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This paper proposes a simple modification of a conventional generalized method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration with estimators obtained by Monte Carlo simulation. This method of simulated moments does not require precise estimates of these probabilities, as the law of large numbers operating across observations controls simulation error, and, hence, can use simulations of practical size. The method is useful for models such as high-dimensional multinomial probit, where computation has previously restricted applications. Statistical properties are established using empirical process methods that can handle discontinuities introduced by simulation. Copyright 1989 by The Econometric Society.