An Analysis of Income Differentials by Marital Status. Regina Madalozzo

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1 An Analyss of Income Dfferentals by Martal Status Regna Madalozzo Insper Workng Paper WPE: 023/2002

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3 AN ANALYSIS OF INCOME DIFFERENTIALS BY MARITAL STATUS Regna Madalozzo * Ibmec SP Aprl 3, 2002 Abstract Unmarred cohabtaton has become a more frequently observed phenomenon over the last three decades, and not only n the Unted States. The obectve of ths work s to examne ncome dfferentals between marred women and those who reman sngle or cohabtate. The emprcal lterature shows that, whle the marrage premum s verfed n dfferent studes for men, the result for women s not conclusve. The man nnovaton of my study s the exstence of controls for selecton. In ths study, we have two sources of selectvty: nto the labor force and nto a martal status category. Ths study supplements the lterature on ncome dfferentals among cohabtng, sngle and marred women by makng use of the swtchng regressons as well the Oaxaca (1973)/ Kuhn (1987) decomposton method, as appled n Bllger (2000). The swtchng regressons and the Oaxaca decomposton results demonstrate the exstence of a sgnfcant penalty for marrage. Correctng for both types of selecton, the dfference n wages vares between 49% and 53%, dependng on the method used, when marred women are compared wth cohabtng ones, and favors non-marred women. Ths result ponts to the exstence of a marrage penalty. Moreover, ths marrage penalty can oscllate between 26% and 34% when the comparson s made between marred and sngle females. * I am grateful to the semnar partcpants at Unversty of Illnos at Urbana-Champagn and Ibmec-SP, and to Kevn Hallock, John Johnson, Roger Koenker, Anl Bera, Werner Baer, Marcelo Moura, and Sherrlyn Bllger for helpful comments. Fnancal support from Capes Brazl s acknowledged. E-mal: RegnaM@bmec.br.

4 Unmarred cohabtaton has become a more frequently observed phenomenon over the last three decades, and not only n the Unted States. Recent legal changes n some countres gve cohabtators the same legal standng as marred couples 1. In some countres, cohabtors sgn affdavts, whch stpulate that the unon becomes a legal marrage after a pre-determned length of tme 2. In the Unted States, lmtatons on welfare recept provde ncentves for cohabtaton as compared to marrage, because welfare benefts can be lost upon gettng marred. However, t s not only to escape from restrctve welfare rules that more people are choosng not to marry. Many young, well-educated persons opt to lve together wthout beng marred. These persons are the so-called cohabtors. Fgure 1 llustrates the ncrease n cohabtaton n the Unted States over the last 20 years 3. As shown n ths fgure, the percentage of opposte sex couples cohabtng doubled from 1980 to The obectve of ths work s to examne ncome dfferentals between marred women and those who reman sngle or cohabtate. The emprcal lterature shows that, whle the marrage premum s verfed n dfferent studes for men 4, the result for women s not conclusve. Because marrage has a strong connecton wth chldren, and women usually are the parent responsble for takng care of chldren, most studes consder chldren s mpact on female wages. The earnngs varaton among women can fluctuate wth the number of chldren (Moore and Wlson, 1982) or wth martal status (Hll, 1979). Concernng the number of chldren, women s wages present an ncreasng famly status penalty n the 1980s f accounted for by the presence of chldren (Waldfogel, 1997). However, for those women who do not gve up workng at chldbrth, there s no wage gap when compared to chldless females (Josh, Pac and Waldfogel, 1999). 1 For nstance, n Brazl, snce the early 1990s, any couple lvng together for more than one year has the same rghts and oblgatons to each other as they would have f they were legally marred. 2 In Kenya, for nstance, t s possble to avod the costs of marrage, whch are not only the expenses of the ceremony but also the brde wealth that s stll common, usng ths maneuver. See Kabeber- Machara and Nyamu (1998). 3 The cohabtaton trend s the subect of research across socology, demography, and economcs. For examples, see Bren, Lllard and Wate (1999), Bumpass and Sweet (1989), Carlson and Danzger (1999), Lllard, Bren and Wate (1995), Wlls and Mchael (1994) and Wate (1995). 4 See Allegretto and Arthur (1999) and Korenman and Neumark (1991). 2

5 The man nnovaton of my study s the exstence of controls for selecton 5. Selecton can occur when ncluson n a sample and presence of the varable of nterest are both determned by the same unobservable factors. Not accountng for ths problem causes serous bas n an analyss 6. In ths study, we have two sources of selectvty: nto the labor force and nto a martal status category. Women seem to have more flexblty n choosng to work, relatve to men. The frst selecton control ams to solve ths bas n the analyss. The second selecton problem s the dfference among women who make dstnct choces about lvng arrangements,.e., marryng, cohabtng, or remanng sngle. Ths study supplements the lterature on ncome dfferentals among cohabtng, sngle and marred women by makng use of the swtchng regressons as well the Oaxaca (1973)/ Kuhn (1987) decomposton method, as appled n Bllger (2000). The swtchng regressons and the Oaxaca decomposton results demonstrate the exstence of a sgnfcant penalty for marrage. When correctng only for selecton nto the labor market, the wage gap between marred and cohabtng women favors marred women. The predcted marrage premum s roughly 5%, usng the swtchng regressons method. Usng the same methods for the sample of sngle and marred women, the marrage premum s 10%. However, ths result s based because t does not account for selecton nto martal status. Correctng for both types of selecton, the dfference n wages vares between 49% and 53%, dependng on the method used, when marred women are compared wth cohabtng ones, and favors non-marred women. Ths result ponts to the exstence of a marrage penalty. Moreover, ths marrage penalty can oscllate between 26% and 34% when the comparson s made between marred and sngle females. Ths paper s organzed as follows: the next secton descrbes the data and presents a demographc analyss of the sub-samples. Secton 2 contans a dscusson of the econometrc methods to be used n the study and presents the results and ther nterpretaton. Secton 3 concludes and ncludes drectons for future work. 5 Harkness and Waldfogel (1999) examne the dfferences n wage structure for females and control for selecton nto the labor force usng Heckman s (1979) procedure. However, adequate controls for the selecton problem s not the man pont of ther paper; nether s the nterpretaton of effects of chldren on mothers wages. Ths happens because they cannot properly estmate the wage equaton n the absence of mportant explanatory varables, such as experence and employee characterstcs. 3

6 1 - Data and descrptve analyss The data used n ths paper come from the Annual Demographc Fles of the Current Populaton Survey (CPS), the Annual Demographc Fles for 1995, 1997, and The sample utlzed n ths study has 81,979 observatons among marred, cohabtng, and sngle women between the ages of 20 and 64 over these years. One of the greatest advantages of usng CPS data, besdes ts characterstc of beng a very representatve sample of the US populaton, s the possblty of dentfyng cohabtors 8. Snce 1990, the US Census has set apart unmarred partners,.e., cohabtors, from spouses or housemates. The CPS began the cohabtors dentfcaton n However, only the head of the household s partner s dentfed as a cohabtor by the CPS. The head of the household, or the householder before 1980, s the person who owns or rents the house unt, whch presumably mples the person wth hgher ncome n the famly 10. In order to capture the heads who are cohabtors wthout msrepresentng the results 11, t was necessary to mplement another method. Usng the household dentfcaton number, t was possble to lnk each husband and wfe, as well as to connect unmarred partners as a couple 12, and to capture sngle women who are the famly reference person. 6 See more about the selecton problem n Vella (1998). 7 The CPS uses the same sample for 4 consecutve months, keepng ths sample out for the followng 8 months and re-ntervewng them for another 4 months. Ths process s called rotaton The Panel Study of Income Dynamcs (PSID) s another dataset that dstngushes cohabtors from marred persons. However, ths dstncton s made only n the frst year that the unmarred partner entered the famly. After ths, the cohabtor s treated as a spouse even f the couple dd not actually marry,.e. t s not possble to dstngush marred from unmarred couples. 9 Untl ths date, the way to nvestgate cohabtaton usng the CPS data was to use the method called POSSLQ (Partners of the Opposte Sex Sharng Lvng Quarters). Ths methodology had the caveat of ncludng only unmarred partners wthout chldren n the sample and, sometmes, accountng roommates as partners. The POSSLQ conssts n dentfyng all households wth exactly two adults of opposte sex who are unrelated. The Adusted POSSLQ allows the ncluson of chldren, but t stll does not capture all cohabtors and also ncludes some roommates as partners (Casper and Cohen, 2000). The opton of usng the perod after 1994 for the present study s ustfed by the ncluson of the correct sample of cohabtors. 10 If no such person exsts, then any adult member, excludng roomers, boarders or pad employees can be characterzed as the householder. If the marred couple ontly owns or rents the house, then the householder can be ether one. 11 Roughly 50% of the female cohabtors sample s the head of the household, as can be seen n Table 1. Identfyng the female as the head s ether a pecular characterstc of unmarred couples or means that, n these cases, the fnancal responsbltes are more equally shared between the partners. 12 Addtonal detals about ths methodology are n the Appendx. 4

7 Table 1 presents some descrptve statstcs for the sample to be used n ths study, classfed as marred, cohabtng, or sngle and usng the CPS fnal weght for each ndvdual. Ths table shows that cohabtng and sngle women are younger than marred women and have a fewer chldren. The pattern on ncome data ndcates that sngle women have hgher wages and salares ($18,701), followed by cohabtors ($16,607). However, when consderng only those women wth postve ncome, marred women on average have larger wages and salares than cohabtors ($22,419 and $20,281, respectvely). Even then, sngle women earn 4% more than marred females. Hourly wage s a constructed varable. It s calculated usng the varables annual wages and salares, usual number of hours worked per week, and number of weeks worked last year, as shown below: Hourly wages = Annual wages and salares Hours worked per week * Weeks worked per year Concernng hourly wages, sngle women appear to have hgher wages (19.42) than cohabtng (16.07) and marred women (18.64). Ths pattern s mantaned when observng only those women wth postve ncome. Sngle women earn approxmately the same hourly wages as marred women (19.82 and 19.69, respectvely), and both earn hgher hourly wages than cohabtng women (16.47). A hgher proporton of marred women are engaged n part-tme obs (21%) than cohabtng (16%) or sngle women (15%). Cohabtng females are mostly allocated n full-tme obs (69%). Relatve to educaton, a larger fracton of sngle women have a college degree or hgher (38%) than marred or cohabtng females (35% and 26%, respectvely). One common queston n studes that compare dfferent martal status s how to categorze cohabtors. Do they look more lke marred persons or sngles? Whle cohabtors and sngle women have approxmately the same work profles, and both are more engaged n the labor force when compared to marred women, they are very dssmlar concernng educaton, race, and hourly wages. Therefore, gven these dssmlartes, t s reasonable to analyze marred versus cohabtng women and marred versus sngle women separately. For the rest of the analyss, the total sample 5

8 s dvded nto these two sub-samples. Ths dvson facltates the nvestgaton of the drect effect of cohabtaton or snglehood on ncome wth respect to marred women. 2 - Theoretcal framework and emprcal results The frst step n ths study s to analyze ncome dfferentals for women through a baselne wage regresson 13. In ths specfcaton, the natural logarthm of hourly wages (n dollars) s explaned by personal characterstcs of the ndvduals and ndcators for beng an unmarred partner or sngle. The basc regresson has as explanatory varables: experence 14, experence-squared, number of chldren younger than 6 years old, ndcators for educatonal attanment 15, race 16, 2-dgt ndustry, 1- dgt occupaton 17, resdence n a metropoltan area and yearly ndcators 18 to account for the structure s dfference over the years. For each sub-sample 19, an ndcator for martal status was ncluded. In the sub-sample marred versus cohabtors, an ndcator that assumes value 1 f the woman s a cohabtor and zero otherwse was ncluded. In the sub-sample marred versus sngle, an ndcator that assumes value 1 f the woman s sngle and zero otherwse s the alternatve. Table 2 presents the results for ths baselne regresson. Column (1) uses the sample composed of marred and cohabtng women and, column (2), the sample of marred and sngle women. In all the regressons, robust standard errors were estmated to control for heteroskedastcty, as descrbed n Whte (1980). All regressons are weghted by the fnal CPS weght. 13 An unadusted wage regresson for women, even knowng the selecton problem for ths sample, s estmated. The reason for ths s that the results from ths estmaton wll serve as a comparson wth the results of studes that deal or do not deal wth the selecton problems. The dfference between ths baselne regresson and the adusted one wll be presented at the end of ths paper. 14 Ths s a created varable: experence s the age mnus the number of years of study mnus sx. 15 They are: less than hgh school, hgh school degree, some college, college degree, and post-college degree. Excluded category: less than hgh school. 16 They are: Whte, Black and Hspanc. Excluded category: Whte. Notce that the category whte ncludes other mnortes not specfed as Black or Hspanc. The ethncty varable that allows the dentfcaton of Hspancs do not allow the same for other mnortes. Therefore, other mnortes were ncluded wth the Whtes. 17 All the regressons were also estmated usng 2-dgt occupaton ndcators. Results for these latter regressons pont to the same drecton as the ones presented here. However, the swtchng regressons and Oaxaca-Kuhn effects estmated by usng 2-dgt occupaton ndcators are abnormally hgher than the ones estmated usng 1-dgt occupaton ndcators. 18 They are: 1995, 1997 and Excluded category: I.e., marred versus cohabtng, and marred versus sngles. 6

9 In both regressons, the return to experence s postve wth decreasng margnal returns, as s clear from the negatve sgn on the varable experencesquared. The presence of young chldren has a negatve nfluence on the ncome of ther mothers. Returns to educaton are ncreasng, as expected. The coeffcent on the ndcator for Hspancs n both regressons s negatve and sgnfcant. The coeffcent for the Black ndcator s not sgnfcant n both regressons. The focus of ths paper s on the mpact of martal status on wages. Both the ndcators for beng a cohabtor and for beng sngle have no sgnfcant estmated coeffcents relatve to beng marred. These results mply smlar wages for marred women when compared to cohabtors or sngles. These results are nterestng and suggest no ncome dfferental for women n dstnct martal status categores. However, the sample s composed of only women and an extensve lterature on the selecton problem nto the labor force shows that women have a dfferent pattern of choosng to work than men. Besdes the dscontnuous partcpaton n the labor force caused by chldbearng 20, t s necessary to account for the possblty that dfferences n unobserved characterstcs, that wll henceforth be called ablty, nfluence female partcpaton n the labor market and, consequently, the wage level. Another source of selectvty n ths study s selecton nto martal status. Gven dfferent characterstcs, women opt to reman sngle, cohabt, or get marred. Ths choce among dfferent martal statuses can also reflect the sub-samples unobservable characterstcs. If these unobservable characterstcs act both n the choce over martal status and the wage level, not accountng for these nfluences would bas the nference. The technque used to deal wth selecton nto the labor force s based on Heckman (1977). For the second selectvty problem, related to the choce of martal status, the swtchng regressons technque s used, as dscussed n Maddala (1986). Notce that not accountng for these selectvty problems would result n based estmates. 20 Blau and Ehrenberg (1997) study the female role n the labor market. Goldn (1990) presents valuable research on the evoluton and trend of female partcpaton n the labor force. 7

10 2.1 - Selecton nto labor force partcpaton One way to deal wth selectvty nto the labor force, as noted prevously, s to use the Heckman (1977) model. Women wth dfferent characterstcs or abltes choose to engage or not engage n the labor force. Whle the presence of young chldren has the effect of ncreasng the cost of workng, educatonal attanment and experence can have the opposte nfluence. Therefore, to estmate the probablty of partcpatng n the labor force, we use the number of chldren younger than 6 years old 21, ndcators for educaton, and age and age-squared. Pror studes show that nonwhte women have a stronger commtment to the labor market. To account for ths effect, ndcators for race were ncluded. Besdes these ntutve varables, ndcators for martal status were also ncluded 22. The expected sgn for both ndcators s postve, gven that the household producton theory affrms that dvson of work s effcent when each member of a famly dedcates ther tme to the more productve ob 23. Men usually receve relatvely better compensaton for ther tme n the labor market than n home producton. Thus, the expectaton s that marred women dedcate more tme to home tasks and less to the labor market, and ths would mply a dfferent probablty of workng gven the martal status choce. Table 3 presents the results for the estmaton of the probt regresson, whch s specfed as: Pr( workng) = Φ[ η 1 + η2age + η3agesq + η4chld + δ educ + ς race + κd + ε ] (1) Where Φ(.) s the cumulatve standard normal dstrbuton, educ accounts for the four ndcators on educaton attanment, and race represents the two race 21 In order to check for robustness, alternatve specfcatons were tred, lke the ncluson of number of chldren less than 18 years old. Results vared slghtly n magntude, but the conclusons reman the same. Also checkng robustness, an alternatve concept of the dependent varable was used. Instead of usng wages and salares, the tested alternatve was ncome from the longest ob. Fnal results reman bascally the same. However, ths latter specfcaton s not the most sensble way to analyze a wage dfferental. Therefore, only the results from the regressons wth cted specfcatons n the man text are reported. 22 Dfferent ndcators were ncluded dependng on the sample composton. For nstance, n the sample wth marred and cohabtng women, an ndcator for cohabtors was ncluded. In the sample of marred and sngle women, an ndcator for sngles was ncluded as a regressor. 23 See Becker (1965) and Angrst and Evans (1998). 8

11 ndcators. D s the ndcator for martal status, as explaned before. The results are very smlar for both samples as shown n columns (1) and (2). As expected, age and age-squared account for the concave experence effect: the former s postve and the latter negatve. Both are sgnfcant. Young chldren have a negatve nfluence on partcpaton n the labor force. Consstent wth the expected postve and ncreasng returns to educaton, the hgher the educatonal degree attaned, the larger the probablty of workng. For the sample of marred women and cohabtors, there s a postve and sgnfcant effect of beng black, mplyng a hgher probablty of partcpaton nto the labor force by Black women. In column (2), relatve to the sample of marred and sngle women, the same coeffcent s not sgnfcant. Hspanc accounts for a lower probablty of partcpaton n the labor force, and t s sgnfcant n both samples. In addton, as antcpated, the effect of not beng marred,.e. beng a cohabtor or sngle, on the probablty of workng s postve and sgnfcant. The correcton for selecton bas for partcpatng n the labor force s attaned by the Inverse Mlls Rato (IMR) as one of the regressors n the wage equaton. The IMR s defned as: φ( Z γ / σ 0) IMR = (2) Φ( Z γ / σ ) 0 Where Z γ represent the regressors n the probt equaton, and σ 0 s the covarance between the regressons for the sample of workng and non-workng women. Table 4 presents the results for both samples for the logarthmc wage regresson augmented wth the addtonal regressor (2), as shown n Equaton (3): ln( wage) = β X + γd + δimr + ε (3) Where X represents the covarates as descrbed prevously 24, D s the dummy for the martal status, and IMR s the varable that controls for selecton nto the labor 24 They are: experence, experence-squared, ndcators for educatonal attanment, race, 2-dgt ndustry, 1-dgt occupaton, resdence n a metropoltan area and yearly ndcators. 9

12 force. Columns (1) and (3) n Table 4 show the baselne regressons 25. Columns (2) and (4) present the results when controllng for partcpaton n the labor force by the sub-samples of marred and cohabtng women or marred and sngles, respectvely. Notce that, n order to have an dentfed model, some authors suggest that the probt regresson, Equaton (1), should nclude at least one varable that s not a regressor n Equaton (3). Therefore, from the wage regressons, the varable chldren<6 was excluded. It also makes sense to proceed wth ths excluson because the number of chldren s more lkely to nfluence partcpaton nto the labor market than the wage level of the mother. In addton, the varable age squared, whch s not ncluded n the wage regresson, enters n the probt model. When ncluded n a wage regresson, the varable age squared or experence squared accounts for the exstence of a concavty n the wage. The same reasonng can be used here. The probablty of partcpatng n the labor force may ncrease wth tme and after some determned age ths probablty decreases. The sgnfcance of ths coeffcent estmatve renforces ths nterpretaton. There are caveats for both estmated regressons n columns (2) and (4). The frst s the negatve sgn on the Inverse Mlls Rato for the Labor Force Partcpaton. One should expect that the larger the unobservable characterstcs that postvely nfluence the partcpaton of women nto the labor force, the greater should be the expected ncome. However, the results pont n the opposte drecton. For these women, selectvty nto the labor force exsts, as the sgnfcance on the IMR coeffcent ndcates, although women who expect to be less well remunerated by ther work actually are more lkely to partcpate n the labor force. Ths unexpected result s not exclusve to ths paper. Vella (1998), usng NLS data, fnds the same negatve sgn n the IMR coeffcent. Hs result also mples that selectvty nto the labor force works n a reverse way. Women wth characterstcs that predct recevng lower wages are more lkely to partcpate n the labor market. One possble explanaton of ths odd result s that women n these samples have a greater need to work. It s plausble to thnk that a sngle mother has no choce but to work, especally f she and her chldren depend entrely on her labor. The 25 These results are the same as those presented n Table 2. They are reported agan n Table 4 n order to facltate vsualzaton and comparsons between the baselne regressons and the results that correct for selecton nto the labor market. 10

13 Welfare Reform Act of 1994 may have contrbuted to ths result. By these reforms, no one could be a welfare recpent for more than 3 years. Ths change s only vald after 1999, however we could reasonably argue that ths may have had some effect on the precedng years by adustment to the future mplementaton. In addton, the partner or husband s ncome could nfluence partcpaton n the labor force. Generally, unons are made n a smlar ncome range. Therefore, poorer, less educated women n general would be pared wth men wth smlar characterstcs and mght have no other choce but to work, ndependent of the smaller compensaton for ther own characterstcs (Becker, 1973) 26. Fnally, the coeffcents on the central varables, cohabtatng n columns (1) and (2) and sngle n columns (3) and (4), changed substantally once we account for selecton nto labor force partcpaton, columns (2) and (4). Ths means that f we only correct for selectvty nto the labor force usng Heckman s procedure 27, there s a marrage premum for the sample of marred women compared to sngle ones. However, as dscussed before, there s also selectvty n the martal status choce. The next step s to deal wth ths selectvty bas, whch wll be done by usng the swtchng regressons approach Selecton nto dfferent famly categores In ths sub-secton, results correct for selecton nto dfferent martal statuses. The dataset has no nformaton on the background of these women (e.g., parents ncome and educaton) besdes ther educaton and race profle, but some of the more relevant nformaton that could nfluence the decson to get marred are ncluded n the emprcal model. Frst, by the demographcs, one can conclude that age s mportant n ths decson: marred women are older than sngles or cohabtors. The presence of younger chldren could nfluence ths decson n ether drecton. On one hand, 26 Neal (2001) has an nterestng theoretcal paper reasonng that economcally dsadvantaged women may choose to reman sngle when an economc crss happens. He argues that the creaton of a welfare system may have renforced ths decson, and also may have created the opportunty for these sngle women to have chldren. 27 Ths result s renforced when usng swtchng regressons. Table 7 presents the results for both subsamples, wth a sgnfcant dfference between wages pad to marred and to unmarred women, the 11

14 havng a chld may motvate mothers to marry because they could share the responsbltes of educatng and sustanng ther chldren. However, on the other hand, sngle mothers can lose part of ther ncome when they marry. For nstance, chld support recepts can decrease f the sngle mother opts to marry 28. The educaton profle s ncluded to explore the dfferences n the composton of these groups. Usng the demographcs n Table 1, t s evdent that Black women are more lkely to stay sngle. In the opposte drecton, Hspanc women are more lkely to marry. The ncluson of race ndcators accounts for these dfferences. The varable that s ncluded n the probablty model to cohabtate or stays sngle, whch s not ncluded n the wage estmaton, s the ndcator for ownng a house. Spendng a consderable sum of money to buy a house can sgnal an nclnaton toward, or a readness, for stablty 29. As the papers that analyze male returns to marrage emphasze, one of the possble motves for the marrage premum could be that stablty n one s personal lfe can result n on-the-ob productvty. The expected sgn on ths varable s negatve for both regressons, probablty of cohabtng and probablty of stayng sngle, mplyng that ownng a house, as one would suspect, s related to beng marred. The probablty model of cohabtng or beng sngle can be expressed by the followng equatons, smlar to Equaton (1): Pr( cohabtaton) = Φ[ η 1 + η2age + η3chld + η4 housng + δ educ + ς race + ε ] (4) Pr( sngle ) = Φ[ η 1 + η2age + η3chld + η4 housng + δ educ + ς race + ε] (5) Where housng s an ndcator for ownng a house. Table 5 presents the results for these regressons. As expected, age negatvely nfluences the probablty of beng a cohabtor or sngle. Havng a young chld has the same effect, whch suggests that the benefts of stayng sngle and, possbly, mantanng alternatves sources of marrage premum, when correctng only for selecton nto the labor force. Sub-secton 2.3 presents these results. 28 See Hu(1999) and Veum(1992). 29 Of course, buyng a house also means that the person has some wealth. Ths fact does not contradct the fact that the person who buys a house s also the one who has more nclnaton toward stablty. Even consderng a house only as a sgn of wealth, lke an nvestment, we also could thnk that an nvestment s a sgn of stablty per se. Both ways, the varable ownng a house can be consdered a good proxy for marrage. 12

15 ncome (e.g., chld support or almony) are more than compensated for by the benefts of sharng the responsbltes of parenthood. Schoolng has dfferent effects for the samples. Havng more years of educaton mples a lower probablty of enterng nto a cohabtaton unon, but ths has the opposte consequence on the probablty of stayng sngle. The hgher the educaton degree, the more lkely a woman wll stay sngle. As antcpated, the ndcator varable for Black s postve and hghly sgnfcant for probablty to contnue sngle. The Hspanc ndcator s negatve for the probablty of enterng nto a cohabtaton unon, but smaller and postve for the probablty of remanng sngle. Ownng a house has the ntutve sgn: t s more negatve for the probablty of stayng sngle then for cohabtng. For both regressons, the estmated coeffcents are hghly sgnfcant. The swtchng regressons method, descrbed n Madalla (1986) and appled n Bllger (2000), uses the results from Table 5 to control for selecton nto famly status. Ths method s both an alternatve to and an adustment of the Heckman procedure for the cases where more than one type of selecton s nvolved n the regressons. It fts n ths study n order to control for the two types of selectvty that could bas the fnal analyss. In the swtchng regressons, the sub-samples are dvded agan, now by each martal status: marred, cohabtors and sngle women 30. The estmaton proceeds by two wage equatons 31 : y 1 = ln( wage cohabtors ) = β c X + ε1 (6) y 2 = ln( wage marred ) = β m X + ε 2 (7) The varable y k (n ths case, wage profle and k=1,2) s assumed to follow dfferent probablty laws for marred and cohabtng women. There s also an Indcator Functon, whch takes value 1 when the selected characterstc s present (n 30 Notce that the regressons for marred women have slghtly dfferent results on Tables 6a and 6b, columns (2) and (3). Ths occurs because n these columns the IMR are ncluded and they are calculated dfferently, dependng on the maor dvson (.e., between marred women and cohabtors or between marred women and sngles). 31 In the text, the explanaton s lnked to the sample of marred and cohabtng women. The same s appled to the sample of marred and sngle women, by replacng cohabtors for sngles. 13

16 ths case, beng a cohabtor) and zero otherwse. Makng use of the Heckman (1977) selectvty theory, we have: E ε y y ) = σ ε φ( Z) / Φ( ) (8) ( Z where Z are possble explanatory varables for the occurrence of the selected characterstc 32, whch s beng a cohabtor. By ths, we can wrte: ln( wage) = β X σ ε ( Z) / Φ( Z) V (9) And E(V)=0. As a practcal matter, the estmated equatons are: c 1 φ + φ( γ ' Z) y1 = ln( wage Z y 2 cohabtor ) = βc X + σ1ε + ε1 Φ( γ ' ) (10) φ( γ ' Z) = ln( wage Z marred ) = βm X + σ1 ε + ε 2 1 Φ( γ ' ) (11) The results for equaton (10) and (11) for the sample of marred women and cohabtors are shown n Table 6a. Columns (1) and (4) represent the baselne regressons. They have the expected sgns for the estmated coeffcents. Columns (2) and (5) nclude the control for selecton nto the labor force. For most of the varables the coeffcents are as expected. Fnally, columns (3) and (6) control for both selectvty nto the labor force and cohabtaton. These last equatons have some unexpected results on the educatonal attanment varables. They pont to a negatve return to educaton f the degree attaned s less than a college degree. These coeffcents are also sgnfcant n the cohabtors sample, but ths sample shows no postve effect of educaton at all. Table 6b presents the same set of results for the sub-sample of marred and sngle women. The results follow a pattern very smlar to the prevous sample. Wth the ncluson of the Mlls Rato probablty of workng and Mlls Rato probablty of remanng sngle, for the marred sub-sample, returns to educaton are mostly postve and sgnfcant. A post-college degree s hghly sgnfcant and presents a postve return to educaton. For the sub-sample of sngles, there s no sgnfcant coeffcent for any level of educaton 32 The other regressors are the same expressed n Table 5: age, number of chldren less than 6 years old, ndcators for educaton and race, ndcator for ownng a house and a constant. 14

17 The estmated coeffcents n Tables 6a and 6b wll be useful n the next subsecton. In that secton, the results are used to estmate the predcted ncome dfferentals by martal status usng the swtchng regressons model and the Oaxaca- Kuhn decomposton Predcted ncome dfferentals In ths analyss, two dfferent methods wll be appled. The frst one uses the swtchng regressons procedure to calculate a percent wage dfferental, as n Bllger (2000). The second technque s closest to the approach of Hallock, Hendrcks and Broadbent(1998), who use an ndvdual-based form of the Oaxaca decomposton as ntroduced n Kuhn (1987). Usng the estmated parameters presented n Table 6a, t s possble to predct wages for cohabtng women as f they were cohabtors or marred. Wth the results from Table 6b, the same calculatons are used to predct wages for sngle women as f they were sngle or marred. After these computatons, the results are used to calculate the wage dfferentals for the dfferent samples: Wˆ c Wˆ Wage dfferental 1 = Wˆ Wˆ s Wˆ Wage dfferental 2 = Wˆ m m m m (12) (13) The second method of analyzng ncome dfferentals s Kuhn s extenson of the Oaxaca decomposton. The orgnal work of Oaxaca (1973), on dscrmnaton aganst women, suggested that the ncome dfferental measure should be: 0 W m Wm W f W f D = (14) 0 Wm W f where W 0 m represents the observed male-female wage rato and Wm represents W f W f the male-female wage rato wthout the exstence of dscrmnaton. 15

18 In order to get ths measure, he suggested the use of the followng regressons. Both male and female data, separately, would be regressed as shown n equaton (15) ln( W ) = β X + u (15) where W s the hourly wage rate for the -th worker, X represents a vector of ndvdual characterstcs, β s the regresson s coeffcents and u represents the error term. Havng the estmated m βˆ coeffcents for the male sample and the estmated f βˆ for the female sample, we use them wth the sample means, and t s possble to get the statstc D : D ˆ m f f = β X ln( W ) (16) where f X represents the average of each varable that composes the vector of ndvdual characterstcs for females, and W f the average female wage. The dscrmnaton factor s the dfference between the observed mean of the female wage from the wage that women would have f they were evaluated as men and consderng the observed characterstcs of women. Kuhn (1987) extends ths dervaton. Instead of usng the average of each varable that composes the vector of ndvdual characterstcs of the sample, he suggests usng the ndvdual specfc measures, wth two alternatve measures. They are: ˆ 1 ˆ m f D = β X ln( W f ) (17) ˆ 2 D m = ˆ β X ˆ β X f f f (18) ˆ 1 D measures the ncome dfferentals over the actual wage of each woman and ˆ 2 D uses an estmatve of the wage for each woman. The choce between these two depends on the women s unobserved characterstcs 33. Nether one of these measures would be preferable to the other, unless there are assumptons about unobserved 33 Kuhn (1987) says that Equaton (17) s preferable when the unmeasured ablty s sector-specfc, and Equaton (18) s preferable when the unmeasured ablty s general. 16

19 characterstcs. In the present work, I use both equatons (17) and (18) to analyze the data. Only the results from equaton (18) are presented 34. Tables 7 and 8 present the results of these two methods. Table 7 presents the results for the swtchng regressons and Table 8 for the Oaxaca-Kuhn s decomposton 35. Panel A of Table 7 presents the results for the cohabtators sample, and Panel B shows the results for the sample composed of sngles. Usng the baselne specfcaton, cohabtng women, keepng ther own characterstcs, receve hourly wages 1% hgher than f they were marred. When controllng for selecton nto the labor force, ths dfference goes n favor of marred women. The marrage premum s 5.2%. However, as dscussed prevously, the comparson between marred women and cohabtors (or sngles) should account for the selectvty n the choce of martal status. Accountng for the second type of selectvty, cohabtors earn an ncome 53% hgher than f they were marred. The results for sngles are smlar. Wthout controllng for any type of selectvty,.e. usng the estmated parameters from the baselne regresson, sngle women earn annual wages and salares 3.4% lower than f they were marred. Controllng only for selectvty nto the labor market, ths dfference s 9.9%, stll n favor of marred women. However, n the fnal specfcaton, whch accounts for both selectvty nto the labor force and selectvty n the choce of martal status, shows that sngle women have ncomes 25.6% hgher than f they were marred. These results pont to the exstence of a marrage penalty for women. Ignorng both selectvty problems would bas the results. Correctng only for the selectvty nto the labor force would bas them mplyng a marrage premum for both subsamples. Only the specfcaton that accounts for both selectvty problems gves the result of a wage premum for non-marred women between 25.6% (sngles case) and 53% (cohabtors case). 34 Table 3.8 presents the average of the dfference between what marred women were supposed to receve f they were cohabtors and what they were supposed to receve beng marred, usng the estmated parameters from equaton (15). The average s the same for both equatons (17) and (18). Only the standard errors change. Equaton (18) has smaller standard errors. However, even n the results from equaton (17),whch have bgger standard errors, the predcted coeffcents for the dfference between marred and cohabtors (or sngles) were stll sgnfcant. Ther t-statstcs were between 10.9 and

20 Table 3.8 presents the results for the measure of ncome dfferentals developed by Kuhn for the two sub-samples 36. Column (1) shows the results of the predcted dfference between what cohabtng women earn, wth ther own characterstcs, beng cohabtors and what they would be predcted to earn beng marred. Usng the baselne specfcaton, cohabtng women earn 4.5% more beng cohabtors nstead of beng marred. Controllng for the selecton nto the labor force, ths dfference flps to 3.1 % n favor to marred women. However, we should also control for the selectvty nto martal status. Usng the fnal specfcaton, the dfference between what cohabtng women would earn by beng cohabtors and what they would earn f they are marred s 49.2%, renforcng the marrage penalty estmated by the swtchng regressons method. Column (2) n Table 3.8 presents the estmated dfference between what sngle women would earn by remanng sngle and what they would have earn f they were marred. The baselne regresson shows a dfference of 3.2% between the two predctors. Controllng only for selecton nto the labor market pushes the dfference to 3.9%, but n favor of marred women. The assumed correct specfcaton s on the last lne, whch controls for both selecton problems (nto the labor force and n the choce of martal status). Ths last specfcaton predcts a dfference of 33.6% between what sngle women s predcted to earn by remanng sngle and what they would have earn f they were marred. By two alternatve methods, the swtchng regressons procedure and the Oaxaca-Kuhn decomposton, results ndcate the exstence of a marrage penalty for women, when adequately controllng for both selecton problems. The magntude of ths penalty vares wth the chosen procedure, however both are consstent on the drecton of the dfference, favorng cohabtors and sngle women. 35 Notce that Table 8 presents the results for the Oaxaca-Kuhn predcted wage dfferences n percents. 36 Table 8 expresses the values for the estmaton of: [(wage as cohabtor/sngle) (wage as marred)] wage as marred In order to get the percents values, t s necessary to calculate the exponental value of ths dfference. 18

21 3 - Concluson and future developments The man goal of ths paper s to emprcally nvestgate women s ncome dfferentals by martal status. The motvaton for ths reles on the fact that the marrage premum for males s a well-known result, but for females the exstence of a penalty for beng marred or a premum for beng sngle or cohabtng s a topc that has receved much less attenton. Usng data from the CPS for 1995, 1997 and 1999, and controllng for two types of selectvty, usng technques as n Maddala (1986) and Oaxaca(1973), emprcal results show that marred women have lower pay than non-marred or cohabtng women. My estmates ndcate a statstcally sgnfcant ncome gap between marred and cohabtng women n the range of 49% to 53%. When comparng marred wth sngle women, ths dfference ncreases. Usng the swtchng regressons method, the dfference s 25.6% n favor of sngle women. By the Oaxaca-Kuhn decomposton, the dfference of annual ncome between marred and sngle women s 34%. Ths paper shows that both selecton nto the labor force and n the choce of martal status matter. Not accountng for them would serously bas the fnal analyss, even mplyng a non-exstent marrage premum. Accountng for selecton nto the labor force s mportant, as other cted references ndcate. However, not accountng for the choce of martal status would wrongly predct that ncome dfferences between marred and cohabtng (or sngle) women favor the former. Controllng for both types of selecton, we have a consstent result of the dfference for each subsample and conclude that a marrage penalty exsts for women. Because the ncome dfference between women n dstnct martal status categores has receved lttle attenton up to now, there are some avenues for further nvestgaton. One of the possble future developments of ths research s to dvde the sample by race. Because whte women have a somewhat dfferent profle for work than non-whte women, ths nvestgaton could shed some lght on the subect. Another potental development would be a theoretcal model for the exstence of ncome dfferentals among women gven ther martal status. Marrage, whch may gve men the appearance of stablty or greater ablty, may have an opposte sgnfcance for women. A model that approprately explores these deas would be nterestng. 19

22 Fnally, the study of cohabtaton n a panel data sample would be appealng. It would be possble to analyze decsons over educaton, labor force partcpaton, mpacts on future generatons, and to see what happens to ndvduals labor market outcomes when ther martal status changes. I hope that my work s a useful frst-step n ths area of research. 4 - References Allegretto, S. and Arthur, M. (1999) An Emprcal Analyss of Homosexual/Heterosexual Male Earnngs Dfferentals: Unmarred an Unequal? Industral and Labor Relatons Revew (forthcomng). Angrst, J. and Evans, W. (1998) Chldren and ther Parents Labor Supply: Evdence from Exogenous Varaton n Famly Sze Amercan Economc Revew, v. 83, n. 3, pp Bauman, Kurt J. (1999) Shftng Famly Defntons: The Effect of Cohabtaton and Other Nonfamly Household Relatonshps on Measures of Poverty Demography, v. 36, n. 3, pp Becker, G. (1973) A Theory of Marrage Journal of Poltcal Economy, v. 81, n.4, pp Bllger, S. (2000) Does Attendng Predomnantly-Female Schools Make a Dfference? Labor Outcomes for Women mmeo. Blau, F. and Ehrenberg, R. (1997) Gender & Famly Issues n the Workplace Russel Sage Foundaton (book). Bren, M.; Lllard, L. and Wate, L. (1999) Interrelated Famly-Buldng Behavors: Cohabtaton, Marrage and Nonmartal Concepton Demography, v. 36, n. 4, pp Bumpass, Larry L. and Sweet, James A. (1989) What s happenng to the famly? Interactons between demographcs and nsttutonal change Demography, v. 27, n.4, pp Carlson, M. and Danznger, S. (1999) Cohabtaton and the Measurement of Chld Poverty Revew of Income and Wealth, seres 4, n. 2, pp Casper, L. and Cohen, P. (2000) How does POSSLQ Measure Up? Hstorcal Estmates of Cohabtaton Demography, v. 37, n. 2, pp Goldn, Clauda (1990) Understandng the Gender Gap: an Economc Hstory of Amercan Women Oxford Unversty Press (book). Hallock, K.; Hendrcks, W. and Broadbent, E. (1998) Dscrmnaton by Gender and Dsablty Status: Do Worker Perceptons match Statstcal Measures? Southern Economc Journal, v. 65, n. 2, pp

23 Harkness, S. and Waldfogel, J. (1999) The Famly Gap n Pay: Evdence from Seven Industralzed Countres CASEpaper 29, London School of Economcs Workng Paper. Heckman, J. (1979) Sample Selecton Bas as a Specfcaton Error Econometrca, v. 47, n.1, pp Hll, M. (1979) The Wage Effects of Martal Status and Chldren The Journal of Human Resources, v. 14, n. 4, pp Hu, W. (1999) Chld Support, Welfare Dependency, and Women s Labor Supply Journal of Human Resources, v. 34, n. 1, pp Josh, H.; Pac, P. and Waldfogel, J. (1999) The Wages of Motherhood: Better or Worse? Cambrdge Journal of Economcs, v. 23, pp Kabeber-Machara, J. and Nyamu, C. (1998) Marrage by Affdavt: Developng Alternatve Laws on Cohabtaton n Kenya n Eekelaar, J. and Nhlapo, T. The Changng Famly, Hart Publshng, Oxford, UK. Korenman, S. and Neumark, D. (1991) Does Marrage Really Make Men More Productve? The Journal of Human Resources, v. 24, n. 2, pp Korenman, S. and Neumark, D. (1992) Marrage, Motherhood, and Wages The Journal of Human Resources, v. 27, n. 2, pp Kuhn, P. (1987) Sex Dscrmnaton n Labor Markets: The Role of Statstcal Evdence The Amercan Economc Revew, v. 77, n. 4, pp Lee, Lung-Fe (1978) Unonsm and Wage Rates: a Smultaneous Equatons Model wth Qualtatve and Lmted Dependent Varables Internatonal Economc Revew, v. 19, n. 2, pp Lllard, L.; Bren, M. and Wate, L. (1995) Premartal Cohabtaton and Subsequent Martal Dssoluton: a Matter of Self-Selecton Demography, v. 32, n. 3, pp Maddala, G. S. (1986) Dsequlbrum, Self-Selecton, and Swtchng Models n: Grlches and Intrlgator (1986) Handbook of Econometrcs, v. 3, pp Moore, W. and Wlson, R. (1982) The Influence of chldren on the Wage Rates of Marred Women Eastern Economc Journal, v. 3, n. 3. Neal, D. (2001) The Economcs of Famly Structure Natonal Bureau of Economc Research, Workng Paper Oaxaca, R. (1973) Male-Female Wage Dfferentals n Urban Labor Markets Internatonal Economc Revew, v. 14, n. 3, pp U. S. Census Bureau (1980 to 1999) Statstcal Abstract of the Unted States. Vella, Francs (1998) Estmatng Models wth Sample Selecton Bas: A Survey The Journal of Human Resources, Wnter, pp Wate, L. (1995) Does Marrage Matter? Demography, v. 32, n. 4, pp

24 Waldfogel, Jane (1997) workng Mothers Then and Now: a Cross-Cohort Analyss of the Effects of Maternty Leave on Women s Pay n Blau and Ehrenberg (1997) Gender & Famly Issues n the Workplace Russell Sage Foundaton. Whte, H. (1980) A Heteroskedastcty-Consstent Covarance Matrx Estmator and a Drect Test of Heteroskedastcty Econometrca, v. 48, pp Wlls, R. and Mchael, R. (1994) Innovaton n Famly Formaton: Evdence on Cohabtaton n the Unted States n Ermsch, J. and Ogawa, N. The Famly, the Market and the State n Ageng Socetes Clarendon Press, Oxford. 22

25 Fgure 1: Cohabtaton Trend n US 5,5% % cohabtors n the pop. over 25 years old 5,0% 4,5% 4,0% 3,5% 3,0% 2,5% 2,0%

26 Table 1: Demographcs, CPS March Fle (1995, 1997 and 1999) Restrcted to women wth age between 20 and 64, nclusve Marred Cohabtor Sngle Age (.042) (.154) (.106) Annual Wages and Salares 15,546 (82.89) 16,607 (294.67) 18,701 (219.78) Annual Wages and Salares (only for women wth postve ncome) 22,419 (104.63) [47,365] 20,281 (329.29) [3,552] 23,227 (246.12) [7,875] Hourly Wages Hourly Wages (only for women wth postve wage) (.315) (.319) [27,087] (.924) (.945) [1,873] (.857) (.875) [4,176] Number of chldren.34 (.003).19 (.008).26 (.006) Employment (%): Part-tme Full-tme Unemployed Others Educaton(%): Less than hgh school Hgh school dploma Some college College degree More than college Status n the household (%): Head Wfe Partner (cohabtor) Race (%): Whte Black Hspanc Other # of Observatons 67,887 4,335 9,757 Notes: (1) Standard errors are n parenthess. (2) Number of observatons n squared-brackets. 24

27 Table 2: Basc Regressons Dependent Varable: Ln(hourly wage) Marred and Cohabtors Marred and Sngles (1) (2) Cohabtaton ndcator (.028) Indcator for sngles (.021) Experence.031 (.002).031 (.002) Experence squared (.0001) (.0001) Chldren < (.014) (.014) Hgh school.199 (.031).224 (.031) Some college.247 (.034).297 (.034) College.455 (.035).502 (.035) Pos-college.704 (.041).733 (.040) Black.048 (.026) (.023) Hspanc (.027) (.027) Industry ndcators Yes Yes Occupaton ndcators Yes Yes Metropoltan Area Indcator Yes Yes Year ndcator Yes Yes Constant 1.57 (.323) 1.59 (.318) Adusted R-squared # of Observatons 27,087 29,390 Note: Robust standard error are n parenthess. 25

28 Table 3: Probt Results for Probablty of Beng n the Labor Force (1) Marred and Cohabtors (1) Marred and Sngles (2) Cohabtaton ndcators (.023) Indcator for sngles (.016) Age.090 (.003).086 (.003) Age squared (.0001) (.0001) Chldren < (.009) (.008) Hgh school.488 (.016).500 (.016) Some college.590 (.018).605 (.017) College.751 (.017).780 (.017) Pos-college 1.01 (.025) 1.04 (.024) Black.131 (.022).035 (.019) Hspanc (.015) (.015) Constant (.071) (.068) Pseudo R-squared # of observatons (2) 77,913 83,845 Note: (1) Robust standard errors are n parenthess. (2) The number of observatons on ths table may dffer from the one on Table 3.1, snce the latter s a weghted estmaton over the sample. 26