We develop generalised indirect inference procedures that handle equality and inequality constraints on the auxiliary model parameters. We also show that the asymptotic efficiency of such estimators can never decrease by explicitly taking into account Lagrange multipliers associated with additional equality constraints, regardless of whether the restrictions are correct. Furthermore, we discuss the variety of effects on efficiency that can result from imposing some constraints on the parameters of a previously unrestricted model. As examples, we consider MA(1) estimated through AR(1), AR(1) through MA(1), and stochastic volatility through GARCH with Gaussian or t distributed errors.
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