Psychological traits and the gender wage gap

Transcription

1 Psychological traits and the gender wage gap Sarah Cattan The Institute for Fiscal Studies October 13, 2013 Abstract This paper examines the role that psychological factors play in explaining the gender wage gap. To do so, I propose a methodology that extends the standard approach used in the literature interested in this question in three main dimensions. First, I rely on an economic model that captures multiple channels through which gender differences in traits can influence gender wage inequality. Second, I account for measurement error in the measures of psychological traits by using latent factor models. Third, I estimate entire counterfactual wage distributions in order to measure the contribution of gender differences in traits to the gender wage gap along the whole wage distribution instead of focusing on its mean. Implementing this methodology in the National Longitudinal Survey of Youth 1979, I find that gender differences in cognition and self-confidence explain a considerable fraction of the gender wage gap, with the majority of this effect being due to gender differences in self-confidence. Moreover, I establish evidence of substantial heterogeneity in the effect that gender gaps in psychological traits have on the gender wage gap along the wage distribution. In particular, gender gaps in self-confidence and, to a lesser extent, cognition explain a greater fraction of the gender wage gap at the top than at the bottom of the wage distribution. By comparing my estimates to those obtained from implementing two standard decomposition methods widely used in the gender wage gap literature, I show that failing to account for the heterogeneity of returns to traits across occupations and for measurement error in observed measures of traits leads to substantial biases in the analysis of the role that psychological factors play in explaining the gender wage gap. I thank James Heckman, Steven Durlauf, Jeffrey Grogger, Mathilde Almlund, Gary Becker, Marianne Bertrand, Miriam Gensowski, Robert LaLonde, Remi Piatek, Edward Vytlacil and Laura Wherry for their ideas, suggestions and comments. I thank the Esther and T.W. Schultz Endowment and the University of Chicago for their financial support. The appendix is available upon request from the author. All remaining errors are mine.

2 1 Introduction After decades of stagnation, the gender wage gap substantially decreased in the 1980s. Since the early 1990s however, the pace of convergence between male and female wages has slowed down, although females have continued to improve their relative qualifications in dimensions that matter for labor market success (Blau and Kahn, 2007). Cohorts of females born in the late 1950s not only eliminated, but reversed the male lead in college attendance and graduation rates. Females continued to increase their rate of labor force participation and to enter occupations, such as managerial and professional ones, which had traditionally been dominated by males (Goldin, 2006). In light of such remarkable gains in traditional measures of human capital, the slowdown in the narrowing of the gender wage gap raised a puzzle, which urged researchers to think of new possible explanations for gender differences in labor market outcomes. As part of this effort, this paper concentrates on the hypothesis that cognitive and non-cognitive traits of personality play a role in explaining the gender wage gap. This hypothesis has arisen from two important developments in the economics literature of the past decade. On the one hand, the growing influence of psychology on economics has led to the emergence of a large body of work on the importance of psychological traits for a variety of outcomes, including wages, education, and occupational choice (Almlund et al., 2011). On the other hand, there is now robust evidence from surveys and experiments that males and females differ in a variety of psychological dimensions (Bertrand, 2011). Despite promising evidence that psychological traits should matter for the gender wage gap, the few existing empirical investigations of this hypothesis have failed to find strong support for its relevance (Fortin, 2008; Manning and Swaffield, 2008; Mueller and Plug, 2006; Nyhus and Pons, 2011). Whether or not this hypothesis will have a long-term impact on our understanding of the origins of gender wage inequality thus remains to be ascertained. Methodologically, this entire body of work is based on linear wage models that implicitly assume a one-sector economy in which traits have a direct effect on wages. The wage equation is usually estimated by ordinary least squares and the coefficient estimates used to implement the traditional Oaxaca-Blinder decomposition of the gender gap in mean wages. In this paper, I argue that there are three, conceptually distinct reasons why this methodology might have led researchers to mis-measure the effect that psychological factors have on gender wage inequality. The first one is related to the underlying economic model; the second one to the measurement of traits; and the third one to the use of the Oaxaca-Blinder decomposition to measure the contribution of 1

3 gender gaps in traits to the gender wage gap. First, the existing empirical literature relies on an implicit model of wage inequality, which assumes that inequality in traits only determines the wage distribution by affecting productivity directly and uniformly across sectors. By ignoring the possible effects that traits have on wages through human capital investments and the sorting of workers across sectors of the economy, this model could fail to capture the full impact of traits on the gender wage gap. Second, the existing literature relies on observed measures of psychological traits, which might be contaminated by measurement error and hence fail to accurately capture gender gaps in psychological dimensions. Third, previous studies rely on the Oaxaca-Blinder decomposition to assess the contribution of gender gaps in traits to the gender wage gap. In doing so, they focus on measuring the effect of average gaps in psychological traits on the gender gap in mean wages and thus potentially miss greater effects at other points of the wage distribution. Therefore, the objective of this paper is to revisit the existing evidence on the role of psychological traits in explaining gender wage inequality by using a more comprehensive methodology. More precisely, the methodology I propose extends the standard approach in three main directions. First, I consider a model in which traits affect the wage distribution through a richer set of mechanisms; I model a multi-sector economy in which psychological traits shape the wage distribution not only through their occupation-specific effects on productivity, but also through their effect on occupational choice, educational attainment, experience, and fertility. Second, I use latent factor models to measure psychological traits and account for potential measurement error and systematic biases for or against a particular gender. Third, I rely on an econometric strategy that allows me to measure the contribution of gender gaps in traits to the gender wage gap along the entire wage distribution. The model is estimated by maximum likelihood using data from the National Longitudinal Survey of Youth 1979 (NLSY 79) on the outcomes of males and females born between 1957 and 1964 at four points of their life-cycle (23-27, 28-32, 33-37, and years old). The NLSY 79 is rich in psychological measurements, which I use to measure the male-female gap in two latent traits cognition and self-confidence. Males are found to be significantly more self-confident than females on average, but the distributions present no major difference in variance between genders. On the other hand, there is no significant gender gap in cognition on average, but males have greater variance on this trait than females. The model estimates indicate that workers sort into occupational categories according to their 2

4 comparative advantage in cognition and self-confidence, as well as education and experience. These variables have heterogeneous effects on wages across occupations, and they are significant determinants of occupational decisions. Additionally, both cognition and self-confidence have an impact on education and experience. Having shown that the model provides a reasonable fit of the data, I use the model and its estimates to assess the impact of psychological traits on the male-female wage differential. Gender differences in the joint distribution of cognition and selfconfidence explain between 7 and 15% of the gender gap in wages on average, depending on the age group. Most of this effect is driven by gender differences in self-confidence, which explain an increasing fraction of the gender wage gap over the career. Going beyond the mean, I find evidence of substantial heterogeneity in the contribution of traits to the gender gap along the wage distribution. As an example, in most age groups, gender differences in cognition and self-confidence explain at least twice as much of the gender wage gap at the 9th decile than at the 1st decile of the distribution. By explicitly modeling how the male and female wage distributions are determined, the framework helps provide an economic rationale for this heterogeneity. In particular, I explain that it is a product of gender differences in the variance of trait distributions, heterogeneous returns to traits across occupations, and workers occupational sorting based on psychological traits. My paper contributes to the literature on the origins of gender wage inequality by extending the standard framework of analysis in dimensions that empirically matter. I consider a general economic model that accounts for previously unexplored but potentially important mechanisms through which traits may impact wages and hence the gender wage gap. In addition, the econometric strategy based on factor models allows me to both account for measurement error in observed measures of traits and identify the contribution of traits to the gender wage gap along the entire wage distribution. The empirical analysis shows that incorporating these features is of critical importance and helps explain why previous studies failed to find evidence that cognitive and non-cognitive traits are relevant to understand male-female wage differentials (Fortin, 2008; Manning and Swaffield, 2008; Nyhus and Pons, 2011). Until recently, the majority of studies on the gender wage gap have relied on the Oaxaca (1973) - Blinder (1973) decomposition of the gender gap in mean wages. A major development in the past decade has been the emergence of methods aimed at going beyond the means." Among them, researchers have proposed quantile decomposition (Mata and Machado, 2005), reweighing (Dinardo et al., 1996), or residual imputation methods (Juhn et al., 1993). My paper complements 3

5 this work by offering an approach based on an explicit economic model that provides a rationale for why various skills have unequal power in explaining the gender gap along the wage distribution. Furthermore, my results strengthen this literature by providing a case in point that going beyond the means is a fruitful avenue to understand gender wage inequality. The rest of this paper is organized as follows. Section 2 reviews the existing literature on psychological factors and the gender wage gap and motivates the central ideas of this paper. Section 3 presents the methodology and Section 4 its implementation in the NLSY 79. Section 5 discusses the model estimates and their implications with respect to the role that psychological traits play in explaining the gender wage gap. Section 6 compares my methodology and results to two widely used decomposition methods in the gender wage gap literature (the Oaxaca-Blinder and Juhn et al. (1993) decompositions) and analyzes the bias that results from using these standard approaches. Section 7 concludes. 2 Background and Motivation 2.1 Evidence on psychological traits and the gender wage gap While economists have long equated skill with intelligence or IQ, the past decade has seen the emergence of a literature interested in studying how other aspects of personality affect economic and social behavior. A growing consensus has emerged around the idea that the relevant set of skills or attributes is multi-dimensional and incorporates both cognitive and non-cognitive traits. As comprehensively reviewed in Almlund et al. (2011), these dimensions of personality have been found to affect a wide array of outcomes. For example, Heckman et al. (2006) show that both cognitive and non-cognitive factors affect wages, educational attainment, labor force participation, occupational choice, and teen pregnancy. Other studies have established their empirical importance in explaining health outcomes, longevity, and criminal activity (see Heckman et al. (2012), Conti et al. (2012), Savelyev (2012), among others). Thanks to both experimental and survey data, researchers have also been able to identify psychological dimensions along which males and females tend to systematically differ. A popular classification of personality traits is the Big Five typology, which includes openness to experience, conscientiousness, extroversion, agreeableness, and neuroticism. As suggested in Bouchard and Loehlin (2001), women are consistently found to be both more agreeable and neurotic than men. In their study of the Wisconsin Longitudinal Study, Mueller and Plug (2006) also note that women 4

6 have slightly higher conscientiousness and extraversion than men. Self-esteem and locus of control are two other traits along which males and females have been found to differ. Self-esteem refers to individuals subjective estimation of their own worth, whereas locus of control refers to their opinion about whether the determinants of their life events are self-determined (internal) or determined by luck and outside factors (external). Both Fortin (2008) and Manning and Swaffield (2008) find that men have higher self-esteem and a more internal locus of control than women in the National Education Longitudinal Study (NELS) 1972 and 1988 and the British Cohort Survey, respectively. Although locus of control and self-esteem are not part of the Big Five typology, they have been associated with the Big Five trait of Neuroticism and Emotional Stability. 1 These traits deserve particular attention, since they are more often measured than the Big Five traits in longitudinal surveys used by economists. In particular, they are measured in the National Longitudinal Survey of Youth 1979, the dataset I use in my paper. Together, these findings suggest that gender differences in psychological traits could be a possible explanation for gender differences in labor market outcomes. A few recent papers have started exploring this hypothesis, but so far the research has been quite limited in its ability to establish the importance of these factors in explaining gender wage inequality. Despite finding that females have lower self-esteem and a more external locus of control than males, Manning and Swaffield (2008) show that these measures explain little more than 2% of the gap in the British Cohort Survey. Using a Dutch panel from the DNB Household Survey, Nyhus and Pons (2011) find that gender differences in locus of control explain 0.05% of the gender wage gap. Based on the NELS 72 and NLS 88, Fortin (2008) concludes that gender differences in self-esteem and locus of control are irrelevant to explain the wage gap. 2 Finally, based on data from the Wisconsin Longitudinal Survey, Mueller and Plug (2006) find that 3 to 4 percent of the gender gap in average earnings is explained by gender differences in the Big Five traits and gender differences in their returns. Thus, so far, the existing evidence has been relatively unsupportive of the importance of psychological factors in explaining male-female differences in wages. 1 As Almlund et al. (2011) reviews, Judge and co-authors argue that locus of control, self-esteem, and and Big Five Emotional Stability are associated with a common construct, terms as core self-evaluation. They point that positive core self-evaluations reflect a generally proactive and positive view of oneself and one s relationship to the world, which can be related to the Big Five trait of Neuroticism and Emotional Stability. 2 Fortin (2008) also includes a measure of cognitive skill (math score) in her analysis and finds that the gender gap in this measure of cognition explains between 1.5 and 5% of the wage gap depending on the specification. 5

7 2.2 Methodology underlying the existing evidence The Oaxaca-Blinder decomposition While the aforementioned studies rely on different datasets, they employ a similar methodology to quantify the role of psychological factors in explaining the gender wage gap. In particular, they rely on the following linear log wage model: ln W g = X g β g + ɛ g E(ɛ g ) = 0 (1) where the superscript g is g = m for males and g = f for females, X g contains the regressors and a constant, β g contains the gender-specific slope parameters and the intercept, and ɛ g is the error. The vector X g usually includes work experience and other individual characteristics related to productivity. The most common measure of productivity is schooling, but several of these papers also include other variables, such as occupation and industry indicators, dummies for part-time work and unionized status (see Altonji and Blank (1999) for an extensive review). In light of the evidence on the importance of personality for labor market outcomes, the papers reviewed above also include observed measures of cognitive and non-cognitive traits. 3 The theoretical motivation for these specifications is human capital theory (Becker, 1964) and the coefficients of the wage equation are interpreted as the returns on different types of investments in human capital. In this model, the error term is thought of capturing unobserved individual specific skills, effort, and motivation. With a few exceptions that I discuss below, most studies of the gender wage gap estimate the wage equation (1) by ordinary least squares (OLS). The OLS estimates of the wage equation are then used to implement the Oaxaca (1973) - Blinder (1973) (OB) decomposition of the gender gap in mean wages, which can be expressed as: ln W m ln W f = (X m X f ) ˆβ }{{} f + X m ( ˆβ m ˆβ f ) }{{} A B (2) 3 The literature has used various measures of cognitive and non-cognitive ability, depending on their availability in the dataset of interest. With respect to cognition, Heckman et al. (2006) and Urzua (2008) relies on different math and verbal test scores from the ASVAB, an achievement test score used to determine qualification for enlistment in the US armed forces. Fortin (2008), on the other hand, proxies cognitive ability by an individual s high school math score, whereas Manning and Swaffield (2008) do not include any measure of cognitive ability (besides schooling). A great discussion of the different measures of cognition used in the literature is available in Almlund et al. (2011). With respect to non-cognitive traits, both Fortin (2008) and Manning and Swaffield (2008) use measures of locus of control and self-esteem. In addition, a few recent studies comparing male and female non-cognitive skills and their role in explaining the gender gap in education has relied on measures of externalizing behavior (Jacobs, 2002). 6

8 where X g is the vector of average characteristics for gender g (g = f, m). This technique decomposes the gender gap in mean log wages into a component attributable to gender differences in average characteristics (A) and a component attributable to gender differences in coefficients (B). 4 Based on this methodology, the existing empirical literature on psychological traits and the gender wage gap has concluded that gender gaps in cognitive and non-cognitive traits only play a minor role in explaining gender wage inequality. I argue however that this standard framework of analysis makes assumptions that might lead researchers to mis-measure the effect of traits on the male-female wage differential. For expositional clarity, I elaborate on this point by distinguishing among the assumptions pertaining to 1) the economic model, 2) the measurement of traits, and 3) the decomposition method used to quantify the contribution of traits to the gender wage gap Economic model A first concern with the standard approach is whether the underlying model allows to adequately capture the mechanisms through which traits determine the wage distribution. The model specified in equation (1) makes four particular assumptions that might be important to relax when answering the question of interest. (a) The direct effect of traits on wages is identical across sectors of the economy. This assumption contrasts with the notion that skills are more productive in certain jobs than in others. For example, one could reasonably posit that self-esteem may be more valuable to a manager than a blue-collar worker. This hypothesis is not only intuitive, but has also been corroborated by several studies that have looked at other measures of productivity (Gould, 2002; Heckman and Sedlacek, 1985; Keane and Wolpin, 1997). Given that female occupational segregation is important (Bayard et al., 2003; Groshen, 1991), accounting for the fact that males and females face non-uniform returns to their productive characteristics across occupations may be particularly relevant when analyzing the gender wage gap. (b) Workers do not select into the labor force on the basis of their traits. This assumption contrasts with a substantial body of literature providing evidence that females sort into the workforce based on their unobservables (Blundell et al., 2007; Heckman, 1974, 1979; Machado, 2010; Mulligan and 4 As discussed in Fortin et al. (2011), one characteristic of this type of decomposition is that whether it is performed from the male viewpoint or from the female viewpoint may not lead to the same conclusions. The decomposition above is formulated from the viewpoint of the female group, i.e. the group differences in the predictors are weighted by the female coefficients to determine the size of explained coefficient. Such decomposition answers the counterfactual question of what the average wage gap would be if females had the average characteristics of males but kept facing the female coefficients. Naturally, the differential can analogously be expressed from the male viewpoint or can be performed using coefficients estimated on the pooled sample. 7

9 Rubinstein, 2008; Neal, 2004; Vella, 1998). These studies do not control for cognitive and psychological traits, so the unobservables they discuss as determinants of labor force participation could well include these factors. If this is the case, gender differences in traits could affect the gender wage gap through their effect on the selection of workers in the labor force. (c) Workers do not select across occupations on the basis of their traits. The notion of comparative advantage influencing occupational choice goes back to papers by Roy (1951) and Tinbergen (1956). It has been supported by a wealth of studies, which have provided evidence of comparative advantage in education, general cognitive ability, and quantitative ability (Gould, 2002; Heckman and Sedlacek, 1985; Paglin and Rufolo, 1990). Furthermore, a few papers have found evidence that personality traits affect the choice of occupation (Filer, 1986; Ham et al., 2009; Heckman et al., 2006). This suggests that a channel through which gender differences in the distribution of traits could drive the gender wage gap is by creating gender gaps in occupational sorting (Cobb-Clark and Tan, 2011). 5 Accounting for this channel might be particularly important because, if workers sort on their comparative advantage in traits, the degree of gender wage inequality within a sector will be determined both by the gender gap in trait prices in that sector and by the gender gap in traits among workers who select into that sector. As a result, the role of the traits in explaining gender wage inequality could be strong in certain sectors and weak in others, but such heterogeneous effects would likely be missed in an analysis that assumes this feature of the data away. (d) The variables in the vector X are not determined by the traits. While there is an extensive literature on the potential bias resulting from the endogeneity of education, experience, and fertility in wage equations, only a few studies of the gender wage gap have adopted estimation methods other than OLS estimators to tackle this issue (Hansen and Wahlberg, 1995). Among other reasons, the endogeneity of education and experience could result from their correlation with psychological traits, if the latter are omitted from the wage equation. Indeed, several studies have found some evidence that these variables are determined by cognitive and non-cognitive traits (Conti et al., 2012; Heckman et al., 2006; Jacobs, 2002; Piatek and Pinger, 2010). In this case, gender differences in traits could contribute to the gender wage gap by creating gaps in education and 5 Note that assumption that workers do not select across occupations on the basis of their traits is intrinsically linked to assumption of uniform productivity of traits across sectors since the existence of heterogeneous returns to traits across sectors could be one reason for non-random sorting of workers across the economy. However, if traits did not have any effect on productivity, but still affected occupational preferences, it would still be the case that gender differences in traits could lead to gender differences in wages by pushing males and females into different occupations, in which they would face different rewards to their productive characteristics. 8

10 experience, another channel that might be important to account for Measurement of psychological traits A second main concern regarding the standard approach is whether the traits are measured accurately. Existing studies of psychological factors for the gender wage gap rely on multi-item selfreported instruments and construct measures of cognitive and non-cognitive traits by averaging across items of various achievement and personality scales. Several studies have shown however that self-reported instruments are contaminated with measurement error (Heckman et al., 2011, 2006; Urzua, 2008). While averaging decreases purely random measurement error, it however imposes that items are related to the underlying construct in the same way across items and genders. This practice might be particularly problematic when analyzing gender differences in traits, as test scores might be systematically upward or downward biased for a particular gender. For example, girls have been found to perform worse in competitive test-taking environments than in less competitive ones, thus suggesting that competitive pressure could lead gender gaps in observed test scores to over- or under-estimate gender gaps in underlying traits and abilities (Niederle and Vesterlund, 2010) Decomposition method A third main concern with existing studies is that they rely on the Oaxaca-Blinder decomposition and thus focus on quantifying the contribution of gender differences in mean traits to the gender gap in mean wages. However, if there are gender differences in the variance of trait distributions and/or if workers face unequal returns to their traits across occupations, it is likely that gender gaps in traits will have heterogeneous effects on the gender wage gap along the wage distribution. Thus, failing to find that psychological factors have large effects on the gender wage gap at the mean might not necessarily imply that psychological traits are irrelevant to explain gender wage inequality as a whole. As reviewed by Fortin et al. (2011), the past decade has seen a lot of work aimed at extending decomposition methods to distributional parameters other than the mean. Among others, this includes extensions of the Oaxaca-Blinder decomposition to quantile regressions (Albrecht et al., 2003; Mata and Machado, 2005; Melly, 2005), the semi-parametric reweighing method proposed by Dinardo et al. (1996), and the residual imputation method of Juhn et al. (1993). While some of these methods have been implemented to analyze the role of gender gaps in experience or 9

11 education, it is surprising that such an exercise has never been performed to analyze the role of psychological factors. Thus, I have outlined three main reasons why the standard approach based on equations (1) and (2) might lead researchers to mis-measure the contribution of psychological traits to gender wage inequality. A re-assessment of the evidence is in order, and the goal of my paper is to do so by using an approach that takes into account each of these issues. In what follows, I present a framework that 1) relaxes assumptions (a) through (d) of the model determining the wage distribution, 2) accounts for measurement error and gender biases in observed measures of traits, and 3) quantifies the contribution of traits to the gender wage gap along the entire wage distribution. Through my results, I will show that accounting for these features matters for our understanding of the gender wage gap. I will precisely assess the extent to which they do by comparing my results with the Oaxaca-Blinder decomposition and the Juhn et al. (1993) technique, two of the most widely used decomposition methods in the gender wage gap literature. 3 Methodology 3.1 Econometric model The econometric model that I estimate is an approximation to a standard life cycle model of education, labor supply, occupation, and fertility decisions. Males and females are heterogeneous in their endowments of psychological traits. I denote θ g the vector of psychological traits for an individual of gender g (g = f for females and g = m for males). Let F denote the index set for traits and θ j g the j th element of the vector of traits (j F). 6 In the initial period, individuals choose to obtain one of four educational levels in order to maximize their discounted present value of net lifetime utility. They can either 1) drop out of high school and/or get a GED, 2) graduate from high school, 3) go to college for some years and/or get a 2-year college degree, or 4) obtain a 4-year college degree. This choice is denoted by a dummy S g,r that equals 1 if an individual of gender g chooses schooling level r (r = 1,..., 4). The cost of schooling includes both monetary and psychic costs, which are determined by the agent s endowments in psychological traits and 6 The model remains silent on the way these traits are acquired and treats the traits as exogenous. However, because the tests are taken between the ages of 14 and 22, I rely on the factor models to control for the possible reverse causality of schooling on the measures of traits at the time the measure is taken. This will be further discussed in section 3.2. Papers, such as Cunha et al. (2006, 2010) and Heckman et al. (2010), treat the issue of skill formation before labor market entry. 10

12 other variables, such as family background. 7 In every subsequent period, individuals make three types of decisions. First, they choose whether to have a child and hence implicitly their total number of children in that period (F g,t ). Next, they choose whether to participate in the labor force. Third, if they work, they choose to work in one of five occupational categories: professionals, managers, sales and service workers, clerical workers, and blue-collar workers. 8 I integrate the labor force participation decision into the occupational choice model by defining the sixth occupational category as household production. I denote the occupational decision of an individual of gender g by a dummy D g,k,t that equals 1 if individual of gender g works in sector k at time t (k = 1,..., 6). 9 In each period, workers utility depends on non-pecuniary benefits and, if they work, on their wages. Wages are determined by workers education, experience, and number of children, as well as their endowment of psychological traits. 10 The effect of these characteristics on wages are allowed to be both sector and gender specific. 11 Additionally, males and females are allowed to have different preferences over their educational attainment, fertility, labor supply, and occupational choices. For notational clarify, I leave the individual subscript implicit, but index all the parameters of the model by gender. With this economic set up in mind, I now describe the econometric equations that I estimate in the NLSY 79 to approximate it. Schooling The educational choice is modeled as an unordered discrete choice model in which the discounted present value of net lifetime utility of an individual of gender g choosing educa- 7 The schooling decision is not sequential and, once individuals leave school, they cannot return. 8 An ideal version of this model would allow more finely defined jobs in order to capture further the heterogeneity with which characteristics affect wages. The sample size of the NLSY 79 however does not allow me to implement the model with more than five occupational categories. 9 I simplify the labor supply decisions to working (full-time) or not working in order to compare males and females with more similar labor force attachment. While it would be very interesting to model other states of labor supply, such as part-time or part-year work, which are particularly prevalent among females, preliminary estimation of a multinomial model of labor supply with more than two labor supply states has revealed that modeling such subtleties are not of first-order importance when answering the question of interest in this paper about the role that traits play on the gender wage gap. In addition, the multinomial model provided a worse fit of the labor supply decisions than the model presented here. Hence, I chose to focus solely on full-time workers. 10 The number of children is included in the wage equation to account for the possibility suggested by Becker (1985) that greater domestic commitments of women with children could imply that they put less energy in their market work and thus receive lower wages. 11 The parameters of the wage equation can be interpreted as measuring the price or return to productive characteristics or the productivity of characteristics in each occupation. Depending on the interpretation of these parameters as prices or technology parameters, gender differences would reflect discrimination or gender differences in the types of jobs males and females sort into within each occupational category. 11

13 tional level r is approximated by: S g,r = ρ g,r X s g,r + α s g,rθ g + υ s g,r r = 1,..., 4 where X s g,r is a vector of observable characteristics affecting the schooling decision and υ s g,r an error term. Occupational choice The choice of occupation among five market occupations and household production is modeled as an unordered discrete choice model, where the underlying utility of an individual of gender g choosing occupation k at time t is approximated by: D g,k,t = δ 1,g,k,tS g + δ 2,g,k,t E g,t + δ 3,g,k,t F g,t + δ 4,g,k,t X d g,t + α d g,k,t θ g + υ d g,k,t k = 1,..., 6 where X d g,t is a vector of observable characteristics and υd g,k,t an error term affecting D g,k,t. Potential wages k at time t is written as: The potential log wage for an individual of gender g if working in occupation W g,k,t = β 1,g,k,t S g + β 2,g,k,t E g,t + β 3,g,k,t F g,t + β 4,g,k,t X w g,t + α w g,k,t θ g + υ w g,k,t k = 1,..., 5 where X w g,t is a vector of observable characteristics and υw g,k,t sector k at time t. an error term affecting wages in Experience following linear model: The experience level of an individual of gender g at time t is approximated by the E g,t = η 1,g,t S g + η 2,g,t X e g,t + α e g,tθ g + υ e g,t where X e g,t is a vector of observable characteristics and υe g,t an error term affecting experience. Fertility The number of children of an individual of gender g at time t is also approximated by the following linear model: F g,t = ζ 1,g,t S g + ζ 2,g,t X f g,t + α f g,tθ g + υ f g,t 12

14 where X f g,t is a vector of observable characteristics and υf g,t an error term affecting fertility. 3.2 Counterfactual analysis of gender wage inequality Assuming the model above is an accurate representation of how the wage distribution is determined, the observed log hourly wage for an individual of gender g at time t is given by: W A g,t = 5 D g,k,t (θ g, X g,t, Z g,t (θ g )) W g,k,t (θ g, X g,t, Z g,t (θ g )) (3) k=1 where I have grouped the three determinants of wage and occupational choice depending on traits (schooling, experience, fertility) into the vector Z g,t = (S g, E g,t, F g,t ). The subscripts on Z g,t, D g,k,t, W g,k,t indicate that the parameters underlying these functions are those associated with gender g, occupation k, and time period t. The traits θ g are drawn from the joint distribution of traits specific to gender g, which I denote F g θ (θ). Let h(wg,t A ) the corresponding density of actual wages for gender g (g = f, m). The actual male-female gap in wage distribution at time t can be expressed as: A t = h(w A m,t) h(w A f,t ) The goal of my paper is to measure the contribution of gender differences in psychological traits to A t to A t (endowment effect) and the contribution of gender differences in the returns to traits (price effect). In the simple set up reviewed in Section 2, these objects simply correspond to elements A and B defined in equation (2). In the framework proposed above however, the definition of these objects is not as straightforward. For example, because traits affect the wage distribution through various direct and indirect channels, one might not only be interested in measuring the contribution of gender differences through all channels, but also the relative importance of each channel. In this section, I define the objects that I aim to recover and show how each of them correspond to a particular counterfactual exercise Contribution of gender differences in the joint distribution of traits The model proposed in Section 3.1 allows traits to affect the wage distribution through various channels. As a result, I aim to quantify their contribution through all channels (total contribution), as well the contribution through each individual channel. 13

15 Total contribution of gender differences in the joint distribution of traits The total contribution of gender differences in the joint distribution of traits can be estimated as the difference between the actual gender wage gap and what the gender wage gap would be if females had the male joint distribution of traits and all of their outcomes were affected by this change. Under this counterfactual scenario, the wage of a female would be: 5 Wt C = D f,k,t (θ, X f,t, Z f,t (θ )) W f,k,t (θ, X f,t, Z f,t (θ )) k=1 where the counterfactual traits θ are drawn from F m θ (θ), the male joint distribution of traits. The formulation above clearly shows that the counterfactual female traits θ are allowed to affect the wage distribution not only directly, but also through the choice of occupation, as well as the endogenous determinants of wage and occupational choice (education, fertility and experience) grouped in Z f,t (θ ). Let h(wt C) the corresponding density of counterfactual wages. With knowledge of h(wc t ), the contribution of gender differences in the joint distribution of traits in period t (C t ) can be computed at any point of the wage distribution by comparing the gender wage gap under this counterfactual ( C t ) with the actual gender wage gap ( A ). That is, C t = A t C t where C t = h(w C t ) h(w A m,t) Direct contribution of gender differences in the joint distribution of traits The contribution of gender differences in the joint distribution of traits through their direct effect on wages can be estimated from the counterfactual distribution of wages females would have if they had the male joint distribution of traits, but these counterfactual traits only affected their wages directly without affecting their occupational choice, education, experience, and fertility. For each female, this counterfactual wage W D t W D t = can be written as: 5 D f,k,t (θ f, X f,t, Z f,t (θ f )) W f,k,t (θ, X f,t, E f,t (θ f )) k=1 where θ F m θ (θ) and θ f F f θ (θ). I denote h(wd t ) the corresponding density of wages. The direct contribution of gender differences in the joint distribution of traits (D t ) can then be 14

16 recovered by comparing the gender gap in wage distribution under this counterfactual ( D t ) with the actual gender gap in wage distribution ( A t ). That is: D t = A t D t where D t = h(w D t ) h(w A m,t) Indirect contribution of gender differences in the joint distribution of traits In the model of Section 3.1, gender differences in the joint distribution of traits can also affect the wage distribution indirectly by creating gender gaps in occupational choice, education, experience and fertility. Applying a similar methodology as above, it is possible to estimate their contribution through these indirect channels. For example, the indirect contribution of gender differences in traits through education (I edu t ) could be recovered by estimating the following counterfactual wages for each female: W Iedu t = 5 D f,k,t (θ f, X f,t, Z f,t (θ f ))W f,k,t (θ, X f,t, S f (θ ), E f,t (θ f ), F f,t (θ f )) k=1 where θ F m θ (θ) and θ f F f θ (θ). In this counterfactual, counterfactual female traits affect WIedu both through their direct impact on wages and through educational attainment. As a result, the contribution of gender differences in the joint distribution of traits through the educational channel can be isolated as: I edu t = Iedu t D t where Iedu t = h(w Iedu ) h(wm,t) A t where h(w Iedu t ) is the density of counterfactual wages Wt Iedu. Similarly, it would be possible to isolate the contribution of gender differences in traits to the gender wage gap through their impact on experience, fertility and occupational choice Contribution of gender differences in the marginal distribution of each trait While I have so far focused on estimating the contribution of gender differences in the joint distribution of traits, I now define the counterfactuals to be recovered in order to measure the contribution of gender differences in the marginal distribution of each trait. Because the traits are allowed 15

17 to be correlated, a counterfactual exercise involving females having the male marginal distribution of one trait will affect the remaining dimensions of traits. In the equations below, I refer to the j th dimension of the vector of traits as θ j and to the F 1 remaining ones as θ j. The total contribution of gender differences in the marginal distribution of θ j can be quantified by estimating the following counterfactual wage distribution: W C j t = 5 k=1 D f,k,t (θ j, θ j f, X f,t, Z f,t (θ j, θ j f )) W f,k,t(θ j, θ j f, X f,t, Z f,t (θ j, θ j f )) where θ j is drawn from the male marginal distribution, H m θ j (θ j ), and θ j f is drawn from the female conditional distribution H f θ j θ j (θ j θ j ), so the correlation between the traits is the female correlation. 12 Using the corresponding density of counterfactual wages (h(w C j t )), the contribution of gender differences in θ j to the gender wage gap (C j t ) could be recovered by comparing the actual gender wage gap with the gender wage gap under this counterfactual. That is: C j t = A t Cj t where Cj t = h(w Cj ) h(wm,t) A t The contribution of gender differences in the marginal distribution through each channel could be defined in a similar fashion as above Contribution of gender differences in the wage returns of traits The last object that I aim to estimate is the contribution of gender differences in the wage returns of traits to the gender wage gap. This object can be quantified by estimating the counterfactual wage distribution that females would have if they faced the male wage coefficients on their traits. To define these counterfactual precisely, I now make explicit the parameters on the observables and on the traits in the wage equations in the definition of equation (4). That is, the observed log 12 Note that there is a variety of alternative counterfactuals that can be performed. For example, it might be interesting to also perform the counterfactual experiment where θ j is drawn from the male marginal distribution and θ j is drawn from a conditional distribution where the correlation between the dimensions of θ is set to the male value. Because the correlation between the traits is estimated to be very similar for males and females, I will only implement the counterfactual defined in the text holding the correlation coefficient at the female value. 16

18 wage for an individual of gender g can be written as: 5 Wg,t A = D g,k,t (θ g, X g,t, Z g,t (θ g )) W(θ g, X g,t, Z g,t (θ g ); α w g,k,t, β g,k,t) k=1 where α w g,k,t and β g,k,t groups the wage coefficients on the traits and on the observable characteristics, respectively. The contribution of gender differences in the wage returns of the j th trait to the gender wage gap can be defined as: Pt θj = A t Pθj t where Pθj t = h(wt Pθj ) h(wm,t) A 5 and W Pθj = D f,k,t (θ g, X f,t, Z f,t (θ f )) W(θ f, X f,t, Z f,t (θ f ); α w j,m,k,t, αw j,f,k,t, β f,k,t) k=1 where α w j,m,k,t refers to the male loading on the jth traits and α w j,f,k,t to the vector of female loadings on the remaining traits. Note that this counterfactual can easily be implemented to measure the contribution of gender differences in the wage returns to any other determinants of wages. Therefore, I have shown that the objects measuring the contribution of traits to the gender wage gap can each be defined in terms of a particular counterfactual wage distribution. Because these counterfactual distributions are not observed, some assumptions are necessary to identify them. This is what I discuss in the next section. 3.3 Modeling psychological traits as latent factors Previous studies accounting for the role of psychological traits on gender wage inequality measure personality by averaging across the components of diverse batteries of achievement and personality tests and include these averages as any other regressor in their analysis (Fortin, 2008; Manning and Swaffield, 2008; Mueller and Plug, 2006; Nyhus and Pons, 2011). However, measures of cognition and personality traits are distinct from other typical regressors in two ways: they usually include a multitude of test scores whose dimensionality needs to be reduced and they proxy underlying traits with error. In this paper, I account for these features by treating the psychological traits as unobservables and relying on factor analysis to extract latent measures of personality. 17

19 More precisely, I assume that the unobservables affecting all of the decisions of the model can be modeled as a linear function of latent traits (θ) and an idiosyncratic term (ɛ). Neither θ or ɛ are observed by the econometrician, but the agents may act upon their realizations if they are in their information set at the time of the decision. θ can be thought of the individual s personality traits and ɛ as macro and micro-economic shocks. Importantly for identification, the factors θ are assumed to be independent from the ɛ s. The factor structure is applied to all the terms υ of the equations of the model specified above. In the interest of space, I only illustrate it with the error term of the wage equation: υ w i,j,t = αw j,t θ i + ɛ w i,j,t where α w j,t is a vector of factor loadings measuring the effect of the traits θ i on wages in sector j and time t. These parameters can be interpreted as the wage returns or prices of the unobserved characteristics θ i in each sector. As with all the parameters of the model, the parameters α w j,t (j = 1,..., 5) are allowed to differ by sex. I interpret the latent factors θ as psychological traits by appending a system of measurement equations to the econometric model outlined above. These measurements proxy workers traits, but are allowed to do so with error and not necessarily equal weights. As elaborated in Almlund et al. (2011), this approach accepts a broad definition of measurements, including achievement and personality test scores, but also any behaviors that are thought to capture these traits. For example, I use early risky behaviors as measurements of a particular non-cognitive trait. While psychologists have long used factor models to measure underlying psychological factors, several recent papers in economics have adopted and extended the use of factor models to more general settings. 13 More specifically, suppose there are M measurements available, including M c continuous measurements and M M c discrete measurements. Each continuous measurement Tm c is written as: T c i,m = λ mk i + α t mθ i + ɛ t i,m m = 1,..., M c 13 See, for example, Carneiro et al. (2003) and Hansen et al. (2004), which prove the identification of factor models where the factor loadings depend on endogenous variables. More recently,? applies parsimonious bayesian factor analysis to estimate a factor model where the number of factors is unknown and treated as a parameter of the model. 18

20 and each discrete measurement Ti,m d is being determined by an underlying function: T d i,m = λ mk i + α t mθ i + ɛ t i,m m = M c + 1,..., M where K i is a vector of individual characteristics, α t m a vector of factor loadings, and ɛ t i,m an idiosyncratic error term. The interpretation of the factors as psychological traits is guided by the pattern of factor loadings α t m. For example, if some of these measurements are verbal and math test scores and the first component of θ i (θ i,1 ) loads more heavily on these measurements than on any others, I interpret this factor as cognition. The way psychological factors are measured in this paper greatly contrasts with the way they are measured in the existing empirical literature on the role of personality for the gender wage gap. I argue that this strategy has a number of advantages over the typical practice of using averages. First, it allows the measurements to depend on observable covariates K and thus control for the fact that characteristics, such as age and schooling level at the time of a test, may impact an individual s performance on a test without necessarily reflecting his or her latent ability. 14 Second, it allows me to reduce the dimensionality of the test scores without arbitrarily imposing that they all are related to the latent trait with equal weights, as they would be in averaging. While averaging can help offset purely random measurement error, the factor strategy accepts more flexible forms of measurement error ɛ t m. In particular, as I will elaborate further in Section 4, the measurement error can vary with each test and between genders. Thus, this strategy is likely to be more effective at purging the measures of traits from measurement error and correcting the coefficients from possible downward bias due to attenuation bias. 3.4 Self-selection and endogeneity While the factor strategy allows me to model the psychological traits, it is also instrumental to address the issues of self-selection and endogeneity in the model. The previous discussion has made explicit that certain determinants of the outcomes of the model, such as the agent s psychological traits, may not be perfectly observed by the econometrician. This possibility potentially creates two types of empirical issues. First, individuals may self-select into schooling, labor supply states, and occupations on the basis of their unobservables. If the unobservables driving educational, 14 Indeed, the estimates of the measurement system shown in Appendix B show that in the NLSY 1979, both schooling and age at the time of the test have a significant effect on achievement and personality test scores, thus further justifying this factor strategy. 19