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Demography

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01.11.2011

Differential Survival in Europe and the United States: Estimates Based on Subjective Probabilities of Survival

verfasst von: Adeline Delavande, Susann Rohwedder

Erschienen in: Demography | Ausgabe 4/2011

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Abstract

Cross-country comparisons of differential survival by socioeconomic status (SES) are useful in many domains. Yet, to date, such studies have been rare. Reliably estimating differential survival in a single country has been challenging because it requires rich panel data with a large sample size. Cross-country estimates have proven even more difficult because the measures of SES need to be comparable internationally. We present an alternative method for acquiring information on differential survival by SES. Rather than using observations of actual survival, we relate individuals’ subjective probabilities of survival to SES variables in cross section. To show that subjective survival probabilities are informative proxies for actual survival when estimating differential survival, we compare estimates of differential survival based on actual survival with estimates based on subjective probabilities of survival for the same sample. The results are remarkably similar. We then use this approach to compare differential survival by SES for 10 European countries and the United States. Wealthier people have higher survival probabilities than those who are less wealthy, but the strength of the association differs across countries. Nations with a smaller gradient appear to be Belgium, France, and Italy, while the United States, England, and Sweden appear to have a larger gradient.

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In addition to quantifying the relationship between mortality and economic variables, most of these studies are concerned with causality between health and socioeconomic status, which is beyond the scope of this article. To conduct those analyses, authors have in some cases combined cross-sectional data on birth-cohort mortality with pooled time-series data on income, education, and poverty (e.g., Deaton and Paxson 2001, 2004).

Examples are Desplanques (1991) and Bommier et al. (2006) for France, Nelissen (1999) and references therein for the Netherlands, Hoffmann (2005) for Denmark, and Martikainen (1995) and Valkonen et al. (2000) for Finland.

See Manski (2004) for an overview and discussion of the state of knowledge about subjective expectations data.

See Juster and Suzman (1995) for an overview of early waves, and the HRS website at http://hrsonline.isr.umich.edu or St. Clair et al. (2008) for information about later waves.

Subscripts denoting individuals have been omitted for ease of presentation.

Source: Data description and usage of the HRS Tracker file for 2006 (Final, Version 2.0).

The vast majority of cases determined to be dead by HRS also have a match in the NDI. The small fraction without a match in the NDI is most likely due to respondents leaving the country or other forms of loss to follow-up.

The vast majority of observations that come from 1994 pertain to respondents who were asked both in 1992 and 1994 about their subjective probability of survival to age 75. We use their 1994 response because at that time, the distance to age 75 (i.e., 11 or 12 years) matches more closely that of the rest of the sample.

A similar graph of 14-year mortality by P75 for the population-representative sample of age-eligible HRS respondents (age 51–61) interviewed in 1992 shows qualitatively the same pattern, indicating that the patterns in our analytical sample are not driven by our sample selection.

Results for the same type of analysis by income and by education are provided in Online Resource 1.

These findings are consistent with those reported by Elder (2007), who investigated the predictive power of subjective probabilities of survival for actual mortality and documented biases. Biases in the level of survival do not affect the viability of our proposed method as long as the differentials across socioeconomic groups are preserved.

Our estimate is based on the following Bernoulli log-likelihood function:

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-011-0066-8/MediaObjects/13524_2011_66_Figc_HTML.gif

When testing the joint hypothesis that the coefficients on age 64, 65, and 66 are equal in both regressions, we do not reject this hypothesis at the 5% level.

In our analytical sample, 69.9% of the men and 69.2% of the women survived to age 75.

Other studies of differential mortality often report results in terms of mortality hazard ratios. In our framework, \( P({A_{{TA}}} = 0|Z,W = 2) \) denotes the probability of dying before the target age TA conditional on being alive at the current age and on having characteristics (Z, W=2). The ratio of the probability of dying before the target age TA of the second wealth tercile to the first wealth tercile is given by

https://static-content.springer.com/image/art%3A10.1007%2Fs13524-011-0066-8/MediaObjects/13524_2011_66_Fige_HTML.gif

The health variables include information on drinking alcohol, smoking, the number of chronic conditions, self-rated health, number of limitations with activities of daily living (ADLs), and body mass index.

Results for differential survival by income and by education are included in Online Resource 1.

Small adjustments were made to accommodate institutional differences.

See http://www.share-project.org/ for more details on the sampling and features of SHARE. In this study, we use release 2.0.1 of the first wave of SHARE.

These surveys include the European Union Labor Force Survey, 2004; the European Community Household Panel, 2000; and the European Social Survey, 2002.

See http://www.ifs.org.uk/elsa/documentation.php for more details on the sampling and features of ELSA.

We choose age 51 as the lower age bound because the HRS 2004 data are representative of the population aged 51 and older.

Among the Wave 1 respondents, 73.3% were alive at Wave 2, 2.4% were dead, and the remaining were of unknown status.

The averages are weighted. For the HRS, SHARE, and ELSA, we use respondent-level weights (Börsch-Supan and Jürges 2005).

The sample is relatively small in some countries, so we use narrow age bands rather than age dummy variables.

The pooled regression includes indicator variables for the different countries to allow for differences resulting from, for example, sampling or different survey agencies. The weights in the pooled regressions reflect the countries’ population (i.e., the sum of the weights in a country is equal to its population aged 51–65).

For example, we reject the joint null hypothesis that the coefficient of the second wealth tercile for Belgium is equal to the coefficient of the second wealth tercile for England and that the coefficient of the third wealth tercile for Belgium is equal to the coefficient of the third wealth tercile for England.

Those differences are statistically significant at 5% for Germany, Spain, the United States, and England.

Like in the HRS, there is no statistical difference in the proportion of 100% answers by wealth tercile. The rate of zeros is higher in the lower wealth tercile, which is consistent with the fact that they experience lower mortality.

The difference is statistically significant at the 5% level for the United States, England, the Netherlands, and Spain.

The predicted probabilities that we impute are based on regressions including respondents who answered 50%. Excluding them does not change our results much. To obtain the variance of the exponential of the coefficients necessary to compute the 95% confidence interval, we use a first-degree Taylor approximation—that is, V(f(x))=(f’(x))² V(x).

Two exceptions are England and France and England and Italy, for which we get p values of .139 and .175, respectively. Note, however, that for these two pairs of countries, we reject equality of the coefficient associated with the third wealth tercile at 10%.

See page 6 and Table S4 of Online Resource 1 for detailed results.

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Titel: Differential Survival in Europe and the United States: Estimates Based on Subjective Probabilities of Survival
verfasst von: Adeline Delavande
Susann Rohwedder
Publikationsdatum: 01.11.2011
Verlag: Springer US
Erschienen in: Demography / Ausgabe 4/2011
Print ISSN: 0070-3370
Elektronische ISSN: 1533-7790
DOI: https://doi.org/10.1007/s13524-011-0066-8

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