Schooling and frailty among seniors

~

Economics of Education Review, Vol. 16, No. 1, pp. 45-57, 1997

Copyright © 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0272-7757/97 $17.0(OO.00

Pergamon

S0272-7757(96)00031-3

Schooling and Frailty Among Seniors J. PAUL LEIGH*t a n d RACHNA DHIR* *Department of Economics, San Jose State University, San Jose, CA 95192-0114, U.S.A. 5Department of Medicine, Division of Immunology, Stanford University, Stanford, CA 94304-1808, U.S.A.

Abstract--What accounts for the correlations between schooling and frailty among seniors? Do the correlations differ among women, men, blacks and whites? Data from the 1986 wave of the Panel Study of Income Dynamics (PSID) are analyzed to answer these questions as well as related ones pertaining to the roles of self-selection bias, self-efficacy, risk preference and time preference in explaining the correlations. The correlations between disability and schooling for women were strong after accounting for self-selection bias. The male schooling and exercise correlations were strong after accounting for selfselection, self-efficacy and preferences. Univariate differences in frailty measures between blacks and whites appear to be due to socioeconomic status rather than genetics. No race differences were observed in the correlations between schooling and frailty. The results provide additional evidence that education itself, rather than simply self-efficacy or time or risk preference, acts as preventive medicine. [JEL 112, J16] Copyright 01997 Elsevier Science Ltd INCREASES IN longevity over the past century have been astonishing. But if the additional years of life are spent in nursing homes many may not welcome longer lives. The prevention of infirmities and disabilities among seniors has been receiving increased research attention (Verbrugge, 1984; Fries, 1983). A number of prevention strategies have been discussed including improving access to medical care before and after retirement, encouraging medical checkups, enrolling in self-help classes, encouraging exercise and counseling, discouraging isolation, improving occupational safety prior to retirement, and increasing social security benefits especially for the elderly who are poor (Cutler et al., 1990; Aaron et al., 1989; Grembowski et al., 1993; Fries, 1983; Leigh and Fries, 1991; Verbrugge, 1984; House et al., 1990). This study investigates a covariate that may ultimately be viewed as preventive medicine for postponing or compressing infirmities into the last few months of life: education (Grossman, 1975). "Education as preventive medicine" may not have received the research attention it deserves because investigators question how something acquired early in life would have an effect late in life. Any educationinfirmity link is a long-run phenomena. Moreover, many investigators are skeptical of a causal relation between education and any form of health. One argument suggests that a person's years of completed schooling merely serves as a proxy for the ability to delay gratification (time preference) or desire to take risks or feelings of self-efficacy (Grembowski et al., 1993; Fuchs, 1982; Fuchs, 1992; Callahan et al.,

1988; Williams, 1990; Feinstein, 1993; Pincus et al., 1987; Kaplan e t a l . , 1987). According to this view, the ability to delay gratification and/or self-efficacy leads to improved health habits that in turn lead to good health. The ability to delay gratification or feelings of self-efficacy are the true causes of good health, not education p e r se. Solomon and Amkrant (1981) review the literature suggesting that feelings of loss of control will lead to poor immune function. Nevertheless, a number of recent studies have found evidence for strong education and health correlations even after attempting to account for time or risk preferences or self-efficacy or other variables that are frequently unobserved (Grembowski et al., 1993; Behrman and Wolfe, 1989; Berger and Leigh, 1989; Leigh, 1990). Evidence from the more recent economic studies suggest a direct effect of education on health. This study extends the existing literature on education and frailty in four ways. First, direct measures of self-efficacy, time and risk preferences are entered into the model as separate covariates in the analyses of men. While a similar model has been used to explain seatbelt use (Leigh, 1990), it has not been applied to studies of frailty. Second, the residual from a schooling regression is entered as a separate covariate in the frailty equation. The inclusion of the residual is designed to remove unobserved variables (self-selection) bias (Heckman, 1979). Again, although similar models have been used for other measures of health, the models have not been used to explain frailty (Behrman and Wolfe, 1989; Berger

Correspondence to Department of Economics, San Jose State University, San Jose, CA 95192-0114, U.S.A. [Manuscript received 8 November 1994; revision accepted for publication 13 March 1996] 45

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Economics of Education Review

and Leigh, 1989; Leigh, 1990). Third, the sample is restricted to persons 65 yrs and older. It could be that schooling and health correlations may be less strong among seniors than younger people. Presumably, only the strong survive to age 65. Fourth, race and gender differences in the conelations are inspected. Race and gender differences deserve research attention. A comparison to economic studies of earnings is useful. For more than 20 yrs, economists have recognized that schooling and earnings correlations may be different across races and gender (Hines et al., 1970; Carnoy and Marenback, 1975; Ferber and Lowry, 1976). We are aware of only one study of education and health that focuses on race differences in the correlation (Mutchler and Burr, 1991). But the Mutchler and Burr (1991) study does not attempt to remove possible self-selection bias or bias from variables such as time and risk preferences or self-efficacy. For our purposes, the Mutchler and Burr study is also limited because it does not measure frailty among only seniors nor are any gender differences addressed. 1. D A T A A N D M E T H O D 1.1. Data Subsamples were drawn from the 1986 wave of the Panel Study of Income Dynamics (PSID). The PSID is an ongoing longitudinal (panel) survey of roughly 7000 American families. The PSID began in 1968 with 5000 families but attempts were made to follow people who left the original family, i.e. adult children, divorces, and so on. The 1986 wave was selected because it was the only year with information on Activities of Daily Living (ADLs) and exercise. The ADLs and the exercise information served as our measures of frailty. A recent introduction to the PSID is available (Hill, 1991). Attention was restricted to household heads and wives who were 65 yrs old or older and who provided information on the dependent or endogenous variables. The samples included 663 women and 465 men. A central problem with the PSID concerns data on women. In the early years, heads of households were always assumed to be men if a man and a woman lived together. If no man was in the house, the woman was assumed to be the head. The spouse or significant other was always assumed to be a wife. Today, these assumptions would be problematic. Nevertheless, to ensure a consistent data set, we retained these definitions in our analysis. Again in the early years, many questions asked of the head of the household were not asked of the wives. Beginning in 1979 most of the same questions were asked of heads and wives. As we will see, the incomplete data on wives will result in our excluding measures of occupation, preferences, self-efficacy, parents' wealth, and region where respondent grew up as covariates in frailty and schooling regressions involving women.

The disability (D) questions for the ADLs in the PSID were the following: Does subject have any trouble either walking several blocks or climbing a few flights of stairs because of his/her health? Does subject have trouble bending, lifting or stooping because of his/her health? Would subject's health keep him/her from driving a car? When subject travels around the community, does someone have to assist him/her because of health problems? Does subject have to stay indoors most or all of the day because of his/her health? Does subject's health confine him/her to bed or a chair for most or all of the day? Answers were recorded as "yes", "no", "don't know" or "not applicable". We created a disability index (D) based upon the answers to the six questions. Our disability index (D) was patterned after the disability index on the Stanford Health Assessment Questionnaire (HAQ) (Fries et al., 1982). We simply added the number of "yes" answers. Our disability index (D) takes on integer values between and including 0-6. The D index was our first dependent variable. Clearly, this D index measure is deficient. A "yes" for question number 6 is probably more serious than a "yes" for question number 2. On the other hand, in both the male and female samples, all persons who answered "yes" to question 6 also answered "yes" to question number 2. In fact, in our samples, persons who answered "yes" to question 6 also answered "yes" to virtually every other question. These cumulating "yes" answers are typical for measures of disability (Fries et al., 1982). Our index (D) was an ordinal measure just as is the index in the Stanford Health Assessment Questionnaire (HAQ). Unlike the Stanford index, ours assumed only six possible values. Since the D index was measured on an ordinal scale, the ordered probit appeared to be the most appropriate regression model. The second dependent variable was a measure of exercise (E). The PSID subjects were asked the following questions: Does respondent get any regular exercise, such as doing hard physical work, walking a mile or more without stopping, or playing an active sport? How often is that? If a subject answered "no" to the first question, then his/her E variable equalled zero. Roughly 61% of the women and 52% of the men in our sample answered "no". If the subject answered "yes" to question 1, then information from question 2 was used to create the exercise variable. In this case, exercise equalled the number of times per month exercise was taken. Non-integer numbers were allowed. Thus, 15.2 indicated the subject stated "every other day". The

Schooling and Frailty Among Seniors maximum value the PSID investigators allowed was 30.4. Roughly 17% of the women and 28% of the men recorded the maximum 30.4 value. The third dependent or endogenous variable was years of schooling completed. Schooling included formal schooling (12 grades, years in college or graduate or professional school) and vocational education. Values were recorded as integers and ranged between 1 and 18. Responses more than 18 were recorded as 18 by the PSID investigators. Following Garen (1984) and Berger and Leigh (1989), years of schooling was estimated with least squares (multiple regression) models. Independent or exogenous variables are listed in Table 1. Most are self-explanatory, but some require attention. The occupation variables referred to the person's occupation prior to retirement if retired and to the current occupation if still working (Vingard et al., 1991). The PSID investigators asked about occupation prior to retirement only in 1968 and 1969. The 1986 wave data could therefore not be used to construct an occupation prior to retirement variable. We retrieved the current occupation prior to retirement from prior years of the PSID. For some respondents this meant drawing data from 1968 and 1969. Fortunately, the PSID investigators maintained the same broad occupation codes from 1968 to 1986. We could not locate occupations for roughly 13% of our male sample. This could be due to coding errors in the PSID. Alternatively, it could be the result of these men never reporting any occupation. They could have been permanently disabled or unemployed. Roughly 42% of the women were in the "no occupation, no response" category. This number was disturbingly high, given that we regarded homemaker as an occupation. It is easily explained, however. The PSID has always attempted to gather the most information on household heads who were assumed to be male if a man and a woman lived together. But from

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1968 to 1986 many families were broken through death or divorce or separation. Ex-wives became household heads. New wives were attached to old heads. In general, the longitudinal data on women in the PSID, especially prior to 1974, is much more difficult to obtain than the longitudinal data on men. We therefore did not regard the PSID occupational data on women as reliable. Income data were drawn from 1979, not 1986. Income was for the respondent only, not family earnings. Beginning with respondents from 1979, we were able to trace the 1979 earnings for 98% of the men and 92.7% of the women. The penultimate group of variables indicated the head's or wife's background. The first two variables recorded responses from head.s and wives regarding parents' years of schooling. The last three of these variables were binary and indicated whether the head stated that his or her parents were poor, middle income, or rich. Information on parents' background was only available for heads, not wives. A unique feature of this study is the attempt to explicitly account for self-efficacy and risk and time preferences by using data on measures available in the 1972 wave of the PSID. The PSID investigators have not measured self-efficacy, risk or time preference since 1972. The risk and time preference measures have been used only rarely by economists, but when used, yielded plausible results. Bellante and Link (1981) successfully used the PSID risk measures to help explain employment in relatively risky private sector jobs versus relatively safe public sector jobs. Leigh (1990) used the risk and time preference measures to explain seatbelt use. The PSID investigators created the variable "efficacy and planning" which contained items 1--6. We added item 7, Abbreviated versions of self-efficacy (SE) questions appear below:

Table 1. Descriptive statistics on key variables

Women Mean

Dependent or endogenous Years of completed schooling Disability index (D) Exercise Efficacy and preferences Self-efficacy* Risk preference = risk avoidance? Time preference = horizon proxy~

Men

Standard Minimum Maximum deviation

Mean

Standard Minimum Maximum deviation

variables 9.269

3.697

4.0

18.0

9.927

4.053

4.0

18.0

2.096 6.766

1.895 11.694

0.0 0.0

6.0 30.4

1.203 11.126

1.503 13.516

0.0 0.0

6.0 30.4

4.147 5.089

2.144 2.125

0.0 1.0

7.0 8.0

4.857

2.276

1.0

8.0

Notes: *Self-efficacy was missing for 64 men. fRisk avoidance was missing for 58 men. ~Time preference was missing for 51 men.

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Economics of Education Review sure life would work out (1 point); plans life ahead (1 point); gets to carry things out (1 point); generally finishes things (1 point); rather save for future (1 point); thinks about things that might happen in the future (1 point); and thinks what happens to me is my own doing (1 point).

Scores ranged from zero to 7. Twelve men in our sample scored 7. Roughly 2% of the male sample scored zero. A high score demonstrated high selfefficacy. Risk preferences were also measured using answers to questions raised in the 1972 survey. The PSID investigators created a variable, "risk avoidance" which contained the following items in abbreviated form: newest (assumed to be best) car in good condition (1 point); neutralize non-car owners (1 point); all cars insured (1 point); uses seatbelts some of the time (1 point); uses seatbeits all of time (2 points); has medical insurance or way to get free care (1 point); smokes less than one pack per day (1 point); has some savings but less than two months' pay (1 point); and has more than two months' pay saved (2 points). Each of the above nine items was given 1-2 points as indicated. If a person received 2 points for item 5, he could not get another point for item 4. The same applies to 8 and 9. Suppose, for example, a person checked 1, 3, 4, 6, 7 and 9. For 1-7, he received 5 points; for 9, he received 2 points. His total score would then be 7 points. A person with a high score had high aversion to risk. In our sample of men over 65, no one scored zero or 9. Time preferences (ability to delay gratification) were measured again using answers to questions raised in the 1972 survey. The investigators created the following "horizon proxies" variable which appears below in abbreviated form: is sure whether will or will not move (1 point); has explicit plans for children's education (2 points); neutralize those with no children in school (1 point); has plans for an explicit kind of new job (1 point); knows and mentions what kind of training new job requires (1 point); has substantial savings relative to income (1 point); expects to have a child more than one year hence, or expects no more children and is doing something to limit the number of children (2 points); and

neutralize those who expect child within one year and in approximate cases (! point). A higher time preference score indicated persons who were willing to delay gratification. In our male sample, no one scored zero but six men scored an 8. The means and standard deviations for the selfefficacy, risk and time preference variables are indicated in the bottom of Table 1. 1.2. Estimation Methods and the Ordered Probit As indicated above, the disability index (D), the measure of exercise, and years of schooling were estimated with ordered probit, Tobit, and least squares techniques, respectively. Least squares or multiple regression is well known and does not require elaboration. Tobit has received increasing use by economists and others when attempting to fit a dependent variable with a limiting value. The limiting values for the exercise variable were zero and 30.4, indicating exercise is taken every day. Roughly 52% of the men and 61% of the women in our samples were recorded with zeros; 28% of the men and 17% of the women reported 30.4 for exercise. Since non-integers are possible, Tobit is preferred over Poisson regression. Nontechnical introductions to the Tobit estimator are available (Kennedy, 1992; Leigh and Fries, 1993). The ordered probit is appropriate since the disability index is clearly ordered: 6 implies more disability than 3. But 6 is not necessarily twice as bad as 3. Our application uses the procedure in Greene (1990, 1992) and assumes seven possible disability index outcomes: 0, 1, 2, 3, 4, 5, 6. As in the simple probit or logit case with just two outcomes, the probit coefficients do not, alone, represent marginal effects or partial derivatives. Marginal effects of a given independent variable will, in general, be different for the seven probabilities. If a probit coefficient is positive, the marginal effect for the first probability will be negative and the effect for the seventh probability will be positive. Marginal effects for probabilities 2-6 cannot be predicted by simply considering the sign on a probit coefficient (Greene, 1990). 1.3. Selection Bias and Measurement Error Independent variables in X in Equation (1) have almost always included some measure of schooling, but have typically ignored variables such as self-efficacy, risk preference, time preference, intelligence, and ability. Health = 3,'~X+ E~

(1)

If any of theseiself-efficacy through ability--are correlated with a person's years of schooling (as seems likely), then a bias will afflict any single equation attempt to measure the correlation between schooling and health. This is a self-selection bias. People select more schooling and invest in their

Schooling and Frailty Among Seniors health because some unobserved factor(s) push them to do so. Two approaches to remove the bias have been attempted. First, direct measures of self-efficacy, time and risk preferences and so on have been included in the models (Grembowski et al., 1993; Leigh, 1990). Second, two-equation models have been constructed in which schooling is treated as endogenous. Instruments are found that are correlated with schooling but not correlated with unobserved factors influencing health. In this paper, we will use both approaches. Equations explaining the amount of schooling obtained (SCH) and health or frailty status in the postschooling period (H) can be expressed as:

SCH = c~,'W + c~2'Y + G2

(2)

H =/3,'W +/32SCH + ~3(SCH.B) +/3~'Z + eh3 (3) where W is a vector of variables that influence both schooling and health or frailty. W includes B, a binary race variable equalling I for blacks. Y is a vector of variables that affect only schooling. Z represents variables that affect health status. The es are random error terms reflecting the effects of unobservables on schooling and health or frailty. In terms of Equation (2) and Equation (3); the finding in most studies is that the /32 is positive and statistically significant. The question is whether this finding represents a direct influence of schooling on health or whether the relationship is spurious for some reason. Perhaps the simplest way to investigate this question is to assume that the disturbance terms in Equation (2) and Equation (3) adhere to classical assumptions but are correlated. Unobservables that affect schooling also affect health, meaning SCH and ~h3, are correlated and estimates of/32 are biased. In order to obtain a consistent estimate of /32, one approach is to estimate Equation (2), calculate SCH, and then substitute SCH into Equation (3) in place of SCH. Alternatively, the residuals from Equation (2) could be included in Equation (3) together with SCH. A statistically significant estimated coefficient on SCH (or on SCH if the residuals are included as a separate covariate) would then be evidence of a direct effect of schooling on health. SCH, by construction, would be purged of the unobservables correlated with SCH and our measure of health (H). A direct way to remove the unobservables is to include the schooling residuals together with actual measured schooling (SCH) as separate covariates in Equation (3). To test for race differences SCH./3 (or SCH and the residuals x/3) would replace SCH./3 in Equation (3). If the "true" correlation between schooling and health is different for blacks vs whites, /33 will not be zero. Our model does not allow for poor health to influence schooling. One study found that the effect of poor health on schooling among teens appears weak (Shakotko and Grossman, 1982).

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The PSID data will require some simplifying assumptions to estimate the model. SCH is years of schooling completed. The W variables measure age and race. Most retired persons in 1986 completed their schooling from 1910 to 1940. During these 30 yrs there was an upward trend in levels of completed schooling. We, therefore, expect age to be negatively correlated with schooling completed. Race was entered to account for the education disparity between blacks and whites during 1910-1940. Variables unique to the schooling equation (Y) include the standard background covariates (Leigh, 1990; Manski et al., 1992) such as mother's and father's years of completed schooling, measures of the parents' wealth when the subject was young and state of residence when young. The wealth measures in the PSID were simply dummy variables indicating whether the subject thought his parents were poor, middle income, or well-off when the respondent grew up. Parents' wealth and years of schooling ought to be positively correlated with the respondent's years of schooling. In addition, 39 dummy variables representing 40 states and foreign residences in childhood were entered as covariates. The foreign category was one dummy variable and 38 states were the other categories. New York was the omitted state. Ten states were not represented in our sample, i.e. no one in our sample of persons 65 yrs and older reported growing up in any of 10 states. Some states, such as New York and Massachusetts, spent far more than others, such as Alabama and Georgia, on primary and secondary schools during 1910-1940 (Berger and Leigh, 1989). The variable for state of residence when respondent was a child was available only for household heads. Since wives did not have the information and since female heads would not be a representative sample of females, state of residence when a child applied only to men in our sample. Covariates unique to the health equation, Z in Equation (3), included marital status dummies, 1979 respondent income (including wages, salaries, pension, and social security benefits), whether medicaid covered medical expenses, number of dependents, region dummies, and for men only, self-efficacy, risk and time preference variables as well as occupation dummies. Deficiencies arise in attempting to account for income (Duleep, 1986). For seniors, income is more relevant than earnings. Several prior studies either ignore personal income (Berger and Leigh, 1989; Taubman and Rosen, 1982; Kenkel, 1991) or include it as a covariate, but avoid any attempt to correct for the bias that might be introduced (Leigh, 1990; Callahan and Pincus, 1988; Behrman and Wolfe, 1989; Taubman and Rosen, 1982). Given the formidable bias problem that could result from including income, this omission has been understandable. Moreover, Fuchs (1992) has argued that in the U.S., the marginal effect of income on health is negligible. Bias could

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Economics of Education Review

arise from reverse causality: frailty can lead to low income. We attempt to remove the bias by using data from the 1979 interviewing year, i.e. eight years prior to the data on the disability index and exercise. The year, 1979, is not arbitrary. Prior to 1979, income information was not collected on wives that would have been comparable to heads. Prior income may suffer some reverse causality bias if the poor health was present prior to 1979, but the bias is likely to be less than the bias that would occur with 1986 income. Frailty is more significantly and positively related to age than any other covariate (Ramey et al., 1992), thus eight years is likely to be significant. Our approach to assessing the strengths of the associations between education and measures of health is straightforward. We will begin with probit and Tobit models that include the least number of covariates, i.e. those that assume unobserved variables, risk, and time preference and self-efficacy do not impose a bias. We then gradually add covariates that allow for the possibility of bias. This approach-sequentially adding covariates--has been widely adopted in the literature assessing the effect of education on earnings (Lam and Schoeni, 1993). 2. RESULTS In a longer version of the paper, available from the authors, results were presented and discussed pertaining to equations explaining schooling. In the interest of brevity, these results are omitted, with the exception of one: mother's schooling garnered estimated coefficients and t-statistics roughly double the size of the father's schooling coefficients and t-statistics. These results suggest that the mother's education is more important than the father's in predicting the subject's educational attainment. All of the results on covariates explaining schooling appeared reasonable and were consistent with prior studies (Berger and Leigh, 1989; Leigh, 1990; Manski et al., 1992; Haveman et al., 1991).

2.1. Disability Table 2 presents some ordered probit results explaining the disability index. Two columns of results appear: one for women and another for men. These results correspond to the single equation model that ignores selection bias, self-efficacy, time and risk preferences. In a longer version of the paper, available from the authors, results on age, race, marital status, occupation, and medicaid coverage are discussed. The 5/xs (threshold parameters) (/2~
statistics were roughly 40-120% higher for women than men on the schooling variable. The t-statistic on the schooling variable was highly statistically significant for women but not statistically significant for men. The critical t-value in a two-tailed test for a P = 0.05 is 1.96. It thus appears that schooling is important in explaining frailty for women but not for men. But, this conclusion is premature. Our disability index may not be a good measure of frailty among men. The low correlation (low t-statistic, high P-value) between schooling and disability for men is probably due to the little variation in disability for men when compared to women. The D variable can assume seven integer values: 0, 1, 2, 3, 4, 5, 6. The percentages of women with these values were 27, 17, 23, 9, 9, 8 and 7. For men the percentages were 47, 20, 23, 5, 3, 2, and 0. Thus, almost twice as many men as women were concentrated with D indexes at zero. Moreover, only 5% of men had scores in the 4, 5, and 6 range while 34% of the women had scores of 4 or above. Low t-statistics (high P-values) were estimated on the race-schooling interactions for women and men. This suggests that there are no race differences in the correlation between schooling and this 0-6 measure of disability. Table 3 presents abbreviated results from six ordered probit models. In the interest of brevity, results on all of the control variables--age through /xs--are omitted from Table 3. There were no qualitative differences in results on the control variables across the models. Columns 1 and 2 are for women and 3--6 are for men. Columns 1 and 3 merely reproduce the single equation results from Table 2. Columns 2 and 4 add the schooling residuals and an interaction variable--residuals times the black race dummy variables. Comparing columns 1 with 2 for women and comparing column 3 with either 4, 5, or 6 for men in Table 3, a similar pattern emerges. Once the schooling residuals or self-efficacy, time and risk preferences are added, the size of the estimated coefficient on schooling and the t-statistic decrease. A decrease in the size of the estimated coefficient together with a decrease in the t-statistic indicates that the statistical association between two variables is weakening (Leigh, 1988). The new t-statistic on schooling for women in Table 3 drops to 2.307 after the residuals are added (column 2). This is not a far enough drop for women to nullify the significance level of 0.05 in a two-tailed test, however. The t-statistics for men in columns 4, 5 and 6 are 1.156, 1.003, and .746 after residuals, efficacy and preferences are added. These t-statistics for men are well below any that would be regarded as statistically significant at either the 0.05 or 0.10 level in a one- or two-tailed test. The results for women and men suggest that a single equation model overestimates the strength of the association between schooling and our D index measure of frailty. The results for men also suggest that correlations between schooling and our D index

Schooling and Frailty Among Seniors

51

Table 2. Ordered probit results explaining the disability index in single equation models (ignoring selection bias, selfefficacy, risk and time preferences)

Covariates

Age Black = 1 Divorced = 1 Widow/widower = 1 Single = 1 Separated = I Omitted category is married spouse present Respondent income from 1979t Medicaid coverage Manager Clerk Sales worker Craft worker Military personnel Operative Laborer Service worker Farmer and farm workers Homemaker (no male responses) no occupation, no response Omitted category is professional Northeast = 1 North central = 1 West = 1 Omitted category is south Number of dependents Head of household = 1 (Women only) /xl g2 g3

~4 /x5 Years of schooling Years of schooling × black = 1 Intercept Log-likelihood Significance level Sample size

Estimated coefficients and (absolute values of t-statistics) Women Men 1 2 0.0460* (4.974) -0.0295 (0.115) 0.1324 (0.346) 0.2746 (0.811) 0.2574 (0.836) 0.1825 (0.394)

0.0515" (4.928) 0.3470 (1.260) 0.0307 (0.143) 0.1963" (2.124) 0.1625 (0.051) 0.4385 (0.706)

-0.003 (1.147) 0.1568" (2.264)

-0.001 (0.927) 0.0929 (1.463) -0.0362 (0.811) 0.0072 (0.924) -0.0869 (0.447) 0.1645" (2.154) 0.2075* (2.288) 0.0963* (2.082) 0.1459" (2.868) 0.0365 (0.457) 0.1868" (2.377) 0.2815" (3.426)

-0.2620 (1.527) -0.5947* (3.982) -0.1838 (1.226)

-0.1184 (0.938) -0.2415 (1.725) 0.2349 (1.263)

0.0746 (0.826) 0.1472" (2.075) 0.5216" (8.264) 1.1838" (14.962) 1.4816" (17.264) 1.8349" (18.926) 2.3340* (19.891) -0.0649* (2.965) 0.0216 (0.695) -2.2386* (2.675) -745.16 0.39E-13 663

0.0014 (0.192) 0.9205* (10.110) 1.3056" (15.622) 1.6174" (16.364) 1.8937" (17.258) 2.1465" (16.838) -0.0504 (1.314) -0.0294 (0.948) -3.1219" (3.748) -626.54 0.33E--09 465

Notes: *Significant at the 0.05 level, 2-tailed test. tSample means were substituted for 7.3% of the women and 2% of the men who were missing 1979 income data.

will appear to be stronger w h e n self-efficacy, time and risk preferences are ignored. Additional analyses of the marginal effects for men indicated the correlation between the probability of a D index equal to zero and schooling was positive while the correlations between the probabilities of the D indexes equal to 1~5 were all negative. These results are in contrast to those for the w o m e n in which the positive correlations were for D indexes at zero or 1 and negative correlations for 2~5. 2.2. E x e r c i s e Table 4 presents the Tobit results explaining exercise frequency. The Table 4 results correspond to the simplest models that ignore selection bias, self-efficacy and preferences. Again, in the interest of brevity, only the schooling results are discussed.

Contrasting gender results were apparent for the schooling and exercise correlations. For women, the partial correlation generated a t-statistic below the 1.96 critical value in a two-tailed test and the 1.645 value in a one-tailed test. The t-statistic for men, on the other hand, exceeded 3. The schooling--exercise partial correlation for men was especially strong but was weak to absent for women. Again, these contrasting results could reflect the quality of the dependent variable as a measure of frailty. For men, the exercise variable may be a better measure than the D index. Table 5 presents abbreviated results in Tobit regressions explaining exercise. The Tobit results mirror those for the disability index. As residuals and measures of self-efficacy, time and risk preferences are added, the partial correlations, as measured by the

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Economics of Education Review

Table 3. Abbreviated results on six ordered probit models explaining the disability index Independent variables

Women I

Years of schooling Years of schooling × black = 1 Residuals from schooling

-0.0649* (2.965) 0.0216 (0.695)

Residuals from schooling x black Self-efficacy+

Men 2

-0.0515" (2.307) 0.0299 (0.562) -0.0149 (1.826) -0.0085 (0.265)

Self-efficacy × black Risk preferencet Risk preference x black Time preferencet Time preference × black

3

4

5

6

-0.0504 (1.319) -0.0294 (0.948)

-0.0485 (1.156) -0.0352 (0.463) -0.0434 (1.065) 0.0129 (0.447)

-0.0361 (1.003) -0.0245 (0.478)

-0.0403 (.746) -0.305 (0.369) 0.0515 (0.926) -0.0442 (0.167) -0.0432 (1.407) 0.0226 (0.498) -0.0236 (0.982) -0.0145 (0.706) -0.0405 (1.196) 0.0207 (0.126)

-0.0516 (1.477) 0.0149 (0.829) -0.0143 (1.107) -0.0089 (0.675) -0.0427 (1.218) 0.0242 (0.200)

Notes: *Significant at the 0.05 level, 2-tailed test. ?High score for these variables indicates high self-efficacy, or highly risk averse, or great willingness to delay gratification. When data were missing, means were substituted.

size of the t-statistics, weaken. While the female partial correlations were never statistically significant, the male schooling-exercise partial correlations were always statistically significant. 2.3. O t h e r F i n d i n g s

The importance of self-efficacy and the preference variables (without the race interactions) is indicated in columns 5 and 6 of Table 3 and Table 5. In each case, the signs on the estimated coefficients are appropriate. High self-efficacy, high averse to risk, and great willingness to delay gratification are associated with low disability (Table 3) and high exercise frequency (Table 5). Likelihood ratio tests indicated that, as a group, these variables were statistically significant covariates. 3. D I S C U S S I O N A number of causes of the schooling-health correlation have been identified in prior literature. These include the following. 1. The schooling and health correlation may be spurious. It could be that both good health and high levels of education result from the same variable that is typically not observed by researchers. The ability to delay gratification (low time preference), low aversion to risk as well as high self-efficacy have been suggested as possible unobserved variables (Fuchs, 1982, 1992; Callahan et al., 1988; Grembowski et al., 1993). Under these interpretations, it is not the schooling that causes the good

health but rather the long time horizons or high risk aversion or high self-efficacy that causes both high educational attainment and good health. 2. Well-educated people are likely to have had welleducated parents who were not poor. The strong correlations in our sample between mother's and father's schooling and being reared in a poor family on the one hand and adult respondent's schooling on the other demonstrate the effects of family background. Well-educated, non-poor parents may have discouraged smoking, provided their children with better nutrition, better access to pediatric medicine, and greater financial security than poorly educated or poor parents (Thomas et al., 1991). The legacy of a healthy childhood may be a healthy adulthood. Under this interpretation, it is not the adults' educations but the parents' educations that matter. 3. Another explanation involves income, jobs, and financial security. Schooling is known to be associated with high incomes, access to safe jobs, and low unemployment rates throughout life (Angrist and Kruegar, 1993; Robinson, 1991; Leigh, 1995; Kaufman, 1989), which in turn have been associated with a variety of health problems and early death (Sagan, 1987, Solie and Rogot, 1990). 4. Apart from doctors and emergency rooms, patients with little schooling may not know where to turn for help. They may be intimidated by libraries o r even health magazines if their reading ability is poor (Feldman, 1966). Written information is inaccessible to illiterates.

Schooling and Frailty Among Seniors

53

Table 4. Tobit results explaining exercise frequency in single equation models (ignoring selection bias, self-efficacy, risk and time preferences)

Covariates

Estimated coefficients and (absolute values of t-statistics) Women Men

1 Intercept Age Black = 1 Divorce = 1 Widow = 1 Single = 1 Separated -- 1 Omitted category is married spouse present Respondent income from 1979t Medicaid = I

2

17.4107 (0.796) -0.8357* (2.149) - 10.974 (0.235) -22.076 (0.499) 8.2477 (0.510) 12.145 (0.768) 2.928 (0.734)

19.635 * (3.992) -0.9464* (3.644) 4.835 (0.720) -3.074 (0.4921 ) -6.3265 (1.159) -3.2198 (0.347) 18.4072" (2.154)

0.002 (1.906) - 1.3469" (2.025)

-0.049* (2.105) -2.1582" (2.375) - 1.4772 (0.0859) 2.7364 (0.41 I) -0.9825

Manager Clerk Sales worker

(0.164) Craft worker

- 1.0966 (1.264) 0.8238 (1.671) -4.0761 * (2.336) - 3.7142* (2.159) -0.0836 (0.427) -1.0854" (2.746) -5.7763* (2.864)

Military personnel Operative Laborer Service worker Farmer and farm worker No occupation, no response Omitted category is professional Northeast = 1 North central - 1 West = 1 Omitted category is south Number of dependents Head of household = 1 (women only) Years of schooling Years of schooling x black -= 1 6" Log-likelihood Significance level Sample size

- 3.1421 (1.775) -5.3470 (0.496) 5.3275 (2.516) -3.4727* (2.367) -0.9260* (2.517) 1.4172 (1.288) -0.8365* (2.215) 26.354* (12.277) - 1195.26 0.3E-I 1 663

- 3.4752 (0.736) -0.6284 (0.510) 2.1636 ( 1.247) -3.4066 (1.198) 2.069* (3.298) -0.8382 (0.969) 1.4752* (11.369) - 1136.02 0.4E-I 1 465

Notes: *Significant at the 0.05 level, 2-tailed test. tSample means were substituted from 7.3% of the women and 2% of the men who were missing 1979 income data.

54

Economics of Education Review Table 5. Abbreviated results on six tobit models explaining exercise frequency Women

Independent variables Years of schooling Years of schooling x black = 1 Residuals from schooling Residuals from schooling × black = 1 Self-efficacyt

1 1.4172 (1.288) -0.8365* (2.215)

Men 2

3

1.0743 (0.926) 0.1579 (0.142) 0.7392 (0.996) -0.1352 (1.426)

2.069* (3.298) -0.8382 (0.969)

Self-efficacy x black = l Risk preferencet Risk preference x black = I Time preference+ Time preference x black = 1

4 1.846* (2.954) - 1.077 (0.589) 0.5177 , (1.865) 0.5743 (0.329)

5 1.675" (2.566) -0.4747 (0.732)

1.0835" (2.116) 0.8369 ( 1.217) 0.8325 (0.952) -0.0495 (0.017) 0.9172 ( 1.246) 0.8324 (0.236)

6 1.375" (2.174) -0.3140 (0.625) 0.7243* (2.037) 0.4598 (0.244) 0.9294* (2.037) 0.8142 (0.729) 0.9142 ( 1.077) -0.0276 (0.012) 0.8143 (0.997) 0.7245 (0.159)

Notes: *Significant at the 0.05 level, 2-tailed test. thigh score for these variables indicates high self-efficacy, or highly risk averse, or great willingness to delay gratification.

5. Schooling may increase adaptability (Wozniak, 1987). 6. It could be that persons with more schooling seek medical care more promptly and report to physicians at an earlier stage of disease than persons with few years of schooling (Besley, 1989). 7. Persons with little education may be less likely than others to join self-help groups (Lorig et al., 1989). 8. Schooling may expand time horizons or improve self-efficacy (Frantz, 1980). 9. Finally, schooling teaches self-discipline. Persons who had good study habits in school may be more likely to frequently practice good health habits later in life (Slater and Carlton, 1985). The analyses of randomized trials of the Headstart program indicated that Headstart students were more likely than those not receiving Headstart to graduate from high school and, among girls, to be less likely to become pregnant in teenage years (Berrueta-Clement et al., 1984; Barnett, 1992). Avoiding pregnancy is not a direct product of schooling. It is likely to be an important by-product, however, since avoiding pregnancy requires dedication to a habit that may be difficult for a teenager to maintain. Dedication to avoidance is likely to be especially difficult for youths fiom homes with little family support since a baby can fill an emotional gap. The evidence above suggests that the unobserved variables argument s , involving time horizons, risk preferences, and self-efficacy (numbers 1 and 8), do not account for most of the schooling and frailty

association we found. But they do account for some. In fact, there appears to be evidence for all nine arguments in these data. This is an important conclusion. The search for a single mechanism to explain schooling and health correlations may be in vain. It appears that there are many mechanisms. We nevertheless favor arguments (3-9) suggesting that schooling has direct and indirect beneficial influences on health, even late in life. This is consistent with the view of many economists that schooling has beneficial influences on earnings. In two different naturally occurring randomized experiments, persons with one more year of schooling where found to consistently have higher earnings than otherwise similar persons (Angrist and Kruegar, 1993, 1991). There are reasons to believe blacks and whites have different schooling and health correlations. The salubrious benefits of additional schooling may be more pronounced among blacks than whites. Blacks are less likely than whites to graduate from high school. Historically, school quality for blacks has been below that of whites. One more year of schooling for the typical black may confer greater health benefits than one more year for the typical white. Rates of time preference (the ability to delay gratification) or selfefficacy may also differ. Four studies suggested that African-Americans have higher time preferences (less ability to delay gratification) than whites (Cropper and. Portney, 1992; Leigh, 1986; West, 1978; Lawrence, 1991). But these studies may be flawed. Measures of time preference are likely also to measure a person's faith that the experimenter or the society will provide the promised reward for wait-

Schooling and FrailW Among Seniors ing (Lopez, 1992). Measures of time preference may be measuring trust, not the ability to delay gratification. African-Americans may have less trust in the (white) experimenter or the society at large to reward their delayed gratification. On the other hand, there may not be any differences. A sizable portion of the historical race differences in the financial return to schooling have been attributed to job discrimination (Welch, 1973). The potential supply of high-paying jobs historically has been limited for African-Americans. Jobs can improve or destroy health. Depending on employment benefits, jobs can provide access to medical care. Jobs can injure health through accidents and exposure to carcinogens. Jobs are unlikely to be the principal cause of good or bad health, however, in the same way that they are the principal cause of high or low earnings. Job discrimination, in other words, is less likely to influence health than earnings. This is especially true if the nongenetic influences on health are cigarette smoking, excessive drinking, gun ownership, exercise, nutrition, seatbelt use and so on. Finally, our sample of persons 65 yrs and over may retard our ability to find racial differences in the schooling and health correlations. Blacks, especially black males, are less likely than whites to live ,1o age 65 (Behrman et al., 1991; Rogers, 1992). Blacks who live to age 65 may be especially healthy. Attrition bias is likely to be more pronounced among elderly blacks than elderly whites. This bias may result in elderly blacks who have health habits and educational backgrounds similar to those of elderly whites. No statistically significant race differences in the correlation between schooling and frailty were apparent in these data. An initial explanation might involve the statistically insignificant results on the black binary variable that was not interacted with schooling. It might be argued that statistical insignificance on the black binary variable alone indicates that these data are not representative of the black population, perhaps because of small sample size. Blacks, in general, report more health problems than whites at most ages (Haan and Kaplan, 1985). But blacks comprised 32% of the female sample (n=212) and 29% of the male sample (n=135). Moreover, a number of epidemiological studies ifidicate that once income, occupation, and schooling" are accounted for, aggregate racial disparities in health are greatly minimized (Guralnik et al., 1993) or disappear altogether (Mutchler and Burr, 1991 ). Research by Mutchler and Burr found statistically insignificant differences between blacks and whites in correlations between education and a measure of ADLs among 9803 persons age 55 yrs and over. Similar arguments but different evidence apply to gender differences. Men and women may differ in their ability to delay gratification or in their feelings of self-efficacy. Historically, far more men than

55

women obtained graduate degrees. Men have also shown a higher likelihood of dropping out of high school (Manski et al., 1992). Unhealthy habits such as smoking, drinking excessively, and owning guns have higher prevalence among men than women (Schoenborn, 1988). On the other hand, job discrimination against women with the same schooling as men may have health consequences for women. Attrition bias, in addition, may also play a role. Men are less likely than women to achieve age 65. For the men who do, gender differences, for example in health habits, are much less dramatic than they are for men and women in their 20s (National Center for Health Statistics, 199 I). Unfortunately, our evidence is not able to shed light on the theoretical reasons for male/female differences in education and health correlations. Our evidence indicates that the measure selected for frailty is crucial. The disability index may be more appropriate for women while exercise may be more appropriate for men. But this interpretation is somewhat less convincing in an older cohort than a younger one. Exercise is both a cause and an effect of good health. Appropriate excercise promotes better health. Poor health inhibits exercise. In an elderly cohort, such as we study, the effect of poor health on exercise may be especially large. Further research may address whether these findings can be substantiated in a younger cohort.

4. CONCLUSION

Our findings and contributions to the schooling and health debate include the following: (1) attempts to remove unobserved variables bias and the bias from self-efficacy, time and risk preferences weakened but did not destroy the correlations between schooling and frailty; unobserved variables, self-efficacy, time and risk preferences are important, but they do not explain the entire correlation between education and measures of frailty; (2) no race differences were found; (3) our disability index was a better measure of frailty for women whereas exercise frequency was a better measure for men; (4) strong correlations between schooling and measures of frailty were observed in samples of people 65 yrs old and older; and (5) there appear to be many mechanisms through which schooling might improve health; suggestions that there is only one mechanism are questionable.

Acknowledgements--The authors thank Gurmeet Bahtra, Hal Waldon, Bryce Reynolds, Rod Burns and Darius Kolyszko for computer assistance and Ann Christine Thompson for word-processing. This research was supported by grants from the National Institute on Aging (AG 10410), the National Science Foundation (SES 902308), and the National Institute of Health (AR21393) to ARAM1S.

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Economics o f Education Review

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