Econometrica: May, 1978, Volume 46, Issue 3

A Modified Stein-like Estimator for the Reduced Form Coefficients of Simultaneous Equations

https://doi.org/0012-9682(197805)46:3<695:AMSEFT>2.0.CO;2-Q
p. 695-703

Esfandiar Maasoumi

In 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 [2] and S. Sclove [16] 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.