Disentangling the Contemporaneous and Life-Cycle Effects of Body Mass Dynamics on Earnings Donna B. Gilleskie, Univ of North Carolina Euna Han, Univ of Illinois at Chicago Edward C. Norton, Univ of Michigan March 2011 Econ 850

Body Mass of Females as we Age (same individuals followed over time) Body Mass Index Age

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

Empirical Distribution of the Body Mass Index The distribution of BMI (among the US adult female population) is changing over time. The mean and median have increased significantly. The right tail has thickened (larger percent obese). Source: DiNardo, Garlick, Stange (2010 working paper)

Trends in Body Mass over time

1999 Obesity Trends* Among U.S. Adults 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%

Body Mass Index Calories in < Calories out Calories in > Calories out Caloric Intake: food and drink Caloric Expenditure: requirement to sustain life and exercise

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).

Potential Problems… 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. Endogenous 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. 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.

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 Contempor- aneous Life-Cycle Intake t Exercise t Info known entering period t

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 behavior of individuals as they age 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 Ω t = (B t, S t, E t, M t, K t, X t, P t ) Ω t+1 = (B t+1, S t+1, E t+1, M t+1, K t+1, X t+1, P t+1 ) c i t, c o t caloric intake, caloric output 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

Data: National Longitudinal Survey of Youth (NLSY)

Information entering period t (endogenous state variables)

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)

Exogenous price and supply side variables

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  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  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  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  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’dCDEB 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 X t, P b  b μ,  b  t AttritionlogitB t+1, S t+1, E t+1, M t+1, K t+1 XtXt  a μ,  a  t

What do hourly wages look like among the employed?

… and ln(wages)?

Empirical Model of Wages ln(w t ) | e t ≠ 0 = η 0 + η 1 S t + ρ w μ + ω w ν t + ε w t + η 2 E t + η 3 1[e t = 1 (pt) ] + η 4 B t + η 5 M t + η 6 K t + η 7 X t + η 8 P e t + η 9 t Schooling (entering t) work experience and part time indicator productivity exogenous determinants and changes in skill prices unobserved permanent and time varying heterogeneity

Unobserved Heterogeneity Specification Permanent: rate of time preference, genetics Time-varying: unmodeled stressors u e t = ρ e μ + ω e ν t + ε e t where u e t is the unobserved component for equation e decomposed into permanent heterogeneity factor μ with factor loading ρ e time-varying heterogeneity factor ν t with factor loading ω e iid component ε e t distributed N(0,σ 2 e ) for continuous equations and Extreme Value for dichotomous/polychotomous outcomes

Individual’s optimal decisions about schooling, employment, marriage, and child accumulation

School

Body Mass Transition B t+1 = η 0 + η 1 B t + ρ b μ + ω b ν t + ε b t + η 2 S t+1 + η 4 E t+1 + η 5 M t+1 + η 6 K t+1 + η 7 X t + η 8 P b t Under Normal Over Obese Female Male body mass production function

What does the distribution of body mass look like? Females Mean = St.Dev. = 5.95

What does body mass look like as we age? under normal over obese

What does body mass look like as we age?

How should we estimate wages? OLS: quantifies how variation in rhs variables explain variation in the lhs variable, on average. It explains how the mean W varies with Z. In estimation, we also recover the variance of W. The mean and variance of W define the distribution of wages (under the assumption of a normal density).

So, using OLS, we can obtain the marginal effect of Z on W, on average. But what if Z has a different effect on W at different values of W? Might BMI have one effect on wages at low levels of the wage and a different effect on wages at higher levels of the wage? How can we capture that? How should we estimate wages?

Might there be a more flexible way of modeling the density that allows for different effects of covariates Z at different points of support of W? ?

Conditional Density Estimation Determine cut points such that 1/K th of individuals are in each cell. Let Replicate each observation K times and create an indicator of which cell an individual’s wage falls into. Interact Z’s with α’s fully. Estimate a logit equation (or hazard), λ(k,Z). Then, the probability of being in the k th cell, conditional on not being in a previous cell, is Define a cell indicator

VariableModel 1 BMI t (0.002) *** BMI t ≤ (0.024) ** 25 ≤ BMI t < (0.013) * BMI t ≥ (0.025) ** BMI t x Black0.006 (0.002) *** BMI t x Hisp0.002 (0.003) BMI t x Asian0.001 (0.005) Model Includes: X t, B t Marginal Effect of 5% Preliminary Results: ln(wages) of females

VariableModel 1Model 2 BMI t (0.002) *** (0.002) *** BMI t ≤ (0.024) ** (0.019) 25 ≤ BMI t < (0.013) * (0.012) BMI t ≥ (0.025) ** (0.021) BMI t x Black0.006 (0.002) *** (0.002) ** BMI t x Hisp0.002 (0.003) (0.003) BMI t x Asian0.001 (0.005) (0.004) Model Includes: X t, B t X t, B t, S t, E t, M t, K t Marginal Effect of 5% Preliminary Results: ln(wages) of females

VariableModel 1Model 2Model 3 BMI t (0.002) *** (0.002) *** (0.00 ***2) BMI t ≤ (0.024) ** (0.019) (0.019) 25 ≤ BMI t < (0.013) * (0.012) (0.012) BMI t ≥ (0.025) ** (0.021) (0.021) BMI t x Black0.006 (0.002) *** (0.002) ** (0.002) * BMI t x Hisp0.002 (0.003) (0.003) (0.003) BMI t x Asian0.001 (0.005) (0.004) (0.004) 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 Marginal Effect of 5% Preliminary Results: ln(wages) of females

VariableModel 1Model 2Model 3Model 4 BMI t (0.002) *** (0.002) *** (0.00 ***2) (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 5% Preliminary Results: ln(wages) of females

White Females Black Females Predicted change in wage by BMI Source: NLSY79 data $ $ * Reference BMI = 22 Predicted change in wage by BMI BMI Specification: Single index with fixed effects

Preliminary Results – quantile regression 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 5%

Unobserved Heterogeneity Distribution 1.0 11  1 = 0 22 33  2 =  3 =  Probability 1.0 11  t1 = 0 22  t2 =  t 3 = tt Probability 33 PermanentTime-varying

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 direct effect of BMI on wages. We find that a 5% decrease in BMI leads to $0.26 decrease in wages. Also, more likely to be enrolled, full time employed; less likely to be married or have a child. Preliminary Results: using preferred model

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

Preliminary Conclusions Unobservables that influence BMI also affect wages (and therefore must be accounted for) In addition to its direct effect on wages, BMI has a significant effect on wages through particular endogenous channels: schooling, work experience, marital status, and number of 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 to model the different effects of past decisions across the distribution of current BMI.) BMI appears to have a statistically significant direct effect on women’s wages (an effect that remains unexplained).

Additional Feedback … The body mass index (BMI) specifies a particular relationship b/w weight and height In light of the positive height effect and conjectured “beauty” effect on wages, are the appropriate measures simply weight and height? How might we simulate a change in BMI or weight when updating?

To Do… Estimate wages under the assumption that the endogenous rhs variables are exogenous and evaluate the effect of B t on w t (with and without fixed effects). Replace all endogenous rhs variables in wage equation with their reduced form arguments and evaluate the effect of B t on w t (with and without fixed effects).

To Do… Estimate equations explaining variation in all endogenous input variables and use their predicted values in estimation of wages, and evaluate the effect of B t on w t (with and without fixed effects). We can calculate BMI's direct, indirect, and total effects here.

To Do… Estimate equations for all endogenous variables jointly allowing for flexible unobserved correlation in both the permanent and time-varying individual dimension and evaluate effects of B t on w t. We can calculate BMI's direct, indirect, and total effect here.

To Do… Estimate equations for all endogenous variables jointly using conditional density estimation (CDE) to model wages and BMI in order to determine if BMI has a different effect at different points of support of the wage distribution. Similarly, we can evaluate whether behavioral inputs have a different effect at different points of support of the BMI distribution.

Unobserved Heterogeneity Distribution

Model of behavior of individuals as they age wtwt 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 Ω t = (B t, S t, E t, M t, K t, X t, P t ) Ω t+1 = (B t+1, S t+1, E t+1, M t+1, K t+1, X t+1, P t+1 ) And we jointly model the set of structural equations that describe these observed outcomes, allowing unobserved components to be correlated

Behavioral Equations: Employment ln[p(e t = d)/p(e t = 2)] e = 0 (non-employed) e = 1 (part-time) e = 2 (full-time) = δ 0d + δ 1d B t + δ 2d S t + δ 3d E t + δ 4d M t + δ 5d K t + δ 6d X t + δ 7d P s t + δ 8d P e t + δ 9d P m t + δ 10d P k t + δ 11d P b t + ρ e d μ + ω e d ν t Full time Part time Non-employed Female Male

ln[p(s t = 1)/p(s t = 0)] s = 0 (not enrolled) s = 1 (enrolled) = γ 0 + γ 1 B t + γ 2 S t + γ 3 E t + γ 4 M t + γ 5 K t + γ 6 X t + γ 7 P s t + γ 8 P e t + γ 9 P m t + γ 10 P k t + γ 11 P b t + ρ s μ + ω s ν t Behavioral Equations: Schooling Not enrolled Enrolled Female Male

ln[p(m t = 1)/p(m t = 0)] m = 0 (not married) m = 1 (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 X t + α 7 P s t + α 8 P e t + α 9 P m t + α 10 P k t + α 11 P b t + ρ m μ + ω m ν t Behavioral Equations: Marriage Not married Married Female Male

ln[p(k t = j)/p(k t = 0)] k = 0 (no change in children) k = -1, 1 = β 0j + β 1j B t + β 2j S t + β 3j E t + β 4j M t + β 5j K t + β 6j X t + β 7j P s t + β 8j P e t + β 9j P m t + β 10j P k t + β 11j P b t + ρ k j μ + ω k j ν t Behavioral Equations: Children # of kids acquired: Female Male