On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev\'e equation

Using a simple operator-norm estimate we show that the solution to the second Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well defined region of the complex plane of the independent variable. The result is illustrated with several numerical examples.Comment: 8 pages, to appear in Nonlinearit

Mixed Correlation Functions of the Two-Matrix Model

We compute the correlation functions mixing the powers of two non-commuting random matrices within the same trace. The angular part of the integration was partially known in the literature: we pursue the calculation and carry out the eigenvalue integration reducing the problem to the construction of the associated biorthogonal polynomials. The generating function of these correlations becomes then a determinant involving the recursion coefficients of the biorthogonal polynomials.Comment: 16 page

Comparative Analysis of Labor Market Outcomes: Lessons for the US from International Long-Run Evidence

We analyze a 1960-96 panel of OECD countries to explain why the US moved from relatively high to relatively low unemployment over the last three decades. We find that while macroeconomic and demographic shocks and changing labor market institutions explain a modest portion of this change, the interaction of these shocks and labor market institutions is the most important factor explaining the shift in US relative unemployment. Our finding of the central importance of these interactions is consistent with Blanchard and Wolfers (2000). We also show that, controlling for country- and time-specific effects, high employment is associated with low wage levels and high levels of wage inequality. These findings suggest that US relative unemployment has fallen in recent years in part because its more flexible labor market institutions allow shocks to affect real and relative wages to a greater degree than is true in other countries. Disaggregating, we find that the employment of both younger and older people fell sharply in other countries relative to the United States since the 1970s, with much smaller differences in outcomes among the prime-aged. In the late 1990s, the US had lower unemployment than our models predict, suggesting exceptionally favorable recent US experience.

Labor Market Institutions and Demographic Employment Patterns

Using data from 17 OECD countries over the 1960-96 period, we investigate the impact of institutions on the relative employment of youth, women, and older individuals. Theoretically, we show that labor market institutions meant to improve workers' income share imply larger disemployment effects for groups whose labor supply is more elastic. Using an empirical model that allows us to control for unmeasured country-specific factors that affect relative employment and unemployment, we find that, for both men and women, more extensive involvement of unions in wage-setting significantly decreases the employment rate of young and older individuals relative to the prime-aged, with no significant effects on the relative unemployment of these groups. In contrast, a larger role for unions has insignificant effects on male-female employment differentials, but raises female unemployment relative to male unemployment. These results suggest that union wage-setting policies price the young and elderly out of employment and drive disemployed individuals in these groups to non-labor-force (education, retirement) states. A possible scenario for women is that high union wages encourage female labor force participation, but that women who would otherwise be disemployed by high wage floors are able to find work in unregulated sectors or are absorbed by public employment.

Private school quality in Italy

Private school enrolment may lead to worse subsequent performance in further education or in the labour market. If students differ in their ability not only to pay but to take advantage of educational opportunities (“talent” for short), private schools attract a worse pool of students when publicly funded schools are better suited to foster progress by more talented students. In the data we analyze, the impact of observable talent proxies on educational and labour market outcomes is indeed more positive for students who (endogenously) choose to attend public schools than for those who choose to pay for private education

The Supernova Impostor Impostor SN 1961V: Spitzer Shows That Zwicky Was Right (Again)

SN 1961V, one of Zwicky's defining Type V supernovae (SN), was a peculiar transient in NGC 1058 that has variously been categorized as either a true core collapse SN leaving a black hole (BH) or neutron star (NS) remnant, or an eruption of a luminous blue variable (LBV) star. The former case is suggested by its association with a decaying non-thermal radio source, while the latter is suggested by its peculiar transient light curve and its low initial expansion velocities. The crucial difference is that the star survives a transient eruption but not an SN. All stars identified as possible survivors are significantly fainter, L_opt ~ 10^5 Lsun, than the L_opt ~ 3 10^6 Lsun progenitor star at optical wavelengths. While this can be explained by dust absorption in a shell of material ejected during the transient, the survivor must then be present as a L_IR ~ 3 10^6 Lsun mid-infrared source. Using archival Spitzer observations of the region, we show that such a luminous mid-IR source is not present. The brightest source of dust emission is only L_IR ~ 10^5 Lsun and does not correspond to the previously identified candidates for the surviving star. The dust cannot be made sufficiently distant and cold to avoid detection unless the ejection energy, mass and velocity scales are those of a SN or greater. We conclude that SN 1961V was a peculiar, but real, supernova. Its peculiarities are probably due to enhanced mass loss just prior to the SN, followed by the interactions of the SN blast wave with this ejecta. This adds to the evidence that there is a population of SN progenitors that have major mass loss episodes shortly before core collapse. The progenitor is a low metallicity, ~1/3 solar, high mass, M_ZAMS > 80 Msun, star, which means either that BH formation can be accompanied by an SN or that surprisingly high mass stars can form a NS.Comment: 26 pages, 7 figures, submitted to Ap