I have a set of panel data and I am adding one instrumental variable to the panel regression.
The coefficient for the endogenous variable is -3.8% (p<0.0001) with R^2=20% but after adding the IV it suddenly changed to +76% (p<0.0001) with R^2=-1.2%. I did the following test:
And the diagnostic test shows:
Weak instruments p-value is 1.45e-11, which means it's not weak Wu-Hausman p-value is <2e-16 , which means IV is consistent and OLS is not
Can anyone please suggest anything? Happy to provide my data.
An instrument has to satisfy two criteria: relevance - the instrument and the instrumented variable are sufficiently correlated - that is what you test with the weak dependence test and exogeneity - the instrument is not correlated with the error of the regression, where you are instrumenting.
As you have only one instrument you cannot test exogeneity and have to think whether it is reasonable to assume exogeneity based on the information about the data set.
If the instrument is exogenous and the Hausman-Wu test rejects the null hypothesis, this tells you that the estimates of the consistent estimator(IV) and the efficient estimator(OLS) differ (which is waht you see in your regression output). Thus you should use the IV estimate.
If however the instrument is not exogenous the assumptions of the Hausman-Wu test are violated and the result of the test is not informative. In this case both regressions (IV and OLS) are inconsistent.