Book contents
- Frontmatter
- Contents
- List of figures
- List of tables
- List of contributors
- Preface
- Acknowledgements
- Michael Magdalinos 1949–2002
- Introduction
- 1 Conditional Heteroskedasticity Models with Pearson Disturbances
- 2 The Instrumental Variables Method Revisited: On the Nature and Choice of Optimal Instruments
- 3 Nagar-Type Moment Approximations in Simultaneous Equation Models: Some Further Results
- 4 Local GEL Methods for Conditional Moment Restrictions
- 5 Limit Theory for Moderate Deviations From a Unit Root Under Weak Dependence
- 6 The Structure of Multiparameter Tests
- 7 Cornish-Fisher Size Corrected t and F Statistics for the Linear Regression Model with Heteroscedastic Errors
- 8 Non-Parametric Specification Testing of Non-Nested Econometric Models
- 9 Testing for Autocorrelation in Systems of Equations
- 10 Alternative Approaches to Estimation and Inference in Large Multifactor Panels: Small Sample Results with an Application to Modelling Asset Returns
- 11 Judging Contending Estimators by Simulation: Tournaments in Dynamic Panel Data Models
- 12 A Statistical Proof of the Transformation Theorem
- 13 On the Joint Density of the Sum and Sum of Squares of Non-Negative Random Variables
- 14 Conditional Response Analysis
- References
- Index
4 - Local GEL Methods for Conditional Moment Restrictions
Published online by Cambridge University Press: 22 September 2009
- Frontmatter
- Contents
- List of figures
- List of tables
- List of contributors
- Preface
- Acknowledgements
- Michael Magdalinos 1949–2002
- Introduction
- 1 Conditional Heteroskedasticity Models with Pearson Disturbances
- 2 The Instrumental Variables Method Revisited: On the Nature and Choice of Optimal Instruments
- 3 Nagar-Type Moment Approximations in Simultaneous Equation Models: Some Further Results
- 4 Local GEL Methods for Conditional Moment Restrictions
- 5 Limit Theory for Moderate Deviations From a Unit Root Under Weak Dependence
- 6 The Structure of Multiparameter Tests
- 7 Cornish-Fisher Size Corrected t and F Statistics for the Linear Regression Model with Heteroscedastic Errors
- 8 Non-Parametric Specification Testing of Non-Nested Econometric Models
- 9 Testing for Autocorrelation in Systems of Equations
- 10 Alternative Approaches to Estimation and Inference in Large Multifactor Panels: Small Sample Results with an Application to Modelling Asset Returns
- 11 Judging Contending Estimators by Simulation: Tournaments in Dynamic Panel Data Models
- 12 A Statistical Proof of the Transformation Theorem
- 13 On the Joint Density of the Sum and Sum of Squares of Non-Negative Random Variables
- 14 Conditional Response Analysis
- References
- Index
Summary
Introduction
Simulation evidence increasingly indicates that for many models specified by unconditional moment restrictions the generalized method of moments (GMM) estimator (Hansen, 1982) may be substantially biased in finite samples, especially so when there are large numbers of moment conditions. See, for example, Altonji and Segal (1996), Imbens and Spady (2001), Judge and Mittelhammer (2001), Ramalho (2001) and Newey, Ramalho and Smith (2005). Newey and Smith (2004), henceforth NS, provides theoretical underpinning for these findings. Alternative estimators which are first-order asymptotically equivalent to GMM include empirical likelihood (EL) (Owen, 1988; Qin and Lawless, 1994; and Imbens 1997), the continuous updating estimator (CUE) (Hansen, Heaton and Yaron, 1996), and exponential tilting (ET) (Kitamuraand Stutzer, 1997 and Imbens, Spady and Johnson, 1998). See also Owen (2001). NS show that these estimators and those from the Cressie and Read (1984) power divergence family of discrepancies are members of a class of generalized empirical likelihood (GEL) estimators and have a common structure; see Brown and Newey (1992, 2002) and Smith (1997, 2001). Correspondingly NS also demonstrate that GEL and GMM estimators are asymptotically equivalent and thus possess the same first-order asymptotic properties. For the unconditional context, NS describe the higher-order efficiency of bias-corrected EL. Also see Kitamura (2001).
The principal aim of this chapter is adapt the GEL method to the conditional moment context and, thereby, to describe GEL estimators which achieve the semi-parametric efficiency lower bound.
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- The Refinement of Econometric Estimation and Test ProceduresFinite Sample and Asymptotic Analysis, pp. 100 - 122Publisher: Cambridge University PressPrint publication year: 2007
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