Endogeneity test for two endogenous variables using REIV (xtivreg, re)

[Mehrzad Baktash]

Dear all,

I am using an REIV using the command "xtivreg, re". I have two endogenous variables, y2 and y3 (y3 is an interaction of y2 with z2, and z2 is assumed to be exogenous), and two instrumental variables.

Jeff Wooldridge explains this in Section 11.2 of his MIT press book (Econometric Analysis of Cross Section and Panel Data) for one endogenous variable. He also gives an example of how to do it in Stata in one of the Statalist posts in 2017.

Krissy: Your case is a bit harder, but doable in Stata. I cover it in Section 11.2 in my MIT Press book, 2010, 2e. I think you have to do it "by hand" as xtreg2 does not support RE and xtregress does not have the endog test available.

Let y1 be the dependent variable, y2 the endogenous explanatory variable, z1, ... zL the exogenous variables, with z1, ..., zM, M < L, included in the model.

reg y2 z1 z2 ... zL
predict v2hat, resid
xtreg y1 y2 v2hat z1 z2 ... zM, re vce(cluster id)

The t statistic on v2hat is the test of the null that y2 is exogenous. If you reject, you conclude IV is needed. The test is fully robust to serial correlation and heteroskedasticity.

A word of caution: You are requiring pretty strong exogeneity of your instrument. It must be uncorrelated with the heterogeneity in the structural equation, as well as the shocks. If your explanatory variable and instruments change over time, FEIV will be more convincing.

JW

My question is if I can apply the same procedure in the case of two endogenous explanatory variables (y2 and y3) and two instruments?

reg y2 z1 z2 ... zL
predict v2hat2, resid
reg y3 z1 z2 ... zL
predict v2hat3, resid
xtreg y1 y2 v2hat2 y3 v2hat3 z1 z2 ... zM, re vce(cluster id)

In this case, are the t-statistics on v2hat2 and v2hat3 the tests of the null that y2 and y3 are exogenous?
Are there any other tests that I might perform in this case?

Best regards,
Mehrzad

[Manh Hoang Ba]

Dear all,

I am using an REIV using the command "xtivreg, re". I have two endogenous variables, y2 and y3 (y3 is an interaction of y2 with z2, and z2 is assumed to be exogenous), and two instrumental variables.

Jeff Wooldridge explains this in Section 11.2 of his MIT press book (Econometric Analysis of Cross Section and Panel Data) for one endogenous variable. He also gives an example of how to do it in Stata in one of the Statalist posts in 2017.




My question is if I can apply the same procedure in the case of two endogenous explanatory variables (y2 and y3) and two instruments?

reg y2 z1 z2 ... zL
predict v2hat2, resid
reg y3 z1 z2 ... zL
predict v2hat3, resid
xtreg y1 y2 v2hat2 y3 v2hat3 z1 z2 ... zM, re vce(cluster id)

In this case, are the t-statistics on v2hat2 and v2hat3 the tests of the null that y2 and y3 are exogenous?
Are there any other tests that I might perform in this case?

Best regards,
Mehrzad

I think you should test v2hat2=v2hat3=0 by chi2-test

test v2hat2 v2hat3