Interpretation of error covariances with nonrandom data: An empirical illustration of returns to college education

Conclusion

This paper reviews two models of selectivity and gives an interpretation of the covariance terms that are particular to self-selectivity models. While the second model examined in this paper has been discussed elsewhere, the estimates presented for the first model have not been discussed in previous papers. More importantly though, the paper proposes an hypothesis about the expected relationship between error covariances. According to this hypothesis, if all individuals who are faced with the choice between two regimes (1 and 2) choose the regime which yields a maximum value, then the expected relationship between covariances is σ_{1 ∈} < σ_{2 ∈}. If all individuals choose that regime which yields a minimum value, then the expected relationship between covariances is σ_{1 ∈} > σ_{2 ∈}. This relationship holds for a very general class of selectivity models, so long as individuals are choosing between regimes by comparing the expected value (to them) of each regime.