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El. knyga: Estimation of Simultaneous Equation Models with Error Components Structure

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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.

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Springer Book Archives
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
?i11XNjul 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.
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