NBER WORKING PAPER SERIES PREDICTORS OF MORTALITY AMONG THE ELDERLY Michael D. Hurd Daniel McFadden Angela Merrill Working Paper 7440 http://www.nber.org/papers/w7440 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 December 1999 Financial support from the National Institute on Aging through a grant to the NBER is gratefully acknowledged. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research. © 1999 by Michael D. Hurd, Daniel McFadden, and Angela Merrill. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Predictors of Mortality Among the Elderly Michael D. Hurd, Daniel McFadden, and Angela Merrill NBER Working Paper No. 7440 December 1999 ABSTRACT The objective of this paper is to find the quantitative importance of some predictors of mortality among the population aged 70 or over. The predictors are socio-economic indicators (income, wealth and education), thirteen health indicators including a history of heart attack or cancer, and subjective probabilities of survival. The estimation is based on mortality between waves 1 and 2 of the Asset and Health Dynamics among the Oldest-Old study. We find that the relationship between socio-economic indicators and mortality declines with age, that the 13 health indicators are strong predictors of mortality and that the subjective survival probabilities predict mortality even after controlling for socio-economic indicators and the health conditions. Michael Hurd Daniel McFadden RAND Corporation University of California, Berkeley 1700 Main Street Department of Economics Santa Monica, CA 90407 549 Evans Hall #3880 and NBER Berkeley, CA 94707-3880 [email protected] and NBER [email protected] Angela Merrill University of California, Berkeley Program in Health Services and Policy Analysis Berkeley, CA 94707-3880 [email protected] 1. Introduction Mortality risk is a fundamental determinant of consumption and saving in a life-cycle model. Understanding the behavioral reactions to variation in mortality risk is important from a scientific point of view and from a policy point of view. The reaction will reveal the degree of risk aversion, which is an important behavioral parameter. The economic status of the oldest-old will depend on their consumption and saving choices in the years closely following retirement. Under the life-cycle model the predicted changes in life expectancy will have an effect on national saving beyond what would be forecast from a compositional effect. Mortality risk in the population may be adequately measured by lifetables; however, individuals are likely to have additional information about their life chances and use that information in making consumption and saving decisions. Some of that information may be related to observable characteristics such as health status and socio-economic status (SES). Accounting for the relationship between SES and mortality (the SES gradient) is particularly important. The gradient is important because it causes difficulties in predicting the economic status of a cohort and in understanding life- cycle behavior from cross-section variation in wealth. Besides cohort effects that would, by themselves, cause wealth to decline with age in cross-section, the mortality gradient will cause wealth to increase both in cross-section and in panel. As a cohort ages those with less wealth die, leaving survivors from the upper part of the wealth distribution. Thus, even if no couple or single person dissaves after retirement, the wealth of the cohort would increase with age. This makes it difficult to study life-cycle wealth paths based on synthetic cohorts, which will eliminate cohort differences in lifetime time resources but not differential mortality. These difficulties carry over to studies of income and consumption in synthetic cohorts. Yet, it is likely that individuals have subjective information about their own survival chances that cannot be discovered from mortality rates stratified by observable covariates such as SES. First, some personal characteristics are not easily measured, so they cannot be used as stratifying variables. Second, individuals may misperceive their survival chances, choosing consumption based on subjective yet biased life expectancy. If we are to understand consumption choices we need to have observations on the subjective variables that individuals use in making their choices. Third, even if we could stratify by many characteristics and understand average bias, there surely would remain considerable heterogeneity in subjective survival probabilities: understanding that heterogeneity would help in the estimation of life-cycle models. To model and use heterogeneous information about survival chances in life-cycle models is a multi-step process. First, we need to find the observable correlates of mortality and measure their effects. Second, we need to measure the perceptions of individuals about their own mortality risk, and, given observable characteristics, to find if these perceptions have explanatory power for mortality. Third, we need measures of mortality risk that embody all of our knowledge about heterogeneity in models of decision making. This paper addresses the first two of these steps. Differential mortality by socio-economic status (SES) has been observed over a wide range of data and populations: mortality rates are high among those from lower SES groups (Kitagawa and Hauser, 1973; Shorrocks, 1975; Hurd, 1987; Hurd and Wise, 1989; Jianakoplos, Menchik and 3 Owen, 1989; Feinstein, 1992). However, because of data limitations the measures of SES have typically been occupation or education. In the Health and Retirement Study (HRS) and the Asset and Health Dynamics Study (AHEAD) there is scope for expanded studies of differential mortality because these are panel surveys with considerable age density and they obtain extensive data on income, wealth and health conditions in addition to occupation and education. The AHEAD data in particular offer opportunities for increasing our knowledge of the gradient because the population (age 70 or over at baseline) has been not been studied to the extent to which younger populations have been. Furthermore, the fact that the AHEAD population is almost completely retired means that a very strong confounding effect of health on income via work status is practically eliminated. Finally, almost the entire AHEAD population is covered by Medicare: therefore, an important causal pathway linking SES to mortality via access to health care services is reduced and even possibly eliminated. The HRS and AHEAD asked respondents to give an estimate of their survival chances to a target age, which was approximately 12 years in the future. In the HRS this variable is a significant predictor of mortality between waves 1 and 2 (Hurd and McGarry, 1997). Here we aim to find if it has predictive power for mortality in the AHEAD population both unconditionally and conditionally on observable characteristics. In this paper we will verify that SES is related to mortality in the AHEAD data. Then we will give evidence about the validity of the subjective survival probabilities. The evidence will be of three kinds: whether the subjective survival probabilities vary in cross-section in a way that is appropriate given the variation in actual mortality; how the subjective survival probabilities change in panel in response to new information such as the onset of an illness; and whether they predict actual mortality. We will then examine whether, conditional on health status, SES and the subjective survival probabilities have explanatory power for predicting mortality 2. Data Our data come from the study of the Asset and Health Dynamics among the Oldest-Old (AHEAD).1 This study is a biennial panel survey of individuals born in 1923 or earlier and their spouses. At baseline in 1993 it surveyed 8222 individuals representative of the community-based population except for oversamples of blacks, Hispanics and Floridians. Wave 2 was fielded in 1995. The main goal of AHEAD is to provide panel data from the three broad domains of economic status, health and family connections. Our main interest in this paper is to understand the predictors of mortality between waves 1 and 2, especially education, income, wealth and the subjective probability of survival. In wave 1 individuals and couples were asked for a complete inventory of assets and debts and about income sources. Through the use of unfolding brackets, nonresponse to asset values was reduced to levels much lower than would be found in a typical household survey such as the SIPP.2 1 See Soldo, Hurd, Rodgers and Wallace, 1997. 2 To handle non-response to asset and total income questions, we use a nested composite imputation procedure. We impute non-response to asset ownership, unfolding brackets, and asset amounts 4 Both HRS and AHEAD have innovative questions about subjective probabilities, which request the subject to give the chances of future events. We will use observations on the subjective probability of survival. The form of the question is as follows: [Using any] “number from 0 to 100 where “0" means that you think there is absolutely no chance and “100" means that you think the event is absolutely sure to happen ... What do you think are the chances that you will live to be at least A ," where A is the target age. A is 80, 85, 90, 95, or 100 if the age of the respondent was less than 70, 70-74, 75-79, 80-84, 85-89 respectively. The question was not asked of those 90 or over or of proxy respondents. AHEAD queries about a wide range of health conditions. Many are asked of the respondent in the following form: “Has a doctor ever told you that you have …” We will use information on 10 conditions such as cancer, heart attack/disease and lung disease. The respondent is queried about limitations to activities of daily living (ADL). We will use as an indicator of poor health three or more ADL limitations. AHEAD measures cognitive status in a battery of questions which aim to test a number of domains of cognition (Herzog and Wallace, 1997). Learning and memory are assessed by immediate and delayed recall from a list of 10 words that were read to the subject. Reasoning, orientation and attention are assessed from Serial 7's, counting backwards by 1 and the naming of public figures, dates and objects.3 In prior work we have found that unrealistic stated subjective survival probabilities are associated with low cognitive performance (Hurd, McFadden and Gan, 1998). Therefore we aggregated the cognitive measures in AHEAD and formed a categorical variable to indicate low cognitive performance. AHEAD also has a battery of questions that are extracted from the CESD scale. The scale aims to assess depressed mood. We form an indicator of depressed mood based on these questions. 3. Results The baseline AHEAD sample was 8222, of which 813 died between waves 1 and 2, and 7364 survived. The vital status of 45 is unknown. Excluding the 45, the two-year mortality rate was 0.099.4 This mortality rate cannot be compared with any lifetable rate for two reasons: first, the sequentially. Ownership and complete brackets are imputed using stepwise logistic regression on a number of demographic characteristics. Dollar amounts are then imputed, conditional on a complete bracket, using a nearest neighbor which makes extensive use of covariates (Hoynes, Hurd and Chand, 1998). 3Serial 7's asks the subject to subtract 7 from 100, and then to continue subtracting 7 from each successive difference for a total of five subtractions. 4The mortality rate including the 45 cases among the living was 0.0988. Including them among the dead the mortality rates was 0.104. In the rest of the paper we will include them among the living for 5 AHEAD baseline is the community-based population, so that it excludes residents of long-term care facilities who have substantially higher mortality rates than the community-based population. Lifetables include residents of long-term care facilities and of other institutions.5 Second, the AHEAD sample includes spouses of AHEAD age-eligible respondents, but the spouses may themselves not be age-eligible. The age-ineligible spouses do not make up any population whose mortality rate can be compared with a lifetable. The mortality rate of the AHEAD age-eligible sample (n=7446) was 0.107; the lifetable rate interpolated to 1993 was 0.155. The difference comes from the high mortality rates among the institutionalized. Table 1 shows weighted mortality rates for the age-eligible part of the AHEAD population by age and sex, and the number of observations. A few respondents were age 69 at their initial interview but we include them in the 70-74 age band. The weights account for the oversamples at baseline. The figures show sharply increasing mortality rates with age and a considerable difference between men and women. At older ages the number of subjects diminishes rapidly due to mortality, cohort effects, and the fact that the institutionalized are not in the AHEAD baseline. Table 2 presents mean wealth and income by age and marital status. Wealth is the total of housing wealth, financial, business and other real estate wealth, but it does not include any pension wealth. Income includes all financial income such as pension income, but no flow from owner occupied housing. Just as in other cross-section data sets, wealth and income fall with age, and both are higher among couples than among singles. The table makes clear that we cannot study the relationship between mortality and economic status without effectively controlling for age. Wealth, Income and Education Table 3 shows average and median wealth in wave 1 by vital status in wave 2. At baseline among single males aged 70-74 who survived to wave 2, average wealth was about $216.5 thousand. Wealth was just $67.2 thousand among those who died. This is, of course, a substantial difference and indicates considerable differential mortality by wealth holdings. The difference among single females is smaller but still substantial. Among married males there is only a small difference, whereas married female survivors had almost twice the wealth on average as deceased married females. The medians also indicate considerable differential mortality by wealth. There is diminished differential mortality by wealth among those 75-79. Given the amount of observation error on wealth, we judge there to be little difference in wealth holdings by mortality outcome among those married at baseline, either male or female. There is some difference among singles. The differences are smaller still among the 80-84 year-olds, and there are no consistent convenience, but their treatment is not consequential compared with the lack of data on the institutionalized population. 5Because AHEAD will follow the baseline respondents into institutions, it will eventually be representative of the entire cohort of 1923 or earlier. 6 differences among the 85-89 year-olds. The medians show somewhat more differential mortality but not as much as at the youngest age interval. Among those 90 or over, sample sizes are small. For example, just 39 single males and just twenty married females were in the age interval at baseline. The group with the largest number of observations (single females) shows no differential mortality. These data are summarized in Figure 1, which shows the wealth of decedents relative to the wealth of survivors.6 For example, single female decedents aged 70-74 had about 40 percent of the wealth of survivors. The figure shows a general trend to smaller differences in wealth at greater ages. We conclude that overall there is evidence of differential mortality by wealth: on average those who died had about 70% of the wealth of those who survived. However, the difference decreases with age. Table 4 has comparable results but for average education. Thus, among males age 70-74 the average level of education was 11.5 years among survivors and 10.4 among the deceased. In the first age band the differential is considerable and it is the same for each sex. At ages 75-79 the differential decreases for men but remains about the same for women, and by 80-84 there is no differential among men. It is notable that in the highest age interval, the educational level of women is higher than that of men even though for these cohorts the educational level of a complete population of men would have been considerably higher. An explanation is found in the differential mortality at younger ages: women consistently have a higher mortality gradient by education than men, causing the better educated women to survive at a higher rate than the better educated men. Tables 5 and 6 show mortality rates by wealth and income quartiles. The quartiles are defined separately by marital status, but the quartile boundaries are the same over the entire age range. Because of the correlations between age and economic status, and between age and mortality, overall mortality varies strongly by wealth or income quartile as shown in the last line of each table. However, this relationship is much less clear when age is controlled for. In the first age band there is a consistent decline across the quartiles, but in the other age bands there is little consistent pattern even though mortality is generally the largest in the first wealth quartile. Mortality by income has a more consistent pattern and for some age intervals the effects are very strong. For example among 80-84 year-olds the morality rate in the lowest income quartile is about 56% greater than in the highest. As with wealth, however, the differential seems to diminish with age. These figures, particularly for wealth, suggest that differential mortality may decrease with age. To test that idea we estimated analysis-of-variance models where the observations are mortality rates classified by age intervals, and income and wealth quartiles. The models had complete interactions between age intervals and income quartiles and between age intervals and wealth quartiles. We tested for significance of the interactions. We could reject the null hypothesis that the interactions for couples and separately for singles are all zero at the five percent level, but not at the one percent level. Because the age interactions are not particularly strong and in the interest of simplifying the analysis, our basic model will have age effects, and income and wealth quartiles but not interactions. We will leave the exploration of the age interaction for future research. 6 Not shown when the category has less than 100 observations. 7 Table 7 has mortality rates by education level for males. As the table shows, in the AHEAD data mortality is higher for men with 9-11 years of education than for males of 0-8 years of education, and this is true holding age constant. We have no good reason for this result, except possibly that those with 0-8 years of education have been highly selected by the time they reach the AHEAD ages. Holding age constant, we see some pattern of differential mortality in the younger age bands, but it is less apparent at older ages. Among females in their 70s there is a strong and consistent relationship between mortality and education, but at older ages there is little if any (Table 8). Overall we conclude that there is differential mortality by educational attainment at the younger ages in the AHEAD population, but the effects diminish with age. Particularly among females, who comprise most of the observations in the population 80 or over, there is little evidence for a mortality gradient by education. Subjective Probabilities of Survival The subjective probability of survival has been studied extensively in data from the HRS (Hurd and McGarry, 1995, 1997). In cross-section it aggregates well to lifetable levels and it varies appropriately with known risk factors. Furthermore, in panel it is a significant predictor of actual mortality even after accounting for SES and a number of disease conditions. In AHEAD baseline it aggregates well to lifetable values among those aged 70-79, but in the older age groups the subjective survival probabilities overstate survival compared with lifetable rates (Hurd, McFadden and Gan, 1998). One cause of the excess survival probability is that a fairly small number of subjects give a probability of 1.0 of surviving to the target age. The propensity to give a probability of 1.0 is related to low cognitive status, and often an individual will give a probability of 1.0 to a number of unrelated subjective probability questions. Such regularities provide evidence of error in some of the responses. Nonetheless we will take the responses as they were given by the AHEAD subjects. We imagine, however, that the predictive power of the subjective survival probabilities could be increased were some of the reporting error removed by application of a model of the error. Table 9 shows the average subjective survival probability by age band and wealth quartile.7 It is important to group by age in this manner because all the respondents in each age band were given the same target age. As would be expected the average survival probability declines with age, but unlike actual mortality there is little systematic variation in the survival probability as a function of wealth. For example, among those 70-74 the average subjective survival probability is about the same in the lowest and the third quartiles. Only in the highest quartile is it greater. Yet the actual two- year survival rate was five percentage points higher in the fourth quartile than in the first quartile: Such a large difference in two-year survival should accumulate to a much greater difference in subjective survival to the target age. 7 Both the wealth and income quartiles are calculated separately by marital status. 8 As shown in tables 10 and 11, there is little variation in the survival probabilities as a function of income quartiles or of education bands. A possible reason for the lack of any pattern by wealth, income, or education is the rather high rate of nonresponse to the survival probabilities.8 A substantial number of interviews were by proxy, often because of the frailty of the targeted respondent. In this case it made no sense to ask a proxy about the subject’s subjective survival probability. In addition a rather large number of respondents replied “Don’t know” (DK) to the query. Table 12 has the counts of nonresponse as a function of wealth quartile. Overall about 25% of singles and 21% of married persons were nonrespondents. It is clear that the rate of nonresponse is greatest among those in the lowest quartiles. For example, among 70-74 year-olds the rate of nonresponse was about 31% in the lowest quartile and 11% in the highest. Furthermore, because the propensity to give a proxy interview and the likelihood of a DK are related to health status, it is probable that the responding sample is systematically selected toward those with higher survival probabilities. Therefore, the averages in the lowest quartiles are higher than the true quartile averages whereas the averages in the highest quartiles are closer to the true averages, acting to reduce any upward trend in the subjective survival probabilities as a function of wealth. We ask whether the pattern of nonresponse could conceivably be responsible for the lack of pattern in the subjective survival probabilities, even though there is a clear pattern in actual mortality. We illustrate that it could be responsible by assigning a subjective survival probability of zero to the nonresponders. Figure 2 shows the variation in the subjective survival probabilities under that assignment. The probabilities increase in wealth in each age band. These results show that differential nonresponse has a quantitatively important effect on the level and variation in the subjective survival probabilities. In future work we will explore methods for imputing missing values, but for the rest of this paper we will, as appropriate, use categorical variables to account for nonresponse. Table 13 shows the estimated regressions of the subjective survival probabilities on the wealth and income quartiles, education bands, and other explanatory variables. We control for age and for the varying interval between the interview and the target age by including as a right-hand variable the lifetable survival rate to the target age from the age of the respondent. If respondents reported their subjective survival probability to be the same as the lifetable rate, the coefficient on this variable would be 1.0. The estimated coefficient shows that the age gradient in the subjective survival probability is less than the age gradient in the lifetable rate. This is partly due to the overestimation of subjective survival probabilities among the oldest compared with the lifetable values. The three sets of SES variables show no systematic pattern, which is the basic finding from the cross-tabulations in tables 9, 10 and 11. Relative to the lifetable, males overstate their survival chances by 0.07. This tendency to over-optimism is also found in the HRS population (Hurd and McGarry, 1995). The last two columns of Table 13 contain regressions which include controls for health condition. Most of the health conditions are asked of the respondent in the following form: “Has a doctor ever told you that you have …” The exceptions are “low cognitive score,” which is a categorical variable indicating a low score on the sum of three items that were administered in the 8 This low response rate in AHEAD is in contrast to the very high response rate in HRS. 9 survey itself; and “depression,” which is based eight items from the CESD (Wallace and Herzog, 1995). A categorical variable for depression indicates a score of five or more on the CESD. Eight of the 13 health variables are significant at the 0.05 level, and they are associated with a reduction in the subjective survival probabilities of nine to 25 percent of the average probability. For example having had a heart attack or heart disease prior to wave 1 is associated with a reduction in the subjective survival probability of 0.062 from a base of 0.415 or about 15 percent. Based on these results we would expect the subjective survival probabilities to predict actual mortality because of their association with the health conditions which, themselves, are associated with mortality. Change in the subjective survival probabilities As individuals age the subjective survival probabilities should increase among survivors holding the target age constant. Between waves 1 and 2 the average increase was 0.064 (16 percent) among singles and 0.051 (15 percent) among couples. Tables 14 and 15 show the levels and changes by age band and by sex. The tables show that the subjective survival probabilities are overstated relative to lifetables at older ages, particularly among men. For example among men aged 85-89 the average subjective survival probability to age 100 is 0.314 whereas the average lifetable value is 0.034. In terms of relative risk, the increases in the subjective survival probabilities from wave to wave are reasonably close to the increases in the lifetable probabilities except in the oldest age intervals. Although it is difficult to know what the appropriate standard of comparison is, it is notable that in all age bands the subjective survival probabilities increase between the waves. This increase was not found in HRS: among survivors the average subjective survival probability decreased slightly (Hurd and McGarry, 1997). Besides increases in the subjective survival probabilities that are due to the AHEAD subjects surviving for two years, the probabilities should change in response to new information that alters survival chances. Such information would be onset of a health condition that is associated with an increased risk of death. Table 16 shows the incidence of new conditions between waves 1 and 2 for all respondents. Thus, for example, among singles who had not had cancer prior to the baseline interview, 5.1 percent had a cancer between the waves. Among all singles, including those with a history of cancer prior to baseline, 5.5% had a new or initial cancer between the waves. Although it is not the focus of this paper the table shows that having a prior history of cancer, stroke, heart attack/disease, hip fracture or fall increases the risk of a new, similar event. Having a low cognitive score, which is associated with increased risk of dementia, has the greatest rate of onset. About 8.2 percent of singles who were living in the community at wave 1 were in a nursing home at wave 2. There is little difference in the rates of onset between singles and couples except for limitations on the activities of daily living (ADL limitations) and nursing home entry. The measure of ADL limitations is an indicator for ADL limitations greater than two, and singles had an incidence rate of 10.4% compared with couples of 6.6%. The difference likely comes from the fact that on average singles are older than couples and from the ability of couples to help each other, disguising some mild cases of ADL limitations. As in the case of ADL limitations the rate of entry into a nursing home is 10