st: test of over-identifying restrctions after Heckman model

["Evren Ceritoglu" <evren.ceritoglu@tcmb.gov.tr>]

Hello Statalist,

I want to perform over-identifying restrictions (overid) test after Heckman 
two-step selection model. I must introduce at least one exogeneous variable 
in the probit equation, which becomes an instrument, for the Heckman model 
to hold. However, this process also reqires an overid test after the 
estimation to check whether the instruments are valid or not.

OLS: lny1 = X1b1 + X2b2 + u
Probit: d = X1b1 + Zb3 + e

(d: dummy variable, which is the selection criterion)
(Z: set of instruments, composed of dummy variables)

The overid command is useful after ivprobit or ivtobit, but it is not 
possible to use it after the Heckman model.

I tried to perform a LR test, but there was a problem! I stored the 
predictions (estimation results) from the overidentified regression 
(heckoverid) and also the predictions (estimation results) from the
just-identified regression (heckjustid). However, stata says that heckoverid 
does not contain scalar e(ll), which I don't understand in both cases.

I) over-identified model

OLS: lny1 = X1b1 + X2b2 + u
Probit: d = X1b1 + Zb3 + e

II) just-identified model

OLS: lny1 = X1b1 + X2b2 + Zb3 + u
Probit: d = X1b1 + Zb3 + e

III) LR test

lrtest heckoverid heckjustid, df(1) (assuming that there is only one 
instrument)

Is there a feasible way to perform over-identifying restrictions test after 
the Heckman two-step selection model?

Thank you,

Evren Ceritoglu



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