The accessibility of high-performance computing power
has always influenced theoretical and applied econometrics.
Gouriéroux and Monfort begin their recent offering,
Simulation-Based Econometric Methods, with a stylized
three-stage classification of the history of statistical
econometrics. In the first stage, lasting through the 1960's,
models and estimation methods were designed to produce
closed-form expressions for the estimators. This spurred
thorough investigation of the standard linear model, linear
simultaneous equations with the associated instrumental
variable techniques, and maximum likelihood estimation
within the exponential family. During the 1970's and
1980's the development of powerful numerical optimization
routines led to the exploration of procedures without closed-form
solutions for the estimators. During this period the general
theory of nonlinear statistical inference was developed,
and nonlinear micro models such as limited dependent variable
models and nonlinear time series models, e.g., ARCH, were
explored. The associated estimation principles included
maximum likelihood (beyond the exponential family), pseudo-maximum
likelihood, nonlinear least squares, and generalized method
of moments. Finally, the third stage considers problems
without a tractable analytic criterion function. Such problems
almost invariably arise from the need to evaluate high-dimensional
integrals. The idea is to circumvent the associated numerical
problems by a simulation-based approach. The main requirement
is therefore that the model may be simulated given the
parameters and the exogenous variables. The approach delivers
simulated counterparts to standard estimation procedures
and has inspired the development of entirely new procedures
based on the principle of indirect inference.