st: Multinomial sample selection with IV estimation, selmlog with ivreg, is it right?

[Umid Aliev <U.Aliev@leeds.ac.uk>]

Dear Stata users,
I try to estimate the wage and employment equations using firm-level data. The sample includes firms of various ownership structures: foreign owned, domestic private, and state. It is hypothesized that there are differences in intercept and slope coefficients between the firms of different ownership groups. Since the ownership structure is a decision variable it is treated as endogenous. The endogeneity of the ownership variable is to be controlled by use of endogenous switching regime model, where sample selection/endogeneity is corrected by the two-step procedures similar to the well-known Heckman two-step estimator, although now the first step – ownership decision equation is estimated as a multinomial logit model. The second step is OLS. All these procedures are implemented with -selmlog- command in Stata. 
However, in my case the second state equation cannot be estimated through OLS as both wage and employment equations contain other endogenous variables, which I plan to control through IV estimation. Therefore is it possible to run IV estimator on the second stage? In my understanding methodologically it is OK to do so, as long as correction terms (conditional probabilities) are included into the second stage equation, although I am not sure, and I don’t know how to imlement it in Stata. With this respect I would be grateful for any comments on whether it is a right strategy to obtain correction terms using selmlog and then to insert them into the regression on ivreg29, and if yes then how to implement it in Stata?
Many thanks,

Umid Aliev
PhD student
Leeds University Business School
Leeds
UK
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