Spatial Economic Analysis - Volume 1, Issue 2

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Spatial Economic Analysis, Vol. 1, No. 2, November 2006

Downloaded by [Tehran University] at 04:21 21 August 2011

Editorial Spatial Economic Analysis was launched during the summer of 2006, with a formal announcement made at the 40th Anniversary Celebration Event of the Regional Studies Association on 14 September at the House of Commons, London, and with the support of members of the Regional Studies Association, the Regional Science Association International-British and Irish Section, and of the editorial team, who attended a number of conferences to disseminate the first issue. We are very happy to report that Spatial Economic Analysis has been warmly received by the academic community, not only by those who were present at these conferences, but more widely. Conferences hopefully bring out the best in people. Not only do they provide a lively forum for debate, both the formal debate in the conference rooms but often the even more lively debate in the bar or wherever, but they are also an opportunity to make contact with old friends and colleagues; a way of quickly upgrading one’s knowledge about subjects one thought one knew quite well; and discovering useful ideas from parallel intellectual worlds. During the summer there were several conferences, workshops and meetings held at various venues around Europe, all of which focussed on issues relating to spatial econometrics and spatial economics. The events included an interdisciplinary workshop on Regional Innovation, held at King’s College, Cambridge (UK) and an ‘International Workshop on Spatial Econometrics and Statistics’ in Rome, both held in early June. These were followed by the 36th annual conference of the British and Irish Regional Science Association in Jersey (Channel Islands), the 46th European Regional Science Congress in Volos (Greece), the 13th International Conference on Panel Data held at Robinson College, Cambridge (UK), and the ADRES conference on ‘Networks of Innovation and Spatial Analysis of Knowledge Diffusion’ at St Etienne (France) in September. Several important themes emerged from these various meetings. Firstly, quantitative economic geography remains a topic of considerable interest among the geographical community, and particularly among young and emerging researchers. There appears to have been a revival of quantitative economic geography following the session held at the Royal Geographical Society in 2003, entitled, ‘50 years of Regional Science or the Return of Quantitative Economic Geography’, which was organised by our coeditor Paul Cheshire. More broadly, recent developments suggest an increasing overlap between what one might call mainstream microeconomics and economic geography. Spatial economic analysis really is a unifying intellectual force. Given the various conference themes, quite naturally the emphasis of many of these sessions was on spatial econometrics, but there were also papers combining econometric virtuosity with economic theory. Secondly, mainstream econometricians really are getting interested in spatial analysis. The hot topic truly is panel data with spatial dependence thrown in also, and this clearly opens possibilities beyond what is available via purely cross-sectional analyses. The increased availability of spatial time series has encouraged this, but what is interesting is that a much wider audience of economists and econometricians are now becoming interested in spatial analysis. For example Sean Holly, Hashem Pesaran and Takashi ISSN 1742-1772 print; 1742-1780 online/06/020147-07 # 2006 Regional Studies Association

DOI: 10.1080/17421770601135588


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Yamagata’s paper ‘A spatio-temporal model of house prices in the US’ employs concepts familiar to any well read spatial econometrician together with techniques from time series econometrics, such as panel unit root tests. There is clearly potential for more methodological spillover between spatial and time series econometrics and a coming together of people, as evidenced by a growing and dedicated band of common attendees at each others’ conferences. The future looks bright. Thirdly, there is currently a great deal of theoretical and empirical interest in the topic of networks, how they are described, how they evolve and how they determine outcomes, such as firm performance and regional economic growth. The topic of networks focuses our thinking on the fact that ‘spatial’ can mean spatial in the wider sense, whereby distance may be measured in km, but in reality spatial distance is something much more complex and subtle, particularly once we allow for knowledge spillovers. This is what Spatial Economic Analysis is about, the role of space, in all of its manifestations, in both explaining and shaping economic phenomena. One important outcome of the Rome meeting was the formal establishment of the Spatial Econometrics Association (which also, coincidently, shares our acronym SEA!). Another outcome was the decision to hold the next conference,1 the first under the Association banner, in Cambridge. Dr Bernard Fingleton, Editor-inChief of Spatial Economic Analysis has been appointed local organiser for this. In 2000 Daniel McFadden shared the Nobel Prize in Economic Science for his work developing methods of discrete choice analysis, thus providing models that predict how people or organisations will behave when faced with a choice among a limited set of alternatives. These methods have wide application since they were first developed to explain why commuters choose one transportation mode rather than another. Now their remit extends to explaining why consumers prefer one type of consumer product over another, why residents opt for one rather than another form of tenure, why investors and institutions place their investments in one region and not another and why students select one from several optional decisions regarding their continuing education, and so on. In all of these cases the choice is between several optional categories, and prior to McFadden and his coworkers the technical tools available for the quantitative analysis of these choices were decidedly limited, especially by comparison to the sophisticated tools available for the analysis of continuous variables. However McFadden’s contribution has not been restricted to extending statistical methodology, important as that is, what is also significant is the way in which the statistical and econometric tools dovetail beautifully with random utility theory. From a theoretical model of the determinants of the utility level of each option, allied to a random error to accommodate uncertainty, we arrive at a specification for the empirical model. While the actual level of utility associated with each option is unknown because of the unobservable random error, the discrete choices made by the commuter or consumer or student are observable, and thus we arrive at a model in which the dependent variable is the frequency of each option choice, or the ratio of frequencies. The particular specification that is adopted depends on the assumptions made about the random error distribution, but the best known and most tractable model from the empirical perspective is the so-called logit model, in which the dependent variable is the log of the odds of choosing between two options. Extending the number of options gives us the multinomial logit model, and this is the tool that Sa´, Florax and Rietveld use in their paper in this issue to analyse the effects of accessibility on higher education choices.


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Sa´, Florax and Rietveld (2006) continue the theme now established among the spatial econometrics community of introducing spatial effects into standard discrete choice models, and they are able to show that close geographical proximity has a positive effect on the destination choices of high school leavers, be it university, a professional college or opting out of education, controlling for a range of other potential influences. Their data set comprises a sample of 3263 Dutch students, basically a cohort graduating from pre-university high school, which raises interesting questions of sample selection bias, since these students may have innate ability which caused them to opt for this particular secondary education track, so it is difficult, as they explain, to extend their conclusions to other students. Nevertheless, they give a valuable and interesting account of how this group behaves. One strong feature of their analysis is their explicit treatment of spatial dependence and heterogeneity. To avoid misspecification problems, dummy variables pick up the effects of unmodelled variables that are responsible for heterogeneity, and they make assumptions about the nature and extent of spatial dependence in order to use a Huber White estimator that allows for intercorrelation between individuals. The assumption they make is that social interaction, and, therefore, correlation among choices, is confined to the high school attended, rather than spilling over ad infinitum from neighbours to neighbours of neighbours and so on across the entire landscape. One feature of their analysis is the error distribution that underpins the multinomial logit model. It is well known that the multinomial logit is based on the Weibull distribution (and consequently on the logistic distribution), which is the one usually used to model the distribution of extreme values. Using the Weibull rather than the normal distribution does not make much difference in practice, but it is interesting to contemplate the option of taking a more general specification in which the distribution of the errors is normal, with, for options j and k, variances varj and vark and covariance covjk. This leads to the multinomial probit model which is probably the most general discrete choice specification. Testing for the ‘independence from irrelevant alternatives’ (IIA) condition, which they do, amounts to a test of the more restricted set of error assumptions, namely common error variance and zero covariance, which are consistent with the multinomial logit model.2 Since the IIA assumption is not rejected, we can assume that university versus professional college versus discontinuing education really are distinct, uncorrelated alternatives. If they were not, so that the covariances were actually non-zero, then we would be unable to assume that the odds of choosing between say, university and non-continuance, do not depend simply on the specific attributes relating to these alternatives alone. Fortunately, this is not the case, and the multinomial logit is the appropriate and, providentially, relatively simple vehicle of analysis. The paper by Mur and Angulo (2006) raises some fundamental issues for spatial econometrics. First, how does one choose between competing specifications, do we start with a simple model and build up (the bottom-up or specific-to-general approach), or do we start with a complex model and eliminate insignificant effects (the top-down or general-to-specific approach) as has become favoured by many time series econometricians, led by David Hendry. Both approaches are potentially problematic. For instance, the top-down approach makes inference more sustainable from a theoretical perspective, because we start from white noise errors which is what we are supposed to have in making inferences, and while the overparameterized model will be inefficient, it will be unbiased. However many

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correlated variables can cause problems of multicollinearity and top-down needs a sensible initial specification, and it is not entirely clear what this should be in spatial econometrics, where there are difficult decisions regarding what we mean by a spatial lag. In time series analysis, everyone knows what a lagged variable is, if x(t) is the variable, x(t 1) is a different variable equal to x lagged by one time period, and we use these lagged variables to create the general model with which we commence the top-down approach. Bottom up is simpler; if the residuals are well behaved in the simple model, why complicate it? However some significant effects may be omitted, in which case we would have serious misspecification bias. Incidentally, the evidence that bottom up is best for spatial econometrics has evoked a reaction among time series econometricians, not least Hendry (2006), and a reply by Florax, Folmer and Rey (2006). Regarding competing spatial econometric models, two are famous. One is the model in which the spatial lag is a right hand side variable. A simple example of a spatial lag would be a variable which is equal to the weighted average of the dependent variable, let us call this Wy, which is the matrix product of the so-called weights matrix W and the dependent variable y. For example, Wy might be the average value of y in contiguous3 areas, so if three areas are contiguous to area k, with y values equal to 1, 2 and 3, then using equal weights of 1/3, Wy for area k might be 2.4 The second famous type of spatial econometric model is where a similar phenomenon occurs for the residuals, u. Let us say that u depends on contiguous u (Wu) plus a random spatially uncorrelated shock or innovation, e. This would amount to an autoregressive process for the errors. One way to try to resolve the issue about which model is best is to initially fit a less restricted model that nests both of these alternatives as special cases, the so-called spatial Durbin model. From this starting point, one can impose (common factor) restrictions to arrive at the error specification, whilst imposing other restrictions leads us to the spatial lag model. Implicitly, therefore, the common factor approach is top-down. Which of these two famous specifications is correct is important, because it can be argued that sometimes the existence of spatially dependent residuals is due to the omission of relevant variables, rather than being a true error process, so the hypothesis of a spatial error process needs to be carefully considered against alternatives. Mur and Angulo (2006) contribute to our understanding of these issues by presenting some Monte Carlo results of some common factor tests that are available in the literature, making a case for more importance to be given to this test in our model selection. Despite the importance of the common factor hypothesis, which, if it is true, reduces the spatial Durbin specification to the model with an error process, surprisingly little work has been done exploring the properties of these tests. This is the main contribution of their paper. The paper by Baltagi and Li (2006) is the first of our two papers analysing spatial panel data, in their case the consumption over time of alcoholic beverages across US states. The specific application has some fascination, for evidently drinkers will go to considerable lengths to travel to ‘wet’ counties to consume alcohol if their own particular county is ‘dry’, and will even cross State boundaries, distorting the State level data on consumption. Heavy drinking goes on in Nevada, evidently because of tourism, but Mormon-dominated Utah is a low consumption state. These and other causes of across-state heterogeneity and between state spatial dependence will ostensibly play havoc with attempts to forecast alcohol consumption, which is of obvious interest to not only the producers of alcohol, but also the health-care sector. The paper sets out a wide panoply of panel data models as a basis


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for forecasting. These are divided between fixed effects models, in which the across-state heterogeneity is captured by state-specific dummy variables, and random effects models, with heterogeneity forming a component of the disturbance vector which is fixed over time but treated as a random draw across states. The remaining component of the disturbance term picks up spatial autocorrelation due to the spillover across state boundaries, treating it as a spatial autoregressive process. The paper explores the precision with which the forecasts are made using different model specifications, either fixed or random effects, with or without spatial autocorrelation, by making out-of-sample forecasts over the last 5 years of data. In this and other regards, the paper provides a coherent summary of the state of the art and good practice that could be used across a wide range of applications. Driffield and Taylor (2006) apply some of these newly available spatial panel estimation techniques to consider the question of wage spillovers both within and across UK regions and industries, looking specifically at the impact of foreign direct investment (FDI). Specifically, their data set consists of wage levels broken down by foreign or domestic ownership, by manufacturing industry, by skill level and by time. Using spatial fixed effects and random effects estimators, they are able to show that wage spillovers have occurred across both regions and industries. The spillover of wages paid by foreign owned firms, however, is somewhat restricted, impacting only skilled workers in ‘nearby’ industries and not, in general, spilling over to nearby regions. Within regions, the impact of FDI is seen mainly on skilled worker wages, and they conclude that this increases wage inequality between skilled and unskilled workers. From the econometric perspective, this is an interesting early application of the recent innovations in spatial panel analysis via GMM estimation with random effects, due to Kapoor, Kelejian and Prucha (2006). Wages are undoubtedly determined to some extent by ‘fixed’ effects such as age, gender and so on, but of course these are not available at the level of aggregation employed by Driffield and Taylor. Instead, their effects are picked up using the endogenous lag. One interesting aspect is the problem of endogeneity, since the left hand side wage variable will affect the right hand side wage variables and vice versa and some other right hand side variables are also likely to be endogenous. This problem is overcome using lagged values, having checked for an absence of serial correlation and established that the instruments are independent of the errors via the Sargan test. Our final paper, by Bru¨lhart (2006), considers another important subject for Spatial Economic Analysis, namely the new economic geography (NEG). The key insight from the NEG literature is that the location of production and demand are jointly determined. Firms locate where demand is high and mobile workers* and thus consumers* will prefer to locate in centres of production. It is therefore no surprise that market access is a central variable in NEG models. The idea that market access matters is, of course, not new and goes back to at least the market potential function as introduced by Harris (1954). In fact, Paul Krugman summarized the NEG literature as an attempt to come up with a micro-economic foundation for such a market potential function. Bru¨lhart (2006) takes Harris’s market potential measure as a starting point to estimate core periphery gradients for his sample of Western European regions. Using a Balassa index for regional sectoral employment as the dependent variable, he first sets out to establish whether employment is significantly concentrated in core regions: that is to say, in regions with a high market potential. For four of his eight sectors this is indeed the case.


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But more interestingly, no sector shows an increase in concentration in core regions during the sample period of 1975 2000. If anything, there has been a tendency to relocate to peripheral regions during this time as is evident by the flattening of the core periphery gradients over time. This is also true for manufacturing employment. The interest of European policymakers in the NEG literature is largely determined by the fact that the relationship between economic integration and agglomeration is at the heart of this literature. NEG models typically predict a nonlinear relationship between integration and agglomeration and at some critical break-point it is predicted that economic integration will induce more agglomeration. In the second part of his paper Bru¨lhart sets out to establish if sectoral location patterns in regional employment have been influenced by EU integration. Exploring past accessions to the EU, it investigates whether EU accession leads to a deviation from the baseline (pre-EU) trend growth in employment. Except for agriculture, this turns out to be the case. And again, for manufacturing employment, EU accession goes along with a tendency to (re-)locate to countries’ peripheral regions. The opposite holds for service sectors. As the author acknowledges, the main findings in the paper do not necessarily run counter to predictions made by the NEG literature. In the NEG models, it very much depends on the level of economic integration whether or not a further increase in economic integration leads to more agglomeration, or, in other words, to a steeper core-periphery gradient. The non-linearity of these models also allows for the possibility that increased integration leads to a more even spreading of production and employment across space. As a next step to Bru¨lhart’s paper, one could therefore try to come up with empirical (gu)es(s)timates of the range of economic integration where more integration implies more agglomeration. B. Fingleton P.Cheshire H. Garretsen D. Igliori P. McCann J. McCombie V. Monastiriotis B. Moore M. Roberts Notes 1. To be held 12 14 July, 2007, Fitzwilliam College Cambridge. 2. One other alternative, which would also take care of a failure to satisfy IIA, would be a generalised Weibull distribution possessing correlated errors. 3. Of course there are many alternative definitions other than contiguity leading to W . 4. This description of a spatially lagged variable assumes that the W matrix is row standardised.

References Baltagi, B. H. & Li, D. (2006) Prediction in the panel data model with spatial correlation: the case of liquor, Spatial Economic Analysis , 1(2), 175 185. Bru¨lhart, M. (2006) The fading attraction of central regions: an empirical note on core-periphery gradients in western Europe, Spatial Economic Analysis , 1(2), 227 235.

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Driffield, N. & Taylor, K. (2006) Wage spillovers, inter-regional effects and the impact of inward investment, Spatial Economic Analysis , 1(2), 187 205. Florax, R. J. G. M., Folmer, H. & Rey, S. J. (2006) A comment on specification searches in spatial econometrics: The relevance of Hendry’s methodology: a reply, Regional Science and Urban Economics , 36(2), 300 308. Hendry, D. F. (2006) A comment on ‘Specification searches in spatial econometrics: The relevance of Hendry’s methodology’, Regional Science and Urban Economics , 36(2), 309 312. Kapoor, M, Kelejian, H. H. & Prucha, I. (2006) Panel data models with spatially correlated error components, Journal of Econometrics , forthcoming. Mur, J. & Angulo, A. (2006) The spatial Durbin model and the common factor tests, Spatial Economic Analysis , 1(2), 207 226. Sa´, C., Florax, R. J. G. M. & Rietveld, P. (2006) Does accessibility to higher education matter? Choice behaviour of high school graduates in the Netherlands, Spatial Economic Analysis , 1(2), 155 174.


Does Accessibility to Higher Education Matter? Choice Behaviour of High School Graduates in the Netherlands

´ , RAYMOND J. G. M. FLORAX & PIET RIETVELD CARLA SA


(Received October 2005; revised September 2006)

This paper identifies pivotal factors behind individual decision making in the transition from high school to post-secondary education in the Netherlands. We apply a multinomial logit framework to individual data and accommodate two types of effects that have not received much attention in the literature. First, we analyse the impact of geographical accessibility of the higher education system. Second, we allow the individual observations to be correlated within schools, in effect accounting for localized social interactions. Our results confirm the paramount influence of the student’s track record and talent. The results, however, also show that geographical proximity significantly increases the probability of high school leavers continuing their education at a university or professional college.

ABSTRACT

L’accessibilite´ a` l’enseignement supe´rieur importe-t-elle? Comportement du choix des diploˆme´s de l’enseignement secondaire au Pays-Bas RE´SUME´ Cet article identifie les facteurs essentiels intrinse`ques a` la prise de dećision individuelle dans la transition ayant lieu entre l’ećole secondaire et l’enseignement postsecondaire au Pays-Bas. Nous appliquons le cadre d’un logit multinomial a` des donneés individuelles et nous adaptons deux types d’effets qui n’ont pas beńe´ficie´ d’une grande attention dans la documentation. Premie`rement, nous analysons l’impact de l’accessibilite´ geógraphique du syste`me de l’enseignement secondaire. Deuxie`mement, nous permettons la corre´lation des commentaires individuels au sein des ećoles, qui repre´sentent de fait des interactions sociales localiseés. Nos re´sultats confirment l’influence primordiale des re´sultats obtenus de l’e´tudiant ainsi que de son talent. Les re´sultats montrent cependant e´galement

Carla Sa´ (to whom correspondence should be sent), NIPE, University of Minho, Portugal, and Tinbergen Institute, Gualtar, 4710-057 Braga, Portugal. Email: [email protected]. Raymond J. G. M. Florax, Department of Agricultural Economics, Purdue University, West Lafayette, IN 47907 2056, USA, and Department of Spatial Economics, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. Email: [email protected]. Piet Rietveld, Department of Spatial Economics and Tinbergen Institute, Vrije Universiteit, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. Email: [email protected]. The first author gratefully acknowledges the financial support of the Portuguese Foundation for Science and Technology, FCT [SFRH/BD/5054/2001]. The authors wish to thank the Research Centre for Education and the Labour Market (ROA) for supplying the data used in this paper. Timo Huijgen and Maarten Wolbers of ROA have been extremely helpful in guiding the authors through the data acquisition process. The authors also benefited from the comments and suggestions of two anonymous reviewers of this journal, and discussions with participants of the 43rd Conference of the European Regional Science Association (Jyva¨skyla¨, Finland) and the ROA seminar (Maastricht, The Netherlands). ISSN 1742-1772 print; 1742-1780 online/06/020155-20 # 2006 Regional Studies Association

DOI: 10.1080/17421770601009791

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que la proximite´ geógraphique augmente conside´rablement la probabilite´ des sortants du secondaire qui poursuivent leurs e´tudes dans une universite´ ou un colle`ge professionnel.

¿Importa el acceso a la Educacioń Superior? La toma de decisiones en graduados de Educacioń Secundaria en los Paı´ses Bajos. Este trabajo identifica los factores claves en la toma de decisiones individuales en la transicioń del Instituto de Educacioń Secundaria a la educacioń Superior en los Paı´ses Bajos. Aplicamos un marco logarı´tmico polinomial a los datos individuales y analizamos dos tipos de efectos que no han sido estudiados detalladamente en este tipo de literatura. Primero, analizamos el impacto de la accesibilidad geogra´fica del sistema de Educacioń Superior. Segundo, permitimos que las observaciones sean correlacionadas dentro de las escuelas pudiendo explicar las interacciones sociales localizadas. Nuestros resultados confirman la significativa influencia de los antecedentes escolares de los estudiantes y sus habilidades. Los resultados, sin embargo, tambień revelan que la proximidad geogra´fica aumenta de gran manera la posibilidad de que los graduados de Instituto continuén su educacioń en una universidad o colegio profesional.


RESUMEN

KEYWORDS: High school graduates; higher education; social interaction; geographical accessibility JEL CLASSIFICATION: C25; I21; R10

1. Introduction The behaviour of high school leavers with respect to the choice between continuing education by entering post-secondary schools or entering the labour market has been analysed quite thoroughly. Initially, studies assumed the choice to be a simple binary decision between continuing schooling or entering the labour market (see, for instance, Kohn et al., 1976). More recently, studies have considered broader sets of alternatives, including vocational education options and labour market alternatives, and have analysed the choice behaviour by means of multinomial models (see, for instance, Riphahn, 2002; Nguyen & Taylor, 2003; Giannelli & Monfardini, 2003). The transitional behaviour of high school leavers is generally explained by individual characteristics, such as the individuals’ capabilities, as well as the students’ socio-economic background, usually measured by means of parental income, education, and occupation. Although most of the more recent studies include information on the spatial variability in labour market conditions, none of the studies seems to fully explore the spatial dimensions of the student’s decision process as well as the potential relevance of localized social interactions.1 It is often assumed that characteristics of the regional surroundings of the parental household are the main source for variations in expected earnings and expected employability after schooling. Because some authors argue that it is quite unlikely that educational decisions are dominated by expectations related to the region where the student might possibly work after graduation (Hartog & Serrano, 2002), many studies introduce controls for spatial heterogeneity based on the regions where students live when making the decision whether or not to continue education. The spatial heterogeneity is generally related to labour market characteristics, although this seems to be an unnecessary restriction. Regional characteristics, such as the level of educational attainment, the intellectuality of the regional milieu, and the availability of local amenities may also be relevant (Sa´ et al.,


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2004). In order to control for such aspects, some studies include regional dummies, usually derived from a rather crude division of the country into large heterogeneous entities such as North, South, East, and West (see Giannelli & Monfardini, 2003, in a study for Italy; and Nguyen & Taylor, 2003, in a study for the USA). In most studies, individual students are the unit of analysis. However, individuals cannot be treated in isolation, and social interaction patterns should be accounted for (Manski, 2000; Brock & Durlauf, 2002). Although it is virtually impossible to identify one single social context that is most important for the student’s choice behaviour after leaving high school, it is likely that the interaction in a cross-sectional data set of individual students can best be captured by assuming clustering among students attending the same high school. Students attending the same high school tend to be rather homogeneous in their socio-economic background, because they usually come from the same types of neighbourhoods. They also share various features of their everyday life, because they spend a significant part of the day attending classes together, they are being taught by the same teachers, and they are likely to spend some of their leisure time together. We therefore follow Moulton (1990) in maintaining that it is reasonable to expect that individuals who share an observational characteristic such as location (or high school) also share other unobservable characteristics, implying that disturbances are correlated. We emphasize an additional spatial aspect in this paper, apart from accounting for spatial heterogeneity and localized social interaction as indicated above. Some previous studies have experimented with including distance to higher education institutions among the explanatory variables in the analysis of transitions of high school leavers (see, for instance, Kjellstro¨m & Regne´r, 1998). However, none of the studies have considered the distance impediment in terms of a system-wide accessibility measure that includes all higher education institutions, eventually even distinguishing between professional colleges and universities. The latter is not only potentially relevant in explaining the choice behaviour of students but also provides important information for making informed policy decisions because, effectively, in most European countries the spatial distribution of higher education institutions is determined to a considerable extent by the national government (see Florax, 1992; Florax et al., 2006; Sa´ et al., 2004). In fact, the objective of policy makers is often to provide all potential students with the same higher education options and opportunities. In pursuing this objective, information on the spatial distribution of higher education participation is imperative. We address the above issues using individual data on choices of high school leavers with a diploma, and combine these data with information on high schools and regional characteristics, for the Netherlands. Our main hypothesis is that individuals who live in closer proximity to a specific type of higher education institution (i.e. a professional college or a university) are more likely to continue studying after high school, and they are more likely to choose that type of institution, even after controlling for spatial heterogeneity and social interaction. We investigate the behaviour of Dutch high school leavers at the end of the last century (1998 2000) by means of a multinomial logit model distinguishing between university education, professional training, and no higher education as the main alternatives. This paper continues as follows. Section 2 provides background information on the Dutch educational system. A state-of-the-art overview of the literature on choice behaviour of high school leavers is presented in Section 3. Sections 4 and 5

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cover data issues, the empirical model, and the estimation results. Section 6 concludes.


2. The Dutch Educational System Dutch students are admitted to secondary school after leaving primary education at an average age of 12, and they are essentially free to attend the high school of their choice, although parents are advised by the primary school as to the type of secondary education that best suits their children. Secondary education comprises schools providing practical training (PRO), pre-vocational secondary education (VMBO), general secondary education (HAVO), and pre-university education (VWO).2 The longest track, VWO, takes 6 years and prepares students for university, although students with a VWO diploma do also have access to postsecondary professional colleges. Students from the HAVO track, instead, can only proceed to professional colleges, whereas those with a diploma for the VMBO track can go on to the MBO track, after which they can eventually attend higher professional education at professional colleges. Students have to choose one out of four programme profiles: science and technology, science and health, economics and society, or culture and society. The different profiles include both a set of courses common to all profiles (for instance, Dutch) and a series of courses specific to the profile. The tertiary step of the educational system comprises the higher education sector. The Dutch higher education system is a dual system, with 13 universities (WO) and 50 vocational/professional colleges (HBO), which are almost all entirely publicly funded.3,4 Every year, the national government determines minimum requirements regarding the secondary school diplomas that allow students to apply for post-secondary study programmes. Institutions can impose additional prerequisites with respect to the profile and/or high school courses included in the diploma. In general, all students with a secondary school diploma have access to university education, that is, for most study programmes there are no supply constraints, although some exceptions apply.5 The same is not entirely true for professional colleges, which tend to have somewhat greater autonomy in defining their admission criteria. Typically, they fix a broader range of entrance requirements, in particular related to skills, talent, or fitness for a profession. Students are required to pay admission fees, which are equal across institutions and generally not very high. Quality differences between educational institutions are considered negligible in the Netherlands. Regular full-time students are eligible for student support provided by the national government, which is compatible with some part-time jobs. All students are eligible for a basic scholarship for the nominal duration of the higher education programme (4 or 5 years), the exact amount of which depends on whether the student lives with his or her parents. Depending on their parents’ and their own income, students can also apply for additional funding, which is eventually supplied in the form of a supplementary grant or even a loan. Since 1990, all students have received a public transport pass, allowing free travel during workdays and discounted travel at weekends. Until the 1970s, a policy of geographical decentralization of the higher education system, resulting in the establishment of new universities, was implemented in the Netherlands, guided mainly by spatial equity concerns. As a result, the geographical accessibility of the university system is relatively high; there are about three universities per 100 100 km grid cell. The same applies to post-secondary professional colleges, /


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the spatial distribution of which has traditionally been very even (see Florax et al., 2006). The above features of the Dutch higher education system, characterized as it is by inexpensive, spatially balanced and easy access to higher education, makes it less likely that price and supply considerations play a major role in the choice behaviour of students. In addition, given the high spatial density of institutions, it is questionable whether distance to such institutions is really an impediment.


3. Choice Behaviour of High School Leavers There is an extensive literature on the choice behaviour of high school leavers. We present a concise overview here, concentrating on aspects that have been identified as relevant to the decision whether or not to continue (post-secondary) education. Human capital theory looks at education as an investment good. The decision to continue education depends on the anticipation that future returns for a postsecondary degree, over and above those for a high school diploma, outweigh the additional costs of extended schooling (including income forgone). Apart from being an investment decision, the demand for education can also be a current consumption choice (Kodde & Ritzen, 1988; Duchesne & Nonnemann, 1998). Students may attend college simply because they like the courses or the student lifestyle. Theories considering schooling as a consumption activity assume the demand for higher education to vary positively with student income and negatively with both direct (tuition) and indirect (opportunity) costs. Kodde & Ritzen (1984) integrate consumption and investment motives in a unique model, according to which students choose the optimal level of education, and current and future consumption, subject to time and budget constraints. The solution for the maximization problem suggests that the individual’s demand for education is a function of direct and indirect costs, income and wage differentials. The direct cost of attending a higher education institution has received considerable attention in empirical work. Direct costs include tuition, books and fees; expenditure for food and housing are not always considered because these exist in any case. The empirical literature shows that human capital investments are more likely when costs are lower (Bishop, 1977; Fuller et al., 1982). The amount of financial aid, either in the form of grants or scholarships which cover at least part of the cost of college education, generally has a positive effect on the probability of enrolment (Fuller et al., 1982; Catsiapis, 1987). Household income is another important determinant of the decision to continue studying after secondary education. Most studies have found that the higher the household income, the higher the demand for post-secondary education as well as the propensity to be in school after the secondary level (see, for instance, Savoca, 1990; Duchesne & Nonnemann, 1998; Checchi, 2000; Hartog & Serrano, 2002). Educational attainment of parents and/or their occupational status are sometimes used either to proxy this income effect or to capture the independent positive influence it has on youngsters’ decisions to attend higher education (e.g. Checchi, 2000; Hartog & Serrano, 2002; Nguyen & Taylor, 2003). Average earning differentials between higher education graduates and high school graduates have been shown to be a good indicator of the relative labour market conditions. Empirical studies have found a positive effect of wage differentials between college and non-college occupations in local labour markets on the student’s likelihood of attending post-secondary education (see, for example,


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Duchesne & Nonnemann, 1998; Hartog & Serrano, 2002). The expectation of future unemployment, however, reduces the returns to education, and can therefore reduce the demand for higher education (Ordovensky, 1995; Riphahn, 2002). Current unemployment also plays a role in this decision process, with poor employment prospects retaining youngsters in school (Corman & Davidson, 1984; Savoca, 1990; Hartog & Serrano, 2002; Giannelli & Monfardini, 2003). Some recent studies also incorporate the effect of family, neighbourhood and ethnicity on individual human capital decisions, probably because knowledge of the behaviour of others reduces the risk and uncertainty involved in this type of decision (Borjas, 1995). Finally, human capital theory also predicts that, ceteris paribus, myopic people are less likely to go to college than forward-looking people, and that most college students are young (Ehrenberg & Smith, 2000). The degree of present-orientation is quite difficult to test, but age has been included in most empirical studies. In addition to the consumption and human capital motive, participation in post-secondary education may also be related to higher education functioning as a screening or filtering device (see, for example, Kodde & Ritzen, 1984). While human capital theory suggests that education increases individual human capital, screening theory asserts that there is a selection effect at work. Participation in higher education is restricted to the more capable students, who also happen to be more productive. This is subsequently useful information for future employers, and higher education hence operates as a filter. Many studies use test scores as a proxy for individual talent and show that students with higher scores are more likely to attend post-secondary education (Fuller et al., 1982; Venti & Wise, 1983; Catsiapis, 1987), in particular academic programmes (Ordovensky, 1995; Nguyen & Taylor, 2003). Previous empirical studies have also found a series of other individual, family and school characteristics to be relevant. Gender seems to play a role in participation, but the results are not consistent across studies (Kodde, 1986; Kodde & Ritzen, 1988; Savoca, 1990; Ordovensky, 1995; Checchi, 2000). Race differentials are an important determinant of differences in college enrolment (Black & Sufi, 2002), as well as parental nationality and family structure (Nguyen & Taylor, 2003). The type of secondary school that students attend may determine how likely the student is to enrol in higher education (Catsiapis, 1987; Kodde & Ritzen, 1988; Checchi, 2000; Nguyen & Taylor, 2003). The direction of this effect varies, however, between countries and with the structure of the educational system. The social status of the neighbourhood where the high school is located has a positive effect on youngsters’ attendance of higher education institutions (Bishop, 1977). The educational track, the academic quality of the institution, and the plans of peers appear to have a positive effect as well (see, for instance, Fuller et al., 1982; Savoca, 1990; Ordovensky, 1995). Finally, as far as spatial effects are concerned, the level of urbanization has been shown to play a role in determining choice behaviour (Riphahn, 2002; Giannelli & Monfardini, 2003; Nguyen & Taylor, 2003). Most studies have also found a negative distance effect (see, for instance, Fuller et al., 1982; Ordovensky, 1995; Sa´ et al., 2004), although there are exceptions as well (see, for instance, Kjellstro¨m & Regne´r, 1998). The above literature review shows that there is a vast series of potential determinants of the choice behaviour of high school students with respect to the decision to continue education (either at a professional college or a university) or choose another option, including entering the labour market. Typically, the


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determinants are personal (including family background), school, and spatial characteristics. The overview also shows that it is important to take into account that decisions are not made in isolation, but rather within a network of social interactions. Finally, the overview shows that spatial effects and the impediments of distance should not be ignored. In the next section, we discuss how we include these aspects. 4. Empirical Framework


4.1. General Model We model the choice behaviour of high school graduates on the basis of a utility maximization framework in a multinomial choice model. Let i represent the student, j stand for high school, and k indicate the geographical location of the student at the moment of graduation, and each student chooses between three different alternatives a, either: no higher education, go to a professional college, or enter a university programme (a 1, 2, or 3, respectively). The utility associated with alternative a is then given by: /

(a) Uijk Vijk(a) o (a) ijk ;

Vijk(a)

(1)

o (a) ijk

is a linear predictor, and is a random term. Alternative f is selected where (f ) (g) (f ) (g) over any other alternative g if Uijk Uijk ; for all g, or, equivalently, Uijk Uijk (f ) (g) (f ) (g) (a) Vijk Vijk (o ijk o ijk ) 0: If the error term o ijk has a Type I extreme value distribution (Gumbel), the differences (o (fijk) o (g) ijk ) have a logistic distribution, and it follows that the multinomial probability of response category f equals: exp(Vijk(f ) ) (f ) PA pijk (a) ; a1 exp(Vijk )

(2)

(f ) is the probability that f is chosen, and aAa1 exp(Vijk(a) ) 1: In order to where pijk ensure identification of the model, we use alternative a 1 (no higher education) as the base category.

4.2. Data and Variables The variables in Vijk refer to personal characteristics of the individual indexed by i, characteristics of the high school that he or she attends indexed by j, at the spatial location of the moment of graduation indexed by k, the latter including accessibility to professional colleges or universities. 4.2.1. Personal characteristics. The data on student choices and other personal characteristics are derived from the RUBS survey (Registratie Uitstroom en Bestemming van Schoolverlaters) conducted by ROA (Researchcentrum van Onderwijs en Arbeidsmarkt) among students graduating from a pre-university high school (VWO; see Section 2), which is the only secondary education track that allows students to opt for professional or university higher education. The students are selected randomly in a stratified sampling process in which high schools are sampled first, and students in the subsequent second stage. We use survey data on 1998, 1999 and 2000 graduates, who responded to a questionnaire 18 months after graduation. The resulting sub-sample contains 3,263 observations.6 The data set


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contains the name and location of the high school, information about the respondent’s main activity at the time of the survey (being a student, working, or out of the labour force), and, if applicable, the educational level attended. This information is used to create the choice variable (1 for no higher education, 2 for professional training, and 3 for university education), where the no higher education option is a mix of activities such as working, unemployment, out of the labour force, and non-tertiary education. In line with previous studies, we derive information on personal characteristics from the sample, including gender, citizenship, parental citizenship, and age. We also obtain information on school performance by means of the mean grade point average (GPA). Finally, because high school programmes are organized in different ‘streams’ from which students may choose, we distinguish four profiles (science and technology, science and health, culture and society, and economics and society) by means of dummy variables. We have data referring to three different cohorts of graduates, which we pool for estimation purposes. Since the distributions of variables tend to change over time, the identical distribution assumption may be not valid, although the independence assumption still holds. We therefore include cohort dummies in the econometric model to capture aggregate changes over time (see Wooldridge, 2002). Descriptive statistics of the data according to the three dimensions of variation (personal, high school, space) are given in Table 1, and the distribution across the different choice categories is given in Table 2. Table 1 shows that the graduates are distributed evenly across the choice categories as far as gender, citizenship, age, and cohort are concerned. Table 2 shows that approximately 30% of the graduates choose a professional college, 65% continue education at a university, and 6% go elsewhere, mainly directly entering the labour market. The choice behaviour reflected in the sample information corresponds very well to the population. For 1999, for instance, the ministry reports that 26.2% of the VWO graduates chose professional training, 66.5% university education, and 7.2% went elsewhere (OCW, 2003, p. 49).7 4.2.2. High school characteristics. We include a limited number of high school characteristics in our analysis, and obtain these characteristics from yearly quality reports of each high school in the Netherlands, as conveyed in the evaluation of high schools by educational assessment authorities (Inspectie Onderwijs). High schools in the Netherlands vary according to denomination. We distinguish public high schools, from private (non-religious) high schools, and private high schools with a religious denomination. We also include information on the size of the high school in terms of the total number of students, ranging from 426 to 3,020. Tables 1 and 2 do not show large differences between the choice categories according to high school characteristics, except perhaps for school size. Specifically, in larger schools, graduates are more likely not to continue their education, and in smaller schools graduates are slightly more likely to go to university. There is a slight indication that graduates from private religious schools are more likely to choose a professional college. 4.2.3. Spatial characteristics. The data set does not contain information on family income and parental education. We therefore use areal data at the municipality


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Table 1. Descriptive statistics by choice and personal, high school, and spatial characteristics, respectively (means, with standard deviations in parentheses for continuous variables) Choice Variables Personal characteristics Male Non-Dutch Parents non-Dutch Age


Grade point average (GPA) Science and technology profile Science and health profile Culture and society profile Economics and society profile 1998 graduate 1999 graduate 2000 graduate High school characteristics Public school Private school Private religious school School size Spatial characteristics Income per capita Population density College accessibility University accessibility Groningen Friesland Overijssel Gelderland Utrecht Noord-Holland Zuid-Holland Zeeland, N-Brabant Limburg Flevoland No. of observations

No education

College

University

Total

0.3851 0.0460 0.0690 19.4023 (0.7126) 6.5067 (0.5789) 0.2701 0.1322 0.1494 0.4483 0.3736 0.2874 0.3391

0.3368 0.0200 0.0316 19.4421 (0.7085) 6.5531 (0.4843) 0.2379 0.1789 0.1853 0.3979 0.4526 0.2968 0.2505

0.4474 0.0453 0.0790 19.2941 (0.6581) 6.9233 (0.6568) 0.4535 0.1388 0.1267 0.2810 0.4324 0.2768 0.2908

0.4119 0.0380 0.0647 19.3429 (0.6793) 6.7933 (0.6333) 0.3809 0.1502 0.1450 0.3239 0.4352 0.2832 0.2816

0.2701 0.0862 0.6437 1,406.8450 (676.7423)

0.1895 0.0684 0.7421 1,396.0270 (633.2048)

0.2445 0.0944 0.6611 1,304.3450 (586.8493)

0.2298 0.0864 0.6837 1,336.5030 (607.1513)

9.6879 (0.6762) 2,444.8620 (1,089.7470) 1.0295 (0.2944) 0.2899 (0.1455) 0.0632 0.0172 0.0575 0.0057 0.0287 0.1724 0.5805 0.0287 0.0402 0.0057 174

9.6343 (0.6184) 2,183.7280 (1,105.4400) 0.9677 (0.2927) 0.2580 (0.1402) 0.0747 0.0116 0.0905 0.0074 0.0316 0.1589 0.4642 0.1074 0.0442 0.0095 950

9.6550 (0.6737) 2,247.3660 (1,108.9640) 0.9724 (0.2992) 0.2597 (0.1250) 0.0827 0.0131 0.0519 0.0089 0.0243 0.1725 0.4525 0.0935 0.0851 0.0154 2,139

9.6508 (0.6582) 2,239.3700 (1,108.0300) 0.9741 (0.2973) 0.2608 (0.1309) 0.0794 0.0128 0.0634 0.0083 0.0267 0.1686 0.4628 0.0941 0.0708 0.0132 3,263

level to capture these effects. The effect of the student’s socio-economic background is included by using per capita income of the municipality where the high school is located.8 The impact of cultural background and amenities is taken into account by including the level of urbanization of the municipality in which the high school is located, which is operationalized as population density. Both variables are obtained from CBS, the national statistics agency (CBS, 2003). Table 1 shows that there are no significant differences in per capita income across

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Table 2. The distribution of graduates across choices, by personal, school, and spatial characteristics, respectively (in per cent), and the numbers of observation per category Choice


No education (%)

College (%)

University (%)

No. of observations

All observations

5.60

29.28

65.12

3,263

Personal characteristics Male Female Dutch Non-Dutch Dutch parents Non-Dutch parents Age5/18 Age 19 Age 20 Age /20 GPA/6 GPA/7 GPA/8 GPA/9 Science and technology profile Science and health profile Culture and society profile Economics and society profile 1998 graduate 1999 graduate 2000 graduate

4.99 5.58 5.29 6.45 5.31 5.69 6.48 4.82 6.36 6.01 7.89 4.06 3.29 0.00 3.78 4.69 5.50 7.38 4.58 5.41 6.42

23.81 32.83 29.66 15.32 30.14 14.22 21.30 26.37 35.05 38.80 40.54 26.02 11.03 0.00 18.18 34.69 37.21 35.76 30.28 30.52 25.90

71.21 61.59 65.05 78.23 64.55 80.09 72.22 68.82 58.58 55.19 51.56 69.92 85.68 100.00 78.04 60.61 57.29 56.86 65.14 64.07 67.68

1,344 1,919 3,139 124 3,052 211 108 2,139 833 183 1,216 1,576 426 45 1,243 490 473 1,057 1,420 924 919

High school characteristics Public school Private school Private religious school

6.27 5.32 5.02

24.00 23.05 31.60

69.73 71.63 63.38

750 282 2,231

Spatial characteristics Groningen Friesland Overijssel Gelderland Utrecht Noord-Holland Zuid-Holland Zeeland, N-Brabant Limburg Flevoland

4.25 7.14 4.83 3.70 5.75 5.45 6.69 1.63 3.03 2.33

27.41 26.19 41.55 25.93 34.48 27.45 29.21 33.22 18.18 20.93

68.34 66.67 53.62 70.37 59.77 67.09 64.11 65.15 78.79 76.74

259 42 207 27 87 550 1,510 307 231 43

the different choice categories. The respective choice categories of no higher education, professional college, and university are inversely related to population density. It is likely that other unobserved spatial characteristics play a role in the choice behaviour of graduates (for instance, regional production structure differences or cultural differences) and/or that the choices of graduates are spatially clustered. In order to avoid misspecification problems, we include dummies for the Dutch provinces as control variables.9 In doing so, we account for spatial heterogeneity, which is altogether different from spatial dependence (or autocorrelation) that may



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be relevant as well. One should note, however, that spatial heterogeneity and spatial dependence are generally difficult to disentangle in an empirical sense (Anselin, 2001; Florax & Nijkamp, 2005), and a corrective device for one of the misspecifications is likely to affect the seriousness of the other misspecification as well. Finally, we incorporate two accessibility measures in our model, referring to spatial or geographical accessibility to professional colleges and universities, respectively. One should note that accessibility varies not only over space* which is obvious* but also over groups of individuals, because the eligibility to enter specific college and university programmes depends on the high school profile that the graduate adopts. Moreover, since we do not have exact geo-referenced information as to where the graduate lives, we use the distance between the graduate’s high school and the respective colleges and universities that can be attended by students with a given profile. For ease of notation, we only use the subscript k, referring to space, instead of a more complex set of subscripts. Accessibility to universities is then defined as: a(u)k

Li p X 1 l1

djl

;

(3)

where Li p is the total number of universities offering study programmes for which student i who followed profile p in high school is eligible, and djl is the distance between the municipalities where the high school and the university are located, respectively. By analogy, we define the accessibility measure for professional colleges, a(c)k . Accessibility measures are strictly positive,10 and we assume that the higher the accessibility the greater the chance of choosing one of the educational alternatives.11 Following utility theory for these kinds of models, the accessibility variables are included in logarithmic form (see, for instance, Rietveld & Bruinsma, 1998; Ortu´zar & Willumsen, 2001).12 Table 1 shows that the geographical accessibility to professional colleges is substantially greater than to universities (0.97 vs 0.26), which is obvious given the total number of institutions of both types (approximately 50 vs 13). 4.3. Utility Function and Econometric Aspects The general formulation of the utility that each individual takes from each choice depends on individual, high school related, and spatial aspects, in the following way: (a) Vijk(a) a(a) b(a)? xi d(a)? yj g(a)? zk u(a) 1 log(a(u)k )u2 log(a(c)k );

(4)

where a 1 (no higher education), 2 (professional college), or 3 (university), xi is a vector containing variables with personal characteristics, yj contains high school characteristics, zk spatial characteristics, and a(u)k and a(c)k refer to university and college accessibility, respectively. For reasons of identification, the coefficients referring to choice 1 are all set to zero. The utility associated with the choice of professional college education does not depend, however, on how accessible university alternatives are, and, mutatis mutandis, the same holds for the university alternative. This implies that we set (3) u(2) 1 0 and u2 0 in order to obtain: /

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C. Sa´ et al. Vijk(2) a(2) b(2)? xi d(2)? yj g(2)? zk u(2) 2 log(a(c)k )

(5)

Vijk(3) a(3) b(3)? xi d(3)? yj g(3)? zk u(3) 1 log(a(u)k );

(6)


and

for the utilities associated with choosing professional colleges and universities, respectively. Moreover, owing to the inherent characteristics of the multinomial logit model, both accessibility measures appear in every choice probability (as utilities of each and every alternative appear in the denominator of equation (2)), allowing for possible substitution effects. Before proceeding with the estimation of the above utility functions in a multinomial logit setting, we elucidate some salient econometric issues at stake. We have identified the potential of correlation among the individual observations because of network effects and/or spatial clustering. The former may be caused by social interaction in localized networks, and the latter by unobserved spatial characteristics such as regional labour market conditions. Lacking data prohibits the explicit incorporation of these phenomena in the model specification, and we therefore resort to accounting for the correlation by choosing an appropriate estimator. A straightforward way of accomplishing this is to use the Huber White (‘sandwich’) estimator (see Wooldridge, 2002, section 13.8.2, for details). This is not possible, however, for spatial clustering, because a disjoint classification of spatially clustered individuals is at odds with the mere concept of spatial clustering.13 We therefore use the modified Huber White type of clustering to model localized social interactions. Specifically, we expect students attending the same high school to be more similar in their characteristics than individuals chosen randomly from the population. One can, of course, argue that social interaction and networks extend beyond the school’s boundaries* to the neighbourhood of residence, for instance. Since students attending the same high school tend to come from the same types of neighbourhoods and socio-economic contexts, we choose to define social interaction, and hence correlation among choices, by means of the high school attended by students. As mentioned above, modelling spatial clustering (or dependence) in a multinomial logit model is somewhat cumbersome (see Fleming, 2004), and we therefore incorporate spatial effects by focusing on spatial heterogeneity through the inclusion of fixed effects for provinces. The fixed effects are intended to capture, among other things, regional labour market conditions. The fact that regional labour market conditions are likely to be correlated to per capita income and population density makes a fixed-effect specification preferable over a randomeffects specification, because the correlation with the exogenous variables would cause the random-effects estimator to be biased. Finally, it is important to discuss the potential sample selectivity problem of our data. It was noted in Section 2 that the tracking of students starts very early in the Dutch education system, because at the age of about 12 pupils have to choose one out of four possible tracks. The sub-sample used in this study considers only those individuals in the VWO track, which may suggest a problem of non-random sample selection in that some factors that have determined the track choice may also play a role in the higher education choice. This is the case if, for instance, an unobserved attribute like innate ability influences the choice in favour of the VWO track, and at the same time favours the following choice of university education.


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Failing to account for sample selectivity implies that our estimates might suffer from sample selection bias. This is an obvious shortcoming of our study that we cannot correct for using a selection equation because we do not have data on students in all tracks and nor do we have a variable explaining the selection only. However, from the university standpoint VWO students constitute an important target group, as only these students can directly continue to university education. This suggests that this study does not lose its validity as a step towards understanding the role of space and the spatial distribution of higher education institutions to higher education choice. Our conclusions, however, cannot be extrapolated to students in tracks other than the VWO track. In the next section, we present the estimation results for a multinomial logit model, with spatial fixed effects and modified Huber White adjusted standard errors based on clustering of individuals attending the same high school, produced with the STATA 8.0 software.14 5. Estimation Results The coefficient estimates of the multinomial logit model are difficult to interpret in that they refer to the effect of each variable on the log-odds ratio between the choice (professional college, or university) and the no higher education option. In order to avoid these difficulties, we compute marginal effects of each variable on each possible outcome (see Table 3). The reference case chosen in the computation of the marginal effects is a female Dutch student, with at least one Dutch parent, who chose the science and health profile and graduated in 1998 from a private school with a religious denomination, located in Zuid-Holland. All continuous variables are set to their sample means. Table 3 shows that male students are more likely to go to university, and women to attend a professional college. The results also show that a student not being Dutch and/or having non-Dutch parents contributes to the odds of choosing the university alternative. The age of the student is negatively correlated with the university option, and positively with the professional college option, whereas the effect on choosing the no higher education option is not significantly different from zero. The results for the different profiles seem to indicate that, as compared to the science and health profile, graduates with other profiles are more likely to choose the professional college option. Furthermore, over time, graduates have a tendency to turn away from academic training as compared to professional training or no continued training.15 In accordance with previous studies, the student’s high school performance and talents, as measured by the GPA, have unequivocally the largest marginal effect on the odds of choosing the university option. With respect to high school characteristics, there is a slight tendency for graduates from public as well as private high schools (although in the latter case the results are statistically not significant), as compared to graduates from private schools with a religious denomination, to choose the no higher education and the university education option as compared to professional colleges. It is unclear whether this is partly an artefact of the proportion of professional colleges with a religious denomination being higher than the proportion of universities with a religious base. The size of high school has no discernable effect. The spatial characteristics of per capita income and level of urbanization are not significantly different from zero. This may be related, in part, to the relatively high

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Table 3. Multinomial logit model, marginal effects


No education Variable

Estimate

Personal characteristics Male Non-Dutch Parents non-Dutch Age Log(GPA) Science and technology profile Culture and society profile Economics and society profile 1999 graduate 2000 graduate

0.0026 (0.0067) 0.0140 (0.0191) 0.0168** (0.0085) 0.0007 (0.0054) 0.2607*** (0.0578) 0.0041 (0.0124) 0.0051 (0.0129) 0.0191** (0.0089) 0.0149 (0.0117) 0.0166* (0.0091)

High school characteristics Private school Public school Log(school size) Spatial characteristics Log(income per capita) Log(population density) Log(college accessibility) Log(university accessibility) Groningen Friesland Overijssel Gelderland Utrecht Noord-Holland Zeeland, N-Brabant Limburg Flevoland No. of observations % Correctly predicteda Log pseudo-likelihood Pseudo-R2

Robust SE

0.0106 (0.0155) 0.0275** (0.0135) 0.0104 (0.0146) 0.0270 (0.1109) 0.0053 (0.0072) 0.0067* (0.0035) 0.0089* (0.0047) 0.0404*** (0.0082) 0.0257*** (0.0077) 0.0238*** (0.0076) 0.0284** (0.0118) 0.0061 (0.0154) 0.0140 (0.0131) 0.0422*** (0.0067) 0.0307*** (0.0073) 0.0379*** (0.0052)

College Estimate

University

Robust SE

0.0718*** 0.0781* 0.1609*** 0.0536*** 1.1861*** 0.1403*** 0.1609*** 0.1413*** 0.0074 0.0378*

(0.0201) (0.0429) (0.0257) (0.0146) (0.0963) (0.0327) (0.0398) (0.0293) (0.0196) (0.0222)

Estimate 0.0745*** 0.0641 0.1777*** 0.0529*** 1.4467*** 0.1362*** 0.1661*** 0.1603*** 0.0075 0.0212

Robust SE (0.0201) (0.0459) (0.0272) (0.0155) (0.1104) (0.0312) (0.0370) (0.0273) (0.0221) (0.0231)

0.0439 (0.0376) 0.1036*** (0.0380) 0.0235 (0.0396)

0.0333 (0.0371) 0.0761** (0.0366) 0.0339 (0.0396)

0.3896 0.0056 0.1103* 0.0535** 0.0519 0.0282 0.0315 0.0641 0.0022 0.0339 0.0434 0.0504 0.0936**

0.4165 0.0003 0.1037* 0.0624** 0.0115 0.0025 0.0077 0.0357 0.0039 0.0479 0.0013 0.0811** 0.1315***

(0.2746) (0.0305) (0.0569) (0.0274) (0.0778) (0.0702) (0.0533) (0.0655) (0.0731) (0.0431) (0.0547) (0.0376) (0.0447)

(0.2826) (0.0305) (0.0535) (0.0320) (0.0776) (0.0699) (0.0564) (0.0609) (0.0828) (0.0445) (0.0548) (0.0357) (0.0461)

3,263 66.99 2,322.9451 0.10

Notes : Significance at the 1%, 5% and 10% level is indicated by ***, ** and *, respectively, with Huber White adjusted standard errors based on correlation among graduates attending the same high school given in parentheses. The marginal effects are computed for a female Dutch student, with at least one Dutch parent, who has chosen the science and technology profile, and who graduated in 1998 from a private school with a religious denomination, located in Zuid-Holland. All continuous variables are set to their sample means. a The percentage correctly predicted outcomes is computed as follows. For each observation: (i) we estimate the probability of each outcome; (ii) the outcome with the highest estimated probability is the predicted one; (iii) the outcome is correctly predicted if the predicted outcome is the observed outcome; and (iv) the percentage of outcomes correctly predicted is the total number of correctly predicted outcomes divided by the total number of observations in the sample.

level of spatial aggregation that we use, given restricted data availability, and to correlation with the spatial fixed effects. With respect to the spatial fixed effects for the different provinces, again it should be noted that the marginal effects should be compared to the omitted category Zuid-Holland, which is one of the most dense and urbanized provinces in the Netherlands. Given the signs and significance of the



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effects, it is actually likely that the dummy variables do pick up regional labour market differences as well as differences in other regional characteristics. Specifically, the marginal effects indicate that graduates living in rural areas (i.e. all provinces outside the highly urbanized Randstad, which is located in the provinces of Noord-Holland, Zuid-Holland, and Utrecht), in comparison to ZuidHolland, have a tendency to prefer the education to the non-education option. Moreover, in all cases but two (Limburg, which has a very popular ‘regional’ university; and Flevoland, which is a polder very close to Amsterdam and Utrecht, both of which have large universities), they prefer to go to a professional college. Hence, there is a rather pronounced dichotomy between the Randstad area and the rest of the Netherlands.16 We end this discussion of the estimation results by looking more closely at the results related to geographical accessibility or distance deterrence. The coefficients of the accessibility variables show that geographical accessibility plays a significant role in determining the choices of youngsters in their transition from high school to post-secondary education or dropout from the educational system. Accessibility to professional colleges exerts a positive impact on decisions to continue with a professional education, while accessibility to university institutions has a positive influence on going to a university. A 1% increase in any of the accessibility variables hardly affects the probability of the non-higher education option (the probabilities decrease by only 0.0067 and 0.0089, respectively). If the accessibility to professional colleges increases by 1%, the probability of choosing that type of institution increases by 0.11, at the same time lowering the probability of choosing the university option by approximately the same amount (0.10). Similarly, although somewhat smaller in magnitude, a 1% increase in the spatial accessibility of universities increases the probability of choosing academic education by 0.06, with a concurrent decreasing effect of the choice for a professional college. The difference in magnitude of the effects between the two types of higher education illustrates that participation in professional training is more sensitive to changes in accessibility than university participation. It is important to note, however, that the number of universities is substantially smaller than the number of professional colleges (13 vs about 50). Hence, the number of new professional colleges required to bring about a 1% increase in accessibility is substantially higher than the number of new universities needed to accomplish a similar increase in university accessibility. The effects of changes in accessibility are further illustrated by a series of simple simulations, the results of which are presented in Figure 1. The estimated average choice probabilities referring to the actually existing situation are 5.3% for the no higher education choice, and 29.1% and 65.6% for the choices of professional college and university, respectively. The simulations in Figure 1 cover various situations. First, we give the reference case, with the actual (act) accessibility levels for both professional colleges and universities presented above (the vertical dashed line). Second, we compute the choice probabilities by fixing the accessibility to the minimum (min) or the maximum (max) level observed in the sample. And finally, we re-compute the accessibility level assuming that either one of the universities is closed down, or a professional college in one of the university towns is closed down. In the closedown case the choice probabilities shown in Figure 1 are the average of the different closedowns considered. The options in Figure 1 are grouped in ascending order of the probability of choosing to continue with a university education. The

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Probability

0.8

0.6

0.4

0.2

Options

0.0 max min

max act

act min

act close


No education

act act

close act College

max max

min min

act max

min act

min max

Accessibility college Accessibility university

University

Figure 1. Simulated choice probabilities for selected accessibility scenarios of professional colleges and universities. Note : the abbreviations for the different options refer to accessibility fixed at the maximum value in the sample (max), at the minimum value in the sample (min), at the actual sample value (act), and at a re-computed value where one of the institutions is closed down (close).

figure clearly shows that changes in the accessibility of the higher education system have virtually no effect on the total number of high school graduates who decide to stay within or drop out of the higher education system. Hence, changes in the spatial accessibility of the higher education system have virtually no impact on the participation of youngsters in higher education as a whole. Changes in the accessibility of either compartment of the higher education system have a clear effect, however. The scenario where the accessibility of professional colleges is fixed at the sample maximum increases the likelihood of their choice, to the detriment of the university choice. Mutatis mutandis, similar effects hold for universities and for the scenario where the accessibility is fixed at the sample minimum. Finally, the figure shows that the effect of closing down either one university or one professional college (in a university town) has only a very small effect on national participation figures. At the local or regional level, the effect is, of course, notable, especially when the closure takes place in regions that are oriented strongly towards a particular institution. But, even then, the results indicate that the effects are rather limited, because most high school graduates opt to go to a different university rather than a nearby professional college. 6. Conclusions Previous studies have documented that a wide range of personal, high school, and spatial factors determine the decisions of school leavers to continue their education or to drop out of the higher educational system. However, only limited attention has been paid to the potential relevance of localized social interactions and for the impact of space. The latter concerns both heterogeneity of the observed phenomenon over space as well as the potential distance deterrence effect that can be captured by accounting for spatial or geographical accessibility of the higher education system. We address these important issues in a case study of high school graduates in the Netherlands, during the period 1998 2000. We use a multinomial



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logit model to investigate the choice behaviour of high school graduates 18 months after graduation, assuming that the school leavers have three options: university education, professional training, or no higher education. Localized social interaction is taken into account by allowing for observations of high school graduates attending the same high school to be correlated. Spatial effects are interpreted as spatial heterogeneity, and are taken into account by including fixed effects for areal units. The distance deterrence effect is incorporated through the inclusion of geographical accessibility indices for professional colleges and universities, respectively. Including variables reflecting both personal as well as high school characteristics mitigates omitted variable problems. The empirical results confirm that past high school performance and talent of the high school graduates are strongly related to students’ likelihood of going on to higher education. Another eye-catching result is that non-Dutch citizens and students with non-Dutch parents are more likely to choose to go on to university. Most importantly, we show that the choice behaviour of graduates has salient spatial dimensions. Concurrently, population density has a relatively small effect on the likelihood of high school graduates going to a professional college. There is also a distinct dichotomy between the highly urbanized Randstad area and the rest of the Netherlands: graduates living in rural areas have a tendency to prefer the education to the non-education option, and they prefer to go to a professional college. The most outstanding spatial result is, however, that the geographical accessibility of the higher education system significantly contributes to high school graduates choosing to continue education. This effect is strongest for professional colleges: a 1% increase in the accessibility of professional colleges increases the odds of high school graduates choosing this option by 0.11. The corresponding effect for universities is about half the size (0.06). We are aware of some shortcomings of our analysis. First, as we have pointed out in Section 4.3, the data we use potentially suffer from a sample selectivity bias problem, which we cannot fully correct with the available data. Therefore the results cannot be used to predict the behaviour of students in tracks other than the academic one. Second, we use population density and per capita income at the municipality level to proxy individual-level variables. The use of municipality averages results from lacking individual data. Although municipalities are in general not sufficiently homogeneous in terms of their socio-economic composition for these variables to serve as entirely adequate proxies, the use of these variables reduces the problem of omitted variable bias. Our research can obviously be extended in various ways. It would be particularly useful to be able to incorporate information on the living arrangements of students (see, for instance, Martinez-Granado & Ruiz-Castillo, 2002), and to focus on the impact of supply constraints in the professional education tier of the higher education sector. Future research geared towards investigating the choice behaviour of prospective students based on precise geo-referenced individual data can contribute to using sophisticated spatial econometric techniques.

Notes 1. Robertson & Symons (2003) are an exception as they consider the importance of localized social interactions on academic attainment.


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2. The abbreviations are derived from the Dutch terms: practical training (PRO, Praktijkonderwijs ), prevocational secondary education (VMBO, Voorbereidend Middelbaar Beroepsonderwijs ), general secondary education (HAVO, Hoger Algemeen Voorbereidend Onderwijs ), and pre-university education (VWO, Voorbereidend Wetenschappelijk Onderwijs ). 3. Note that among the public higher education providers there are public and (almost completely) publicly funded non-profit private schools, which usually have a religious character. This distinction was the result of the movement of Protestants and Roman Catholics against the state. 4. Universities are referred to through the use of the abbreviation WO (Wetenschappelijk Onderwijs ), and vocational or professional colleges are labelled HBO (Hoger Beroepsonderwijs ). Over the last two decades, mergers have resulted in a sizeable reduction in the number of HBO institutions, falling from 350 in the mid1980s to 56 in 2000, and subsequently to 50 in 2002 (OCW, 2003, pp. 74, 81). 5. For a limited number of profession-oriented programmes, such as medicine, dentistry, veterinary science, and information science, the national government fixes the number of students based on prospective demand in the labour market (numerus clausus ). 6. The costs of the RUBS survey are partly born by the high schools, whose decision to participate in the survey is voluntary. The survey covers different schooling types, but we restrict the sample to graduates from VWO because those are the only students for which the three choices (i.e. no higher education, professional college, or university) are available. We use the 1999, 2000, and 2001 surveys, referring to the school year 1997/1998, 1998/1999, and 1999/2000, and include only those students who obtained a diploma and who supplied information on all relevant variables. See Potma & Kolk (2000), Potma (2002), and Huijgen (2002), for details on the surveys. 7. These figures are not perfectly comparable due to slightly different definitions and the moment at which the information was obtained (see OCW, 2003). 8. Municipal per capita income can be only a rough proxy of household socio-economic background, but unfortunately individual socio-economic data are not available for this sample. In the Netherlands, a municipality is a city or a group of small cities located very close to each other. In 2003, there were 489 municipalities in the Netherlands, with an average size of 85 km2 and an average population of 33,114 inhabitants. One may also note, however, that in the context of the Dutch higher education system the relevance of household economic status is at least partly mitigated by the fact that all students are eligible for a basic scholarship, and it is only the supplementary grant that depends on family income. 9. We have experimented with different levels of spatial aggregation (for instance, the so-called NUTS I and II levels), but have found that a low level of aggregation, with many fixed effects as a result, explains away most of the variation. We therefore include 10 dummy variables for the 12 Dutch provinces because one of the provinces (Drenthe) is not represented in the data set, and the provinces of Zeeland and Noord-Brabant are pooled because of the low number of observations in the ‘no higher education’ category. 10. In order to avoid scale problems we define the intrazonal distance, which is relevant when a high school and a college or university location coincide in the same municipality, as: di ((p1)=p)×

pffiffiffiffiffiffiffiffi si =p;

where si is the area of region i measured in square metres (see Rietveld & Bruinsma, 1998). The formula assumes that regions are circular, and all zones are used equally intensively. Although various alternative intrazonal measures are possible as well (see Sa´ et al ., 2004), the choice of one or the other does not have any serious bearing upon the results. 11. These are gravity-type measures, as they weight the number of opportunities of higher education of each type with the inverse of distance as impediment factor. We have also experimented with simpler accessibility measures such as the number of institutions of each type in the region and the distance to the nearest college/ university. These measures are, however, highly negatively correlated with the accessibility measures, and the estimation results, therefore, barely change. 12. Rietveld & Bruinsma (1998, pp. 36 37) describe this type of accessibility measure in the context of the use of infrastructure services. The accessibility of a facility in a transport network is the expected value of the maximum utility of visiting that facility, which is assumed to depend on the mass of the facility, the travel costs of a trip to that facility, and a stochastic term. If the stochastic term is Weibull distributed, stochastic utility theory presumes accessibility measures that are typically of the form A/log Sj exp(utility’s deterministic part), where A refers to accessibility, and j to destinations. 13. The Huber White estimator requires the identification of observations that belong to clusters or groups of correlated observations (see, for example, Rogers, 1993; Williams, 2000, for details). This is perfectly feasible if one assumes network effects among individuals belonging to the same group or network. However, the nature of spatial dependence means that all observations, regardless of whether the observations refer to an individual or to an areal unit, typically belong to the same group. This can be seen as follows. In the spatial econometrics


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literature, spatial correlation is often modelled using contiguity or distance to determine spatial interaction. If, for instance, correlation is suspected among areal units that are contiguous, and unit a is correlated to unit b , and unit b to unit c , then unit a and c end up belonging to the same group of correlated observations regardless of whether or not they are contiguous, simply because they have a mutual link to unit b . 14. Using the STATA mlogtest command, we tested for the Independence of Irrelevant Alternatives (IIA) assumption, which is implicit in multinomial logit models. The null hypothesis was not rejected by the Hausman test, and there is therefore no statistical evidence against IIA. 15. A possible reason for this is that the originally rather generous system of student financial assistance has been subject to several changes, leading, in effect, to lower grants, increased parental contributions, and a check on students’ progress (Boezerooy, 2003). 16. This is consistent with earlier findings on the basis of a gravity model using aggregate areal data (see Sa´ et al ., 2004).


References Anselin, L. (2001) Spatial econometrics, in: B. Baltagi (ed.) Companion to Theoretical Econometrics, pp. 310 330, Oxford, Blackwell. Bishop, J. (1977) The effect of public policies on the demand for higher education, Journal of Human Resources , 12(3), 285 307. Black, S. E. & Sufi, A. (2002) Who Goes to College? Differential Enrollment by Race and Family Background, Working Paper 9310, National Bureau of Economic Research, Cambridge, MA. Boezerooy, P. (2003) Higher Education in the Netherlands, Country Report, Centre for Higher Education Policy Studies (CHEPS), Enschede. Borjas, G. J. (1995) Ethnicity, neighborhoods, and human capital, American Economic Review , 85(3), 365 390. Brock, W. A. & Durlauf, S. N. (2002) A multinomial-choice model of neighborhood effects, American Economic Review Papers and Proceedings , 92(2), 298 303. Catsiapis, G. (1987) A model of educational investment decisions, Review of Economics and Statistics , 69(1), 33 41. CBS (Centraal Bureau voor de Statistiek) (2003) StatLine , Statistics Netherlands. Internet site: http://statline.cbs.nl Checchi, D. (2000) University education in Italy, International Journal of Manpower , 21(3 4), 177 205. Corman, H. & Davidson, P. K. (1984) Economic aspects of post-secondary schooling decisions, Economics of Education Review , 3(2), 131 139. Duchesne, I. & Nonnemann, W. (1998) The demand for higher education in Belgium, Economics of Education Review , 17(2), 211 218. Ehrenberg, R. G. & Smith, R. S. (2000) Modern Labor Economics: Theory and Public Policy, 7th edn, Reading, MA, Addison-Wesley. Fleming, M. M. (2004) Techniques for estimating spatially dependent discrete choice models, in: L. Anselin, R. J. G. M. Florax & S. J. Rey (eds) Advances in Spatial Econometrics: Methodology, Tools and Applications, pp. 145 168, Heidelberg, Springer. Florax, R. J. G. M. (1992) The University: a Regional Booster? Economic Impacts of Academic Knowledge Infrastructure, Aldershot, Ashgate. Florax, R. J. G. M., Hall, P., Titheridge, H. & Wikhall, M. (2006) A comparative analysis of the geography of student recruitment and labor market entry, in: G. To¨rnqvist & S. So¨rlin (eds) The Wealth of Knowledge: Universities and the New Economy, forthcoming. Florax, R. J. G. M. & Nijkamp, P. (2005) Misspecification in linear spatial regression models, in: K. KempfLeonard (ed.) Encyclopedia of Social Measurement, pp. 695 707, San Diego, Academic Press. Fuller, W. C., Manski, C. F. & Wise, D. A. (1982) New evidence on the economic determinants of postsecondary schooling choices, Journal of Human Resources , 17(4), 477 498. Giannelli, G. C. & Monfardini, C. (2003) Joint decisions on household membership and human capital accumulation of youths. The role of expected earnings and local markets, Journal of Population Economics , 16(2), 265 285. Hartog, J. & Serrano, L. D. (2002) Earnings Risk and Demand for Higher Education, Discussion Paper 122/3, Tinbergen Institute, Amsterdam. Huijgen, T. (2002) Methodiek schoolverlatersinformatiesysteem 2001, ROA W 2002/3, Researchcentrum voor Onderwijs en Arbeidsmarkt, University of Maastricht. Kjellstro¨m, C. & Regne´r, H. (1998) Does Distance to a University Affect Enrolment Decisions? Evidence from Data on Three Cohorts of Swedes, Working Paper 8/98, Institute for Social Research, University of Stockholm. Kodde, D. A. (1986) Uncertainty and the demand for education, Review of Economics and Statistics , 68(3), 460 467. Kodde, D. A. & Ritzen, J. M. M. (1984) Integrating consumption and investment motives in a neoclassical model of demand for education, Kyklos , 37(4), 598 608.


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Kodde, D. A. & Ritzen, J. M. M. (1988) Direct and indirect effects of parental education level on the demand for higher education, Journal of Human Resources , 23(3), 356 371. Kohn, M. G., Manski, C. F. & Mundel, D. S. (1976) An empirical investigation of factors which influence collegegoing behavior, Annals of Economic and Social Measurement , 5(4), 391 419. Manski, C. F. (2000) Economic analysis of social interactions, Journal of Economic Perspectives , 14(3), 115 136. Martinez-Granado, M. & Ruiz-Castillo, J. (2002) The decisions of Spanish youth: a cross-section study, Journal of Population Economics , 15(2), 305 330. Moulton, B. R. (1990) An illustration of a pitfall in estimating the effects of aggregate variables on micro units, Review of Economics and Statistics , 72(2), 334 338. Nguyen, A. N. & Taylor, J. (2003) Post-high school choices: new evidence from a multinomial logit model, Journal of Population Economics , 16(2), 287 306. OCW (Ministerie van Onderwijs, Cultuur en Wetenschappen) (2003) Facts and Figures 2003 . Internet site: http:// www.minocw.nl/english/figures2003/pdf/figures2003.pdf Ordovensky, J. F. (1995) Effects of institutional attributes on enrolment choice: implications for post-secondary vocational education, Economics of Education Review , 14(4), 335 350. Ortu´zar, J. D. & Willumsen, L. G. (2001) Modelling Transport, 3rd edn, Wiley, Chichester. Potma, L. (2002) Methodiek schoolverlatersinformatiesysteem 2000, ROA-W-2002/2, Researchcentrum voor Onderwijs en Arbeidsmarkt, University of Maastricht. Potma, L. & Kolk, P. (2000) Methodiek schoolverlatersinformatiesysteem 1999, ROA-W-2000/9, Researchcentrum voor Onderwijs en Arbeidsmarkt, University of Maastricht. Rietveld, P. & Bruinsma, F. (1998) Is Transport Infrastructure Effective? Transport Infrastructure and Accessibility: Impacts on the Space Economy, Heidelberg, Springer. Riphahn, R. T. (2002) Residential location and youth unemployment: the economic geography of school-towork transitions, Journal of Population Economics , 15(1), 115 135. Robertson, D. & Symons, J. (2003) Do peer groups matter? Peer group versus schooling effects on academic attainment, Economica , 70(1), 31 53. Rogers, W. H. (1993) Regression standard errors in clustered samples, Stata Technical Bulletin , 13, 19 23. Sa´, C., Florax, R. J. G. M. & Rietveld, P. (2004) Determinants of the regional demand for higher education in the Netherlands: a gravity model approach, Regional Studies , 38(4), 373 390. Savoca, E. (1990) Another look at the demand for higher education: measuring the price sensitivity of the decision to apply to college, Economics of Education Review , 9(2), 123 134. Venti, S. F. & Wise, D. A. (1983) Individual attributes and self-selection of higher education: college attendance versus college completion, Journal of Public Economics , 21(1), 1 32. Williams, R. L. (2000) A note on robust variance estimation for cluster-correlated data, Biometrics , 56(2), 645 646. Wooldridge, J. M. (2002) Econometric Analysis of Cross Section and Panel Data, Cambridge, MA, MIT Press.


Prediction in the Panel Data Model with Spatial Correlation: the Case of Liquor

BADI H. BALTAGI & DONG LI


(Received October 2005; revised July 2006)

This paper considers the problem of prediction in a panel data regression model with spatial autocorrelation in the context of a simple demand equation for liquor. This is based on a panel of 43 states over the period 1965 1994. The spatial autocorrelation due to neighbouring states and the individual heterogeneity across states is taken explicitly into account. We compare the performance of several predictors of the states’ demand for liquor for 1 year and 5 years ahead. The estimators whose predictions are compared include OLS, fixed effects ignoring spatial correlation, fixed effects with spatial correlation, random-effects GLS estimator ignoring spatial correlation and random-effects estimator accounting for the spatial correlation. Based on RMSE forecast performance, estimators that take into account spatial correlation and heterogeneity across the states perform the best for forecasts 1 year ahead. However, for forecasts 2 5 years ahead, estimators that take into account the heterogeneity across the states yield the best forecasts. ABSTRACT

Pre´vision pour le panel DataModel avec corre´lation spatiale: le cas de l’alcool Cet article analyse le proble`me de la pre´vision d’un mode`le de re´gression de donneés de panel avec auto corre´lation spatiale dans le contexte d’une simple e´quation de demande d’alcool. Ceci se base sur un panel de 43 e´tats sur la pe´riode de 1965 a` 1994. L’auto corre´lation spatiale due aux e´tats avoisinants et l’he´te´rogeńeíte´ individuelle a` travers les e´tats sont explicitement pris en compte. Nous comparons la performance de plusieurs indices de demande des e´tats pour l’alcool sur une pe´riode d’un an et de cinq ans a` l’avance. Les estimateurs dont les pre´visions sont compareés incluent le MCO, les effets fixes ne prenant pas la corre´lation spatiale en compte, les effets fixes avec corre´lation spatiale, l’estimateur MCG des effets aleátoires ne prenant pas la corre´lation spatiale en compte et l’estimateur des effets aleátoires justifiant la corre´lation spatiale. En se basant sur la performance de la pre´vision RMSE (erreur quadratique moyenne), les estimateurs qui prennent en compte la corre´lation spatiale et l’he´te´rogeńeíte´ a` travers les e´tats reálisent les meilleures pre´visions pour l’anneé a` venir. Cependant, pour les pre´visions sur deux a` cinq ans, les estimateurs prenant en compte l’he´te´rogeńeíte´ a` travers les e´tats produisent les meilleures pre´visions. RE´SUME´

Badi H. Baltagi (to whom correspondence should be sent), Department of Economics and Center for Policy Research, Syracuse University, Syracuse, New York, NY 13244-1020, USA. Email: [email protected]. Dong Li, Department of Economics, Kansas State University, Manhattan, KS 66506, USA. Email: [email protected] USA. The authors wish to thank Lance Bachmeier, the editor and an anonymous referee for helpful comments and suggestions. ISSN 1742-1772 print; 1742-1780 online/06/020175-11 # 2006 Regional Studies Association

DOI: 10.1080/17421770601009817

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Prediccioń en el modelo de datos en panel con correlacioń espacial: el caso del licor. Este trabajo analiza la problema´tica de la prediccioń en un modelo de regresioń con datos en panel con auto-correlacioń espacial, en el contexto de una simple ecuacioń de demanda por licor. Este se basa en un panel de 43 estados por el perıódo 1965 1994. Se toma en cuenta explıćitamente la auto-correlacioń espacial debido a estados vecinos y la heterogeneidad individual entre los estados. Comparamos el comportamiento de diversos predictores de demanda de licor en los estados por uno y cinco anos por adelantado. Los estimadores cuyos predicciones se comparan incluyen OLS, efectos fijos que ignoran la correlacioń espacial, efectos fijos con correlacioń espacial, estimador GLS de efectos fortuitos que ignora la correlacioń espacial y estimador de efectos fortuitos que explica la correlacioń espacial. Basado en un comportamiento de prediccioń RMSE, los estimadores que incluyen la correlacioń espacial y la heterogeneidad en los estados resultan ser las mejores predicciones para un ano. Sin embargo, los estimadores que incluyen la heterogeneidad en los estados arrojan las mejores predicciones de dos a cinco anos


RESUMEN

KEYWORDS: Prediction; spatial correlation; panel data; liquor demand JEL CLASSIFICATION: C21; C23; C53

1. Introduction This paper focuses on prediction in a simple demand equation for liquor based on a panel of 43 states over the period 1965 1994. The spatial autocorrelation due to neighbouring states and the individual heterogeneity across states is taken explicitly into account. In order to explain how spatial autocorrelation may arise in the demand for liquor, we note that liquor prices vary among states primarily as a result of variation in state taxes on liquor. For example, in 1983, state excise taxes ranged from $1.50 per gallon in a low-tax state like Maryland to $6.50 per gallon in Florida. In 1984, apparent per capita consumption of alcohol for those aged 14 years and older in New Hampshire was 4.91 gallons, a little less than twice the national median of 2.64 gallons per capita. This does not imply that New Hampshire residents are heavy drinkers. Carlson (1985, p. 31) reports that ‘about 55% of New Hampshire’s $155 million in annual liquor sales is to out of state tipplers’. Border-effect purchases not explained in the demand equation can cause spatial autocorrelation among the disturbances.1 At the county level, liquor is not available in dry counties and consumers are forced to buy it from adjacent wet counties. The availability and pricing of liquor also varies as we move from private licensed states to monopoly states. Private licensed states are states with privately owned liquor stores that are licensed by the state. Monopoly states have a legal monopoly on the wholesale or retail of liquor. For more on the effects of the two governmental systems on prices, revenues and consumption of liquor, see Simon (1966) and Zardkoohi & Sheer (1984). This paper models the demand for liquor as follows: yit x?it bo it

i 1; . . . ; N ; t 1; . . . ; T ;

(1)

where yit denotes the real per capita consumption of liquor measured in gallons of distilled spirits by individuals of drinking age (16 years and older). The explanatory variables include the average retail price of a 750 ml of Seagram 7 expressed in real terms, and the real per capita disposable income of each state and a time trend. All

Panel Data Model with Spatial Correlation

177

variables, except the time trend, are expressed in logarithms and the estimated coefficients represent elasticities. Per capita consumption of liquor is obtained from the Distilled Spirits Institute, the price series is obtained from various issues of The Liquor Handbook and updated using the price of alcoholic beverages from the intercity cost of living index published quarterly by the American Chamber of Commerce Researchers Association. Per capita disposable income data on a state basis are published in various issues of the Survey of Current Business. Population data are obtained from various issues of the Current Population Reports. Price deflators are obtained from the Bureau of Labor Statistics. N 43 states and T 30 years. We use only the first 25 years for estimation and reserve the last 5 years for out-ofsample forecasts. For data sources, see Baltagi & Griffin (1995). Here, we update the data 12 years from 1983 to 1994. The disturbance term follows an error component model with spatially autocorrelated residuals (see Anselin, 1988, p. 152). The disturbance vector for time t is given by Downloaded by [Tehran University] at 04:22 21 August 2011

/

/

o t mft ; ?

(2)

?

where o t (o 1t ; . . . ; o Nt ) ; m (m1 ; . . . ; mN ) denotes the vector of state effects and ft (f1t ; . . . ; fNt )? are the remainder disturbances which are independent of m. The ft s follow the spatial error dependence model ft lW ft nt ;

(3)

where W is the matrix of known spatial weights of dimension N N and l is the spatial autoregressive coefficient. nt (n1t ; . . . ; nNt )? is iid(0; s2n ) and is independent of ft and m. The spatial matrix W is constructed as follows: a neighbouring state takes the value 1, otherwise it is zero. The rows of this matrix are normalized so that they sum to 1. The mi s are the unobserved state-specific effects which can be fixed or random (see Hsiao, 1986). State-specific effects include but are not limited to the following: (i) states like Montana, New Mexico and Arizona with Indian reservations sell tax-exempt liquor. (ii) States like Florida, Texas, Washington and Georgia with tax-exempt military bases. (iii) Utah, a state with a high percentage of Mormons (a religion which forbids drinking) had an adult per capita consumption of liquor in 1994 of 1.2 gallons. This is much less than the national average of 1.82 gallons per adult. (iv) Nevada, a highly touristic state, had per capita consumption of liquor in 1994 of 4.68 gallons, which is more than twice the national average. Not accounting for these state-specific effects may lead to biased estimates. There are also numerous government interventions and restrictions as well as health warnings and Surgeon General’s reports. These include the Alcohol Traffic Safety Act of 1983, which provided states with the financial incentives to enforce stringent drunk driving laws, as well as the Federal Uniform Drinking Age Act of 1984 passed by Congress to pressure all states into raising the drinking age to 21, and numerous warning labels on all alcoholic beverages warning pregnant women about the dangers of drinking and the public about the dangers of drinking and driving. Kenkel (1993) reports that between 1981 and 1986, 729 state laws were enacted pertaining to drunk driving. /

2. Estimation Table 1 reports the estimates of a simple, albeit naı¨ve, demand model for liquor using pooled OLS.2 These estimates ignore the states’ heterogeneity and the spatial

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Table 1. Estimates of liquor demand (based on 25 years) Price 0.774 0.819 0.584 0.766 0.679 0.314 0.682 0.317


Pooled OLS Pooled spatial Average heterogeneous OLS Average spatial MLE FE FE-spatial RE RE-spatial

(0.088) (0.093) (0.064) (0.062) (0.044) (0.044) (0.044) (0.045)

Income 1.468 1.605 1.451 1.589 0.938 0.612 0.959 0.654

(0.065) (0.070) (0.041) (0.044) (0.063) (0.075) (0.062) (0.075)

Year 0.062 (0.004) 0.067 (0.004)

0.049 0.029 0.049 0.030

(0.002) (0.002) (0.002) (0.002)

Notes : a The numbers in parentheses are standard errors. b The F -test for H0; m/ 0 in the FE model is F (42,1029)/165.79, with p / 0.000. c The Breusch Pagan test for H0; s2m /0 in the RE model is 97.30, with p/ 0.000. d The Hausman test based on FE and RE yields a/x23 of 3.36, with p/ 0.339.

autocorrelation. The price elasticity estimate is 0.77, while the income elasticity estimate is 1.47, and both are statistically significant. Next, we take into account the spatial autocorrelation, and estimate the model using the maximum likelihood method described in Anselin (1988). This assumes normality of the disturbances but ignores the heterogeneity across states. The resulting estimates are reported as pooled spatial in Table 1. This yields a slightly higher price ( 0.82) and income elasticities (1.61) than OLS ignoring the spatial correlation. Both elasticities are significant. The estimate of l is 0.34.3 In addition, we conducted a grid search procedure over l to ensure a global maximum. The likelihood ratio test for l 0 yields a value of 102.9, which is asymptotically distributed as x21 under the null hypothesis. The null is rejected, justifying concern over spatial autocorrelation. Table 2 allows for different parameter (heterogeneous) estimates for each year. The first set of estimates gives the cross-sectional demand equation estimates using OLS for each year. The price elasticity estimates varied between 1.41 in 1989 and 0.09 in 1977, while the income elasticity estimates varied between 0.97 in 1989 to a high of 1.75 in 1971. Pesaran & Smith (1995) suggest averaging these heterogeneous estimates to obtain a pooled estimator. This yields a price elasticity estimate of 0.58 and an income elasticity estimate of 1.45, both of which are significant. These are reported as average heterogeneous OLS in Table 1. These individual cross-section regressions and their average do not take the spatial autocorrelation into account. Using the normality assumption, we re-estimate these cross-sectional demand equations using the maximum likelihood estimates (MLE) described in Anselin (1988) which account for spatial autocorrelation in the disturbances. These heterogeneous spatial estimates are reported in Table 2 along with the corresponding estimate of l. We also report for each year the Lagrange multiplier test for l 0, given in Anselin & Bera (1998). The spatial coefficient estimates are insignificant at the 5% level in 15 out of the 25 years used for estimation. They are significant in 1975, 1979, 1981, 1982, 1984, 1985, 1986, 1987, 1988 and 1989. The heterogeneous MLE estimates accounting for spatial autocorrelation do not differ much from the heterogeneous OLS estimates ignoring spatial autocorrelation. The price elasticity estimates varied from a low of 0.16 in 1983 to a high of 1.56 in 1989, while the income elasticity estimates varied from a low of 0.97 in 1989 to a high of 1.88 in 1971. The average pooled spatial heterogeneous MLE estimator yields a price elasticity estimate of 0.77 and an /

/


179

Table 2. Heterogeneous estimates of liquor demand Heterogeneous OLS


Price 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989

0.354 0.299 0.405 0.489 0.367 0.992 1.306 1.230 0.933 1.054 1.098 0.081 0.091 0.047 0.424 0.313 0.271 0.294 0.161 0.617 0.698 0.273 0.478 1.178 1.409

(0.524) (0.523) (0.506) (0.507) (0.533) (0.569) (0.584) (0.596) (0.590) (0.571) (0.605) (0.704) (0.680) (0.622) (0.605) (0.614) (0.515) (0.476) (0.504) (0.531) (0.540) (0.522) (0.487) (0.446 (0.367)

Income 1.454 1.447 1.543 1.633 1.640 1.664 1.749 1.693 1.419 1.576 1.528 1.401 1.329 1.305 1.374 1.225 1.383 1.415 1.471 1.463 1.443 1.476 1.557 1.127 0.966

(0.286) (0.291) (0.294) (0.291) (0.312) (0.319) (0.331) (0.380) (0.390) (0.400) (0.418) (0.459) (0.443) (0.437) (0.397) (0.372) (0.362) (0.355) (0.351) (0.361) (0.341) (0.314) (0.278) (0.255 (0.253)

Heterogeneous spatial Price 0.371 0.393 0.487 0.657 0.443 1.084 1.424 1.434 1.171 1.263 1.556 0.459 0.313 0.244 0.718 0.498 0.442 0.377 0.157 0.713 0.884 0.526 0.711 1.255 1.564

(0.496) (0.499) (0.480) (0.484) (0.505) (0.553) (0.577) (0.613) (0.578) (0.570) (0.599) (0.731) (0.706) (0.604) (0.531) (0.564) (0.456) (0.424) (0.468) (0.493) (0.511) (0.508) (0.469) (0.424 (0.320)

l

Income 1.559 1.551 1.642 1.749 1.740 1.752 1.884 1.854 1.578 1.723 1.843 1.640 1.603 1.587 1.650 1.392 1.528 1.553 1.586 1.548 1.497 1.517 1.621 1.153 0.967

(0.324) (0.325) (0.325) (0.320) (0.340) (0.342) (0.364) (0.413) (0.417) (0.423) (0.454) (0.504) (0.499) (0.488) (0.426) (0.390) (0.364) (0.355) (0.353) (0.355) (0.338) (0.311) (0.279) (0.266 (0.258)

0.238 0.260 0.251 0.314 0.244 0.245 0.264 0.298 0.308 0.304 0.392 0.267 0.280 0.281 0.364 0.287 0.336 0.334 0.302 0.354 0.337 0.366 0.358 0.344 0.477

(0.195) (0.189) (0.192) (0.185) (0.189) (0.183) (0.182) (0.177) (0.169) (0.172) (0.169) (0.178) (0.181) (0.179) (0.162) (0.170) (0.163) (0.162) (0.169) (0.157) (0.160) (0.158) (0.162) (0.165) (0.145)

LMa 1.437 1.893 1.679 2.724 1.681 1.889 2.297 3.111 3.730 3.419 5.006 2.314 2.347 2.417 5.132 3.042 4.435 4.660 3.542 5.593 4.764 5.214 4.744 4.487 9.732

(0.231) (0.169) (0.195) (0.099) (0.195) (0.169) (0.130) (0.078) (0.053) (0.064) (0.025) (0.128) (0.126) (0.120) (0.023) (0.081) (0.035) (0.031) (0.060) (0.018) (0.029) (0.022) (0.029) (0.034) (0.002)

Note: a This gives the LM statistic for H0; l/0 and the corresponding p -value in parentheses.

income elasticity estimate of 1.59 with a spatial autocorrelation parameter estimate of l of 0.31, all of which are significant. These are reported in Table 1 as the average spatial maximum likelihood estimates. Note that these estimates are slightly higher than the average heterogeneous OLS estimates ignoring spatial autocorrelation. Next, we account for heterogeneity across states by using the fixed-effects (FE) estimator. This model assumes that the mi s are fixed parameters to be estimated. The F-statistic for testing the significance of the state dummies yields a value of 165.79, which is statistically significant. Note that if these state effects are ignored, the OLS estimates and their standard errors in Table 1 would be biased and inconsistent (see Moulton, 1986).4 Ignoring the spatial effects, the FE estimator can be obtained by running the regression with state dummy variables or by performing the within transformation and then running OLS (see Hsiao, 1986). These estimates are denoted by bˆ FE : These are reported in Table 1 as FE. Compared to the OLS estimates, the price elasticity estimate drops to 0.68 and the income elasticity estimate to 0.94; both are significant. This FE estimator does not take into account the spatial autocorrelation. This paper estimates the fixed effects with spatial autocorrelation using MLE.5 In addition, we checked this global maximum using a grid search procedure over l.6 The estimates are reported in Table 1 as FE-spatial. Figure 1 shows the relationship between the loglikelihood function and these results yield a much lower price


180


Figure 1. MLE for FE-spatial.

elasticity estimate of 0.31 and a lower income elasticity estimate of 0.61 than the FE estimator. Both estimates are statistically significant. The l estimate is 0.62. The likelihood ratio test for l 0, yields a x21 test statistic of 445.4. This is statistically significant and rejects the null of l 0 in the FE model. For the random-effects model, the mi s are iid(0; s2m ) and are independent of the fit s (see Anselin, 1988). For this model, we need to derive the variance covariance matrix. Let B IN lW, then the disturbances in equation (3) can be written as follows: ft (IN lW )1 nt B1 nt : Substituting ft in equation (2), we get /

/

/

o (iT IN )m(IT B1 )n;

(4)

where iT is a vector of 1s of dimension T and In is an identity matrix of dimension N. The variance covariance matrix is V E(oo? ) s2m (iT i?T IN )s2n (IT (B?B)1 ):

(5)

In this case, GLS on equation (1) using V1 derived by Anselin (1988, p. 154) yields bˆ GLS : If l 0, so that there is no spatial autocorrelation, then B IN and V from equation (5) becomes the usual error component variance covariance matrix /

/

VRE E(oo? ) s2m (iT i?T IN )s2n (IT IN ):

(6)

Applying GLS using this V RE yields the random-effects (RE) estimator which we will denote by bˆ RE : See Wansbeek and Kapteyn (1983) for more details. The onesided Breusch & Pagan (1980) test for s2m 0 yields an N(0,1) test statistic of 97.3, which is statistically significant. Feasible GLS is based on Amemiya’s (1971) method of estimating the variance components. This is an analysis of variance method that uses FE residuals in place of the true disturbances. The results are reported as RE in Table 1. In fact, the price elasticity estimate is 0.68 and the income elasticity estimate is 0.96 and both are significant. These RE estimates are close to those of the FE estimator. In fact, a Hausman (1978) test statistic for misspecification based on the difference between the FE and RE estimators of b yields a x23 test statistic of 3.36, which is statistically insignificant. The null hypothesis is not rejected and we conclude that the RE estimator is consistent.



181

Figure 2. MLE for RE-spatial.

If l " 0; MLE under normality of the disturbances using this error component model with spatial autocorrelation is derived in Anselin (1988). Here we apply this MLE using the CO module of GAUSS, version 4.0.28. In addition, we check the global maximum by running a grid search procedure over l and r s2m =(s2m s2n ): The latter is a positive fraction allowing a grid search over values of r between zero and one.7 The results are reported in Table 1 as RE-spatial. Figure 2 shows the relationship between l, r, and the loglikelihood function. These results yield a much lower price elasticity estimate of 0.32 and a lower income elasticity estimate of 0.65 than the RE estimator. Both estimates are statistically significant. The l estimate is 0.61, which is close to that of the FE-spatial model. The likelihood ratio test for l 0 yields a x21 test statistic of 423.1. This is statistically significant and rejects that l 0 in the RE model. We now turn to comparing these various estimators using forecasts for 5 years ahead. These are out-of-sample predictions for 1990, 1991, . . ., and 1994. /

/

3. Prediction Goldberger (1962) has shown that, for a given V; the best linear unbiased predictor (BLUP) for the ith state at a future period TS is given by /

yî;T S x?i;T S bˆ GLS v?V1 oˆGLS ;

(7)

where v E(o i;T S o) is the covariance between the future disturbance o i;T S and the sample disturbances o: bˆ GLS is the GLS estimator of b from equation (1) based on V; and oˆGLS denotes the corresponding GLS residual vector. For the error component model without spatial autocorrelation (l 0), Taub (1979) derived this BLUP and showed that it reduces to /

yî;T S x?i;T S bˆ GLS

s2m s21

(i?T l?i )oˆGLS ;

(8)

where s21 T s2m s2n and li is the ith column of In . The typical element of the last term of equation (8) is (T s2m =s21 )o¯i:;GLS ; where o¯i:;GLS aTt1 oˆti;GLS =T : Therefore,

182


Table 3. RMSE performance of out-of-sample forecasts (estimation sample of 25 years; prediction sample of 5 years)



1990

1991

1992

1993

1994

0.2485 0.2548 0.7701 0.8516 0.1232 0.1213 0.1239 0.1207

0.2520 0.2594 0.8368 0.9237 0.1351 0.1532 0.1356 0.1517

0.2553 0.2638 0.8797 0.9715 0.1362 0.1529 0.1368 0.1513

0.2705 0.2816 0.9210 1.0142 0.1486 0.1655 0.1493 0.1633

0.2678 0.2783 0.9680 1.0640 0.1359 0.1605 0.1366 0.1581

5 years 0.2590 0.2678 0.8781 0.9678 0.1360 0.1515 0.1367 0.1497

the BLUP of yi ,T S for the RE model modifies the usual GLS forecasts by adding a fraction of the mean of the GLS residuals corresponding to the ith state. In order to make this forecast operational, bˆ GLS is replaced by its feasible GLS estimate bˆ RE reported in Table 1 and the variance components are replaced by their feasible estimates. The corresponding predictor is labelled the RE predictor in Table 3. Baltagi & Li (1999) have derived the BLUP correction term when both error components and spatial autocorrelation are present. In this case the predictor reduces to yî;T S x?i;T S bˆ GLS Tu

N X

dj¯o j:;GLS ;

(9)

j1

where u s2m =s2n ; dj is the jth element of the ith row of V 1 with V TuIN (B?B)1 and ¯o j:;GLS aTt1 oˆtj;GLS =T : In other words, the BLUP of yi ,TS adds to x?i;T S bˆ GLS ; a weighted average of the GLS residuals for the N regions averaged over time. The weights depend upon the spatial matrix W and the spatial autocorrelation coefficient l. To make this predictor operational, we replace bˆ GLS ; u and l by their estimates from the RE-spatial MLE reported in Table 1. The corresponding predictor is labelled RE-spatial in Table 3. When there is no spatial autocorrelation, i.e. l 0, the BLUP correction term given in equation (9) reduces to the RE predictor term given in equation (8). Also, when there are no random state effects, so that s2m 0, then u0 and the BLUP prediction term in equation (9) drops out completely from equation (7). In this case, V in equation (5) reduces to s2n (IT (B?B)1 and GLS in this model, based on the MLE of l, yields the pooled spatial estimator reported in Table 1. The corresponding predictor is labelled the pooled spatial predictor in Table 3. If the fixed-effects model without spatial autocorrelation is the true model, then the BLUP is given by /

/

/

y˜i;T S x?i;T S b˜ FE m˜ i

(10)

(see Baillie & Baltagi, 1998), with mi estimated as m˜ i y¯ i: x¯ ?i: bˆ FE and y¯ i: aTt1 yit =T and x¯ i: similarly defined. Note that in this case, l 0, so that fit in equation (3) reduces to fit and the latter are not serially correlated over time. Therefore, v E(ni;T S n) 0; and the last term of equation (7) for the FE model /


183

is zero. However, the m˜ i appear in the predictions as shown in equation (10). The corresponding predictor is labelled the FE predictor in Table 3. If the fixed-effects model with spatial autocorrelation is the true model, then the problem is to predict


yi;T S x?i;T S bmi fi;T S ;

(11)

with fT S lW fT S yT S obtained from equation (3). Unlike the previous case, l " 0 and the mi s and b have to be estimated from MLE, i.e. using the FEspatial estimates. The disturbance vector from equation (3) can be written as f (IT B1 )y; so that v E(fi; T S f) 0 since the ys are not serially correlated over time. So the BLUP for this model looks like that for the FE model without spatial correlation given in equation (10) except that the mi s and b are estimated assuming that l " 0: The corresponding predictor is labelled the FE-spatial predictor in Table 3. Table 3 gives the RMSE for forecasts 1 year, 2 years, . . ., and 5 years ahead along with the RMSE for all 5 years. These are out-of-sample forecasts from 1990 to 1994. Each year’s RMSE is obtained from 43 state-by-state predictions. We compare the forecasts for all 5 years. The pooled OLS predictor in Table 3 is computed as yî;T S x?i;T S bˆ OLS : Pooled OLS, which ignores spatial autocorrelation and heterogeneity across the states, gives an RMSE over the 5 years of 0.2590. Accounting for spatial autocorrelation using the pooled spatial estimator increases this RMSE to 0.2678. This predictor replaces the OLS estimator of b by that of pooled spatial MLE reported in Table 1. Substituting the average heterogeneous OLS estimator (which ignores spatial autocorrelation but allows for parameter heterogeneity across time) more than triples the RMSE of pooled OLS yielding an RMSE to 0.8781. This forecast performance is not improved by accounting for spatial autocorrelation. Substituting the average heterogeneous spatial MLE yields an RMSE of 0.9678. Parameter heterogeneity is costly in terms of RMSE forecast performance and is beaten by estimators that rely on parameter homogeneity. A substantial improvement in RMSE forecast performance occurs when one uses a simple FE or RE estimators. In fact, the simple FE estimator without spatial autocorrelation yields an RMSE of 0.1360 followed closely by the RE estimator without spatial autocorrelation with an RMSE of 0.1367. These predictors were described in equations (10) and (8), respectively. Taking into account both heterogeneity and spatial autocorrelation, the best forecast performance for 1 year ahead is obtained by the RE estimator with spatial autocorrelation, which yields an RMSE of 0.1207, followed closely by the FE with spatial autocorrelation estimator with an RMSE of 0.1213. The FE-spatial predictor is obtained as in equation (10) but with the FE-spatial estimates from Table 1 replacing the FE estimates. The REspatial predictor is obtained from equation (9) by substituting the RE-spatial estimates from Table 1. For forecasts 2 or more years ahead, the FE estimator without spatial correlation performs the best, followed by the RE estimator. In sum, for the simple liquor demand model chosen to illustrate our forecasts, taking into account the heterogeneity across states by an FE or RE estimators yields the best out-of-sample RMSE forecast performance. The FE estimator gives the lowest RMSE for 1991, 1992, 1993 and 1994 and is surpassed only by the RE-spatial estimator in the first year, 1990. Overall, both the FE and RE estimators perform well in predicting liquor demand. Adding the spatial correlation in the model does not improve prediction except for the first year. However, as we show next, the

184


Table 4. Diebold Mariano test

(1) (2) (3) (4) (5) (6) (7) (8)


1

2

3

4

5

6

7

8

2.667 10.209 11.170 2.741 2.535 2.729 2.562

10.009 10.978 2.984 2.766 2.972 2.792

15.176 12.651 12.751 12.645 12.765

13.490 13.626 13.484 13.638

1.076 2.606 0.971

1.004 2.629

0.899


Note : The test statistic follows a standard normal distribution asymptotically.

difference in forecast accuracy between FE and FE-spatial or RE-spatial is not significant. To compare the out-of-sample forecast performance, we conduct the Diebold & Mariano (1995) test on the eight forecasts considered in this paper. The null hypothesis is that there is no difference in forecast accuracy of the two competing forecasts. Briefly, this test considers two forecast errors series, feˆt gand fe˜t g; based on two competing methods. Suppose the loss function is g(+ ): In our case, g(et ) e2t : Diebold & Mariano (1995) propose an asymptotic test

¯d S pffiffiffiffiffiffiffiffiffiffiffiffiffi ; Var(¯d )

1

(12)

aTt1 [g(eˆt )g(e˜t )] and Var(¯d) is the Hubert White robust variance of T the numerator. The test statistic S N(0,1). See Diebold & Mariano (1995) and West (2005) for more details. We conduct this test for pairwise comparisons based on the eight forecasts. The results for the 5-year forecast averaged over the 43 states are reported in Table 4. For example, the FE model is significantly better than the pooled OLS, the pooled spatial, the average heterogeneous OLS, the average spatial MLE, and the RE models in terms of out-of-sample forecast performance. However, the difference in forecast accuracy between FE and FE-spatial or REspatial is insignificant. These results are in agreement with the findings in the last column of Table 3. We also conduct the Diebold Mariano test on a year-by-year basis. The results are consistent with the first five columns in Table 3 and are available upon request from the authors. We add the caveat that comparisons of forecast accuracy are but one of many diagnostics that should be considered, and that the superiority of a particular forecast does not necessarily mean that other forecasts contain no additional information (see Diebold & Mariano, 1995). Some of the limitations of our study are that we used a simple static model of liquor demand when a dynamic liquor demand may be more appropriate. However, the latter model introduces additional econometric complications for our forecasting illustrations and these are beyond the scope of this paper. Despite these limitations, this paper lays out a simple methodology for forecasting with panel data models that are spatially autocorrelated. where ¯d

/


185

Notes 1. In fact, Baltagi & Griffin (1995) used the minimum price in neighbouring states to capture border-effect purchases. 2. For a dynamic demand model of liquor, see Baltagi & Griffin (1995). 3. This was obtained using the Constrained Optimum (CO) module with GAUSS version 4.0.28. 4. Note that prices vary across states mainly due to tax changes across states. To the extent that endogeneity in prices is due to its correlation with the state effects this makes the fixed-effects estimator a viable estimator which controls for endogeneity by wiping out the state effects. 5. This was obtained using the Constrained Optimum (CO) module with GAUSS version 4.0.28. 6. In fact, Figure 1 shows that the maximum likelihood function is well behaved for values of l around the global maximum. 7. Figure 2 shows that the maximum likelihood function is well behaved for values of l and r around the global maximum.


References Amemiya, T. (1971) The estimation of the variances in a variance components model, International Economic Reviews , 12, 1 13. Anselin, L. (1988) Spatial Econometrics: Methods and Models, Dordrecht, Kluwer. Anselin, L. & Bera, A. (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics, in: A. Ullah & D. Giles (eds) Handbook of Applied Economic Statistics, pp. 237 289, New York, Marcel Dekker. Baillie, R. & Baltagi, B. (1998) Prediction from the regression model with one-way error components, in: H. Pesaran, K. Lahiri, C. Hsiao & L.-F. Lee (eds) Analysis of Panel Data and Limited Dependent Variable Models, pp. 255 267, Cambridge, Cambridge University Press. Baltagi, B. H. & Griffin, J. M. (1995) A dynamic demand model for liquor: the case for pooling, Review of Economics and Statistics , 77, 545 554. Baltagi, B. H. & Li, D. (1999) Prediction in the spatially autocorrelated error component model, Econometric Theory , Problem 99.2.4,15, 259. Breusch, T. S. & Pagan, A. (1980) The Lagrange multiplier tests and its applications to model specification in econometrics, Review of Economic Studies , 47, 239 253. Carlson, E. (1985) New Hampshire tries harder, marketing liquor with spirit, Wall Street Journal , 8, 31. Diebold, F. X. & Mariano, R. S. (1995) Comparing predictive accuracy, Journal of Business and Economic Statistics , 13, 253 263. Goldberger, A. S. (1962) Best linear unbiased prediction in the generalized linear regression model, Journal of the American Statistical Association , 57, 369 375. Hausman, J. A. (1978) Specification tests in econometrics, Econometrica , 46, 1251 1271. Hsiao, C. (1986) Analysis of Panel Data, Cambridge, Cambridge University Press. Kenkel, D. S. (1993) Drinking, driving, and deterrence: the effectiveness and social costs of alternative policies, Journal of Law and Economics , 36, 877 913. Moulton, B. R. (1986) Random group effects and the precision of regression estimates, Journal of Econometrics , 32, 385 397. Pesaran, M. H. & Smith, R. (1995) Estimating long-run relationships from dynamic heterogeneous panels, Journal of Econometrics , 68, 79 113. Simon, J. L. (1966) The economic effects of state monopoly of packaged-liquor retailing, Journal of Political Economy , 74, 188 194. Taub, A. J. (1979) Prediction in the context of the variance components model, Journal of Econometrics , 10, 103 107. Wansbeek, T. & Kapteyn, A. (1983) A note on spectral decomposition and maximum likelihood estimation of ANOVA models with balanced data, Statistics and Probability Letters , 1, 213 215. West, K. D. (2005) Forecasting evaluation, in: G. Elliot, C. W. J. Granger & A. Timmermann (eds) Handbook of Economic Forecasting, Amsterdam, Elsevier. Zardkoohi, A. & Sheer, A. (1984) Public versus private liquor retailing: an investigation into the behavior of the state governments, Southern Economic Journal , 50, 1058 1076.


Wage Spillovers, Inter-regional Effects and the Impact of Inward Investment

NIGEL DRIFFIELD & KARL TAYLOR


(Received October 2005; revised September 2006)

This paper evaluates the extent of inter-industry and inter-regional wage spillovers across the UK. An extensive body of literature exists suggesting that wages elsewhere affect wage determination and levels of satisfaction, but this paper extends the analysis of wage determination to examine the effects of inward investment in the process. Thus far the specific effect of foreign wages on domestic wage determination has not been evaluated. We employ industry- and regional-level panel data for the UK, and contrast results from alternative approaches to space-time modelling. Each supports the notion that such wage spillovers do occur, though assumptions made concerning the modelling of spatial interaction are important. Further, such wage spillovers are more widespread for skilled than for unskilled workers and also lower in areas of high unemployment.

ABSTRACT

Les retombeés de salaires, les effets interre´gionaux et l’impact des investissements e´trangers Cet article e´value la porteé des retombeés de salaires au niveau interindustriel et interre´gional a` travers le Royaume-Uni. Une documentation importante existe qui sugge`re que les salaires d’ailleurs affectent la de´termination des salaires et les niveaux de satisfaction. Cet article approfondit neánmoins l’analyse de la de´termination des salaires afin d’examiner ce faisant les effets des investissements e´trangers. L’effet particulier des salaires e´trangers sur la de´termination des salaires au niveau domestique n’a pas jusqu’ici fait l’objet d’une e´valuation. Nous employons des donneés de panel industriel et re´gional pour le Royaume-Uni et comparons les re´sultats allant d’approches alternatives a` une mode´lisation geóstatique. Chacun soutient la notion d’existence de telles retombeés de salaires, bien que les hypothe`ses effectueés concernant la mode´lisation de l’interaction spatiale soient importantes. En outre, de telles retombeés de salaires sont plus re´pandues chez le personnel qualifie´ que le personnel non qualifie´ et sont e´galement plus faibles dans les re´gions ou` le choˆmage est e´leve´. RE´SUME´

Nigel Driffield (to whom correspondence should be sent), Aston Business School, Aston University Birmingham B4 7ET, UK. Email: [email protected]. Karl Taylor, Department of Economics, University of Sheffield, 9 Mappin Street, Sheffield S1 4DT, UK. Email: [email protected]. The authors gratefully acknowledge the support of the ESRC under award RES-000-22-0468. They are grateful for the comments of two anonymous referees. Comments were also helpful from Kristof Dascher, Gilles Duranton and other participants at the conference on Agglomeration and Labour Markets at the DIW in Berlin and also from conference participants at the European Society of Population Economics, New York, 2003, in particular Sarah Brown and Erling Barth. Thanks are also due to Sourafel Girma, Patrick Minford, Stanley Siebert, and other participants at various seminars in Lancaster, Nottingham, Birmingham and the University of Wales Colloquium. ISSN 1742-1772 print; 1742-1780 online/06/020187-19 # 2006 Regional Studies Association

DOI: 10.1080/17421770601009825

188

N. Driffield & K. Taylor

Derramamiento del salario, efectos inter-regionales y el efecto de la inversioń interna Este trabajo evaluá el alcance del derramamiento del salario inter-industrial e interregional en el RU. Gran parte de la literatura existente sugiere que el salario en otras partes afecta la determinacioń del salario y el nivel de satisfaccioń, pero este trabajo extiende el ana´lisis de la determinacioń del salario para examinar los efectos de la inversioń interna en el proceso. Hasta aquı´, el efecto especı´fico de los salarios extranjeros en la determinacioń local de los salarios no ha sido evaluada. Utilizamos datos de panel a nivel regional e industrial para el RU y contrastamos resultados de enfoques alternativos con un modelado espacio-tiempo. Cada uno apoya la idea de que dichos derramamientos si ocurren, aunque los supuestos en relacioń a modelado de inter-relacioń espacial son importantes. Adema´s, dichos derramamientos de salario estań mas extendidos en la fuerza laboral cualificada que en la fuerza laboral no cualificada y tambień son ma´s reducidos en aquellas a´reas con alto desempleo.


RESUMEN

KEYWORDS: Wage determination; regional spillovers; alternative wage JEL

CLASSSIFICATION:

J21, J30

1. Introduction A substantial body of literature exists which suggests that wages are influenced by spillover effects from wages set elsewhere. For example, a number of authors have considered the extent to which wages set in one region may influence wage determination in neighbouring (contiguous) areas (Manning, 1994; Burridge & Gordon, 1981; Molho, 1982). In a similar vein researchers have also considered the extent to which inter-industry spillovers effect wage determination. For example, Smith (1996) found that within the chemicals industry the existence of a wage leader influences the wage determination of other groups. Moreover, Latreille & Manning (2000) evaluate inter-industry and inter-occupational impacts, again finding that wages elsewhere impact on wage determination. This work, however, pre-dates recent developments in inter-regional modelling and spatial econometrics. The purpose of this paper is to add to this literature by considering inter-industry and inter-regional wage spillovers using the concept of contiguity. We also consider the importance of wage spillovers between the foreign and domestic sectors of UK industry. This is pertinent for two reasons: firstly there is a growing literature, discussed below, that illustrates the apparent premium paid by foreign-owned firms. Secondly, foreign-owned firms also have higher levels of skill intensity and pay a larger skill premium than domestic firms. This paper proceeds as follows: The following section provides a brief rationalization for how such spillovers can be justified. Section 3 discusses the potential role of foreign direct investment in domestic wage determination. Section 4 outlines the model of wage determination and spillovers that is developed, while the data are outlined in Section 5. Finally, the results and conclusions are presented in Sections 6 and 7. 2. Why Do Fallback Wages Matter? Notions of fairness and the importance of comparison incomes have long been important in the psychology and sociology literature on labour supply (Ross, 1948;


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Adams, 1963), and more recently in economics (Akerlof & Yellen, 1990; Rees, 1993; Smith, 1996). For example, Ross (1948) argues: ‘comparisons play a large and often dominant role as a standard of equity in the determination of wages under collective bargaining’. The underlying mechanism driving the importance of comparison incomes is the concept of a reference level of income against which an individual compares him/herself, which is also related to issues of individual utility or satisfaction (Clark & Oswald, 1996; Hamermesh, 2001).1 The concept of wage spillovers between industries or regions can be justified theoretically with reference to bargaining theory and migration. In bargaining models, where the aim is to maximize utility over and above some minimum level, neighbouring wages take the form of fallback wages. This provides an obvious link to models based upon migration (Harris & Todaro, 1970). If it is possible for workers to migrate between different industries and regions then wage increases in adjacent industries or regions may result in workers migrating to the more attractive (in terms of wages) location. The importance of external effects in wage determination is discussed in a different context by Yankow (2003) who demonstrates the pecuniary returns to migration. The returns to migration, however, are neither universal nor equal across occupational groups, suggesting a similar pattern for wage spillovers. Further analysis of the regional distribution of wage rates is provided by Dickie & Gerking (1998), who show that for Canada inter-regional wage differentials are lower for more educated workers. While Dickie & Gerking (1998) do not model the interregional effects explicitly, they do, however, identify regional differences in wage determination, largely using intercept dummies. In a similar vein, Brakman et al. (2004) for Germany have shown that real wage equalization between regions is an unrealistic assumption, and that while spillovers do occur, there are frictions in the process limiting the degree of convergence. Interestingly, Dickie & Gerking (1998) identify certain segmentation effects based on distance, and show that relocation costs will limit the size of spillovers. This implies, therefore, that any study of contiguity effects in wage determination must consider the limits to this process. This is discussed in more detail in Section 4. This suggests that an important consideration in any study of wage spillovers is labour market segmentation, particularly between regions. For example, it is well understood that unskilled workers are less mobile than skilled ones, and so interregional effects are likely to be smaller for unskilled workers than for skilled workers (McCormick, 1997). Further, there is also evidence that technological change generates an increase in wage inequality through an increase in relative demand for skilled workers (see, for example, Machin & Van Reenen, 1998). New technology is seen as complementary to skilled labour, and skilled labour augmenting, and so disadvantages the less skilled worker. The above suggests that notions of comparison wages must be seen within the context of labour market segmentation. For example, while it is well documented that inward investors pay higher wages than their host country counterparts (for UK evidence see Girma et al., 2001), the spillover effects of these higher wages may not be uniform across regions or occupational groups. The rationale for this and the potential limitations to the process of foreign-to-domestic wage spillovers are discussed in the following section.

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3. The Role of Foreign Direct Investment in Wage Comparisons There are a number of studies that identify substantial differences in factor demand between foreign and domestic firms (Conyon et al., 2002; Girma et al., 2001). The inference here is that foreign multinationals demonstrate higher levels of labour productivity, and in turn greater demand for high-quality labour. Equally, foreign entrants pay higher wages than incumbent domestic firms, and therefore may attract higher quality workers. Therefore, entry by such firms is expected to impact on domestic labour markets not only in terms of labour demand but also in restricting the supply of labour to domestic firms offering lower wages. Over the period 1984 1992 foreign firms, on average, paid 11% more to unskilled workers than domestic firms, and approximately 9% more to skilled workers (figures from the Office for National Statistics).2 Driffield (1999) shows that as a result of these higher wages, increased inward investment acts to bid up wages, and in the short term to reduce employment. However, in this study the labour market effects of foreign direct investment (FDI) have been effectively constrained to intra-industry effects, which also therefore encompass the crowding out of domestic employment through product market competition. The productivity effects of inward investment may have compounded the direct wage effects. As Barrell & Pain (1997) show, one of the major impacts of inward investment into the UK has been to introduce new technology, while Driffield & Taylor (2005), for example, outline the major technological differences between the foreign-owned and domestic sectors, and their magnitudes. There is a relatively large body of literature on the importance of productivity spillovers from FDI (see, for example, Driffield et al., 2004). This outlines the importance of interand intra-regional effects in industry-level productivity spillovers, while Sun (2001) demonstrates for China that the beneficial effects of inward FDI on host regions are not distributed evenly but are concentrated in those regions that are best placed to benefit from the introduction of new technology. Further, Driffield & Taylor (2000) demonstrate that productivity spillovers from FDI are partly facilitated by domestic firms becoming more skill intensive, and, as such, one may expect wage spillovers to affect the market for skilled, rather than unskilled, workers. Despite this conjecture, the impacts of FDI on labour markets in general, and earnings in particular, have surprisingly been far less explored (for a review of this literature see Driffield & Taylor, 2000). The above discussion suggests, therefore, that wage spillovers from inward investment will be greater for skilled workers than for unskilled workers, in terms of both inter-regional impacts and foreign-to-domestic impacts. This is an important issue for policy makers, as concern has been expressed that both skill shortages and labour market tightening have been exacerbated in certain parts of the country by inward investment. Equally, if inward investment merely bids up skilled wages in the domestic sector, then this will increase wage inequality not only between skilled and unskilled workers but also across industries and, perhaps more importantly, across regions. In a similar vein, there is a well-developed body of literature on the determinants of the spatial distribution of FDI (see, for example, Basile, 2004; Coughlin & Segev, 2000; Crozet et al., 2004, who argue that agglomeration of activity and the level of development of a region has a positive impact on FDI location). The existence of foreign-to-domestic wage spillovers, and also the extent to which segmentation between the foreign and domestic sectors exists, can be tested


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directly. This can be achieved with the use of contiguity matrices interacting with wage terms which have been used in the regional science literature to examine issues such as unemployment (e.g. Aragon et al., 2003), economic growth (e.g. Lo´pez-Bazo et al., 2004), and the economics literature (e.g. Latreille & Manning, 2000). Our analysis extends that of Latreille & Manning (2000) to include different spillover terms for wages in the foreign and domestic sectors. Further, comparing wage spillovers in the skilled and unskilled sectors can test the hypothesis of segmentation as a restriction to spillovers. We hypothesize that segmentation will be less important in the market for skilled workers, and as such that foreign-todomestic wage spillovers will be greater for skilled workers. We also suggest that wage spillovers for unskilled workers will be limited geographically, as unskilled workers are less mobile. Specifying the model in this way allows for a further consideration that is addressed in the wider literature. There is a large body of literature on productivity spillovers, both in the context of FDI and, more generally, both in terms of spillovers between and within industries, and between regions (see, for example, Driffield et al., 2004). While capital investment is an important determinant of labour productivity, the model presumes that any additional external productivity effect will impact on the regional labour market in the form of higher external wages.3 4. Theory and Empirical Models The theoretical approach is based upon a simple structural model of the labour market, highlighting the role of alternative wages as comparison incomes in labour supply. In order to examine the effect that inward FDI has on the labour market, we focus on wages paid by domestically owned enterprises. To characterize this, we specify a Cobb Douglas production function for the domestic sector, of the form Q AKa Lb , where Q is output, K is capital, and labour L is split into skilled and unskilled. The marginal revenue product of labour is defined as MPL @Q=@L AK a bL b1 : In equilibrium, wages in the domestic sector, y, are given by: /

y pAK a bL b1 :

(1)

However, it is also necessary to introduce the supply side of the labour market, which is influenced by the wage on offer y, two vectors of alternative wages available y˜ 1, y˜ 2 and unemployment U,4 so: L f (y; y˜1 ; y˜2 ; U):

(2)

The measures of alternative wages consist of wages paid in neighbouring regions and related industries. y˜ 1 captures regional-level intra-industry effects. Firstly, this includes the inter-occupational term. Following Latreille & Manning (2000) it is necessary to investigate whether skilled wage rates have an impact upon unskilled wage determination and vice versa. Secondly, y˜ 1 captures the effect of FDI by including wages paid in the local industry by foreign-owned firms. y˜ 2 then captures the inter-industry and inter-regional effects in wage determination, including contiguity effects between foreign and domestic wage spillovers, and inter-industry wages paid in both the foreign- and domestically owned sectors. The variables that make up y˜ 1 and y˜ 2 are discussed in depth below. Intra-industry spatial contiguity is modelled using a spatial lag structure outlined in equation (3) below.

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To estimate the reduced form model of skilled and unskilled domestic wages we contrast two approaches to time-space econometrics. Firstly, we adopt estimation based on a standard spatial fixed-effects model (see Baltagi, 2002; Elhorst, 2003), and employ the most general reduced form of wage equation, based on Latreille & Manning (2000) and Driffield & Girma (2003). In equilibrium the basic model can be given by:


y rW1 yXfg1 W2 y˜1 g2 W3 y˜2 (I lW4 )o;

(3)

where y is the spatially lagged dependent variable, a matrix of industry-level wages paid by domestically owned firms in contiguous regions at the industry level, X is a matrix of observations on other independent variables, y˜1 is a matrix consisting of alternative wages within the industry and the region, including inter-occupational effects, and wages paid to the same occupational group by the foreign-owned sector. y˜2 is a matrix consisting of alternative wages in contiguous industries or regions as defined below. The data we employ have three dimensions* industry (i), region (r) and time (t)* hence we consider the influence of domestic and foreign wages in adjacent regions and industries using contiguity matrices, which inform us of neighbouring industry and/or regional wages. We also consider the significance of time lags in wage spillover effects, although where spillovers are found these appear to occur within a 1-year lag. Given the data (see Section 5 below) we are able to split the sample into foreign and domestic sectors, with details for each of the twodigit industries and 11 regions. Hence, alternative wages are based upon the following: . . . . . .

contiguous industry domestic wage * industry-level wages paid by UK-owned firms in all two-digit industries (i) operating in the same one-digit industry (j), given in y˜ 2 (see equation (3) above); contiguous industry foreign wage * industry-level wages paid by foreign firms in all two-digit industries (i) operating in the same one-digit industry (j), given in y˜ 2 (see equation (3) above); contiguous region domestic wage * industry-level wages paid by domestic firms in adjacent regions. This is the spatially lagged dependent variable, given in y (see equation (3) above); contiguous region foreign wage * industry-level wages paid by foreign firms in the same industry (i) operating in adjacent regions (j), given in y˜ 2 (see equation (3) above); cross-wage term * wages paid to other occupational groups (skilled or unskilled) within the industry and region, given in y˜ 1 (see equation (3) above); foreign wage* the wages paid by the foreign-owned sector in industry (i) and region (r), given in y˜ 1 (see equation (3) above).

Hence the alternative wages include inter-industry effects, inter-occupational effects (i.e. the cross-over wage terms (skilled or unskilled)), inter-regional effects, and the foreign-to-domestic effect. This also has a spatial component given by g. In equation (3) the matrices Wz are spatial weights where the importance of spatial lags in domestic wage effects are captured by r. Two alternatives for the contiguity matrix are generally offered by the literature, namely the ‘rook’ specification, where any contiguous region would enter with a ‘1’ in the matrix, and the standard

Wage Spillovers

reduced form, where this is normalized such that all columns sum to 1. In practice, a standard reduced form is employed.5 We also allow for autoregressive disturbances with effects given by l. We initially estimate the spatial lag and the spatial error regression model by maximum likelihood, allowing for the spatial nature of our data. In practice we follow Florax & Folmer (1992) and Aragon et al. (2003) where firstly we test whether l 0 and then whether r 0, with each model allowing for the possibility that g1 " 0 and g2 " 0. The model given in equation (3) is based on a relatively standard levels approach but incorporating spatial dependency. However, in addition to the essential problems of spatial lag and spatial error, and the fundamental question of whether findings regarding the importance of alternative wages are robust to alternative treatments of these issues, there are other considerations. Previous work in the area also investigates the importance of time lags and persistence in these effects. This requires a reformulation of the basic model to include a lagged dependent variable. In standard wage determination models (see, for example, Willis, 1986), a vector of further characteristics, or ‘fixed effects’ such as age, experience, education, gender and ethnic group would be included. Such data are clearly not available at this level of disaggregation, but these effects can be captured by a lagged dependent variable which, by definition, is correlated with these fixed effects. Thus, the model that is estimated becomes a dynamic panel data model (now introducing the subscripts defining the dimension of our data into the analysis): /

/

/


193

/

yirt ayirt1 rW1 yist X irt fg1 W2 y˜1irt g2 W3 y˜2irt (I lW4 )o irt ; (4) where yist captures the spatially lagged dependent variable, region s being contiguous to region r. With a model of this type there are a number of endogeneity issues surrounding standard ‘levels’ fixed-effects estimators. The development of panel data models to handle these types of problems is relatively well understood (see, for example, Arrelano & Bond, 1988, 1991; Holtz-Eakin et al., 1988). These involve converting the data to first differences and employing a GMM estimator, using past values as instruments for current values. However, the standard form of this estimator is not robust to spatial error or autocorrelation. We therefore propose an alternative GMM estimator following Kapoor et al. (forthcoming), who develop a spatial GMM estimator. This is based on the GMM estimator of Kelejian & Prucha (1999) for estimating the disturbance process, and subsequently applying GLS for the final regression. However, the choice of instruments for this estimation is far from straightforward. With a spillover model of this type there is the concern that contiguous wages are endogenous in wage formation, and must therefore be instrumented. We employ further spatial lags and time lags of wages as instruments of contiguous wages, and time and spatial lags to instrument unemployment. Capital is instrumented using time lags only. This approach is confirmed by the Sargan identification test statistic. A final consideration is that different regions of the UK exhibit markedly different patterns of unemployment. This is illustrated by Table 1. As such, it is likely that the effects of external wages, and indeed the importance of external wages in wage determination, will differ across regions, varying with the levels of unemployment. Further, regions with ‘assisted area’ status have often sought to attract inward FDI in order to reduce structural unemployment.6

194


Table 1. Average unemployment rates by region over the period 1984 1992 Region South East East Anglia South West West Midlands East Midlands Yorkshire & Humberside North Westa North of Englanda Walesa Scotlanda

Unemployment (%) 6.80 6.40 7.50 10.10 8.00 9.90 11.10 12.50 10.50 11.00


Note: aCovered mostly by assisted area status during the period.

The regions with higher unemployment* North West; North; Wales and Scotland* were all covered by assisted area status during the period. One common criticism of estimating equations (3) and (4) is that the unemployment variable is endogenous. Consequently, in the empirical analysis, in addition to employing unemployment as an explanatory variable, we also split the sample by region in terms of assisted and non-assisted area status.7 When we do so, the unemployment term is dropped. After describing the data in the next section, we estimate skilled and unskilled domestic wage equations based upon fixed-effect spatial panel data models and spatial GMM panel data models. The latter approach employs instruments to allow for endogeneity in the regressors, including the contiguous wage variables that are instrumented with further lags. 5. Data The UK Office of National Statistics (ONS) provided the data used for the empirical analysis. The data set comprises information for both the foreign-owned and domestically owned sectors of UK manufacturing, and comprises industry- and regional-level data for the UK, covering the period 1984 1992. There are 11 standard planning regions, and 19 manufacturing sectors (two-digit level) (see Figure 1 and Table 2). While data for Northern Ireland are available, these are omitted from the econometric analysis as Northern Ireland is not contiguous with the rest of the UK. Figure 1 illustrates the standard statistical regions of the UK as defined by the UK Office for National Statistics. These are NUTS2 regional classifications. In terms of spillover effects, Figure 1 illustrates the contiguity of the 11 regions. For example, imagine a worker employed in industry i who lives in Yorkshire & Humberside. There are a variety of spillovers that may occur in his/her wage determination. For example, the average wage bill in the domestic sector in Yorkshire & Humberside is £500 less than that in the North West (see Table 3), so a negative effect on wage aspirations may be expected* since the two regions are neighbouring (see Figure 1). However, if the individual remains in the Yorkshire & Humberside region but is able to move from the domestic to the foreign sector then this may yield a positive wage effect, since foreign wages are around £1,500 higher. An even greater effect on his/her wages may be the possibility of moving.


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Figure 1. Standard statistical regions of the UK.

For example, a move to the North West, and a job in the foreign-owned sector would be expected to increase earnings by £4,100. Akin to this argument, the differential between the average wage bill by industry and domestic/foreign sectors is also applicable. The advantage of such data, in addition to isolating domestic foreign interactions, is that they allow one to evaluate inter- and intra-regional effects, as well as inter- and intra-industry effects. These are based on the best alternative pay, in the industry and sector, in surrounding regions or related industries. In both the domestic and foreign sectors, skilled wages are defined as annual earnings of non-manual workers and conversely unskilled wages are defined by the annual earnings of manual workers. The capital stock in the domestic sector is estimated as the sum of the net capital investment of the previous 7 years, depreciated by 10% per annum. The unemployment rate is based upon regional-level data and does not vary across industries. To construct the alternative wage we chose the maximum wage available in contiguous industries or regions such that it represents the best alternative wage.

196


Table 2. Definitions of regions and industries Industries Region


SIC code South East East Anglia South West West Midlands East Midlands Yorkshire & Humberside North West North East

22 23 24 25 26 31 32 33

Wales Scotland

34 35 36 37 41 43 45 46 47

Description Metal manufacturing Extraction of minerals not specified elsewhere Manufacture of non-metallic mineral products Chemical industry Production of man-made fibres Manufacture of metal goods not specified elsewhere Mechanical engineering Manufacture of office machinery & data processing equipment Electrical & electronic engineering Manufacture of motor vehicles & parts Manufacture of other transport equipment Instrument engineering Food, drink and tobacco Textile industry Footwear and clothing industries Timber & wooden furniture industries Manufacture of paper & paper products; printing & publishing Processing of rubber & plastics Other manufacturing industries

48 49

Table 3 shows the sample means for a number of variables. For instance, over the period 1984 1992 the unemployment rate across regions averaged 10%. The region with the highest average wage in the foreign sector was the North West, and for the domestic sector the North East.8 Looking at the ratio between the foreign and domestic wage bill the largest differential is seen in the North West (21%). 6. Empirical Results In this section we report estimates of both skilled and unskilled wage determination, based upon spatial fixed-effects models (equation (3)), and spatial GMM estimation (equation (4)). Finally, we report the wage equations for assisted areas and non-assisted areas separately. All results across the three sets of estimators are shown with t-statistics based upon robust standard errors. 6.1. Spatial Fixed-effects Results The results from estimating equation (3) for both unskilled and skilled wage determination are shown in Table 4. These illustrate results based on alternative specifications, allowing for a spatial lag (r " 0) and a spatial error (l " 0). There is no evidence of a spatial lag operator in these data, for either skilled or unskilled workers since the hypothesis that r 0 cannot be rejected. Spatial autocorrelation, however, is clearly present, and shows negative dependence. Time dummies are used across the specifications and are always jointly significant. Throughout, we test the null hypothesis of spatial independence, i.e. no spatial autocorrelation based upon the LMSEC test outlined by Baltagi et al. (2003). /

/

/

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Table 3. Summary statistics of sample means Earnings, capital and unemployment: Domestic skilled wage Domestic unskilled wage Foreign skilled wage Foreign unskilled wage Capital

£17,198 £13,095 £18,761 £17,488 £1,261,219

Unemployment

10%

Average foreign and domestic wages per head and ratio by region:


Region South East East Anglia South West West Midlands East Midlands Yorkshire & Humberside North West North East Wales Scotland

Foreign wage £19,800 £17,200 £16,800 £18,400 £18,000 £17,800 £20,400 £19,200 £18,100 £18,300

Domestic wage £17,100 £16,800 £16,800 £16,400 £15,500 £16,300 £16,800 £17,400 £17,300 £16,700

Ratio 1.16 1.02 1.00 1.12 1.16 1.09 1.21 1.10 1.05 1.10

Average foreign and domestic wages per head and ratio by industry: Industry SIC22 SIC23 SIC24 SIC25 SIC26 SIC31 SIC32 SIC33 SIC34 SIC35 SIC36 SIC37 SIC41 SIC43 SIC45 SIC46 SIC47 SIC48

Foreign wage £20,000 £17,900 £19,200 £17,200 £18,400 £20,600 £15,800 £22,600 £17,300 £15,400 £21,000 £14,300 £10,700 £13,500 £20,700 £19,100

Domestic wage £20,300 £15,900 £18,000 £19,000 £16,300 £16,100 £18,400 £18,200 £15,600 £20,100 £18,600 £15,500 £15,200 £13,000 £10,300 £15,400 £18,800 £17,100

Ratio 0.98 0.99 1.01 1.07 1.00 1.13 1.02 1.12 0.93 0.93 1.38 1.10 1.04 0.87 1.10 1.12

Notes : Definitions of industry SIC codes are given in Table 2. Average wage per head/total wage bill }/ FTE employment by industry (region).

Turning to the estimates of the coefficients generated by the model, capital and labour are shown to be complementary within this framework. While the capital stock is positively correlated with wages, this effect is significantly greater for unskilled workers. It is likely that increased industry-level capital expenditure within the region impacts on unskilled labour productivity to a greater extent than it does on the productivity of skilled labour. Unemployment is significant in both

Spatial fixed effects Unskilled Spatial lag estimator Capital 0.744 (6.36) Unemployment /0.254 (2.20) Skilled wage 0.490 (9.37) Unskilled wage Foreign wage 0.015 (1.41) Contiguous region domestic wage 0.048 (2.79) Contiguous region foreign wage 0.012 (0.83) Contiguous industry domestic wage 0.022 (1.03) Contiguous industry foreign wage 0.009 (2.45) Observations Time dummies Log likelihood /2,688.971 p/ [0.000] Wald g2 /0: x2(4) p/ [0.000] r 0.230 (0.82) Wald r /0: x2(1) 0.679 p/ [0.410] Wald : x2(1) Spatial autocorrelation LMSEC

Skilled Spatial error estimator 0.810 /0.485 0.480

(6.30) (4.56) (8.51)

0.008 0.041 0.008 0.023 0.014

(0.68) (2.50) (0.55) (1.03) (2.22) 1,520 Yes /2,686.584 p / [0.000] p/ [0.000]

Spatial lag estimator 0.271 /0.220

(3.69) (2.12)

0.307 /0.079

(3.41) (1.62)

0.590 0.060 0.047 0.003 0.018 0.021

(5.50) (3.51) (1.87) (0.19) (1.13) (3.11)

0.564 0.051 0.050 0.004 0.019 0.018

(5.18) (3.12) (2.03) (0.29) (1.17) (2.30)

/2,829.121 p/ [0.000] p / [0.000] (0.34) /0.097 0.116 p/ [0.733]

/0.708 (2.30) 5.294 p / [0.021] p/ [0.241]

Spatial error estimator

/2,818.373 p / [0.000] p/ [0.000]

/1.178 (7.05) 49.707 p / [0.000] p/ [0.187]



198

Table 4. Spatial fixed-effects results for domestic wage determination


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equations and has a negative impact as expected, with a significantly greater impact on unskilled wages, again as one would expect. This is consistent with Blanchflower & Oswald (1994) and Cameron & Muellbauer (2000), but contrasts with Latreille & Manning (2000) who find no significant difference in the impacts of unemployment. The cross-wage terms indicate the existence of such wage effects. These are also suggestive of the importance of skill differentials in wage determination. The interoccupational effects are positive and significant and suggest that skilled wages are more responsive to cross-wage spillovers than unskilled wages. Interestingly, industry-level wages paid by inward investors at the regional level have no influence upon unskilled wages, but do have a positive and significant effect on skilled wage determination. This would suggest that wage differentials between the skilled and unskilled will increase with foreign presence, thus increasing wage inequality in the domestic sector (see Taylor & Driffield, 2005). Finally, this model generates significant evidence of wage spillover effects. We find evidence that contiguous regional domestic wages and contiguous industry foreign wages impact on local wage determination. Not surprisingly, wage spillover effects are greater for skilled labour. Skilled labour is generally more mobile, and as discussed above, the returns to mobility are greater for skilled labour (see, for example, Dickie & Gerking, 1998). These results are interesting in that neighbouring industry and regional wages matter for wage determination, but the mechanism of foreign effects operates solely via industry comparisons. In contrast, domestic wage comparisons exhibit inter-regional effects. This suggests that while inward investment has an impact on local labour markets, these effects are limited to the area of the investment. There are two potential explanations for this. Firstly, there is significant evidence that productivity spillovers from FDI (and indeed productivity spillovers generally) are limited geographically (Driffield et al., 2004; Baranes & Tropeano, 2003). Secondly, (higher paying) foreign firms outside the region may not be seen as relevant comparators by firms seeking to set wages within a local labour market context. 6.2. Spatial GMM Results The results from estimating the dynamic panel data model of equation (4) for both unskilled and skilled wage determination are shown in Table 5, which reports results based upon spatial GMM estimation.9 Tests for spatial correlation and autocorrelation are also reported, where, as with the fixed-effects results, spatial dependence is apparent in the data. This effect is captured by the use of contiguous wage variables, instrumented with further spatial lags. As a result, tests for seconddegree spatial lags were also carried out, though none were detected. All estimates are based upon robust standard errors and include a set of time dummies that all prove significant. After losing observations for first differencing and instrumenting, estimation is based upon 1,330 observations. All alternative wage variables are instrumented with lagged values due to possible endogeneity problems, as is the capital stock, and the unemployment rate. The global validity of the instruments in the simultaneous estimation is confirmed (at the 5% level) by the Sargan tests reported in both the skilled and unskilled wage equations towards the bottom of the table. This is further

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Table 5. First-difference estimates of domestic wage determination Spatial GMM


Unskilled Capital (t 1 ) Capital (t 2 ) Unemployment (t 1 ) Unemployment (t 2 ) Skilled wage (t 1 ) Skilled wage (t 2 ) Unskilled wage (t 1 ) Unskilled wage (t 2 ) Foreign wage (t 1 ) Contiguous region domestic wage (t 1 ) Contiguous region foreign wage (t 1 ) Contiguous industry domestic wage (t 1 ) Contiguous industry foreign wage (t 1 ) Observations Time dummies Wald g2 /0: x2(4) Sargan p -value Further time lag in contiguous wages / x2(4) Serial correlation AR(1) p -value Spatial autocorrelation LMSEC / x2(1) Fit * (approximated by Corr(y, y˜)2)

0.0701 0.0094 /0.1545 /0.0192 0.1652 0.0603 0.1840

(4.95) (1.19) (5.10) (3.08) (3.27) (0.81) (4.02)

0.1714 0.0399 0.0361 0.0324 0.0022

(4.30) (2.47) (1.53) (3.60) (1.48)

Skilled 0.0474 0.0241 /0.1403 /0.0354 0.3070

(4.20) (2.40) (2.08) (2.97) (3.85)

0.1271 0.0458 0.2256 0.1840 0.1323 0.0346 0.0034

(4.97) (1.78) (3.74) (1.06) (1.20) (3.10) (3.77)

1,330 Yes p/ [0.000] p/ [0.310] 4.813 p/ [0.307]

p / [0.000] p / [0.204] 5.163 p/ [0.271]

1.087 p/ [0.315] 1.763 p/ [0.184] 0.800

0.577 p/ [0.447] 1.687 p/ [0.194] 0.744

reinforced by the absence of a second-order serial correlation in the firstdifferenced models under consideration. In both the skilled and unskilled domestic wage equations, estimating by spatial GMM and spatial fixed effects, capital and unemployment have positive and negative impacts upon wages, respectively. We find that the impact of the crosswage term is positive, which suggests that the two groups are complements and the effect is larger in levels than under the spatial GMM specification. Turning to the foreign wage variable, there is evidence that the existence of higher paying foreign firms exerts upward pressure on wages in domestically owned firms. Noticeably, these effects are evident for both unskilled and skilled wages, whereas for the fixed-effects analysis foreign wages influenced only skilled wage determination. However, the impact upon skilled wages is larger, and significantly so, thus supporting the earlier conclusion that a foreign presence in the same industry and region elevates wage inequality in the domestic sector. There is a growing body of literature that suggests that there is a gap between wages paid in the foreign sector to those wages paid in the domestic sector of around 5 7% in favour of foreign firms (see Section 3). When considering contiguity terms, as found when using spatial fixed effects, there is a role for the average domestic wage in adjacent regions to influence unskilled wage determination. Focusing upon skilled wages, both domestic and foreign contiguous industry wages have an impact* although the former is always larger. This confirms the earlier evidence that the mechanism of foreign effects operates solely via industry comparisons.

Assisted areas Unskilled Capital (t 1 ) Capital (t 2 ) Skilled wage (t 1 ) Skilled wage (t 2 ) Unskilled wage (t 1 ) Unskilled wage (t 2) Foreign wage (t 1 ) Contiguous region domestic wage (t 1 ) Contiguous region foreign wage (t 1 ) Contiguous industry domestic wage (t 1 ) Contiguous industry foreign wage (t 1 ) Observations Time dummies Wald g2 /0: x2(4) Further time lag in contiguous wages / x2(4) Sargan p -value Serial correlation AR(1) p -value Spatial autocorrelation LMSEC / x2(1) ¯ 2 (approximated by Corr/(y; yˆ2 ) Fit */R

Non-assisted areas Skilled

0.1620 0.0315 0.3241 0.1489 0.4070

(2.69) (1.63) (4.52) (0.85) (3.62)

0.0134 0.0034 0.0018 0.0090 0.0068

(2.19) (0.27) (0.14) (0.48) (0.72)

Unskilled

0.0993 0.0340 0.4870

(4.30) (2.42) (5.02)

0.1894 0.0099 0.3205 0.1140 0.3880

0.1359 0.0342 0.1570 0.1363 0.1449 0.0065 0.0020

(5.61) (2.31) (5.04) 0.3325 (1.72) 0.0503 (1.28) 0.0603 (1.41) 0.0304 (2.02) 0.0033

798 Yes p/ [0.342] 2.889 (0.577) p/ [0.400] 0.654 p/ [0.419] 0.998 p/ [0.318] 0.801

Skilled (4.34) (2.46) (3.41) (1.53) (4.00) (4.16) (2.95) (2.46) (2.96) (3.28)

0.0840 0.0298 0.2110

(4.72) (1.67) (3.04)

0.1742 0.0619 0.2628 0.1499 0.1717 0.0332 0.0067

(4.40) (2.47) (2.68) (1.68) (1.55) (2.40) (3.31)

532 Yes p / [0.000] 5.006 (0.287) p / [0.364] 0.744 p/ [0.388] 2.009 p/ [0.156] 0.69

p / [0.000] 4.128 (0.389) p / [0.381] 0.501 p/ [0.479] 1.985 p/ [0.159] 0.734

p / [0.000] 4.384 (0.357) p / [0.393] 0.847 p / [0.357] 1.729 p / [0.189] 0.722

Wage Spillovers


Table 6. GMM estimates of domestic wage determination by assisted area status

201

202



6.3. Assisted Area Status* Spatial GMM The importance of unemployment in terms of the differential effects on skilled and unskilled wages has been noted across estimators. We now investigate this further by estimating equation (4) as above, but for assisted and non-assisted areas separately. The results are shown in Table 6 below, which has the same format as Table 5.10 The analysis in Table 6 shows that the impact-contiguous inter-industry and inter-regional domestic wages are generally less important in assisted areas. This again confirms a priori expectations, namely that workers, particularly those in areas of high unemployment, would be the least mobile (Gordon & Molho, 1998), and therefore the least likely to experience wage spillovers. When considering the impact of inter-industry contiguous FDI, the greatest effects are again found for skilled workers, with wages paid by foreign firms exerting a greater effect on skilled rather than unskilled workers. This again seems a plausible result, and ties in with results reported elsewhere that show that foreign firms are more skill intensive than domestic firms (Driffield & Taylor, 2005). Consequently, it is logical to assume that skilled workers in the domestic sector are more likely to be able to move into the foreign sector, because the foreign sector demands skilled labour. Because of this, issues of fairness and comparability feed through into the skilled wage equation, and effects are smaller and/or insignificant in the unskilled wage equation. We also find evidence of inter-regional effects for unskilled workers in nonassisted areas, that is g2 " 0. However, the magnitude of these effects suggests that inter-regional or inter-sectoral wage spillovers are limited. This may tie in with work by Ingram et al. (1999) who report that issues of wage comparability are becoming less important over time in the UK, as does Hamermesh (2001) for the USA. Whilst wage spillovers from foreign to domestic firms are confined largely to intra-industry, intra-region effects, such spillovers exist even within assisted areas. This is a potentially important result, as it suggests that even in areas of high unemployment, inward investment acts to bid up wages in the domestic sector. For skilled workers, this effect is particularly strong* a 10% increase in foreign wages will increase domestic wages by some 1.6%. /

7. Conclusions There is evidence of wage spillovers, for both skilled and unskilled workers, both across regions, industries, and between the foreign- and domestic-owned sectors. However, for inter-industry effects, the impact of wages paid by foreign-owned firms is limited to skilled workers. There are several potential explanations of why wage spillovers are greater for skilled workers. For example, it is widely accepted that skilled workers have greater mobility, and often their skills are more transferable between industries. It is also interesting to note that wages paid by foreign firms have a greater impact on domestic skilled wages. Noticeably, there are no inter-regional effects from foreign firms across the sample as a whole. Splitting the sample by assisted area status reveals that while contiguity effects are important in wage determination, the UK exhibits evidence of distinct spatial labour markets, similar to those reported for Canada and Germany by Dickie & Gerking (1998) and Brakman et al. (2004), respectively. Equally, there is evidence of labour market segmentation in the UK, between assisted and non-assisted areas,

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between occupation groups, and between the foreign- and domestically owned sectors. This difference between the results for skilled and unskilled workers is highlighted further by the assisted areas distinction, as there are no significant external effects on wages for unskilled workers in assisted areas. At the same time, such regions have higher proportions of unskilled workers than non-assisted areas. While inward investment does generate wage increases in the domestic sector, there is also evidence of labour market segmentation* that foreign firms employ more skilled workers, and so inward investment has only a limited impact on surrounding labour markets. It is also worth noting that foreign wages impact, even within the region, to a larger extent on domestic skilled wages. This adds credence to the recently expressed concerns that inward investment may act to increase wage inequality between the two groups.

Notes 1. This is also indirectly related to the concept of the reservation wage, i.e. the wage at which the individual would cease to work or find another job. 2. In both cases approximately 40% of this differential is due to foreign firms being more highly concentrated in high-wage industries or regions; for details of the methodology used in this disaggregation, see Davies & Lyons (1991). 3. In this paper we only consider the role of wages in neighbouring regions and industries upon wage determination. However, it is conceivable that there may be knowledge spillovers in contiguous industries or regions (e.g. R&D expenditure, new process or product innovations). As pointed out by an anonymous referee, such knowledge spillovers may well influence productivity and wages. Within the specification adopted, however, this effect would be captured through wage increases in the contiguous region or industry. 4. The labour force LF is defined as the unemployed UE plus the employed E , LF/UE/E ; thus the unemployment rate is defined as U /UE/LF . The motivation for the inclusion of unemployment rate U in the skilled and unskilled wage equations follows Blanchflower & Oswald (1994). Their work suggests that a negative spatial relationship exists, within and across countries, between the level of pay and the local rate of unemployment. This differs from conventional wisdom that implies that there should be a positive relationship between wages and unemployment stemming from compensating-differentials arguments (see Harris & Todaro, 1970). As such, although the direction of influence from the unemployment rate may be debatable, the literature implies that a relationship exists between unemployment and wage determination. 5. We experimented with various distance measures instead of the contiguity matrix. Specifying precise geographical distances between regions of this type is problematic. The regions, while having a meaningful economic status for policy makers (and the basis for various proposals for regional devolution in the UK) are quite large, often with more than one city. We also experimented with various distance functions, and attempted to use various functional forms of distances between cities, and also with various ‘threshold’ distance functions. However, these could not improve on the ‘rook’ contiguity matrix between regions, which itself is outperformed by the standard first-order matrix that we employ. We also considered measures of distance based not on geography but on similarity of region, attempting, for example, to identify regions that are dominated by similar industries, or sectors where average earnings or unemployment rates are similar. The latter of these is problematic as by definition the contiguity matrix becomes endogenous in the estimation, and the former essentially served to show that the essential difference between regions in the UK can be explained in terms of the ‘core periphery’ distinction that is well understood in regional science. Again, as a result, spatial weights perform at least as well as other measures of distance. 6. See, for example, Morgan (1997) for a full discussion of this. 7. Assisted areas are those areas of Great Britain where regional aid may be granted under European Community law. Regional selective assistance (RSA) is the main form of such aid in Great Britain. It is a discretionary grant, awarded to secure employment opportunities and increase regional competitiveness and prosperity. 8. The average wage bill was calculated as: Total wage bill divided by employment, by industry and region. 9. Over-identification test statistics are also computed to test the validity of the instrumental variables candidates. 10. Note that levels fixed-effects estimates for the assisted/non-assisted area split are omitted for brevity, but are consistent with those presented and available upon request from the authors.

204



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The Spatial Durbin Model and the Common Factor Tests

´ S MUR & ANA ANGULO JESU


(Received October 2005; accepted July 2006)

The spatial Durbin model occupies an interesting position in the field of spatial econometrics. It is the reduced form of a model with cross-sectional dependence in the errors and it may be used as the nesting equation in a more general approach of model selection. Specifically, in this equation we obtain the common factor tests (of which the likelihood ratio is the best known) whose objective is to discriminate between substantive and residual dependence in an apparently misspecified equation. Our paper tries to delve deeper into the role of the spatial Durbin model in the problem of specifying a spatial econometric model. We include a Monte Carlo study related to the performance of the common factor tests presented in the paper in small sample sizes.

ABSTRACT

Le mode`le de Durbin spatial et les tests de facteur commun Le mode`le de Durbin spatial occupe une position inte´ressante dans l’ećonome´trie spatiale. Il s’agit de la forme re´duite d’un mode`le avec une de´pendance transversale dans les erreurs; elle s’utilise comme une e´quation de capacite´ d’emboıˆtement dans une approche plus geńe´rale pour la se´lection d’un mode`le. Dans cette e´quation en particulier, nous obtenons les tests de facteur commun (parmi lesquels le Rapport de vraisemblance (likelihood ratio) est le plus connu), dont l’objectif est de faire une distinction entre la de´pendance substantive et la de´pendance re´siduelle dans une e´quation apparemment mal spećifieé. Notre article tente d’aller un peu plus loin dans l’analyse du roˆle du mode`le de Durbin spatial sur le proble`me de spećification d’un mode`le ećonome´trique spatial. Nous incluons une e´tude de Monte Carlo associeé a` la performance des tests de facteur commun pre´senteé dans l’article, par petites brides d’ećhantillon. RE´SUME´

El modelo Espacial Durbin y las pruebas de factor comuń El modelo espacial Durbin ocupa una importante posicioń en la econometrıá espacial. Es la forma reducida de un modelo con dependencia seccional cruzada en los errores y se puede usar como la ecuacioń jerarquizada en un enfoque ma´s general de seleccioń de modelos. Especı´ficamente, en esta ecuacioń, obtenemos las Pruebas de factor comuń (entre las cuales, la Razoń de Verosimilitud es la ma´s conocida) cuyo objetivo es discriminar entre la dependencia substantiva y residual en una ecuacioń aparentemente mal especificada. Nuestro trabajo intenta cavar mas profundo en el rol del Modelo espacial Durbin en el problema para especificar un modelo econome´trico espacial. Incluimos un estudio

RESUMEN

Jesu´s Mur (to whom correspondence should be sent), Department of Economic Analysis, University of Zaragoza, Gran Vıá, 2 4 (50005), Zaragoza, Spain. Email: [email protected]. Ana Angulo, Department of Economic Analysis, University of Zaragoza, Gran Vıá, 2 4 (50005), Zaragoza, Spain. Email: [email protected]. This research has been possible thanks to the financial support obtained from project SEJ 2006-02328/ECON from the Ministerio de Educacioń y Ciencia del Reino de Espanâ. ISSN 1742-1772 print; 1742-1780 online/06/020207-20 # 2006 Regional Studies Association

DOI: 10.1080/17421770601009841

208

J. Mur & A. Angulo

en Monte Carlo relacionado con el comportamiento de las Pruebas de factor comuń que es presentado en el trabajo en tamanõ de muestra. KEYWORDS: Common factor tests; spatial lag model; spatial error model

JEL

CLASSIFICATION:

C21; C50; R15


1. Introduction In recent years there has been an increase in concern about questions related to methodology in the field of spatial econometrics. The works of Anselin & Florax (1995), Anselin et al. (1996) and Anselin & Bera (1998) played a leading role in the revitalization of this interest in the 1990s. Almost all these papers underline the difficulties arising from the lack of specificity of the tests based on the Lagrange multiplier principle and, consequently, the problems of finding the true model when there are various alternatives. They demonstrate that there is a very serious risk of obtaining a misspecified model if the user is not sufficiently careful with the method. Later, Florax et al. (2003) carried out a more systematic approach by comparing the results of Hendry’s methodology with those corresponding to the traditional approach in the field of spatial econometrics. Surprisingly, the latter seems to work better. Mur & Angulo (2005) study the same topic (model selection), introducing new elements into a discussion with many branches. Dubin (2003) focuses on the ability of several interaction models to capture structures of spatial autocorrelation in the error term of the equation, in an approach that is reminiscent of that of Florax & Rey (1995). McMillen (2003) demonstrates that, beyond a problem of autocorrelation in the error term, what the user may really be finding is a misspecification of the model: ‘yet autocorrelation is often produced spuriously by model misspecification’ (p. 215) is one of his conclusions. Finally, Lo´pez-Bazo & Fingleton (2006) openly question the credibility of specifications with structures of dependence in the error term. According to these authors, if the reasons for the externalities that intervene are as Anselin (2003) describes them, we should find, in the main, substantive cross-sectional dependence relationships (with lags in the endogenous variable on the right-hand side of the equation). However, in most of the cases reviewed by the authors it is mechanisms of residual dependence that dominate. Using particular but relevant modelling cases, Lo´pez-Bazo & Fingleton arrive at the same conclusion reached previously by McMillen (2003): in effect, what habitually underlies models with residual autocorrelation is a problem of misspecification of the equation due, in general, to the omission of relevant variables. In this paper, we would like to contribute further evidence to the debate, outlined briefly above, about how to specify and develop better models in spatial econometrics. Our objective focuses on the so-called spatial Durbin model and on the tests of common factors. The most popular is the likelihood ratio, LRCOM, to which we add the Lagrange multiplier, LMCOM, and the Wald test, WCOM. As is described in Section 2, both elements (the Durbin model and common factor tests) are intimately linked and they can become very helpful instruments in the process of developing a trustworthy econometric model. In Section 3 we present the main

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results obtained from a Monte Carlo experiment on the common factor tests. The paper finishes with a section of conclusions. 2. Background: Facts and Some Critical Points The Durbin model appears in a specific context in which, using time series, we need to estimate an econometric model with an autoregressive error term, AR(1): yt x’t g0 ut : (1) ut rut1 o t


Cochrane & Orcutt (1949) propose a stepwise algorithm involving least squares (LS) estimators in successive semi-differentiated variables: yt rˆ (r1) yt1 [xt rˆ (r1) xt1 ]’g0 o t ; where rˆ (r1) is the estimation of r obtained in the (r 1)th iteration. The process implicitly begins with a value of r equal to zero, which can lead to problems of inconsistency. To avoid such a risk, Durbin (1960) suggests directly estimating the reduced unrestricted form of equation (1) by LS: yt ryt1 x’t g0 x’t1 g1 o t :

(2)

This alternative, which is much simpler, guarantees consistent estimators even in the first step. The adaptation of these results to the spatial case does not involve any special complexity, as discussed by Anselin (1980): y xg0 u (3) [ y rWyxg0 Wxg1 o; u rWuo where W is the weighting matrix; y, u and o are vectors of order (R 1); x is the (R k) matrix of observations of the k explicative variables; g0 and g1 are (k 1) vectors of parameters and r the parameter of the spatial autoregressive process of the first order, SAR(1), that intervenes in the random term of the main equation. Following Durbin’s initial proposal, the next step should be the estimation of the reduced form that appears on the right-hand side of equation (3), but this is not particularly straightforward. That equation cannot be estimated by LS because there is an endogeneity problem: the regressor Wy is dependent on the error term o. We have to use, for example, maximum likelihood (ML) or GMM (generalized method of moment) methods. It is clear that the Durbin model does not help to simplify the problem of estimating a spatial model with SAR(1) errors. However, it highlights some other questions which are very relevant to the specification of the model. Firstly, it shows why substantive spatial dependence tests have so much power when they are used in spatial static models1 in which an SAR(1) process is present in the error term. The reason is that the reduced form of both types of models is nearly the same, except for the term Wxg1. The opposite is equally true: residual dependence tests show a surprisingly high power when they are applied to spatial dynamic structures2 whose error term is white noise. This lack of specificity sharpens if we employ tests based on the Lagrange multiplier principle. This is the case with the Lagrange multiplier for omitted spatially lagged dependent variables (LMLAG) of Anselin (1988) and of the Lagrange multiplier for spatial error /

/

/

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dependence (LMERR) of Burridge (1980). A reasonably convincing solution to this problem of uncertainty involves applying the general principles of specification testing in the case of locally misspecified models as proposed by Bera & Yoon (1993). This approach leads, in our case, to the robust multipliers of Anselin et al. (1996). The LMLAG evolves into the LMLE, a Lagrange multiplier test for a spatially lagged dependent variable robust to the presence of a spatially SAR(1) process in the error term. Similarly, the LMERR transforms into a new Lagrange multiplier for the presence of a spatial SAR(1) error process LMEL, which is robust to the presence of a spatially lagged dependent variable in the model. Another aspect to note in relation to equation (3) is that in this expression it must hold that g1 rg0. In another words, if in unrestricted equation (3) we cannot reject this set of k non-linear restrictions, the evidence points to a static process with an SAR(1) error term. The most popular test in this context is the likelihood ratio of common factors, LRCOM, proposed by Burridge (1981). As is well known with every likelihood ratio, in the first place we need the ML estimation of the nesting model: y rWyxg0 Wxg1 o : (4) o N (0; s2 I)


/

/

For simplicity, we assume normality in the error term. The log-likelihood function of model (4) is standard: R R [By xg0 Wxg1 ]’[By xg0 Wxg1 ] l(y=8 A ) ln 2p ln s2 2 2 2s2 ln jBj;

(5)

2

with 8A [g0,g1,r,s ]’; jBj is the determinant of the Jacobian term whose logarithm may be obtained as: lnjBjlnjI rW jaRr1 ln(1rlr ); with {lr , r 1, 2, . . . , R} being the eigenvalues of matrix W. Let us look now at the restricted model: y xg0 u (6) u rWuo /

/

whose log-likelihood function is also standard: R R (y xg0 )’B’B(y xg0 ) 2 ln jBj; l(y=8 0 ) ln 2p ln s 2 2 2s2 with 80 [g0,r,s2]’. Formally, the LRCOM test can be expressed as: H0 :rg0 g1 0 [ LRCOM 2[l(y=8˜ A )l(y=8˜ 0 )] x2 (k): HA :rg0 g1 " 0

(7)

/

(8)

The list of common factor tests available (see also Burridge, 1981) can be completed with that based on the principle of the Lagrange multiplier, LMCOM, and with the Wald test, WCOM. Both are relatively unknown in this field. This omission can be justified by the complexity involved in obtaining them, as can be seen in the Appendix. Another reason is that the LRCOM test seems more reliable than the other two according to the evidence provided in the third section of this paper.



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A question that must be taken into account when interpreting the common factor tests is that they should be applied once the usual misspecification tests (for omitted spatial lag dependence and/or omitted spatial error dependence) reject the static model with the white noise error term. That is, the common factor tests are useful in cases in which there is evidence for maintaining that the parameter r is different from zero. The problem is that we do not know exactly in which specification the parameter r is not zero, namely in that of equation (4) or that of equation (6). Obviously, the null hypothesis of the common factor hypothesis will continue to hold if r and g1 are equal to zero both in equation (4) and in equation (6), but this case lacks interest. Accordingly, it is evident that we are dealing with a problem of model selection. From our point of view, the common factor tests can help to clarify the situation but not to resolve it by themselves. The nesting model employed up to this point is that specified in equation (4), which is ‘an autoregressive distributed lag model of the first order’, ADL(1,1), as described by Bivand (1984, p. 27). Blommestein (1983) had previously advanced in this direction by suggesting the convenience of adopting an approach like Hendry’s, structured in a sequence of ADL(m,n) processes, despite ‘the increasing complexity in specifying higher order ( 1) spatial lags in the case of non-binary weights and/or irregular lattices’ (p. 259). Blommestein’s proposal* to start the process using a general ADL(m,n) and trying to simplify it through a sequence of tests* is not a simple task in a spatial context. However, this proposal shows the convenience of checking the spatial dynamics of the model to which the common factor tests have led us. For example, if the data come from an ADL(2,2): y r1 W1 yr2 W2 yxg0 W1 xg1 W2 xg2 o ; (9) o N (0; s2 I) /

in which W1 and W2 are two different weighting matrices; r1 and r2 are two autoregressive parameters; and g0, g1 and g2 are vectors of parameters associated with the spatial lags of the exogenous variables. It is relatively simple to show that, after introducing a restriction of common factors such as: g1 r1g0, we will obtain a model with an SAR(1) error term in which spatially dynamic elements remain in the main equation: ) [I r1 W1 ]y r2 W2 y[I r1 W1 ]xg0 W2 xg2 o [ y r2 [I r1 W1 ]1 W2 y[I r1 W1 ]1 W2 xg2 [I r1 W1 ]1 o [ y r2 W yW xg2 [I r1 W1 ]1 o y r2 W yW xg2 v [ (10) v r1 Wv o /

where W [I r1 W1 ]1 W2 : The reduced form of equation (10) has a spatially dynamic nature with an autoregressive structure in the random term. On the other hand, using the result of Bivand (1984), it is clear that a spatially autoregressive process of the first order, SAR(1) admits a spatial moving average representation of an infinite order, SMA(): X (I rW )1 (rW )j I rW (rW )2 (rW )3 j1 [ u rWuo [ u [I rW ]1 o [I rW (rW )2 (rW )3 ]o:

(11)

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Conversely, an SMA(1) process admits an SAR() representation. If we assume initially a spatially static model such as that of equation (6), with a moving average error term of the first order, we could arrive at an ADL(1,1) with an autocorrelated error term: y xg0 u u yxg0 [ 1 o [I rW ] u urWur2 W 2 ur3 W 3 u u o rW o [ u o rW o o rW [urWur2 W 2 ur3 W 3 u ] u o rWuv ; v (rW )2 [I rW r2 W 2 r3 W 3 ]u |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}


¡

(yxg0 ) o rW (yxg0 )v [ y xg0 rWyWxg1 v [ v o v o (rW )2 [I rW r2 W 2 r3 W 3 ]u o (rW )2 o y xg0 u rWyxg0 Wxg1 v [ v o r2 W 2 o

(12)

being g1 rg0. This means that, also under the null hypothesis, a final discrimination exercise should be carried out between, at the very least, two alternative processes for the error term, involving either autoregressive or moving average dependence. To sum up, there is a final test that should be carried out, depending on the outcome of the common factor tests. If the common factor tests have led us to a spatially dynamic model such as that which appears in equation (4) we must test, in this equation, that the error term is really white noise in order to complete the specification. In this final stage we may use, for example, the Lagrange multiplier RSl ½r of Anselin & Bera (1998). Alternativelly, if the common factor tests have led us to a spatially static model with an apparent SAR(1) structure in the random term, we should then test wheter we need to include a longer dynamic structure in the main equation using, for example, the RSr ½l test of Anselin & Bera (1998). /

3. Common Factor Tests in Small to Medium Sample Sizes: a Monte Carlo Analysis In the previous section we illustrated the role that common factor tests can play in the specification of a cross-sectional econometric model. As has been made clear, they should not be used as definite elements but rather as signposts as to the appropriate direction in which to explore in order to improve the model. In this sense, the indications of the common factor tests should be combined with those of other complementary tools before taking a final decision. However, the literature on spatial econometrics has paid very scant attention to the use of these tests, which is a little surprising. To cite only the most recent cases, they are not included in the comprehensive simulation carried out by Anselin & Florax (1995), nor are they mentioned in the meta-analysis of Florax & de Graaff (2004), or in the manuals of Tiefelsdorf (2000) and Griffith (2003). This section aims to partially correct this deficiency by resolving a Monte Carlo exercise in order to evaluate the behaviour of the common factor tests under


213

different configurations, relative to the data generation process (DGP), the sample size and the shape of the regional system. In this exercise, we have taken a simple linear model as the starting point: y xbu;

(13)

where x is an (R 2) matrix whose first column, comprising 1s, is associated with the intercept of the model whereas the second corresponds to the observations of the regressor xr ; b is a (2 1) vector of parameters, b’ [b0 ; b1 ]; and u is the (R 1) vector of error terms. From this point, it is straightforward to obtain either a spatial error model (SEM) or a spatial lag model (SLM). In matrix terms: 8 < y xbu SEM: u uWuo (14a) : o iid(0; s2 I) /

/


/

SLM:

y rWyxbu : u iid(0; s2 I)

(14b)

Also, combining both specifications, we can employ a mixed model which includes a spatial lag of the endogenous variable in the main equation and an SAR(1) process in the error term, which Anselin & Florax (1995) call SARMA(1,1): ) y rWyxbu u uWuo : (15) o iid(0; s2 I) In our simulations we will use, respectively, the SEM of equation (14a), the SLM of equation (14b) and the SARMA(1,1) of equation (15). The main characteristics of the exercise are as follows: (a) We used two pairs of values for b0 and b1 in equation (13). The first, (b0 10; b0 0.5), guarantees an average R2 of 0.2 without spatial effects, while the second, (b0 10; b0 2.0), raises it to 0.8. (b)The observations of xr , the regressor, and of the random terms o and u were obtained from a univariate normal distribution with mean zero and a variance, s2, equal to 1 in all cases. (c) We used three different sample sizes containing 25, 100 and 225 observations. These data were distributed in regular grids of (55), (10 10) or (15 15), respectively. Furthermore, we distinguished two cases for the space* a planar and a torus arrangement* with the objective of isolating a potential edge effect in the behaviour of the tests. (d)The contiguity matrix, W, was specified as being of a binary type using a rook and a queen scheme. The first assures approximately four contacts per cell whereas the second doubles this measure of average connection. (e) The range of values for the parameter r depends on the contiguity matrix used in each variant. Specifically, this range corresponds to the interval: 1 (l1 Min ; lMax ); with lMin and lMax being the greatest negative and positive eigenvalues, in absolute terms, of the contiguity matrix. In each case, 40 values of the parameter distributed regularly over the whole interval were simulated. (f) Each combination was repeated 1,000 times. /

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Below, the results obtained for the planar case in a rook scheme are presented,3 distinguishing between what we call an unconditional and a conditional approach to the problem of specifying the model. In the first, we take the raw results of the common factor tests, independently of whether there are symptoms of misspecification in the estimated equation. In the conditional approach we use only those cases in which a previous test has detected misspecification problems in the spatial dynamics of the equation.


3.1. Common Factor Tests in an Unconditional Approach The results obtained in this case are grouped in Table 1, which shows the behaviour of the tests when there are no spatial effects of any kind in the DGP, and in Figures 1 3. Figure 1 summarizes the results obtained in the case where the data have been generated using an SEM model, Figure 2 presents the results observed in the case of the SLM, and Figure 3 refers to the mixed model in the DGP. In these figures we include the average R2 obtained for the 1,000 simulations corresponding to each case, and the percentage of rejections of the null hypothesis of common factors corresponding to the three tests. The terms ‘(h)’ or ‘(l)’ next to the corresponding statistic indicate that these data come from a simulation with a high (h) or a low (l) signal-to-noise ratio. The results for the mixed model in the DGP appear in Figure 3, but only for the high signal-to-noise ratio case. Here we summarize the percentage of rejections of the null hypothesis when the data have been generated with the mixed model of equation (15). Horizontally, we indicate the range of r (the coefficient of Wy in the main part of equation (15)) and vertically, the range of u (the autocorrelation coefficient of the error term also in equation (15)). As mentioned above, Table 1 summarizes the results obtained when no spatial effects have intervened in the DGP. These percentages can be understood as a partial approximation to the size (the null hypothesis is also true when r and u are equal to zero, although the case has no special interest). The estimates are, in general, outside the confidence interval for a significance value of p 0.05, (0.042; 0.058) in this case. The sample size tends to correct the performance of the tests, although the improvement is small. The Lagrange multiplier fits better to the theoretical value of 0.05, whereas the likelihood ratio tends to overestimate the size and the Wald test to underestimate it. A measure of size that is more interesting in our problem appears in Figure 1: the percentage of times that the tests of common factors reject the SEM model when this model has intervened in the DGP. The results are satisfactory on the whole and adjust to what was expected. The sample size tends to stabilize and improve the behaviour of the three tests, especially in the extremes of the interval. /

Table 1. Percentage of rejections of the hypothesis of common factors when there are no spatial effects in the DGP. Significance level: 5% LRCOM High R R/25 R/100 R/225

0.078 0.059 0.062

2

LMCOM Low R 0.103 0.073 0.073

2

High R 0.049 0.053 0.062

2

WCOM Low R 0.047 0.068 0.073

2

High R 0.039 0.035 0.047

2

Low R2 0.072 0.069 0.073


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1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20


0.10

-0.25

-0.20

-0.15

-0.10

-0.05

0.00 0.00

0.05

0.10

0.15

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0.25

0.05

0.10

0.15

0.20

0.25

0.05

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0.20

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

-0.25

-0.20

-0.15

-0.10

-0.05

0.00 0.00 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

-0.25 LRcom (h)

-0.20

-0.15 LRcom (I)

-0.10 LMcom (h)

-0.05

0.00 0.00 LMcom (I)

Wcom (h)

Wcom (I)

0.25 R2 (h)

R2 (I)

Figure 1. DGP: SEM. Percentage of rejections of the hypothesis of common factors. Top: R/25; middle: R/100; bottom: R/225.

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J. Mur & A. Angulo 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10


-0.25

-0.20

-0.15

-0.10

-0.05

0.00 0.00

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0.10

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0.05

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0.05

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1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 -0.25

-0.20

-0.15

-0.10

-0.05

0.00 0.00 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

-0.25 LRcom (h)

-0.20

-0.15

LRcom (I)

-0.10 LMcom (h)

-0.05

0.00 0.00 LMcom (I)

Wcom (h)

Wcom (I)

0.25 R2 (h)

R2 (I)

Figure 2. DGP: SLM. Percentage of rejections of the hypothesis of common factors. Top: R/25; middle: R/100; bottom: R/225.


R = 25

5 0.22 0.29 0.16 0.14 0.11 0.18 0.05 0.03 0.00 0.0 3 .0 -0 0 5 . -0 0 8 . -0 11 . -0 14 . -0 16 . -0 19 . -0 2 2 . -0 25 . -0 0.22 0.20 0.17 0.15 0.12 0.10 0.07 0.05 0.02 0.00 θ -0.02 -0.05 -0.07 -0.10 -0.12 -0.15 -0.17 -0.20 ρ -0.22

ρ

ρ

0.22 0.20 0.17 0.15 0.12 0.10 0.07 0.05 0.02 0.00 θ -0.02 -0.05 -0.07 -0.10 -0.12 -0.15 -0.17 -0.20 -0.22

ρ

0.22 0.19 0.17 0.14 0.12 0.10 0.07 0.05 0.02 0.00 θ -0.02 -0.05 -0.07 -0.10 -0.12 -0.14 -0.17 -0.19 ρ -0.21

ρ

0.20-0.40

0.40-0.60

0.60-0.80

0.22 0.19 0.17 0.14 0.12 0.10 0.07 0.05 0.02 0.00 θ -0.02 -0.05 -0.07 -0.10 -0.12 -0.14 -0.17 -0.19 -0.21

2 0.29 0.17 0.14 0.12 0.10 0.17 0.05 0.02 0.00 0.0 2 .0 -0 05 . -0 07 . -0 10 . -0 12 . -0 14 . -0 17 . -0 19 . -0 21 . -0

2 0.29 0.17 0.14 0.12 0.10 0.17 0.05 0.02 0.00 0.0 2 .0 -0 05 . -0 .07 -0 10 . -0 .12 -0 14 . -0 17 . -0 19 . -0 21 . -0

2 0.29 0.17 0.14 0.12 0.10 0.17 0.05 0.02 0.00 0.0 2 .0 -0 05 . -0 07 . -0 10 . -0 .12 -0 14 . -0 17 . -0 19 . -0 21 . -0

0.00-0.20

0.22 0.20 0.17 0.15 0.12 0.10 0.07 0.05 0.02 0.00 θ -0.02 -0.05 -0.07 -0.10 -0.12 -0.15 -0.17 -0.20 -0.22

2 0.20 0.27 0.15 0.12 0.10 0.17 0.05 0.02 0.00 0.0 2 .0 -0 05 . -0 07 . -0 10 . -0 12 . -0 .15 -0 17 . -0 20 . -0 22 . -0

0.22 0.19 0.17 0.14 0.12 0.10 0.07 0.05 0.02 0.00 θ -0.02 -0.05 -0.07 -0.10 -0.12 -0.14 -0.17 -0.19 -0.21

R = 225

ρ

2 0.20 0.27 0.15 0.12 0.10 0.17 0.05 0.02 0.00 0.0 2 .0 -0 05 . -0 07 . -0 10 . -0 12 . -0 .15 -0 17 . -0 20 . -0 22 . -0

2 0.20 0.27 0.15 0.12 0.10 0.17 0.05 0.02 0.00 0.0 2 .0 -0 05 . -0 .07 -0 10 . -0 12 . -0 15 . -0 17 . -0 20 . -0 22 . -0


R = 100

0.25 0.22 0.19 0.16 0.14 0.11 0.08 0.05 0.03 0.00 θ -0.03 -0.05 -0.08 -0.11 -0.14 -0.16 -0.19 -0.22 -0.25

5 0.22 0.29 0.16 0.14 0.11 0.18 0.05 0.03 0.00 0.0 3 .0 -0 0 5 . -0 0 8 . -0 11 . -0 14 . -0 16 . -0 19 . -0 22 . -0 25 . -0

ρ

0.25 0.22 0.19 0.16 0.14 0.11 0.08 0.05 0.03 0.00 θ -0.03 -0.05 -0.08 -0.11 -0.14 -0.16 -0.19 -0.22 -0.25

5 0.2 2 0.29 0.16 0.14 0.11 0.18 0.05 0.03 0.00 0.0 3 .0 -0 0 5 . -0 0 8 . -0 11 . -0 14 . -0 16 . -0 19 . -0 22 . -0 25 . -0

0.25 0.22 0.19 0.16 0.14 0.11 0.08 0.05 0.03 0.00 θ -0.03 -0.05 -0.08 -0.11 -0.14 -0.16 -0.19 -0.22 ρ -0.25

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0.80-0.100

Figure 3. DGP: mixed model. Percentage of rejections of the hypothesis of common factors. High signal-to-noise ratio. Top left: LRCOM; top centre: LMCOM; top right: WCOM; middle left: LRCOM; middle centre: LMCOM; middle right: WCOM; bottom left: LRCOM; bottom centre: LMCOM; bottom right: WCOM.

The tests work better when the R2 value of the LS regression is high. Furthermore, the order described previously is maintained: the LMCOM tends to move around the theoretical size of the test (p 0.05), the LRCOM is situated higher and the WCOM slightly lower. Figure 2 measures the power of each test as the number of times the SEM model is rejected because the data come from an SLM. The figures highlight a number of interesting aspects. The behaviour of the tests is very disperse when the sample is small (the case of R25). The LRCOM test is clearly better than the other two, for both positive and negative values of the parameter of spatial autocorrelation. The behaviour of the LMCOM is unacceptable for positive values of this parameter and a low R2. The sample size substantially improves the results of the three tests and the jump from 25 to 100 observations is critical. In the last case, there are still some anomalies in the estimated power function of the LMCOM test, namely an unexpected fall in the intermediate range of values in the positive part of /

/

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the parameter interval and a low R2. The power functions take on a very regular appearance when they are estimated with a sample of 225 observations. Independently of the sample size, all the tests work better in a powerful regression (with a high R2) than when the regression is weak (a low R2). In all cases, the estimated power function of the LRCOM test is higher than the other two. The differences are almost imperceptible when the sample is large (R 225) but become very evident as the sample size decreases. Finally, Figure 3 represents the estimated power of the three tests when the data come from an SARMA(1,1) model; that is, neither the SEM nor the SLM are correct. To help with the interpretation of these figures, it should be remembered that as the colour darkens a higher percentage of rejections of the SEM model in favour of the SLM is implied. It is evident that the LRCOM test tends to identify processes of the latter type to the detriment of the former, while the LMCOM is more favourable to SEM-type specifications. The sample size and the value of R2 itself act in favour of SLM structures, so the acceptance region of SEM processes is limited to a narrow band situated around r (the parameter associated with the spatial lag of the endogenous variable) equal to zero.


/

3.2. Common Factor Tests in a Conditional Approach The peculiarity of this part of the study is that we are going to use the common factor tests only in those cases in which we have strong evidence that the model proposed initially, namely the static one of equation (13), without any kind of spatial effects, is misspecified. To do so, in the first place we will resolve the LS estimation of this model: y Xb u, where sˆ 2 and bˆ are the corresponding LS estimations and uˆ the residual series and we will obtain the SARMA test proposed by Anselin (1988): /

SARMA

/

u’Wy ˆ

u’W ˆ uˆ 2

sˆ 2 sˆ 2 RJˆr-b T1

1 T1

u’W ˆ uˆ 2 sˆ 2

;

(16)

ˆ ˆ sˆ 2 ; T1 is the sum of the elements of matrix where RJˆrb T1 (b’X’WMWX b)= -1 W and MX [I X(X’X) X’]. It is a Lagrange multiplier test for a joint spatial lag and spatial moving average or autoregressive error (absence of spatial effects in the model, both in the main equation and in the error term). The SARMA test has an asymptotic chi-square distribution with two degrees of freedom. For reasons of space, we exclude the results corresponding to the mixed case (where the bias towards SLM structures is maintained). Equally, we restrict the discussion to the high signal-to-noise ratio variant. Tables 2 and 3 show a selection of the results for the cases in which an SEM or SLM process was used in the DGP. It should be noted that the number of observations used in the estimation of these percentages varies with the performance of the SARMA test. That is, with the power of this test being p; ˆ the real sample size for the LRCOM, LMCOM and WCOM tests is reduced to 1,000 p: ˆ The results included in both tables are convincing in the sense that the common factor tests become more reliable when applied once there are clear symptoms of misspecification in relation to the spatial dynamics of the model. /

/


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Table 2. Percentage of rejections of the null hypothesis of common factors. Conditional approach. DGP: SEM and high R2. Significance level: 5% SARMA(/p) ˆ a


Parameter

LRCOM

LMCOM

WCOM

R/25 /0.274 /0.202 /0.101 0.000 0.101 0.202 0.274

0.980 0.615 0.153 0.052 0.123 0.518 0.938

0.081 0.094 0.229 0.577 0.325 0.160 0.232

0.045 0.055 0.157 0.519 0.187 0.056 0.026

0.108 0.094 0.150 0.154 0.065 0.031 0.055

R/100 /0.248 /0.182 /0.091 0.000 0.091 0.182 0.248

1.000 0.993 0.472 0.041 0.535 0.992 1.000

0.043 0.044 0.064 0.171 0.069 0.066 0.102

0.041 0.040 0.051 0.146 0.062 0.050 0.033

0.050 0.045 0.044 0.073 0.026 0.017 0.035

R/225 /0.242 /0.178 /0.089 0.000 0.089 0.178 0.242

1.000 1.000 0.845 0.055 0.905 1.000 1.000

0.050 0.055 0.053 0.364 0.050 0.050 0.065

0.050 0.050 0.047 0.364 0.050 0.045 0.030

0.060 0.050 0.041 0.273 0.033 0.030 0.035

Note : aThis measures the percentage of times that the SARMA test rejects its composite null hypothesis of the absence of spatial effects in the static model of equation (13).

The size (conditioned) of the tests, as can be seen in Table 2, tends to adjust better to the corresponding theoretical value, although the Wald test still shows a tendency to underestimate, even with large samples. It is evident that the size of the sample continues to play a fundamental role and helps to improve the behaviour of the tests (especially that of LRCOM). The same can be said with respect to the explanatory capacity of the model (and in the same sense: greater reliability for a higher R2).4 The (conditioned) power functions shown in Table 3 ratify the improvements obtained for the common factor tests when they are used in a second stage. The (conditioned) power of the three quickly approaches unity in the neighbourhood of the origin (r 0), even with a moderate sample size. The test which works least well, especially when the sample size is reduced, is the Lagrange multiplier, LMCOM, whose (conditioned) power function maintains a clear asymmetry between positive and negative values of the parameter of spatial dependency r. /

3.3. Stylized Results of the Simulation The Monte Carlo study has produced a considerable amount of information about the behaviour of the common factor tests in different situations, part of which has been presented in the previous two sections. Next we summarize what we think are the essential results:

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Table 3. Percentage of rejections of the null hypothesis of common factors. Conditional approach. DGP: SLM and high R2. Significance level: 5%


Parameter

SARMA(/p) ˆ a

LRCOM

LMCOM

WCOM

R/25 /0.274 /0.202 /0.101 0.000 0.101 0.202 0.274

1.000 0.986 0.596 0.040 0.999 1.000 1.000

0.998 0.987 0.893 0.450 0.984 0.998 0.999

0.999 0.969 0.802 0.300 0.251 0.427 0.632

1.000 0.973 0.517 0.100 0.370 0.988 1.000

R/100 /0.248 /0.182 /0.091 0.000 0.091 0.182 0.248

1.000 1.000 0.990 0.049 1.000 1.000 1.000

1.000 1.000 0.986 0.347 1.000 1.000 1.000

1.000 1.000 0.986 0.327 0.999 0.999 1.000

1.000 1.000 0.972 0.245 0.996 1.000 1.000

R/225 /0.242 /0.178 /0.089 0.000 0.089 0.178 0.242

1.000 1.000 1.000 0.055 1.000 1.000 1.000

1.000 1.000 1.000 0.364 1.000 1.000 1.000

1.000 1.000 1.000 0.364 1.000 1.000 1.000

1.000 1.000 1.000 0.364 1.000 1.000 1.000

Note : aThis measures the percentage of times that the SARMA test rejects its composite null hypothesis of the absence of spatial effects in the static model of equation (13).

(i)

There is a strong effect related to the sample size. The power of the common factor tests improves substantially with the number of observations. (ii) There is, equally, an effect associated with the explicative capacity of the model. All the tests work better with a high R2 coefficient. The differences should not be underestimated because they can reach 30 points in some cases. (iii) The three common factor tests have problems with size. The LRCOM tends to overestimate it whereas the WCOM tends to underestimation. The LMCOM does a little better in this respect. (iv) The power functions of all the tests maintain a certain asymmetry with respect to the origin. In general, they perform slightly better in the range of positive values of the parameter of autocorrelation. (v) The performance of the LMCOM is not acceptable in small samples. The WCOM is slightly more reliable but the best option is the LRCOM. (vi) In general, the common factor tests show a strong preference for processes with a spatial dynamic structure in the main equation. They tend to select the SEM model only when the signal coming from the spatial lag of the endogenous variable is very weak.


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(vii) The performance of all the tests improves, both in size and in power, when they are applied in a conditional approach once there are clear symptoms of misspecification in the spatial dynamics of the equation. (viii) The shape of the regional system, whether it is on a plane or in a torus, and the number of contacts per cell (the rook or queen case) have a minor impact on the behaviour of the tests. In general, the power functions of the three common factor tests become smoother and more regular when the edge effect disappears in a torus, but at the cost of slight losses in power. The same occurs when the average connectivity increases.


4. Conclusions The tests of common factors were introduced into a spatial context at the beginning of the 1980s when many of the tools that we use today were still being developed. However, they had never occupied a really important position in the process of specifying a model and only the likelihood ratio variant is moderately popular. Habitually, they have been used as auxiliary tests that are useful for corroborating conclusions obtained with other instruments. Nevertheless, we believe that the common factor tests should play a more relevant role as a guide in applied work. As we have stated, these tests should not be used as ultimate criteria but as useful tools for exploring the most adequate direction for the specification process. At the very least we should bear in mind the requirement of Davidson (2000, p. 168) who, when alluding to the time series equivalent dilemma, indicates: ‘The point is that although AR(1) errors may well be the correct specification, they impose a common-factor parameter restriction on the equation that requires to be tested. It would nowadays be regarded as bad practice to impose the AR(1) model without testing the implicit restriction.’ Our position is that, given the peculiarities of the discipline, we must be a little more ambitious. Externalities and dynamic spatial relationships play a strategic role in any model specified in the field of spatial economics. Nevertheless, these elements are often elusive, and this makes them difficult to see. For this reason, it is important to have efficient tools to discriminate between different alternatives to deal with spatial interaction mechanisms. The common factor tests may help in resolving this problem. Notes 1. We use this term in relation to a model in which no spatial lag of the endogenous variable appears on the righthand side of the equation. 2. We refer to models with spatial lags of the endogenous variable on the right-hand side of the equation. 3. In this paper, and for reasons of space, we show only a few of the total results obtained. For more a more detailed treatment of the information contained in this paper, please contact the authors. 4. See Note 3.

References Anselin, L. (1980) Estimation Methods for Spatial Autoregressive Structures , Regional Science Dissertation and Monograph Series No. 8, Cornell University, Ithaca, NY. Anselin, L. (1988) Lagrange multiplier tests diagnostics for spatial dependence and spatial heterogeneity, Geographical Analysis , 20, 1 17.


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Anselin, L. (2003) Spatial externalities, spatial multipliers and spatial econometrics, International Regional Science Review , 26, 153 166. Anselin, L. & Bera, A. (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics, in: A. Ullah & D. Giles (eds) Handbook of Applied Economic Statistics, pp. 237 289, New York, Marcel Dekker. Anselin, L., Bera, A., Florax, R. & Yoon, M. (1996) Simple diagnostic tests for spatial dependence, Regional Science and Urban Economics , 26, 77 104. Anselin, L. & Florax, R. (1995) Small sample properties of tests for spatial dependence in regression models: some further results, in: L. Anselin & R. Florax (eds) New Directions in Spatial Econometrics, pp. 21 74, Berlin, Springer. Bera, A. & Yoon, M. (1993) Specification testing with locally misspecified alternatives, Econometric Theory , 9, 649 658. Bivand, R. (1984) Regression modelling with spatial dependence: an application of some class selection and estimation methods, Geographical Analysis , 16, 25 37. Blommestein, H. (1983) Specification and estimation of spatial econometric models. A discussion of alternative strategies for spatial economic modelling, Regional Science and Urban Economics , 13, 251 270. Burridge, P. (1980) On the Cliff Ord test for spatial correlation, Journal of the Royal Statistical Society B , 42, 107 108. Burridge, P. (1981) Testing for a common factor in a spatial autoregression model, Environment and Planning A , 13, 795 800. Cochrane, D. & Orcutt, G. (1949) Application of least squares regression to relationships containing autocorrelated error terms, Journal of the American Statistical Association , 44, 32 61. Davidson, J. (2000) Econometric Theory, Oxford, Blackwell. Dubin, R. (2003) Robustness of spatial autocorrelation specifications: some Monte Carlo evidence, Journal of Regional Science , 43, 221 248. Durbin, J. (1960) Estimation of parameters in time-series regression models, Journal of the Royal Statistical Society B , 22, 139 153. Florax, R., Folmer, H. & Rey, S. (2003) Specification searches in spatial econometrics: the relevance of Hendry’s methodology, Regional Science and Urban Economics , 33, 557 579. Florax, R. & de Graaff, T. (2004) The performance of diagnostics tests for spatial dependence in linear regression models: a meta-analysis of simulation studies, in: L. Anselin, R. Florax & S. Rey (eds) Advances in Spatial Econometrics: Methodology, Tools and Applications, pp. 29 65, Berlin, Springer. Florax, R. & Rey, S. (1995) The impacts of misspecified spatial weight structures in linear regression models, in: L. Anselin & R. Florax (eds) New Directions in Spatial Econometrics, pp. 111 135, Berlin, Springer. Griffith, D. (2003) Spatial Autocorrelation and Spatial Filtering, Berlin, Springer. Lo´pez-Bazo, E. & Fingleton, B. (2006, forthcoming) Empirical Growth Models with Spatial Effects , Papers in Regional Science, 87, 177 198. McMillen, D. (2003) Spatial autocorrelation or model misspecification, International Regional Science Review , 26, 208 217. Mur, J. & Angulo, A. (2005) Model Selection Strategies in a Spatial Context , Working Paper DTECONZ 2005 06, Department of Economic Analysis, University of Zaragoza. Tiefelsdorf, M. (2000) Modelling Spatial Processes. The Identification and Analysis of Spatial Relationships in Regression Residuals by Means of Moran’s I, Berlin, Springer.

Appendix: Maximum Likelihood Tests for the Hypothesis of Common Factors The hypothesis of common factors links the models with substantive and residual autocorrelation. The former acts as the ample model in which the latter is nested. That is, starting with the autoregressive model: ) y rWyxg0 Wxg1 o rWyZg’o ’ ’ (A1) z [x; Wx] g [g0 ; g1 ] 2 o N (0; s I)


223

we obtain the model with residual autocorrelation: ) y xg0 u u rWuo o N (0; s2 I)

(A2)

after imposing the restriction of common factors, g1 rg0. With this term we refer to a set of k non-linear restrictions on the parameters of model (A1), whose pertinence can be analysed using various procedures. In the paper by Burridge (1981), reference is made to the likelihood ratio, to the Lagrange multiplier and to the Wald test. As the author indicates (p. 800), ‘there is little to choose between the tests’ given that they are ‘three asymptotically equivalent test procedures’ whose behaviour in a context of finite samples is unknown. The literature has opted for the likelihood ratio, apparently the most costly option, because it requires the estimation of both models, (A1) and (A2). In this Appendix, we present the results relative to the other two tests. The Lagrange multiplier is usually the easiest test to resolve, although the advantages that it offers in this case in particular are dubious. To obtain it, we need to evaluate the score and the information matrix corresponding to the nesting model (A1) under the null hypothesis. The score is a vector of order (2k2) 1 whose expression, under the null hypothesis of common factors (H0: g1 rg0), is the following:


/

/

/

/

/

3 7 6 7 6 7 6 @r 7 6 s2 i1 1 rli 7 7 6 6 7 6 @l 7 6 x’o 7 6 7 6 7 6 @g 7 6 2 7 6 7 6 s g(8 ) 6 0 7 6 7 [ g(8 )jH0 7 6 @l 7 6 x’W o 7 6 7 6 7 6 @g 7 6 s2 7 6 17 6 7 6 @l 7 6 o’o R 5 4 5 4 2 4 2 @s 2s 2s 3 2 R o’Wy X li 7 6 7 6 s2 6 i1 1 rli 7 7 6 0 6 7; 7 6 x’W o 7 6 5 4 2 s 0 2

@l

3

2

o’Wy

R X

li

(A3)

where 8 ’ [r; g’0 ; g’1 ; s2 ] the vector, of order (2k 2) 1, of parameters of the model. The Hessian matrix, of order (2k2) (2k2), of second derivatives of the log-likelihood function with respect to 8 is: /

/

/

/

/

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J. Mur & A. Angulo 2 2

R X

6y’WWys 6 i1 6 6 6 x’Wy @l 1 6 6 H(8 ) 6 @8 @8 ’ s2 6 6 x’WWy 6 6 6 o’Wy 4 s2

li 1 rli

2 y’Wx

y’WWx

x’x

x’Wx

x’Wx

x’WWx

o’x s2

o’Wx s2

3 y’W o 7 s2 7 7 x’o 7 7 7 s2 7: 7 x’W o 7 7 s2 7 7 7 o’o R5 s4 2s2

(A4)


If we introduce the null hypothesis, change the signs and obtain its expected value, we will have the information matrix corresponding to the model of the null hypothesis: I(8 )jH0 E[H(8 )]jH0 2 R X li 6g0 ’x’WWxg0 2s2 g0 ’x’Wx g0 ’x’WWx 6 i1 1 rli 6 1 6 x’Wxg0 x’x x’Wx 6 x’Wx x’WWx x’WWxg 0 s2 6 6 6 R X li 4 0 0 1 rli i1 2

3 li 7 1 rli 7 7 7 0 7 7 0 7 7 R 5 2s2

(A5)

3 2s2 e¯l(r) 7 0 7 7 2s2 e¯l(r) g0 7 7 R 7 2 7 4 2s 2e¯l(r) 5 1 R R

(A6)

R X i1

whose inverse is: 2

[I(8 )jH0 ]1

e 0 eg0 ’ 1 6 [x’x] x’Wxm22 0 m 11 6 6 1 6 x’Wxm22 [x’x] m22 eg0 g0 ’ s2 6 eg0 6 6 2s2 e¯l(r) 4 g0 ’ 2s2 e¯l(r) 0 R

In this expression, ¯l(r) is the mean of the series li ; i 1; 2; . . . ; R l(r)i 1 rl ˜ i in which the eigenvalues of matrix W, fli ; i 1; 2; . . . ; Rg; and the estimation of parameter r of model (A2) intervene; e f2s2 RV [l(r)]g1 corresponds to the ML estimation of the variance of the ML estimator of r (once multiplied by s2), in model (A2), where V [l(r)] is the variance of series fl(r)i g; m11 and m22 are two symmetrical matrices that depend on the original variables m11 [x’x]1 [x’x]1 x’Wxm22 x’Wx[x’x]1 and m22 [x’WMx Wx]1 with Mx IR x[x’x]1 x’ and IR the identity matrix of order R. Lastly, the Lagrange multiplier appears as the quadratic form of the score of (A3) over the inverse of the


225

information matrix (A6). The final expression of the statistic is not very comfortable: H0 :g1 rg0 g[ LMCOM [g(8 )jH0 ]’[I(8 )jH0 ]1 [g(8 )jH0 ]x2 (k) HA :g1 "rg0 as ’ o Wx x’ W o LMCOM s2 g12 e2g1 g3’ g0 (m22 eg0 g’0 ) (A7) s2 s2

with g1 and g3 being the first and third elements, respectively, of the score of (A3), evaluated under the null hypothesis of common factors, namely


g1

o’Wy s2

R X i1

li

1 rli

and g3

x’W o s2

:

Obviously, the other elements that intervene in the multiplier of (A7) must be evaluated in the ML estimation of the model of the null hypothesis (that is, the model with residual autocorrelation (A2)). In the Wald test we find ourselves in the alternative hypothesis to analyse whether the value of the restriction is acceptable using the estimations coming from the ample model (A1). If we rewrite the restriction of common factors in an implicit form, r(8 ) g1 rg0, the Wald test can be expressed as: ) H0 :r(8 ) g1 rg0 0 HA :r(8 ) g1 rg0 " 0 /

/

[ WCOM [r(8 )jHA ]’[R(8 )jHA (I(8 )jHA )1 R(8 )’jHA ]1 [r(8 )jHA ]x2 (k); (A8) as

where R(8 )

@r(8 ) @8 ’

[g0 ; rIk ; Ik ; 0]

is a matrix of order k (2k 2). In this case it is difficult to progress beyond the general result of (A8). The following expressions may soften the discussion: /

/

R(8 )[I(8 )]1 R(8 )’ V (r)g0 g’0 2[rCov(r; g0 )Cov(r; g0 )]’g0 rI ’ [rIk Ik ][V (g )] k Ik V (r)

gz’B1 WMz WB1 zg’

s2 z [x; Wx] g [g0 ’; g1 ’]

1 2RV [l(r)]

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1

1

[IR rW ]

V [l(r)]

R 1X

R

i1

li

1 rli

1

X R

R

i1

li

2

1 rli

Cov(r; g’) V (r)[gz’B1 Wz(z’z)1 ] V (g) s2 [z’z]1 V (r)[(z’z)1 z’WB1 zg’gz’B1 Wz(z’z)1 ]:


It should be remembered that all these elements must be evaluated using the ML estimation of the model (A1). In particular, V(r) is the ML estimation of the variance of the ML estimator of r in (A1).


The Fading Attraction of Central Regions: an Empirical Note on Core Periphery Gradients in Western Europe

¨ LHART MARIUS BRU


(Received March 2006; revised August 2006)

ABSTRACT This paper describes sectoral core periphery gradients across Western European regions over the period 1975 2000, and it estimates the impact of EU membership on countries’ internal geography. Overall, it is found that the centrality of European regions has been losing importance as a determinant for the location of employment. Central regions have gained employment share in none of the eight broad sectors analysed, whereas peripheral regions have significantly gained employment share in four of these sectors. Accession to the EU has favoured countries’ peripheral regions in terms of manufacturing employment and their central regions in terms of service employment.

L’attirance des re´gions centrales en dećlin: une note empirique sur les inclinaisons de pe´riphe´rie du cœur en Europe occidentale Cet article dećrit les inclinaisons de pe´riphe´rie du cœur a` travers les re´gions de l’Europe occidentale sur la pe´riode de 1975 a` 2000 et l’impact des adhe´sions a` l’UE sur la geógraphie interne des pays concerne´s. Il s’ave`re dans l’ensemble que l’aspect central des re´gions europeénnes a perdu de l’importance comme e´le´ment de´terminant pour l’emplacement d’un emploi. Les re´gions centrales n’ont acquis aucune part d’emploi dans les huit larges secteurs analyse´s, alors que les re´gions pe´riphe´riques ont conside´rablement gagne´ de part du marche´ de l’emploi dans quatre de ces meˆmes secteurs. L’accession a` l’UE a favorise´ les re´gions pe´riphe´riques des pays au niveau de l’emploi industriel et leurs re´gions centrales au niveau de l’emploi dans les services. RE´SUME´

La atraccioń en declive de las regiones centrales: una nota empı´rica sobre gradientes de periferia central en Europa occidental. Este trabajo describe los gradientes sectoriales de periferia central en regiones de Europa occidental entre los anõs 1975 a 2000, y evaluá el impacto de la pertenencia a la UE en la geografıá interna de los paı´ses. Sobretodo, se revela que la centralidad de las regiones europeas ha ido perdiendo importancia como factor determinante en la localizacioń de empleo. Las regiones centrales no han ganado participacioń laboral en ninguno de los amplios ocho sectores analizados, mientras que las regiones perife´ricas han aumentado significativamente su participacioń laboral en cuatro de estos sectores. RESUMEN

De´partement d’ećonome´trie et ećonomie politique, Ecole des HEC, Universite´ de Lausanne, CH-1015 Lausanne, Switzerland. Email: [email protected]; http://www.hec.unil.ch/mbrulhar/. Also affiliated with the Centre for Economic Policy Research, London. The author would like to thank Carsten Schu¨rmann for the generous provision of data, and Harry Garretsen for his helpful comments. Financial support from the Swiss National Science Foundation (grant 612-65970) is gratefully acknowledged. ISSN 1742-1772 print; 1742-1780 online/06/020227-09 # 2006 Regional Studies Association

DOI: 10.1080/17421770601009866

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M. Bru¨lhart

El ingreso a la UE ha favorecido a las regiones perife´ricas de los paı´ses en lo que se refiere a trabajos de manufactura y a sus regiones centrales en lo referente a empleos del a´rea servicios. KEYWORDS: Geographic concentration; EU regions; core periphery gradients JEL

CLASSIFICATION:

F15; R12; R14


1. Introduction Since the early 1990s, the economic geography of Western Europe has become an object of intense scrutiny. Academic interest has been kindled primarily through the advent of a new generation of spatial general-equilibrium models, the ‘new economic geography’, that provide a formal treatment of locational forces affecting imperfectly competitive industries over a priori featureless space. These models appear particularly well suited to the analysis of locational forces in industrialized and relatively homogeneous world regions such as Western Europe. Policyoriented economists have taken note of these models primarily because they identify cumulative forces that create or reinforce polarized economic landscapes featuring agglomerated core locations and hollowed-out peripheries, and because these forces may be strengthened by the reduction of spatial transaction costs. The relevance for Western Europe is obvious: if economic integration strengthens agglomeration forces and exacerbates core periphery gradients, important distributional (and, possibly, efficiency-related) issues arise.1 The purpose of this note is to offer some relevant stylized facts. It describes (a) the degree to which sectoral location patterns in Western Europe are influenced by the centrality and peripherality of regions, and (b) whether and how accession to the EU has been associated with changes in within-country location patterns. The analysis draws on a balanced panel of sectoral employment across 222 Western European regions over the period 1975 2000. Eight sectors are distinguished, covering the full range of economic activities. Related studies abound.2 This literature has mainly described the extent to which particular sectors are geographically concentrated, and* the flipside of this coin* the extent to which regions (or countries) are specialized in particular sectors. These are important issues in their own right, but they do not address what are arguably two of the most pressing questions that arise in the context of modern location theory and of European integration: how are sectors (re-)locating relative to the regional core periphery structure of aggregate economic activity? And: how does economic integration affect these location patterns?3 The paper is organized as follows. Section 2 briefly describes the data. Section 3 reports regression estimates of locational core periphery gradients. Estimates of the impact of EU accession on countries’ internal location patterns are reported in Section 4. Section 5 concludes. 2. Data The data set, compiled by Cambridge Econometrics, provides a balanced panel of sectoral employment for 17 Western European countries, the 15 pre-2004 EU Member States plus Norway and Switzerland (referred to collectively as ‘WE17’). Except for Luxembourg, all country data are disaggregated into NUTS-2 or

The Fading Attraction of Central Regions

229

NUTS-3 regions, yielding a total of 222 region-level observations per sector and year. The number of regions within countries ranges from 2 (Ireland) to 37 (UK). Employment is reported for eight sectors, covering the full range of economic activities, over the period 1975 2000.4 In addition, the exercise draws on a regional estimates of Harris’s (1954) wellknown market-potential measure: Mr

S X Ys s1

drs

;

(1)

where r R and s S ( R ƒ S) denote regions; Y stands for 1998 regional GDP in terms of purchasing power parity, as computed by Eurostat; and drs stands for the economic distance between regions r and s. Drawing on the data set of Schu¨rmann & Talaat (2000), economic distances are represented by estimated road-freight travel times between regional capitals. These estimates take account of road quality, border delays and legal constraints that affect the speed of road transport. Intraregional distances are defined as one-third of the radius of a circle whose area represents that of the region, and drr is defined as twice the intra-regional distance, which implies that the intra-regional travel speed is 30 km/h on average.5 The set of partner regions S includes WE17 as well as all other countries on the European Continent.6 The estimated market potentials vary considerably: that of the most central region in our data set (London) is 12.5 times larger than that of the most peripheral region (northern Norway).


/

3. Core Periphery Gradients in Western Europe One of the principal insights of modern geography models is that a location’s market access can be a powerful attractor for increasing-returns activities.7 The policy relevance of this issue is obvious. 3.1. The Regression Model Based on the market potential measure Mr , we compute core periphery gradients of the eight sample sectors by estimating the following simple specification separately for each sector and year: 1

0

yrit C B X C B B yrit C C B C B i lnB X C ait bit ln(Mr )o rit ; B yrit C C B BXrX C A @ yrit i

(2)

r

where y is employment, i denotes sectors, t denotes years, a and b are regression coefficients, and o is a stochastic error. The dependent variable is commonly referred to as a Balassa index or location quotient.8 We take logs in order to make

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M. Bru¨lhart

the Balassa index symmetric around zero, and so as to be able to interpret bˆ it as an elasticity. Since there is evidence of between-country heteroskedasticity, inference is based on White-adjusted t-statistics. To assess the statistical significance of changes in bˆ it between sample years, F tests are computed on the hypothesis that bˆ it bˆ i;tx 0; using seemingly unrelated regression estimates of the disturbance covariances in order to account for cross-equation error correlation (Greene, 2000, p. 620).


3.2. Results Table 1 reports the results, based on sector-level regressions for 1975, 1987 and 2000. The estimations broadly conform with expectations based on casual observation. Agriculture is the only sector that exhibits a consistently positive and statistically significance locational bias towards peripheral regions. Conversely, four sectors are statistically significantly concentrated in central regions for all three sample years: manufacturing and energy, transport and communication, banking and insurance, and ‘other market services’. Looking at changes over time, it turns out that no sector exhibits a significant increase over the sample period in its tendency to concentrate at the core. However, four sectors have relocated significantly towards peripheral regions: manufacturing, Table 1. Core periphery gradients, 1975 2000a (222 regions) /

Sector

Year

Agriculture

1975 1987 2000 1975 1987 2000 1975 1987 2000 1975 1987 2000 1975 1987 2000 1975 1987 2000 1975 1987 2000 1975 1987 2000

Manufacturing, energy

Construction

Distribution

Transport, communication

Banking, insurance

Other market services

Non market services

a b

bˆ

R2

1.38** 1.31** 1.29** 0.38** 0.28** 0.14** 0.10 0.04 0.18** 0.14** 0.06 0.07 0.12* 0.09* 0.13** 0.39** 0.39** 0.36** 0.26** 0.28** 0.31** 0.18** 0.12** 0.02

0.33 0.33 0.29 0.23 0.14 0.03 0.03 0.01 0.08 0.07 0.01 0.01 0.02 0.03 0.07 0.22 0.27 0.18 0.16 0.24 0.29 0.04 0.03 0.001

/

/

(FjH0 :bˆ t bˆ tx 0) b

x f12; 13g

x /25

3.9* 0.04

0.7

14.7** 47.9**

39.2**

16.4** 18.4**

37.9**

12.3** 0.5

4.2*

1.2 6.2*

0.2

0.0 0.8

0.5

0.4 2.3

1.7

5.4* 88.8**

41.7**

See equation (2); ** and * denote statistical significance at 99% and 95%, respectively, White-corrected. F -statistic on Wald test of equality of bˆ across years, taking account of cross-equation error covariance.


231


construction, distribution, and non-market services. Hence, centrality seems to have lost some importance as a determinant of sectoral location in Europe. It may be thought particularly striking that manufacturing employment has been relocating away from central regions. We illustrate this pattern in Table 2, which lists the 12 regions with strongest specialization into manufacturing, and the 12 regions with strongest specialization out of manufacturing, where specialization changes are defined as differences in log Balassa indices between 1975 and 2000.9 The average market potential of the regions specializing out of manufacturing (13,181) is considerably larger than that of the regions specializing into manufacturing (7,518). In view of the varied composition of the 24 regions with most pronounced changes in manufacturing specialization, we can observe furthermore that the diagnosed locational shift away from central regions is a phenomenon that applies across European countries and is not driven by the relative performance of a certain country (or subset of countries) alone.

4. EU Accession and Intra-country Core Periphery Gradients While it is interesting in itself to describe the evolution of the European space economy, such descriptions inevitably raise the question as to whether and how such trends are affected by policy decisions. We therefore seek a way of identifying the effect of Western Europe’s most prominent recent policy experiment, EU integration. Our data do not allow us to examine the impact of integration on Continent-wide location patterns. However, we can offer a simple assessment of how EU integration has impacted on countries’ internal core periphery gradients. Exploiting the richness of the data set in terms of time coverage and intra-country information, we can explore whether past accessions to the EU were associated with systematic changes in the time profile of sectoral location patterns within Member States. 4.1. The Regression Model In order to isolate EU effects, we need to control for the myriad of unobserved factors that shape sector- and country-specific inter-temporal location patterns. Hence, we estimate a separate intercept and linear time trend for each country sector over the full sample period, attributing to these intercepts and time trends all the forces that shape sectoral location patterns except for EU membership. Then, we estimate the deviation from this baseline time trend of a time trend starting in the year of the relevant country’s accession to the EU. Any deviation of the postEU trend from the full-period trend is then interpreted as a membership effect. In order to obtain sufficient degrees of freedom for meaningful statistical analysis, and assuming that similar spatial forces were triggered when successive countries joined the EU, we force those deviation terms to be identical across countries and therefore estimate a unique membership effect per sector. Specifically, we estimate the following regression model separately for each sector: Z IaTbEgo;

(3)

where we let K denote the number of sample countries and T the number of sample years; Z is a KT 1 vector of estimated within-country core periphery gradients /

232

Table 2. Regions with largest changes in manufacturing specialization


Region

Market potential

Balassa index

1975

2000

1975

2000

12 regions with largest decrease in manufacturing specialization: Scottish Highlands (UK) Trier (DE) Oslo (NO) London (UK) North Aegean (GR) Lie`ge (BE) Aosta Valley (IT) Luxembourg (LU) Merseyside (UK) Brabant (BE) Namur (BE) Bedfords./Hertfords. (UK) Average

4,924 13,885 4,795 31,307 2,523 15,888 9,811 14,740 12,606 16,911 15,334 15,451 13,181

49 59 57 441 20 124 11 52 212 106 28 223 115

11 17 23 158 7 44 5 35 69 71 13 119 48

0.17 0.13 0.22 0.35 0.12 0.08 0.34 0.09 0.07 0.00 0.34 0.14 0.06

0.86 0.63 0.89 0.96 0.62 0.42 0.80 0.37 0.40 0.46 0.79 0.29 0.62

12 regions with largest increase in manufacturing specialization: Ionian Islands (GR) Epirus (GR) Gotland (SE) Molise (IT) Ireland Centre/West (IE) Braunschweig (DE) Niederbayern (DE) Kassel (DE) Western Greece (GR) Abruzzi (IT) Oberfranken (DE) Galicia (ES) Average Overall average (WE17)

3,103 3,363 5,423 6,950 5,127 12,484 11,135 13,417 3,659 7,878 12,365 5,308 7,518 9,967

2 12 3 13 57 200 144 90 31 84 160 184 82 173

5 15 6 18 95 247 208 173 21 104 229 183 109 131

2.28 1.30 0.92 1.03 0.46 0.05 0.11 0.18 1.38 0.37 0.22 0.60 0.68 0.12

1.10 0.74 0.16 0.82 0.39 0.69 0.64 0.18 0.25 0.03 0.33 1.10 0.02 0.10

M. Bru¨lhart

Manuf. empl.


233

bˆ ct, with c denoting countries, from country-by-country regressions of equation (2); a and b are K 1 vectors of regression coefficients; I is a KT K matrix that consists of K diagonally stacked T 1 vectors of 1s, and zeros elsewhere; T is a KT K vector consisting of K diagonally stacked T 1 vectors of sample years in ascending order ([1975, 1976, . . ., 2000]), and zeros elsewhere; E is a KT 1 vector whose values are equal to the number of years either since the relevant country’s accession to the EU or since 1975, whichever of the two is more recent, and zero for non-EU country-years;10 g is a regression coefficient (1 1); and o is a KT 1 vector of stochastic disturbances. This is a piecewise linear spline function. The main object of interest is the membership effect g, a slope shifter contingent on accession to the EU. Inspection of the data reveals significant intra-country autocorrelation and crosscountry error correlation. Since the number of panels is relatively small (K 17), we follow Beck & Katz (1995) and estimate the coefficients with feasible generalized least squares accounting for the intra-country autocorrelation (Prais Winsten method) whilst taking account of the cross-country correlation and implied heteroskedasticity by basing inference on panel-corrected standard errors. /

/

/

/

/

/

/

/


/

4.2. Results Estimated gs ˆ and the corresponding inferential statistics are reported in Table 3. The regression model accounts for a large share of the sample variation in the dependent variable, ranging between 55% and 99%. The coefficient on the slopeshifting EU-accession variable is statistically significant in all sectors except for agriculture. For manufacturing and for construction, accession to the EU is associated with an increasing tendency for employment to locate in countries’ peripheral regions (where ‘peripherality’ is again defined relative to the whole of Europe, and not just relative to the country’s domestic markets). The opposite holds for the service sectors, where EU accession is associated with an increasing tendency towards location in central regions. EU accession therefore appears to have reinforced the general trend towards dispersion of manufacturing employment away from central regions, whereas it has to some extent counterbalanced such dispersion forces with respect to service employment.11 Table 3. EU membership and intra-country C-P gradients Dependent variable/ bˆ ft (employment, 16 countries) Sector Agriculture Manufacturing, energy Construction Distribution Transport, communication Banking, insurance Other market services Non-market services

EU accession effect 0.005 0.047 0.041 0.122 0.125 0.123 0.120 0.052

P- value

R2

0.78 0.00 0.03 0.00 0.00 0.00 0.00 0.02

0.99 0.98 0.86 0.77 0.79 0.84 0.78 0.55

Notes : Prais Winsten GLS regressions with panel-corrected standard errors (see Beck & Katz, 1995); country fixed effects and interactions of country fixed effects with year variable included but not reported; 390 observations.

234

M. Bru¨lhart


5. Conclusion This note reports core periphery gradients of sectoral location patterns and estimates the impact of countries’ accession to the EU on changes in their internal economic geography. Overall, the centrality of regions has over time become a less important determinant of sectoral location patterns. None of the eight broad economic sectors became significantly more concentrated in core regions, whereas in four of them the employment share of peripheral regions increased significantly. Countries’ accession to the EU appears to have reinforced the general trend towards peripheral regions for the manufacturing and construction sectors, but not for the service sectors, where the effect of EU accession was to strengthen the locational attractiveness of central regions. It is perhaps striking that the manufacturing sector, which is frequently seen as the most geographically mobile part of the economy and subject to potential agglomeration economies, while on average still concentrated in central regions, was in fact relocating towards the periphery, both across all Western European regions and (even more so) within individual countries subsequent to EU accession. Two caveats should be mentioned. First, it might be tempting to interpret the observed locational changes as bad news for the new economic geography, which mainly stresses centripetal agglomeration forces that are triggered by integration. Such a reading of our results would be overly simplistic, both because many new economic geography models can accommodate integration-induced locational dispersion and because our data are highly sectorally aggregated (the price to pay for disaggregation in the regional dimension). For instance, while we find that manufacturing overall was relocating towards the periphery, some manufacturing subsectors might of course have exhibited opposite tendencies. Second, we measure location through employment. This is the variable that most concerns European policy makers, but it would be interesting to investigate whether relative employment gains by peripheral regions were reinforced or offset by unequal changes in labour productivity. We leave this issue for future research.

Notes 1. For a thorough analysis of the policy implications of new economic geography models, see Baldwin et al . (2003). 2. For a survey of this literature, see Combes & Overman (2004). 3. Accounts of sectoral core periphery patterns across European regions have previously been provided by Hallet (2002) and Bru¨lhart (1998). These analyses are based on shorter data sets with fewer regions, and they do not attempt to gauge the impact of EU integration explicitly. 4. For a detailed description of this data set, see Bru¨lhart & Traeger (2005). 5. The appropriate measurement of distance, particularly at the intra-region level, remains a moot issue (see, for example, Head & Mayer, 2002). It could be interesting for future research to test the sensitivity of estimated centre periphery gradients to alternative underlying distance measures, as well as to the inclusion of timevarying measures of market potential. 6. The following non-WE17 countries were not disaggregated into regions: Albania, Belarus, BosniaHerzegovina, Croatia, Cyprus, Estonia, Iceland, Latvia, Lithuania, Macedonia, Malta, Moldova, Russia, Serbia-Montenegro, Slovenia, Turkey, and Ukraine. 7. In those models, the arrival of increasing-returns firms in a location is typically of sufficient magnitude that it increases the market potential of that location significantly and thereby triggers further arrivals of firms in a process of cumulative causation. Market access therefore becomes an endogenous variable. This analysis abstracts from such processes by taking the market potential of regions as exogenous and time invariant. 8. Since the denominator of the index does not vary across regions, its inclusion only affects aît :


235

9. Owing to the slow-moving nature of sectoral employment shares, recomputing these numbers for 3-year averages makes no difference to the rankings in Table 2. 10. We have experimented with alternative definitions of this variable, by starting the counter 1 or 2 years ahead of countries’ accession dates, in order to take account of anticipatory relocation decisions. The results (available upon request) are qualitatively equivalent. 11. The similarity of estimated coefficients for the four market service sectors raises suspicion about the accuracy of those individual data series * it would appear that they were generated to some extent by imputing employment in market services to individual subsectors using common disaggregation weights.


References Baldwin, R. E., Forslid, R., Martin, P., Ottaviano, G. I. P. & Robert-Nicoud, F. (2003) Economic Geography and Public Policy, Princeton, Princeton University Press. Beck, N. & Katz, J. N. (1995) What to do (and not to do) with time-series cross-section data, American Political Science Review , 89(3), 634 647. Bru¨lhart, M. (1998) Trading places: industrial specialisation in the European Union, Journal of Common Market Studies , 36(3), 319 346. Bru¨lhart, M. & Traeger, R. (2005) An account of geographic concentration patterns in Europe, Regional Science and Urban Economics , 35(6), 597 624. Combes, P.-P. & Overman, H. G. (2004) The spatial distribution of economic activities in the European Union, in: V. Henderson & J.-F. Thisse (eds) Handbook of Urban and Regional Economics, Amsterdam, Elsevier-North Holland. Greene, W. H. (2000) Econometric Analysis , 4th edn, Englewood Cliffs, NJ, Prentice Hall. Hallet, M. (2002) Regional specialisation and concentration in the EU, in: J. R. Cuadrado-Roura & M. Parellada (eds) Regional Convergence in the European Union, Heidelberg and New York, Springer. Harris, C. D. (1954) The market as a factor in the localization of industry in the United States, Annals of the Association of American Geographers , 44, 315 348. Head, K. & Mayer, T. (2002) Illusory Border Effect: Distance Mismeasurement Inflates Estimates of Home Bias, CEPII Working Paper 2002-1, CEPII, Paris. Schu¨rmann, C. & Talaat, A. (2000) Towards a European Peripherality Index, Report for DGXVI Regional Policy of the European Commission, University of Dortmund.

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