When people speak of "simulation variance", what does this mean? Does simulation variance disappear as $N \rightarrow \infty $?
Are models that have less simulation variance for a fixed $N$ considered more "robust"?
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Simulation variance is brought about by the fact that estimating expectations (integrals that are part of likelihood functions) by averaging a bunch of realizations of the respective random variables is not precise for a finite bunch. It gets smaller with the number of simulations and not related to the sample size, N.
Economic models may not have less simulation variance, they assume integrals to be computed exactly, so it is a separate issue.
My answer is like Alex's. Simulation variance appears in all analyses that apply Monte Carlo. there is nothing special about structural economics. The simulation results are based on random sample of size N being drawn from a population distribution. The distribution this sample (called the empirical distribution) is different from the population distribution because N is finite. If you took you did it again for another sample of size N you would not get the exact same empirical distribution and hence the simulation result would be different. This difference from one sample to the next has its variability characterized by the simulation variance. Now it is well known that for indpenedent identically distributed random variables as N increases the empirical distribution converges to the population distribution. So increasing N leads to distributions that are close together and hence the simulation variance is getting smaller and going to 0 and N approaches infinity.