An interpretation and implementation of the Theil-Goldberger 'mixed' estimator

Theil and Goldberger (Int. Ec. Rev., 1961) and Theil (JASA, 1963) proposed a generalized least squares approach to 'mixing' sample information and prior beliefs about the coefficients of a regression equation. Their 'mixed' estimator may be considered as a stochastic version of constrained least squares (Stata's cnsreg). Although based on frequentist statistics, the TG estimator is identical to that used in a Bayesian estimation approach when an informative prior density is employed (Greene text, 2008). It may also be viewed as a 'one-shot' application of the Kalman filter, providing an updating equation for point and interval coefficients based on prior and sample information (Cuthbertson et al. text, 1992). I discuss the motivation for the estimator and my implementation in Stata code, tgmixed, and give illustrations of how it might be usefully employed.