We present a minimum distance approach for conducting hypothesis testing in the presence of potentially weak instruments. Under this approach, we propose size-correct tests for limited dependent variable models with endogenous explanatory variables such as endogenous tobit and probit models. Additionally, we extend weak-instrument tests for the linear instrumental-variables model by allowing for variance-covariance estimation that is robust to arbitrary heteroskedasticity or intracluster dependence. We invert these tests to construct confidence intervals on the coefficient of the endogenous variable. We also provide a postestimation command for Stata, called rivtest, for computing the tests and estimating confidence intervals.
We propose tests for structural parameters in limited dependent variable models with endogenous explanatory variables. These tests are based upon the generalized minimum distance principle. They are of the correct size regardless of whether the structural parameters are identified and are especially appropriate for models whose moment conditions are non-linear in the parameters. Moreover, they are computationally simple, allowing them to be implemented using a large number of statistical software packages. We compare our tests to Wald tests in a simulation experiment and use them to analyse the female labour supply and the demand for cigarettes. Copyright (C) 2010 The Author(s). The Econometrics Journal (C) 2010 Royal Economic Society
Limited-information identification-robust methods on the indexation and price rigidity parameters of the New Keynesian Phillips Curve yield very wide confidence intervals. Full-information methods impose more restrictions on the reduced-form dynamics and thus make more efficient use of the information in the data. However, such methods are also subject to weak instrument problems. We propose identification-robust minimum distance methods for exploiting these additional restrictions and show that they yield considerably smaller confidence intervals for the coefficients of the model compared to their limited-information generalized method of moments counterparts. In contrast to previous studies, we find evidence of partial but not full indexation, and obtain sharper inference on the degree of price stickiness. However, this parameter remains weakly identified. Copyright (c) 2010 The Ohio State University.
Summary
Microeconomic data often have within‐cluster dependence, which affects standard error estimation and inference. When the number of clusters is small, asymptotic tests can be severely oversized. In the instrumental variables (IV) model, the potential presence of weak instruments further complicates hypothesis testing. We use wild bootstrap methods to improve inference in two empirical applications with these characteristics. Building from estimating equations and residual bootstraps, we identify variants robust to the presence of weak instruments and a small number of clusters. They reduce absolute size bias significantly and demonstrate that the wild bootstrap should join the standard toolkit in IV and cluster‐dependent models.
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