The Hausman test for endogeneity

[ALKEBSEE RADWAN]

I have read in a paper that we can use Hausman test for endogeneity. and the authors mentioned that we can use error term as follows:

we perform the Hausman test (Gujarati, 2003) as follows. First, we obtain the error term (ύ) from an estimate of audit committee cash compensation regression (ACCASH) that includes the following determinants: firm size (LNTA), leverage (LEV), return on assets (ROA), market‐to‐book ratio (MKTBOOK), litigation risk (LITRISK), sales growth in industry (INDSAL), inside ownership (INSIDER), CEO power (CEOPOWER), accounting expertise on the audit committee (ACEXPERT), audit committee meetings (ACMEET), audit committee multiple‐directorships (ACBUSY), and industry fixed effects. Next, we include the obtained error term (ύ) in all our main regressions to determine if it is significant. A significant ύ will indicate that the propensity to beat earnings by a large margin and audit committee cash compensation is endogenous. In all of our primary and additional tests, the error term (ύ) is not significant (p > .10). As there is no evidence of endogeneity between our test and dependent variables, we can proceed to estimate and present single multivariate regression results

kindly can someone explain to me how to extract the error term and how to apply this process ?
thanks in advance.

[Fernando Martins]

Hi Alkebsee,

I think you can follow this procedure to have the same results from the paper:

- Run the first regression of your dependent variable against all the regressors
- Use the comand 'predict resid, residuals' to create a variable of your residuals named 'resid'
- Run your regression again, but now including 'resid' as one of your control variables

You should get what they got. The problem is that I don't know if this is the right description of the Hausman Test nor the right procedure to check for endogeneity since it's missing instrumental variables to be considered a reduced form test.

Can you explain a little more what you are trying to achieve here?

[ALKEBSEE RADWAN]

Hi Alkebsee,

I think you can follow this procedure to have the same results from the paper:

- Run the first regression of your dependent variable against all the regressors
- Use the comand 'predict resid, residuals' to create a variable of your residuals named 'resid'
- Run your regression again, but now including 'resid' as one of your control variables

You should get what they got. The problem is that I don't know if this is the right description of the Hausman Test nor the right procedure to check for endogeneity since it's missing instrumental variables to be considered a reduced form test.

Can you explain a little more what you are trying to achieve here?

Dear Fernando,

First of all, Thank you so much for replying.
Secondly, you said ((Run the first regression of your dependent variable against all the regressors)) kindly what do you mean by against all regressors? do mean that i run the first regression as follows:

reg dependent variable which is my  independent variable, and control variables i.yea i.industrty

?

Thirdly,
What i am trying to achieve is (1) Is this process the Hausman test ? because when I looked for this test i found a different way.
(2) If it is not the Hausman test so what i should call it?
(3) Which coefficient that is important ? is it the coefficient of resid (the new variable) ? or of which variable? in the meantime should this coefficient be insignificant? to make sure there is no endogeneity issue?
(4) As you mentioned that ((The problem is that I don't know if this is the right description of the Hausman Test nor the right procedure to check for endogeneity since it's missing instrumental variables to be considered a reduced form test)) if I have instrumental variable (which is related to the independent variable) How can i use it in this process?

Once again thank you so much
Kind

[Eric de Souza]

Let the model be :
y = a + bx + cw +u
where x is suspected of endogeneity and z is assumed exogenous.
Let z be an instrument for x
In 2SLS estimation, the first stage regression is a regression of x on w and z ("all" the instruments and "all" the exogenous regressors); and the second stage regression is the regression of y on xhat, the fitted value from the first stage regression ) and w. Of course, to obtain correct standard errors you need to use a 2SLS routine.

The endogeneity test consists in:
running the second stage regression with the residual from the first stage added and testing the null hypothesis that the coefficient of the residual is zero.. The null hypothesis is that x is exogenous.

[Chris Boudreaux]

Fernando in post #2 and Eric in post #4 both provide the solution. This is also known as the control function approach and covered in Wooldridge (2010). Alternatively, Stata will provide this test for you after ivregress using the post estimation command, estat endogenous



Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. MIT press.

[Eric de Souza]

For the record, there is a typo in my post #4
"where x is suspected of endogeneity and z is assumed exogenous."
should read
"where x is suspected of endogeneity and w is assumed exogenous."