RACIAL SORTING AND NEIGHBORHOOD QUALITY * Patrick Bayer Yale University. Robert McMillan University of Toronto. November 2005.

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1 RACIAL SORTING AND NEIGHBORHOOD QUALITY * Patrck Bayer Yale Unversty Robert McMllan Unversty of Toronto November 2005 Abstract In ctes throughout the Unted States, blacks tend to lve n sgnfcantly poorer and loweramenty neghborhoods than whtes. An obvous frst-order explanaton for ths s that an ndvdual s race s strongly correlated wth socoeconomc status (SES), and poorer households can only afford lower qualty neghborhoods. Ths paper conjectures that another explanaton may be as mportant. The lmted supply of hgh-ses black neghborhoods n most U.S. metropoltan areas means that neghborhood race and neghborhood qualty are explctly bundled together. In the presence of any form of segregatng preferences, ths bundlng rases the mplct prce of neghborhood amentes for blacks relatve to whtes, promptng our conjecture that racal dfferences n the consumpton of neghborhood amentes are sgnfcantly exacerbated by sortng on the bass of race, gven the small numbers of blacks and especally hgh-ses blacks n many ctes. To provde evdence on ths conjecture, we estmate an equlbrum sortng model wth detaled restrcted Census mcrodata and use t to carry out nformatve counterfactual smulatons. Results from these ndcate that racal sortng explans a substantal porton of the gap between whtes and blacks n the consumpton of a wde range of neghborhood amentes n fact, as much as underlyng socoeconomc dfferences across race. We also show that the adverse effects of racal sortng for blacks are fundamentally related to the small proporton of blacks n the U.S. metropoltan populaton. These results emphasze the sgnfcant role of racal sortng n the ntergeneratonal persstence of racal dfferences n educaton, ncome, and wealth. Keywords: racal sortng, segregaton, bundlng, equlbrum sortng model, local publc goods, neghborhood amentes (JEL: H0, J7, R0, R2) * We would lke to thank Fernando Ferrera for outstandng research assstance. We are grateful to Pat Bajar, Steve Berry, Matt Kahn, Tom Nechyba, Km Rueben and Chrs Tmmns for many valuable dscussons about ths research, and to Maureen Cropper, Davd Cutler, Denns Epple, Ed Glaeser, James Heckman, Vernon Henderson, Costas Meghr, Robert Mofftt, Davd Neumark, Steve Ross, Holger Seg, Kerry Smth, and Jacob Vgdor for addtonal helpful comments. We also thank conference partcpants at the AEA, ERC, IRP, NBER, PET, SIEPR, and SITE, and semnar partcpants at Brown, Chcago, Colorado, Columba, Duke, Johns Hopkns, Northwestern, NYU, PPIC, Smon Fraser, Stanford, Toronto, UBC, UC Berkeley, UC Irvne, UCLA, and Yale for helpful suggestons. Ths research was conducted at the Calforna Census Research Data Center; our thanks to the CCRDC, and to Rtch Mlby n partcular. We gratefully acknowledge fnancal support for ths project provded by the Natonal Scence Foundaton under grant SES , the Publc Polcy Insttute of Calforna, and SSHRC.

2 1 INTRODUCTION In ctes throughout the Unted States, blacks tend to lve n sgnfcantly poorer and loweramenty neghborhoods than whtes. Many researchers post that such neghborhood dfferences play a central role n the perpetuaton of racal nequalty (see Wlson (1987) and Massey and Denton (1993), for example). 1,2 In tryng to understand how these substantal gaps n neghborhood qualty across race arse, an obvous frst-order explanaton s that an ndvdual s race s strongly correlated wth socoeconomc status (SES), 3 and poorer households can only afford lower qualty neghborhoods. Ths paper conjectures that another explanaton may be mportant, due to a combnaton of racal sortng and the short supply of predomnantly black, hgh-amenty neghborhoods n almost all U.S. metropoltan areas. The short supply s stark: whle over 11,000 Census tracts n U.S. metropoltan areas are at least 40 percent college-educated, for example, a mere 44 of these tracts are also at least 60 percent black. 4 As a consequence of ths short supply, neghborhood race and many other neghborhood characterstcs are explctly lnked n the set of resdental optons avalable to most households: n order to choose hgh-amenty neghborhoods, households must typcally lve wth a hgher fracton of whte neghbors, gven that the full range of possble neghborhood optons s not spanned. The bundlng of neghborhood race and other neghborhood amentes would be of lttle mport f households had dentcal preferences for neghborhood racal composton or f race played no role n household locaton decsons. But gven any form of segregatng preferences n the populaton, 5 ths bundlng drves a wedge between the mplct prce that whtes versus blacks must pay n order to consume hgher levels of a gven neghborhood amenty. Imagne, for example, that black and whte households preferred to lve wth neghbors of the same race, other thngs equal. In ths stuaton, whle all households would pay the drect cost of resdng n hgh- 1 In the words of Massey and Denton (1993), a sgnfcant share of black Amerca s condemned to experence a socal envronment where poverty and joblessness are the norm, where educatonal falure prevals, and where socal and physcal deteroraton abound. Through prolonged exposure to such an envronment, black chances for socal and economc success are drastcally reduced (page 2). 2 The ntergeneratonal persstence of ncome nequalty across race s also an mportant theme n the work of Glenn Loury (see, for example, Loury (1977)), drawng attenton to the role of negatve externaltes n the human captal accumulaton process for blacks, some of whch operate at the neghborhood level. 3 For example, 15 percent of black adults compared to 33 percent of whte adults had attaned a 4-year college degree n U.S. metropoltan areas n Of the 44 tracts, 33 are located n one of four metropoltan areas: Baltmore-Washngton, Detrot, Los Angeles, and Atlanta. Only 142 tracts are at least 40 percent black and at least 40 percent college-educated. 5 Note that the mplct prce wedge descrbed here would arse under any of the followng forms of segregatng preferences: () f whtes and blacks each preferred neghbors of the same race () f whtes and blacks both preferred black neghbors but blacks were wllng to pay for them or () f whtes and blacks both preferred whte neghbors but whtes were wllng to pay more for them. 1

3 amenty neghborhoods va hgher housng prces, the ncreased fracton of whtes n these neghborhoods would be welfare-enhancng for whtes and welfare-decreasng for blacks. In turn, as each household responded n a decentralzed way to ts own mplct prce when decdng where to lve, the resultng consumpton of neghborhood amentes by blacks would be lower than that of otherwse-dentcal whtes. 6 Ths dscusson prompts our man conjecture: gven the short supply of hgh-amenty, predomnantly black neghborhoods n most metropoltan areas, racal sortng whether drven by decentralzed preferences or dscrmnaton s lkely to exacerbate the gap between blacks and whtes n the consumpton of many neghborhood amentes. 7,8 Further, the resultng adverse effects of racal sortng for blacks may dmnsh as the proporton of (especally hgh-ses) blacks n the metropoltan populaton grows larger and hgh-amenty black neghborhoods form, gven evdence (see Bayer, Fang, and McMllan (2005)) that the avalablty of mxed- and hgh-ses black neghborhoods s ncreasng n the proporton of hghly educated blacks n the metropoltan populaton. The central task of the current paper s to shed lght on our conjecture emprcally. To do so, one would deally lke to compare observed racal dfferences n the consumpton of neghborhood amentes wth those arsng n a world n whch households chose neghborhoods wthout regard for race. To nvestgate the role played by the proporton of hghly educated blacks, n turn one would deally lke to examne the mpact of ncreasng the proporton of blacks n the populaton on the consumpton effects of racal sortng, whle holdng the strength of preferences for neghborhood race constant. The prmary analyss presented n ths paper s desgned to mplement these deal thought experments n an ntutve way. Specfcally, usng restrcted-access Census data that precsely match nearly a quarter of a mllon households to ther neghborhoods n the San Francsco Bay Area, we estmate a flexble equlbrum model of resdental sortng and use t to conduct counterfactual smulatons that correspond drectly to these thought experments. 9 At ts heart, 6 As we dscuss n more detal below, dscrmnatory practces that ncrease the mplct prce that blacks versus whtes pay for housng n predomnantly whte neghborhoods clearly have the same mplcatons regardng the consumpton of neghborhood amentes by blacks versus whtes. The goal of ths paper s the measure the total mpact of racal sortng not to dstngush between these alternatve explanatons. 7 A gap between blacks and whtes n the consumpton of neghborhood amentes would arse even n the absence of racal sortng because of the substantal underlyng dfferences between blacks and whtes n socoeconomc characterstcs (e.g., ncome, educaton) that contrbute to resdental sortng. 8 Whle not generally explctly lnked to the sze of the black populaton or the avalablty of hgh-ses black neghborhoods, the lterature examnng the spatal msmatch hypothess, frst proposed by Kan (1968), has spawned nnumerable studes that suggest that resdental segregaton can exacerbate exstng nequaltes n employment access and outcomes. See Ihlanfeldt and Sjoqust (2000) for a recent survey. 9 Ths model s presented fully n Bayer, McMllan, and Rueben (2005). 2

4 our prmary estmaton approach reles on the standard economc noton of revealed preference: by examnng how locaton decsons vary on average wth household characterstcs (such as ncome, educaton and race) gven the set of neghborhoods avalable n the market, we nfer how the demand for housng and neghborhood attrbutes vares wth these household characterstcs. In estmatng the model, we are also careful to address an mportant endogenety problem that arses due to the correlaton of neghborhood socodemographc characterstcs wth unobserved aspects of housng and neghborhood qualty (a correlaton that s nduced by resdental sortng), mplementng a boundary fxed effects strategy closely related to that of Black (1999). The resultng preference estmates are reasonable n magntude across a wde set of housng and neghborhood attrbutes, provdng evdence of strong nteractons n the utlty functon between ndvdual and neghborhood socodemographc characterstcs, consstent wth stratfcaton along both racal and socoeconomc dmensons n equlbrum. Usng the estmated household preferences along wth our equlbrum model, we then carry out two complementary smulatons that provde evdence on our conjecture. In the frst, we compare the actual state of the world to one n whch race s elmnated as a factor n each household s resdental locaton decson. 10,11 Elmnatng racal sortng whether drven by preferences or dscrmnaton leads to a substantal decrease n racal segregaton across all socoeconomc levels n the new equlbrum, although some segregaton perssts due to the szeable average dfferences remanng between blacks and whtes n educaton, ncome, and wealth. At the same tme, average black-whte dfferences n the consumpton of many neghborhood amentes are also substantally reduced. Specfcally, the results mply that elmnatng neghborhood race from the locaton decson cuts the black-whte gap n neghborhood school qualty and crme by more than half and the gap n average neghborhood ncome and educaton by nearly ths amount. Ths ndcates that racal sortng s as mportant as the underlyng socoeconomc dfferences between whtes and blacks n drvng dfferences n the consumpton of neghborhood amentes. 10 In lght of the potental for racal dscrmnaton n the housng market, t s mportant to pont out that the preference parameters estmated n our analyss combne the mpact of preferences and dscrmnaton. That s, dscrmnatory practces that ncrease the mplct prce that blacks versus whtes pay for housng n predomnantly whte neghborhoods wll generally result n the estmaton of stronger preferences among blacks for predomnantly black neghborhoods. In our frst smulaton, settng the preference parameters n the model assocated wth neghborhood race to zero corresponds to elmnatng both decentralzed racal preferences and any centralzed dscrmnatory practces that exst n the current state of the world. 11 Mechancally, ths nvolves calculatng a new housng market equlbrum that allows households to resort and housng prces to adjust, havng frst set all of the utlty functon parameters assocated wth neghborhood racal composton equal to zero. 3

5 In the second smulaton, we equalze (counterfactually) the proportons of blacks and whtes n the metropoltan area, thereby relevng the exstng bundlng constrant whle leavng all preference parameters at ther estmated values. Though ths smulaton also leaves the socoeconomc dstrbuton for both whtes and blacks unchanged, the new equlbrum s characterzed by a sharp ncrease n the avalablty of hghly-amenty, predomnantly-black neghborhoods. As a result, the observed whte-black gaps n the consumpton of neghborhood amentes declne by nearly the same amount as n our frst smulaton: the adverse effects of racal sortng for blacks n the Bay Area would be vrtually elmnated were blacks to consttute a larger proporton of the metropoltan area s populaton. Ths result makes clear that the small proporton of black households found n the typcal U.S. metropoltan area s central to racal sortng havng adverse effects on the consumpton of neghborhood amentes by blacks relatve to whtes. That the effect of racal sortng declnes wth the proporton of (hghly educated) blacks n the populaton gves rse to an mplcaton that s testable across metropoltan markets. In partcular, t mples that the adverse effects of segregaton on black outcomes (relatve to whtes) should declne as the proporton of hghly educated blacks ncrease. To provde complementary evdence on ths aspect of our man hypothess, we augment the prmary regressons reported n Cutler and Glaeser (1997, henceforth CG ) n order to examne how the effect of segregaton vares wth the proporton of hghly educated blacks n the metropoltan populaton. Ths analyss demonstrates that the substantal negatve effects of segregaton for blacks relatve to whtes shown n CG declne to zero as the fracton of college-educated blacks n metropoltan populaton reaches 3 to 6 percent (the average fracton n U.S. metro areas n 2000 was 1.7 percent), agan mplyng that the adverse effects of racal sortng are strongly lnked to the small number of hghly educated blacks n the populaton. These emprcal results draw attenton to an mportant consequence of racal sortng the dstorton affectng the neghborhood qualty choce 12 and they provde clear evdence of the sheer sze of ths dstorton. The substantal reductons n neghborhood qualty for blacks that we fnd are lkely to have a sgnfcant mpact on the nter-generatonal persstence of racal dfferences n educaton, ncome, and wealth. Further, our analyss provdes a new explanaton as to why the dstorton to neghborhood qualty choce arses n the frst place, due to a combnaton of a small numbers problem and racal sortng. 12 See Massey and Denton (1993) for a dscusson n the socology lterature of the losses experenced by both mddle-class and poor blacks as a result of the lmtaton of black resdental optons through segregaton (page 9). 4

6 Our analyss nforms a much larger body of research that examnes the mpact of segregaton on ndvdual outcomes. Most mportantly, t mples that segregaton measured at ether the neghborhood or metropoltan level does not provde a suffcent statstc for estmatng the mpact of racal sortng. In partcular, because racal sortng s drectly responsble for a szeable porton of the dfference n neghborhood amenty consumpton by blacks versus whtes, analyses of the mpact of neghborhood measures of segregaton on ndvdual outcomes that condton on these other neghborhood characterstcs may nadvertently attrbute too lttle of the black-whte dfferences n outcomes to racal sortng. 13 Moreover, our second smulaton makes clear that the adverse effect of racal sortng for blacks s not fully captured by an estmate of the mpact of metropoltan segregaton on ndvdual outcomes. In partcular, t shows planly that an ncrease n the proporton of blacks n the populaton of a metropoltan area can reduce the adverse effects of racal sortng for blacks whle smultaneously ncreasng the level of segregaton. The rest of the paper s organzed as follows: Secton 2 presents descrptve evdence from all metropoltan areas n the Unted States on neghborhood avalablty and segregaton usng 2000 Census data, helpng motvate our conjecture. Secton 3 outlnes the key feature of our detaled San Francsco Bay Area dataset, and Secton 4 provdes descrptve evdence related to neghborhood supply and sortng just usng Bay Area data. Sectons 5, 6 and 7 descrbe the man analytcal tool used n ths paper - an equlbrum model of resdental sortng - descrbng the model, ts estmaton, and the estmated parameters n turn. Secton 8 then uses the estmated model to conduct two counterfactual smulatons that shed lght on our conjecture. Secton 9 provdes complementary evdence based on augmented Cutler-Glaeser regressons and Secton 10 concludes. 2 PATTERNS OF RACIAL SORTING IN U.S. METROPOLITAN AREAS Our prmary analyss wll be based on detaled mcrodata drawn from the San Francsco Bay Area. In ths secton, we provde motvaton for that analyss by characterzng the supply of neghborhoods n all U.S. ctes. The prmary goal of ths ntal analyss s to demonstrate that the fundamental condtons motvatng our man conjecture exst n most U.S. metropoltan areas. In partcular, we show that () neghborhoods combnng hgh-fractons of both college-educated and black ndvduals are n short supply n almost every metropoltan area n the Unted States and () that faced wth the resultng trade-off between black versus other college-educated neghbors, college-educated blacks choose a very dverse set of neghborhoods n each metropoltan area. 13 See, for example, Kan (1968), Ihlanfeldt (1992), Ihlanfeldt and Sjoqust (1990), O Regan and Qugley (1998), Ross (1998), Wenberg (2000, 2004), and Ross and Zenou (2004), among many others. 5

7 Ths analyss also serves to hghlght the fact that the racal composton and set of avalable neghborhoods n the San Francsco Bay Area are n fact comparable to the average patterns for U.S. metropoltan areas as a whole. Our approach s straghtforward. Usng publcly avalable Census Tract Summary Fles (SF3) from the 2000 Census, we characterze the dstrbuton of race and neghborhood qualty for all neghborhoods n U.S. metropoltan areas (MSAs). 14 We also plot the dstrbuton of avalable neghborhoods n ndvdual MSAs, drawng attenton to mportant patterns n terms of neghborhood avalablty. In ths porton of the analyss, a neghborhood corresponds to a Census tract, whch typcally contans 3,000 to 5,000 ndvduals and we summarze neghborhood qualty n a sngle dmenson - the fracton of resdents who are college-educated. (Usng far rcher data for the San Francsco Bay Area, we consder a much wde set of neghborhood attrbutes below.) In terms of racal composton, we focus on non-hspanc black and non-hspanc whte ndvduals 25 years and older resdng n U.S. metropoltan areas. Non-Hspanc blacks and whtes respectvely consttute 11.1 and 69.5 percent of the U.S. populaton 25 years and older resdng n metropoltan areas. Among blacks, 15.4 percent have a four-year college degree, whle the comparable number for whtes s 32.5 percent. We begn by showng that, whle neghborhoods combnng hgh fractons of both collegeeducated and whte ndvduals are abundant n all metropoltan areas, neghborhoods that combne hgh fractons of both college-educated and black ndvduals are n extremely short supply. To that end, Table 1 documents the number of tracts n the U.S. by the percentage of ndvduals wth a college degree and the percentage of ndvduals who are black or whte respectvely. Panel A descrbes the number of tracts n whch more than 0, 20, 40 and 60 percent of ndvduals 25 years and older are at least college-educated, respectvely. Panel B then reports the number of tracts n each of the categores lsted n the column headngs that contan a mnmum fracton of blacks equal to 20, 40, 60, and 80 percent, respectvely. As the correspondng numbers show, a much smaller fracton of the tracts wth a hgh fracton black also have a hgh fracton of ndvduals wth a college degree. For example, whle 22.6 percent (row 1, column 3) of all tracts are at least 40 percent college-educated, only 2.5 percent (row 3, column 3) of tracts that are at least 40 percent black are at least 40 percent college-educated, and only 1.1 percent (row 4, column 3) of tracts that are at least 60 percent black are at least 40 percent college-educated. Panel C of Table 1 presents analogous numbers for whtes. They show a 6

8 markedly dfferent pattern of neghborhood choces for whtes, wth a far greater fracton of neghborhoods wth at least 40, 60, and 80 percent whtes meetng the educaton crtera lsted n the column headngs. In addton to beng n short supply overall, neghborhoods combnng hgh fractons of both college-educated and black ndvduals are concentrated n only a handful of metropoltan areas, most notably Baltmore-Washngton DC, ndcatng that the supply of such neghborhoods n most metropoltan areas s even more lmted. 15 The absence of these neghborhoods means that neghborhood race and many other neghborhood characterstcs are explctly lnked n the set of resdental optons avalable to most households: n order to choose neghborhoods wth more college-educated neghbors, households must typcally lve wth a greater fracton of whtes. It s the explct bundlng of neghborhood race and other neghborhood amentes n the absence of hgh-amenty black neghborhoods that motvates our man hypothess. To llustrate ths potental trade-off, Fgure 1 shows scatterplots of avalable neghborhoods n three metropoltan areas: Boston, Dallas, San Francsco and St. Lous. In the scatterplots, a crcle represents a Census tract and ts coordnates represent the fracton of college-educated ndvduals (vertcal axs) and the fracton of blacks (horzontal axs) n the tract. The dameter of the crcle s proportonal to the number of college educated blacks n the tract; thus the largest crcles correspond to the tracts where hghly educated blacks are most lkely to lve. The scatterplots demonstrate the short supply of neghborhoods that combne hgh fractons of both hghly educated and black ndvduals, neghborhoods that would have appeared n the north-east corner of each plot, had they exsted. Fgure 1 also demonstrates that, facng ths constraned choce set, college-educated blacks choose to lve n a dverse set of neghborhoods: whle a szeable fracton of college-educated blacks n each of these MSAs choose neghborhoods wth few black and many college-educated neghbors (neghborhoods n the north-western corner of the plots), another szeable fracton choose neghborhoods wth many black and few collegeeducated neghbors (neghborhoods n the south-eastern corner of the plots). To show that the patterns shown n Fgure 1 are representatve of those for U.S. metropoltan areas as a whole, Panel A of Table 2 summarzes the characterstcs of neghborhoods n whch 14 In ths secton, we defne metropoltan areas as ether () free-standng Metropoltan Statstcal Areas (MSAs) or () Consoldated Metropoltan Statstcal Areas (CMSAs) consstng of two or more economcally and socally lnked metropoltan areas - Prmary Metropoltan Statstcal Areas (PMSAs). 15 Of the 44 tracts that are at least 60 percent black and 40 percent college-educated, for example 14 are n Baltmore-Washngton DC, 8 n Detrot, 6 n Los Angeles, and 5 n Atlanta. Of the 142 tracts (see row 3, column 3 of Table 2) that are at least 40 percent black and 40 percent college-educated, almost two-thrds are n the MSAs lsted above along wth Chcago and New York. See Bayer, Fang, and McMllan (2005) for more detals. 7

9 college-educated blacks resde n all U.S. MSAs. We frst rank college-educated blacks n each MSA by the fracton of blacks n ther Census tract and assgn ndvduals to ther correspondng quntle of ths dstrbuton. Ths corresponds to drawng four vertcal lnes n the scatterplot for each metropoltan area such that an equal number of college-educated blacks fall nto each of the resultng fve regons. Panel A of Table 2 then summarzes the neghborhood characterstcs correspondng to these quntles, averaged over all U.S. metropoltan areas. The table shows a clear trade-off for college-educated blacks between the fracton of ther neghbors who are black and the fracton who are hghly educated: the average fracton of hghly educated neghbors falls from 38.0 percent for those college-educated blacks lvng wth the smallest fracton of black neghbors to 13.8 percent for those lvng wth the largest fracton. Panel B of Table 2 reports analogous numbers for college-educated whtes. Comparson of Panels A and B reveals that the 40 percent of college-educated blacks n each metropoltan area who lve n the tracts wth the smallest fracton of other blacks have roughly the same fracton of collegeeducated neghbors as college-educated whtes do on average; however, college-educated blacks lvng wth the greatest fracton of other blacks have only about one-thrd of the fracton of hghly educated neghbors. That such a hgh fracton of college-educated blacks n U.S. metropoltan areas n Table 2 choose segregated neghborhoods wth relatvely low average educaton attanment s consstent wth two aspects our man conjecture. Frst, t suggests that, whether due to preferences or dscrmnaton, race remans an mportant factor n the locaton decsons of a large number of college-educated blacks. Ths helps to cast doubt on an obvous potental explanaton for the absence of neghborhoods combnng hgh fractons of both college-educated and black ndvduals namely, that college-educated blacks smply chose college-educated neghborhoods wthout regard for the racal composton. Second, the especally low levels of average neghborhood educatonal attanment for those college-educated blacks lvng n the most segregated neghborhoods suggests that racal sortng may ndeed have a substantal mpact on the consumpton of neghborhood amentes by blacks. It s mportant to recognze, however, that the evdence presented n Table 2 s far from conclusve n ths regard. Other explanatons for ths pattern related to heterogenety n other mportant ndvdual attrbutes (e.g., ncome and wealth) or n neghborhood amentes other than average educatonal attanment mght explan these observed patterns. It s precsely these alternatve potental explanaton that our prmary analyss, whch condtons on a wde set of ndvdual and neghborhood attrbutes, s desgned to address. Fnally, we motvate the dea that the short supply of hgh-amenty black neghborhoods may be systematcally relaxed as the number of college-educated blacks n a metropoltan areas 8

10 ncreases wth a combnaton of regresson analyss and scatterplots for a dfferent set of U.S. ctes. 16,17 In partcular, Fgure 2 depcts analogous scatterplots to those presented n Fgure 1 for Atlanta, Chcago, Detrot and Washngton DC MSAs that contan a much more szeable number of college-educated blacks than those MSAs shown n Fgure 1. As Fgure 2 clearly shows, the supply of neghborhoods combnng relatvely hgh fractons of both black and hghly educated ndvduals s substantally greater n these MSAs. As a result, we would expect the adverse effects of racal sortng for the consumpton of neghborhood amentes by blacks versus whtes to be less severe n these MSAs. We provde evdence on ths aspect of our man conjecture n the second smulaton and wth addtonal across-metropoltan analyss, whch reveal that the adverse effects of racal sortng for black neghborhood amenty consumpton are ndeed drectly related to the fact that blacks (college-educated blacks n partcular) represent such a small fracton of the populaton of the San Francsco Bay Area and, more generally, the U.S. metropoltan populaton. 3 DATA FOR PRIMARY ANALYSIS Gven ths broad characterzaton of racal sortng n MSAs throughout the U.S., we now turn to the much more detaled dataset for our prmary analyss. The partcular dataset that we construct s based prmarly on restrcted Census mcrodata for the San Francsco Bay Area for These restrcted Census data provde the same detaled ndvdual, household, and housng varables found n the publc-use verson of the Census, but also nclude nformaton on the locaton of ndvdual resdences and workplaces at a very dsaggregate level. In partcular, whle publc-use data specfy the PUMA (a Census regon wth at least 100,000 ndvduals) n whch a household lves, the restrcted data specfy the Census block (a Census regon wth an average of 100 ndvduals), thereby dentfyng an ndvdual s neghborhood far more precsely than has been prevously possble wth such a large data set. These data allow us to estmate a model of resdental sortng on the part of ndvdual households, whle controllng carefully for a wde set 16 Indeed, regressons of the number or fracton of tracts n an MSA that are at least 40 percent collegeeducated and 40 percent black on metropoltan socoeconomc characterstcs reveal a strong postve relatonshp wth the fracton of college-educated blacks n the MSA. The number of such tracts s also, not surprsngly, ncreasng n the populaton of the MSA and a smlar pattern holds for any combnaton of educaton and race crteron that count the number of tracts n the upper-rght porton of the scatterplots. 17 We also examned a seres of quantle regressons desgned to ft the 90th percentle of the relatonshp between neghborhood educaton and race shown n the scatterplots for college-educated blacks -- that s, to approxmate the mplct neghborhood avalablty constrant defned by the absence of neghborhoods n the upper-rght porton of these scatterplots. These regressons demonstrate that the neghborhood avalablty constrant shfts sgnfcantly outward as the fracton of college-educated blacks n the MSA populaton s ncreased. Ths result holds no matter whether the fracton black or fracton of collegeeducated households n the MSA s held constant. 9

11 of household characterstcs and makng use of reasonable varaton n the data to dentfy the mpact of a wde varety of factors (ncludng neghborhood racal composton) on each ndvdual s locaton decson. In assemblng our Bay Area dataset, we use data from sx contguous countes: Alameda, Contra Costa, Marn, San Mateo, San Francsco, and Santa Clara. The resultng study area s reasonably self-contaned and szeable along a number of dmensons, ncludng over 1,100 Census tracts, and almost 39,500 Census blocks, the smallest unt of aggregaton n the data. Our fnal sample conssts of just over 242,000 households. We also note that, among the largest metropoltan areas n the US, the fracton of black and whte households n the San Francsco Bay Area (68.6 percent whte, 7.6 percent black) most closely matches that of the country as a whole (69.5 percent whte, 11.1 percent black). The Census provdes a wealth of data on the ndvduals n the sample race, age, educatonal attanment, ncome from varous sources, household sze and structure, occupaton, and employment locaton. 18 In addton, t provdes a varety of housng characterstcs: whether the unt s owned or rented, the correspondng rent or owner-reported value, 19 number of rooms, number of bedrooms, type of structure, and the age of the buldng. We use these housng characterstcs drectly and n constructng neghborhood characterstcs, characterzng stock of housng n the neghborhood surroundng each house, as well as neghborhood racal, educaton and ncome dstrbutons based on the households wthn the same Census block group, a Census regon contanng approxmately 500 housng unts. We merge addtonal data descrbng local condtons wth each house record, constructng varables related to crme rates, land use, local schools, topography, and urban densty. 20 The lst of the prncpal housng and neghborhood varables used n the analyss, along wth means and standard devatons, s gven n the frst two columns of Table Throughout our analyss, we treat the household as the decson-makng agent and characterze each household s race as the race of the householder, assgnng households to one of four mutually exclusve categores of race/ethncty: Hspanc, non-hspanc Asan, non-hspanc black, and non-hspanc whte. To mantan a streamlned exposton of results, we focus on black and whte households, although t s mportant to pont out that our prmary analyss also controls separately for Asan and Hspanc households. 19 As descrbed n the Data Appendx, we construct a sngle prce vector for all houses, whether rented or owned. Because the mpled relatonshp between house values and current rents depends on expectatons about the growth rate of future rents n the market, we estmate a seres of hedonc prce regressons for each of over 40 sub-regons of the Bay Area housng market. These regressons return an estmate of the rato of house values to rents for each of these sub-regons. 20 For each of these measures, a detaled descrpton of the process by whch the orgnal data were assgned to each house s provded n a Data Appendx. 10

12 4 RACIAL SORTING AND NEIGHBORHOOD AMENITIES IN THE BAY AREA Before turnng to our model of resdental sortng, we frst descrbe the patterns of racal sortng and consumpton of neghborhood amentes n the San Francsco Bay Area. The man goal of ths secton s to llustrate that the pattern demonstrated for average neghborhood educaton for all U.S. metropoltan areas extends to a wder set of neghborhood amentes. Ths analyss also llustrates how housng prces vary wth neghborhood amentes and racal composton. Segregaton Patterns. We begn by descrbng the pattern of racal segregaton n the Bay Area. We do so by examnng the average compostons of the neghborhoods (Census block groups n ths case) n whch households n a partcular category of race and ncome resde. 21 These measures are reported n Panel A of Table 4. The measures n the frst row show neghborhood compostons averaged over all of the households n the Bay Area. The remanng rows report neghborhood compostons averaged over the set of households descrbed n the row headng. The second row, for example, ndcates that black households lve n neghborhoods n whch an average of 20.9 percent of the households are both black and n the lowest ncome quartle, 9.0 percent are black and n the second ncome quartle, etc. Average neghborhood compostons are reported for blacks and whtes as a whole and for blacks and whtes n the lowest and hghest ncome quartle, respectvely. Panel B of Table 4 re-summarzes these average neghborhood composton measures reported n Panel A n a way that s more meanngful for dscussng segregaton, reportng the average neghborhood composton for a partcular type of household relatve to the average for the Bay Area as a whole. For example, the frst entry of Panel B s calculated as the average exposure of black households to blacks n the lowest ncome quartle (20.9 percent), dvded by the average exposure of all households n the Bay Area to blacks n the lowest ncome quartle (3.4 percent). Ths mples that a black household n the Bay Area s exposed on average to 6.1 tmes the fracton of blacks n the lowest ncome quartle that the average household n the Bay Area s exposed to. Panel B reveals a clear pattern of racal segregaton for Bay Area blacks that cuts across all ncome categores. Whle blacks n the lowest ncome quartle are exposed to 6.2 tmes the fracton of blacks relatve to the average household n the metropoltan area, the comparable fgure for blacks n the hghest ncome quartle s 3.2, whch ndcates a substantal amount of 21 We use ncome throughout the remander of the paper as a proxy for socoeconomc status n descrbng the results or our analyss. Results based on educaton or ncome condtonal on educaton are completely analogous. 11

13 segregaton even for hgh-ncome blacks. Moreover, whle hgh-ncome blacks are especally hghly exposed to blacks n the hghest ncome quartle (4.4 tmes the Bay Area average), ther exposure to blacks n the lowest ncome quartle also remans hgh at 2.9 tmes the Bay Area average. Thus race contnues to play a large role n the resdental choce process even for hghncome blacks. Racal Sortng and the Consumpton of Housng and Neghborhood Amentes. To explore ths possblty drectly, Table 5 descrbes the dstrbuton of neghborhoods n whch blacks and whtes n the hghest quartle of the ncome dstrbuton resde, respectvely. 22 In each case, as n Table 2, neghborhoods are frst ranked by the fracton of a household s neghbors that are of the same race, and quntles of the dstrbuton are then reported. Panel A shows the dstrbuton of neghborhoods n whch blacks n the hghest ncome quartle resde. We order these households nto fve quntles based on percentage black n the neghborhood. Thus the frst column provdes average housng and neghborhood characterstcs for the 20 percent of hgh-ncome blacks who lve n neghborhoods wth the lowest fracton of black households, neghborhoods n whch less than 4 percent of the populaton s black. As one reads across the columns, the neghborhoods have a hgher fracton of black households by constructon; the fnal column ndcates that fully 20 percent of blacks n the hghest ncome quartle resde n neghborhoods n whch over 54 percent of the populaton s black. As n Table 2, what emerges from Panel A of Table 5 s a clear pcture of the wde range of neghborhoods n whch hgh-ncome blacks resde. Comparng the neghborhoods at ether end of the spectrum, the levels of school qualty, publc safety, average neghborhood ncome, and fracton college-educated are each 1.5 to 2 standard devatons greater n the neghborhoods wth the least versus the greatest fracton of black households. Panel B of Table 5 shows the same dstrbuton for whtes n the hghest ncome quartle, frst rankng neghborhoods by percent whte and agan reportng the quntles of ths dstrbuton. For whtes, ncreases n the fracton of whte neghbors are accompaned by ncreases rather than decreases n the consumpton of housng and neghborhood amentes. Thus, whle ncreased consumpton of neghborhood amentes such as school qualty, publc safety, and neghborhood educaton and ncome comes at the expense of ncreased housng prces for households of each race, these ncreases are accompaned by sharp decreases n the fracton of households of the same race for blacks and ncreases n the fracton of households of the same race for whtes. 22 An analogous table for blacks and whtes n the lowest ncome quartle s ncluded as Appendx Table 1. Ths table generally shows a smlar, although muted, pattern as Table 5. 12

14 Whle hghly suggestve, consumpton patterns lke those presented n Table 5 do not provde conclusve evdence concernng the mpact of that racal sortng on the consumpton of neghborhood amentes. Frst, the wde varaton n neghborhood amenty consumpton among hgh-ncome blacks mght reflect heterogenety n other mportant ndvdual attrbutes (e.g., ncome and wealth) or n neghborhood amentes other than those shown n the table. Second, as Panel A reveals, those hgh-ncome blacks that lve n the lowest amenty neghborhoods spend substantally less on housng. Thus, another potental explanaton for the lower average consumpton of neghborhood amentes by blacks relatve to whtes s that blacks have a lower average wllngness-to-pay for these amentes relatve to whtes. The prmary emprcal analyss that we now present solates the mpact of racal sortng from these alternatve explanatons by allowng each of these channels to contrbute to observed resdental locaton decsons. Specfcally, by condtonng on a wde set of ndvdual and neghborhood attrbutes, ths analyss explctly condtons out any of the varaton n neghborhood amenty consumpton that can be explaned by heterogenety n these attrbutes. Second, by allowng wllngness-to-pay for each housng and neghborhood amenty to vary completely flexbly by race, our analyss explctly allows for the possblty that racal dfferences n demand for amentes mght explan the observed pattern of neghborhood amenty consumpton. Our subsequent emprcal analyss does mply that each of these alternatve channels do play a role n explanng consumpton patterns. Even after controllng for these alternatves n a very flexble way, however, our analyss leads to the clear concluson that sortng on the bass of neghborhood racal composton whether due to preferences or dscrmnaton drves a substantal fracton of observed racal dfferences n neghborhood amenty consumpton. 5 A MODEL OF RESIDENTIAL SORTING To measure the mpact of racal sortng on the consumpton of neghborhood amentes, we now turn to a model of the resdental locaton decson of households n the Bay Area. In developng such a model, our goal s to provde the smplest analytcal tool that can account for () heterogenety n both household attrbutes and the attrbutes of houses/neghborhoods and () the endogenous determnaton of housng prces and neghborhood demographc compostons. To ths end, we adopt the equlbrum model of an urban housng market developed n Bayer, McMllan, and Rueben (2004b). Ths equlbrum model conssts of two key elements: the household resdental locaton decson problem and a market-clearng condton. Whle mantanng a smple structure, the model allows households to have heterogeneous preferences defned over housng and neghborhood attrbutes n a very flexble way; t also allows for 13

15 housng prces and neghborhood demographc compostons to be determned n equlbrum. In estmatng the model, we are careful to account for the correlaton that naturally arses between unobserved housng and neghborhood attrbutes and both housng prces and neghborhood composton. Havng estmated the model, we then use t to conduct two equlbrum counterfactual smulatons that provde drect evdence on our man conjecture. 23 The Resdental Locaton Decson. We model the resdental locaton decson of each household as a dscrete choce of a sngle resdence from a set of houses avalable n the market. The utlty functon specfcaton s based on the random utlty model developed n McFadden (1973, 1978) and the specfcaton of Berry, Levnsohn, and Pakes (1995), whch ncludes chocespecfc unobservable characterstcs. 24 Let X h represent the observable characterstcs of housng choce h ncludng characterstcs of the house tself (e.g., sze, age, and type), ts tenure status (rented vs. owned), and the characterstcs of ts neghborhood (e.g., school, crme, and topography). We use Z to represent the average socodemographc characterstcs of the correspondng neghborhood, wrtng t separately from the other housng and neghborhood attrbutes to make explct the fact that these characterstcs are determned n equlbrum. 25 Let p h denote the prce of housng choce h and let d h denote the dstance from resdence h to the prmary work locaton of household. Each household chooses ts resdence h to maxmze ts ndrect utlty functon V h : (1) Max ( h) V h = α X + α Z α p α d + ξ + ε. X h Z h p h d h h h The error structure of household ndrect utlty s dvded nto a correlated component assocated wth each house valued the same by all households, ξ h, and an ndvdual-specfc term, ε h. A 23 A long lne of theoretcal studes, ncludng mportant papers by Epple, Flmon and Romer (EFR) (1984, 1993), Benabou (1993, 1996), Anas and Km (1995), Anas (2002), Fernandez and Rogerson (1996, 1998), and Nechyba (1999, 2000) have developed and used models of sortng to analyze the way that nterdependent ndvdual decsons n the housng market aggregate up to determne the equlbrum structure of a metropoltan area. In recent years, a new lne of emprcal research has sought to take these models to the data. Epple and Seg (1999) develop an estmator for the equlbrum sortng model of EFR, provdng the frst unfed treatment of theory and emprcs n the lterature. In the same ven, Seg et al. (2004) use ths approach to explore the general equlbrum mpacts of ar qualty mprovements n the Los Angeles Basn. 24 Dscrete choce applcatons n the urban economcs lterature nclude Anas (1982), Qugley (1985), Gabrel and Rosenthal (1989), Nechyba and Strauss (1998), and Bajar and Kahn (2001). Only the latter paper ncludes choce-specfc unobservables. Brock and Durlauf (2001) study a general class of dscrete choce models wth socal nteractons that do not nclude choce-specfc unobservables. 25 Ths component of the utlty functon allows for endogenous sortng on the bass of race, as n Schellng (1969, 1971), as well as on the bass of other characterstcs such as ncome and educaton. 14

16 useful nterpretaton of ξ h s that t captures unobserved housng qualty, ncludng any unobserved qualty assocated wth the surroundng neghborhood. 26 Each household s valuaton of choce characterstcs s allowed to vary wth ts own characterstcs, Z, ncludng educaton, ncome, race, employment status, and household composton. Specfcally, each parameter assocated wth housng and neghborhood characterstcs and prce, α j, for j {X, Z, d, p}, vares wth a household s own characterstcs accordng to: (2) α j = α 0 j + α kj Z k, K k = 1 wth equaton (2) descrbng the parameters of household s preference for choce characterstc j. Characterzng the Housng Market. As wth all models n ths lterature, the exstence of a sortng equlbrum s much easer to establsh f the ndvdual resdental locaton decson problem s smoothed n some way. To ths end, we assume that the housng market can be fully characterzed by a set of housng types that s a subset of the full set of avalable houses, lettng the supply of housng of type h be gven by S h. 27 Gven the household s problem descrbed n equatons (1)-(2), household chooses housng type h f the utlty that t receves from ths choce exceeds the utlty that t receves from all other possble house choces - that s, when h k h h k k (3) V > V W + ε > W + ε ε ε > W W k h h where W h ncludes all of the non-dosyncratc components of the utlty functon V h. As the nequaltes n (3) mply, the probablty that a household chooses any partcular choce depends n general on the characterstcs of the full set of possble house types. Thus the probablty P h that household chooses housng type h can be wrtten as a functon of the full vectors of house/neghborhood characterstcs (both observed and unobserved) and prces {X, p, ξ}: h (4) P = f ( Z, X,p, ξ) h k k h 26 We employ an ndrect utlty functon that s lnear n housng prces. Alternatve specfcatons of the ndrect utlty functon could certanly be estmated, as the lnear form s not essental to the model. 27 We also assume that each household observed n the sample represents a contnuum of households wth the same observable characterstcs, wth the dstrbuton of dosyncratc tastes ε h mappng nto a set of choce probabltes that characterze the dstrbuton of housng choces that would result for the contnuum of households wth a gven set of observed characterstcs. For expostonal ease and wthout loss of generalty, we assume that the measure of ths contnuum s one. 15

17 as well as the household s own characterstcs Z. Aggregatng the probabltes n equaton (4) over all observed households yelds the predcted demand for each housng type h, D h : (5) D h P h. = In order for the housng market to clear, the demand for houses of type h must equal the supply of such houses and so: (6) Dh = S h, h Ph = S h h. Gven the decentralzed nature of the housng market, prces are assumed to adjust n order to clear the market. The mplcatons of the market clearng condton defned n equaton (6) for prces are very standard, wth excess demand for a housng type causng prce to be bd up and excess supply leadng prces to fall. Gven the ndrect utlty functon defned n (1) and a fxed set of housng and neghborhood attrbutes, Bayer, McMllan, and Rueben (2004b) show that a unque set of prces (up to scale) clears the market. Gven that some neghborhood attrbutes are endogenously determned by the sortng process tself, we defne a sortng equlbrum to be a set of resdental locaton decsons and a vector of housng prces such that the housng market clears and each household makes ts optmal locaton decson gven the locaton decsons of all other households. In equlbrum, the vector of neghborhood socodemographc characterstcs along wth the correspondng vector of market clearng prces must gve rse to choce probabltes that aggregate back up to the same vector of neghborhood socodemographcs. 28 Whether ths model gves rse to multple equlbra depends on the dstrbutons of preferences and avalable housng choces, as well as the utlty parameters. In general, t s mpossble to establsh that the equlbrum s unque a pror. Fortunately, estmaton of the model does not requre the computaton of an equlbrum nor unqueness more generally, as we descrbe n the next secton. 28 Bayer, McMllan, and Rueben (2004b) establsh the exstence of a sortng equlbrum as long as () the ndrect utlty functon shown n equaton (1) s decreasng n housng prces for all households; () ndrect utlty s a contnuous functon of neghborhood socodemographc characterstcs; and () ε s drawn from a contnuous densty functon. 16

18 6 ESTIMATION Estmaton of the model follows a two-step procedure related to that developed n Berry, Levnsohn, and Pakes (1995). A rgorous presentaton of the estmaton procedure s ncluded n a techncal appendx, ncludng a dscusson of methods for smplfyng the computaton and a descrpton of the asymptotc propertes of the estmator. In ths secton, we outlne the estmaton procedure, focusng on the dentfcaton of the model. It s helpful to frst ntroduce some notaton. In partcular, we rewrte the ndrect utlty functon as: (7) Vh where h h = δ + λ + ε (8) δ h = α 0 X X h + α Z h α 0 p ph + ξ h and h 0Z K K K (9) λ h = kx Z k X h Z kz k Z h kpz α + α α k ph. k = 1 k = 1 k = 1 In equaton (8), δ h captures the porton of utlty provded by housng type h that s common to all households, and n (9), k ndexes household characterstcs. When the household characterstcs ncluded n the model are constructed to have mean zero, δ h s the mean ndrect utlty provded by housng choce h. The unobservable component of δ h, ξ h, captures the porton of unobserved preferences for housng choce h that s correlated across households, whle ε h represents unobserved preferences over and above ths shared component. The frst step of the estmaton procedure s equvalent to a Maxmum Lkelhood estmator appled to the ndvdual locaton decsons takng prces and neghborhood socodemographc compostons as gven, 29 returnng estmates of the heterogeneous parameters n λ and mean ndrect utltes, δ h. Ths estmator s based smply on maxmzng the probablty that the model correctly matches each household observed n the sample wth ts chosen house type. In partcular, for any combnaton of the heterogeneous parameters n λ and mean ndrect utltes, 29 Formally, the valdty of ths frst stage procedure requres the assumpton that the observed locaton decsons are ndvdually optmal, gven the collectve choces made by other households and the vector of market-clearng prces and that households are suffcently small such that they do not nteract strategcally wth respect to partcular draws on ε. Ths ensures that no household s partcular dosyncratc preferences affect the equlbrum and the vector of dosyncratc preferences ε s uncorrelated wth the prces and neghborhood socodemographc characterstcs that arse n any equlbrum. For more dscusson, see the Techncal Appendx. 17