Model Selection in Equations with Many 'Small' Effects

General unrestricted models (GUMs) may include important individual determinants, many small relevant effects, and irrelevant variables.  Automatic model selection procedures can handle perfect collinearity and more candidate variables than observations, allowing substantial dimension reduction from GUMs with salient regressors, lags, non-linear transformations, and multiple location shifts, together with all the principal components representing 'factor' structures, which can also capture small influences that selection may not retain individually.  High dimensional GUMs and even the final model can implicitly include more variables than observations entering via 'factors'.  We simulate selection in several special cases to illustrate.