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SAMPLING PROPERTIES OF THE INEQUALITY CONSTRAINED LEAST SQUARES ESTIMATOR WHEN THE USE OF A PROXY VARIABLE IS INEVITABLE

In this paper we suppose that an unobservable independent variable is one of the core independent variables, and thus the use of a proxy variable is inevitable. We also suppose that there is prior information in the form of an inequality constraint on the regression coefficient for the unobservable independent variable (latent variable). The bias and mean squared error of the inequality constrained least squares (ICLS) estimator are compared with those of the ordinary least squares estimator. It is shown that when the inequality constraint is true, or false and not nearly true, the effect of the inequality constraint gets large as the proxy variable gets poor.