## Bruce E. Hansen

A Stein-Like 2SLS Estimator

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Econometric Reviews, 2017

Abstract:

Maasoumi (1978) proposed a Stein-like estimator for simultanous equations and showed that his Stein shrinkage estimator has bounded finite sample risk, unlike the 3SLS estimator. We revisit his proposal by investigating Stein-like shrinkage in the context of 2SLS estimation of a structural parameter. Our estimator follows Maasoumi (1978) in taking a weighted average of the 2SLS and OLS estimators, with the weight depending inversely on the Hausman (1978) statistic for exogeneity. Using a local-to-exogenous asymptotic theory, we derive the asymptotic distribution of the Stein estimator, and calculate its asymptotic risk. We find that if the number of endogenous variables exceeds two, then the shrinkage estimator has strictly smaller risk than the 2SLS estimator, extending the classic result of James and Stein (1961). In a simple simulation experiment, we show that the shrinkage estimator has substantially reduced finite sample median squared error relative to the standard 2SLS estimator.

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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111.
Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.