Self–selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of self–selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work. Available estimation methods are either infeasible for a selection model with so many alternatives or place potentially severe restrictions on earnings and the selection process. This paper develops an alternative econometric methodology that combines Lee's (1983) parametric maximum order statistic approach to reduce the dimensionality of the error terms with more recent work on semiparametric estimation of selection models (e.g., Ahn and Powell (1993)). The resulting semiparametric correction is easy to implement and can be adapted to a variety of other polychotomous choice problems. The empirical work, which uses 1990 U.S. Census data, confirms the role of comparative advantage in mobility decisions. The results suggest that self–selection of higher educated individuals to states with higher returns to education generally leads to upward biases in OLS estimates of the returns to education in state–specific labor markets. While the estimated returns to a college education are significantly biased, correcting for the bias does not narrow the range of returns across states. Consistent with the finding that the corrected return to a college education differs across the U.S., the relative state–to–state migration flows of college– versus high school–educated individuals respond strongly to differences in the return to education and amenities across states.

Self-selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile.To assess the impact of self-selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work.Available estimation methods are either infeasible for a selection model with so many alternatives or place potentially severe restrictions on earnings and the selection process.This paper develops an alternative econometric methodology which combines Lee's (1983) parametric maximum order statistic approach to reduce the dimensionality of the error terms with more recent work on semiparametric estimation of selection models (e.g., Ahn and Powell, 1993).The resulting semiparametric correction is easy to implement and can be adapted to a variety of other polychotomous choice problems.The empirical work, which uses 1990 U.S. Census data, confirms the role of comparative advantage in mobility decisions.The results suggest that self-selection of higher educated individuals to states with higher returns to education generally leads to upward biases in OLS estimates of the returns to education in state-specific labor markets.While the estimated returns to a college education are significantly biased, correcting for the bias does not narrow the range of returns across states.Consistent with the finding that the corrected return to a college education differs across the U.S., the relative state-to-state migration flows of college-versus high school-educated individuals respond strongly to differences in the return to education and amenities across states.

Band spectral regression with both deterministic and stochastic trends is considered. It is shown that trend removal by regression in the time domain prior to band spectral regression can lead to biased and inconsistent estimates in models with frequency dependent coefficients. Both semiparametric and nonparametric regression formulations are considered, the latter including general systems of two-sided distributed lags such as those arising in lead and lag regressions. The bias problem arises through omitted variables and is avoided by careful specification of the regression equation. Trend removal in the frequency domain is shown to be a convenient option in practice. An asymptotic theory is developed and the two cases of stationary data and cointegrated nonstationary data are compared. In the latter case, a levels and differences regression formulation is shown to be useful in estimating the frequency response function at nonzero as well as zero frequencies.