Why does Indirect Inference estimation produce less small sample bias than maximum likelihood? : a note

Maximum Likelihood (ML) shows both lower power and higher bias in small sample Monte Carlo experiments than Indirect Inference (II) and IIís higher power comes from its use of the model-restricted distribution of the auxiliary model coeffi cients (Le et al. 2016). We show here that IIís higher power causes it to have lower bias, because false parameter values are rejected more frequently under II; this greater rejection frequency is partly o§set by a lower tendency for ML to choose unrejected false parameters as estimates, due again to its lower power allowing greater competition from rival unrejected parameter sets.