Do Education and Income Really Explain Inequalities in Health? Applying a Twin Design

Transcription

1 Scand. J. of Economics 118(1), 25 48, 2016 DOI: /sjoe Do Education and Income Really Explain Inequalities in Health? Applying a Twin Design U.-G. Gerdtham Lund University, SE Lund, Sweden ulf.gerdtham@nek.lu.se P. Lundborg Lund University, SE Lund, Sweden petter.lundborg@nek.lu.se C. H. Lyttkens Lund University, SE Lund, Sweden carl_hampus.lyttkens@nek.lu.se P. Nystedt Jönköping University, SE Jönköping, Sweden paul.nystedt@ju.se Abstract We apply a twin design to examine the relationship between health and education and income. The estimated associations between health and education and income, controlling for unobserved endowments, at the twin-pair level, are lower than estimates obtained via ordinary least-squares (OLS) on the same sample. Thus, OLS-based effects of education and income are biased, exaggerating the contribution of education and income to health inequality. The main part of health inequality is explained by within-twin-pair fixed effects, incorporating family background and genetic inheritance. It appears that education and income policies have less to offer for reducing health inequality than is usually assumed. Keywords: Education; health inequality; income; twins JEL classification: I10; I12; I14 Affiliated with IZA Bonn. We are grateful to Gustav Kjellsson, Rachel Knott, and two anonymous referees for comments. Financial support from the Swedish Council for Working Life and Social Research (FAS) (dnr ) and the Swedish Research Council (dnr ) is gratefully acknowledged. The Health Economics Program (HEP) at Lund University also receives core funding from FAS (dnr ), the Government Grant for Clinical Research (ALF), and Region Skane (Gerdtham). This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

2 26 Do education and income really explain inequalities in health? I. Introduction Numerous studies report a strong socioeconomic gradient in health and longevity, regardless of the population studied and regardless of how socioeconomic status and health are measured (e.g., Ettner, 1996; Smith, 1999; Bloom and Canning, 2000; Gerdtham and Johannesson, 2000, 2002, 2004; Benzeval and Judge, 2001; Deaton, 2003; van Doorslaer and Koolman, 2004; Baum and Ruhm, 2009). Despite improvements in average health status over recent decades, this health gradient has persisted and has even increased in most western countries (e.g., Mackenbach et al., 2003; van Doorslaer and Koolman, 2004; Kunst et al., 2005; Shkolnikov et al., 2011). Thus, reducing the magnitude of health inequality still poses a challenge, and has become a major policy objective for many European governments (Marmot et al., 2010). Recently, the Marmot Review suggested that the strong association between health and socioeconomic status implies that socioeconomic inequalities have to be reduced in order to reduce socioeconomic-related inequalities in health (Marmot et al., 2010; Marmot, 2012). Accordingly, policy measures affecting socioeconomic inequalities, such as income redistribution and publicly financed education, are taken to influence health inequalities. This conclusion is based on the strong assumption that the association between socioeconomic status and health reflects a causal effect running from the former to the latter, which has attracted extensive debate and disagreement in the literature (e.g., Smith, 1999; Deaton, 2002; Cutler et al., 2008; Case and Paxson, 2011). This lack of consensus reflects the incomplete nature of our knowledge about underlying causal mechanisms and channels behind the disparities in health. Policies aimed at reducing disparities might therefore easily be ineffective, inconsistent, and even counterproductive (Deaton, 2011), and so there is an urgent need to improve our understanding of the origins of socioeconomic health inequalities. For policy purposes, the usefulness of any analysis of health and socioeconomic status critically hinges upon whether the estimated health function reflects causal effects of socioeconomic factors on health. In practice, this is tremendously difficult to prove (Deaton, 2011). There are two fundamental conceptual problems. First, causality might run from health status to, for example, income, rather than the other way around. Second, there might be some third, unobserved factor, perhaps of genetic or environmental origin, that determines both health and income (Fuchs, 1982; Smith, 1999; Mackenbach, 2003; Deaton, 2011). Similar causality issues hold for education and other socioeconomic factors. One limitation of the majority of prior studies is that they do not consider reverse causality or the unobserved endowment and heritability that are correlated with socioeconomic factors. Thus, the estimated contributions of socioeconomic factors

3 U.-G. Gerdtham et al. 27 on health might well be confounded with the effects of innate ability and other hard-to-define or hard-to-measure characteristics relating to personality and family background. Consequently, the estimated socioeconomic contributions on health could rather reflect a correlation between health and such characteristics. The present paper adds to the existing body of literature by analyzing the impact of education and income on health inequalities, using a twin data design as an identification strategy. The twin approach has been exploited previously in the literature, mainly in order to estimate wage and earnings returns to education (Ashenfelter and Kreuger, 1994; Ashenfelter and Rouse, 1998; Bonjour et al., 2003; Isacsson, 2004). Recently, a number of papers have also used the design to estimate the causal effect of education on health (Amin and Behrman, 2009; Webbink et al., 2010; Behrman et al., 2011; Lundborg, 2013). The twin design brings certain distinct advantages to the analysis of the relation between socioeconomic factors and adult health. First, it allows us, under certain assumptions, to estimate also the causal influence of factors that do not change over time, such as educational status, by relying on differences in socioeconomic factors between twins at a given point in time. Note that this is in contrast to the fixed effects panel data approach, where identification requires that the variable of interest varies over time; this might be true for certain factors such as income, but not for others, such as education; see, for example, Wildman (2003) and Islam et al. (2010). In other words, it is difficult to assess the relative contribution of a factor such as education using a fixed effects panel data approach. However, the twin approach requires that the variables of interest vary within twin pairs, which it does for a majority of the twins. Second, twin estimates are likely to reflect the average effect in the population of interest, because differences within twin pairs in factors such as education and income are likely to be represented across the education and income distributions. An instrumental variable (IV) approach, in contrast, estimates local average treatment effects, where the estimated effect is only identified for the marginal group affected by the instrument. Because the instruments used typically only affect a small subgroup in the population, it is not clear that the IV estimate can be generalized to larger populations. Moreover, most IV studies are only able to instrument for one explanatory variable, such as education, which means that the endogeneity problem remains for other socioeconomic variables. This, again, naturally complicates the assessment of the relative contribution of the different variables indicating socioeconomic status. Third, twins share familial environmental conditions but while dizygotic (DZ) twins are sampled from the same gene pool, they only share on average 50 percent of their genes, whereas monozygotic (MZ) twins have

4 28 Do education and income really explain inequalities in health? identical genetical predispositions. By comparing estimates based on the two types of twins, we can hence explicitly address the influence of genes. In this paper, we use a unique dataset, including data on a vast majority of Swedish native twins born between 1896 and The dataset links survey data on self-reported health, to register data on education (1990, 2007) and income ( ). In the regression analysis, we report results based both on a health production function estimated by ordinary leastsquares (OLS), with the health of twins treated as independent observations, and by within-twin-pair (WTP) estimations, which removes the influence of factors shared by twins. In addition, we also study whether there are heterogeneities in the effects of socioeconomic factors along the health distribution by using WTP quantile regression analysis. To preview our findings, in line with most prior cross-sectional studies, the OLS-based analysis indicates that factors such as education and income are strongly associated with health. The WTP-based analysis, however, indicates much weaker and statistically insignificant contributions of education and income. A reasonable interpretation is that OLS-based analysis is subject to severe upward biases due to the influence of unobserved factors. In other words, our results suggest that most of the socioeconomic disparities in health are attributed to factors that are associated with socioeconomic status as well as health, such as genes and early life conditions. From a policy perspective, reducing inequalities in education and income would therefore do less to reduce socioeconomic disparities in health than what might be expected from OLS-based analyses. In fact, because the WTP estimates can be viewed as an upper bound of the effect of socioeconomic factors on health, our results suggest that factors such as education and income play a smaller role than suggested by the WTP estimates, in causally explaining socioeconomic disparities in health. The paper unfolds as follows. In Section II, we provide a background discussion and review the literature on the value of WTP estimation. In Section III, we present the empirical model and the data material, and explain the details of the variable constructions. In Section IV, we report the results, including some comparisons with another dataset based on a general population. We conclude in Section V. II. Twin Data Approach to the Regression of Health To see how the twin design might help to reduce the problem of unobserved heterogeneity, consider an individual i, whose health h i is determined by h i = βy i + α A i + u i, (1)

5 U.-G. Gerdtham et al. 29 where y i denotes education (or income or any other socioeconomic factor) and A i denotes unobserved factors affecting health, such as genetic traits and personal characteristics as well as family background. Next, let education be y i = δ A i + ξ i, (2) where ξ i denotes an education-specific random term. This gives rise to the standard result that an OLS estimate of β is biased such that plim(β OLS ) = β + α σ Ay. (3) σy 2 Because the unobserved factors (A i ) are likely to be positively correlated with both education and health, it is usually assumed that an estimate of β OLS will be upward biased. In the twin-differencing strategy, let h 1 j and h 2 j denote the health of the first and second twin in the jth twin pair. Assume now that the unobserved component is made up of two parts. The first part μ j denotes unobserved factors that vary between MZ twin pairs but not within pairs, such as genetic characteristics and certain early life environmental factors. The second part, ε 1 j and ε 2 j, denotes unobserved factors specific to each twin. This can be written as h 1 j = βy 1 j + μ j + ε 1 j, (4) h 2 j = βy 2 j + μ j + ε 2 j. (5) Next, we take the difference between equations (4) and (5), h 1 j h 2 j = β WTP (y 1 j y 2 j ) + ε 1 j ε 2 j, (6) where β WTP is the within-twin-pair, or fixed effects, estimate of the effect of education. Insofar as μ j captures the influence of common family background, which might be of a genetic or environmental character, their influence will vanish, as they will be differenced out of the equation. This means that an OLS estimate of equation (6) will no longer be biased due to unobserved twin-pair specific variables. There are two well-known potential problems with a twin design. First, WTP estimates might still be biased if there are important unobserved differences between the twins that relate to health as well as education and/or income. As noted by Bound and Solon (1999), even MZ twins can differ in factors such as birth weight, for instance, which has been linked to both adult earnings and education (e.g., Behrman and Rosenzweig, 2004; Black

6 30 Do education and income really explain inequalities in health? et al., 2007; Royer, 2009). 1 Moreover, there could exist ability differences between MZ twins, so that the twin with greater ability also has better health, irrespective of education or income. 2 Such results were obtained by Sandewall et al. (2014), who showed that the difference between MZ twins in cognitive test scores at age 18 was a significant predictor of their later schooling. If cognitive ability has positive effects on both later income and health, our twin-based estimates still risk being biased upward, as we do not have data on cognitive test scores. The results of Sandewall et al. (2014) seem compelling at first sight, but note that the cognitive test scores they rely on are measured at an age where they are likely to have been affected by previous schooling. Indeed, Meghir et al. (2011), using the same Swedish cognitive test score data as Sandewall et al. (2014), find that this is the case. 3 Nevertheless, it is important to note that even if twins differ in ability, the twin design is still useful in tightening the upper bound of the estimated effects (Bound and Solon, 1999). This is also the view we take in this paper; our WTP estimates should be regarded as an upper bound of the effect of education and income on health. In this sense, the WTP estimates will indicate the minimum extent to which OLS estimates are biased, and hence inappropriate to use as a decision basis. The second potential problem with a twin design is the well-known fact that the importance of measurement errors in explanatory variables is exacerbated by differencing, and even more so when differencing between MZ twins (Griliches 1979). This can cause the twin fixed effects estimates of our explanatory variables to be downward biased. As shown by Griliches (1979), in the presence of classical measurement error, the WTP estimates would be biased according to plim(β WTP ) = β{1 Var(ν)/[Var(y)(1 ρy)]}, (7) 1 Other studies using the twin design find no significant impact, however (Bonjour et al., 2003; Miller et al., 2005; Petersen et al., 2009). Note also that in most studies that find an effect on schooling, the effects are small in magnitude. In Royer (2009), for instance, an increase in birth weight by 250 g, which would be quite a policy achievement, only leads to years of additional schooling. 2 Note, however, that parents might respond by compensating for differences in, for instance, health or ability among their twins, which might partly offset any upward bias. Some evidence for such behaviour in the US is presented in Lundborg (2013). Rosenzweig and Zhang (2009), however, found that Chinese parents invested more educational expenditures on the twin of higher birth weight. However, other twin-based studies, using various measures of parental inputs, do not suggest that parents systematically reinforce or compensate for early life insult (e.g., Royer, 2009; Currie and Almond, 2011). 3 They show that the Swedish compulsory schooling reform had a significant impact on the development of cognitive and non-cognitive abilities of young men during their teens.

7 U.-G. Gerdtham et al. 31 where Var(ν) denotes the assumed common variance of the twins measurement error, Var(y) is the variance in the true income levels, and ρy is the correlation between the measured income of the twins. Here, we expect the measurement error problems in the WTP estimation to be relatively small, because register information is used for the key factors of education and income. Holmlund et al. (2008) found high reliability for Swedish register-based measures of education: 0.95 for males and 0.94 for females. If the reliability ratios are similar for income, which we can expect as income is also register-based, then the measurement error problems would not severely threaten our estimates. III. Sample and Variable Definitions Sample Construction In this paper, we exploit micro data originating from the Swedish Twin Registry. The study population consists of a subset of the dataset: the participants in a telephone interview called Screening Across the Lifespan Twin Study (SALT). This is the only part of the twin register where data on self-reported health are available, which is our main dependent variable. The Swedish Twin Registry was established in the 1950s to study the health consequences of smoking and alcohol consumption, and is now the largest population-based twin register in the world. It has been described in detail previously (Lichtenstein et al., 2002, 2006). The SALT survey was conducted in the period , and attempted to include all Swedish twins born in 1958 or earlier, and hence aged 40 years or older at the time of the interview. The twin data have been matched with register data from Statistics Sweden on annual taxable labor earnings and education level. This study uses a restricted subsample due to our measurement of longterm income (see below). Thus, the main analysis includes the population of twins born in who survived until being interviewed ( ), yielding 32,476 observations including 25,138 complete twin-pair observations, and 15,752 same-sex DZ MZ twin-pair observations (i.e., 7,876 twin pairs (4,548 DZ, 3,328 MZ)). Summary statistics for the samples of the twins are included in Table 1, both for the total number of observations available for each variable in different twin samples and for the observations of complete pairs that are used in the analysis. Data from the Statistics Sweden Survey of Living Conditions (the ULF survey) are also used to complement the twin data in order to investigate the representativeness of the twin data. The ULF survey data are based on yearly one-hour personal interviews with about

8 32 Do education and income really explain inequalities in health? Table 1. Means of basic samples and working samples of the Swedish Twin Registry (SALT) Variable (1) (2) (3) (4) (5) (6) Health: 1 (excellent) Health: Health: Health: Health: 5 (very bad) TTO utility weight Male Age Mean income (35 39 years) 196, , , , ,145 Schooling years n 32,476 25,138 15,752 9,096 6,656 4,314 Notes: The columns show the following: (1) all twins in the data; (2) twins included in the complete twin-pair regressions; (3) twins included in the complete same-sex twin-pair regressions; (4) twins comprising complete same-sex DZ twin pairs; (5) twins comprising complete MZ twin pairs; (6) ULF pooled sample. TTO is time trade-off health utility estimated using an algorithm for Sweden (see equation (8)). Mean income is expressed in 2010 prices, SEK. 6,000 randomly selected adults in Sweden aged years, and include variables similar to those in the twin dataset. Variables In the regression analysis, we use self-reported health (cardinalized along a procedure shown below) as our dependent variable, and gender, age, year of interview, and education or/and income, as independent variables. Age and year of interview are categorized into annual dummy variables. Self-reported Health Self-reported health is a multiple-category indicator in which individuals answer the question: How is your health in general? The answer is chosen from five categories (proportions for all twins in parentheses; see Table 1): very poor (2.1 percent), poor (7 percent), fair (18 percent), good (37 percent), and very good (37 percent). An important aspect of twin data analyses is the presence of sufficient variation within twin pairs. In the sample, 1,627 (36 percent) same-sex DZ and 1,393 MZ (42 percent) twin pairs report equal health. In order to work with a continuous variable in the regression estimations, and to enable estimation of a health concentration index, we transform the self-reported health measure to time trade-off (TTO) health utility by using an algorithm adapted for Sweden. This assigns TTO quality-of-life values based on self-reported health, age, and gender (Burström et al., 2014,

9 U.-G. Gerdtham et al. 33 Supplementary Material, Table S8, Model 3, p. 16): 4,5 TTO utility = good health fair health poor health very poor health age35 44 years age45 54 years age55 64 years age65 74 years age75 84 years female. (8) A TTO health state value of unity represents perfect health, and zero represents being dead. In the entire complete twin-pair sample, the TTO ranges from to (mean, 0.912; std dev., 0.103); for the MZ sample, the corresponding figures range from to (mean, 0.916; std dev., 0.102). For the representativity analysis of the twin data, the above estimated function is also used to predict the health utility scores for the general population in the same age intervals as in the twin dataset using the ULF survey data (for 2004/2005). Education Our education variable is measured in years and constructed from register data measured in 1990 and 2007 according to Swedish Educational Terminology (SUN), the standard system for classifying education in Sweden. The data range between 8 and 20 years of schooling. According to the register information, 32 percent of all same-sex DZ twins and 46 percent of MZ twins have the same level of education, implying that identification of the association between education and health in the WTP setting is based on the remaining twin couples (see the Online Appendix). Income We use income data provided by Statistics Sweden and measured as individual total pre-tax income from employment and own business (sammanräknad förvärvsinkomst) (prior to the health interview 4 Note that the variables on the right-hand side of equation (8) are expressed as binary indicators (reference: a male individual, age18 24 years in very good health). This means, for instance, that quality of life for a female, age55 64 years with fair health, becomes = Health economists often value health states of people by the TTO method where respondents value quality of life in relation to length of life; respondents are asked to imagine living in a given state of health for (typically) ten years, and then to state the shorter amount of time in full health that makes them indifferent between the two options (Drummond et al., 2005).

10 34 Do education and income really explain inequalities in health? carried out in ). The consumer price index has been used to deflate income across the years to the price level of Annual income (and also education) is expected to carry only small measurement errors, because the data are obtained from registers. However, it has been suggested that lifetime or permanent income might be more appropriate to use in an analysis of health behavior (Frijters et al., 2005). If that is the case, then income measures might still include measurement errors due to transitory income. Previous studies have shown that for Swedish males, income at the age span captures permanent income fairly well (Björklund, 1993; Böhlmark and Lindqvist, 2006). To adapt to this line of research and to smooth temporary earnings shifts, we measure long-term income in our main specification as average annual income at age This implies that cohort-wise, the sample is restricted to people born 1933 or later (as they should not be older than 35 in 1968, which is the first year for which we have income data). Moreover, in a sensitivity analysis we ran all estimations based on average income at years of age, which restricts the birth cohorts to (as earlier cohorts are 41 or older in 1968 and younger cohorts have not reached 50 years of age in 1998 when the first interviews were conducted). Individuals with zero income have been dropped from the sample (1.3 percent). The context of our study encompassing how income can affect health emphasizes the functioning of income representing consumption boundaries rather than pure labor market productivity (as in studies of how, for example, education affects hourly wages). From this perspective, it should be noted that the studied income measure includes income from employment, own business, parental leave benefits, unemployment insurance, and sickness leave benefits; these sources of income are also included in the earnings measure analyzed by Björklund (1993) and Böhlmark and Lindqvist (2006), cited above. Including the last three of these income sources serves the purpose of smoothing temporary earnings shifts and more accurately capturing actual consumption possibilities. During the rather long time period from which the income data are drawn ( ), it is inevitable that there have been changes in tax and social 6 It is not possible to calculate after-tax household income or equivalent after-tax household income, because only before-tax income is available in the data, and the income of any other household members is unknown. 7 Note that our income measure does not include capital income and realizations of capital gains. Such income sources were included in the studies by Böhlmark and Lindqvist (2006) and Björklund (1993). Björklund (1993) finds that the fraction of total income from capital income and gains in for men born between 1924 and 1936 (admittedly only partly overlapping our sample) did not exceed 2.6 percent, suggesting that our results should be relatively insensitive to whether this source of income is included or not.

11 U.-G. Gerdtham et al. 35 security system rules. Whereas changes in, for example, reimbursement levels and waiting days for sickness benefits affect consumption possibilities and are captured in the registered income data, tax scale alterations are not. From the perspective taken here, a prominent change also occurred during an expansion of the social security system when unemployment, sickness, and parental leave benefits, all based on current and/or previous work experience and income, became taxable Hence, the more limited support given /73 before the expansion is not captured in our income data. However, the average fraction of income from such support was initially moderate as reimbursements levels were lower and unemployment rates amounted to about 2 percent during the 1970s. We are able to deduct these benefits for the year 1981, and find them to account for about 6 percent of our income measure. 8 Because the taxation of these social security benefits was accompanied by expansion of the coverage and reimbursement levels, we conclude that the untaxed and unregistered benefits were rather mildly affecting the average consumption possibilities of the studied sample. The influence of this should be of limited importance, especially in a twin difference analysis setting, as income data on two twins are taken simultaneously. Education and Income as Explanatory Variables The issue of reverse causality (i.e., health can influence education and income) is not explicitly dealt with by twin differencing. When it comes to education, it should be noted that our main empirical analysis is based on the health reports of people aged Most people have reached their final level of education well before age 30 and it seems unlikely that health status in middle-age can causally affect education decisions made at a fairly young age. All income data used are also recorded in advance of the used health reports, although the time lag is smaller in this case, increasing the risk of causality running from health to income. Moreover, interpreting the results with the inclusion of both education and income as explanatory variables is problematic because education is bound to affect income later in life. Therefore, we primarily estimate health production functions including education or income. For illustrative purposes, we also present results from regressions including both, although these should be interpreted with care. 8 This result mirrors Björklund (1993), who found that unemployment and sickness benefits amounted to about 5 percent of total income for men in 1975.

12 36 Do education and income really explain inequalities in health? Table 2. Means of health scores in different standardized long-term income decile groups from low to high in the twin register DZ same-sex MZ twins All twins twins (complete) (complete) Deciles (1) (2) (3) N 32,476 9,096 6,656 Mean health C of health SE Notes: C is the concentration index of health (Kakwani et al., 1997). IV. Estimation Results Table 2 displays the estimated mean TTO health utility in the different deciles of the income distribution for: (1) all twins in the entire dataset; (2) all complete same-sex DZ twin pairs used in the analysis; (3) complete MZ twins used in the analysis. Mean health is very similar across the three different samples of twins, ranging from about 0.89 in the first decile, to 0.95 in the last. Table 2 also reports the concentration index of health C, which is a popular measure in health economics 9 (similar to the Gini coefficient of income inequalities) that quantifies relative socioeconomic inequalities in a health variable by calculating the cumulative percentage of health concentrated in a cumulative percentage of the population ranked by a socioeconomic status, typically measured by income (cf. Kakwani et al., 1997). 10 C is equal to twice the area between the concentration curve and the line of equality (the 45 degree line); it is 1 ( 1) if all health is concentrated to the individuals with the highest (lowest) income, and it is zero if all health is equally distributed over individuals with different income. The estimated C corresponds well to results from previous studies for Sweden based on other data (Gerdtham and Johannesson, 2000). 9 See Wagstaff and Van Doorslaer (2000) and Fleurbaey and Schokkaert (2011). 10 C of health is sensitive to changes in the distribution of the population across the socioeconomic dimension (income in this case).

13 OLS and WTP Estimation of Health Production U.-G. Gerdtham et al. 37 Table 3 presents estimates of the health production function for different twin samples in the birth year cohorts using average earnings at age OLS estimations based on all complete same-sex twin pairs are reported in Columns 1 3 of Table 3 for education (Model A) or income (Model B) and combined (Model C), respectively, and the corresponding WTP estimations are reported in Columns 4 6. Columns 1 and 4 represent (same-sex) DZ and MZ twins combined, Columns 2 and 5 represent DZ twins, and Columns 3 and 6 represent MZ twins. The estimates based on OLS are in line with past studies, and significant at least on the 1 percent level in the expected direction, education and income having protective effects. When simultaneously including education and income, the effect of education is just slightly reduced by 10 percent, whereas the income effect is reduced by percent (depending on the studied twin sample). The question now is whether these results reflect causal mechanisms, suggesting that people who invest more in education and/or are equipped with less limited budget restrictions will also experience health improvements. Alternatively, it could be the case that people with higher innate ability and advantageous family background are able to obtain both better health and better education and income. In the latter case, a causal relationship between health and socioeconomic status is not necessarily implied. Our results strongly suggest that the latter hypothesis is closer to the truth, because the results change radically when we move to the WTP estimation. Closer inspection reveals that the reductions in the estimated education and income parameters, moving from OLS to WTP, are more pronounced among MZ twins. For DZ twins, the association between education and health is halved (from to ) whereas the association between health and income reduces slightly more in magnitude (from to , the last estimate being statistically insignificant). The corresponding reductions going from OLS to WTP among MZ twins are much more pronounced (education, to , or about 80 percent; income, to , or about 75 percent) and the WTP estimates are statistically insignificant. The hypothesis of no difference in coefficient estimates across models (OLS, WTP) is rejected at the 5 percent level for both education (Model A) and income (Model B) in the DZ as well as MZ samples. This suggests that environmental family background and genetic inheritance explain much of the crude covariation between health on the on hand, and education and earnings on the other As a sensitivity analysis (results not shown but available upon request from the authors), we have re-estimated the models of Table 3 for the sample consisting of the birth cohorts

14 38 Do education and income really explain inequalities in health? Table 3. Pooled OLS and WTP regression estimations of the effect of income and education, respectively, on health Complete same-sex twin pairs With different level of education OLS estimation WTP estimation OLS WTP (1) DZ+MZ (2) DZ (3) MZ (4) DZ+MZ (5) DZ (6) MZ (7) MZ (8) MZ Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Coeff. Variables (SE) (SE) (SE) (SE) (SE) (SE) (SE) (SE) Model A Schooling a a a a, a, a ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) R 2, R within 2 (WTP) Model B Log income a a a b, c, a ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) R 2, R within 2 (WTP) Model C Schooling a a a a, a, a ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Log income a a a c, b ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) R 2, R within 2 (WTP) N 15,752 9,096 6,656 15,752 9,096 6,656 3,618 3,618 Mean health score WTP, FE No No No Yes Yes Yes No Yes Notes: Robust standard errors (SE) are given in parentheses. Each column in each panel comes from a separate model. In the upper panels (Models A and B) the education and income gradients are estimated separately, and in the Model C panel, the gradients come from a pooled model. OLS models control for gender, year of interview, and age fixed effects, and WTP models for year of interview fixed effects. Testing null of the coefficient: a p < 0.01; b p < 0.05; c p < 0.1. Testing null of no difference in coefficient estimates per sample across models (WTP versus OLS): p < 0.1; p < 0.05; p < 0.01.

15 U.-G. Gerdtham et al. 39 Because the WTP models are identified via variation within twin pairs, and the sample of twins, which differ in education, is less than the full sample, the reductions in the educational parameter estimates when we move from OLS to WTP could partly be driven by limited variation in a smaller sample. To check this, we re-estimated our models, restricting the sample to MZ twins with different educational level. 12 The results are presented in Columns 7 and 8 of Table 3. Compared to our original analysis on the MZ twins (Table 3, Columns 3 and 6), we obtain highly similar results, indicating that our findings are not a consequence of the WTP parameters being identified in a subsample of the OLS sample. Heterogeneity of Effects Using Quantile Analysis of Socioeconomic Status on Health Table 4 presents quantile regressions on the association between health, education, and income for the MZ sample. The upper panel gives ordinary quantile results whereas the lower panel yields results from WTP quantile regression. For the latter results, we follow the fixed-effect quantile regression procedure of Canay (2011), which assumes that the fixed effects work as location shift variables (i.e., variables that affect all quantiles in the same way). 13 The estimates reveal an expected pattern where the estimated association between health and education and income is strongest at the lower end of the health distribution. For instance, looking at the ordinary quantile estimates for education, one year of schooling shifts the threshold of the first quantile by about 0.01, whereas it has no effect whatsoever on the threshold for the fifth quantile. Now this is not a small change given the descriptive statistics of Table 2, where it is shown that 0.01 in the health score corresponds fairly well to, for example, the mean difference in health , using average income at age The estimated education effects are very similar to the sample studied above, across method of estimation as well as of zygosity of the studied twins. The income estimates are overall somewhat larger in magnitude, but we cannot discern whether this is due to a cohort or an age effect (i.e., whether the association between health and income decreases with birth year, or increases with age). Nevertheless, and most importantly, the main result that the influence of income and education is heavily reduced in the WTP compared to the OLS analysis remains unchanged. 12 In principle, all twin pairs have different income and therefore we have not made a similar analysis regarding income. 13 Canay (2011) shows that a simple transformation of the data removes the fixed effects in a quantile regression framework under the assumption that the fixed effects are location shifters. In Canay s two-step procedure, the fixed effects are first estimated using a standard fixed effects model. In the second step, a standard quantile regression is run on the transformed outcome variable, where the transformation involves subtracting the estimated fixed effects from the outcome variable.

16 40 Do education and income really explain inequalities in health? Table 4. Quantile regression results for TTO health utility on income and education (MZ sample: 6,656) Q20 Q40 Q60 Q80 Quantile regression Model A Schooling SE ( ) ( ) ( ) ( ) Model B Log income SE ( ) ( ) ( ) ( ) Model C Schooling SE ( ) ( ) ( ) ( ) Log income SE ( ) ( ) ( ) ( ) Mean health score WTP quantile regression Model A Schooling SE ( ) ( ) ( ) ( ) Model B Log income SE ( ) ( ) ( ) ( ) Model C Schooling SE ( ) ( ) ( ) ( ) Log income SE ( ) ( ) ( ) ( ) Mean health score Notes: Testing null of the coefficient: p < 0.01; p < 0.05; p < 0.1. OLS models control for gender, age, age square, and year of interview fixed effects, and WTP models for year of interview fixed effects. between the first (0.894) and the fourth (0.903) income decile. However, in the WTP setting, this shift is decreased by more than 70 percent to Representativity of the Twin Data To illustrate the representativity of the twin data in relation to the general Swedish population of the same age range, the regression analyses in Tables 3 and 4 are reproduced in Table 5 based on OLS regressions including only gender, age, age square, and schooling years (i.e., variables that are identically defined in the twin and ULF samples; note that it is not possible in the current ULF dataset to include average income at age 35 39). The results show that the estimated effects in the ULF dataset are very similar to that of the twin data samples, although the effects of schooling are slightly higher in the ULF dataset.

17 U.-G. Gerdtham et al. 41 Table 5. Representativity of the OLS-based regression analysis of education on TTO health utility on twin samples and the ULF sample (1) (2) (3) (4) Coeff. Coeff. Coeff. Coeff. Variables (SE) (SE) (SE) (SE) Age ( ) ( ) ( ) ( ) Age ( ) ( ) ( ) ( ) Male ( ) ( ) ( ) ( ) Schooling ( ) ( ) ( ) ( ) Constant ( ) ( ) ( ) ( ) R Mean health score N 15,752 9,096 6,656 4,294 Notes: The columns show the following: (1) all complete same-sex DZ and MZ twin pairs; (2) All complete DZ twin pairs; (3) all complete MZ twin pairs; (4) ULF ( representative ) sample. Robust standard errors (SE) are given in parentheses. p < 0.01; p < 0.05; p < 0.1. Decomposition Analysis of Socioeconomic Status on Health Inequalities One way of expressing socioeconomic inequalities in health is via the concentration index, which measures health inequalities in relation to an individual s socioeconomic rank, for example in terms of income (Fleurbaey and Schokkaert, 2011). In order to obtain information on the relative importance of different factors and the magnitude of their individual contributions for this index, Wagstaff et al. (2003) proposed a decomposition method. Here, the concentration index of health is expressed as a function of the means and inequalities of the factors in a health production function as well as the regression effects (elasticities) of health factors; see, for example, Wagstaff and Van Doorslaer (2000), Wagstaff et al. (2003), and Kjellsson and Gerdtham (2013) for details. In order to more directly relate the results from our twin data approach to this common line of research, we conducted a decomposition analysis. It should be noted that in contrast to most previous decomposition studies, in which various inter-related socioeconomic characteristics (e.g., income, education, employment, retirement) are included simultaneously as explanatory variables, we include, as above, only education or/and income in order to limit endogeneity issues. The resulting concentration indices are presented as C in Table 2. Results from the decompositions are summarized in Figure 1 (education) and Figure 2 (income). The figures clearly show that the contributions from education

18 42 Do education and income really explain inequalities in health? Fig. 1. Summary of the percentage contribution of education, sex, age, and year (of interview) on health concentration index (income-related inequalities in health) Fig. 2. Summary of the percentage contribution of income, sex, age, and year (of interview) on health concentration index (income-related inequalities in health) and income are heavily reduced when the health production function is estimated by WTP, while the contribution from the fixed effects (sum of gender and age in the OLS models) increases. It is also clear that the contribution from the fixed effects increases further when the estimating sample consists of only MZ twins. Closer inspection of Figure 1 reveals that, for MZ twins, education accounts for 28 percent of the health concentration index in the OLS setting but only 6 percent in the WTP setting, a reduction by about 80 percent, which corresponds to the findings on the direct association between education and health presented in Table 3. The contribution from age and sex (and fixed effects in the WTP) increases

19 U.-G. Gerdtham et al. 43 from 24 to 96 percent between the settings. The corresponding patterns for DZ twins run from 26 to 14 percent (education), and 36 to 69 percent (fixed effects). The contribution of income (Figure 2) among MZ twins decreases from 57 to 14 percent, or by about 75 percent between the two settings, which again mirrors the findings of Table 3, whereas the contribution of the fixed effects increases from 4 to 90 percent. For DZ twins, the corresponding patterns go from 42 to 17 percent (income) and from 22 to 66 percent (fixed effects). Again, this illustrates how the crude associations between health and education and income to a large extent could be explained by underlying environmental and genetical factors operating at a family level. Hence, the potential impact of educational and redistributive policies on diminishing health inequalities seems to be smaller than could be expected from traditional decomposition analysis based on pooled population data. Sample Selection Conditional upon Survival Conceptually, any health comparisons between people are bound to be conditional upon survival up to the time point when the considered health measure is taken. Thus, such comparisons and resulting estimated socioeconomic gradients do not necessarily capture mortality risks up to that point in time. Comparing the health status of two twins at a certain point in time (or at a given age) obviously requires that both of them are alive at this time. In this study, twin pairs in which at least one of the twins has died before the health interview are not included in the analysis. From this perspective, our sample (as well as any other cross-sectional based sample) could be viewed as being selected on good mortality (or health) outcomes, a selection that becomes more severe the older the individuals. In order to address this phenomenon and to facilitate understanding of the potential of it for our results, we examined the 646 same-sex twin pairs who were excluded because only one of them had made the interview and had outlived their co-twin, who in turn had not made the interview, having died before 2003 (the last interview year was 2002) at an age above Hence, out of in total 17,044 (15, ) individual twins (of which at least one in the twin pair had made the interview), 646 (or 3.8 percent) 14 Note that the purpose of this examination is not to make a comprehensive analysis of the association between mortality and socioeconomic status, but merely to address how mortalityinduced selection might relate to our study of health and socioeconomic status. Addressing how mortality can influence our estimated gradient between health and education/income (at age 35 39) is not straightforward. In order to focus on our estimations and to decrease the influence of reverse causality (i.e., that adverse health status, as manifested ultimately by mortality, affect education and earnings), we have limited our analysis to co-twins who have lived at least until 40 years of age.

20 44 Do education and income really explain inequalities in health? had died before being interviewed. Numerically, the magnitude of this selection process does seem to be rather mild. Linear WTP models of the probability of not making it to the interview, being outlived by your partner (who did make the interview), and dying before 2003 reveals that there is a statistically significant negative association between this probability and education and income at the age (results not shown). The estimated parameter value of years of education is (SE ), and for income (per SEK ) it is (SE ). 15 Summarizing, there are relatively few twin pairs that have been excluded from the sample because one of the twins has died between reaching the age of 40 and being interviewed. Nevertheless, it seems as if education and income are indeed associated with survival until being interviewed, although the pattern of causality is uncertain and the number of deaths is limited. Hence, it is certainly possible that the education/income gradients from a wider or alternative health perspective (not being limited to self-reported health) overall are more pronounced. However, given the small fraction of deaths, it seems unlikely that the reduction in the estimated associations between self-reported health and socioeconomic status, moving from OLS to WTP, which is a core result of our study, should be severely affected by mortality-induced selection processes. V. Discussion In this paper, we use the twin design in order to remove the influence of many of the unobserved underlying factors, such as family background and genetic inheritance. The WTP-based analysis demonstrates that the contributions of education and income are significantly reduced compared with the OLS-based analysis. In addition, the WTP-based analysis shows that the main contributor to the income-related inequality in health measure is the WTP fixed effect, which incorporates the influence of all factors shared by the twins. In summary, our paper provides a number of key insights, which are highlighted below. First, OLS-based studies on the estimation of the health production function using cross-sectional data probably substantially exaggerate the influence of education and income. Second, WTP-based analysis gives more rigorous estimates and provides an upper bound for the contribution of the health factors to the inequalities in health. Taken literally, these results are obviously important for policy makers, but leave them 15 Taken literally, this implies that a one standard deviation increase in education and income is associated with a decrease of the death risk by about 1.4 and 0.8 percentage points, respectively; because these standard deviations amount to 2.8 years and SEK (not shown), and