Shrinkage Estimators for Structural Parameters

IV estimators of parameters in single equation structural models, like 2SLS and the LIML, are the most commonly used econometric estimators. Hausman-type tests are commonly used to choose between OLS and IV estimators. However, recent research has revealed troublesome size properties of Wald tests based on these pre-test estimators. These problems can be circumvented by usage of shrinkage estimators, particularly James-Stein estimators. We introduce the -ivshrink- command which encompasses nearly 20 distinct variants of the shrinkage-type estimators proposed in the econometrics literature, based on optimal risk properties, including fixed (k-class estimators are a special case) and data-dependent shrinkage estimators (random convex combinations of OLS and IV estimators, for example). Analytical standard errors, to be used in Wald-type tests are provided where appropriate, and bootstrap standard errors are reported otherwise. Where the variance-covariance matrices of the resulting estimators are expected to be degenerate, options for matrix norm regularization are also provided. We illustrate the techniques using a widely used dataset in the econometric literature.