Interest Rates and Budget Deficits: A Study of the Advanced Economies (Routledge Studies in the Modern World Economy, 1)

INTEREST RATES AND BUDGET DEFICITS Does fear of higher inflation lead to higher interest rates? For the past decade, rising interest rates have dominated economic headlines. It now seems that the persistently low rates of the 1970s have given way to persistently high rates in the 1980s and 1990s. Interest Rates and Budget Deficits explores this phenomenon and discusses various aspects of interest rates across a range of developed countries. In particular, the authors examine: • the relationship between high budget deficits, debts and high interest rates; • the role of inflation expectations and the Fisher hypothesis; • empirical evidence from eleven advanced economies: Australia, Belgium, Canada, France, Germany, Italy, Japan, the Netherlands, Sweden, the U.K. and the U.S.A. Kanhaya L.Gupta and Bakhtiar Moazzami challenge a number of widely held conceptions, and their analysis produces some surprising results. It shows, above all, that cross-country generalizations about interest rate behaviour can be misleading and that factors specific to individual countries are still of vital importance. Kanhaya L.Gupta is Professor of Economics at the University of Alberta. Bakhtiar Moazzami is Associate Professor at Lakehead University. Both have published widely in the fields of macroeconomics and monetary policy.

ROUTLEDGE STUDIES IN THE MODERN WORLD ECONOMY 1 INTEREST RATES AND BUDGET DEFICITS A Study of the Advanced Economies Kanhaya L.Gupta and Bakhtiar Moazzami 2 WORLD TRADE AFTER THE URUGUAY ROUND Prospects and Policy Options for the Twenty-first Century Edited by Harald Sander and András Inotai 3 THE FLOW ANALYSIS OF LABOUR MARKETS International perspectives Edited by Ronald Schettkat

INTEREST RATES AND BUDGET DEFICITS A study of the advanced economies

Kanhaya L.Gupta and Bakhtiar Moazzami

London and New York

First published 1996 by Routledge 11 New Fetter Lane, London EC4P 4EE This edition published in the Taylor & Francis e-Library, 2005. “ To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/.” Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 © 1996 Kanhaya L.Gupta and Bakhtiar Moazzami All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalogue record for this book has been requested. ISBN 0-203-98434-X Master e-book ISBN

ISBN 0-415-10135-2 (Print Edition) ISSN 1359-7965 (Print Edition)

To Pat, Lew and Neda

CONTENTS List of figures

vii

List of tables

xi

Acknowledgements

xvi

1 INTRODUCTION

1

2 PROBLEMS OF MEASURING EX-ANTE REAL INTEREST RATES

4

3 ESTIMATES AND BEHAVIOUR OF EX-ANTE REAL INTEREST RATES

8

4 INTEREST RATES, INFLATION AND TAXES

59

5 ON THE EXOGENEITY OF THE REAL INTEREST RATE

84

6 BUDGET DEFICITS AND INTEREST RATES: THEORY

131

7 BUDGET DEFICITS AND INTEREST RATES: THE EVIDENCE

139

8 SOME LESSONS

216

Notes

219

Select bibliography

222

Index

228

FIGURES 3.1

Short-term pre-tax ex-ante real interest rates

10

3.2

Pre-tax short-term real rates: survey method

21

3.3

Medium-term pre-tax ex-ante real interest rates

25

3.4

Real rates as index-linked bonds

31

3.5 Nominal, pre- and post-tax real short-term rates

34

3.6 Nominal, pre-and post-tax real medium-term rates

39

3.7

After-tax short-term real rate: survey method

43

5.1

Responses of the ex-ante short-term real interest rates to innovations: Australia

94

5.2

Responses of the ex-ante short-term real interest rates to innovations: Belgium

96

5.3

Responses of the ex-ante short-term real interest rates to innovations: Canada

98

5.4

Responses of the ex-ante short-term real interest rates to innovations: France

101

5.5

Responses of the ex-ante short-term real interest rates to innovations: Germany

104

5.6

Responses of the ex-ante short-term real interest rates to innovations: Italy

106

5.7

Responses of the ex-ante short-term real interest rates to innovations: Japan

109

5.8

Responses of the ex-ante short-term real interest rates to innovations: the Netherlands

112

5.9

Responses of the ex-ante short-term real interest rates to innovations: Sweden

114

5.10 Responses of the ex-ante short-term real interest rates to innovations: U.K.

116

5.11 Responses of the ex-ante short-term real interest rates to innovations: U.S.A.

119

7.1

140

Ex-ante real (short) rate and budget deficit

7.2 Ex-ante medium rate and budget deficit

151

7.3

Actual, fitted and conditional forecast of short-run interest rate: 166 Australia

7.4

Actual, fitted and conditional forecast of medium-term interest rate: Australia

7.5

Actual, fitted and conditional forecast of short-run interest rate: 170 Belgium

7.6

Actual, fitted and conditional forecast of medium-term interest rate: Belgium

7.7

Actual, fitted and conditional forecast of short-run interest rate: 174 Canada

7.8

Actual, fitted and conditional forecast of medium-term interest rate: Canada

7.9

Actual, fitted and conditional forecast of short-run interest rate: 178 France

7.10 Actual, fitted and conditional forecast of medium-term interest rate: France

166

170

174

178

7.11 Actual, fitted and conditional forecast of short-run interest rate: 181 Germany 7.12 Actual, fitted and conditional forecast of medium-term interest rate: Germany

182

7.13 Actual, fitted and conditional forecast of short-run interest rate: 186 Italy 7.14 Actual, fitted and conditional forecast of medium-term interest rate: Italy

186

7.15 Actual, fitted and conditional forecast of short-run interest rate: 190 Japan 7.16 Actual, fitted and conditional forecast of medium-term interest rate: Japan

190

7.17 Actual, fitted and conditional forecast of short-run interest rate: 194 the Netherlands 7.18 Actual, fitted and conditional forecast of medium-term interest rate: the Netherlands

194

7.19 Actual, fitted and conditional forecast of short-run interest rate: 198 Sweden 7.20 Actual, fitted and conditional forecast of medium-term interest rate: Sweden

198

7.21 Actual, fitted and conditional forecast of short-run interest rate: 202 U.K. 7.22 Actual, fitted and conditional forecast of medium-term interest rate: U.K.

203

7.23 Actual, fitted and conditional forecast of short-run interest rate (real actual federal deficits): U.S.A.

208

7.24 Actual, fitted and conditional forecast of medium-term interest rate (real actual federal deficits): U.S.A.

208

7.25 Actual, fitted and conditional forecast of short-run interest rate (real national income deficits): U.S.A.

209

7.26 Actual, fitted and conditional forecast of medium-term interest rate (real national income deficit): U.S.A.

209

TABLES 3.1

Mean and standard deviation of pre-tax ex-ante real short-term interest rates: auto and Mishkin estimates

16

3.2 Data used for nominal medium-term interest rates

22

3.3

Mean and standard deviation of pre-tax ex-ante real mediumterm interest rates

23

3.4

Short-term and medium-term pre-tax ex-ante real interest rates for 1990:4

30

3.5

Mean and standard deviation of post-tax ex-ante real short-term interest rates: auto and Mishkin estimates

32

3.6

Mean and standard deviation of post-tax ex-ante real mediumterm interest rates: auto and Mishkin estimates

33

3.7

Correlations between nominal and ex-ante real interest rates

43

3.8

Testing for unit root based on equation (4)

50

3.9

Maximum likelihood estimate of model (8) (ex-ante real shortterm rates)

53

3.10 Testing for unit root based on equation (4)

54

3.11 Unit root test: allowing for one-time break

55

3.12 Maximum likelihood estimate of model (8) (ex-ante real medium 56 rates) 4.1

Testing for unit root short-run nominal interest rates

64

4.2

Unit root test: allowing for one-time break short-run nominal interest rates

65

4.3

Testing for unit root short-run inflationary expectations (Mishkin 65 method)

4.4

Unit root test: allowing for one-time break short-run inflationary 66 expectations

4.5

Summary results of stationarity tests

67

4.6

Fisher hypothesis using short-term interest rates

68

4.7 Fisher hypothesis using post-tax short-term interest rates

71

4.8

Testing for unit root medium-run nominal interest rates

74

4.9

Unit root test: allowing for one-time break medium-term nominal 75 interest rates

4.10 Testing for unit root medium-run inflationary expectations

75

4.11 Unit root test: allowing for one-time break short-run inflationary 76 expectations 4.12 Summary results of stationarity tests

76

4.13 Fisher hypothesis using pre-tax medium-term interest rates

78

4.14 Fisher hypothesis using post-tax medium-term interest rates

82

5.1

Granger causality test of the ex-ante real short-term interest rate

90

5.2

Proportions of forecast error K quarters ahead, produced by each 92 innovation (Australia: 1969:3–1990:4)

5.3

Proportions of forecast error K quarters ahead, produced by each 95 innovation (Belgium: 1969:3–1990:4)

5.4

Proportions of forecast error K quarters ahead, produced by each 97 innovation (Canada: 1969:3–1990:4)

5.5

Proportions of forecast error K quarters ahead, produced by each innovation (France: 1969:3–1990:4)

100

5.6

Proportions of forecast error K quarters ahead, produced by each innovation (Germany: 1969:3–1990:4)

102

5.7

Proportions of forecast error K quarters ahead, produced by each innovation (Italy: 1969:3–1990:4)

105

5.8

Proportions of forecast error K quarters ahead, produced by each innovation (Japan: 1969:3–1990:4)

107

5.9

Proportions of forecast error K quarters ahead, produced by each innovation (Netherlands: 1969:3–1990:4)

110

5.10 Proportions of forecast error K quarters ahead, produced by each innovation (Sweden: 1969:3–1990:4)

112

5.11 Proportions of forecast error K quarters ahead, produced by each innovation (U.K.: 1969:3–1990:4)

115

5.12 Proportions of forecast error K quarters ahead, produced by each innovation (U.S.A.: 1969:3–1990:4)

117

5.13 Granger causality test of the ex-ante real medium-term interest rate

121

5.14 Granger causality tests of exogeneity of ex-ante real rates (1969:3–1990:4)

128

5.15 Existence of a causal relationship between real rate and money supply (1969:3–1990:4)

129

5.16 Existence of a causal relationship between real output and real interest rates (1969:3–1990:4)

129

5.17 Existence of a causal relationship between real rate and expected rate of inflation

130

7.1

164

Instrumental variable estimation: Australia

7.2

Mean values of actual, fitted and conditional forecast of interest 167 rates in Australia

7.3

Instrumental variable estimation: Belgium

7.4

Mean values of actual, fitted and conditional forecast of interest 171 rates in Belgium

7.5

Instrumental variable estimation: Canada

7.6

Mean values of actual, fitted and conditional forecast of interest 175 rates in Canada

7.7

Instrumental variable estimation: France

7.8

Mean values of actual, fitted and conditional forecast of interest 179 rates in France

7.9

Instrumental variable estimation: Germany

168

172

176

180

7.10 Mean values of actual, fitted and conditional forecast of interest 182 rates in Germany 7.11 Instrumental variable estimation: Italy

183

7.12 Mean values of actual, fitted and conditional forecast of interest 185 rates in Italy 7.13 Decomposition of the variance of money supply in Italy

187

7.14 Instrumental variable estimation: Japan

188

7.15 Mean values of actual, fitted and conditional forecast of interest 191 rates in Japan 7.16 Instrumental variable estimation: the Netherlands

192

7.17 Mean values of actual, fitted and conditional forecast of interest 195 rates in the Netherlands

7.18 Instrumental variable estimation: Sweden

196

7.19 Mean values of actual, fitted and conditional forecast of interest 199 rates in Sweden 7.20 Instrumental variable estimation: U.K.

200

7.21 Decomposition of the variance of money supply in the U.K.

202

7.22 Mean values of actual, fitted and conditional forecast of interest 204 rates in the U.K. 7.23 Instrumental variable estimation: U.S.A.

205

7.24 Decomposition of the variance of money supply in the U.S.A.

207

7.25 Mean values of actual, fitted and conditional forecast of interest 210 rates in the U.S.A. 7.26 Impact of deficits on short-run interest rates

211

7.27 Impact of deficits on medium-term interest rates

213

7.28 Impacts of money, inflation and trade balance on short-run interest rates

214

7.29 Impacts of money, inflation and trade balance on medium-term 214 interest rates

ACKNOWLEDGEMENTS We would like to express our sincere thanks to the anonymous reader at Routledge for very constructive criticisms and suggestions. The sequencing of the chapters is in no small measure due to the suggestions of the referee. Our thanks also go to Charlene Hill for her excellent typing of numerous drafts. We would like to acknowledge the permission granted by the editor of Public Finance for using the material in our paper, ‘Dynamic Specification and the Long-run Effect of Budget Deficits on Interest Rates’, Public Finance, XXXXVI/No. 2/1991. Finally, we would like to thank Dr V.Tanzi for supplying the data on tax rates for the U.S.A.

1 INTRODUCTION The behaviour of nominal and real interest rates in the developed countries over the last several decades has been the subject of considerable scrutiny and debate. But in spite of the various controversies surrounding this issue, it is rather strange that most of the empirical literature in this area has been confined to the U.S.A. Our aim in this study is to fill this gap to some extent. However, we would like to add that the aim is not only to extend the coverage to more countries, but also to suggest, what we hope, are better ways of answering the questions to be explored. At a more specific level, we plan to ask some of the same kinds of questions which have been asked over the last decade or so about the behaviour of real interest rates. And we do that for a sample of eleven developed countries. Thus we ask: (a) How should we measure the ex-ante real interest rates, given that they are generally not observable in most countries? (b) Do the measured rates remain constant over time? (c) Do they tend to be equal across the countries? If so, does the equality hold only in the long run? (d) Does the Fisher hypothesis hold in all countries and in all time periods covered? Once again, does the validity of this hypothesis depend on whether we are dealing with the long term only? (e) Do the real rates tend to be exogenous in a world characterized by a certain set of variables? (f) Do budget deficits matter in determining the intertemporal behaviour of the real rates? Do they account for the persistently high rates in the 1980s and persistently lower rates in the 1970s? Would the rates have behaved differently if the time path of the deficits had been different? (g) Is the answer to one or more of the above questions sensitive to the particular time period covered or to how the real rates are generated or the type of the interest rate used? Of course, there are other questions one could ask. But given the number of the countries covered in our sample, we confine ourselves to a manageable set of questions. In order to assist the reader in the reading of our work, we offer a brief summary of the chapters to follow.

Interest rates and budget deficits

2

Chapter 2. The first major problem about the subject under consideration is that the variable of our inquiry, namely the ex-ante real interest rate, is not directly observable except in the case of index-linked bonds. This means that some proxy must be found. This chapter discusses alternate means of generating them, including the advantages and disadvantages of each method. It also discusses the problems with the real rates obtained from index-linked bonds. Since the real rates used in economic decision making are often post-tax rates, we also comment upon them. Chapter 3. The estimation methods discussed in the last chapter are used to present estimates of the ex-ante real interest rates for the eleven countries. The interest rates covered are both short term and medium term. These estimates are then used to examine their intertemporal behaviour. For example, were the estimated rates higher during the 1980s than during the 1970s, as is commonly believed? Did their variability differ between different decades? Do the estimates indicate any significant structural breaks? These rates are further used to examine questions about the international linkages and the equality of the rates across the countries. But before doing that, the chapter presents extensive evidence on the time series properties of the estimated rates. Then using a model which is a combination of Mishkin (1984) and Wickens and Breusch (1988), we test three hypotheses: first, whether the rates are linked internationally; second, whether this linkage is full or partial; and, third, whether the rates are equal internationally. An interesting aspect of the methodology used is that it allows us to test both the long-run and the short-run relationship as well as to allow us to estimate the speed of adjustment of the estimated rates to their long-run equilibrium values. Chapter 4. This chapter deals with one of the most important hypotheses in monetary economics, namely, the Fisher hypothesis. A distinctive feature of the evidence presented is that it is also based on the methodology used in Chapter 3. In other words, we are able to distinguish between the long-run validity of the hypothesis versus the short-run verification. Chapter 5. Here we explore the question first discussed in detail by Litterman and Weiss (1985), namely, the question about the exogeneity of real interest rates. This is done using the Granger causality test and the innovation accounting technique. We first test the null hypothesis that the real rate is exogenous relative to a universe that includes money, real output and expected inflation. Then, as an additional test of exogeneity of the real rates, we decompose their variance into components explained by orthogonalized innovations in money, real output and expected inflation. Chapter 6. From the properties of the real rates, in this chapter we turn to what is arguably the most talked about and controversial policy issue in the literature on interest rates. We are, of course, referring to the role of budget deficits. It has been suggested that in order to appropriately discriminate between the competing paradigms on this issue, we must be able to distinguish between the effects of permanent vis-à-vis transitory changes in budget deficits (Bernheim, 1989). In this chapter we propose a model which allows us to achieve this goal without the necessity to generate such proxies and thus enables us to distinguish between the competing paradigms. Chapter 7. This chapter provides the most extensive evidence to date on the role of budget deficits on interest rates. This is done in three stages. First, we look at the descriptive evidence on deficits and the estimated rates and check whether the data display any regularities which require explanation. Second, we provide a very brief

Introduction

3

survey of the existing evidence. Finally, we estimate the model of Chapter 6 and also employ the innovation accounting technique used in Chapter 5. An interesting feature of these results is the simulations done to trace the time path of the estimated rates if the deficit is set equal to zero over the time horizon under consideration. Chapter 8. Since the evidence is very extensive, no attempt is made in the final chapter to summarize the results. That is done in each chapter individually. However, we simply try to gather together some broad lessons which emerge from our findings and the use of the methodology employed.

2 PROBLEMS OF MEASURING EX-ANTE REAL INTEREST RATES It was pointed out in Chapter 1 that the relevant interest rates for economic decision making are the post-tax ex-ante real interest rates. Leaving aside the question of taxes for the moment, even the estimation of pre-tax ex-ante real interest rates poses problems because they are not directly observable in general. Even for the index-linked bonds, where such rates are directly observable, there are serious difficulties, as discussed below. This chapter briefly describes the various approaches to the estimation of such rates in the literature and the approaches used by us. ALTERNATE METHODS OF ESTIMATING EX-ANTE REAL INTEREST RATES For ease of discussion, we distinguish four approaches: 1 direct estimates from index-linked bonds; 2 survey method based on direct estimates of inflation expectations; 3 standard method using current and/or past rates of inflation to estimate inflation expectations; and 4 the rational expectations approach. Since the four methods of estimation are relatively well known, our discussion is brief. Clearly, the most attractive solution would be if we could directly observe such rates. In principle, yields on index-linked bonds could provide such a measure. But, unfortunately, as, for example, Wormell (1985), has pointed out there is no commonly agreed method for calculating the real yields on such bonds, and the yields published by brokers and newspapers tend to differ widely. This happens because of the differences in the assumptions made about expected inflation. Generally, two approaches are used to formulate such expectation: either that inflation would continue at a constant rate, starting from a certain date, or that it will continue at a level equal to the average of some recent period. Both assumptions have disadvantages. Therefore, brokers tend to publish yields based on a range of retail price index changes and let the users choose what they like. The result, according to Wormell is that, ‘the yields on index-linked stocks have swung widely since their introduction. This volatility has been a result of not changes in real returns in the economy, but of other, more technical reasons’ (p. 101). Thus, it is clear that even if we had such estimates available for all of the countries in our sample, they would not necessarily provide an accurate measure of the ex-ante real interest rates. But a more practical limitation for us is that such rates are available only for the U.K. and those

Problems of measuring ex-ante real interest rates

5

too only since March 1981. However, just for the sake of comparison with alternate estimates, we would use the available information on these rates in the next chapter. A rather popular method for estimating ex-ante real interest rates, whether pre- or post-tax, in the United States has been based on the use of survey data on inflation expectations. Of course, once data on expected inflation is given, the rest of the calculations are not that difficult. The main question when this method is used is whether the survey data represent unbiased measure of the inflation expectations, i.e., whether they are consistent with the rational expectations hypothesis. Existing empirical evidence suggests that the survey data on inflation expectations are not an unbiased measure of expected inflation. (See, for example, Baghestani (1992), among others.) In fact, in a recent study, Lahiri and Zaporowski go on to conclude that, the expected inflation series resulting from the rationally expected real rate model supports the hypothesis of unbiasedness. However, the original data does not support the unbiasedness property. Since the Livingston series typically underestimates the true market expectations, the use of this data to compute real interest rates will tend to overestimate actual exante real interest rates. (1988, p. 310) The estimates reported in the next chapter support this conclusion. Quite apart from the use of survey data as being the most appropriate measure of expected inflation, like the yields on index-linked bonds, here we also face a practical problem. Such survey data are available for very few countries in our sample. Consequently, given the shortcomings of using such data, as discussed above, and the lack of such data for most of the countries in our sample, we would only provide evidence for the U.S.A. in the next chapter just to highlight the differences with respect to alternate estimates. This takes us to what we call the standard method. This method constructs proxies for expected inflation, based on current and/or past inflation rates. There is no commonly agreed-upon formula, so that there are various alternatives, for example, the adaptive procedure, the extrapolative procedure, a mixture of the two and so on (see, for example, Cukierman (1977) and Lovell (1986), among others). But regardless of the scheme used, the starting point for the estimates is the Fisher equation, which in its approximate form is given by (1) where R represents the ex-ante real interest rate, NI the nominal interest rate, and PE the expected rate of inflation, which an investor expects to prevail over the holding period. In order to estimate PE, we use the autoregressive approach. This approach is somewhat different when used for the short- and medium-term ex-ante real interest rates. Since estimates for both rates are reported in the next chapter, the differences in the method used are explained below. Our procedure closely follows that of Blanchard and Summers (1984). For the short rate, we use rolling autoregressive forecasts, for one quarter ahead, reestimating the equation on the basis of the last twenty quarters, using six lags of inflation.

Interest rates and budget deficits

6

We also tried eight lags and twenty-four quarters, but the results were neither better nor different. When we used four quarter lags of inflation, the results were decidedly inferior. The medium rates pose a somewhat different problem because the maturity period of medium-term securities is more than a quarter. Therefore, medium ex-ante real interest rates are constructed by (2)

where

and

are the real and the nominal rates on bonds of maturity j and

is the mean nominal PEt,t+k is the forecasts of inflation in period t+k, as, of time t. rate of interest over the period examined. It is important to note that although the forecasts of inflation are generated by the same formula as for the short rate, in this case forecasts are generated over the life of the bond and not one period ahead only. It is clear that the estimates of the ex-ante real interest rates generated by the above method are sensitive to the estimates of PE. The autoregressive procedure used for estimating expected inflation has been criticized on many grounds, the most important being that economic agents may formulate their price expectations on the basis of more information than the current and past behaviour of inflation alone. This suggests the need for an approach which completely avoids the use of expected inflation in the measurement of ex-ante real interest rates. Such an approach has been proposed by Mishkin (1984). This approach exploits the hypothesis of rational expectations to generate a series on the ex-ante real interest rate and then the series on the expected rate of inflation is derived as a by-product by using equation (1). This approach can be briefly described as follows: Define the ex-post real interest rate as (3) when EPR is the ex-post real interest rate and is the actual rate of inflation. The ex-ante real interest rate is then given by (4) where E is the expectations operator. Combining equations (3) and (4) we get (5) where (6) Invoking the assumption of rational expectations for future inflation, we have

Problems of measuring ex-ante real interest rates

7

(7) where Z is the set of all available information at time t (for simplicity, time subscripts have been omitted in the above equations except (2)). Mishkin (1984) proposes that the best linear prediction of E(EPR) given X be used as an estimate of the ex-ante real interest rate, where X is a subset of the information set Z which is observed and which is assumed to be correlated with E(EPR). In other words the projection equation for ex-ante real interest rate is (8) where v is the projection equation error. Substituting (8) into (5) we get (9) The estimated ex-ante real interest rates are the predicted value from equation (9): (10) We can immediately see that by using the values of EPR and equation (1), we can get (11) where PÊ is the estimated value of expected inflation by Mishkin’s method. The estimates of expected inflation from (11) and the autoregressive scheme are used to examine the Fisher hypothesis and the Mundell-Tobin effect. PRE-TAX VERSUS POST-TAX EX-ANTE REAL INTEREST RATES As mentioned above, the relevant interest rates for economic decision are the post-tax exante real interest rates. This means that we must have information on how the nominal interest incomes are treated for tax purposes. In the case of the index-linked bonds, the added problem of how the inflation premium is taxed must be considered. For the other three methods, we must have time series data on the marginal rate of tax on interest income. Given the different treatment of interest income in different countries, preparation of such data are well beyond the scope of such a study. However, some time series data for the U.S.A. and some summary data for a number of other countries are available. These data are used to provide estimates of the post-tax ex-ante real interest rates wherever possible.

3 ESTIMATES AND BEHAVIOUR OF EXANTE REAL INTEREST RATES This chapter presents the estimates of the ex-ante real interest rates for the eleven countries included in this study. This is done, wherever possible, using the four procedures discussed in the last chapter. While the estimates for the pre-tax interest rates are presented for all of the countries included, the post-tax are presented only for a subset of the sample, because of the unavailability of the tax rate data. The rates included are both short and medium term. The estimated rates are used to shed light on two specific issues: first, whether the observed nominal interest rates have served as a reliable proxy or a signalling device for the behaviour of the ex-ante real interest rates, and second, whether they have been equal across the countries. THE ESTIMATES OF THE SHORT-TERM PRE-TAX EX-ANTE REAL INTEREST RATES In order to estimate the short-term pre-tax ex-ante real interest rates, we need a measure of the nominal interest rate and of the price index. Since there is no consensus on what constitutes ‘the’ short-term interest rate or ‘the’ price index, the usual practice in singlecountry studies is to use alternate measures of both variables and check whether the resulting estimates of the ex-ante real interest rates are sensitive to the alternate measures. Such an approach is not feasible for this study for two reasons. First, given the large number of countries included in our sample, the sheer size of the exercise would constrain such an approach. Second, and even more important, in order to render the results comparable, we need data which to a considerable degree are comparable, which is not possible for too many of the alternatives. Consequently, we use the three-month treasury bill rate as a measure of the short-term nominal interest rate for Canada, the Netherlands, the U.K. and the U.S.A. For the other countries, the short-term rate is represented by the money market rate. For the price index, we use the consumer price index. The data used are quarterly and generally cover the period from 1967:2 to 1990:4. The period prior to 1967:2 was used up in calculating the expected rates of inflation so that estimates of the ex-ante real interest rates for that period cannot be provided, unless data on the price index are available since 1957 which is not the case. Since most of the discussion in this chapter and the subsequent chapters is based on the estimates derived by using the standard method and the rational expectations hypothesis, we start by presenting estimates using these methods. The specific standard method used was described in Chapter 2. But some further details of the rational expectations hypothesis are required before we can present the estimates. In order to

Estimates and behaviour of ex-ante real interest rates

9

implement the rational expectations or the Mishkin approach, we need to specify the variables in the information subset X. The variables finally selected were the current nominal interest rate, three lagged values of actual inflation, time, time squared, time cubed and time raised to the power four. We also tried more lagged values of inflation and both higher and lower degree polynomials in time. But the results, using Akaike’s Final Prediction Error criterion showed that our preferred selection of the variables was the best. Therefore, the ex-ante real interest rates by the Mishkin method are the fitted values from the regressions of the ex-post real rates on information, as defined above, at the beginning of the period. The series on expected inflation by this method can be obtained by using equation (11) in Chapter 2. In the tables and the figures that follow, we have used certain notations. The shortterm pre-tax ex-ante real interest rates estimated by the autoregressive and the Mishkin approaches are denoted by RAUT and RHMISHK, respectively, and the expected inflation rates by PH and PMISHK, respectively. The short-term nominal interest rate is denoted by NI. The two estimates of the short-term pre-tax ex-ante real interest rates are given in Figure 3.1, while their means and standard deviations are given in Table 3.1. Looking at Figure 3.1, its first striking feature is the very close similarity between the two estimates for each of the eleven countries. This inference is further confirmed from the data in Table 3.1. The means and the standard deviations for the different periods for each country are very close, many a time virtually identical. This close correspondence between the two estimates is quite remarkable when we consider how different are the two estimation procedures. This should provide us considerable confidence in our estimates, because clearly they are not very sensitive to these two alternate estimation procedures. We now turn to a detailed discussion of these estimates, both ove time for each country and across countries for a comparative analysis, paying particular attention to the 1980s. In a study involving as large a number of countries as this one, it is always problematic to decide how to organize the discussion. Since the behaviour of ex-ante real interest rates in each country is of interest in its own right, quite apart from how it relates to that in the other countries, we have organized our analysis on a country-by-country

Interest rates and budget deficits

10

Figure 3.1 Short-term pre-tax ex-ante real interest rates r

Estimates and behaviour of ex-ante real interest rates

11

Interest rates and budget deficits

12

basis and draw comparative conclusions wherever appropriate. In the case of Australia, the short-term pre-tax ex-ante real interest rate has increased systematically over the four sub-periods. We can see from Table 3.1 that it was the lowest in the 1960s and the highest in the second half of the 1980s, being over twice the mean rate in the 1970s. The behaviour in the 1980s is also interesting in that the rate increased from the early to the late 1980s. The increase

Estimates and behaviour of ex-ante real interest rates

13

in the mean rate of nearly 860 basis points between the 1960s and the 1980s is quite remarkable. It is important to note that along with this increase, their variability also increased, although this increase was more marked from the 1960s to the 1970s than from the 1970s to the 1980s. In fact, the decline in the variability in the late 1980s compared to the early 1980s is noteworthy, considering that the real rate increased. This positive relationship between increases in the

Interest rates and budget deficits

14

real rate and in variability in the earlier periods, followed by a negative relationship in the later period suggest that the role of uncertainty may not have been symmetrical during the 1980s. This issue is explored in more detail later on. It is clear from Figure 3.1 that these averages mask important variations within each period. It is thus important to look more deeply into the 1980s. Using the autoregressive estimates, we find

Estimates and behaviour of ex-ante real interest rates

15

that the real rate in 1990:4 was 10.36 per cent as against 10.67 per cent in 1980:1, hardly any change. The estimates seem to reveal a number of fundamental breakpoints. For example, in 1983:1, then in 1988:1, after which the real rate continued to rise until 1989:3 and then started to decline. But the rate still remained very high. A comparison with the other countries is also revealing. Thus, we find that during the 1980s Australia had the highest real rate and also the greatest variability among the countries covered here. For example, compared to the U.S.A., the real rate was almost 500 basis points higher. This comparison is all the more revealing when we note that the Australian real rate was higher by only 150 basis points in 1980:1, but this difference in 1990:4 had shot up to 422 basis points, almost three times as much. A further comparison with the non-European countries, that is, Canada, Japan and the U.S.A., shows that the general trend towards lower short-term real rates was similar, though less pronounced. In short, Australian short-term pre-tax ex-ante real rates are characterized by high and variable levels and show a recent tendency towards declining, a tendency shared by many of the other countries in the sample. The two estimates for Belgium again reveal an identical pattern. From Table 3.1, the mean short-term real rate was 2.89 in the 1960s, rising to 4.09 in the 1970s and then to 6.2 per cent in the late 1980s. It is interesting to note that unlike Australia, the mean real rate in Belgium declined from the early to the late 1980s. But like Australia, these rising mean rates are not accompanied by increasing volatility. In fact, the value of the standard deviation in the 1980s is hardly different from that in the 1960s, but lower than that in the 1970s. Thus, in the case of Belgium, increased real rates in the 1980s have been accompanied by reduced volatility. This again points to a potential role for uncertainty, though the direction of causality is no longer as transparent as in the case of Australia.

Interest rates and budget deficits

16

Table 3.1 Mean and standard deviation of pre-tax ex-ante real short-term interest rates: auto and Mishkin estimates* Country

1967:3– 1990:4 Me an

Aus tralia Belgium

8.93

1967:3– 1969:4

1970:1– 1979:4

1980:1– 1984:4

1985:1–1990:4

St. dev.

Me an

St. dev.

M ean

St. dev.

M ean

St. dev.

M ean

St. dev.

4.1

3.88

0.75

6.28

2.24

11.63

2.81

13.22

2.20

(9.00) (4.1) (3.75) (0.66) (6.39) (2.17) (11.50) (2.50) (13.44) (2.25) 5.47

2.67

2.89

1.73

4.09

2.23

8.53

1.86

6.28

1.14

(5.44) (2.60) (2.86) (1.39) (4.05) (2.16) (8.64) (1.50) (6.17) (1.08) Canada

7.41

3.18

5.39

1.07

5.21

2.19

10.86

2.63

9.06

1.82

(7.39) (3.17) (5.24) (0.81) (5.19) (2.15) (10.87) (2.70) (9.07) (1.66) France

7.53

2.39

5.92

1.76

6.20

1.89

10.53

1.87

7.93

0.95

(7.52) (2.42) (5.90) (1.64) (6.13) (1.89) (10.73) (1.67) (7.84) (0.89) Germany 5.07

2.42

2.84

1.80

4.74

2.56

6.89

2.20

5.03

1.47

(5.06) (2.30) (2.77) (1.48) (4.75) (2.38) (7.00) (2.01) (4.93) (1.36) Italy

9.01

3.86

3.32

0.60

7.40

2.85

13.96

1.97

10.54

0.97

(9.15) (3.86) (3.18) (0.37) (7.47) (3.03) (13.94) (1.53) (10.43) (0.89) Japan

5.38

1.89

5.22

1.13

5.15

2.17

6.56

1.68

4.86

1.45

(5.36) (1.65) (5.01) (0.65) (5.15) (2.01) (6.50) (1.23) (4.87) (1.06) Nether lands Sweden

5.18

2.83

4.10

1.89

4.20

3.44

6.79

2.19

5.98

1.35

(5.09) (2.78) (3.62) (1.64) (3.98) (3.20) (7.16) (2.20) (5.85) (1.20) 7.00

3.22

5.47

1.31

4.38

2.27

9.58

1.78

9.82

1.67

(6.93) (3.21) (5.03) (0.94) (4.25) (2.12) (9.89) (1.32) (9.71) (1.59) U.K.

7.64

2.81

6.14

0.79

5.83

2.44

9.16

1.98

10.02

1.92

(7.66) (2.60) (5.51) (0.43) (5.90) (2.08) (9.39) (1.53) (10.04) (1.40) U.S.A.

5.97

2.26

4.78

0.63

4.53

1.25

9.19

2.03

6.11

1.00

(5.90) (2.24) (4.46) (0.51) (4.47) (1.32) (9.14) (1.85) (6.11) (0.81) *The figures in parentheses are those based on Mishkin procedure.

Figure 3.1 reveals considerable variation during each sub-period. Thus, there seems to be a sudden break in 1979:3 when the real rate jumped from 4.78 per cent in the previous

Estimates and behaviour of ex-ante real interest rates

17

quarter to 8.2 per cent in 1979:3. The rates remained relatively high until 1983:1 and then went down to 5.9 per cent in the next quarter. During the last two years of the 1980s, we see a pattern somewhat different from Australia, in that the rate continuously rises from 1988:4 to 1990:1 and then declines and rises, alternately. A look at the figures for France, Germany and the Netherlands shows a close correspondence between the four towards the last four years of the 1980s. It is also interesting to note that the estimates for France and Germany suggest a breakpoint in 1979:3 and those for the Netherlands a quarter later. Use of monthly data may reveal a closer correspondence between the timing of this breakpoint. What is thus clear is that in the case of Belgium, the short-term ex-ante real rate did not remain constant over the period, but it did not show the same increasing volatility with rising levels as was the case with the Australian rate. According to Table 3.1, the mean short-term pre-tax ex-ante real rate in Canada remained virtually constant from the 1960s to the 1970s and then increased by almost 467 basis points in the 1980s. In this respect, Canadian experience is different from Australia and Belgium in the earlier periods, but shares the same characteristic in the 1980s. But if we look at the two sub-periods of the 1980s, Canada’s experience is more like that of Belgium than Australia. However, when we turn to the volatility of these mean rates, the results are even more different. The first interesting part of these estimates is that although the mean rate hardly changes between the 1960s and the 1970s, the standard deviation almost doubles, suggesting much greater volatility in the 1970s. On the other hand, when the mean rate nearly doubles from the 1970s to the 1980s, the variability hardly changes. The value of the standard deviation increases only marginally from 2.19 to 2.37. The pattern of the French short-term real rate seems to mirror the Canadian experience. From Table 3.1, the mean rate remains virtually constant from the 1960s to the 1970s, although, unlike Canada, it rises marginally rather than falls in the second period. But in the 1980s, it increases by about 290 basis points, whereas the corresponding increase in Canada was greater. But unlike any of the other three countries discussed so far, in this case the variability remains almost constant until the mid-1980s, declining sharply thereafter. It is also interesting to note that the mean rate in the 1980s was higher than that for members of the G-7 or for the European countries, the rate for the two being 8.53 and 8.57 per cent, respectively. Compared to the U.S.A., the French rates were higher in each period. Turning to the behaviour in the 1980s, there is a sharp jump in 1979:4, then again a breakpoint in 1981:2. During 1988 it varied between a very narrow range of around 6.75 per cent. In 1989 it moved closer to 8 per cent and then in 1990 to 9 per cent. Thus, in the case of France, short-term pre-tax real rates have remained far from constant during the 1980s and relative to a number of the OECD countries have tended to be on the high side. The behaviour of the short-term real rates in the 1980s is quite different from that of the other countries in the sample, except to some extent for Japan. The real rate varied from a low of 2.87 per cent to a high of 11.09 per cent during the 1980s. But this maximum occurred in 1981:3. From Table 3.1, it is clear that the mean short-term real rate for Germany increased right from the 1960s to the mid-1980s, the increase being almost 215 basis points from the 1970s to the mid-1980s. But from the mid- to the late 1980s, the mean rate showed a

Interest rates and budget deficits

18

sharp decline, being equal to 186 basis points. Thus, Germany’s experience during the 1980s parallels that of Belgium, Canada and France, even though the absolute rates in Germany were much lower than in the other three countries. In terms of the volatility, Germany’s experience corresponds to that of Belgium, first suggesting a positive and then a negative relationship between changes in real rate and the level of variability. The behaviour of the short-term real rates in Germany in the 1980s is quite different from that of the other countries in the sample, except to some extent for Japan. The real rate varied from a low of 2.87 per cent to a high of 11.09 per cent during the 1980s. But this maximum occurred in 1981:3. For most of the rest of the decade, the real rate remained at or well below 5 per cent and went as high as 8 per cent in 1990:3, then declining to 7.5 per cent in 1990:4. A comparison with the other countries in the sample is most revealing. In the 1960s, Germany had the lowest mean pre-tax ex-ante real short-term rate, but by the 1970s, this was no longer the case, although it still was one of the lowest. But Germany again regained this distinction in the 1980s if we exclude Japan, although even Japan’s rate was only marginally lower, a mere 25 basis points. An even more remarkable aspect of the estimates for Germany vis-à-vis the other countries in the sample is that Germany experienced, excluding Japan, by far the smallest increase in the real rate from the 1970s to the 1980s, a mere 113 basis points. A comparison with the U.S.A. is also revealing. From the mean rates given in Table 3.1, the U.S. estimate for the 1980s exceeds the German estimate by 165 basis points. But if we consider the last five quarters, we find that the U.S. real rates have declined while German rates have moved up with the result that unlike the mean for the whole decade, the German real rate in the last three quarters of 1990 were higher than those of the U.S.A. On the whole though, during most of the period covered, Germany experienced rather low short-term rates accompanied by low and declining variability. Only in the late 1980s did the rates show a tendency to catch up with those in many of the other countries. For Italy, the real rate of interest went up from a low of 3.32 per cent in the 1960s to 7.40 per cent in the 1970s and then again to 12.09 per cent in the 1980s. Thus, Italy experienced almost the highest increases in the two periods in the entire sample. What is more, the mean rate in the 1960s was among the lowest, but by the 1970s it had become the highest among the eleven countries and, with the exception of Australia, the same being the case in the 1980s. This behaviour is even more strikingly different if we compare it to the U.S.A. Thus, in the 1960s, the U.S. real rate exceeded that of Italy by about 146 basis points, but by the 1970s the Italian rate exceeded the U.S. rate by almost double the amount, 187 basis points, and in the 1980s this gap increased to 457 basis points. It should be noted, however, that in the second half of the 1980s, the Italian shortterm rate, though still the highest in the sample (except for Australia), had nevertheless gone down considerably compared to the mid-1980s, by almost 340 basis points. In terms of the variability of the real rate, Italy also displays a distinctly different pattern. In the 1960s, Italy experienced the lowest standard deviation in its short-term real rate, but by the 1970s this had not only gone up by a factor of almost five, but had also become the largest in the sample, if we exclude the Netherlands. But in the 1980s, although, as already pointed out, the real rate again increased sharply, its variability declined considerably, being close to those of the other members of the G-7. Relative to the other countries in the sample, Italy thus presents one of the most important exceptions and it

Estimates and behaviour of ex-ante real interest rates

19

would be interesting to examine in the subsequent chapters the reasons for this distinctive experience. Turning to the experience during the 1980s, we can see from Figure 3.1 that the high mean rate for the 1980s masks considerable variations. For example, during this period, the rate ranged from a maximum of 17.65 per cent in 1981:2 to a low of 8.84 per cent in 1987:1, thus suggesting a breakpoint during the latter quarter. After reaching the peak in 1981:2, the real rate has shown a marked tendency to decline, although during 1989 and 1990 it has tended to stabilize around 11 per cent, except for the last quarter when it went down by over 100 basis points. Thus, while the rate peaked in the early 1980s and has shown a steady decline since, it has nevertheless tended to remain at a relatively high level, most often equalling or exceeding 10 per cent. These kind of high real rates during the 1980s have not been the experience of most of the members of the G-7 or for that matter of the other countries in the sample. In terms of the mean real rates of interest reported in Table 3.1, Japan stands out as the most unique case. The mean rate seems to have remained virtually constant over the 1960s and the 1970s, rising in the first half of the 1980s and then going down in the second half. It is also distinguished by the fact that the mean rate remained at the lower level of about 5 per cent. While in the 1960s, this rate was nowhere near the lowest rates experienced by the other countries, for example only 2.84 per cent for Germany, nevertheless by the 1970s it had become one of the lower ones and by the 1980s it was the lowest. A comparison with the U.S.A. is revealing here. Thus, while in the 1960s and the 1970s, the U.S. mean real rate was lower than that of Japan by about 55 basis points, in the 1980s the difference had turned the other way, with the U.S. mean real rate exceeding the Japanese rate by as much as 200 basis points. In terms of the volatility of the mean rates, Japan’s experience is more like Belgium and Germany, namely, a decline in volatility accompanied by an increase in the real rate. These mean rates, however, give an exaggerated view of the constancy of the pre-tax short-term ex-ante real rates in Japan, as can be easily verified from Figure 3.1. A number of turning points can be identified; for example, some of the possible breakpoints are 1974:4 and 1980:1. Since 1981:1 the real rate has tended to be relatively lower, until 1990. During 1990, the rate moved between 6 and 7.6 per cent. A comparison of Figure 3.1 for Japan and for the U.S.A. shows a certain correspondence between the temporal behaviour of the short-term real rates in the two countries, but the Japanese rates appear to be more volatile and the turning points not always the same. The mean real rate for the Netherlands remained almost constant from the 1960s to the 1970s, although it became much more volatile in the 1970s. In the 1980s, on the other hand, while the real rate increased by nearly 50 per cent, the volatility was reduced by half. With the exception of Germany and Japan, the Netherlands had the lowest mean real rate in the 1980s. It was considerably below the average for the G-7 and the European countries by about 200 basis points. A look at Figure 3.1 shows lack of constancy of the real rate over time, although it can also be seen that the degree of variability is considerably less marked during the 1980s compared to the earlier periods. A comparison of Figure 3.1 for the Netherlands and Sweden shows considerable correspondence between the behaviour of the real rates in the two countries, particularly in the 1980s, including an increase in the real rate in the last quarter of 1990, a feature not shared by any other country in the sample.

Interest rates and budget deficits

20

For Sweden the mean real rate declined by about 110 basis points from the 1960s to the 1970s but then rose by 533 basis points in the 1980s over the 1970s, suggesting one of the highest increases in the sample. Sweden is one of the three countries in the sample, besides Australia and the U.K., in which the mean real rate increased and the volatility declined from the first half of the 1980s to the second half. The variability of the real rate, however, displays a reverse pattern. It increased when the rate went down but went down when the real rate increased, thus mirroring the experience of the Netherlands as noted above. In absolute terms, the mean rate in the 1980s was above the mean for the G-7 and for the European countries. Looking at Figure 3.1 for Sweden, once again it would seem that the real rate has not remained constant over time. The real rate shows a tendency to increase towards the end of the period. The mean real rate for the U.K., although it went down in the 1970s compared to the 1960s, nevertheless became quite volatile with the standard deviation having increased by almost three times. Like many of the other countries in the sample, the mean rate in the 1980s increased sharply over the 1970s, but was accompanied by reduced volatility. As mentioned above, the U.K., unlike most other countries in the sample, experienced an increase in the real rate in the second half of the 1980s. A comparison of Figure 3.1 for the U.K. and the U.S.A. shows a much greater correspondence between the behaviour of the short-term real rate in the two countries in the 1980s than in the earlier periods, but in absolute value the U.K. rates have tended to exceed the U.S. rates by about 200 basis points, thus suggesting considerable independent variation. The estimates for the U.S.A. confirm the findings of Cumby and Mishkin (1985) and others for the 1970s and early 1980s, namely that the real rates were substantially lower in the 1970s than in the 1980s. Our estimates extend the findings for the 1980s and suggest that the rates were substantially higher and more volatile not only for the early 1980s but for the entire decade, with the real rate exceeding by as much as 300 basis points over the mean rate for the 1970s and the standard deviation being nearly twice as much. But it should be noted that the real rate in the second half of the 1980s was almost 300 basis points lower than in the first half with greatly reduced volatility. An interesting feature of the estimates for the U.S.A. is that unlike most of the members of the G-7, the mean volatility of the real rate increases over the entire sample period, in spite of the fact that the U.S.A. did not by any means experience the highest increase in mean real rate from the 1970s to the 1980s. In fact, the mean rate in the 1980s was still one of the lowest in the sample and with the exception of Germany and Japan, the lowest in the G-7 countries. This would seem to suggest a certain lack of correspondence between the behaviour of the pre-tax short-term real rates in the U.S.A. and that of the other countries. Figure 3.1 for the U.S.A. also confirms two other findings by Cumby and Mishkin (1985) and others, namely possible structural breaks in the early parts of the last quarters of 1979 and 1982. Our estimates also suggest a possible break in early 1982. It is well known that the structural breaks of October 1979 and October 1982 also coincided with monetary policy regime changes in the U.S.A. As Bonser-Neal (1990) has pointed out, some of the break-off points we have identified above for Canada, Germany and the U.K., also seemed to coincide with policy regime changes in those countries. The question whether there is a causal and predictable relationship between policy regime changes and changes in real rates is an important one and will be pursued in the following

Estimates and behaviour of ex-ante real interest rates

21

chapters. Suffice it to say here that the structural breakpoints noted in the above discussion call for an explanation, one which may be due to policy regime changes, but may be due to other factors also, say uncertainty. The role of these and other factors is considered later on. The above discussion has been based on the estimates derived from the standard procedure and the rational expectations hypothesis. Before we turn to a general summary of these estimates, a brief word is in order about the use of survey data on inflation expectations for calculating ex-ante real interest rates, as discussed in Chapter 2. Because of the biasedness of such survey forecasts, as pointed out in Chapter 2 and also because of the lack of suitable data for many of the countries in the sample, we only report some estimates for the U.S.A. just to illustrate the difference between the three types of estimates. The survey data on expected inflation was taken from Lahiri et al. (1988) which is itself based on an inflation expectations survey by the American Statistical Association and the National Bureau of Economic Research (ASA/NBER) of the implicit GNP price deflator. They explain that in order to use the information in the probability distribution reported by the ASA/ NBER survey, we must match the forecast span of the distribution with the nominal interest rates of identical length maturity. This was

Figure 3.2 Pre-tax short-term real rates: survey method done by using the method described by them. The secondary market treasury bill yields were used as the nominal interest rate. The estimates by the three methods are shown in Figure 3.2. Because of the data limitations, the period covered for this comparison is from 1969:4 to 1986:3. The autoregressive and the rational expectations hypothesis estimates of the pre-tax short-term real ex-ante interest rates are virtually identical. But the estimates based on the survey data are systematically lower, a conclusion which confirms the findings of many other studies, which report that the survey estimates of expected inflation systematically overestimate the actual expected inflation.

Interest rates and budget deficits

22

Concentrating on the general discussion above, it is possible to conclude that for virtually all of the countries in the sample, the pre-tax short-term real ex-ante interest rates behaved differently in the three decades, and within the 1980s the behaviour was quite distinct, with the rates being generally lower in the second half than in the first. It is also clear that while the general movement across the countries is in the same direction, there are wide quantitative differences between them in virtually all time periods; thus, for example, the pre-tax short-term real rate ranged from a low of 4.85 per cent for Japan to a high of 13.22 per cent for Australia in the second half of the 1980s.

Table 3.2 Data used for nominal medium-term interest rates* Country

Data

Australia

1970–90, Australian Government Security, 5 years’ maturity or Commonwealth Government bond, maturity 5 years

Belgium

1965–69, Central Government Bond, 10 or more years’ maturity 1970–90, Central Government Bond in secondary market, 10 or more years’ maturity

Canada

1965–90, Federal Government Bonds, 3–5 years’ maturity, in secondary market

France

1965–69, Bonds guaranteed by government and similar issues, 10 or more years’ maturity 1970–90, Public sector bond in secondary market, 10 or more years’ maturity

Germany

1965–69, Public sector bond (outstanding bond) 1970–90, 3–7 years Public sector bond in secondary market

Italy

1965–90, ‘Crediop’ bonds on Treasury Account, 5 years’ average maturity

Japan

1965–90, Central Government Bond, 7 years’ average maturity 1970–90, Central Government Bond in secondary market, 7 years’ average maturity

Netherlands

1965–90, Central Government Bond, 5–8 years’ maturity

Sweden

1965–69, Effective yield on short-term Central Government Bond 1970–90, 5 years Central Government Bond in secondary market

U.K.

1965–90, Government Bond rate, 5 years’ maturity

U.S.A.

1965–69, 3–5 years U.S. Government notes and bond rate 1970–90, 5 years U.S. Government notes and bond rate in secondary market

*For calculating expected inflation, the following maturities were assumed: Australia (20 quarters), Belgium (40 quarters), Canada (20 quarters), France (40 quarters), Germany (20 quarters), Italy (20 quarters), Japan (28 quarters), the Netherlands (32 quarters), Sweden (20 quarters), the U.K. (20 quarters) and the U.S.A. (20 quarters).

Estimates and behaviour of ex-ante real interest rates

23

Table 3.3 Mean and standard deviation of pre-tax ex-ante real medium-term interest rates* Country

Australia Belgium

1967:2– 1990:4 Mean

St. dev.

8.50a

St. dev.

Mean

St. dev.

3.28

5.19b

1.60

11.35

1.35

11.28

0.78

(7.58)

(1.63)

(6.54)

(0.60)

(9.86)

(0.88)

(7.07)

(1.16)

7.92

2.20

7.07

1.14

10.82

0.93

9.15

0.73

c

9.01 6.78

Italy

9.53 (8.59)

Japan

5.71 (5.09)

Netherlands

6.76 (6.41)

Sweden

8.12 (7.80)

U.K.

8.32 (7.77)

U.S.A.

7.12 (6.81)

6.95

(1.35) (7.14) 3.38

d

6.85

(1.76) (7.82) 1.17

(6.61)

5.51

(2.11) (5.73) 2.11

(8.15) Germany

(4.29) (2.37) 2.30

(7.40) France

1985:1– 1990:4

Mean

5.64

6.13

(2.56) (6.59) 1.35

5.34

(1.08) (5.53) 1.33

6.11

(1.36) (5.94) 2.13

5.93

(1.90) (5.89) 2.08

6.92

(1.79) (6.98) 2.29

5.16

(2.00) (5.27)

St. dev.

1980:1– 1984:4

St. dev.

7.61

Mean

1975:1– 1979:4 Mean

(7.01) Canada

1967:2– 1974:4

0.83

(3.20) (5.74) 0.83

6.44

(0.88) (6.10) 0.48

8.17

(1.11) (7.91) 1.08

5.97

(1.00) (5.55) 1.31

9.36

(1.07) (8.48) 0.95

6.01

(0.59) (4.45) 1.03

6.13

(0.83) (5.39) 0.76

7.14

(0.65) (6.76) 1.60

7.48

(1.61) (6.50) 0.69

6.00

(0.83) (5.65)

(0.54) (10.47) (1.51) (11.17) (0.76) 1.27

10.67

1.59

8.74

0.84

(1.05)

(9.87)

(2.07)

(8.58)

(0.91)

0.71

12.08

1.15

9.98

0.79

(6.62)

(0.99)

(0.59) (10.42) (1.26) 0.97

7.61

1.05

6.54

1.06

(1.08)

(7.47)

(1.21)

(6.07)

(1.30)

1.37

14.39

2.52

10.02

1.09

(8.14)

(1.31)

(0.59) (12.37) (2.52) 1.48

6.96

0.91

4.90

1.23

(1.27)

(5.75)

(0.33)

(4.69)

(1.23)

1.04

8.28

1.17

6.87

0.95

(0.83)

(7.99)

(1.33)

(6.54)

(1.15)

0.62

9.98

1.08

10.22

1.27

(0.52)

(9.32)

(0.52)

(9.86)

(1.22)

2.14

10.19

1.55

9.27

1.23

(1.71)

(8.84)

(1.43)

(6.94)

(0.98)

0.87

10.55

1.69

7.71

1.05

(1.02)

(9.69)

(1.49)

(7.38)

(0.87)

*The figures in parentheses are based on Mishkin estimates, (a) The period is from 1971:4 to 1990:4. (c) The period is from 1971:4 to 1990:4. (b) The period is from 1971:4 to 1979:4. (d) The period is from 1969:4 to 1990:4.

Interest rates and budget deficits

24

THE ESTIMATES OF THE MEDIUM-TERM PRE-TAX EX-ANTE REAL INTEREST RATES Given the importance of long-term ex-ante real interest rates in economic decision making, particularly those relating to business, it would be useful to provide estimates of such rates. But as already discussed in Chapter 2, this is quite difficult regardless of which of the three methods (excluding the survey method, of course) we use. As a compromise we present estimates for the medium-term rates which in our case implies returns on bonds of three to five years’ maturity. Since the autoregressive method provides the most reliable estimates, the discussion will be based on the estimates using this procedure. However, for the sake of comparison, estimates using Mishkin’s method and the returns from the index-linked bonds for the U.K. are also presented. The data on the nominal medium-term interest rates as well as the other variables were again collected from the various issues of the OECD Financial Statistics. The exact details of the interest rate series used are given in Table 3.2. The period covered is not the same as for the short-term rates in some cases because of the unavailability of the relevant data. The means and the standard errors of the estimated values of the pre-tax medium-term ex-ante interest rates, based on the autoregressive and Mishkin procedures, are given in Table 3.3. We note that for all countries in our sample, except for Australia, the autoregressive estimates were obtained for the post-1967 period. Due to data limitations, the Mishkin estimates for Australia, France, Belgium and Japan could be obtained for the post-1971 period. For other countries, the Mishkin estimates cover the 1967:1–1990:4 period. Before analysing these estimates in detail, a word is in order about the relative magnitudes of the two estimates. A comparison with Table 3.1 shows that the two estimates are not as close as those for the short-term rates. However, with the exception of a few cases, the two estimates are still relatively close. But more importantly, the general inference suggested by the two estimates is the same. For example, both estimates suggest that for the U.S.A. the rate was higher in the early 1970s than in the late 1970s and further that it was higher in the first half of the 1980s than in the second half. The following discussion is based on the autoregressive estimates. The results of Table 3.3 confirm the findings about the ex-ante real short-term rates, namely, that the medium-term real rates were higher in the 1980s compared to the 1960s and 1970s. It is interesting to note though, that the rates in the second half of the 1980s were somewhat lower than in the first half. A notable exception is Germany where the rate has remained relatively stable, as also reported by Blanchard and Summers (1984) for the period earlier than 1984:2. However, across the countries there was considerable variation. Thus, in the second half of the 1980s, the mean real medium-term interest rate in Australia was as high as 11.28 per cent while in Japan it was only 4.90 per cent. The mean rate was 8.86 per cent in Europe and 7.71 per cent in the U.S.A. during the same period. A comparison between Japan and the U.S.A. shows that the U.S. rate exceeded the Japanese rate by as much as 281 basis points in the 1985–90 period. But in terms of the variability of these mean rates, we observe a different pattern. By the second half of the 1980s not only had the degree of variability been reduced in all but two cases, Japan

Estimates and behaviour of ex-ante real interest rates

25

and Sweden, but also it had become relatively uniform across the countries. Thus the value of the standard deviation varied from a high of 1.27 to a low of 0.73. As expected, these mean rates mask important intertemporal differences as can be readily ascertained from Figure 3.3. A detailed country-by-country comparison, along the lines of that done for the pre-tax ex-ante short-term real interest rate, would reveal important intra- and inter-country differences. This is left as an exercise for the reader. But a comparison of the short- and medium-term pre-tax

Figure 3.3 Medium-term pre-tax exante real interest rates

Interest rates and budget deficits

26

ex-ante real rates for the latest period in the sample, namely 1990:4, is instructive. The relevant information is given in Table 3.4. This table reveals a number of important characteristics of the most recent experience. First, the lowest medium-term real rate was experienced by Japan, followed by the U.S.A., and in contrast the rest of the countries experienced relatively high rates. Thus, the mean rate for Europe was 9.93 per cent as against a rate of only 5.97

per cent for Japan and 6.90 per cent for the U.S.A. A comparison of Canada, the U.K. and the U.S.A. is also striking. Thus, while the rates for Canada and the U.K. are virtually the same, they both exceed the U.S. rate by over 250 basis points, thus suggesting considerable scope for independent movement of the domestic rates. It is also important

Estimates and behaviour of ex-ante real interest rates

27

to point out that over time there has been a fundamental change in the relative positions of these countries.

Thus, Blanchard and Summers (1984) reported that in 1984:2 the U.S.A. had the highest real medium-term rate in a sample of six countries, but our Table 3.4 shows that by 1990:4, the U.S.A. had one of the lowest rates among these countries. The second characteristic of this table is the behaviour of the medium rates relative to that of the short rate. For six of the countries in our sample and for 1984:2 Blanchard and Summers (1984) reported that the medium-

Interest rates and budget deficits

28

term real rates were at least as high as the short-term real rates. It is interesting to note that the same cannot be said for 1990:4. In particular, this is no longer the case for Japan and the U.K., although it still holds true for the other four countries, namely France, Canada, Italy and the U.S.A. For the other five countries in our sample, the medium-term real rate exceeds the short-term real rate in Australia, Belgium and the Netherlands, but not in Canada and

Estimates and behaviour of ex-ante real interest rates

29

Sweden. A comparison of Canada and the U.S.A. is particularly revealing. Thus, in Canada the medium-term rate falls short of the short-term rate by almost 100 basis points, whereas it exceeds by 76 basis points in the U.S.A., thus suggesting a difference of 176 basis points. These differences clearly suggest, further, that just as in the case of the short-term real rate, the countries in our sample do not display identical behaviour with respect to the medium rate either.

Interest rates and budget deficits

30

Table 3.4 Short-term and medium-term pre-tax exante real interest rates for 1990:4 Country

Short rate

Medium rate

Australia

10.35

12.21

Belgium

7.07

9.98

Canada

10.37

9.34

France

9.02

10.57

Germany

7.48

8.47

Italy

9.69

10.56

Japan

7.04

5.97

Netherlands

8.20

8.43

Sweden

12.00

11.74

U.K.

11.92

9.75

6.14

6.90

U.S.A.

As mentioned in Chapter 2, rates of return on index-linked bonds can be used as a direct measure of ex-ante real interest rates, although there are serious shortcomings of such data. For our sample of countries, such data are available only for the U.K. The yields on the index-linked bonds cannot be compared with those estimated by other methods because of the differences in maturity, assumptions about the future rate of inflation and so on. However the information that we have since 1981 leads to similar

Estimates and behaviour of ex-ante real interest rates

31

Figure 3.4 Real rates as index-linked bonds conclusions. For example, if we consider index-linked bonds of over 5 years’ maturity, we find that the mean real yield was 3.64 per cent during the late 1980s as against the mean of 3.006 during the early 1980s. The standard deviation, on the other hand, was 0.33 and 1.29 for the two periods, respectively, suggesting greater volatility during the earlier period. If we consider the real yields, assuming a 5 and 10 per cent constant rate of inflation, on index-linked bonds of 5 or less years’ maturity estimated by our autoregressive scheme, we find that while the later estimates are much higher, the general behaviour of the three sets of estimates is quite similar. These estimates are shown in Figure 3.4. The data in this figure represent the average gross redemption yield in the last week of each quarter and were collected from the Financial Times. But these rates can vary widely. Thus, according to the Financial Times, 14/15 November 1992, the average gross redemption yield on index-linked bonds of up to 5 years’ maturity, assuming a 5 per cent rate of inflation, varied between a low of 2.25 per cent and a high of 5.06 per cent, a difference of over 124 per cent. If the assumption about expected inflation is changed to 10 per cent, this difference rises to 182 per cent. Thus, the reported ex-ante yields on index-linked bonds need to be treated with extreme caution as indicators of actual ex-ante real interest rates. ESTIMATES OF POST-TAX EX-ANTE REAL INTEREST RATES Given the importance of after-tax real interest rates in economic decision making, this section presents some estimates for such rates. The basic requirement in calculating such rates is the data on marginal tax rates on interest income. Unfortunately such data are not easy to obtain. We have only two sets of data at our disposal. The first is the time series data for the U.S.A. supplied by Tanzi. And the second is the average data for the period 1971–81, as given in Tanzi (1984) for eight countries. The use of the average data poses

Interest rates and budget deficits

32

two problems. One is that it masks intertemporal variations even for the period 1971–81. But the other and more serious problem is that it implies assuming that the tax rates were the same in the other periods covered in the study, a not very plausible assumption. But given the enormity of the task involved in the calculation of tax rates for such a large number of countries, we must make do with what we have, but keeping in mind these limitations while interpreting the reported estimates. This said, the estimated post-tax exante real short-term and medium-term rates are given in Tables 3.5 and 3.6, respectively. In order to bring out the comparison between the nominal, the pre-tax and the post-tax real interest rates, we have plotted them in Figure 3.5 for the short-term, based on the

Table 3.5 Mean and standard deviation of post-tax ex-ante real short-term interest rates: auto and Mishkin estimates* Country

Canada France Germany Italy Japan Netherlands U.K. U.S.A.

1967:3– 1990:4

1967:3– 1969:4

1970:1– 1979:4

1980:1– 1984:4

1985:1– 1990:4

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

6.06

2.69

4.46

0.93

4.15

1.83

8.93

2.15

7.55

1.54

(6.04)

(2.67)

(4.29)

(0.66)

(4.13)

(1.78)

(8.93)

(2.22)

(7.55)

(1.38)

4.42

1.53

3.61

1.11

3.42

1.17

6.15

1.22

5.06

0.60

(4.44)

(1.53)

(3.60)

(0.98)

(3.37)

(1.13)

(6.36)

(1.02)

(4.97)

(0.53)

3.04

1.59

1.67

1.24

2.71

1.71

4.18

1.40

3.22

0.95

(3.03)

(1.46)

(1.59)

(0.94)

(2.72)

(1.51)

(4.29)

(1.20)

(3.11)

(0.83)

5.65

2.53

2.14

0.44

4.23

1.75

8.66

1.39

6.98

0.65

(5.63)

(2.48)

(1.99)

(0.21)

(4.31)

(1.81)

(8.63)

(0.97)

(6.86)

(0.53)

4.91

1.76

4.76

1.10

4.65

2.00

6.02

1.56

4.49

1.34

(4.89)

(1.49)

(4.55)

(0.59)

(4.65)

(1.83)

(5.97)

(1.10)

(4.51)

(0.95)

3.73

2.24

2.86

1.56

2.85

2.70

4.94

1.63

4.55

1.07

(3.64)

(2.18)

(2.46)

(1.30)

(2.64)

(2.44)

(5.30)

(1.63)

(4.42)

(0.89)

5.25

2.23

4.45

0.67

3.69

1.94

6.36

1.42

7.28

1.43

(5.27)

(1.97)

(3.81)

(0.27)

(3.76)

(1.42)

(6.58)

(0.96)

(7.29)

(0.89)

4.26

1.69

3.60

0.51

3.15

1.02

6.62

1.55

4.42

0.72

(4.19)

(1.66)

(3.30)

(0.48)

(3.10)

(1.07)

(6.57)

(1.34)

(4.40)

(0.54)

*The figures in parentheses are those based on Mishkin procedure.

Estimates and behaviour of ex-ante real interest rates

33

Table 3.6 Mean and standard deviation of post-tax ex-ante real medium-term interest rates: auto and Mishkin estimates* Country

Canada France

a

Germany Italy Japan

b

Netherlands U.K. U.S.A.

1967:2– 1990:4

1967:2– 1974:4

1975:1– 1979:4

1980:1– 1984:4

1985:1– 1990:4

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

6.22

1.94

4.49

0.73

5.15

1.11

8.77

1.28

7.23

0.72

(6.02)

(1.76)

(4.71)

(0.73)

(4.81)

(0.88)

(7.97)

(1.75)

(7.08)

(0.80)

a

a

5.85

1.43

b

3.99

0.46

4.65

0.53

7.15

0.77

6.78

0.60

(4.45)

(1.06)

(4.76)

(0.68)

(4.39)

(0.46)

(5.55)

(0.85)

(3.42)

(0.72)

4.19

0.76

4.21

0.71

3.57

0.67

4.65

0.67

4.29

0.66

(4.02)

(0.89)

(4.40)

(0.56)

(3.15)

(0.70)

(4.51)

(0.81)

(3.83)

(0.90)

5.95

2.30

3.77

1.30

5.35

1.13

8.96

1.76

6.74

0.79

(5.01)

(1.48)

(4.23)

(0.75)

(4.46)

(0.42)

(6.94)

(1.74)

(4.85)

(1.11)

5.24

1.34

4.75

1.08

5.47

1.41

6.40

0.87

4.53

1.15

(4.60)

(1.01)

(5.01)

(0.53)

(3.91)

(1.18)

(5.19)

(0.32)

(4.32)

(1.15)

4.95

1.08

4.38

0.86

4.34

0.93

6.08

0.86

5.25

0.74

(4.60)

(1.11)

(4.21)

(0.62)

(3.59)

(0.68)

(5.79)

(1.00)

(4.92)

(0.93)

5.78

1.69

4.85

1.19

4.71

1.90

7.13

1.16

6.75

0.99

(5.23)

(1.45)

(4.91)

(1.15)

(3.73)

(1.38)

(5.78)

(1.02)

(6.43)

(0.73)

5.17

1.77

3.69

0.56

4.20

0.66

7.71

1.40

5.77

0.82

(4.87)

(1.46)

(3.79)

(0.62)

(3.85)

(0.77)

(6.86)

(1.13)

(5.44)

(0.64)

*The figures in parentheses are those based on Mishkin estimates. (a) The period is from 1971:4 to 1990:4. (b) The period is from 1969:4 to 1990:4.

Interest rates and budget deficits

34

Figure 3.5 Nominal, pre- and post-tax real short-term rates Mishkin method, and in Figure 3.6 for the medium-term using the autoregressive method. To get some idea whether the use of the average tax rate for the period 1971–81 for the entire period makes any significant difference, we have plotted the after-tax real ex-ante short-term interest rates for the U.S.A. using three methods in Figure 3.7. In these figures RTMISH and RTAUT represent the post-tax estimates by the Mishkin and autoregressive methods, respectively.

Estimates and behaviour of ex-ante real interest rates

35

Before turning to a detailed comparative analysis of these estimates, it is best to deal with the U.S. evidence first, because of the additional evidence we have on this one country. Figures 3.5 to 3.7 for the U.S.A. show clearly that the post-tax estimates of real ex-ante short-term rate are sensitive to the two alternate tax rates used in these estimates. However, the general direction of the estimates based on the autoregressive and Mishkin methods is fairly similar. An interesting feature of Figure 3.7 is that the post-tax shortterm real rate in the U.S.A. was negative for a good part of the period if measured using the survey data on inflation expectations, an inference not supported by the other two estimates. This brings into serious question whether the use of the survey method is really appropriate. We now consider the results in Tables 3.5 and 3.6 in greater detail. The short-term as well as the medium-term after-tax rates were positive for all the countries in each of the sub-periods. Like the pre-tax rates, the post-tax rates were also lower in the second half of the 1980s compared to the first half. And they were the lowest in the 1970s. While no attempt is made to carry out the same detailed inter-country comparison of these rates, nevertheless a look at Figures 3.5 and 3.6 is instructive. Each graph shows three rates: the nominal rate, the pre-tax real ex-ante rate and the after-tax real ex-ante rate. Ignoring for the moment the lines representing the nominal rate, it can be seen that neither of the two rates was negative at any time included in the sample. However, the pre-tax and post-tax rate differences are not necessarily the same for each of the eight countries. Consider the more extreme cases. In Japan, the difference between the two rates was minimal, presumably reflecting low tax rates. On the other hand, this difference was quite marked for France and Italy. It is also interesting to note that, except for Japan, the difference between the pre- and post-tax rates varied considerably over the period in most of the countries, suggesting that pre-tax ex-ante real interest rates may not always be an accurate guide to the behaviour of the corresponding post-tax rates; this holds true both with respect to the level as well as the variability of the rates.

Interest rates and budget deficits

36

Estimates and behaviour of ex-ante real interest rates

37

Interest rates and budget deficits

38

Estimates and behaviour of ex-ante real interest rates

39

Figure 3.6 Nominal, pre- and post-tax real medium-term rates THE ROLE OF NOMINAL INTEREST RATES AS A SIGNAL FOR THE BEHAVIOUR OF EX-ANTE REAL INTEREST RATES One way to get insight into the process generating ex-ante real interest rates is to see the extent to which nominal interest rates serve

Interest rates and budget deficits

40

as a guide to the behaviour of the unobserved expected real interest rates. We can get some idea about this issue by looking at the simple correlations between the nominal interest rates and the ex-ante real interest rates given in Table 3.7 and their temporal behaviour in Figures 3.5 and 3.6. Not unexpectedly, the correlations and the movements of the post-tax real rates and the nominal interest rates

Estimates and behaviour of ex-ante real interest rates

41

are not as close as those of the pre-tax real rates and the nominal rates. Concentrating on the pre-tax rates only, the results are quite striking. It would seem that, with few exceptions, the two rates have moved closely so that movements in nominal rates have served as a reliable signal for the movements in the expected real rates. The most

Interest rates and budget deficits

42

important exception is Japan in the 1960s until the mid-1970s, when the correlation was in fact negative. This is not surprising, because during this period the medium rates were highly regulated. France and the U.S.A. also provide some interesting exceptions. Thus, in France, the correlation was in fact negative. Again, this is not surprising, because during this period the medium rates were highly

Estimates and behaviour of ex-ante real interest rates

43

Figure 3.7 After-tax short-term real rate: survey method Table 3.7 Correlations between nominal and exante real interest rates Short-term rate Country

r

(NI,RHMISHK)

r

Medium-term rate

(NI,RTMISHK)

r

(NI,RAUT)

r

(NI,RTAUT)a

Australia 1967:3–1990:4

0.99

0.96

1967:3–1969:4

0.99

1970:1–1979:4

0.98

0.88

1980:1–1984:4

0.99

0.91

1985:1–1990:4

0.99

0.88

1967:3–1990:4

0.97

0.86

1967:3–1969:4

0.99

0.57

1970:1–1979:4

0.97

0.79

1980:1–1984:4

0.99

0.93

1985:1–1990:4

0.99

0.71

Belgium

Canada 1967:3–1990:4

0.98

0.98

0.97

0.95

Interest rates and budget deficits

44

1967:3–1969:4

0.99

0.98

0.74

0.64

1970:1–1979:4

0.99

0.98

0.96

0.94

1980:1–1984:4

0.99

0.99

0.97

0.95

1985:1–1990:4

0.99

0.99

0.97

0.96

Short-term rate Country

r

(NI,RHMISHK)

r

Medium-term rate

(NI,RTMISHK)

r

(NI,RAUT)

r

(NI,RTAUT)a

France 1967:3–1990:4

0.96

0.90

0.89

0.52

1967:3–1969:4

0.99

0.98

0.90

0.59

1970:1–1979:4

0.99

0.96

0.85

0.90

1980:1–1984:4

0.98

0.94

0.95

0.81

1985:1–1990:4

0.98

0.95

0.96

0.26

1967:3–1990:4

0.98

0.96

0.89

0.72

1967:3–1969:4

0.95

0.93

0.90

0.74

1970:1–1979:4

0.99

0.98

0.85

0.65

1980:1–1984:4

0.99

0.98

0.95

0.88

1985:1–1990:4

0.99

0.97

0.96

0.91

1967:3–1990:4

0.97

0.94

0.92

0.81

1967:3–1969:4

0.95

0.82

0.18

0.12

1970:1–1979:4

0.99

0.99

0.74

0.58

1980:1–1984:4

0.95

0.87

0.98

0.96

1985:1–1990:4

0.98

0.94

0.84

0.66

1967:3–1990:4

0.94

0.92

0.64

0.60

1967:3–1969:4

0.98

0.97

−0.47

−0.57

1970:1–1979:4

0.99

0.99

0.81

0.79

1980:1–1984:4

0.99

0.98

0.73

0.89

1985:1–1990:4

0.95

0.94

0.94

0.92

0.97

0.95

0.83

0.72

Germany

Italy

Japan

Netherlands 1967:3–1990:4

Estimates and behaviour of ex-ante real interest rates

45

1967:3–1969:4

0.99

0.97

0.81

0.70

1970:1–1979:4

0.99

0.99

0.71

0.62

1980:1–1984:4

0.99

0.98

0.96

0.93

1985:1–1990:4

0.99

0.99

0.92

0.87

Sweden 1967:3–1990:4

0.99

0.95

1967:3–1969:4

0.98

0.65

1970:1–1979:4

0.99

0.76

1980:1–1984:4

0.96

0.87

1985:1–1990:4

0.99

0.98

U.K. 1967:3–1990:4

0.93

0.87

0.78

0.64

1967:3–1969:4

0.95

0.87

0.87

0.76

1970:1–1979:4

0.99

0.97

0.69

0.57

1980:1–1984:4

0.98

0.96

0.89

0.80

1985:1–1990:4

0.98

0.96

0.89

0.83

1967:3–1990:4

0.97

0.95

0.95

0.91

1967:3–1969:4

0.95

0.91

0.68

0.44

1970:1–1979:4

0.98

0.98

0.86

0.74

1980:1–1984:4

0.97

0.94

0.85

0.76

1985:1–1990:4

0.95

0.81

0.97

0.95

U.S.A.

(a) Time periods as specified in Table 3.6.

regulated. France and the U.S.A. also provide some interesting exceptions. Thus, in France, the correlation is 0.66 in the period 1966–76 for the medium rate, which jumped to 0.92 during 1980:1 to 1984:4, but then went down to 0.67 in the latter half of the 1980s. For the U.S.A., just like France, the correlation was lower during the late 1960s and early 1970s, but then showed a continuous increase going as high as 0.97 during the second half of the 1980s.

Interest rates and budget deficits

46

STATISTICAL BEHAVIOUR OF EX-ANTE REAL INTEREST RATES Before proceeding to estimation and testing of the long-run relationships about the behaviour of ex-ante real interest rates, we have to examine the univariate statistical properties of these series. More specifically, we need to examine whether ex-ante real interest rates tend to revert back to some long-term equilibrium path following a shock or whether they tend to follow a random walk process. If real rates follow random walk the effect of temporary shocks such as an oil price increase or a change in the conduct of monetary policy (such as the change in the Federal Reserve operating procedure in October 1979) will be permanent. If real rates do not follow a random walk process these shocks will have a temporary effect on these rates, and after a long period of time they revert back to their long-run equilibrium value. The standard econometric theory is based on the assumption that the underlying economic time series are stationary with constant unconditional mean and variance over time. This implies that shocks will generate transitory fluctuations around a relatively stable trend path. If economic time series are non-stationary, a regression of one against another can result in spurious results. In this case, ordinary least squares does not yield a consistent parameter estimator and the Gauss-Markov theorem does not hold.1 Over the last century, most economic variables have experienced significant shifts in their mean and variance so that their first two moments can no longer be characterized as being constant. This phenomenon has resulted in a series of studies on stationary and spurious regressions.2 The seminal study by Nelson and Plosser (1982) found that most macroeconomic variables behave like random walks. The Nelson and Plosser study was followed by a series of empirical studies which basically confirmed the original findings.3 Most of these studies employ the unit root tests introduced by Dickey and Fuller.4 The problems of estimation and statistical inference in the presence of non-stationary variables are discussed by Phillips (1986), Granger and Newbold (1974), Nelson and Kang (1981), and Nelson and Plosser (1982). There seem to be two basic reasons for an overwhelming support for the hypothesis that most macroeconomic variables appear to be random walks, or at least appear to have random walk components rather than being trend reverting. First, small sample size used in estimation and testing for the presence of unit root or non-stationarity in a series. It is entirely possible that economic variables behave like a random walk with growing mean and variance within a small time interval. As time lapses, however, the variables may revert to their long-run equilibrium path.5 Second, even when long time series are available, the presence of a structural break or shift in a series can make it appear to be non-stationary using standard tests when, in fact, it is stationary. The influential study by Perron (1989) shows that the standard tests of unit root hypothesis cannot reject the unit root hypothesis if the true data-generating mechanism is that of stationary fluctuations around a trend function which contains a one-time break. Perron derived test statistics which allow for the presence of breaks in the series, applied them to the data set used by Nelson and Plosser and found that most macroeconomic time series are not characterized

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by the presence of a unit root and their fluctuations are indeed stationary around a deterministic trend function. In what follows, we first discuss the unit root testing procedures and then apply them to the ex-ante real rate series derived in the previous sections. TESTING THE ORDER OF INTEGRATION OF ECONOMIC TIME SERIES In order to estimate and test the equality of real rates across different countries, we first have to examine the order of integration of the real rate series. For this purpose, we proceed as follows. Assume that the real rate series Yt can be described by the following data generating process: (1) where ut is a well behaved random disturbance, and T is a time trend. Equation (1) tests two possible hypotheses concerning the behaviour of the variable Yt. First, Yt has been growing over time because it has a positive trend (β1>0), but would be stationary after detrending (ρ0 and ρ=1). In this case, the presence of Yt in standard regressions can produce spurious results.6 If ρ=1, the variable Yt is said to contain a unit root. Yt is said to be integrated of order 1 if it has a unit root, but becomes stationary if differenced once. If Yt is integrated of order 1, its variance increases over time. Dickey and Fuller (1979) considered the problem of testing for the presence of unit root in the time series Yt by testing the null hypothesis of H0: ρ=1 versus the alternative hypothesis of stationarity around a deterministic trend; i.e., H1: ρ0 Equation (13) can be rewritten to allow us to examine the effect of a given change in either Cg or Ig while keeping G constant. In other words, we can examine the effect of a change in the composition of G while keeping the total constant. This can be done by using the identity (14) and substituting for

or

in (13). Substituting, say, for

, we get (15)

From (15), we can estimate the effect of a change in Cg while keeping G constant. This is given by

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With G constant,

Since the terms in the parentheses are positive, we have that . In so far as the role of crowding out is concerned, the implications of (15) are rather interesting. It not only enables us to examine the role of a given change in G, which is the approach followed in other studies, but it also allows us to examine the effects of a change in the composition of a given G. To the extent that private expenditures are crowded out to different degrees by the two types of government expenditures, even if the total government expenditure does not change, the results can provide useful policy implications.2 Having derived the determinants of re(t), the determinants of the other two terms in equation (1) are assumed to follow Sargent’s specification. The spread between the market rate and the equilibrium rate (rm(t)–re(t)) is determined, following Wicksell, by the rate of growth of real money supply. Assuming linearity, we thus have:3 (16) where m is the rate of growth of real stock of money. The last term of equation (1) is assumed to depend, linearly and positively, on the expected rate of inflation, so that (17) where πe is the expected rate of inflation. We can now derive two alternate reduced-form equations for the nominal interest rate rn(t): one by substituting (13), (16) and (17) into (1) and the other one by substituting (15), (16) and (17) into (1). For reasons already given, our preference is for equation (15). Consequently, we only give the equation obtained by substituting (15), (16) and (17) into (1), namely, (18)

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Since our primary concern is with assessing the role of budget deficits on interest rates, we now incorporate budget deficit in question (18) explicitly. By definition, DEFt=Gt−Tt where DEF is budget deficit and T is tax revenue. Substituting for G (i.e. (Ig+ Cg)) and T(Sg=T−Cg or T=Sg+Cg) we obtain

. Equation (18) can be

expressed in terms of DEF. Through appropriate substitutions for Sg,

Ig and

we can get:

We can now see how the Ricardian equivalence proposition can be tested from (19). If ∂rn(t)/∂DEFt=0, we must have {1+λs(Σbi)}/Dλ =0. Because Dλ>0 since d>0, θ