IVENDOG: Stata module to calculate Durbin-Wu-Hausman endogeneity test after ivreg

ivendog computes a test for endogeneity in a regression estimated via instrumental variables (IV), the null hypothesis for which states that an ordinary least squares (OLS) estimator of the same equation would yield consistent estimates: that is, any endogeneity among the regressors would not have deleterious effects on OLS estimates. A rejection of the null indicates that endogenous regressors' effects on the estimates are meaningful, and instrumental variables techniques are required. The test was first proposed by Durbin (1954) and separately by Wu (1973) (his T4 statistic) and Hausman (1978). This "Durbin-Wu-Hausman" (DWH) test is numerically equivalent to the standard "Hausman test" obtained using {help hausman} with the sigmamore option, in which both forms of the model must be estimated. Under the null, it is distributed Chi-squared with m degrees of freedom, where m is the number of regressors specified as endogenous in the original instrumental variables regression. The ivendog output also contains another test statistic: the "Wu-Hausman" T2 statistic of Wu (1973). This routine is a replacement for "dmexog". W Its facilities are also available in our "ivreg2" routine via the "orthog" option. That routine can handle cases which "ivendog" cannot, such as ivreg or ivreg2's robust option or ivreg2's GMM option.