Robust inference with GMM estimators

Article Abstract:

The local robustness properties of generalized method of moments (GMM) estimators and of a broad class of GMM based tests are investigated in a unified framework. GMM statistics are shown to have bounded influence if and only if the function defining the orthogonality restrictions imposed on the underlying model is bounded. Since in many applications this function is unbounded, it is useful to have procedures that modify the starting orthogonality conditions in order to obtain a robust version of a GMM estimator or test. We show how this can be obtained when a reference model for the data distribution can be assumed. We develop a flexible algorithm for constructing a robust GMM (RGMM) estimator leading to stable GMM test statistics. The amount of robustness can be controlled by an appropriate tuning constant. We relate by an explicit formula the choice of this constant to the maximal admissible bias on the level or (and) the power of a GMM test and the amount of contamination that one can reasonably assume given some information on the data. Finally, we illustrate the RGMM methodology with some simulations of an application to RGMM testing for conditional heteroscedasticity in a simple linear autoregressive model. In this example we find a significant instability of the size and the power of a classical GMM testing procedure under a non-normal conditional error distribution. On the other side, the RGMM testing procedures can control the size and the power of the test under non-standard conditions while maintaining a satisfactory power under an approximatively normal conditional error distribution. [C] 2001 Elsevier Science S.A. All rights reserved.

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Statistical inference for testing inequality indices with dependent samples

Article Abstract:

This paper develops asymptotically distribution-free inference for testing inequality indices with dependent samples. It considers the interpolated Gini coefficient and the generalized entropy class, which includes several commonly used inequality indices. We first establish inference tests for changes in inequality indices with completely dependent samples (i.e., matched pairs) and then generalize the inference procedures to cases with partially dependent samples. The effects of sample dependency on standard errors of inequality changes are examined through simulation studies as well as through applications to the CPS and PSID data. [C] 2001 Published by Elsevier Science S.A. JEL classification: C40; D63 Keywords: Generalized entropy indices; Gini coefficient; Theil indices; Asymptotic distribution; Statistical inference; Dependent samples

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Statistical inference for poverty measures with relative poverty lines

Article Abstract:

Relative poverty lines such as one-half median income have been increasingly used in poverty studies. This paper contributes to the literature by developing statistical inference for testing decomposable poverty measures with relative poverty lines. The poverty lines we consider are percentages of mean income and percentages of quantiles. We show that the estimates of poverty indices with relative poverty lines are asymptotically normally distributed and that the covariance structure can be consistently estimated. As a consequence, asymptotically distribution-free statistical inference can be established in a straightforward manner. [C] 2001 Published by Elsevier Science S.A. JEL classification: C40; 132 Keywords: Relative poverty line; Decomposable poverty measure; Statistical inference

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