  Indirect inference requires simulating realisations of endogenous variables
from the model under study. When the endogenous variables are discontinuous
functions of the model parameters, the resulting indirect inference criterion
function is discontinuous and does not permit the use of derivative-based
optimisation routines. Using a change of variables technique, we propose a
novel simulation algorithm that alleviates the discontinuities inherent in such
indirect inference criterion functions, and permits the application of
derivative-based optimisation routines to estimate the unknown model
parameters. Unlike competing approaches, this approach does not rely on kernel
smoothing or bandwidth parameters. Several Monte Carlo examples that have
featured in the literature on indirect inference with discontinuous outcomes
illustrate the approach, and demonstrate the superior performance of this
approach over existing alternatives.
