From The New Palgrave Dictionary of Economics, Second Edition, 2008

The problem of statistical model selection in econometrics and statistics is reviewed. Model selection is interpreted as a decision problem through which a statistical model is selected in order to perform statistical analysis, such as estimation, testing, confidence set construction, forecasting, simulation, policy analysis, and so on. Broad approaches to model selection are described: (1) hypothesis testing procedures, including specification and diagnostic tests; (2) penalized goodness-of-fit methods, such as information criteria; (3) Bayesian approaches; (4) forecast evaluation methods. The effect of model selection on subsequent statistical inference is also discussed