Dear, I want to apply Heckman two stage for Market participation assessment. For doing this, I get IMR from 1st stage probit regression, whether participated or not. Then include IMR as a independent variable in 2nd stage per capita consumption expenditure equation (OLS). But problem is that IMR is not significant after OLS. I also noticed some study that dependent variable used in probit model and OLS are not same or vary, why?? Sometimes found the statement "The selection equation should contain at least one variable that is not in the outcome equation" or "exclusion restriction" or "omit variables" (OV). I think this terms were similar meaning or not? However I want to draw your attention regarding my procedure about heckman 2 stage that is first stage was selection model ( 1 market participant, 0= otherwise) ( probit regression) , then generate IMR and run OLS (2nd stage). But I got the probability value of IMR is about 0.43 (>.10). When I checked the collinearity of the independent variable, then I got three variable were collinear and I excluded these three variable from the 2nd stage (OLS) and find significant IMR. can I do that?
You need to be clear about the use of heckman selection model. It seems to me that without identifying the necessity of heckman model you are interested to use it anyhow.
If IMR is not significant from first stage why you are interested to use it in second step. Non significant IMR indicates there is no bias. In that case OLS is enough. You may try double hurdle regression if heckman is not appropriate.
Md. Sadique Rahman Significant IMR not always indicates that there is no selection bias. The inclusion of the inverse Mills ratio often yields collinearity with the X variables, even when the correction term has been properly implemented or significant that can have profound consequences of the model estimates. Because any multiple regression with collinearity will give inconsistent estimate. So model with exclusion restriction always better than model without exclusion restriction. Moreover, most of the good quality (almost all) paper used exclusion restriction without explaining it properly. So before going to another model like craggit model/double hurdle/log normal hurdle models we have to check it properly.
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