Constrained Indirect Estimation

We develop generalized indirect estimation procedures that handle equality and inequality constraints on the auxiliaty model parameters by extracting information from the relevant multipliers, and compare their asymptotic efficiency to maximum likelihood. We also show that, regardless of the validity of tbe restrictions, the asymptotic efficiency of such estimators can never decrease by explicitly considering the multipliers associatcd with additional equality constraints. Furthermore, we discuss the variety of effects on efficiency that can result from imposing constraints on a previously unrestricted model. As an example, we consider a stochastic volatility process estimated through a GARCH model with Gaussian or t distributed errors.