Instrumental variable estimation with heteroskedasticity and many instruments

Abstract

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

Asymptotic Distribution of Jive in a Heteroskedastic Iv Regression With Many Instruments

“…In contrast, consistency of LIML and Fuller (1977) requires K n /r n −→ 0 when P ii is asymptotically correlated with E[X i ε i |Z]/E[ε 2 i |Z], as discussed in Chao and Swanson (2004) and Hausman et al (2007). This condition is also required for consistency of the bias corrected 2SLS estimator of Donald and Newey (2001) when P ii is asymptotically correlated with E[X i ε i |Z], as discussed in Ackerberg and Devereux (2009).…”

“…Bekker and van der Ploeg (2005), Ackerberg and Devereux (2009), Chao and Swanson (2006), and Hausman et al (2007)). The main objective of this paper is to develop asymptotic theory for the JIV estimators in a setting that includes the many instrument sequence of Kunitomo (1980), Morimune (1983), and Bekker (1994) and the many weak instrument sequence of Chao and Swanson (2005).…”

“…In recent years, there has been interest in developing procedures that use "deleteone" fitted values in lieu of the usual first-stage OLS fitted values as the instruments employed in the second stage of the estimation. A number of different versions of these estimators, referred to as jackknife instrumental variables (JIV ) estimators, have been proposed and analyzed by Phillips and Hale (1977), Angrist, Imbens, and Krueger (1999), Blomquist and Dahlberg (1999), Ackerberg and Devereux (2009), Davidson and MacKinnon (2006), and Hausman, Newey, Woutersen, Chao, and Swanson (2007).…”

“…For example, it has already been used in Hausman et al (2007) to derive the asymptotic properties of the jackknife versions of the LIM L and Fuller (1977) estimators and in Chao et al (2010) to derive a moment based test.…”

Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain

“…The promised improvement in efficiency is appealing, but IV estimators based on many instruments may have poor properties. See, for example, , , Hansen, Hausman, and Newey (2008), and Hausman, Newey, Woutersen, Chao, and Swanson (2009) which propose solutions for this problem based on "manyinstrument" asymptotics.…”