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st: Control function approach
I would very much appreciate some advice on applying the control function approach
I have 3 equations:
1. y1 = dZ + e
where y1 is a dicrete choice variable taking the value 1 if an MBO, 2 if an MBI, and zero is neither MBO or MBI. This is estimated by multinomial logit. Z the independent variable set.
My second equation:
2. wages = eemplyment + bX + aMBO + cMBI + v
3. employment = fW + u
a, b, c, d, e, and f are coefficients.
Equations 2 and 3 are estimated by 3SLS
1. Can I use the multinomial logit in a control function approach?
2. If the answer to (1) is yes, can I use the fitted values from the multinomial logit as explanatory variables in equation (2) in order to test for endogeneity and correct the standard errors for bias?
3. If the answer to (2) is no, is it possible to obtain the choice specific residuals from the multinomial logit? Wooldridge (2002) suggests using the residuals but I cannot find a way of obtaining them after multinomial logit estimation.
Any help on this is much appreciated.
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