A Critical Assessment of Simulated Critical Values

There is a wide variety of statistical problems (e.g., unit root and cointegration tests) where hypothesis testing involves the use of simulated rather than theoretical critical values. We argue that in practice the number of replications used to simulate critical values is often insufficient to provide the degree of precision that is implied. In particular, the number of replications needed is greatest for values in the tails of the distribution. We provide recommendations for approximating the number of replications needed to achieve a desired degree of precision.