Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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 efficiency 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 finite moments and high asymptotic efficiency in a range of cases. The standard errors are easy to compute, being like White's (1982), with additional terms that account for many instruments. They are consistent under standard, many instrument, and many weak instrument asymptotics. We find that the estimator is asymptotically as efficient as the limited-information maximum likelihood (LIML) estimator under many weak instruments. In Monte Carlo experiments, we find that the estimator performs as well as LIML or Fuller (1977) under homoskedasticity, and has much lower bias and dispersion under heteroskedasticity, in nearly all cases considered. Terms of use: Documents in
Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in August, 2007Revised October, 2010 JEL classification: C13, C31.Keywords: heteroskedasticity, instrumental variables, jackknife estimation, many instruments, weak instruments. → 0 as n → ∞, where K n and r n denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical IV estimators as LIM L, B2SLS, and 2SLS, all of which are inconsistent in the presence of heteroskedasticity, unless K n rn → 0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r n and K n .
This paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity. It is based on a jackknife version of the Sargan test statistic, having a numerator that is the objective function minimized by the JIVE2 estimator of Angrist, Imbens, and Krueger (1999). Correct asymptotic critical values are derived for this test when the number of instruments grows large, at a rate up to the sample size. It is also shown that the test is valid when the number instruments is fixed and there is homoskedasticity. This test improves on recently proposed tests by allowing for heteroskedasticity and by avoiding assumptions on the instrument projection matrix.The asymptotics is based on the heteroskedasticity robust many instrument asymptotics .
Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in August, 2007Revised October, 2010 JEL classification: C13, C31.Keywords: heteroskedasticity, instrumental variables, jackknife estimation, many instruments, weak instruments. → 0 as n → ∞, where K n and r n denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical IV estimators as LIM L, B2SLS, and 2SLS, all of which are inconsistent in the presence of heteroskedasticity, unless K n rn → 0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r n and K n .
This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’s smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework.
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