### (DP 1979-21) On the Effect of Multicollinearity Upon the Properties of Structural Coefficient Estimators

#### Abstract

This paper considers as analytical investigation of multicollinearity in a simultaneous-equation model and focuses on coefficients of endogenous variables. Previous Monte Carlo studies tend to support the notion that higher multicollinearity among exogenous variables causes estimator precision to deteriorate. It is shown in this paper, however, that in the case of simple, partial and multiple correlations, higher multicollinearity can increase or decrease the mean squared error of estimators, depending upon the true model parameter values and the observations on the exogenous variables. Some special cases are identified where a higher degree of multicollinearity brings about less precise estimators. The analysis leading to this indeterminacy of multicollinearity effects starts from the result that multicollinearity among the exogenous variables will affect the probability distributions of the LIML and k-class estimators (k non-stochastic and 0 ¡Ü k ¡Ü 1) only through the so-called concentration parameter. Through numerical calculations of concentration parameter values in two simulation studies, we reconcile the apparent conflict between the conclusion from Monte Carlo experiments and the analytical result presented here. The paper also contains some comments on an approach to making a choice among competing data sets for the exogenous variables. It also suggests a way of choosing additional observation vectors to increase estimator precision in simultaneous system.

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