Bartik shocks and industrial spillovers
Jacob Cosman
Abstract
Researchers use Bartik shocks as an instrument for local aggregate demand. If
the performance of locally dominant industries affects employment in other industries,
Bartik shocks may reflect local industrial composition and therefore not be exogenous
to local conditions. This study estimates the effect of spillovers from locally dominant
industries. I find evidence that these spillovers contribute substantially to local labour
demand. Adjusting for these spillovers can give significant differences in an estimated
labour supply curve.
1
Introduction
A Bartik shock is an instrument for local aggregate demand. It is intended as a source of
exogenous variation in situations where aggregate demand may be simultaneously determined
with the outcome variable of interest. For example, Paciorek (2013) uses Bartik shocks as an
instrument for demand in a study of cross-sectional differences in housing price dynamics,
Dworak-Fisher (2004) uses Bartik shocks as an instrument in a study of-metro migration
decisions, and Luttmer (2005) uses Bartik shocks as an instrument in a study of neighbours’
economic performance and subjective well-being. Bartik (1991) and Blanchard and Katz
(1992) initially popularized this instrumentation strategy. As documented in Baum-Snow
and Ferreira (2014), Bartik shocks are now widely used in urban economics.
Bartik shocks are defined by interacting national-level industry trends with local industrial composition. Specifically, if yij is the growth in employment in city i in industry j, κij
is the share of the population of city i in industry j, and I is the number of cities, then the
Bartik shock Bi for city i is defined as follows:
Bi =
X
j
κij
1 X
y i0 j
I − 1 i0 6=i
!
(1)
Insofar as employment growth in city i in industry j is correlated with employment growth
in city i0 6= i in industry j, Bi will be correlated with aggregate employment growth in city
1
i. The utility of the Bartik shock as an instrument arises from the insight that employment
in all cities in all industries is affected by national industry-level trends, but the trend for a
given industry has more impact in a city where the industry employs a greater share of the
population. For example, the Bartik shock calculation for Cleveland would place a higher
weight on the nationwide performance of manufacturing in the rest of the country and a
lower weight on the nationwide performance of tourism than the Bartik shock calculation
for Las Vegas.
To be an effective instrument, the Bartik shock must have strong first-stage power and
it must be exogenous to the outcome variable of interest. Studies including Duranton and
Turner (2011), Luttmer (2005), Aizer (2010) have tested the first-stage power of the Bartik
shock instrument — that is, the ability of the Bartik shock to predict changes in employment.
They report that the instrument has strong first-stage predictive power.
The exogeneity of the Bartik shock is more complicated to interpret. If employment
in each industry is driven primarily by macroeconomic trends, then it seems reasonable
to assume this is exogenous, as individual cities are small compared to a national economy.
However, if employment in a given city is driven by the performance of the dominant industry
in that city, then Bartik shocks could be capturing local conditions rather than the impact
of national trends. This effect could arise via productivity spillovers between industries
(as discussed in, e.g., Moretti (2004) and Beaudry, Green and Sand (2012)) or migration
due to amenities correlated with industrial composition (as discussed in, e.g., Rappaport
(2008) and Diamond (2013)). For example, in a study of the relationship between demand
growth and house prices, strong spillover effects could mean that the identifying power of
the Bartik shock could be arising from decreasing amenity values in cities where locally
dominant industries are declining which leads to net outward migration. In this situation,
the estimated Bartik shock values would incorporate changes to amenity values, which are
likely simultaneously determined with housing prices.
Researchers using instrumentation strategies based on Bartik shocks are aware of this
potential complication. In their discussion of using the Bartik shock as an instrument,
Baum-Snow and Ferreira (2014) express the concern as follows:
[I]t may be the case that manufacturing intensive cities have declined not only
because the demand for skill has declined more in these locations, but also because
they have deteriorated more in relative amenity values with the increasing blight
and decay generated by obsolete manufacturing facilities.
Beaudry, Green and Sand (2012) and Beaudry, Green and Sand (2014) address the possibil2
ity that workers migrate away from cities where a high-paying industry is leaving regardless
of the industry in which they are currently working as the workers perceive the probability
of acquiring a high-paying job to be decreasing. They test for this scenario using a Heckman selection-type procedure based on Dahl (2002) and for their application they find no
significant effect.
In this study, I contribute to this discussion by quantifying the magnitude of these
spillover effects. I construct and estimate a model that decomposes local changes in labour
demand into city-specific and industry-specific components to measure potential spillovers
from employment in a specific industry to employment in other industries in the city. I find
evidence of substantial spillover effects. On the median, these spillover effects are 47% the
magnitude of the desired exogenous variation from national industry trends.
To assess the practical impacts of these spillovers on economic questions of interest, I
use the results to adjust an estimated labour supply curve. Specifically, I estimate a labour
supply curve using Bartik shocks as an instrument for labour market growth and then reestimate after adjusting the Bartik shocks for the spillovers estimated above. I find that
adjusting for spillovers can significantly alter the magnitude of the results. The direction
of the changes indicates that the usual Bartik shock may not fully account for simultaneity
between labour supply and local conditions and therefore may produce biased results.
The remainder of this paper is organized as follows. I discuss a decomposition of labour
market demand shocks into city-specific and industry-specific components and propose a
model for the spillovers from national-level industry outcomes to city-level outcomes. I use
US Census data to estimate the model. As a demonstration of the impact of spillovers, I use
the results to produce adjusted estimates of labour supply.
2
Theory
To understand the use of Bartik shocks as an instrument for local aggregate demand, it
is helpful to define a theoretical model for labour market shocks. Consider a collection
cities indexed by i ∈ 1, 2, . . . , I with their workforces employed in industries indexed by
j ∈ 1, 2, . . . , J. Throughout, I assume all cities have a workforce of unit size1 . Each city i
P
has a share κij of its workforce in industry j (with j κij = 1).
P
Let yij be the change of employment in city i in industry j and let Yi =
j κij yij
1
Abstracting from the distribution of city sizes not meaningfully impact the theoretical results outlined
below.
3
be the citywide change in employment. Each yij can be decomposed into a city-specific
component ui , an industry-specific component vj , and an idiosyncratic residual term εij —
that is, yij = ui + vj + εij . Aggregating these yij over all industries j for a given city i
P
yields Yi = ui + j κij (vj + εij ). Throughout, assume the data is suitably de-meaned to
give E [ui ] = E [vj ] = E [εij ] = 0.
In many situations researchers would like an instrument for the growth in local employment Yi where the predictive power of the instrument does not arise from the city-specific
component ui , as ui may be jointly determined with the outcome variable of interest. For
example, if the outcome variable of interest is housing supply elasticity, it is helpful to have
an instrument for labour demand that is uncorrelated with local amenities. In the empirical
application below, I estimate a labour supply curve using the Bartik shock as an instrument
for labour supply to resolve the simultaneity bias.
The Bartik shock is designed to provide such an instrument. For a given city, the Bartik
shock is defined as the performance of each industry in other cities, weighted by industrial
composition in this city:
!
X
1 X
y i0 j
(2)
Bi =
κij
I
−
1
0
j
i 6=i
Substituting yi0 j = ui0 + vj + εi0 j and rearranging Equation 2Theoryequation.2.2 yields following result:
X
1 X
1 XX
Bi =
ui0 +
κij vj +
κi0 j εi0 j
(3)
I − 1 i0 6=i
I
−
1
0
j
i 6=i j
Equation 3Theoryequation.2.3 contains no ui terms, so this would appear to remove the
troublesome city-specific component of Yi . However, if the industry-specific component vj
causes spillovers to ui , the instrument may be less plausibly exogenous. To understand how
these spillovers could cause the city-specific ui terms to enter the first-stage regression of
employment Yi on the Bartik shock instrument, consider cov (Yi , Bi ):
cov (Yi , Bi ) =
1
I−1
P
P P
1
cov (ui , ui0 ) + j κij cov (ui , vj ) + I−1
i0 6=i
j κj cov (ui , εi0 j ) +
P
P
P
P
1
i0 6=i
j κij cov (vj , ui0 ) +
j1
j2 κij1 κij2 cov (vj1 , vj2 ) +
I−1
P
P
P
1
i0 6=i
j1
j2 κij1 κij2 cov (vj1 , εi0 j2 ) +
I−1
P
P
P P
1
0) +
κ
cov
(ε
,
u
0
ij
ij
i
i
=
6
i
j
j1
j2 κij1 κij2 cov (εij1 , vj2 ) +
I−1
P
P
P
1
(4)
i0 6=i
j1
j2 κij1 κij2 cov (εij1 , εi0 j2 )
I−1
P
i0 6=i
This complicated expression can be simplified. First, since εij is the residual after accounting
4
for ui and vj , it must be that cov (ui , εij ) = cov (vj , εij ) = 0. As well, it seems reasonable
to assume city is sufficiently small that nothing happening in city i affects any other city.
Formally, this corresponds to the following assumption:
Assumption 1. For all i, i0 ∈ 1, 2, . . . , I such that i0 6= i, and for all j ∈ 1, 2, . . . , J, the
following conditions hold:
1. cov (ui , u0i ) = 0
2. cov (ui , εi0 j ) = 0
3. cov (εij , εi0 j ) = 0
Under Assumption 1assumption.1, Equation 4Theoryequation.2.4 simplifies as follows:
cov (Yi , Bi ) =
XX
j1
|
κij1 κij2 cov (vj1 , vj2 ) +
X
j2
j
{z
Industry effects
}
|
κij cov (ui , vj ) +
1 XX
κij cov (ui0 , vj )
I − 1 i0 6=i j
{z
}
Spillover effects
(5)
In Equation 5Theoryequation.2.5, the first term reflects the contribution to the covariance
from the industry-specific components of labour market performance while the second and
third term reflect potential spillovers from industry-specific components to city-specific components. The former term is the plausibly exogenous component while the latter component
includes ui and therefore it may introduce undesirable correlation with the outcome variable
of interest. Accordingly, it is worth understanding how much of the identifying power of
the Bartik shock could potentially impact the instrument’s ability to satisfy the exclusion
restriction.
To investigate the role of spillovers from industrial performance to the city-specific component of labour market shocks, I first assume that the spillover can be expressed as a linear
combination of industry-specific spillovers:
Assumption 2. For j ∈ 1, 2, . . . , J there exists a function φj (κij ) such that spillovers
from industrial performance to city-specific outcomes in city i may be expressed as ui =
P
j φj (κij ) vj + ei .
This functional form assumption is effectively equivalent to a first-order expansion around
vj = 0. The general dependence on κij allows for potentially larger spillover effects from
locally dominant industries.
5
Under the functional form assumed in Assumption 2assumption.2, cov (ui , vj ) may be
written follows:
X
cov (ui , vj1 ) =
φj2 (κij2 ) cov (vj1 , vj2 )
(6)
j2
Substituting this back into Equation 3Theoryequation.2.3 yields an expression for the correlation between the Bartik shock and the local labour market entirely in terms of the national
industry shocks vj and the local labour market composition κij :

cov (Yi , Bi ) =
X
j1


X

κij1

j2 


1 X
+ φj2 (κij2 ) +
φj2 (κi0 j2 )
κij2
 cov (vj1 , vj2 ) (7)
|{z}
I − 1 i0 6=i

Industry effects
|
{z
}
Spillover effects
Equation 7Theoryequation.2.7 indicates a strategy for examining whether the first-stage
regression power of the Bartik shock is driven by the plausibly exogenous industry trends
or by within-city spillovers: estimate φj for each industry, then compare the magnitude of
P
1
κij with the magnitude of φj2 (κij2 ) + I−1
i0 6=i φj2 (κi0 j2 ). This comparison is independent
of the magnitude of the industry performance covariance cov (vj1 , vj2 ).
Specifically, for a collection of cities i ∈ 1, 2, . . . , I and industries j ∈ 1, 2, . . . , J, I estimate
ui and vj by regressing employment changes yij for each (i, j) from the following regression
fixed-effects regression:
yij = ui + vj + ij
(8)
In Equation 8Theoryequation.2.8, ui and vj are full vectors of city-time and industry-time
fixed effects. Let uˆi and vˆj denote the estimated effects. Then, I obtain spillover estimates
φˆj (κij ) by estimating the following regression:
uˆi =
X
φj (κij ) vˆj + νi
(9)
j
For each (i, j) pair, I compare the correlation induced by industrial performance with
the correlation induced by spillover from industry effects to city effects. Let Ni be the
size of the labour force of city i. Then (after adjusting the results shown in Equation
7Theoryequation.2.7 to account for variation in city size) the industrial-performance effects
P
are proportional to κij and the spillover effects are proportional to φj2 (κij2 )+ P 0 1 N 0 i0 6=i Ni0 φj2 (κi0 j2 ).
i
i 6=i
This exercise provides an indication of the importance of spillovers from industry performance
6
(a) Distribution of estimated values u
ˆit .
(b) Distribution of estimated values vˆjt .
Figure 1: Distribution of estimated values of city and industry components to labour demand
changes. Values are aggregated over the three time periods.
to local conditions in the predictive power of the Bartik shock.
3
Results
To generate the city-specific labour conditions yij , I use data from the 1980, 1990, 2000, and
2010 US Census. This data set includes 360 MSAs (under the 1999 MSA boundaries) and for
fourteen top-level industry classifications from the IPUMS 1990 consistent industries. This
is comparable to the data commonly used in the literature. I consider only adults between
25 and 55 years of age who are not in school and who usually work at least 35 hours per
week.
I obtain estimates uˆit and vˆjt by estimating the model specified in Equation 8Theoryequation.2.8
with data pooled across the three decadal intervals with regression weights equal to workforce
size Nit . Figure 1Distribution of estimated values of city and industry components to labour
demand changes. Values are aggregated over the three time periods.figure.caption.1 shows
the distribution of estimates for uˆit and vˆjt . As shown, the city-specific and industry-specific
components of yij are of comparable magnitudes.
Next, I estimate the spillover function φj (as specified by Assumption 2assumption.2) for
each sector j. To flexibly estimate φj , I explore several specifications: polynomials of degree
d, linear splines with knots placed at q − 1 evenly-spaced quantiles 1q , 2q , . . . , q−1
of κij , and
q
linear splines with knots placed at k evenly spaced values of κij for each j. Throughout, I use
7
Figure 2: Bayesian information criterion for models of spillover functions φj . The models
indexed by d are polynomial functions, the models indexed by q are linear splines with knots
at quantiles of κij , and the models indexed by k are linear splines with k evenly-spaced knots.
pooled data across the three time periods. I select a model using the Bayesian information
criterion (BIC). Figure 2Bayesian information criterion for models of spillover functions φj .
The models indexed by d are polynomial functions, the models indexed by q are linear splines
with knots at quantiles of κij , and the models indexed by k are linear splines with k evenlyspaced knots.figure.caption.2 shows the BIC for each of the models under consideration. As
shown, the q = 7 model minimizes the BIC. This model has a highly meaningful difference
in BIC when compared with all models except q = 10.
ˆ for each industry j. Along each row from left to right, the inFigure 3Estimated phi
j
dustries are as follows: “agriculture, forestry, and fisheries”, “mining”, “construction”, and
“manufacturing” in the first row, “transportation, communication, and other public utilities”, “wholesale trade”, “retail trade”, and “finance, insurance, and real estate” in the second row, “business and repair services”, “personal services”, “entertainment and recreation
services”, and “professional and related services” in the third row, and “public administration” and “active-duty military” in the final row. The dashed lines show bootstrapped
8
95% confidence intervals.figure.caption.3 shows φˆj estimated using the q = 7 linear spline
model. I estimate confidence intervals from repeated draws from the estimated covariance
matrix. As shown, for most industries j the 95% confidence intervals are very broad. Howˆ
ever, the spillovers for manufacturing (in the top right corner of Figure 3Estimated phi
j
for each industry j. Along each row from left to right, the industries are as follows: “agriculture, forestry, and fisheries”, “mining”, “construction”, and “manufacturing” in the first
row, “transportation, communication, and other public utilities”, “wholesale trade”, “retail
trade”, and “finance, insurance, and real estate” in the second row, “business and repair services”, “personal services”, “entertainment and recreation services”, and “professional and
related services” in the third row, and “public administration” and “active-duty military” in
the final row. The dashed lines show bootstrapped 95% confidence intervals.figure.caption.3)
appear to be very strongly increasing with industrial concentration — that is, the city-specific
component uˆit is particularly closely correlated with the industry-specific component vˆjt for
manufacturing in city-decade pairs where the share of employment in manufacturing κijt is
high.
I use the comparison suggested by Equation 7Theoryequation.2.7 to assess the importance of spillovers from industrial composition in driving the predictive power of the Bartik
Figure 4Cumulative distribution
function function for the spillover magnitude
P shock.
P
1
ˆ
ˆ
j φj (κijt ) + I−1 i0 6=i φj (κi0 jt ) . Each observation is an MSA-decade pair.figure.caption.4
P ˆ
P
1
ˆ
shows a histogram of the magnitude of j φj (κijt ) + I−1 i0 6=i φj (κi0 jt ) for the estimated
P
κijt = 1 for each city i by construction, this measures the
spillover functions φˆj . Since
j
relative magnitude of the spillover effect to the industry effect — that is, the relative effect
of the city-specific correlation terms compared to the industry-specific terms in Equation
7Theoryequation.2.7. As shown, the relative magnitude of the spillover effect is nontrivial. The median value of the relative magnitude of the spillover effect is 47%. In 10% of
observations the magnitude of the estimated contribution from spillovers is larger than the
magnitude of the direct contribution from national industry performance.
To understand the practical implications of these spillovers for the use of the Bartik shock
in estimation, I apply these results to the estimation of the labour supply curve. I regress
MSA-level average wage growth on employment growth under three specifications:
1. Uninstrumented ordinary least squares (OLS)
2. Employment growth instrumented with the Bartik shock (Bartik IV)
3. Employment growth instrumented with the spillover-adjusted Bartik shock (adjusted
9
Intercept
Employment change
N
First-stage F -stat
OLS
Bartik IV
∗
0.374
0.304∗
(0.005)
(0.007)
∗
0.666
1.064∗
(0.020)
(0.031)
1080
1080
1352∗
Adj. Bartik IV
0.197∗
(0.019)
1.671∗
(0.098)
1080
174∗
Table 1: Regression results for labour supply curve. Throughout, the dependent variable is
the change in average wages and the unit of observation is the MSA. The first column is
an OLS regression, the second is a IV regression using the Bartik shock to instrument for
labour demand, and the third is an IV regression using a spillover-adjusted Bartik shock to
instrument for labour demand. An asterisk denotes statistical significance at p < 0.001.
Bartik IV)
Specifically, to adjust the estimated Bartik shock for spillovers, I replace employment growth
for industry j in city i0 in Equation 2Theoryequation.2.2 yi0 j with a spillover-adjusted
P
value y˜i0 j = yi0 j − j 0 φj 0 (κi0 j 0 ) vj 0 . Instrumenting for aggregate demand with the Bartik
shock improves the estimate relative to the uninstrumented version by removing the bias
of simultaneously-determined wages and employment. Similarly, using spillover-adjusted
Bartik shocks should improve the estimate by removing simultaneously-determined spillover
effects.
Table 1Regression results for labour supply curve. Throughout, the dependent variable is the change in average wages and the unit of observation is the MSA. The first
column is an OLS regression, the second is a IV regression using the Bartik shock to instrument for labour demand, and the third is an IV regression using a spillover-adjusted
Bartik shock to instrument for labour demand. An asterisk denotes statistical significance
at p < 0.001.table.caption.5 shows the estimated demand curve parameters. Unsurprisingly,
under all three specifications, the labour supply curve is upwards-sloping. For both instrumental variables, an F -test for the first stage regression strongly rejects the null hypothesis
of a weak instrument at any reasonable threshold of statistical significance. That is, both
the Bartik shock and the adjusted shock are strongly predictive of employment in the first
stage of the IV regressions.
However, the regression results differs significantly between the IV regression results with
and without the spillover adjustment. Specifically, using the spillover-adjusted Bartik shock
as an instrument yields a steeper labour supply. The baseline IV result is intermediate
10
between the OLS result and the spillover-adjusted result. This could potentially indicate
that the substantial spillover effects described above lead to simultaneity between the wage
and employment changes. Such simultaneity would bias the result with the baseline Bartik
shock instrument towards the uninstrumented OLS result.
4
Conclusion
Bartik shocks are widely used as an instrument for local aggregate demand. They are highly
predictive, but other researchers in the literature have expressed concerns that spillovers
from dominant industries may influence the instrument’s predictive power and complicate
its interpretation as exogenous.
This study contributes to the literature on this widely-used instrument by quantifying
the importance of those concerns. I estimate the magnitude of spillover effects’ contribution
to the Bartik shock’s identifying power and find that these effects are substantial compared
to the assumed identifying variation arising from plausibly-exogenous national-level industry
trends. Moreover, accounting for these spillover effects in the first stage of IV estimation of
the labour supply curve leads to meaningfully different results. These results suggest that
in some contexts the Bartik shock may not represent an reasonable source of exogenous
variation.
References
Aizer, Anna. 2010. “The Gender Wage Gap and Domestic Violence.” American Economic
Review, 100(4): 1847–59.
Bartik, Timothy J. 1991. Who Benefits from State and Local Economic Development
Policies? W.E. Upjohn Institute for Employment Research.
Baum-Snow, Nathaniel, and Fernando Ferreira. 2014. “Causal Inference in Urban and
Regional Economics.” National Bureau of Economic Research Working Paper 20535.
Beaudry, Paul, David A. Green, and Benjamin M. Sand. 2014. “Spatial equilibrium
with unemployment and wage bargaining: Theory and estimation.” Journal of Urban
Economics, 79(C): 2–19.
11
Beaudry, Paul, David A. Green, and Benjamin Sand. 2012. “Does Industrial Composition Matter for Wages? A Test of Search and Bargaining Theory.” Econometrica,
80(3): 1063–1104.
Blanchard, Olivier Jean, and Lawrence F. Katz. 1992. “Regional Evolutions.” Brookings Papers on Economic Activity, 23(1): 1–76.
Dahl, Gordon B. 2002. “Mobility and the return to education: Testing a Roy model with
multiple markets.” Econometrica, 70(6): 2367–2420.
˜
Diamond, Rebecca. 2013. “The Determinants and Welfare Implications of US WorkersA
Diverging Location Choices by Skill: 1980-2000.” Job market paper.
Duranton, Gilles, and Matthew A. Turner. 2011. “The Fundamental Law of Road
Congestion: Evidence from US Cities.” American Economic Review, 101(6): 2616–52.
Dworak-Fisher, Keenan. 2004. “Intra-metropolitan shifts in labor demand and the adjustment of local markets.” Journal of Urban Economics, 55(3): 514–533.
Luttmer, Erzo F. P. 2005. “Neighbors as Negatives: Relative Earnings and Well-Being.”
The Quarterly Journal of Economics, 120(3): 963–1002.
Moretti, Enrico. 2004. “Workers’ education, spillovers, and productivity: evidence from
plant-level production functions.” American Economic Review, 656–690.
Paciorek, Andrew. 2013. “Supply constraints and housing market dynamics.” Journal of
Urban Economics, 77(C): 11–26.
Rappaport, Jordan. 2008. “Consumption amenities and city population density.” Regional
Science and Urban Economics, 38(6): 533 – 552.
12
ˆ j for each industry j. Along each row from left to right, the industries
Figure 3: Estimated phi
are as follows: “agriculture, forestry, and fisheries”, “mining”, “construction”, and “manufacturing” in the first row, “transportation, communication, and other public utilities”,
“wholesale trade”, “retail trade”, and “finance, insurance, and real estate” in the second
row, “business and repair services”, “personal services”, “entertainment and recreation services”, and “professional and related services” in the third row, and “public administration”
and “active-duty military” in the final row. The dashed lines show bootstrapped 95% confidence intervals.
13
Figure
distribution
function function for the spillover magnitude
P 4: Cumulative
P
1
ˆ
ˆ
j φj (κijt ) + I−1 i0 6=i φj (κi0 jt ) . Each observation is an MSA-decade pair.
14