Abstract
In this chapter we present estimates of both the proportional and accelerated-time-to-failure hazard models that are discussed in Chapter 3 for the Dorn sample, with emphasis on associations with smoking, occupational risks, birth cohort and unobserved frailty (heterogeneity). The mortality hazard relations that we estimate, as discussed in Section 3.1, can be viewed as production functions or conditional demand relations that come out of the dynamic optimizing behavior in the model presented there. We first survey relevant previous literature and then describe the Dorn sample. We then begin our analysis with no allowance for heterogeneity. We then redo the analysis allowing for parametric and non-parametric heterogeneity, whose significance and importance are examined, and then we use the Maximum Penalized Likelihood functions that also diminish the importance of heterogeneity. These explorations of the impact of unobserved heterogeneity address some possibly important estimation problems since both mortality and the right-side variables may be responding to unobserved heterogeneity.
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A zero, one dummy variable is the dependent variable. In addition to other problems, the right-side variables are not independent of the disturbance term, and OLS is not guaranteed to reproduce a function limited to that range.
Kaprio, et al. (1987) also indicate an excess mortality of widowers and widows in a four year follow-up in Finland.
Manton, writing with several others, has made other notable contributions to the estimation of mortality models and to substantive knowledge on mortality. We use some of the statistical models that he has helped to develop, though we also use some other recent methods. We discuss these developments and other methodological issues in Chapter 3 on estimation. We note here that Manton’s work generally has been with small samples or with few covariates.
This is a 5 percent random sample of all Medicare patients who are followed over time.
The public use version of the Framingham sample only records date of death within a two year interval. Monthly data were available to Liu, et at.
Rogot is our source for much of the description below.
Alternative statistical methods have been developed to estimate a baseline survivor distribution (what percentage of the sample is alive at a given age) that shifts with covariates. See for example Cox (1972), Kalbfleisch and Prentice (1980), Manton, Stallard and Vaupel (1986), and Vaupel, Manton and Stallard (1979) and the discussion in Chapter 4.
This physical activity result is also found in Moore and Haywood (1988) using the NLS older men.
Of course the signs of the elasticities are reversed since the theoretical concept has changed from the age-specific death rate to how long you will survive. Most of the same results hold for the other baseline hazard distributions, but not all (e.g., the Northeast regional effects are significantly nonzero for the Weibull and lognormal cases).
We have one estimate using three points of support for this cohort. Most parameter estimates are very similar to those in Table 5.9, but the coefficient on regular tobacco use rises sharply to 0.58. The third support increases CPU time on the NEC SX-2 supercomputer used in these analyses by about 50 percent. For a sample of about 13,000 observations, the running time is about 4.5 hours.
Although distributions other than the normal can be specified in the CTM program (Yi, et al., 1986), the extreme computational demands implied by the relatively large number of covariates and sample observations mean that only a limited number of parametric heterogeneity distributions could be considered. These included the lognormal and gamma. However, due to convergence problems and cu constraints, the only parametric heterogeneity distribution on which we report estimates is the normal. Although the normal is not a flexible distribution, its ubiquity in applied work and justification therein provides us with some rationale for its selection for this study.
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© 1998 Springer Science+Business Media New York
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Behrman, J.R., Sickles, R.C., Taubman, P. (1998). Mortality Hazard Estimates from the Dorn Sample: Smoking, Occupational Risks, Birth Cohort, Functional Form and Frailty. In: Causes, Correlates and Consequences of Death Among Older Adults. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4393-6_4
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DOI: https://doi.org/10.1007/978-94-011-4393-6_4
Publisher Name: Springer, Dordrecht
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