REGRESSION AND F ACTOR ANALYSIS APPLIED IN ECONOMETRICS

REGRESSION AND F ACTOR ANALYSIS APPLIED IN ECONOMETRICS

Tilburg studies in econometrics Vol. 1

Regression and factor analysis applied in econometrics J. H. F. SCHILDERINCK Tilburg School of Economics, Social Sciences and Law, the Netherlands Second edition tjaartinuscfjlijhoff Social Sciences Division ~eiden 1978

ISBN-13: 978-1-4613-4053-9 e-isbn-13:978-1-4613-4051-5 DOl: 10.1007/978-1-4613-4051-5 1977 by H.E. Stenfert Kroese B. V., Leiden, the Netherlands. Softcover reprint of the hardcover 1st edition 1977 No part of this book may be reproduced in any form by print, photoprint, microfilm or any other means, without written permission from the publisher.

Preface This book deals with the methods and practical uses of regression and factor analysis. An exposition is given of ordinary, generalized, two- and three-stage estimates for regression analysis, the method of principal components being applied for factor analysis. When establishing an econometric model, the two ways of analysis complement each other. The model was realized as part of the 'Interplay' research project concerning the economies of the European Common Market countries at the Econometrics Department of the Tilburg School of Economics. The Interplay project aims at: a. elaborating more or less uniformly defined and estimated models; b. clarifying the economic structure and the economic policy possible with the linked models of the European Community countries. Besides the model for the Netherlands published here, the models for Belgium, Italy, West Germany and the United Kingdom are ready for linking and for publishing later on. The econometric model presented in this book and upon which the Interplay model is based comprises eleven structural and twenty-one definitional equations; it is estimated with ordinary, two- and three-stage least squares. The analysis of the model is directed at eliminating multicollinearity, according to D.E. Farrar's and R. Glauber's method. In practice, however, complete elimination of multicollinearity leads to an exclusion of certain relations which is not entirely satisfactory. Economic relations can be dealt with more fully by analyzing the variables involved in detail by factor analysis. In this study factor analysis is also a suitable method for a comparative analysis of different periods. Prof. dr. J. J. J. Dalmulder Professor of Econometrics and Mathematical Economics

Contents PREFACE / V 1. Some theoretical and statistical aspects of a linear econometric model / 1 1.1 Motivation for the use of a model / 1.2. Definition of a model / 2 1.3. The linea~ econometric model / 3 1.4. The variables / 6 1.5. The general form of a single equation linear econometric model / 8 1.5.1. Ordinary least squares (O.L.S.) / 9 1.5.2. Generalized least squares (G.L.S.) / 13 1.6. The general form of a simultaneous linear econometric model / 15 1.6.1. The formulation of a simultaneous linear econometric model / 16 1.6.2. Two stage least squares / 23 1.6.3. Three stage least squares / 35 1.7. Statistics for a single equation linear econometric model / 40 1.7.1. The adj usted correlation coefficient / 40 1.7.2. The relative variance-share coefficient / 43 1.7.3. The t-test / 44 1. 7.4. Tests on multicollinearity / 47 1.7.5. Tests on autocorrelation / 51 2. Factor analysis as a method of economic research /59 2.1. Motivation for the use of factor analysis / 59 2.2. Aim of factor analysis / 62

2.3. Regression analysis versus factor analysis / 64 2.4. Normalization of variables / 67 2.5. The model of factor analysis / 70 2.6. The solution of the factor analysis model / 77 2.6.1. The geometric approach / 77 2.6.2. The algebraic approach / 82 2.7. The interpretation of the commonfactor coefficients / 98 2.8. Factor rotation / 101 3. Structure of the model / 114 3.1. The structure of expenditure in the Dutch economy in the pre-war and post -war period / 114 3.2. The structure of the model / 134 3.3. The consumption equation / 142 3.4. The investment equation / 165 3.5. The inventory equation / 172 3.6. The export equation / 175 3.7. The import equation / 185 3.8. The employment and unemployment equation / 187 3.9. The price equations / 189 4. Some applications of factor analysis /196 4.1. A factor analytical comparison of each variable in the whole of variables / 196 4.2. Investments / 202 4.2.1. The relation between investment and financing variables / 202 4.2.2. The relation between investment and final expenditure / 213 4.3. Consumption / 220 4.4. Government expenditure / 227 BIBLIOGRAPHY 1236