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  • Usage of estimated coefficients of a first regression as explanatory variables in the second stage of a regression

    Dear Statalists
    I m working on the relationship between schooling decisions, child labor and the regional rates of returns to school in my country. I so first estimate these regional rates of return to school using Lewbel (2012) approach. And secondly, I would like to use the regional estimated rate of returns to school as explanatory variables to see if they impact on the parents decisions to send their children at school or to work.
    So in the first equation, I have estimated Mincer equation using Lewbel (2012) approach to solve the potential problem of endogeneity biais link to school. And in the second step, I would like to use a Bivariate Probit model to examine if these regional rates of return to school impact on parents decisions to send their children at school or make them work. But after the first step estimation, I face with 2 problems:
    1- Some coefficients of my first step estimation are not significant. Should I consider them as 0 in the second stage of my estimation (I speak about the bivariate probit model)
    2-The first stage coefficients (rate of returns to school) are of higher level compared to the second stage estimation. Is there any problem with this?
    Thank you to answer me!
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