Method of simulated moments

Method of simulated moments: In econometrics, the method of simulated moments (MSM) (also called simulated method of moments^[1]) is a structural estimation technique introduced by Daniel McFadden^[2]. It extends the generalized method of moments to cases where theoretical moment functions cannot be evaluated directly, such as when moment functions involve high-dimensional integrals. MSM's earliest and principal applications have been to research in industrial organization, after its development by Ariel Pakes and others, though applications in consumption are emerging.

GMM v.s. SMM

$\hat{\beta}_{GMM}=argmax\,m(x,\beta)'Wm(x,\beta)$ ,

where $m (x,β)$ is the moment condition.

$\hat{\beta}_{SMM}=argmax\,\hat{m}(x,\beta)'W\hat{m}(x,\beta)$ ,

where $\hat{m}(x,\beta)$ is the simulated moment condition and $E[\hat{m}(x,\beta)]=m(x,\beta)$

References

^ Cooper, Russell; Haltiwanger, John; Willis, Jonathan L. (2007). "Implications of Search Frictions: Matching Aggregate and Establishment-level Observations". NBER Working Paper. http://www.nber.org/papers/w13115.

^ D. McFadden. 1989 "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration". Econometrica, 57(5):995–1026

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