Disentangling the Contemporaneous and Life-Cycle Effects of Body Mass on Earnings Donna B. Gilleskie, Univ of North Carolina Euna Han, Gachon Univ of Medicine and Science Edward C. Norton, Univ of Michigan July 11, 2011 International Health Economics Association

Description of Average Body Mass by Age (using repeated cross sections from NHIS data) Source: DiNardo, Garlick, Stange (2010 working paper) overweight normal weight 2

Trends in Body Mass over Time

1999 Obesity Trends* across Time and the US States BRFSS, 1990, 1999, 2008 (*BMI 30, or about 30 lbs. overweight for 5’4” person) No Data <10% 10%–14% 15%–19% 20%–24% 25%–29% ≥30%

What exactly is this Body Mass Index? Calories in < Calories out Calories in > Calories out Caloric Intake: food and drink Caloric Output: requirement to sustain life and exercise

Pros and Cons of the Body Mass Index Body mass is captured by the commonly used index: BMI A function of weight & height; independent of age & gender (among adults) Commonly used diagnostic tool to identify weight problems (original proponents stressed its use in population studies and considered it inappropriate for individual diagnosis) A simple means for classifying (sedentary) individuals ̵BMI < 18.5:underweight ̵18.5 to 25:ideal weight ̵25 to 30:overweight ̵BMI 30+:obese Self-reported weight (subjective measure, rounding issues)

But, a single index of body weight may not be sufficient. Does this mean the measure is not a good one? ̵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) Does this mean we need multiple measures of “fatness”? ̵percentage of body fat (skinfold, underwater weighing, fat-free mass index) ̵account for mass and volume location (body volume index) Does this mean we need to clarify what we intend to capture? ̵the big picture: health and productivity ̵but we have a measure of body mass only (in these data) ̵does it adequately capture the productive effects of health? ̵might it merely capture physical appearance (positive and negative)? Pros and Cons of the Body Mass Index

What do we already know about Body Mass and Wages? Evidence in the economic literature that wages of white women are negatively correlated with BMI. Evidence that wages of white men, white women, and black women are negatively correlated with body fat (and positively correlated with fat-free mass). 8

Reasons for Hesitation… Cross sectional data: we don’t want a snapshot of what’s going on, but rather we want to follow the same individuals over time. Exogenous body mass: to the extent that individual permanent unobserved characteristics as well as time-varying ones influence both BMI and wages, we want to measure unbiased effects. Exogenous confounders: BMI might affect other variables that also impact wages; hence we want to model all avenues through which BMI might explain differences in wages. 9

Year 1984Year 1999 Mean BMI 75% percentile Females Males Body Mass Index Distribution of same individuals in 1984 and 1999 Source: NLSY79 % obese: 6.7 (1984) ; 30.2 (1999) % obese: 5.4 (1984) ; 25.6 (1999)

Year 1984Year 1999 Mean BMI 75% percentile White n = 1341 Black n = 873 Body Mass Index Distribution of same females in 1984 and 1999 % obese: 3.9 (1984) ; 21.2 (1999) % obese: 11.2 (1984) ; 43.4 (1999) Source: NLSY79

The Big Picture Schooling Observed Wages t Body Mass t Employment Body Mass t+1 SchoolingEmploymentMarriageChildren History t of: Current decisions t regarding: t-1t t+1 Marriage Children Contemporaneous Life-Cycle CaloriesIn t CaloriesOut t Info known entering period t 12

Individual’s optimization problem consumption Let indicate the schooling (s), employment (e), marriage (m), and kids (k) alternative in period t leisure kids & marriage preference shiftersinfo entering period t future uncertain body mass, wages, and preference shocks

Individual’s optimization problem Let indicate the schooling (s), employment (e), marriage (m), and kids (k) alternative in period t non-earned income tuitionchild-rearing costs optimal caloric intake optimal caloric expenditure time workingtime in schooltime with family earned income

Individual’s optimization problem Let indicate the schooling (s), employment (e), marriage (m), and kids (k) alternative in period t body mass production function wage function

Model of individual behavior as she ages w*tw*t s t, e t, m t, k t B t+1 beginning of age t beginning of age t+1 draw from wage distribution schooling, employment, marriage, and child accumulation decisions evolution of body mass 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 t+1, X t+1 ) c i t, c o t calories in, calories out dtdt ctct d t = d(Ω t, P d t, P c t ) + e d t c t = c(Ω t, d t, w t, P c t ) + e c t B t+1 = b(B t, c i t, c o t ) + e b t w t | e t = w(Ω t ) + e w t more frequent shocks unobs’d biol. changes = b ’ (Ω t, d t, w t, P c t ) + e b t

Panel data: – Estimated using 20 years of data on the same individuals Jointly estimated multiple equation dynamic model: – Allows BMI to affect wages contemporaneously, but also incorporates the dynamic effects of BMI through other endogenous pathways (e.g., education, employment, marriage, and children) Discrete Factor Random Effects: – Captures correlation across equations explicitly with both permanent individual unobservables as well as time-varying individual unobservables Conditional Density Estimation: – Estimates a distribution-free density (of wages and BMI) conditional on endogenous variables that may have different effects at different levels of the dependent variable Features of our empirical model

Description of the research sample: National Longitudinal Survey of Youth (NLSY) 18

Information entering period t (endogenous state variables) 19

Exogenous variables X t : race, AFQT score, non-earned income, spouse income if married, ubanicity, region, and time trend Information entering period t (endogenous state variables) 20

Exogenous price and supply side variables 21

Exogenous price and supply side variables 22

Exogenous price and supply side variables 23

Decision/OutcomeEstimator Explanatory Variables EndogenousExogenousUnobs’d Het Initially observed state variables 2 logit 7 ols X 1, P 1, Z 1 iμiμ EnrolledlogitB t, S t, E t, M t, K t X t, P s t, P e t, P m t, P k t, P b t  s μ,  s  t EmployedmlogitB t, S t, E t, M t, K t X t, P s t, P e t, P m t, P k t, P b t  e μ,  e  t MarriedlogitB t, S t, E t, M t, K t X t, P s t, P e t, P m t, P k t, P b t  m μ,  m  t Change in kidsmlogitB t, S t, E t, M t, K t X t, P s t, P e t, P m t, P k t, P b t  k μ,  k  t Wage not obs’dlogitB t, S t, E t, M t, K t XtXt  n μ,  n  t Wage if emp’d & obs’d CDEB t, S t, E t, M t, K t X t, P e t  w μ,  w  t Body MassCDEB t, S t+1, E t+1, M t+1, K t+1, w t X t, P b t  b μ,  b  t AttritionlogitB t+1, S t+1, E t+1, M t+1, K t+1 XtXt  a μ,  a  t stst etet mtmt ktkt wtwt B t+1 a t+1 24

VariableModel 1Model 2Model 3Model 4 BMI t (0.002) *** (0.002) *** (0.002) ***) (0.002) BMI t ≤ (0.024) ** (0.019) (0.019) (0.014) *** 25 ≤ BMI t < (0.013) * (0.012) (0.012) (0.009) BMI t ≥ (0.025) ** (0.021) (0.021) (0.015) BMI t x Black0.006 (0.002) *** (0.002) ** (0.002) * (0.003) BMI t x Hisp0.002 (0.003) (0.003) (0.003) (0.003) BMI t x Asian0.001 (0.005) (0.004) (0.004) (0.006) Model Includes: X t, B t X t, B t, S t, E t, M t, K t X t, B t, S t, E t, M t, K t, P e t X t, B t, S t, E t, M t, K t,P e t, fixed effects Marginal Effect of a 5% drop in BMI White: Black: Preliminary Results: ln(wages) of females 25

Variable25 th percentile 50 th percentile 75 th percentile BMI t (0.012) *** (0.010) *** (0.015) *** BMI t ≤ (0.083) *** (0.082) *** (0.124) *** 25 ≤ BMI t < (0.085) ** (0.083) (0.109) BMI t ≥ (0.126) *** (0.110) ** (0.170) BMI t x Black0.035 (0.008) *** (0.009) *** (0.013) *** BMI t x Hisp0.021 (0.011) ** (0.010) (0.018) BMI t x Asian (0.023) (0.022) (0.024) Model Includes: X t, B t, S t, E t, M t, K t, P e t Marginal Effect of a 5% drop in BMI White: Black: Preliminary Results – quantile regression and CDE CDE Results: White: Black: 0.057

No updating: simply compute the effect of a change in BMI given the values of one’s observed RHS variables entering the period. Hence, this calculation provides only the (unbiasesd) contemporaneous effect of BMI on wages. We find that a 5% decrease in BMI leads to $0.020 increase in wages for white women and $0.015 decrease for black women. Also, more likely to be enrolled, full time employed; less likely to be married or have a child. Preliminary Results: jointly estimated model with heterogeneity and CDE on wages and BMI 27

Initial Conclusions Using 20+ years of data on the same individuals, our replications -- of models that treat BMI as exogenous -- and that use cross section or repeated cross section data confirm a negative correlation between BMI and wages of white women. 28

Examination of alternative models -- that allow BMI to have a different effect at different levels of wages (quantile regression and conditional density estimation) suggest that the BMI penalty is larger at higher wages. Initial Conclusions 29

Examination of alternative models -- that allow for permanent unobserved heterogeneity (fixed effect) -- that allow for permanent & time-varying unobserved heterogeneity (discrete factor random effects) suggest that controlling for endogeneity of BMI (and potentially other endogenous explanatory variables) erases the observed contemporaneous wage penalty. Initial Conclusions 30

Specification of BMI (more moments, interactions) Selection into employment Endogenous BMI Endogenous state variables (related to history of schooling, employment, marriage, and children) Random effects vs fixed effects Permanent and time-varying heterogeneity Modeling of effect of BMI on density of wages Sources of differences from preliminary models 31

Evidence of a Life-Cycle Effect? Unobservables that influence BMI also affect wages and the variables that determine wages (and therefore must be accounted for). BMI has a significant effect on wages through particular endogenous channels: schooling, work experience, marital status, and children. Conditional density estimation results suggest that it is important to model the effect of BMI across the distribution of wages, not just the mean. (And it may also be important to model the different effects of past decisions across the distribution of current BMI.) 32