Topics In Advanced Econometrics

Inhaltsverzeichnis

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.
- 1.4.1 Assumptions and Conventions.
- 1.4.2 Notation.
- 1.5 Inconsistency of OLS Estimators.
- 1.6 Two Stage Least Squares (2SLS).
- 1.6.1 The Original Derivation.
- 1.6.2 An Alternative Formulation.
- 1.7 Three Stage Least Squares (3SLS).
- 1.8 Restricted 2SLS and 3SLS Estimators.
- 1.9 Tests of Prior Restrictions.
- 1.9.1 Generalities.
- 1.9.2 A Restricted Least Squares Interpretation of 2SLS and 3SLS.- Questions and Problems.- Appendix to Chapter 1.- Preliminaries to Hausman's Test.- Examples.- 2 Extension of Classical Methods II.
- 2.1 Limiting Distributions.
- 2.1.1 Preliminaries.
- 2.1.2 Limiting Distributions for Static GLSEM.
- 2.1.3 Limiting Distributions for Dynamic GLSEM.
- 2.2 Forecasting from the GLSEM.
- 2.2.1 Generalities.
- 2.2.2 Forecasting from the URF.
- 2.2.3 Forecasting from the RRF.
- 2.3 The Vector Autoregressive Model (VAR).
- 2.4 Instrumental Variables (IV).
- 2.4.1 2SLS and 3SLS as IV Estimators.
- 2.4.2 2SLS and 3SLS as Optimal IV Estimators.
- 2.5 IV and Insufficient Sample Size.
- 2.5.1 The Nature of the Problem.
- 2.5.2 Iterated Instrumental Variables (IIV).
- 2.6 k-class and Double k-class Estimators.
- 2.7 Distribution of LM Derived Estimators.
- 2.8 Properties of Specification Tests.
- 2.8.1 Single Equation 2SLS.
- 2.8.2 Systemwide 2SLS and 3SLS.
- 2.8.3 Relation to Hausman's Test.- Questions and Problems.- Appendix to Chapter 2.- Convergence of Second Moment Matrices.- Convergence for Dependent Sequences.- Preliminaries and Miscellaneous.- Convergence of Second Moments of Final Form Errors.- 3 Maximum Likelihood Methods I.
- 3.1 Introduction.
- 3.2 The Identification Problem.
- 3.2.1 Generalities.
- 3.2.2 The Simple Supply-Demand Model.
- 3.2.3 Identification by Exclusion Restrictions.
- 3.2.4 Identification by Linear Restrictions.
- 3.2.5 Identification and the Reduced Form.
- 3.2.6 Covariance and Cross Equation Restrictions.
- 3.2.7 A More General Framework.
- 3.2.8 Parametric Nonlinearities and Identification.
- 3.3 ML Estimation of the RF.
- 3.3.1 General Discussion and ILS.
- 3.3.2 Estimation of the Reduced Form.
- 3.4 FIML Estimation.
- 3.5 Simplified FIML Estimators.
- 3.6 Properties of Simplified Estimators.
- 3.6.1 Consistency.
- 3.7 Limiting Distribution of FIML.- Questions and Problems.- 4 LIML Estimation Methods.
- 4.1 The "Concentrated" Likelihood Function.
- 4.1.1 A Subset of m* Structural Equations.
- 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.- Questions and Problems.- Appendix to Chapter 4.- Limiting Distribution of (T? - 1).- 5 Nonlinear ML Methods.
- 5.1 Motivation.
- 5.2 A Mathematical Digression.
- 5.3 Aspects of Likelihood Functions.
- 5.3.1 An Interesting Inequality.
- 5.4 Fisher Information.
- 5.4.1 Alternative Representation of the Information Matrix.
- 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.
- 5.8.1 Independent Observations.
- 5.8.2 Generalizations.
- 5.9 The General Nonlinear Model (GNLM).
- 5.9.1 Consistency.
- 5.9.2 Identification.
- 5.9.3 Asymptotic Normality.
- 5.10 The GNLM with Restrictions.
- 5.11 Tests of Restrictions.
- 5.11.1 Generalities.
- 5.11.2 The Conformity Test.
- 5.11.3 The Likelihood Ratio Test.
- 5.11.4 The Lagrange Multiplier Test.
- 5.11.5 Equivalence of the Three Tests.- Questions and Problems.- 6 Topics in NLSE Theory.
- 6.1 Nonlinear ML.
- 6.1.1 Identification.
- 6.1.2 Consistency of the ML Estimator.
- 6.1.3 Limiting Distribution of ML Estimators.
- 6.1.4 Relation of Structural and Covariance Parameter (ML) Estimators.
- 6.1.5 Estimators in Structurally Misspecified Models.
- 6.2 Nonlinear 2SLS.
- 6.2.1 Identification and Consistency of NL2SLS.
- 6.2.2 Asymptotic Normality of NL2SLS.
- 6.2.3 Choice of an Optimal NL2SLS Estimator.
- 6.3 Nonlinear 3SLS.
- 6.3.1 Identification and Consistency of NL3SLS.
- 6.3.2 Asymptotic Normality of NL3SLS.
- 6.3.3 Optimum NL3SLS and Computational Aspects.
- 6.4 GMM.
- 6.4.1 Reformulation of GMM as NL2SLS and NL3SLS.
- 6.4.2 Identification and Consistency.
- 6.4.3 Asymptotic Normality.
- 6.4.4 Tests of Restrictions.
- 6.5 Causality and Related Issues.
- 6.5.1 Introduction.
- 6.5.2 Basic Concepts.- Questions and Problems.