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  • Average structural function in ivprobit

    Hello,

    I am trying to understand how the probabilities generated by the `pr` option in `predict` relate to the estimated model parameters when using maximum likelihood. For example:

    Code:
    ivprobit fem_work fem_educ kids (other_inc = male_educ)
    
    predict pred_direct_asf, pr
    predict pred_direct_fixedasf, pr fixedasf
    predict pred_linear, xb
    
    g predict_manual = normal(pred_linear)
    Holding the ASF fixed, I can manually generate the predicted probabilities by transforming the linear predictions (predict_manual = pred_direct_fixedasf). However, the probabilities in pred_direct_asf are different because they condition on the error term. My question is:

    How could I "manually" generate the predicted probabilities resulting from "predict pred_direct_asf, pr" given the estimated model parameters? I have found some discussions that are based on control function approaches to estimation, but I am curious about how it is implemented when the model is estimated through maximum likelihood.





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