Can anyone offer a test of my exclusion restrictions for a heckman selection
model (beyond that theoretically they don't belong in the "first stage"
regression)? If I include them in the "first stage" regression, aren't I
committing the error of having Z=X and thus relying on the distributional
assumptions to identify my model? It has been suggested that my excluded
variables should not be correlated with the regressors in the first stage, but
this seems too stringent. I have more than one excluded variable, so I have been
including them in small batches in the regression and doing an F-test on their
coefficients.
Any thoughts?
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