Constrained EMM and Indirect Inference Estimation

We develop generalised indirect inference procedures that handle equality and inequality constraints on the auxiliary model parameters. We obtain expressions for the optimal weighting matrices, and discuss as examples an MA(1) estimated as AR(1), an AR(1) estimated as MA(1), and a log-normal stochastic volatility process estimated as a GARCH(1,1) with Gaussian or t distributed errors. In the first example, the constraints have no effect, while in the second, they allow us to achieve full efficiency. As for the third, neither procedure systematically outperforms the other, but equality restricted estimators are better when the additional parameter is poorly estimated.