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Unformatted text preview: Instrumental Variable Estimation with Heteroskedasticity and Many Instruments Jerry A. Hausman Department of Economics M.I.T. Whitney K. Newey Department of Economics M.I.T. Tiemen Woutersen Department of Economics Johns Hopkins University John Chao Department of Economics University of Maryland Norman Swanson Department of Economics Rutgers University August 2006 Revised September 2009 Abstract This paper gives a relatively simple, well behaved solution to the problem of many instruments in heteroskedastic data. Such settings are common in micro econometric applications where many instruments are used to improve e ciency and allowance for heteroskedasticity is generally important. The solution is a Fuller (1977) like estimator and standard errors that are robust to heteroskedasticity and many instruments. We show that the estimator has f nite moments and high as ymptotic e ciency in a range of cases. The standard errors are easy to compute, being like Whites (1982), with additional terms that account for many instruments. They are consistent under standard, many instrument, and many weak instrument asymptotics. Based on a series of Monte Carlo experiments, we f nd that the es timators perform as well as LIML or Fuller (1977) under homoskedasticity, and have much lower bias and dispersion under heteroskedasticity, in nearly all cases considered. JEL Classi f cation: C12, C13, C23 Keywords: Instrumental Variables, Heteroskedasticity, Many Instruments, Jackknife The NSF provided f nancial support for this paper under Grant No. 0136869. Helpful comments were provided by A. Chesher and participants in seminars at CalTech, CEMMAP, Harvard, MIT, Pittsburgh, UC Berkeley, UCL, and USC. Capable research assistance was provided by H. Arriizumi, S. Chang, A. Kowalski, R. Lewis, and K. Menzel. K. Menzel derived the vectorized form of the variance estimator. 1 I n t r o d u c t i o n This paper gives a relatively simple, well behaved solution to the problem of many instruments in heteroskedastic data. Such settings are common in microeconometric applications where many instruments are used to improve e ciency and allowance for heteroskedasticity is generally important. The solution is a Fuller (1977) like estimator and standard errors that are robust to heteroskedasticity and many instruments. We show that the estimator has f nite moments and high asymptotic e ciency in a range of cases. The standard errors are easy to compute, being like Whites (1982), with ad ditional terms that account for many instruments.They are consistent under standard, many instrument, and many weak instrument asymptotics. They extend Beckers (1994) standard errors to the heteroskedastic case....
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 Fall '08
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 Economics

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