Exogeneity, weak identification and instrument selection in econometrics.

摘要

What happens to inference procedures when some instruments are endogenous or both weak and endogenous? In particular, what happens if an invalid instrument is added to a set of valid instruments? How robust are these inference procedures to instrument endogeneity? Do alternative inference procedures behave differently? If instrument endogeneity makes statistical inference unreliable, can we propose the procedures for selecting "good instruments" (i.e. strong and valid instruments)? Can we propose instrument selection procedure which will be valid even in presence of weak identification?;The second chapter analyzes the effects of weak identification on Durbin-Wu-Hausman (DWH) specification tests an Revankar-Harttley exogeneity test. We propose a finite-and large-sample analysis of the distribution of DWH tests under the null hypothesis (level) and the alternative hypothesis (power), including when identification is deficient or weak (weak instruments). Furthermore, we provide a characterization of the power of the tests, which clearly exhibits factors which determine power. Moreover, we present simulation evidence indicating: (1) over a wide range cases, including weak IV and moderate endogeneity, OLS performs better than 2SLS; (2) pretest-estimators based on exogeneity tests have an excellent overall performance compared with usual IV estimator.;We illustrate our theoretical results through simulation experiment and two empirical applications: the relation between trade and economic growth and the widely studied problem of returns to education.;In the third chapter, we extend the generalized Wald partial exogeneity test [Dufour (1987)] to non-gaussian errors. We develop in this chapter, a modified version of earlier procedure which is valid even when model errors are not normally distributed. We present simulation evidence indicating that when identification is strong, the standard GW-test is size distorted in presence of non-gaussian errors. Furthermore, our analysis of the performance of different pretest-estimators based on GW-tests allow us to propose two new pretest-estimators of the structural parameter. The Monte Carlo simulations indicate that these pretest-estimators have a better performance over a wide range cases compared with 2SLS. Therefore, this can be viewed as a procedure for selecting variable where a GW-test is used in the first stage to decide which variables should be instruments and which ones are valid instruments.;This thesis focuses on structural models and answers these questions through four chapters. The first chapter is published in Journal of Statistical Planning and Inference 138 (2008) 2649--2661. In this chapter, we analyze the effects of instrument endogeneity on two identification-robust procedures: Anderson and Rubin (1949, AR) and Kleibergen (2002, K) test statistics, with or without weak instruments. First, when the level of instrument endogeneity is fixed (does not depend on the sample size), we show that all these procedures are in general consistent against the presence of invalid instruments, whether the instruments are "strong" or "weak". We also describe situations where this consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. Second, when the instruments are locally exogenous, we find asymptotic non-central chi-square distributions with or without weak instruments, and describe situations where the non-centrality parameter is zero and the asymptotic distribution remains the same as in the case of valid instruments (despite the presence of invalid instruments).;We illustrate our theoretical results through two empirical applications: the well known wage equation and the returns to scale in electricity supply.;The fourth chapter develops identification-robust inference for the covariances between errors and regressors of an IV regression. The results are then applied to develop partial exogeneity tests and partial IV pretest-estimators which are more efficient than usual IV estimator.;When more than one stochastic explanatory variables are involved in the model, it is often necessary to determine which ones are independent of the disturbances. The generalized Wald (GW) procedure (Dufour, 1987) which typically allows the construction of confidence sets as well as testing linear restrictions on covariances assumes that the available instruments are strong. When the instruments are weak, the GW-test is in general size distorted.;To answer this problem, we develop a finite-and large-sample valid procedure for building confidence sets for covariances allowing for the presence of weak instruments. We provide analytic forms of the confidence sets and characterize necessary and sufficient conditions under which they are bounded. Moreover, we propose two new pretest-estimators of structural parameters based on our above procedure.;We illustrate our results through two empirical applications: the relation between trade and economic growth and the widely studied problem of returns to education. The results show unbounded confidence sets, suggesting that the IV are relatively poor in these models, as questioned in the literature [Bound (1995)]. (Abstract shortened by UMI.)