Econometrics (Routledge Revivals)

A Varying Coefficients Approach

Baldev Raj, Aman Ullah

• Publisher: Taylor & Francis
• Year: 2013
• Print ISBN: 9780415606936
• eBook ISBN: 9781317850663
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

Originally published in 1981, this book considers one particular area of econometrics- the linear model- where significant recent advances have been made. It considers both single and multiequation models with varying co-efficients, explains the various theories and techniques connected with these and goes on to describe the various applications of the models. Whilst the detailed explanation of the models will interest primarily econometrics specialists, the implications of the advances outlined and the applications of the models will intrest a wide range of economists.

Part One

Single Equation Varying Coefficient Models

1. Introduction

1.1 PREAMBLE

Econometric model building is concerned mainly with statistical inference of such behavioural economic relationships as the consumption and investment functions, wage equations and the production function. The econometric methods employed to estimate economic relationships often assume that the regression coefficients do not change from observation to observation. The assumption that the coefficients are fixed is restrictive and sometimes even unnecessary. Consider, for example, the regression of the quantity demanded of a certain commodity on its price. If time series data are used on these variables, it is quite likely that the price elasticity of demand will not remain the same over the sample period.

Similarly, in a cross-section study of the production function of firms, labour and capital elasticities might vary from small firms to large firms due to economies of scale, managerial abilities, etc. In another example of a regression relationship between savings and incomes of a sample of households, the marginal propensity to save is likely to differ for each household because of different average ages and wealth holdings. This indicates that the assumption of fixed coefficients in modelling economic relations is restrictive and that a more flexible approach to econometric modelling requires that regression coefficients vary from observation to observation.

1.2 CAUSES OF COEFFICIENT VARIATION

Essentially, an econometric model is an approximation of reality and as a result is subject to a number of misspecifications such as the exclusion of relevant variables, a wrong choice of functional form, etc. These lead to a variation in coefficients. Five of the main causes for such variation are discussed below.

(i) Coefficient Variation due to Omitted Variables

Consider an econometric relationship

where y is (say, linearly) related to a set of explanatory variables. The error in regression u captures the influence of the omitted explanatory variables which are normally assumed to have a minor effect on the dependent variable. However, the omitted variables may be more significant than assumed. Then it is clear that the regression relationship needs to be respecified by including the significant omitted variables. This may not always be possible, however, because of the limitation of the number of observations and hence the degrees of freedom. If so, their inclusion may actually reduce the explanatory power of the model. Variables, moreover, may have to be omitted because of problems of measurement.

Often an alternative is to assume a first order autoregressive process for u, that is, u=ρ u₋₁ + v, where the subscript −1 represents a lagged value of u and the v is a serially uncorrected error. The problem with this alternative is that even though the incorporation of this may change the value of a coefficient it...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Original Copyright Page
• Table of Contents
• List of Tables and Figures
• Preface
• One: Single Equation Varying Coefficient Models
• Two: Multi Equations Varying Coefficient Models
• Appendix A
• Bibliography
• Authors Index