A new use of importance sampling to reduce computational burden in simulation estimation

Simulation estimators (Lerman and Manski 1981; McFadden, Econometrica 57(5):995–1026, 1989; Pakes and Pollard, Econometrica 57:1027–1057, 1989) have been of great use to applied economists and marketers. They are simple and relatively easy to use, even for very complicated empirical models. That said, they can be computationally demanding, since these complicated models often need to be solved numerically, and these models need to be solved many times within an estimation procedure. This paper suggests methods that combine importance sampling techniques with changes-of-variables to address this caveat. These methods can dramatically reduce the number of times a particular model needs to be solved in an estimation procedure, significantly decreasing computational burden. The methods have other advantages as well, e.g. they can smooth otherwise non-smooth objective functions and can allow one to compute derivatives analytically. There are also caveats—if one is not careful, they can magnify simulation error. We illustrate with examples and a small Monte-Carlo study.