Why Do Cities Matter? Local Growth and Aggregate Growth

Transcription

1 Why Do Ctes Matter? Local Growth and Aggregate Growth Chang-Ta Hseh Unversty of Chcago Enrco Morett Unversty of Calforna, Berkeley Aprl 2015 Abstract. We study how growth of ctes determnes the growth of natons. Usng a spatal equlbrum model and data on 220 US metropoltan areas from 1964 to 2009, we frst estmate the contrbuton of each U.S. cty to natonal GDP growth. We show that the contrbuton of a cty to aggregate growth can dffer sgnfcantly from what one mght navely nfer from the growth of the cty s GDP. Despte some of the strongest rate of local growth, New York, San Francsco and San Jose were only responsble for a small fracton of U.S. growth n ths perod. By contrast, almost half of aggregate US growth was drven by growth of ctes n the South. We then provde a normatve analyss of potental growth. We show that the dsperson of the condtonal average nomnal wage across US ctes doubled, ndcatng that worker productvty s ncreasngly dfferent across ctes. We calculate that ths ncreased wage dsperson lowered aggregate U.S. GDP by 13.5%. Most of the loss was lkely caused by ncreased constrants to housng supply n hgh productvty ctes lke New York, San Francsco and San Jose. Lowerng regulatory constrants n these ctes to the level of the medan cty would expand ther work force and ncrease U.S. GDP by 9.5%. We conclude that the aggregate gans n output and welfare from spatal reallocaton of labor are lkely to be substantal n the U.S., and that a major mpedment to a more effcent spatal allocaton of labor are housng supply constrants. These constrants lmt the number of US workers who have access to the most productve of Amercan ctes. In general equlbrum, ths lowers ncome and welfare of all US workers. We are grateful to Klaus Desmet, Rebecca Damond, Danel Fetter, Cecle Gaubert, Ed Glaeser, Erc Hurst, Pat Klne, Steve Reddng and semnar partcpants at the AEA Meetngs, Brown, Chcago Booth, Chcago Fed, Mnneapols Fed, NBER Summer Insttute, Smon Fraser Unversty, Stanford SIEPR, Unversty of Arzona, Unversta Cattolca d Mlano, Unversty of Brtsh Columba, UC Berkeley Haas, UCLA Anderson, Unversty of Vence, and Yrjo Jahnsson Foundaton for useful suggestons. Ths paper prevously crculated under the ttle "Growth n Ctes and Countres."

2 1. Introducton Macroeconomsts have long been fascnated by the vast dfferences n economc actvty between countres. Yet, dfferences between ctes or regons wthn each country are equally strkng. Whle there s a long tradton of usng ctes or regons as laboratores to understand the sources of dfferences across countres (for example, Barro and Sala--Martn, 1991 and 1992; Gennaol, LaPorta, Lopez-de-Slanes, and Shlefer, 2013), researchers have pad less attenton to how the geographcal dstrbuton of economc actvty across ctes or regons tself affects aggregate outcomes of a gven country. At the same tme, a large urban economcs lterature dentfes local forces that explan dfferences n wages and economc actvty across ctes but has pad comparatvely less attenton to how these forces aggregate to affect growth for the country as a whole. In ths paper we brdge ths gap. We study how economc growth of ctes determnes the growth of natons. We use data on 220 US ctes over the past fve decades and a spatal equlbrum model to address two related questons---a postve one and a normatve one. Frst, we estmate the contrbuton of each US metropoltan area to aggregate output growth between 1964 and We show that our model-based calculaton of a gven cty s contrbuton to aggregate growth dffers sgnfcantly from what one mght navely nfer from the growth of the cty s GDP. We then turn to a normatve analyss of potental growth. We document a sgnfcant ncrease n the spatal dsperson of wages between 1964 and 2009, ndcatng that worker productvty s ncreasngly dfferent across Amercan ctes. We argue that these productvty dfferences reflect an ncreasngly neffcent spatal allocaton of labor across US ctes, and that much of ths neffcency s caused by restrctve housng polces of muncpaltes wth hgh productvty, lke New York and San Francsco. We base our analyss on a Rosen-Roback model where workers can freely move across ctes and geographcal dfferences n wages reflect dfferences n local labor demand and supply. In turn, local labor demand reflects forces that affect the TFP of frms n a cty---nfrastructure, ndustry mx, agglomeraton economes, human captal spllovers, access to non-tradable nputs and local entrepreneurshp---whle local labor supply reflects amentes and housng supply. We analyze how these local forces aggregate n the Rosen-Roback model to affect natonal output and welfare. We show that aggregate output ncreases n local TFP n each cty but decreases n the dsperson of wages across ctes. 1 The reason s that wage dsperson across 1 Formally, we show that aggregate output growth can be decomposed nto the contrbuton of the weghted average of the growth rate of local TFP and nto the change n the dsperson of the margnal product of labor across ctes. 1

3 ctes reflects varaton n the margnal product of labor: The wder the dsperson of margnal products across ctes, the lower aggregate output, everythng else constant. Intutvely, f labor s more productve n some areas than n others, then aggregate output may be ncreased by reallocatng some workers from low productvty areas to hgh productvty ones. In ths settng, geography matters n the sense that the same localzed shock can have profoundly dfferent aggregate effects dependng on where t takes place. An ncrease n local labor demand caused by a TFP ncrease wll have a large effect on aggregate output f the TFP ncrease generates an ncrease n local employment, but the same ncrease n local TFP n another cty can have a much smaller aggregate effect f t largely results n hgher nomnal wages n the cty and only a small ncrease n local employment. Emprcally, we begn by calculatng the contrbuton of each US cty to aggregate growth and compare t wth an accountng measure based solely on the growth of the cty s GDP. We show there are large dfferences between these two numbers. For example, growth of New York s GDP was 12 percent of aggregate output growth from 1964 to However, vewed through the lenses of the Rosen-Roback model, New York was only responsble for less than 5 percent of aggregate output growth. The dfference s because much of the output growth n New York was manfested as hgher nomnal wages, whch ncreased the overall spatal msallocaton of labor. On the other extreme, Detrot s GDP fell dramatcally from 1964 to 2009, but ts net contrbuton to aggregate output growth was actually postve. In the case of Detrot, the declne n ts nomnal wage from 1964 to 2009 lowered the overall wage dsperson. We then turn from a postve analyss of the local forces underlyng aggregate growth to a normatve analyss of potental growth. We focus on the effects of the growng dsperson n the margnal product of labor across ctes. We show that after condtonng on workers characterstcs, the geographcal dstrbuton of nomnal wages s sgnfcantly wder today than n In partcular, the standard devaton of condtonal wages across US ctes n 2009 s twce as large compared to 1964, ndcatng that dfferences n worker productvty across ctes are growng. When we quantfy the output and welfare cost of ths ncrease n dsperson of the margnal product of labor, we fnd that aggregate output n 2009 would have been sgnfcantly hgher f the dsperson of nomnal wages had not ncreased. Holdng the dstrbuton of local TFP fxed at 2009 levels, we hypothetcally reallocate labor from hgh wage to low wage ctes such that the The growth rate of aggregate output s hgher when the weghted average of the growth rate of local TFP s hgher and s lower when the weghted average of wage dsperson across ctes ncreases (for a gven dstrbuton of TFP). 2

4 hypothetcal wage n each cty (relatve to the average wage) s equal to the relatve wage n Intutvely, ths scenaro nvolves settng amentes and housng supply at ther 1964 level, whle keepng labor demand constant at ts 2009 level, and allowng workers to reallocate across ctes n response. Under ths scenaro, aggregate yearly GDP growth from 1964 to 2009 would have been 0.3 percentage ponts hgher. In levels, U.S. GDP n 2009 would be 13.5% or $1.95 trllon hgher. Ths amounts to an annual wage ncrease of $8775 for the average worker. Ths output effect s drven to a large extent by three ctes -- New York, San Francsco and San Jose whch experenced some of the strongest growth n labor demand over the last four decades, thanks to growth of human captal ntensve ndustres lke hgh tech and fnance (Morett, 2012). But most of the labor demand ncrease was manfested as hgher nomnal wages nstead of hgher employment. The resultng ncrease n overall wage dsperson negatvely mpacted aggregate growth. In contrast, Southern ctes also experenced rapd output growth, but much of ths growth showed up as employment growth and only a small amount as an ncrease n the nomnal wage. The resultng decrease n overall wage dsperson fostered aggregate growth, although the mpact was smaller than that one n New York, San Francsco and San Jose. Of course, the potental output gans from spatal reallocaton of labor do not necessarly translate nto welfare gans. The effect on aggregate welfare depends on why wages are not equalzed across ctes n the frst place. 2 If the relatve ncrease n nomnal wages n hgh TFP ctes such as San Francsco and New York s due to restrctons to housng supply, then the aggregate output loss due to dfferences n the margnal product of labor also mply welfare losses. In ths case, removng constrant to housng supply n ctes lke San Francsco and New York would allow more workers to move there and take advantage of ther hgher productvty, ncreasng both aggregate output and welfare. In contrast, f labor supply n New York and San Francsco s low because of ncreasngly undesrable local amentes, then the loss n aggregate output from the gaps n the margnal product of labor does not necessarly reflect a loss n welfare. For example, f equlbrum wages n New York are hgh because people dslke congeston, nose and polluton and need to be compensated for t, then movng more people to New York wll ncrease aggregate output, but wll lower welfare. 2 Formally, we show that aggregate welfare n the Rosen-Roback model s smply aggregate output dvded by a weghted average of the rato of local housng prces to local amentes. Holdng aggregate output constant, hgher housng prces lower aggregate welfare and better local amentes ncrease welfare. 3

5 When we decompose the ncrease n wage dsperson nto the changes due to housng supply and amentes, we fnd that the ncrease s almost entrely drven by the former. Settng amentes back to ther 1964 levels slghtly decreases the overall wage dsperson and ncreases aggregate output, but the effect s quanttatvely small. In contrast, we fnd that constrants to housng supply n ctes wth hgh TFP are a major drver of our fndngs. We use data from Saz (2010) to separate overall elastcty of housng supply n each U.S. cty nto the avalablty of land and muncpal regulatons. We estmate that holdng constant land but lowerng land use regulatons n New York, San Francsco and San Jose to the level of the medan cty would ncrease U.S. output by 9.7%. In essence, more housng supply would allow more Amercan workers to access the hgh productvty of these hgh TFP ctes. We also estmate that ncreasng regulatons n the South would be costly for aggregate output. In partcular, we estmate that ncreasng land use regulatons n the South to the level of New York, San Francsco and San Jose would lower U.S. output by 3%. We conclude that the aggregate gans n output and n welfare from spatal reallocaton of labor are lkely to be substantal n the U.S., and that a major mpedment to a more effcent spatal allocaton of labor s the growng constrants to housng supply n hgh wage ctes. These constrants lmt the number of US workers who can work n the most productve of Amercan ctes. In general equlbrum, ths lowers ncome and welfare of all US workers and amount to a large negatve externalty mposed by a mnorty of ctes on the entre country. Ths paper bulds on two bodes of work. Frst, we buld on the large emprcal work, begnnng wth Rosen (1979) and Roback (1982), on local labor supply and labor demand. The effect of strngent land use regulatons on local housng prces s well documented (Glaeser, Gyourko and Saks, 2005 and 2006; Gyourko and Glaeser, 2005; Saz, 2010), and our paper hghlghts the aggregate negatve mpacts of such regulatons (and the postve effect of the relatve absence of such regulatons n the US South). Our fndngs on the mportance of housng supply constrans are consstent wth those n Ganong and Shoag (2013). Second, we draw on the theoretcal work on systems of ctes n spatal equlbrum. In partcular, Henderson (1981, 1982), Au and Henderson (2006a and 2006b), Behrens et. al. (2014), Eeckout et. al. (2014), Desmets and Ross-Hansberg (2013) and Reddng (2014) model the equlbrum allocaton of resources across ctes. Our approach s most closely related to Desmets and Ross-Hansberg (2013), Reddng (2014) and Gaubert (2014). Desmets and Ross-Hansberg (2013) analyze the effect on the heterogenety of local TFP, amentes and local frctons n the US and Chna, 4

6 Reddng (2014) analyzes on the effect of nternal trade frctons, and Gaubert (2014) analyzes optmal cty sze. We abstract from trade frctons and heterogenety n local TFP to focus on the effect of local housng supply on wage dsperson, aggregate output and welfare. Another closely related paper s Duranton et al. (2015) who quantfy the msallocaton of manufacturng output n Inda caused by msallocaton of land. Our fndng of barrers to labor moblty n the U.S. complements the fndng of broader set of barrers to factor moblty n 83 countres n Gennaol, LaPorta, Lopez-de-Slanes, and Shlefer (2014). The paper s organzed as follows. In Secton 2 we present the model. In Secton 3 we descrbe the data and the key changes n wage dsperson. Emprcal fndngs are n Secton 4. Secton 5 dscusses polcy mplcatons. 2. Model Ths secton examnes the channels by whch local forces n a cty affect aggregate output and welfare. The model s a standard Rosen-Roback model wth a spatal equlbrum. Ctes dffer by local labor demand and local labor supply. Specfcally, cty produces a traded good sold at a fxed prce n the natonal market wth the followng technology (1.1) Y AL K. Here, A denotes total factor productvty, L employment, and K captal. We assume 1. We nterpret A as capturng forces such as cost advantages enjoyed by frms n the cty (access to waterways, ralways, arports, topography, nature of the terran, weather, local nsttutons, labor and envronmental regulatons), demand for products made by the cty, ease of entry, agglomeraton economes or technologcal spllovers that beneft all frms n the cty. Workers can freely move across ctes and ther ndrect utlty gven by WZ (1.2) V. P Here W denotes the nomnal wage, Z amentes, share of expendtures on housng. 3 an exogenously gven rental prce. P the prce of housng n cty, and s the We assume that captal s suppled wth nfnte elastcty at 3 Whle dfferent ctes have dfferent ncome and dfferent prces, the share of expendtures on housng does not vary wth ncome (Davs and Ortalo-Magnes, 2010; Lewbel, Arthur and Krshna Pendakur, 2008), whch suggests that s roughly constant. 5

7 We make several smplfyng assumptons. Frst, the expresson for ndrect utlty mplctly assumes workers do not own the housng stock, but rent from an absentee landlord. Second, we assume that workers have homogeneous tastes over locatons and are perfectly moble across locatons. Ths makes labor supply to a local labor market nfntely elastc. Thrd we assume that TFP and amentes can vary across ctes but are exogenous. Fourth, we assume all ctes produce the same product and do not specalze. Fnally, we assume no heterogenety n labor demand elastcty. We relax all these assumptons later. We now solve for the equlbrum allocaton of employment and wage across ctes. Frst, equatng the margnal product of labor to the cost of labor n each cty and the cost of captal to an exogenously determned nterest rate, employment s: (1.3) A L W Employment s ncreasng n local TFP and decreasng n the nomnal wage, wth an elastcty that depends on the slope of the labor demand curve. After substtutng (1.2) nto (1.3) (1 ) AZ employment can also be expressed as L. Not surprsngly, ctes wth more P employment are those wth hgh local TFP, low housng prces, or hgh qualty amentes. We assume housng prces reflect local demand and supply condtons. Specfcally, we assume P L where s a parameter that governs the elastcty of housng supply wth respect to the number of workers. An ncrease n the number of workers has a larger effect on housng prces when s large. We thnk of heterogenety n as capturng dfferences n both land avalablty and housng regulatons (such as land use regulatons). Ctes wth lmted amount of land and strngent land use regulatons have a large ; ctes wth abundant land and permssve land use regulatons have a small (Glaeser, Gyourko and Saks, 2005 and 2006; Saz, 2010). We can now wrte the equlbrum wage as a functon of three exogenous factors: (1.4) W Z 1 (1 )(1 ) A 1 The equlbrum wage s ncreasng n local TFP and decreasng n amentes wth an elastcty that depends on the local elastcty of housng supply. The frst factor local TFP reflects 6

8 labor demand. Hgher local TFP mples stronger demand for labor and therefore hgher equlbrum nomnal wages, ceters parbus. The other two factors -- amentes and housng supply reflect labor supply. In equlbrum, better amentes mply larger supply and therefore lower nomnal wages. Intutvely, the utlty stemmng from the amentes makes workers wllng to lve n a cty even f ther nomnal wages are lower. More elastc housng supply also mples lower wages, but for a dfferent reason. More elastc labor supply means that n ctes wth postve demand or amenty shocks, the cost of housng ncrease by less. The spatal varaton of wages reflects the varaton n TFP, amentes, and housng supply and the covarance between these varables. 2.1 Aggregate Output and Welfare We now solve for aggregate output and welfare. Frst, we use (1.2) and (1.3) to express welfare as: (1.5) P V Y L Z 1 where Y Y denotes aggregate output. Intutvely, welfare s aggregate output n unts of utlty and P L s the cost mnmzng prce of a unt of utlty (the prce of goods s Z normalzed to one). 4 Second, we solve for aggregate output by mposng the condton that aggregate labor demand s equal to aggregate labor supply (normalzed to one): (1.6) 1 1 W Y Y A W where W WL denotes the employment-weghted average nomnal wage and W s determned by (1.4). Aggregate output s a harmonc mean of the product of local TFP and the nverse of the wage gap of the cty relatve to the mean wage. Housng supply restrctons affect 4 Equaton (1.5) only consders the effect of labor ncome on welfare. If we nstead assume that frm profts accrue to the workers, the sum of labor ncome and profts s proportonal to aggregate output. Therefore, welfare would stll be proportonal to aggregate output dvded by the prce of utlty. 7

9 welfare through ther effect on the average prce of housng and on aggregate output by changng the dsperson of nomnal wages. We can now decompose the sources of aggregate growth n output and welfare. The growth of aggregate output s: (1.7) Y Yt where L A A t1 1 1 j j W 1 t1 A L t, 1 t, 1 W t, A W t, t L t, W t, denotes the hypothetcal cty sze when wages are the same n all ctes. Equaton (1.7) suggests that aggregate output growth can be decomposed nto the effect of local TFP (the frst term n (1.7)) and nto the effect of changes n the spatal dsperson of wages (the second term n (1.7)). The effect of spatal dsperson s gven by W L W 1 1 measured n the two years. Intutvely, ths term measures the rato of aggregate output observed n each year to the hypothetcal output when wages were the same n all ctes n that year (and labor and captal s reallocated n response to the change n the wage dstrbuton). Because the exponent on the relatve wage s greater than one, aggregate output rses when wage dsperson falls (holdng local TFP fxed). 5 The growth of aggregate welfare depends on the same two forces as well as on changes n the prce of utlty, because we have seen n equaton (1.5) that aggregate welfare s equal to aggregate output tmes the prce of utlty (.e. the weghted average of the rato of local amentes to the local housng prce.) Thus there are three channels va whch local shocks affect aggregate welfare: the prce of utlty, the weghted average of local TFP, and the weghted dsperson of wages across ctes. To llustrate these mechansms, consder how changes n local TFP or local amentes affect aggregate output and welfare. Frst, suppose that local TFP rses n a cty. Ths rases the 5 We assume decreasng returns to scale. Wth constant or ncreasng returns to scale, the dstrbuton of employment would be degenerate as the cty wth the hghest TFP would attract all economc actvty. 8

10 weghted average of local TFP, whch ncreases aggregate output and welfare (holdng the prce of utlty constant). The ncrease n local TFP also rases the local housng prce by ncreasng the local demand for housng. Ths ncreases the prce of utlty n all ctes, whch lowers welfare (holdng aggregate output fxed), and ths effect s larger when the local housng supply s nelastc. Fnally, hgh local housng prces ncreases the local wage, but the aggregate effect of a hgher local wage s ambguous. If the hgh local housng prce ncreases the gap between the local wage and the average wage, aggregate output -- and welfare -- falls. When ths s the case, the growth rate of local GDP overstates the contrbuton of the local growth to aggregate output growth. But f the TFP ncrease occurs n a low wage cty, the ncrease n the local wage potentally lowers the overall wage dsperson, whch ncreases aggregate output. In ths case, the growth rate of local GDP understates the local contrbuton to aggregate GDP. Second, consder the effect of a declne n local TFP. Low TFP lowers the average of local TFP, whch lowers aggregate output and welfare. In addton, Glaeser and Gyourko (2005) show that housng prces drop sharply n ctes that suffer from an adverse labor demand shock. In our framework, the declne n housng prces has two addtonal effects. Frst, lower housng prces lowers the prce of utlty, whch offsets the effect of lower aggregate output on welfare. The drop n housng prces also lowers the local nomnal wage, but as before the aggregate effect depends on whether the local nomnal wage was above or below the natonwde mean. If the local wage s above the mean, the declne n the nomnal wage potentally narrows the margnal product gap, whch ncreases aggregate output and welfare. In ths case, local GDP falls because of the drect effect of the declne n local TFP and the fall n the local wage. However, even when local output growth s negatve, the net effect on aggregate output growth may well be postve f the effect of the narrowng wage dsperson s larger than the drect effect of the declne n local TFP. In the emprcal results, we wll show that ths appears to have been the case n many US ctes where local TFP fell. Thrd, consder the effect of an mprovement n amentes. When amentes mprove n hgh wage ctes, ths ncreases the average level of amentes and lowers overall wage dsperson. Here the declne n wage dsperson unambguously mproves welfare, and the local output growth understates the contrbuton of the local economy to aggregate output. On other hand, when amentes mprove n low wage ctes, ths also ncreases the average level of amentes, but ncreases the overall wage dsperson. Here, although local GDP ncreases, the mprovement n amentes lowers aggregate output. The output declne due to ncreased wage dsperson offsets some of the drect effect of the mprovement n the average level of amentes. 9

11 In the emprcal secton of the paper, we use ths framework to provde two calculatons. Frst, we measure the contrbuton of each US cty to aggregate US growth. We show that the model-based calculaton of the contrbuton of each cty to aggregate growth s emprcally qute dfferent from a naïve accountng-based calculaton based on the measured growth of local output. Second, we use ths framework to calculate the counterfactual output and welfare growth n the US under dfferent assumptons on wage dsperson. We ask how much faster output and welfare growth would have been f wage dsperson had not ncreased n the US but had remaned constant and lnk the ncrease n wage dsperson to specfc housng supply polces on the part of US ctes. 2.2 Extensons We now consder the effect of several extensons of our basc model. Ownershp of Housng Stock: We have assumed that workers do not own the housng stock so that an ncrease n average housng prces lowers welfare holdng aggregate output fxed. Suppose we assume nstead that the housng stock s owned by the workers n equal proportons, rrespectve of where they lve. Thnk of workers as ownng equal shares n a mutual fund that own all the housng n the US. All the equatons are the same, except that welfare s gven by P V Y LhP L Z 1 where h denotes per-capta housng consumpton n cty. After mposng the condton that the share of nomnal expendtures on housng s equal to, the change n housng prces has the same effect on nomnal ncome as on the average prce of housng. In ths case, changes n housng prces only affect welfare through the effect of the dsperson of the nomnal wage on aggregate output, but changes n the average prce of housng has no effect on welfare. The most realstc case s of course the one where workers own housng n the cty where they lve. In ths case, changes n house prces nduced by our counterfactuals have redstrbutve effects: workers n some areas are made better off, whle workers n other areas are made worse off. But n the aggregate, the conclusons are dentcal to the case n whch the housng stock s owned by the workers n equal proportons, rrespectve of where they lve: housng prces only affect welfare through the effect of the dsperson of the nomnal wage on aggregate output. Thus, estmates of the effects based on the baselne model remans vald n the aggregate. 10

12 Specalzaton by Ctes: Our baselne model assumes that the output of a cty s a perfect substtute for the products made by other ctes. Suppose nstead that each cty makes a dfferentated product wth a producton functon gven by Y AL. The demand for the (1 ) 1 1 product of each cty s determned by utlty defned as U j Yj hj Z j where U j denotes utlty n cty j, Y j denotes consumpton of cty 's output n cty j, and h j s per-capta housng n cty j. The labor demand n each cty s gven by A L W 1 and aggregate output 1 W by Y A W These last two equatons are dentcal to (1.3) and (1.6) when we 1 substtute wth 1. 6 In words, a model wth constant returns to scale and where ctes 1 are specalzed n producton s somorphc to a model where ctes produce dentcal products and wth a decreasng returns to scale producton functon. Fnally, assumng that the output good s avalable n all ctes at the same prce, we can normalze the cost-mnmzng prce of one unt of the CES aggregate of the output good welfare s stll gven by (1.5). 1 1 Y to one. Wth ths normalzaton, Imperfect Labor Moblty: We can also relax the assumpton of nfnte labor moblty. Suppose that workers dffer n preferences over locatons. Specfcally, suppose the ndrect WZ utlty of worker j n cty s gven by Vj j where s a random varable measurng the jt P taste of ndvdual j n cty as, for example, n Morett (2010). A larger jt means that worker s partcularly attached to cty jfor dosyncratc reasons. We assume that workers locate n the cty where her utlty V j s maxmzed. In ths case, workers tend to move toward ctes wth hgh real wages and good amentes, but they are not nfntely senstve to small wage 6 Snce labor s the only factor of producton n the dfferentated products model, we set the captal share to zero n the baselne model for comparablty. 11

13 dfferences. The mplcaton s that only margnal workers are ndfferent across ctes and all the other workers are nfra-margnal. To make ths model tractable, we assume that are ndependently dstrbuted and drawn jt from a multvarate extreme value dstrbuton. Specfcally, we follow Klne and Morett (2013) N and assume the jont dstrbuton of s gven by F ( jt g 1,.., N) exp where the parameter 1/ governs the strength of dosyncratc preferences for locaton and therefore the degree of labor moblty. If 1/ s large, many workers requre large real wage or amenty dfferences to be compelled to move. On the other hand, f 1/ s small, most workers are not partcularly attached to one communty and wll be wllng to move n response to small dfferences n real wages or amentes. 7 In ths model, employment n a cty s stll gven by (1.3) and aggregate output by (1.6). What s new s that the Rosen-Roback condton that dfferences n wages across ctes are drectly proportonal to the rato of housng prces to amentes (equaton (1.5)) no longer holds. Instead, the (nverse) labor supply equaton of a cty s gven by: PL (1.8) W Z Ths says even when housng prces and amentes are the same n all ctes, wages wll dffer between large and small ctes wth an elastcty that depends on the heterogenety n preferences for locaton. Intutvely, hgher wages n large ctes are needed to compensate margnal ndvduals to lve n the cty. When we endogenze the housng prce as a functon of cty sze and the local housng supply elastcty and mpose the condton that labor demand s equal to labor supply, the equlbrum nomnal wage s gven by: 1 1 (1 ) (1 )( 1/ ) 1/ (1 ) (1 )( 1/ ) 1 (1.9) W A Z Fnally, whle utlty dffers across workers, average utlty s the same n all ctes and gven by: 1 1 P (1.10) V Y L Z In sum, condtonal on the observed changes n the wage dstrbuton, the mplcatons for cty sze and aggregate output s the same as before and does not depend on. But the effect of 1 7 None of the substantve results here hnge on the extreme value assumpton. See Klne (2010) and Busso, Gregory, and Klne (2013) for analyses wth a nonparametrc dstrbuton of tastes. 12

14 local TFP, amentes, and the local housng supply elastcty on the wage dstrbuton (and by extenson on aggregate output and average welfare) depends crtcally on. Heterogenety n Labor Demand Elastcty: Our basc model assumes that the output elastcty wth respect to labor s constant. We can relax ths assumpton. Specfcally, suppose that total output of n a cty s the sum of the output produced n dfferent ndustres ndexed by j: j Y Y j j j where Y AL K denotes output of ndustry j n cty. Note that the labor and captal shares are now ndexed by ndustry. In ths case, there are two changes n the key endogenous varables. Frst, total employment n a cty s gven by: L j 1 jaj 1 j j 1 j W j Second, aggregate output Y s mplctly defned by j j j W Aj j Y W 1 j 1 j j Yj where j s the aggregate labor share. All the other equatons are the same. Y j Endogenous TFP and Amentes: We can also relax the assumpton that TFP and amentes are exogenous. In practce, t s plausble to thnk that both TFP and amentes are endogenous to changes n cty sze. For example, a large lterature n urban and regonal economcs posts that n the presence of agglomeraton economes, A depends postvely on L as denser ctes are more productve. Ths would make our counterfactual exercse conceptually more complcated, as changes n cty sze would nduce an endogenous feedback effect through the agglomeraton economes. In practce, our estmates of aggregate effects are not affected f the elastcty of agglomeraton s constant across ctes. Wth constant elastcty, reallocaton of workers across ctes has no aggregate mpact, because the ncreases n agglomeraton economes experenced by ctes that grow n sze are exactly offset by the losses n agglomeraton economes experenced by ctes that shrnk n sze. Emprcally, the assumpton of constant elastcty 13

15 appears consstent wth the emprcal evdence on US manufacturng (Klne and Morett, forthcomng). In terms of amentes, a large lterature posts that amentes mght depend on cty sze and/or densty. Our baselne assumpton of exogenous amentes does not requre that amentes are necessarly fxed (as n the case of weather). It allows amentes --n partcular publc servces lke schools, publc transt or polce--to expand (contract) as the counterfactual populaton of the area expands (contracts), as long as the per-capta avalablty remans stable at current levels. Whle ths s realstc for many publc servces, t s possble that the per capta amount of other amentes depend on cty sze. Ths could happen, for example, f congeston s an ncreasng functon of cty sze.e. more people n a cty mean more nose, traffc and polluton. It could also happen for the opposte reason, f more people mprove urban amentes such as varety of restaurants and varety of cultural events. Glaeser (2010) has argued that ctes lke London, New York and San Francsco are attractve precsely because of ther urban amentes stemmng from hgh densty of resdents. Thus hgher populaton densty can create both negatve and postve externaltes. Irrespectve of the sgn, the possblty of ths type of endogenous amentes makes our counterfactual exercse more complcated because changes n the number of workers nduce an endogenous feedback effect on resdents welfare through changes n amentes. 8 Note that what matters s the aggregate effect. Our counterfactual exercse ncreases sze of some ctes and reduced sze of other ctes. If amentes declne n the frst group and mprove n the second group (or vce versa), the queston that matters for us s the net effect n the aggregate. To see ths more clearly, consder the followng extenson of our model. Suppose that the producton functon s stll gven by (1.1) and welfare by (1.2) but amentes are now gven by Z ZL. Here, Z denotes the component of per capta amentes exogenous to cty sze and L the component that vares endogenously wth the sze of the cty. Cty sze s gven by AZ L P 1 1 (1 )(1 ) (1 ) and aggregate output and welfare by 8 If the elastcty of endogenous amentes wth respect to cty sze s constant across ctes, then the net effect on aggregate welfare s zero, as gans n some ctes are off by losses elsewhere. 14

16 1 (1 )(1 ) Z P Y A 1 Z j Pj Lj j 1 1 j j j V Y P Z L. j (1 )(1 ) 1 1 (1 )(1 ) In the end, the sze and sgn of the parameter s an emprcal queston. If 0 then our counterfactual wll mply welfare losses that wll reduce the welfare benefts stemmng from ncreased output, as t ncreases the sze of ctes that are already large, further exacerbatng congeston. On the other hand, f 0 then our counterfactual wll mply welfare gans that wll magnfy the welfare benefts stemmng from ncreased output. If 0 then our counterfactual wll be measurng welfare gans correctly. The exstng evdence ndcates that the assumpton that endogenous amentes are ether ncreasng or do not depend on cty sze. Ahlfeldt, Reddng, Sturm and Wolf (2014) and Damond (2014) fnd that urban amentes slghtly ncrease wth densty n Germany and the US. The most drect estmate of for the US s found n Albouy (2012). He shows that qualty of lfe n a cty s postvely correlated wth the cty populaton, when no controls are ncluded. But when natural amentes such as weather and coastal locaton are controlled for, Albouy (2012) fnds no relatonshp between cty populaton and qualty of lfe. Ths suggests that ctes wth better natural amentes are bgger (just as predcted by the equlbrum expresson above for cty sze), but endogenous amentes are not sgnfcantly better or worse n large ctes compared to small ctes. 9 If Albouy's estmates are correct, then allowng for endogenous amentes should not change our estmates of aggregate mpacts very much. Fnally, t s worth hghlghtng an mportant caveat. It s n prncple possble that nelastc housng supples may contrbute to the hgh TFP n ctes lke San Francsco and New York. Ths could happen, for example, f productvty s endogenous to college share (as n Morett 2004 and Damond 2013) and college workers more wllng to pay hgh house prces. In ths case, TFP would be endogenous wth respect to housng supply, and our framework would not be adequate to estmate counterfactual output. 9 Ths s true wthn the range of cty szes observed n the data. There s of course no guarantee that f one were to sgnfcantly expand the largest ctes n the US, ths would reman true. 15

17 3. Data and Key Facts About the Spatal Dsperson of Wages n the U.S. 3.1 Data The deal data for ths project would have three features: they go back n tme as much as possble; they have detaled and consstently defned geocodes; and they have detaled ndustry defnton. To approxmate t, we use a combnaton of data sources taken from the 1964, 1965, 2008 and 2009 County Busness Patterns (CBP); the 1960 and 1970 Census of Populaton; the 2008 and 2009 Amercan Communty Survey (ACS); and the 1964 and 2009 Current Populaton Survey (CPS). Snce the earlest year for whch we could fnd cty-ndustry level data on wages and employment s 1964, we focus on changes between 1964 and Employment, Wages and Rents: Data on employment and average wages are avalable at the county and county-ndustry level from the CBP and are aggregated to MSA and MSA-ndustry level. The man strength of the CBP s ts fne geographcal-ndustry detal and the fact that data are avalable for as far back as The man lmtaton of the CBP s that t does not provde worker level nformaton, but only county aggregates, and t lacks nformaton on worker characterstcs. Obvously dfferences n worker skll across ctes can be an mportant factor that affects average wages. In addton, unon contracts may create a wedge between the margnal product of labor and the wage, as unon wages may contan economc rents. We augment CBP data wth MSA-level nformaton on worker characterstcs from the Census of Populaton, the ACS and CPS: three levels of educatonal attanment (hgh school drop-out, hgh school, college); race; gender; age; and unon status. To purge average wage from dfferences n worker characterstcs across ctes, we calculate a resdual wage that condtons for geographcal dfferences n the composton of the workforce. Specfcally, we use natonwde ndvdual level regresson based on the CPS n 1964 and 2009 to estmate the coeffcents on worker characterstcs, and use those coeffcents to compute resdual wages based on cty averages. 11 We end up wth a balanced sample of 220 MSA s wth non-mssng values n 1964 and The Data Appendx provdes addtonal nformaton on how we defned the varables, the 10 The publshed tabulatons of the Census of Populaton provde MSA level averages of worker characterstcs, but the ndvdual level data on employment and salary wth geocodes s not avalable from the publc verson of the Census of Populaton on a systematc bass untl Only a thrd of metro areas are dentfed n the 1970 Census. 11 / Resdual wage s defned as W X b where W s the average wage n the MSA, X s the vector of average workers characterstcs n the MSA, and b s a vector of coeffcents on workers characterstcs from ndvdual level regressons estmated on natonwde samples. 12 These MSAs account for 71.6% and 72.8% of US employment n 1964 and 2009, respectvely, and 74.3% and 76.3% of the US wage bll n 1964 and

18 lmtatons of the data, and presents summary statstcs. Appendx Fgure A1 shows that n 2009 the estmated average resdual wage obtaned from MSA-level data correlates well wth average resdual wage obtaned from ndvdual level data. (We cannot do the same for 1964, whch s why we rely on MSA-level data.) Housng Supply: Data on housng supply are from Saz (2010). For each MSA, these data provde overall elastcty of housng supply as well as ts two man determnants: land avalablty and land use regulatons. Land use regulatons are measured usng the Wharton Resdental Land Use Regulatory Index, orgnally obtaned by Wharton researchers through a detaled survey of muncpaltes n 2007 and aggregated up at the MSA level by Saz. It s the best avalable measure of dfferences n land use restrctons. We follow hs estmates (Table 5, column 2) to dvde overall supply elastcty nto the part that reflects land use regulatons and the part that reflects land avalablty. Technology: Fnally, to take the model to the data, we need to specfy the technology parameters. In our baselne estmates, we assume a labor share of 65 percent and a captal share of 25 percent, whch mply that the proft share 1 s 10 percent. The assumpton that the labor share s 65 percent s consstent wth BEA data (BEA, 2013), data n Pketty (2014), and Karabarbouns and Neman's (2014). The assumpton that the proft share s 10 percent s consstent wth Basu and Fernald's (1997) estmates of the returns to scale n U.S. manufacturng as well as wth estmates n Atkeson, Khan and Ohanan (1997). In addtonal estmates, we relax ths assumpton. Frst, we provde varous alternatve estmates under dfferent assumptons on and. In these models, we ether vary and ndvdually or we vary the degree of returns to scale. Second, n separate models, we relax the assumpton that technology s the same across all ctes and years by allowng the technology parameters to vary by ndustry and over tme. Because the geographcal locaton of ndustres s dfferent for dfferent ctes, ths assumpton allows dfferent ctes to have dfferent technologes. In practce, we use a dataset that s analogous to the one used n the baselne analyss, but that ncludes separate observatons (and a separate technology) for each 1-dgt 17

19 ndustry n each cty n each year. We use data on the labor share by ndustry n 1964 from Close and Shulenberg (1971) for 1964 and smlar data for 2009 from BEA (2013) Changes n the Spatal Dsperson of Nomnal Wages The model n the prevous secton hghlghts the mportance of wage dfferences across ctes for aggregate output. It ndcates that larger wage dfferences result n lower output, everythng else constant. Intutvely, wage dsperson across ctes reflects varaton n the margnal product of labor. If labor s more productve n some areas than n others, then aggregate output may be ncreased by reallocatng some workers from low productvty areas to hgh productvty ones. For example, n 2009 average nomnal wages n San Jose, CA were twce as large as nomnal wages n Brownsvlle, TX, presumably because the margnal product of labor n San Jose s twce as large. If some workers were moved from Brownsvlle to San Jose, aggregate GDP would ncrease because more workers would have access to whatever productve factor generates hgh productvty n San Jose. In prncple, aggregate output s maxmzed when the margnal product of labor s equalzed across locatons. Emprcally, the spatal dstrbuton of nomnal wages across US metropoltan areas s sgnfcantly more dspersed n 2009 than t was n 1964, suggestng a negatve effect on output growth. Fgure 1a plots the weghted dstrbuton of the uncondtonal average wage n a MSA n 1964 and 2009 (after removng the mean US wage n each year), where the weghts are MSA employment n the relevant year. It s clear that the 2009 dstrbuton s more sgnfcantly dspersed. It s also clear that the rght tal -- whch ncludes ctes wth average wages that are 50% above the mean -- has become thcker. 14 The bump of the rght tal ncludes New York, San Francsco and San Jose. Table 1a quantfes the change n the dsperson n average nomnal wage. Panel A ndcates that the employment-weghted standard devaton (column 1), nterquartle range (column 2), and the range (column 3) of the log average MSA wage ncreased sgnfcantly from 1964 to 2009 (by.07 log ponts,.10 log ponts, and.38 log ponts respectvely). Panel B controls for the average wage n nne Census dvsons and t suggests that ncreases n wage dsperson s not just a regonal phenomenon, but t occurs even wthn Census dvsons. Indeed, controllng 13 No hstorcal data exst on captal share by ndustry or by cty. In both years, we retan the assumpton of a 10% proft share (Basu and Fernald, 1997). 14 Weghtng s emprcally mportant. The unweghted dstrbuton shows a more lmted ncreased n dsperson (see Appendx Fgure A2). As our model makes clear, the weghted dstrbuton s the relevant one for our purposes. 18

20 for regonal wage dfferences generates a larger ncrease n the wage dsperson, so regonal wage dfferences have declned over tme. Panel C shows that a non-trval part of the ncrease n dsperson s due to three large ctes wth hgh output growth over the last 50 years: New York, San Francsco, and San Jose. Droppng these three ctes has a sgnfcant effect on the rght tal of the dstrbuton. The standard devaton and the range of the log average wage when we exclude these three ctes ncrease by much less from 1964 to These fndngs are not drven by dfferences n observable worker characterstcs across ctes. Fgure 1b and Table 1b present the spatal dsperson of the average of the resdual wage n each MSA. 15 Controllng for changes n worker composton does not alter the pcture of ncreased spatal dsperson between 1964 and The pcture that emerges ndcate that () spatal dsperson has ncreased sgnfcantly; () such ncrease s not all concentrated n one specfc regon; and () New York, San Francsco and San Jose account for an mportant part of such ncrease. These fndngs are generally robust. Frst, all the results are dentcal f we use 2007 data (pre-recesson) nstead of Second, our approach of controllng for workers characterstcs assumes that the effect of workers characterstcs s the same everywhere n the country, but t s possble that the return to these characterstcs (such as educaton) vares across ctes (Dahl, 2003). To see whether ths matters emprcally, we estmate models where we allow the effect of workers characterstcs on wages to vary by regon or by state. When we do ths, the resultng spatal dstrbuton of wage resduals s very smlar to that shown n Table 1b. A potental concern s that we cannot control for unobserved dfferences n worker ablty. It s possble that average unobserved ablty dffers between ctes, and that some of the documented wage dfferences across ctes are not dfferences n the margnal product of labor, but dfference n the qualty of labor. We cannot completely rule out the possblty of unobserved worker heterogenety. However, three consderatons are worth mentonng. Frst, the fact that the uncondtonal 15 The fve ctes for whch the dfference between uncondtonal and condtonal wages s the largest are, Madson WI; Ann Arbor, MI; Boston, MA; Champagn-Urbana, IL; State College, PA. In other words, controllng for educaton and other workers characterstcs has the largest mpact n unversty towns and other ctes wth very hgh densty of college educated workers. By contrast, the fve ctes for whch the dfference between uncondtonal and condtonal wages s the smallest are McAllen, TX; Brownsvlle, TX; Vsala, CA; Yakma, WA; and Bakersfeld, CA. Controllng for educaton and other workers characterstcs has the smallest mpact n ctes that have a labor force wth low levels of schoolng and hgh levels of mnorty workers. 16 As explaned n the Appendx, to ncrease the sample sze, our 2009 data actually ncludes 2008 and

21 dstrbuton (Fgure 1a) s bascally the same as the dstrbuton condtonal on observable worker characterstcs (Fgure 1b) should allevate the concern at least n part. Second, recent evdence based on longtudnal data that follow workers movng from low wage ctes to hgh wage ctes ndcates that ths problem may be lmted once educaton s controlled for. Baum-Snow and Pavan (2012), for example, fnd that sortng on unobserved ablty wthn educaton group contrbutes lttle to observed dfferences n wages across ctes of dfferent sze. Smlarly, De La Roca and Puga (2012) fnd that workers n ctes that are bgger and have hgher wages do not have hgher unobserved ntal ablty, as reflected n ndvdual fxed-effects. These fndngs are consstent wth Glaeser and Mare (2001), who show that workers who move from low wage areas to hgh wage areas experence sgnfcant wage ncreases and that ths s not just the result of sortng by ablty. We also pont out that what matters for our analyss s not merely the possblty of dfferences n unobserved ablty n a cross-secton of ctes. Rather s whether these dfferences have changed dfferentally over tme. Thrd, we have explored the relatonshp between worker ablty and nomnal wages. Specfcally, we have used NLSY data to relate the average AFQT scores to the nomnal wage across metropoltan areas. Ths data ndcates that workers n hgh nomnal wage MSAs tend to have hgher AFQT scores, but the correlaton attenuates and becomes statstcally nsgnfcant once we ntroduce controls for educaton, race, and ethncty. 17 The flpsde of the ncrease n the dsperson n wages s an ncrease n the dsperson n housng costs, snce n equlbrum workers need to be compensated for housng costs. Panel A n Appendx Table A2 shows that the dsperson n average rent has ncreased between 1964 and Rents are a good approxmaton to the user cost of housng. In panel B we show the correspondng fgures for housng prces. The ncrease n the spatal dsperson of housng prces s larger than that of housng rents. 4. Emprcal Fndngs We now take the model to the data. Frst, we decompose aggregate GDP growth nto the contrbuton of each US cty and compare t wth a naïve accountng calculaton (secton 4.1). Second, we turn to the ncreased dsperson of wages and calculate how much larger US GDP 17 We frst regress log AFQT scores on log nomnal wages. We then replcated the same regresson controllng for the same vector of controls used n panel B of table 1b. Both regressons are weghted by MSA employment. Whle the coeffcent s postve n the frst regresson, t s statstcally ndstngushable from zero n the second regresson. However, the small sample sze precludes defntve conclusons. 20

22 would be n the counterfactual where the spatal dsperson of wages s fxed from 1964 to 2009 (secton 4.2). We then turn to the causes of ncreased dsperson of wages to dscuss ts welfare mplcatons (secton 4.3). Fnally, we dscuss lmtatons of our approach (secton 4.4). 4.1 Local Growth and Aggregate Growth Equaton (1.7) allows us to calculate the contrbuton of each cty to aggregate growth n 1964 and Ths calculaton s presented n Table 2 and Fgures 2a-2e. Fgure 2a plots the percentage contrbuton of the 220 ctes to aggregate growth from 1964 to 2009 (on the y-axs) aganst the growth of local GDP as a percentage of aggregate GDP growth over the same perod (on the x-axs). To be clear, the calculaton on the y-axs s based on the model (specfcally on equaton (1.7)) whle the x-axs s the growth n local GDP as a rato of aggregate GDP growth. 18 We call the latter the naïve accountng calculaton. The sold lne s the 45 degree lne so ctes that le above the 45 degree lne contrbute more to growth than s apparent from ther measured GDP growth, and ctes below the 45 degree lne contrbute less to growth than suggested by ther output growth. If all the observatons le on the 45 degree lne, the growth rate of aggregate GDP would smply be gven by the weghted average of local GDP growth. The frst feature that s apparent n Fgure 2a s that the dsperson of the accountng measure of the contrbuton of each cty s much wder than the actual contrbuton. The range of the accountng calculaton of the contrbuton of a cty to aggregate growth s 20 percent whle the range of the model based calculaton s only 5 percent. The second and most mportant feature of Fgure 2a s that there are szable and systematc dfferences between local growth and local contrbuton to aggregate growth. For example, growth of New York s GDP was 12 percent of aggregate output growth from 1964 to However, vewed from the lenses of the Rosen-Roback model, New York was only responsble for less than 5 percent of aggregate output growth. The dfference s because much of the output growth n New York was manfested as hgher nomnal wages, whch ncreased the overall spatal msallocaton of labor. On the other extreme, Detrot s GDP fell dramatcally from 1964 to Although one mght expect the contrbuton of Detrot to be negatve because of the 18 The "accountng" calculaton s based on the accountng dentty 21 y y y t 1 t, 1 t, Lt, where the t and t 1 yt y, t y subscrpts denote tme, y denotes aggregate GDP per worker (n the country), y s GDP per worker n cty, and yt, 1 yt, L the employment share n cty. The "contrbuton" of cty s measured by Lt, y y. t,

23 declne measured local output, the net contrbuton of Detrot to aggregate output growth s postve. The dfference n the case of Detrot s because much of the declne n local GDP n Detrot was drven by a declne n nomnal wages. And n Detrot, nomnal wages n 1964 were sgnfcantly hgher than the natonwde mean so the declne n the nomnal wage from 1964 to 2009 lowered the overall wage dsperson whch ncreases aggregate output. Other ctes dsplay large dfferences: Chcago and Los Angeles, for example, are well above the 45 degree lnes. Whle ther contrbuton to aggregate growth as calculated from equaton (1.7) s not unlke New York s contrbuton, the growth of ther GDP as a fracton of overall growth s much smaller. Overall, Fgure 2a shows that the relaton between local growth and local contrbuton to aggregate growth s postve, but wth an elastcty that s much less than one. A regresson of the varable on the y-axs on the varable on the x-axs yelds a coeffcent (standard error) of.295 (.018), wth an ntercept equal to.320 (.033). The slope s statstcally dfferent from one and the ntercept s statstcally dfferent from zero. Ctes wth large postve shocks to ther local economy tend to contrbute less to aggregate growth than ther local gans would suggest. At the same tme, ctes wth large negatve shocks tend to contrbute more than ther local losses would suggest. Ths dscrepancy between local growth and local contrbuton reflects changes n each cty relatve wage. Fgures 2b-2e and Table 2 separately present the contrbuton of four groups of ctes. Fgure 2b presents the actual vs. the accountng calculaton of New York, San Francsco, and San Jose to aggregate output growth from 1964 to All three ctes le sgnfcantly below the 45 degree lne. Although local output grew rapdly n all three ctes, so dd the gap between local wages and the natonwde wage. The frst row n Table 2 ndcates that although local GDP growth was almost 20 percent of aggregate US output growth, the actual contrbuton of these three ctes was much lower, at 6 percent of US output growth. Fgure 2c shows the contrbuton of 37 ctes n the Rust Belt. As can be seen, all the Rust Belt ctes le above the 45 degree lne: the actual contrbuton of Rust Belt ctes s larger than suggested by observed changes n local GDP. What s drvng ths dscrepancy s that nomnal wages n Rust Belt ctes were typcally above the natonwde mean n And snce 1964 wages have fallen and have thus narrowed the gap between wages n the Rust belt and the natonwde mean. What s perhaps more surprsng s that although local GDP growth s negatve n every Rust Belt cty, the actual contrbuton of every Rust Belt cty to aggregate growth s postve. Although the declne n labor demand caused by the declne of manufacturng presumably mples that the contrbuton of the Rust Belt ctes to aggregate 22

24 growth would be negatve, the allocatve effects of the sharp declne n the wage gap has a larger effect on aggregate growth. Table 2 shows that the Rust Belt ctes contrbuted as much as New York, San Jose, and San Francsco (taken together) to aggregate output, despte the sharp declne n GDP n the Rust Belt ctes. Fgure 2d presents the contrbuton of 86 Southern ctes. In the perod under consderaton, the South of the US has grown more rapdly than the rest of the country. Washngton, DC, Houston, Atlanta, and Dallas are among fve fastest growng ctes n the US (the fastest growng cty s New York). All ctes le sgnfcantly below the 45% lne because the gap n local wages and the natonwde wage ncreased n all these ctes. Therefore, the contrbuton of the large Southern ctes to aggregate growth s less than suggested by ther output growth. The fact that relatve wages ncreased n the large southern ctes also suggests that the standard narratve that growth n these ctes was drven by mproved amentes (hot weather became more tolerable wth ar condtonng) and cheap housng s not the entre story. If the only change n the South was that amentes have mproved or housng became cheaper, then relatve wages should have fallen n these ctes whereas the opposte s true. Taken together, Southern ctes were responsble for 42 percent of aggregate growth n the US (Table 2). Ths s szeable to be sure, but 20 percentage ponts lower than what one mght nfer from the observed growth of GDP n the Southern ctes. Fgure 2e presents the contrbuton of the remanng large US ctes. Ths group ncludes 19 large ctes wth 2009 employment above 600,000 that are not n any of the prevous three groups. Here, the story s more mxed. There are ctes where the observed local growth almost exactly measures the actual contrbuton. These are ctes such as Boston, Portland, and Salt Lake Cty. There are also ctes where the growth contrbuton s larger than suggested by local growth. These are ctes such as Chcago, Los Angeles, and Phladelpha where relatve wages have fallen and the gap n the margnal product of labor relatve to the rest of the country has narrowed. Fnally, there are also ctes where the growth contrbuton s smaller than suggested by the local output growth numbers. For example, Phoenx, s one of the fastest growng metro areas n the country; based on the accountng measure, GDP growth n Phoenx accounts for sx percent of aggregate US growth. Yet, much of ths growth has accompaned by a declne n wages n Phoenx, whch n the framework of the Rosen-Roback model must be drven by a declne n relatve housng prces or an mprovement n relatve amentes. And snce wages n Phoenx were already below the natonwde mean n 1964, the further declne n wages ncreases the wage gap. Las Vegas and Rversde have smlar experences. Essentally, Phoenx, Las 23

25 Vegas and Rversde have attracted many resdents because of good weather and abundant supply of cheap housng but ths reallocaton results n a loss n aggregate output because t has brought more people workng n ctes where the margnal product of labor s low. Ths effect s remnscent of the Dutch dsease n two-sector models of growth. The bottom lne s that almost three quarters of aggregate US output growth from 1964 to 2009 was drven by local forces n southern US ctes and the group of "large" 19 ctes. And despte the large dfference n local GDP growth between New York, San Jose, and San Francsco and the Rust Belt ctes, both groups of ctes had roughly the same contrbuton to aggregate output growth (about 6 percent). In Table 3 we probe the robustness of our estmates usng dfferent assumptons on technology. Recall that our baselne estmates assume that α =.65 and η =.25 n all ctes n both years (column 1). In columns 2 and 3, we keep the returns to scale constant and alter α or η. The estmates are almost dentcal to the baselne estmates. In columns 4 to 7 we alter the labor or captal share to vary the returns to scale. In columns 4 and 5, we ncrease return to scale, as α + η ncreases from.9 to.95. In columns 6 and 7 we alter the labor or captal share to decrease the returns to scale -- α + η decreases from.9 to.85. Entres are vrtually unchanged. So far we have constraned the technology to be the same n all ctes and ndustres. Next, we relax our assumptons on technology by allowng technology to vary across ctes and years. Specfcally, we allow labor and captal shares n 1964 and 2009 to be dfferent n dfferent ndustres. Because the geographcal locatons of ndustres are not the same, ths allows dfferent ctes to have dfferent technologes. In practce, we use a dataset that s analogous to the one used n the baselne analyss, but that ncludes separate observatons for each 1-dgt ndustry n each cty n each year. We assume that workers can move freely across ndustres wthn each cty, so that the wage s the same. The entres n column 8 ndcate that the results are not very senstve to ths generalzaton. We have performed several addtonal checks, and found our results to be generally robust. For example, n some models resdual wage s estmated usng models where the coeffcent of workers characterstcs s allowed to vary not just by year, but also by state. Results dd not change sgnfcantly. We have also re-estmated our models droppng the two ctes that n Fgure A1 are outlers, and found smlar estmates We have also re-estmated our 2009 model droppng the restaurant sector, as one where mnmum wage workers are partcularly prevalent and therefore the assumpton that equates wages wth margnal product of labor may be volated. The correlaton of the share that each cty contrbutes to 2009 output wth and wthout the restaurant sector s.99. We can t do the same for 1964, snce ndustry defnton n 1964 s less dsaggregated. 24

26 4.2 Wage Dsperson and Aggregate Growth Equaton (1.7) decomposes the growth rate of aggregate output nto two components: growth of local TFP and change n the spatal dsperson of wages. It ndcates that ncreases n the spatal dsperson of wages negatvely affect aggregate growth: for a gven local TFP growth, a more dspersed spatal wage dstrbuton results n slower growth. Emprcally, we have seen that the spatal dsperson of wages across US ctes ncreased sgnfcantly from 1964 to the standard devaton, for example, s now double relatve what t used to be n We now quantfy the effect of ths ncrease n wage dsperson on the rate of growth of aggregate output between 1964 and 2009 and on the level of output n We estmate counterfactual output under the scenaro where the dsperson of wages across ctes remaned constant between 1964 and Specfcally, we calculate the counterfactual where the relatve wage of a cty n 2009 s equal to the relatve wage of the same cty n We take local TFP n each cty as fxed and allow labor and captal to endogenously reallocate across ctes n response to the change n the dstrbuton of local housng supply and amentes. Clearly wages are an endogenous varable. As we have seen, they are determned by local TFP, amentes and elastcty of housng supply (equaton (1.4)). But the effect of changes n the wage dsperson on aggregate output growth does not depend on the sources of wage dsperson. (The effect on welfare does depend on the source of wage dsperson. We take up the queston of the exact mechansm underlyng the change n the spatal wage dsperson n the next secton.) In terms of output growth, when we take equaton (1.7) to the data, we fnd that the growth of local TFP boosts aggregate GDP by 2.5 percent a year from 1964 to 2009, holdng the spatal dsperson of wages fxed. The ncreased spatal dsperson of wages lowers aggregate GDP growth by 0.3 percent a year, holdng constant local TFP. The net effect of these two forces s that aggregate GDP grew by 2.2 percent a year from 1964 to In other words, under the counterfactual scenaro where wage dsperson dd not ncrease n the U.S., aggregate yearly GDP growth from 1964 to 2009 would have been 0.3 percentage ponts hgher. In terms of output level, the ncrease n the spatal dsperson of wages resulted n a sgnfcantly lower level of output n Ths effect s quantfed n Table 4. The frst row ndcates that f the spatal dsperson of relatve wages had not changed, 2009 U.S. GDP would be 13.5% hgher. Gven that US GDP n 2009 was 14.5 trllon, ths mples an addtonal annual aggregate ncome of $1.95 trllon. Gven a labor share of.65, ths amounts to an ncrease of 25

27 $1.27 trllon n the wage bll, or $8775 addtonal salary per worker (f number of workers was fxed). 20 More than half of US workers would move under ths scenaro (column 2). In the second row of Table 4, we set the dstrbuton of nomnal wages n 2009 equal to ts 1964 level only n New York, San Francsco and San Jose. Remember that the ncrease n relatve wages from 1964 to 2009 was partcularly pronounced n these ctes. In addton, these ctes are among the largest ctes n the US n terms of TFP so the effect on aggregate output growth of the change n the change n the wage n these three ctes s largely to be large. Aggregate output would ncrease by 13.2% f the relatve average wage n only these three ctes s set to ther 1964 level. 54% of U.S. workers would relocate. 21 The thrd row llustrates the effect on aggregate output when the dstance from the mean wage n the Rust Belt ctes s set to gap n As can be seen, the effect s small, as aggregate 2009 output ncreases by 0.5% and only 9% of workers relocate. The last row shows the effect on aggregate output when the dstance from the mean wage n Southern ctes s set to gap n Row 3 shows that f the dstance from the average wage n Southern ctes were set at the 1964 gap, aggregate 2009 output would fall by 0.4%. The changes n the economc geography of the US mpled by Table 4 are massve and probably not realstc. Changng the geographcal locaton of Amercan workers to the pont that brngs wages back to ther 1964 level would lkely take several decades. One way to see how extreme mpled by ths scenaro s to compare the mpled moblty rate wth the one observed n realty. Consder that less than 20% of workers change MSA every 10 years. By comparson, the scenaro n row 1 of Table 4 nvolves the relocaton of more than half of the US work force. Table 5 shows the equvalent of Table 4, but for partal adjustment. We scale partal adjustment based on the fracton of movers. For example, the second row n the table shows that f 2009 wages were set so that only 50% of workers were to relocate, the output gan n 2009 s 13.2%. The other rows show that f 2009 wages were set so that only 40%, 30%, 20% or 10% of workers were to relocate, the output gan would be respectvely 11.8%, 9.4%, 6.5%, and 3.4%. We consder the scenaro where 20% of workers change MSA -- correspondng to the counterfactual shown n the ffth row of Table 5--as our benchmark scenaro, as t s the closest to the typcal moblty rate that we observe over a decade. 20 The salary ncrease would be smaller f more workers decde to enter the labor market n response to the hgher salary. 21 The sze of these three ctes would grow. It s mportant to understand, however, that n general equlbrum the spatal relocaton of labor would affect not only these three ctes, but all ctes n the U.S. 26

28 Table 6 shows counterfactual employment for selected ctes under full adjustment and partal adjustment. In partcular, n column 1, counterfactual employment s computed settng 2009 relatve wage to 1964 levels n all ctes (frst row of Table 4). In column 2, counterfactual employment s computed movng 2009 relatve wage toward ther 1964 levels n all ctes up to the pont where 20% of U.S. workers change MSA (row 5 of Table 5). By a vast margn, New York s the cty that would experence the largest percentage ncrease n employment: a staggerng 787% ncrease n the case of full adjustment. San Jose and San Francsco would grow by more than 500%, whle Austn would ncrease by 237%. All these ctes are mportant nnovaton clusters and have experenced rapd wage growth snce 1964 mostly drven by human captal ntensve ndustres. Surprsngly, Fayettevlle s also n the top group. What dstngushes ths MSA s the fact that ts economy has changed enormously over the past 3 decades due to the locaton of Walmart headquarters. The medan cty, Sheboygan, WI would lose 80% of ts employment. The bottom of the table reports the ctes that would experence the largest declne n employment. Ths group ncludes Rust Belt former manufacturng centers, lke Mansfeld OH, Munce, IN and Flnt, MI. Under our counterfactual scenaro, vrtually all of Flnt s workers would move and relocate to other ctes. Column 2 shows the counterfactual employment for selected ctes under the more plausble ntermedate scenaro where 20% of workers change cty of resdence. New York remans the cty that would experence the largest percentage ncrease n employment, but the ncrease n only 179%. San Jose, San Francsco, Fayettevlle and Austn would grow by 149%, 147%, 118% and 102%, respectvely. The medan cty Sheboygan, would lose a thrd of ts employment. The bottom of the table ndcates that 78% of Flnt s workers would move and relocate to other ctes. Three consderatons are worth keepng n mnd. Frst, these are ntended to be long term benchmarks. They are based on the assumpton that as the populaton expands n an area, local servces also expand to keep the per-capta avalablty of schools, parks, publc transt and other publc amentes stable at ther current levels. Thus, one should not thnk of these counterfactuals as takng place overnght and holdng fxed publc servces. Rather, one should thnk of these counterfactuals takng place slowly over the long run, matched wth a steady ncrease n the supply of publc servces so that the per-capta level of publc servces s unchanged. Second, whle the counterfactual employment for the top group of ctes n column 2 mply cty szes that are very large, they are not completely mplausble. For example, the Assocaton of Bay Area Governments (whch s made of all muncpaltes n the San Francsco 27

29 Bay Area) has recently adopted a formal economc development plan for the regon that calls for the addton of enough housng unts to ncrease the regon s populaton by 80% n 2030 (ABAG, 2013). Ths ncrease s smaller than the one estmated n column 2 of Table 6 for the San Francsco MSA, but not too far off. Thrd, these estmates are obtaned assumng that the total number of workers n the US s fxed. In realty, f wages were to rse of average, total employment s lkely to ncrease due to nternatonal mgraton and ncreased domestc labor supply. Ths would further ncrease counterfactual output. Thus, our estmates of output gans are to be nterpreted as a lower bound. In Appendx Table A3 we probe the robustness of our estmates usng dfferent assumptons to calbrate the model parameters. In rows 2 and 3, we keep the returns to scale constant and alter α or η. In rows 4 to 7 we alter the labor or captal share to vary the returns to scale. We fnd that the results are not senstve to changes n labor or captal share for a gven degree of return to scale. But they are quanttatvely senstve to the degree of decreasng return to scale. The closer the sum α + η s to 1, the larger the output gan. Ths makes ntutve sense, because the sum α +η governs the returns to scale. Wth α + η close to 1 our technology approaches constant returns to scale and there s the most productve ctes attractng an ncreasngly larger share of the economc actvty of the country. Fnally, n the bottom row, we allow labor and captal shares n 1964 and 2009 to be dfferent n dfferent ndustres and years. Snce ctes have dfferent shares of each ndustry, ths models allows technology to vary across ctes and years, as a functon of ther ndustry mx. 4.3 Sources of Wage Dsperson: Housng Supply vs. Amentes We have shown that the spatal dsperson of nomnal wages has ncreased sgnfcantly over the past 50 years and, as a consequence, aggregate growth and aggregate output are lower than what they could have been. However, we have been slent on what has caused the ncrease n wage dsperson and on the mplcatons for welfare. Formally, we have shown that the dfference between welfare and output s smply the weghted average of the rato of housng prces to local amentes. Understandng how changes n housng prces and amentes have affected wages s thus crucal to understand the mplcatons of changes n wages for welfare. In other words, we need to determne why U.S. labor s not flowng to hgh wage ctes to a larger degree. Our calculatons of the counterfactual output n the prevous secton dd not depend on the specfc reason for the ncreased spatal dsperson n wages. But to understand the mplcatons for welfare, we need to understand what has been ncreasngly constranng labor 28

30 supply to hgh wage ctes n the U.S. In our settng, labor supply to a cty depends on two exogenous factors ---amentes and elastcty of hosng supply --- wth opposte mplcatons for worker welfare. Intutvely, f labor s not movng to hgh wage ctes lke San Francsco or New York because of undesrable amentes for example, workers may fnd these ctes crowded, nosy and polluted -- then ncreasng ther sze wll ncrease aggregate output but not aggregate welfare. On the other hand, f labor s not movng to ctes lke San Francsco or New York due to housng supply constrants caused by land use regulatons, then ncreasng ther sze wll ncrease aggregate output and aggregate welfare. Ths possblty s consstent wth anecdotal evdence on the evoluton of land use regulatons over the past half century. Glaeser (2014), among others, ponts out that snce the 1960 s, expensve coastal U.S. ctes have gone through a property rghts revoluton whch has sgnfcantly reduced the elastcty of housng supply: In the 1960s, developers found t easy to do busness n much of the country [ ]. In the past 25 years, constructon has come to face enormous challenges from any local opposton. In some areas t feels as f every neghbor has veto rghts over every project. 22 We now examne whch of these two factors amentes or housng supply restrctons created by land use regulatons---have contrbuted the most to the output losses uncovered above. (A) Amentes: The effect of the dstrbuton of amentes on aggregate output depends on whether amentes have mproved more n hgh wage ctes or n low wage ctes. If amentes have mproved by more n hgh wage ctes, ths lowers the dsperson of the nomnal wage across ctes and, ceters parbus, ncreases aggregate output. Consstent urban economcs lterature, we use the spatal equlbrum condton (equaton (1.2)) to measure amentes: Z W P. Ths condton ndcates that local amentes are proportonal to the dfference between properly weghted housng rents and nomnal wages, where the weght on housng rents reflects the share of housng n total expendtures. We set the housng share equal to 0.32 from Albouy s (2012) estmates. 23 Albouy (2012) shows that 22 Glaeser also ponts to poltcal economy causes of ths trend: To most resdents, a new project s nothng but a bother. They don t care about the welfare receved by the new resdent, or the benefts earned by the bulders or by the employers who have to pay lower wages when housng costs are lower. Moreover, unaffordable housng sn t a problem to most homeowners t represents an ncrease n the value of ther bggest asset." (Glaeser, 2014) 23 Followng Albouy (2012) we multply wages by 0.52 to account for taxes and transfers. Note that amenty levels are not dentfed because we do not know the absolute value of welfare. 29

31 small. 25 Row 3 performs the same exercse for the Rust Belt. Our estmates ndcate that, ths measure of local amentes s hghly correlated wth avalable measures of specfc amentes (such as weather and crme) and wth exstng ndces of the qualty of lfe. Table 7 quantfes the role played by changes n amentes. 24 In the top row, we compute counterfactual output under the assumpton that the level of amentes n 2009 s set equal to ts 1964 level. To obtan ths counterfactual, we proceed n two steps. We frst use equaton (1.4) and compute what wages would be n 2009 had amentes n each cty stayed at 1964 levels (holdng TFP and housng supply constant). We then allow workers and captal to reallocate and compute counterfactual employment and output. The results n the frst row of Table 7 show that counterfactual output s hgher than observed output, but only margnally. If the level of amentes n 2009 was equal to ts 1964 level, 2009 output would grow by only 1.6% and less than 10% of workers would move. In rows 2 to 4, we repeat the same exercse changng amentes levels only n selected ctes. Row 2 shows that changes n amentes n New York, San Francsco and San Jose between 1964 and 2009 had a postve mpact on aggregate output, but the effect s quanttatvely unsurprsngly, amentes n Rust Belt ctes worsened from 1964 to Changng amentes back to ther 1964 level would further lower wages n the Rust Belt and slghtly ncrease the overall wage dsperson. Row 3 shows that aggregate output would fall under ths scenaro, although the magntude s trval. In row 4 we look at the South. Emprcally, amentes have mproved n Southern ctes from 1964 to Ths s plausble, and lkely reflects ar condtonng, and the general mprovement n qualty of lfe n the South. Rollng amentes back to ther 1964 level would ncrease wages n the South and slghtly reduce the overall wage dsperson. Aggregate output would ncrease under ths scenaro, although the estmate n row 4 ndcates that the effect s very small. Here the mprovement n amentes experenced by Southern ctes ncreases aggregate welfare, but ths effect s slghtly offset by the declne n aggregate output. 24 Appendx Table A4 shows that the spatal dsperson of amentes has ncreased between 1964 and 2009, although the ncrease n the spatal dsperson s sgnfcantly less than that observed for wages 25 Whle crme, cultural amentes and qualty of lfe n general are generally thought to be better to have mproved n New York, San Francsco and San Jose snce the 1990s, the evdence n row 2 suggests that the post 1990s mprovement n amentes have offset the declne n amentes pror to the 1990s. So here, the change n amentes n New York, San Francsco and San Jose has two effects on welfare. Frst, t drectly lowers the average level of amentes. Second, t ncreases the nomnal wage n these ctes, ncreases the overall wage dsperson, and lowers aggregate output. 30

32 In sum, we conclude that amentes have changed dfferentally across US ctes. But the overall effect across all ctes of changes n the dstrbuton of amentes s lmted and cannot explan but a small fracton of our counterfactual output gans. (B) Housng Supply: In our model, the equlbrum housng prce s gven by 1 (1 )(1 AZ ) P. Ths says that hgher housng prces can be drven by hgher local TFP, better amentes, and more nelastc housng supply (hgher ). Based on Saz's estmates, New York, San Francsco and San Jose have some of the most nelastc housng supples n the country (hgh ). Specfcally, San Francsco s at the 99th percentle of the nverse elastcty dstrbuton, whle New York and San Jose are at the 96 th percentle. Saz shows that ths s due to a combnaton of geographcal features and restrctons to housng supply due to land use regulatons, as measured by the Wharton Resdental Land Use Regulatory Index. We cannot measure land use restrctons n 1964, because the Wharton survey does not go back n tme. Instead, n Table 8, we estmate counterfactual output under the assumpton that land use regulatons n New York, San Francsco and San Jose are set equal to the level of regulatons n the medan US cty. Thus, our counterfactual takes as gven geographcal factors that can affect housng supply, and only changes factors that are set by polcy. To obtan ths counterfactual, we proceed n three steps. Frst, we use Saz (2010) coeffcents (Table 5 column 2 n hs paper) to estmate the elastcty of housng supply n New York, San Francsco and San Jose f land use regulatons n these three ctes were equal to the level of regulatons n the medan US cty, holdng constant geography. The resultng counterfactual elastcty of housng supply s mechancally hgher n these three ctes. Second, we use ths counterfactual elastcty to estmate the counterfactual levels of housng prces and wages n New York, San Francsco and San Jose holdng local TFP and amentes constant at 2009 levels, along wth the counterfactual employment levels. Emprcally, we fnd that counterfactual wages are on average 25% lower n the three ctes and employment s hgher. Ths s not surprsng: because counterfactual housng supply s more accommodatng, n equlbrum more workers can move to these three ctes from the rest of the US. Emprcally, San Francsco s the cty that grows the most n ths counterfactual, followed by New York and San Jose. Thrd, we compute the counterfactual output that s generated by ths new allocaton of labor. 31

33 The frst row n Table 8 ndcates that ths would sgnfcantly speed up growth. The dfference between the actual and counterfactual annualzed output growth rate between 1964 and 2009 s.21%. Ths would nduce 30% of workers to relocate, and would ncrease 2009 output level by 9.7%. Comparng ths fgure wth the correspondng estmate n Table 4 (13.5%), we conclude that ths change n supply elastctes accounts for more than two thrds of the overall output gans. The second row of the table focuses on the role played by land use regulatons n the South. Housng supply s generally rather elastc n Southern ctes. Ths reflects abundant land and permssve land use regulatons. We estmate counterfactual output under the assumpton that land use regulatons n the South are set to the level of New York, San Francsco and San Jose, holdng constant land avalablty n the South. More strngent regulatons would result n hgher wages and lower employment n the South. The entry shows that n turn, US output would be 3% lower n ths counterfactual scenaro. We note that our estmates are senstve to the assumpton of perfect moblty. In the theory secton, we have shown how preferences for locaton may reduce the effect of changes n amentes or housng supply, although they do not alter the estmates of the overall effect of changes n relatve wages. The key parameter n ths case s the dsperson parameter, whch governs the strength of preference for locaton. Stronger preferences for locaton nduce some ndvduals to optmally choose ctes where real wages net of amentes are low. To our knowledge, there are only two emprcal estmates of ths parameter based on MSA-level data, although nether fts our settng perfectly. Serrato and Zdar (2014, Table 5) estmate ths parameter to be n the range , whle Damond (2013, Table 3) estmates the parameter to be.57 for college graduates and.27 for workers wth lower educaton. If we use the largest value of the parameter n Serrato and Zdar's we fnd output gans that are sgnfcantly smaller. For example, the estmate n row 1 of Table 8 drops to 1.6%. In ths case, employment n New York, San Francsco and San Jose ncrease only by 54%, 50%, and 31% respectvely. We note however, that both Serrato and Zdar's and Damond s parameters are lkely to be conservatve for our settng, as they are obtaned usng 10 year changes or less. A longer tme horzon would lkely mply more moblty and yeld larger estmates. 4.4 Caveats and Lmtatons. Ths paper hghlghts the possblty of output and welfare losses stemmng from an neffcent geographcal allocaton of labor. The number we present should not be taken as 32

34 precse estmates of the losses but rather as gudance on the general order of magntude of the losses, as they are based on a number of untestable assumptons. Frst, our fndngs depend on specfc assumptons on technology. Whle our estmates are qualtatvely robust to alternatve technology parameters, we have shown that they are quanttatvely senstve to the assumed degree of returns to scale (Appendx Table A3). Second, we use resdual wages as a measure of the margnal product of labor. Ths requres that dfferences across ctes n unobserved worker characterstcs have not changed over tme, or, f they have changed, they have changed n ways that are uncorrelated wth nomnal wages. Whle ths mght not be true, there s lttle we can do to relax ths assumpton, as detaled data on worker cogntve ablty are not avalable at a scale large enough to allow for a cty-level analyss. Falure of ths assumpton may lead us to overestmate potental benefts of geographcal reallocaton of labor. In partcular, f workers n MSA s wth hgh nomnal wages have hgher IQ than workers n MSA s wth low nomnal wages after condtonng on educaton and other characterstcs, then the documented spatal dsperson n nomnal wages overestmates the true degree of dsperson. If, n addton, the amount of unobserved ablty has ncreased more n MSA s wth hgh nomnal wages than n MSA s wth low nomnal wages, then the estmated counterfactual output gans reported n the paper are too large. Thrd, we have made restrctve assumptons on the relatonshp between TFP and cty sze; and the relatonshp between amentes and cty sze. A large lterature n urban economcs ndcates that TFP mght not be exogenous, but could depend on the sze or the densty of a cty. Smlarly, t has long been posted that local amentes can depend on cty sze and/or densty. Our assumptons don t rule out these possbltes, but restrct the relatonshp between TFP and employment and the relatonshp between amentes and employment. Recall that we have assumed that the elastcty of agglomeraton and the elastcty of amentes s constant across ctes. Wth constant elastcty, reallocaton of workers across ctes has no aggregate mpact on aggregate productvty or aggregate amentes, because the changes experenced by ctes that grow n sze are exactly offset by changes experenced by ctes that shrnk n sze. As noted above, the assumpton of constant elastcty for TFP s consstent wth Klne and Morett, forthcomng; the assumpton of constant elastcty for amentes s consstent wth Albouy (2012). However, we stress that the estmates n both Klne and Morett (forthcomng) and Albouy (2012) are based on ranges of cty sze hstorcally observed n the U.S. data. There s no guarantee that the same estmates extend to cty szes that are sgnfcantly larger than the ones observed n the data. 33

35 Fourth, we have assumed that workers can freely move across ndustres. Ths assumpton s useful because ctes have dstnct ndustry specalzaton. Thus, spatal reallocaton of labor also mples ndustry reallocaton. For example, scalng up employment n New York, San Francsco and San Jose mplctly requres ncreasng the number of workers n fnance and hgh tech, snce tradable sector employment n these three ctes s heavly concentrated n fnance and hgh tech. The assumpton of nter-ndustry moblty s clearly false n the short run. For example, t would be hard to relocate a Detrot car manufacturng worker to a San Francsco hgh tech frm overnght. On the other hand, the assumpton s more plausble n the long run, as workers sklls especally the sklls of new workers enterng the labor market --- can adjust. In ths respect, t s mportant to note that not all the workers need to adjust, because not all the workers are spatally reallocated n our counterfactual exercses. In addton, not all workers are employed n the tradable sector. Whle wages are set n the tradable sector, two thrd of the labor force s employed n the non-tradable sector, whch s arguably much less specalzed. 5. Polcy Implcatons We fnd that three quarters of aggregate U.S. growth between 1964 and 2009 was due to growth n Southern US ctes and a group of 19 other ctes. Although labor productvty and labor demand grew most rapdly n New York, San Francsco, and San Jose thanks to a concentraton of human captal ntensve ndustres lke hgh tech and fnance, growth n these three ctes had lmted benefts for the U.S. as a whole. The reason s that the man effect of the fast productvty growth n New York, San Francsco, and San Jose was an ncrease n local housng prces and local wages, not n employment. In the presence of strong labor demand, tght housng supply constrants effectvely lmted employment growth n these ctes. In contrast, the housng supply was relatvely elastc n Southern ctes. Therefore, TFP growth n these ctes had a modest effect on housng prces and wages and a large effect on local employment. Constrants to housng supply reflect both land avalablty and delberate land use regulatons. We estmate that holdng constant land avalablty, but lowerng regulatory constrants n New York, San Francsco, and San Jose ctes to the level of the medan cty would expand ther work force and ncrease U.S. GDP by 9.5%. Our results thus suggest that local land use regulatons that restrct housng supply n dynamc labor markets have mportant externaltes on the rest of the country. Incumbent homeowners n hgh wage ctes have a prvate ncentve to 34

36 restrct housng supply. By dong so, these voters de facto lmt the number of US workers who have access to the most productve of Amercan ctes. For example, Slcon Valley---the area between San Francsco and San Jose---has some of the most productve labor n the globe. But, as Glaeser (2014) puts t, by global urban standards, the area s remarkably low densty due to land use restrctons. In a regon wth some of the most expensve real estate n the world, surface parkng lots, 1-story buldngs and underutlzed peces of land are stll remarkably common due to land use restrctons. Whle the regon s natural amentes---ts hlls, beaches and parks---are part of the attractveness of the area, there s enough underutlzed land wthn ts urban core that housng unts could be greatly expanded wthout any reducton n natural amentes. Our fndngs ndcate that n general equlbrum, ths would rase ncome and welfare of all US workers. In prncple, one possble way to mnmze the negatve externalty created by housng supply constrants n hgh TFP ctes would be for the federal government to constrant U.S. muncpaltes ablty to set land use regulatons. Currently, muncpaltes set land use regulatons n almost complete autonomy snce the effect of such regulatons have long been thought as only local. But f such polces have meanngful natonwde effects, then the adopton of federal standard ntended to lmt negatve externaltes may be n the aggregate nterest. An alternatve s the development of publc transportaton that lnk local labor markets characterzed by hgh productvty and hgh nomnal wages to local labor markets characterzed by low nomnal wages. For example, a possble beneft of hgh speed tran currently under constructon n Calforna s to connect low-wage ctes n Calforna s Central Valley -- Sacramento, Stockton, Modesto, Fresno -- to hgh productvty jobs n the San Francsco Bay Area. Ths could allow the labor supply to the San Francsco economy to ncrease overnght wthout changng San Francsco housng supply constrants. An extreme example s the London metropoltan area. A vast network of trans and buses allows resdents of many ctes n Southern England ncludng far away ctes lke Readng, Brghton and Brstol-- to commute to hgh TFP employers located n downtown London. Another example s the Tokyo metropoltan area. Whle London and Tokyo wages are sgnfcantly above the UK and Japan averages, they would arguably be even hgher n the absence of these rch transportaton networks. Our argument suggests that UK and Japan GDP are sgnfcantly larger due to the transportaton network. 35

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40 Data Appendx In ths appendx we descrbe where each varable used n the paper comes from. We begn by measurng average wages n a county or n a country-ndustry cell by takng the rato of total wage bll n prvate sector ndustres and total number of workers n prvate sector ndustres usng CBP data for (referred to as 1964) and (referred to as 2009). To ncrease sample sze and reduce measurement error, we combne 1964 wth 1965 and 2008 wth s the earlest year for whch CBP data are avalable at the county-ndustry level. Data on total employment by county are never suppressed n the CBP. By contrast, data by county and ndustry are suppressed n the CBP n cases where the county-ndustry cell s too small to protect confdentalty. In these cases, the CBP provdes not an exact fgure for employment, but a range. We mpute employment n these cases based on the mdpont of the range. We aggregate countes nto MSA s usng a crosswalk provded by the Census based on the 2000 defnton of MSA. The man strength of the CBP s a fne geographcal-ndustry detal and the fact that data are avalable for as far back as But CBP s far from deal. The man lmtaton of the CBP data s that t does not provde worker level data on salares, but only a county aggregate and therefore does not allow us to control for changes n worker composton. We augment CBP data wth nformaton on worker characterstcs from the Census of Populaton and the ACS. Specfcally, we merge 1964 CBP average wage by MSA to a vector of workers characterstcs from the 1960 US Census of Populaton; we also merge 2009 CBP average wage by MSA to a vector of workers characterstcs from the 2008 and 2009 ACS. These characterstcs nclude: three ndcators for educatonal attanment (hgh school drop-out, hgh school, college); ndcators for race; an ndcator for gender; and age. We drop all cases where educaton s mssng. In the small number of cases where one of the components of the vector other than educaton s mssng, we mpute t based on the relevant state average. Because the Census does not report nformaton on unon status, we augment our merged sample usng nformaton on unon densty by MSA from Hrsch, Macpherson, and Vroman (2001). Ther data represent the percentage of each MSA nonagrcultural wage and salary employees who are covered by a collectve barganng agreement. Ther estmates for 1964 and 2009 are based on data from the Current Populaton Survey Outgong Rotaton Group (ORG) earnngs fles and the now dscontnued BLS publcaton Drectory of Natonal Unons and Employee Assocatons (Drectory), whch contans nformaton reported by labor unons to the Federal Government. The exact methodology s descrbed n Hrsch, Macpherson and Vroman (2001). 27 Ths allows us to estmate average resdual wage n each MSA, defned as average wage condtonal on worker characterstcs. Specfcally, we estmate resdual wages as W c X b, where W s average wage n the MSA, X s the vector of average workers characterstcs n the MSA and b s a vector of coeffcents on workers characterstcs from ndvdual level regressons estmated on a natonwde sample n 1964 and 2009 based on CPS data. The 26 Unfortunately, ndvdual level data on employment and salary wth geocodes s not avalable from the Census of Populaton on a systematc bass untl A thrd of metro areas are dentfed n the 1970 Census. 27 For 1964, estmates are calculated based on fgures n the BLS Drectores, scaled to a level consstent wth CPS estmates usng nformaton on years n whch the two sources overlap. Only state averages are estmated n Thus, n 1964 we assume assgn unon densty to each MSA based on the state average. 39

41 coeffcents for 1964 are: hgh-school or more.44; college or more.34; female: -1.13; non whte: -.44; age:.004; unon.14. The coeffcents for 2009 are: hgh-school or more.50; college or more.51; female: -.45; non whte: -.07; age:.007; unon.14. Because a unon dentfer s not avalable n the 1964 CPS, the 1964 regresson assumes that the coeffcent on unon s equal to the coeffcent from 2009, whch s estmated to be equal to.14. For 2009, we can compare the wage resduals estmated our approach wth those that one would obtan from ndvdual level data. (Of course we can t do ths for 1964, because we don t have mcro data n that year). Appendx Fgure 1 shows that whle nosy, our mputed wage resduals do contan sgnal. The two measures have correlaton.75. In some models resdual wage s defned as W c X b s where b s s a vector of coeffcents on workers characterstcs from ndvdual level regressons whch s allowed to vary across states. The correlaton n 2009 ncreases only margnally to.78. Data on housng costs are measured as medan annual rent from the 1960, 1970 US Census of Populaton and the 2008 and 2009 Amercan Communty Survey. For 1964, we lnearly nterpolate Census data between 1960 and Because rents may reflect a selected sample of housng unts, n some models we use average housng prces. Data for 2009 are from ndvdual level data from the Amercan Communty Survey. To get more precse estmate, we combne 2008 and Our sample conssts of 220 MSA s wth non-mssng values n 1964 and These ctes account for 71.6% of US employment n 1964 and 72.8% n They account for 74.3% of US wage bll n 1964 and 76.3% n The average cty employment s 144,178 n 1964 and 377,071 n Appendx Table A1 presents summary statstcs. Data on housng supply elastctes, land use regulatons and land avalablty are from Saz (2010). They are ntended to measure varaton n elastcty that arses both from poltcal constrants and geographcal constrants. In 19 ctes, Saz data are mssng. In those cases, we mpute elastcty based on the relevant state average. 40

42 Table 1a: Spatal Dsperson of Nomnal Wages n 1964 and 2009 Std. Devaton (1) Interquartle Range (2) Range (3) Panel A Log Wage n Log Wage n Panel B: Dff. wth 9 Census Dvson mean Log Wage n Log Wage n Panel C: Drop NY, San Francsco, San Jose Log Wage n Log Wage n Notes: The sample ncludes 220 metropoltan areas observed n both 1964 and All fgures are weghted by employment n the relevant metropoltan area and year. Wage s the uncondtonal average wage n the metropoltan area. Panel B shows the dstrbuton of the dfference between log nomnal wages and the average log nomnal wage n each census dvson.

43 Table 1b: Spatal Dsperson of Resdual Wages n 1964 and 2009 Std. Devaton (1) Interquartle Range (2) Range (3) Panel A Log Wage n Log Wage n Panel B: Dff. wth 9 Census Dvson mean Log Wage n Log Wage n Panel C: Drop NY, San Francsco, San Jose Log Wage n Log Wage n Notes: The sample ncludes 220 metropoltan areas observed n both 1964 and All fgures are weghted by employment n the relevant metropoltan area and year. Resdual wage s the average wage n the metropoltan area after controllng for three levels of educatonal attanment (hgh school drop-out, hgh school, college); race; gender; age; and unon status. Panel B shows the dstrbuton of the dfference between log nomnal wages and the average log nomnal wage n each census dvson.

44 Table 2: Cty GDP Growth and Cty Contrbuton to Aggregate Growth, by Group Accountng Estmates Model-Drven Estmates Growth of Cty GDP As a Fracton of Aggregate Growth Growth of Cty Contrbuton to Aggregate Growth As a Fracton of Aggregate Growth (2) (1) NY, San Francsco, San Jose 19.3% 6.1% Rust Belt Ctes (N=37) -28.5% 6.1% Southern Ctes (N=86) 66.8% 42.0% Other Large Ctes (N=19) 31.4% 32.1% Notes: Entres n column 1 are the growth of the cty s GDP as a percentage of aggregate GDP growth over the perod Entres n column 2 are the percentage contrbuton of each cty to aggregate growth from 1964 to We measure the contrbuton of a cty to aggregate growth as the change n local TFP adjusted by the change n the gap between the local wage and the average wage as a share of the change n aggregate GDP. The group Other Large Ctes ncludes 19 MSA wth 2009 employment above 600,000 that are not n the other three groups. The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

45 Table 3: Cty Contrbuton to Aggregate Output 2009, by Group Robustness to Dfferent Assumptons on Technology (1) Baselne α =.65 η =.25 (2) α =.70 η =.20 (3) α =.60 η =.30 (4) α =.70 η =.25 (5) α =.60 η =.35 (6) α =.60 η =.25 (7) α =.65 η =.20 (8) α and η vary by ndustry and year NY, San Francsco, San Jose Rust Belt Ctes (N=37) Southern Ctes (N=86) Other Large Ctes (N=19) Notes: Entres are the percentage contrbuton of each cty to aggregate growth from 1964 to We measure the contrbuton of a cty to aggregate growth as the change n local TFP adjusted by the change n the gap between the local wage and the average wage as a share of the change n aggregate GDP. Entres n column 1 are based on our baselne assumpton on technology and are reproduced from Table 2, column 2. Entres n other columns vary assumptons on technology. The group Other Large Ctes ncludes 19 MSA wth 2009 employment above 600,000 that are not n the other three groups. The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

46 Table 4. Counterfactual Output The Effect of Changes n the Spatal Dsperson of Relatve Wages 2009 Counterfactual Output Percent Who Have Moved by 2009 (1) (2) 1) In All Ctes 13.5% 52.5% 2) In NY, San Francsco, San Jose 13.2% 54.0% 3) In Rust Belt Ctes 0.5% 8.7% 4) In Southern Ctes -0.4% 21.2% Notes: Entres n column 1 are the percent dfference between counterfactual output level n 2009 and actual output level. Entres n column 2 are the percent of workers who n the counterfactual scenaro resde n a MSA dfferent from ther actual MSA of resdence. The counterfactual nvolves settng 2009 relatve wage equal to ther 1964 level n selected ctes. The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

47 Table 5. Counterfactual Output The Effect of Changes n the Spatal Dsperson of Relatve Wages - Partal Adjustment Percent Who Have Moved by Counterfactual Output (1) (From Tab 4) (1) (2) 52.5% 13.5% (2) 50% 13.2% (3) 40% 11.8% (4) 30% 9.4% (5) 20% 6.5% (6) 10% 3.4% (7) 0 0 Notes: Entres n column 1 are the percent of workers who n the counterfactual scenaro resde n a MSA dfferent from ther actual MSA of resdence n Entres n column 2 are the percent dfference between counterfactual output level n 2009 and actual output level. Row 1 reproduces Table 4, row 1. We scale partal adjustment based on the fracton of movers. For example, row (2) shows counterfactual output gans f 2009 relatve wages were set so that 50% of workers relocate to a dfferent MSA. The counterfactual nvolves settng 2009 relatve wage equal to ther 1964 level n all ctes. The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

48 Table 6: Counterfactual Employment The Effect of Changes n the Spatal Dsperson of Relatve Wages Full Adjustment (52.5% of US Workers Move) Partal Adjustment (20% of US Workers Move) Percent Change n MSA Employment (1) Percent Change n MSA Employment (2) Ctes wth Largest Increases NEW YORK-NEWARK, NY-NJ-PA 787.7% 179.8% SAN JOSE, CA 522.4% 149.2% SAN FRANCISCO, CA 509.9% 147.9% FAYETTEVILLE-SPRINGDALE, AR 320.2% 118.1% AUSTIN-SAN MARCOS, TX 237.7% 102.7% Cty wth Medan Change SHEBOYGAN, WI -79.7% -32.4% Ctes wth Largest Decreases KENOSHA, WI -97.3% -74.7% MANSFIELD, OH -97.6% -75.7% MUNCIE, IN -97.8% -76.9% GADSDEN, AL -97.9% -76.1% FLINT, MI -97.9% -77.4% SHARON, PA -98.1% -78.3% Note: Entres represents the percent dfference between counterfactual employment and actual employment. In column 1, counterfactual employment s computed settng 2009 relatve wage to 1964 levels n all ctes (Panel B, frst row of Table 4). In column 2, counterfactual employment s computed movng 2009 relatve wage toward ther 1964 levels n all ctes up to the pont where 20% of U.S. workers change MSA (row 5 of Table 5). The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

49 Table 7: Counterfactual Output The Effect of Changes n Amentes 2009 Counterfactual Output Percent Who Have Moved by 2009 (1) (2) 1) In All Ctes 1.6% 9.3% 2) In NY, San Francsco, San Jose 1.5% 3.1% 3) In Rust Belt Ctes -0.2% 0.8% 4) In Southern Ctes 0.3% 3.7% Notes: Entres n column 1 are the percent dfference between counterfactual output level n 2009 and actual output level. Entres n column 2 are the percent of workers who n the counterfactual scenaro resde n a MSA dfferent from ther actual MSA of resdence. The counterfactual nvolves settng 2009 amentes are equal to ther 1964 level n selected ctes. The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

50 Table 8: Counterfactual Output The Effect of Changng Housng Supply Regulatons 2009 Counterfactual Output Percent Who Have Moved by ) Regulatons n New York, San Francsco and San Jose are set equal to regulatons of the medan cty 2) Regulatons n South are set equal to regulatons n New York, San Francsco and San Jose (1) (2) 9.70% 30.0% -3.0% 33.5% Notes: Entres n column 1 are the percent dfference between counterfactual output level n 2009 and actual output level. Entres n column 2 are the percent of workers who n the counterfactual scenaro resde n a MSA dfferent from ther actual MSA of resdence. The counterfactual nvolves changng 2009 housng supply regulatons n selected ctes, holdng land avalablty constant. Housng supply regulatons vary at the MSA level and are measured usng Saz (2010) data, whch n turn are based on the Wharton Index aggregated at the MSA level. The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

51 Fgure 1a: Spatal Dsperson of Demeaned Log Nomnal Wages n 1964 and Densty Demeaned Log Wage Note: The dstrbuton s weghted by MSA employment n the relevant year.

52 Fgure 1b: Spatal Dsperson of Demeaned Log Resdual Nomnal Wages n 1964 and 2009 Densty Demeaned Log Wage Note: The dstrbuton s weghted by MSA employment n the relevant year.

53 Fgure 2a: Cty GDP Growth and Cty Contrbuton to Aggregate Growth Actual 5 0 DETROIT, LOS ANGE ATLANTA, CHICAGO, BOSTON W PHOENIX DALLAS, WASHINGT HOUSTON, MINNEAPO PHILADEL ST. LOUI CLEVELAN PITTSBUR MILWAUKE CINCINNA o o oo LOUISVIL GREENSBO BALTIMOR o INDIANAP KANSAS MEMPHIS, COLUMBUS NORFOLK o o o JACKSONV SACRAMEN C oo NASHVILL SALT CHARLOTT PORTLAND TAMPA ST ORLANDO, RIVERSID SEATTLE LAS DENVER, VEGA SAN DIEG SAN FORT RALEIGH o o LAK AUSTIN S ANTO FRAN LAU SAN JOSE NEW YORK Nave Notes: The Fgure plots the percentage contrbuton of each cty to aggregate growth from 1964 to 2009 (on the y-axs) aganst the growth of the cty s GDP as a percentage of aggregate GDP growth over the same perod (on the x-axs). We measure the contrbuton of a cty to aggregate growth as the change n local TFP adjusted by the change n the gap between the local wage and the average wage as a share of the change n aggregate GDP. The sold lne s the 45 degree lne. The sample ncludes 220 ctes observed n 1964 and 2009.

54 Fgure 2b: Cty GDP Growth and Cty Contrbuton to Aggregate Growth New York, San Francsco, San Jose Actual 5 NEW YORK 0 SAN FRAN SAN JOSE Nave Notes: The Fgure plots the percentage contrbuton of each cty to aggregate growth from 1964 to 2009 (on the y-axs) aganst the growth of the cty s GDP as a percentage of aggregate GDP growth over the same perod (on the x-axs). We measure the contrbuton of a cty to aggregate growth as the change n local TFP adjusted by the change n the gap between the local wage and the average wage as a share of the change n aggregate GDP. The sold lne s the 45 degree lne.

55 Fgure 2c: Cty GDP Growth and Cty Contrbuton to Aggregate Growth Rust Belt Ctes 2 0 DETROIT, PITTSBUR CLEVELAN o ST. LOUI o oo o o o o o o o o o o o o o o o o ooo o o Actual Nave Notes: The Fgure plots the percentage contrbuton of each cty to aggregate growth from 1964 to 2009 (on the y-axs) aganst the growth of the cty s GDP as a percentage of aggregate GDP growth over the same perod (on the x-axs). We measure the contrbuton of a cty to aggregate growth as the change n local TFP adjusted by the change n the gap between the local wage and the average wage as a share of the change n aggregate GDP. The sold lne s the 45 degree lne.

56 Fgure 2d: Cty GDP Growth and Cty Contrbuton to Aggregate Growth Southern Ctes 10 Actual 5 ATLANTA, DALLAS, WASHINGT HOUSTON, 0 o TAMPA ST ORLANDO, BALTIMOR GREENSBO MEMPHIS, NORFOLK NASHVILL CHARLOTT SAN FORT RALEIGH ANTO LAU AUSTIN S o o oo o o o o ojacksonv o ooo ooo o Nave Notes: The Fgure plots the percentage contrbuton of each cty to aggregate growth from 1964 to 2009 (on the y-axs) aganst the growth of the cty s GDP as a percentage of aggregate GDP growth over the same perod (on the x-axs). We measure the contrbuton of a cty to aggregate growth as the change n local TFP adjusted by the change n the gap between the local wage and the average wage as a share of the change n aggregate GDP. The sold lne s the 45 degree lne.

57 Fgure 2e: Cty GDP Growth and Cty Contrbuton to Aggregate Growth Other Large Ctes 5 Actual 0 CHICAGO, LOS ANGE BOSTON W MINNEAPO PHILADEL RIVERSID SAN SEATTLE DIEG LAS DENVER, VEGA PORTLAND MILWAUKE CINCINNA INDIANAP KANSAS COLUMBUS CSACRAMEN SALT LAK PHOENIX Nave Notes: The Fgure plots the percentage contrbuton of each cty to aggregate growth from 1964 to 2009 (on the y-axs) aganst the growth of the cty s GDP as a percentage of aggregate GDP growth over the same perod (on the x-axs). We measure the contrbuton of a cty to aggregate growth as the change n local TFP adjusted by the change n the gap between the local wage and the average wage as a share of the change n aggregate GDP. The sold lne s the 45 degree lne. Ths group, called Other Large Ctes ncludes 19 MSA wth 2009 employment above 600,000 that are not n the other three groups.

58 Appendx Table A1: Summary Statstcs 1964 Average (1) Average Annual Salary Prvate Sector Workers 25,538 (3,868) Average Annual Rent 4,770 (932) Prvate Sector Employment 144,178 (294,016) Prvate Sector Wage Bll (bllon) 4.04 (8.95) Hgh School Drop Out 0.59 (0.11) Hgh School or More 0.40 (0.08) College or More 0.07 (0.02) Hspanc 0.03 (0.05) Non Whte.09 (0.11) Age 28.1 (3.3) Female 0.51 (0.01) Unon 0.26 (0.12) 2009 Average (2) 29,018 (5,278) 6,553 (1826) 377,071 (604,448) (25.5) 0.10 (.05) 0.90 (0.04) 0.26 (0.07) 0.10 (0.10) 0.22 (0.15) 39.9 (0.9) 0.51 (0.01) 0.11 (.06) Number of Ctes Note: The unt of analyss s a MSA. The sample ncludes 220 metropoltan areas observed n both 1964 and All monetary fgures are n 2000 dollars.

59 Appendx Table A2: Spatal Dsperson of Cost of Housng n 1964 and Std. Devaton (1) Interquartle Range (2) Range (3) Panel A: Medan Rent Log Rent n Log Rent n Panel B: Medan Housng Prce Log Annual Cost n Log Annual Cost n Notes: Medan housng prce s annualzed usng a dscount factor of 7.85% (Peser and Smth, 1985). All fgures are weghted by employment n the relevant metropoltan area and year.

60 Appendx Table A3: Robustness - The Effect of Changes n the Spatal Dsperson of Relatve Wages Under Alternatve Assumptons on Producton Technology 2009 Counterfactual Output Percent Who Have Moved by 2009 (2) (1) Baselne 1) α =.65; η = % 52.5% Dfferent Labor and Captal Shares, Same Returns to Scale 2) α =.70; η = % 55.9% 3) α =.60; η = % 49.1% Dfferent Returns to Scale 4) α =.70; η = % 85.9% 5) α =.60; η = % 83.9% 6) α =.60; η = % 34.4% 7) α =.65; η = % 37.0% Technology Parameters Vary Across Industres and Years 7.4% 53.9% Notes Entres n column 1 are the percent dfference between counterfactual output level n 2009 and actual output level. Entres n column 2 are the percent of workers who n the counterfactual scenaro resde n a MSA dfferent from ther actual MSA of resdence. The counterfactual nvolves settng 2009 relatve wage equal to ther 1964 level n all ctes. The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

61 Appendx Table A4. Spatal Dsperson of Amentes n 1964 and 2009 Std. Devaton (1) Interquartle Range (2) Range (3) Amentes n Amentes n Notes: All fgures are weghted by TFP 1/(1- α- η). The sample ncludes 220 metropoltan areas observed n both 1964 and 2009.

62 Appendx Fgure A1: Estmated 2009 Average Wage Resdual vs Actual 2009 Average Wage From Indvdual Level Data Estmated Wage Resduals Wage Resduals Note: Each dot s a MSA. The x axs reports average resduals by MSA from an ndvdual level regresson based on ndvdual level data from the Census of Manufacturers. The y axs has resduals based on CBP data used n the man analyss. The employment weghted correlaton s.75.

63 Appendx Fgure A2: Spatal Dsperson of Demeaned Log Nomnal Wages n 1964 and Unweghted Densty Demeaned Log Wage