Statistical Inference in Random Coefficient Regression Models

ISBN-13: 9783540056034 / Angielski / Miękka / 1971 / 210 str.

P. a. V. B. Swamy

Opis

This short monograph which presents a unified treatment of the theory of estimating an economic relationship from a time series of cross-sections, is based on my Ph. D. dissertation submitted to the University of Wisconsin, Madison. To the material developed for that purpose, I have added the substance of two subsequent papers: "Efficient methods of estimating a regression equation with equi-correlated disturbances," and "The exact finite sample properties of estimators of coefficients in error components regression models" (with Arora) which form the basis for Chapters 11 and III respectively. One way of increasing the amount of statistical information is to assemble the cross-sections of successive years. To analyze such a body of data the traditional linear regression model is not appropriate and we have to introduce some additional complications and assumptions due to the hetero geneity of behavior among individuals. These complications have been discussed in this monograph. Limitations of economic data, particularly their non-experimental nature, do not permit us to know a priori the correct specification of a model. I have considered several different sets of assumptionR about the stability of coeffi cients and error variances across individuals and developed appropriate inference procedures. I have considered only those sets of assumptions which lead to opera tional procedures. Following the suggestions of Kuh, Klein and Zellner, I have adopted the linear regression models with some or all of their coefficients varying randomly across individuals."

Spis treści

I -- Introduction.- 1.1 Purpose and Outline of the Study.- 1.2 Review of the Literature on Regression Models with Random and Fixed Coefficients.- 1.3 Conclusions.- II -- Efficient Methods of Estimating a Regression Equation with Equicorrelated Disturbances.- 2.1 Introduction.- 2.2 Some Useful Lemmas.- 2.3 A Regression Model with Equicorrelated Disturbances.- 2.4 Analysis of Time Series of Cross-Sections.- 2.5 Estimation When the Variance-Covariance Matrix of Disturbances is Singular.- 2.6 Estimation When the Remaining Effects are Heteroskedastic.- 2.7 Conclusions.- III -- Efficient Methods of Estimating the Error Components Regression Models.- 3.1 Introduction.- 3.2 Some Matrix Results.- 3.3 Covariance Estimators.- 3.4 Estimation of Error Components Models.- 3.5 A Class of Asymptotically Efficient Estimators.- 3.6 Small Sample Properties of the Pooled Estimator.- 3.7 A Comparison of the Efficiencies of Pooled and OLS Estimators.- 3.8 A Comparison of the Efficiency of Pooled Estimator with Those of its Components.- 3.9 Alternative Estimators of Slope Coefficients and the Regression on Lagged Values of the Dependent Variables.- 3.10 Analysis of an Error Components Model Under Alternative Assumptions.- 3.11 Maximum Likelihood Method of Estimating Error Components Model.- 3.12 Departures from the Basic Assumptions Underlying the Error Components Model.- 3.13 Conclusions.- IV -- Statistical Inference in Random Coefficient Regression Models Using Panel Data.- 4.1 Introduction.- 4.2 Setting the Problem.- 4.3 Efficient Methods of Estimating the Parameters of RCR Models.- 4.4 Estimation of Parameters in RCR Models when Disturbances are Serially Correlated.- 4.5 Problems Associated with the Estimation of RCR Models Using Aggregate Data.- 4.6 Forecasting with RCR Models.- 4.7 Relaxation of Assumptions Underlying RCR Models.- 4.8 Similarities Between RCR and Bayesian Assumptions.- 4.9 Empirical CES Production Function Free of Management Bias.- 4.10 Analysis of Mixed Models.- 4.11 Conclusions.- V -- A Random Coefficient Investment Model.- 5.1 Introduction.- 5.2 Grunfeld’s Hypothesis of Micro Investment Behavior.- 5.3 Estimation and Testing of Random Coefficient Investment Model.- 5.4 Aggregate Investment Function.- 5.5 Comparison of Random Coefficient Model with Fixed Coefficient Macro Model.- 5.6 Comparison of Random Coefficient Model with Fixed Coefficient Micro Model.- 5.7 Conclusions.- VI -- Aggregate Consumption Function with Coefficients Random Across Countries.- 6.1 Introduction.- 6.2 Aggregate Consumption Model.- 6.3 Source and Nature of Data.- 6.4 Fixed Coefficient Approach.- 6.5 Random Coefficient Approach.- 6.6 Conclusions.- VII -- Miscellaneous Topics.- 7.1 Introduction.- 7.2 Identification.- 7.3 Incorporation of Prior Information in the Estimation of RCR Models.- 7.4 Conclusions.