Model selection in equations with many 'small' effects

High dimensional general unrestricted models (GUMs) may include important individ-ual determinants, many small relevant effects, and irrelevant variables. Automatic modelselection procedures can handle more candidate variables than observations, allowing substantial dimension reduction from GUMs with salient regressors, lags, nonlinear transformations, and multiple location shifts, together with all the principal components, possibly representing ‘factor’ structures, as perfect collinearity is also unproblematic. ‘Factors’can capture small influences that selection may not retain individually. The final model can implicitly include more variables than observations, entering via ‘factors’. We simulate selection in several special cases to illustrate