Endogeneity test for iv regression with cluster robust standard errors

[Clara Nelson]

I have performed a 2sls iv regression using ivregress 2sls. When I use estat endogenous, I get the below result. As I am using cluster robust standard errors my understanding is that this is not the Hausman test? What test is being used here?

[Parul Gupta]

Clara Nelson Were you able to find out?

[Jeff Wooldridge]

It's the variable addition test (VAT), also known as the control function test. If the equation is y1 = a1*y2 + z1*b1 + u1 and the first stage for y2 is y2 = z1*c2 + z2*d2 + v2, then one first estimates the first stage by OLS and gets the residuals, v2hat. Then, the test is OLS of y1 on y2, z2, v2hat, and you compute the t statistic on v2hat. If you clustered when using ivregress then the standard error in the VAT is also cluster-robust.