Maximum Simulated Likelihood: Don’t Stop ’Til You Get Enough?

Maximum simulated likelihood estimation can be employed in empirical health economics, amongst others, to tackle issues concerning endogenous treatment effects. While theory suggests that maximum simulated likelihood estimation is asymptotically consistent, efficient and equivalent to the maximum likelihood estimator when both the number of simulation draws S and sample size N → ∞ and √N/S → 0 there is no guidance on how large of an S to choose and even theory suggests to experiment. This piece of research reviews strategies of health economists that aim at dealing with this issue. Most pieces of applied research rely on experimentation until numerical stability is achieved, while some employ Monte-Carlo techniques to justify their choice of S. A more formal test was suggested, but seemed not to be employed yet. This lack of guidance induces a research problem that needs to be properly addressed.