Urbaniza(on and Inequality Fron(ers of Urban Economics Conference
Nathaniel Baum-­‐Snow Brown University Goals hlight some important facts in the data that demonstrate a poten=ally important role for local labor rkets in understanding wage and income inequality Average wage gaps between ci=es of different sizes Differences in wage distribu=ons between ci=es of different sizes =onalize these facts in a spa=al equilibrium environment mine evidence on poten=al mechanisms driving these differences Labor & macro literatures Nature of agglomera=on economies ecify what we don’t know yet A lot! U.S. Na=onwide Growth in Wage Inequality illed Worker Definition
nskilled Worker Definition
Some College+
High School-­‐
College+
Some College-­‐
College+
High School-­‐
College Only
High School Only
0.50
0.62
0.66
0.72
0.38
0.46
0.50
0.55
0.60
0.67
0.72
0.80
0.48
0.53
0.57
0.64
Panel A: All Workers
1980
1990
2000
2005-­‐7
0.30
0.38
0.43
0.48
0.47
0.54
0.57
0.62
Panel B: Manufacturing Workers Only
1980
1990
2000
2005-­‐7
0.36
0.42
0.46
0.53
0.56
0.59
0.63
0.70
U.S. Na=onwide Growth in Wage Inequality 0.2
0.1
1989-­‐1999 0
1999-­‐2007 -­‐0.1
1979-­‐1989 -­‐0.2
0
25
50
Percentile
75
100
U.S. Na=onwide Growth in Wage Inequality Year
1979
1989
1999
2004-7
79-07
Change
Variance
0.21
0.29
0.34
0.39
Total
90-50 Gap
0.53
0.62
0.72
0.81
50-10 Gap
0.63
0.70
0.67
0.74
0.18
0.28
0.11
ln widst = α dst + ε idst
Year
1979
1989
1999
2004-7
Total
Variance
0.21
0.29
0.34
0.39
Between
Variance
0.05
0.08
0.10
0.12
Residual
Variance
0.16
0.21
0.25
0.27
79 to 07 Change
0.18
0.07
0.11
Average Wage Differences Across Metropolitan Areas Mean Log Wage Relative to Small Cities and Rural Areas
Decennial Census 5% PUMS
MSAs: 250,000 - 1.5 million
MSAs: > 1.5 million
R-squared
1980
1990
2000
0.14***
(0.01)
0.23***
(0.01)
0.18***
(0.01)
0.31***
(0.01)
0.19***
(0.01)
0.32***
(0.01)
0.03
0.05
0.04
MSA
ation
to 1.5
Million
Million
quared
Average Metro Area Wage Differences – Panel Data All Male Workers No Controls
1
0.19***
(0.03)
0.29***
(0.03)
0.04
Individual
Controls
2
0.14***
(0.03)
0.22***
(0.03)
0.26
1980 MSA
Population
Individual
Controls and
Fixed Effects
3
0.07***
(0.02)
0.15***
(0.02)
0.60
No Controls
Individual
Controls
1
2
Individual
Controls and
Fixed Effects
3
College or More
0.25 to 1.5
Million
> 1.5 Million
R-squared
0.21***
(0.05)
0.27***
(0.05)
0.03
0.20***
(0.04)
0.27***
(0.05)
0.18
0.07**
(0.03)
0.12***
(0.04)
0.60
High School Graduates Only
0.25 to 1.5
Million
> 1.5 Million
R-squared
0.12***
(0.03)
0.22***
(0.03)
0.03
0.12***
(0.03)
0.22***
(0.03)
0.14
0.06*
(0.03)
0.18***
(0.04)
0.52
Variance of Weekly Wages by City Size 0 = Rural Areas 1-­‐10 = Deciles of Urban Popula(on by City Size
0.6
0.5
0.4
0.3
0.2
1970 0.1
0
2
4
6
8
10
Variance of Weekly Wages by City Size 0 = Rural Areas 1-­‐10 = Deciles of Urban Popula(on by City Size
0.6
0.5
0.4
0.3
1980 0.2
1970 0.1
0
2
4
6
8
10
Variance of Weekly Wages by City Size 0 = Rural Areas 1-­‐10 = Deciles of Urban Popula(on by City Size
0.6
0.5
0.4
1990 0.3
1980 0.2
1970 0.1
0
2
4
6
8
10
Variance of Weekly Wages by City Size 0 = Rural Areas 1-­‐10 = Deciles of Urban Popula(on by City Size
0.6
0.5
2000 0.4
1990 0.3
1980 0.2
1970 0.1
0
2
4
6
8
10
Variance of Weekly Wages by City Size 0 = Rural Areas 1-­‐10 = Deciles of Urban Popula(on by City Size
0.6
2007 0.5
2000 0.4
1990 0.3
1980 0.2
1970 0.1
0
2
4
6
8
10
Some College+ vs. High School-­‐ Wage Gaps by City Size All Workers
2005-7
.6
2000
.5
1990
.4
1980
.3
.2
8.5
Rural Areas 10.5
12.5
Log 1980 CBSA Population
14.5
16.5
Skilled & Unskilled Wages by City Size – All Workers
2000
2005-7
1990
2.95
Some College or More 1980
2.85
2.75
2.65
2.55
2.45
8.5
10.5
12.5
Log 1980 CBSA Population
14.5
16.5
2.55
1980
High School or Less 1990
2.45
2000
2.35
2005-7
2.25
2.15
8.5
10.5
12.5
Log 1980 CBSA Population
14.5
16.5
Firm TFP in France Combes et al. (2012)
Ra=onalizing Cross-­‐Sec=onal Wage PaYerns in the Data bouy (2015) formalizes the “Rosen-­‐Roback” long-­‐run spa=al equilibrium condi=ons Producers of tradeables indifference condi=on •  Lets us learn about traded produc=vity differences across loca=ons Consumer indifference condi=on •  Lets us learn about quality of life differences across loca=ons •  Allows us to think about the labor supply environment Indifference Condi(on for Firms Producing Tradeables
ose firms are in long-­‐run loca=on equilibrium, produce tradeables using a CRS technology, are perfectly mobile and have (L), capital (K) and local goods (R) as inputs. From this, we see that wage gaps across loca=ons are closely related to uc=vity differences across these loca=ons π = max{a j F ( L, K , R) − w j L − rK − p j R}
L,K ,R
implies
ln w j − ln w j ' =
ln a j − ln a j '
φL
−
φR
[ln p j − ln p j ' ]
φL
ves factor input shares bra=ons of parameters indicate that nominal city size wage gaps overstate produc=vity differences by about 15 percent •  Implica=on is that wage differences across loca=ons are closely related to produc=vity differences across loca=ons i=onal labor factors of produc=on do not change this conclusion much since all skill types have higher wages in larger •  More on skill heterogeneity below What Factors Could Account For The City Size Wage Gap?
1.  Sor=ng of more able workers into larger ci=es 2.  Agglomera=on economies (Duranton and Puga, 2004): •  “Sharing” : •  Indivisibili=es in intermediate inputs •  Risk sharing •  Input market pooling Empirically amounts to differences in wage intercepts across loca=on types •
“Learning” : •  Different rates of human capital accumula=on by workers Differences in returns to experience across loca=on types •
•
“Matching” : •  Thicker labor markets mean more rapid ascending of job ladders •  Higher variance distribu=ons of firm-­‐worker match quality exist in thicker labor markets Differences in job turnover and firm-­‐worker component of wages across loca=on types We can imagine many of these mechanisms may be likely to be skill-­‐biased Long-­‐Run Consumer Indifference Condi(ons
•  Indirect u=li=es across equated across loca=ons j for those of each type c for each skill group g local local wages prices ameni=es •  Albouy (2015) shows that this generates the equilibrium condi=ons across loca=ons: ∂ ln V / ∂ ln q
d ln w = β g d ln p −
d ln q gc
∂ ln V / ∂ ln w
g
expenditure share on local goods U is typically specified as qu(x,H) u() homothe=c, making this a constan
•  There are important lifecycle considera=ons for consumers though that turn out to maYer a lot in prac=ce – more on that later Using Consumer Indifference to Recover Labor Supply Func(ons to Ci(es
•  Following Notowidigdo (2013), suppose there is a migra=on fric=on such that each individual draws from a distribu=on of migra=on costs to each loca=on such that the last (highest cost) migrant of type gc to j pays M(.) in migra=on cost. This generates a wedge in differences, assuming constant consumer ameni=es over =me. (Diamond (2015) generates upward sloping labor supply with taste shocks.) •  Differen=a=ng over =me, we get the following law of mo=on, imposing g
gc
d ln w j − β g d ln p j − M g (d ln j N gc , N j 0 ) = (1 /
d ln V
)d ln v gc
d ln w 1
gc
2
gc
g
•  Solving for the change in indirect u=lity and specifying M = α g d ln N j − α g N j 0
own effect compe==on effect Quan=ty effect •  We will come back to this later, as it turns out to be useful for iden=fica=on City Costs
•  On one side of the ledger were the produc=vity advantages of density, on the other side is city costs, or what generates differences in pj across ci=es •  The liYle empirical evidence we have (Combes, Duranton & Gobillon, 2014) indicates that dlnpj/dlnNj is comparable to dlnwj/dlnNj, both at about 0.04 •  Urban costs are typically derived using a monocentric model of city structure •  A big important topic for developing countries trying to decide on infrastructure, and how much urbaniza=on to facilitate as a result Ques=ons How much urbaniza=on should we encourage in developing countries? What are the returns to reducing migra=on fric=ons and why? •  Bryan & Morten (2015) look at effects of migra=on fric=ons in Indonesia and the US, find big gains to reducing them in Indonesia •  Bryan, Chowdhury & Mobarak (ECMA, 2014) run an RCT in Bangladesh that give out bus =ckets for migra=on, find huge effects •  Ques=on of scalability Related theore=cal literature thinks about op=mal city size distribu=ons in the US and Chinese contexts taking
nto account agglomera=on externali=es (Desmet & Rossi-­‐Hansberg, 2013; Albouy, Behrens, Robert-­‐Nicoud, 015; Hsieh & Morem, 2015) Big important ques=ons about how to provide efficient urban infrastructure in developing countries to facilita
urbaniza=on, and how much such infrastructure is op=mal to provide Decomposing Sources of Agglomera=on Economies Baum-­‐Snow & Pavan (2012) arge empirical literature providing evidence of the produc=vity advantages of size or density •  Rosenthal & Strange (2004), Combes et al. (2008, etc.) Much less empirical literature that separates out mechanisms driving these changes •  Goal is to do so using a lifecycle model that incorporates “sharing”, “matching”, “learning” and endogenou
migra=on ery liYle use of lifecycle models in urban economics, but lifecycle considera=ons turn out to be important •  Can ra=onalize viola=on of the sta=c consumer indifference condi=on without sor=ng on unobservables –
more valuable experience early in the lifecycle in big ci=es in order to take to small ci=es se NLSY work history data, observe wage, job, loca=on •  Availability of large matched data sets means one could do more in this dimension – go big data! Wage Changes With Labor Market Transi(ons
•  Es=mate regression All
College
Δ Experience
HS
0.031**
0.046**
0.016
in Small
Δ Experience
in Medium
Δ Experience
in Large
Job to Job
in Small
Job to Job
in Medium
Job to Job
in Large
Job-Un-Job
in Small
Job-Un-Job
in Medium
Job-Un-Job
in Large
(0.012)
(0.019)
(0.023)
0.056***
0.062***
0.046***
(0.010)
(0.018)
(0.013)
0.059***
0.064***
0.055***
(0.011)
(0.023)
(0.012)
0.066***
0.081*
0.078***
(0.018)
(0.043)
(0.028)
0.097***
0.126***
0.094***
(0.010)
(0.024)
(0.016)
0.079***
0.083***
0.078***
(0.012)
(0.022)
(0.015)
-0.017
0.043
-0.050**
(0.017)
(0.092)
(0.025)
-0.027
-0.022
-0.028
(0.019)
(0.047)
(0.026)
0.021
0.026
0.025
(0.015)
(0.054)
(0.020)
•  Only coefficients monotonic in city size on a posi=ve base are on experience •  Many problems with causal interpreta=on in this regression b/c of endogenous migra=on •  Similar results with adjustments for cost of living Sta(s(cal Wage Growth Decomposi(on
Wage at LF Entry
COL Adj. Unadjusted
Within
Job
Job to Job
Within
Between
Job to Unemp. to Job
Within
Between
UnKnown
Total
Growth
Small
2.14
2.09
0.28
0.18
0.06
-0.03
-0.02
-0.01
0.47
Medium
2.22
2.20
0.44
0.25
0.06
-0.05
-0.02
0.00
0.67
0.74
0.34
-0.01
-0.06
-0.01
0.01
0.51
0.22
0.04
0.01
0.03
-0.01
0.66
0.11
-0.06
0.14
0.16
0.00
Frac of Diff With Sm all
Large
2.11
Frac of Diff With Sm all
2.22
•  Ini=al levels and within job wage growth are the only components of wages at 15 years of experience that are monotonic in loca=on size •  Within job is by far the greatest in percentage terms as well, though job-­‐job within also appears poten=ally important between small and medium 0.80
Model
airly standard dynamic par=al equilibrium on-­‐the-­‐job search model •  Endogenous migra=on between three city size categories •  Three unobserved worker types making this a “Finite Mixture Model” (Heckman & Singer, 1984; Keane & Wolpin, 1997; Kasahara, 2009) •  Es=mate returns to experience, wage process intercepts, labor market search fric=on and match parameters by loca=on and type Modeling considera=ons •  Flexible enough to fit the data •  Not too flexible such that it can’t be es=mated •  Able to separate out mechanisms of interest: •  Sor=ng •  Level Effects •  Experience Effects •  Search & Matching Effects The Wage Process
2
3
3
3
⎛
⎞
⎛
⎞
j
lnw j (h, x1, x 2 , x 3,ε,u) = ε + β 0 (h) + ∑ β1kj (h)x k + β 2j ⎜∑ x k ⎟ + β 3⎜∑ x k ⎟ + u
⎝ k=1 ⎠
⎝ k=1 ⎠
k=1
3
•  h is latent type: A, B or C •  xk is years of work experience in loca=on k •  We allow wages to depend both on current work loca=on and experience from other loca=ons •  ε is firm-­‐worker specific component of the wage, or the “match quality” •  The distribu=on of ε depends on loca=on and worker type •  u is the wage (mean 0) i.i.d. measurement error. Its distribu=on depends on loca=on •  The distribu=on of worker types depends on loca=on of LF entry Addi(onal Elements of the Model
•  Indirect search with job offer arrival rates {λj(h), λjj’(h)} for employed workers and {λuj(h), λujj’(h)} for unemployed workers. •  Differ by “from” loca=on, “to” loca=on and latent type •  Differ if individuals switch jobs within the same city and within the same city size category •  Exogenous separa=on rates δj(h) ater which individuals must go unemployed •  Idiosyncra=c shocks that allow the model to capture in a reduced form way isolated behavior in the data that would otherwise be inconsistent with the model •  Shock to unemployment benefit: vU •  Shock to moving cost: vM •  Shock to op=on value of job offer:
vS Value Func(ons at the Beginning of Each Period
Vj
UN
=
α j ( h)
1
3
+ ln b j + β V j
U
3
WK
V j (ε ) = α j (h) + ln w j (⋅) + βV j (ε )
•  The value of being unemployed for 1 month consists of •  amenity value of j •  unemployment benefit •  discounted op=on values to be specified on the next slide •  The value of working for 1 quarter consists of •  amenity value of j •  wage •  discounted op=on values to be specified shortly •  The firm worker match ε, individual type h, loca=on j, and loca=on specific experience x1, x2, x3 are the state variables (6 state variables for employed workers) Possibili(es for the Unemployed Individual
•  The unemployed individual faces 3 possible scenarios •  No job offer anywhere: Vj
UN
+ vU
•  Receive a job offer in the same city with match quality ε. Accept if offer is good enough: Vj
UN
+ vU ≤ V j
WK
(ε )
•  Receive an offer in a different city. Accept if offer is good enough: Vj
UN
WK
+ vU ≤ V jʹ′
(ε ) − [CM + vM ]
Possibili(es for the Unemployed Individual
Vj
U
3
⎛
u
u ⎞
UN
⎜
⎟
= ⎜1 − λ j − ∑ λ jjʹ′ ⎟ EvU V j + vU +
j ʹ′ =1
⎝
⎠
(
(
u
+ λ j EvU ,ε j max V j
3
u
UN
+ vU , V j
(
+ ∑ λ jjʹ′ EvU ,vM ,ε jʹ′ max V j
j ʹ′ =1
UN
WK
)
(ε ))+
+ vU , V
WK
j ʹ′
(ε ) − [CM + vM ])
•  The unemployed individual faces 3 possible scenarios •  No job offer anywhere •  He receives a job offer in his same city •  He receives an offer in a different city •  No=ce that the worker is not allowed to move to a different city without a job. This is comes from the fact that we usually do not observe the loca=on of unemployment Possibili(es for the Employed Individual
•  At the beginning of the period the worker can be exogenously separated with probability δj: •  He also observes the new shock to the value of unemployment and decides to keep working if: Vj
UN
+ vU ≤ Value of still working
Possibili(es for the Employed Individual
•  If he keeps working, three possible scenarios can happen: •  No job offer from a different firm: V j WK (ε)
•  Job offer from a different firm in the same city. He will switch employer if: Vj
WK
WK
(ε) ≤ V j (εʹ′) − v S
•  Job offer from a different firm in a different city. He will switch employer if: Vj
WK
W
(ε) ≤ V j ʹ′ (εʹ′) − v S − [CM + v M ]
Possibili(es for the Employed Individual
V j (ε ) = δ jV j
UN
{
+ (1 − δ j )EvU max V j
UN
+ vU ,
3
⎛
⎞ WK
⎜1 − λ j − ∑ λ jjʹ′ ⎟V j (ε ) +
⎜
⎟
ʹ′
j
=
1
⎝
⎠
(
+ λ j EvS ,ε ʹ′j max V j
3
WK
(ε ),V jWK (ε ʹ′) − vS )+
(
+ ∑ λ jjʹ′ EvS ,vM ,ε ʹ′jʹ′ max V j
j ʹ′ =1
WK
(ε ),V
WK
j ʹ′
⎫
(ε ʹ′) − vS − [CM + vM ] ⎬
⎭
)
•  The employed individual at loca=on type j faces several possible scenarios •  He gets exogenously separated and goes unemployed •  If he is not separated he has to choose whether he wants to con=nue working •  If he con=nues working he might receive a wage offer from the same loca=on or from a different loca=on which he has to accept or decline Es(ma(ng the Model by Maximum Likelihood
•  The biggest difficul=es in specifying the likelihood func=on are: •  We do not observe the firm specific wage component (which varies over =me) •  We do not observe worker type (which is constant) •  The wage is not always observed and this event is not random •  Wages are observed on interview dates and just before leaving jobs •  We use •  An integrated likelihood func=on •  “Non-­‐linear state space model” (extensive use of Bayesian upda=ng) Es(ma(ng the Model by Maximum Likelihood
Individual observation : Yt = (ln wt , x1t , x2t , x3t , JM t , loct )
History is : Y t = (Yt , Yt −1 ,..., Y1 )
For an individual entering the labor force in location j,
A
(
)
(
B
) (
A
L(θ ) = π j f Y T | hA ;θ + π j f Y T | hB ;θ + 1 − π j − π j
B
) f (Y
Notice that we condition on initial location. Using the usual
decomposition we can write :
(
T
T
)
(
f Y | h;θ = f (Y1 | h;θ )∏ f Yt | Y t −1 , h;θ
t =1
(
)
)
Unfortunately f Yt | Y t −1 , h;θ is a complicated object
T
| hC ;θ
)
Iden(fica(on
•  Parameters indexed by type vs. parameters indexed by loca=on •  Kasahara & Shimotsu (2009) derives iden=fica=on results for general finite mixture models •  Migra=on is key. We need to observe some people in different loca=ons. By looking at the labor market outcomes of the same individual over =me across different loca=ons, we can infer the direct contribu=ons of the city size effects as separate from type effects •  Firm-­‐worker match distribu=ons •  As is standard in search models, non-­‐parametrically not iden=fied. We do not observe rejected wage offers. Therefore, we have to infer the let tail of the match distribu=ons from their rightward por=ons and parameterize as normals •  Transi=ons through unemployment help by giving draws from uncondi=onal match distribu=ons How the Model Captures Different Mechanisms
•  Intercepts β0j(h) in the wage process capture “level effects” •  Slope coefficients in the wage process capture “experience effects” •  Arrival and separa=on rate parameters λj(h) and δj(h) capture “search” •  Distribu=ons of match quality Fεj(ε) capture “matching” •  Indexa=on of all of these parameters by worker type h captures “unobserved heterogeneity” •  Labor force entry probabili=es by worker type h captures “sor=ng on unobservables” •  The model also incorporates other parameters that allow us to reasonably characterize other aspects of the life-­‐cycle (ameni=es, moving costs, job switching costs, shocks) •  We emphasize that we can separately iden=fy different classes of explana=ons for city size wage premia, but poten=ally not the accurate underlying micro-­‐founded mechanisms that are encompassed by the channels we examine Using the Model
•  It is not simple to understand the rela=ve importance of each component of the city size wage gap by looking at parameter es=mates •  In order to evaluate the importance of each component we examine what happens when we equalize its associated parameters across different loca=ons •  We do this first in an environment with fully restricted mobility •  More successfully represents the true environment, in which migra=on rates across loca=ons are very low and allows us not to have to worry about general equilibrium effects •  This is done with real wages but for each channel we also show the implied reduc=on in the nominal wage gap which we think is closer to the gap in marginal produc=vity Actual and Simulated Wage Premia
Regression Coefficients
Medium
Large
College Sample
1. Baseline Data
2. Model
3. Restricted Mobility (Compare to Row 2)
4. Price Differential
0.14
0.14
[0.07, 0.21]
0.15
[0.07, 0.24]
0.06
0.09
0.09
[0.02, 0.17]
0.13
[0.04, 0.23]
0.18
High School Sample
1. Baseline Data
2. Model
3. Restricted Mobility (Compare to Row 2)
4. Price Differential
0.09
0.09
[0.05, 0.19]
0.10
[0.04, 0.19]
0.03
•  Evidence that sor=ng on unobservables is not so important 0.04
0.04
[-0.05, 0.29]
0.04
[-0.02, 0.29]
0.18
Consistent with li
considera=ons of
able moving out o
ci=es ater gainin
valuable experien
there Counterfactuals With Restricted Mobility – College Sample Experiment
Restricted Mobility
Equalize Ability Distribution at LF Entry
Implied Reduction in Marginal Productivity Gap
Equalize Search & Matching Across Locations
Implied Reduction in Marginal Productivity Gap
Equalize Returns to Experience Across Locs
Implied Reduction in Marginal Productivity Gap
Equalize Nominal Intercepts Across Locs
Implied Reduction in Marginal Productivity Gap
Regression Coefficients
Medium
Large
0.15
[0.07, 0.24]
0.13
[0.04, 0.23]
0.17
0.14
0.14
0.11
0.06
-0.04
0.01
0.02
Gap With Reference
Medium
Large
0.02
-10%
0.00
2%
-0.08
39%
-0.13
65%
0.01
-3%
-0.03
8%
-0.17
57%
-0.11
37%
Counterfactuals With Restricted Mobility – High School Sample Experiment
Restricted Mobility
Equalize Ability Distribution at LF Entry
Implied Reduction in Marginal Productivity Gap
Equalize Search & Matching Across Locations
Implied Reduction in Marginal Productivity Gap
Equalize Returns to Experience Across Locs
Implied Reduction in Marginal Productivity Gap
Equalize Nominal Intercepts Across Locs
Implied Reduction in Marginal Productivity Gap
Regression Coefficients
Medium
Large
Gap With Reference
Medium
Large
0.10
[0.04, 0.19]
0.04
[-0.02, 0.29]
0.00
0.00
0.08
0.10
0.13
0.04
0.06
-0.14
-0.02
-0.04
-0.02
16%
0.04
-31%
-0.04
29%
-0.12
97%
0.07
-29%
0.00
-1%
-0.17
78%
-0.07
34%
Returning to Fixed Effects Es(mates
Controls, Data
FE, Data
FE, Sim Data
College Sample
Medium
Large
0.14***
(0.04)
0.09*
(0.05)
0.05*
(0.03)
0.01
(0.04)
0.06
-0.05
High School Sample
Medium
Large
0.09***
(0.03)
0.04
(0.03)
0.05*
(0.03)
0.05
(0.04)
0.03
0.00
•  Model successfully replicates aYenuated fixed effects es=mates that look like posi=ve sor=ng on ability •  Model at the same =me delivers through counterfactual experiments nega=ve sor=ng on ability over the lifecycle •  Assump=on(s) needed for consistency of FE es=mates likely to be violated What Else Can LifeCycle Models Tell Us?
•  Lifecycle migra=on paYerns (Wang, 2015) •  Career specific human capital accumula=on and career shopping (Pavan, 2010) •  Return migra=on paYerns (Kennan & Walker, 2011; de la Roca 2014) De la Roca & Puga (2015)
Es=mate panel wage regressions of the following form using an enormous sample of workers in Spain Results show the importance of dynamic experience effects Distribu(ons of Effects
They interact es=mated fixed effects with experience to recover informa=on about the heterogeneity of experience effects Points to one poten=ally important mechanism driving higher wage inequality in larger ci=es Fixed Effects and Sor(ng
Find liYle evidence of sor=ng, based on distribu=ons of fixed effects located in large and small ci=es rom the fully saturated specifica=on Slightly more dispersed in bigger ci=es, but not much Poten=al difficulty of endogeneity of loca=on of labor force entry and migra=on •  Dahl (2000) handles this by using varia=on in place of birth nves(ga(ng City Size and Inequality Over Time
•  What role does “city size” have in causing the observed increases in “between” and “residual” wage dispersion? •  How much is from city size’s effects on prices vs. quan==es of observed and unobserved skills? Graphical Analysis
•  Larger rela=ve demand gaps today across loca=ons than in 1980 Rela=ve Wage Large Locs in Small Locs in 1980 1980 Rela=ve Quan=ty Graphical Analysis
•  Larger rela=ve demand gaps across loca=ons today than in 1980 Rela=ve Wage Large Locs Today Small Locs Today Large Locs in Small Locs in 1980 1980 Rela=ve Quan=ty •  Strong evidence of rela=ve rela=ve demand shits (Katz & Murphy, 1992) Framework for Examining The Roles of Demographics and City Size (Baum-­‐Snow & Pavan, 2013)
•  As shown by DiNardo, For=n & Lemieux (1996), the distribu=on of wages at =me t can be broken up into, means m, residual “price” distribu=ons g and “quan=ty” distribu=ons h f t (ε ) = ∫ g t (ε | x, s )ht (x, s )dsdx
at (w) = ∫ g t (w − mt ( x, s ) | x, s )ht (x, s )dsdx
ε = residual
x = demographics (75 ageXeduc cells)
s = city size (0 - 10)
m = demographic group mean
Accoun(ng for Quan((es Only
•  Replace the distribu=on of people within each demographic group across city size categories with that from 1980. This gives us a counterfactual distribu=on that takes out changes in sor=ng on observed skill across loca=ons, but allows the na=onwide shits in the composi=on of the popula=on that occurred to remain. q
f t (ε ) = ∫ gt (ε | x, s )ha1979 (s | x )hbt (x )dsdx
Addi(onally Accoun(ng for Prices
hin each skill group, maintain the same percen=le rela=onships between rural loca=ons and each n size category that existed in 1980. Take the evolu=on of wage inequality in rural loca=ons as enous. •  This is an implementa=on of the “Changes in Changes” model of Athey and Imbens (2006) where
rural loca=ons are the “control” group and each city size category is a different “treatment” group •  Murphy, Juhn & Pierce (1993) do something similar using na=onal distribu=ons •  Suppose that each residual is the product of a price and quan=ty of unobserved skill, and the distribu=ons of unobserved skill do not change over =me ε t ( x, s ) = ρ t ( x, s )u (φ | x, s) implies
ρ ( x,0)
ε t p ( x, s ) = ρ1979 ( x, s ) t
u (φ | x, s )
ρ1979 ( x,0)
Accoun(ng for Prices and Quan((es
•  Calculate the counterfactual price distribu=on gtp(ε|x,s) by combining all of these individual counterfactual residuals •  Generate counterfactual distribu=on of residuals taking into account both prices and quan==es ft
c
(ε ) = ∫
p
gt (ε | x, s )ha1979 (s | x )hbt (x )dsdx
Inves(ga(ng the Importance of the Level of Sor(ng on Observed Skill for Price Results
•  Carry out the same exercise on the same set of residuals εt(x,s) but place everyone in the same demographic group. This yields the following counterfactual distribu=on: n
n
f t (ε ) = ∫ gt (ε | s )h1979 (s )ds
•  Comparison of inequality measures in the resul=ng counterfactual distribu=on to that in the one that fully accounts for prices and quan==es reveals the importance of accoun=ng for differences in the composi=on of observed demographic groups across different loca=ons Counterfactual Residual Growth – Reduc(ons Rela(ve to Actual
1
Calculated Using
X Set
Adjustment
f t q (ε )
Full Demog
Quantities
c
2
3
n
f t (ε )
ft (ε )
20%
49%
35%
26%
59%
43%
Full Demog
No Demog
Residual Prices Residual Prices
& Quantities
& Quantities
Panel A: Variance
1979 to 1989
1979 to 1999
1979 to 2004-7
0%
-2%
-2%
Panel B: 90 - 50 Percentile Gap
1979 to 1989
1979 to 1999
1979 to 2004-7
0%
-1%
-1%
21%
36%
30%
46%
62%
50%
Panel C: 50 - 10 Percentile Gap
1979 to 1989
1979 to 1999
1979 to 2004-7
0%
-3%
-3%
7%
104%
58%
-2%
88%
51%
Construc(ng Counterfactual log Wage Distribu(ons
•  Our counterfactual mean wages are very conserva=ve as they allow the overall mean wages to move as they did in equilibrium. If we instead index to rural loca=ons, we get much larger effects. c
mt ( x, s) = ∫ mt ( x, s)hat ( s | x)ds + [m1979 ( x, s) − ∫ m1979 ( x, s)hat ( s | x)ds ]
•  The resul=ng counterfactual distribu=on is: at
c
(w) = ∫ g (w − m
p
t
t
c
(x, s ) | x, s )ha1979 (s | x )hbt (x )dsdx
•  Carry out the same exercise assigning everyone to the same demographic group Counterfactual log Wage Growth
1
Calculated Using
X Set
Adjustment
q
at (w)
Full Demog
Quantities
2
at (w)
3
c
ε
Full Demog
Residual Prices
& Quantities
at (w)
4
n
at (w)
Full Demog
Total Prices
& Quantities
No Demog
Total Prices
& Quantities
16%
34%
23%
26%
50%
43%
-10%
17%
20%
17%
50%
51%
16%
78%
20%
14%
102%
41%
Panel A: Variance
1979 to 1989
1979 to 1999
1979 to 2004-7
-2%
-2%
-1%
10%
31%
21%
Panel B: 90 - 50 Percentile Gap
1979 to 1989
1979 to 1999
1979 to 2004-7
-4%
2%
-2%
-14%
14%
17%
Panel C: 50 - 10 Percentile Gap
1979 to 1989
1979 to 1999
1979 to 2004-7
0%
-19%
0%
6%
71%
19%
Evalua(ng the Role of Industry Composi(on Shibs
•  Data not rich enough to do this totally nonparametrically as in the earlier analysis •  Break up “Between” and “Residual” components using the following regression, now incorpora=ng industries j ln widjst = α dst + β djt + δ jst + ε idjst
•  Calculate variances as follows, where θ represents share: Vt (ln widjst ) =
∑θ
d , j ,s
V (αdst + β djt + δ jst ) + ∑θdjstV (ε idjst )
djst
d , j ,s
•  Generate counterfactuals analogously to before by replacing the θ and variance components to have 1980 profiles Evalua(ng the Role of Industry Composi(on Shibs
1
2
q
f t (ε )
Calculated Using
Between
Quantities
Residual
3
q
at (w)
Total
4
5
c
6
c
f t (ε )
at (w)
16%
36%
22%
13%
26%
15%
21%
45%
31%
15%
33%
22%
Prices & Quantities
Between
Residual
Total
Panel A: Demographics, Industry and City Size
1979 to 1989
1979 to 1999
1979 to 2004-7
-2%
0%
2%
0%
-2%
-2%
-1%
-1%
0%
9%
7%
4%
Panel B: Demographics and City Size
1979 to 1989
1979 to 1999
1979 to 2004-7
-4%
-1%
1%
-1%
-2%
-2%
-2%
-2%
-1%
8%
10%
9%
Canonical Models for understanding the Na(onwide Rise in Wage Inequality
Acemoglu & Autor (2011) •  Rise in wage inequality interpreted as increases in AH over =me, σ>1 for subs=tutes •  Lots of evidence that high and low skilled labor are subs=tutes, more on that later Krusell et al. (2000 tell the following story: declines in the price of capital + capital-­‐skill complementarity = ncreases in demand for skill, essen=ally enriching the model to make the argument they don’t need the facto
augmen=ng elements [
Yt = At K s cU t + (1 − c)[λK t + (1 − λ ) St ]σ / ρ
α
σ
•  If σ > ρ, there is capital-­‐skill complementarity ρ
ρ
1−α
]
σ
Polariza(on (Autor & Dorn, 2014)
Polariza(on (Autor & Dorn, 2014)
Goods sector 1
< 1 so routine labor and capital are substitues
1− µ
=> routine labor or capital and abstract labor are relative complements
Service sector Low skilled workers can either go into rou=ne or manual labor CES preferences for some variety between goods and services Story of declining αk over =me Use varia=on across metro areas and Bar=k instruments to es=mate parameters Cross-­‐Sec(onal Evidence
Beaudry, Doms & Lewis (2010) and Lewis (2011) look at PC and technology adop=on as a func=on of skilled lab
nputs ccone & Peri (2005) generate es=mates and summarize myriad other es=mates of the elas=city of s=tu=on between skilled and unskilled workers in a two-­‐factor model •  Between 1.4 and 2 -­‐> more subs=tutable than Cobb-­‐Douglas produc=on •  None of these es=mates in the literature use varia=on across local labor markets to iden=fy effects, though Ciccone & Peri (2005) use state/year varia=on Burstein, Vogel, Morales (2015) use a CES model with occupa=ons as factors that can incorporate capital-­‐skill omplementarity •  Isomorphism between local labor markets and occupa=ons in their setup Why Is Wage Inequality Higher in Larger Ci(es?
Eeckhout, Pinhiero & Schmidheiny (2014) consider a model that delivers this paYern plus thicker tails of the ability distribu=on in larger ci=es •  The central feature is “extreme skill complementarity”, which has a produc=on technology like: γ
γ
A j [(m1 j y1 + m3 j y3 ) λ + m2 j y2 ]
λ > 1 for m1 and m 3 complements
Baum-­‐Snow, Freedman & Pavan (2015) consider a technology with capital, more along the lines of Krusell et a
2000) and Autor & Dorn (2014) Baum-­‐Snow, Freedman, Pavan (2015) Produc(on Technology
•  Standard CES produc=on func=on as in Krusell et al. (2000), with the addi=on of agglomera=on economies which are poten=ally factor-­‐biased and aggrega=on to the CBSA rather than na=onal level •  We think of this produc=on func=on as holding for each point in =me, with one observa=on per CBSA j [
σµu
σ
Y j = Aj cD j U j + (1 − c)[λD j
TFP Output CBSA Unskilled Pop. Labor ρµ k
ρ
K j + (1 − λ ) D j
Capital ρµ s
]
ρ σ / ρ 1/ σ
Sj ]
Skilled Labor •  Can think of this produc=on func=on as being CES in U and a composite input made up of K and S •  Different factor augmen=ng coefficients on each of them •  We explore the other (much less standard) nes=ng in a robust check Empirical Paeerns Over Time – Manufacturing Workers
Manufacturing Workers
Δln(wS/wU)
log(1980 CBSA Pop) 0.014***
(0.001)
1990-­‐2000
0.000
Indicator
(0.003)
2000-­‐2007
0.003
Indicator
(0.003)
Constant
0.031***
(0.003)
Observations
R-­‐Squared
2,766
0.113
Raw Counts
Δln(S/U)
-­‐0.002
(0.002)
-­‐0.335***
(0.008)
-­‐0.524***
(0.008)
0.598***
(0.007)
Δln(K/S)
0.014***
(0.002)
0.218***
(0.011)
0.268***
(0.011)
-­‐0.246***
(0.009)
Δln(wS/wU)
0.011***
(0.001)
-­‐0.025***
(0.003)
-­‐0.000
(0.003)
0.033***
(0.002)
Efficiency Units
Δln(S/U)
0.001
(0.002)
-­‐0.308***
(0.008)
-­‐0.516***
(0.008)
0.591***
(0.007)
Δln(K/S)
0.016***
(0.002)
0.196***
(0.011)
0.254***
(0.011)
-­‐0.261***
(0.009)
2,766
0.639
2,202
0.256
2,766
0.144
2,766
0.624
2,202
0.230
•
Significantly more rapid increases in wage gaps in larger ci=es •
No significant increase in skill intensity in larger ci=es •
Significantly more rapid capital intensifica=on in larger ci=es Deriving Es(ma(ng Equa(ons
•  Because our exogenous varia=on from immigra=on shocks exists in changes rather than levels, we must derive es=ma=ng equa=ons that are func=ons of dln(S/U) •  We assume that the capital rental rate v is not a func=on of CBSA j •  Define these shares: •  We make extensive use of these shares, which can be measured empirically from •  capital share •  unskilled labor share •  Though we treat them as predetermined here, robustness checks account for the poten=al endogeneity of these shares A Decomposi(on
•  Cost minimiza=on with respect to S and U plus full differen=a=on yields a fairly standard looking rela=ve inverse demand equa=on changes in the skill bias of agglomera=on economies changes in the rela=ve supply of skill changes in capital intensity: >0 with K-­‐S complementarity (endogenous) Interac=on between K-­‐S complementarity and changes in factor bias of agglom economies •  Standard two-­‐factor models with skilled and unskilled labor would have only the second term, with a coefficient of 1/(elas=city of subs=tu=on between skilled & unskilled labor) •  This equa=on forms the basis for one es=ma=ng equa=on Understanding Capital Rela(ve to Skill Intensity
•  Profit maximiza=on with respect to capital yields Standard price effect agglomera=on effect The Associated Reduced form Expression
•  Coefficients in the first and third terms are nega=ve-­‐> given capital-­‐skill complementarity, skilled wages increase with •  Declines in the price of capital (Krusell et al. story) •  Increases in TFP •  Decreases in the rela=ve supply of skill •  Sign of second term is ambiguous, though it increases as agglomera=on economies become more skill biased, raising skilled wages •  Broad lesson is that capital-­‐skill complementarity interacts with agglomera=on economies & rela=ve labor factor supplies Es(ma(ng Equa(on #2
•  This is directly derived from the K/S equa=on. We express it in this way: •  To be able to evaluate the sign of the third coefficient directly in a linear model à it is posi=ve only if σ > ρ, or there exists capital-­‐skill complementarity •  So that the outcome can be measured exclusively with manufacturing census data with a =ming that matches up •  The first term can be proxied for with =me fixed effects plus an error term •  The coefficient on ln Dj is 0 if the change in agglomera=on economies is factor unbiased or σ = ρ
. Es(ma(ng Equa(on #3
•  Cost minimiza=on with respect to K and S yields: •  Holding dln(K/S) fixed, larger ci=es will have greater increases in the skilled wage if agglomera=on economies become more skill biased rela=ve to capital biased, regulated by the relevant elas=city of subs=tu=on •  dln(K/S) is subs=tuted with the equa=on given above Fourth Es(ma(on Equa(on
•  The addi=onal es=ma=on equa=on to the three demand side equa=ons, which can be thought of as a rela=ve supply equa=on or a “first stage” equa=on •  Here α1 is our key first stage coefficient of interest and has a sta=s=cally significant value of 0.21 for raw units and 0.17 for efficiency units Iden(fica(on
•  Idea is to exploit the decline in S/U in Los Angeles during the 1990s both because a lot of Mexican immigrants came during that decade and because there were a lot of Mexicans in Los Angeles in 1970 -­‐> Need to condi=on flexibly on =me effects •  That is, for this empirical strategy to be valid, it must be true in the context of the model that •  The rela=ve stocks of immigrants from each country in 1970 is not correlated with changes in CBSA TFP in the 1980s, 1990s or since 2000 condi=onal on city size •  In a more general sense •  There cannot be unobservables correlated with 1970 immigrant shares by educa=on across CBSAs that predict changes in wages or capital share, condi=onal on city size IV Results
Δln(Predicted S
/Predicted U)
Δln(Skilled Labor
/Unskilled Labor)
ln(CBSA Population)
ln(Skilled Imm. /
Unskilled Imm.)t-­‐1
Year = 2000
Year = 2005-­‐2007
Constant
Observations
First stage F
Δln(S/U) F.S.
0.21***
(0.045)
0.0012
(0.0065)
0.044***
(0.012)
-­‐0.31***
(0.017)
-­‐0.45***
(0.030)
0.51***
(0.026)
2,751
Evidence of capital-­‐skill complementarity, as in Lewis (2011) Raw Counts
Δln(K/Y)
Δln(ws )
0.64***
(0.20)
0.0076
(0.0078)
-­‐0.033***
(0.013)
-­‐0.19*
(0.11)
0.059
(0.049)
-­‐0.19***
(0.014)
2,047
20.0
-­‐0.25**
(0.11)
0.0094***
(0.0026)
0.021**
(0.0100)
0.12**
(0.060)
0.12***
(0.025)
-­‐0.027***
(0.0077)
2,751
21.7
Δln(ws /wu)
-­‐0.43***
(0.099)
0.013***
(0.0020)
0.026***
(0.0088)
0.24***
(0.059)
0.081***
(0.022)
0.064***
(0.0067)
2,751
21.7
Evidence of increase in the skill bias of agglomera=on economies Informa=on about subs=tutability of factors Structural Es(mates
Para-­‐
Description
meter
α1 Coefficient on instrument in Equation (6)
Sparse Model
Counts
Eff Unit
0.28
0.24
(0.05)
(0.05)
Full Model
Counts
Eff Unit
0.28
0.23
(0.04)
(0.04)
0.85
(0.03)
0.22
(0.26)
change in skilled labor biased agglom.
0.85
(0.03)
0.06
(0.21)
0.015
0.88
(0.02)
0.16
(0.21)
0.015
change in capital biased agglom.
(0.002)
-­‐0.012
(0.002)
-­‐0.009
(0.003)
-­‐0.008
(0.003)
(0.002)
-­‐0.004
(0.002)
σ
1/(1-­‐σ )=elast of sub btw K or S and U
ρ
1/(1-­‐ρ)=elast of sub btw K and S
dµs
dµk
dµu
0.90
(0.02)
0.43
(0.23)
change in unskilled labor biased agglom.
•  Evidence of capital-­‐skill complementarity (σ > ρ) •  increasing skill-­‐bias of agglomera=on economies •  declining capital bias of agglomera=on economies •  Unreported =me fixed effects indicate that dlnv-­‐E[dlnA] < 0 for all 3 study periods “Full” Model Robustness
α1
σ
ρ
dµs
dµk
dµu
Exclude 1980 & Pred. ω c, ω cs
Counts
Eff Unit
Exclude 2005-­‐7
Counts
Eff Unit
Exclude 1980
Counts
Eff Unit
0.26
(0.04)
0.85
(0.03)
-­‐0.34
(0.54)
0.014
(0.003)
-­‐0.011
(0.003)
-­‐0.011
0.22
(0.04)
0.89
(0.02)
-­‐0.21
(0.62)
0.016
(0.002)
-­‐0.009
(0.002)
-­‐0.004
0.30
(0.05)
0.77
(0.05)
-­‐2.26
(4.02)
0.005
(0.003)
-­‐0.005
(0.003)
-­‐0.010
0.29
(0.05)
0.86
(0.04)
0.08
(0.27)
0.011
(0.004)
-­‐0.011
(0.003)
-­‐0.007
0.34
(0.05)
0.82
(0.04)
0.03
(0.22)
0.015
(0.006)
-­‐0.015
(0.005)
-­‐0.008
0.31
(0.05)
0.87
(0.04)
0.09
(0.28)
0.011
(0.005)
-­‐0.010
(0.004)
-­‐0.007
(0.004)
(0.003)
(0.002)
(0.002)
(0.002)
(0.002)
A Decomposi(on
•  Revisit this equa=on •  Note that to bring this equa=on to the data, we have augmented it such that we do not es=mate it directly, but can s=ll recover these four components •  Our analysis is beYer suited to understanding how important these three mechanisms are for understanding the increasingly posi=ve rela=onship between the log skill gap and city size than for understanding changes in wage gaps overall •  The augmented components that we have added for iden=fica=on purposes (year FE and immigrant skill ra=os) are important for understanding na=onal trends in wage gaps Decomposi(on Results
•  Regress skill gap components on =me fixed effects and ln(D) •  All coefficients are significant Object
Actual
Predicted
Predicted Using K,S,U from Data
Agglomeration
S-­‐U Shifts
K-­‐S Shifts
Agglom. K-­‐S Shifts Interaction
Equation and Term
Raw Counts
Efficiency Units
Eqn 2, Term 1
Eqn 2, Term 2
Eqn 2, Term 3
Eqn 2, Term 4
0.015
0.015
0.017
0.019
0.001
0.006
-­‐0.009
0.012
0.012
0.016
0.017
0.000
0.007
-­‐0.007
•  Model fits this element of paYerns in the data well •  Discrepancy between the two Predicted versions are the use of exogenous vs. all varia=on in dln(S/U) •  Clear central role for the increased skill bias of agglomera=on economies From Wages to Income, Well-­‐Being and Neighborhoods Morem (2012) argues that trends in price differences across ci=es means that from a measurement perspec=v
rowth in real wage inequality has been slower than growth in nominal wage inequality What about the microstructure of metropolitan areas •  CheYy et al. (2014, 2015) provide evidence that neighborhoods and youth environment maYer •  There is a lot we don’t know about why and how they maYer •  Neighborhood dynamics can be important for understanding trends in inequality aYerns of Neighborhood Dynamics (Baum-­‐Snow & Hartley, 2015) Inequality Criterion
Fraction
Fraction
Mean HH
White
College Ed
Income
Period
1970-­‐1980 Constant
1.001
(0.014)
1.114
(0.008)
0.883
(0.017)
1980-­‐1990 ΔLn(Employment),
standard devs.
Constant
-­‐0.080
(0.032)
0.976
(0.011)
-­‐0.036
(0.013)
1.109
(0.005)
-­‐0.115
(0.055)
0.910
(0.025)
1990-­‐2000 Constant
0.934
(0.012)
1.056
(0.006)
0.896
(0.006)
2000-­‐2010 ΔLn(Employment),
standard devs.
Constant
-­‐0.043
(0.023)
0.869
(0.011)
-­‐0.009
(0.011)
1.002
(0.005)
-­‐0.082
(0.025)
1.006
(0.009)
0 ΔLn(Employment),
standard devs.
Constant
-­‐0.123
(0.053)
0.773
(0.021)
-­‐0.085
(0.026)
1.184
(0.012)
-­‐0.155
(0.064)
0.846
(0.026)
Conclusions and Research Ideas Agglomera=on economies exist, but what are the main mechanisms driving them? •  Poten=al “sta=c” forces: beYer market access for intermediate goods, lower cost inputs due to economi
scale, fewer fric=ons to technology adop=on, ??? •  Poten=al “dynamic” forces: more rapid human capital accumula=on (but how?), differently opera=ng internal labor markets; these forces seem to be worker and not firm specific ocal labor markets maYer for changes in wage inequality •  What mechanisms are driving more rapid increases in the price of skill in larger ci=es? •  Rise of the service sector interacted with agglomera=on economies in service provision? •  Differences in skill-­‐complementary capital costs? What about the microstructure of metropolitan areas and neighborhood dynamics?