The common denominator in simulation-based inference (SBI) is the use of simulations for inference when dealing with econometric models which contain expectations that are intractable numerically and analytically. Here, we take inference to cover not only model parameter estimation and hypothesis testing, but also other facets of statistical analysis such as model validation, forecasting, and statistical properties of procedures.
Stochastic simulation for multiple integral evaluation is indeed a standard technique in numerical analysis. In econometrics, it has found direct application in various distinguishable directions. One of the earlier econometric applications dealt with Monte Carlo techniques for the analysis of exact sampling distributions of econometric estimators and test statistics in models beyond standard linear regression. A prominent example which received a great deal of attention in the early 1960s is the linear simultaneous equations model, where finite-sample properties of least squares and likelihood-based estimators and tests were investigated through stochastic simulations. In this area of application, model estimators, such as two-stage least squares and more general instrumental variable methods for simultaneous equations models, can be calculated with ease. However, an analytical study of their finite-sample properties is mostly intractable because the estimators depend on sample observations in a complicated way. Monte Carlo experimentation presents a viable approach toward approximating the exact sampling distributions of these estimators and evaluating expectations of functions of these estimators. Hendry (1984) provides an excellent survey.
A second area of application is prediction and specification testing in non-linear econometric models, where stochastic simulations are used to obtain unbiased forecasts and appropriate prediction regions.