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A Matter of Weight? Hours of Work of Married Men and Women and Their Relative Physical Attractiveness by Sonia Oreffice 米 Climent Quintana-Domeque^** Documento de Trabajo 2011-05

Economía de la Salud y Hábitos de Vida CÁTEDRA Fedea-la Caixa

March 2011

* Universitat d’Alacant & IZA. ** Universitat d’Alacant, FEDEA, IAE-CSIC & IZA.

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A Matter of Weight? Hours of Work of Married Men and Women And Their Relative Physical Attractiveness

Sonia Ore¢ce

Climent Quintana-Domequey

Universitat díAlacant & IZA

Universitat díAlacant, FEDEA, IAEñCSIC & IZA

March 16, 2011.

Abstract

We explore the role of relative physical attractiveness within the household on the labor supply decisions of husbands and wives. Using data from the Panel Study of Income Dynamics, we Önd that husbands who are heavier relative to their wives work more hours, while wives who are thinner relative to their husbands work fewer hours. We also Önd a 9%-elasticity of annual hours of work with respect to own BMI for married men, and a ñ7%-elasticity with respect to wifeís BMI. For married women, we Önd an 8%-elasticity of annual hours of work with respect to own BMI, and a ñ6%-elasticity with respect to husbandís BMI. While own BMI is positively related to own hours of work for married individuals, no statistically signiÖcant relationship emerges for either unmarried men or unmarried women.

Keywords: hours worked, body mass index, marital status. JEL Codes: D1, J1, J22.

Sonia Ore¢ce. Postal Address: Department of Economics, Universitat díAlacant, Campus de Sant Vicent, 03690, Spain. Telephone: + (34) 965 903 400 (Ext: 3259). E-mail: sonia@merlin.fae.ua.es.

yCliment Quintana-Domeque. Postal Address: Department of Economics, Universitat díAlacant, Campus de Sant Vicent, 03690, Spain. Telephone: + (34) 965 903 400 (Ext: 3264). E-mail: climent@ua.es.

1 Introduction

Economists have been inquiring about the determinants of labor supply, the intra-household allocation of resources, and the economic impact of physical attractiveness for decades. Is there any common link between all these di§erent forces? As illustrated in the seminal work by Chiappori (1992), the family has considerable ináuence on the behavior of its members, and in particular on their labor supply choices. The wifeís decision power, which depends on her characteristics and wellbeing outside marriage relative to her spouseís (relative age, wage, education, non-labor income, divorce laws, etc.), will a§ect both her own and her husbandís allocation of hours of work. Although many studies have analyzed the role of spousesídi§erences along several dimensions, the literature has remained silent on the role of di§erences in physical attractiveness.¹ This is somewhat surprising, since relative attractiveness seems to be a relevant determinant of the bargaining power of each spouse, and existing works directly link attractiveness to several economic outcomes, such as individual employment status, earnings, and criminal activity (e.g., Hamermesh and Biddle, 1994; Rooth, 2009; Mocan and Tekin, 2010).

In this paper, we explore the role of relative physical attractiveness within the household on the labor supply decisions of husbands and wives, proxied by relative body mass index (BMI, weight-for-height). Evidence from psychology explicitly points to fatness being stigmatized by spouses, and that social pressures for slimness a§ect marital interaction (Sobal, 1995). In particular, it is the relative attractiveness within the couple which is thought to a§ect household behavior. McNulty and Ne§ (2008) actually claim that how the discrepancy in spousesí attractiveness a§ects household outcomes and satisfaction is an open question in family and social psychology. By establishing a link between relative attractiveness and intra-household allocation of resources of married men and women, our work is consistent with the long tradition in labor supply research that emphasizes the family context in which work decisions are made (e.g., Blundell and MaCurdy, 1999; Chiappori, Fortin and Lacroix, 2002; Blau and Kahn, 2007).

¹For example, Browning et al. (1994) have shown that di§erences in age and income among the members of the household appear to be determinants of household outcomes, such as consumption expenditures. Lundberg, Pollak and Wales (1997) estimate that which spouse receives the child allowance a§ects household decisions. See Vermeulen (2002) for a survey of bargaining power measures in collective models.

Our analysis extends and complements the literature on the marriage market penalties of low physical attractiveness. Heavier (or obese) men and women are found to be penalized in the marriage market by matching with partners who are weaker along socioeconomic dimensions, i.e., educational attainment and wages (Averett and Korenman 1996; Hamermesh and Biddle, 1994; Ore¢ ce and Quintana-Domeque, 2010). Indeed, the very recent work by Chiappori, Ore¢ ce and Quintana-Domeque (2010) considers multidimensional matching and tests that absolute attractiveness of individuals (proxied by weight-for-height, body mass index, BMI) is an important characteristic in explaining matching patterns of married couples. Heavier men tend to marry heavier women, and heavier women (men) can compensate their negative trait by being endowed with higher education (wage).

We use a standard collective labor supply model with relative physical attractiveness a§ecting the decision power of each spouse (Chiappori et al., 2002). Following Gregory and Rhum (2009) and Chiappori et al. (2010), among others, we consider BMI as a proxy for physical attractiveness. Viewing the role of relative physical attractiveness through the lens of a collective labor supply framework allows us to investigate its consequences in terms of hours of work of both married men and women. In such a context, relatively high body weight transforms into low Pareto weight in the household, inducing individuals to compensate for their negative physical trait by working more hours, while their spouse works less (Chiappori et al., 2002). Discrepancies in physical appearance lead to a better position inside the household for the better looking spouse, in terms of intrahousehold allocation of resources, and thus of hours worked by husbands and wives.

Using data from the Panel Study of Income Dynamics (PSID) on married heads and their wives from 1999 to 2007, we show how relative attractiveness proxied by husbandís BMI relative to wifeís BMI matters in explaining their labor supply patterns, i.e., the annual hours of work, of married men and women. We Önd that husbands who are heavier relative to their wives work more hours, while wives who are thinner relative to their husbands work fewer hours. Acknowledging that own weight (or BMI) has already been linked to labor supply ñindividuals working more hours may work in sedentary jobs (Ruhm, 2005; Lakdawalla and Philipson, 2007; Loh, 2009) or consume more highly-caloric food to economize on the scarcity of their time (Chou, Grossman and Sa§er, 2004)ñ we also present estimates controlling for sedentary job-type and the ratio of expenditures of food at home versus total food. The results in each case are virtually identical. Finally, we also account for spousal characteristics and estimate the spousesílabor supply equations simultaneously. Interestingly, we cannot reject that the estimated e§ects of husbandís relative BMI are the same for men and women but with opposite signs, and show a signiÖcant response of both male and female labor supplies, which is also consistent with recent work on body size and the marriage market emphasizing that male physical attractiveness matters as well (e.g., Chiappori et al., 2010; Hitsch, HortaÁsu, and Ariely, 2010).

Since the identiÖcation of the e§ect of the relative husbandís BMI on labor supplies may depend on symmetric but of-opposite-sign e§ects imposed by the BMI ratio, we then replace the ratio by the logs of own BMI and spousal BMI, as separate variables. We Önd a 9%- elasticity of annual hours of work with respect to own BMI for married men, and a ñ7%- elasticity with respect to their wivesí BMI. For married women, an 8%-elasticity of annual hours of work is associated with own BMI, while a ñ6%-elasticity to their husbandsí BMI. In addition, to uncover the bargaining power channel from the sorting at the time of the match, we focus on couples who have been married for at least 4 years, and show that sorting would not predict the positive correlations we Önd between hours and own BMI. Finally, we compare the spousesílabor supply elasticities with respect to own BMI to those of unmarried individuals, to distinguish within-family mechanisms from alternative ones. While own BMI is positively related to hours of work for both married men and married women, no statistically signiÖcant relationship emerges for either unmarried men or unmarried women.

While negative e§ects of own BMI on both labor-² and marriage-market outcomes³ have been well-documented in the social sciences, our evidence indicates that the relative BMI within the couple reinforces these negative penalties through the household decision process. This induces relatively heavier married individuals to work more hours to compensate their spouses for their defect, regardless of gender. More generally, our work contributes to the understanding of labor supply responses of married men and women. The estimated sizeable impacts of relative BMI on both spouses, and with opposite signs, are all the more remarkable given the acknowledged rigidities in the labor supplies.

The paper is organized as follows. Section 2 discusses the conceptual framework. Section 3 describes the data. Section 4 presents the empirical results and discusses potential alternative explanations. Section 5 concludes the paper.

2 Conceptual Framework

2.1 Measuring (relative) physical attractiveness

Our study analyzes the role of relative physical attractiveness in labor supply decisions. Hence, we Örst need to deÖne how to measure physical attractiveness. There exists a considerable literature in which weight scaled by height (body mass index, BMI) is used as a proxy for socially deÖned physical attractiveness. Recent examples in economics include Gregory and Rhum (2009) and Chiappori et al. (2010). Indeed, BMI is shown to be negatively related to physical attractiveness. Interestingly, Rooth (2009) found that photos that were manipulated to make a person of normal weight appear to be obese (BMI 30) caused a change in the viewerís perception, from attractive to unattractive. In particular, BMI is reported to be the dominant cue for female physical attractiveness, while the waist-to-chest ratio (WCR) plays a more important role than BMI in the case of male attractiveness (Swami, 2008). However, it must be emphasized that BMI and WCR are strongly positively correlated, and, not surprisingly, BMI is correlated with the male attractiveness rating by women, though this correlation is lower than the one with WCR (TovÈe, Maisey, Emery and Cornelissen, 1999; TovÈe and Cornelissen, 2001; Wells, Treleaven and Cole, 2007).

²See Cawley (2000, 2004), Brunello and díHombres (2006), Garcia and Quintana-Domeque (2007), Atella, Pace and Vuri (2008), Han, Norton and Stearns (2009), and Rooth (2009) among others.

³See Averett and Korenman (1996), Fu and Goldman (2000), Lundborg, Nystedt, and Lindgren (2007), Averett, Sikora, and Argys (2008), Mukhopadhyay (2008), Tosini (2009), Hitsch et al. (2010), Chiappori, et al. (2010), Ore¢ce and Quintana-Domeque (2010), among others.

We are not aware of any study with detailed measures of body shape and socioeconomic characteristics which simultaneously provides these data for both spouses. Since BMI has been shown to constitute a good proxy for both male and female physical attractiveness, and evidence from psychology explicitly points to fatness being stigmatized by spouses (and that social pressures for slimness a§ect marital interaction; Sobal, 1995), we will use this measure in our analysis.⁴ SpeciÖcally, to capture relative attractiveness, we will use the husbandís relative BMI (husbandís BMI over wifeís BMI), and then the spousesíBMIs as two separate variables.

2.2 A standard model

We apply the collective household labor supply model with distribution factors of Chiappori, Fortin and Lacroix (2002). A household is composed of two decision makers, husband and wife, each having a distinct utility function on consumption and leisure, and making Paretoe¢ cient decisions. Preferences are egoistic, in that one spouseís utility does not depend on the otherís consumption or leisure, although the model can be extended to allow for caring preferences, and public goods. Let and for i = 1; 2 denote member iís labor supply and consumption of a private composite good (whose price is normalized to unity), with leisure time the household non-labor income, the wage rate of spouse and possible preference parameters of spouse i. Finally, let s represent the relative attractiveness of the two spouses, speciÖcally spouse 1ís attractiveness with respect to spouse . Opportunities outside marriage and personal qualities shape an individualís relative attractiveness, and are found to enhance a spouseís role and decision power in the household, a§ecting household choices.⁵ The utility function of member i is , where is strictly quasi-concave, increasing, and continuously di§erentiable.⁶

⁴Our study refers to the Western culture, as in some developing countries the relationship between female attractiveness and BMI may be di§erent.

The optimal allocations of labor supplies are determined by the following program:

\[\max _ {\{C _ {1}, C _ {2}, h _ {1}, h _ {2} \}} \mu U ^ {1} (C _ {1}, 1 - h _ {1}) + (1 - \mu) U ^ {2} (C _ {2}, 1 - h _ {2})\]

subject to

\[C _ {1} + C _ {2} \leq w _ {1} h _ {1} + w _ {2} h _ {2} + y\]

\[0 \leq h _ {i} \leq 1,\]

\[i = 1, 2\]

where the corresponding (Pareto) weighting factor is , representing the household decision process, and in particular spouse 1ís bargaining power. The scalar function is assumed continuously di§erentiable in its arguments, non-negative, and can be normalized to belong to [0; 1] without loss of generality. s measures the discrepancy in spouses attractiveness, and we deÖne it to be , the BMI of individual 1 relative to the BMI of individual 2. In general, may also depend on other factors, such as prices, incomes or any characteristic of the household environment that may a§ect the intra-household distribution of resources and thus the decision process (Browning et al., 1994; Browning and Chiappori, 1998; Vermeulen, 2002). Here, we focus on relative physical attractiveness.

⁵ The relative age, relative income, relative education, relative wages, as well as the sex ratios, divorce laws, abortion legalization, alimony, and child beneÖts laws, are examples of distribution factors that have been studied in the literature (Browning, Chiappori, Weiss, 2011; Chiappori et al., 2002; Lundberg and Pollak, 1996; Ore¢ce, 2007; Vermeulen, 2002).

⁶Following convention, the utility from companionship is assumed to be additive and not to ináuence the trade-o§ between leisure and consumption.

In this framework, relative physical attractiveness of individual 1 with respect to individual 2 increases the weighting factor (the weight on spouse 1ís utility function in the household welfare function), while decreasing the relative importance of individual 2, and thus a§ects the household choices of consumption and leisure. Therefore, we predict that

Assuming interior solutions, and following Chiappori et al. (2002), we can state that the coupleís Pareto-e¢ cient decisions yield the following equilibrium labor supply functions of the two spouses:

\[h _ {i} = H _ {i} (w _ {1}, w _ {2}, y, \mu (w _ {1}, w _ {2}, y, z, s)) \quad \forall i = 1, 2 \quad \mathrm{with} \frac {\partial H _ {1}}{\partial \mu} < 0 \mathrm{and} \frac {\partial H _ {2}}{\partial \mu} > 0\]

so that:

\[\frac {\partial h _ {1}}{\partial s} = \frac {\partial H _ {1}}{\partial \mu} \frac {\partial \mu}{\partial s} > 0\]

and

\[\frac {\partial h _ {2}}{\partial s} = \frac {\partial H _ {2}}{\partial \mu} \frac {\partial \mu}{\partial s} < 0\]

Therefore, the labor supply function of each spouse is negatively related to his/her level of relative attractiveness, ceteris paribus, in particular controlling for own and spouseís wage, and for the coupleís total non-labor income . If having a relatively low BMI strengthens a spouseís relative outside opportunities and welfare, thus increasing his/her weight in household decisions, he/she will work fewer hours. At the same time, we should observe the opposite impact on the labor supply of his/her spouse, who would experience a decline in his/her decision power, and thus work more hours.

We will investigate these patterns for both married males and females, by testing whether a husband (individual 1)ís labor supply is positively related to the relative BMI, s, while his wife (individual 2)ís hours of work are negatively related to it. More physical weight implies less Pareto weight in the household, compensating their spouse for the negative physical attribute by working more hours. In other words, lower relative weight of individual 1 in the decision process should, by standard income e§ects, lead to an increase in individual 1ís labor supply and a reduction in individual 2ís, all else equal. These di§erences in response to BMI would support the claim that hours of work are a§ected by the physical attractiveness of both spouses through its relevance in the household decision process, regardless of gender, and in addition to the individual and spousal characteristics that are traditionally thought to a§ect labor supply (Blau and Kahn, 2007; Browning, Chiappori and Weiss, 2011).

Our empirical analysis focuses on couples where both individuals are working, according to the predictions by Chiappori et al. (2002) which were developed for married working couples. In addition, Blundell et al. (2007) state that the case where both spouses work is the one yielding the strongest identifying power for preferences and for the impact of distribution factors on the division of household resources. Our labor supply analysis is exactly in terms of intra-household bargaining and allocation of resources.⁷

3 Data Description

Our empirical work uses data from the Panel Study of Income Dynamics (PSID). The PSID is a longitudinal household survey collecting a wide range of individual and household demographic, income, and labor-market variables. In addition, in all the most recent waves since 1999 (1999, 2001, 2003, 2005, and 2007), the PSID provides the weights (in pounds) and heights (in feet and inches) of both household heads and wives, which we use to calculate the BMI of each spouse, deÖned as an individualís body weight (in kilograms) divided by the square of his or her height (in meters squared).⁸

⁷Excluding domestic production does not necessarily bias the estimated e§ects of distribution factors on welfare (Donni, 2008).

In each of the survey years under consideration, the PSID comprises about 4,500 married households. We select households with a household head and a wife where both are actually present. In our sample years, all the married heads with spouse present are males, so we refer to each couple as husband and wife, respectively. We conÖne our study to white couples, and to those whose wife is between 26 and 48 years old, and whose husband is between 28 and 50 years old, given the average two-year intra-household age gap in the US (Chiappori, Iyigun, and Weiss, 2009). The lower and upper bounds are chosen to focus on prime-age individuals, since our analysis concerns labor supply behavior. We exclude individuals with work-limiting disability conditions, as measured by reporting a physical or nervous condition that limits an individualís type or amount of work.

The analysis comprises white individuals because in the PSID blacks are disproportionately over-represented in low-income households ("poverty/SEO sample"). Moreover, following Conley and Glauber (2007), we discard those individuals whose height and weight values include any extreme ones: a weight of more than 400 or less than 70 pounds, a height above 84 or below 45 inches. We focus on men whose BMI is between 20 and 40, and women between 18.5 and 40, thus excluding (medically) severely obese or underweight individuals (WHO, 2004).

Our main samples consist of working men and women, married to one another, since our main predictions concern hours worked in the labor market, and reáect the long tradition in labor supply research that emphasizes the family context in which work decisions are made (e.g., Blundell and MaCurdy, 1999; Blau and Kahn, 2007). Unlike many previous studies (e.g., Averett and Korenman, 1996; Averett et al., 2008; Hamermesh and Biddle, 1994), the focus is on matched partnerships, rather than on groups of husbands and wives that are not necessarily associated to each other. This has the advantage to assess labor supply outcomes actually decided at the household level. In particular, we consider couples where both husbands and wives are working because the compensation e§ects for BMI arise in the household in terms of labor supply decisions of both spouses. In addition, the empirical analysis closely refers to the predictions of Chiappori et al. (2002), which were developed for working couples.

⁸Weight and height are originally reported in pounds and inches, respectively, in the PSID. The pounds/inches BMI formula is: Weight (in pounds) 704.5 divided by Height (in inches) Height (in inches). Ore¢ ce and Quintana-Domeque (2010) has shown that non-response to body size questions appears to be very small in the PSID data. SpeciÖcally, item non-response for husbandís height is below 1.4% in each year, for wifeís height is below 1.4% in each year, and for husbandís weight is below 2.2% in each year. Regarding wifeís weight, item non-response is below 5.5% in each year.

Because the PSID main Öles do not contain any direct question concerning the duration of the marriages, we rely on the "Marital History File: 1985-2007" Supplement of the PSID to obtain the year of marriage and number of marriages, to account for the duration of the couplesícurrent marriage. We merge this information to our married sample using the unique household and person identiÖers provided by the PSID, and we consider married couples who have been married for at least 4 years, to capture the role of bargaining power rather than of sorting at the time of the match.

In the PSID all the variables, including the information on the wife, are reported by the head of the household. Reed and Price (1998) found that family proxy-respondents tend to overestimate heights and underestimate weights of their family members, so that family proxy-respondent estimates follow the same patterns as self-reported estimates (see Gorber et al., 2007, for a review). The authors suggest that the best proxy-respondents are those who are in frequent contact with the target. Since we are considering married couples, the best proxy-respondents are likely to be the spouses. Additionally, although it is well-known that self-reported anthropometric measures are likely to su§er from measurement error, Thomas and Frankenberg (2002) and Ezzati et al. (2006) showed that in the United States, selfreported heights exaggerate actual heights, on average, and that the di§erence is close to constant for ages 20-50.⁹

⁹We note that Cawley (2000, 2004) used the National Health and Nutrition Examination Survey III (NHANES III) to estimate the relationship between measured height and weight and their self-reported counterparts. First, he estimated regressions of the corresponding measured variable to its self-reported counterpart by age and race. Then, assuming transportability, he used the NHANES III estimated coe¢cients to adjust the self-reported variables from the NLSY. The results for the e§ect of BMI on wages were very

In all of our regressions, the dependent variable is the log of annual hours worked, deÖned in the PSID as ìtotal annual work hours on all jobs, including overtimeî. We focus on individuals working more than 1000 annual hours if male, and 750 if female, and on those earning more than $5 per hour. These restrictions are meant to exclude couples who are not really attached to the labor market. SpeciÖcally, those couples where the husband works less than part-time ( 20 hours per week), and the wife works less than about 15 hours per week.

The main explanatory variables are either the ratio of the husbandís BMI to the wifeís BMI, or the logs of husbandís and wifeís BMIs, separately. The control variables used in our analysis are: age; log hourly wage; non-labor income (constructed as total family income minus the labor income of each spouse¹⁰); education (deÖned as the number of completed years of schooling and is top-coded at 17 for some completed graduate work); health status (1 if excellent, very good, or good; 0 if fair or poor); number of children in the household under 18 years; and a dummy variable for the presence of children aged 2 years old or less (to control for a recent pregnancy).

In addition, occupation categories are considered to create a categorical variable for sedentary job type, following the very recent medical classiÖcation by Choi et al. (2010), and we also create the ratio of the expenditures of food at home versus total food. This is to account for the fact that individuals working more hours may work in sedentary jobs (Lakdawalla and Philipson, 2007) or consume more highly-caloric food to economize on the scarcity of their time (Chou et al., 2004), and therefore exhibit a higher BMI. Finally, state dummy variables are included to capture constant di§erences in labor and marriage markets across geographical areas in the US, such as the proportion of obese men and women and cultural attitudes toward BMI and obesity (e.g., Lundborg et al., 2007). As our analysis concerns several PSID waves, year dummy variables are also used. The regression analysis uses the PSID-provided

similar, whether corrected for measurement error or not. Hence, we rely on his Öndings, and we are conÖdent that our results (based on unadjusted data) are unlikely to be signiÖcantly biased. Recent papers conÖrm that the BMI-adjustment makes no di§erence (see Kelly et al., 2011).

¹⁰An alternative measure of non-labor income using the spousesítaxable income minus their labor incomes yields comparable estimates

sample household weights.¹¹

Table 1 contains the main descriptive statistics for our sample of married couples. The average husband works 2361 hours per year, while the average wife works 1857 annual hours. Part of this di§erence is due to the fact that we are focusing on couples were husbands work more than 1000 hours (hence, excluding part-time husbands) and wives work more than 750 hours. The average husband in our sample has a BMI of 27.7, so he is overweight (BMI 25), while the average wife is almost overweight, with a BMI of 24.7. The average household has a non-labor income of approximately $9000 per year. The spousesí wage di§erence is $7, with the average husband earning $26.6 per hour and the average wife having an hourly wage of $19.6. No mean di§erences between husbands and wives are found in terms of either completed education, around 14 years, or health status, 97% and 98%, for married men and women, respectively. The average age is 40 for married men, and 38 for married women. The average number of children per household is 1.4, and in 10% of cases, there has been a recent pregnancy. Finally, we note that nearly 60% of husbands work in sedentary jobs, while this percentage is almost 90% for wives.

[Table 1 about here]

4 Empirical Evidence

We start exploring the relationship between annual hours of work and relative attractiveness in Table 2. We run two regressions, for married men and women separately, of an indicator of husbandís (wifeís) annual hours of work ñwhich takes value 1 if the husbandís (wifeís) works more than the average husbandís (wifeís) work hours, i.e., 2361 (1857)ñon a type of couple indicator ñwhich takes value 1 if the relative husbandís BMI is higher than the average, i.e,

¹¹Longitudinal weights are available throughout the period 1999-2007, whereas cross-sectional weights are absent for the most recent waves of 2005 and 2007. Consequently, we consider the entire time period 1999-2007 using longitudinal weights.

1.15ñcontrolling for own age, state and year Öxed e§ects. 45% of husbands work above the average, while 55% of wives work above the average. Note that in 48% of the couples, the husbandís BMI is 15% higher than the wifeís BMI. The main results of the table are that husbands who are relatively heavier (15% or more) than their wives are a 6% more likely to work more hours than the average husband, while wives who are relatively thinner than their husbands are a 6% less likely to work more hours than the average wife.

[Table 2 about here]

This table is consistent with the basic story presented above. A husbandís lower relative physical attractiveness (or higher BMI) leads him to work more hours and her wife to work fewer hours, and conversely. However, while these Öndings are supportive of a standard collective model, they do not constitute clean tests of it, because labor supply depends at least on wages, which may be related to the BMI ratio.

4.1 Relative BMI and Labor Supplies

Table 3 presents the results of several regressions where the dependent variable is the log annual hours of work (our measure of labor supply) of married men. In the Örst column we estimate a standard labor supply equation, which postulates a log-linear relationship between hours of work and wages controlling for a vector of demographic characteristics (age, education, household non-labor income, and number of children), state and year Öxed e§ects. This is a prototype empirical speciÖcation that encompasses many economic models of labor supply (Blundell and MaCurdy, 1999). In the second column, we add our measure of relative attractiveness between spouses, namely the ratio of husbandís BMI to his wifeís, to the standard labor supply equation. Consistently with our predictions, we Önd a positive signiÖcant correlation between relative BMI and hours worked by married men, which corresponds to an elasticity of roughly 6.5%, signiÖcant at the 5% level, while the estimated coe¢cients associated to the hourly wage and other variables (results available upon request) do not exhibit any signiÖcant change with respect to the previous column.

Acknowledging that weight (or BMI) has already been linked to labor supply ñindividuals working more hours may work in sedentary jobs (Lakdawalla and Philipson, 2007)ñwe also present estimates controlling for sedentary job-type, column (3). The estimated relationship between labor supply and relative BMI remains virtually the same. Finally, in the last column, we add the food expenditure ratio to account for the possibility that individuals working more hours may consume more highly-caloric food to economize on the scarcity of their time (Chou et al., 2004). This does not alter the estimated association between hours of work and relative BMI.

[Table 3 about here]

To sum up, relatively heavier husbands tend to work more hours, on average. Moreover, this strong positive correlation persists and exhibits comparable magnitudes when accounting for sedentary job-type and the ratio of food at home versus total food expenditures.

Table 4 displays the same set of regressions for married women. As expected, relatively thinner wives tend to work fewer hours. The relationship is robust and present in all the speciÖcations, as it is the case for married men.

[Table 4 about here]

Tables 3 and 4 indicate that both men and women seem responsive to their relative BMI within marriage, and willing to alter their labor supply behavior. This is suggestive of a compensation mechanism, so that a relative defect is compensated with a quality. Everything else being equal, if a male (female) individual is heavier relatively to his wife (husband), he (she) works more hours to compensate for the relatively poor physical trait.

Next, in Table 5 we include spousal characteristics and estimate the spousesílabor supply equations simultaneously, to account for the existence of common random shocks a§ecting labor supply decisions within a couple. The Örst panel in Table 5 uses the ratio, while the second panel uses the log-ratio. Interestingly, we cannot reject that the estimated e§ects of husbandís relative BMI are the same for men and women but with opposite signs, which is also consistent with recent work on body size and the marriage market emphasizing the relevance not only of female physical attractiveness but also of male attractiveness (e.g., Chiappori et al., 2010; Hitsch et al., 2010).¹²

[Table 5 about here]

4.2 Addressing IdentiÖcation Concerns

4.2.1 Relaxing and testing the symmetry imposed by the BMI ratio

Since the identiÖcation of the e§ect of the relative husbandís BMI on labor supplies may depend on imposing symmetric but of-opposite-sign e§ects, we now relax this assumption by including the logs of own BMI and spousal BMI, as two separate variables. In Table 6 we estimate the same simultaneous labor supply equations as in Table 5, but replacing the husbandís relative BMI with the logs of own BMI and spousal BMI. Our conceptual framework has two main predictions. First, own BMI and own hours of work are positively related, ceteris paribus. Own BMI decreases own bargaining power in the household, leading to an increase in own labor supply that acts as a compensation mechanism within the household. The second prediction concerns the cross-e§ect of spousal BMI on own hours of work. Ceteris paribus, spousal BMI increases own bargaining power because it improves own relative attractiveness in the couple, leading to a decrease in own labor supply.

[Table 6 about here]

Table 6 conÖrms both predictions. Looking at the Örst column, we Önd a 9%-elasticity of annual hours of work with respect to own BMI for married men, and a ñ7%-elasticity with respect to wifeís BMI. For married women, the second column displays an 8%-elasticity of annual hours of work with respect to own BMI, and a ñ6%-elasticity with respect to husbandís BMI. This last elasticity, although sizeable, is not statistically signiÖcant. This is not surprising, and it can be easily understood in a classical measurement error world, as long as the variance of the classical measurement error is higher when the household head reports the measure of his/her spouse than when he reports his own.

(ρ = 0.0651

ρ = 0.0653)

¹²The residuals of each labor supply equation are positively correlated ( = 0:0651 and = 0:0653), and the Breusch-Pagan tests reject independence at the 1% level.

To assess the validity of our symmetry assumption and the plausibility of our mechanism, we perform several tests. The tests in row A indicate that we cannot reject the equality of the coe¢ cients but with opposite signs within equations, i.e., we cannot reject the symmetry imposed by the ratio. Moreover, the tests in rows B and C indicate that we cannot reject either the equality of own BMI e§ects across equations or the equality of cross-BMI e§ects across equations. Hence, our regressions based on the ratio do not appear to be misspeciÖed.

4.2.2 Sorting during the match or bargaining power after the match

It could be argued that the negative relationship between own hours of work and spousal BMI may reáect sorting at the moment of the match, rather than bargaining power. There are at least two reasons to believe that this phenomenon does not interfere with our results and their interpretation. First, we are focusing on non-recently married couples, in particular, those who have been married for at least 4 years, so that (part of) these negative associations capture our bargaining power explanation, and not sorting at the moment of the match. Second, although it is true that if we were capturing sorting the cross-e§ect should be expected to be negative, the own e§ect should be expected to be negative as well (see Appendix for a simple derivation). However, our estimated own e§ect is positive. Hence, our empirical Öndings are not simply the mere reáection of sorting at the time of the match.

4.2.3 Alternative non-marriage market explanations: the unmarried

We have acknowledged that own weight (or BMI) has already been linked to labor supply ñ individuals working more hours may work in sedentary jobs (Lakdawalla and Philipson, 2007) or consume more highly-caloric food to economize on the scarcity of their time (Chou et al., 2004)ñ and we have controlled for sedentary job-type and the food ratio. However, these controls may not fully address the underlying correlations.

To single out the family-origin correlation of BMI and labor supply from alternative explanations, we implement a placebo test using the unmarried. If our bargaining power mechanism is at work, ceteris paribus, we should Önd a positive relationship between own BMI and own hours of work for both married men and married women. Conversely, no relationship for either unmarried men or unmarried women should emerge since they have no spouse to relate to, and therefore are not involved in any intra-household bargaining.

In Table 7 we compare own-e§ects of BMI on hours of work between unmarried and married individuals. Both for men and women, no statistically signiÖcant relationship emerges between BMI and hours of work, and the magnitudes are much smaller. The coe¢ cient for married men is 2.5 times bigger than the one corresponding to unmarried men, while the coe¢ cient for married women is 1.4 times bigger than the one corresponding to unmarried women.

[Table 7 about here]

4.2.4 Potential non-linearities in BMI

In Table 8 we estimate the same regressions as in Table 6 but including squared log BMIs to assess the existence of non-linearities in the relationship between hours of work and (own and spousal) BMI. We do not Önd evidence of non-linearities. We have also estimated the same regressions as in Table 6 but including the square of log(own BMI) for unmarried men and women, without Önding evidence of non-linearities (results available upon request).

[Table 8 about here]

5 Conclusions

Our paper relies on the simple idea that relative physical attractiveness matters for the intrahousehold allocation of resources, and therefore for the labor supply decisions of both spouses. This is appealing, we think, in light of the absence in the literature of a link between the existing work highlighting the family context in which work decisions are made (e.g., Blundell and MaCurdy, 1999; Chiappori et al., 2002; Blau and Kahn, 2007), and those estimating the impact of physical attractiveness in the workplace (e.g., Hamermesh and Biddle, 1994; Rooth, 2009; Mocan and Tekin, 2010). Furthermore, evidence from psychology explicitly points to fatness being stigmatized by spouses, and to the fact that it is the relative attractiveness within the couple which is thought to a§ect household behavior (McNulty and Ne§, 2008).

Using data from the Panel Study of Income Dynamics (PSID) on married heads and their wives from 1999 to 2007, we Önd that husbands who are heavier relative to their wives work more hours, while wives who are thinner relative to their husbands work fewer hours, also when controlling for sedentary job-type and the ratio of expenditures of food at home versus total food. Moreover, accounting for spousal characteristics and estimating the labor supply equations simultaneously, we cannot reject that the estimated e§ects of husbandís relative BMI are the same for men and women but with opposite signs, and show a signiÖcant response of both male and female labor supplies. Finally, replacing the ratio by both the log of own BMI and the log of spousal BMI, we Önd a 9%-elasticity of annual hours of work with respect to own BMI for married men, and a ñ7%-elasticity with respect to their wivesíBMI. For married women, an 8%-elasticity of annual hours of work is associated with own BMI, while a ñ6%-elasticity to their husbandsí BMI. Our household bargaining interpretation is reinforced by the evidence that no statistically signiÖcant relationship emerges for unmarried individuals.

Appendix: Challenging the alternative explanation of sorting

Consider the case where sorting of couples at the moment of the match takes place along two characteristics, namely BMI (observable to the econometrician) and x (unobservable to the econometrician), where a high BMI is perceived as a negative trait, while a high x is a positive one. If both characteristics were observable to the econometrician, to investigate the presence of sorting, and similarly to Hitsch et al. (2010), we could regress each wife (husband) characteristic on her (his) spouse characteristics at the time of the match. For spouse 1, we could simultaneously estimate the following two equations:

\[\log (B M I _ {1}) = \alpha_ {0} + \beta_ {1} \log (B M I _ {2}) + \gamma_ {1} \log (x _ {2}) + \varepsilon_ {1}\tag{1}\]

\[\log (x _ {1}) = \alpha_ {1} + \beta_ {2} \log (B M I _ {2}) + \gamma_ {2} \log (x _ {2}) + \varepsilon_ {2}\tag{2}\]

where and capture some sort of randomness.

And similarly for spouse 2:

\[\log (B M I _ {2}) = \pi_ {0} + \delta_ {1} \log (B M I _ {1}) + \rho_ {1} \log (x _ {1}) + v _ {1}\tag{3}\]

\[\log (x _ {2}) = \pi_ {1} + \delta_ {2} \log (B M I _ {1}) + \rho_ {2} \log (x _ {1}) + v _ {2}\tag{4}\]

where and capture some sort of randomness.

Unfortunately, we do not observe but we assume that it is positively related with hours of work. SpeciÖcally, and for simplicity, x and hours of work are related in the following way:

\[\log (h _ {1}) = \log (x _ {1}) + u _ {1}\tag{5}\]

\[\log (h _ {2}) = \log (x _ {2}) + u _ {2}\tag{6}\]

where and are classical measurement errors.

Replacing expressions (5) and (6) into (1)-(4) we obtain:

\[\log (B M I _ {1}) = \alpha_ {0} + \beta_ {1} \log (B M I _ {2}) + \gamma_ {1} \log (h _ {2}) + (\varepsilon_ {1} - \gamma_ {1} u _ {2})\tag{7}\]

\[\log (h _ {1}) = \alpha_ {1} + \beta_ {2} \log (B M I _ {2}) + \gamma_ {2} \log (h _ {2}) + (\varepsilon_ {2} + u _ {1} - \gamma_ {2} u _ {2})\tag{8}\]

\[\log (B M I _ {2}) = \pi_ {0} + \delta_ {1} \log (B M I _ {1}) + \rho_ {1} \log (h _ {1}) + (v _ {1} - \rho_ {1} u _ {1})\tag{9}\]

\[\log (h _ {2}) = \pi_ {1} + \delta_ {2} \log (B M I _ {1}) + \rho_ {2} \log (h _ {1}) + (v _ {2} + u _ {2} - \rho_ {2} u _ {1})\tag{10}\]

If heavier men tend to marry heavier women, then . Similarly, if high-x men tend to marry high-x women, then . Moreover, if there is some degree of substitutability between spousal characteristics, we should expect . The estimates in Table A1 are consistent with these signs. Note, however, that the estimates of and reported in Table A1 su§er from attenuation bias due to (5) and (6).

[Table A1 about here]

What happens if we regress labor supply on both own and spousal BMI? Replacing (10) into (8), we obtain:

\[\log (h _ {1}) = \varphi_ {1} + \left(\frac {\beta_ {2}}{1 - \gamma_ {2} \rho_ {2}}\right) \log (B M I _ {2}) + \left(\frac {\gamma_ {2} \delta_ {2}}{1 - \gamma_ {2} \rho_ {2}}\right) \log (B M I _ {1}) + \eta_ {1}\tag{11}\]

Similary, replacing (8) into (10), we obtain:

\[\log (h _ {2}) = \varphi_ {2} + \left(\frac {\delta_ {2}}{1 - \gamma_ {2} \rho_ {2}}\right) \log (B M I _ {1}) + \left(\frac {\rho_ {2} \beta_ {2}}{1 - \gamma_ {2} \rho_ {2}}\right) \log (B M I _ {2}) + \eta_ {2}\tag{12}\]

where

Hence, as long as

Therefore, the expected relationship between hours of work and own BMI is negative, as well as the expected relationship between hours of work and spousal BMI. In other words, if sorting were driving our empirical results, labor supply should be negatively related to own BMI, while the standard collective model predicts, and our evidence shows, the opposite.¹⁴

1 > γ2ρ2

1 22 1−γ2P2 ₂

δ2 1−γ2ρ2 ¹ 22

r(log(BMI2), u1) ≠ 0

corr(log(BMI1), u2) ≠ 0

γ2δ2 ₂ 1−γ2ρ2 ¹ 22

P2β2 ₂₂ ¹ 22 1−γ2ρ2

¹³ Indeed, the tables indicate that 1 > ₂₂ is satisifed.

¹⁴ Note that estimation of (11) and (12) by OLS (or SUREG) will lead to biased estimates of the crosse§ects, and , since corr(log(BMI2); u1) 6= 0 and corr(log(BMI1); u2) 6= 0, but not of the own-e§ects and

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Note: Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years.

Regressions of annual hours of work indicators per type of couple indicator, PSID 1999-2007. I (·) indicator variable that takes value 1 if the condition (·) is satisfied

Note: The regressions include own age, year and state fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Robust standard errors clustered at the household-head id level are reported in parentheses. Sampling weights are used. *** p-value<0.01, ** p-value<0.05, * p-value<0.1

Table 3: Regressions of husband’s log annual hours of work on husband’s BMI relative to wife’s BMI. PSID 1999-2007.

Note: Demographic characteristics include age, completed years of education, a good health status indicator, household non-labor income, number of children, a recently pregnant indicator, state and year fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Robust standard errors clustered at the household-head id level are reported in parentheses. Sampling weights are used. *** p-value<0.01, ** p-value<0.05, * p-value<0.1

Table 4: Regressions of wife’s log annual hours of work on husband’s BMI relative to wife’s BMI. PSID 1999-2007.

Note: Demographic characteristics include age, completed years of education, a good health status indicator, household non-labor income, number of children, a recently pregnant indicator, state and year fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Robust standard errors clustered at the household-head id level are reported in parentheses. Sampling weights are used. *** p-value<0.01, ** p-value<0.05, * p-value<0.1

Seemingly unrelated regressions of log annual hours of work on husband’s BMI relative to wife’s BMI.PSID 1999-2007.

Note: Regressions, which are simultaneously estimated, include own and spousal characteristics (age, log-hourly wage, completed years of education, a good health status indicator, a sedentary-job type indicator, and a recently pregnant indicator), household non-labor income, number of children, state and year fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Standard errors are reported in parentheses. Sampling weights are used. *** p-value<0.01, ** p-value<0.05, * p-value<0.1

Note: Regressions, which are simultaneously estimated, include own and spousal characteristics (age, log-hourly wage, completed years of education, a good health status indicator, a sedentary-job type indicator, and a recently pregnant indicator), household non-labor income, number of children, state and year fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Standard errors are reported in parentheses. Samplin weights are used.

*** p-value<0.01, ** p-value<0.05, * p-value<0.1

Regressions of log annual hours of work on log own-BMI by marital status.

Note: All regressions include own characteristics (age, log-hourly wage, completed years of education, a good health status indicator, a sedentary-job type indicator, and –for women- a recently pregnant indicator), household non-labor income, number of children, state and year fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Robust standard errors clustered at the household-head id level are reported in parentheses. Sampling weights are used. *** p-value<0.01, ** p-value<0.05, * p-value<0.1

Note: Regressions, which are simultaneously estimated, include own and spousal characteristics (age, log-hourly wage, completed years of education, a good health status indicator, a sedentary-job type indicator, and a recently pregnant indicator), household non-labor income, number of children, state and year fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Standard errors are reported in parentheses. Sampling weights are used. *** p-value<0.01, ** p-value<0.05, * p-value<0.1

Seemingly unrelated regressions of log annual hours of work and log BMI. PSID 1999-2007.

Note: Regressions, which are simultaneously estimated, include own and spousal characteristics (age, log-hourly wage, completed years of education, a good health status indicator, a sedentary-job type indicator, and a recently pregnant indicator), household non-labor income, number of children, state and year fixed effects. Men aged 28-50 and working more than 1000 hours per year, women aged 26-48 working more than 750 hours per year, both earning more than $5 per hour and non-disabled. Married individuals are those with a marital duration of at least 4 years. Standard errors are reported in parentheses. Sampling weights are used. *** p-value<0.01, ** p-value<0.05, * p-value<0.1

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25. 2010-11: “The Spanish Business Bankruptcy Puzzle and the Crisis”, Marco Celentani, Miguel García-Posada y Fernando Gómez.
26. 2010-10: “Promoting Employment of Disabled Women in Spain; Evaluating a Policy”, Judit Vall Castello.
27. 2010-09: “The Role of Construction in the Housing Boom and Bust in Spain”, Carlos Garriga.
28. 2010-08: “Did Good Cajas Extend Bad Loans? Governance, Human Capital and Loan Portfolios”, Vicente Cuñat y Luis Garicano.
29. 2010-07: “Unemployment and Temporary Jobs in the Crisis: Comparing France and Spain”, Samuel Bentolila, Pierre Cahuc, Juan J. Dolado y Thomas Le Barbanchon.
30. 2010-06: “La Subida del Impuesto Sobre el Valor Añadido en España: Demasiado Cara y Demasiado Pronto”, Juan Carlos Conesa , Javier Díaz-Giménez, Julián Díaz-Saavedra y Josep Pijoan-Mas.
31. 2010-05: “Off-the-peak preferences over government size”, Francisco Martínez-Mora y M. Socorro Puy.