Lectu re Notes in Economics and Mathematical Systems
Managing Editors: M. Beckmann and W. Krelle
221
Shinichiro Nakamura
An Inter-Industry Translog Model of Prices and Technical Change for the West German Economy
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Editorial Board
H.Albach A.v. Balakrishnan M. Beckmann (Managing Editor) P.Ohrymes G.Fandel J.Green WHildenbrand WKrelie (Managing Editor) H. P. Kunzi G. L. Nemhauser K. Ritter R. Sato U. Schittko P. Schonfeld R. Selten
Managing Editors
Prof. Dr. M. Beckmann Brown University Providence, RI 02912, USA
Prof. Dr. W Krelle Institut fUr Gesellschafts- und Wirtschaftswissenschaften der Universitat Bonn Adenauerallee 24-42, 0-5300 Bonn, FRG
Author
Dr. Shinichiro Nakamura Institut fUr Gesellschafts- und Wirtschaftswissenschaften der Universitat Bonn Adenauerallee 24-42, 0-5300 Bonn 1, FRG
ISBN-13: 978-3-540-12709-3 e-ISBN-13: 978-3-642-46486-7 DOl: 10.1007/978-3-642-46486-7
Library of Congress Cataloging in Publication Data. Nakamura, Shinichiro, 1952- An interindustry translog model of prices and technical change for the West German economy. (Lecture notes in economics and mathematical systems; 221) Includes bibliographical references and index. 1. Germany (West)-Economic conditions-1974-1974--Mathematical models. 2. Input-output tables-Germany (West) 3. Prices-Germany(West)-Mathematical models. 4. Technological innovations-Germany (West)-Mathematical models. 5. Production functions (Economic theory) I. Title. II. Title: Translog model of prices and technical change for the West German economy. III. Series. HC286.7.N34 1984 339.2'3'0724 83-20275 ISBN-13: 978-3-540-12709-3
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© by Springer-Verlag Berlin Heidelberg 1984
2142/3140-543210
To my parents
PREFACE
This book presents the results of a research project which has
been carried out in the Special Research Unit (Sonderforschungsbereich) 21 at Bonn University. It is a part of the current research on disaggregated econometric forecasting models with a fully integrated input-output system with variable input coefficients where prices are explained as dual variables of the
underlying production model. A similar approach has already been
used by Knut KUbler "Ein disaggregiertes Prognosesystem fUr die Bundesrepublik, die Unternehmenssektoren", Meisenheim am Glan,
1977. But KUbler assumed Cobb-Douglas production functions. Mean
while a new approach has been suggested by Jorgenson and others, using more flexible forms of functions, e.g. the translog function as an approximation to any reasonable neo-classical production function, see Hudson and Jorgenson "US Energy Policy and Economic Growth, 1975 - 2000", Bell Journal of Economics and Management SCience, Vol.5 (1974), page 461 ff.~ Jorgenson and Fraumeni,
"Substitution and Technical Change in Production", Discussion paper No. 752, Harvard Institute of Economic Research, Harvard
University, Cambridge/Mass. (1 980) ~ Friede, "Investigation of Producer Behavior in the FRG using the Translog Price Function",
Cambrigde/Mass. (1980). Krelle and Pallaschke "A General Demand
System", Zeitschrift fUr Nationalokonomie 41 (1981), page 223 ff. suggested another approximation using a Taylor expansion of any reasonable demand system. Nakamura follows the lines of Jorgenson and his collaborators but extends them into new areas and reaches much better results.
Nakamura assumes that there exists a production function of the type putty-putty for each sector with constant returns to scale and that there is perfect competition on all factor markets and
that the entrepreneurs minimize the cost of producing a
given amount of output. As to the production functions, he assumes weak separability such that a three stage optimizing procedure is applicable. Thus there exist price aggregator functions on the lowest level for each of the twelve sectors of domestic production
VI
and of imports. On the base of these functions price aggregator functions are derived for material inputs, ,energy inputs and service inputs. On the final stage there are price levels for each sector which are explained by the price levels for material inputs, energy inputs, service inputs and capital and labour inputs. According to the duality theorem in production theory it does not matter whether one uses production, cost or profit functions. Nakamura uses cost functions as the basic concept and approximates them by translog functions with technical progress. Using Shephard's Lemma he derives the factor demand functions in the form of functions for all input coefficients. Since the production functions are supposed to be homogeneous of degree one, prices can be determined independently from the quantities. The prices of the final products are determined simultaneously from the input coefficients of material inputs, energy and service inputs as well as from capital and labour inputs. Thus a logically consistent model arise's which (due to the assumption of three stage separability of the unknown production functions and to the assumption of linear homogeneity) could also be estimated econometrically on the base of the underlying data (yearly input-output tables for West Germany from 1960-1974).
Careful specification of the assumptions on the stochastic term and utilization of the limited information maximum likelihood method with instrument variables yield results which (given the relatively small number of observations) should be reasonably free from biases induced by the simultaneity of the total system.
The model is much more general than all others mentioned above, especially in dealing with technical progress, imports and separability of the production functions. Thus Nakamura is able to analyse the interrelationships between the elasticities of substitution of the factors of production, the price elasticities of demand and different types of technical progress. He tests whether the underlying cost function is concave (otherwise the theoretical construct of a cost minimizing representative firm for each sector breaks down, and the approach must be taken as purely heuristic). He also estimates the biases of technical
VII
change and finds that the dominant pattern of technical change
is represented by imports using and capital using and labour
saving biases. His results suggest that the simplifying assump
tion of Hicks neutrality of technical change is not consistent with the data.
In 75 out of 89 cells of the input-output table the price aggregator function for domestic inputs and corresponding imported inputs is of the Cobb-Douglas type. This may justify simpler approaches using Cobb-Douglas price aggregator functions.
These are only examples for the interesting results which may be
found in this book. Of course, one may ask whether a fully consistent theory for deriving prices and demand yields better results in forecasting than other simpler or even naive models. But the advantage of this approach comes out when the simulation
results and the different elasticities are considered and com
pared.
This book sets a standard in production and price theory in connection with econometric forecasting systems from which further research may start.
Bonn, July 1983
Wilhelm Krelle
ACKNOWLEDGEMENTS
This volume presents research carried out at the Sonderforschungsbereich 21, University of Bonn, from 1980 to early 1982 with financial support of the Deutsche Forschungsgemeinschaft. I would like to express my appreciation for the opportunities offered to me by the above-mentioned institutions.
During the process of research and the preparation of this volume, I enjoyed help from many individuals, and I would like to thank all of them. My special thanks go to Wilhelm Krelle, University of Bonn. Wilhelm Krelle supervised the research as director of the project "Econometric Forecasting Systems" and lowe him a lot of helpful comments and encouragement. I am also indebted to Dale Jorgenson, Harvard University, for helpful comments while I was at Harvard in the summer of 1980. Also I would like to thank Lawrence Lau, Stanford University, for helpful comments which led to a revision of the first draft of this volume. Earlier versions of this volume were presented in several meetings including the Karlsruhe Symposium on Natural Resources and Production, 1980, European Meeting of the Econometric Society, Dublin, 1982, and the Kyoto Meeting of the Japanese Association of Theoretical Economics and Econometrics, 1982. I greatly appreciate helpful comments of Georg Hasenkamp, University of Hamburg, Masahiro Kuroda, Keio University, and Mitsuo Saito, Kobe University. I take this opportunity to express my indebtness to my colleagues in Bonn, Fran90is Laisney and Sigrid Muller, for their friendly help and encouragement. I am especially indebted to Sigrid Muller for her constant encouragement during the laborious process of writing this volume. Needless to say, all the errors and shortcomings are solely mine.
This volume is my doctoral dissertation accepted at the Rechtsund Staatswissenschaftliche Fakult§t der RheinischenFriedrichWilhelms-Universit§t Bonn in January 1983. I would like to thank Wilhelm Krelle once again for realizing its publication in the present form.
Bonn, July 1983 Shinichiro Nakamura
TABLE OF CONTENTS
1 INTRODUCTION
2 2.0
2.1
2.1 .1 2.1.2
2.1.3
2.1 .4
2.1 .5
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.2.6
2.2.7 2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.4
2.4.1 2.4.2
2.4.3
THE MODEL
Introduction
The Basic Model
Technology Behavior
Prices of Domestic Outputs
Input Coefficients
Remarks
The Dete~inistic Model I: General Formulation
Partition of Inputs
4 4
4
4 7
10
13
15
21
21
Separability as Further Assumption on Technology 24
Dual Implications of the Separability Assumption 34
Three Stage Optimization 38
Technical Change 44
Prices and Input Coefficients 60
Remarks 66
The Deterministic Model II: Model Specification 70 Sectoral Specification 70
Choice of Functional Forms 72
Specified Model and Its Implications 76
Remarks 96
A Note on the General Demand System of Krelle and Pallaschke and Its Relationships to the Demand System Used in the Model 99
The Econometric Model 108
The Stochastic Specification of the Model 108
The Estimation Procedure 114
Remarks 120
x
TABLE OF CONTENTS (CONTINUED)
3
3.0
3.1
3.2
3.2.1
EMPIRICAL RESULTS
Introduction
Data
Estimation Results and Their Implications
Price Aggregator Functions for Domestic Inputs and Imports
3.2.1.1 Initial Estimation Results
3.2.1.2 Integrability Conditions
3.2.1.3 Procedures of Reestimation
3.2.1.4 Implications of the Reestimated Parameters
3.2.2 Price Aggregator Functions for Material Inputs
3.2.2.1 Estimation Results
3.2.2.2 Integrability Conditions
3.2.2.3 Patterns of Substitution between Material Inputs
3.2.2.4 Biases of Technical Change in the Use of Material Inputs
3.2.2.5 Computation of ~mj 3.2.3 Price Aggregator Functions for Service Inputs
3.2.3.1 Estimation Results
3.2.3.2 Integrability Conditions
3.2.3.3 Patterns of Substitution Between Service Inputs
3.2.3.4 Biases of Technical Change in the Use of Service Inputs
3.2.3.5 Computation of ~sj 3.2.4 KLEMS Price Functions
3.2.4.1 Estimation Results
3.2.4.2 Integrability Conditions
3.2.4.3 Patterns of Substitution Between K,L,E,M,S
3.2.4.4 Biases of Technical Change for K,L,E,M,S
121
121
122
127
127
127
133
137
140
153
153
166
170
173
175
175 175
182
189
191
193
193
193
200
208
212
XI
TABLE OF CONTENTS (CONCLUDED)
3.2.5
3.2.5.1
3.2.5.2
3.2.6 3.3
3.3.1
3.3.2
3.3.3
3.4 3.4.1
3.4.2
3.4.2.1
3,4.2.2
3.4.2.3
3.4.2.4
3.4.2.5
4
5
APPENDIX
2
Equations for the Negative of the Rates of
Technical Change The Rates of Technical Change
Estimation Results
Overall Biases of Technical Change Performance of the ~adel: Interpolations
Test Results for Prices of Domestic Outputs
Test Results for Input Coefficients: Domestic Intermediate Inputs, Capital and Labor Services
Test Results for Input Coefficients: Imports Simulation Experiments Increase in a Single Import Price
Simultaneous Increase in Exogenous Variables
Increase in All Import Prices
Increase in Prices of All Labor Services
Increase in Prices of All Capital Services
Increase in the Rates of Indirect Taxes Comparison of Effects of Exogenous Variables
CONCLUSION
REFERENCES
Test Statistic for Testing Local Concavity of ~ij
Test Statistic for Testing Constancy of ~ ... , J,1.1.
215
215
217
223
228
229
245
258 262 263
268
268
270
270
271
271
273
277
288
LIST OF TABLES
2.1 The Number of Free AES Divided into Eight Groups 31
2.2 Equations of the r.fodel of Production 61
2.3 Equations for Determining Input Coefficients 65
2.4 Classification of Production Sectors 71
3.1 The Cells with Import Shares Larger than Five 128 Per Cent
3.2 Demand Functions for Domestic Inputs: Initial Estimation Results 130
.... 3.3 Test Results of Local Concavity of gij 135
3.4 Share Equations for Domestic Inputs:Final Estimation Results 141
3.5 Elasticity of Substitution between Domestic Products and Imports 149
3.6 Elasticity of Substitution between Domestic Products and Imports 150
3.7 Comparison of Goodness of Fit (R2) of Share Equations for Material Inputs Estimated Subject to Alternative Zero Restrictions 155
3.8 Estimation Results of the Share Functions for Material Inputs: Simultaneous ML Estimation 157
3.9 Estimation Results of Share Equations for Material Inputs: Singl~ QLS Estimation 162
3.10 Signs of Estimated Allen Partial Elasticities of Substitution (AES) between Seven Material Inputs 171
3.11 Biases of Technical Change for Material Inputs at the Second Stage 174
3.12 Estimation Results of the Share Functions for Service Inputs: Simultaneous ML Estimation 176
3.13 Estimates of Cholesky Values: Demand Functions for Service Inputs j87
3.14 Likelihood Ratio Test of Global Concavity: Price Aggregator Functions for Service Inputs 188
3.15 Signs of Estimated Allen Partial "Elasticities of Substitution between Four Service Inputs 190
3.16 Bias of Technical Change in the Use of Service Inputs 192
3.17 Estimation Results of the Share Functions for M, E,S, and L: Simultaneous ML Estimation 194
3.18 Estimates of Cholesky Values: KLEMS Demand Functions 205
XIII
LIST OF TABLES (CONCLUDED)
3.19 Likelihood Ratio Tests of Global Concavity: KLEMS Price Functions
3.20 Signs of the Estimated Allen Partial Elasticities of Substitution between Capital Services (K), Labor Services (L), Energy (E), Material (M) and Services (S)
3.21 Predominant Patterns of Substitution Possibilities between K, L, E, M, and S
3.22 Signs of the Constant Biases of Technical Change for K, L, E, M, and S
3.23 Negative of the Rates of Technical Change
3.24 Goodness of Fit Measured by R2 of the Equations for the Rates of Technical Change: with and without Equality Restrictions
3.25 Test Results of Equality Condition between the Parameters of Biases of Technical Change et , , in (2.4.4) and (2.4.16) 1J
3.26 Signs of the Estimates of the Rates of Change of the Rates of Technical Change
3.27 Signs of Overall Biases of Technical Change b ij : Domestic Intermediate Inputs
3.28 Signs of Overall Biases of Technical Change b ij : Imports
3.29 Summary Measure of Error for Ex Post Predictions of Prices of Domestic Outputs: 1961 - 1974
3.30 Summary Measure of Error for Ex Post Predictions of Prices of Domestic Outputs with Exogenous Rates of Technical Change: 1961 - 1974
3.31 Summary Measure of Error for Ex Post Predictions of Input Coefiicients of Domestic Inputs
3.32 Summary Measure of Error for Ex Post Predictions of Domestic Outputs: 1961 - 1974
3.33 Summary Measure of Error for Ex Post Predictions of Input Coefficients of Imports: 1961 - 1974
3.34 Summary Measure of Error for Ex Post Predictions of Sectoral Imports: 1961 - 1974
207
209
211
213 216
218
219
222
224
225
230
238
246
251
259
261
3.35A Effects of a 50 Per Cent Increase in an Import Price on Domestic Prices: 1974 264
3.35B Effects of a 50 Per Cent Increase in an Import Price on Domestic Prices: 1964 265
3.36 Effects of a 50 Per Cent Increase in Exogenous Variables on Domestic Prices: 1974 269
LIST OF FIGURES
2.1
2.2
2.3
2.4 2.5
3.1
3.2
3.3
3.4
The Tree Structure of Production
Partition of AES into Eight Groups
Division of Free AES under the Separability Assumption into Eight Groups
The Dual Tree Structure of Production Structure of the Sectoral Model
Plots of the Actual (*) and Predicted (+) Values of Prices of Domestic Products
Plots of the Actual (*) and Predicted (+) Values of Prices of Domestic Products with Exogenous Rates of Technical Change Plots of the Actual (*) and Predicted (+) Values of Domestic Input Coefficients Plots of the Actual (*) and Predicted (+) Values of Domestic Outputs
27
30
33
39
62
231
239
247
252
