Physical Appearance and Wages over the Life Cycle
Wang-Sheng Lee
Deakin University and IZA, Bonn
This draft: January 23, 2014
Preliminary and incomplete. Please do not cite or quote.
Abstract:
Previous studies have shown that both height and weight are associated with wages. However,
concurrent increases in height and weight can make these effects difficult to disentangle. In
this paper, we examine the joint relationship of height and weight on wages using a semiparametric spline approach. The key contribution of the paper is that we provide a more
complete picture of how labor market returns to body size differ by gender and how they vary
over the life cycle. Our results are presented using contour plots that allow for complex nonlinear interactions between height and weight. We find using Australian data that there
generally are clear returns to men for being taller. For men who are aged between 45 and 54,
there appears to be a body type that is associated with the highest hourly wages. These are men
who are between 1.8 to 1.9 meters tall and who weigh between 80 to 90 kg. The appearancewage dynamics for women is a little more complicated. Young women (aged 25-34) who are
between 1.67-1.77 meters tall and who weigh between 50-70 kg tend to have the highest wage
premiums. For middle aged women (aged 35-44), there are returns to being tall and slim.
However, some heavy and large sized women earn even higher hourly wages than tall and slim
women. Finally, for older women (aged 45-54), there is generally a wage premium for being
taller.
Keywords: height, weight, wages, P-spline, GAM, BMI.
JEL codes: J31, J71
This paper uses unit record data from the Household, Income and Labour Dynamics in Australia
(HILDA) Survey. The HILDA Project was initiated and is funded by the Australian Government
Department of Social Services (DSS) and is managed by the Melbourne Institute of Applied Economic
and Social Research (Melbourne Institute). The findings and views reported in this paper, however, are
those of the author and should not be attributed to either DSS or the Melbourne Institute.
1. Introduction
There is a substantial literature in economics that focuses on the relationship between
physical appearance and wages. One stream of this literature has focused on the relationship
between height and wages (e.g., Loh, 1993; Persico et al., 2004; Case and Paxson, 2008; Case
et al., 2009; Kortt and Leigh; 2010), generally finding a positive relationship between height
and wages for both males and females. A second stream of this literature focuses on the
relationship between obesity and wages (e.g., Register and Williams, 1990; Sargent and
Blanchflower, 1994; Averett and Korenman, 1996; Pagan and Davila, 1997; Baum and Ford,
2004; Cawley, 2004; Han et al., 2009), generally finding a penalty for being overweight for
women and mixed results for men.
As a person’s physical appearance is a visual three-dimensional construct and not
necessarily a function of height and obesity considered separately, a third stream of this
literature focuses on examining the relationship using more direct measures of physical
appearance. For example, Hamermesh and Biddle (1994), Biddle and Hamermesh (1998) and
Harper (2000) focus on examining the relationship between beauty and wages. In these studies,
a beauty score is typically measured by asking interviewers in the field to rate the perceived
attractiveness of survey respondents on a scale that varies from “very attractive” to “very
unattractive.” Another approach is based on field experiments. In such studies, fictitious job
applications with facial photographs attached are sent out to employers to examine the
relationship between attractiveness and differential treatment in hiring in the labor market (e.g.,
Rooth, 2009; Boo et al., 2013).
As subjective data on beauty is not routinely collected and available in most survey data
sets while information on height and weight is, the question we address in this paper is whether
there is a way of examining the relationship between physical appearance and wages using
information on height and weight as a proxy for physical appearance. One might consider this
question to have already been addressed in the literature as the formula for the body mass index
(BMI) contains information on both height and weight. Although previous research has
examined the relationship between BMI and wages, the focus in the economics literature has
generally been on viewing BMI as a proxy for obesity and not as a proxy for beauty. However,
it has also been argued that BMI is a major factor in determining sexual attractiveness (Tovée
et al., 1998, 1999). Thus, one might also be inclined to reinterpret studies examining the
relationship between BMI and wages as studies representing the relationship between beauty
and wages.
1
Regardless of whether one regards BMI as a valid proxy for either obesity or physical
appearance, it is worth highlighting that the simultaneous use of height and weight as specified
in the BMI formula (weight/height2) is a very restrictive specification. Recently, in estimating
the effect of weight on wages, Kan and Lee (2012) allow for a more flexible semi-parametric
specification of height and weight, allowing each term to enter separately and in an additive
fashion. They argue that such a specification provides deeper insights into the labor market
returns to obesity relative to the conventional approach of estimating a regression of log wages
on BMI. In related work, in an attempt to improve on the literature that has been based on linear
models that use BMI either as a continuous measure or as categorical indicators for normal
weight, overweight and obese, researchers have also used semi-parametric methods to more
flexibly examine the relationship between BMI and wages (e.g., Shimokawa, 2008; Hildebrand
and Van Kerm, 2010; Gregory and Ruhm, 2011). 1
In a meta-analysis, Langlois et al. (2000) report that physically attractive individuals
are more likely than unattractive individuals to be judged as competent in their professions, to
experience success in their occupations, and to be treated more favorably by others. In this
paper, we add to the literature by examining the relationship between physical appearance and
wages using information on height and weight simultaneously in a semi-parametric fashion.
The key contribution of the paper is highlighting how labor market returns to attractiveness
differ by gender and how these returns vary over the life cycle.
Previewing our main findings, we find using Australian data that there generally are
clear returns to being taller for men. For men who are aged between 45 and 54, there appears
to be a body type that is associated with the highest hourly wages. These are men who are
between 1.8 to 1.9 meters tall and who weigh between 80 to 90 kg. The appearance-wage
dynamics for women is a little more complicated. Young women (aged 25-34) who are between
1.67-1.77 meters tall and who weigh between 50-70 kg tend to have the highest hourly wages.
For middle aged women (35-44), there are returns to being tall and slim. However, some heavy
and large sized women earn even higher hourly wages than tall and slim women. Finally, for
older women (aged 45-54), there generally are clear returns to being taller.
The remainder of this paper is organized as follows. Section 2 provides a brief overview
of the literature that has attempted to define beauty and attractiveness. Section 3 describes the
1
As an alternative, instead of using the World Health Organization (WHO) recommended BMI categories to
denote underweight (BMI < 18.5), normal weight (18.5 ≤ BMI < 25), overweight (25 ≤ BMI < 30) and obese
(BMI ≥ 30), Chen (2012) uses terciles of the BMI distribution to examine the non-linear relationship between
BMI and wages.
2
data and the semi-parametric approach used. Section 4 presents the results. Finally, section 5
concludes.
2. Measuring Beauty
Evolutionary psychologists have long argued for the existence of universally shared
criteria of attractiveness and beauty, despite the fact that beauty is largely a subjective
phenomenon. Facial symmetry is one way that beauty has been defined in the literature. 2 This
is the definition of beauty that field experiments examining the relationship between
attractiveness and hiring in the labor market (e.g., Rooth, 2009; Boo et al., 2013) are based on.
Rhodes (2006) finds that averageness and symmetry are both attractive in male and female
faces. Masculinity and femininity and are also attractive in male and female faces respectively
and is preferred to averageness. Pallett et al. (2010) find that when the face’s eye-to-mouth
distance is 36% of the face length and interocular distance is 46% of face width, the face
reaches its optimal attractiveness given its unique facial features.
Anthropometric measures have also been used to define beauty. For women, two
potential cues are body shape and weight. Singh (1993) focused on the waist-to-hip ratio
(WHR) and found a ratio of 0.7 (a curvaceous body) to confer maximal attractiveness to males.
On the other hand, Tovée et al. (1998, 1999) found that attractiveness ratings for women were
better accounted for by BMI than WHR. Comparing directly the relative importance of BMI
and WHR for women, Kościński (2013) finds that BMI is twice as important as WHR for the
attractiveness of the female body. Although BMI may be an important factor for female
attractiveness, for men, Maisey et al. (1999) find that attractiveness is determined by shape
cues (specifically the waist-to-chest ratio, a measure of upper body shape) rather than BMI.
In recent research, with the aid of a 3D interactive software program that allowed
manipulation of a virtual 3D image, it was found that the ideal body shape and size set by a
sample of Caucasian men and women is a relatively curvaceous body with low BMI (Crossley
et al., 2012). For women, the ideal BMI is approximately 19, the ideal WHR approximately 0.7
and the ideal waist-to-chest ratio (WCR) around 0.68. For men, the corresponding numbers are
25, 0.86 and 0.75. However, in the context of resource scarce and socioeconomic status
societies, other studies have shown that heavier female figures are judged to be more attractive
than thinner figures (e.g., Swami and Tovée, 2005). Based on cross-country data from the first
2
For example, see www.anaface.com, a web-based photo analysis application that computes a facial beauty score
according to a person’s facial geometry.
3
International Body Project which surveyed 7,434 individuals in 10 major world regions about
body weight ideals and body dissatisfaction, Swami et al. (2010) find that that there are
statistically significant differences in body weight ideals and body dissatisfaction across world
regions. Nevertheless, due to the globalization of Western media, they find that the thin body
ideal has clearly become more widely embraced and international in nature.
Although it has been argued that BMI is associated with sexual attractiveness for
females, the ideal BMI for females based on using 3-D images tends to be on the low side
which is not representative of the female population at large. It is thus worth exploring what
more realistic height/weight combinations are associated with better labor market outcomes
using actual real world data. Furthermore, when we think of a particular BMI value for females,
it is difficult visualize exactly what a person with a BMI value of 23 looks like. On the other
hand, it is arguably easier to visualize someone who is 1.6 meters tall who weighs 59 kg (BMI
= 23) or a person who is 1.7 meters tall and who weighs 66.5 kg (BMI = 23). This rationale
explains why many internet dating sites such as match.com prefer to report information on
height and weight separately rather than a person’s BMI.
In this paper, we therefore attempt to proxy for physical appearance using information
on height and weight separately. While it appears straightforward to obtain and interpret the
marginal effects of height in a log wage equation which controls for, among other
demographics, a measure of obesity using BMI, matters are not that simple. This is because
BMI = weight/height2 and it is not possible to talk about the partial effect of changing height
while keeping BMI and all other factors constant. Instead, just as one would examine the effect
of a variable that has interaction terms, a plot would be more suitable. An additional important
point to note is that height and weight will generally vary together and that the ceteris paribus
assumption will not hold in some instances when both these variables are included as
regressors. Interpreting the partial effect of increasing weight holding height constant is
meaningful as height generally remains the same for adults till shrinkage begins in old age.
However, interpreting the partial effect of increasing height holding weight constant is not
particularly meaningful because as a person gets taller, he will generally get heavier.
The issue of interpreting marginal effects for height and weight meaningfully is not
confined to linear models. Henderson et al. (2012) make the same point in the context of nonparametric models where partial mean plots of a variable of interest are usually made holding
other variables in the model constant at their means. However, it is likely that even in settings
with few covariates, as the dimensionality of the data increases, many of the observations will
not be close to the mean. This indicates that partial mean plots might not be relevant to any
4
actual cases of the observed data. In our subsequent semi-parametric analysis, we therefore
allow both height and weight to interact and co-vary together and restrict our attention to
realistic combinations of height and weight that represent possible human forms. Note that our
estimates are clearly not causal effects of height and weight on wages. Instead, they capture
the residual effect of height and weight on wages after controlling for relevant individual
characteristics. This residual effect can be viewed as a form of labor market discrimination.
3. Data and Methods
The data used in this article comes from the 2006-2011 waves of the Household, Income
and Labour Dynamics in Australia (HILDA) survey, which are the waves where self-reported
data on height and weight were collected. 3 HILDA is one of the largest surveys in Australia
that is representative of the population that has detailed information on wages, body size and
other relevant demographic characteristics such as education and marital status that are helpful
in estimating labor market returns. It also includes measures of health status as measured by
the SF-36 health survey. Kortt and Leigh (2010) pool the 2006-2007 waves of HILDA to
examine the relationship between body size and wages, conducting their analysis using linear
models. We update the data set used in their paper and use more recent waves of data that are
available.
The main approach we use in this paper is to use pooled cross-sectional data estimate
the following log wage equation:
Wi f ( Z i ) + X i β + +ε i
=
(1)
where Wi is the logarithm of the hourly wage of individual i, Z i is an individual’s height and
weight, X i is a vector of individual characteristics, and ε i is a residual term. The dependent
variable is log hourly wages in a person’s main job measured in year 2011 dollars. This is
constructed by dividing total weekly earnings from the main job by the total weekly hours of
work in the main job. In order to correct for potential reporting error in height (i.e., where there
3
For a detailed discussion of the quality of the height and weight data in HILDA, see Wooden et al. (2008).
Unfortunately, data on physical attractiveness (rated by the interviewer) as well as data on WHR and WCR is not
available in HILDA. In theory, we could also perform our analysis using, for example, waist and hip circumference
measured separately rather than as a ratio. While physical attractiveness is largely a biological phenomenon, it
can also be influenced by presentation such as the type of clothing, hair color and makeup (e.g., Hamermesh,
Meng and Zhang, 2002).
5
are discrepancies across waves by person), we use the average of a person’s height across
waves in our pooled regression models.
In equation (1), the function f (.) is a continuous but unspecified function of height and
weight that is estimated from the data. The parametric part of the model allows discrete or
continuous covariates that are deemed to have a linear effect on the outcome to be modeled
alongside non-parametric terms. The vector X i includes controls for a quadratic in age, years
of experience in the current occupation (and its square), education, marital status, education,
the presence of a long-term health condition differentiated by whether it is work limiting or
not, born overseas, contractual employment status (with two dummies identifying casual and
fixed-term contract employment, respectively), firm size (with dummies included to identify
firms with between 1-99 employees and firms with between 100-499 employees), union
membership, and wave dummies. We restrict our sample to respondents aged 25–54 who are
employed full-time, dropping those respondents who have missing data on individual
characteristics used in our model. Persons with implausibly low hourly wages (i.e., less than
$10 per hour, which is significantly below the federal minimum wage) are dropped.
In the economics literature, this is referred to as a partially linear regression model or a
semi-parametric model because part of the model contains a parametric functional form but
another part does not make any parametric assumptions. As highlighted by Ichimura and Todd
(2007: 5419), such models have been broadly applied in economics but mainly to the problem
of estimating Engel curves and the problem of controlling for sample selection bias. A widely
cited semi-parametric model is the model proposed by Robinson (1988) which in its
formulation treats the variables that enter the non-parametric part of the model f (.) as nuisance
variables. Instead, Robinson’s (1988) focus is on obtaining a √𝑛𝑛-consistent estimator of the
parameter vector β . Such an approach is very useful if one is interested solely in the parameter
vector β but less useful if one is more interested in examining the effects of the variables that
enter f (.) . 4
As the model is additively separable and includes a non-parametric component, in the
statistical literature, it is sometimes also referred to as a generalized additive model (GAM).
This is because it extends a generalized linear model by replacing the linear functional form
with an unknown functional form determined by the data. Lowess and smoothing splines can
4
Chen (2007) refers to a model as being ‘semi-parametric’ if its parameters of interests are in finite-dimensional
spaces but its nuisance parameters are in infinite-dimensional spaces, and a model as ‘semi-nonparametric’ if it
contains both finite-dimensional and infinite-dimensional unknown parameters of interest.
6
be very useful when there are no more than two explanatory variables. When there are more
than two explanatory variables, GAMs provide a compromise between the ease of
interpretation of the linear model and the flexibility of the general non-parametric model.
Complicated non-linear problems can be easily accommodated, even for models with many
explanatory variables. GAMs are able accommodate the interaction of two or more predictors
in a way that is conceptually comparable to interactions in a linear regression model. The joint
smooth function of the predictors can be specified using tensor product smooths which is
optimal for variables measured on different scales (Wood, 2006a). We use this interaction to
map out the height-weight combination that is related to the highest hourly wages.
The function f (.) in equation (1) can be constructed using kernel functions that require
marginal integration (e.g., Fan and Gijbels, 1996; Li and Racine, 2007, Kan and Lee, 2012) or
various spline smoothing functions. In this paper, we focus on using a P-splines for performing
our empirical analysis (Eilers and Marx, 1996). P-splines are a simple combination of two ideas
for curve fitting: the use of B-splines as the basis function with the inclusion of a difference
penalty on the regression coefficients.
The asymptotic behavior of P-spline estimation has been explored in detail recently.
Hall and Opsomer (2005) use a white-noise process representation of P-splines to provide
insights into its asymptotic properties. Li and Ruppert (2008) provide theoretical asymptotic
results where they derive equivalence between kernel smoothing and penalized splines in the
univariate case with a large number of knots. Claeskens et al. (2009) relate the asymptotic
properties of P-splines to known asymptotic results for regression splines and smoothing
splines. Relaxing the simplifying assumption that the dimension of the spline basis is fixed
which characterized earlier theoretical work, Kauermann et al. (2009) show that P-spline
smoothing is asymptotically justified even if the number of spline basis functions is allowed to
increase with the sample size. We briefly describe the two components of P-splines below as
they are likely to be unfamiliar to economists.
Under a B-spline approach, the unknown f (.) function can be written as the sum of k
basis functions:
k
f ( x) = ∑ α j b j ( x)
(2)
i =1
For expositional purposes, an example of a basis function that has flexible turning points that
is the polynomial basis:
7
f ( x) =
α1 + α 2 x + α 3 x 2 + α 4 x3 + α 5 x 4
(3)
Such a function will clearly fit data better than simply using linear or quadratic terms in a linear
regression model. For example, Murphy and Welch (1990) argue that allowing for quartic
terms in experience is empirically important and superior than using a quadratic in experience
for fitting the earnings curve. Although the polynomial basis is useful for illustrating ideas, in
practice, it has poor numerical stability properties as they tend to lead to highly correlated
parameter estimators. Instead, B-splines are polynomial pieces that are joined together in a
special way. A B-spline function is a piecewise polynomial function of degree k and the places
where the pieces meet are known as knots. As B-splines are continuous functions at the knots,
it is possible to control the wiggliness of the fitted model by controlling the number of
piecewise polynomial functions used. 5 As discussed by Eilers and Marx (1996), when a large
number of equally spaced knots and a large number of B-splines are used, the primary role of
the basis function is to serve as a convenient smooth interpolation device. 6
P-spline smoothing models are fit using penalized likelihood maximization in which
the model likelihood is modified by the addition of a penalty for each smooth function,
penalizing its ‘wiggliness’. Specifically, Eilers and Marx (1996) propose adding the following
penalty to the objective function to be minimized when using B-splines:
P=
λ
λ( f )
k
∑ (∆
i= d +1
d
βi )2
(4)
The penalty can be written as a linear combination of some basis functions, where ∆ d is the
difference operator of order d. 7 To control for the tradeoff between penalizing wiggliness and
penalizing badness of fit, each penalty is multiplied by an associated smoothing parameter.
One obvious drawback of spline smoothers such as the B-spline smoother is that the
number and position of the knots (or basis dimension) has to be chosen by the researcher. If
5
The B in B-spline is short for basis. A good overview of B-splines is provided in De Boor (2001).
A competing approach to smoothing described in Ruppert and Carroll (2000) and Ruppert and Wand (2003) is
based on truncated power functions.
7
An alternative approach to using P-splines is based on thin plate regression splines (Wood, 2003) which are low
rank smoothers which avoid having to choose knot locations for spline bases. However, this approach has been
shown to perform less well in Monte Carlo simulations compared to the P-spline approach we use in this paper
(Strasak et al., 2011).
6
8
too many knots are used such that the smoothing spline can approximate the unknown true
function, it is likely that the model will overfit data that contains any noise. Eilers and Marx
(1996) recommend using a large number of equally spaced knots (e.g., between 10 and 30).
Ruppert (2002) notes that the choice of the number of knots is usually not critical in affecting
the model results as long as it is set large enough. This is because it only sets an upper bound
on the flexibility of a term. Instead, the smoothing parameter plays a more important role in
controlling the actual effective degrees of freedom.
As is the case with many semi- and non-parametric approaches, the choice of the
smoothing parameter λ or the amount of smoothing that is applied to the data strongly affects
the fit of the model. The smoothness of f (.) is calculated with the aim of optimal balance
between the fit to the data versus a penalty for excessive “wiggliness” of the functions. Several
approaches to choosing λ are available. One possibility is to estimate it based on some
goodness of fit criterion, such as AIC (Eilers and Marx, 1996). Another possibility is to use a
data driven approach such as generalized cross validation (Wahba, 1990). Finally, the
smoothing parameter can also be estimated via a restricted maximum likelihood (REML)
approach (Ruppert et al., 2003; Wand, 2003).
In this paper, we estimate the smoothing parameter using REML. In the presence of
correlated data (which applies to our context analysing pooled cross-sectional data), standard
smoothing parameter selectors fail to work and tend to overfit the data (Opsomer et al., 2001).
Krivobokova and Kauermann (2007) show in simulations and a theoretical investigation that
REML-based smoothing parameter selection is less sensitive to misspecifications of the
correlation structure in the data compared to approaches that minimize the mean-squared error,
such as generalized cross validation and those based on the AIC. Furthermore, the Monte Carlo
simulation results in Strasak et al. (2011) suggest that compared to the alternative approach of
using generalized cross validation, REML for smoothing parameter selection in conjunction
with the use of P-splines seems to provide the best compromise between goodness of fit and
stability of the estimator.
Marx and Eilers (1998) further introduce P-splines to the GAM setting. In our GAM
application, we use cubic B-splines as the basis with a second order difference penalty. We use
a basis dimension of 10 for both height and weight. 8 The mgcv library (Wood, 2006b) in R
version 2.9.2 is used to estimate the models.
8
We also experiment with basis dimensions of 5 and 15 for height and weight and find very similar results to
those presented in the paper.
9
4. Results
4.1 Descriptive statistics
Table 1 provides descriptive statistics of the data from waves 6 to 11 of HILDA used
in this paper. Since previous studies have sometimes observed differences in the effect of body
size on the wages of men and women, we estimate our results separately for men and women.
Hourly earnings in 2011 dollars is $33.90 for males in our sample and $29.11 for females. The
average height is 1.79 meters for men and 1.65 meters for women, while the average weight is
87.2 kg for men and 71.9 kg for women. This makes both the average man and woman in
Australia slightly overweight according to BMI.
4.2 Linear parametric models
In estimating the relationship between height/weight on labor market outcomes in a
multivariate setting, there is some disagreement in the literature over whether one should also
control for experience and education. The central issue is whether experience and education
are a channel through which body size affects earnings, or whether they are confounding
variables that happen to be correlated with both body size and wages. Some authors argue
against accounting for differences in decision variables when estimating the effect of labor
market discrimination (e.g., Neal and Johnson, 1996; Heckman, 1998). This is because
including variables such as work experience, education, and occupation which are subject to
worker choice and which can be affected by labor market discrimination will lead to the wage
effects of discrimination being misstated. If the goal is to estimate the total effect of
height/weight on wages and not the partial effect of height/weight on wage conditional on
education, occupation, and marital choices, then one might prefer to omit these variables from
the model, controlling only for purely exogenous determinants of wages. We refer to this model
as the parsimonious model. However, as other authors deem it might also be of interest how
much these factors can account for of the variation in wages (e.g., Cawley, 2004; Kortt and
Leigh, 2010), we also examine models where educational attainment, occupation
characteristics, and marital status are included in the model. We refer to his model as the full
model.
Table 2 provides OLS results for males. Columns 1, 3 and 5 are based on a model where
education, occupation, and marital choices are included as covariates in addition to other
exogenous characteristics. They clearly illustrate the typical finding in the literature of there
being a positive association between height and wages. In columns 2, 4 and 6 which are based
on the more parsimonious specification which does not include education, occupation, and
10
marital status, as one would expect when not controlling for potential confounding factors, the
corresponding coefficients for height are larger. The results in Table 2 suggest that the effect
of height tends to dominate the effect on weight. For example, in column 7 where both height
and BMI are included as regressors, the coefficient on BMI is not statistically significant when
height is included even though it is statistically significant in a model where only BMI and not
height is included (results not shown).
The statistical significance on the interaction term for height and weight in columns 5
and 6 is a hint that it might be of interest to explore more deeply the nature of this interaction,
which is the main focus of this paper. Table 3 provides the OLS results for females, which are
largely similar to the results for males except that the relationship between height and wages
tends to be slightly smaller in magnitude.
4.3 General additive models
The use of linear models to examine the relationship between body size and wages
might not be ideal if there exist non-linearities in the relationship. This has been the motivation
behind researchers using semi-parametric approaches in examining the relationship between
BMI and wages (e.g., Shimokawa, 2008; Hildebrand and Van Kerm, 2010; Gregory and Ruhm,
2011. Figure 1 illustrates the non-linear relationship between body size and wages in the
HILDA data for men and women. In the top panel, there is evidence that a linear function might
be appropriate in the case of men but is clearly not so for women, where the relationship is an
inverted U-shape. In the middle panel of Figure 1, it can be seen that there does not appear to
be a simple linear relationship between weight (measured in kg) and hourly wages. The bottom
panel examines the bivariate relationship between BMI and wages. For men, wages appear to
peak at a BMI of between 25 and 33 whereas for women, it peaks earlier at BMI values between
20 and 22. These findings generally echo the results found in this literature.
In general, the non-linear results from equation (1) are best shown using graphs as the
complex non-linear interaction effect between height and weight cannot be simply summarized
using a regression coefficient or mathematical function. The joint interactive effect of height
and weight on wages can be shown in a three-dimensional plot or a contour plot as they both
contain the same information. We choose to use the latter for our application because the isocontour lines in the plots make it very easy to see the different levels of log hourly wages
associated with different combinations of height and weight.
Based on using the full model specification, the top panel of Figure 2 depicts the height
and weight combinations of males aged 25-54 that are associated with the highest hourly log
11
wages. The iso-contour lines clearly suggest that height has a much greater influence on wages
than weight does. The bottom panel of Figure 2 which uses the parsimonious specification (not
controlling for education, experience and marital status) reveals a similar finding. In contrast,
the results for females shown in Figure 3 are starkly different. There is a local maxima for
relatively tall and slim women regardless of whether the full or parsimonious model is used. In
other words, women who are approximately between 1.67 to 1.77 meters tall and who roughly
weigh between 50 to 70 kg earn relatively high wages compared to most other women.
However, Figure 3 also reveals that there is another peak that appears for women who are
greater than 150 kg. In fact, these women tend to earn higher hourly wages than the relatively
tall and slim women.
We also apply both these model specifications for different age groups in the data
because we are interested to know how the importance of physical attractiveness and its link
with wages varies over the life course. The motivation behind this is that a person’s physical
appearance might be more important at the earlier stages of one’s life where careers are being
built, but less important at the later stages of one’s life where careers have stabilized and
discrimination on looks matters less. Early in one’s career, workers are to some extent
considered to be unknown quantities to their employers, and physical appearance might
therefore play a larger role in assessing their productivity. In addition, more physically
attractive persons might also gain access to valuable networks that will help them climb the
career ladder more quickly. Note that unlike studies that examine the effect of facial
attractiveness of individuals (which tends to be relatively time invariant) and how they are
related to labor market outcomes over the life course (e.g., Glass et al., 2010), we are more
concerned with the types of body shapes that are related to successful labor market outcomes
and what the “look of a winner” is at different stages of life.
For males aged 25-34 (Figure 4) and aged 35-44 (Figure 5), it can be seen that height
is a dominant factor and that taller men generally earn the highest wages. By the time males
are late in their careers though (aged 45-54), the body profile of the most successful male
according to the parsimonious model is one who is between 1.8 to 1.9 meters tall and who
weighs between 80 to 90 kg. Based on the full model, however, two local peaks appear. The
highest earners now capture a slightly larger height and weight range as compared to before
and also an additional group of shorter men (less than 1.65 meters tall) who weigh between 80140 kg.
The appearance-wage dynamics for women is a little more complicated. For young
women aged 25-34, Figure 7 suggests that those who are between 1.67 to 1.77 meters tall and
12
who are between 50 to 70 kg tend to earn the highest wages. By middle age (35-44), the
importance of having a particular body type seems to have dissipated somewhat. Instead, wages
are relatively higher for two groups of women. The first group are women who are relatively
tall and slim. The iso-contour lines map an area suggesting that women taller than 1.68 meters
and who weigh less than 70 kg do well in the labor market. However, there is another group of
women who does even better than this first group of relatively tall and slim women. The isocontour lines at the top right hand corner of both panels in Figure 8 suggest that there are some
middle-aged heavy women (> 130 kg) that earn the highest relative wages. By the time females
are late in their careers (aged 45-54), height appears to be a dominant factor. Taller women
over a relatively large weight range tend to earn the highest wages.
4.4 Does past physical appearance matter?
As past and current body shape and physical appearance can have an effect on current
labor market outcomes, it might also be of interest to examine how height and weight from
several years ago affects one’s wage growth and wages in the current period. There might be
certain age ranges where physical appearance has the largest impact on labor market outcomes.
For example, Chen (2012) finds that a higher BMI in one’s twenties for females has a persistent
negative effect on wages and is more important factor than current BMI. She also notes that
differences in marital characteristics, occupation status, or education cannot explain it.
In order to empirically examine how past body shape affects current wages in our data,
we estimate a variation of equation (1) where we restrict the data to be a cross-section from the
latest wave – wave 11 that corresponds to the year 2011. Instead of using height and weight
measured in 2011, however, we use height and weight measured in 2006, the earliest wave
where data on height and weight is available. This provides us with a how body shapes have
an effect on labor market outcomes five years later. Using such an approach also allows us to
circumvent any potential issues with reverse causality as although current wages might
possibly have an effect on current weight (e.g., low-wage workers who are depressed eat more
junk food and become fatter), current wages cannot possibly have an effect on past weight.
Based on the full model specification that includes education, experience and marital
status, Figure 10 shows that young and tall men in 2006 who are in a reasonably tight weight
range that increases proportionally with height appear to have done the best five years later.
On the other hand, the young women in 2006 who earn the highest relative wages in 2011 are
those who are petite (< 60 kg) and who are between 1.60 – 1.75 meters tall. This finding
therefore adds to Chen’s (2012) finding that there can be persistent longer term effects of
13
weight on wages for women who are in their twenties who are building their careers. It appears
that having the right look early in one’s career does matter for women’s wages over time.
5. Conclusions
In this paper, we use a semi-parametric approach based on P-splines to examine in more
detail the relationship between height, weight and wages. A drawback of using a restrictive
functional form such as that specified in the BMI formula to estimate an obesity penalty is that
it can lead to inferences that are not relevant to actual body sizes. Rather than focusing on the
role of height, or on the role of weight based on the BMI, we provide a more complete picture
of how body shapes that represent actual human forms are related to wages.
For example, although the literature suggests that women with relatively low BMI
values (20-22) tend to have the highest wages, one needs to keep in mind that such BMI values
can correspond to women who are very tall or very short. Based on our analysis, there would
be little benefit for a young woman who is 1.60 meters tall and 65 kg (BMI = 25.4 ) to lose
weight so that she weighs 56 kg (BMI = 21.9) and falls into the BMI range that the literature
suggests would optimize her wage rate. By doing so, she would instead still remain on the same
iso-contour line according to our model (Figure 7). Similarly, while the literature suggests that
there are labor market returns to being tall (holding a person’s weight constant), our results
suggests that depending on the age range considered, there are certain height and weight
combinations (or a certain look) that are associated with the highest wage premiums.
14
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18
Table 1: Descriptive Statistics
Males (N = 11154)
Hourly earnings
Log earnings
Height (cm)
Weight (kg)
BMI
Age
Experience
Couple
Divorced/Separated/Widowed
University degree
Diploma
Certificate
High school
Overseas born
Indigenous
Health condition
Union
Employment (fixed contract)
Employment (casual contract)
Firm size (small)
Firm size (medium)
Mean
33.90
3.43
178.51
87.21
27.35
39.47
9.70
0.78
0.06
0.31
0.09
0.32
0.12
0.19
0.01
0.11
0.31
0.09
0.06
0.61
0.23
SD
16.71
0.42
7.15
15.81
4.66
8.50
8.83
0.41
0.25
0.46
0.29
0.47
0.33
0.40
0.12
0.31
0.46
0.29
0.23
0.49
0.42
Min
10.02
2.30
131
38
15
25
0.02
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Max
242
5.49
208
250
81.3
54
40
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Mean
29.11
3.31
164.92
71.91
26.43
39.47
8.44
0.70
0.13
0.43
0.12
0.16
0.14
0.21
0.01
0.11
0.33
0.12
0.06
0.59
0.23
SD
11.74
0.35
7.13
16.82
6.00
8.98
8.55
0.46
0.33
0.50
0.33
0.37
0.34
0.41
0.12
0.32
0.47
0.33
0.23
0.49
0.42
Min
10.08
2.31
142
28
12.3
25
0.02
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Max
183.92
5.21
193
185
72.3
54
40
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Females (N = 7031)
Hourly earnings
Log earnings
Height (cm)
Weight (kg)
BMI
Age
Experience
Couple
Divorced/Separated/Widowed
University degree
Diploma
Certificate
High school
Overseas born
Indigenous
Health condition
Union
Employment (fixed contract)
Employment (casual contract)
Firm size (small)
Firm size (medium)
Notes: Omitted groups are single, less than high school, employment (permanent) and firm size (large).
19
Table 2: OLS Results for Males
Height (m)
(1)
Log
Earnings
0.316***
(6.58)
(2)
Log
Earnings
0.491***
(9.40)
Weight (kg)
(3)
Log
Earnings
0.342***
(6.48)
-0.000
(-1.19)
(4)
Log
Earnings
0.622***
(10.89)
-0.001***
(-5.62)
Height*Weight
(5)
Log
Earnings
0.752***
(3.23)
0.008*
(1.75)
-0.005*
(-1.81)
(6)
Log
Earnings
1.098***
(4.34)
0.008
(1.64)
-0.005*
(-1.93)
BMI/10
Age
Age square
Experience
Experience square
Couple
Divorced/Separated
/Widowed
University
Diploma
Certificate
High School
Overseas born
Indigenous
Health condition
Union
Fixed contract
Casual contract
Firm size (small)
Firm size (medium)
N
adj. R2
0.047***
(11.37)
-0.001***
(-10.15)
0.011***
(9.20)
-0.000***
(-5.86)
0.099***
(10.21)
0.054***
(3.32)
0.421***
(38.52)
0.256***
(18.30)
0.134***
(12.79)
0.150***
(11.35)
-0.034***
(-3.85)
0.024
(0.83)
-0.048***
(-4.38)
0.015*
(1.92)
0.056***
(4.76)
-0.018
(-1.19)
-0.244***
(-25.44)
-0.103***
(-9.47)
11154
0.282
0.054***
(12.13)
-0.001***
(-10.71)
0.014
(1.45)
-0.034
(-1.06)
-0.066***
(-5.56)
0.028***
(3.41)
0.077***
(5.94)
-0.120***
(-7.43)
-0.311***
(-30.12)
-0.136***
(-11.41)
11154
0.143
0.048***
(11.43)
-0.001***
(-10.21)
0.011***
(9.16)
-0.000***
(-5.83)
0.100***
(10.23)
0.054***
(3.32)
0.419***
(38.21)
0.255***
(18.25)
0.134***
(12.75)
0.149***
(11.32)
-0.034***
(-3.89)
0.025
(0.85)
-0.047***
(-4.34)
0.015*
(1.95)
0.056***
(4.74)
-0.018
(-1.23)
-0.245***
(-25.46)
-0.104***
(-9.51)
11154
0.282
0.056***
(12.60)
-0.001***
(-11.12)
0.011
(1.17)
-0.030
(-0.94)
-0.064***
(-5.36)
0.029***
(3.52)
0.075***
(5.83)
-0.121***
(-7.51)
-0.313***
(-30.37)
-0.137***
(-11.56)
11154
0.145
0.048***
(11.44)
-0.001***
(-10.22)
0.011***
(9.18)
-0.000***
(-5.84)
0.099***
(10.20)
0.054***
(3.31)
0.419***
(38.23)
0.255***
(18.25)
0.134***
(12.80)
0.149***
(11.32)
-0.033***
(-3.75)
0.026
(0.89)
-0.048***
(-4.36)
0.015**
(1.97)
0.056***
(4.73)
-0.018
(-1.21)
-0.245***
(-25.47)
-0.104***
(-9.50)
11154
0.282
0.056***
(12.61)
-0.001***
(-11.14)
0.012
(1.31)
-0.028
(-0.89)
-0.064***
(-5.38)
0.029***
(3.55)
0.075***
(5.82)
-0.121***
(-7.49)
-0.313***
(-30.38)
-0.137***
(-11.55)
11154
0.146
(7)
Log
Earnings
0.307***
(6.35)
-0.007
(-0.94)
0.048***
(11.34)
-0.001***
(-10.13)
0.011***
(9.07)
-0.000***
(-5.78)
0.100***
(10.25)
0.055***
(3.37)
0.419***
(37.98)
0.254***
(18.02)
0.133***
(12.59)
0.149***
(11.26)
-0.034***
(-3.82)
0.024
(0.82)
-0.047***
(-4.29)
0.016**
(2.08)
0.055***
(4.64)
-0.018
(-1.16)
-0.245***
(-25.35)
-0.102***
(-9.31)
11069
0.282
20
Table 3: OLS Results for Females
Height (m)
(1)
Log
Earnings
0.281***
(5.42)
(2)
Log
Earnings
0.368***
(6.52)
Weight (kg)
(3)
Log
Earnings
0.300***
(5.52)
-0.000
(-1.18)
(4)
Log
Earnings
0.448***
(7.58)
-0.001***
(-4.53)
Height*Weight
(5)
Log
Earnings
0.439**
(2.06)
0.003
(0.62)
-0.002
(-0.67)
(6)
Log
Earnings
0.922***
(3.99)
0.010*
(1.90)
-0.007**
(-2.12)
BMI/10
Age
Age square
Experience
Experience square
Couple
Divorced/Separated
/Widowed
University
Diploma
Certificate
High School
Overseas born
Indigenous
Health condition
Union
Fixed contract
Casual contract
Firm size (small)
Firm size (medium)
N
adj. R2
0.030***
(6.83)
-0.000***
(-6.21)
0.010***
(6.94)
-0.000***
(-3.71)
0.034***
(3.43)
0.023*
(1.67)
0.311***
(26.91)
0.172***
(12.17)
0.022*
(1.68)
0.086***
(6.17)
-0.008
(-0.87)
0.024
(0.78)
-0.036***
(-3.12)
0.015*
(1.75)
0.025**
(2.23)
-0.100***
(-6.26)
-0.188***
(-19.03)
-0.127***
(-11.13)
7031
0.265
0.030***
(6.52)
-0.000***
(-6.04)
0.019*
(1.95)
-0.013
(-0.39)
-0.047***
(-3.71)
0.096***
(11.14)
0.040***
(3.31)
-0.184***
(-10.76)
-0.228***
(-21.41)
-0.159***
(-12.83)
7031
0.124
0.030***
(6.91)
-0.000***
(-6.28)
0.010***
(6.91)
-0.000***
(-3.67)
0.033***
(3.39)
0.023
(1.62)
0.310***
(26.77)
0.172***
(12.17)
0.022*
(1.69)
0.086***
(6.18)
-0.009
(-1.00)
0.026
(0.87)
-0.035***
(-2.99)
0.015*
(1.80)
0.025**
(2.22)
-0.100***
(-6.29)
-0.188***
(-19.06)
-0.127***
(-11.13)
7031
0.265
0.032***
(6.88)
-0.000***
(-6.35)
0.014
(1.38)
-0.001
(-0.04)
-0.041***
(-3.23)
0.097***
(11.21)
0.040***
(3.25)
-0.185***
(-10.82)
-0.228***
(-21.48)
-0.158***
(-12.81)
7031
0.127
0.030***
(6.91)
-0.000***
(-6.29)
0.010***
(6.91)
-0.000***
(-3.67)
0.033***
(3.38)
0.023
(1.62)
0.310***
(26.68)
0.172***
(12.14)
0.022*
(1.67)
0.086***
(6.15)
-0.009
(-0.94)
0.026
(0.86)
-0.035***
(-2.99)
0.015*
(1.81)
0.025**
(2.20)
-0.100***
(-6.29)
-0.188***
(-19.05)
-0.127***
(-11.10)
7031
0.265
0.032***
(6.90)
-0.000***
(-6.39)
0.015
(1.54)
-0.002
(-0.07)
-0.041***
(-3.23)
0.097***
(11.24)
0.039***
(3.19)
-0.184***
(-10.79)
-0.228***
(-21.46)
-0.158***
(-12.74)
7031
0.127
(7)
Log
Earnings
0.268***
(5.13)
-0.009
(-1.50)
0.031***
(7.01)
-0.000***
(-6.40)
0.010***
(6.77)
-0.000***
(-3.56)
0.031***
(3.16)
0.022
(1.55)
0.309***
(26.43)
0.171***
(12.01)
0.021
(1.60)
0.085***
(6.04)
-0.009
(-1.01)
0.024
(0.78)
-0.035***
(-3.03)
0.016*
(1.85)
0.025**
(2.22)
-0.099***
(-6.16)
-0.187***
(-18.90)
-0.128***
(-11.10)
6940
0.263
21
Figure 1: Kernel Weighted Local Polynomial Smooths of Height and Body Size
3.1
3.2
Log Hourly Wage
3.3
3.4
3.5
Male
Female
180
160
Height (cm)
140
200
4
120
3
3.2
Log Hourly Wage
3.4
3.6
3.8
Male
Female
0
50
100
Weight (kg)
150
3.45
200
3.2
3.25
Log Hourly Wage
3.3
3.35
3.4
Male
Female
10
20
30
BMI
40
50
60
22
Figure 2: Males – Full Sample
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
23
Figure 3: Females – Full Sample
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
24
Figure 4: Males Aged 25-34
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
25
Figure 5: Males Aged 35-44
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
26
Figure 6: Males Aged 45-54
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
27
Figure 7: Females Aged 25-34
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
28
Figure 8: Females Aged 35-44
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
29
Figure 9: Females Aged 45-54
(With controls for education, experience and marital status)
(Without controls for education, experience and marital status)
30
Figure 10: Males Aged 25-34 – Height and Weight in 2006 and Wages in 2011
Figure 11: Females Aged 25-34 – Height and Weight in 2006 and Wages in 2011
31