Testing models with fat tails via indirect inference

Fat tails can in principle undermine the power of the standard indirect inference test. We examine this issue with Monte Carlo experiments, first for a New Keynesian model solved by the nonlinear algorithm method of Fair and Taylor. Here we find that the standard test has its usual high power, even in a model exhibiting potentially fat tails due to misspecification. If the model is solved by Dynare, then fat tails have only a minor effect on the power of the standard test so that the problem can be ignored except for very extreme fatness. It is therefore unlikely to occur; if it does, it can be solved either by eliminating outlier shocks, or by switching to the Fair-Taylor solution method. Second, we examine the case of the highly nonlinear CGE trade model where we find the fat tails problem is acute and pervasive, as shocks interact with the model nonlinearity to create high volatility. Here eliminating outliers restores the test power.