The cohomology ring of weight varieties and polygon spaces

We use a theorem of Tolman and Weitsman to find explicit formul\ae for the rational cohomology rings of the symplectic reduction of flag varieties in C^n, or generic coadjoint orbits of SU(n), by (maximal) torus actions. We also calculate the cohomology ring of the moduli space of $n$ points in CP^k, which is isomorphic to the Grassmannian of k-planes in C^n, by realizing it as a degenerate coadjoint orbit.Comment: 31 pages, 1 figur

Long-Run Changes in the U.S. Wage Structure: Narrowing, Widening, Polarizing

The U.S. wage structure evolved across the last century: narrowing from 1910 to 1950, fairly stable in the 1950s and 1960s, widening rapidly during the 1980s, and “polarizing” since the late 1980s. We document the spectacular rise of U.S. wage inequality after 1980 and place recent changes into a century-long historical perspective to understand the sources of change. The majority of the increase in wage inequality since 1980 can be accounted for by rising educational wage differentials, just as a substantial part of the decrease in wage inequality in the earlier era can be accounted for by decreasing educational wage differentials. Although skill-biased technological change has generated rapid growth in the relative demand for more-educated workers for at least the past century, increases in the supply of skills, from rising educational attainment of the U.S. work force, more than kept pace for most of the twentieth century. Since 1980, however, a sharp decline in skill supply growth driven by a slowdown in the rise of educational attainment of successive U.S. born cohorts has been a major factor in the surge in educational wage differentials. Polarization set in during the late 1980s with employment shifts into high- and low-wage jobs at the expense of the middle leading to rapidly rising upper tail wage inequality but modestly falling lower tail wage inequality.

The shaping of higher education in the United States and New England.

Education ; Public schools

The Origins of Technology-Skill Complementarity

Current concern with relationships among particular technologies, capital, and the wage structure motivates this study of the origins of technology-skill complementarity in manufacturing. We offer evidence of the existence of technology-skill and capital-skill (relative) complementarities from 1909 to 1929, and suggest that they were associated with continuous-process and batch methods and the adoption of electric motors. Industries that used more capital per worker and a greater proportion of their horsepower in the form of purchased electricity employed relatively more educated blue-collar workers in 1940 and paid their blue-collar workers substantially more from 1909 to 1929. We also infer capital-skill complementarity using the wage-bill for non-production workers and find that the relationship was as large from 1909-19 as it has been recently. Finally, we link our findings to those on the high-school movement (1910 to 1940). The rapid increase in the supply of skills from 1910 to 1940 may have prevented rising inequality with technological change.

The Returns to Skill in the United States across the Twentieth Century

Economic inequality is higher today than it has been since 1939, as measured by both the wage structure and wealth inequality. But the comparison between 1939 and 1999 is largely made out of necessity; the 1940 U.S. population census was the first to inquire of wage and salary income and education. We address what the returns to skill were prior to 1940 and piece together the first century-long history of skill premiums, the dispersion of the wage structure, and returns to formal schooling. We use the 1915 Iowa State Census, a remarkable and unique document, as well as several less-obscure but untapped reports. Using all of these sources, we find that the wage structure narrowed at several moments in the first half of the 20th century, not just in the 1940s, both coinciding with major economic disruptions brought about by war. The returns to education were in fact higher in 1914 than in 1939, and the enormous expansion in secondary schooling beginning in the 1910s was a contributing factor to the decrease in educational returns. Inequality and the returns to education across the entire century, therefore, first declined before their more recent and steep ascent.