performing Hausman test with many instruments

[Jack Reimer]

I would like to specify a 2SLS with multiple instruments. My reduced form is

reg kids educ age age2 south east west i.time  black ///
    c.age#c.educ south#c.educ east#c.educ west#c.educ black#c.educ

And I'm instrumenting for `educ` with `meduc` and `feduc`

ivregress 2sls kids age age2 south east west i.time black ///
    (educ c.age#c.educ south#c.educ east#c.educ west#c.educ black#c.educ = ///
    meduc feduc ///
    c.age#c.meduc c.age#c.feduc ///
    south#c.meduc south#c.feduc ///
    east#c.meduc east#c.feduc ///
    west#c.meduc west#c.feduc ///
    black#c.meduc black#c.feduc), vce(robust)

I would like to perform a Hausman test for endogeniety but I am only familiar with how to estimate this with one instrument. That is

1) estimate the first stage for my plausibly endogenous explanatory variable and
2) then run a regression with all of my explanatory variables, instruments and the residuals from 1)

Is there a means through which to do this for multiple instruments? If this is what the hausman command does, can someone help me understand how to interpret the results beyond the documentation?

[Jeff Wooldridge]

That first regression is not a "reduced form." It's the regression that treats educ as exogenous. The first-stage for educ would be

reg educ age age2 south east west i.time black ///
        meduc feduc ///
       c.age#c.meduc c.age#c.feduc ///
       south#c.meduc south#c.feduc ///
       east#c.meduc east#c.feduc ///
       west#c.meduc west#c.feduc ///
       black#c.meduc black#c.feduc)

You have one endogenous variable but it appears as an interaction with exogenous variables, so Stata properly sees many endogenous variables. Is this for a research project?

[Jack Reimer]

Thank you for this response! This is very helpful. No this is not for a research project, it's an exercise extending beyond question 6.8 in EACS&PD