Topics In Advanced Econometrics

1 Extension of Classical Methods I.- 1.1 Introduction.- 1.2 A Brief Historical Review.- 1.3 The Nature of the GLSEM.- 1.4 The GLSEM: Assumptions and Notation.- 1.5 Inconsistency of OLS Estimators.- 1.6 Two Stage Least Squares (2SLS).- 1.7 Three Stage Least Squares (3SLS).- 1.8 Restricted 2SLS and 3SLS Estimators.- 1.9 Tests of Prior Restrictions.- Appendix to Chapter 1.- 2 Extension of Classical Methods II.- 2.1 Limiting Distributions.- 2.2 Forecasting from the GLSEM.- 2.3 The Vector Autoregressive Model (VAR).- 2.4 Instrumental Variables (IV).- 2.5 IV and Insufficient Sample Size.- 2.6 k-class and Double k-class Estimators.- 2.7 Distribution of LM Derived Estimators.- 2.8 Properties of Specification Tests.- Appendix to Chapter 2.- 3 Maximum Likelihood Methods I.- 3.1 Introduction.- 3.2 The Identification Problem.- 3.3 ML Estimation of the RF.- 3.4 FIML Estimation.- 3.5 Simplified FIML Estimators.- 3.6 Properties of Simplified Estimators.- 3.7 Limiting Distribution of FIML.- 4 LIML Estimation Methods.- 4.1 The “Concentrated” Likelihood Function.- 4.2 The Single Equation LIML Estimator.- 4.3 Consistency of the LIML Estimator.- 4.4 An Interesting Interpretation of LIML.- 4.5 Indirect Least Squares (ILS).- 4.6 Relation of LIML to Other Estimators.- 4.7 Limiting Distribution of LIML Estimators.- 4.8 Classic Identifiability Tests.- Appendix to Chapter 4.- 5 Nonlinear ML Methods.- 5.1 Motivation.- 5.2 A Mathematical Digression.- 5.3 Aspects of Likelihood Functions.- 5.4 Fisher Information.- 5.5 The Cramer-Rao Bounds.- 5.6 Martingale Properties of Likelihood Functions.- 5.7 Kullback Information.- 5.8 Convergence A.C. of ML Estimators.- 5.9 The General Nonlinear Model (GNLM).- 5.10 The GNLM with Restrictions.- 5.11 Tests of Restrictions.- 6 Topics in NLSE Theory.- 6.1Nonlinear ML.- 6.2 Nonlinear 2SLS.- 6.3 Nonlinear 3SLS.- 6.4 GMM.- 6.5 Causality and Related Issues.