dummy endogenous variables

[Mosi Fagbemide]

I have a primary explanatory variable - education attainment (the qualification not years).

I have created 3 dummies to represent each qualification.

my education attainment (i.e. each dummy) is endogenous.

is it sensible to equate the 3 dummies to the same instrumental variable?

such that my the Stata command would be:

. ivprobit Account_0_1 age age2 inc_q_dum1 inc_q_dum2 inc_q_dum3 inc_q_dum4 femdum2 (educ_dum1 educ_dum2 educ_dum3 = Instrument)


Thank you

[Mark Schaffer]

No, this is not sensible - you can't identify 3 coefficients with only 1 instrument. Plus IV probit as implemented in Stata (either ML or Newey's minimum chi-sq) is in general inappropriate for your setup because your endogenous regressors are dummies. The online help for ivprobit says:

"By default, ivprobit uses maximum estimation, but Newey's (1987) minimum chi-squared (two-step) can be requested. Both estimators assume that the endogenous are continuous and so are not appropriate for use with discrete covariates."

[Mosi Fagbemide]

okay.

it is a bit confusing though. what if my endogenous variable is a categorical variable which takes a numeric form between 1, 2 or 3?

[Mosi Fagbemide]

so how does one deal with such endogenous variables, please.