Econometrica: May 1978, Volume 46, Issue 3
A Modified Stein-like Estimator for the Reduced Form Coefficients of Simultaneous Equations
Esfandiar MaasoumiIn this paper a reduced form estimator is developed which combines the corresponding restricted 3SLS and the unrestricted LS estimators. This estimator is similar to the `positive part' Stein-like estimators proposed by Baranchik  and S. Sclove  in the classical multivariate regression context. It is shown that, whereas the restricted (derived) 3SLS and 2SLS reduced form estimates possess no finite moments (hence have unbounded risk), the modified Stein-like reduced form (MSRF) estimator has finite moments of up to order (T - n - m), where T is the sample size, n and m are the number of the endogenous and the non-stochastic exogenous variables in the system. Furthermore it is argued that, asymptotically, the difference between the MSRF and the 3SLS estimators is negligible.
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