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Instrumental Variables Estimation with Flexible Distributions



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Instrumental Variables Estimation with Flexible Distributions Christian Hansen Graduate School of Business University of Chicago James B McDonald Brigham Young University Department of Economics Whitney K Newey Department of Economics M I T October 2 2006 Abstract Instrumental variables are often associated with low estimator precision This paper explores efficiency gains which might be achievable using moment conditions which are nonlinear in the disturbances and are based on flexible parametric families for error distributions We show that these estimators can achieve the semiparametric efficiency bound when the true error distribution is a member of the parametric family Monte Carlo simulations demonstrate low efficiency loss in the case of normal error distributions and potentially significant efficiency improvements in the case of thick tailed and or skewed error distributions Research assistance provided by Brigham Frandsen Samuel Dastrup and Randall Lewis is gratefully appreciated 1 1 Introduction Instrumental variables IV estimation is important in economics A common finding is that the precision of IV estimators is low This paper explores potential efficiency gains that might result from using moment conditions that are nonlinear in the disturbances It is known that this approach can produce large efficiency gains in regression models The hope is that such efficiency gains might also be present when models are estimated by IV These gains could help in overcoming the low efficiency of IV estimators A simple approach to improving efficiency in IV estimation based on nonlinear functions of the residuals is to use flexible parametric families of disturbance distributions This approach has proven useful in a variety of settings For example McDonald and Newey 1988 present a generalized t distribution which can be used to obtain partially adaptive estimators of regression parameters McDonald and White 1993 use the generalized t and an exponential generalized beta



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