Statistical inference with simulated likelihood functions

This paper considers classical test statistics, namely, the likelihood ratio, efficient score, and Wald statistics, for econometric models under simulation estimation. The simulated likelihood ratio, simulated efficient score, and simulated Wald test statistics are shown to be asymptotically equivalent. Because the simulated score vector can be asymptotically biased, limiting distributions of these simulated statistics can be asymptotically noncentral chi(2) distributed. This paper studies inference issues with various simulated test statistics. Monte Carlo results are also provided to compare and demonstrate finite sample properties of simulated test statistics.