Journal of Urban Economics

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1 Journa of Urban Economics 67 (2010) Contents ists avaiabe at ScienceDirect Journa of Urban Economics Marriage an the city: Search frictions an sorting of singes Pieter A. Gautier a, *, Michae Svarer b, Coen N. Teuings c a Vrije Universiteit Amsteram, Dep. of Economics (2A-33), De Boeeaan 1105, 1081 HV Amsteram, The Netherans b Schoo of Economics an Management, Aarhus university, Barthoins Aé 10, DK-8000 Aarhus C, Denmark c Netherans Bureau for Economic Poicy anaysis, Van Stokweg 14, 2585 JR, The Hague, The Netherans artice info abstract Artice history: Receive 5 June 2009 Revise 29 August 2009 Avaiabe onine 13 September 2009 JEL Cassification: J1 R2 R3 This paper eveops an tests a moe where cities pay an important roe as marriage markets. The iea is simpe. Cities are ense areas where singes can meet more potentia partners than in rura areas. To enjoy those benefits, they are wiing to pay a premium in terms of higher housing prices. Once marrie, the benefits from meeting more potentia partners vanish an marrie coupes move out of the city. Attractive singes benefit most from a ense market an are therefore more ikey to move to the city. Those preictions are teste an confirme with a unique Danish ata set. Ó 2009 Esevier Inc. A rights reserve. Keywors: Search frictions Marriage market Composition of cities 1. Introuction * Corresponing author. E-mai aress: pgautier@feweb.vu.n (P.A. Gautier). Why o peope ive in cities? The iea we put forwar in this paper is that cities pay an important roe as marriage markets. Cities are ense areas where singes can meet more potentia marriage partners than in rura areas. To enjoy these benefits, they are wiing to pay a premium in terms of higher housing prices. Once marrie, the benefits from meeting more potentia partners isappear an consequenty, the countrysie becomes more attractive. This generates a fow of marrie coupes out of the city. We fin that the fraction of iniviuas iving in one of the 5 argest cities in Denmark at age 18 is 22%, at the ate of marriage this fraction has increase to 36% an after 5 years of continue marriage it bounces back to 23%. In orer to expain this pattern, we exten the marriage-market moe of Burett an Coes (1997) an istinguish between search markets that are more efficient (cities) an ess efficient (rura areas). One obvious impication of the moe is that singes are more ikey to move from rura areas to cities whie coupes are more ikey to make the reverse movement. This is in particuar reevant for the most attractive types because they are most choosy an therefore benefit most from a high contact rate. Consequenty, they are aso the ones that are most wiing to pay the higher house prices in the city. In a segmente equiibrium, a agents have a esire to sort in homogeneous segments an the joint existence of cities an rura areas offers them this opportunity. Our story can aso be rephrase as one of cubs that sort attractive types an raise high entrance fees, see Jacquet an Tan (2007). Since the opportunity cost of being singe are arger for the most attractive types, they are wiing to pay those high fees an a separating equiibrium wi resut irrespective of the contact technoogy. Finay, Eeckhout (2006) iscusses sorting on pay-off irreevant characteristics. We use canonica correations to create attractiveness inices which are a inear combination of eucation, income, father s eucation an father s income. We fin that (1) singes are more ikey to move from the countrysie to the city than coupes, (2) coupes have the argest probabiity to make the reverse movement an (3) attractive singes are more ikey to move to the city than ess attractive singes. We aso test the sensitivity of our resuts to ifferent efinitions of attractiveness an cities. Moreover, we take sub-sampes of (i) iniviuas oer than 25 to eiminate a potentia coege-effect an of (ii) iniviuas who never have kis to contro for the possibiity that chiren infuence the moving ecision. Our main resuts are robust to those excusions, athough our finings are ess precise in the reuce sampe for iniviuas without chiren. Finay, we are worrie that our resuts are riven by ife cyce motives. When peope get oer they enjoy cubs an bars ess an waking through nature more. To aress this issue, we consier iniviuas who ivorce in the country. If their ocation choice was riven by ife-cyce consierations we /$ - see front matter Ó 2009 Esevier Inc. A rights reserve. oi: /j.jue

2 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) expecte them to stay in the country whie accoring to the marriage-market story we expect them to move back to the city. We give evience that ivorcees ten to move back to the city. A number of papers are reate to ours. Mincer (1978) argues that marriage reuces mobiity because the cost are higher for famiies. He fins support for this pattern in US ata. Costa an Kahn (2000) argue that higher eucate coupes (power coupes) are overrepresente in cities. The iea is that the coocation probem (both have to ive cose to their job) is particuary severe for them. Their moe therefore preicts that higher eucate coupes are more ikey to move into the city an ess ikey to move out of the city. In terms of the atter preiction, our moe preicts exacty the opposite. They use cross-section ata from the U.S. Recenty, Compton an Poak (2007) took another ook at the issue. They argue that another expanation for the overrepresentation of power coupes in the arge cities is that a coege eucate iniviuas, marrie an unmarrie, are attracte to the amenities an high returns to eucation of the arge cities. As a resut of this, the formation of power coupes is more ikey to occur in arger than smaer metropoitan areas. In their expanation eucation is key whie in ours, the marriage market roe of cities is the riving force. Base on PSID ata, they anayze the ynamic patterns of migration, marriage, ivorce, an eucation in reation to city size an fin that power coupes are not more ikey to migrate to the argest cities in the U.S. than part-power coupes or power singes. Instea, the ocation trens are better expaine by the higher rate of power coupe formation in arger metropoitan areas. With the Danish ata we fin that the marriage market roe of cities is more important than the coocation of job opportunities. High skie singes move to the city but once they are marrie they are more ikey to move out of the city. Dah an Sorenson (2008) give evience that migration in Denmark is more riven by socia factors (ocation of famiy an friens) than by financia incentives. Stark (1988) an Smith an Thomas (1998) aso ook at the reation between marriage an mobiity. Stark argues that the abor an the marriage market interact because the ocation where peope search for jobs is often the same as where they search for a marriage partner. Smith an Thomas fin for Maaysia that migration by maes is mainy riven by abor market consierations whie for femaes, fertiity an famiy consierations are more important. We aso fin that femaes behave more ike the marriage-market moe than maes. Back et a. (2002) suggest that the reason a city ike San Francisco hosts a isproportiona high number of gays is ue the high housing cost of iving there. San Francisco is known as one of America s oveiest cities. Hence, ue to the high eman for housing in San Francisco, housing prices are high. Gay coupes face constraints that make having chiren more costy for them than for simiar heterosexua coupes. This frees resources for other goos such as housing in high-amenity ocations. Athough we o not expicity consier the gay mating market, our moe suggests an aternative expanation. Since the market for gays is reativey thin, they gain a ot by moving to a ense market ike cities. In aition, any area that happens to have a arge gay community wi attract more gays because the matching rate epens not ony on the contact rate but aso on the share of potentia mates an this is what pushes up house prices an creates nice amenities. Eun (2005) argues that young women outnumber young men in urban areas. The argument is that urban areas offer skie workers better abor markets. Assuming that there are more skie maes than femaes, this aone wou preict a surpus of maes. However, the presence of maes with high incomes may attract not ony skie femaes but aso unskie femaes, an thus a surpus of femaes in urban areas from the combination of better abor an marriage markets. Finay, custering an partner formation is stuie intensivey in bioogy. In many promiscuous species, femaes custer aroun the top maes. Seconary maes may however aso custer aroun the top maes for two reasons. Accoring to the hotshot moe of Beeher an Foster (1988), remaining isoate is ess attractive since then they wou meet even fewer femaes. Aternativey, Braburry (1981) argues that maes respon to femae s esire to compare. In the presence of search frictions, custering is necessary for comparison. Finay, Wagner (1997) gives evience that sociay monogamous species have simiar incentives to custer. 1 The paper is organize as foows. First, in Section 2 we present a simpe marriage market moe. In Section 3 we iscuss the ata. Section 4 presents the main estimation resuts. Section 5 carries out a number of robustness checks an Section 6 concues. 2. The moe The marriage market that we consier is in the spirit of Burett an Coes (1997). Our economy is mae up of two ocations, the countrysie an the city. A maes an femaes have ientica preferences but they iffer in their attractiveness as a marriage partner. The attractiveness istribution an preferences are the same for both sexes. We assume that a singes are ranomy istribute over the city an the country sie at the age that they enter the marriage market. We iscuss the marriage ecision probem from the femae point of view, the mae perspective is mutatis mutanis the same. Consier a singe femae who is ooking for a marriage partner. Given the ocation choices of a the other singes, an the excess cost of iving in the city, she chooses the ocation of resience that maximizes her expecte iscounte utiity. For reasons of tractabiity, we anayze the moe uner two ifferent extreme assumptions for the cost of mobiity. Either this cost is zero for singes an finite for coupes, or it is infinite for both. Both extremes aow us to focus on a particuar aspect of the moe, the sorting of iniviuas across ocations (for zero mobiity cost of singes) an the tightness of the correation between mae an femae attractiveness within a ocation (for infinite mobiity cost). Each woman searches for a husban who she wants to marry an who wants to marry her. After having foun a partner the coupe must ecie whether to stay at the current ocation or move. We treat the moving cost for coupes to be a ranom variabe which captures the iea that it epens on work ocation or the presence of chiren, etc. The size of this moving cost is reveae after marriage. Divorce is rue out, marriage is an absorbing state. We focus on the steay state where the yeary infow of singes is equa to the yeary outfow of marrie coupes an where the eath rate is. For simpicity, we assume that both partners of a coupe ie simutaneousy. To keep thinks simpe, we set the rate of time preference at zero. In orer to keep the moe tractabe we ignore abor market consierations. This is not because we beieve that empoyment motivate migration is unimportant but rather because we want to focus here on the marriage market roe of the city an there areay exists a arge iterature on abor markets, aggomeration an the urban wage premium. 2 In our empirica anaysis we o iscuss how we can istinguish between both stories. Let a be the attractiveness of a femae an a the attractiveness of mae, a an a 2½a ; a þ Š, where we assume a þ > a > 0. For simpicity we assume a to be constant over time. Coes an Frances- 1 Sociay monogamous species are characterize by the fact that both partners engage in parenta care. However, there is ot of evience that both maes an femaes sti pursue extra-pair copuations (EPS). This EPS, give accoring to Wagner simiar incentives to custer as the motivations escribe above. 2 See e.g. Rosentha an Strange (2004), Gautier an Teuings (2004, 2009), Combes et a. (2008) an Gemici (2008).

3 208 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) coni (2008) aow a to ecrease over time. Symmetry impies that the femae probem is ientica to the mae probem. Let 2f0; 1g be the ocation of resience of an iniviua or a coupe (0 = countrysie, 1 = city) an et c be the excess cost of iving in a city which we take as given but ater in Section 2.4 we enogenize c for a specia case of the moe. Utiity is non-transferabe between maes an femaes. It is convenient to iscuss the moe in reverse orer, starting from the ast stage of the ife cyce, the ocation choice of a marrie coupe, an then work back to the ocation choice of singes. Lifetime utiity of a marrie coupe at the optima ocation. A femae who is marrie with a mae who has attractiveness a an who ives in area enjoys ife time utiity u m ða; Þ ¼a c: where c is the excess cost of iving in a city (in stock terms). 3 Location choice of a marrie coupe. A coupe chooses the ocation of resience that maximizes their utiity. They trae off the cost of moving with the utiity gain that a change of ocation yies. Denote the cost of moving by c. We assume c to be a stricty positive ranom variabe. Coupes earn the vaue of c after marriage. A coupe that marries in the city, = 1, ecies to move to the countrysie, = 0, if its moving cost are ower than the excess cost of urban ife: u m ða; 1Þ < u m ða; 0Þc ) c > c: A coupe who marries in the countrysie never moves to the city because the cost of iving are higher there. The aitive separabiity of the utiity function in the attractiveness of the partner an the ocation specific cost makes that the preference of both husban an wife for iving at either ocation is the same. Hence, we can ignore any probem of intra-househo bargaining on ocation choice. In case of infinite mobiity cost, marrie coupes never move. Lifetime utiity of a singe an a marrie femae. Define the expecte utiity for a femae who is marrie in ocation to a mae with attractiveness a as 4 : E u m ða; Þ E ½max½u m ða; 1Þ; u m ða; 0ÞcŠŠ ¼ a ðc CÞ; C E max½c c; 0Š: C is the expecte cost saving of moving out of the city. C is equa to either zero if the moving cost excees the excess cost of iving in the city or it is equa to the ifference between the cost of iving in the city an the moving cost if the atter are ess than the former. Let f ðaþ be the mass of maes of attractiveness a who search for a partner in ocation, an m ðaþ the marriage set of a femae with attractiveness a. This set consists of a maes with attractiveness fag with whom she is wiing to marry an who are wiing to marry her. Hence: a 2 m ðaþ () a 2 m ðaþ: The ifetime utiity for a singe femae who searches for a partner in ocation is etermine by the foowing Beman equation: Z u s ða; Þ ¼k ½E u m ða; Þu s ða; ÞŠf ðaþa c m ðaþ Z ¼ k ½a ðc CÞu s ða; ÞŠf ðaþa c: ð2þ m ðaþ The eath rate, > 0, pays the same roe as the iscount factor in stanar search moes. k is the arriva rate of marriage caniates ð1þ per unit of the stock of searching caniates. We assume that the arriva rate is higher in the city than in the country, 0 < k 0 < k 1, either because of a higher ensity or because the market is bigger. The first right-han term of the first ine is the wefare gain of marriage an moving to the optima ocation. The secon term, c, is the excess cost of iving in the city that a singe pays uring the perio she searches for a partner. Note that the assumption a > 0 impies that a woman who ives in the countrysie prefers being marrie to the east attractive mae to remaining singe for ever, since remaining singe yies u s ða; 0Þ ¼0, whie being marrie to the east attractive man yies E ½u m ða; 0ÞŠ ¼ a > 0. Marriage sets. Marriage requires mutua agreement. Hence, for both partners, the ifetime utiity of being marrie must be weaky greater than the ifetime utiity of being singe. C1 : E u m ða; Þ > u s ða; Þ^ C2 : E u m ða; Þ > u s ða; Þ: Conition C1 states that a femae with attractiveness a must be wiing to marry a mae of attractiveness a, C2 states that a mae with attractiveness a must be wiing to marry a femae of attractiveness a. By symmetry, the marriage sets of a man an a woman with the same attractiveness are the same. Equaity of the in an outfow of singes for each a an. We assume that the marriage market in each region is in steay state. Hence, the number of new singes entering the market equas the number of singes getting marrie. Let g ðaþ be the mass of singes of attractiveness a entering ocation to search for a partner. In steay state the foowing hos 5 : Z! g ðaþ ¼f ðaþ k f ðaþa þ : ð4þ m ðaþ The eft-han sie is the infow of new singes of attractiveness a, an the right-han sie is the outfow rate which equas the number of contacts between femaes with attractiveness a with maes in her matching set, R m ðaþ f ðaþa an a fraction ies. By symmetry, a simiar equation hos for the infow of maes of attractiveness a; g ðaþ an the mass of maes an femaes with the same attractiveness, f ðaþ is ientica. In Appenix A.1 we erive a cose form expression for f ðaþ. Location choice of a singe. For the case of costess mobiity of singes, a femae iving in the countrysie, = 0, ecies to move to the city, =1,if u s ða; 1Þ > u s ða; 0Þ: an vice versa. Let h(a) be the mass of singes of attractiveness a in both ocations before ocation choice an et I(a) be an inicator function that takes the vaue one if attractiveness eve a prefers ocation 1, that is, if conition (5) is satisfie an zero otherwise. Then g 1 ðaþ ¼IðaÞhðaÞ; ð6þ g 0 ðaþ ¼½1 IðaÞŠhðaÞ: When the cost of mobiity is infinite (see Section 2.3), we assume the new singes to be equay istribute among both ocations: g ðaþ ¼ 1 2 hðaþ: ð3þ ð5þ ð7þ 3 Utiity epens ony on the characteristics of one s partner. Specifications where the own type matters in an aitive way o not change the resuts, i.e. a femae with attrictiveness a f marrie to a mae a m receiving utiity, u ¼ a m þ hða f Þ, with h 0 > 0. In the wors of Burett an Coes (1999): narcissm is not necessariy rue out. 4 Where we can think of a a 0 = with a 0 being the fow vaue of marriage with a type a. 5 Hence, we eviate from a common but unpeasant simpification in the iterature which is the coning assumption: each person who gets marrie is immeiatey repace by another person of the same attractiveness, see e.g. Boch an Ryer (2000). That assumption fixes the istribution of attractiveness over the stock instea of over the infow.

4 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) Definition 1. An equiibrium is a coection of marriage sets m ðaþ an ensities f ðaþ that satisfies Eqs. (3) an (4), an either Eq. (6) for the case with zero mobiity cost for singes, or Eq. (7) for the case with infinite mobiity cost. Beow, we first characterize the equiibrium for a singe ocation. Next, in Section 2.2 we turn our attention to the sorting of singes an coupes into cities an rura areas in the case of zero mobiity cost for singes. Then, we compare the correation between mae an femae attractiveness between both ocations for the case of infinite mobiity cost in Section 2.3. Finay, we expain in Section 2.4 why cities are more expensive to ive in, have a higher contact rate an have a arger fraction of singes The marriage market equiibrium The shape of the marriage sets is etermine by a number of simpe observations. If a femae with attractiveness a is wiing to marry a mae with attractiveness a, then she is aso wiing to marry a maes who are more attractive: a > a because u m ða; Þ is stricty increasing in a. Hence, the marriage set of a woman with attractiveness a in ocation is convex, the ower boun a ðaþ being the east attractive man to whom she is wiing to marry, the upper boun a þ ðaþ being the most attractive man who is wiing to marry her. In other wors, the ower boun is the attractiveness a for which conition C1 is just vioate (i.e. hos by equaity), the upper boun is the highest rank a for which conition C2 is not vioate (i.e. hos by equaity). Hence, the marriage set of a woman with attractiveness a is efine as fag 2ha ðaþ; a þ ðaþš. Consier the most attractive femae, a ¼ a þ. By the previous argument, a maes are wiing to marry her, so the upper boun of her marriage set is a ¼ a þ. The ower boun of her marriage set, enote a 1, is etermine by the mae type that gives her the same amount of marriage utiity as the vaue of remaining singe. Evauating (2) at a 1 gives an expression for u s ða 1 ; Þ. Then, a 1 ðc CÞ ¼u s ða 1 Þ¼k a 1 ¼ k Z 1 a 1 Z 1 a 1 ða a 1 Þf ðaþa C: ða a 1 Þf ðaþa c It is easiy verifie that a singe women with attractiveness fag 2ha 1 ; 1Š set the ower boun of their marriage set at the same vaue as the most attractive woman because they sove exacty the same probem. Hence, a these singe women have the same utiity, u s ða; Þ ¼u s ða þ ; Þ; 8 a 2ha 1; aþ Š. By symmetry, the same appies to a maes. The femaes an maes with attractiveness fag 2ha 1; 1Š form a cose segment an marry with each other, but they o not marry with anyboy ese. A woman with attractiveness a 1 can therefore not marry with a more attractive mae. Her own attractiveness is the upper boun of her marriage set. The whoe ogic that appies to the first segment that contains the most attractive caniates therefore carries over to the secon segment. The ower boun of the next segments i, a i, can be cacuate in a simiar way: a i ¼ k Z a i1 a i ða a i Þf ðaþa C: The whoe market fas apart in a number of consecutive, non-overapping segments. Men an women marry within an never outsie their segment. In Appenix A.2 we characterize the equiibrium an give a conition for uniqueness. Fig. 1 shows the segments in the attractiveness space of maes an femaes. The segments are given by the shae areas. By Eq. (19), a femae s attractiveness when being singe is irecty reate to the utiity of the east attractive mae in her segment, because a femaes in this segment are inifferent between marrying this man an remaining singe. Hence, this ð8þ ð9þ Fig. 1. Marriage market segments. utiity can be erive immeiatey from Fig. 1. This segmente cass structure has been estabishe in a number of papers. 6 In a Warasian marriage market without search cost, the utiity of a singe woman equas her attractiveness, because each eve of attractiveness forms a separate segment an marriage sets are reuce to singetons. Consequenty, a matches are on the iagona (Gae an Shapey, 1962). Hence, for the countrysie (for the city the argument is ony triviay ifferent) the vertica istance between the iagona an the actua utiity u s ða; 0Þ ¼a i 0 ; ai 0 < a < ai1 0 can be interprete as a measure of the cost of search frictions for a woman of attractiveness eve a. Ony for the east attractive singe woman in each segment her utiity is equa to what it wou be in a Warasian market. For her, the cost of waiting for a suitabe marriage partner is exacty offset by the chance of fining a better partner than she wou have been abe to fin in a Warasian market. A sight change in the segmentation wou therefore make her worse off, since she wou no onger be the east attractive woman in her segment, an hence she wou get a ower pay off than in the Warasian equiibrium. Hence, there is no unambiguous Pareto ranking for equiibria with a ifferent number of segments. The shae area between the iagona an the actua utiity is a measure of the tota cost of search frictions. The arger therefore the number of segments, the smaer the tota osses ue to search for the most attractive type are The best ocation to search for a partner Having characterize the marriage market equiibrium in each ocation, we can now procee with the anaysis of the ocation choice at the moment that a singe starts ooking for a partner. The case with infinite mobiity is simpe: there is no mobiity, everyboy starts searching for a partner at the ocation where she is born. With finite mobiity cost for coupes an zero mobiity cost for singes, the atter move to the ocation where their expecte utiity is highest. In that case, there are mutipe equiibria. 7 6 See e.g. Burett an Coes (1997), Boch an Ryer (2000), Eeckhout (1999), an Smith (1997). 7 Formay, this can be seen by comparing the fow equiibrium conition (16) in the appenix to Eq. (6) for g ðaþ.

5 210 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) The ocation choice etermines the ensity of new singes that enter the market in a particuar ocation, g ðaþ, which in turn etermines the number of peope with attractiveness a in the stock of peope who are ooking for a partner, f ðaþ. An extreme exampe carifies the probem. For the sake of argument, assume c = 0 at this point. Suppose that a singes ecie to ook for a partner in the city, then g 0 ðaþ ¼f 0 ðaþ ¼0 for a a, an hence, u s ða; 0Þ ¼0, which rationaizes the choice of singes to move to the city in the first pace. Ceary, when we start with the reverse presumption that a singes ecie to ook for a partner at the countrysie, then g 1 ðaþ ¼f 1 ðaþ ¼0 for a a, an hence, u s ða; 1Þ ¼0, which aso rationaizes the presumption. This expains the existence of sma areas ike Bevery His which contains a arge fraction of attractive singes. If we want to obtain a unique equiibrium, we have to impose further restrictions. For this purpose, we introuce the notion of hierarchica efficiency. Definition 2. An hierarchicay efficient equiibrium is an equiibrium that satisfies Definition 1 an where on top of that the ifetime utiity of a singe with attractiveness a cannot be improve without making a more attractive singe a 2ha ; a þ Š worse off. By the cass structure of the equiibrium on the marriage market, where a singe in the ith segment of the market has to take the behavior of singes in higher segments as given, the concept of hierarchica efficiency is reate to Aumann s (1959) concept of a strong equiibrium (there exists no profitabe eviation by a coaition of payers). In an hierarchicay efficient equiibrium, the utiity of each iniviua is maximize subject to the constraint that the utiity of more attractive peope is areay maximize. Since in any equiibrium, a coaition of ess attractive peope cannot infuence the strategy of more attractive peope, an hierarchica efficient equiibrium is a strong equiibrium. Proposition 1. Consier the case of finite mobiity cost. For intermeiate vaues of C, there exists a critica eve of attractiveness a such that in a strong equiibrium a singes with a 6 a move to the countrysie, = 0 an a others to the city, = 1. For ower vaues of C, they move to the city. For higher vaues of C they move to the countrysie. Proof. See Appenix A.3. h Proposition 2 shows that the most attractive singe women prefer the city an the east attractive women prefer the countrysie. We abe this outcome the eite city orering. Singes face a trae off between the efficiency of the marriage market in the city an the cheap cost of iving in the countrysie. The eite prefers the efficiency of the city marriage market above the cheap cost of iving in the country because they gain more by a higher contact rate. Their greater attractiveness aows them to marry with more attractive partners since their own attractiveness is basicay their enowment in the marriage market. Hence, their opportunity cost of remaining singe are the highest an therefore they have the greatest incentive to move to the city. We have not moee the housing market at this stage. However, one can expect that with a positive suppy of housing both in the city an at the countrysie, house prices wi ajust such that at east some singes prefer the city above the countrysie, for otherwise noboy wants to ive in the city (remember that coupes migrate ony from the city to the countrysie), see Section 2.4. Jacquet an Tan (2007) stuy a reate probem where market paces fufi the same roe as ocations in our moe. They aow for free entry of market paces an show that a equiibria feature perfect segmentation (the first contact resuts in a match) when the contact technoogy exhibits constant returns to scae. With a quaratic contact technoogy they show that (ike here) a Burett Coes cass structure arises. The intuition is that uner CRS, ess attractive types impose congestion externaities on more attractive types an this gives the atter more incentives to form new market paces for themseves. Uner a quaratic technoogy, there are no congestion externaities Location ifferences in the tightness of matching Next, we consier whether the segmentation of the marriage market is tighter in the city. With finite mobiity cost the anaysis is very messy as we argue beow an therefore we focus on infinite mobiity cost in this section an assume that the istribution of attractiveness of the infow of new singes is equa in both regions. At what ocation is the correation between the mae an femae attractiveness of a coupe highest? Proposition 2. Consier the case of infinite mobiity cost. Conitiona on a common upper boun a i1 of segment i at both ocations, the ower boun of the segment is ower in the country than in the city a i 0 < ai 1 < 1. Proof. This foows from the fact that the ower boun of a segment is increasing in k, see (9). h Since the contact rate is higher in the city, singes respon by becoming more choosy an this impies a higher correation between mae an femae attractiveness since matches are coser to the main iagona of Fig. 1. The reation between segment size an regions is more compicate with finite ranom mobiity cost. In that case, part of the singes of a particuar eve of attractiveness wi move an part wi stay at the ocation where they are born (those with high mobiity cost). It then epens on the exact segmentation of the market whether singes of a particuar eve of attractiveness move to the city or to the countrysie. For exampe, the best segment, i = 1, wi be tighter in the city than at the countrysie, but a femae with attractiveness a in between the ower bouns of the upper segment in the city an at the countrysie fas in the secon segment in the city whie she beongs to the first segment in the country. If the ower boun of this secon segment in the city is beow the ower boun of the first segment in the countrysie, ða 1 1 < a1 0 < a2 1Þ, she remains in the country. Hence, there is myria of potentia outcomes. However, with finite ranom mobiity cost, one can expect by an arge that for the upper en of the attractiveness istribution there is net immigration to the city an matching is tighter there, whie for the ower en of the istribution, the reverse hos. Immigration an tighter matching are two sies of the same coin, as tighter matching impies that the most attractive singes in a segment get higher utiity in that ocation, an hence singes wi move there. As we wi show in the next subsection, the higher cost of iving in the city can be riven by the net aggregate migration of singes to the city The nature of the excess cost of iving in the city This section proposes an expanation for why iving in the city is more expensive than in the countrysie. For reasons of tractabiity, we consier a simpifie version of our moe where a agents have the same attractiveness a an where the stock of housing (an hence the popuation) at both ocations is equa. We normaize the tota popuation size to one an start our anaysis with equa contact rates in both ocations, k 1 ¼ k 0 ¼ k. Without oss of generaity we enote the ocation with (weaky) more singes as the city, =1.

6 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) Contrary to the previous anaysis the excess cost of iving in the city c is now enogenous. Since we wi show that the cost of iving in the city are equa to or above the cost of iving in the country, c P 0, coupes who marrie in the country never move to the city. Let CðcÞ be the istribution function of moving cost, c. Coupes move to the countrysie if c < c. So a fraction C CðcÞ of the coupes moves from the city to the countrysie. Let F i be the stock of singes in ocation i. The stock of marrie iving in the country, M 0, foows from the foowing steay state fow conition: kf 2 1 C þ kf2 0 ¼ M 0: The eft-han sie is the infow of marrie coupes into the country; where the first term is the infow of the newy marrie coupes with sufficienty ow moving cost moving in from the city, an the secon term represents the number of marriages in the country. The right-han sie is the outfow of marrie coupes (into eath). The stock of marrie in the city, M 1, foows from a simiar equation: kf 2 1 ð1 CÞ ¼M 1: The stock of marrie coupes at the countrysie, M 0, pus the stock of singes, F 0, must be equa to haf of the tota popuation. The same appies to the city. Hence: k F2C 1 þ k F2 0 þ F 0 ¼ 1 2 ; ð10þ k F2 1 ð1 CÞþF 1 ¼ 1 2 : ð11þ The ifetime utiity of a singe iving in, respectivey, the country an the city is given by: u s0 ¼ k F 0ða u s0 Þ; u s1 ¼ k F 1ða u s1 Þðc CÞ: Since singes are free to choose their ocation, a no-arbitrage conition hos an both utiities must be equa in equiibrium, u s0 ¼ u s1, impying that: c C ¼ kðf 1 F 0 Þ þ kf 0 a; ð12þ Suppose c is istribute uniformy on the interva ½0; 1=gŠ. This impies: CðcÞ ¼gc; C ¼ gc; C E max½c c; 0Š ¼Prðc < cþeðcjc < cþ ¼ 1 2 gc2 : Using these conitions, equiibrium can be characterize by an equation that ony epens on c. 8 There exist mutipe equiibria. The first is a trivia equiibrium where both ocations have the same popuation composition an where c = 0. Since moving cost are positive, marrie coupes have no incentives to move out of the ocation where they marry. For sufficienty ow moving cost, this equiibrium is unstabe because if the initia conitions are such that the city has sighty more singes, it wi break own an the city attracts more singes. Then, the 8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2kF 1 þ 1 4 k 2 F 2 1gc þ 2 k 0 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 1 4 k 2 a c þ 1 F 2 1gc þ 2 k 2 gc2 ; ð13þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where F 1 ¼ þ 1 þ 2 k ð1 gcþ ð14þ 2kð1 gcþ where (13) foows from soving (10) for F 0 an substituting the resut in (12) whie (14) foows from soving (11) for F 1. city speciaizes in marriage formation an consequenty it attracts reativey many singes who push up house prices an increase the cost of iving. This gives newy forme coupes with sufficienty ow moving cost incentives to eave the city in orer to save on the high cost of iving. Beow, we iustrate the equiibrium for fg ¼ 1; a ¼ 1; k ¼ 1; ¼ 0:2g. Besies the equiibrium where c = 0, there is one other equiibrium in this exampe where c = Location 1 has more singes than ocation 0, F 1 ¼ 0:29; F 0 ¼ 0:16 an ocation 0 has more marrie coupes: M 1 ¼ 0:21 an M 0 ¼ 0:34. We have not foun parameters combinations that generate more than 2 feasibe equiibria. The higher cost of iving in the city are ue to the rents that home owners appropriate. Suppose that we exten this moe with an upwar soping housing suppy curve. The iea is that construction becomes more an more expensive as the number of houses in an area increases. Since rents are higher in the city, equiibrium housing suppy wi be higher in the city as we. Consequenty, the popuation ensity in the city wi be arger than in the country, raising the contact rate in the city above the contact rate at the countrysie, k 1 > k 0, an making the city even more attractive for singes. This expains why the excess cost of iving in the city go han in han with a higher popuation ensity. Finay, the suppy of singe amenities (bars, cubs, etc.) wi aso ajust to the composition of a region. In our moe, the emergence of cities is the resut of the esire of singes to custer together in orer to fin an attractive marriage partner. Aing heterogeneity to this moe makes that cities speciaize in their roe as efficient marriage markets in particuar for attractive singes, as iscusse in Section Empirica strategy an ata In the remainer of the paper we provie a simpe exporatory empirica anaysis of the main preictions of the theoretica moe presente above. Our goa is to test whether the preictions are consistent with a ata set consisting of a ranomy rawn subsampe of Danes born between 1955 an Specificay, we ook at the moving patterns between the countrysie an cities an we investigate whether singes an in particuar the most attractive ones are more ikey to move to the city. We consier some aternative expanations in Section 5. Beow, we give a escription of the ata set use an how we construct a measure of attractiveness. In the next section we present the empirica resuts which are base on inear probabiity moes of the mobiity pattern. 9 The ata that we use to test the main impications of the moe come from IDA (Integrate Database for Labor Market Research) create by Statistics Denmark. The information comes from various aministrative registers that are merge at Statistics Denmark. The IDA sampe use here contains (among other things) information on marriage market conitions for a ranomy rawn subsampe of iniviuas born between January 1, 1955 an January 1, The iniviuas are foowe from 1980 to The ata set enabes us to ientify iniviua transitions between ifferent states on the marriage market on an annua basis. In aition, we have information about current geographica ocation. This impies that we aso observe an iniviua s mobiity pattern within Denmark on an annua basis. 11 If the iniviua enters a reationship 9 In earier versions of the paper we estimate non-inear probabiity moes, which gave very simiar resuts. Since one of our main variabes is the interaction term between being singe an eve of attractiveness we fin it more informative to use the inear probabiity moe which gives a ceaner interpretation of the interaction term. 10 Immigrants are incue but cannot be separatey ientifie. 11 We consier Denmark to be a singe market. Given the sma fraction of immigrants this is not too restrictive (the foreign born popuation ony accounte for 5% in 2000 whie for the OECD as a whoe this is 10%, see OECD, 2008).

7 212 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) we aso observe the persona characteristics of the partner. There are 23,672 iniviuas in our sampe. We use the foowing variabes. Eucation. We use years of compete eucation to escribe eucationa attainment. Since most of the sampe is acquiring eucation in the sampe perio we wi use eucation in 1995 (when the youngest person in the sampe was 30) as the inicator for eve of eucation (to avoi probems with unfinishe eucation). The basic eve of eucation in Denmark is 9 years of eucation. Iniviuas grauating from high schoo have 12 years of eucation, the next eucation cass is 14 years of eucation, to compete a meium egree requires 16 years an finay it takes 18 years to grauate from university. Income. We use (og) gross income. The income figures are a in terms of 1980 prices an incue saary, capita gains, an income transfers. The consumer price inex is use as a efator. City- rura efinition. We ivie Denmark into cities an rura areas. The five argest Danish cities are Copenhagen (inc. Freeriksberg), Aarhus, Oense, Aaborg, an Esbjerg. Fig. 2. Map of Denmark. The most ense area in Denmark is the Copenhagen metropoitan area 12.7% of the popuation ive there in The other cities host 15% of the popuation in The five cities are istribute across the country as shown in Fig. 2. We therefore conjecture that the reevant city efinition is to incue the argest cities in each region of Denmark. The epenent variabes in the anaysis are inicator variabes that take the vaue 1 if an iniviua who ives in the city moves to the countrysie or, for the other regression, if an iniviua that ives in the countrysie moves to the city in a given year. For iniviuas who stay either in the city or in the countrysie for two consecutive years the reevant epenent variabes take the vaue 0. Note that a city accoring to our efinition is a much smaer unit than a CMSA in the Census ata so one shou be carefu when comparing our resuts to those of Costa an Kahn (2000) an Compton an Poak (2007). Therefore, we repeate our anaysis with a ifferent efinition of ense an non-ense areas base on the popuation ensity. This changes the city efinition somewhat. Some suburbs of Copenhagen are more ensey popuate than the arge cities. It turns out however, that our main resuts are robust to changes in the city efinition. Finay, we o our anaysis ony treating Copenhagen as a city an fin quaitativey simiar resuts. Marriage. Iniviuas can occupy one of three states in the marriage market: singe, cohabiting, or marrie. In this paper we merge cohabitation an marriage into one group an refer to this group as marrie. Cohabitation as either a preue to or a substitute of marriage is very common in Denmark (see e.g. Svarer, 2004). There are some quaifications to this efinition of marriage. Some of the coupes presumaby a sma minority that are registere as cohabiting are simpy sharing a housing unit, an o not ive together as a marrie coupe. Persona characteristics. We aso have etaie information about the number of kis in the househo. We know the abor market status of the iniviuas, their age an their income. In aition, we have information on the income an eucation of the father of each iniviua in the sampe. Tabe 1 presents escriptive statistics for the main variabes. The perio covers We report means for 1987 for the main expanatory variabes. These are representative for the whoe perio. Tabe 1 shows that a higher fraction of the popuation is singe in the city athough the age ifference between the city an rura areas was quite sma in That is, the higher fraction of singes in the city is not a resut of a ower mean age. More peope have chiren in the rura areas. Peope ten to be more eucate an have higher incomes in the city. In aition, housing prices are aso higher in the city. Tabe 1 aso reveas that men marry ater Tabe 1 Descriptive statistics. City Rura Women Men Women Men Number of observations, 1987-numbers Singe, 1987-numbers (%) Chiren, 1987-numbers (%) Age, 1987-numbers (in years) Years of eucation Gross income (conitiona on working, in 1000 kk) Father s years of eucation Father s gross income (in 1000 kk) Father has missing income (%) Other escriptives 1995 house prices per m 2 (in 1000 kk) 6.3 kk 4.3 kk Average annua rura-to-city mobiity rate (%) (a years) 2.9 Average annua city-to-rura mobiity rate (%) (a years) 6.4 Note. Numbers represent percentages uness state otherwise.

8 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) Tabe 2 Resuts from canonica correations. because the cohort contains reativey many singe men. The average annua mobiity rate for the sampe perio is presente in the ast two rows. On average 2.9% of the iniviuas move from the rura areas to the city per year. The reverse move from a city to a rura area happens more than twice as often. In the next section we construct an attractiveness measure which we use in Section 4 to test the main impications of the moe Constructing a measure of attractiveness Canonica coefficients t-vaue a 1 : Man s eucation a 2 : Man s father s eucation a 3 : Man s income a 4 : Man s father s income a 5 : Man s father has missing income b 1 : Woman s eucation b 2 : Woman s father s eucation b 3 : Woman s income b 4 : Woman s father s income b 5 : Woman s father has missing income Canonica correation between A M an A F Canonica correation between A M an A F 0.14 Bivariate correations Eucation 0.38 Income 0.07 Father s eucation 0.14 Father s income 0.15 # Coupes 14,018 Note. A weights are significanty ifferent from 0 at the 5% eve. The moe presente in Section 2 suggests that more attractive singes are more ikey to move to the city. Iniviua attractiveness presumaby epens on a whoe range of characteristics ike weight, height, age, inteigence, humor, physica appearance, income, etc. Data imitations restrict us from using a compete set of persona attributes. Regrettaby, pictures of the iniviuas in the sampe are not avaiabe, so that we cannot rank iniviua accoring to their ooks, as in e.g. Hamermesh an Bie (1994). We therefore foow Wong (2003) an Anerberg (2004) an use income an eucation as attractiveness components. In aition, we aso expoit information on father s eve of eucation an income. 12 Beow, we expain how we etermine their reative importance. In a frictioness wor, the most attractive femaes marry the most attractive maes, resuting in a perfect correation between mae an femae attractiveness. In a wor with frictions this correation wi not be equa to one but it wi be positive. Here, we conjecture that attractiveness for both maes ða M Þ an femaes ða F Þ is a inear function of the four factors escribe above an the ummies for missing income an eucation for fathers. 13 A M ¼ eu a 1 þ nðincþa 2 þ f eu a 3 þ nðf incþa 4 þ f miss inc a 5 A F ¼ eu b 1 þ nðincþb 2 þ f eu b 3 þ nðf incþb 4 þ f miss inc b 5 : 12 In abor economics simiar issues arise, see e.g. Heckman an Scheinkman (1987). Worker skis are often measure by eucation but as Bacoo et a. (2009) argue, this is restrictive. They use many other psychoogica traits an measures of inteigence an take an heonic approach using information on job requirements to ientify skis from ski requirements. Gautier an Teuings (2009) aso take an heonic approach an use a worker characteristics that are avaiabe in the CPS to construct a singe imensiona ski inex using wages to obtain weights for the various factors. 13 We i not incue age because it is ikey that preferences are base on age ifferences between own s an partner s type rather than the absoute vaue of age. We aso consiere using occupation information. It was however not obvious how to rank ifferent occuptations so we choose not to incue it in the anaysis. Tabe 3 Summary statistics for the stanarize attractiveness measure. Singes Mean St. Dev. Rura Mae attractiveness Femae attractiveness City Mae attractiveness Femae attractiveness We estimate the reative importance of those factors (the a 0 s an the b 0 s) by canonica correation, as was areay suggeste by Becker (1973). Canonica correations (see e.g. Johnson an Wichern (1998)) construct inices of A M an A F such that the correation between each of them is maximize subject to the inices being orthogona to each other. In the moe, we assume that the two sets of variabes are reate to each other ony through a singe inex. In Tabe 2 we present the resuts from the canonica correation anaysis. We stanarize a variabes, i.e. they are a transforme to have mean 0 an variance equa to 1 to ensure that the weights are consistenty estimate. A estimate coefficients are significanty ifferent from zero. The stanarize coefficients show that the attractiveness eve is mainy etermine by eucation. The bivariate correation between the partners eucationa eve is The aitiona terms in the attractiveness measures o not a much to the tota correation. On the other han they a have a significant impact on the measure an we choose to incue them in the subsequent anaysis. We aso investigate a version where ony eucation is incue as a measure of attractiveness. 14 The first canonica root is 0.42 an athough the secon is significanty positive it is much smaer. Hence, the first canonica correation captures most of the correation between the two sets of variabes an we can use a singe inex. Base on the estimate weights we construct an attractiveness number for each iniviua by aing up the weighte vaues of their characteristics. The summary statistics for the attractiveness inex (singes ony) for both cities an rura areas are presente in Tabe Tabe 3 shows that on average singes iving in the city are more attractive than singes iving in the countrysie. Since, a crucia eterminant of attractiveness in the current anaysis is the eve of eucation this might simpy refect that returns to eucation are arger in the city. In the next section we try to investigate whether other motivations for iving in the city ominate the marriage market effect. 4. Resuts In this section we investigate whether the mobiity patterns observe in the ata are consistent with the main preictions of Section 2. First, singes have a reativey arger probabiity to move to the city an a reativey smaer probabiity to move to the countrysie to expore the higher contact rate. Secon, in particuar the attractive singes have a arger probabiity of moving to an staying in the city since the opportunity cost of remaining singe are argest for them. 14 We aso investigate a version of the moe where we use average income in the ast three years to purge for potentia temporary income fuctuations. The resuts presente in Tabe 2 an in subsequent tabes where not affecte by this other income measure. 15 The attractiveness measure is constructe base on 1995 observations. The resuts throughout the paper are however unaffecte if we use each year s income to construct the measure. Moreover, if we estimate the weights for city an rura areas separatey, we get very simiar resuts.

9 214 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) Tabe 4 Linear probabiity moe: probabiity of mobiity. a Women Rura to city City to rura Rura to city City to rura Coeff. SE Coeff. SE Coeff. SE Coeff. SE Singe 0.026* * * * Attractiveness 0.005* * * * Singe* attract * * * * Chiren 0.022* * * # Observations 84,736 29,714 76,130 27,065 a Note that in this an a subsequent tabes we aso conition on age an empoyment status. * Significanty ifferent from 0 at the 5% eve. Men Tabe 5 Geographica ocation of iniviuas base on attractiveness at ifferent ife-stages. a Leve of attractiveness by quartie Fraction iving in city At age 18 At marriage a After 5 years of marriage Since there are no ifferences in the gener specific patterns we present numbers for both men an women in this tabe. In Tabe 4, we present the resuts for the movements rura to city an city to rura for both men an women. Tabe 4 shows that for both men an women the mobiity pattern is consistent with the moe preictions. That is, singe peope are more ikey to move to the city an ess ikey to eave the city compare to marrie iniviuas. In aition, the coefficients of the interaction terms revea that among singes the most attractive are most ikey to move to the city an are aso ess ikey to eave the city athough for the city-to-rura movement, the sum of the coefficients (singe, attractiveness an their prouct) is not significanty ifferent from zero. Another interesting fining is that the presence of chiren is associate with a ower mobiity propensity in a imensions, athough the margina effect is, as expecte, much arger in the mobiity equation from the city to rura areas. An aternative story is that expecte income is higher in the city (in particuar for attractive types). However, higher income oes not expain why singes an attractive singes in particuar are more ikey to move to the city than coupes. Another competitor to the marriage market hypothesis of why attractive peope ocate in the city is that they can benefit from the higher returns to eucation. But this cannot expain why they move out of the city as we fin. The fining that more attractive peope are more mobie is consistent with other stuies on iniviua mobiity (e.g. Greenwoo, 1997; Compton an Poak, 2007). In Tabe 4, we aso see that the probabiity of moving from the city to the countrysie is in particuar ower for the most attractive singes. That is, among the marrie the most attractive are more ikey to eave the city. We beieve this fining highights the importance of consiering the marriage market component in the investigation of mobiity patterns between cities an rura areas. Our resuts are consistent with recent iterature that ooks at mobiity patterns of iniviuas base on their marriage market status. Both Eun (2005) an Compton an Poak (2007) fin that singes are more ikey to ocate in the cities an that this is particuary so for the more attractive ones (aso known as power singes in the terminoogy of Costa an Kahn (2000) an Compton an Poak (2007)). In fact, Compton an Poak (2007) show that the reason that power coupes are more often observe in cities Tabe 6 Spearman rank correation at time of marriage. Spearman correation City Rura Attractiveness Eucation # Observations (the Costa an Kahn, 2000 fining) is that marriage formation among power singes is more ikey to happen in cities. Our anaysis provies aitiona evience that after marriage formation, power coupes (here iustrate by the power man or woman who tens to marry power spouses (see e.g. Niesen an Svarer, 2009)) eave the city at a higher rate an ocate in ess popuate areas. 16 Tabe 4 aso shows that the presence of chiren is associate with a ower mobiity propensity between the city an the countrysie an vice versa. This suggests that chiren raise moving costs. The margina effect of chiren is higher for the migration from the countrysie to the city, which inicates that amenities of rura iving ike more space, cheaper housing an ess poution are more vauabe to iniviuas with chiren. In Section 5.2, we investigate further whether the presence of chiren is the riving force behin the mobiity ifferences between singes an marrie iniviuas. For now, we simpy notice that whereas chiren are affiiate with a ower mobiity probabiity from the countrysie to the city they are aso associate with a ower probabiity of moving from the city to the countrysie. Finay, we give aitiona ife cyce evience in Tabe 5. We present the istribution of iniviuas between rura an city conitiona on their eve of attractiveness at ifferent ife stages. Tabe 5 shows that at age 18 (when iniviuas are typicay not yet active on the marriage market an often sti ive with their parents) most peope ive in rura areas an there is not a ot of ifference between iniviuas at the high an the ow en of the attractiveness istribution. However, at the time of marriage, many of them ive in the city. In particuar, a arge share of the iniviuas in the fourth quartie have move to the city an marrie there. Amongst the iniviuas who stay marrie for 5 years we see that a significant fraction has move back to the rura areas an a pattern arises that is very cose to the pattern at age 18. Ony the most attractive iniviuas prefer to ive in the city, athough aso for this group, we see transitions from city to rura upon marriage. Compton an Poak (2007) ook at the proportion of power men an women iving in US cities with more than 2 miion inhabit- 16 In the anaysis we o not moe the ynamic mobiity process of each iniviua. As a short cut we treat each annua observation as inepenent. This approach cou be invaiate if there is a ot of return migration. However, among the marrie coupes that eave the city aroun 90% o not return to a city uring their marriage. If we excue the return migrants from the anaysis our quaitatative finings remain the same.

10 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) Tabe 8 Linear probabiity moe: iniviuas oer than 25. Women Rura to city City to rura Rura to city City to rura Coeff. SE Coeff. SE Coeff. SE Coeff. SE Singe 0.032* * * * Attractiveness 0.002* * * * Singe* attract * * * Chiren 0.013* * * # Observations 51,764 17,154 46,528 16,591 Note. We conition on age an whether the iniviua works fu-time. * Denotes significanty ifferent from 0 at the 5% eve. Men Tabe 9 Linear probabiity moe: no kis sampe. Women Rura to city City to rura Rura to city City to rura Coeff. SE Coeff. SE Coeff. SE Coeff. SE Singe 0.024* ** Attractiveness 0.006* * Singe* attract * # Observations Note. We conition on age an whether the iniviua works fu-time. * Significanty ifferent from 0 at the 5% eve. ** Significanty ifferent from 0 at the 10% eve. Men ants. They aso fin that conitiona on eucation, singes are more ikey to ive in a arge city than coupes. This observation is consistent with the Danish ata Size of the segments In Section 2.3, we suggeste that cities have more an smaer segments which impies a higher correation between eves of attractiveness of men an women. In this section we present evience for this caim. We investigate whether ifferences in our attractiveness measure between partners iffer between the city an rura areas. In Tabe 6, we present the Spearman rank correation between attractiveness an eucation separatey. For both measures of attractiveness the rank correation is arger in the city which suggests a finer segmentation. The evience presente above is to a arge extent consistent with the marriage-market hypothesis presente in Section 2. In the subsequent sections we ook at a number of aternative expanations. The main goa is to see whether the marriage market story sti prevais once these confouning mechanisms have been incue in the anaysis. 5. Aternative expanations an robustness checks In this section we carry out a number of sensitivity checks an test whether our resuts can be riven by other factors. First, we test whether the infow of singes into the city merey refects a coege effect, an secon we test whether the fact that coupes move out of the city is mainy ue to the presence of chiren an finay we test whether our resuts cou be riven by ife cyce motives Going to the city to get a coege eucation In Denmark, most universities are ocate in the arger cities so we must worry about whether our resuts are riven by youngsters who move into the city to get an eucation, get marrie an then move back to the countrysie. First, this story is not necessariy inconsistent with our marriage market moe because coeges an universities are goo marriage markets themseves because they seect a fairy homogeneous group of highy eucate iniviuas (see e.g. Goin an Katz, 2002; Niesen an Svarer, 2009). Nevertheess, it is usefu to check whether our preictions sti ho in the absence of coeges. We can o this by restricting the sampe to iniviuas who are oer than 25 years an assume that the motivation for those iniviuas to move to the city cannot be the presence of coeges. 17 The resuts of this exercise are presente in Tabe 8. Comparing the resuts in Tabe 8 to the resuts foun for the unrestricte sampe reveas that the singe an attractive men an women are even more ikey to move to the city than their marrie counterparts, an that this is especiay so for the more attractive singes. Aso the mobiity patterns from the city to the countrysie are consistent with the resuts foun for the compete sampe. Even though schoo attenance presumaby is a major factor to ocate in cities, those who are beyon the schooing age an are singe are aso strongy attracte to the cities The roe of chiren Athough we contro for having chiren, marrie coupes cou sti move to rura areas because they expect to have kis in the future. In that case, the reason to move to the countrysie refects a shift towars more space an not the fact that one oses the benefits of a higher contact rate. In orer to isoate the search motivation, we ony consier the subset of coupes who never get chiren. Uner the assumption that having no kis refects preferences rather than constraints, this group must have other motives than kis to move to the countrysie (see Tabe 9). 17 This wi be vioate if a coege grauate from Copenhagen who move out after grauating is more ikey to move back in because she knows her way aroun the city than a non-coege grauate.

11 216 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) Tabe 10 Linear probabiity moe: ivorcees. Women Rura to city City to rura Rura to city City to rura Coeff. SE Coeff. SE Coeff. SE Coeff. SE Divorce, 1 year 0.051* * * * Attractiveness 0.009* * * * Divorce* attract * * * Chiren 0.026* * Divorce, 2 years 0.019* ** * ** Attractiveness 0.010* * * * Divorce* attract * * Chiren 0.027* * # Observations 84,736 29,714 76,130 27,065 Note. We conition on age an whether the iniviua works fu-time. * Significanty ifferent from 0 at the 5% eve. ** Significanty ifferent from 0 at the 10% eve. Men The absence of kis oes not change the sign of the coefficients. We o, however, see that the stanar errors increase an that in terms of statistica significance our resuts are ess cear for the reuce sampe. For the transition from the countrysie to the city we sti fin that singes have a higher moving propensity an that this is especiay pronounce for the more attractive singe women. We aso estimate mobiity equations (not shown) for a sampe of mothers. That is, we investigate whether singe mothers are more ikey to move than marrie mothers. We basicay fin the same pattern as in Tabe 8. Singe mothers are more ikey to move to the city, but not statisticay more ikey to stay in the city compare to marrie mothers. One interpretation of the resuts in Tabe 8 is that even if ifferent preferences reate to chiren are controe for, singes are more ikey to move to the cities ue to the better marriage market conitions there. Athough the signs are as preicte, our estimations are not strong enough to concue that marrie iniviuas without kis are more ikey to eave the city. A possibe reason for this resut is the higher mobiity costs associate with having chiren. For future research it wou be reevant to investigate this issue in more epth with a arger ata set to get more precise estimates Life cyce motives for eaving the city Athough our theoretica moe oes not aow for ivorce an return migration, both are saient facts in the ata. 18 The behavior of ivorcees can she ight on the geographica mobiity of singe peope. Inee, the mobiity pattern that we reporte so far cou be the resut of orinary ife cyce behavior. Peope enter the city when they are young an have reativey strong preferences for bars, cubs, cinemas an other city amenities an then eave the city when they are oer an richer an have stronger preferences for space. One way to isoate the search effect is to consier the mobiity patterns of coupes who have move to the country an who ivorce there. 19 If they move to the countrysie for ife cyce motives other than the marriage market, we expect them to stay in the country after ivorce whereas accoring to the marriage market moe they shou move back to the city once they become singe again. We fin that our moe sti hos. Since the observations we use are annua, we ony know that a ivorce has occurre uring the year but not the exact ate. We therefore present resuts for both iniviuas who have been ivorce 1 year an those who are sti ivorce after 2 years (see Tabe 10). 18 See for a ynamic moe of return migration. 19 An ening cohabitation aso counts as a ivorce. Not surprisingy, because of the nature of a ivorce, ivorcees are more ikey to move. Therefore we must compare the ikeihoo to move to the city with the ikeihoo to move out of the city. For men, there is no arge ifference after the first year of ivorce. In the secon year after ivorce they are however more ikey to move to the city, but not to the rura areas compare to the reference group. For both men an women, the propensity of the ivorce to move to the city is arger than to move out of the city after 2 years of ivorce but not after 1 year of ivorce. This can be expaine by the fact that it is typicay harer to fin a pace to ive in the city than in the countrysie Other aternatives A parae expanation to our story is that peope who ive in the country can meet as many potentia marriage market partners as peope who ive in the city but it is more costy for them to o so (i.e. they have to rive to a city, take a vountary job where one meets many peope, etc.). The opportunity cost of oing so is higher for more skie workers so they opt for iving in the city. 20 We cou moe this by introucing search cost to our moe but this wou a yet another source of mutipicity simiar to Diamon (1982) an make it intractabe. Another possibiity is that high skie workers (which are the more attractive workers in our empirica appication) must work harer in ense areas to istinguish them from rivas, see Rosentha an Strange (2008). If the participants of the urban rat race are more ikey to eave the city after a few years of 80 hour working weeks this cou expain the patterns of Tabe 5. However, it cannot expain why coupes are more ikey to eave the city than singes. 6. Fina remarks In this paper we exten the Burett an Coes (1997) marriage market moe with a istinction between efficient marriage markets (cities) an ess efficient search markets (rura areas) an erive how iniviuas sort into those markets. Our moe preicts that singes an in particuar attractive singes move to the city whie coupes move out of the city. Those preictions are confirme by the ata. We fin that in particuar for femaes, the cross-partia of singe an attractiveness on the probabiity of moving is positive an statisticay significant. Why the cross-effect is ess pronounce for maes is sti an open issue. 20 We thank one of the referees for pointing out this possibiity.

12 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) We offer a range of aternatives stories that can generate simiar mobiity patterns as those erive from our marriage market hypothesis. These incue: higher returns to eucation in the city, the presence of universities in cities, an ife cyce motives for moving in an out of the city. By using appropriatey chosen sub sampes, we show that there is sti room for the marriage-market motivation. Finay, one might woner why cities have more amenities per capita that are aime at singes ike bars an cubs? We view this as the natura market response to the esire of singes to custer in cities. For future research we beieve it cou be fruitfu to incue ivorce ecisions. One interesting motivation for marrie coupes to move to a rura area is that it is an efficient way to make a commitment. Burett et a. (2004) showe that if one of the partners is ikey to continue searching on-the-job, this by itsef stimuates the other partner to continue search as we. Given the many ong term investments that are require, ike raising chiren an buying a house, which a require a stabe reationship, it can be efficient to move to an inefficient search market to imit onthe-job search. In Gautier et a. (2009) we investigate this further. Furthermore, it wou be interesting to aow for investments in one s type, as in Burett an Coes (2001) an Maiath et a. (2000). 21 The atter show, aso using an increasing returns to scae contact technoogy, that if workers are sorte on the basis of payoff irreevant characteristics (i.e. green an re) that there exist equiibria where firms spen more effort to search in the green-worker areas an the green workers invest more in human capita than the re workers. In our moe, attractiveness is exogenous but their resuts impy that there may exist equiibria where attractive femaes mainy search in cities an where city maes invest more in their types. Finay, we focusse on the marriage market in this paper an abstracte away from the abor market. This oes not mean that we beieve that abor market consierations are not important to unerstan migration. To the contrary, we beieve that an interesting avenue for future research is to jointy stuy the abor an the marriage market in one moe. In such a moe it wou be important to consier joint ocation constraints an househo bargaining as in Gemici (2008). Acknowegments We thank the eitor Wiiam Strange an two anonymous referees for their very usefu coments an suggestions. We aso thank Heena Skyt Niesen an seminar participants at the Free University Amsteram, Tinbergen Institute, University of Aarhus, University of Copenhagen, CEMFI, Copenhagen Business Schoo, CREST, IZA, Singapore Management University, University of Hesinki, University of Utrecht an participants at the conference on Labor Market Moes an Matche Empoyer-Empoyee Data in Honour of Dae T. Mortensen 2004 for very usefu comments. Michae Svarer thanks the Danish Nationa Research Founation for support through its grant to CAM an Pieter Gautier thanks the NWO for support through a VIDI grant. Appenix A. Derivations an omitte proofs A.1. The erivation of equation f ðaþ Integrating (4) over m ðaþ an expoiting symmetry, f ðaþ ¼f ðaþ, yies: Z Z 2 Z g ðaþa ¼ k f ðaþa! þ f ðaþa ð15þ m ðaþ m ðaþ m ðaþ 21 See aso Akerof (1985) for a reate moe on iscrimination with IRS. Soving (15) for R f m ðaþ ðaþa an substitute this back in (4) yies the foowing expression for the steay state mass of femaes of type a: 2g f ðaþ ¼ ðaþ q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð16þ þ 2 þ 4k Rm g ðaþ ðaþa A.2. The marriage market equiibrium in a singe region By Eq. (16), f ðaþ satisfies 2g f ðaþ ¼f ðaþ ¼ q ðaþ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 2 þ 4k G a i; ; ð17þ ai1 Z G a i ; a i1 ai1 g ðaþa: Define: a 0 a þ ; a a; a i1 1 a i sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k G a; a i1 Z a i1 a ða aþg ðaþa C: ð18þ The ast expression gives the utiity of singes whose upperboun is a i1 for various vaues of the ower boun a. In equiibrium, the ower boun of one s matching set is the vaue that makes a singe inifferent between marriage an remaining singe. An equiibrium in the marriage market is a coection of connecte non-overapping segments such that the ower boun a i of each segment i at ocation is the upper boun of the next segment. Then, the ower bouns a i of segments i are etermine recursivey starting from i = 1 by the foowing agorithm: a i ¼ a a i ; ai1 ; except for the owest segment, enote I, for which a > a a ; a I 1 ; a I ¼ a : Furthermore, u s ða; Þ ¼a i C; 8a 2hai ; ai1 Š: ð19þ A sufficient conition for uniqueness is: 2Hða; bþ 2 > hðaþ Hða; bþ Z b a Z b a hðaþa: ða aþhðaþa; 8ða; bþ; a 6 a < b 6 a þ ; ð20þ This can be seen as foows. The proposition generaizes the ogic of Eqs. (8) an (9). For a ¼ a i, Eq. (18) is ientica to Eq. (9), where we substitute f ðaþ for Eq. (16). Given the upper boun a i1 of a segment i, we can cacuate a ða; a i1 Þ as a function of a. Suppose conition (20) hos. Then, this conition aso hos for g ðaþ within a segment: if mobiity cost are infinite, it hos by Eq. (7); if mobiity cost for singes are zero, either a attractiveness eves within a segment prefer region or none since a have the same utiity as a singe u s ða; Þ ¼a i C within a ocation, so either the one ocation ominates or the other, so that g ðaþ ¼hðaÞ within that segment, see Eq. (6). For a ¼ a i1 a; a ; a ða; a i1 ¼ 1 k G a; a i1 " 2 Z # a i1 2G a; a i1 2 g ðaþ ða aþg ðaþa a Þ¼C < a an < 0; 8a < a i1 : ð21þ

13 218 P.A. Gautier et a. / Journa of Urban Economics 67 (2010) where the inequaity foows from the fact that conition (20) appies. Hence, a ða; a i1 Þ¼a has either a unique interior soution for a < a i1 or it has no soution at a, in which case i is the owest segment I at ocation, for which a i ¼ a. Without conition (20), we cannot rue out mutipe equiibria. The source of the mutipicity of equiibria is the same as in Burett an Coes (1997): if a women use a non-seective acceptance strategy, where they aso marry with unattractive maes, they a marry fast. By symmetry, this impies that maes o the same an the stock of singes is sma. This reuces the probabiity of fining a very attractive mae, an makes appying a more seective strategy not profitabe. However, if the most attractive femaes in the segment are a seective, then they stay singe for a onger perio. This raises the probabiity of fining an attractive partner, an hence the seective strategy is an equiibrium as we. Since this mutipicity is not centra to our argument, we rue it out by imposing conition (20). 22 A.3. Proof of Proposition 2 It is sufficient to prove that if singes in segment i prefer the countrysie above the city, so wi singes in segment i + 1. The ocation of segment i 1 is irreevant, so we omit the suffix for that segment. Suppose segment i prefers the countrysie above the city a i 0 < ai 1. By Eq. (6), this impies a i 0 ¼ 1 pffiffiffiffiffi > 1 p > 1 p Z a i1 k 0 a i 0 ffiffiffiffiffi Z a i1 k 1 a i 1 ffiffiffiffiffi Z a i1 k 1 a i 0 a a i 0 hðaþa a a i 1 hðaþa C a a i 0 hðaþa C: The secon inequaity foows from (21). The first equaity impies a i0 pffiffiffiffiffi ¼ k 0 Z a i1 a i 0 a a i 0 hðaþa: Substitution in the secon inequaity yies: pffiffiffiffiffi pffiffiffiffiffi k 1 k 0 pffiffiffiffiffi a i 0 k < C: 0 Since a i 0 > aiþ1 0, this inequaity hos aso for segment i + 1. 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