This paper develops two new methods for conducting formal statistical inference in nonlinear dynamic economic models. The two methods require very little analytical tractability, relying instead on numerical simulation of the model's dynamic behaviour. Although one of the estimators is asymptotically more efficient than the other, a Monte Carlo study shows that, for a specific application, the less efficient estimator has smaller mean squared error in samples of the size typically encountered in macroeconomics. The estimator with superior small sample performance is used to estimate the parameters of a real business cycle model using observed US time-series data.