Different results of Durbin-Wu-Hausman tests for endogeneity in IV estimation

[Luigi Rombi]

Dear all,
I have some doubts about the interpretation of slightly different results of the Durbin (1954) and the Wu-Hausman (Wu, 1974; Hausman, 1978) test obtained after ivreg2 sls command.

I am performing an endogeneity test on a sample of 540 observations using the ivregress 2sls command in Stata. After running ivreg command, I obtain the results of the two tests via the estat endogenous postestimation command.

However, the two tests yield slightly different results. The Durbin test shows a p-value of 9.9%, while the Wu-Hausman test reports a p-value of 11.1%.

As far as I understand, both tests are interpreted in the same way (i.e., a statistically non-significant p-value suggests no endogeneity concerns), and this difference may arise from the fact that they are based on different distributions (Chi-square and F-distribution, respectively).

Given that my sample size is not particularly large, my question is: can I reasonably conclude that there are no endogeneity concerns based on the Wu-Hausman test alone, and disregard the Durbin test?

Best,
L

[Daniel Santos Torres]

Hi Luigi, I think the p-values are quite similar and at the border of rejecting the null at 90% of confidence so, from my point of view, it might be difficult to draw a strong conclussion about the endogeneity of the regressor.

Could you provide more information about the data, the specification you're trying and the instruments? Are they strong predictors of the endogenous variable and orthogonal to the outcome you want to measure? From my understanding of Staiger and Stock (1997) If instruments are weak, I think the Durbin test is preferred.

References:

Staiger, D., & Stock, J. (1997). Instrumental Variables Regression with Weak Instruments. Econometrica, Vol. 65, No. 3, pp. 557-586.

Best regards,
Daniel