I-SHORT ANSWER
This is a common problem in social sciences,
y= x1……..xn, but
x1=x2…..xn
How to deal with it? In Stata, use ivprobit if the suspected endogenous variable is continuous, if it is binary/discrete, use treatreg.
II-LONG ANSWER
look for lnsigma and athrho
1) meaning of lnsigma
lnsigma = log of sigma
sigma could be understood as standard error of….what?
of ….correlation….between what?
2) meaning of athrho
athrho= transformation of rho, and rho is basically a correlation measure
In this context, rho is the correlation between the errors (residuals) of the probit equation (full equation) and the reduced equation for the suspected endogenous variable (now let us call this correlation between two residuals ‘A’)
full model: y=x1+……………….xn ---> error 1
reduced model: x1=x2….xn --->error 2
Does error1 correlate significantly with error2?
The task here is to test a Ho : there is no endogeneity problem in the set of predictors in relation with the dependent variable. In other words, we test that A is not significant.
if athrho >0.05, that means the possibility that A is not significant is larger than 5%
if athrho <0.05, that means the chance for A to be insignificant is very tiny.
IN SHORT, IF athrho is larger than 5%, we can say that: we cannot reject Ho, or, it is less likely that there is an endogeneity issue in here.
Then WHAT ---> RUN a normal model using probit or logit, depending on what you like, then use it for final results.
IF athrho <0.05, you should keep the output result of ivprobit, which include estimate for both models
NOTE THAT: ivprobit should be used for continuous (suspected) endogenous variable. Consider transform your variable if it is discrete. Nevertheless, the test idea is the same: Does residual in FULL MODEL significantly correlate with residual in REDUCED MODEL?
Consider using –treatreg FOR BINARY endogenous variable:
svy, subpop(sex): treatreg [Y] [ALL_X] , treat(BINARYVARGOESHERE = ALL_X)
est store m1
estout m1, cells(b(star fmt(3)) ) l starlevels(+ 0.1 * 0.05 ** 0.01 *** 0.001) stats(N F,star(r2 p))
