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

http://www.stata.com/support/faqs/stat/bias.htmlwith the following explanation for identification:

"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

identifiedâ€”because of this nonlinearityâ€”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.

Thanks alot,

Sridhar

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