Simulation-Based Estimators in Structural Econometrics: SML, SMM, and MSS Explained

Описание: When structural models require numerical integration, whether from preference heterogeneity or dynamic expectations, classical estimators often become computationally intractable. This video introduces three simulation-based estimation methods: Simulated Maximum Likelihood (SML), Simulated Method of Moments (SMM), and Method of Simulated Scores (MSS). We compare their statistical properties, computational trade-offs, and practical relevance for applied structural estimation.

Slides used in the video are available here: https://raw.githack.com/tyleransom/st...
Source code for the slides is here: https://github.com/tyleransom/structu...

Topics covered:
Why structural models require simulation: preference heterogeneity and dynamic expectations
Simulated Maximum Likelihood (SML/MSL): replacing exact probabilities with simulated approximations
Jensen's inequality and the log-bias problem in SML: how the rate of growth of R relative to N determines consistency and efficiency
Simulated Method of Moments (SMM/MSM): matching simulated model moments to data moments without a log transformation
Why SMM avoids Jensen's inequality bias
Consistency of SMM even for fixed R, and the efficiency cost relative to MLE
Method of Simulated Scores (MSS): using a simulated score/gradient
Why MSS is rarely used in practice: difficulty of constructing an unbiased score simulator
Summary comparison of all three methods across bias, consistency, and efficiency

Related resources:
Kenneth Train, Discrete Choice Methods with Simulation (2nd ed., see Ch. 10) covers all three estimators in detail
Problem Set 4 (numerical integration and SML in Julia, referenced in the video): https://raw.githack.com/OU-PhD-Econom...

Tyler Ransom is an Associate Professor of Economics at the University of Oklahoma. Subscribe for more videos on data science, econometrics, and research methods!

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