City-Speciﬁc Racial Diﬀerences in the Labor Supply of Women ∗

: Theoretical and empirical analyses typically ignore geographic variation in female employment and racial diﬀerences in female employment outcomes. We document that there is substantial heterogeneity in female employment with respect to geographic location, race, and their interaction. We show that a parsimonious set of area-level controls explains a substantial portion of that heterogeneity. Our results suggest that analyses that ignore geographic variation may misstate the determinants of female employment, possibly producing erroneous conclusions and policy prescriptions. They also suggest that understanding geographic heterogeneity is crucial to understanding racial diﬀerences in female employment as well as female employment itself. correlation These results show that there are locational eﬀects in employment outcomes for women that a standard set of demographic characteristics cannot explain. These eﬀects are persistent across time and correlated across racial groups. The rest of the paper is dedicated to understanding the MSA locational eﬀects and their implications for racial diﬀerences in female employment.


INTRODUCTION
Female labor supply is a topic of substantial active research. 1 As women become a larger part of labor force and the gender gap in educational attainment narrows, understanding female employment becomes crucially important. Traditionally, much of labor economics focused on men and considered women to be secondary earners. Newer studies of women's employment outcomes show that women and men often have different key decision factors. Women have become in many cases equal earning partners in their families. However, their decisions concerning careers, marriage, fertility, and household production are much more entangled than the decisions of men. For example, Black et al. (2014) show that while commuting time is very important in the employment decisions of white married women, especially those with young children, it plays virtually no role in employment decisions of married men. Rosenthal and Strange (2012) provide evidence that female-owned businesses experience fewer agglomeration externalities than male-owned businesses, in part because women are more affected by commuting costs. Patrick et al. (2016) similarly show that women's motivations for self-employment are different from the motivations of men. Studies like these show that models of labor supply developed for men do not necessarily apply to women and highlight the importance of better understanding labor supply decisions of women. 2 Most studies of labor supply are conducted at the national level. When men constituted the majority of the labor force and were the primary subject of analysis, this was not a problem. According to Black et al. (2014), employment rates for married men vary little across locations. In contrast, for white married women, Black et al. (2014) show that there is large variation across metropolitan areas. This suggests that locational factors play a more important role in employment outcomes for women than for men. In this paper, we document two stylized facts. First, women have very different employment rates in different cities. Second, these patterns of geographic variation in employment rates are quite different between white and black women.
Our first point is most closely related to Black et al. (2014). While that paper focuses on white married women, we do not restrict our analysis to married women. We find that white women have employment rates that vary widely across metropolitan areas, even after controlling for the usual set of labor supply variables.
Next, we analyze employment rates for black women. 3 There is an extensive literature on black-white differences in female labor supply behavior. 4 Most of this literature has focused on national differences and the possible role that geography plays in determining these differences has been largely unexplored. In this paper, we find that there is a wide variation in employment rates for black women across metropolitan areas. More importantly, however, the patterns of geographic variation in employment rates are quite different between white and black women. Consider, for example, two large cities, Minneapolis and New York. In 2015, in Minneapolis, the employment rate of white women was 83 percent, but the employment rate of black women was only 67 percent (a 16 percentage point difference). On the other hand, in New York City, the employment rates for white and black women were almost identical at 75 and 73 percent, respectively. We document more generally that such geographic and racial differences in female employment rates are widespread and persistent over time.
These differences demonstrate that it is a mistake to treat the female labor force as a homogeneous entity. Empirical studies predicated on the idea of a homogeneous female labor force might lead to erroneous conclusions and result in public policies with unexpected consequences. Understanding all the factors that lead to this geographical and racial heterogeneity is a complex theoretical and empirical problem. Our goal here is much less ambitious. Using Public Use Micro Samples (PUMS) of the 50 largest metropolitan areas in the United States, we show that there is substantial heterogeneity in the employment rates of white and black women, as well as in the racial differences in those rates. While we do not attempt to uncover the underlying explanations for this heterogeneity, we do show that about threequarters of it can be explained by a relatively simple panel of city-specific factors. However, we emphasize that the explanatory power of these factors should not be interpreted causally. Our hope is to motivate a stream of future papers to explain the empirical regularities that we identify here.
The paper proceeds in three additional sections. Section 2 describes the data, Section 3 reports the empirical findings, and Section 4 offers concluding remarks.

DATA
This study focuses on the employment of black and white non-Hispanic women who live in the 50 largest Metropolitan Statistical Areas (MSAs) in the U.S. The data used in the analysis are the Public Use Micro Samples (PUMS) from the 2000 Census and a 5-year pooled sample of the American Community Surveys (ACS) from 2011-2015. 5 We use the 2000 Census sample because it is the last year for which the large sample is available. We include the most recent data from the ACS, but because of the smaller samples sizes of the ACS we pool the last 5 years of the data. For simplicity, we refer to this pooled sample as the 2015 sample.
The sample is restricted to individuals aged 25 to 55. 6 Two racial/ethnic groups are considered: white non-Hispanic women and black non-Hispanic women. Individuals with imputed values of key outcome and explanatory variables are excluded from the analysis.
We use the Metropolitan Statistical Area (MSA) as the unit of geographic analysis because it represents a well-defined geographic area where people both live and work, i.e. a "local labor market." Data support quickly becomes an issue for any analysis performed at the MSA level, especially for black women. Because of this, our analysis is focused on the largest 50 MSAs. 7 The IPUMS data provide information on employment status. The three main categories are employed, unemployed, and not in the labor force. Individuals' true labor force participation status is difficult to discern, particularly for women, who are more likely to be the margin along which households adjust their labor supply (Black et al., 2014). Consequently, the analysis here primarily looks at the "employment rate" as the measure of labor force participation in a local labor market, thereby including women who are reported as unemployed with those who are out of the labor force. 8 Included in the sample are women in the armed forces, but they constitute only a fraction of a percent of the sample.

EMPIRICAL INVESTIGATION
3.1. Overview of the Racial and Locational Differences in the Employment of Women  Table 1 summarizes these results. MSA-specific employment rates of white women, for example, varied between 66.7 and 83.6 percent in 2000 and between 64.4 and 83.5 percent in 2015. Thus, in some MSAs the employment rate of white women was as much as 10 percentage points below the national employment rate, while in other MSAs the employment rate of white women was as much as 10 percentage points above the national employment rate. This locational variation is significantly larger than variation over time over the past several decades. While there are many factors (such as an increase in educational attainment of women over time) that explain the cross-time variation in women's employment, these factors are not likely to be able to explain the cross-city variation at a given point of time.
The locational variation in employment rates of black women is similarly large. MSAspecific employment rates of black women varied between 64.8 and 78.5 percent in 2000 and between 58.4 and 79.2 percent in 2015. Table 2 compares MSA-specific ratios of employment rates of white women to employment rates of black women (entries less than one indicate that black women are less likely to be employed). The table shows that, while in some MSAs black women have higher employment rates than white women, in other MSAs black women have lower employment rates than white women.
In short, the descriptive statistics show that there is substantial cross-city variation in the employment rates of both white and black women. Of course, it could be that the differences in demographic composition across MSAs produce this variation in employment. We next turn to more careful examination of the role of MSA-specific factors on female employment.

Role of Locational Factors in Women's Employment
In order to properly analyze the effect of location-specific factors on female employment, we estimate a linear probability model of employment with and without MSA fixed effects. The dependent variable is an individual woman's employment status multiplied by 100 (that is, it has the value of 100 if a woman is employed and 0 otherwise). The coefficients, therefore, can be interpreted as percentage points. We include a set of standard demographic controls, such as age, age squared, marital status, number of children, and a set of controls for education pay for someone else or worked in a family or own business (Ruggles et al., 2015). level. We estimate these models separately for white and black women who live in the 50 largest MSAs. The results are in Table 3. Columns (1) and (2) report results for white and black women, respectively, from a specification that does not include MSA fixed effects. The specification reported in columns (3) and (4) includes MSA fixed effects. Comparing columns (1) and (2), three points are worth mentioning. First, black women's employment is much less sensitive to the presence and number of children than white women's employment. Second, the direction of the relationship between marriage and employment is different for white and black women. A married white woman in 2000 was 7.88 percentage points less likely to be employed than a similar unmarried white woman. The effect had decreased to 3.78 percentage points in 2015. In contrast, a married black woman in 2000 was 3.26 percentage points more likely to be employed than a similar unmarried black woman. This effect remained virtually unchanged over time. Third, and consistent with the existing literature, comparing results for 2000 in Panel A and 2015 in Panel B shows that women's employment became less sensitive with respect to most demographic characteristics over time (see, e.g., Blau and Kahn (2007)).
Columns (3) and (4)  Not surprisingly, we find that MSA fixed effects are jointly very significant, with near-zero p-values for the F-tests of joint significance. 9 The results in Table 3 confirm that MSA-specific factors play an important role in   Table 3 women's employment outcomes and that otherwise similar women living in different cities can have substantially different probabilities of being employed. It comes as no surprise that female employment varies between cities. There is, after all, geographic variation in economic conditions, culture, history, geography, policy, law, institutions, and a whole host of other factors, including city-level differences in individual-level characteristics driven by self-selection into residential location. The results also accord well with previous findings by Black et al. (2014) and Hirsch et al. (2017) that local factors explain differences in employment among females and the probability of multiple job holdings. The impressive explanatory power of the MSA effects suggests that, rather than city-tocity fluctuations around the national average, these factors cause large, systematic geographical differences in female employment. Reiterating this point, Table 4  These results show that there are locational effects in employment outcomes for women that a standard set of demographic characteristics cannot explain. These effects are persistent across time and correlated across racial groups. The rest of the paper is dedicated to understanding the MSA locational effects and their implications for racial differences in female employment.

Determinants of Locational Effects
What determines the MSA-specific component of female employment? While there is an expansive body of studies of local labor markets in urban and regional economics, economists have only recently started exploring the intersection of labor and urban economics. 10 As a result, there is limited research on how specific characteristics of local labor markets affect employment behavior and outcomes.
One important feature of local labor markets that affects employment appears to be commuting time. In particular, Black et al. (2014) show that labor force participation of white married women is negatively affected by commuting times within the metropolitan area. 11 A labor supply model with a fixed time cost of commuting introduces a non-convexity to the budget constraint. This non-convexity makes an individual with a longer commute more likely to prefer a corner solution, corresponding to non-participation. The authors use the MSA average commuting time of white men as a measure of how difficult it is to commute in that MSA. Since white men's labor force participation rates are high and consistent across MSAs, the measure is not subject to endogeneity concerns.
Initially, we follow the Black et al. (2014) approach and investigate the relationship between the MSA fixed effects calculated in Table 5 and MSA commuting times that we compute as white men's average commuting time. 12 Specification (1) in Table 5 reports the results of regressions of the MSA employment fixed effects on the average commuting time for white men, separately for white and black women in 2000 and in 2015. For white women, the relationship between the fixed effects and commutes is indeed negative and statistically significant. Thus, the typical white woman living in MSAs with a relatively long commute is less likely to be employed than a demographically identical woman living in an area with a shorter commute. In contrast, fixed effects for black women are not sensitive to commuting times. This racial difference in the relationship between commuting time and employment is consistent with the existing literature on racial differences in female labor supply, which finds that black women are more attached to the labor force and, as a consequence, their labor supply is less elastic with respect to external factors (such as wages and fertility). Of course, our measure of MSA commutes could be picking up some other MSA-specific factors. To account for this possibility, and to further explore the determinants of the MSA fixed effects, we add additional MSA-level characteristics in specifications (2) through (4). First, to control for the local labor market's economic condition, we include the MSA-specific unemployment rate of white men. 13 The results are reported in specification (2) of Table 5. Not surprisingly, MSAs with higher unemployment rates (i.e., worse economic conditions) have lower MSA fixed effects of women's employment. Clearly, local economic conditions matter. The MSA-specific component of female employment is smaller for similar women living in MSAs with higher unemployment rates.
Next, we add controls for the industrial composition of the local labor market. Geographic variation in industrial composition may lead to geographic variation in female employment rates either if there are industry-level differences in female employment or if women select into industries with different overall employment rates then men. To control for industrial composition, we calculate MSA-specific proportions of all men and women aged 25-55 working in each of a number of high-level industrial classifications. 14 Inclusion of these controls in specification (3) of Table 5 improves the power of our regressions to explain employment. 15 Finally, we also include region dummies in specification (4) of Table 5. 16 These effects will absorb local variation in female employment that operates on geographic scales more coarse than the MSA. For example, there may be agglomeration externalities or differences in infrastructure that affect multiple labor markets within a given region. Alternatively, there may be region-level differences in histories of, and cultural attitudes towards, female employment. 17 As the table shows, these region dummies do help explain the MSA effects, particularly in the later sample.
While additional controls improve the fit of the regressions in Table 5, they do not change the conclusion that MSA commutes affect employment for white women, but not for black women. However, commuting times alone explain, at most, a quarter of the variation in MSA fixed effects for white women (and nearly none of the variation in those effects for black women). Including unemployment, industrial composition, and region dummies explains over 70 percent of the variation in MSA fixed effects for both races and sample 13 We cannot use the female unemployment rate as it is mechanically related to women's employment rate.
The unemployment rate for Black males might be affected by factors not directly related to local economic conditions. 14 The classifications, which include (1) agriculture, (2) mining, (3) construction, (4) manufacturing, (5) transportation, communication, and other public utilities, (6) wholesale trade, (7) retail trade, (8) finance, insurance, and real estate, (9) personal services, (10) entertainment and recreational services, (11) professional services, and (12) public administration, are based on the 1990 industrial classification scheme provided by IPUMS. 15 It might seem logical that local housing prices could affect women's employment as well. However, a careful analysis by Johnson (2014) finds "little evidence of a positive effect of house prices on married women's labor force participation." 16 Region dummies are based on Census and ACS regions (New England, Middle Atlantic, East North Central, West North Central, South Atlantic, East South Central, West South Central, Mountain, and Pacific). 17 Several papers (see Fernàndez and Fogli (2009) and Blau et al. (2013)) show that cultural norms and beliefs transfer over generations and affect work and fertility behavior even after controlling for other demographic characteristics.

periods. 18
Though these additional controls explain a substantial fraction of the variation in MSAspecific determinants of female employment, they should be interpreted with care for two reasons. First, the inclusion of a large number of explanatory variables in the richest specifications will mechanically increase the R 2 . Notice, however, that including these variables causes similar (though naturally smaller) increases in the adjusted R 2 as well, as Table 5 shows. 19 Second, the MSA regressors should not be interpreted as causal determinants of female employment rates. The significance of the region dummies, for example, only means that female employment outcomes in one area are correlated with those in other nearby areas. Similarly, while the explanatory power of the industrial composition controls may be a consequence of industry-specific differences in female employment or differential selection of women into occupations, it may also reflect unobserved factors like local cultural norms or unobserved preferences that correlate with industrial composition. At the same time, while the MSA-level factors that we examine help explain local differences in female employment, they do not diminish the significance of those differences to policy analysis and future theoretical and empirical work on female employment.

Determinants of Racial Differences in Location Effects
The results presented above establish two stylized facts. First, there is substantial geographic variation in the employment of females of both races. Second, while local factors such as commuting time, unemployment rates, and industrial composition help explain this variation, they do so differently for black and white women. In this section, we explore the determinants of racial differences in the city-specific components of female employment.
A natural starting point for such an explanation is to ask to what extent racial differences in female employment are explained by racial differences in the geographic distribution of women, rather than by racial differences in the local components of female employment. To answer this question, we perform Oaxaca-Blinder decompositions of female employment into two parts: one that is explained by differences in the MSAs in which black and white women reside and another that is explained by within-MSA differences in the employment of black and white women.
A complication of this approach is that the unconditional relationship between location and female employment reflects both city-specific labor supply and demand shifters and geographic differences in demographic factors such as age, education, marital status, and fertility. To isolate and analyze the former component, on which our interest centers in this paper, we begin by removing the component of residential location that is explained by such demographics. To this end, let λ ji be an indicator for whether a woman i resides in metropolitan area j. Similarly, letλ ji = λ ji − x i β r , r ∈ {w, b}, be the residual from a (race-specific) regression of λ ji on demographic covariates. The residualsλ ji can be viewed as the part of a woman's residential location that are not explained by her demographic char-acteristics (equivalently, these residuals can be viewed as the difference between a woman's residence in area j and the probability that she lives there predicted by her demographic variables).
Suppose further that a woman's employment status is determined by the (race-specific) equation emp i = Σ j γ jr ·λ ji + i . The Oaxaca-Blinder decomposition of the white-black difference in female employment can then be written as: The first term in the sum is the "explained" part of the white-black difference in female employment. It represents the expected difference in employment (after controlling for demographic characteristics) that would arise from the fact that whites and blacks live in different areas, holding the effect of location constant. The second term in the sum is the "unexplained" part of the difference. It represents the difference arising because employment outcomes differ between whites and blacks in each MSA, holding the geographic distribution constant between blacks and whites. 20 The results of the decompositions are presented in Table 6. In both 2000 and 2015, the explained part of the decomposition is relatively small and statistically insignificant. The difference in expected employment between white and black women comes almost entirely from the unexplained part of the decomposition. Hence, the observed differences in the employment of white and black women are not because they live in different places, but rather because there are city-specific differences in the supply and demand for female workers of different races. Put differently, while cities matter, they matter differently for black women than they do for white women. 21 The results of this decomposition raise a natural second question: what explains racial differences in the local components of female employment? Put differently, how can we explain the "unexplained" variation from the decompositions presented above? To shed light on this question, in Table 7 we report the results of the regressions similar to those in Table 5, but with the black-white differences in the MSA fixed effects serving as the dependent variable (instead of the race-specific MSA fixed effects themselves). As the results indicate, the same factors that help explain race-specific MSA fixed effects also help explain white-black differences in those effects, though the magnitudes and standard errors of the coefficients are more sensitive to the specification and sample used to estimate them than those presented previously in Table 5.
MSA commutes are negatively related to the racial differences in MSA fixed effects in most specifications in 2000, though the relationship is not as strong in 2015. Furthermore, while local economic conditions (as measured by the unemployment rates of white men) explain some of the variation in racial differences in MSA fixed effects, they are statistically insignificant in most specifications. Adding a panel of controls for industrial composition increases the R 2 of the regression to about 0.58 in the 2000 sample and 0.41 in the 2015 sample. As noted above, since these controls may reflect the influence of unobserved arealevel factors that correlate with industrial composition, their explanatory power should be interpreted with some care. Moreover, even if local differences in industrial composition themselves cause racial differences in MSA fixed effects, the underlying source of this relationship remains unknown. Lastly, adding indicators for Census regions increases the R 2 of the regressions to over 0.7 in both years, though this suggests mainly that the MSA-level fixed effects are correlated within such regions.

CONCLUDING REMARKS
The findings presented in this paper highlight striking heterogeneity of female employment with respect to geographic location, race, and their interaction. Accounting for, and ultimately explaining, this heterogeneity is essential to better understanding and modeling female employment outcomes. Given the amount of variation in employment of women by city and by race, for example, our results suggest that it is meaningless to talk about "the" employment rate of women in the U.S as a way to describe the labor force participation of women.
Our results also suggest that explanations of employment outcomes for white women cannot be easily extended to black women. Either white and black women have systematically different preferences or, if they have the same preferences, there are important unobserved area-level factors that typically are not included in empirical models of employment. Obvious candidates for these omissions are cultural norms, differences in social and/or family c Southern Regional Science Association 2019. Notes: Dependent variables are white-black differences MSA fixed effects from female employment regressions using the 50 largest MSAs for the 2000 and 2011-2015 periods. Industrial composition denotes MSA-specific proportions of all men and women aged 25-55 working in (1) agriculture, (2) mining, (3) construction, (4) manufacturing, (5) transportation, communication, and other public utilities, (6) wholesale trade, (7) retail trade, (8) finance, insurance, and real estate, (9) personal services, (10) entertainment and recreational services, (11) professional services, and (12)  structure, and fertility decisions. A growing literature highlights the fact that cultural norms affect economic behavior. Blau (2015), for example, shows that "immigrant source-country gender roles influence immigrant and second-generation women's behavior in the United States." Understanding female employment is important because women account for an increasing portion of the labor force. While our results suggest that local factors such as commuting time, unemployment, industrial composition, and Census region help explain geographical variation in female employment, and racial differences in that variation, more research is