  This paper explores the effects of simulated moments on the performance of
inference methods based on moment inequalities. Commonly used confidence sets
for parameters are level sets of criterion functions whose boundary points may
depend on sample moments in an irregular manner. Due to this feature,
simulation errors can affect the performance of inference in non-standard ways.
In particular, a (first-order) bias due to the simulation errors may remain in
the estimated boundary of the confidence set. We demonstrate, through Monte
Carlo experiments, that simulation errors can significantly reduce the coverage
probabilities of confidence sets in small samples. The size distortion is
particularly severe when the number of inequality restrictions is large. These
results highlight the danger of ignoring the sampling variations due to the
simulation errors in moment inequality models. Similar issues arise when using
predicted variables in moment inequalities models. We propose a method for
properly correcting for these variations based on regularizing the intersection
of moments in parameter space, and we show that our proposed method performs
well theoretically and in practice.
