Indirect inference: A methodological essay on its role and applications

In this short paper we review the intellectual history of indirect inference as a methodology in its progress from an informal method for evaluating early models of representative agents to formally testing DSGE models of the economy; and we have considered the issues that can arise in carrying out these tests. We have noted that it is asymptotically equivalent to using FIML-i.e. in large samples; and that in small samples it is superior to FIML both in lowering bias and achieving good power. In application its power needs to be evaluated by Monte Carlo experiment for the particular context. Structural models need to be defined in terms of their scope of application and auxiliary models chosen suitably to test their applicability within this scope. Power can be set too high by using too many auxiliary model features to match; and it can be pushed too low by using too few. Excessively high shocks, such as wars and crises, may also limit a model's applicability by causing unusual behaviour that cannot be captured by the model. If so, these need to be excluded so that the model is evaluated for the 'normal times' in which it is applicable.