Simultaneous Equations (REG3) and Endogeneity Test Result(Hausman Test)

[Ali Ahmed]

Hi All,

I have following set of simultaneous equations:

Y = X + A + B + C + D (1)
X = Y + E + F + G + H (2)

In above equations variables X and Y are endogenous variables. The variables F G and H are instruments for endogenous X variable. I solve it using 3SLS (reg3) command as follows :

reg3 (Y X A B C D) (X Y E F G H), first

I wish to get the p value for hausman test of simultaneity for both equations. Can anyone help please to get the value of endogeneity test for both equations after this reg3 command. Solution can help many other users as well. Cheers

[John Antonakis]

You cannot get this result out of reg3. However, you can get it from sem. Run:

sem (y <- x a b c d) (x<- y e f g h), cov(e.y*e.x)

The test of the covariance of y and x = 0 is the Hausman test.

See: Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. 2010. On making causal claims: A review and recommendations. The Leadership Quarterly, 21: 1086-1120.

HTH,
John.

[Ali Ahmed]

You cannot get this result out of reg3. However, you can get it from sem. Run:

sem (y <- x a b c d) (x<- y e f g h), cov(e.y*e.x)

The test of the covariance of y and x = 0 is the Hausman test.

See: Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. 2010. On making causal claims: A review and recommendations. The Leadership Quarterly, 21: 1086-1120.

HTH,
John.

Thanks John. I tried using your method but this does not allow factor variables (industry and year dummies i.e. i.year i.industry) into the model. However it works successfully without factor variables. Can i ask please is there any other way to solve this simultaneous equation. I am not good with econometrics. Let's say using ivregress 2sls ??? can i run two separate ivreg commands in stata to solve both simultaneous equations ? then how can i model the commands. Thanks again for kind help.

[John Antonakis]

You can create dummy variables--you don't have to use factor variables. For say, the categorical variable "company", which say has 100 categories, do:

tab company, gen(compd)

This will create compd1-compd100.

Then simply include compd1-compd99 in the model.

Again to get the Hausman test you wish, the simplest way to do this is in sem, as I showed you.

[Ali Ahmed]

Dear Prof John

Thank you so much.. your help is appreciated.

[Ali Ahmed]

You cannot get this result out of reg3. However, you can get it from sem. Run:

sem (y <- x a b c d) (x<- y e f g h), cov(e.y*e.x)

The test of the covariance of y and x = 0 is the Hausman test.

See: Antonakis, J., Bendahan, S., Jacquart, P., & Lalive, R. 2010. On making causal claims: A review and recommendations. The Leadership Quarterly, 21: 1086-1120.

HTH,
John.

Dear Prof John,

I copied the following image for REG3 command results from Stata manual. Can I ask please, what does the p-value and chi2 values (circled in blue) mean. I was guessing it could be the endogeneity test results. Sorry if i am totally wrong. Thanks for your help again.

[John Antonakis]

As I mentioned, you cannot do the endogeneity test in this way with reg3. You could use an augmented regression to do this (just google the term). The chi-square test above is the test for all regressors being different from zero. It would be a good idea to read the manual entries about what these statistics mean.

[Aswer Mohamed Ambrella]

Dear Professor John, Your comments here are very useful for us. One question I have with the command you mentioned- sem (y <- x a b c d) (x<- y e f g h), cov(e.y*e.x).
As mentioned Ali, F G and H are instruments for endogenous X variable But he does not have any instruments for Y. So his stata command is reg3 (Y X A B C D) (X Y E F G H). My question is why you focus only on "E" variable when your wirite cov(e.y*e.x)? This could be because of Ali has only one exogenous variable in second equation in his second eqation, that is "E"? If so, say, if Ali's instrument are only G and H, then both E and F becomes exogenous variables. So how we modify this command (cov(e.y*e.x))? Thanks for your attention and reply