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The Existence of Moments of the Ordinary Least Squares and Two-Stage Least Squares Estimators

Roberto S. Mariano

Abstract

This paper deals with two single-equation estimators in a set of simultaneous linear stochastic equations--namely, ordinary least squares (OLS) and two-stage least squares (2SLS). Under the assumption that all predetermined variables in the model are exogenous, necessary and sufficient conditions are obtained for the existence of even moments of the above estimators. It is shown that for the general case with an arbitrary number of included endogenous variables, even moments of the 2SLS estimator are finite if and only if the order is less than K2 - G1 + 1. Furthermore, even moments of the OLS estimator exist if and only if the order is less than N - K1 - G1 + 1, where N is the sample size, G1 + 1 is the number of included endogenous variables, K1 and K2 respectively are the number of included and excluded exogenous variables in the equation to be estimated.