Econometrics, Statistics And Computational Approaches in Food And Health Sciences

Alok Bhargava

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Econometrics, Statistics and Food and Health Sciences

Alok Bhargava University of Houston, USA

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ISBN

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PREFACE

This volume brings together four of my papers that developed longitudinal econometric methods in early part of my career and 23 applications addressing problems of food, nutrition and health in developing and developed countries. It may seem unusual to begin one's career in theoretical econometrics developing statistical tests and estimation methods and then apply them to resolve rather technical biomedical issues in food sciences and population health. The applied papers were published in diverse journals in economics, statistics, nutrition, psychology, anthropology, demography and public health. Thus, the main purpose in putting these papers into a single volume is that most libraries do not subscribe to all the journals and, perhaps more importantly, there are clear connections between the themes covered in the papers. However, it may be somewhat difficult for the reader to see the inter-connections and the introductory Chapter 1, therefore, outlines the links. The papers are organized into six broad themes i.e. econometric methodology, food intakes and health and productivity in developing countries, child health and cognitive development in developing countries, effects of population health on economic growth, economic demography in developing countries, and diet and obesity in developed countries such as the U.S. I would like to briefly describe the evolution of my research interests since many economists were surprised with my switch to biomedical sciences and public health. From 1979-1983,1 worked with Professor J.D. Sargan, at the London School of Economics, who had a sound intuition for mathematical concepts. He was a very modest person and one of the few truly introverted economists that I have come across. Econometrics to him was a quasi inter-disciplinary subject covering statistical theory, estimation methods and advanced computational techniques to address economic policy issues. In a sense, I tried, to follow his approach in the early part of my career. However, in 1988, I encountered a policy debate concerned with the effects of rises in household incomes on the way individuals nourish themselves in developing countries such as India. It struck me that economists are often unfamiliar with nutritional sciences though are not shy about invoking simplifying assumptions that can be at variance with the knowledge in biomedical sciences. Even in the behavioral field, psychologists have reservations about economists' assumptions concerning human behavior. I outlined some of these issues in an editorial in the Journal of Econometrics (Bhargava, 1997) and received strong encouragement from Professor Herbert Simon who was a well-known economist and psychologist. Despite the current popularity of randomized controlled experiments in economics, it remains to be seen if the micro-economics literature will gradually begin to rely on scientifically acceptable assumptions. A stark contrast between the research in econometrics and applied health sciences is that while economists spend much time developing complex estimation techniques, health scientists are more concerned with measurement issues and the design of surveys. The contrast is more striking in research analyzing aggregate time series where I began my career developing tests for "unit roots". An inordinate effort is spent devising alternative statistical methods for time series though there have been few significant improvements in data collection methods or in compiling disaggregated measures of economic activity that may afford closer links between economic theory and data analyses. By contrast, the data from numerous carefully designed longitudinal studies are available in food and health sciences and knowledge of the scientific issues can greatly strengthen the formulation and

Preface

VI

estimation of models for health outcomes. While bio-statistical literature is often available in health sciences, there is a division of labor between biomedical scientists and statisticians. Although some specialization is inevitable, it is difficult for biomedical scientists to visualize how their knowledge can be used to extract further information from the data that have been painstaking compiled. The main objective of my research in the last two decades has been to fill this gap especially since there are urgent problems of malnutrition and ill health affecting billions of inhabitants in developing countries. There are, of course, many hindrances in making a career switch in the competitive environments existing in academia. The peer review system can hamper the transition unless the editors of leading journals take independent and critical views of the research in their fields. The existence of such editors in biological sciences is assured by the fact that even in the most scientific disciplines, empirical results depend on the relationships postulated for the variables and hence there is scope for misinterpreting the results. This spirit is less common in social sciences where conceptually weak paradigms can sometimes dominate the research for decades. My transition into biomedical sciences was facilitated by editors who accepted my papers often on controversial issues. I was also fortunate to have the benefit of criticisms from eminent nutritionists like Nevin Scrimshaw whose main goal has been to improve the nutritional well-being of individuals in developing countries. My former teachers from the London School of Economics, Partha Dasgupta, Terence Gorman, David Hendry and Amartya Sen have encouraged me to address pressing problems such as hunger, population, AIDS, and obesity. I would also like to thank Tony Atkinson, Howdy Bouis, Bob Fogel, Jerry Hausman, Jim Heckman, Peter Hogfeldt, Dan McFadden, and Martin Ravallion for their encouragement. Lastly, on a personal note, there are things about our personalities and motivations that are largely inexplicable. The psychologist Carl Jung, for example, revived the ancient Indian notion of "maya" (or illusion) arguing that the unconscious mind drives many of our conscious behaviors (Jung, 1961). I was fortunate in having the support of my parents in the early years to create a carefree inner world that allowed me to mull over abstract concepts. I think that there is an asymmetry in human development in that we seek to know our children consciously but the relationships with our parents are driven by unconscious forces. So, while I consciously learnt the classical theories of Piaget (1977) and Vygotsky (1987) for improving the specification of models for children's cognitive development, I suspect that most of my work has been an unconscious tribute to the love and affection that I received from my parents. I became conscious of this phenomenon when my father suddenly passed away on 19 January 1999 leaving a vacuum in my life that no amount of research is likely to fill. Of course, my wife and children have helped me in many ways over the past several years. References Bhargava, A. (1997). Introduction to 'Analysis of data on health'. Journal of Econometrics, 77, 1-4. Jung, C. G. (1961). Memories, Dreams, Reflections. New York: Random House. Piaget, J. (1977). The Essential Piaget, Gruber, H., and J. Voneche (eds.). New York: Basic Books. Vygoysky, L. (1987). Thinking and speech. In the Collected Works of L. S. Vygotsky, Volume 1, Rieber, R. W., and A. Carton (eds.). New York: Plenum.

CONTENTS Preface

v

Introduction

xi

I. Methodological Contributions 1. Estimating Dynamic Random Effects Models from Panel Data Covering Short Time Periods Alok Bhargava and J. D. Sargan

3

2. Wald Tests and Systems of Stochastic Equations Alok Bhargava

29

3. Identification and Panel Data Models with Endogenous Regressors AlokBhargava

49

4. Serial Correlation and the Fixed Effects Model Alok Bhargava, L. Franzini and W. Narendranathan

61

II. Food Intakes, Health and Productivity in Developing Countries 5. Estimating Short and Long Run Income Elasticities of Foods and Nutrients for Rural South India Alok Bhargava

81

6. Does Household Consumption Behave as a Martingale? A Test for Rural South India Alok Bhargava and Martin Ravallion

99

7. Dietary Intakes and Socioeconomic Factors are Associated with the Hemoglobin Concentration of Bangladeshi Women Alok Bhargava, Howarth E. Bouis andNevin S. Scrimshaw

105

8. Malnutrition and the Role of Individual Variation with Evidence from India and the Philippines Alok Bhargava

113

9. Nutritional Status and the Allocation of Time in Rwandese Households Alok Bhargava

125

10. Requirements for What? Is the Measurement of Energy Expenditure a Sufficient Estimate of Energy Needs? Alok Bhargava and Peter J. Reeds

145

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Contents

III. Child Health and Cognitive Development in Developing Countries 11. Modelling the Health of Filipino Children Alok Bhargava

153

12. Modelling the Effects of Nutritional and Socioeconomic Factors on the Growth and Morbidity of Kenyan School Children Alok Bhargava

169

13. Coliforms in the Water and Hemoglobin Concentration are Predictors of Gastrointestinal Morbidity of Bangladeshi Children Ages 1-10 Years Alok Bhargava, Howarth E. Bouis, Kelly Hallman and Bilqis A. Hoque

179

14. Modeling the Effects of Maternal Nutritional Status and Socioeconomic Variables on the Anthropometric and Psychological Indicators of Kenyan Infants from Age 0-6 Months Alok Bhargava

191

15. A Dynamic Model for the Cognitive Development of Kenyan Schoolchildren Alok Bhargava

207

16. Anthelmintic Treatment Improves the Hemoglobin and Serum Ferritin Concentrations of Tanzanian Schoolchildren Alok Bhargava, Mathew Jukes, Jane Lambo, C. M. Kihamia, W. Lorri, Catherine Nokes, Leslie Drake and Donald Bundy

213

17. Modeling the Effects of Health Status and the Educational Infrastructure on the Cognitive Development of Tanzanian Schoolchildren Alok Bhargava, Matthew Jukes, Damaris Ngorosho, Charles Khilma and Donald A. P. Bundy

225

18. AIDS Epidemic and the Psychological Weil-Being and School Participation of Ethiopian Orphans AlokBhargava

239

IV. Population Health and Economic Growth 19. Stochastic Specification and the International GDP Series Alok Bhargava

255

20. Modeling the Effects of Health on Economic Growth Alok Bhargava, Dean T. Jamison, Lawrence J. Lau and Christopher J. L. Murray

269

Contents

IX

V. Economic Demography 21. A Longitudinal Analysis of Infant and Child Mortality Rates in Developing Countries Alok Bhargava and Jiang Yu

289

22. Family Planning, Gender Differences and Infant Mortality: Evidence from Uttar Pradesh, India Alok Bhargava

303

23. Healthcare Infrastructure, Contraceptive Use and Infant Mortality in Uttar Pradesh, India Alok Bhargava, Sadia Chowdhury and K. K. Singh

319

VI. Behavior, Diet and Obesity in Developed Countries 24. Estimating the Variations and Autocorrelations in Dietary Intakes on Weekdays and Weekends Alok Bhargava, Ronald Forthofer, Susie McPherson and Milton Nichaman

339

25. Behavioral Variables and Education are Predictors of Dietary Change in the Women's Health Trial: Feasibility Study in Minority Populations Alok Bhargava and Jennifer Hays

353

26. Socio-economic and Behavioural Factors are Predictors of Food Use in the National Food Stamp Program Survey Alok Bhargava

363

27. Unhealthy Eating Habits, Physical Exercise and Macronutrient Intakes are Predictors of Anthropometric Indicators in the Women's Health Trial: Feasibility Study in Minority Populations Alok Bhargava and Joanne F. Guthrie

373

INTRODUCTION The 27 articles in this volume are divided into six themes, namely, methodological contributions, food intakes and health and productivity in developing countries, child health and development, population health and economic growth, economic demography, and diet and obesity in developed countries. A potential problem for the reader of the volume may be the different styles and formats followed in social sciences and biomedical journals. Moreover, biomedical and public health researchers are often unfamiliar with concepts such as "endogeneity" that economists take for granted. Even the terminology used in the statistical and psychometric literatures is often different than that used in econometrics. Many of these problems have already been circumvented in the articles because they were published outside the economics field; the concepts were clarified at the suggestions of various reviewers and editors. However, it would be useful to note the salient points in the articles in this Introduction to enable the reader to assess the empirical results in a unified manner. We now briefly discuss the articles in the six groups.

I. Methodological Contributions A common feature of longitudinal ("panel") data compiled in social and health sciences is that large numbers of household or individual units are observed for a few time periods. For data sets compiling long time series on the units, estimation methods such as "fixed effects" models (where an indicator (0-1) variable is included for each unit) can be easily extended. By contrast, if the number of units is large but the number of time periods is small, then it is useful to assume that the unobserved individual specific effects are randomly distributed. While the use of random effects models has been common in the econometrics and statistical literatures, the appropriate asymptotic distribution theory was spelled out around the same time by Anderson and Hsiao (1981) and Bhargava and Sargan (1983). The article by Bhargava and Sargan (1983) exploited the analogy with simultaneous equations models for which Mann and Wald (1943) and Koopmans and Hood (1953) had derived the fundamental results. The main purpose of this section is to outline the properties of the econometric estimators from the viewpoint of their applications without going into the technical details. The first article by Bhargava and Sargan (1983) proposed several estimators for "dynamic" models (containing previous realizations of the dependent variable) with random effects for analyzing data on large number of individual units observed for a few time periods. The main advancements in this paper were, firstly, the initial (and lagged) observations on the dependent variable were treated as "endogenous" variable i.e. correlated with the unobserved random effects. For identification and estimation purposes, the available T-time observations were stacked as a system of simultaneous equations where each set of time observations corresponded to an "equation". Estimation methods such as the Limited Information Maximum Likelihood (LIML) and Three Stage Least Squares (3SLS) developed for simultaneous equations were used to estimate the model parameters that were restricted to be constant over time i.e. across the T equations. Second, the estimation methods assumed that the T x T variance covariance matrix of the errors was the unrestricted dispersion (or serial covariance) matrix of a multivariate normal distribution, and also where this matrix had

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Introduction a simple random effects structure. For the random effects decomposition, the "concentrated likelihood function" (eliminating "nuisance" parameters from the likelihood function) was more complex than in the case where the dispersion matrix was unrestricted. Likelihood ratio statistics were developed to test the null hypotheses that the random effects decomposition was accepted by the data. This is important because incorrectly enforcing the restrictions, as done in many applications, can yield inconsistent parameter estimates. Third, the methodology for estimation of dynamic models was extended to the situation where some of the time invariant and time varying explanatory variables were correlated with the individual specific random effects. The main contribution of the article was to derive sufficient conditions under which the model parameters were identified; the proof of the theorem exploited cross-equations restrictions on the model parameters. Moreover, a likelihood ratio test was developed to test whether the postulated variables were exogenous. These test statistics are important because economists often postulate many variables to be endogenous. However, the "instrumental variables" necessary for consistent estimation of model parameters may be weakly correlated with endogenous variables especially when individual or household level data are employed leading to unreliable results. Furthermore, the postulated correlation between the endogenous variables and the random effects enabled the use of deviations of the time varying variables from their time means as instrumental variables; these deviations are in the spirit of the fixed effects model and are likely to be more strongly correlated with the endogenous variables. Fourth, from a computational standpoint, the estimation methods were implemented by creating the second moment matrices of the variables from the data and summing them over each individual unit. This afforded enormous savings in the computer memory since the data were read individual by individual. Moreover, numerical optimization algorithms available in the Numerical Algorithm Group (1991) approximating the analytical derivatives of the concentrated (or "profile") likelihood function were used. For example, the FORTAN computer program for estimating a dynamic model using data on 1000 individual units in 10 time periods typically required less than 2 megabytes of computer memory and less than a second to converge. It is hoped that these and other methods for estimating random effects models from short panels will be incorporated in software packages in due course. Lastly, the estimation methods and statistical tests were applied to an "earnings function" using the data from the Michigan Panel Survey of Income Dynamics. The empirical results were a significant improvement over the previous results obtained in economics from estimating dynamic models using short panels. Moreover, the results indicated a need for caution in situations when the correlations between time varying endogenous variables ("years of schooling") and instrumental variables were low. In such circumstances, it is important to re-appraise why the variables might be endogenous, and compare the results with the estimates that ignore endogeneity problems. The second article (Bhargava, 1987) investigated additional issues in the specification and estimation of dynamic random effects models from short panels. First, it was shown that if the errors were not distributed according the multivariate normal distribution, then the quasi (or pseudo) maximum likelihood estimator was still consistent and asymptotically normally distributed given a large number of units. Moreover, the variance covariance of the model parameters was not affected by distributional misspecification insofar as the fourth order moments of the actual errors were finite. However, the variance covariance matrix of the estimated dispersion (serial covariance) matrix was affected by distributional misspecification. In fact, this variance covariance matrix depends on third

Introduction

xin

and fourth order moments of the errors though the contribution of third-order moments disappears if a constant term is included in the model thereby simplifying the computations. Second, because the variance covariance matrix of the dispersion matrix can be estimated under general distributional misspecification, one can investigate the stochastic properties of the errors affecting random effects model within a general framework. In particular, a sequence of Wald (1943) statistics that are robust to distributional misspecification were developed to test whether the errors followed moving average processes, allowing for the presence of unobserved random effects. Moreover, tests for changes in the variances of the errors (heteroscedasticity) over time were developed. The testing procedures provided an interesting application of the theory of sequential tests developed originally by Wald (1947) where the size of each sub-test can be set at different levels. Lastly, the article estimated a dynamic earnings function using the data from the Michigan Panel Survey of Income Dynamics to produce an unrestricted estimate of the serial covariance matrix of the errors. The results showed that there was heteroscedasticity over time in the errors and that a third-order moving average process was adequate in this application. From a methodological standpoint, these results showed the feasibility of applying Wald statistics to dynamic models from panel data. This is useful since the error structures are difficult to specify a priori and hence likelihood ratio statistics are more difficult to apply for testing the validity of alternative specifications. The third article (Bhargava, 1991a) considered identification and estimation of dynamic and static models under more general assumptions on the correlation patterns between the error terms and the endogenous explanatory variables. Bhargava and Sargan (1983) assumed that only the random effects were correlated with the ("special") endogenous explanatory variables which may not be appealing in some applications. Estimation under more general correlation pattern was feasible especially in situations where the number of time observation was not too small (e.g. >3). The main results in this article were, first, that the identification conditions were more complex and stringent than the case where only the random effects were correlated with time varying explanatory variables. However, investigators can decide on the correlation pattern that would be appropriate depending on the identification conditions that might be satisfied. Second, the article demonstrated that the restricted correlation pattern (as in random effects formulations) was in fact a special case of the general correlation pattern so that one can use nested sequential tests for exogeneity hypotheses. These tests would first test if the random effects decomposition for the correlation pattern was accepted by the data, and if so, then one would test whether the random effects were uncorrelated with the explanatory variables. The nested sequential testing procedure for exogeneity assumptions is unique in the econometrics literature and was in the spirit of the classical approach developed by Wald (1943, 1947). Third, instrumental variables estimators were developed for the general and special correlation patterns for static models and these were generalizations of the 3SLS method (Zellner and Theil, 1962) with cross-equations restrictions on the parameters. Fourth, sequential Chi-square tests for exogeneity hypotheses were developed for maximum likelihood and instrumental variables estimators. For static models, for example, the test statistics were more comprehensive than the ordinary time series case considered by Sargan (1958); the statistics for the ordinary time series have been reworked in the mathematically equivalent framework of "Generalized Methods of Moments". Fifth, the estimation methods and tests for static models were applied to the data on dietary intakes in three villages in south India. The empirical models will be discussed in the next section though it should

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Introduction

be noted that the Chi-square statistics for exogeneity hypotheses sometimes assumed negative values in this application. Unlike likelihood ratio tests, these statistics were computed as differences between two positive definite quadratic forms and can assume negative values. This is likely to happen if the models were poorly specified or if there was severe multi-collinearity between the instrumental variables reducing precision of the sub-routines for matrix inversion. Lastly, the FORTRAN programs for estimating static models were also very efficient in terms of computer memory and the time necessary to compute model parameters and can be made available to statistical software packages. The final article in the methodological section (Bhargava et al, 1982) generalized the DurbinWatson (1950) statistic to models withfixedeffects i.e. with separate intercept terms for each individual unit. Longitudinal data covering a large number of units lead to the problem of "incidental" parameters in thefixedeffects models since the number of parameters increase with the sample size (Neyman and Scott, 1948). Thus, the estimates of parameters such as the elements of the serial covariance matrix are inconsistent insofar as the number of time observations is small. By contrast, the Durbin-Watson type tests rely on finite sample theory and circumvented the problem of incidental parameters. This was also true for optimal tests for unit roots (where the serial correlation coefficient is unity) developed by Sargan and Bhargava (1983) that were also extended to the fixed effects model. Furthermore, lower and upper bounds were tabulated for testing serial independence of the errors and for tests for unit root null hypothesis assuming different numbers of individual units and time periods. The article also developed an estimation method for correcting the "bias" in the estimated serial correlation coefficient due to the small number of time observations. The methods and tests were applied to a static earnings function that was estimated using the Michigan Panel Survey of Income Dynamics. The results showed that the estimated serial correlation coefficients were very close to those obtained previously using a random effects model (Lillard and Willis, 1978). Some versions of these methods for fixed effects models are available in STATA (2003). However, a majority of the papers in this volume rely on the random effects framework. II. Food Intakes, Health and Productivity in Developing Countries The first paper in this section (Bhargava, 1991b) estimated short and long run income elasticities of foods and nutrients using household and individual level data on intakes from three villages in south India that were surveyed in 1976-1978 by the International Crops Research Institute for Semiarid Tropics (ICRISAT). First, dynamic models estimated for the annual expenditures on six food groups (grains, pulses, sugar, vegetables, milk and meat); the results provided evidence of higher intakes especially of milk and meat with rises in household incomes. Moreover, the empirical results indicated the importance of "habit persistence" in diets among Indian households. Second, the models for dietary energy and nutrient intakes were estimated using the data from 24-hour recall surveys where every individual in the household stated the foods consumed together with portion sizes in the previous 24-hour period at two time points. These data provided direct measures of food intakes and were subsequently converted to energy and nutrient intakes using food conversion tables for India. The article also discussed methodological problems in the estimation of empirical models due large "internal" (within-subject) variation in the intakes that is partly due to the fact that most foods contain most nutrients though in different proportions.

Introduction Third, alternative versions of dynamic models were estimated for energy and nutrient intakes and for the ratios of nutrient to energy intakes. Because most foods contain most nutrients, the simple dynamic models may not lead to robust estimates since one cannot increase the intake of a nutrient without increasing the intakes of several other nutrients. This point was noted in the economics literature by Stigler (1945). The empirical results from the models indicated that individuals' intakes of essential nutrients such as protein, minerals and vitamins significantly increased with household incomes. In fact, the ratios of nutrient to energy intakes are good indicators of diet quality that were significantly associated with household incomes. Fourth, the article emphasized the "hierarchical" nature of demand for nutrients in that households are likely to meet their members' energy needs, followed by the requirements of protein, minerals and vitamins. This is a more complex approach than that assumed in economic analyses where households or individuals solve the food consumption decisions via the postulate of utility maximization. In fact, the notion of hierarchy in human wants is known since the writings of Plato and its relevance in economics was noted by Georgescu-Roegen (1966). Finally, the article demonstrated the importance of analyzing the effects of economic variables on dietary intakes while controlling for physiological variables such as individuals' heights and weights that reflect their energy and nutrient requirements. While the income elasticities of energy and nutrients in the dynamic and static models were in the interval [0.10, 0.20], it was likely that previous studies using aggregate food expenditures data had over-estimated these elasticities. Moreover, in modeling the intakes data, it is important to note the biological limits on food intakes. For example, the intakes cannot increase dramatically without a concomitant increase in energy expenditures i.e. physical activity levels. Thus, higher household incomes are likely to lead to gradual improvements in diet quality that is beneficial for individuals' health. The dynamic longitudinal modeling approach afforded a unified treatment of nutritional, economic and computational issues for formulating food policies in developing countries. The second article in this section by Bhargava and Ravallion (1993) used the ICRISAT data on aggregate consumption expenditures of Indian households over a six-year period. The main purpose of this article was to test the "martingale" hypothesis that is implied by certain versions of the permanent income hypothesis (Hall, 1978) i.e. if future changes in consumption are significantly influenced by the currently available information. The article used both fixed and random effects formulations for the estimation of model parameters and for diagnostic tests. The results did not support the martingale hypothesis using the data on consumption, income and a variety of assets held by the households. This was perhaps not surprising since households cannot borrow from "perfect" capital markets and so it is unlikely that consumption can adjust to a stochastic self-fulfilling expectation of future household incomes. The results were also suggestive of the more complex decision making process that poor households were likely to adopt due to income uncertainties. The third article in this section (Bhargava, Bouis and Scrimshaw, 2001) was also concerned with issues of income and nutrition though in a more complex nutritional setting using a longitudinal data set from Bangladesh. Iron deficiencies are widely prevalent in developing countries and assessing adequacy of iron intakes is complicated by the fact that iron absorption rates from staple foods such as cereals are very low (e.g. around 1%). Thus, it is important to account for intakes of other nutrients in the meal such as ascorbic acid (vitamin C) and meat for assessing the "absorbable" (or "bioavailable") iron intake. Moreover, models for the effects of nutrient intakes on blood indicators

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Introduction of iron status such as hemoglobin concentration are useful from a policy standpoint. The main results in this article were, first, that the bioavailable iron intakes depended on the assumptions regarding the body stores of iron i.e. women with lower iron stores were likely to absorb higher quantities of iron. Second, the absorbable iron intakes were significant predictors of hemoglobin concentration of Bangladeshi women, controlling for confounding factors such as women's height and weight and the intake of iron tablets. Thus, higher intakes of vitamin C and meat were likely to increase hemoglobin concentration and reduce the prevalence of iron deficiency anemia. Third, the algorithms for calculating bioavailable iron were approximate since these were based on laboratory experiments involving healthy adults in developed countries. Thus, from an economic viewpoint, it was important to investigate the effects of increases in household incomes on dietary intakes that in turn increase hemoglobin concentration. Because iron from meat, fish and poultry is readily absorbed, the income elasticity of intakes of iron from meat,fishand poultry by Bangladeshi women was estimated and was around 0.60. Similar results were obtained for iron intakes from all animal foods including milk and eggs where the income elasticity was 0.70. The results in this article are important for devising food polices for combating iron deficiencies in developing countries. For example, while the iron content of rice can be increased via plant breeding (Bouis, 2002), it is critical to increase the intakes of vitamin C and meat for enhancing iron absorption. Adverse consequences of iron deficiencies for outcomes such as children's cognitive development are addressed in Section III. The fourth article in the section deals with the controversy surrounding "biological adaptation" to low energy intakes promoted by Sukhatme and Margen (1978, 1982). Briefly, these authors hypothesized that with a decline in food intakes, the human body can increase the efficiency with which food intakes are converted into expendable energy. Thus, under-nourished individuals can easily adapt to low food intakes. The hypothesis was claimed to be supported by the evidence from the variations in energy intakes by 27 young British Army recruits and 12 individuals living in the Antarctica. The implications of the results, however, were extrapolated for under-nourished inhabitants of developing countries. The article by Bhargava (1992) used the data on energy and protein intakes by individuals in the ICRISAT survey in south India, and another survey in the Bukidnon region of the Philippines covering 450 households (Bouis and Haddad, 1990). First, it was argued that the within subject variations in energy and protein intakes were likely to increase with poverty since poor individuals cannot afford adequate quantities of food. Thus, Sukhatme and Margen (1978) were correct to emphasize the importance of high within subject variation in intakes but for the wrong reasons i.e. these variations stem from poverty rather than from obscure biological processes. Second, the within subject variations and autocorrelations in energy and protein intakes were estimated via simple dynamic random effects models using the data at four time points from India and the Philippines. The results indicated that the within subject variances were larger in India which was not surprising since the households were poorer and there were greater fluctuations in food intakes due to seasonality. Third, the within subject variances of energy and protein intakes were found to decline with household incomes in India and in the Philippines. Fourth, similar results were obtained by disaggregating the data for age groups which was important since individuals' requirements were likely to depend on their age. These findings were sufficient to contradict the theories of Sukhatme and Margen that high within subject variations reflect the ability of the human

Introduction

body to adapt to low food intakes. Lastly, the article briefly discussed the upward revisions of "Recommended Dietary Allowances" in developing and developed countries. The fifth article in this section (Bhargava, 1997) analyzed the determinants of time allocation on productive and resting activities of men and women in Rwanda using a longitudinal data set covering four time periods in 1982-1983. Because food shortages are common in Rwanda, the roles of energy and protein intakes and anthropometric indicators such as body weight were underscored. Moreover, the data were available on food prices paid by households and there was considerable variation in prices since the surveys covered all 90 "sectors" of Rwanda. Also, the daily patterns of activities were recorded for 14 consecutive days, and the food intakes for seven days in each of the four survey rounds. The energy expenditures on 30 broad activities defined by FAO/UNU/WHO (1985) were calculated in terms of the Basal Metabolic Rate (i.e. the minimum energy necessary for sustaining life) for a typical day; the food intakes were based on averaging the intakes data over seven days. The main results from the analysis were, first, higher prices of sweet potatoes were negatively associated with the total consumption expenditures of households. Second, there was some weight loss apparent in the third and fourth survey rounds indicating that individuals' energy requirements were not being met. Third, the resting patterns of men and women indicated that individuals with low Body Mass Index (BMI) spent a greater proportion of time resting in order to conserve energy. Moreover, men with higher BMI spent a greater proportion of time on strenuous activities such as working on the land; there were also positive and significant effects of energy intakes on certain productive activities. Fourth, there was considerable work sharing in these households in that the men (women) increased their energy expenditures especially on agricultural activities in response to greater demands on women's (men's) time. These results provided some evidence against the argument that women were likely to bear a greater work burden of economic development (Berio, 1984). Finally, the results had important implications for incorporating energy expenditures in the definition of energy and nutrient requirements that are discussed in the next article. The article by Bhargava and Reeds (1995) took a broader view of the inter-relationships between energy expenditures and intakes than that reflected in the statement "requirements for what?" (FAO/UNU/WHO, 1985); the latter implied that one must spell out energy expenditures prior to defining energy requirements. However, it was pointed out in the article that energy expenditures are useful indicators of energy requirements mainly in populations where there are no food shortages and diet quality is good such as in developed countries. By contrast, in situations where there are food shortages, energy intakes are likely to drive the energy expenditures. Thus, focusing exclusively on energy expenditures will not be helpful for defining energy requirements in developing countries. Furthermore, in situations with no energy shortfalls but with micronutrient deficiencies such as those of iron, individuals' health status may be compromised and hence their energy expenditures may be low. Thus, it is important to view the problems of energy requirements and expenditures in a broader analytical framework. The article also presented estimates of the effects of individuals' height and weight on their Basal Metabolic Rates using a data set from India covering under-nourished individuals.

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III. Child Health and Cognitive Development in Developing Countries The eight articles in this section are concerned with issues of children's health and cognitive development in developing countries. The first paper (Bhargava, 1994) developed the conceptual framework for modeling indicators of child health such as height, weight and morbidity taking into account the inter-relationships between the indicators. In the anthropometric assessment and biostatistical literatures, for example, height is often used as a predictor of body weight but not vice versa. This is a reasonable approach since height of a child reflects the skeletal size and that is "fixed" during the observation period of (say) 24 hours. In contrast, the child's weight can fluctuate on the day of observation depending on food intakes and other factors such as the time of the day the children are weighed. Similarly, child morbidity that incorporates the intensity and duration of symptoms can greatly vary in a 24-hour period. The essence of the modeling approach in this article was that one can view a child's height asfixedin relation to weight, and both height and weigh were fixed in relation to morbidity that was essentially a "flow" variable. This "stock/flow" approach afforded a unified framework for modeling health indicators. Moreover, issues such as "feedback effects" (endogeneity) of some of the explanatory variables were tackled in the empirical modeling. The main results in the article using four time observations on 312 Filipino children in the age group 1-10 years were, first, that income elasticities of minerals and vitamins were around 0.20. These model parameters were more precisely estimated than with the ICRISAT data from India that were available at two time points for the estimation of income elasticities. Second, in the model for height, protein intakes were significant predictors; the intakes were based on 24-hour recall method and it often difficult to find significant effects of nutritional intakes due to the large within subject variation. Third, the models for height and weight showed significant effects of parents' anthropometrics on children's measurements. Fourth, the paper proposed a likelihood ratio test for testing whether height and weight could be combined as the Body Mass Index (BMI). The practice of using BMI was criticized by Kronmal (1993) and the application of this likelihood ratio test circumvented the problems. Interestingly, the likelihood ratio test statistic accepted in the null hypothesis at 2.5% significance level that Filipino children's height and weight could be combined as the BMI in the model for the morbidity index. Fifth, the results for children's morbidity index indicated that /3-carotene intakes lowered morbidity, while children using open pit type toilets faced higher morbidity levels. Lastly, the analysis tested for the feedback effects (or exogeneity) and the results under alternative assumptions were close. The second article (Bhargava, 1999) conducted an analysis similar to that for Filipino children for Kenyan school children where the data were available at three time points. The children's food intakes at each of the three time points were based on six days of food intakes and hence were more reflective of the "habitual" intakes. Furthermore, the morbidity data were available on a weekly basis for the three-month period preceding each survey round and were more elaborate than the Filipino data that covered only five symptoms. The main results from the empirical modeling were that, first, maternal height and children's calcium intakes were significant predictors of children's height. Second, in the model for weight, a likelihood ratio test showed that it was appropriate to combine children's energy and protein intakes as the protein/energy ratio. This ratio is an indicator of diet quality and hence Kenyan children consuming better diets were heavier. Third, both the children's height and arm circumference were significant predictors of weight. As noted above, height is a good approximation for skeletal size and arm circumference reflects "lean body mass"

Introduction

(muscle); these variables were important factors affecting weight. Lastly, the results for children's morbidity provided many insights. For example, while maternal and paternal years of education were not significant predictors, parental scores on tests of "intelligence" were highly significant predictors. In fact, the coefficient of the maternal score was four times the coefficient of paternal test scores. Moreover, the intakes of vitamin A significantly reduced child morbidity, while not having a latrine increased morbidity levels. The third paper (Bhargava, Bouis, Hallman and Hoque, 2003) presents an analysis using the data on 99 Bangladeshi children in the age group 1-10 years that were observed at three time points. The emphasis in this paper was on the effects of water contamination by fecal and total coliforms for children's gastrointestinal morbidity. Sanitation in developing countries is generally poor and in Bangladesh, the efforts to improve water quality via tube wells were unexpectedly thwarted by the presence of arsenic. The main results from the empirical modeling were, first, that children's hemoglobin concentration was an important and significant predictor of gastrointestinal morbidity. Good iron status is known to enhance immunity systems and the results underscored the importance of improving iron status via higher intake of animal products and by removing hookworm infections (see also below). Second, the fecal and total coliforms in the stored water were significant predictors of child morbidity. By contrast, coliforms in the water available at the source were not significant predictors. These results indicated the importance of providing households with subsidized soap for washing hands, and better storage containers with tight fitting lids to reduce water contamination. Lastly, the model for children's hemoglobin concentration showed significant effects of hookworm infections though the dietary intakes were not significant predictors. The latter could be due to small number children in the sample and also because the food intakes were assessed via the 24-hour recall method. The next five papers in the section analyzed health and cognitive data on children; the data were compiled by psychologists, nutritionists and epidemiologists. The paper on Kenyan infants (Bhargava, 2000) analyzed anthropometric and psychological data at birth, anthropometric data from 1-6 months, and psychological tests at six months (Bayley, 1969) on approximately 100 infants. The purpose of these analyses was to gain insights into the usefulness of psychological measures at young ages. First, the Brazelton Neonatal Behavioral Assessment Scale (Brazelton, 1984) that is administered to new-born infants was not found to be a useful indicator for under-nourished infants though it may be useful for infants suffering from neurological defects. By contrast, infants' length, weight, and head circumference were useful indicators that were significantly predicted by variables such as length of the gestation period, maternal pre-pregnancy BMI and socio-demographic variables. Second, the models for children's length, weight, and head circumference showed the importance of maternal health and nutritional status. Third, the children's scores on 33 items from the Bayley Motor Scales at the age of six months showed the importance of energy intakes from animal sources such as milk and meat. Moreover, infants' protein intakes were significant predictors of the scores on eight items from the Bayley Infant Behavior Record. Overall, the results indicated that anthropometric indicators were reliable and inexpensive indicators of infant development though the psychological measures at the age of six months were also useful. The article on the cognitive development of Kenyan school children (Bhargava, 1998) analyzed the data at three time points on the scores on digit span, Raven's matrices, arithmetic, verbal abilities and behavioral indicators. The main results were, first, that children's hemoglobin con-

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centration was a significant predictor of the scores on digit span, arithmetic and Raven's matrices that typically require higher-order mental functions. By contrast, the scores on verbal abilities were not significantly affected by children's iron status which may be due to the fact that a child must learn language to communicate with the adults (Vygotsky, 1987). Second, parental scores on psychological tests were significant predictors of children's scores and this was perhaps not surprising since the home environment was likely to play an important role. Third, children's anthropometric indicators such as the BMI and head circumference were significant predictors of the test scores indicating the importance of good nutritional status for cognitive development. Lastly, the scores on school examinations were predicted mainly by children's school attendance and not by the health status related variables that predicted the scores on cognitive tests. These results were indicative of the inadequacies in the educational infrastructure since the children seemed to have received high marks for attending school. The next two papers analyzed the data from a randomized trial in Tanzania offering anthelmintic treatment against hookworm and schistosomiasis to heavily infected children in the Intervention group. While the use of randomized trials is becoming popular in social sciences, it is important to recognize that well-specified hypotheses are essential for designing the trials. Thus, for example, anthelmintic treatment will eliminate intestinal parasitic load. Because these parasites thrive on blood, one would expect to see a direct impact on children's iron status in the Intervention group. However, certain psychologists have emphasized links between intestinal parasites and children's cognitive function (Watkins and Pollitt, 1997); randomized trials have investigated the potential effects of de-worming on cognitive function. However, such effects are likely to be more complex since they also involve the educational infrastructure (see below). The article by Bhargava et al. (2003) found significant benefits of anthelmintic treatment on Tanzanian school children's hemoglobin and ferritin concentrations; the increases in hemoglobin concentration were approximately 8%. Moreover, longitudinal models for hemoglobin and ferritin concentrations and C-reactive protein levels were estimated using the data at three time points from the Control group. Another purpose of the analysis was to predict, using the data from the Control group, the likely improvement in hemoglobin and ferritin concentrations if the hookworm and schistosomiasis loads were reduced to zero. A statistical test was proposed to test the null hypothesis of no difference. However, the model for the Control group under-predicted the benefits of anthelmintic treatment for children's hemoglobin concentrations that were observed in the Intervention group. These results suggested that anthelmintic treatment may have other benefits such as increasing nutrient absorption. Moreover, the article stressed that it is helpful to use alternative approaches to analyses of data from randomized controlled trials. The second article on Tanzanian school children (Bhargava et al., 2005) modeled the data from the Control group on three sets of indicators of child development i.e. scores on cognitive tests designed by psychologist, educational achievement tests such arithmetic, spelling and reading, and on school examinations in arithmetic, science, geography and civics. It was argued that while anthelmintic treatment can conceivably affect the test scores, measures of health status, socioeconomic factors and educational infrastructure were likely to play an important role. First, the results showed that the differences in the changes in test scores of treated children in the Intervention group and children in the Control group between baseline and thefinalobservation period (15 months) were not statistically significant. Second, the data from Control group showed that while the intestinal par-

Introduction

asite loads were not statistically significant predictors of test scores, variables such as hemoglobin concentration, height, and school attendance were significant predictors of especially of the scores on educational achievement tests. Thus, the results indicated that factors such as the children's iron status and school attendance were more important than the intestinal parasitic loads from the standpoint of enhancing cognitive development. Third, from a methodological standpoint, the scores on educational achievement tests were predicted by variables such as school attendance, while school attendance was not a significant predictor of the scores on cognitive tests and school examinations. Because educational achievement tests are closer in spirit to the material taught in the classroom and were administered by outside enumerators, they are likely to be useful tools for assessing children's development in developing countries. Fourth, the effects of the educational infrastructure such as teachers' years of experience and homework assignments were important predictors of the scores on educational achievement tests. There were also interactive effects between children's height and work assignments indicating that the school infrastructure may offset some of the deficits in children's health status from the standpoint of learning. Lastly, school attendance was mainly predicted by households' socioeconomic status and not by variables such as the intestinal parasitic loads. With the AIDS pandemic rife in many African countries, it is likely that school attendance would be reduced by premature parental deaths. Thus, comprehensive policies such as those subsidizing fostering households are urgently needed for child welfare and for economic development in Africa (Bhargava and Bigombe, 2003). The final article in this section modeled the proximate determinants of school participation and psychological well-being of Ethiopian children that were being fostered due to the deaths of their mothers (Bhargava, 2005). The data were from a national survey conducted in 2001-2002; approximately 1000 children over the age of 10 years were given 60 items from the Minnesota Multiphasic Personality Inventory (MMPI) to investigate their emotional and social adjustment. The main results were that the death of the mother increased the chances of the child participating in remunerative activities and dropping out of school. Moreover, the data from MMPI indicated that girls were psychologically worse off due to the loss of their mothers. The responses to the questions inquiring the food situation in the fostering household showed that children's psychological well-being could be raised via greater food subsidies to fostering households. Similarly, a variable reflecting if the children were dressing well was a significant predictor of the scores on MMPI. Overall, the empirical results underscored the need to alleviate poverty among fostering households for enhancing children's school participation and psychological well-being. This is an urgent issue in Africa since there may be 25 million orphans of AIDS by the year 2010. IV. Population Health and Economic Growth The two articles in this section present analyses of longitudinal data on national averages from developing and developed countries; such studies are popular in the empirical macro-economics literature. The focus of the articles is on model specification issues in quantifying the effects of population health indicators such as life expectancy (or adult survival rate-probability of reaching 60 years having survived to the age of 15 years) on economic growth rates. Because there are methodological problems arising in such analyses, the articles underscored the need for compiling more elaborate variables especially in the widely used databases such as the World Development

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Indicators (WDI; World Bank, 2005). For example, demographic surveys are conducted about every five years in developing countries and variables such as fertility rates are constructed from the data. However, fertility rates tabulated in the WDI often interpolate the data for the in-between years thereby complicating the longitudinal modeling. Similarly, indices of Purchasing Power Parity (PPP) are constructed using the costs of baskets of goods in different countries to afford comparisons in living standards. However, the underlying surveys were conducted in less than half the countries over a number of years so that only approximate comparisons are feasible. It is important for the reader to be aware of such caveats in interpreting the empirical results and for drawing policy implications from cross-country analyses. The first article (Bhargava, 2001) analyzed the stochastic properties of per capita Gross Domestic Product (GDP) series for over 100 countries atfive-yearlyintervals in the period 1965-1990 using random and fixed effects frameworks. The GDP series based on PPP were taken from the Penn World Table (PWT; Summers and Heston, 1991), while the series based on. exchange rate conversions was from the WDI. The advantage in using exchange rate based series was that the data on PPP were interpolated for some countries. However, exchange rate fluctuations can induce large changes in GDP series especially for developing countries and so it was useful to analyze both types of series. Moreover, it was useful to use the data at five-year intervals since annual data on GDP growth rates exhibited large fluctuations. Also, the actualfiguresfor variables such as fertility rates and life expectancy were not available at annual intervals in the commonly used databases. The main result from this analysis were that in the fixed effects framework, both the PPP and exchange rate based GDP series exhibited very high persistence and the tests for "unit root" null hypotheses accepted the null hypotheses. This was true for the cases where there was a simple trend in the GDP series and also where there were country-specific trends included in the models. The test statistics were based on the previous tests proposed by Bhargava et al. (1982) though in the model with country specific trends, the statistics were generalized and their lower and upper confidence limits were tabulated for various sample sizes. However, the fixed effects model cannot afford further analyses of the stochastic properties of shocks affecting the GDP series due to the incidental parameter problem arising from the large number of indicator variables for the countries. The analysis using the random effects framework showed that the coefficients of the lagged dependent variable were close to one in the models for GDP levels using exchange rate and PPP based series. These results supported the unit root null hypotheses accepted in the fixed effects models. By contrast, the models for GDP growth rates showed that the estimated coefficients of the lagged dependent variables were small and significantly below one in all models. Further, an analysis of the stochastic properties of the GDP series using a sequence of Wald statistics in the random effects framework showed that the errors had different variances over time and that a second order moving average process was accepted for the PPP and exchange rate based series. While the fourth order moments of the residuals from the exchange rate GDP series were considerably higher than those for the PPP series, the second order moving average process was adequate for the two series. Overall, the results from the analyses of GDP series based on PPP and exchange rates in fixed and random effects framework indicated that it was better to model GDP growth rates since the levels series had rather complex stochastic properties. The second article was concerned with policy issues and analyzed the effects of population health indicators such as adult survival rate (ASR) and variables such as the investment/GDP ratio

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on five-yearly GDP growth rates using five time observations (Bhargava et al, 2001). The article emphasized the importance of gathering more elaborate health indicators such as Disability Adjusted Life Years for understanding the effects of population health on economic growth rates. Furthermore, there were likely to be interactions between the previous GDP and ASR levels in the models explaining growth rates. For example, high ASR (or life expectancy) may be beneficial especially for low-income countries since it would enable individuals and the society to reap the benefits of investments in education over longer periods. Moreover, the previous work by Preston (1976) investigating the effects of GDP levels on life expectancy implied that ASR (or life expectancy) should be treated as potentially endogenous variables. Also, one should explore "reverse causality" in the relationship between ASR and GDP growth rates i.e. high ASR may be due to high levels of previous GDP growth rates. The main results in this article using models for growth rates proposed by Barro and Sal-iMartin (1995) were, first, that there were significant interactions between the previous ASR and GDP levels. For example, the effects of higher ASR on growth rates depended on the previous GDP levels and vanished when the GDP was equal to 1715 in 1985 international dollars using the PPP series, and at $580 using the exchange rate based series. While the effects of higher ASR on growth rates became negative after these points, confidence intervals for the effects were wide. Thus, the results mainly showed significant beneficial effects of higher ASR on GDP growth rates in low-income countries. For developed countries, it was emphasized that elaborate measures such as Disability Adjusted Life Years would be useful for policy analyses. Second, the Chi-square statistics showed that it was important to treat variables such as the lagged GDP levels as endogenous. Moreover, the error terms affecting the model were correlated with the lagged GDP variable in a more complex form than that captured by postulating correlation between country specific random effects and the previous GDP levels. Third, a model was formulated to investigate the potential problems of reverse causality. While instrumental variables can address some endogeneity issues, as discussed above, the results from their application depend critically on the correlation between the instruments and endogenous variables. Moreover, R.A. Fisher's dictum ("elaborate your theories") for going from associations to "causality" implies that statistical models should be re-formulated according to alternative set of hypotheses and the results should be interpreted in a broad framework. The results in the article from estimating a model for ASR showed that lagged GDP growth rates were not significant predictors of the current ASR. Thus, the possible "causality" underlying GDP growth rates-ASR relationships was more likely to run from high ASR levels to higher economic growth in low-income countries. Lastly, a simple test for parameter stability indicated that the model parameters were not constant outside the estimation period though the null hypothesis could be accepted at the 2.5% significance level. As noted above, there were discrepancies in definitions of variables for heterogeneous countries and the empirical results mainly provide an indication of the benefits of higher ASR (or life expectancy) for economic growth in developing countries. Of course, such analyses are useful for developing further hypotheses such as the effects of individual health status on productivity as seen in earlier chapters using micro data.

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V. Economic Demography The three articles in the section are concerned with issues of fertility and child mortality that are the focus of demographic research in developing countries. Economists are concerned with high population growth rates since it is difficult for poor households to educate a large number of children. Thus, the availability of a skilled labor in the future depends on households' access to health care and family planning services (Bhargava, 2001). Of course, as seen in the previous chapters, children's health status and the educational infrastructure are important for learning. Further, analyses of demographic and socioeconomic data can be conducted at the country level, at regional levels within a country, and at the household level. The results from such analyses are useful and have relative merits. For example, analyses of national averages can provide insights into the proximate determinants of child mortality in a long time frame. However, issues of comparability and interpolation of variables need to be addressed. Similarly, there is much heterogeneity across geographical regions in large countries such as China and India and regional analyses can be useful for allocation of resources to health and education. Lastly, the data at the household and individual levels contain elaborate information that can be analyzed for policy formulation. However, the budgets for demographic surveys covering thousands of households are typically small and this can lower the quality of the recorded information. The first article by Bhargava and Yu (1997) analyzed cross-country data on child mortality rates and socioeconomic variables such as illiteracy levels, healthcare expenditures and Gross National Product (GNP) for developing countries at three time points (1975, 1980, and 1985). Unlike the child mortality figures available in databases of international agencies, the figures from United Nations (1990) were used and these were based on actual demographic surveys in the countries. While the number of countries in the sample was reduced, the advantage in using actual data was that the interpolation procedures for infant (under-1 year) and child mortality (under-5 years) rates were not likely to affect the results. Moreover, there were some difficulties in obtaining comparable data for healthcare expenditures in African and non-African countries; separate longitudinal analyses were performed for the two groups of countries. The main findings from the analysis of cross-country longitudinal data were that the elasticities of infant and child mortality rates with respect to female illiteracy were close to one for African countries but were smaller (~0.20) for non-African countries. Dynamic and static versions of the random effects models were estimated in part because the number of countries in the sample was small. Female literacy is especially important for African countries in part because in rural regions, there are often no educated women so that the chances of interactions between educated and uneducated women are small. Such interactions can increase the uptake of ante-natal care and vaccinations that are likely to reduce child mortality. The per capita GNP and governmental healthcare expenditures were significant predictors of infant and child mortality rates in African countries but not in non-African countries. In general, the non-African countries were quite heterogeneous since they were in Asia and Latin America where infant and child mortality rates declined in the period 1975-1985. Further, the coefficients of the lagged dependent variables were considerably smaller for African countries than for non-African countries though because of the small number of countries, it was difficult to make rigorous comparisons. Overall, the results indicated that female education was likely to be an important instrument for reducing child mortality in developing countries. However, the differential effects of healthcare utilization by poor and better off households

Introduction

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on child mortality cannot be analyzed using aggregate data at the country level; such issues are addressed using individual level data in the next two articles. The second article (Bhargava, 2003) analyzed the data from the most populous Indian state Uttar Pradesh (U.P.) using the National Family Health Survey-1 that was conducted in 1992-1993. The main objectives of the research were to investigate the underlying reasons for higher mortality of girls especially in the age group 7-36 months. The paper reconciled two seemingly different analytical frameworks used in demographic research. For example, it has been argued that couples are unlikely to use contraceptives unless they have achieved their fertility goals (Taylor et al., 1976). While this is likely to be true for irreversible procedures such as sterilization, demographers such as Scrimshaw (1978) and Cleland (1996) have emphasized that high fertility rates can exacerbate infant mortality. It was pointed out in the article that these frameworks are complementary. Historically, reductions in child mortality were followed by lower fertility rates. However, at a given point in time, households without access to healthcare and family planning services are likely to have large numbers of children and experience higher child mortality especially as high birth orders. The article also used women's stated preferences for the "ideal number of boys" and "ideal number of girls" to assess "unwanted fertility" and the possible neglect of girls born after the "ideal" number. The main findings in the article were, first, that presence of older sisters in the household was significantly more beneficial for survival chances of the "index" child than the presence of older brothers. This was not surprising since older sisters were likely to provide child care especially when mothers were engaged in housework or remunerative activities. Second, while the survival chances of girls were generally higher, girls born after the "ideal" number had significantly lower survival chances. This was not true for the boys born after the "deal" number in certain versions of the models. Thus, there appeared to be a selective neglect of "unwanted" girls; healthcare may not have been provided to such girls during sicknesses thereby increasing their mortality chances. Third, longer birth intervals were associated with higher chances of infant survival. This was not surprising since birth spacing facilitates child care and is also important for replenishing the women's stores of nutrients such as iron and calcium that are critical for fetal growth. Fourth, maternal vaccinations such as those against tetanus were important predictors of infant survival. By contrast, maternal education was mainly significant in models where vaccinations were not included. Thus, educated women were more likely to utilize the healthcare infrastructure thereby increasing survival chances of their infants. Fifth, the article addressed issues of endogeneity of variables such as the numbers of older brothers and sisters in the household and controlled for unobserved heterogeneity using a random effects framework. The empirical results were generally robust across the specifications. Overall, the results emphasized the importance of healthcare and family planning services for reducing infant mortality in U.P. Moreover, it was evident from women's responses that they would have liked to limit family size but had poor access to healthcare services. However, the healthcare infrastructure was not assessed in detail and the next article deals with such issues. The last article in this section by Bhargava et al. (2005) analyzed the 'PERFORM' data from U.P. that gathered information in 1995 on the "performance" of the healthcare infrastructure. In addition, the variables compiled in demographic surveys were available for over 40,000 households. The surveys of healthcare infrastructure covered "fixed service delivery points" such as government and private hospitals, community health centers, and numerous "private agents" such as doctors

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providing care in clinics. Information was gathered on the qualifications of the staff and on their training to perform medical procedures such sterilization and termination of pregnancies. As in the design of demographic surveys, the households were located in approximately 2,000 Primary Sampling Units' (PSU) and the data from the healthcare module of the questionnaire were mapped with the PSU's in which the households were located. Thus, the analysis focused on the effects of available services on utilization. A more comprehensive assessment would map the exact service received from various providers. However, this is generally infeasible in demographic data given the limited resources. The article was also concerned with conceptual issues in the economic demography literature. First, the "endogenous facility placement" hypothesis has emphasized that governments place medical facilities in response to the prevailing conditions such as high child mortality in the region (e.g. Angeles et al., 1998). Thus, the distance between the households and public clinics may be correlated with the errors affecting the model for child mortality. While it is true that governments mandate the placements of hospitals, public health centers and community health centers on the basis of populations, the quality of services in such facilities is likely to depend on the level of economic development. For example, clinics in remote areas are likely to be poorly equipped and child mortality is likely to be high. Moreover, the role of private providers has been overlooked in the endogenous facility placement literature. In India, approximately 85% of the healthcare may be from private providers. Second, Easterlin and Crimmins (1985) have proposed models for the demand and supply of children. However, it would be more appropriate to consider the demand and supply schedules for contraceptives since factors underlying the "supply" schedule for children are opaque. The resulting framework from incorporating these conceptual issues led to the estimation of comprehensive models for the proximate determinants of fertility and infant mortality in U.P., India. The first sets of models in the article were for the demand for female sterilization, intrauterine device (IUD) use, birth control pills, and condoms. Because sterilization and IUD insertion require skilled personnel, the availability of medical staff in public and private clinics was likely to play an important role. By contrast, birth control pills and condoms can be easily distributed via medical and other outlets. The empirical results from binary logistic models showed the importance government and private hospitals in the PSU and also of the number of trained staff in such facilities. Moreover, the use of birth control pills and condoms was positively associated with the supplies from private sources. This was not surprising since such contraceptives can be obtained in a more discreet manner from private sources. Multinomial and ordinal regression models were also estimated for the use of the contraceptives and the results again showed the importance of availability of services from public and private providers. The models for infant mortality were similar to those presented in the preceding article. In addition, the average number of private doctors in the PSU significantly lowered the chances of infant mortality. Finally, an analysis was presented for the variables reflecting healthcare infrastructure at the PSU level in government hospitals, community health centers, private hospitals, and via private doctors ("agents"). The results showed that infant mortality was not a significant predictor of the family planning staff available in any of the four types of facilities. There was clear inter-dependence in the infrastructure in government and private hospitals that is likely to result from competition between the providers. For example, if the infrastructure in public clinics

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were poor, then households may seek services in private clinics. Thus, greater resources should be invested in public facilities to improve the quality of service; otherwise, these are likely to be under-utilized. The results also showed that private doctors were mainly located in regions that were economically better off. In summary, demographic issues are of utmost importance for economic development since small family size especially among poor households is beneficial for maternal and child health and facilitates children's educational outcomes. Greater resources for demographic surveys in the future will afford the compilation of more elaborate data sets that would be useful for policy formulation. VI. Behavior, Diet and Obesity in Developed Countries The final section of this volume consists of four articles concerned with issues of individual behavior, diet and obesity in developed countries. These studies provide an interesting contrast to the articles in Section II investigating the links between household incomes and dietary intakes in developing countries. With increased affluence in countries such as the U.S., food expenditures are a small proportion of households' budgets. Also, prices in fast-food type restaurants have declined partly due to low wages in the service sector. Moreover, ethnic cuisines are widely available and can promote over-eating. Thus, individuals with poor dietary knowledge and self-control are likely to over-consume food and the problems are compounded by the fact that higher body weight, in turn, increases the energy requirements. Maintaining a healthy body weight is therefore a challenge in affluent societies; it is not surprising that about two-thirds of the U.S. population is over-weight. The costs of treatment of medical conditions associated with obesity such as high blood pressure, diabetes, cardiovascular disease and cancers are high and a preventive approach via healthful eating is a sound long-term strategy for improving health. Further, while economic factors underlie the obesity epidemic in developed countries, individual characteristics such as dietary knowledge, self-control and lifestyles are important for making appropriate food choices. For example, in "all-you-can-eat" type restaurants, one might observe individuals lacking self-control to over-eat while for those with high degree of self-control, the food consumed may reflect their energy needs. While food prices affect the decision to consume food at home and select restaurants, personal characteristics are critical determinants of food intakes in developed countries. From this viewpoint, the use of a "procedural" definition of rationality invoked in psychology (Simon, 1986) is more appealing for analyzing food consumption decisions than the "substantive" postulate used in economics, where individuals solve a utility maximization problem subject to budget constraints. Furthermore, the analysis of individual characteristics affecting food choices is facilitated by the availability of data from randomized trials offering nutrition education in the Intervention group. Thefirstarticle (Bhargava etal, 1994) presents a simple analysis of the variations and autocorrelations in dietary intakes by 37 women in the Houston area before and after a nutrition education program that encouraged lowering of fat intakes and increasing the consumption of fruits and vegetables. While there was no Control group in this study, the women filled in 7-day food records (7DFR) before and after the intervention. The intakes data based on 7DFR are more informative and expensive than those from Food Frequency Questionnaires (FFQ) where the subjects outline the food consumption patterns in the past few months. While one can distinguish between food intakes on weekdays and weekends using 7DFR, individuals can become self-conscious of the intakes on

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the days of keeping records and can alter their behavior. Such issues are recognized in the nutritional epidemiology literature and the use of alternative dietary instruments is useful for analyzing the diet-disease relationships. The main findings in the article were that the food consumption patterns were different on weekdays and weekend. For example, the dietary intervention increased the variations in the fat and cholesterol intakes on weekdays when most women were at work, but these variations were lowered during weekends presumably due the composition of family meals. These findings have implications for nutrition education programs that should emphasize the need for lowering fat intakes especially on weekends. Moreover, four-day food records are used in the nutritional literature and the intakes on either Saturday or Sunday are recorded. However, if the subjects become more self-conscious about their intakes on the day of filling in food records, then weekend intakes of fat and cholesterol are likely to be under-estimated. Furthermore, the results showed that the intakes of vital nutrients such as /3-carotene and vitamin C were lower on weekends. Thus, it would be useful to cover food consumption patterns on the full weekend though the improvements in dietary assessment may in part be offset by the potential "fatigue" in filling out food records. It is useful to employ additional dietary instruments such as the FFQ and unannounced repeated 24-hour recalls for assessing intakes, though alternative sets of methods on all the subjects have seldom been used. The second article (Bhargava and Hays, 2004) analyzed the data on dietary intakes from the Control and Intervention groups of the Women's Health Trial: Feasibility Study in Minority Populations (WHTFSMP) conducted in 1991-1995. The nutrition education program encouraged the post-menopausal women (28% Black, 16% Hispanic, and 54% White) in the Intervention group to reduce their intakes of saturated fat and to consume whole grain products, fruits and vegetables. The intakes data were based on the FFQ method and were recorded at baseline, 6 and 12 months. The survey was designed by nutritionists and psychologists; there were several items reflecting psychological theories such as the "social learning theory" (Bandura, 1977) and the "health belief model" (Rosenstock et al, 1988). While the women in the Control group received minimal dietary advice via pamphlets, women in the Intervention group met regularly with nutritionists and learnt preparing low-fat meals. However, it was possible that some women in the Control group changed their dietary intakes and hence it was important to model the effects of personal characteristics on dietary changes using the data from the two groups. First, there were significant reductions in energy and fat intakes from baseline to 12 months in both the Control and Intervention groups. The differences in changes between the two groups were statistically significant thereby indicating that the nutrition education program successfully lowered the fat and energy intakes. Second, four indices were constructed for women's 'Unhealthy eating', 'Preparation and budget [time]', 'Concerned about health' and 'Participation motivation'. Except for the 'Preparation and budget' index, differences between the Control and Intervention groups in the changes in the indices from baseline to 12 months were significant. These results indicated that the women changed their behavior due to the nutrition education program and these changes in turn led to the observed changes in dietary intakes. Third, dynamic random effects models were estimated for the intakes of carbohydrate, saturated, monounsaturated and polyunsaturated fats, fiber, /^-carotene, ascorbic acid and calcium intakes by women in the Control and Intervention groups using the data at baseline, 6 and 12 months. Likelihood ratio tests rejected the null hypothesis that the model parameters were constant across the

Introduction

xxix

two groups. Moreover, coefficients of the personal characteristics reflected in indices were different for Control and Intervention groups. For example, for the Control group, the coefficients of the index 'Concerned about health' were significant and positive in the models for monounsaturated and polyunsaturated fat intakes, and were significantly negative in the models for fiber, ascorbic acid and calcium intakes. By contrast, the signs of all these coefficients were the opposite in the respective models for the Intervention group. Thus, while the women that were concerned about their health in the Control group were consuming poor diets, women in the Intervention group made appropriate changes to improve their intakes. Furthermore, the coefficient of a variable reflecting the years of education showed that better educated women in the Intervention group made significantly greater improvements in their diets. Overall, the empirical results supported the view that dietary intakes critically depend on personal characteristics and that increasing dietary knowledge via nutrition education especially among women with low education is likely to enhance healthful eating. The next article by Bhargava (2004) explored the effects of dietary knowledge and behavior on food consumption ("use") patterns of households that were receiving food stamps due to their low incomes. The data from the National Food Stamp Program Survey conducted in 1996 were cross-sectional. From a diet quality standpoint, it was useful to express the households' "use" of /3-carotene, calcium, carbohydrate, protein, fiber, iron, and saturated, monounsaturated and polyunsaturated fats as ratios to energy use. In addition, a model was estimated for households' energy use to identify variables contributing to food shortages. Alternative versions of the models were estimated to account for the ages of household members and for presence of guests. From the responses to the survey items, indices were constructed for households' behavioral characteristics such as the knowledge of the 'Food pyramid', reading 'Nutrition labels', consuming 'Low-fat diet' and 'Fruits and vegetables', and for shopping practices ('Save money'). The main findings in the articles were that the energy intakes were significantly lower as the households moved further from the day of food stamps receipts. Thus, recent developments in the delivery of food stamps via "electronic benefit transfer" are likely to stabilize food availability among poor households. Moreover, behavioral characteristics reflected in the 'Nutrition labels' index were positively associated with fiber use. The index of 'Save money' was an important predictor of fiber, iron and protein densities. In general, the dietary knowledge of these low-income households was quite poor. For example, over half the households had not seen the U.S. Department of Agriculture pyramid that is displayed in offices disbursing food stamps. Thus, it is important to offer nutrition education to low-income households to improve their dietary intakes. Moreover, individuals with low education may not spend much time reading labels and consume unhealthy foods. In contrast, programs such as the Supplemental Food Program for Women, Infant and Children in the U.S. offer cheese, milk and orange juice that are good sources of calcium and ascorbic acid. It may be useful in the future to enable greater purchase of fruits and vegetables via food stamps to improve diet quality among low-income households. The final article in this section (Bhargava and Guthrie, 2002) analyzed the data from WHTFSMP to investigate the effects of intakes of various macronutrients such as saturated, monounsaturated and polyunsaturated fats and carbohydrate on women's weight, and waist and hip circumferences. The importance of fat intakes for body weight was uncovered in laboratory experiments since fat is oxidized more slowly than carbohydrate and protein i.e. higher fat intakes could lead

Introduction

XXX

to weight gain. While it is true that fat is energy-dense with each gram yielding 9 kcals of energy, over-consumption of foods high in sugars can also increase the total energy intake. At any rate, a diet that is low in fats and high in fruits and vegetables is likely to lower energy intake and could lead to weight loss. The main results in the article were that there was a significant reduction in weight in the Intervention group in comparison with the Control group; energy and fat intakes were also significantly lowered in the Intervention group. However, using dynamic random effects models, the intakes of saturated fat were not significantly associated with weight and waist and hip circumferences of the subjects in the two groups. In some of the models, monounsaturated fat and carbohydrate intakes were significantly positively associated with body weight. The relationships between the intakes of fats and anthropometric indicators were mainly ambiguous. By contrast, the index of 'Unhealthy eating' and a variable reflecting regular pattern of mild physical exercise were invariably significant predictors of the anthropometric indicators. Because the energy content of sugary foods is often high, it was apparent from these analyses that personal characteristics played an important role in throwing women into high-energy intake disequilibrium. Thus, nutrition education programs should emphasize the importance of healthful diets and encourage greater physical activity for stemming the obesity epidemic in the U.S. References Angeles, G., Guilkey, D., Mroz, T. (1998). Purposive program placement and the estimation of family planning program effects in Tanzania. Journal of American Statistical Association, 93, 884-899. Anderson, T.W., and Hsiao, C. (1981). Estimation of some dynamic models with error components. Journal of American Statistical Association, 76, 598-606. Gorman, W.M. (1967). Tastes, habits and choices. Int. Econ. Rev., 8, 218-222. Bandura, A. (1977). Social Learning Theory. Englewood Cliffs, NJ: Prentice Hall. Barro, R.J., and Sala-i-Martin, X. (1995). Economic Growth. New York: McGraw Hill. Bayley, N. (1969). Bayley Scales of Infant Development. New York: Psychological Corporation. Berio, A.-J. (1984). The analysis of time allocation and activity patterns in nutrition and rural development planning. Food and Nutrition Bulletin, 6, 53-68. Bhargava, A., Franzini, L., and Narendranathan, W. (1982). Serial correlation and the fixed effects model. Review of Economic Studies, 49, 533-549. Bhargava, A., and Sargan, J.D. (1983). Estimating dynamic random effects models from panel data covering short time periods. Econometrica, 51, 1635-1659. Bhargava, A. (1987). Wald tests and systems of stochastic equations. International Economic Review, 28, 789-808. Bhargava, A. (1991a). Identification and panel data models with endogenous regressors. Review of Economic Studies, 58, 129-140. Bhargava, A. (1991b). Estimating short and long run income elasticities of foods and nutrients for rural south India. Journal of the Royal Statistical Society, Series A, 154, 157-174. Bhargava, A. (1992). Malnutrition and the role of individual variation with evidence from India and the Philippines. Journal of the Royal Statistical Society, Series A, 155, 221-231.

Introduction

xxxi

Bhargava, A. (1994). Modelling the health of Filipino children. Journal of the Royal Statistical Society, Series A, 157, 417-432. Bhargava, A., and Ravallion, M. (1993). Does household consumption behave as a martingale? A test for rural South India. The Review of Economics and Statistics, 76, 500-504. Bhargava, A., Forthofer, R., McPherson S., and Nichaman, M. (1994). Estimating the variations and autocorrelations in dietary intakes on weekdays and weekends. Statistics in Medicine, 13, 113-126. Bhargava, A., and Reeds, RJ. (1995). Requirements for what? Is the measurement of energy expenditure a sufficient estimate of energy needs? Journal of Nutrition, 125(5), 1358-1362. Bhargava, A. (1997). Nutritional status and the allocation of time in Rwandese households. Journal of Econometrics, 11, 277-295. Bhargava, A., and Yu, J. (1997). A longitudinal analysis of infant and child mortality rates in developing countries. Indian Economic Review, 32, 141—153. Bhargava, A. (1998). A dynamic model for the cognitive development of Kenyan schoolchildren. Journal of Educational Psychology, 90, 162-167. Bhargava, A. (1999). Modelling the effects of nutritional and socioeconomic factors on the physicaldevelopment and morbidity of Kenyan school children. American Journal of HumanBiology, 11,317-326. Bhargava, A. (2000). Modeling the effects of maternal nutritional status and socioeconomic variables on the anthropometric and psychological indicators of Kenyan infants from age 0-6 months. American Journal of Physical Anthropology, 111(1), 89-104. Bhargava, A., and Bigombe, B. (2003). Public policies and the orphans of AIDS in Africa. BMJ, 326(7403), 1387-1389. Bhargava, A., Bouis, H.E., and Scrimshaw, N.S. (2001). Dietary intakes and socioeconomic factors are associated with the hemoglobin concentration of Bangladeshi women. Journal of Nutrition, 131,758-764. Bhargava, A., Jamison, D.T., Lau, L.J., and Murray, C.J.L. (2001). Modeling the effects of health on economic growth. Journal of Health Economics, 20, 423^40. Bhargava, A. (2001). Stochastic specification and the international GDP series. The Econometrics Journal, 4, 273-286. Bhargava, A., and Guthrie, J.F. (2002) Unhealthy eating habits, physical exercise and macronutrient intakes are predictors of anthropometric indicators in the Women's Health Trial: Feasibility study in minority populations. British Journal of Nutrition, 88, 719-728. Bhargava, A., Jukes, M., Lambo, J. Kihamia, CM., Lorri, W., Nokes C., Drake, L., and Bundy, D.A.P. (2003). Anthelmintic treatment improves the hemoglobin and serum ferritin concentrations of Tanzanian schoolchildren. Food and Nutrition Bulletin, 24, 332-342. Bhargava, A., Bouis, H.E., Hallman, K., and Hoque, B.A. (2003). Coliforms in the water and hemoglobin concentration are predictors of gastrointestinal morbidity of Bangladeshi children ages 1-10 years. American Journal of Human Biology, 15, 209-219. Bhargava, A. (2001). Nutrition, health and economic development: Some policy priorities. Food and Nutrition Bulletin, 22, 173-177. Bhargava, A. (2003). Family planning, gender differences and infant mortality: Evidence from Uttar Pradesh, India. Journal of Econometrics, 112, 225-240.

XXX11

Introduction

Bhargava, A. (2004). Socio-economic and behavioural factors are predictors of food use in the National Food Stamp Program Survey. British Journal of Nutrition, 92,497-506. Bhargava, A., and Hays, J. (2004). Behavioral variables and education are predictors of dietary change in the Women's Health Trial: Feasibility study in minority populations. Preventive Medicine, 38,442-451. Bhargava, A. (2005). AIDS epidemic and the psychological well-being and school participation of Ethiopian orphans. Psychology, Health and Medicine, 10, 263-276. Bhargava, A., Jukes, M., Ngorosho, D., Khilma, C , and Bundy, D. (2005). Modeling the effects of health status and the educational infrastructure on the cognitive development of Tanzania school children. American Journal of Human Biology, 17, 280-292. Bhargava, A., Chowdhury, S., and Singh, K.K. (2005). Healthcare infrastructure, contraceptive use and infant mortality in Uttar Pradesh, India. Economics and Human Biology, 3, 388^104. Bouis, H. (2002). Plant breeding: A new tool for fighting micronutrient malnutrition. Journal of Nutrition, 132, 491S-494S. Bouis, H., and Haddad, L. (1990). Agriculture Commercialization Nutrition and Rural Poor: A Case Study of Philippine Farm Households. Boulder: Riener. Brazelton, T.B. (1984). Neonatal Behavioral Assessment Scale, 2nd edition. London: Blackwell Publications. Cleland, J. (1996). Population growth in the 21st century: Cause for crisis or celebration? Tropical Medicine and International Health, 1, 15-26. Durbin, J., and Watson, G.S. (1950). Testing for serial correlation in least squares regression I. Biometrika, 37, 409-428. Easterlin, R., and Crimmins, E. (1985). The Fertility Revolution. Chicago: University of Chicago Press. FAO/WHO/UNU, (1985). Energy and Protein Requirements. World Health Organization Technical Report Series No. 724 (WHO, Geneva). Georgescu-Roegen, N. (1966). Analytical Economics: Issues and Problems. Cambridge: Harvard University press. Hall, R. (1978). Stochastic implications of the life cycle-permanent income hypothesis: Theory and evidence. Journal of Political Economy, 86, 971-987. Koopmans, T., and Hood, W. (1953). Studies in Econometric methods. New York: John Wiley and Sons. Kronmal, R. (1994). Spurious correlation and the fallacy of the ratio standard revisited. Journal of Royal Statistical Society A, 156, 379-392. Lillard, L., and Willis, R. (1978). Dynamic aspects of earning mobility. Econometrica, 46, 9851011. Mann, H., and Wald, A. (1943). On the statistical treatment of linear stochastic difference equations. Econometrica, 11, 173-220. Numerical Algorithm Group. (1991). Numerical Algorithm Group Mark 13. (Oxford University, UK: NAG.). Neyman, J., and Scott, E. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1-32. Preston, S. (1976). Mortality Patterns in National Populations. New York: Academic Press.

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xxxiii

Rosenstock, I.M., Strecher, V.J., and Becker, M.H. (1988). Social learning theory and the health belief Model. Health Educ. Quart., 15, 175-183. Sargan, J.D. (1958). The estimation of economic relationships using instrumental variables. Econometrica, 26, 3 9 3 ^ 1 5 . Sargan, J.D., and Bhargava, A. (1983). Testing residuals from least squares regression for being generated by the Gaussian random walk. Econometrica, 51, 153-174. Scrimshaw, S. (1978). Infant mortality and behavior in the regulation of family size. Population and Development Review, 4, 383-403. Simon, H. (1986). Rationality in psychology and economics. Journal of Business, 59, S209-S224. STATA (2003). Stata version 8. College Station, TX. Stigler, G.J. (1945). The cost of subsistence. Journal of Farm Economics, 27, 303-314. Sukhatme, P.V., and Margen, S. (1978). Models of protein deficiencies. American Journal of Clinical Nutrition, 31, 1237-1256. Sukhatme, P.V., and Margen, S. (1982). Autoregulatory homeostatic nature of energy balance. American Journal of Clinical Nutrition, 35, 355-365. Summers, R., and Heston, A. (1991). The Penn World Table (mark 5). An expanded set of international comparisons, 1950-1988. Quarterly Journal of Economics, 106, 327-368. Taylor, C , Newman, J., and Kelly, N. (1976). The child survival hypothesis. Pop. Stud., 30, 262-278. United Nations Development Program (1990). Child mortality since 1960's: A database for developing countries. United Nations, New York. Vygotsky, L.S. (1987). Thinking and speech. In Collected Works of L.S. Vygotsky, Volume 1, Rieber, R.W., and A.S. Carton (eds.). New York: Plenum. Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society, 54, 426-482. Wald, A. (1947). Sequential Analysis. New York: Dover Publications. Watkins, W.E., and Pollitt, E. (1997). "Stupidity or worms": Do intestinal worms impair mental performance? Psychological Bulletin, 121, 171-191. Zellner, A., and Theil, H. (1962) Three-stage least squares: Simultaneous estimation of simultaneous equations. Econometrica, 30, 54—78.

I. Methodological Contributions

Econometrica, Vol. 51, No. 6 (November, 1983)

ESTIMATING DYNAMIC RANDOM EFFECTS MODELS FROM PANEL DATA COVERING SHORT TIME PERIODS' BY ALOK BHARGAVA AND J. D. SARGAN This paper advocates the use of simultaneous equations estimators (especially LIML) to estimate dynamic random effects models from panel data. The methods are found to perform quite satisfactorily in Monte Carlo experiments. The LIML procedures are also extended to the case where some of the regressors are correlated with the effects and a theorem on identification is proved. Finally, the Michigan Panel is used for some illustrations. 1. INTRODUCTION

of the estimation of dynamic economic relationships from panel data has long been recognized [3], the poor performance of maximum likelihood estimation procedures [3, 13, 15] cast serious doubts on the usefulness of these methods at least for typical panels that comprise a large number of individual units who are observed only for a few time periods. Recently, however, it was pointed out by several authors [1, 16] that maximum likelihood methods for dynamic random effects models need rely only upon the increase in the number of individual units for their desirable asymptotic properties, but it is the role of the assumptions made on the initial observations on the dependent variable that is of paramount importance in determining the appropriateness of the estimation procedures. Thus, for example, Anderson and Hsiao [1, 2] discuss various likelihood functions that correspond to different assumptions on the initial observations and stress that investigators should choose the correct initial conditions. In most economic applications, however, it would be somewhat unreasonable to assume a priori the initial conditions and it would be indeed quite useful to develop test procedures that enable researchers to test the appropriateness of their assumptions on the initial observations (see Section 3). In any event, since the treatment of the individual effects as "fixed" parameters leads to estimation procedures which are inconsistent insofar as the number of time periods for which the data are available is small, the random effects model has a central role to play in the estimation of dynamic models from panel data. Further, the fact that the essential hypothesis of this model is embodied in the special form of the serial covariance matrix has led investigators to adopt other estimation procedures including Generalized Least Squares (GLS) and Instrumental Variables [3, 15, 16]. It would therefore seem to be of considerable importance that a general framework is developed wherein it is possible to discuss the relative merits of the alternative estimation procedures for dynamic WHILST THE IMPORTANCE

'This paper is a revised version of a paper presented to the Conference on "Analysis of Panel Data on Incomes" held at the International Centre for Economics and Related Disciplines, London School of Economics. We are grateful to ICERD for financing this research and to the referees for their comments.

4

A. Bhargavaand J.D. Sargan

models and also to test the validity of the restrictions implied by the random effects model—the rejection of which in practical situations might lead to poor results in constrained maximum likelihood estimation [3]. This paper attempts to provide a framework for the estimation of dynamic relationships from panel data by drawing upon the analogy with the general simultaneous equations system. Indeed, if we have a cross-section of size H repeated successively in (T+ 1) time periods, then we may regard the problems that arise in the estimation and testing of this model as akin to those for a simultaneous equations system with (T + 1) structural equations and H observations available on each of the equations. There are cross-equation linear restrictions and the earlier serial covariance matrix now becomes the variance matrix of the errors on (T+ 1) structural equations. But since the theory of identification and estimation is well-developed for simultaneous equations systems [8, 9], it is possible to extend the relevant theorems to panel data. In particular, we have found it extremely useful to employ the unconstrained and constrained versions of the Limited Information Maximum Likelihood (LIML) method to estimate simultaneously the subset of T equations and have also been able to extend these procedures to incorporate the cases where some of the explanatory variables are correlated with the effects. The structure of this paper is as follows. Section 2 writes the dynamic model into a simultaneous equations form and argues for the preference of maximum likelihood methods over other simultaneous equations estimators. Five models are considered and their concentrated likelihood functions are derived. Section 3 develops tests for some of the maintained hypotheses in these models and investigates the performance of the estimation and test procedures by Monte Carlo methods. In Section 4, we take into account the problems of identification that arise when some of the explanatory variables are correlated with the effects and extend the LIML estimators to these cases. The proposed estimation and test procedures are illustrated in Section 5 using the Michigan Panel and the conclusions are summarized in Section 6. 2. ESTIMATION

2.1. The Model We consider the model m

(2-i)

n

yhl = Y0 + 2 ?.•**+ °yht-\ + 2 fax*!* uhi (h = 1, . . . H; t = 1, . . . , T)

where zih are the time invariance variables, xiht are those which are time varying, H is the number of individual units on whom (T + 1) observations are available

Dynamic Random Effects Models

5

and, for the moment, (2.2)

uhl = i]h + vhl

(h = l,...,H;t

=

l,...,T)

with T) A ~NID(0,^ 2 ) and c A ,~NID(O,0 2 ). It is also assumed that the variables zih and xjht are stochastic and are independent of the variables for other households and that they are also independent of the errors r\k and t?fa for all /, j , k, h, s, and t. As noted in the Introduction, we need to specify the equation determining yh0 (h = 1, . . . , H). The conventional model assumes yh0 to be exogenous and we replace this assumption by n

(2.3)

T

m

yh0 = | 0 + 2 2 0***,+ 2 Crt»+ «*o

(A - 1, . . . , #)•

Equation (2.3) is chosen merely for convenience (see also below) since our initial theoretical model implies that yh0 is determined by a sequence of equations of the form (2.1) with 00

(2-4)

^o=2«

k

2 &* + Vo + 2 Y,-*a. + "A(-fc)

i-1

fc=-0

/-1

where J A0 is the systematic or exogenous part of yh0 and 00

(2.5)

wA*0 = 2

a\_

.

k )

Now we derive the form (2.3) by assuming that the optimal predictor of yh0 conditional upon xihl (/ = 1 n; t = 0, . . . , T) and zih (i = 1, . . . , m) is n

(2.6)

T

m

j % = lo + 2 2 *«*«/ + S f e i-l/«0

(A - 1 , . . . , # )

i-l

wherej?^ = P*o + eh and £ A ~NID(0,ff 2 ). Denoting by fl* the (!T + 1) X (T + 1) symmetric matrix of the variance of uht (t = 0, . . . , T; h arbitrary) we see that SI* has elements of the form _2 f\

n\

1

(2.7)

WQO

=

(2.8)

«0, = y ^

,

0

,

2

-j + 5 +". < (1 - a) 2 1 - az (' = 1

T),

6

A. Bhargava and J.D. Sargan

and (2.9)

u„ = a2 + o-2 -a*

if

s = t,

X

s¥>t

(s=l

T;t=\,...,T).

Indeed, it is also possible to estimate the model with the matrix $2* unconstrained and we shall in fact use likelihood ratios to test the constraints (2.7), (2.8), and (2.9) and will also be able to test the validity of the stationarity assumptions represented by (2.7) and (2.8) while maintaining the constraints (2.9) (see Section 3). In order to facilitate further discussion, we write the system (2.1) as a system of simultaneous equations where each equation represents the dynamic relationship in a given time period, i.e., (2.10)

AD'=U'

where (2.11)

D=

(Y:X:Z),

Y being the H X (T + 1) matrix of the endogenous variables, Z the H X (m + 1) matrix of the time invariant variables, X the Hx n(T + 1) matrix of time varying variables, U the H X T matrix of the errors, and A the TX[(T+ 1) (n + 1) + (m + 1)] matrix of the structural form coefficients. This can also be written as (2.12)

A' = (8f,S 2 *

8})

with S*' = {ad[s_„ - < , 4 ' ® /?', y)

(s = 1, . . . , T),

ds being a (T + 1) X 1 vector containing one in the jth position and zero otherwise, a the coefficient of the lagged dependent variable, and /? and y, respectively, the n X 1 and {m + 1) X 1 vectors of the coefficients of the x's and the z's. Now defining the set of Instrumental Variables by (2.13)

Z* =

(X:Z)

and letting (2.14)

R =

Y'Z*(Z*'Z*y*Z*'Y Z*'Y

Y'Z* Z*'Z*

we consider together the reduced form equation (2.3) with the structural system (2.10).2 Clearly the matrix of endogenous variables (comprised of the first {T + 1) columns of A and an additional first row for^ 0 ) has a triangular structure so that 2

This model is identified if Plim(Z*'Z*///) is positive definite (see the Proposition below).

Dynamic Random Effects Models

7

although GLS based on a consistent estimate of J2* is itself consistent, it is inefficient relative to Three Stage Least Squares (3SLS) [10]. Furthermore, since the maintained hypothesis in the random effects model implies that the matrix S* is both constrained and dependent upon the parameter a occurring in the structural form, it follows that 3SLS based on a consistent estimate of 12* is inefficient in comparison with FIML. On the other hand, if $2* is assumed to be unrestricted, then 3SLS and FIML are asymptotically equivalent and the latter procedure can be considerably simplified by using the LIML method discussed by Koopmans and Hood [9] (see below). However, since we also wish to test the maintained hypothesis in the random effects model, it would seem more appropriate to rely upon maximum likelihood methods and below we shall derive the LIML estimator which also takes into account the special forms of ft* matrix.3 For starting off the iterative procedure for maximum likelihood estimation, it would be desirable to provide initial consistent estimates of S, where 8' = (a, /3',y'). Thus we define the Crude Instrumental Variable (CIV) estimate of 5 which minimizes (2.15)

tr(Ai?A')

where R is defined by (2.14). These estimates ignore the fact that the Tx submatrix A of Q*, i.e., (2.16)

Q=

T

E(U'U),

is not proportional to IT. The explicit solution to (2.15) can be written as vecA = SS — c where vecA is the T[(T + 1)(« + l) + ( m + l ) ] X l vector, ( 2.17)

S=

i|fA

and (2.18)

c = v e c ( 0 r / r : 0),

0 r being a T x l vector of zeros and 0 being a T X [n(T + 1) + m + 1] matrix of zeros. The CIV of S if then given by (2.19)

5 a v = [S"(/®/?)5']"1[5"(/Xi?)c]

and was found in practice to provide quite accurate initial estimates. 2.2. Estimation by Maximum Likelihood We consider the estimation of the system (2.10) by maximum likelihood methods under two alternative sets of assumptions, namely that the yQ's are 3 It is perhaps worth pointing out that the reduced form estimation procedures [12] are likely to be both impractical and inefficient owing to the constraints on 0* (see Models 4, 5, 7, and 8 below).

8

A. Bhargava and J.D. Sargan

exogenous and that the y0's are endogenous and are explained by the reduced form (2.3). Although the former assumption is likely to lead to biased estimates of the parameters, it has been used rather extensively by previous investigators [3, 13, 15] and the results obtained have often appeared to be unsatisfactory. It would therefore be of some interest to see whether similar results are also obtained in the experiment that we conduct below. Furthermore, rather than to assume the exogeneity of the j 0 's, it would seem more reasonable to test the validity of this assumption and the required test criterion entails the maximization of the likelihood function for this model. y0's Exogenous With/A0 (h = 1, . . . , H) treated as exogenous, we need only take into account the matrix Q of the errors on (2.10). We consider the estimation of this model under two alternative sets of assumptions on fl. Firstly, $2 is assumed to be an arbitrary positive definite matrix as for most simultaneous equations systems. This assumption is fairly general and will enable us to test the validity of the various restricted forms of £2 and we shall refer to this case (j 0 's exogenous, Q unrestricted) as Model 1. Secondly, S2 is assumed to be the serial covariance matrix associated with the random effects model as in the Balestra-Nerlove [3] case, i.e., 0 has elements of the form (2.9) (Model 2). The log-likelihood function for Model 1, apart from an irrelevant constant, can be written as L , = - ^ l n d e t f l - ±tr(ST'AZTDA'); concentrating this with respect to Q, we obtain (2.20)

Lf = - ^ Indet[S2(A)]

where (2.21)

fl(A)

= M^Al.

Note that Lf differs from the concentrated likelihood function for the general simultaneous equations system in that the term ln(det.B), where B is the matrix of the endogenous variables, does not occur here due to the triangular structure of (2.10). It is now straightforward to numerically optimize (2.20) as a function of S by the use of some nonderivative algorithm [14] or by using algorithms that require the first derivatives and noting that (2.22)

9Lf - j ^ - = -S"[B(A) D'DjvecA.

In practice, it was found simpler to use a nonderivative algorithm since it could also be used quite easily to optimize the other concentrated Ukelihood functions derived below. The asymptotic standard errors were calculated by using the

Dynamic Random Effects Models differencing estimates of the second derivatives of Lf and the final fi(A) was also printed out for inspection. Next, we enforce the constraints (2.9) on the matrix fi (Model 2). Defining (2.23)

p = av/a,

the matrix Q can now be written as (2.24)

$2 = a\lT + p2qq')

where q is a T X 1 vector of ones. Thus d e t f i = a 2 r ( l + Tp2) and

(2.25, „-_£(/,-_£-,*). The likelihood function can now be written as L 2 = - ^ l n d e t f l - |tr(a-'AZ>'Z)A') = - ^ l n a 2 - % ln(l + Tp2) - - \ \x(AD'DA') 2i 22) was found to be a very useful parameterization to restrict a.

11

12

A. Bhargava and J.D. Sargan function to be rr

(2.35)

H(T+l) K

Lf = - f ln\ 5

—

'- hvsf

where (2.36)

\55 = Woo(l + Tp2) - 7«? Tv20

and s%2 is the MLE of a2 obtained by making the appropriate changes in (A.l 1). Note that for Q* to be positive definite, (2.36) must be positive which can be achieved hv writing achieved by (2-37)

Tat,

"oo=

T

^I+^

2

and maximizing Lf with respect to a, /?, y, p, L% and, if the null is rejected, using (3.9)

2(L2-L 2 *) + i/lnw 0 0 ~x 2

with 1 d.f.,

A

then (3.8) must also reject the null. In most practical situations, the above tests will probably reject the exogeneity of theyQ's and (3.2), (3.3), and (3.4) should be quite useful in the testing of the constraints on Q* since they assume the y0's to be endogenous. 3.2. Simulation Evidence In view of the past record of maximum likelihood methods [13, 15], it was felt necessary to investigate the performance of Models 1 to 4 by Monte Carlo methods.6 The true model was generated by (3.10)

yht = l. + 0.5^,_, - 0.16z„ + 0.35x„ + (Vh + vhl) (h = 1, . . . , 100; t = 1,. . . , 20)

where TJA are NID(0,0.09), vht are NID(0,0.4225) (i.e. p2 = 0.213), xht = 0.1/ + ft**,., +pht

(h = 1, . . . , 100; t = 1, . . . , 20),

with ^~NID(0,0.01), pht are NID(0,1) and zh= - 0.2xM + p'h 6

{h = 1, . . . , 100),

It was not considered worthwhile to also simulate the semi-constrained case (Model 5).

Dynamic Random Effects Models

15

TABLE I SIMULATION RESULTS FOR MAXIMUM LIKELIHOOD METHODS' Model l b Parameter

Yo Yi

ft a

- 0.1993 (0.024)' 0.0203 (0.005) 0.0028 (0.003) 0.0674 (0.008)

P2

Model 2C Model 3 d BIASES IN THE ESTIMATES

-0.1156 (0.018) 0.0108 (0.004) 0.0044 (0.003) 0.0377 (0.006) - 0.0499 (0.009)

-0.0221 (0.026) 0.0007 (0.005) 0.0046 (0.003) 0.0072 (0.0009)

Model 4«

0.0045 (0.017) - 0.0036 (0.004) 0.0044 (0.003) - 0.0028 (0.005) 0.0011 (0.009)

MEANS OF THE ESTIMATED STANDARD ERRORS

Yn Yi

ft a P2

0.142 (0.002) 0.0365 (0.0006) 0.0214 (0.0001) 0.0463 (0.0007)

0.1155 (0.0008) 0.0354 (0.0005) 0.0214 (0.0001) 0.0355 (0.0003) 0.0591 (0.0001)

0.1582 (0.002) 0.0398 (0.0007) 0.0210 (0.0001) 0.0507 (0.0007)

0.105 (0.0007) 0.0392 (0.0005) 0.0214 (0.0001) 0.0312 (0.0002) 0.0588 (0.0017)

'H - 100, T - 9, m - 1, n - I, 50 replications. b j>0 exogenous and £2 unconstrained. c _y0 exogenous and il constrained. d j* 0 endogenous and ft* unconstrained. K yti endogenous and ft* constrained. f Monte Carlo standard errors.

and p'h are NID(0,1). The z's and the x's were held fixed over the replications and the first ten observations were discarded. Thus the yh0's are in fact stochastic and correlated with the individual effects rjh (see also [15]). Table I reports the results for Models 1 to 4 obtained in 50 replications. First, considering Models 1 and 2 which incorrectly assume the y0's to be exogenous, in no case were there the types of difficulties described by Nerlove [15] and the biases reported in Table I are indeed smaller than what one might have expected from previous studies. However, this is not to advocate the use of Models 1 and 2 since, as we shall see in Section 5, they can easily fail to converge when real data are used, perhaps due to the presence of other sources of misspecification. The constraints on the 0 matrix were rejected seven times (out of 50) using the test criterion (3.1). The experiment was also repeated for Model 2 by reducing the number of individual units to 25 for greater comparability with the study of Nerlove [15], but the results were broadly unaffected apart from boundary solutions at p = 0 in some of the replications though the bias in the estimate of p 2 was unaltered. It would therefore appear that at least some of Nerlove's findings were due to the choice of the exogenous variables.

16

A. Bhargava and J.D. Sargan The cases where the y0's are treated as endogenous clearly perform extremely well and the biases in the parameters are almost negligible. The means of the estimated standard errors are slightly lower for Model 4 owing to the constraints on fi* but the gain in efficiency will usually depend upon the general features of the problem under study. In 6 of the replications, the constraints on 0* were rejected and the exogeneity of them's was rejected 46 and 50 times, respectively, using the tests (3.7) and (3.9). 4. CORRELATION BETWEEN THE REGRESSORS AND THE EFFECTS

The estimation procedures of Section 2 will break down if some of the exogenous variables are in fact partly determined by the same factors that determine the individual effects. It is, for example, quite plausible that some of the time invariant z's are correlated with the ij's, since in some sense they both represent "permanent" characteristics and it is not surprising that this case has drawn much empirical investigation [6, 7]. Similar reasoning might also be applied in some cases to argue that some of the xiht are affected by the random effects but from the standpoint of identification and estimation of the extended model, it would be desirable to give a precise form to this correlation. Indeed, if we follow the basic random effect model and assume that (4.1)

*,„, = K,T)A + x?h,

(i=l,...,n-k;h

=l

H; t = 0, . . ., T)

where xfhl is independent of i\h, then we are in effect assuming that the coefficient of regression of the xiht on the corresponding TJ'S is also independent of t. This assumption is not an unreasonable one since while assuming the xih, to be correlated with the TJA in all time periods, it allows the presence of an unaffected part xfht which could incorporate the influence of macro or other phenomena on the xiht. Note that from (4.1) it would follow that x£t where T

1 (4.2)

xiht *= xiht —

1 +

. 2J xihs

l

s-0

(i=l,...,n-k;h =

i Y* — ' A iht rp , , 1 "•• '

=

l,...,H;t=\,...,T)

T

V Y* £j *ihs s-0

are independent of -qh and can therefore be regarded as exogenous variables. Denoting by xlh the time means of the xiht's, we see that the formulation (4.1) has provided us with an additional T(n — k) instrumental variables while adding only (« — k) endogenous variables xih into the system. In order to extend our dynamic model to the present situation, it would be simplest to add reduced form equations explaining the nonexogenous variables in terms of the completely

Dynamic Random Effects Models

17

exogenous z's and the x's. The whole system can now be written as 7 T

T

+ 2

/*,'*IA,+ S

lh+'xvu+

(4-3)

-yoh

(4.4)

Byh + T2z2h + 2 C2,x2ht + £ C U JC 1 A ,+ r,* 1A = uXh ,

(4.5)

- z2A + 2