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Marriage Delayed or Marriage Forgone? New Cohort Forecasts of First Marriage for U.S. Women

American Sociological Review 2001 66(4), 506-519
Do recent declines in first marriage rates signal that an increasing proportion of women will remain single their entire lives, or merely that they are postponing marriage to older ages? Our forecasts for cohorts born in the 1950s and 1960s suggest that marriage will remain nearly universal for American women—close to 90 percent of women are predicted to marry. However, separate forecasts by educational attainment reveal a new socioeconomic pattern of first marriage: Whereas in the past, women with more education were less likely to marry, recent college graduates are now forecast to marry at higher levels despite their later entry into first marriage. This educational crossover, which occurs for both black women and white women in recent cohorts, suggests that marriage is increasingly becoming a province of the most educated, a trend that may become a new source of inequality for future generations. Forecasts presented here use data from the 1995 Current Population Survey and compare estimates from the Hemes model with those from the Coale-McNeil model.

A General Formula for Valuing Defaultable Securities

Econometrica 2004 72(5), 1377-1407 open access
Previous research has shown that under a suitable no-jump condition, the price of a defaultable security is equal to its risk-neutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating that one can always value defaultable claims using expected risk-adjusted discounting provided that the expectation is taken under a slightly modified probability measure. This new probability measure puts zero probability on paths where default occurs prior to the maturity, and is thus only absolutely continuous with respect to the risk-neutral probability measure. After establishing the general result and discussing its relation with the existing literature, we investigate several examples for which the no-jump condition fails. Each example illustrates the power of our general formula by providing simple analytic solutions for the prices of defaultable securities.