Can we use Heckman two step method with a simple probit model in the
first stage and an ordered probit model in the second stage even if
there are no obvious instrument variables available that affect the
first stage but not the second stage. In fact can the dependent
variables in both the stages be the same?
I know of a discussion available on STATA forum at
with the following explanation for identification:
"As in any model, one must be aware from where identification arises.
While it is well known that for instrumental variables estimation one
requires a variable that is correlated with the endogenous variable,
uncorrelated with the error term, and does not affect the outcome of
interest conditional on the included regressors, identification in
sample selection issues is often not as well grounded. Because the IMR
is a nonlinear function of the variables included in the first-stage
probit model, call these Z, then the second-stage equation is
identified—because of this nonlinearity—even if Z=X. However, the
nonlinearity of the IMR arises from the assumption of normality in the
probit model. Since most researchers do not test or justify the use of
the normality assumption, it is highly questionable whether this
assumption should be used as the sole source of identification. Thus,
it is advisable, in my opinion, to have a variable in Z that is not
also included in X. This step makes the source of identification clear
(and debatable). For the double-selection model discussed above in
Model III, two exclusion restrictions would be needed (one for the
labor force probit, one for the union probit). "
Can anybody suggest me to the literature or papers that address this issue.