This is more of an econometric question than a Stata question. Suppose that there is one endogenous variable and three instruemnts. The aim is to test whether instrument_3 is an exogenous instrument. The relevant statistic is the C statistic. It is reported by the orthog option of ivreg. The syntax is:
ivreg2 dependent (endogenous_variable = instrument_1 instrument_2 instrument_3) exogenous_variables, orthog(instrument_3).
Before I got to know about the C statistic, I used to test for the exogeneity of an instrument using a heuristic test. I call it heuristic because I do not recall if I came up with it or if it is indeed a formal test. That is the question. That is, consider the regression
ivreg2 dependent (endogenous_variable = instrument_1 instrument_2) instrument_3 exogenous_variables, orthog(instrument_3).
What I do here is that I include instrument_3 directly in the reduced form regression, and check if it is significant. If it is, instrument_3 is not exogenous because then it directly affects the dependent. I figure that the result of this heuristic test is always in line with the result of the C test. This is not surprising, but I wonder whether this heuristic test is indeed heuristic test, or is it somewhat a formal test that I do not know the name?
ivreg2 dependent (endogenous_variable = instrument_1 instrument_2 instrument_3) exogenous_variables, orthog(instrument_3).
Before I got to know about the C statistic, I used to test for the exogeneity of an instrument using a heuristic test. I call it heuristic because I do not recall if I came up with it or if it is indeed a formal test. That is the question. That is, consider the regression
ivreg2 dependent (endogenous_variable = instrument_1 instrument_2) instrument_3 exogenous_variables, orthog(instrument_3).
What I do here is that I include instrument_3 directly in the reduced form regression, and check if it is significant. If it is, instrument_3 is not exogenous because then it directly affects the dependent. I figure that the result of this heuristic test is always in line with the result of the C test. This is not surprising, but I wonder whether this heuristic test is indeed heuristic test, or is it somewhat a formal test that I do not know the name?
