Abstract
Here we use a large sample of UK manual workers and compare estimates of the union wage differential obtained from a conventional Heckman two-step method of controlling for the potential endogeneity of union status with semi-parametric estimates. The semi-parametric methodology yields slope coefficients very close to Heckman two-step and least squares. That is, much of the the difference in differentials between least squares and Heckman/semi-parametric methods arises from the magnitude of the constant terms. This is the source of the large union wage differentials obtained when self-selection is taken into account. All of our attempts to control for selection generate very different constant terms from OLS so that, despite our misgivings about identification of the constants, we doubt the validity of the OLS differentials.
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