Peter Hackl (Ed.)

Statistical Analysis and Forecasting of Economic Structural Change

With 98 Figures

Springer-Verlag Berlin Heidelberg GmbH

Professor Dr. Peter Hackl Institut fUr Statistik Wirtschaftsuniversitat Augasse 2-6 A-1090 Wien

ISBN 978-3-662-02573-4

Library of Congress Cataloging-in-Publication Data Statistical analysis and forecasting of economic structural change 1 Peter Hackl (ed.). Includes bibliographical references. ISBN 978-3-662-02573-4 ISBN 978-3-662-02571-0 (eBook) DOI 10.1007/978-3-662-02571-0 I. Economic forecasting --Statistical methods. l. Hackl, Peter. HB3730.S735 1989 330'.01 '51--dc20

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad­casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.

© 1989 Springer-Verlag Berlin Heidelberg Originally published by Springer-Verlag Berlin Heidelberg New York Tokyo in 1989 Softcover reprint of the hardcover 1 st edition 1989 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

2142/7130-543210

Preface

In 1984, the University of Bonn (FRG) and the International Institute for Applied System Analysis (IIASA) in Laxenburg (Austria), created a joint research group to analyze the relationship between economic growth and structural change. The research team was to examine the commodity composition as well as the size and direction of commodity and credit flows among countries and regions. Krelle (1988) reports on the results of this "Bonn-IIASA" research project.

At the same time, an informal IIASA Working Group was initiated to deal with prob­lems of the statistical analysis of economic data in the context of structural change: What tools do we have to identify nonconstancy of model parameters? What type of models are particularly applicable to nonconstant structure? How is forecasting affected by the presence of nonconstant structure? What problems should be anticipated in applying these tools and models? Some 50 experts, mainly statisticians or econometricians from about 15 countries, came together in Lodz, Poland (May 1985); Berlin, GDR (June 1986); and Sulejov, Poland (September 1986) to present and discuss their findings. This volume contains a selected set of those conference contributions as well as several specially invited chapters.

After a euphoric period in the 1960s, model builders in economics became aware of a need of model diagnostics and, in particular, for methods to detect - and cope with - structural changes. Statisticians' interest grew slowly after a few early contributions, especially R.E. Quandt's (1958) paper on switching regression. Related problems were discussed and adaptable methods were developed in areas such as probability theory (the change point problem), continuous sampling inspection (the CUSUM technique), or engi­neering (recursive estimation, filtering). Hackl and Westlund's (1985) bibliography, Sta­tistical Analysis of Structural Change, contains some 300 titles; in a revised version to be published in 1989, the number of entries has increased by about 100 papers.

Nevertheless, in practical model building exercises, the methods recommended by statisticians seem not to be extensively used. Reasons for this might be the scarcity of corresponding computer programs and also the lack of a systematic survey. Broemeling and Tsurumi's (1986) book is the most comprehensive volume on the subject, in spite of the fact that it is based on a Bayesian paradigm. The same basis underlies a 1982 supplement of the Journal of Econometrics, edited by Broemeling, which also covers a broad area of the subject. Specialized books have been published on multiphase regression

vi Statistical Analysis and Forecasting of Economic Structural Change

(Schulze, 1986), spline function-based models (Poirier, 1976), and the analysis of residuals (Hackl, 1980). Several volumes contain special sections on model building, such as those by Broemeling (1985) and by Kramer and Sonnberger (1986). Accessible bibliographies have been compiled by Shaban (1980) and by Johnson (1977, 1980).

The present volume contains an introduction and three sections:

I. Introduction

The introductory chapter, "What can statistics contribute to the analysis of economic structural change?" by G.J. Anderson and G.E. Mizon, discusses not only the role of statistics in the detection and assimilation of structural changes, but also the relevance of respective methods in the evaluation of econometric models. Trends in the development of these methods are indicated, and the contributions to the present volume are put into a broader context of empirical economics to help to bridge the gap between economists and statisticians.

II. Identification of Structural Change

The chapters combined under this heading are concerned with the detection of param­eter nonconstancy. The procedures discussed range from classical methods, such as the CUSUM test, to new concepts, particularly those based on nonparametric statistics. Sev­eral chapters assess the conditions under which these methods can be applied and their robustness under such conditions.

In "Testing for structural change in simultaneous equation models", A.C. Harvey and G.D.A. Phillips develop exact tests to detect changes in the coefficients of structural equa­tions based upon k-class estimation. B. Schips and Y. Abrahamsen demonstrate in a Monte Corlo case study ("Specification and stability tests versus jackknifing: Some illustrative examples") the superiority of jackknifing-type criteria over classical inference statistics, given nonconstancy of linear model parameters. W. Kramer shows in Chapter 4, "The robustness of the Chow test to autocorrelation among disturbances", that independence of the error terms is crucial for deviations between true and nominal significance level.

P. Hackl and W. Katzenbeisser compare, in "Tests against nonconstancy in linear models based on counting statistics", various tests and conclude that some simple ones are strong competitors to the well-known CUSUM procedure. M. Huskova and P.K. Sen in "Nonparametric tests for shift and change in regression at an unknown time point", cover various nonparametric and robust tests available and suggest an adaptive procedure that fulfills an (asymptotic) optimality criterion. H. Tsurumi's "Detection of join point in regression models" reviews methods for estimating the join point and proposes a new procedure based on the mean squared errors of post-sample forecasts.

Tools to characterize parameter changes in linear regression models in various pat­terns of nonconstancy are studied by A.H. Westlund and B. Tornkvist in Chapter 8: "On the identification of time of structural changes by MOSUM-SQ and CUSUM-SQ proce­dures". Conditions for the CUSUM-SQ test to have nontrivial local power are given by W. Ploberger in "The local power of the CUSUM-SQ test against heteroscedasticity". J. Praagman's "Bahadur efficiency of tests for a shift in location of normal populations"

Preface vii

treats two generalized forms of the most relevant test statistics.

Finally, in Chapter 11, Z. Wasilewski demonstrates "The use of graphical displays in the analysis of structural change" for the investigation of regression residuals.

IlL Model Building in the Presence of Structural Change

This section addresses models that are in some sense generalizations of constant-parameter models, so that they can assimilate structural changes.

In Chapter 12, "Adaptive estimation and structural change in regression and time series models", J. Ledolter reviews heuristic and model-based approaches to adaptive estimation of regression parameters and discusses in detail the case where the parameters follow ARMA processes. The use of exponential weights for adaptive estimation is treated in "An adaptive method of regression analysis" by Y.P. Lukashin. J. Dziechciarz, in "Changing and random coefficient models. A survey" , reviews comprehensively the related literature (about 200 references).

P.M. Robinson discusses, in "Nonparametric estimation of time-varying parameters", the construction and properties of a kernel-based estimator of the regression coefficient. V.V. Fedorov, in "Latent variables in regression analysis", treats two types of regression models with unobservable variables, together with reformulations that can be handled by traditional regression analysis techniques.

L.D. Broemeling returns in Chapter 17, "Structural change and time series analysis", to demonstrate a Bayesian approach in analyzing a time series model for data so that the trend or the auto covariance function changes at an unknown time point. H. Tong, in "Thresholds, stability, nonlinear forecasting, and irregularly sampled data", examines threshold models, i.e., global models composed of submodels for areas delineated by thresh­olds. "Forecasting in situations of structural change: A general approach" , by F .X. Diebold and P. Pauly, presents a method of combining forecasts to compensate for poor primary forecasts on the basis of time-varying weighting. J. Kleffe, in "Updating parameters of linear change point models", discusses an algorithm for efficiently updating the residual sum of squares applied in two-phase regression with a shifting change point.

IV. Data Analysis and Modeling

This section deals with real-life structural change situations.

P.K. Sen, in "Change point problem relating to the poverty structure", constructs and analyzes poverty indices, based on income distribution. T. Ozaki and V.H. Ozaki, in "Statistical identification of nonlinear dynamics in macroeconomics using nonlinear time series models", describe a model representing both Keynesian and monetarist viewpoints vis a vis the dynamics of the Hicksian IS-LM concept by a difference in model parameters. A. Keller's Chapter 23, "Econometrics of technical change: Techniques and problems", surveys studies concerning "technical progress" - an essential notion of economic growth with implications and pitfalls for data observations, model specifications, and estimation procedures.

On the basis of interest rates for Austria, W. Polasek demonstrates, in "Local autore­gression models for detection of changes in causality" , an approach to analyze nonstation-

viii Statistical Analysis and Forecasting of Economic Structural Change

arity by applying local stationary autoregressive processes.

Finally, in Chapter 25, J.-M. Dufour presents an empirical study, "Investment, tax­ation, and econometric policy evaluation: Some evidence of the Lucas critique", which discusses Lucas's arguments that parameters in econometric relationships reflect economic agents' decision rules.

It is hoped that this volume will be useful and stimulating to both statisticians and economists.

I wish to thank the former deputy project leader, Dr. Anatoly Smyshlyeav, now back in Moscow, the instigator of this project, for his encouragement and interest; Professor Wilhelm Krelle, for his help and patience; the scientists who contributed by participating in the workshops, by delivering chapters for this volume, or by acting as referees, for their efforts; and both the International Institute for Applied Systems Analysis and the Austrian Ministry of Science and Research (BMfWF) for their financial support.

References

Peter Hackl Institut fiir Statistik,

Wirtschaftsuniversitiit Wien, and IIASA, Laxenburg

Broemeling, L.D. (1985), Bayesian Analysis of Linear Models. New York: M. Dekker. Broemeling, L.D. and Tsurumi, H. (1986), Econometrics and Structural Change. New

York: M. Dekker. Hackl, P. (1980), Testing the Constancy of Regression Relationships over Time. Gottingen:

Vandenhoeck & Ruprecht. Hackl, P. and Westlund, A.H. (1985), Statistical Analysis of "Structural Change": An

Annotated Bibliography. Collaborative Paper CP-85-31. Laxenburg: International Institute for Applied Systems Analysis.

Johnson, L.W. (1977), Stochastic parameter regression: An annotated bibliography. In­ternational Statistical Review, 45, 257-272.

Johnson, L.W. (1980), Stochastic parameter regression: An additional annotated biblio­graphy. International Statistical Review, 48, 95-102.

Kramer, W. and Sonnberger, H. (1986), The Linear Regression Model under Test. Heidel­berg: Physica.

Krelle, W. (Ed.) (1989), The Future of the World Economy: Economic Growth and Structural Change (Results ofthe Bonn-IIASA Research Project). Berlin: Springer.

Poirier, D.J. (1976), The Econometrics of Structural Change. Amsterdam: North-Holland. Quandt, R.E. (1958), The estimation of the parameters of a linear regression system

obeying two separate regimes. Journal of the American Statistical Association, 53, 873-880.

Schulze, U. (1986), Mehrphasenregression: Stabilitiitspriifung, Schiitzung, Hypothesenprii-fungo Berlin: Akademie-Verlag.

Shaban, S.A. (1980), Change point problem and two-phase regression: An annotated bibliography. International Statistical Review, 48, 83-93.

Foreword

As Professor Hackl has already pointed out in his preface, this work on statistical identifi­cation of economic structural change was originally conceived as p~t of a common research project in which the other part was concerned with economic analysis and forecasting of economic growth and structural change. For reasons beyond our control, these projects had to be separated. This was unfortunate for several reasons. The most important one is that the results of the statistical project were to have been applied and tested in the economic project, and the practical problems encountered in the economic project were to have been analyzed and solved in the statistical project. Although this ideal arrangement was not possible, we strove to compensate for this loss. Within the Sonderforschungsbereich 303 (Special Research Unit 303) at Bonn University, three research projects have been carried out. The corresponding research reports are given by C. Weihs (1987) ("Auswirkungen von Fehlern in den Daten auf Parameterschatzungen und Prognosen", in K.-A. Scheffer et al., Arbeiten zur Angewandten Statistik, Vol. 30. Heidelberg: Physica-Verlag); and by A. Kirchen (1988) ("Schatzung zeitveranderlicher Strukturparameter in 6konometrischen Prognosemodellen", Frankfurt/Main: Athenaum); the third project, performed by Mr. K6r6si, on latent variable approaches, is not yet completed. We were able to use these results for our research.

The economic research team consisted of a central group at Bonn University, composed offive scholars in 1985 and 1986 and two scholars in the first half of 1987, and collaborating groups in almost all important world market countries and international institutions. The results of their work are contained in The Future of the World Economy: Economic Growth and Structural Change, edited by Wilhelm Krelle and published by Springer-Verlag.

In Part I of that book, the forecasts to the year 2000 resulting from the solution of an econometric world model are given. This work was carried out by the central group: W. Krelle, H. Ross, and H. Welsch (all from the FRG); R. Dobrinsky (Bulgaria); 1. Szekely (Hungary); and J. Gajda and J. Sztaudynger (Poland). In Part II of the book, these fore­casts are collated with those made by the collaborating country groups: B. Hickman and P. Pauly (USA); S. Dubovsky and O. Eismont (USSR); C. Moriguchi (Japan); J. Donges, H. Klodt, K.-D. Schmidt, W. Krelle, and H. Sarrazin (FRG); J.-L. Brillet (France); M. Lan­desmann and A. Snell (UK); O. Panov and J. Djarova (Bulgaria); A. Czyzewski and W. Welfe (Poland); K. Zeman and 1. Sujan (Czechoslovakia); A. Simon (Hungary); and S. Schleicher (Austria). In Part III, world trade and the debt situation are analyzed in more detail by G. Erber (FRG); P. Pauly (USA); and J. Richtering (UNCTAD). In Part

x Statistical Analysis and Forecasting of Economic Structural Change

IV, some general and methodological problems related to economic growth and struc­tural change are dealt with by S. Menshikov and K. Klimenko (USSR); G. d'Alcantara (Belgium); I. Tchijov (USSR); J. Ceska (Czechoslovakia); and R. Dobrinsky (Bulgaria).

It is hoped that the results of the statistical group, headed by Professor Hackl and published in this book, can be used to improve the results obtained by the economic group within the framework of a new approach to the problem of economic growth and structural change, and vice versa.

Wilhelm K relle Institut fUr Gesellschafts- u.

Wirtschaft swissenschaften, Universitat Bonn

Contents

Preface v

Foreword ix

I Introduction 1

1 What Can Statistics Contribute to the Analysis of Economic Structural Change? 3

1.1 Introduction............ 3

1.2 A View of Econometric Modeling 6

1.2.1 A class of models 6

1.2.2 Model evaluation

1.2.3 Robustness: new data

1.2.4 Robustness: rival models

1.2.5 Model congruence ....

1.3 Models of Parametric Structural Change .

7

9

9

10

11

1.4 Detecting the Presence of Structural Change: Misspecification Tests 14

1.5 Detecting Breakpoints . . . . . 16

1.6 Assimilating Structural Change

1.7 Summary and Conclusions . . .

II Identification of Structural Change

17

18

23

2 Testing for Structural Change in Simultaneous Equation Models 25

2.1 Introduction................................ 25

xii Statistical Analysis and Forecasting of Economic Structural Change

2.2 Testing for Structural Change in Simultaneous Equation Models: Some Preliminary Results ........................ 26

2.3 Tests Based upon Two-stage Least Squares (2SLS) Estimation ....... 29

2.4 Tests Based upon Ordinary Least Squares (OLS) and Limited Information Maximum Likelihood (LIML) Estimation . . 32

2.5 Conclusions.................................... 34

3 Specification and Stability Tests versus Jackknifing: Some Illustrative Examples 37

4 The Robustness of the Chow Test to Autocorrelation among Distur-bances 45

4.1 Introduction . 45

4.2 Rejection Probabilities under Autocorrelation 47

4.3 A Numerical Example 49

4.4 Conclusion 51

5 Tests against Nonconstancy in Linear Models Based on Counting Statis-tics 53

5.1 Introduction..... 53

5.2 The Test Procedures

5.3 Distributional Properties.

5.3.1 Random variable Nn

5.3.2 Test statistics M and D

5.3.3 Other test statistics ..

5.4 The Power of the Tests against Trend Alternatives

5.4.1 Exact power functions ..

5.4.2 Monte Carlo experiments

5.4.3 Results ........ .-.

5.5 The Power of the Tests against Nonconstancy in R-Models .

5.5.1 Procedure

5.5.2 Results

5.6 Summary . . .

56

58

58

60

62

62

63

64

65

65

68

68

69

6 Nonparametric Tests for Shift and Change in Regression at an Unknown Time Point 71

6.1 Introduction.................................... 71

Contents xiii

6.2 Nonparametric Change Point Test for Shift: Location Known . . . . . . .. 73

6.3 Nonparametric Change Point Tests for Shift: Locations Unknown ...................... .

6.4 Nonparametric Change Point Tests for Constancy of Regression.

6.5 (jeneral Rer.narks . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Detection of Join Point in Regression Models

7.1 Introduction.................

7.2 Bayesian Predictive Density of the MSEF

7.3 Nur.nerical Example.

7.4 Concluding Rer.narks

76

81

83

87

87

88

91

94

8 On the Identification of Time for Structural Changes by MOSUM-SQ and CUSUM-SQ Procedures 97

8.1 Introduction ........ .

8.2 Models and Test Statistics .

8.3 Properties of the Test Statistics .

8.3.1 Properties of CSt.

8.3.2 Properties of MQt

8.3.3 Sur.nr.nary .....

8.4 Structural Change Characterization: A Nur.nerical Study ........................ .

8.4.1 The design .

8.4.2 Basic results

8.5 Conclusions.....

97

99

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. 101

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. .. 117

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. 122

9 The Local Power of the CUSUM-SQ Test against Heteroscedasticity 127

9.1 Introduction........ . 127

9.2 The Model and Notation. . 128

9.3 The Local Power of the CUSUM-SQ Test . 130

9.4 Sor.ne Examples . . . . . . . . . . . . . . . . 131

10 Bahadur Efficiency of Tests for a Shift in Location of Normal Popula-tions 135

10.1 Introduction.

10.2 Prelir.ninaries

.135

.137

xiv Statistical Analysis and Forecasting of Economic Structural Change

10.3 Variance Known .140

10.3.1 Sum-type statistics . . 140

10.3.2 Max-type statistics . . 143

10.4 Variance Unknown . . . . . . 148

10.4.1 Sum-type sta.tistics . . 149

10.4.2 Max-type statistics . . 152

10.5 Some Comparisons and Examples. . 158

10.6 Power Estimates for Small Sample Sizes . 161

11 The Use of Graphical Displays in the Analysis of Structural Change 167

11.1 Introduction. . . . . . . . . . . . . . . . . . 167

11.2 Transformed Residuals Used in the Plots. . 168

11.2.1 Internally studentized residuals . . 168

11.2.2 Externally studentized residuals . 168

11.2.3 Predicted residuals . 169

11.2.4 Recursive residuals . 169

11.3 Smoothing Residuals . . . . 170

11.4 Using Plots in the Analysis of Structural Changes . 172

11.5 Final Remarks .................... . 187

III Model Building in the Presence of Structural Change 189

12 Adaptive Estimation and Structural Change in Regression and Time Series Models 191

12.1 Introduction ...... . · 191

12.2 Heuristic Approaches to Recursive Estimation in Regression Models . 192

12.2.1 Recursive least squares. . . . . . . . . . . . . . . . . . . . . . . 193

12.2.2 Heuristic approaches to the estimation of time-varying coefficients . 195

12.3 Model-Based Adaptive Recursive Estimation . 200

12.4 Extensions and Concluding Remarks . . . . .

13 An Adaptive Method of Regression Analysis

13.1 Introduction ................... .

13.2 Adaptive Estimation of Regression Coefficients

13.3 illustrating Examples. . . . . . . . . . . . . . .

.206

209

.209

· 210

· 212

Contents

13.4 Conclusions and Further Aspects

14 Changing and Random Coefficient Models. A Survey

14.1 Introduction. . . . . . . . . .

14.2 Defining an Adequate Model

14.3 Arguments for Varying Parameter Specification

14.4 Types of Varying-Parameter Models

14.4.1 Fixed coefficient models ...

14.4.2 Systematically Varying Parameter Models

14.4.3 Switching regression models

14.5 Random-Parameter Models ....

14.5.1 Hildreth-Houck random coefficient models

14.5.2 Return-to-normality models . . . .

14.5.3 Swamy random coefficient models

14.5.4 The Hsiao random coefficient model

14.6 Nonstationary Random-Parameter Models .

14.6.1 Cooley-Prescott models ....

14.6.2 Convergent parameter models .

14.6.3 Kalman filter models.

14.7 Summary and Conclusions ..

15 Nonparametric Estimation of Time-Varying Parameters

15.1 Introduction ...... .

15.2 Estimators of the f1t, Ut

15.3 Consistency . . . . . .

15.4 Asymptotic Normality

15.5 Extensions ...... .

15.5.1 Serially correlated Ut

15.5.2 Alternative estimators

15.5.3 More general models .

16 Latent Variables in Regression Analysis

16.1 Introduction ............ _ .. .

xv

.215

217

.217

· 218

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· 231

.231

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253

· 254

· 256

· 258

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· 263

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· 263

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265

· 265

16.2 The Regression Model with a Variance Containing Unknown Parameters . . 266

16.3 Multiresponse Regression Model ........................ 270

xvi Statistical A nalysis and Forecasting of Economic Structural Change

17 Structural Change and Time Series Analysis

17.1 Introduction ....

273

.273

.274

.275

.275

.277

17.2 Trends in the Data

17.3 Changing Covariance Structure

17.4 The Bayesian Analysis ...

17.5 Summary and Conclusions.

18 Thresholds, Stability, Nonlinear Forecasting and Irregularly Sampled D~a 2" 18.1 Introduction. . . . . . 279

18.2 Threshold Inference . 280

18.3 Stability . . . . . . . . 282

18.4 Nonlinear Forecasting . 291

18.5 Irregularly Sampled Data . 294

18.6 Concluding Remarks . . . . 295

19 Forecasting in Situations of Structural Change: A General Approach 297

19.1 Introduction. . . . . . . . . . . . . 297

19.2 The Basic Theory of Combining. . 298

19.2.1 Variance-covariance combining . 298

19.2.2 Regression-based combining . 302

19.3 Non-Constant Weights . . . . . . 304

19.3.1 Weighted least squares. . 304

19.3.2 Deterministic time-varying parameter models . 307

19.3.3 Stochastic time-varying parameter models . 309

19.4 Testing Procedures . 310

19.5 Examples . . . . . . 312

19.6 Conclusions and Directions of Future Research . 316

20 Updating Parameters of Linear Change Point Models 319

20.1 Introduction. . . . . . 319

20.2 Updating SSR1(m) . . 320

20.3 Updating SSR2(m) . . 323

20.4 Example . . . . . . . 324

20.5 Linear Constraints . 326

Contents

IV Data Analysis and Modeling

21 Change Point Problem Relating to the Poverty Structure

21.1 Introduction. . . . .

21.2 Preliminary Notions

21.3 Parametric Formulation

21.4 Nonparametric Formulations

21.4.1 The pseudo two-sample approach .

21.4.2 The recursive-residual approach .

21.5 Some General Remarks ........ .

xvii

327

329

.329

.332

.335

.337

.338

.341

.342

22 Statistical Identification of Nonlinear Dynamics in Macroeconomics Us-ing Nonlinear Time Series Models 345

22.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . 345

22.2 Dynamic Modeling of the Hicksian IS-LM Paradigm . 346

22.3 Time Discretization . 349

22.4 Model Identification . 355

22.5 Bayesian Estimation of Time-varying IS-LM Curves . 360

22.6 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . 364

23 Econometrics of Technical Change: Techniques and Problems 367

23.1 Introduction. . . . . . . . . . . . . . . . . . . . 367

23.2 Description and Effects of Technical Change . . 369

23.2.1 Characteristics and bias of technical change . 369

23.2.2 Measurement of technical change and sources of errors . 373

23.2.3 Estimates of technical change for the US economy .. . 374

23.3 Econometric Specification of Technical Change . . . . . . . . . 375

23.3.1 Specification of production functions with disembodied technical change ................................... 375

23.3.2 Specification of production functions with embodied technical change ................................... 383

23.3.3 Specification of production functions with endogenous tech-nical change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

23.3.4 Specification of technical change in multisectoral and disaggregated models. . . . . . . . . . . . . . . . . . . . . . . . . . 391

23.4 Estimation Techniques and Problems of Technical Change . . . . . . . . . . 393

xviii Statistical Analysis and Forecasting of Economic Structural Change

23.4.1 Time series and cross-section data bias. . 393

23.4.2 Methods of estimating technical change . 394

23.4.3 Econometric problems . 398

23.5 Conclusions . . . . . . . . . . . 399

24 Local Autoregression Models for Detection of Changes in Causality 407

24.1 Introduction. . . . . . . . . . . . 407

24.1.1 Purpose of this chapter . 407

24.1.2 Locally stationary AR models. . 408

24.2 Univariate Locally Stationary Models . 409

24.2.1 Deposit Rate ......... .

24.2.2 Corrected Lending Rate (without outliers) .

24.2.3 Lending Rate . . . . . . . . . . .

24.2.4 3-Month Money Rate (72.1-81.9)

.420

.420

.420

.420

24.2.5 Call Money Rate . 420

24.2.6 Bond Rate ... . 421

24.2.7 Stability of the results . 421

24.3 Multivariate Locally Stationary Models . 421

24.3.1 Results for the Deposit Rate and Corrected Lending Rate . 426

24.3.2 Results for the Call Money and the 3-Month Money Rates. . 428

24.3.3 Results for the trivariate 3Rt! Rt! Bt model . 429

24.4 Local Causality Analysis . . . . . . . 431

24.4.1 Deposit and Lending Rates . 431

24.4.2 Call Money and 3-Month Money Rate . 432

24.5 Locally moving AR-models . 435

24.6 Conclusions . . . . . . . . . . 437

25 Investment, Taxation, and Econometric Policy Evaluation: Some Evi-dence on the Lucas Critique 441

25.1 Introduction.

25.2 The Model .

25.3 Methodology

25.4 Recursive Stability Analysis of Investment Demand .

25.5 Conclusion ...................... .

.442

.443

.446

.451

.469

Contents

Author Index

Subject Index

List of Authors

xix

475

483

487