Lecture 5: Urban Sorting, Skills, and Wageserossi/Urban/Lecture_5_538.pdf · ERH (Princeton University) Lecture 5: Urban Sorting, Skills, and Wages 8 / 24. Using individual level

Lecture 5: Urban Sorting, Skills, and WagesWWS 538

Esteban Rossi-Hansberg

Princeton University

ERH (Princeton University ) Lecture 5: Urban Sorting, Skills, and Wages 1 / 24

Introduction

Wages are higher in larger cities

Why?I Workers more productive there? Externalities?I Positive assortative matching?I Human capital accumulation?

Urban costs can explain why not everyone goes to cities but not why firmstay there

I All top cities have more establishments per capita than the US as a wholeI So we need a different mechanism

Are the effects dynamic or static?

Large body of evidence shows basic fact for a wide variety of circumstancesand periods

Start by looking at evidence in Glaeser and Mare (2001)


The Wage-Size Premium in CitiesCities and Skills 317

Fig. 1.—Wages and SMSA population. Wage p 2,732 log (population) 1 4,332 (340); R2

p .579; number of observations p 49. Data from Statistical Abstract of the United States(Austin, TX: Reference, 1992), tables 42, 670. The unit of observation in both of theseregressions is the SMSA. Standard errors are in parentheses beneath parameter estimates.

Kuznets 1970 for early data). In 1970, the urban wage premium wasslightly larger than it is today; families in Standard Metropolitan StatisticalAreas (SMSAs) with over 1 million residents earned 36% more than fam-ilies living outside of SMSAs.2 While the premium from living in a centralcity has fallen over time, the earnings gap between those who work in alarge city and those who work outside a large city is still larger than theearnings gaps between the races or between union and nonunion members.

Higher costs of living and urban disamenities may explain why labordoes not flock to this high pay, but if urban wages are so high, why doso many firms stay in cities?3 After all, more than 22% of U.S. nonfarmbusiness establishments are in America’s five largest metropolitan statis-tical areas. In the New York City area alone, which has the highest wagesin the country, there are 555,000 establishments.4 Firms, even those thatsell their goods on the national market, appear willing to pay the highwages in cities. The best explanation for the continuing presence of firmsin cities is that these higher wages are compensated for by higher pro-

2 The wage premium for living in a smaller SMSA was 21%. Both of thesefigures come from Current Population Reports Wages by Metropolitan/Non-metropolitan Residence. These numbers are not directly comparable with ourown since they are family figures, not worker figures.

3 Firms do appear to leave areas with wages that are not compensated for byhigher productivity (Carlton 1983).

4 Both the New York area and the five largest metropolitan areas taken as awhole have more nonfarm establishments per capita than the country as a whole.


Glaeser and Mare (2001)

Two basic questions:I Is it that most skilled sort into cities or that cities improve productivity?I Is the effect important when people get to the city or do wages grow over timefaster?


Sorting

Most skilled might sort into cities because:I Information flows are relatively more valuable to themI Consumer cities might be more attractive for skilled people

If sorting is important:I Urban wage premium even after controlling for local pricesI Fixed-effect estimates of the urban wage premium should be zeroI Factors that lead individuals to move into cities, but which are not correlatedwith individual ability, should not be correlated with higher wages


Timing of effects

Most standard theories imply that effects happen at impactI So wages should jump up when people move to cities and should jump downwhen they move out

Alternatively, cities might act through human capital accumulation orlabor-market matching

I In this case wages should grow over time and should not jump down whenworker leave


Labor SupplyIn order to have a spatial equilibrium real wages per unit of skill equalize:φkωiPi

needs to be constant across cities iI φk = units of skill, ωi = wage in city i , Pi = price index in city iI Implies that Wi − Wj = φi − φj + log

(PiPj

)where Wi log of geometric mean

of nominal wagesI So if Wi − Wj − log

(PiPj

)= φi − φj = 0, there are no ability differences

across cities320 Glaeser and Mare

Fig. 2.—Wages adjusted by cost of living. Wage/cost of living p 213 log (population) 121828 (455); R2 p .006; number of observations p 37. Data from Statistical Abstract of theUnited States (Austin, TX: Reference, 1992), tables 42, 670; ACCRA Cost of Living Index,vol. 25, no. 3 (Louisville, KY: ACCRA, 1992). The unit of observation in both of theseregressions is the SMSA. Standard errors are in parentheses beneath parameter estimates.

derstand why firms do not flee these high-wage areas. These two questionstogether can be thought of as explaining labor supply and labor demandin cities.

The labor-supply question (why do workers not come to high wagecities?) can be seen in the simple formalization. Assume that each indi-vidual (indexed k) is endowed with a quantity of efficiency units of laborto sell on the labor market (denoted fk), and the wage per efficiency unit,fi, is different in each location i. The price level Pi may also be differentacross locations. To ensure that workers do not flock to particular cities,it must be true that fkqi/Pi, which means that real wages must be constantover space. Thus, half of the explanation of the urban wage premiumrequires showing that prices are higher in large cities.6

These arguments also imply that , where˜ ˜ ˜ ˜W 2 W p f 2 f 1 log (P/P)i j i j i j

denotes the logarithm of the geometric mean of any variable X withinXi

city i.7 Higher wages in an area must reflect either higher ability levelsor higher prices (otherwise workers would have to respond to wage dif-ferences). This equation also means that if real wages are not higher inlarge cities, then ability levels are not higher in those cities either.

The labor demand question is more puzzling. Firms will remain in

6 If real wages are high in some areas, then urban theory (see Roback 1982)argues that amenities must be lower in those areas.

7 We define where Ni is the population of city i, and XkiN˜ iX p O log (X )/N ,i kp1 ki i

are the levels of X for all of the residents (indexed with k) of city i.


Labor Demand

In order for firms to demand workers in a city and pay higher wages it mostbe that they

I Obtain higher productivityI Charge higher prices

Suppose firms maximize: AiK σL1−σ −ωiL− RKI L is labor in unit of effi ciency and Ai includes effi ciency and pricesI Then, firm maximization and zero profits imply ωi = cR−σ/(1−σ)A1/(1−σ)

i(where c is some constant)

Implies that

Wi − Wj = φi − φj +1

1− σlog(AiAj

)So the goal is to obtain an estimate of Ai/AjIf workers in cities are better in an "unobserved" way this will be complicated


Using individual level data

Estimate the regression

log (Wkt ) = Xktβ+ LktΓ+ φk + εkt

where Wkt is the hourly wage, Xkt is a vector of individual characteristics,Lkt is an indicator of an urban area, and φk denotes individual ability

If φk omitted there is a potential bias, but could be solved with fixed effects(lose some information)


Main results

Table 3Base Regressions

1990 CensusBasic Wage

Equation(1)

1990 CensusBasic WageEquation

withOccupational

Education(2)

PSIDBasic Wage

Equation(3)

PSIDBasic WageEquation

with LaborMarket

Variables(4)

NLSYBasic WageEquation

(5)


withOccupational

Education(6)


(7)

NLSYFixed-Effects

Estimator(8)

PSIDIndividual

Fixed-EffectsEstimator

(9)

Dense metropoli-tan premium .287 (.00) .269* (.00) .282* (.01) .259* (.01) .249* (.01) .245* (.01) .243* (.01) .109* (.01) .045* (.01)

Nondense metro-politanpremium .191* (.00) .179* (.00) .148* (.01) .133* (.01) .153* (.01) .147* (.01) .141* (.01) .070* (.01) .026* (.01)

Experiencedummies Yes Yes Yes Yes Yes Yes Yes Yes Yes

Educationdummies Yes Yes Yes Yes Yes Yes Yes Yes Yes

Nonwhite 2.169* (.00) 2.156* (.00) 2.193*(.01) 2.173* (.01) 2.159* (.01) 2.137* (.01) 2.087* (.01) N.A. N.A.Average education

in (one-digit)occupationalgroup .055* (.00) .039* (.00) .034* (.00) .027* (.00) .009* (.00) .016* (.00)

Tenure .015* (.00) .001* (.00) .001* (.00) .000* (.00) .010* (.00)AFQT .002* (.00) N.A.Time dummies No No Yes Yes Yes Yes Yes Yes YesAdjusted R2 (%) 20.4 21.6 30.2 34.7 29.4 33.0 33.7 28.4 20.6N 332,609 332,609 39,485 39,485 40,194 40,194 40,194 40,194 39,485

Note.—Numbers in parentheses are standard errors. PSID p Panel Study of Income Dynamics; NLSY p National Longitudinal Study of Youth; AFQT p Armed ForcesQualification Test.

* Significant at 1% level.


Interpretation

Two interpretations of the result:I The urban wage premium is all omitted ability factorsI Urban wage premium is not closely tied (temporally) to moving to a city

Ideally, one would like to instrument for urban resident with variables thatpredict urban status and are orthogonal to unobserved ability

I But hard to find: Urbanization in parent’s state of residence?


Growth of level effect?

Estimate

log (Wkt ) = Xktβ+ LktΓ+ φk +∑j

γenterj I entert+j +∑j

γexitj I exitt+j + εkt

where I entert+j and I exitt+j are dummies indicating when the agent entered orexited the urban area

The parameters γenterj and γexitj indicate the urban premium j years beforethe move


Dynamic effectsTable 5Analysis of Movers

NLSY OLS

NLSYIndividual

(Spell)Fixed Effects PSID OLS

PSIDIndividual

Fixed Effects(1) (2) (3) (4)

Nonmovers livingin a metropolitanarea .168* (.01) N.A. .203* (.01) N.A.

Move to a metropoli-tan area:

Observed 5 or moreyearsbefore a move .069* (.02) .093* (.02) 2.138* (.01) 2.067* (.02)

Observed 3–5 yearsbefore a move 2.021 (.02) .028 (.02) 2.141* (.02) 2.056* (.02)

Observed 1–3 yearsbefore a move 2.040** (.02) 2.010 (.02) 2.151* (.02) 2.048* (.02)

Observed within 1yearbefore a move 2.022 (.02) N.A. 2.092* (.02) N.A.

Observed within 1yearafter moving .079* (.02) .073* (.02) 2.113* (.02) 2.036** (.02)

Observed 1–3 yearsafter moving .111* (.01) .114* (.02) 2.082* (.02) 2.008 (.02)

Observed 3–5 yearsafter moving .125* (.01) .123* (.02) 2.053* (.02) .030*** (.02)

Observed 5 or moreyears aftermoving .118* (.01) .105* (.02) 2.050* (.01) .019 (.02)

Leave a metropolitanarea:

Observed 5 or moreyearsbefore a move .049** (.02) .021 (.02) .188* (.01) .018 (.01)

Observed 3–5 yearsbefore a move .039*** (.02) 2.001 (.02) .148* (.01) 2.006 (.01)

Observed 1–3 yearsbefore a move .053* (.02) 2.002 (.02) .165* (.01) .010 (.01)

Observed within 1yearbefore a move .062* (.02) N.A. .150* (.02) N.A.

Observed within 1yearafter moving .050** (.02) 2.036*** (.02) .128* (.02) 2.024*** (.01)

Observed 1–3 yearsafter moving .005 (.02) 2.068* (.02) .116* (.01) 2.041* (.01)

Observed 3–5 yearsafter moving .028 (.02) 2.023 (.02) .097* (.02) 2.035** (.02)

Observed 5 or moreyearsafter moving .006 (.02) 2.027 (.02) .148* (.01) 2.008 (.01)

Cities and Skills 337

Table 5 (Continued)

NLSY OLS

NLSYIndividual

(Spell)Fixed Effects PSID OLS

PSIDIndividual

Fixed Effects(1) (2) (3) (4)

Regressions containeducation,experience,nonwhiteand timedummiesand occupationaleducation Yes Yes Yes Yes

Adjusted R2 (%) 26.6 25.9 34.4 19.3N 40,822 40,822 39,485 39,485

Note.—Numbers in parentheses are standard errors. NLSY p National Longitudinal Study of Youth;OLS p ordinary least squares; PSID p Panel Study of Income Dynamics.

* Significant at 1% level.** Significant at 5% level.*** Significant at 10% level.

The parameter estimates and reflect the extent to whichenter exitt 1 j. g gj j

wages rise or decline immediately before a move and rise or decline aftera move. In specification 1 and 3, we include a battery of individual specificcontrols. In specifications 2 and 4, we also include individual fixed effects.

Regressions 1 and 2 show our results from the NLSY. The metropolitanarea wage premium in the NLSY is 16.8%. Rural-to-urban migrants alsoexperience significant wage gains. In the 5 years prior to moving, thosemoving into a metropolitan area earn 2%–4% less than those who remainin a nonmetropolitan area. After moving, their wages increase by around15%, and they earn 8%–12% more than those remaining outside a met-ropolitan area. This is still, however, less than the 16.8% earned by thosewhom we observe staying within a metropolitan area.

Interestingly, urban-to-rural migrants in the NLSY experience onlysmall wage losses. While in a metropolitan area, rural-to-urban migrantsearn a premium of 4%–6%, much less than the full urban wage premium.After moving, their relative earnings drop by between 1% and 5%, whichis a small fraction of the urban wage premium. While this small reductionin wages is one implication of the wage growth hypothesis, it can alsobe explained by the selection bias deriving from workers’ endogenouschoice of location. If workers only leave if they are expecting solid wagesoutside of the city, this would explain the absence of a wage decline.

Regression 2 shows the estimates for an equation similar to that inregression 1, but it allows for a time-invariant individual-specific fixed


de la Roca and Puga (2014) for Spain

Utrera

Aranjuez

Cuenca

Huesca

Ávila

Mérida

Puertollano

Linares

Segovia

Lorca

Motril

Vélez−Málaga

Ponferrada

El EjidoZamora

Sanlúcar de Barrameda

Tenerife Sur

Alcoi

Talavera de la Reina

Cáceres

Ciudad Real

Arrecife

Costa del Sol

Palencia

Toledo

Roquetas de Mar

Lugo

Sagunt

Gran Canaria Sur

Guadalajara

Torrevieja

Costa Blanca

Orihuela

Elda − Petrer

Manresa

Santiago de Compostela

Badajoz

Gandía

JaénOurense

FerrolLleida

Algeciras

Girona

AlbaceteCartagena

Logroño

Almería

BurgosTarragona − Reus

HuelvaLeón

Salamanca

Santander − Torrelavega

Asturias

Cádiz

Castellón de la Plana

Vigo − Pontevedra

A Coruña

Córdoba

Palma de Mallorca

Alacant − Elx

Santa Cruz de Tenerife − La Laguna

Valladolid

Las Palmas de Gran CanariaMurcia

Granada

Málaga

Zaragoza

Sevilla

Valencia

Barcelona

Madrid

16,0

0020

,000

24,0

0028

,000

32,0

00

50,000 125,000 250,000 500,000 1,000,000 2,000,000City size

(€, f

ull−

tim

e eq

uiva

lent

, log

sca

le)

Mea

n an

nual

ear

ning

s

(people within 10km of average worker, log scale)

Figure 1: Mean earnings and city size

experience. Since these dynamic advantages are transformed in higher human capital, they mayremain beneficial even when a worker relocates.

In this paper, we simultaneously examine these three potential sources of the city-size earningspremium: static advantages, sorting based on initial ability and dynamic advantages. For thispurpose, we use a rich administrative data set for Spain that follows workers over time and acrosslocations throughout their careers, thus allowing us to compare the earnings of workers in cities ofdifferent sizes, while controlling for measures of ability and the experience previously acquired invarious other cities.

To facilitate a comparison with previous studies, we begin our empirical analysis in section 3

with a simple pooled ols estimation of the static advantages of bigger cities. For this, we estimatea regression of log earnings on worker and job characteristics and city fixed-effects. In a secondstage, we regress the estimated city-fixed effects on a measure of log city size. This yields a pooled-ols elasticity of the earnings premium with respect to city size of 0.046. The first stage of thisestimation ignores both the possible sorting of workers with higher unobserved ability into biggercities as well as any additional value of experience accumulated in bigger cities. Thus, this basicestimation strategy produces a biased estimate of the static advantages of bigger cities and noassessment of the possible importance of dynamic advantages or sorting.

Glaeser and Maré (2001) and, more recently, Combes, Duranton, and Gobillon (2008) introduceworker fixed-effects to address the issue of workers sorting on unobserved ability into bigger cities.When we follow this strategy, the estimated elasticity of the earnings premium with respect to citysize drops substantially to 0.023, in line with their findings. This decline is usually interpretedas evidence of more productive workers sorting into bigger cities (e.g., Combes, Duranton, and

2


Controlling for Worker Characteristics (Static)

Utrera

Aranjuez

Cuenca

Huesca

Ávila

Mérida

Puertollano

Linares

SegoviaLorca

Motril

Vélez−MálagaPonferradaEl Ejido

Zamora


Tenerife SurAlcoiTalavera de la Reina

Cáceres

Ciudad Real

Arrecife

Costa del Sol

Palencia

Toledo

Roquetas de Mar

Lugo

Sagunt

Gran Canaria Sur

Guadalajara

Torrevieja

Costa Blanca

Orihuela

Elda − Petrer

Manresa

Santiago de Compostela

Badajoz

GandíaJaén

Ourense

FerrolLleida

Algeciras

Girona

AlbaceteCartagena

Logroño

Almería


Huelva

León

Salamanca

Santander − TorrelavegaAsturias

Cádiz


Vigo − Pontevedra

A CoruñaCórdoba

Palma de Mallorca

Alacant − Elx

Santa Cruz de Tenerife − La Laguna

Valladolid

Las Palmas de Gran CanariaMurcia

Granada

Málaga

Zaragoza

Sevilla Valencia

Barcelona

Madrid

−10

%0%

10%

20%

30%

40%

50,000 125,000 250,000 500,000 1,000,000 2,000,000City size

Ear

ning

s pr

emiu

m,

stat

ic e

stim

atio

n, p

oole

d o

ls


Elasticity: 0.046

Figure 2: Static ols estimation of the city-size premium

equation (2) includes the omitted variables:

ηict = µi +C

∑j=1

δjceijt + ε ict . (4)

Hence,Cov(ιict, ηict) = Cov(ιict, µi) + Cov(ιict,

C

∑j=1

δjceijt) 6= 0 . (5)

Equation (5) shows that a static cross-section or pooled ols estimation of σc suffers from two keypotential sources of bias. First, it ignores sorting, and thus the earnings premium for city c, σc, isbiased upwards if individuals with high unobserved ability, µi, are more likely to work there, sothat Cov(ιict, µi) > 0 (and biased downwards in the opposite case). Second, it ignores dynamiceffects, and thus the earnings premium for city c, σc, is biased upwards if individuals with morevaluable experience, ∑C

j=1 δjceijt, are more likely to work there, so that Cov(ιict, ∑Cj=1δjceijt) > 0 (and

biased downwards in the opposite case).12

To see how these biases work more clearly, it is useful to consider a simple example. Supposethere are just two cities, one big and one small. Everyone working in the big city enjoys an

12Strictly speaking, the actual bias in the pooled ols estimate of σc, σc pooled, is more complicated because it is notnecessarily the case that Cov(xit, µi + ∑C

j=1δjceijt) = 0, as we have assumed. For instance, even if we do not allow thevalue of experience to vary by city, we may have overall experience, eit ≡ ∑C

j=1 eijt, as one of the explanatory variablesincluded in xit in equation (2). In this case, δjc measures the differential value of the experience acquired in city jwhen working in city c relative to the general value of experience, which we may denote γ. Then plim σc pooled =σc + Cov(ιict, µi)/Var(ιict) + ∑C

j=1δjcCov(ιict, eijt)/Var(ιict) + (γ− γpooled)Cov(ιict, eit)/Var(ιict). Relative to the simplerexample discussed in the main text, the bias incorporates an additional term (γ − γpooled)Cov(ιict, eit)/Var(ιict). Inpractice, this additional term is negligible if Cov(ιict, eit) is close to zero, that is, if the total number of days of workexperience (leaving aside where it was acquired) is not systematically related to workers’ location. In our sample, thisis indeed the case: the correlation between mean experience and log city size is not significantly different from 0.

10


Homogenous Dynamic Effects

Madrid always

Sevilla always

Madrid 5 years,then Santiago

Sevilla 5 years,then Santiago

0%5%

10%

15%

20%

25%

30%

35%

40%

0 1 2 3 4 5 6 7 8 9 10

Years worked

Ear

ning

s pr

emiu

mre

lati

ve to

San

tiag

o —

med

ian

size

Panel (a) Profiles allowing for learning benefits of bigger cities

Sevilla always

Madrid 5 years,then Santiago

Sevilla 5 years, then Santiago

Madrid always

0%5%

10%

15%

20%

25%

30%

35%

40%

0 1 2 3 4 5 6 7 8 9 10

Years worked

Ear

ning

s pr

emiu

mre

lati

ve to

San

tiag

o —

med

ian

size

Panel (b) Profiles not allowing for learning benefits of bigger cities

Figure 3: Earnings profiles relative to median-sized city

16


Homogenous Dynamic Effects

Utrera

Aranjuez

Cuenca

Huesca

Ávila

Mérida

Puertollano

Linares

Segovia

Lorca

Motril

Vélez−Málaga

Ponferrada

El Ejido

Zamora


Tenerife SurAlcoi

Talavera de la Reina

Cáceres

Ciudad Real

Arrecife

Costa del Sol

Palencia

Toledo

Roquetas de Mar

Lugo

Sagunt

Gran Canaria Sur

GuadalajaraTorrevieja

Costa Blanca

OrihuelaElda − Petrer

Manresa

Santiago de CompostelaBadajoz

Gandía

Jaén

Ourense

Ferrol

Lleida

Algeciras

Girona

Albacete

Cartagena

LogroñoAlmería


Huelva

LeónSalamanca

Santander − Torrelavega

Asturias

Cádiz


Vigo − PontevedraA Coruña

Córdoba

Palma de Mallorca

Alacant − ElxSanta Cruz de Tenerife − La Laguna

ValladolidLas Palmas de Gran Canaria

Murcia

Granada

Málaga

Zaragoza

Sevilla

Valencia

Barcelona

Madrid

−10

%0%

10%

20%

30%

40%

50,000 125,000 250,000 500,000 1,000,000 2,000,000City size

Med

ium

−te

rm e

arni

ngs

prem

ium

,d

ynam

ic e

stim

atio

n, fi

xed

−ef

fect

s


Elasticity: 0.047

Figure 4: Dynamic fixed-effects estimation of the medium-term city-size premium

same city evaluated at the average experience in a single location for workers in our sample (7.24

years). The estimated elasticity of this medium-term earnings premium with respect to city size,in column (3) of table 2, is 0.047.

Comparison of the 0.047 elasticity of the medium-term earnings premium with respect to citysize in column (3) of table 2 with the 0.023 elasticity of the short-term static premium in column (2)indicates that in the medium term, about half of the gains from working in bigger cities are staticand about half are dynamic.

Note also that the 0.047 elasticity of the medium-term earnings premium with respect to citysize is almost identical to the static pooled ols estimate in column (2) of table 1. This suggeststhat the drop in the estimated elasticity between a static pooled ols estimation and a static fixed-effects estimation is not due to sorting but to dynamic effects. When estimating the medium-term elasticity, we have brought dynamic effects back in, but left sorting on unobserved time-invariant ability out. The fact that this takes us back from the magnitude of the static fixed-effectsto the magnitude of the pooled ols estimate indicates that learning effects can fully account for thedifference. This not only underscores the relevance of the dynamic benefits of bigger cities, it alsosuggests that sorting may not be very important. We return to this issue later in the paper.

While our estimate of the medium-term benefit of working in bigger cities resembles a basicpooled ols estimate, our methodology allows us to separately quantify the static and the dynamiccomponents and to discuss the portability of the dynamic part. Furthermore, the estimation ofthe combined medium-term effect is more precise. Figure 4 plots the estimated medium-termpremium against log city size. Compared with the plot for the pooled ols specification in figure2, log city size explains a larger share of variation in medium-term earnings across cities (R2 of

19


Heterogenous Dynamic Effects

Madrid always,worker fixed-effect at 25 percentile

Madrid always,worker fixed-effect at 75 percentile

Sevilla always,worker fixed-effect at 75 percentile

Sevilla always,worker fixed-effect at 25 percentile

th

th

th

th

0%5%

10%

15%

20%

25%

30%

35%

40%

0 1 2 3 4 5 6 7 8 9 10

Years worked

Ear

ning

s pr

emiu

mre

lati

ve to

San

tiag

o —

med

ian

size

Figure 5: Earnings profile relative to median-sized city, high- and low-ability worker

6. Sorting

Our estimations separately consider the static advantages associated with workers’ current loca-tion, learning by working in bigger cities and spatial sorting. However, we have so far left sortingmostly in the background. Some of the evidence discussed above suggests that sorting acrosscities on unobservables is not very important. Nevertheless, it is possible that there is sorting onobservables. We would also like to provide more direct evidence that sorting on unobservables isunimportant by comparing the distribution of workers’ ability across cities of different sizes.

The concentration in bigger cities of workers with higher education or higher skills associatedwith their occupation has been widely documented for the United States (e.g., Berry and Glaeser,2005, Bacolod, Blum, and Strange, 2009, Moretti, 2012, Davis and Dingel, 2013). A similar patterncan be observed in Spain. In table 5 we compare the distribution of workers across our five skillcategories in cities of different sizes.28 Very-high-skilled jobs (those requiring at least a bachelors orengineering degree) account for 10.9% of the total in Madrid and Barcelona, compared with 6.2%in the 3rd-5th biggest cities, and with 3.5% in cities below the top-five. High-skilled jobs (thosetypically requiring at least some college education) also account for a higher share of the totalthe bigger the city-size class. At the other end, workers employed in medium-low-skilled and

28These skill groups are the same we used as controls in our regressions. They are based on categories assigned byemployers to workers in their social security filings and are closely related to the level of formal education requiredfor the job. For instance, social security category 1 (our ’very-high-skilled occupation’ category) corresponds to jobsrequiring an engineering or bachelors degree and top managerial jobs. Note it is the skills required by the job and notthose acquired by the worker that determine the social security category. For instance, someone with a law degree willhave social security category 1 (our ’very-high-skilled occupation’ category) if working as a lawyer, and social securitycategory 7 (included in our ’medium-low-skilled’ category) if working as an office assistant.

25


Distribution of Workers

5 biggest citiesSmaller cities

Den

siti

es

−1 0 10.00

0.25

0.50

0.75

1.00

1.25

Worker fixed−effects

5 biggest citiesSmaller cities

Den

siti

es

−1 0 10.00

0.25

0.50

0.75

1.00

1.25


Panel (a) Panel (b)Fixed-effects, heterogeneous dynamic and static premium Fixed-effects, homogeneous dynamic and static premium

5 biggest cities

Smaller cities

Den

siti

es

−1 0 10.00

0.25

0.50

0.75

1.00

1.25


5 biggest cities

Smaller cities

Den

siti

es

−1 0 10.00

0.25

0.50

0.75

1.00

1.25

Earnings

Panel (c) Panel (d)Fixed-effects, static premium Earnings

Figure 6: Comparisons of worker fixed-effects distributions across cities

appears larger than it is (this estimation mixes the extra value that big-city experience has for themwith their innate ability), while the ability of workers at the bottom of the distribution appearssmaller than it is. Hence, by ignoring the heterogeneity of the dynamic benefits of bigger cities wecan get the erroneous impression that there is greater dispersion of innate ability in bigger cities.

Panel (c) leaves out any dynamic benefits of bigger cities and plots worker fixed-effects from apurely static specification. We have seen that a static fixed-effects estimation such as that of column(3) in table 1 gives roughly correct estimates of city fixed-effects. Nevertheless, it yields biasedestimates of worker fixed-effects that incorporate not only time-invariant unobserved workercharacteristics that affect earnings, but also the time-varying effect of experience in bigger citiesand its interaction with time-invariant skills. In particular, estimation of µ on the basis of equation(6) if wages are determined as in equation (11) results in a biased estimate of µ:

plim µi fe = µi(1 +C

∑j=1

φj eij) +C

∑j=1

δj eij . (13)

If we do not take this bias into account, it could appear from the estimated fixed-effects thatworkers in bigger cities have higher ability on average even if the distribution of µ in small and

27


Baum-Snow and Pavan (2011)Study similar set of issues than Glaeser and Mare but with more recent dataInverted U-shaped pattern in real wages

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BAUM-SNOW & PAVAN UNDERSTANDING THE CITY SIZE WAGE GAP 5

2.2. Data

The primary data set used for this analysis is the National Longitudinal Survey of Youth 1979(NLSY79) restricted use geocoded and work history files. Using this data set, we constructinformation on jobs, unemployment, wages, and migration patterns for a sample of white menaged 14–21 years on 31 December, 1978 from the time of their entry into the labour force until 15years of work experience, year 2004, or their attrition from the survey, whichever comes first. Wesample the weekly job history data four times every year for those who become attached to thelabour force after 1 January, 1978 and observe wages in about one-quarter of the observations.Appendix A details how we construct the data including our sample selection rules.

2.3. Descriptive patterns

Table1 reports city size wage premia with and without adjustment for cost of living differencesacross locations. The estimated nominal wage premium for medium-sized cities over smallerareas is 0∙19, while that for large cities is 0∙29. Controlling for education and a cubic in workexperience reduces these coefficients to 0∙14 and 0∙22, respectively. Controlling for individualfixed effects additionally reduces these coefficients to 0∙07 and 0∙15.

TABLE 1Estimates of city size wage premia

Individual IndividualIndividual controls and Individual control and

No controls controls fixed effects No controls controls fixed effects

1980’s MSA Temporally deflated only Spatially and temporallydeflated

population 1 2 3 1 2 3

Panel A: full sample

0∙25–1∙5 0∙19∗∗∗ 0∙14∗∗∗ 0∙07∗∗∗ 0∙14∗∗∗ 0∙09∗∗∗ 0∙05∗∗∗

million (0∙03) (0∙03) (0∙02) (0∙03) (0∙02) (0∙02)> 1∙5 million 0∙29∗∗∗ 0∙22∗∗∗ 0∙15∗∗∗ 0∙11∗∗∗ 0∙05∗ 0∙03

(0∙03) (0∙03) (0∙02) (0∙03) (0∙03) (0∙02)R-squared 0∙04 0∙26 0∙60 0∙01 0∙24 0∙59

Panel B: College ormore

0∙25–1∙5 0∙21∗∗∗ 0∙20∗∗∗ 0∙07∗∗ 0∙15∗∗∗ 0∙14∗∗∗ 0∙05∗

million (0∙05) (0∙04) (0∙03) (0∙04) (0∙04) (0∙03)> 1∙5 Million 0∙27∗∗∗ 0∙27∗∗∗ 0∙12∗∗∗ 0∙09∗ 0∙09∗ 0∙01

(0∙05) (0∙05) (0∙04) (0∙05) (0∙05) (0∙040)R-squared 0∙03 0∙18 0∙60 0∙01 0∙18 0∙61

Panel C: high school graduatesonly

0∙25–1∙5 0∙12∗∗∗ 0∙12∗∗∗ 0∙06∗ 0∙09∗∗∗ 0∙09∗∗∗ 0∙05∗

million (0∙03) (0∙03) (0∙03) (0∙03) (0∙03) (0∙03)> 1∙5 million 0∙22∗∗∗ 0∙22∗∗∗ 0∙18∗∗∗ 0∙03 0∙04 0∙05

(0∙03) (0∙03) (0∙04) (0∙04) (0∙03) (0∙04)R-squared 0∙03 0∙14 0∙52 0∙01 0∙14 0∙52

Notes:Eachregression in Panel A uses data on 1754 white men and has 25,363 observations based on quarterly data.Panel B has 7,555 observations on 583 individuals. Panel C has 10,436 observations on 674 individuals. Individualcontrols are four educational dummies and cubic polynomials in work experience. We only include observations fromthe first 15 years of work experience. Standard errors are clustered by location. Complete sample selection rules areexplained in Appendix A. *** indicates significance at the 1% level, ** indicates significance at the 5% level, and* indicates significance at the 10% level.

by guest on March 7, 2012

http://restud.oxfordjournals.org/D

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City Size, Job Turnover, and Unemployment

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BAUM-SNOW & PAVAN UNDERSTANDING THE CITY SIZE WAGE GAP 7

TABLE 2Attributes at 15 years of work experience as functions oflocation

Job–jobchanges Job-unemployment-job changes Fraction inlocation

Location Within To Within Length To Length At Entry At 15Yrs

Size 1 2 3 4 5 6 7 8

Panel A: full sample

Small 2∙7 0∙7 1∙8 22∙9 0∙4 4∙7 0∙32 0∙30Medium 3∙0 0∙6 1∙7 19∙1 0∙3 3∙4 0∙36 0∙39Large 3∙0 0∙4 1∙6 16∙0 0∙3 2∙2 0∙32 0∙30

Panel B: college ormore


Panel C: high school graduatesonly


Notes:Thesample includes all individuals used for the regressions in Table1 except those who we do not observe for atleast 15 years of work experience. Columns marked “Within” report numbers of job changes within location, whereascolumns marked “To” report job changes across locations to locations of the indicated size. Each entry is calculated asthe total amount of the quantity indicated in the column header for the sample indicated in the panel header dividedby the sum of the fraction of time spent by everybody in the sample in the location category given in the row header.Therefore, each entry is the amount of each quantity experienced by the average individual over the first 15 years of workexperience if he were to live in the indicated location for the full time. “Length” refers to total length of all unemploymentspells. “LF” stands for labour force. Bootstrapped standard errors with samples clustered by individual reveal that theonly statistically significant medium–small and large–small differences in Columns 1–6 are in Panel/Columns A2, A5,B1, and C2. College graduates are significantly more likely to be located in large locations at LF entry and 15 years ofexperience. The full sample includes 1425 men, including 466 in the college sample and 566 in the high school sample.

or rural counties of the indicated size, while those headed by “To” indicate transitions that alsoinvolve migration to MSAs or rural counties of the indicated size. Such “To” migration mayoccur between or within size categories but always involves a change of MSA or rural county.Entries are calculated as

(∑

iyi j)/(∑

i

ti jTi

)andrepresent estimates of the expected number of

transitions or weeks of unemployment experienced if an average individual were to spend hisentire first 15 years of experience living in the indicated city size category. In this ratio,yi j is thetotal quantity of each object given in Table2 column headers for each mani in location typejover his firstTi yearsof work experience andti j is the number of years spent working in locationtype j .7

Resultsreported in Table2 reveal few patterns in labour market transitions that could plau-sibly lead to the prevalence of city size wage premia reported in Table1. Within location, theonly statistically significant large–small and medium–small gaps are for job to job transitions for

7. Ti is not exactly 15 for everybody because the data set does not include all of the required information everyquarter. For the purpose of Tables2–4, we only include individuals with a wage observation within 2 years of 15 yearsof work experience and truncate the sample at the wage observation closest to 15 years. For cases in which two wageobservations are equidistant from 15 years, we use the longer sample.



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Firm-Worker match quality not a driver

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8 REVIEW OF ECONOMIC STUDIES

TABLE 31Log wage regressions

Temporally deflated only Spatially and temporallydeflated

All College HS All College HS

1Experience 0∙031∗∗ 0∙046∗∗ 0∙016 0∙031∗∗ 0∙046∗∗ 0∙017in small (0∙012) (0∙019) (0∙023) (0∙012) (0∙019) (0∙023)1Experience 0∙056∗∗∗ 0∙062∗∗∗ 0∙046∗∗∗ 0∙054∗∗∗ 0∙060∗∗∗ 0∙045∗∗∗

in medium (0∙010) (0∙018) (0∙013) (0∙010) (0∙018) (0∙013)1Experience 0∙059∗∗∗ 0∙064∗∗∗ 0∙055∗∗∗ 0∙057∗∗∗ 0∙062∗∗∗ 0∙054∗∗∗

in large (0∙011) (0∙023) (0∙012) (0∙010) (0∙022) (0∙012)1Experience 2 0∙001 0∙000 0∙003 0∙002 0∙001 0∙004

(0∙001) (0∙002) (0∙002) (0∙001) (0∙002) (0∙002)1Exp3 −0∙000∗ −0∙000 −0∙000∗ −0∙000∗∗ −0∙000 −0∙000∗∗

(0∙000) (0∙000) (0∙000) (0∙000) (0∙000) (0∙000)

Jobto job 0∙066∗∗∗ 0∙081∗ 0∙078∗∗∗ 0∙066∗∗∗ 0∙082∗ 0∙079∗∗∗

in small (0∙018) (0∙043) (0∙028) (0∙018) (0∙043) (0∙028)Job to job 0∙097∗∗∗ 0∙126∗∗∗ 0∙094∗∗∗ 0∙096∗∗∗ 0∙126∗∗∗ 0∙093∗∗∗

in medium (0∙010) (0∙024) (0∙016) (0∙010) (0∙024) (0∙016)Job to job 0∙079∗∗∗ 0∙083∗∗∗ 0∙078∗∗∗ 0∙078∗∗∗ 0∙085∗∗∗ 0∙077∗∗∗

in large (0∙012) (0∙022) (0∙015) (0∙012) (0∙023) (0∙015)

Job-un-job −0∙017 0∙043 −0∙050∗∗ −0∙015 0∙043 −0∙047∗in small (0∙017) (0∙092) (0∙025) (0∙017) (0∙092) (0∙025)Job-un-job −0∙027 −0∙022 −0∙028 −0∙028 −0∙022 −0∙029in medium (0∙019) (0∙047) (0∙026) (0∙019) (0∙046) (0∙026)Job-un-job 0∙021 0∙026 0∙025 0∙021 0∙028 0∙023in large (0∙015) (0∙054) (0∙020) (0∙015) (0∙054) (0∙019)

Job-job+move 0∙099∗∗∗ 0∙212∗∗∗ 0∙032 0∙126∗∗∗ 0∙245∗∗∗ 0∙053to small (0∙032) (0∙055) (0∙057) (0∙032) (0∙057) (0∙058)Job-job+move 0∙116∗∗∗ 0∙118∗∗∗ 0∙019 0∙133∗∗∗ 0∙144∗∗∗ 0∙027to medium (0∙036) (0∙044) (0∙058) (0∙032) (0∙043) (0∙058)Job-job+move 0∙085∗∗ 0∙113∗∗∗ −0∙134 0∙055∗ 0∙107∗∗∗ −0∙204∗∗

to large (0∙034) (0∙041) (0∙101) (0∙032) (0∙040) (0∙100)

Job-un-job+ −0∙033 −0∙013 0∙000 0∙004 0∙019 0∙029move to small (0∙042) (0∙101) (0∙058) (0∙041) (0∙100) (0∙057)Job-un-job + −0∙072∗ −0∙007 −0∙089 −0∙028 0∙028 −0∙025move to medium (0∙044) (0∙095) (0∙063) (0∙044) (0∙091) (0∙062)Job-un-job + 0∙161∗∗∗ 0∙184∗∗ 0∙234∗∗∗ 0∙109∗ 0∙143∗∗ 0∙158∗

move to large (0∙055) (0∙074) (0∙071) (0∙058) (0∙060) (0∙087)

Unobservable job −0∙105∗∗∗ −0∙180∗∗ −0∙140∗∗ −0∙100∗∗ −0∙163∗∗ −0∙142∗∗

to small (0∙038) (0∙082) (0∙068) (0∙040) (0∙081) (0∙069)Unobservable job −0∙086 −0∙035 −0∙164∗ −0∙085 −0∙052 −0∙152∗

to medium (0∙074) (0∙197) (0∙087) (0∙073) (0∙191) (0∙086)Unobservable job −0∙077 −0∙014 −0∙107 −0∙085 −0∙038 −0∙093to large (0∙080) (0∙186) (0∙099) (0∙081) (0∙186) (0∙100)

Observations 21,481 6,276 9,020 21,481 6,276 9,020R-squared 0∙019 0∙028 0∙020 0∙020 0∙030 0∙020

Notes:Eachcolumn is a separate regression of the change in log wage on functions of experience or labour markettransitions listed at left. The regression specification is given by equation (6) in the text with standard errors clusteredby location. The 185 cases of gaps between wage observations exceeding ten quarters are excluded. *** indicatessignificance at the 1% level, ** indicates significance at the 5% level, and * indicates significance at the 10% level.



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Conclusions

Returns to experience and wage-level effects are the most importantmechanisms contributing to the overall city size wage premium

Differences in wage intercepts across location categories are more importantfor generating medium—small wage gaps

Differences in returns to experience are more important for generatinglarge—small city size wage gaps

Sorting on unobserved ability within education group and differences inlabour market search frictions independently contribute slightly negatively, ifat all, to observed city size wage premia


More Segregation over Time (Diamond 2016)486 THE AMERICAN ECONOMIC REVIEW MARCH 2016

Cities’ local wages have a similar but less strong relationship with the local college employment ratio. Panel C plots changes in local college employment ratios against changes in local noncollege wages from 1980 to 2000. A 1 percent increase in college employment ratio is associated with a 0.24 percent increase in noncollege wages. Low skill workers were both initially and increasingly concentrating in low wage cities.

Panel D shows that a 1 percent increase in a city’s college employment ration is associated with a 0.30 percent increase in college wages. Additionally, college employment ratio changes can explain 36 percent of the variation in local college wage changes. College workers are increasingly concentrating in high wage cities and high skill wages are closely linked to a city’s skill-mix. Moretti (2013) has also documented this set of facts and refers to them as “the Great Divergence” in Moretti (2012).

The polarization of skill across cities coincided with a large, nationwide increase in wage inequality. Table 2, along with a large literature, documents that the nation-wide average college/high school graduate wage gap has increased from 38 percent in 1980 to 57 percent in 2000.11

11 This is estimated by a standard Mincer regression using individual 25–55-year-old full-time, full-year work-ers’ hourly wages and controls for sex, race dummies, and a quartic in potential experience.

Boston

Chicago

DallasDetroit

Houston

Los AngelesMinneapolis

New YorkPhiladelphiaSan Francisco

Washington

−0.5

0

0.5

1

∆ ln

col

lege

em

ploy

men

t ra

tio 1

980−

2000

−2 −1.5 −1 −0.5 0

In college employment ratio, 1980

Panel A

Boston

Chicago

DallasDetroit

Houston

Los AngelesMinneapolis

New York

Philadelphia

San Francisco

Washington

β = 0.70(0.044)

R2 = 0.49

β = 0.17(0.027)

R2 = 0.13 −0.4

−0.2

0

0.2

0.4

0.6

∆ ln

ren

t 19

80–2

000

−0.5 0 0.5 1

∆ ln college employment ratio, 1980−2000

Panel B

Boston

Chicago

Dallas

DetroitHouston

Los Angeles

Minneapolis

New York

Philadelphia

San FranciscoWashington

−0.2

−0.5

−0.1

0

0.1

0.2

0.3

∆ ln

non

colle

ge w

age

1980

−20

00

0 0.5 1


Panel C

Boston

ChicagoDallas

Detroit

HoustonLos Angeles

Minneapolis

New York

Philadelphia

San Francisco

Washington

−0.2

0

0.2

0.4

0.6

∆ ln

col

lege

wag

e19

80−

2000

−0.5 0 0.5 1


Panel D

β = 0.237(0.026)

R2 = 0.24

β = 0.30(0.025)

R2 = 0.36

Figure 1. Changes in Wages, Rents, and College Employment Ratios, 1980–2000

Notes: Weighted by 1980 population. Largest 15 MSAs in 1980 labeled.


Lecture 5: Urban Sorting, Skills, and Wageserossi/Urban/Lecture_5_538.pdf · ERH (Princeton University) Lecture 5: Urban Sorting, Skills, and Wages 8 / 24. Using individual level

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