Phoebus J. Dhrymes

Topics in Advanced Econometrics (eBook, PDF)

Probability Foundations

• Format: PDF

Produktbeschreibung

For sometime now, I felt that the evolution of the literature of econo metrics had mandated a higher level of mathematical proficiency. This is particularly evident beyond the level of the general linear model (GLM) and the general linear structural econometric model (GLSEM). The problems one encounters in nonlinear econometrics are not easily amenable to treatment by the analytical methods one typically acquires, when one learns about probability and inference through the use of den sity functions. Even in standard traditional topics, one is often compelled to resort to heuristics; for example, it is difficult to prove central limit theorems for nonidentically distributed or martingale sequences, solely by the use of characteristic functions. Yet such proofs are essential, even in only moderately sophisticated classroom exposition. Unfortunately, relatively few students enter a graduate economics de partment ready to tackle probability theory in measure theoretic terms. The present volume has grown out of the need to lay the foundation for such discussions. The motivating forces were, chiefly, (a) the frustration one encounters in attempting to communicate certain concepts to stu dents wholly in analytic terms; and (b) the unwillingness of the typical student to sit through several courses in mathematics departments, in order to acquire the requisite background.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 380
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461245483
• Artikelnr.: 43986871

Inhaltsangabe

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.