Urban Effects on Participation and Wages: Are there Gender. Differences? 1

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1 Urban Effects on Partcpaton and Wages: Are there Gender Dfferences? 1 Euan Phmster ** Department of Economcs and Arkleton Insttute for Rural Development Research, Unversty of Aberdeen. Centre for European Labour Market Research Dscusson Paper Edtor: W Davd McCausland ** Postal address. Department Of Economcs, Busness School, Unversty of Aberdeen, Edward Wrght Buldng, Aberdeen AB24 3QY. Unted Kngdom. Emal e.phmster@abdn.ac.uk. Fax

2 2 ABSTRACT Ths paper estmates partcpaton and wage equatons usng panel data from the Unted Kngdom to explore dfferences n urban and rural wages and partcpaton by gender. The results suggest a small but economcally sgnfcant partcpaton premum for urban women relatve to rural female workers. Results from the wage estmatons suggest that after controllng for sample selectvty, observed and unobserved heterogenety, the wage premum receved by urban women s larger than that obtaned by men. Consstent wth the hypothess that poorer matchng n less dense labour markets affects rural workers, there s also evdence of hgher rural wage deprecaton for both men and women, whle returns to experence for rural men are also lower than for urban workers. Keywords. Partcpaton, wages, urban, rural, panel, sample selecton. Acknowledgements The data used n ths paper were made avalable through the ESRC Data Archve. The data were orgnally collected by the Insttute for Socal and Economc Research, Unversty of Essex. Nether the orgnal collectors of the data nor the Archve bear any responsblty for the analyses or nterpretatons presented here. I would also lke to acknowledge fnancal support from the Leverhulme Trust (grant number F/152/Y), the help of Nck Buck, Alana Glbert, Deborah Roberts and Esperanza Vera-Toscano, plus the comments and suggestons from the two anonymous referees. All usual caveats apply.

3 I. INTRODUCTION Recent evdence suggests that varous types of agglomeraton externaltes are mportant n explanng the observed urban wage premum. Wheaton and Lews [31] fnd evdence of ncreasng urban wages consstent wth ncreasng frm level returns and greater specalzaton of labor n denser urban markets. Glaeser and Maré [10] fnd a robust urban wage premum and show that rural-urban mgrants experence hgher wage growth consstent wth greater learnng spllovers n urban areas. Wheeler [32] provdes emprcal support for a model where larger labor market sze ncreases job match qualty, ndvdual productvty and wages. Whle the recent lterature has explored how agglomeraton nfluences the urban wage premum, there has been lttle consderaton of whether these externaltes mpact dfferently on women and men. There are a number of reasons why such gender dfferences mght exst. Frst, emprcal evdence suggests that women are less spatally moble than men, wth job search conducted over a smaller area than men (Madden and Chu [19]). In denser urban labor markets, mproved urban job matchng may counterbalance ths reduced moblty and hence, one mght expect that any urban wage premum would be larger for women than men. Second, women typcally work fewer hours and years over ther workng lves and have a hgher rate of job turnover than men (Altonj and Blank [2]). Such career nterruptons are lkely to reduce the effect of mproved learnng spllovers n urban markets and hence may reduce any urban wage growth effect. On the other hand, the more nterrupted nature of female work hstores may mean that women partcularly beneft from mproved urban job matchng. As a result, the extent of wage deprecaton suffered by women durng perods out of employment may be less n denser urban markets.

4 4 By ncreasng the offered wage for any gven ndvdual, agglomeraton effects on wages should also ncrease labor market partcpaton. However, other densty effects, especally on female partcpaton, are also possble. In partcular, populaton densty allows greater provson of certan servces, e.g. chldcare provson, the avalablty of whch are partcularly lkely to reduce the reservaton wages of women. Indeed, female partcpaton rates n urban areas n developed countres have been consstently hgher than those observed n rural areas (Stabler [26]), whle the lack of chldcare facltes and access to transport are frequently cted as barrers to women acceptng employment n rural areas (Porterfeld [22], Lchter et al. [17]). Ths paper explores gender dfferences n both urban wage and partcpaton premums usng panel data from the Unted Kngdom. Specfcally, usng the Brtsh Household Panel Survey (BHPS), partcpaton and wage equatons are estmated for samples of urban and rural women and men and the extent of any urban premums calculated. Dfferences n the structure of wages and partcpaton are consdered by testng for urban-rural dfferences n the mpact of explanatory varables for women and men. Hgher urban wages and partcpaton may also reflect lvng costs, dfferences n abltes, job characterstcs or lower preferences for urban amenty (Roback [24], Hwang et al [14]) Therefore, when tryng to dentfy agglomeraton effects t s mportant to account for observed and unobserved dfferences n such factors. Whle many prevous studes have been able to control for observed dfferences, ther ablty to control for unobserved dfferences n these factors has often been lmted because the approprate data was cross-sectonal only (Wheeler [32], Wheaton and Lews [31]). However, the avalablty of panel data does allow the estmaton of models accountng for such unobserved dfferences or heterogenety. For example Glaeser

5 5 and Maré [10] used a fxed effects estmator to dentfy the male urban wage premum whle controllng for unobserved heterogenety. Ths approach s less attractve f sample selecton effects are mportant, as the fxed effects estmator s nconsstent f these effects do not vary wth tme (Verbeek and Njman [30]). Clearly, the nterrupted nature of female labor market partcpaton means sample selecton effects should be taken nto account when consderng the female urban wage premum. The fxed effect estmator also reles on urbanrural/rural-urban mgrants for dentfcaton of the wage premum. Ths means that t s unsutable f there are nsuffcent numbers of such mgrants for credble estmaton. For smlar reasons, n ths approach t s partcularly dffcult to dentfy urban-rural dfferences n parameters for explanatory varables such as educaton where there s lttle varaton over tme at the ndvdual level. Therefore, to account for sample selecton and unobserved heterogenety, whle allowng urban-rural dfferences n the mpact of explanatory varables to be dentfed, the panel sample selecton model suggested by Vella and Verbeek [29] and Njman and Verbeek [21] s estmated. In ths model the correlaton between unobserved components n the wage and partcpaton equatons controls for tradtonal sample selecton effects and unobserved heterogenety across all ndvduals. The dentfcaton of any urban premums n ths model does not rely on mgrants but uses all avalable wage nformaton. The man results are as follows. There s evdence of a small but economcally sgnfcant urban partcpaton premum for women of around 3%. In contrast, there appears to be no economcally sgnfcant partcpaton premum for men. There s also evdence of gender dfferences n the structure of the urban wage premum. In partcular, urban women experence lower wage deprecaton assocated wth tme out

6 6 of the labor force, but ther returns to experence are no hgher. In contrast, there s evdence of both lower wage deprecaton and hgher returns to experence for urban men. The source of the female urban partcpaton premum s dffcult to determne. However, the urban wage premums found are consstent wth the hypothess that those wth lower spatal moblty are more dsadvantaged n less dense labor markets, wth for example, the wage premum substantally lower for sngle women than for those who are marred or cohabtng. The plan of the paper s as follows. Secton II dscusses n more detal the source and emprcal mplcatons of possble gender dfferences n agglomeraton effects. Secton III descrbes the data, the defntons used and provdes some basc descrptve analyss. Secton IV dscusses the econometrc specfcaton, dscusson of hypotheses and model estmaton. Secton V presents the results. Secton VI concludes. II. BACKGROUND The varous mechansms through whch agglomeraton can ncrease wages (and partcpaton) are lkely to affect gender dfferences n a number of dfferent ways. Arguably, agglomeraton externaltes that occur prmarly at the frm level, are unlkely to nduce large gender dfferentals. For example f urban frms are more productve because of lower set-up or transport costs, or through ncreased nformatonal spllovers (Krugman [16], Glaeser [8]) there should be no gender dfferental as long as women and men are equally lkely to be found n frms where such effects are mportant. In contrast, agglomeraton effects whch accrue to the ndvdual are more lkely to be assocated wth gender dfferences. For example, because of the greater number of contacts between ndvduals, nformal learnng s lkely to be greater n

7 7 urban areas and ndvdual productvty and wages n urban areas may grow faster as a result (Glaeser [9], Rauch [23]). However, women have hstorcally had lower labor market attachment, hgher job turnover, and have receved less tranng than men (Altonj and Blank [2]). If learnng spllovers ncrease the rate of human captal formaton, the nterrupted nature of the typcal female work hstory and lower levels of tranng mean that urban women are lkely to gan less from such spllovers than men and hence wage growth effects may be less evdent for women. On the other hand, women are lkely to gan sgnfcantly from better job matchng n denser markets. Varous models predct hgher wages and growth f the qualty of job matchng mproves n urban markets. For example, Hesley and Strange [13] llustrate how agglomeraton tself can be drven by ncreasng expected urban match qualty, whle Wheeler [32] shows how decreasng search costs lead to more productve matches, ncreased sortng and wages n urban labor markets. Evdence suggests that women are less spatally moble than men, wth job search conducted over a smaller area than men (Madden and Chu [19]). Hence, denser markets and better job matchng may counterbalance ths reduced moblty. Further, mproved urban job matchng should also reduce the wage deprecaton assocated wth perods out of the labor force (Mncer and Ofek [20]). The more nterrupted nature of female work patterns should mean that ths type of effect wll be partcularly mportant for women. Although the evdence s mxed, a number of authors have argued that returns to educaton wll be hgher n denser markets. Possble gender effects n such educaton dfferentals are perhaps rather ambguous. For example, Rauch [23] argues that hgher returns to educaton n urban areas arse because the transmsson of deas s lkely to mprove wth hgher levels of human captal. Hence, these spllovers may

8 8 be larger n urban areas where average educaton levels are hgher. Such effects, whch are external to the ndvduals, are unlkely to nduce gender dfferences. However, Frank [7] argues that overeducaton effects are more lkely n less dense markets and that such effects are more lkely to affect the second earner n the household,.e. typcally women. In ths case, any ncrease n the return to educaton assocated wth denser markets mght well be larger for women. If market sze ncreases wages t should also ncrease partcpaton for dentcal ndvduals. Moreover, f the female urban wage premum s larger, any assocated ncreased partcpaton effect should also be hgher for women. Fnally, the effect of populaton densty on servce provson may also tend to exacerbate any gender dfference n the urban partcpaton premum. In partcular, n areas of low populaton densty, access to servces such as transport, housng and chldcare, may be more dffcult. If they exst, such barrers to employment are lkely to mpact dfferentally on women, ncreasng ther reservaton wages and hence further reducng female partcpaton n low densty areas (Porterfeld [22], Lchter et al [17]). In summary, the prevous dscusson suggests a number of general hypotheses concernng the nature of possble gender dfferences n urban wage and partcpaton premums. Frst, f agglomeraton effects are only felt at the frm level, the urban wage premum s lkely to be smlar for both sexes. In contrast, where job matchng effects are mportant, the urban wage premum may be larger for women as denser markets counterbalance the effect of ther smaller job search area. Further, the urban wage premum should, as a result, be larger for certan groups whose spatal moblty s lkely to be partcularly restrcted, e.g. marred women. Learnng spllover and job matchng effects are both lkely to be mportant n the male urban wage premum. However, the nterrupted nature of ther work

9 9 hstores means that job matchng effects, e.g. through lower wage deprecaton, are lkely to be relatvely more mportant than learnng spllover effects for women. In contrast, t s more dffcult to make predctons whether, f they exst, hgher urban returns to educaton should vary by gender. Fnally, any larger female urban wage premum should also mply a larger urban partcpaton premum for women. Ths dfferental may also be exacerbated by hgher servce provson n denser urban areas. III. DATA The data was drawn from the frst eght waves of the Brtsh Household Panel Survey, a longtudnal survey followng some 10,000 ndvduals representatve of the Brtsh populaton. The labour market component of the survey has detaled nformaton on ndvdual earnngs, hours worked, other ndvdual characterstcs and work hstores from whch standard measures of usual hourly earnngs, hghest educaton level attaned, total experence and tme out of the labour force can be calculated (see the footnote to Table 1 for detals on defntons). Unlke n the Unted States there s no sngle accepted defnton of what consttutes a (dense) metropoltan area n the UK. However, addtonal nformaton made avalable by UK Insttute for Socal and Economc Research, made t possble to splt the sample nto urban and rural resdents based on place of resdence consstent wth those defntons used by polcy makers. Specfcally, n England, Local Authorty Dstrcts are classfed nto Remote Rural, Accessble Rural, Coalfeld areas, Urban and Metropoltan (Cabnet Offce [4], Tarlng et al [27]). For Scotland and Wales, rural Local Authorty Dstrcts are dentfed usng the Randall defnton, where populaton densty n the dstrct s less than one person per hectare, and then rural dstrcts are classfed as remote or accessble rural dependng on ther proxmty to urban centers (Scottsh Offce [25]).

10 10 Whle these defntons do not allow the examnaton of cty sze effects, t s argued that the contrast between urban and rural samples can stll be exploted to dentfy agglomeraton effects. To ensure those n the rural sample are resdent n areas characterzed by populaton scarcty and dstance from urban centers (Cabnet Offce [4]), t s mportant to exclude those lvng n rural areas but wthn commutng dstance to urban centers. Hence, the rural sample conssts only of those ndvduals resdent n remoter rural dstrcts only, whle the urban sample ncludes only those resdent n dstrcts defned to be urban and metropoltan. To estmate the sample selecton model specfed n the next secton requres at least three (consecutve) observatons for each ndvdual n the sample. To maxmze the use of the avalable data and n partcular to ensure adequate rural observatons, an unbalanced panel was constructed from the rural and urban samples of ndvduals ntervewed n three or more consecutve waves. For each ndvdual, only nformaton from one set of consecutve ntervews was used. Hence, f data was mssng n a gven wave, only the nformaton from the longest set of consecutve of ntervews was ncluded for that ndvdual. Ths procedure resulted n repeated observatons on 2177 women, of whch 1040 were observed n all eght waves, and 1626 repeated male observatons, wth 565 observed n all eght waves. Moves between urban and rural locatons are extremely rare n the data, wth 71 total moves for women and only 48 total moves for men n ether drecton. Table 1 reports key summary statstcs for the urban and rural samples by gender. As expected, the Table shows hgher urban partcpaton rates and wages for both sexes. The urban-rural dfferences n partcpaton rates are rather smlar for women and men,.e. 4 and 3 percent respectvely. However, the female urban wage premum at 15 percent s sgnfcantly larger than the male urban-rural dfference at 8

11 11 percent. Apart from a few exceptons, e.g. a lower proporton of marred or cohabtng urban women, a hgher proporton of urban men wth a degree, most of the characterstcs appear smlar across the urban and rural samples. IV. MODEL Urban premums n wages and partcpaton may arse from dfferences n observed and unobserved ndvdual characterstcs or n dfferences n the mpact of gven explanatory varables on an ndvdual s wages and partcpaton probablty. The followng model captures both types of effect. Frst, consder the offered wage equaton u u r r (1) w t = xt β + xt β + α + et, =1,..,N, t=1,.., T 1 where w t represents the potental offered (log) wage of ndvdual n tme t, k x t (k=u,r) s a vector of observed characterstcs for the urban (u) and rural (r) samples k ( x = 0 f ndvdual s not part of sample k), t k β are returns to these characterstcs n the two samples, whle α and e t are random components. In the model estmated below k x t contans quadratc functons of each ndvdual s total experence and tme out of the labor force, educaton dummes plus tme and regonal dummes. Dfferences n the structure of returns to characterstcs across the two samples can be consdered n equaton (1) by testng whether the parameters k β are dentcal. Unobserved heterogenety across ndvduals n terms of cost of lvng, productvty, preference for amenty and other job characterstcs, e.g. ndustry and occupaton, s controlled for by the random effect term α, whle e t accounts for other tme varyng 1 In the emprcal work, separate equatons are estmated by gender. For brevty the specfcaton descrbed below does not explctly dstngush between the sexes.

12 12 random shocks. Assume, as s standard, that an ndvdual s decson to work s determned by whether the offered wage s above ther reservaton wage, where both are nfluenced by observed and unobserved ndvdual characterstcs. Ths mples a standard reduced form model for partcpaton as a functon of all the varables affectng both the reservaton and offer wage plus any ndvdual unobserved effect. However, there s extensve evdence to suggest that even after accountng for ndvdual heterogenety, ndvduals also exhbt a consderable degree of persstence n ther labor market state (Heckman [11], Hyslop [15]). Ths suggests that the reduced form model should also allow for state dependence as follows * u u r r u u r u (2) yt δ yt + δ yt + ztδ + ztδ + θ + ηt = (3) y I( y * > 0) t = t where y t s equal to one when ndvdual partcpates n perod t, * y t s the latent varable whch when postve mples the ndvdual wll partcpate, k z t are vectors contanng the varables assumed to nfluence both offered and reservaton wages for u the urban (u) and rural (r) samples. The vector δ 1 captures the (net) effects of the varables n the reservaton and offered wage functons by locaton. In the specfcaton below, k z t contans all the explanatory varables used n k x t plus a set of demographc and other varables, ncludng martal status, number and age of chldren and non-labor ncome. The extent of state dependence or persstence n partcpaton s captured by the presence of the lagged partcpaton varables k yt 1 (equal to one f the ndvdual was workng n the prevous perod and resdent n locaton k). Unobserved heterogenety s captured by θ whle η t s pure random component. The model s completed by assumng that the error terms are jontly normally

13 13 dstrbuted wth zero means and constant varances. The sample selecton problem nduced by the potental correlaton between unobserved components n the partcpaton and wage equatons can then be ncorporated by allowng for non-zero covarances between the random effects n the α and θ, and between the two shocks e t and η t. All other covarances between elements of the error terms are assumed zero. 2 Testng Urban-Rural Dfferences The sources of possble gender dfferences n urban wage and partcpaton premums suggest a number of dfferences n the urban and rural coeffcents n equatons (1) and (2). Frst, as Glaeser and Maré [10] note, frm level agglomeraton effects mply an urban wage level effect. Hence, any wage premum for both sexes should dsappear once observed and unobserved heterogenety s controlled for,.e. u H o : = r should not be rejected n equaton (1). Moreover, f an urban wage premum s observed t should not dffer sgnfcantly by gender. In contrast, job matchng effects should mean any overall urban wage premum s larger for women, and that ths premum wll be greater n samples where spatal moblty s thought to be lower. Learnng spllover effects should ncrease urban wage growth. Improved job matchng effects may also ncrease wage growth but equally should decrease wage deprecaton assocated wth tme out of the labor force. Dsentanglng these effects s obvously dffcult. Frst, the exact relatonshp between any learnng spllover and job matchng effects and the estmatng equatons s not clear-cut. Second, the small number of mgrants n the dataset means t not possble to use ths group to dentfy 2 The sample selecton model controls for labor market partcpaton but not the potental endogenety of locaton. However, nformal tests usng sub-samples of less moble ndvduals, e.g. those wth lower educaton levels, ndcate that the results are robust to ths lmtaton.

14 14 the source of the urban premums (Glaeser and Maré [10]). However, the lack of urban-rural moblty does suggest that that any urban premum n wage growth and/or reduced wage deprecaton should be reasonably reflected n the dfferent estmates of returns to experence and wage losses assocated wth tme out of the labor force. For example, f mproved job matchng effects are more mportant for women than learnng spllovers, any urban wage growth effect captured through ncreased returns to experence should be less mportant than any reduced urban wage deprecaton effect. There are no clearcut predctons as to whether there wll be any dfference n any urban educatonal premum by gender. However, any such effects wll be captured by dfferences n the coeffcents reflectng returns to educaton n the wage equaton (1). Any urban mpacts on returns to experence, wage deprecaton and educaton wll also affect the coeffcents n the partcpaton equaton. However, as these varables may also affect the reservaton wage, dfferences n these coeffcents are more dffcult to nterpret drectly. However, after accountng for other factors, the mpact of a hgher female urban wage premum should mean a greater urban female partcpaton effect. The other hypotheszed partcpaton effects that can be captured by equaton (3) are also lkely to renforce any hgher urban female partcpaton effect. In partcular, for women, the presence of (young) chldren s lkely to ncrease reservaton wages, and therefore decrease the probablty of labor market actvty, by ncreasng the opportunty costs of workng. If populaton densty effects on chldcare servce provson are mportant, ths reducton n reservaton wages may be lower for urban women. Hence, the urban coeffcents capturng the overall mpact of chldren

15 15 on partcpaton on women should be less negatve than the rural ones. Econometrc Implementaton Estmaton of the wage and partcpaton equatons poses a number of econometrc problems. As specfed, the estmaton model would need to assume that the random effect θ s ndependent of z t. Ths assumpton s not tenable for a number of the explanatory varables. Ths poses a problem as, f ths assumpton s volated, the estmated coeffcents wll not correctly dentfy the margnal mpacts of the tme varyng ndependent varables. The standard approach to control for ths s to model the random effect θ as a functon of all the ndependent varables n all tme perods (Chamberlan [5]) or, slghtly more restrctvely, as a smple functon of the ndvdual level means of the ndependent varables (Arulampalam et al [3]). Ths latter approach s followed here. Hence, u u r r (4) θ = z φ + z φ + µ where µ s assumed ndependent of random effect and the regressors may vary by locaton. 3 k z t and the correlatons between the orgnal After substtuton of (4) n (2), the estmaton of the resultng partcpaton and wage equatons s undertaken usng the two-step procedure suggested by Njman and Verbeek [21]), and Vella and Verbeek [29]). In the frst step, estmates of the parameters n the partcpaton equaton (2) are obtaned from a dynamc random effects probt. heterogenety One addtonal problem s that the presence of unobserved µ n conjuncton wth lagged partcpaton t 1 y nduces an ntal 3 One problem of ths approach s that sgnfcant collnearty problems may be nduced between the addtonal regressors and the orgnal ndependent varables. Hence, n the emprcal work only a subset of the ndependent varables are used,.e. those wth suffcent varaton wthn the panel.

16 16 condtons problem, where the ntal observaton y t 0 wll be correlated wth the unobserved random effect and hence maxmum lkelhood wll produce nconsstent estmates. Ths s addressed usng the suggeston of Heckman [12], where a reduced form equaton s specfed for the ntal perod, where the error term from ths equaton s assumed correlated to the unobserved random effects. (5) yt = z t 0λ + ε o 0 where z t 0 s a vector of strctly exogenous varables, ε o s the error term, where ths error and the random effect µ are correlated. The second step of the estmaton procedure s an extenson of the standard Heckman approach dealng wth sample selecton. Consder the condtonal expectaton of equaton (1), condtonal on the y, the vector of all partcpaton states observed for ndvdual, u u r r (6) E w y ) = x β + x β + E( α y ) + E( e y ). ( t t t t As the errors are assumed to be drawn from a multvarate normal dstrbuton, the condtonal expectatons E α y ) and E e t y ) are lnear functons of the ( ( covarances σ αµ and σ e η. Specfcally, Verbeek and Njman [30] show that T 1 = αµ 2 σ η + Tσ µ s= 1 (7) E[ α y ] σ a E[ µ + η y ] 2 s s T 1 1 = eη t 2 2 σ η σ η + Tσ µ s= 1 (8) E[ e y ] σ E[ µ + η y ] a E[ µ + η y ] t 2 s s where T = s = a 1 T s s the number of perods an ndvdual s observed ( T = max ( T ), a s = 1 f observed n perod s, 0 otherwse), and σ αµ σ e η are the covarances between the random effects and error terms respectvely. It can be shown

17 17 that the bracketed terms on the rght hand sde of (7) and (8) are functons of the parameters n the partcpaton equaton only. Hence, as n the standard Heckman case, once estmates of the partcpaton parameters have been obtaned, estmates of these correcton terms can be obtaned va numercal ntegraton. Then equaton (6) can be estmated ncludng the two correcton terms usng OLS, where standard errors are adjusted to allow for the estmated nature of the correcton terms. The coeffcents provde estmates of σ αµ and η, and therefore the sgnfcance of these two σ e coeffcents provdes a test for the mportance of sample selecton effects. In prncple, the error assumptons dentfy all the parameters n the offered wage equaton as the selecton terms are non-lnear functons of the exogenous varables. However as Vella [28] notes, the degree of the non-lnearty n the selecton terms may be lmted gven the actual range of values of the regressors. Hence, further excluson restrctons are desrable. Here, a number of varables are excluded from the wage equaton, namely, the demographc varables and non-labor ncome, plus the lagged partcpaton value. It s often argued that household demographc varables should be ncluded to capture unobserved motvatonal factors. Here such factors are controlled for by the unobserved heterogenety. Even wthout these restrctons, the wage regresson coeffcents can be dentfed by the excluson of the lagged partcpaton varable. 4 V. RESULTS Partcpaton The results of the estmaton of the partcpaton equaton for women and men are 4 Expermentaton shows that the results are robust to a varety of excluson restrctons, ncludng the case where lagged partcpaton s the only explanatory varable n the partcpaton equaton excluded from the wage regresson.

18 18 reported n Tables 2 and 3 respectvely. For comparatve purposes each Table also reports (n Columns 1 and 2) the results from a smple statc Random effects probt wth no adjustment for potental correlatons between the regressors and the random effect. The urban and rural estmates from the full dynamc model (equatons (2)-(4)) are reported n columns 3 and 4 respectvely. Hence, comparng across the two specfcatons shows the mpact on the partcpaton estmates of allowng for dynamcs and correlatons between regressors and the random effects. For brevty n all cases, the estmated coeffcents on the regonal and wave dummes are not reported. In the dynamc partcpaton equaton, the ntal condtons equaton estmates and the adjustment for correlated errors gven by equaton (4) are also omtted. Unless otherwse ndcated, the standard error s gven n brackets below each estmated coeffcent. The second secton of Tables 2 and 3 reports the value of the nter-temporal correlaton coeffcent for the partcpaton equatons. The correlaton coeffcent ρˆ s typcally nterpreted as the proporton of the varance unexplaned by the regressors n the random effects probt and accounted for by varaton between ndvduals (Arulampalam et al [3]). The assocated standard error ndcates whether takng account of unobserved heterogenety n the partcpaton equaton s mportant. Consstent wth prevous studes, ths correlaton s sgnfcant for all specfcatons n both Tables 2 and 3. In the fnal panel of the Tables, a number of estmaton evaluaton measures are reported. For all estmatons, the hypothess that all coeffcents are zero s strongly rejected. Further, consstent wth the exstence of urban densty effects, the hypotheses that all the urban and rural coeffcents are dentcal ( δ = = ) s rejected at 5 percent sgnfcance for all cases, except for u r u r H o : 0 δ 0, δ 1 δ 1

19 19 the dynamc model n the female sample. Here, ths hypothess s rejected at 10 percent sgnfcance (p-value 0.056). Fnally, the urban partcpaton premum s reported at bottom of each Table. Ths s derved for each of the estmatons as follows. Frst, the urban and rural coeffcent estmates are appled to the urban sample separately to generate two sets of ndvdual partcpaton probablty predctons. The urban partcpaton premum s the dfference between the average of the predctons obtaned usng the urban coeffcents and the average obtaned usng the rural coeffcents. Formally, the average predcted probablty from random effects estmaton represents the (condtonal) probablty that a randomly chosen ndvdual wll be observed partcpatng (Arulampalam, et al [3]). Ths premum can therefore be nterpreted as the ncrease n the probablty that a randomly chosen ndvdual wll partcpate f located n an urban area rather than a rural one. As predcted, the mpled urban partcpaton premum for women s postve ( ) and larger than for men. Indeed, for men the premum s ether negatve ( ) or extremely small (0.008). Turnng to the coeffcents for women presented n Table 2. For the urban women estmates (columns 1 and 3), most are broadly n lne wth pror expectatons. In both the statc and dynamc specfcatons, the partcpaton probablty s strongly postvely assocated wth educaton level, and negatvely assocated wth tme out of the labor force, pre-school chldren and non-labor ncome. In the dynamc specfcaton, the coeffcent on the lagged partcpaton varable s postve and sgnfcant. The ncluson of ths varable substantally decreases the proporton of the unexplaned varance attrbuted to ndvdual heterogenety. A number of the estmated coeffcents also change substantally between the statc and dynamc specfcaton. For example, the margnal mpact of total actual experence s now

20 20 apparently negatve (although nsgnfcant), the educaton coeffcents now exhbt a more dstnct pattern, wth ncreasng educaton assocated more clearly wth ncreasng partcpaton probablty, whle the margnal negatve mpact of young chldren s much reduced. Ths latter result s consstent wth the probablty of women havng chldren beng correlated wth preferences for not workng. The majorty of the rural coeffcents are of same sgn as the urban ones, wth the educaton coeffcents beng a notable excepton. However, unsurprsngly gven the smaller underlyng sample many of these coeffcents are less well determned. The coeffcents on educaton, experence and tme out of the labor force capture the effects of these varables on both offered and reservaton wages. Hence, clearcut conclusons n terms of urban densty effects are dffcult to draw from any urban-rural dfferences for these varables. However, the man source of the rejecton of the hypothess that all the urban and rural coeffcents are dentcal does appear to arse from the educaton varables. Two of the educaton varables are ndvdually sgnfcantly dfferent n both specfcatons, whle the jont Wald test of equalty of all educaton coeffcents across the urban and rural samples s rejected n both the statc and dynamc specfcatons. (p-values and respectvely). Overall the urban-rural dfferences n the experence varables and tme out of the labor force do not exhbt clear dfferences across the urban and rural sample. Whle the mpact of all experence and tme out of the labor force varables s statstcally dfferent across the two samples (p-value 0.020), ths dfference s not apparent n the dynamc specfcaton. Because these varables appear n the partcpaton model only, stronger nterpretatons are possble f urban-rural dfferences n the mpact of chldren are observed. For example, the margnal coeffcents on young chldren are less negatve

21 21 for urban women n both specfcatons (consstent wth lower urban reservaton wages from better chldcare provson). However, n nether the statc or dynamc specfcaton are these dfferences statstcally sgnfcant, whle the urban-rural dfferences n the coeffcents on older chldren do not conform to ths hypothess. The Table 3 estmates for the male sample follow a rather smlar pattern to the female sample. Both urban and rural estmates generally follow pror expectatons. Relatve to the statc model, the full dynamc specfcaton wth correlated regressors reduces the correlaton coeffcent ρˆ, whle none of the varables reflectng number of chldren s statstcally sgnfcant n ths latter specfcaton. Both urban and rural coeffcents on lagged partcpaton varable are postve. In ths case the urban coeffcent s less than the rural one but ths dfference s not statstcally sgnfcant. Although dffcult to nterpret n terms of urban densty effects because they are net effects, the overall rejecton of equalty of the urban and rural coeffcents does appear to arse from dfferng mpacts of the experence and out of the labor force varables. In the statc specfcaton, the equalty of urban-rural coeffcents of both the experence varables and the out of the labor force varables s rejected (p-values 0.08 and respectvely). In the dynamc specfcaton, although there are no ndvdually sgnfcant dfferences, the test that both coeffcents on the out of the labor force varables are equal across the samples s stll rejected at 10 percent (pvalue 0.08). In contrast to women, there s lttle evdence of urban educaton effects. Although the coeffcent on one of the educaton dummes s sgnfcantly dfferent n the dynamc case, the jont test that all educaton coeffcents are dentcal cannot be rejected n ether specfcaton.

22 22 Wages Tables 4 and 5 present the Sample Selecton model wage equaton estmates for women and men. To provde an ndcaton of the senstvty of the results to the underlyng assumptons used to dentfy ths model, OLS and Fxed Effects wage equaton results are also reported n these Tables. In partcular, the OLS results provde a smple way to judge the effects of allowng for sample selecton and unobserved heterogenety usng the Sample Selecton model. In contrast, the Fxed Effects model accounts for unobserved heterogenety but not all types of sample selecton and reles on mgrants to dentfy the urban effects. There are two addtonal coeffcents n the Sample Selecton model assocated wth the two selecton terms generated usng the dynamc random effects probt results n Tables 2 and 3. These coeffcents provde estmates of the covarance between the random effects, σ αµ and the covarance between the random shocks σ e η. 5 The results ndcate that sample selecton s mportant for men and women. For both samples the estmate of σ αµ s postve, although t s only sgnfcant for women, whle the estmates of σ e η are negatve and sgnfcant at 5% for both sexes. 6 In the bottom panel of the Tables, a number of estmaton evaluaton measures are reported. The tests that all coeffcents are zero are strongly rejected n all specfcatons for both women and men. The test of equalty between all the urban 5 The frst selecton term also accounts for unobserved heterogenety n the wage equaton. 6 As the covarance between the two tme-varyng components of the partcpaton and wage equaton must be zero for the fxed effects estmator to be consstent, the sgnfcance of the second tme varyng selecton term provdes some evdence, condtonal on the sample selecton model s dentfyng assumptons, to suggest that the fxed effects estmator may not be approprate n ths case.

23 23 u r and rural coeffcents ( H : = ) s also clearly rejected n the OLS and Sample o Selecton models n both Table 4 and 5. However, the results for the Fxed Effects estmator are more ambguous wth lttle evdence to support the rejecton of ths hypothess for men (p-value 0.111), whle the test s rejected only at the 10 percent level only for women. Fnally, the mpled urban wage premum s gven for all specfcatons. These are calculated by applyng the urban and rural coeffcent estmates separately to the urban sample to generate two sets of ndvdual predcted offer wages. The urban wage premum reported s the dfference between the average of the offer wage predctons obtaned usng the urban estmates and the average obtaned usng the rural estmates. As wth prevous evdence by Glaeser and Maré [10], a postve urban wage premum remans for both women and men after controllng for both observed and unobserved heterogenety. Although frm level agglomeraton effects mply an urban premum n wage levels, the unobserved heterogenety, whch allows each ndvdual s ntercept to dffer, should purge the observed premum of such effects. Hence, as an urban premum remans n both the Fxed Effects and Sample Selecton models, ths suggests that the premum s not smply a frm level effect. Further, n all specfcatons the female urban wage premum s sgnfcantly larger than that for men, consstent wth the hypothess that mproved job matchng n denser urban areas s mportant n explanng hgher urban wages. Turnng to the coeffcent estmates n Table 4 and 5. The OLS and Sample Selecton models provde smlar results that are consstent wth pror expectatons. For both men and women, the results for these models ndcate that wages ncrease wth experence and educaton level but declne wth tme out of the labor force.

24 24 Consstent wth prevous evdence (Lght and Ureta [18]), they also suggest that returns to experence and that wage deprecaton are lower for women. Returns to educaton below degree level also appear lower for women. In contrast, the estmated coeffcents n for the Fxed Effects model are often poorly determned, partcularly for varables such as educaton level where there s lttle tme varaton wthn ndvduals. For example, the coeffcents on the educaton varables do not follow the expected pattern for ether men or women, whle only four of the sxteen educaton coeffcents estmated are sgnfcant. In addton, although the estmated coeffcents have the expected sgns nether tme out of the labor force or ts square are found to have a sgnfcant effect on wages for women n ths model. In the OLS and Sample Selecton results, the source of urban-rural dfferences n wages are well determned and apart from results for the educaton varables - consstent wth pror hypotheses on potental gender dfferences. For women, the estmates n Table 4 are smlar across OLS and Sample Selecton models. They both ndcate sgnfcant reduced wage deprecaton n the urban sample consstent wth mproved job matchng wth the urban coeffcents on tme out of the labor force and tme out of the labor force squared around half the rural estmates. Further, the jont test of urban-rural equalty of the two out of the labor force coeffcents s rejected n both specfcatons (p-values <0.001). On the other hand there s no evdence of hgher urban returns to experence or to educaton. Indeed, wth respect to returns to educaton, there s some evdence that the returns to lower range qualfcatons are n fact hgher n the rural sample. In contrast, the results for the Fxed Effects model suggests that the lack of mgrants n the data mean t s dffcult to dentfy the source of any urban wage premum usng ths approach. For example, only one of the dfferences between an ndvdual urban and rural estmate s statstcally sgnfcant,

25 25.e. the effect of A-Levels, and n ths case nether ndvdual estmate s sgnfcant. The OLS and Sample Selecton results for men n Table 5 ndcate that urban wage deprecaton assocated wth tme out of the labor force s lower consstent wth mproved urban job matchng. However, urban returns to experence for men are also sgnfcantly hgher consstent wth the exstence of mproved nformal spllover effects. Jont tests of the experence varables and the out of the labor force varables strongly reject the hypotheses that these coeffcents are dentcal across urban and rural samples n ether the OLS or Sample Selecton specfcaton (p-values and respectvely). As for women, there s no evdence of hgher urban returns to educaton. The results for the Fxed Effects model also ndcate hgher urban returns to experence for men (despte the fact that the hypothess that all urban and rural coeffcents are equal cannot be rejected). However n ths case, no sgnfcant urban-rural dfferences are found n the effect of tme out of the labor force. Model Evaluaton The ablty of the Sample Selecton model to dentfy the urban wage premum and control for unobserved heterogenety depends on a number of assumptons, e.g. jont normalty of errors, ndependence between the error components and regressors n the wage equaton, non-zero correlatons between unobserved heterogenety n partcpaton and wage equatons etc. As model msspecfcaton nduced by volatons of these assumptons s lkely to be reflected n the wage resduals, we use these as the bass of an nformal test of overall model valdty. The three estmaton approaches used,.e. OLS, Fxed Effects, and Sample Selecton, also provde specfc predctons about the behavor of the wage resduals. In partcular, because OLS does not take account of unobserved heterogenety, the unadjusted resduals from the OLS wage regressons should be strongly correlated for

26 26 ndvduals. In contrast, f the tme varyng sample selecton effects are not mportant, Fxed Effects should control effectvely for unobserved heterogenety and the resduals n ths model should be uncorrelated at the ndvdual level. Smlarly, f the Sample Selecton model does control effectvely for unobserved heterogenety through the correlaton between the unobserved effects n the partcpaton and wage equatons, the unadjusted resduals from the Sample Selecton wage regressons should also be uncorrelated at the ndvdual level. The resduals ( u t ) from each of the sx wage estmatons n Tables 4 and 5 are analyzed usng technques appled when examnng the covarance of earnngs (Dckens [6], Abowd and Card [1]). Frst, wthn ndvdual resdual covarances are calculated, and an estmate of the resdual covarance matrx obtaned. Second, from these matrces the average covarances by lag length are calculated. These are reported n Table 6 for each wage regresson. Zero correlaton n the resduals would mean that each of these covarances should not be statstcally sgnfcant. Overall the results from Table 6 do not suggest serous underlyng msspecfcaton n the Sample Selecton model. Furthermore, they ndcate that ths model s more effectve n elmnatng correlaton n the resduals n both the female and male wage estmatons than ether OLS or Fxed Effects approaches. The reported OLS resdual covarances are large and all strongly statstcally sgnfcant for both sexes. Although somewhat smaller than for the OLS estmaton, all resdual covarances beyond one lag reman statstcally sgnfcant for both sexes n the Fxed Effects results. In contrast, the covarances from the Sample Selecton model are generally smaller, wth only one ndvdual covarance remanng statstcally sgnfcant n each case.

27 27 Spatal Moblty and Urban Partcpaton-Wage Premums The results reported n Table 3-5 provde evdence that urban partcpaton and wage premums are larger for women and that the structure of urban-rural dfferences n returns to experence and tme out of the labor force dffer by gender. If the source of these dfferences s mproved urban job matchng effects, we would expect that the urban premum wll be greater for groups where spatal moblty s thought partcularly restrcted. To explore ths Table 7 reports the urban partcpaton and wage premums for a sub-sample thought a pror lkely to be less spatally moble,.e. marred and cohabtng ndvduals, and a sub-sample thought to be more moble,.e. unmarred ndvduals. The results for the urban characterstcs (columns 1 and 3) are calculated n the same way to the premums presented n Tables 3-5,.e. the urban and rural estmates are appled to the urban sample to provde two sets of predctons, wth the urban premum equal to the average predcted value usng the urban coeffcents mnus the average usng the rural coeffcents. In addton, the urban premums obtaned when the urban and rural coeffcents are appled to the rural samples of men and women are also reported. Each set of results s based on the estmaton of a separate dynamc Random Effects partcpaton probt and Sample Selecton model wage regresson for the approprate sub-sample. To provde a general ndcaton as to the robustness of the urban premums reported, the result of the jont test that all urban and rural coeffcents are dentcal n the model used to generate the predctons s also reported for each case. The partcpaton results provde lttle support for the hypothess that the observed urban premum arses from dfferences n spatal moblty. For women, the hypothess that there are no urban-rural dfferences n the coeffcents used to generate

28 28 the results n Table 3 cannot be rejected for ether sub-sample, whle the calculated premums are larger for those thought to be less spatally constraned,.e. unmarred women. For men, the urban partcpaton premums are larger for the samples of marred men but reman small. In contrast, the urban wage premum results do provde further evdence that the urban-rural gender dfferences observed n Tables 4 and 5 are drven by dfferences n spatal moblty. Frst, the urban-rural dfferences n estmated coeffcents underlyng the calculated premums appear robust, wth the hypothess that the urban and rural coeffcents are dentcal rejected (at 5 % sgnfcance) n all cases. Second, the urban wage premum vares as predcted. So although the urban wage premum does not dsappear for sngle women, t s substantally lower than for the marred/cohabtng sample. For example, when the characterstcs of rural sngle women are used the premum falls to but rses to for the sample of rural marred women. Smlarly, the wage premum s larger for marred than sngle men. VI. SUMMARY AND CONCLUSIONS Ths paper has consdered the extent of gender dfferences n both the urban wage and partcpaton premums usng panel data from the Unted Kngdom. Specfcally, partcpaton and wage equatons were estmated for urban and rural women and men usng a panel sample selecton model, whch controlled for observed and unobserved heterogenety. As the dentfcaton of the wage component of the model requres a number of relatvely strong assumptons, e.g. jont normalty of errors, the wage equaton results were also compared wth both OLS and Fxed Effects estmatons. These comparsons showed that the Sample Selecton estmator does provde an effectve way n whch to control for unobserved heterogenety and sample selecton n cases where dentfcaton problems reduce the usefulness of Fxed Effects

29 29 estmator. From the results, there s evdence of a small but economcally sgnfcant urban partcpaton premum for women. In contrast, there appears to be no economcally sgnfcant partcpaton premum for men. However, for both women and men there s evdence that partcpaton structure dffers n urban areas, although specfc urban densty effects are dffcult to dentfy. In contrast, the wage regressons do suggest that urban densty effects nduce gender dfferences n wages. Even after controllng for observed and unobserved heterogenety, the urban premum s larger for women. Further, consstent wth hypothess that hgher urban market densty counteracts the effects of lower spatal moblty, the urban wage premum for women was substantally larger for those who were marred or cohabtng relatve to those who were sngle. Fnally, whle there s no evdence of hgher urban returns to experence, wage deprecaton for women s apprecably lower n the urban sample. In contrast, both hgher returns to experence and lower wage deprecaton help explan the male urban wage premum. Whle not conclusve, these results do suggest that mproved urban job matchng effects are relatvely more mportant n the female urban wage premum than learnng spllover effects. The results ndcate a number of possble questons for further research. The urban-rural categorzaton used here s necessarly rather broad. Are there dfferent effects f a fner scale s avalable, e.g. are there cty sze effects? Also, the tests of the mpact of hgher servce provson on partcpaton appled are rather ndrect. Can measures be found whch would allow such effects to be tested more fully, e.g. effects of dfferences n publc transport provson?