Disentangling the Contemporaneous and Life-Cycle Effects of Body Mass on Earnings

Transcription

1 Disentangling the Contemporaneous and Life-Cycle Effects of Body Mass on Earnings by Donna B. Gilleskie, Euna Han, and Edward C. Norton Donna B. Gilleskie Department of Economics University of North Carolina at Chapel Hill Euna Han School of Pharmacy Gachon Medical and Science University Edward C. Norton Department of Health Management and Policy Department of Economics University of Michigan December 2011 Very Preliminary Please do not quote We are grateful for the comments from seminar participants at Yale University, New York University, McGill University, Elon University, the Association for Health Econometrics Workshop (AHEW), and the Triangle Health Economics Workshop.

2 1 Introduction In this study we aim to assess the effect of body mass on earnings. It has been shown that the body mass of white females is negatively correlated with wages (Cawley, 2004). The evidence in the literature reflects the contemporaneous relationship between current body mass and current wages. Even in the cases where longitudinal observations on individuals have been available, the researchers have obtained their results treating the panel observations as repeated cross sections. In an effort to understand the effects on wages (and employment) of a determinant of productivity such as body mass that evolves over time, we argue that it is important to consider the effects of weight on decisions made jointly with employment over the life cycle. Using a long panel of observations on young adults as they approach middle age, we capture the influence of body mass on life-cycle decisions pertaining to schooling, employment, marital status, and family size. Admittedly, these behaviors may also impact the evolution of body mass over the life cycle. The history of these decisions, as well as one s body mass, define cumulative measures of human and health capital that often explain variation in observed wages. Having modeled the effect of body mass on the individual productive determinants of wages, contemporaneous body mass may still have a statistically significant effect on contemporaneous wages. This impact may capture wage penalties associated with lower productivity conditional on other observed measures of productivity (e.g., educational attainment, work experience, marital status, and family size). That is, despite modeling the effect of body mass on the previous life-cycle decisions that impact current employment and wages, the variables that summarize one s human capital may not fully capture productivity. Hence, current body mass may contribute to current productivity. Alternatively, a significant contemporaneous effect may reflect employer preference for employees with a particular outward appearance due to concerns about consumer distaste for obesity or high expected medical care expenditure affecting firm health insurance costs. We are not able to distinguish these two interpretations: individual productivity or employer preference. Ultimately, however, they both reflect the marginal product of the employee s work time. Our contribution, therefore, is that we are able to disentangle the effects of body mass on wages attributable to the impact of body mass on life-cycle human capital accumulation 1

3 and those reflecting additional current productivity. To disentangle these life-cycle and contemporaneous effects we propose to model employment and wages of individuals while jointly explaining the accumulation of education and work experience, marital and family size outcomes, and the evolution of body mass over time. We would like to know whether variations in individual characteristics (in particular body mass) significantly explain variation in wages. Observed wages of employed individuals reflect accepted wage offers only. Also, the human capital and productivity characteristics that determine pay for work reflect the life cycle choices of an individual. Hence, two potential sources of bias compromise evaluation of the role of these characteristics in explaining wages: the first is selection; the second is endogeneity. Labor economics informs us that we need to account for the decision to work in order to correctly understand which individual characteristics explain variations in observed wages. That is, individuals who chose to work for wages are a self-selected group of people: only those with wages above an individual reservation wage will choose to work. Reservation wages are determined by both observed and unobserved individual characteristics. For example, a college educated new mother may be quite capable of earning a good wage (i.e., based on her observed education and work experience, etc.), but, given her desire (i.e., an unobserved characteristic to an econometrician) to be at home with her new baby, the minimum wage at which she would enter employment is quite high. Another women with the same observed characteristics and a lower reservation wage might be observed to work. Estimation using the self-selected sample will result in biased coefficients on explanatory variables for wages if the selection into employment is not modeled jointly with the observed wages. In addition to selection, which produces a non-random group of people for whom wages are observed, many of the characteristics that explain variation in wages and employment are endogenous. These productivity characteristics include educational attainment, work experience, marital status, number of children, and, as we consider, body mass. Endogeneity suggests that observed characteristics that explain these (time-varying) decisions may also explain differences in wages of individuals who choose to work. In order to compute an unbiased effect of these individual characteristics on observed wages, we must account for any unobservables that influence them as well as wages. For example, someone with low 2

4 self-confidence may be more likely to be overweight and more likely to earn low wages. In addition to permanent individual unobservables such as self-confidence, we must account for time-varying unobservables that affect both body mass and employment or wages. An unobserved temporary negative health event may lead to weight gain as well as a reduction in observed wages if accumulation (or depreciation) of human capital is not fully measured. By accounting for such permanent and time-varying unobservables, we seek to uncover causation rather than spurious correlation. We use data from the National Longitudinal Survey of Youth (NLSY, 1979 cohort) and construct a research sample of individuals for whom we have annual observations from the ages of in 1983 through the ages of in These twenty years of data on individual decisionmaking and body mass evolution provide a quite comprehensive picture of life changes from young adulthood to middle age. While there has been much research focusing on the health of children, adolescents, the near elderly, and the elderly, relatively little research focuses on the health and productivity of prime age individuals who constitute the bulk of our nation s workforce. Because we model many individual decisions and outcomes (e.g., education, employment, marriage, children, wages, and body mass) that are potentially correlated through unobserved permanent and time-varying individual characteristics, we use an estimation framework that simultaneously explains variation in the multiple behaviors by variation in both observed and unobserved factors. We model the unobserved factors using a discrete random effects method that does not require us to make assumptions about the distribution of these unobservables. We also allow body mass to influence wages differently at different points of support of the wage distribution by modeling the density of wages without imposing a distributional assumption. Similarly, we allow determinants of body mass to have different effects at different points of the support of its distribution. We are able to estimate the conditional densities for wages and body mass jointly with endogenous behaviors that determine both wages and body mass, and hence allow modeled permanent and time-varying observables and unobservables to affect all outcomes. We extend the literature in several dimensions. First, we analyze the effects of body mass on wages using yearly observations on a cohort of individuals followed for twenty 3

5 consecutive years. This point of reference allows for a better understanding of both body mass and wage dynamics and provides a perspective that differs from (repeated) crosssectional analyses. We are able to quantify the effects of (and determinants of) body mass as an individual ages, and broaden the interpretation from one of aggregate time effects to individual behaviors. Second, we jointly model, along with the evolution of body mass and wages, several individual behaviors that may be affected by body mass and that also explain observed wage variation. Hence, we are able to decompose the correlation between body mass and wages reported in the literature into life-cycle effects captured through human capital variables and contemporaneous (direct) productivity influences. Third, we apply estimation techniques that go beyond traditional methods to better eliminate bias in both the observed and unobserved dimensions. After estimating unbiased effects of variables of interest, we are able to simulate the effects of changes in body mass during the late teens on later life outcomes. In particular, we direct our attention to understanding the life-cycle and contemporaneous effects of body mass on the productivity of employed individuals as measured by wages. Estimated with our research sample consisting of twenty years of annual observations on the same individuals, we have replicated the results in the literature using similar specifications and estimation techniques. That is, we find that current BMI has a statistically significant negative effect on the current wages of white women. We find a smaller, but statistically significant effect on the wages of black women in the most sparse specifications, but the significance of this effect falls with a richer specification. When take advantage of the longitudinal nature of the data, and estimate a model with fixed individual effects, the significant effect of BMI on wages of white women remains, but is much smaller. No effect exists for black women in a model that allows for permanent individual heterogeneity. To date we have also jointly estimated the set of 17 equations that allows for the selection into employment and the endogeneity of several determinants of wages. Calculation of the marginal effect of BMI on wages is more difficult in this model because of its contemporaneous and life-cycle effects. We intend to quantify those marginal effects through simulation using the estimated model. It also remains to verify a different effect of BMI at different levels of wages as is allowed with the conditional density estimation procedure. 4

6 2 Review of the Relevant Literature 2.1 Measured Associations between Body Mass and Wages An association between obesity and labor market outcomes, particularly wages, has been documented in the economic literature. The majority of these studies estimate a reducedform static model of the relationship between body mass and wages. A few exceptions explore the underlying mechanisms behind the relationship (Harper, 2000; Baum and Ford, 2004; Bhattacharya and Bundorf, 2004; Carpenter, 2006; Han, Norton, and Stearns, 2009; Han, Norton, and Powell, 2009). Harper (2000) shows a positive effect of being physically attractive on the probability of working in managerial or professional specialty and clerical occupations for women. However, physical attractiveness is not found to be associated with sorting into customer-oriented occupations and also no wage differences are found between non-attractive and attractive women in customer-oriented jobs in the same study. Baum and Ford (2004) examine four potential pathways linking obesity to labor market outcomes: less productivity due to health problems from obesity (measured by health limitations), less investment in human capital by obese workers (measured by work experience), employer distaste for obese employees due to high health care cost (measured by employer provision of health insurance), and consumer distaste for obese workers (measured by classification of occupation as customer-related). Bhattacharya and Bundorf (2004) report no statistically significant wage differential between obese and non-obese individuals by employer provided health insurance coverage. Carpenter (2006) shows that the employment rate increased 4% for obese women and 2% for obese men compared to their respective non-obese counterparts after a 1993 court case (Cook vs. Rhode Island) in which a federal appeals court ruled that obesity is covered under the Rehabilitation Act of 1973 and the Americans with Disabilities Act. Han, Norton, and Stearns (2009) also report larger negative relationships between adult contemporaneous body mass and wages in occupations requiring interpersonal skills. Han, Norton, and Powell (2009) examine the direct effect of body mass on wages and the indirect effects operating through education and occupation choice. They find that body weight in the upper tail of the distribution significantly affects educational and occupational outcomes of men and women, which in turn have significant effects on wages. The 11 percent adult 5

7 wage penalty of obesity during a woman s late teen years can be partly attributed to the effect of body mass on human capital accumulation. 2.2 Endogenous Body Mass Only a few of the studies attempt to address the potential endogeneity of body mass, typically measured by a body mass index (BMI) or an obesity indicator (Averett and Korenman, 1996; Pagan and Davila, 1997; Behrman and Rosenzweig, 2001; Cawley, 2004; Baum and Ford, 2004; Conley and Glauber, 2005; Norton and Han, 2008). Instrumental variable estimation techniques require a variable that is correlated with body mass in the current period but uncorrelated with wages in the current period. Instrumental variables (IVs) used in the previous literature include a lag of respondents own body weight or BMI (Averett and Korenman, 1996; Conley and Glauber, 2005), or siblings or children s BMI (Cawley, 2000; Cawley, 2004). The lag of current BMI is not a valid instrument if there is any serial or inter-temporal correlation in the wage residuals. Likewise, children s body weight is not a valid instrument if unobserved heterogeneity in the wage residual is associated with both children s body weight and the mother s employment behavior. Siblings BMI also is not a valid instrument if siblings share unobserved endowment factors that influence earnings. Norton and Han (2008) use genetic variation among young adults to identify their model (using multiple instruments). They find no statistically significant effect of adolescents BMI on wages in young adulthood. There are potential limitations of using own genetic information as IVs for own behavioral outcomes given that genes that predict body weight outcomes are related to brain chemistry and, thus, are likely to affect labor market outcomes such as wages via various channels. 2.3 Body Mass and Other Outcomes Regardless of the estimation techniques in the previous economic studies, most studies report gender differences in the association between obesity and wages. Only women consistently show a statistically significant negative association of BMI or obesity with hourly wages (Averett and Korenman 1996; Cawley 2004; Baum and Ford 2004; Conley and Glauber 2005; Han, Norton, and Stearns 2009). BMI is also associated with women s total household 6

8 income by affecting their spouses earnings and occupational prestige (Conley and Glauber, 2005). Some studies also report racial differences in the association between body mass and labor market outcomes for women. For example, Cawley (2004) reports that only white women s hourly wages are associated with their body mass. Some studies assess the association of obesity on labor market outcomes at the extensive margin by measuring its effect on the probability of employment or the different effect by different job sectors. Cawley (2000) finds no statistically significant effect of obesity on the amount of paid work and limitations on types of paid work. Morris (2007) estimates a negative relationship between obesity and the probability of employment for British people for both genders. Paraponaris and colleagues (2005) report that a one standard deviation increase of BMI from the mean at age 20 raises the percentage of time spent unemployed during the working years and lowers the probability of employment after a period of unemployment for both genders. Pagan and Davila s (1997) study reports that both obese men and women are less likely to sort into managerial, professional and technical occupations among fourteen Census occupation categories. There are also a few papers estimating the effect of obesity on educational achievement. Some studies report no effect of obesity on grade point average among adolescents (Crosnoe and Muller, 2004), scores on Peabody Individual Achievement Tests among pre-teen children (Kaestner and Grossman, 2009), and grade progression and drop out status (Kaestner, Grossman, and Yarnoff, 2009) among adolescents. In contrast, Sabia (2007) reports that white female adolescents have a grade point average penalty for being obese, whereas non-white female and male adolescents do not. However, Sabia (2007) uses parent-reported self-classification for obesity as an IV for adolescent BMI, which is not likely to be a valid IV if parents self-classification for obesity reflects the level of their self-esteem or time preference and will not be excluded from their children s educational achievement. 7

9 2.4 Measurement of Body Mass The body mass index is a simple means for classifying sedentary individuals by weight: underweight, ideal weight, overweight, and obese. 1 There are potential criticisms of using the body mass index, however, to make individual weight comparisons. The original proponents of this index stressed its advantageous use in making population comparisons. They warned against using it for individual health diagnosis. BMI, as a function of weight and height, does not allow one to distinguish between fat mass and fat-free mass (such as muscle and bone). It may overestimate adiposity on those with more lean body mass (e.g. athletes), while underestimating adiposity on those with less lean body mass (e.g. the elderly). To the extent that it is desirable to measure adiposity (or body weight) as it relates to productivity versus appearance multiple measures of overweight and obesity exist. Fat mass can be measured by percentage of body fat (using skinfold, underwater weighing, or fat-free mass techniques) or by measures that account for mass and volume location (waist and arm circumference and the body volume index). Johansson, et al. (2009) show that the measure of adiposity affects analysis of the obesity wage penalty. Burkhauser and Cawley (2008) find that obesity measured by BMI is only weakly correlated with obesity defined by other measures of fatness. Unfortunately, however, many data sets that contain information on employment and wages contain only measures of height and weight that can be used to construct the body mass index. Another concern is that the data on height and weight are often self-reported. These self-reports are likely to suffer from reporting error, subjectivity error, and rounding error. The current version of the paper does not use any of the available methods to correct for these potential measurement errors. 3 Description of the Research Sample The National Longitudinal Survey of Youth (NLSY) provides data on a 1979 cohort of individuals aged 17 to 21 followed annually through These individuals (and an additional cohort of adolescents that we do not include) continue to be followed every two 1 Specifially, BMI equals weights in kilograms divided by height in meters squared. A BMI less than or equal to 18.5 indicates underweight; between 18.5 and 25, normal weight; greater than or equal to 25 and less than 30, overweight; and 30 or greater, obese. 8

10 years since Our research sample includes those who have not attrited by 1983 and who have responses for important variables in our analysis. Because the literature on the relationship between body mass and wages has detected a wage effect that differs between black and whites, we restrict our analysis in this paper to these races. We drop 2921 sample eligible individuals who report an Asian race or Hispanic ethnicity (a mutually exclusive category in the NLSY data). From 1983, we follow 3213 females and 3244 males through 2002 or until they attrit from the NLSY survey. Table 1 displays the research sample size by year and the percent of individuals who attrit each year ,666 person-year observations. The research sample contains Since the evolution of body mass as individuals age is important in this study, we depict the trends in body mass over time in Figure 1. The body mass index (BMI) is an alternative measure of body fat based on height and weight and allows for evaluation of adult men and women on the same scale. Average body mass increases by age for both genders, with the mean increasing from 22.1 and 23.1 at age 20 to 27.4 and 27.7 at age 40, for women and men respectively. More importantly, the 75th percentile of the BMI distribution is increasing as is the body mass of people in the right tail of the distribution. 3 The NLSY data provide a unique understanding of individual body mass dynamics over time because the data follow the same individuals for such a long time (e.g., over 20 years in some cases) relative to most data sets. Figure 2 displays the weight gain of individuals through their 20s, 30s, and 40s relative to their weight at age 30. Those individuals who are overweight at age 30 are about 15 percent heavier than their age 20 weight, relative to those who were normal weight at age 30 (who are only 5 or 6 percent heavier than their weight at age 20). By age 40, normal age-30 weight individuals are about 11 percent heavier than 10 years earlier. Interestingly, overweight men at age 30 are about 10 percent heavier by age 40, while overweight women at age 30 have gained about 13 percent by the time they reach their 40s. 2 We restrict the initial 1983 sample to include individuals who are observed for at least two consecutive periods. Hence, attrition does not occur between 1983 and In fact, the 1983 data serve as initial conditions for the subsequent period of observation. Additionally, we have no need to model attrition at the end of 2002 since this is the last year of data that we use. 3 The vertical lines in Figure 1 indicate normal, overweight, and obese thresholds. The dark shaded regions indicate the interquartile range. The light shaded regions extend up to 1.5 times the interquartile range. Points on either side of the shaded areas represent remaining outliers. 9

11 Table 1 Empirical Distribution of Research Sample Females Males Year Sample Attriters Attrition Sample Attriters Attrition Size Rate Size Rate , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Number of person-year observations: 51,884 49,782 10

12 Female Male Age Body Mass Index 80 Figure 1: Distribution of Body Mass as Individuals Age, by Gender 11

13 Percent Weight Gain by Age and Gender (relative to weight at age 30) Male Normal Female Normal Male Over Female Over Age Figure 2: Weight Gain by Age and Gender (relative to age-30 weight) In addition to explaining the evolution of body mass, we attempt to explain an individual s wage profile (as he ages) as a function of his body mass. Wages increase with years of work experience for both males and females in full and part time positions. Clearly, if individuals gain weight as they age, but are also gaining work experience as they age, then if total work experience leads to higher wages, we will also see that those with larger body mass also have higher wages. Hence, we should depict full-time wages as total experience increases by body mass status. Doing so, we would observe that both overweight and obese females make lower wages than normal weight females as work experience increases. Obese males receive lower wages than either normal or overweight males. Yet, such a graph only shows how current wages differ by current body mass at different years of experience. In this paper we seek to understand how a person s entire history of body mass affects current wages through both human capital accumulation and current productivity. Since work experience influences wages, and work experience increases with age as does body mass, it is important to understand individual decisions to work. Hence, we model employment in full and part time positions in order to allow for both observed and unobserved differences in individuals that might be correlated with both employment behavior and body mass. Similarly, wages vary by educational attainment. If body mass affects years 12

14 of schooling and degree attainment, then school enrollment as one ages should be modeled. Table 2 displays the probabilities of these outcomes by age for women and men. To the extent that marital status affects employment behavior and body mass as individuals age, we account for endogenous changes in marriage. The number of children in one s household also affects employment decisions. We model both the probability of acquiring at least one child as one ages (which could reflect a birth or adoption or an increase in household size due to marriage) as well as the probability of losing a child (where a reduction may simply represent a change in household size due to marriage dissolution or a child leaving home). In addition to the effects children have on employment behavior, child bearing imposes physical changes in a woman s body mass that may not be temporary and children impose both time and financial requirements that may alter caloric intake and expenditure. Table 3 describes marriage and child accumulation probabilities by gender and age. 4 Empirical Framework Our empirical framework is motivated by a theoretical model of decisionmaking and health production over the lifecycle: per-period decisions regarding education, employment, marriage, and children, observed wages, and body mass transitions. The theory serves to formulate choice probabilities which we approximate as a function of information known at the beginning of each period of decisionmaking. The theory also describes how these lifecycle decisions affect the production of health (or evolution of body mass) over time. We then estimate the approximated demand and production equations jointly, and allow for both permanent and time-varying unobserved individual heterogeneity through the use of discrete factor random effects (Heckman and Singer, 1983 and Mroz, 1999). This empirical approach allows us 1.) to include several endogenous explanatory variables that provide a detailed description of the history of individual decisions, 2.) to consider the continuous evolution of body mass rather than discrete categories as several authors have done, and 3.) to explore the possibility that variables of interest may have different marginal effects at different points of support of the wage and body mass distributions (e.g., by using conditional 13

15 Table 2 Empirical Distribution of Enrollment and Employment by Age and Gender Enrolled Employed Full Time Part Time Age M F M F M F M F

16 Table 3 Empirical Distribution of Marriage and Household Size by Age and Gender Married No Change Acquire Lose in Size Child Child Age M F M F M F M F

17 density estimation (Gilleskie and Mroz, 2004)). We seek to confirm the causal pathways of body mass on wages of white women suggested by several authors in the literature and verify the apparent lack of correlation between body mass and wages of men and other races found by Cawley and others. We do so using data from the National Longitudinal Survey of Youth, which allows us to follow individuals over time from the age of 18 up to the age 45 in some cases. To account for endogenous histories that we observe at the beginning of the sample period, we jointly estimate these initial conditions with the multi-period main equations. We also model attrition from the research sample. We allow unobserved individual heterogeneity to explain each of these additional behaviors (i.e., initial conditions and attrition each period). 4.1 Timing and Notation In each year t after age 18, an individual obtains a wage offer drawn from the population distribution of wages. The individual also observes his or her spouse s wage if married. 4 Wages, w t, depend on education and employment experience, as described by Mincer (1974), as well as marital status (Korenman and Neumark, 1991), number of children, and body mass (Cawley, 2004) entering period t. Educational attainment and work experience are common measures of human capital that affect wages. We argue that these variables do not fully capture a person s productivity at work. This productivity, or effort, might be influenced by one s health or his time demands. Hence, we include body mass to capture unobserved health demands on effort. We recognize that body mass may also explain wage variation imposed by employers based on appearance. We include marital status and family size to capture unobserved time demands. We recognize that the effects of marital status and family size on productivity may be different for men and women. Each period the individual then jointly decides 1.) whether or not to attend school, 2.) whether to be non-employed, part-time employed, or full-time employed, 3.) whether or not to be married, and 4.) whether or not to acquire (or lose) a child (or children) living in the household. We let indicator variables define which alternatives are chosen. That is, 4 Spouse income is treated as exogenous. While we model the marriage decision, which may be influenced by body mass, we do not model the potential correlation between an individual s body mass and her spouse s income. 16

18 s t = 1 if the individual attends school in period t and s t = 0, otherwise. The employment indicator takes on the value e t = 0 if the individual does not work in period t, e t = 1 if he works part time (less than 1375 hours per year), and e t = 2 if he works full time (1375 hours or more per year). We indicate the marriage decision by m t = 1 if the individual is married in year t, and m t = 0, otherwise. The number of children in the household may increase or decrease due to pregnancy (singleton or multiples), marriage, divorce, age of child, or child mortality. 5 The variable k t = 0 indicates that no children are acquired in year t, and values of k t = 1 and k t = 1 indicate that at least one child is acquired or lost in year t. These yearly decisions (i.e., school attendance, employment, marriage, and children) produce stock variables upon entering period t that summarize the history of the decisions. The vectors of these history variables are denoted: educational history (S t ), work experience (E t ), marital history (M t ), and household child accumulation (K t ). These vectors include both duration values as well as indicators of behavior or outcomes in the last period (t 1) and polynomials of the continuous values. We allow body mass at the beginning of a period (B t ) to affect marital status (perhaps through marriage opportunities) and child accumulation (perhaps through health channels). It may also affect the wage distribution through unobserved determinants of wage such as productivity or appearance. Given the dynamic nature of body mass transitions and the possible influence of current body mass on future health and productivity expectations, current body mass may affect current schooling and employment decisions. Having made these beginning-of-period decisions (i.e., education, employment, marriage, and child accumulation) that affect the per-period budget and time constraints, individuals then allocate income and time to the daily activities of caloric intake and caloric expenditure (i.e., eating and exercising). These latter activities are not observed in our data, but the input decisions determine end-of-period body mass. Because the daily input decisions depend on the less frequent education, employment, marital, and child accumulation decisions, the body mass 5 A reason for a change in number of children is available in the data. For example, the survey records whether a child was born, died, adopted, etc. The number of children recorded from year to year reveals additions and losses of more than one child in a non-trivial number of cases. We are motivated, therefore, to model the change in number of children in the household rather than pregnancy. To the extent that children affect employment decisions and body mass transitions, we believe this could be due to both pregnancy as well as children acquired (or lost) through another channel (e.g., adoption, marriage, death). Both mechanisms place demands on time, finances, and energy. 17

19 transition is a function of those period t decisions and the resulting income (own wages and spouse s wages if married). Other information known at the beginning of year t includes individual exogenous characteristics (e.g., age, gender, race, spouse s income) denoted by the vector X t. The vector of individual information known at the beginning of period t is denoted Ω t = (B t, S t, E t, M t, K t, X t ). Variables that capture known county- or state-level price and supply conditions such as tuition, average wage and employment information, welfare amounts, restaurant sales, and costs of different food items are denoted by the vector P t. We denote with superscripts, for descriptive purposes only, the variables in P t that are related to particular behaviors by a unique subscript; that is, P t = (Pt s, Pt e, Pt m, Pt k, Pt b ). We recognize, however, that each of the jointly made decisions may be a function of own and cross prices. The timeline below depicts the observed and unobserved outcomes per period (e.g., one year), and the exogenous and endogenous information available at the beginning of each period. beginning of t unobserved wage draw s t, e t,m t, k t w t unobserved demand for caloric intake and caloric expenditure B t+1 beginning of t + 1 w t observed demand for schooling, employment, marriage, and family size observed wage if employed ci t, ce t observed body mass evolution P t and Ω t = (B t, S t, E t, M t, K t, X t ) P t+1 and Ω t+1 = (B t+1, S t+1, E t+1, M t+1, K 1t+1, X t+1 ) Variables that explain the observed outcomes are described in Tables 4 and 5 for females and males. The exogenous individual variables are summarized for the 6456 individuals in our research sample in The endogenous variables are summarized over all personobservations in the sample over the period. The exogenous price and supply-side variables vary by state or county and time, and are described in Table 6. 18

20 Table 4 Description of Exogenous Individual Explanatory Variables Female (N=3213) Male (N=3244) Variable name Mean Std Dev Mean Std Dev Time-invariant individual variables in year 1984 Black race AFQT score minus median by gender AFQT score missing Non-US citizenship at birth Non-US citizenship at age Mother is non-us citizen Father is non-us citizen Years of education of mother Mom s education missing Years of education of father Dad s education missing Time-varying individual variables over all person-years Age in years Rural residence Residence type missing Northeast region North central region West region State of residence missing

21 Table 5 Description of Endogenous Individual Explanatory Variables Female (N=3213) Male (N=3244) Variable name Mean Std Dev Mean Std Dev Endogenous individual variables over all person-years Body mass B t BMI in t Underweight: BMI in t Normal weight: 18.5 BMI in t < Overweight: 25 BMI in t < Obese: BMI in t Ever overweight prior to t Ever obese prior to t Weight in pounds at t Height in inches at t Education history S t Enrolled in t Years enrolled in school missing Years enrolled in school entering t Years enrolled < 12 entering t Years enrolled 12 entering t Years enrolled 16 entering t Freshmen year of college in t Employment history E t Employed in t Employed full time in t Employed part time in t Years employed entering t Years full time employed entering t Years part time employed entering t Marital history M t Married in t Years married entering t if married in t Years newly single entering t if single in t Child history K t Number of children entering t Acquire any children in t Lose any children in t

22 Table 6 Description of Exogenous Price and Supply-Side Variables Variable name Mean Std Dev Min Max Schooling variables Pt s Two year college semester tuition in 000s Four year college semester tuition in 000s Graduate school semester tuition in 000s Employment variables Pt e Unemployment rate Total employment per capita Ratio of manuf empl to total empl Ratio of service empl to total empl Total earnings per employee Ratio of manuf earnings to total earnings Ratio of service earnings to total earnings Marriage and Children variables Pt m and Pt k Total population in 000,000s Household income in 000s AFDC per month per family of four in 00s Consumption variables Pt b Indicator of missing price data Mean price of food Mean price of junk food Mean price of carton of cigarettes Mean price of 6-pack of beer Mean price of bottle of wine Mean price of liter of liquor Ratio of food sales to total retail sales Ratio of restaurant sales to total retail sales Note: Data presented are means over 50 states and the District of Columbia for the years Dollar amounts are in year 2000 dollars. 21

23 4.2 Demand Equations: Schooling, Employment, Marriage, Children Before specifying the wage equation, let us describe the probabilities of the observed outcomes from the joint schooling, employment, marriage, and children decisions. The error terms that capture the unobserved determinants of each equation e, u e t = ρ e µ+ω e ν t +ɛ e t, are decomposed into a permanent individual component (µ), a time-varying individual component (ν t ), and an idiosyncratic component (ɛ t ). Factor loadings (ρ and ω) in each equation (and for each outcome in each equation) indicate the relative importance of the associated type of heterogeneity for that equation or outcome. The serially-uncorrelated idiosyncratic terms (ɛ e t) are Extreme Value distributed each period, producing logit and multinomial logit probabilities of observed decision outcomes. The log odds ratio of being enrolled in school in period t (s t = 1) relative to not being in school (s t = 0) is ln [ ] p(st = 1) p(s t = 0) = γ 0 + γ 1 B t + γ 2 S t + γ 3 E t + γ 4 M t + γ 5 K t +γ 6 Pt s + γ 7 Pt e + γ 8 Pt m + γ 9 Pt k + γ 10 Pt b (1) +γ 11 X t + ρ 1 µ + ω 1 ν t The log odds ratio of being non-employed (e t = 0) or employed part-time (e t = 1) relative to being employed full-time (e t = 2) in period t is ln [ ] p(et = d) p(e t = 2) = δ 0d + δ 1d B t + δ 2d S t + δ 3d E t + δ 4d M t + δ 5d K t +δ 6d Pt s + δ 7d Pt e + δ 8d Pt m + δ 9d Pt k + δ 10d Pt b (2) +δ 11d X t + ρ 2 dµ + ω 2 dν t d = 0, 1 The log odds ratio of being married in period t (m t (m t = 0) is ln [ ] p(mt = 1) p(m t = 0) = 1) relative to not being married = α 0 + α 1 B t + α 2 S t + α 3 E t + α 4 M t + α 5 K t +α 6 Pt s + α 7 Pt e + α 8 Pt m + α 9 Pt k + α 10 Pt b (3) +α 11 X t + ρ 3 µ + ω 3 ν t 22

24 The log odds ratio of acquiring at least j children in period t (k t = j) relative to none (k t = 0) is ln [ ] p(kt = j) p(k t = 0) = β 0j + β 1j B t + β 2j S t + β 3j E t + β 4j M t + β 5j K t +β 6j Pt s + β 7j Pt e + β 8j Pt m + β 9j Pt k + β 10j Pt b (4) +β 11j X t + ρ 4 jµ + ω 4 j ν t j = 1, 1 Note that these four probabilities are functions of the same explanatory variables since the decisions that produce the outcomes are jointly made. Additionally, because the schooling, employment, marriage, and child accumulation decisions (s t, e t, m t and k t ) are made jointly at the beginning of the period, all the variables representing supply side conditions (Pt s, Pt e, Pt m, Pt k ) appear in each of Equations 1-4 in order to capture own- and cross-price effects. Similarly, individuals are forward looking and anticipate making optimal decisions about caloric intake and expenditure throughout the year. Hence, the vector P b t affects each of those per-period decisions. The equations are also correlated through both the permanent unobserved individual heterogeniety (µ) and the time-varying unobserved individual heterogeneity (ν t ), which enter each equation with different effects. 4.3 Wage Equation conditional on Employment Conditional on an individual s employment outcome in period t, we (the econometrician) observe his accepted wage. According to Mincer s seminal work, wages are a function of education and work experience. Wages are also a function of productivity. Productivity is generally not observed, and certainly difficult to measure. But productivity is affected by time and financial demands, which are influenced by marital status and children in the household. We include the latter as potential explanations of wage variation. Productivity may also be influenced by one s physical health. Body mass is one indicator of physical health and we include it as a possible determinant of wages. Significance of body mass in explaining wages may also capture preferences by employers. For these reasons our period t wage equation includes variables summarizing the history of education, employment, marriage, and children as well as body mass entering the current period. We also include characteristics of 23

25 the demand-side of the employment market at the state level (denoted P e t ), aggregate trends (denoted by a cubic in a linear year indicator), and regional year interactions to pick up variation in skill prices over locations and time. 6 In order to detail the determinants of the wage equation, we present the dependent variable in log wages conditional on being employed as is typical in the labor literature. That is, observed log wages in period t, conditional on being employed in period t, are specified as where ɛ w t ln(w t e t 0) = η 0 + η 1 B t + η 2 S t + η 3 E t + η 4 1[e t = 1] + η 5 M t + η 6 K t + η 7 X t + η 8 P e t + ρ 5 µ + ω 5 ν t + ɛ w t (5) is a serially-uncorrelated error term. Rather than estimate the determinants of wages using OLS on log wages, we estimate the entire density of wages conditional on explanatory variables. We discuss the estimation procedure we employ after introducing the specification of the body mass production equation below. We observe wages of those individuals who are employed in period t. However, in the NLSY data, wages are missing for some employed individuals. In a typical year, about 6 percent of wages are missing. We include an equation to represent any non-randomness in missing wages. In 1995, 1997, 1999, and 2001, however, wages are missing for all individuals in the sample because they were not surveyed that year. We are able to construct values for other variables during these non-surveyed years given the nature of the information. For example, while we do not observe whether someone was married in 1995, we do observe their marital status in 1994 and We make assumptions during years of missing data for only a small number of observations. If an assumption would be too much of a stretch we delete that individual from our research sample. 4.4 Body Mass Production Equation Weight and height are observed in most years with the exception of 1983, 1984, 1991, and the non-survey years of 1995, 1997, 1999, and We linearly interpolate or extrapolate values of weight in years that we do not observe weight. We assume that height is the same across all years an individual is observed. Hence, we can construct values of the body mass 6 We include a cubic of the year variable in all equations modeled over the twenty year period. 24

26 index for all individuals in our research sample. follow a Markov process such that We assume that body mass transitions B t+1 = φ 0 + φ 1 B t + φ 2 S t+1 + φ 3 E t+1 + φ 4 M t+1 + φ 5 K t+1 +φ 6 P b t + φ 7 X t + ρ 6 µ + ω 6 ν t + ɛ b t. (6) The body mass transition at the end of the period is a function of the observed endogenous decisions during the period, reflected by the vector of updated (t + 1) history variables. Conditional on the observed behavior during period t, only the supply-side variables that affect body mass inputs (P b t ) affect the body mass transition at the end of period t. Note that the unobserved permanent and time-varying individual heterogeneity that affects the schooling, employment, marriage, and child accumulation decisions also influences wages in period t and body mass at the end of period t. 4.5 Attrition and Initial Condition Equations In order to correctly estimate the distribution of permanent and time-varying heterogeneity, we must account for the fact that individuals attrit from our research sample over time. We include, in the jointly estimated set of equations, an equation for the probability of attrition at the end of the period. This probability depends on updated history variables reflecting the period t decisions and the unobserved heterogeneity. This dynamic specification and the fact that our analysis begins in 1983 when some of the endogenous variables are non-zero implies that we need to jointly model several initial conditions. The endogenous state variables entering the first period (1984) include: initial years schooling (cts: 7-16), initial marital state (logit: 0,1), initial years married if married (cts: 1-4), initial years single if single (cts: 1-4), initial number of children (cts: 0-7), initial employment state (mlogit: ft, pt, not emp), initial full time experience (cts: 0-5), initial part time experience (cts: 0-5), and initial BMI (cts). For identification we need to include variables in the reduced form equations that explain these initial outcomes that do not influence the subsequent per-period outcomes (conditional on the endogenous history variables). We also allow the permanent unobserved individual heterogeneity to explain these initial conditions. 25