Improved Small Sample Inference for Efficient Method of Moments and Indirect Inference Estimators

Résumé En

The efficient method of moments (EMM) and indirect inference (II) are two widely used simulation-based techniques for estimating structural models that have intractable likelihood functions. The poor performance in finite samples of traditional coefficient and overidentification tests based on the EMM or II objective function indicates a failure of first order asymptotic theory for the distribution of these tests, especially for EMM. We propose practically feasible saddlepoint coefficcient tests for hypotheses on structural coefficients estimated by II and EMM that are asymptotically chi-square distributed and have much better finite sample performance than traditional tests. To construct the tests, we make use of the fact that II and EMM estimators have asymptotically equivalent M-estimators and then use the coefficient saddlepoint tests for M-estimators developed by Robinson, Ronchetti and Young (2003). We evaluate the nite sample behavior of our coeffucient saddlepoint tests by Monte Carlo methods using a MA(1) model. Whereas traditional likelihood-ratio type tests can exhibit substantial size distortions,we show that our saddlepoint tests do not. We also find that the size-adjusted power of our saddlepoint tests is similar to and sometimes greater than the power of traditional tests.