Estimation of Simultaneous Equation Models with Error Components Structure: (312 Lecture Notes in Economics and Mathematical Systems)

Economists can rarely perform controlled experiments to generate data. Existing information in the form of real-life observations simply has to be utilized in the best possible way. Given this, it is advantageous to make use of the increasing availability and accessibility of combinations of time-series and cross-sectional data in the estimation of economic models. But such data call for a new methodology of estimation and hence for the development of new econometric models. This book proposes one such new model which introduces error components in a system of simultaneous equations to take into account the temporal and cross-sectional heterogeneity of panel data. After a substantial survey of panel data models, the newly proposed model is presented in detail and indirect estimations, full information and limited information estimations, and estimations with and without the assumption of normal distribution errors. These estimation methods are then applied using a computer to estimate a model of residential electricity demand using data on American households. The results are analysed both from an economic and from a statistical point of view.

Table of Contents:
1. Introduction.- 1.1 General.- 1.2 Organization of the Book.- 2. A Survey of Panel Data Models.- 2.1 General.- 2.2 Constant Slope Variable Intercept Models.- 2.3 Variable Coefficient Models.- 2.4 Estimation of Variance Components in Panel Data Models.- 2.5 Estimation of Models using Incomplete Time-Series Cross-Section Data.- 2.6 Extensions.- 3. Presentation of Simultaneous Equations Models with Error Components Structure and Estimation of the Reduced Form.- 3.1 The Model.- 3.2 Estimation of the Reduced Form.- Appendix 3.A Proof of the Consistency of the Feasible GLS Estimator of Reduced Form Coefficients.- Appendix 3.B Limiting Distribution of the Feasible GLS Estimator of the Reduced Form.- Appendix 3.C. Limiting Distribution of the Reduced Form Maximum Likelihood Estimators.- 4 Estimation of the Structural Form — Part 1.- 4.1 Generalised Two Stage Least Squares — A Single Equation Method.- 4.2 Generalised Three Stage Least Squares — A System Method.- Appendix 4.A Proof of the Consistency of the 2SLS Covariance Estimators $$ {{\hat a}_{m\left( {\operatorname{cov} } \right)}} $$ and $$ {{\hat a}_{m\left( {\operatorname{cov} } \right)}} $$.- Appendix 4.B Proof of the Consistency of AOV Estimators of Eigenvalues and Variance Components of ?mm.- Appendix 4.C Proof of the Consistency of the Feasible (and pure) G2SLS Estimator.- Appendix 4.D Limiting Distribution of the Feasible G2SLS Estimator.- Appendix 4.E Limiting Distribution of the Feasible G3SLS Estimator.- 5 Estimation of the Structural Form — Part 2.- 5.1 Full Information Maximum Likelihood (FIML) Estimation of the Structural Form.- 5.2 Limited Information Maximum Likelihood (LIML) Estimation of the Structural Form.- Appendix 5.A Limiting Distribution of the FIML Estimators.- 6 The Just-Identified Caseand Indirect Estimation of Structural Parameters.- 6.1 The Identification Problem.- 6.2 Derivation of the Indirect Estimators of Structural Coefficients and their Limiting Distributions.- 6.3 Comparison of the IfGLS Estimator with the fG2SLS and fG3SLS Estimators.- Appendix 6.A Limiting Distribution of the Indirect Feasible GLS Estimator.- 7 Bias of the Feasible Estimators of Reduced Form and Structural Variance Components and Coefficients.- 7.1 The Unbiasedness of the Feasible AOV Estimators of Reduced Form Variance Components.- 7.2 The Unbiasedness of the Feasible GLS Estimator of the Reduced Form Coefficients.- 7.3 Bias of Structural Variance Components Estimators.- 7.4 Bias of Structural Coefficients Estimators.- Appendix 7.A Preliminary Computations of Orders.- Appendix 7.B Derivations of Expectations.- Appendix 7.C Order Calculations Involved in the Determination of the Bias of the Feasible G2SLS Estimator.- Appendix 7.D Expectation of ?i11X’Njul for i=1,4 and j=1,4.- 8 Application to a Model of Residential Electricity Demand.- 8.1 The Model.- 8.2 The Data.- 8.3 Estimation Methods.- 8.4 Results.- Appendix 8.A Computer Programs of Estimation Methods.- 9 Conclusions.- References.