Policy Research Working Paper 9418 Life Expectancy at Birth and Lifetime Education and Earnings Mohammad Mainul Hoque Elizabeth M. King Claudio E. Montenegro Peter F. Orazem Education Global Practice September 2020 Policy Research Working Paper 9418 Abstract Exploiting cross–birth cohort and cross-country variation percent per year of added life expectancy at birth. The esti- from a pool of 188 household surveys from 111 countries, mates imply that rising life expectancy at birth explains this paper measures how life expectancy at birth affects 75 percent of the increase in average years of schooling lifetime education and earnings. On average, individuals worldwide for birth cohorts between 1922 and 1987 and add one year of schooling for every 8.3 years of increased 38 percent of the increase in average gross domestic product life expectancy at birth. Lifetime earnings increase by 1.7 per capita in the 20th century.\. This paper is a product of the Education Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at cmontenegro@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Life Expectancy at Birth and Lifetime Education and Earnings Mohammad Mainul Hoque mmahoq@gmail.com Bangladesh Institute of Development Studies Elizabeth M. King bethking1818@gmail.com Brookings Institution Claudio E. Montenegro cmontenegro@worldbank.org Department of Economics, University of Chile; The World Bank, and the German Development Institute. Peter F. Orazem pfo@iastate.edu Department of Economics, Iowa State University, and IZA JEL Classification: I12, I15, I21, J24, O11, O15 Key Words: Health, Education, Human Capital, Human Development, Life Expectancy, Return to Education ________________________ Corresponding author: Peter F. Orazem, 267 Heady Hall, Department of Economics, Iowa State University, Ames, IA 50011-1070. Email: pfo@iastate.edu Phone: (515) 294-8656/ FAX: (515) 294-0221. Life Expectancy at Birth and Lifetime Education and Earnings 1. Introduction Improvements in nutrition, education, transportation, sanitation, and knowledge of diseases have had a dramatic effect on life expectancy worldwide. Vallin and Meslé (2009) have estimated that various improvements in knowledge and technology increased potential life expectancy at birth by 0.33 year per year from 1885 to 1960 and by 0.2 year per year thereafter. A woman born in 2000 is expected to live 33 years longer than a woman born in 1885. 1 This 63% increase in expected length of life has been accompanied by improved health status and enhanced physical abilities which, in turn, should have had profound effects on life-cycle investments in skills, the application of skills to the labor market, and the ability to enjoy life. Ben-Porath (1967) and Becker (1993) posited that increased length of life would have an unambiguously positive effect on investments in human capital. Both models limited agents to choices of working versus acquiring additional human capital, ignoring the possibility that individuals would consume more leisure rather than spending more time working or learning. Heckman (1976) extended the model to allow both time and financial investments in human capital production and to allow agents to choose labor supply and the consumption of goods and leisure over the life cycle. Still, his model predicts that increased life expectancy at birth would cause individuals to increase also their lifetime human capital production. 1 Vallin and Meslé (2009) focused on women’s life expectancy to avoid the effects of war and the higher probability of violent or accidental deaths in their analysis of vital statistics. Potential life expectancy is based on the highest country life expectancy in each of the years they evaluated between 1750 and 2000. 2 The link between health and human capital investment has been examined intensively in previous research and at different points in the life-cycle. Shocks to fetal or infant health have been shown to lower educational investments or returns. These include maternal malnutrition (Field et al. 2009; Maluccio et al. 2009; Almond and Majumder 2011); low birth-weight (Behrman and Rosenzweig 2004); excessive or insufficient rainfall during the first year of childhood (Maccini and Yang 2009; Shah and Steinberg 2014); exposure to diseases (Almond 2006; Currie and Vogl 2013); and famine during early childhood (Almond and Currie 2011; Gorgens et al. 2012). Exogenous shocks from exposure to environmental pollution or hazards (Chay and Greenstone 2003; Foster et al. 2009; Jayachandran 2009; Almond et al. 2009), and exposure to violence or civil war (Akresh et al. 2011; Camacho 2008; Blattman and Annan 2010; Leon 2012; Yuksel 2014) have also reduced educational attainment and labor market earnings. While the link between these shocks and education might be due to health or related income shocks, past studies have been able to isolate the effects of health on human capital investments. Exploiting variation in the timing and intensity of hookworm and malaria eradication in the American South and in developing countries, Bleakley (2007, 2010a) and Lucas (2010) demonstrated improved education and earnings outcomes for populations with early, compared to later, exposure to the public health interventions. Miguel and Kremer (2004) found that children who received treatment for intestinal worms in Kenya were absent 25% less frequently than students in the schools that were randomly assigned to receive the treatment 2-3 years later. Follow-up surveys of these students reveal that those students from the treatment schools worked 13% more hours and earned 20%-29% more than those from the control schools (Karlan and Appel 2011). Bhalotra and Venkataramani (2012) found that the availability of 3 antibiotics to combat pneumonia at the time of infancy increased education and earnings when those infants reached adulthood. A few studies have examined the role of life expectancy on education. Jayachandran and Lleras-Muney (2009) used improvements in maternal health to instrument for presumed endogenous life expectancy of children and found that an additional year of expected life increased schooling by 0.11 year. Oster et al. (2013) used information on when individuals learned that they had the fatal Huntington’s disease as the measure of a life cycle shock and found that schooling increased by 0.17 year for every additional year of expected life. Studies that examine the effect of increased life expectancy on human capital investment have had more mixed results. Acemoglu and Johnson (2006, 2007) found no effect of increasing life expectancy due to improved control of infectious disease on schooling. They argued that because improved length of life effectively increases cohort size, returns to human capital may fall due to rising labor supply outpacing any growth in demand for skills. Bloom, Canning and Fink (2014) found that the Acemoglu and Johnson result reverses, however, when controls for initial health are added. Hazan (2009) argued that this Ben-Porath model requires an increase in lifetime labor supply for the gain in life expectancy to increase investments in human capital. Given that American men born between 1840 and 1970 actually reduced lifetime labor supply, he concluded that life expectancy has either a negligible, or possibly even, a negative effect on investments in education. His subsequent analysis (Hazan 2012) found no correlation between life expectancy at age 5 and educational attainment. 2 However, other analyses of similar 2 Following Soares (2005), Hazan included “post demographic transition countries,” which are basically a group of countries that exhibited life expectancy at birth above 50 in 1960. He preferred life expectancy at age 5 or 10 instead of that at birth since the later displayed widespread variability due to high infant mortality. 4 country-level data still found a positive correlation between life expectancy and schooling (Cervellati and Sunde 2013; Hansen 2013; Cohen and Leker 2014). This paper makes several improvements over the previous cross-country studies of life expectancy’s effect on human capital investments. First, the analysis is based on a much larger number of 111 developed and developing countries. The analysis is conducted at each cohort level so that there is a one-to-one correspondence between a cohort’s year of birth in a country and the corresponding life expectancy at birth. Secondly, the schooling attainment of each cohort per country was calculated from household survey data for each country in place of the noisier approximations based on school enrollment data, extrapolated estimates for missing values, and ex post adjustments for mortality that were used in previous studies. Estimates are generated separately for men and women and for urban and rural residents to establish the robustness of the findings. Thirdly, estimates of parental life expectancy at birth are incorporated into the analysis to examine evidence of the intergenerational transmission of human capital from parent to child. Finally, we estimate the impact of life expectancy on both lifetime years of schooling and lifetime earnings. We find that an additional year of life expected at time of birth increases years of schooling by 0.12 year and earnings by about 1%. The implied Wald estimate of returns to schooling are 9.9% for men, 4.3% for women, 10.2% for urban residents and 2.9% for rural residents. These cross-country results are very consistent with the findings based on individual data. The next section applies Heckman’s (1976) model of life-cycle earnings, learning, and consumption to the question of how increased life expectancy at birth will affect lifetime schooling and earnings. Section 3 explains how we utilize these implications to derive the reduced form specifications for our estimations. Section 4 elaborates on the data sources, and 5 section 5 specifies the empirical model. Section 6 reports the findings and presents some robustness tests, and section 7 presents the individual analysis. Section 8 discusses and interprets the findings and draws some conclusions. 2. Theoretical Framework Heckman (1976) developed a life cycle model of earnings, learning, and consumption by merging the theory of labor supply with that of human capital production. His model relaxes several assumptions of the Ben-Porath (1967) model that are important to our analysis, including that labor supply decisions are endogenous, that budgets can be used to consume leisure and invest in human capital as well as to purchase market goods and services, and that initial endowments of assets and human capital can alter the entire trajectory of consumption, investment and labor supply. This study uses Heckman’s framework to motivate the analysis of how life expectancy at birth will alter lifetime human capital investments and earnings. At each instant, the individual is endowed with one unit of time, which s/he allocates among leisure (), investment in human capital (), and work (1 − () − ()). Human capital H(t) augments individual time in the production of additional human capital in income generation and in leisure consumption. Human capital is accumulated at the rate (̇ ) = [ () (), ()] − () (1) (0) = 0 (2) where () is the time allocated to human capital production, and () is the input of market goods into human capital production in period t. F is a concave production function. No human 6 capital is produced unless time is allocated to it, i.e., () > 0. Human capital depreciates at the rate of σ in every period. 3 Consumers’ income in period t comes from two sources: interest earnings from assets accumulated and wage earnings conditional on accumulated human capital. The market price for a unit of human capital is R. Labor income in period t can be at most () if the individual devotes no time to human capital production or leisure. Income can be allocated to direct investment in education goods (()) and to consumption of durable and nondurable goods (()) at price P. Given an endowment of initial assets 0 and the human capital endowment 0 , an individual will accumulate wealth () according to ̇ ) = () + ()[1 − () − ()] − () − (), ( (3) (0) = 0 . (4) In equation (3), r is the risk-free rate of return on accumulated assets. The individual’s instantaneous utility function takes the form [(), () ()], where utility is concave in its arguments () and ()(). Note that () is leisure in natural units of time while () () is the human capital augmented leisure. The individual seeks to maximize lifetime utility as ∫0 − [(), () ()]. (5) This is maximized subject to the constraints (1)-(4). 4 The current value Hamiltonian of the above problem is 3 Although human capital might exhibit a differentiated rate of depreciation at older ages, we adopt Heckman’s assumption that is constant throughout life. This will not change the implication of the model for our setting. 4 We ignore the bequest motive for simplicity. Bequests do not make much sense in a model without hierarchical families. 7 (): − [(), ()()] + (){ () + ()[1 − () − ()] − () − ()} + (){[ () (), ()] − ()}, (6) 5 where () is the shadow value of an additional unit of wealth and µ(t) is the shadow value of an additional unit of human capital in period t. The first-order conditions are ()() : 1 () = () . (7) ()() : 2 ()() = () (). (8) ()() : ()1 ()() = ()(). (9) ()() : ()2 () = (). (10) ()() : (̇ ) = −(). (11) Equation (11) is a first-order differential equation in (). The solution for () is () = (0) − . (12) The last first-order condition is ()() : (̇ ) = () − (). (13) The terminal condition for human capital is () = 0, (14) while the assumption of non-satiation () > 0, together with the “no Ponzi scheme” condition () ≥ 0, implies that the terminal condition for wealth is ()() = 0. (15) In equation (12), (0) is the shadow value or marginal utility of wealth at the beginning of life. It is also period 0’s shadow value of lifetime earnings. Since resources are finite and an 5 For simplification, we assume that there is no income tax in the model. Heckman assumed a tax rate of (1-α) so that a households could keep only a fraction (α) of the income. 8 assumption of non-satiation holds, (0) must be positive. To simplify the analysis further, we define the shadow value of human capital in terms of wealth, that is, the ratio of the shadow () value of human capital to that of assets: () = . Along with equation (14), this yields the () first-order differential equation for (), ̇ ) = ( + )() − . ( Utilizing the terminal condition for the shadow value of human capital, as stated in equation (14), the solution for () is () = (+) �1 − (+)(−) �. (16) Since the two basic assumptions of the model are strict concavity and differentiability of the utility and production functions, we can invert equations (7), (8), and (12) to obtain the (0) constant demand function for consumption good () and effective leisure () (): () = �(0) (−) , (0) (−) �, (17) ()() = �(0) (−) , (0) (−) �. (18) Similarly, the demand functions for the two human capital investment inputs can be obtained by inverting equations (9) and (10). () = �() , ()�. (19) () () = �() , ()�. (20) () gets smaller as t→T, so the price of purchased educational inputs and the opportunity cost of time devoted to human capital production increase as an individual ages. As a result, time invested in human capital production, (), decreases as an individual ages and approaches zero at T. Before time T, human capital production takes place in every period to offset human capital depreciation. 9 The stock of human capital at any period t, H(t), is the depreciation-weighted accumulated investments in human capital through period t, plus the depreciated initial stock. Human capital stock at period t is specified as follows, () = ∫0 (−) [ ()(), ()] + (0) − . (21) Thus, the lifetime human capital stock is the accumulated human capital over a lifetime T is () = ∫0 (−) [ ()(), ()] + (0) − . (22) The value of human capital is equal to the earnings generated from selling this human capital in the market in each period, net of its explicit and implicit production costs. The shadow value of human capital in terms of wealth, g(t), can be used to convert human capital into wealth. The value of the lifetime accumulated human capital evaluated at the initial period is = (0)(0) + ∫0 − {() [ () (), ()] − () − ()} . (23) The term within the integral is the lifetime net earnings from human capital investments. 2.1 Comparative dynamics from increase in life expectancy at birth T This section derives the effect of changes in life expectancy, T, on human capital investment decisions, lifetime human capital production, and lifetime earnings from human capital investments. Proposition 1: The shadow value of human capital in terms of wealth, (), increases when life () expectancy, T, increases. 6 This happens for all ∈ [0, ] as = (+)(−) > 0. As () increases, the effective cost of the inputs into human capital production falls, as expressed in equations (18-19), leading us to proposition 2. 6 All proofs to these propositions are presented in Appendix A. 10 Proposition 2: As life expectancy at birth, T, increases, purchases of educational investment goods, D(t), and effective time investment, I(t)H(t), increase in every period of life t < T. Proposition 3: As life expectancy at birth, T, increases, the human capital stock H(t) accumulated by time t increases in every period ∈ [0, ], as does the total human capital H(T) accumulated over the lifetime. This is a direct consequence of the increased use of D(t) and I(t)H(t) in every period t, as governed by the production function [ ()(), ()]. 7 Proposition 4: As life expectancy at birth, T, increases, lifetime labor income increases. Proposition 5: As life expectancy at birth, T, increases, the marginal utility of lifetime wealth at the beginning of life, (0), decreases. Proposition 6: As life expectancy at birth, T, increases, the consumption of leisure in human capital-adjusted efficiency units, (), increases. However, measured hours of leisure, (), may increase or decrease. The proof in Appendix A shows that an increase in life expectancy at birth has two opposing effects on the units of leisure. Effective leisure becomes cheaper due to a fall in the marginal utility of wealth; at the same time, the opportunity cost of hours spent in leisure increases due to rising human capital investments. It is possible that lifetime leisure will rise or fall as T increases, contrary to the assertion made by Hazan (2009). 3. Reduced Form and Econometric Specifications The model predicts that in every period of life, increased life expectancy at the start of life will increase accumulated human capital and will raise lifetime earnings. Simultaneously solving the first-order conditions given by equations (7-15) results in reduced-form solutions of 7 We are assuming that the per unit value of human capital is not bid downward due to the outward shift of the supply of skilled workers. As we demonstrate, the estimated impact of increased life expectancy on human capital investment is sufficiently small in magnitude that the positive effects of human capital on income have dominated the downward pressure from increased supply. 11 the lifetime sequences of the expected paths of goods consumption, investments in human capital, leisure consumption, and planned accumulations of assets and human capital in every period, conditional on available information on the exogenous variables at time 0. The exogenous variables include the rates of interest (r) and human capital depreciation (), the price of human capital inputs (P), the rental rate of human capital (R), the endowments of human capital and assets (0 , 0 ), and life expectancy at birth (T). At the time of birth, the individual can set the optimal trajectory of the human capital stock at every point in the life cycle based on information available at that time Ω0 : [ ()|Ω0 ] = �, , , , 0 , 0 , , ()� ∀ ∈ [0, ]. (24) The investment trajectory for time and goods inputs into human capital investment in each period is set by the expected paths of the shadow values of assets and human capital, (0) () = (0) (+) + (+) �1 − (+) � = (0) (+) + (+) �1 − (+) �. (25) A change in increases the projected lifetime wealth at the beginning of life, causing the marginal utility of wealth at birth, (0), to fall. That increases (0), the value of human capital relative to wealth at the start of life, and this increase in (0) increases all the subsequent values of (), as given by equation (25). While the planned sequence of () is based on information available at time 0, unanticipated shocks to the exogenous variables in equation (24) will cause the individual to reconsider investments and the sequence of () evolves. Critically, however, the new information will be orthogonal to the information set Ω0 . As a result, changes to the sequence of () will be uncorrelated with Ω0 . For example, suppose at time t’ the individual finds out that life expectancy has changed from T to T’. The individual will re-optimize, including new values of the () sequence from t’ through the end of life at T’. However, [ℊ() − ()|Ω0 ] = 12 0 ∀ > ′ where ℊ() represents the re-optimized sequence of relative shadow values of human capital to assets. That means that changes made to planned sequences of human capital investments, labor supply, and lifetime consumption paths from the plans made at time 0 will be uncorrelated with the values of the exogenous variables at time 0, including the life expectancy at birth. 8 This result has important implications for estimating lifetime human capital investments and earnings as a function of life expectancy at birth. Suppose that the planned human capital stock at time t conditional on initial information is (|), and the updated plan after changes in information on life expectancy is ℋ (| ′ ). A survey will reveal information on actual human capital investments ℋ (), but [ℋ (| ′ ) − ℋ ()|Ω0 ] = 0 and so the projection of observed ℋ () on T will yield the effect of life expectancy at birth on planned human capital investments at birth. On the other hand, [(ℋ (| ′ ) − ()|Ω0 , ′ ] ≠ 0 and so a regression of ℋ () on ′ will not generate the unbiased effect of life expectancy on planned human capital investments. In particular, if individual decisions made after birth due to new information on any of the exogenous variables result in changes in life expectancy, the observed human capital outcomes ℋ () and the observed life expectancy ′ will be jointly determined. A similar argument suggests that to derive the effect of life expectancy on lifetime earnings, one should also regress observed earnings on life expectancy at birth and not life expectancy at later ages. 8 Hazan (2012) proposed that life expectancy at age five instead of life expectancy at birth is more suitable to explain human capital investment decisions due to the selection problem with respect to who survives infancy or early childhood. In practice, by the time a child reaches age five, parents or government or both have made significant investment in the child, which makes life expectancy at age five higher compared to what it was at birth, and thus makes life expectancy at five an endogenous variable. 13 4. Data We require data with considerable variation in life expectancy at birth and information on lifetime human capital investment and earnings. We exploit the World Bank’s International Income Distribution Database (I2D2) for this purpose. I2D2 is a harmonized collection of household surveys conducted in 111 countries from all regions and income groups. A list of the countries and survey years is presented in Table B1 in Appendix B. Of our 111 countries, 30 are developed countries, 11 in Asia and Pacific, 17 in Central Asia and Eastern Europe, 23 in Latin America, 4 in the Middle East and North Africa, and 26 in Sub-Saharan Africa and South Asia. From each survey, we include only those individuals who have complete information on both education and wages. Since our interest lies in how life expectancy at birth affects human capital accumulation and earnings, we focus on those individuals who were working at the time of the survey and reported positive incomes. We limit our analysis to the age group 25-60 years. Focusing on individuals over age 25 limits the probability that they would still in school; 9 the upper bound of 60 years avoids selection issues related to retirement and rising mortality with age. Because life expectancy at birth sets the trajectory for lifetime human capital investment and earnings, we do not aggregate across individuals with different life expectancies, but instead define each cohort in each country as the unit of observation. Our earliest available survey is in 1970 and the latest is in 2012. To fit our age range of 25-60, we include 77 birth cohorts born between 1911 and 1987. Many of the countries have multiple surveys, giving us repeated observations for many cohorts. However, completed schooling will be the same for the same cohort across surveys. 9 Both Barro and Lee (2010) and Cohen and Soto (2007) assume that years of schooling are fixed by age 25. 14 We opted to use the earliest available survey for each country to limit mortality bias in the estimated completed schooling and then the most recent survey to capture the completed schooling for the youngest cohorts in the country. In total, we used 188 surveys from 111 countries to generate 4,670 cohort observations covering almost 4 million individual observations. We further disaggregate the cohorts by gender, and if possible, also by urban and rural residence. For each birth cohort, we computed average years of schooling, average earnings, and incidence of marriage. To compare lifetime earnings across countries, we require a common unit of time. Across the 188 surveys, wages are measured per hour, day, week, month, quarter, or year. These surveys are internally consistent, so a survey dummy variable standardizes both time units and currency units. The survey dummy variable also controls for country-specific effects. In effect, the source of identification in our estimates is the variation in schooling and earnings across cohorts within surveys. The data on life expectancy at birth by country were compiled from 1950 from the United Nation’s population database. 10 For earlier birth cohorts, GapMinder constructs a measure of life expectancy at birth for almost 200 countries back to 1900. Figure 1 shows the pattern of life expectancy at birth by birth cohort starting in 1910. Worldwide life expectancy has risen from 38 to 72 years over the 90-year period. Over that same period, the global average years of schooling rose from 6.8 to 12.4 years. As shown in Figure 2, these patterns are common across regions and income groups. As life expectancy increases, the fraction of the birth cohort that enters working age increases. If workers of different ages are not perfect substitutes for one another, members of unusually large working-age cohorts will face depressed earnings (Welch, 1979). We use the 10 The UN database is available at http://data.un.org/Default.aspx. 15 number in the cohort relative to the total population as our measure of the relative cohort supply. Figure 3 shows the path of average wages across birth cohorts after netting out the survey fixed effect. 11 Starting with the oldest cohorts, average earnings rise over birth cohorts until the mid- 1950s when the average earnings begin to decline. The reversal is due to the declining age of the more recent birth cohorts, illustrating that we will need to control for position in the life cycle to remove the effects of age on lifetime earnings. As we demonstrate in the next section, using quadratic terms in age of the cohort or using cohort-specific fixed effects serves to correct for the age effect on earnings. 5. Empirical Specification The theory suggests that the reduced-form equation for completed schooling and earnings will depend on conditions known at the time of birth, plus changes to those variables conditioned on information orthogonal to the variables known at birth. We specify the equations for completed years of schooling and log earnings ln( ) for cohort j, country c, and survey year t as = 0 + + + + + + + , (26) Ln( ) = 0 + + + + + ∑=1 + + + . (27) The focus on years of schooling is a matter of convenience in that we know that human capital investment will rise in every period t as life expectancy for cohort j, , rises, but schooling is the most readily observable and consistent measure of human capital investment 11 The survey fixed effects give us an estimate of average wages net of fixed factors such as the home currency; the time unit used for wages, whether hourly, weekly, monthly or annually; country-specific fixed effects; and inflation. The wages are presented on a logarithmic scale. 16 across countries and time. As it is also a form of human capital investment that is fixed at a relatively young age, we can assume that for birth cohorts aged 25 and over, years of schooling are fixed for the rest of their lives. In equations (26) and (27), includes cohort-specific effects that are known at birth and common across countries, and and are survey-specific fixed effects that also incorporate country-specific effects that are common across cohorts within a country. and are, respectively, the average proportion male and average proportion rural in cohort j, country c, and survey year t. We also include an approximation of the life expectancy at birth for each birth cohort, which we assume as the 25-year lagged life expectancy at birth in a country. Our rationale is evidence of intergenerational transmission of human capital (Lindahl et al. 2015) and life expectancy (Björkegren et al. 2019) that may suggest a further gain from improving health conditions on lifetime schooling and earnings. 12 The log earnings equation (27) shares many of the same features as equation (26). Unique elements in Z include the cohort-specific marriage incidence rate and size of the cohort within a country-survey year. Cohort-specific fixed effects will correct for position in the life cycle. Alternatively, we can conserve on parameters and specify the lifetime log earnings function as ′ ′ ′ ′ ′ ′ ln( ) = 0 + + + ( )2 + + + ∑ ′ ′ =1 + + , (28) 12 Our findings of intergenerational transfers through parental life expectancy were not overly sensitive to the assumption of the lag length. 17 where the quadratic terms in the age of the cohort control for position in the life cycle. We can compute the returns to schooling applying the Wald estimator: = = . This estimate uses life expectancy at birth as an instrument for completed years of schooling by cohort. We can compare it with the traditional estimate using the Mincerian earnings function specification, 2 ) = 0 + �ℎ � + ( ) + ( ) + + ln( + + , (29) which yields biased estimates of the returns to schooling due to presumed endogeneity of the schooling choice (Card, 1999). Observations are weighted to reflect the cohort-survey cell share of the total population in the country. We further weighted the data by the square root of the cell-size to correct for differences in measurement error variance between thin and thick cell samples. 13 Finally, we cluster all errors at the country level to correct for likely correlated errors across cohorts within a country. 6. Results 6.1 Life expectancy at birth and years of schooling Table 1 reports the estimates obtained from regression equations (26). We start with the simplest bivariate specification relating life expectancy at birth and lifetime schooling. All of the specifications include a survey fixed effect which controls for country fixed factors, cyclical factors related to the timing of the survey, and survey type (i.e., household expenditure survey vs. labor force survey). We also control for common birth cohort-specific effects across 13 Cell size is the total number of observations belonging to a specific cohort in a survey. We divide the cell size by how many times each cohort appears and use that to construct the weight to be applied in the regression. In our sample of 111 countries, for 77 countries we add younger birth-year cohorts from the most recent survey. 18 countries. 14 In specification IV, we include cohort dummies, where cohort is defined by the year of birth to control for time-varying factors across countries. 15 The coefficient of life expectancy at birth, in equation (26), is always positive and statistically significant. The effect ranges from 0.094 to 0.12 year of schooling per additional year of life expectancy. The 30-year increase in world life expectancy between the 1922 and 1987 birth cohorts (Figure 1) by itself would have increased completed schooling by 2.8 to 3.6 years. The coefficient of parental life expectancy in specification IV suggests that there is also an intergenerational channel through which parental health affects children’s education. The effect of parental life expectancy is 22% of the own life expectancy effect, raising the combined effect of rising life expectancy to 3.4 to 4.4 years of schooling. The effect of life expectancy gain at birth might have different effects on different groups. We investigate this by estimating equation (26) for four subsamples separately: (i) males, (ii) females, (iii) urban residents, and (iv) rural residents (Table 2). Across all specifications, we observe a larger effect of life expectancy gain at birth on women’s schooling than on men’s schooling, but there is little difference in this life expectancy effect between rural and urban residents. For all four groups, the parental life expectancy effect is positive but not statistically significant. 6.2 Life expectancy at birth and earnings Table 3 reports estimates obtained from regression equations (27) and (28). The first column implies a negative coefficient on life expectancy at birth, but as shown by the inverted 14 Cohorts born during the Great Depression or during World War II might experience common shocks to schooling availability. Similarly, there were several United Nations programs and activities to improve health and education across the countries, implying that cohorts born after the 1960s in the low-income countries might have been exposed to similar global campaigns for education. 15 Later, in the robustness section, we include cohort dummies defining cohorts by five-year birth range. 19 U-shaped plot of log of wages across birth cohorts in Figure 3, we need to control for the age of the cohort when we observe its wage. The latest birth cohorts will be observed early in their life cycle when their ages are low, even as their life expectancy is high. Once we control for lifecycle effects by including age or cohort-fixed effects and other potential confounders, the coefficient of life expectancy at birth reverses sign: the effect of life expectancy at birth on log of wages turns out to be positive and statistically significant. Increasing life expectancy at birth by one year increases lifetime earnings by roughly 1%. In all the specifications, the log of earnings increases with age at a decreasing rate. Consistent with the findings in the literature, married people and urban residents earn relatively more compared to their unmarried and rural counterparts. A larger cohort size lowers cohort earnings, consistent with the presumption that unusually large cohorts receive depressed earnings. 16 As with schooling, there is an intergenerational gain from parental life expectancy that is statistically significant in all of the specifications with cohort fixed effects. The parental life expectancy effect is 60%-88% as large as the own life expectancy effect. In Table 4, we report separate estimates by gender and region. The returns to life expectancy are somewhat larger for men than women and for urban than rural residents. However, for males, the life expectancy coefficient turns out to be statistically significant only in specification III where we control for lifecycle position by birth-year fixed effect. For rural residents, life expectancy at birth is never statistically significant. Parental life expectancy retains a small positive effect on the earnings of their children, but the effect is statistically significant for men, women and rural residents, and only in the specification with the birth-year fixed effect. 16 Cohort-specific dummies would absorb this effect if one specific cohort experiences a surge in population across the world. 20 Using the worldwide increase in life expectancy at birth of 30 years between 1922 and 1987, these estimates suggest that rising life expectancy increased lifetime earnings by 27%. The gains are largest for males (36%) and smallest for rural residents (21%). 6.3 Returns to schooling The Mincerian earnings function (29) generates a measure of the returns to education. This can be compared to the Wald estimator. 17 Estimates from the Mincerian earnings function are reported in Table 5, and these estimates are compared to the corresponding Wald estimators in Table 6. In Table 5, additional schooling increases lifetime earnings irrespective of the specification used. For the pooled sample, the coefficient of years of schooling shows that one additional year of schooling increases lifetime earnings by 11.8% in the simple specification I; this shrinks to 9.4% once we include a broad set of controls. 18 The estimates on the age terms, percentage male, percentage urban-rural, percentage married, and cohort size exhibit the usual signs. The estimates of the earnings function by gender and urban-rural residence do not show any notable variation across groups. Specification II reveals that one additional year of schooling increases lifetime earnings for males, females, urban, and rural groups by 10.6%, 7.3%, 9.5%, and 8.8%, respectively. In Table 6, the Wald estimate of the returns to schooling is obtained by dividing the life expectancy coefficients from specification IV in Table 3 by the life expectancy coefficient from specification IV in Table 1. Similarly, for the male, female, urban, and rural groups, we divide the group-specific life expectancy coefficient obtained from specification II in Table 4 by the life 1 ℎ 17 The Wald estimator for = . ℎ 1 ℎ 18 In all specifications reported in Table 5, we have used survey fixed effects to facilitate comparison across countries and time periods. 21 expectancy coefficient from specification IV in Table 2. The standard errors for the Wald estimates are obtained from 500 bootstrap replications with the corresponding sample. In the pooled sample, the Wald estimates are 16% lower compared with the Mincerian estimates (7.90% vs. 9.40%). The Wald estimate is slightly higher for urban residents (10.21% vs. 9.50%), but it is lower for males (9.90% vs. 10.60%), females (4.30% vs. 7.30%), and rural residents (2.90% vs. 8.8%). For both Mincerian and Wald estimates, the return to schooling is always higher for males than females, and higher for urban than rural residents. 6.4 Robustness checks We reexamine our findings using several estimation methods and samples. We re- estimated the models (i) without weights, (ii) using a different sample consisting only of data from one survey per country, (iii) using an alternative definition of parents’ life expectancy, 19 (iv) including cohort fixed effect with an alternative definition of cohort, 20 (v) using a sample consisting only of young age groups, and (vi) using a higher-order age variable to wipe out all age effects while estimating the life expectancy effects on earnings. 21 These robustness checks generate similar estimates of life expectancy effects on schooling and earnings. In most cases, the sign and statistical significance of the life expectancy coefficient is positive and statistically significant. The results for all robustness checks are briefly discussed and reported in Appendix C. 19 Previously, parents’ life expectancy was constructed by taking a 25-year lag of life expectancy at birth. The youngest cohort in our survey was born in 1987. In the 1980s, in many regions, especially in Sub-Saharan Africa and South Asia, mother’s age at first child birth was less than 20. For example, in Niger half of the women had given birth by age 18 (Source: http://www.unicef.org/pon95/fami0009.html). An alternative measure of parents’ life expectancy assumed a 15-year lagged value of own life expectancy. 20 While constructing the five-year birth cohorts, we collapse all individuals aged 25-59 into different five-year birth cohorts, except for the first and last cohorts. In total, we define 13 cohorts based on 5-year birth groups. Since the number of observations before 1930 is too thin, we group those observations into one cohort. Similarly, all individuals who were born during 1985-87 were collapsed to form the youngest cohort. 21 In addition to those attempted for schooling, we try one additional robustness check for lifetime earnings. Following Card (1999) and Murphy and Welch (1990), we add higher-order age terms to sponge out all age effects. 22 The final check of robustness involves adding exogenous variables that vary by country and cohort at the time of birth, and substituting life expectancy at birth by life expectancy measured at older ages. The theory predicts that the effect of life expectancy at birth is exogenous to any random shock realized in a later period in life. To demonstrate the validity of this, we incorporate average temperature and average precipitation that was observed for a birth- cohort at the time of birth in its country of origin. Note that similar to life expectancy at birth, average temperature and average precipitation also vary by birth-year and country. The results and discussion on this are presented in Appendix C. In sum, the estimates reveal that the statistically significant positive association of life expectancy at birth with schooling and earnings is not altered even after inclusion of these exogenous variables. Concerns related to high infant and child mortality rates led some recent papers to argue against using life expectancy at birth. Hazan (2012) suggests that life expectancy beyond early childhood is more appropriate to capture its true effect on human capital investment decisions since parents make schooling decisions for their children at age five or later. 22 However, by the time a child reaches age five or ten, the parents have made substantive investments in the child’s health based on new information on the child’s survival prospects. That makes life expectancy at ages 5 or 10 endogenous responses to observed child survival, making their use inappropriate as explanatory variables for other parental investments in children. However, results using life expectancy at higher ages still have positive and significant effects on years of schooling and lifetime earnings, as reported in Appendix C. These findings contrast with Hazan’s (2012) finding that life expectancy at older ages does not exhibit any statistically significant association with schooling years using a cross-country panel database. 22 The argument is based on the observation that cross-country life expectancy at birth exhibits more variation compared to life expectancy at five due to high infant and child mortality. 23 7. Individual-level analysis We extend the analysis utilizing individual-level observations instead of cohort-level mean observations as reported above. Since the theoretical model suggests that life expectancy at birth is exogenous in determining human capital investment and lifetime earnings, an individual- level analysis will confirm if country-cohort specific unobservables are contaminating the cohort-mean based empirical results. We estimate three equivalent specifications of equations 26, 28, and 29 using individual-level data: = 0 + + + + + + , (26a) ′ ′ ′ ′ ′ ′ ln( ) = 0 + + + ( )2 + + + ∑ ′ =1 + + , (28a) 2 ) = 0 + ( ) + ( ) + (ℎ ) + + ln( + + . (29a) We do not observe individual life expectancy at birth, but a cohort’s life expectancy at birth, an average measure of individual life expectancies at birth within a cohort ( = ∑ =1 ), is exogenous to an individual’s completed years of schooling or lifetime earnings. Group means are often used to instrument for endogenous variables in empirical analysis using individual-level data. 23 In the above specifications, = + , which states that individual i’s life expectancy at birth in country c deviates from cohort j’s mean life expectancy by which, by construction, is orthogonal to the mean. Since will be contained in the error term, the following conditions hold: 23 Royalty (2000) used the state tax rate as an instrument for marginal tax rate in explaining employees’ health insurance eligibility. Similarly, a series of studies following Ruhm (2000) exploited variation in state or county level unemployment rate while explaining individual health behavior during a recession. 24 ′ � , � = 0, � , � = 0, and � , � = 0. In contrast to the cohort-mean level analysis in the previous sections, to save time and space here, we estimate one specification each for the pooled sample and for the male-female, rural-urban subsamples. 24 As Table 7 shows, the estimates conform to those obtained from the cohort-mean level analysis: life expectancy at birth exhibits a positive and statistically significant association both with completed years of schooling and lifetime earnings. The life expectancy effects on schooling reveal a similar pattern to those obtained from the cohort-mean level analysis reported in Tables 1 and 2. However, except for the urban subsample, the life expectancy effects on earnings are always larger compared to similar estimates using cohort- mean level analysis. In the pooled sample, a one-year gain in life expectancy at birth leads to 0.12 year more completed years of schooling and to 1.3% higher lifetime earnings. The largest effect on earnings is observed for the male subsample—a 1.5%-increase in lifetime earnings for each additional year in life expectancy at birth. Panel (b) of Table 6 reports the Wald estimates of the returns to schooling based on the estimates in Table 7 along with the related returns to schooling in the Mincerian earnings function estimated using the individual sample. The detailed results from the Mincerian earnings function estimations are reported in Table B2 in Appendix B. The Mincerian returns to schooling estimates are about 10%. The Wald estimates exhibit more variation among the groups—for example, the return to schooling is 15% for males, compared to 7.8% for females.. Except for the female subsample, the Wald estimates of the return to schooling exceed the corresponding Mincerian estimates. The Mincerian returns to schooling are similar to those estimated using the birth cohort-level data. However, the Wald estimates based on the individual-level data are 24 We choose specification IV from Table 1 for schooling, and specification IV from Table 3 for earnings. 25 somewhat larger with the overall return to schooling rising to 11.2% per year of schooling compared to 7.9% using the cohort-level data. In contrast to the cohort-mean level analysis, the findings from individual-level empirical analysis consistently suggest that parents’ life expectancy has a statistically significant positive influence on both human capital investments and lifetime earnings in the pooled sample as well as in the male, urban and rural subsamples. Parents’ life expectancy effects on years in school are 19%-26% of the cohort’s own-life expectancy effect; the effects on earnings are even larger— 38.5% to 54.5% of the own-life expectancy effect. This is strong evidence of an intergenerational transfer effect with respect to increases in life expectancy at birth. Such high transmission across generations is not uncommon considering the recent findings by Lindahl et al. (2015) of intergenerational persistence in human capital and lifetime earnings across several generations. 7.1 Instrumental Variables Estimation Thus far, we have assumed that life expectancy at birth is exogenous. This assumption may be supportable by evidence that, in Sweden, all of the persistence in mortality across generations is attributable to pre-birth factors (Björkegren et al. 2019), and yet findings for one country is hardly generalizable. We investigate the possible biases due to endogenous life expectancy at birth by using a plausible instrument in equations (24) and (25): the observed mortality rate of children of age five or less. The presumption is that parents use the prevailing under-5 mortality rate as a signal of a newborn’s expected length of life when they make their fertility decisions, and so it should be a reasonable indicator of the exogenous component of the health endowment, 0 . The instrumental variables estimates for completed years of schooling are presented in panel (a) of Table 8 while those for earnings are presented in panel (c). To facilitate a 26 comparison of these IV estimates with the OLS estimates obtained from the corresponding sample, related OLS estimates on completed years of schooling and earnings are presented in panels (b) and (d), respectively. In all first stages, the under-5 mortality rate shows a statistically significant negative relationship with life expectancy at birth, and the first-stage F-test statistics imply that our estimates are not subject to weak instrument bias. The reported IV estimates suggest that a one-year gain in life expectancy is associated with 0.146 additional year of completed schooling versus 0.113 additional year in the OLS estimates. An additional year of life expectancy raises lifetime earnings by 1.7% using the IV specification versus 1.2% using the OLS specification. The schooling estimates are larger for females than for males, and larger for rural than urban birth cohorts. The gain in lifetime earnings is higher for males than for females, and higher for urban than for rural workers. Applying the historical increase in life expectancy at birth, the implied gain in education and earnings for the 1987 birth cohort over the 1922 birth cohort is 4.4 more years of schooling and 51% higher lifetime earnings. We report the Wald estimates of the returns to schooling based on the IV estimates at the bottom of Table 6. The overall return to schooling rises to 12% per year of schooling. Returns for males and urban residents increase while returns to females and rural residents become smaller. However, the overall result from all of these estimates is that our Wald estimates correspond to consensus estimates from the very large literature on returns to schooling of about 10% per year, somewhat larger for men and urban residents and somewhat smaller for women and rural residents. 7.2 Selection bias due to the labor force participation decision Our analysis for lifetime earnings includes those who are in the labor force at the time of the survey. If life expectancy at birth affects an individual’s labor force participation decision, 27 our estimates will be subject to bias and the direction of that bias is uncertain. Note that Hazan (2009) observed that a gain in life expectancy at birth was associated with a decrease in the labor force participation of U.S. males born between 1840 and 1970. We investigate the labor force selection issue with individual-level data in two ways: (i) first, by including a birth-year specific correction measure for selection in each survey, which is constructed as the proportion of individuals in that cohort participating in the labor force in a survey, and (ii) by estimating a two- step Heckman selection correction for an individual’s labor force participation status. To fulfill the exclusion criterion, the selection equation includes household size (number of household members) and the interviewee’s relationship to the household head. 25 These estimates are done separately for the pooled sample and the male, female, urban and rural subsamples. The results are reported in Tables 9 and 10. After controlling for the proportion of the birth-year cohort in the labor force, neither the pooled sample nor any of the subsamples shows a different pattern in the effect of a gain in life expectancy at birth on lifetime earnings from that obtained without addressing the selection issue, as reported in Table 7. However, estimates obtained following Heckman’s two-step procedure (Table 10) in which we utilize information on individual-level labor force status are positive and statistically significant in the second stage equation, and are larger in magnitude compared to those obtained without any selection correction. 26 The life expectancy effects on lifetime earnings for the pooled sample and the male and rural subsamples are larger in magnitude than our estimates without correcting for selection. 25 In the first stage, we estimate a fixed effects logit model of labor force participation decision including age, gender, urban/rural residence, marital status, life expectancy at birth, parents’ life expectancy, household size, relationship to the household head, and survey/country fixed effects. Using the parameters from the logit model, we calculate a linear predicted probability which we then convert into normal densities to construct the inverse Mills ratio used in the second stage for selection correction. 26 Replicating the analysis in Table 10 on the same sample but without including the selection correction term produces life expectancy coefficients of 0.13, 0.15, 0.12, 0.12 and 0.10 for the pooled, male, female, rural, and urban samples. 28 For the urban subsample, the selection correction does not alter the life expectancy effects on lifetime earnings. Household size and the individual’s relationship to the household head, our identification variables in the selection equation, always turn out to be statistically significant predictors of individual labor force participation. The life expectancy coefficient in the selection equation is positive and statistically significant, except in the rural subsample, though it is smaller in magnitude. Since we control for the life cycle stage in the selection specification, this positive association suggests that a gain in life expectancy at birth influences labor force participation marginally at any stage of the lifecycle. In the earnings equation, the negative and statistically significant inverse Mills ratios suggest a negative selection bias: individuals with jobs have lower wages compared with those for whom we do not observe wages. This is not the case for the urban subsample. Controlling for selection, the corresponding coefficient for urban residents is lower by 9%, suggesting that those urban residents with complete wage information are drawn from a relatively higher income group than those urban residents without wage information. One possible explanation for this disparity is that the urban residents without wage information include not only those whose shadow price of labor is higher than the market wage offer but also those residents who work in the informal sector or those who own large businesses. Overall, the effects of a gain in life expectancy at birth on lifetime earnings without correcting for selection bias tend to be conservatively lower using a cohort-based analysis. 8. Conclusion Using time-series data on birth cohorts from 111 countries, we find that gains in life expectancy at birth increase both investments in human capital and lifetime earnings. An individual completes an additional 0.12 year of schooling for each year added to life expectancy 29 at birth. This estimate is comparable to the estimate of 0.11 year by Jayachandran and Lleras- Muney (2009) for Sri Lanka and to 0.17 year by Hansen (2013) using a 70-country study. In our data, global average life expectancy at birth increased 29.7 years between the 1922 and 1987 birth cohorts. Based on our results, this gain implies an increase of 3.6 years in completed schooling. The actual years of schooling in our sample increased by 4.8 years for the same cohorts, so our results suggest that increased life expectancy at birth explains 75% of the increase in average schooling worldwide. We have also estimated the effect of an additional year of life expectancy at birth on lifetime earnings and find this to be a gain of 1.7%. Global per capita GDP increased by 380% or by 1.3 log points between 1900 and 2000. Our analysis implies that real earnings increase by 1.7% per year of added life expectancy, or by 0.50 log points evaluated at the average gain in life expectancy. Thus, the gain in life expectancy alone explains 38% of the gain in per capita GDP. We illustrate the effect in Figure 4. In the U.S., estimates by Steckel (2002) suggest that life expectancy at birth rose 31.4 years between 1870 and 1990. This gain in life expectancy alone would have increased years of schooling by 3.8 years according to our results, or by 45% of the 8.3 years increase noted by Lee and Lee (2016) for that period. Steckel (2002) also reported that per capita GDP rose 2.25 log points; based on our results, we can tie 0.53 of this increase to rising life expectancy at birth. Hence, while the gains in human capital and lifetime earnings are largest for poorer countries, they can be substantial even for much richer countries. 30 9. References Acemoglu, D., and S. Johnson 2007. “Disease and Development: The Effect of Life Expectancy on Economic Growth.” Journal of Political Economy 115(6): 925–985. Acemoglu, D., and S. Johnson. 2006. “Disease and Development: The Effect of life expectancy on economic growth.” NBER Working Paper, No. 12269. 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Meslé. 2009. “The Segmented Trend Line of Highest Life Expectancies.” Population and Development Review 35(1): 159-187. 34 70 60 Life Expectancy at Birth 50 40 30 20 10 0 1905 1912 1919 1926 1933 1940 1947 1954 1961 1968 1975 1982 Year of Birth Figure 1: Life Expectancy at Birth across Cohorts, World Average 35 80 15 80 15 80 15 High Income Countries East Asia and Pacific Europe & Central Asia 60 60 60 10 10 10 40 40 40 Life Exp 5 Life Exp 5 5 20 20 20 Life Exp School Year School Year School Year 0 0 0 0 0 0 1911 1919 1927 1935 1943 1951 1959 1967 1975 1983 1931 1937 1943 1949 1955 1961 1967 1973 1979 1985 1935 1942 1949 1956 1963 1970 1977 1984 80 15 80 15 80 15 Latin America and the Caribbean Middle East & North Africa South Asia 60 60 60 10 10 10 152 40 40 40 5 5 5 20 Life Exp Life Exp 20 20 Life Exp School Year School Year 0 0 0 0 0 0 1924 1932 1940 1948 1956 1964 1972 1980 1922 1929 1936 1943 1950 1957 1964 1971 1978 1985 1942 1947 1952 1957 1962 1967 1972 1977 1982 80 15 Sub Saharan Africa Life Expectancy at Birth Years in School 60 10 40 Life Exp 5 20 School Year 0 0 1933 1937 1941 1945 1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 Year of Birth Figure 2: Life Expectancy and Schooling by Birth Cohort across Regions 37 6 5.8 5.6 5.4 5.2 ln(wage) 5 4.8 4.6 4.4 4.2 4 1900 1920 1940 1960 1980 Birth-Year Cohort Note: The birth-year specific wages are the coefficients of Birth-Year dummies in the regression of log (wages) on birth-year dummies and survey dummies, where the survey dummies are taking care of across survey differences in exchange rates, inflation, unit of wages, differences in survey instruments. Figure 3: Log(wage) by 1905-1987 Birth-year Cohorts, World Averages 1.5 80 1.4 75 Index of Lifetime Earnings (1922=1) 1.3 70 Life Expectancy at Birth 1.2 65 1.1 60 1 55 0.9 50 1920 1940 1960 1980 Year of Birth Note: We assume 1922 as the base year. We plot the implied present value of lifetime earnings (adjusted for the base year) from the specification II in Table 3 against the Birth Year. The lifetime earnings estimates are assumed for male residing in urban areas. The life expectancy at birth numbers are the maximum life expectancy enjoyed by a cohort across the countries, which is to capture what an average person would expect to enjoy staying on the frontier of health technology at the time of birth. While calculating the net present value of log of lifetime earnings, we try two different discount rates 2% and 5%. The period in the figure ranges from 1922 to 1987 as prior to 1922, the information on urban/rural residence is missing. Figure 4: World Average Life Expectancy at Birth and Implied Lifetime Earnings Index 38 Table 1: Life Expectancy at Birth and Schooling I II III IV Life expectancy at birth 0.120*** 0.097*** 0.094*** 0.117*** [0.015] [0.014] [0.008] [0.026] % Urban 6.009*** 6.043*** 6.737*** [1.687] [1.748] [1.057] % Male -1.212 -1.342 -0.858* [1.047] [0.922] [0.516] Parents Life Expectancy 0.004 0.026* [0.019] [0.014] Birth Year Fixed Effects YES Survey Fixed Effects YES YES YES YES Constant 3.476*** 1.574 1.625 -1.748 [0.916] [2.298] [2.455] [2.256] N 4670 4185 3861 3861 Adjusted R-square 0.987 0.985 0.985 0.987 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. 39 Table 2: Heterogeneity in Effects of Life Expectancy at Birth on Schooling Males Females I II III IV I II III IV Life Expectancy at Birth 0.098*** 0.082*** 0.084*** 0.107*** 0.157*** 0.141*** 0.135*** 0.157*** [0.015] [0.013] [0.009] [0.028] [0.018] [0.018] [0.014] [0.032] % Urban 5.679*** 5.766*** 5.958*** 4.249*** 4.351*** 4.737*** [1.860] [1.911] [1.155] [0.845] [0.927] [0.645] % Male Parents Life Expectancy -0.005 0.02 0.007 0.019 [0.022] [0.017] [0.018] [0.015] Birth Year FE YES YES Constant 4.420*** 1.801 1.888 -1.172 1.622 -0.419 -0.52 -3.001 [0.905] [1.713] [1.949] [2.288] [1.148] [1.491] [1.755] [2.623] N 4690 4204 3878 3878 4622 4149 3822 3822 Adjusted R-square 0.984 0.98 0.98 0.983 0.983 0.981 0.982 0.982 Urban Rural Life Expectancy at Birth 0.112*** 0.103*** 0.097*** 0.108*** 0.129*** 0.119*** 0.114*** 0.118*** [0.018] [0.018] [0.011] [0.028] [0.017] [0.011] [0.010] [0.029] % Urban % Male -0.25 -0.291 -0.106 -0.56 -0.68 -0.448 [0.807] [0.707] [0.441] [0.548] [0.576] [0.467] Parents Life Expectancy 0.007 0.02 0.01 0.012 [0.016] [0.013] [0.019] [0.018] Birth Year FE YES YES Constant 4.539*** 5.461*** 5.492*** 3.861* 2.195** 2.567*** 2.444** 1.785 [1.104] [1.433] [1.513] [2.167] [0.996] [0.884] [1.202] [2.510] N 4684 4200 3874 3874 4446 3959 3657 3657 Adjusted R-square 0.982 0.963 0.963 0.965 0.992 0.987 0.988 0.988 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. 40 Table 3: Effect of Life Expectancy at Birth on Earnings I II III IV V VI Life Expectancy at Birth -0.017*** 0.010* 0.011* 0.009* 0.013** 0.009** [0.005] [0.006] [0.006] [0.005] [0.005] [0.004] Age 0.091*** 0.094*** 0.077*** [0.015] [0.015] [0.013] Age square*(1/100) -0.10*** -0.10*** -0.10*** [0.000] [0.000] [0.000] % Urban 1.303*** 1.396*** 1.112*** 1.348*** 1.087*** [0.421] [0.423] [0.196] [0.323] [0.186] % Male 0.409*** 0.412*** 0.206* 0.154 -0.059 [0.111] [0.116] [0.118] [0.130] [0.145] Parents Life Expectancy 0.004 0.003 0.008** 0.008** [0.003] [0.003] [0.003] [0.003] % Married 0.471*** 0.610*** [0.153] [0.124] Cohort Size -8.577*** -7.733*** [1.534] [1.544] Birth Year FE YES YES Constant 8.490*** 3.738*** 3.341*** 4.206*** 5.278*** 5.637*** [0.331] [0.746] [0.819] [0.671] [0.481] [0.415] N 4670 4185 3861 3861 3861 3861 Adjusted R-square 0.996 0.998 0.998 0.998 0.998 0.998 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. 41 Table 4: Heterogeneity in Effect of Life Expectancy at Birth on Earnings Males Females I II III I II III Age 0.103*** 0.084*** 0.069*** 0.054*** [0.018] [0.018] [0.011] [0.007] Age-squared*(1/100) -0.10*** -0.10*** -0.10*** -0.10*** [0.000] [0.000] [0.000] [0.000] % Urban 1.252*** 0.947*** 0.892*** 0.907*** 0.933*** 0.949*** [0.475] [0.201] [0.154] [0.121] [0.130] [0.151] % Male Life expectancy at birth 0.011 0.010 0.012** 0.009** 0.007** 0.009*** [0.008] [0.007] [0.006] [0.004] [0.003] [0.003] Parents’ life expectancy 0.002 0.008* 0.001 0.004* [0.004] [0.004] [0.003] [0.002] % Married 0.472** 0.578*** 0.429*** 0.434*** [0.180] [0.144] [0.125] [0.074] Cohort size -12.837*** -12.065*** -9.243 -10.247 [0.643] [1.059] [7.188] [7.816] Birth-year Fixed Effects YES YES Constant 3.796*** 4.350*** 5.671*** 4.596*** 4.905*** 5.708*** [0.893] [0.980] [0.562] [0.370] [0.334] [0.324] N 4204 3878 3878 4149 3822 3822 Adjusted R-square 0.997 0.998 0.998 0.997 0.998 0.998 Urban Rural Age 0.096*** 0.083*** 0.069*** 0.054*** [0.012] [0.010] [0.013] [0.015] Age-squared*(1/100) -0.10*** -0.10*** -0.10*** -0.10*** [0.000] [0.000] [0.000] [0.000] % Urban % Male 0.495*** 0.377*** 0.103 0.193 0.124 0.074 [0.091] [0.074] [0.091] [0.140] [0.133] [0.147] Life expectancy at birth 0.012*** 0.011*** 0.010*** 0.002 0.003 0.007 [0.004] [0.003] [0.003] [0.008] [0.009] [0.007] Parents’ life expectancy 0.002 0.005 0.007 0.011** [0.002] [0.003] [0.006] [0.005] % Married 0.294*** 0.501*** 0.534** 0.592*** [0.089] [0.095] [0.237] [0.124] Cohort size -7.169* -5.264 -7.316*** -6.624*** [4.065] [3.542] [1.637] [2.369] Constant 4.337*** 4.653*** 6.396*** 5.706*** 5.380*** 5.988*** [0.543] [0.473] [0.336] [0.900] [1.086] [0.642] N 4200 3874 3874 3959 3657 3657 Adjusted R-square 0.998 0.999 0.998 0.996 0.996 0.996 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. 42 Table 5: Mincerian Earnings Functions and Returns to Schooling Pooled sample Males Females Urban Rural I II I II I II I II I II Age 0.081*** 0.072*** 0.088*** 0.077*** 0.069*** 0.054*** 0.087*** 0.081*** 0.073*** 0.049*** [0.007] [0.006] [0.008] [0.008] [0.005] [0.005] [0.007] [0.005] [0.009] [0.009] Age-squared -0.10*** -0.10*** -0.10*** -0.10*** -0.10*** -0.10*** -0. 10*** -0.10*** -0.10*** -0.000*** *(1/100) [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] Years of 0.121*** 0.094*** 0.137*** 0.106*** 0.093*** 0.073*** 0.102*** 0.095*** 0.096*** 0.088*** schooling [0.025] [0.013] [0.028] [0.020] [0.012] [0.008] [0.018] [0.010] [0.022] [0.024] %Urban 0.528*** 0.406** 0.604*** [0.172] [0.171] [0.093] %Male 0.363*** 0.392*** 0.244** [0.116] [0.099] [0.108] 159 % Married 0.329*** 0.308*** 0.341*** 0.172* 0.406** [0.110] [0.097] [0.127] [0.103] [0.182] Cohort size -5.78*** -7.35*** -6.91 -4.073* -4.967*** [1.208] [1.141] [6.369] [2.291] [1.486] Constant 4.291*** 4.243*** 4.135*** 4.416*** 4.665*** 4.748*** 4.302*** 4.352*** 4.746*** 5.110*** [0.337] [0.307] [0.373] [0.335] [0.211] [0.126] [0.343] [0.230] [0.348] [0.386] Survey Fixed YES YES YES YES YES YES YES YES YES YES Effect N 4670 4185 4690 4204 4622 4149 4687 4201 4446 3959 Adjusted R- 0.998 0.998 0.998 0.998 0.997 0.998 0.998 0.999 0.996 0.996 square Note: Standard errors in brackets. Significance levels: *p<0.05, ** p<0.01, ***p<0.001. 43 Table 6: Comparison of Returns to Schooling using Mincerian and Wald Estimators Pooled sample Males Females Urban Rural Panel a. Birth cohort data Mincerian earnings function 9.40%*** 10.60%*** 7.30%*** 9.50%*** 8.80%*** [std. error] [0.013] [0.020] [0.008] [0.010] [0.024] Wald estimate [std. error] 7.90%*** 9.90%*** 4.30%*** 10.21%*** 2.90% [0.018] [0.024] [0.011] [0.017] [0.026] Panel b. Individual-level data Mincerian earnings function 9.7%*** 8.9%*** 10.7%*** 8.6%*** 10.0%*** [std. error] [0.001] [0.001] [0.001] [0.001] [0.001] Wald estimate 11.2%*** 15.0%*** 7.8%*** 10.6%*** 10.1%*** [std. error] [0.004] [0.003 [0.003] [0.004] [0.004] Wald estimate using IV 12.02.%*** 17.2%*** 7.4%*** 13.8%*** 9.4%*** estimator [0.003] [0.004] [0.004] [0.004] [0.004] [std. error] Note: The Mincerian return to schooling estimates are taken from specification II for each group in Table 5 while the Wald estimates for pooled sample is derived by dividing the coefficients of life expectancy at birth from specification IV in Table 3 by the coefficient of life expectancy at birth in specification IV in Table 1. Similarly, for each gender and Rural-Urban group, the Wald estimates are obtained by dividing the life expectancy coefficients from specification II in Table 4 by life expectancy coefficients from specification IV in Table 2. Standard errors for Wald estimates are obtained by 500 bootstrap replications. 44 Table 7: Life Expectancy at Birth Effects on Schooling and Earning, Individual-Level Analysis Pooled Sample Males Females Rural Urban Schooling Earnings Schooling Earnings Schooling Earnings Schooling Earnings Schooling Earnings Urban -1.621*** -0.424*** -1.812*** -1.253*** -0.483*** -0.396*** [0.087] [0.017] [0.087] [0.074] [0.016] [0.017] Male/Female 0.247*** -0.366*** -0.358*** -0.355*** 0.0932* 0.287*** [0.032] [0.010] [0.012] [0.008] [0.041] [0.031] Life expectancy at 0.115*** 0.013*** 0.103*** 0.015*** 0.150*** 0.012*** 0.120*** 0.012*** 0.0996*** 0.011*** birth [0.008] [0.001] [0.008] [0.002] [0.011] [0.002] [0.009] [0.002] [0.007] [0.001] Parents’ life 0.0219*** 0.005*** 0.0270*** 0.008*** 0.008 0.002 0.0233** 0.006*** 0.0233*** 0.006*** expectancy [0.006] [0.001] [0.007] [0.002] [0.006] [0.001] [0.007] [0.002] [0.006] [0.001] Age 0.077*** 0.087*** 0.060*** 0.064*** 0.081*** [0.004] [0.005] [0.005] [0.003] [0.005] Age square*(1/100) -0.10*** -0.10*** -0.10*** -0.10*** -0.10*** [0.000] [0.000] [0.000] [0.000] [0.000] Marital status -0.107*** -0.245*** 0.024 -0.100*** -0.113*** [0.008] [0.008] [0.015] [0.008] [0.009] Cohort size -2.483*** -2.666*** -1.270*** -1.771*** -2.497*** [0.286] [0.357] [0.375] [0.335] [0.279] Constant 3.315*** 4.925*** 3.749*** 4.474*** 2.112* 4.979*** 1.297 5.062*** 4.242*** 4.838*** [0.645] [0.217] [0.640] [0.279] [0.835] [0.245] [0.796] [0.218] [0.569] [0.225] Birth-Year Fixed YES YES YES YES YES Effect Survey Fixed Effect YES YES YES YES YES YES YES YES YES YES N 2725213 2543741 1589055 1473199 1136158 1070542 872016 832947 1853197 1710794 Adjusted R-square 0.444 0.898 0.442 0.916 0.451 0.869 0.589 0.888 0.340 0.904 F-statistic 36.730 1371.40 39.200 1040.50 49.770 350.70 39.120 292.50 30.190 468.70 Note: Standard errors in brackets. Significance levels: *p<0.05, ** p<0.01, *** p<0.001. 45 Table 8: Instrumental Variables Estimation using Infant Mortality as an Instrument for Life Expectancy at Birth Pooled sample Male Female Urban Rural Stage 1 Stage 2 Stage 1 Stage 2 Stage 1 Stage 2 Stage 1 Stage 2 Stage 1 Stage 2 Panel a: Dependent Variable in Stage 1 is life expectancy at birth; in stage 2, years of completed schooling Death rate for -0.864*** -0.848*** -0.889*** -0.791*** -0.954*** under-5 children [0.106] [0.116] [0.088] [0.095] [0.113] Life expectancy at 0.146*** 0.138*** 0.176*** 0.128*** 0.152*** birth [0.028] [0.028] [0.036] [0.032] [0.029] Parents’ life -0.117*** 0.039*** -0.122*** 0.040** -0.110*** 0.034*** -0.079** 0.042*** -0.163*** 0.038** expectancy [0.037] [0.014] [0.037] [0.016] [0.038] [0.012] [0.037] [0.012] [0.046] [0.018] Urban 0.006 -1.520*** 0.011** -1.698*** -0.003 -1.186** [0.004] [0.580] [0.005] [0.583] [0.005] [0.489] Gender 0.009 0.278** 0.010* 0.316*** 0.008 0.14 [0.005] [0.117] [0.006] [0.091] [0.007] [0.214] First Stage F- 67.067 53.721 101.876 69.877 71.851 Statistic (Weak Identification Test) Panel b: Corresponding OLS Estimates (Life expectancy at birth is exogenous for individual schooling) Life expectancy at 0.113*** 0.103*** 0.141*** 0.090*** 0.124*** birth [0.02] [0.02] [0.04] [0.02] [0.03] Parents’ life 0.037** 0.036** 0.032** 0.042*** 0.031* expectancy [0.01] [0.02] [0.01] [0.01] [0.02] Panel c: Dependent Variable in Stage 1 is life expectancy at birth, in stage 2, it is log of wage Death rate for -0.818*** -0.807*** -0.835*** -0.752*** -0.900*** under-5 children [0.087] [0.092] [0.081] [0.072] [0.105] Life expectancy at 0.017*** 0.024*** 0.013*** 0.018*** 0.014** birth [0.005] [0.008] [0.004] [0.005] [0.007] Parents’ life -0.092** 0.007*** -0.099** 0.009*** -0.082* 0.003*** -0.06 0.007*** -0.130** 0.007* expectancy [0.046] [0.002] [0.048] [0.003] [0.043] [0.001] [0.040] [0.001] [0.062] [0.004] Urban 0.002 -0.361*** 0.006 -0.352*** -0.005 -0.352*** [0.003] [0.063] [0.004] [0.071] [0.006] [0.046] Individual age -0.077 0.074*** -0.094 0.085*** -0.056 0.055*** -0.062 0.079*** -0.098 0.061*** [0.088] [0.009] [0.100] [0.012] [0.072] [0.008] [0.091] [0.009] [0.099] [0.011] Individual age- -0.002* -0.001*** -0.002* -0.001*** -0.002** -0.001*** -0.002* -0.001*** -0.002* -0.001*** squared [0.001] [0.000] [0.001] [0.000] [0.001] [0.000] [0.001] [0.000] [0.001] [0.000] Gender 0.011 -0.415*** 0.011* -0.387*** 0.014 -0.476*** [0.007] [0.060] [0.006] [0.057] [0.012] [0.072] Married 0.035 0.123*** 0.044 0.258*** 0.031 -0.038 0.017 0.121*** 0.053 0.124*** [0.029] [0.014] [0.033] [0.050] [0.031] [0.028] [0.020] [0.012] [0.039] [0.022] Cohort size 11.325* -2.645*** 10.407** -2.894*** 13.286* -1.370** 8.9 -2.821*** 13.778* -1.833*** [5.824] [0.531] [5.076] [0.539] [7.778] [0.621] [5.476] [0.695] [7.399] [0.204] First Stage F- 95.603 83.083 114.28 108.877 73.451 Statistic (Weak Identification Test) Panel d: Corresponding OLS Estimates (Life expectancy at birth is exogenous for individual wage earnings) Life expectancy at 0.012*** 0.015*** 0.011*** 0.011*** 0.011** birth [0.00] [0.01] [0.00] [0.00] [0.00] Parents’ life 0.006*** 0.009*** 0.003*** 0.007*** 0.006* expectancy [0.00] [0.00] [0.00] [0.00] [0.00] Note: Standard errors reported in brackets are clustered at the country level. Significance levels: *p < 0.1, **p < 0.05, ***p < 0.01. All covariates are at the individual level except life expectancy at birth and infant mortality rate, which are birth-year level means. All of the specifications include country fixed effects and birth year fixed effects. Specifications under panel (b) & (d) are to facilitate comparison with estimates obtained from IV and reported in panels (a) and (c). 46 Table 9: Life Expectancy at Birth Effects on Lifetime Earnings with Correction for Selection including Cohort Size in Labor Force Pooled sample Males Females Rural Urban Life expectancy at birth 0.013*** 0.015*** 0.013*** 0.013*** 0.010*** [0.003] [0.004] [0.003] [0.004] [0.003] Age 0.077*** 0.090*** 0.060*** 0.062*** 0.083*** [0.011] [0.015] [0.009] [0.012] [0.012] Age-squared*(1/100) -0.10*** -0.10*** -0.10*** -0.10*** -0.10*** [0.000] [0.000] [0.000] [0.000] [0.000] Rural -0.367*** -0.360*** -0.357*** [0.066] [0.073] [0.050] Male 0.431*** 0.486*** 0.403*** [0.017] [0.016] [0.018] Marital status -0.103*** -0.240*** 0.076*** -0.114*** -0.096*** [0.021] [0.046] [0.029] [0.034] [0.019] Cohort size -2.564 -0.009 -1.548 -3.384 -1.228 [3.161] [4.284] [2.835] [4.292] [3.315] Parents’ life expectancy 0.005*** 0.008*** 0.002 0.006*** 0.006*** [0.002] [0.003] [0.001] [0.003] [0.002] Correction term for 0.202 -4.038 0.984 2.349 -1.619 selection [4.499] [6.217] [4.005] [6.324] [4.074] (Proportion of birth-year cohort in labor force) Constant 4.473*** 4.467*** 4.898*** 4.552*** 4.398*** [0.475] [0.698] [0.301] [0.593] [0.425] N 2478294 1434525 1043769 822189 1656105 Adjusted R-square 0.899 0.918 0.869 0.888 0.906 Note: Standard errors in brackets. Significance levels: *p<0.05, ** p<0.01, *** p<0.001. 47 Table 10: Life Expectancy at Birth Effects on Lifetime Earnings with Correction for Selection Due to Participation in Labor Force Pooled Sample Male Female Rural Urban Selection Earnings Selection Earnings Selection Earnings Selection Earnings Selection Earnings Equation Equation Equation Equation Equation Equation Equation Equation Equation Equation Household size -0.039*** 0.002 -0.075*** -0.022*** -0.056*** [0.001] [0.001] [0.001] [0.001] [0.001] Respondent is 0.787*** 0.862*** 0.538*** 0.721*** 0.810*** household head [0.003] [0.007] [0.004] [0.006] [0.004] Life expectancy at 0.003*** 0.014*** 0.002** 0.018*** 0.007*** 0.012*** -0.006*** 0.014*** 0.016*** 0.010*** birth [0.000] [0.004] [0.001] [0.007] [0.000] [0.003] [0.001] [0.005] [0.001] [0.003] Age 0.204*** 0.045*** 0.203*** 0.035*** 0.209*** -0.005 0.199*** 0.046*** 0.209*** 0.043*** [0.001] [0.005] [0.002] [0.009] [0.001] [0.016] [0.002] [0.006] [0.002] [0.006] Age-squared*(1/100) -0.3*** -0.0*** -0.3*** 0 -0.3*** 0 -0.3*** -0.0*** -0.3*** -0.0*** [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] [0.000] Rural 0.106*** -0.378*** -0.061*** -0.351*** 0.172*** -0.401*** [0.003] [0.062] [0.006] [0.076] [0.003] [0.037] Male 1.691*** 0.154*** 1.851*** 0.301*** 1.630*** 0.105** [0.003] [0.036] [0.006] [0.047] [0.004] [0.041] Marital status, never 0.070*** -0.116*** -0.914*** -0.026 0.558*** -0.122** -0.030*** -0.108*** 0.109*** -0.121*** married [0.004] [0.031] [0.007] [0.035] [0.005] [0.056] [0.007] [0.036] [0.005] [0.030] Cohort Size -2.286*** -2.471*** -0.666 -1.761*** -2.120** (Proportion of birth- [0.749] [0.839] [0.950] [0.273] [0.972] year cohort in labor force) Parents’ life 0.007*** 0.004** -0.001 0.008*** 0.010*** -0.001 0.012*** 0.005 -0.002*** 0.007*** expectancy [0.000] [0.002] [0.001] [0.003] [0.000] [0.001] [0.001] [0.003] [0.000] [0.002] Inverse Mills Ratio -0.742*** -1.575*** -1.077*** -0.443** -0.849** [0.278] [0.566] [0.390] [0.214] [0.325] Constant -3.420*** 5.356*** -0.742*** 5.262*** -4.003*** 6.872*** -3.137*** 5.034*** -3.747*** 5.497*** [0.038] [0.297] [0.084] [0.511] [0.045] [0.569] [0.058] [0.483] [0.050] [0.266] N 4453600 2478294 2149376 1434525 2304224 1043769 1831164 822189 2622436 1656105 Adjusted. R square 0.9 0.919 0.871 0.888 0.907 F-statistics 344.508 130.152 319.203 61.128 201.815 Note: Standard errors in brackets. Significance levels: *p<0.05, ** p<0.01, *** p<0.001. From the selection equation, we calculate the linear predicted probabilities, and then convert these into normal densities to calculate the inverse Mills ratio. The group-specific inverse-mills ratios are used in the earnings specifications, which is estimated only on those who are in the labor force, to correct for the selection. 48 49 Appendix A. Proofs of Propositions in Section III Proposition 1: The shadow value of human capital in terms of wealth, (), increases when life expectancy, T, increases. Proof: differentiation of equation (15) w.r.t. T yields () = �(+) �1 − (+)(−) �� =(+) �−( + )(− (+)(−) )� =�( (+)(−) )�. ( ) Since market rental rate of human capital > 0, = �( (+)(−) )� > 0. Proposition 2: If life expectancy at birth, T, increases, purchases of educational-investment goods, D(t), and effective time investment, I(t)H(t) would increase in every period of life. Proof: from equation (19)-(20), we note that price of D(t) is (), and price of I(t)H(t) is (). P and R are assumed to be constant over lifetime. Therefore, () determines the movement of () prices in the demand functions for investment goods. Proposition 1 shows that > 0. So, in response to a rise in T, prices of both D(t) and I(t)H(t) would decrease as well. Since both of these inputs are assumed normal, own price decrease would increase purchase of both inputs () ( )() ∀ ∈ [0, ] i.e., > 0 and > 0. We explicitly show the case for (). () = �() , ()� ∀ ∈ [0, ] () () () =− ∗ 1 ∗ − ∗ 2 ∗ [()]2 [()]2 () () = − �() ∗ 1 + () ∗ 2 � ∗ . () Strong concavity and twice differentiability of production function implies that () () () ∗ 1 + () ∗ 2 < 0, and from proposition 1, > 0. These together imply that > 0. Proposition 3: If life expectancy, T, increases, total human capital stock accumulated over lifetime increases as well. Proof: From equation 21, human capital stock at any time t is () = ∫0 (−) [ ()(), ()] + (0) − . [ ()] = �� (−) [ ()(), ()] + (0) − � 0 =∫0 (−) { [ ()(), ()]} + ((0) − ) ()() () =∫0 (−) �1 + 2 � . () ()() Proposition 2 demonstrates that > 0, and > 0. Again, [ ()(), ()] is increasing in both of its argument if () > 0. So, the term in braces inside the integral is ()() () positive, i.e., �1 + 2 � > 0. These together imply that [ ()] > 0. Since in response to a rise in life expectancy at birth, human capital increases ∀ ∈ [0, ], lifetime human capital stock, () = ∫0 � (−) [ ()(), ()] + (0) − �, will increase as well. Further, since lifetime accumulation of human capital increases, the value of the stock would change as well in response to a rise in life expectancy. Proposition 4 below explains this. Proposition 4: If life expectancy T increases, lifetime labor income increases. Proof: the present value of lifetime labor earnings, as stated in equation 23, is = (0)(0) + ∫0 − {() [ () (), ()] − () − ()} , where the term inside the integral is the time 0 present value of net profits from human capital accumulation as of time t. Differentiating w.r.t T yields = (0) �(+) �1 − (+)(−) �� + �∫0 − {() [ () (), ()] − () − ()} �. Applying the Leibniz Rule on the above yields = (0) �� (+)(−) �� + �∫0 − {() [ ()(), ()] − () − ()} � + − [()[ ()(), ()] − () − ()], ()() () = (0) �� (+)(−) �� + �∫0 − ��()1 + ()2 �+ () () () [ () (), ()] − − � �+ − [()[ ()(), ()] − () − ()]. From the first order conditions (9), we substitute ()1 = , and from (10), ()2 = into the above equation to yield 50 ()() () () = (0) �� (+)(−) �� + �∫0 − � + + [ ()(), ()] − () ()() − � �+ − [()[ ()(), ()] − () − ()], = (0) �� (+)(−) �� + () �∫0 − � [ ()(), ()] � �+ − [()[ ()(), ()] − () − ()]. In the RHS of the above equation, clearly the first term (0) �� (+)(−) �� > 0. Since () () > 0 from proposition 1, the middle term �∫0 − � [ () (), ()] � �>0. Finally, the last term − [()[ ()(), ()] − () − ()] is the present value of net profit from human capital investment in the last period T. Although, Heckman assumes that human capital investment might be taken even at a financial loss because of nonmarket benefit of education, in the current setting, condition 14 states that shadow value of human capital is 0 in the last period T. It implies that an individual at her last stage of life would not invest in human capital since she will not survive in periods after T to reap the benefits of the investment. Accordingly, in the last period T, () = 0, and, therefore, the last term is 0. It suggests that lifetime labor income from human capital investment is positive, i.e., > 0. Proposition 5: If T increases, marginal utility of lifetime wealth, (0), decreases. Proof: Since (0) is the marginal utility of wealth or shadow value of lifetime wealth as of period 0, and utility function follows concavity, it would decrease if lifetime wealth increases. Throughout the lifetime, wealth comes from two sources-labor income from exploiting human capital in the labor market and initial asset. Proposition 4 shows that lifetime labor income increases in response to gain in T. However, T does not affect initial endowment of assets (0). These together imply that an increase in T would increase lifetime wealth, which, in turn, suggests that (0) falls when life expectancy at birth increases. Proposition 6: If life expectancy T increases, consumption of leisure in human capital adjusted efficiency units, i.e., effective leisure () increases. However, measured hours of leisure,(), responds in an ambiguous manner. Proof: Since leisure is by assumption a normal good and an increase in life expectancy at birth (T) increases lifetime income, value of leisure should increase∀ ∈ [0, ] . From equation 17, ()() = �(0) (−) , (0) (−) �. 51 (0) Since proposition 5 shows that < 0, when T increases effective leisure becomes cheaper through reduced value for (0). It implies that in response to gain in T, for an individual value of leisure increases at all ages. However, the direction of change in consumption of leisure in natural units of time, (), is not quite clear. For exposition, note that effective leisure can be expressed as () = () − () [()] = [()] − [ ()], [()] (0) [()] = ∗ − . (0) [()] (0) Since leisure is a normal good, ∗ > 0, and in proposition 3, we have already shown (0) [()] [()] (0) that the second term > 0. Therefore, we cannot sign [()]. If ∗ > (0) [()] , () increases in response to a rise in T and vice versa. 52 Appendix B Table B1: List of Countries and Years of Surveys Country Survey Year Country Survey Year Afghanistan 2007 Latvia 2004, 2012 Albania 2003 Moldavia 2002, 2005 Argentina 2012 Maldives 1998, 2004 Austria 2004, 2012 Mexico 1989, 2012 Azerbaijan 1995 North Macedonia 2003, 2005 Belgium 2004, 2011 Malta 2009, 2012 Burkina Faso 1994, 2009 Mongolia 2002, 2011 Bulgaria 2003, 2012 Mozambique 2002 Bosnia-Herzegovina 2001, 2004 Mauritius 1999, 2012 Belarus 1998 Malawi 2004, 2010 Belize 1993, 1999 Namibia 1993 Bolivia 1992, 2012 Niger 1995, 2011 Brazil 1981, 2012 Nigeria 1993 Canada 1981, 2001 Nicaragua 1993, 2009 Switzerland 2011 Holland 2005, 2012 Chile 1987, 2011 Norway 2004, 2012 China 2002 Pakistan 2010 Cameroon 2001 Panama 1989, 2012 Colombia 2001, 2012 Peru 1997, 2012 Costa Rica 1989, 2009 Philippines 2003, 2011 Cyprus 2005, 2012 Poland 2005, 2012 Czech Republic 2005, 2012 Puerto Rico 1970, 2005 Germany 2005, 2012 Portugal 2004, 2012 Denmark 2004, 2012 Paraguay 1990, 2011 Dominican Republic 1996, 2011 Romania 1994, 2012 Ecuador 1994, 2012 Russian Federation 1994, 2009 Spain 2004, 2012 Senegal 2011 Estonia 2004, 2012 Solomon Islands 2005 Ethiopia 2005 Sierra Leone 2003, 2011 Finland 2004, 2012 El Salvador 1991, 2009 France 2004, 2012 Serbia 2008 Micronesia, Fed. States. 2000 São Tomé and Príncipe 2000, 2010 Gabon 2005 Surinam 1999 United Kingdom 2005, 2012 Slovak Republic 2003, 2012 Greece 2004, 2012 Slovenia 2005, 2012 Guatemala 2000, 2011 Sweden 2004, 2012 Guyana 1992 Eswatini 2000 Honduras 1991, 2011 Chad 2003 Croatia 2004, 2012 Togo 2006 Haiti 2001 Thailand 1990, 2009 Hungary 2004, 2012 Tajikistan 2003 Indonesia 1998, 2010 Turkmenistan 1998 India 1983, 2007 Timor-Leste 2001, 2007 Ireland 2004, 2009 Tunisia 2001 Iceland 2004, 2012 Turkey 2002 Italy 2004, 2012 Tanzania 2000 Jamaica 1990, 2002 Uganda 1992 Jordan 2002, 2010 Ukraine 2000, 2005 Kenya 2005 Uruguay 1989, 2012 Kyrgyzstan 1997 United States 1990, 2010 Cambodia 1997, 2008 Venezuela, RB 1989, 2006 53 Lao PDR 1997, 2008 Vietnam 2002, 2010 Lebanon 2011 West Bank and Gaza 1998, 2008 Sri Lanka 1993, 2009 Zaire 2005 Lithuania 2005, 2012 Zambia 1998, 2010 Luxembourg 2004, 2012 Note: Total of 188 surveys from 111countries spanning the years 1970-2012. Table B2: Return to Schooling from Mincerian Earnings Functions: Individual Level Analysis Pooled Males Females Rural Urban Sample Years of 0.097*** 0.089*** 0.107*** 0.086*** 0.100*** Schooling [0.001] [0.001] [0.001] [0.001] [0.001] Age 0.062*** 0.068*** 0.052*** 0.052*** 0.066*** [0.003] [0.004] [0.004] [0.003] [0.004] Age- squared -0.10*** -0.10*** -0.10*** -0.10*** -0.10*** *(1/100) [0.000] [0.000] [0.000] [0.000] [0.000] Urban residence -0.222*** -0.210*** -0.231*** [0.004] [0.006] [0.004] Male -0.450*** -0.493*** -0.427*** [0.014] [0.016] [0.015] Marital status -0.061*** -0.204*** 0.073*** -0.067*** -0.062*** [0.006] [0.006] [0.012] [0.007] [0.007] Cohort size -0.326 -0.417 0.083 -0.331 -0.348* [0.203] [0.260] [0.294] [0.274] [0.197] Constant 5.102*** 5.164*** 4.573*** 5.444*** 4.865*** [0.075] [0.096] [0.093] [0.059] [0.084] Survey Fixed YES YES YES YES YES Effect N 2572536 1491901 1080635 842749 1729787 Adjusted R- 0.912 0.928 0.888 0.901 0.919 square F 3299.304 2002.804 3300.83 1117.629 2029.129 Note: Standard errors in brackets. Significance levels: *p<0.05, ** p<0.01, *** p<0.00 54 Appendix C. Robustness Checks Table C1 reports the first set of robustness results for schooling. In general, estimates of life expectancy’s effect on schooling from all of the specifications for robustness show similar patterns as we observed: the coefficients of life expectancy at birth always turn out to be positive and statistically significant at less than the 1 percent level. The estimates lie in the range of 0.04- 0.111. Life expectancy’s effect on schooling is smaller in magnitude both in the un-weighted case, and when a young group sample is used. The estimates are similar in magnitude when we use only one survey per country (the latest possible survey), or we replace parents’ life expectancy by a 15-year lagged value of life expectancy at birth. Similar to previously reported estimates, if life expectancy at birth increases by one year, the birth-year cohort will spend 0.1 year more time in school. For lifetime earnings, Table C2 reports that the positive and statistically significant relationship between life expectancy at birth and earnings is robust across samples consisting only young-age group, controls through higher order age terms, alternative definition of parents’ life expectancy, and alternative assumption on cohort fixed effect. In contrast to that for schooling, we fail to notice any statistical significance for un-weighted regression and sample consisting only one survey per country. Incorporating higher order age terms in our specification, we obtain a 0.8% increase in income from an additional year of gain in life expectancy at birth, which is similar to what we observe in our main specification (specification IV in Table 3). Including cohort fixed effects by defining each cohort as a five-year birth range shrinks the life expectancy effect on lifetime earnings, as reported in column IV. Parents’ life expectancy constructed by taking a 15-year lag does not affect the life expectancy effect on earnings. Next, we restrict our sample on young working group by including only those who are in age group 25- 55 45. The coefficient of life expectancy at birth now shrinks further in magnitude (1.6% per year of added life expectancy) and still remain statistically significant. Although we do not report in Table C2, the coefficient of life expectancy at birth turns out to be positive and statistically significant if we alternatively define the young working group to be those in the age ranges of 25-50 or 25-40. Life expectancy at birth or something else? The literature finds that weather shocks impact well-being through multifaceted channels including reduced labor productivity, agricultural output shock, mortality due to disease outbreak, and political instability instigating civil war (Dell et al. 2014; Maccini and Yang 2009). As a control for other factors prevailing at the time of birth, we incorporate country-cohort specific average temperature and average precipitation. The weather attributes that prevailed at the time of birth appear to be exogenous. This robustness check will give us an indication of whether the positive and statistically significant positive association of life expectancy at birth with schooling and lifetime earnings is truly an exogenous impact of life expectancy at birth, or it is actually due to any cohort and country specific omitted or unobserved factors which influence both health and human capital. 27 The time series on country averages on yearly temperature and precipitation is compiled from CRU-CY data set, produced and maintained by Climate Research Unit at the University of East Anglia, UK. 28 The CRU-CY data set maintains information on monthly, seasonal or annual 27 For illustration, while one was in the womb, if there was a severe flood in his/her locality, which caused food scarcity and high infant mortality in that area, then any life expectancy effects we observe in our model would actually be the true effect of weather shocks. 28 The underlying data set behind the construction of the CRU-CY data set is the CRU TS data set. The construction is described as “The original data (CRU TS 3.21) took the form of a value for each month and each box on a 0.5 degree latitude/longitude grid. CRU assigned each box to a single country. For each country CRU calculated the weighted mean of the values from its constituent grid boxes for each month in turn. Each grid box was weighted by surface area, using the cosine of the latitude. The seasonal and annual values are the means of their constituent months. The CRU TS dataset prioritizes completeness, and has no missing data over land. Where observations are 56 spatial averages on 10 climate variables including temperature and precipitation. We utilize annual averages of these two variables- temperature and precipitation. The first two columns in Table C3 report the results from the earnings specifications with weather variables while the last two columns report those for years in school. The estimates show that the inclusion of birth-year-and-country specific weather variables do not alter the impact of life expectancy at birth on either schooling or lifetime earnings compared to what we observed above. Controlling for any possible weather shock at the time of birth, we observe that one additional year gain in life expectancy increases investment in schooling by 0.11 year and lifetime earnings by 0.8%. We do not observe any such independent effects of temperature and precipitation on either schooling or earnings in our complete specification. However, specifications excluding life expectancy variables in column II and IV reveal that any possible temperature shock at the time of birth is associated with lifetime earnings but not schooling, while high precipitation at the time of birth leads one to spend more time in school. Life expectancy at older ages Some recent papers question the appropriateness of use of life expectancy at birth emphasizing on concerns related to high infant and child mortality rate. We check the strength of our findings to life expectancy at ages beyond infancy by incorporating life expectancy at age five and ten in place of that at birth in our empirical analysis. However, since life expectancy at age 5 and 10 are not available before 1950 for most of the countries in our sample, we use a truncated sample of what we have used so far. Data on life expectancy at age 5 and 10 is available from world population prospects (2012) published by Population division, Department unavailable, the 1961-90 monthly climatic mean is used as a substitute. In data sparse regions of the world, this can lead to repeated values, and this can show up in derived products such as CRU CY.” 57 of Economic and Social Affairs, United Nations. 29 Note that these data are available at 5-year range, for example, those who were born between 1950 and 1955 in Brazil share the same life expectancy at five or ten. So, in this empirical exercise life expectancy at age five or ten varies by five-year-cohort within a country, whereas previously it varied by birth-year. Other variables would remain the same and will vary by birth-year. To consistently assign life expectancy measures at higher ages, for a birth-year cohort we assign a five-year forwarded value as measures of life expectancy at five, and ten-year forwarded value as measure of life expectancy at ten. The columns I-III in Table C4 reports the results for schooling while columns IV-VI for lifetime earnings. To facilitate a comparison of the coefficients of life expectancy at birth with life expectancy at five and ten, we also estimate one specification with life expectancy at birth. The impact of life expectancy at age five or ten on time spent in school is similar to what we observe for life expectancy at birth. An additional year of life expectancy at birth increases school-years by 0.11 year while an additional year of gain in life expectancy at age five and ten increases years in school respectively by 0.115 and 0.10 year. Overall, we observe estimates in similar magnitudes compared to our estimates in Tables 1 and 2. Similarly, the impact of life expectancy at higher ages, at five and ten, on lifetime earnings is positive and statistically significant in this truncated sample. An additional year of life expectancy gain at age five or ten increases lifetime earnings by 1.1% and 1.3%, which is close to the 0.9% effect that we have observed for life expectancy at birth. Various region, gender and age specific life expectancy data are available at http://esa.un.org/wpp/Excel- 29 Data/mortality.htm (last accessed on November 13th, 2014). 58 Table C5 reports the results from a replication of Table C4 with individual level data. 30 In this table, both for schooling and earnings, as we move from life expectancy at birth to higher ages, the coefficient of life expectancy at birth increases in magnitude. An additional year of gain in life expectancy at age 10 increases schooling by 0.129 years, which is 16% larger compared to the effect of life expectancy at birth. For earnings, the life expectancy at age 10 exhibits a 61% larger effect compared to similar effect from life expectancy at birth. One interesting finding from this robustness exercise is that parents’ life expectancy turns out to be positive and statistically significant in almost all the specifications with life expectancy at higher ages for both of schooling and earnings. It implies that parents with higher life expectancy are healthier, possibly more educated and richer and that these characteristics are transmitted to their children either through better health or more investments in children. To facilitate a comparison of the coefficients of life expectancy at birth with those for life expectancy at ages five 30 and ten, we also replicate Table C5 exclusively for the sample for which life expectancies at ages five and ten are available. The estimates from the balanced and unbalanced samples are close. 59 Table C1: Life Expectancy at Birth and Schooling- Robustness Check with Different Weighting, Surveys and Sample Groups I II III IV V No Single Survey Alternative Alternative Sample Weight (Oldest) Definition of Definition Consisting only Parents Life of Cohort Young Group Expectancy Fixed Effect (Age 25 to 50) % Urban 3.811*** 6.028*** 6.477*** 6.737*** 6.237*** [0.654] [1.415] [1.234] [1.057] [1.464] % Male 0.991* -1.336** -0.896* -0.858* -0.182 [0.526] [0.643] [0.476] [0.516] [0.483] Life expectancy at birth 0.039** 0.104*** 0.107*** 0.117*** 0.111*** [0.017] [0.023] [0.021] [0.026] [0.023] Parents’ life expectancy -0.008 -0.008 0.026** 0.031*** (lagged 25 years) [0.010] [0.009] [0.014] [0.010] Parents’ life expectancy 0.026*** (lagged 15 years) [0.010] Cohort Fixed Effects YES YES YES YES YES Constant 4.896*** 1.566 -1.064 -1.748 -1.681 [1.111] [1.841] [1.617] [2.256] [1.777] N 3861 3022 3977 3861 3090 Adjusted R-square 0.945 0.986 0.987 0.987 0.988 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. The Young Age group specific analysis is robust to age group 25-45 and 25-40. In column IV, instead of cohort level defined at five-year birth range, birth-year fixed effect is assumed. 60 61 Table C2: Life Expectancy at Birth and Earnings: Robustness Check with Different Weighting, Specification and Survey Selection I II III IV V VI No Weight Single Survey Higher Order Alternative Alternative Sample (Oldest) Age Variable Definition of Definition of Consisting only Cohort Fixed Parents Life Young Group Effect Expectancy (Age 25 to 45) Age 0.068*** 0.072*** -0.094 0.079*** 0.089*** [0.007] [0.012] [0.168] [0.014] [0.009] Age-squared -0.001*** -0.001*** 0.006 -0.001*** -0.001*** [0.000] [0.000] [0.006] [0.000] [0.000] % Urban 0.883*** 1.006*** 1.109*** 1.043*** 1.118*** 0.953*** [0.101] [0.206] [0.193] [0.221] [0.203] [0.166] % Male 0.480** -0.007 0.210* -0.11 0.210* 0.363** [0.186] [0.145] [0.121] [0.155] [0.111] [0.140] Life expectancy at birth 0.004 0.005 0.008* 0.005* 0.008* 0.016*** [0.003] [0.005] [0.005] [0.003] [0.004] [0.006] Parents’ life expectancy 0.00 -0.001 0.003 0.004 0.008** (lagged 25 years) [0.003] [0.003] [0.003] [0.003 [0.004] Parents’ life expectancy 0.005 176 (lagged 15 years) [0.004] % Married 0.249*** 0.491*** 0.491*** 0.779*** 0.446*** 0.305** [0.063] [0.169] [0.179] [0.200] [0.152] [0.138] Cohort size -5.843*** -10.320*** -8.636*** -7.792*** -8.684*** -7.948*** [2.105] [1.624] [1.513] [1.785] [1.352] [1.619] Age cubed 0 [0.000] Age^4 -0.094 [0.168] Constant 4.943*** 5.184*** 5.881*** 6.072*** 4.087*** 3.241*** [0.477] [0.565] [1.747] [0.316] [0.700] [0.712] Cohort Fixed Effect YES Survey Fixed Effect YES YES YES YES YES N 3861 3022 3861 3861 3977 2638 Adjusted R-square 0.995 0.998 0.998 0.998 0.998 0.999 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. Specification VI is robust to age group 25-40 and 25-50. In column IV, position in the life cycle is controlled by including cohort fixed effect while defining cohort at 5-year birth range. 62 Table C3: Life Expectancy at Birth, Earnings and Years in School: Robustness Check including Temperature and Precipitation Log Wage Years in School I II III IV Age 0.077*** 0.071*** [0.013] [0.011] Age-squared*100 -0.10*** -0.10*** [0.000] [0.000] % Urban 1.107*** 1.082*** 6.772*** 6.737*** [0.198] [0.207] [1.233] [1.355] % Male 0.212* 0.035 -0.981** -3.303*** [0.122] [0.166] [0.506] [1.223] Life expectancy at birth 0.008* 0.112*** [0.005] [0.023] Average precipitation at the -0.007 -0.01 0.028 0.071*** time of birth [0.005] [0.006] [0.036] [0.023] Average temperature at the 0.004 0.007** -0.003 0.006 time of birth [0.004] [0.003] [0.010] [0.012] Parents’ life expectancy 0.003 0.002 0.024** 0.013 [0.003] [0.003] [0.011] [0.012] % Married 0.477*** 0.549*** [0.156] [0.164] Cohort size -8.680*** -8.503*** [1.494] [1.616] Constant 4.256*** 5.133*** -1.624 6.885*** [0.623] [0.314] [1.605] [1.412] Cohort Fixed Effect YES YES YES YES Survey Fixed Effect YES YES YES YES N 3751 3751 3751 3751 Adjusted R-square 0.998 0.998 0.987 0.982 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. 62 63 Table C4: Life Expectancy, Schooling and Earnings: Robustness Check with Life Expectancy at Higher Ages Years in School Log of Earnings I II III IV V VI % Urban 6.715*** 5.633*** 5.777*** 1.112*** 0.834*** 0.902*** [1.220] [1.143] [1.323] [0.196] [0.146] [0.150] % Male -0.932* -1.136* -1.444* 0.206* 0.296*** 0.261** [0.495] [0.573] [0.756] [0.118] [0.098] [0.106] Life expectancy at birth 0.112*** 0.009* [0.023] [0.005] Life expectancy at age 5 0.115** 0.011*** [0.045] [0.004] Life expectancy at age 10 0.101** 0.013*** [0.044] [0.004] Parents’ life expectancy 0.023** 0.048*** 0.039** 0.003 0.007** 0.005* [0.011] [0.018] [0.018] [0.003] [0.003] [0.003] Age 0.077*** 0.085*** 0.082*** [0.013] [0.012] [0.013] Age squared -0.10*** -0.10*** -0.10*** [0.000] [0.000] [0.000] % Married 0.471*** 0.298*** 0.369*** [0.153] [0.103] [0.110] Cohort size -8.577*** -6.136*** -6.368*** [1.534] [1.719] [1.916] Cohort Fixed Effect YES YES YES Survey Fixed Effect YES YES YES YES YES YES Constant -1.198 -1.834 -0.091 4.206*** 3.856*** 3.814*** [1.736] [3.447] [3.117] [0.671] [0.610] [0.650] N 3861 3341 3546 3861 3341 3546 Adjusted R-square 0.987 0.984 0.984 0.998 0.999 0.999 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. Although not reported here, life expectancy at age 15 results in similar estimate for both of schooling and earnings as those of life expectancy at age 5 or 10. 63 64 Table C5: Life Expectancy, Schooling and Earnings: Robustness Check with Life Expectancy at Higher Ages using Individual-Level Data Years in School Log of Earnings I II III I II III Age 0.077*** 0.079*** 0.081*** [0.004] [0.006] [0.006] Age Square -0.001*** -0.001*** -0.001*** [0.000] [0.000] [0.000] % Urban -1.621*** -1.612*** -1.625*** -0.366*** -0.361*** -0.365*** [0.087] [0.209] [0.202] [0.010] [0.022] [0.022] % Male 0.247*** 0.329*** 0.296*** -0.424*** -0.387*** -0.402*** [0.032] [0.069] [0.068] [0.017] [0.037] [0.036] Life Expectancy at Birth 0.113*** 0.013*** [0.008] [0.001] Life Expectancy at Age 5 0.126*** 0.015*** [0.025] [0.003] Life Expectancy at Age 10 0.129*** 0.021*** [0.026] [0.003] Parent’s Life expectancy 0.020*** 0.048*** 0.041*** 0.005*** 0.008*** 0.007*** [0.007] [0.010] [0.010] [0.001] [0.002] [0.001] Marital Status -0.107*** -0.118*** -0.115*** [0.008] [0.018] [0.018] Cohort Size -2.483*** -1.729*** -1.770*** [0.286] [0.388] [0.379] Cohort Fixed Effect YES YES YES Survey Fixed Effect YES YES YES YES YES YES Constant 3.718*** 1.221 1.810 4.925*** 4.564*** 4.259*** [0.635] [1.775] [1.765] [0.217] [0.286] [0.279] N 2726329 2345389 2478221 2543741 2222008 2333455 Adjusted R-Square 0.444 0.418 0.427 0.898 0.903 0.901 101.021 25.791 35.514 1371.380 312.059 355.925 Note: Standard errors in brackets. Significance levels: * p<0.05, ** p<0.01, *** p<0.001. Although not reported here, life expectancy at age 15 results in similar estimate for both of schooling and earnings as those of life expectancy at age 5 or 10. 64