@article{KWW2006a,
    TITLE = {Understanding Mortality Rate Deceleration and Heterogeneity},
   AUTHOR = {David R. Steinsaltz and Kenneth W. Wachter},
  JOURNAL = {Mathematical Population Studies},
   VOLUME = {13},
   NUMBER = {1},
    PAGES = {19--37},
     YEAR = {2006},
       ID = {info:doi/10.1080/08898480500452117},
 ABSTRACT = {Generic relationships between heterogeneity in population frailty
             and flattening of aggregate population hazard functions at extreme
             ages are drawn from classical mathematical results on the limiting
             behavior of Laplace transforms. In particular, it shows that the
             population hazard function converges to a constant precisely when
             the distribution of unobserved heterogeneity in initial mortalities
             behaves asymptotically as a polynomial near zero.},
   }

        

@article{KWW2006b,
    TITLE = {Relationships between Period and Cohort Life Expectancy: Gaps and
             Lags},
   AUTHOR = {Joshua R. Goldstein and Kenneth W. Wachter},
  JOURNAL = {Population Studies},
   VOLUME = {60},
   NUMBER = {3},
    PAGES = {257--269},
    MONTH = {November},
     YEAR = {2006},
       ID = {info:doi/10.1080/00324720600895876},
 ABSTRACT = {This paper offers an empirical and analytic foundation for
             regarding period life expectancy as a lagged indicator of the
             experience of real cohorts in populations experiencing steady
             improvement in mortality. We find that current period life
             expectancy in the industrialized world applies to cohorts born some
             40-50 years ago. Lags track an average age at which future years of
             life are being gained, in a sense that we make precise. Our
             findings augment Ryder's classic results on period-cohort
             translation.},
   }