Ling Zhong Publications

This paper proposes a novel framework for the global optimization of a continuous function in a bounded rectangular domain. Specifically, we show that: (1) global optimization is equivalent to optimal strategy formation in a two-armed decision problem with known distributions, based on the Strategic Law of Large Numbers we establish; and (2) a sign-based strategy based on the solution of a parabolic PDE is asymptotically optimal. Motivated by this result, we propose a class of Strategic Monte Carlo Optimization (SMCO) algorithms, which uses a simple strategy that makes coordinate-wise two-armed decisions based on the signs of the partial gradient (or practically the first difference) of the objective function, without the need of solving PDEs. While this simple strategy is not generally optimal, it is sufficient for our SMCO algorithm to converge to a local optimizer from a single starting point, and to a global optimizer under a growing set of starting points. Numerical studies demonstrate the suitability of our SMCO algorithms for global optimization well beyond the theoretical guarantees established herein. For a wide range of test functions with challenging landscapes (multi-modal, non-differentiable and discontinuous), our SMCO algorithms perform robustly well, even in high-dimensional (d = 200 ∼ 1000) settings. In fact, our algorithms outperform many state-of-the-art global optimizers, as well as local algorithms augmented with the same set of starting points as ours.

This paper examines the gender gap in log earnings among full-time, college-educated workers born between 1931 and 1984. Using data from the National Survey of College Graduates and other sources, we decompose the gender earnings gap across birth cohorts into three components: (i) gender differences in the relative returns to undergraduate and graduate fields, (ii) gender-specific trends in undergraduate field, graduate degree attainment, and graduate field, and (iii) a cohort-specific “residual component” that shifts the gender gap uniformly across all college graduates. We have three main findings. First, when holding the relative returns to fields constant, changes in fields of study contribute 0.128 to the decline in the gender gap. However, this decline is partially offset by cohort trends in the relative returns to specific fields that favored men over women, reducing the contribution of field-of-study changes to the decline to 0.055. Second, gender differences in the relative returns to undergraduate and graduate fields of study contribute to the earnings gap, but they play a limited role in explaining its decline over time. Third, much of the convergence in earnings between the 1931 and 1950 cohorts is due to a declining “residual component.” The residual component remains stable for cohorts born between 1951 and the late 1970s, after which it resumes its decline.

This chapter uses a college-by-graduate degree fixed effects estimator to evaluate the returns to 19 different graduate degrees for men and women. We find substantial variation across degrees, and evidence that OLS overestimates the returns to degrees with the highest average earnings and underestimates the returns to degrees with the lowest average earnings. Second, we decompose the impacts on earnings into effects on wage rates and effects on hours. For most degrees, the earnings gains come from increased wage rates, though hours play an important role in some degrees, such as medicine, especially for women. Third, we estimate the net present value and internal rate of return for each degree, which account for the time and monetary costs of degrees. Finally, we provide descriptive evidence that satisfaction gains are large for some degrees with smaller economic returns, such as education and humanities degrees, especially for men.

This paper uses a college-by-graduate degree fixed effects estimator to evaluate the returns to 19 different graduate degrees for men and women. We find substantial variation across degrees, and evidence that OLS overestimates the returns to degrees with high average earnings and underestimates the returns to degrees with low average earnings. Second, we decompose the impacts on earnings into effects on wage rates and effects on hours. For most degrees, the earnings gains come from increased wage rates, though hours play an important role in some degrees, such as medicine, especially for women. Third, we estimate the net present value and internal rate of return for each degree, which account for the time and monetary costs of degrees. We show annual earnings and hours worked while enrolled in graduate school vary a lot by gender and degree. Finally, we provide descriptive evidence that gains in overall job satisfaction and satisfaction with contribution to society vary substantially across degrees.