UNDERID: Stata module producing postestimation tests of under- and over-identification after linear IV estimation

underid reports tests of underidentification and overidentification after estimation of single-equation linear instrumental variables (IV) models, including static and dynamic panel data models. Stata estimators supported include ivregress, ivreg2, xtivreg, xtivreg2, xthtaylor, xtabond2 and xtdpdgmm. Denote by y the dependent variable in a linear IV equation, Y the set of K endogenous regressors, and Z the set of L excluded instruments; any exogenous regressors X including the constant are partialled out. The model is underidentified if the rank of E(Z'Y) is less than K. Denote the first-stage coefficients by Pi and their OLS estimates by Pihat = inv(Z'Z)*Z'Y. The default underidentification test reported by underid is a test of the rank of E(Z'Y) or, equivalently, a test of the rank of Pi. The null hypothesis for underidentification is H0:rank(E(Z'Y))=K-1, with alternative H1: rank(E(Z'Y))=K, and therefore a rejection of the null indicates that the model parameters are identified. Overidentification tests in IV/GMM models are available when L exceeds K, i.e., the model is overidentified. The usual interpretation for a test of overidentification is that the null hypothesis is H0:E(Ze)=0, i.e., that the excluded instruments Z are orthogonal to the disturbance e. underid reports a range of related tests of underidentification and overidentification: Anderson, Cragg-Donald, Kleibergen-Paap, and Sargan-Hansen J-type 2-step GMM and Cragg-Donald CUE GMM tests. underid can report test statistics for both the classical setting (nonrobust, iid assumed) and statistics that are robust to various forms of heteroskedasticity, autocorrelation, and clustering.