* We would like to thank Tom Wansbeek, Ton Steerneman, Eric Zivot and anonymous referees for helpful comments. ABSTRACTThe paper considers the estimation of the coefficients of a single equation in the presence of dummy intruments. We derive pseudo ML and GMM estimators based on moment restrictions induced either by the structural form or by the reduced form of the model.The performance of the estimators is evaluated for the non-Gaussian case. We allow for heteroscedasticity. The asymptotic distributions are based on parameter sequences where the number of instruments increases at the same rate as the sample size. Relaxing the usual Gaussian assumption is shown to affect the normal asymptotic distributions. As a result also recently suggested new specification tests for the validity of instruments depend on Gaussianity. Monte Carlo simulations confirm the accuracy of the asymptotic approach.

No abstract

No abstract

This paper gives a new jackknife estimator for instrumental variable inference with unknown heteroskedasticity. The estimator is derived by using a method of moments approach similar to the one that produces LIML in case of homoskedasticity. The estimator is symmetric in the endogenous variables including the dependent variable. Many instruments and many weak instruments asymptotic distributions are derived using high-level assumptions that allow for the simulataneous presence of weak and strong instruments for different explanatory variables. Standard errors are formulated compactly. We review briefly known estimators and show in particular that the symmetric jackknife estimator performs well when compared to the HLIM and HFUL estimators of Hausman et al. (2011) in Monte Carlo experiments.

We consider the single equation errors-in-variables model and assume that a researcher is willing to specify an upper bound on the variance covariance matrix of ineasurement errors in the endogenous and exogenous variables. The measurement errora may show any pattern of correlations. It is shown tha[ as a result the set of ML estimates is bounded by an ellipsoid. When, in addition, the variance covariance matrix of the errors is constrained to be diagonal, the set of ML estimates is shown to be bounded by [he convex hull of 2R points (R being the number of error-ridden exogenous variables), lying on the surface of the ellipsoid. The results are applied to an empirical example and extensions to a simultaneous equa[ions system are briefly discussed.