190 IV13 Hausman test

This video dives into the Hausman test, a crucial diagnostic tool in econometrics. We explore how it formally compares OLS and IV estimates to determine if their differences are statistically significant, providing evidence of endogeneity. Understanding the test's core idea, its null and alternative hypotheses, and the Hausman statistic is key to interpreting results. While a powerful test for endogeneity, we also discuss its limitations, emphasizing that it assumes instrument validity and doesn't prove OLS validity if the null is not rejected. Building on the trade-offs between OLS and IV, where OLS is efficient for exogenous variables and IV is consistent for endogenous ones, the Hausman test quantifies whether the gap between these two estimators is too large to be merely sampling variation. Under the null hypothesis that there is no endogeneity, both OLS and IV are consistent. If the null is rejected, it indicates that OLS and IV estimates differ significantly, suggesting OLS is biased and endogeneity is present. The Hausman test statistic, derived from the squared difference between the IV and OLS estimates scaled by their variance, follows a chi-square distribution. We cover interpreting p-values and a practical implementation involving first-stage residuals. It is critical to remember that the Hausman test is a test of endogeneity, not instrument validity, and it assumes the IV instrument is consistent. Its power can also be low with weak instruments or small samples, meaning failure to reject the null does not guarantee OLS validity. Stay tuned for the next video, where we address the problem of weak instruments. Visit AxiomTutoring.com for more resources and subscribe to @AxiomTutoringCourses for advanced econometrics courses.