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Concentration of human capital, externalities, and the wage gap in U.S.
metro areas
1
Rodrigo Perez-Silva*
Center for Economics and Social Policy, Faculty of Humanities, Universidad Mayor, Chile
José Toribio Medina 29, Santiago, Chile
rodrigo.perez@umayor.cl
Mark D. Partridge
The Ohio State University
Jinan, University, and Urban Studies and Regional Science
Gran Sasso Science Institute, L’Aquila, Italy
2120 Fyffe Road, Columbus, Ohio, 43202. U.S.A.
partridge.27@osu.edu
Abstract: The effects of the concentration of human capital on wages and productivity have
been widely studied, but despite their heterogeneity, little attention has been paid to its effects
on the wage gap. This paper assesses the impacts of human capital externalities on wages
and on the U.S. wage gap. Our main results suggest a positive association between the share
of high-educated workers and the wage gap between high- and low-educated workers.
Moreover, the effect associated with the concentration of high-educated workers is entirely
captured by changes in their wages, as wages of low and medium-educated workers are
statistically unaffected.
Keywords: human capital externalities, knowledge spillovers, wage gap, metro areas.
JEL: I24, J24, J31
1. INTRODUCTION
The existence of knowledge spillovers has received considerable attention over the
last couple of decades.
2
It is argued that such spillovers increase the level of productivity and
enhance economic growth (Shapiro, 2006; Bronzini and Piselli, 2009; Abel & Gabe 2010;
Borjas and Doran, 2015; Winters, 2013; 2014; Liu, 2015). The literature has suggested that
information is used more efficiently by peers when they are in geographical proximity
(Nocco, 2005; Fu, 2007; Agrawal et al. 2008; Rodríguez-Pose & Crescenzi, 2008a; b; Breschi
and Lenzi, 2016). Accordingly, the benefits of proximity in terms of productivity gains
associated with knowledge spillovers is at least one reason for both the concentration of high-
educated workers in cities and for firm clustering (e.g. Jaffe et al. 1993; McCann and
Simonen, 2005; Greenstone et al. 2010; Puga, 2010; Betz et al. 2016).
These human capital externalities have been regularly linked to increasing job growth
(Shapiro, 2006; Winters, 2013), wages (Rosenthal and Strange, 2008; Sand, 2013; Peri et al.
1
This is draft version. The final paper will be published in a forthcoming issue of Regional Studies.
* Corresponding author.
2
We broadly use the term “knowledge spillovers” to refer to human capital externalities.
2
2014; Winters, 2014), prices (Saha et al. 2017), productivity (Liu, 2015), and inequality.
Breau et al. (2014) and Lee (2011) find a positive link between innovation and wage
inequality. Similarly, Donegan and Lowe (2008) show that inequality grows in the presence
of the “creative class” (Florida, 2002). Glaeser et al. (2009) suggest that within-city
inequality can be explained by a combination of skill differentials and by differing returns to
skill across cities, that, in turn, could be caused by human capital externalities. Finally,
Cunningham (2015) and Florida & Mellander (2016) show that inequality is related to skills,
creativity, and the presence of high-tech jobs.
Moretti (2004) assessed the relationship between the share of college-educated
workers and wages of high, medium and low-skilled workers over the 1970-1990 period,
finding that relatively higher concentrations of skilled workers are more beneficial to low-
skilled worker wages than their own. He explains that there are two offsetting impacts related
to greater shares of highly-educated workers. First, an increase in the supply of highly
educated reduces their relative wages. Second, both high and low-educated workers benefit
the same from higher concentrations through productivity gains. Thus, the net effect
relatively benefits less-educated workers more, whose labor supply is at least initially
unchanged.
It is also important to note that concentrations of high-educated workers, with
relatively higher opportunity costs and wages, could also increase the demand for services
within the city, increasing the demand and wages of low-educated workers (Moretti, 2010;
Mazzolari & Ragusa, 2013; Florida & Mellander, 2016). Therefore, at least two wage-
increasing effects on low-educated workers are expected: a knowledge spillover effect and a
consumption demand spillover effect. Moreover, recent literature has suggested that what
has been interpreted as a productivity gain for less-educated workers could be a demand
effect, since most of these wage increases have been found only among workers of non-
tradable sectors (Liu & Yang, 2019).
Recent studies (e.g. Sand, 2013; Winters, 2014; Peri et al. 2014), suggest that the net
effect for the wages of the high-educated have evolved over time from being driven by supply
competition to one that is driven by the diffusion of ideas and knowledge sharing (de Lucio
et al. 2002; Adamson et al. 2004; Czaller, 2016). More importantly, if knowledge spillovers
or, more generally, human capital externalities sufficiently dominate the supply effect to
more than offset any increase in low-educated worker wages, then the concentration of
human capital can increase the wage gap and in turn can help explain rising U.S. inequality.
We use individual-level data from the American Community Survey (ACS) for 2005,
2010 and 2014 and a set of instrumental variables to provide new evidence on the relationship
between the concentration of highly-educated workers and the wage gap across U.S. metro
areas. Assuming that the concentration of high-educated workers generates externalities that
increase productivity and wages for all local workers (Rosenthal and Strange, 2008;
Mazzolari & Ragusa, 2013; Liu, 2015; Broersma et al. 2016; Liu & Yang, 2019), this paper
studies whether these productivity and wage gains are disproportionally captured by the same
skill group that generates them. For high-educated workers, the net effect depends on the
magnitude of knowledge spillovers (positive) and on the labor supply effect (negative). For
low-educated workers, any effect is expected to be positive because of knowledge and
3
consumption demand spillovers. Yet, unlike the previous literature, our focus is not on
knowledge spillovers per se, but on the relative effects on inequality—e.g., the
skilled/unskilled wage gap. In particular, we assess whether knowledge spillovers arising
from the concentration of high-educated workers are large enough to compensate for not only
the supply effect that decreases their own wages, but also to overcome possible increases in
wages for low-educated workers. A positive effect of the city’s-share of high-educated
workers over the wage gap is interpreted as evidence consistent with knowledge spillovers,
though we acknowledge that there may be other alternative possibilities.
Our main empirical results suggest that the marginal change in the share of high-
educated workers is associated with a 1.7-1.8% increase in the log wage gap. Our preferred
specification uses city fixed-effects and suggests that larger gains are experienced by highly-
educated workers, with marginal increases in wages between 0.23 and 1.8%.
In addition to contributing to the current debate on the effects of concentrations of
human capital on wages, our contribution is threefold. First, to the best of our knowledge, we
are the first to assess the effects of concentrations of human capital on inequality—
specifically the wage gap. While many studies focused on the effects of concentration of
human capital on wages, while others present a correlation between innovation and
inequality, there have been no attempt to consider both effects. Second, we extend Moretti
(2004)’s theoretical model and offer a unified general theoretical model that reflects the links
between capital and skills and the differential magnitude of knowledge spillovers among
workers, suggesting a plausible mechanism for differential productivity increases. Third, we
test our results with multiple IV approaches that help in identification, but also provide
insights for future research.
The rest of the paper is organized as follows. Section 2 describes the theoretical model
and the resulting predictions. Section 3 describes the empirical strategy, whereas Section 4
presents the data. Our main results are presented in section 5. Section 6 concludes.
2. THEORETICAL MODEL
Assume each city is a closed competitive economy producing a single output , with
a CES technology that employs high (H) and low-educated workers (L). For simplicity, the
price of is normalized to unity.
3
The production function of each metro area is
(1)
in which is the parameter associated with the area’s productivity, and are parameters
indicating each factor’s relative importance, is the elasticity of substitution
between high and low-educated workers (with ), and and are productivity shifters
for high and low-educated workers respectively.
3
Capital is implicitly included in the model as it differentially affects worker productivity through and ,
and the productivity of the economy as a whole through .
4
By assuming a CES production function, we allow for a range of possible values for
the substitutability of workers. As is standard in the literature (e.g. Acemoglu, 2002), a crucial
assumption is that H and L are imperfect substitutes, so that , and .
Moreover, for H and L to be gross substitutes, we assume that and . Note
that a Cobb Douglas technology would force changes in relative wages (skill premium) to be
only determined by the ratio of the inputs (high and low-educated workers). By using a CES
technology, we allow for relative wages to not only vary with respect to the ratio of high and
low-skilled workers, but also with respect to changes in the capital to skill ratio (Lindquist,
2004), reflecting productivity shifters in our model.
By maximizing Eq. (1) with respect to the production factors and equating the
marginal productivity of each worker type to its wage, we get the equality of the MRTS with
the ratio of wages. The expression in logs is given by
(2)
with and the share of high- and low-educated workers, respectively. We then specify
(3)
for . We define as a group-specific productivity shifter parameter.
4
Likewise, is defined as the knowledge/consumption spillover in group caused by the
concentration of high-educated workers. Notice that in Moretti’s (2004) model, the
productivity shift parameter is defined as
(4)
Therefore, a key difference between Moretti’s model and ours is that his restricts knowledge
spillovers from high-educated to low-educated workers to equal the spillovers within the
high-educated group, while ours allow for differential effects.
By assumption, knowledge spillovers have a higher impact on high-educated
workers’ productivity, increasing the relative firm demand for high-skilled workers. If
only captures knowledge spillovers, then we should expect . In our model, however,
we do not distinguish between knowledge and consumption spillovers on low-educated
workers, so that can be interpreted as the joint effect of concentrations of high-educated
workers on low-educated worker productivity, including both knowledge and consumption
spillovers that increase the productivity (and demand) of low-skilled workers. This means
that for to hold, we need productivity gains for high-educated workers to be greater
than these two potential positive effects on low-educated wages. Finally, our model assumes
that there are no spillovers arising from concentrations of low-educated workers (Moretti,
4
These parameters capture any exogenous shifters to productivity and could affect differentially high and
low-educated workers. Our theory is then consistent with changes in productivity and the wage gap that are
initially driven by skill-biased technological change that is enhanced by knowledge spillovers, increasing
demand for skilled workers.
5
2004; Shapiro, 2006; Rosenthal and Strange, 2008).
Rearranging Eq. (2) and replacing accordingly, we get
(5)
Then, the effect of an increase in the share of high-educated workers on the wage gap
equals
(6)
in which
.
Note that given our previous interpretation, it is not possible to determine the sign of
. The second term to the right in Eq. (6) is negative since , and that an
increase in the share of high-educated workers necessarily implies a reduction in the share of
low-educated workers (
.
Eq. (6) states that any increase in the share of high-educated workers has an
ambiguous effect on the wage gap. The total effect depends on the relative magnitude of the
spillovers (first term to the right in Eq. (6)), and the supply effect (second term to the right).
5
As described in the next section, our dependent variable measures the total effect of
the concentration of high-educated workers on wages. However, a positive effect of on
the wage gap implies that
, or that the differential positive
knowledge/consumption spillover effect dominates the negative supply effect.
3. EMPIRICAL STRATEGY
When estimating effects on wages we use individual-level data and two types of
models. For our OLS estimations and the time-variant instrumental variables, we use fixed-
effects models at the MSA level. The identifying assumption of these models is that by
accounting for elements that are persistent in the city, such as the industry composition,
amenities, and structural labor market effects, we capture the actual within-city variation in
wages, reducing concerns regarding endogeneity and sorting of high-skilled workers to
highly productive cities. In particular, the theoretical model suggests that knowledge
spillovers affect the relative firm demand for skilled and unskilled workers, and thus
identification requires removing the labor supply effects associated with share of high-skilled
workers.
The fixed-effect models represent our preferred specifications. However, we also
briefly discuss cross-section models using three time-invariant instrumental variable
5
A discussion of these effects are in Rodríguez-Pose & Tselios (2009).
6
approaches (Lagged Share, Predicted Share, and Land grant). Here we run year-by-year
cross-sectional regressions with state-level fixed-effects along with additional city-level
controls to account for elements that could induce changes in labor demand or supply. We
include the full set of natural amenities from the USDA, unemployment rate, poverty rate,
industry composition (share of workers in agriculture, construction, manufacturing, and
public administration), and most importantly to condition out labor supply effects, several
variables associated labor force participation. We estimate:
(7)
for OLS and time-variant instruments, and
(8)
for time-invariant instruments. Here, is the log-wage equation of a group-j worker
i in city c, at time t. is the share of high-educated workers, is a vector of individual-
specific characteristics, and is a vector of city-specific characteristics. and are city
and state fixed-effects.
For the effect of the concentration of high-educated workers on the wage gap at the
MSA level, we aggregate Eq. (4) and use average characteristics. To estimate the effects on
the wage gap, we define as the difference in the mean log wage between low- and high-
educated workers
(9) .
with ,
(differences in observables) and
. Eq. (9) includes year () and state () fixed-effects.
6
As mentioned before, in Eqs. (7) and (8), and in Eq. (9) could potentially be
correlated with the share of high-educated workers in the city, biasing the estimates. In
particular, the theoretical model assumed that a greater share of skilled workers increases
productivity, which in turn, increases the relative labor demand for skilled workers. Thus, to
achieve identification, we need exogenous supply shocks to identify the labor demand
effects. The relative skilled and unskilled measures we incorporate are affected by migration
flows and local changes in the skilled composition as (primarily) young adults. However, the
labor supply components of these changes in relative skill composition would lead to biased
estimates of our knowledge-spillover labor demand effects. To address these concerns, we
use two main instrumental variable approaches.
First, we adopt a strategy that has some similarities with the international trade and
the empirical industrial organization literature (e.g., Autor et al. 2013; 2014; Hausman, 1995)
by using the values of the potentially endogenous variable from other locations. Specifically,
6
Note that the observable characteristics of the city () and the unobservable characteristics contained in the
city fixed-effect are assumed to have common effects over workers.
7
a two-step strategy first used by Partridge et al. (2017) is implemented.
7
This “Match IV”
strategy uses the Mahalanobis
8
distance approach to detect within the rest of the sample, the
two best matches for each city in terms of a set of exogenous covariates. These are factors
associated with relative labor supply of skilled and unskilled workers including city
population, age structure, the proportion of black workers, women, foreign-born, married
workers, and most importantly, educational attainment. To ensure that these potential
matched cities are not “contaminated,” they must be at least 125 miles from the ‘treated’ city
and out of the state to avoid spatial labor-demand spillovers. Each city is ‘treated’ once and
the rest of the sample are potential matches, in which we sample with replacement. Once the
matches are determined, the second step is to employ the matched cities’ values of the
endogenous variable as the instruments for 2SLS estimation.
The Match IV strategy relies on the assumption that common observable factors
influence the spatial distribution of high-educated workers for similar cities, and that any
omitted variables are most correlated to omitted variables in nearby cities (which is generally
eliminated by our 125-mile threshold). Changes in the proportion of high-educated workers
in a city should reflect common demand and supply shocks, meaning that our match cities
should have similar shares of highly educated workers. However, the variables used to
identify the optimal match are labor-supply oriented as described in footnote 8. Thus, the
matched metropolitan areas have similar relative skilled/unskilled labor supply
characteristics, but not influenced by the demand shocks experienced by the original city
(especially after conditioning on standard labor demand variables), meaning their measures
of skilled/unskilled shares are good instruments for the original city.
9
The construction of the Match IV directly rules out reverse causality as a form of
endogeneity. Likewise, it is especially strong when any omitted variables are more highly
correlated with the explanatory variables when the control and treated counties are closer.
The IV strategy is valid only if for each city, the share of high-educated workers in the
matched cities are highly correlated with that variable in the city of interest, but uncorrelated
with the outcome and residual in the original regression. We perform various specification
tests to show that this is the case for our sample.
A synthetic control approach is similarly used to extract the share of high-educated
workers from a ‘control’ city. For our Synthetic IV, we follow Abadie et al. (2010; 2015) and
7
Autor et al. (2013) and Autor et al. (2014) instrumented for growth in U.S. imports from China by using the
growth in Chinese imports in other high-income countries. The Hausman et al. (1994) approach generally
uses values from adjacent or very close city/regions as the instrument for values of the original city/region.
We go further by eliminating demand spillovers (as described below) and more specifically targeting better
matches using matching techniques.
8
The Mahalanobis distance for cities i and j is defined as
, where x is a vector of
covariates and
is the estimated covariance matrix. The covariates associated with relative labor supply of
skilled and unskilled workers are education, age, mean of wages, the proportion of blacks, women, foreign-
born, and married workers.
9
Whereas we cannot fully rule out the possibility that at least part of the variation in the instrument is demand-
driven, the construction of the instrument along with other factors in how we specify the empirical model
should greatly mitigate any remaining concerns that our model is misspecified. Moreover, the results are
similar when using a purely supply shifter instrument such as the existence of a land-grant university and deep
lags of the relative skilled/unskilled labor supply.
8
predict the share of high-educated workers in the synthetic control counterfactual city to use
it as instrument for the ‘treated’ city, where again the variables used to derive the synthetic
control city are the same labor supply shifters we previously used.
10
As before, the “donor”
cities is at least 125 miles from the city of interest and in a different state.
Since the variation in the share of college-educated workers in a given city stems
from changes in the share of college-educated workers in counterfactual cities, that are not
affected by the city’s labor market shocks, our results are unlikely to be driven by changes in
local demand or wages in specific industries within the city of interest. In addition, the fixed-
effect removes from the residual the persistent differentials that affect the city’s college
graduate share, greatly eliminating concerns that idiosyncratic structural differences across
cities may bias the results. Thus, concerns about endogeneity are minimized due to our
reliance on instrumental variables to simulate exogenous shocks to the city’s share of high-
educated workers and control variables that also account for alternative possibilities.
11
As mentioned, we further employ three time-invariant IVs in cross-sectional
regressions as robustness checks. First, we use the presence of a Land grant institution to
predict the city’s supply of high-educated workers (Moretti, 2004). Second, we use the 1970
share of high-educated workers as a deep lag IV, and finally, the predicted 1970’s share of
high-educated workers as a function of the industry composition of the city (i.e., a Bartik-
style instrument).
12
We follow Détang-Dessendre et al. (2016) and regress each 1970 MSA
industry-share of high-educated workers on a set of industry dummies, its interactions, and a
city fixed-effect (Eq. (10)), bootstrapping standard errors with 100 replicates with a seed of
1. We then construct our instrument using the predictions of the college graduate share and
the city’s 1970 industry composition (Eq. (11)).
(10)
(11)
In Eqs. (10) and (11) is the share of workers in industry k, city c; is the industry fixed-
effect, is a city fixed-effect, and is the error term. , in Eq. (11), is the predicted
share of high-educated workers in city c, and
is the predicted share of high-educated
workers in each industry-city pair from Eq. (10).
10
In particular, we regress the share of high-educated workers in the ‘treated’ city on a set of labor supply
covariates including the population size of the city, the age, share of married workers, share of blacks, share
of women, and the share of foreign in each group of workers (low, medium, and high-educated workers). For
each city, the procedure creates a counterfactual city, that resembles the ‘treated’ one in these covariates. The
instrument used is then the predicted share of high-educated workers in the counterfactual city.
11
Unfortunately, three are no clear natural experiments to further tease out causality. Of course, appropriate
caution in interpreting our results should be exercised.
12
For the first and second IVs, the underlying assumption is that they are correlated with the current share
skill/unskilled shares, but uncorrelated with current wages (conditional on controlling for other factors such as
contemporaneous industry shares and state fixed-effects).
9
4. DATA
We employ the one-year ACS samples for 2005, 2010, and 2014. The ACS, a large
annual survey that started in 2005 and covers about 3.5 million households, provides
information regarding respondents’ employment, occupation, wage, and education among
other variables. The one-year samples provide information for all areas with populations of
65,000 or more, containing all major cities. The selection of years was made in order to cover
an extended period of time and to see whether our estimates are robust to different
macroeconomic conditions—i.e., 2005 was close to the pre-Great Recession peak, 2010 was
in the immediate wake of the recession, and 2014 was during the expansion in which growth
achieved some of its most robust levels.
We use a sample of individuals from the 48 contiguous states plus the District of
Columbia with a positive number of weeks and hours worked, and positive wages. Our
sample consists of 3,407,379 observations at the PUMA (Public Use Microdata Area) level.
To maintain constant metropolitan area boundary definitions, we employ crosswalks between
the 2013 MSAs and the 2000 PUMAs (for 2000 and 2005) and the 2010 PUMAs (for 2014).
For the wage gap regressions, we aggregate MSA-level data and construct a balanced panel
of 1,068 MSA-year observations (356 MSAs each year).
13
We define high-educated workers as those with a four-year college degree or more,
and low-educated workers as those with a high-school diploma or less. Workers with some
college or with an associate degree are considered medium-educated workers.
Our first regressions include all workers in the sample and controls for number of
weeks worked and regular weekly work hours. For these regressions, we use log of real
annual wages. We then restrict the sample to consider only full-year workers (working 50 to
52 weeks a year) and control for the number of hours worked a week.
14
A more restrictive
version is also considered, in which we only include full-year workers with 30 hours or more
worked. Finally, we restrict the sample further to include full-year workers working between
30 and 60 hours a week.
As mentioned, we use aggregate MSA-level data for purposes of estimating the wage
gap, and individual-level data to capture group-specific effects. In both cases, the treatment
of the data is identical, but the second case uses more complete controls.
15
For the wage
inequality measure, we use the difference in the average real log-wage between high and
low-educated workers.
13
For MSAs with geographical boundaries that extend to multiple states, the MSA is assigned to the state in
which the MSA’s population is larger. Following this criterion, cities like Cincinnati (which covers parts of
Ohio, Kentucky, and Indiana), Chicago (covering Illinois, Indiana, and Wisconsin), and Boston (covering
areas of Massachusetts and New Hampshire) are assigned to Ohio, Illinois, and Massachusetts, respectively.
14
Note that both the ACS 2010 and 2014 do not provide the actual number of weeks worked, unlike the ACS
2005. Instead, a categorical measure is reported with ranges of 50-52 weeks, 48-49, 40-47, 27-39, 14-26, and
less than 14 weeks worked. To consistently measure of number of weeks, we construct the 2010/2014 ranges
for the year 2005 as well. Hence, regressions using the full sample of workers use a categorical variable for all
the brackets described as the control for number of weeks worked. Regressions for full-year workers consider
only those working 50-52 weeks a year.
15
For example, when using aggregate data, we only consider the percentage of black workers as a proxy for
race. When using individual level data, we use the variable ‘RAC1P’ with dummies for each race in the ACS.
10
Table 3 in the appendix presents the main descriptive statistics by group. To compare
across MSAs, we classify them according to their position in the distribution of shares of
high-educated workers in the city and split the sample in quartiles. Descriptive statistics using
this classification are reported in Table 4 in the appendix.
Workers with a college degree or more are more likely to be full-year workers, self-
employed, and married. On average they work three hours per week more than workers with
high-school or less. On the other hand, a lower proportion are female, non-white, foreign-
born, and has a disability. High-educated workers earn on average more than double their
low-educated counterparts (Table 3).
Alternatively, cities with larger shares of high-educated workers have lower shares
of women, blacks, and foreign-born workers, and exhibit less unemployment and poverty.
On the other hand, the likelihood of being married and being employed in manufacturing
increases in less-educated cities. No differences in terms of the level of natural amenities are
observed (Table 4).
In high-skilled cities, wages are higher for all groups. High-educated workers have a
15.3% wage premium for living in high-skilled areas. More importantly, low and medium-
educated workers also benefit from living in high-skilled areas. Their wages are 11.5% and
13.8% higher when compared to a low-skilled area worker. Nonetheless, inequality is greater
in high-educated cities, with wage gaps of $4,000 a year or $2 per hour.
5. EMPIRICAL RESULTS
5.1 Effects on group-specific wages
For parsimony, we only present the results for the key explanatory variable (share of
high-educated workers), leaving the full set of estimates and the first-stage tests of the
instruments for the appendix. Similarly, we estimated effects for different subsamples of
workers, but we show only estimated coefficients for all workers in the sample and for those
working 50-52 weeks a year and 30-60 hours a week.
Table 1 presents the results of the fully specified model for the effect of the share of
high-educated workers on log wages by group of workers. Here each entry is a separate
regression, and each row has a different dependent variable, but the same independent
variables. In the top row, we regress the log wages of low-educated workers on the share of
high-educated workers and controls. We repeat the process for medium-educated workers in
the middle row, and for high-educated workers at the bottom.
16
The first set of results in Table 1 suggests only a positive association between the
share of high-educated workers and their own wages. The results suggest that both workers
with high-school or less and with some college do not obtain significant (wage) benefits from
the concentration of high-educated workers. A one-percentage point increase in the college
16
Regressions including all groups simultaneously, with a group dummy, yield similar results.
11
graduate share increases the own wages of graduates by about 1.8% when considering the
Synthetic IV, significantly above the OLS estimate of 0.23%.
Table 1. The effect of the concentration of high-educated workers on group-specific log
wages. Fixed-effect models
OLS
IV
Match
Synthetic Controls
Dep. Variable:
All
Full Time
All
Full Time
All
Full Time
Log wages of:
[1]
[2]
[3]
[4]
[5]
[6]
High-School or less
0.0115
-0.0196
0.0505
-0.0786
-0.432
-0.282
(0.120)
(0.0994)
(0.257)
(0.262)
(1.040)
(1.032)
# Observations
1,227,624
771,724
1,227,624
771,724
1,227,624
771,724
Some college
0.0686
0.184
0.320
0.368
0.491
0.805
(0.129)
(0.136)
(0.226)
(0.226)
(0.818)
(0.886)
# Observations
1,006,354
696,841
1,006,354
696,841
1,006,354
696,841
College or more
0.203*
0.225**
0.0395
-0.0101
1.734*
1.813*
(0.106)
(0.0885)
(0.255)
(0.201)
(0.946)
(0.935)
# Observations
1,173,319
836,202
1,173,319
836,202
1,173,319
836,202
Subsample used
Weeks worked (#)
Any
50+
Any
50+
Any
50+
Hours worked (#)
Any
30-60
Any
30-60
Any
30-60
Note: Clustered standard errors at the state level are below each estimate. Each entry is a separate regression
of log wages of each group on the share of high-educated workers plus individual controls, MSA fixed-effects
and year fixed-effects. Dependent variable is log of real annual wages in columns [1], [3], and [5], and log of
real hourly wages in columns [2], [4], and [6]. Controls consider population size of the MSA, share of
working population in the MSA, schooling, potential experience, a dummy for the number of weeks worked
(columns [1], [3], and [5]), the number of hours worked on a regular week, gender, race, marital status, place
of birth (native or foreign-born), citizen status, a dummy for the class of worker, language spoken at home,
and a dummy to identify disability. Full set of estimates for full-year full-time workers included in the
appendix. *** p<0.01, ** p<0.05, * p<0.1.
Importantly, these results suggest that the concentration of high-educated workers are
not only important in increasing wages of high-educated workers themselves, but also that
the effect is large enough as to compensate for the negative supply effect. On the other hand,
we find no effect of externalities from the concentration of high-educated workers over wages
of low-educated workers.
Having presented our main results, it is worth discussing the validity of our
instruments. For the case of our Match IV, the first-stage F statistic moves approximately
between 24 and 27 suggesting that the instrument is not weak. Similarly, the Kleibergen-
Paap rk LM statistic for Underidentification test (with values between 16 and 21) rejects the
null hypothesis at the 1% level in all cases suggesting that the instruments are relevant.
Finally, the overidentification test (Sargan-Hansen J Statistic) presents p-values above 0.2 in
all cases suggesting that the instruments are valid. Similar results are found when using
Synthetic IV, with F statistics of 4.5-6 (rejecting the null of weak instruments under the
Sanderson-Windmeijer test), and with p-values below 0.03 and 0.07, suggesting the
12
relevance of the instrument (Table 9).
Overall, these results suggest that the concentration of human capital is positively
associated with high-educated worker wages, but it has no tangible effect over other workers’
wages. We extract from these results that the share of high-educated workers is positively
associated with the wage gap, as it only increases wages of high-educated workers
themselves.
One possible concern regarding the low-educated wage results is that they may mask
heterogeneity across workers. Liu & Yang (2019) suggested that most of the spillovers on
low-skilled wages concentrate on workers in non-tradable sectors. In regressions not
presented but available upon request, we divide the sample of low-educated workers into
those in tradable (agriculture, manufacturing and mining) and those in non-tradable sectors
(services and others). Results for these samples are not statistically different from each other
and the college graduate share coefficient remains insignificant and near zero, further
suggesting that neither knowledge spillovers nor consumption effects from the high-skilled
are important in explaining low-educated worker wages.
One difference we have from prior studies (Moretti, 2004; Winters, 2013) is that they
report estimates for four educational groups: less than high-school, high-school diploma,
some college, and college or more. Instead, we follow Autor et al. (2008) and choose to report
our main results for three educational groups. To test whether our results are sensitive to this
selection, we performed additional estimates considering workers with less than high-school
as a separate group but find no meaningful difference (these estimates are available upon
request).
We perform several other robustness checks. First, we use three different time-
invariant IVs in three year-by-year regressions. Nonetheless, the reader should be warned
that, since these IVs are time-invariant, these cross-sectional models fail to account for city
fixed-effects, which we note is potentially a key aspect of our identification (though if the IV
is valid, the omitted variable problem associated with not including city fixed-effects is
greatly mitigated if not eliminated).
When using time-invariant IVs, we add controls for city-specific variables such as
natural amenities, unemployment rate, and industry composition (to account for labor market
shocks). Nonetheless, if a city’s wage structure differs for unobservable reason (and our
instrument is not valid), then our cross-sectional estimates may be biased, meaning these
results should be cautiously interpreted.
According to our cross-sectional IV results with full-year workers, all workers’ wages
are positively associated with the concentration of human capital. These marginal effects
vary from 0.56% to around 1% for low-educated workers and from 1.1% to 1.4% for high-
educated workers, suggesting larger gains for them. It is worth noticing that these differences
are smaller when using the Land grant IV, but they still suggest a large effect for high-
educated workers, and a non-negative effect for the wage gap. In addition, these results
continue to suggest that the positive wage effects of knowledge spillovers dominate the
negative effect associated with any increases in labor supply.
13
Taken together, our results strongly support the idea that the concentration of human
capital favors more workers in the upper end of the skill distribution. Finally, and consistent
with de Lucio et al. (2002), we are able to provide evidence consistent with the hypothesis
of knowledge spillovers being more important than the supply effects in shaping MSA wages
for high-educated workers.
Finally, we find evidence of a city-size effect over wages, especially for the case of
our cross-section regressions, suggesting a wage premium associated with bigger cities.
Similarly, we find evidence that natural amenities are associated with lower wages for all
workers as suggested by Roback (1982), Rosen (1979), and Graves (2014).
5.2 Effects on the wage gap
We now focus our attention at the effect of concentrations of high-educated workers
on the wage gap. The same specifications, instruments and controls used in the previous
section are included here. We reproduce the estimates for different subsamples of workers,
from considering all workers to the most restricted sample of workers working 50+ weeks
per year, and 30-60 hours per week. These results are summarized in Table 2.
As expected, our estimates show that the concentration of high-educated workers is
associated with increases in the wage gap. The impact ranges from 0.63% when considering
full-year workers working any number of hours per week under the OLS regression, to 1.7%
when using the Match IV and the “all workers” subsample.
Our preferred estimations consider full-year (50+ weeks), full-time (30-60 hours per
week) workers. From these results we conclude that a one percentage point increase in the
share of high-educated workers is associated with a 1-1.3% increase in the wage gap (IV
estimates).
Interestingly, when comparing results across subsamples, we find that considering all
workers tends to amplify the differences in the wage gap. This suggests that working a
flexible number of hours and weeks a year poses a higher penalty for low-educated than for
high-educated workers. Restricting the sample reduces but does not eliminate, the effect of
the concentration of human capital on the wage gap.
14
Table 2. The effect of the concentration of high-educated workers on the wage gap
Dep. Variable:
OLS
IV
Log of wage gap
Match
Synthetic
Type of worker
[1]
[2]
[3]
All Workers
0.976***
1.653***
1.264***
(0.147)
(0.634)
(0.220)
Working 50+ weeks
0.630***
1.254**
0.870***
(0.152)
(0.605)
(0.220)
Working 50+ weeks, 30+ hours a week
0.727***
1.340**
1.021***
(0.156)
(0.608)
(0.221)
Working 50+ weeks, 30-60 hours a week
0.704***
1.307**
0.972***
(0.155)
(0.604)
(0.222)
Observations
1,068
1,068
1,068
Note: Clustered standard errors at the MSA level are below each estimate. Each column is a regression of the
log-wage gap between high- and low-educated workers on the share of high-educated workers (workers with
college degree or more) plus controls. Controls consider differences in potential experience, years of
schooling, the share of women in the labor market, the share of blacks, share of married, share of foreign
workers, nativity, weeks worked in the last year (in “All Workers” regressions), and the number of hours
worked per week (in “Working 50+ weeks” regressions, rows 2-4). Dependent variable is the log of the
annual wage gap in row 1, and the log of the hourly wage gap in rows 2-4. All regressions include state fixed-
effects. Full set of estimates for full-year full-time workers included in the appendix. *** p<0.01, ** p<0.05,
* p<0.1.
As before, the usual tests applied to the instruments tend to reject the presence of
weak instruments and suggest that they are relevant (Table 10 in the appendix). When using
the Match IV, the F statistic lies between 27 and 28, the test for Underidentification (with
values of around 46 and p-values of 0.0000) suggest the instruments are relevant, and the
Sargan-Hansen J statistic yields values of around 4, not allowing us to reject the test’s null
hypothesis. For the case of the Synth IV, we obtain an F statistic of around 290 and a
Underidentification value of around 155 (p-values of 0.000).
We successfully perform several additional regressions to test the robustness of our
results. First, we account for the possibility that externalities arise from the concentration of
workers in certain occupations (Winters, 2014) by using workers in Professional, Scientific,
and Technical Services as high-educated workers.
17
Second, we excluded self-employed
workers (to account for innovation), and women (to test gender differences). Third, we
exclude the first 20 MSAs in terms of population, to test whether our results are being
driven by a group of large, unequal MSAs with large concentrations of human capital.
18
Finally, we consider the use of the Gini coefficient and the Theil index as alternatives to the
wage gap. Estimates from these models confirm our previous results.
17
We also tried using the NAICS codes 54 and 55 (Management of companies and enterprises) altogether as
our proxy for highly-skilled workers. The results remain mostly unchanged.
18
This procedure excludes MSAs like New York, Dallas, Los Angeles, Chicago, Washington, Miami, San
Francisco, and Phoenix, among others.
15
6. CONCLUSIONS
The empirical results indicated that an increase in the share of high-educated workers
induces an increase in the log wage gap, which is ultimately only explained by wage increases
among the group high-educated workers. Other workers in the economy do not seem to
benefit from concentrations of high-educated workers. This is robust to splitting the sample
of low-educated workers into those with less than high-school and those with high-school
diploma, or to consider workers in tradable and non-tradable sectors. In line with the study
of Ananat et al. (2018), future studies could also consider assessing whether these results
hold across different groups of workers, such as the differences that might arise when looking
only at women or for different racial groups.
It is important to notice that our specifications do not allow us to directly observe
knowledge spillovers, and without a careful identification scheme, they would only provide
an estimate for the total net effect. As discussed, since an increase in the share of high-
educated workers is necessarily the consequence of an increase in the relative supply of high-
educated workers, places with larger supplies of high-educated workers should pay them
relatively lower wages. Yet, their wages seem to benefit from the concentration of high-
skilled workers. Thus, human capital externalities are positive and large enough to produce
a positive net effect. Moreover, since we do not distinguish between knowledge and
consumption-demand spillovers on low-educated worker wages, our results can be thought
as lower bound estimates of the importance of human capital externalities on the wage gap.
Our results complement previous research on the causes of wage inequality in metro
areas, adding a new dimension to its existence. Knowledge spillovers among workers
provides an additional potential channel for transmission of inequality that is consistent with
changes in the labor market composition, and skill-biased technological change.
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19
APPENDIX
Table 3. Descriptive statistics for the average high, medium and low-educated worker, 2005-
2014
Variable
High-School -
Some College
College +
Annual wage (,000 $ of 2014)
31.0
42.9
77.8
Hourly wage ($ of 2014)
17.7
22.9
38.6
Schooling (years)
12.0
13.0
17.0
Age (years)
43.7
44.5
44.9
Potential experience (years)
26.6
24.7
22.0
Full-year worker (%)
71.1
76.9
77.9
Hours worked a week (#)
38.5
39.5
41.5
Self-employed (%)
4.0
4.9
6.8
Women (%)
56.4
49.2
50.7
Non-white (%)
25.2
19.8
17.7
Foreign-born (%)
19.8
9.6
14.4
Speaks other language at home (%)
24.4
13.7
16.6
Married (%)
55.4
60.3
68.2
Has a disability (%)
9.6
7.5
4.1
Observations
1,227,624
1,006,354
1,173,319
Source: ACS 2005, 2010, and 2014.
20
Table 4. Descriptive statistics by quartile of shares of high-educated workers in the city,
2005-2014
Quartile
1st
2nd-3rd
4th
High-educated workers (%)
17.9
25.8
37.2
Annual wage (,000 $ of 2014)
21.3
23.6
28.0
Hourly wage ($ of 2014)
14.3
15.6
18.2
Hourly wage ($ of 2014): High-School -
11.9
12.4
13.3
Hourly wage ($ of 2014): Some college
14.9
15.4
16.9
Hourly wage ($ of 2014): College +
22.2
22.8
25.6
Annual wage gap (,000 $ of 2014)
20.8
20.9
24.7
Hourly wage gap ($ of 2014)
10.3
10.4
12.4
Schooling (years)
12.9
13.5
14.1
Potential experience (years)
23.5
23.5
22.8
Weeks worked (#)
48.7
48.7
48.8
Hours worked a week (#)
40.0
39.7
39.7
Women (%)
17.3
16.1
15.8
Black (%)
4.1
3.4
3.1
Foreign-born (%)
4.8
2.9
4.1
Married (%)
22.0
19.9
19.6
Unemployment (%)
6.6
5.8
5.6
Poverty (%)
18.2
15.2
13.8
Manufacturing (%)
12.7
11.5
9.9
USDA Natural Amenities Rank
3.5
3.4
3.5
Temperature in January (z-score)
-0.2
-0.1
-0.2
Hours of sun in January (z-score)
0.2
0.0
0.0
Temperature in July (z-score)
-0.1
0.0
0.1
Humidity in July (z-score)
0.3
0.1
0.1
Topography (z-score)
0.1
0.0
0.1
Presence of water (z-score)
-0.2
-0.1
0.0
Observations (# of MSAs)
268
533
267
Source: ACS 2005, 2010, and 2014.
21
Table 5. The effect of the concentration of high-educated workers on log wages of low-
educated workers. Fixed-effect models. Full set of coefficients for full-year full-time
workers
19
Dep. Variable:
OLS
Match
Synthetic
Log wages of workers with
high-school or less
[2]
[4]
[6]
Share of high-educated workers
-0.0196
-0.0786
-0.282
(0.0994)
(0.262)
(1.032)
Population
-2.68e-08*
-2.66e-08*
-2.59e-08
(1.47e-08)
(1.48e-08)
(1.60e-08)
Working population (%)
-0.0150
-0.0119
-0.00108
(0.0280)
(0.0345)
(0.0637)
Potential experience
0.00694***
0.00694***
0.00694***
(0.000257)
(0.000257)
(0.000257)
Schooling (base = no school)
Nursery - Grade 4
-0.0460***
-0.0460***
-0.0459***
(0.00630)
(0.00634)
(0.00638)
Grade 5-6
-0.00320
-0.00319
-0.00314
(0.00879)
(0.00880)
(0.00895)
Grade 7-8
0.0303*
0.0303*
0.0303*
(0.0179)
(0.0179)
(0.0179)
Grade 9
0.0531***
0.0531***
0.0531***
(0.0157)
(0.0157)
(0.0157)
Grade 10
0.0753***
0.0753***
0.0753***
(0.0178)
(0.0178)
(0.0178)
Grade 11
0.0991***
0.0991***
0.0992***
(0.0184)
(0.0184)
(0.0184)
Grade 12, no diploma
0.164***
0.164***
0.164***
(0.0183)
(0.0183)
(0.0183)
High-school graduate
0.261***
0.261***
0.261***
(0.0194)
(0.0194)
(0.0194)
Gender (base = male)
Female
-0.238***
-0.238***
-0.238***
(0.00770)
(0.00770)
(0.00770)
Race (base = white)
Black or African American
-0.129***
-0.129***
-0.129***
(0.00664)
(0.00665)
(0.00653)
American Indian
-0.0627***
-0.0628***
-0.0631***
(0.00862)
(0.00857)
(0.00850)
Alaska Native
-0.150
-0.150
-0.150
(0.159)
(0.159)
(0.159)
A. Indian, Alaska Native - specified
-0.0650***
-0.0650***
-0.0650***
(0.0201)
(0.0202)
(0.0202)
Asian
-0.103***
-0.103***
-0.103***
(0.0219)
(0.0219)
(0.0219)
Native Hawaiian (other Islands)
-0.0543***
-0.0544***
-0.0544***
(0.0186)
(0.0186)
(0.0186)
19
Results for ‘All’ workers (columns [1], [3], and [5] of Table 1) are suppressed to conserve space.
22
Other race
-0.0451***
-0.0450***
-0.0449***
(0.0111)
(0.0111)
(0.0112)
Two or more races
-0.0506***
-0.0506***
-0.0506***
(0.0116)
(0.0116)
(0.0116)
Marital status (base = married)
Widowed
-0.157***
-0.157***
-0.157***
(0.00468)
(0.00468)
(0.00469)
Divorced
-0.0658***
-0.0658***
-0.0657***
(0.00203)
(0.00203)
(0.00203)
Separated
-0.126***
-0.126***
-0.126***
(0.00630)
(0.00630)
(0.00629)
Never married or under 15
-0.217***
-0.217***
-0.217***
(0.00462)
(0.00462)
(0.00462)
Nativity (base = native)
Foreign born
-0.166***
-0.166***
-0.166***
(0.00961)
(0.00961)
(0.00962)
Citizenship status (base = born in the U.S.)
Born in Puerto Rico, Guam…
-0.0556***
-0.0556***
-0.0555***
(0.0135)
(0.0135)
(0.0135)
Born abroad of American parents
0.00371
0.00374
0.00383
(0.0103)
(0.0103)
(0.0101)
US citizen, naturalized
0.148***
0.148***
0.148***
(0.0107)
(0.0107)
(0.0107)
Class of worker (base = employee for profit)
Employee of private non-profit
-0.0337***
-0.0336***
-0.0336***
(0.00513)
(0.00514)
(0.00503)
Employee of local government
0.0354*
0.0354*
0.0354*
(0.0196)
(0.0196)
(0.0196)
Employee of state government
0.0284
0.0285
0.0285
(0.0219)
(0.0219)
(0.0219)
Employee of federal government
0.199***
0.199***
0.199***
(0.0230)
(0.0230)
(0.0230)
Self-employed, not incorporated business
-0.698***
-0.698***
-0.698***
(0.0301)
(0.0301)
(0.0300)
Self-employed, incorporated business
-0.00525
-0.00525
-0.00523
(0.0134)
(0.0134)
(0.0134)
Language at home (base = another language)
Speaks only English at home
0.113***
0.113***
0.113***
(0.00906)
(0.00907)
(0.00911)
Disability (base = with disability)
No disability
0.114***
0.114***
0.114***
(0.00306)
(0.00306)
(0.00306)
Usual hours worked per week
0.00372***
0.00372***
0.00373***
(0.000412)
(0.000412)
(0.000411)
Constant
2.311***
(0.0617)
Observations
771,724
771,724
771,724
Note: Clustered standard errors at the state level are below each estimate. Regressions of log of real hourly
wages on the share of high-educated workers plus individual controls, MSA fixed-effects and year fixed-
effects. Column numbers match those of Table 3. *** p<0.01, ** p<0.05, * p<0.1.
23
Table 6. The effect of the concentration of high-educated workers on log wages of medium-
educated workers. Fixed-effect models. Full set of coefficients for full-year full-time
workers
20
Dep. Variable:
OLS
Match
Synthetic
Log wages of workers with some college
[2]
[4]
[6]
Share of high-educated workers
0.184
0.368
0.805
(0.136)
(0.226)
(0.886)
Population
-4.53e-09
-5.09e-09
-6.44e-09
(1.18e-08)
(1.19e-08)
(1.25e-08)
Working population (%)
-0.000945
-0.0118
-0.0377
(0.0359)
(0.0395)
(0.0636)
Potential experience
0.00862***
0.00862***
0.00862***
(0.000227)
(0.000227)
(0.000228)
Schooling (base = less than 1 year of college)
1+ years of college, no degree
0.0605***
0.0605***
0.0605***
(0.00245)
(0.00245)
(0.00245)
Associate's degree
0.155***
0.155***
0.155***
(0.00477)
(0.00477)
(0.00478)
Gender (base = male)
Female
-0.200***
-0.200***
-0.200***
(0.00647)
(0.00646)
(0.00646)
Race (base = white)
Black or African American
-0.141***
-0.141***
-0.141***
(0.00509)
(0.00508)
(0.00501)
American Indian
-0.0707***
-0.0705***
-0.0700***
(0.00925)
(0.00932)
(0.00920)
Alaska Native
-0.0334
-0.0334
-0.0334
(0.0448)
(0.0448)
(0.0446)
A. Indian, Alaska Native - specified
-0.0690***
-0.0689***
-0.0688***
(0.0201)
(0.0201)
(0.0200)
Asian
-0.0647***
-0.0648***
-0.0649***
(0.00613)
(0.00613)
(0.00612)
Native Hawaiian (other Islands)
-0.110***
-0.110***
-0.110***
(0.0166)
(0.0166)
(0.0166)
Other race
-0.0825***
-0.0826***
-0.0828***
(0.00733)
(0.00733)
(0.00738)
Two or more races
-0.0830***
-0.0830***
-0.0829***
(0.00575)
(0.00575)
(0.00573)
Marital status (base = married)
Widowed
-0.162***
-0.162***
-0.162***
(0.00841)
(0.00841)
(0.00842)
Divorced
-0.0663***
-0.0663***
-0.0663***
(0.00250)
(0.00250)
(0.00249)
Separated
-0.130***
-0.130***
-0.130***
(0.00617)
(0.00616)
(0.00616)
Never married or under 15
-0.229***
-0.229***
-0.229***
(0.00433)
(0.00433)
(0.00432)
20
Results for ‘All’ workers (columns [1], [3], and [5] of Table 1) are suppressed to conserve space.
24
Nativity (base = native)
Foreign born
-0.173***
-0.173***
-0.173***
(0.00790)
(0.00791)
(0.00793)
Citizenship status (base = born in the U.S.)
Born in Puerto Rico, Guam…
-0.0551***
-0.0551***
-0.0551***
(0.0174)
(0.0174)
(0.0173)
Born abroad of American parents
0.00652
0.00646
0.00630
(0.00619)
(0.00616)
(0.00622)
US citizen, naturalized
0.146***
0.146***
0.146***
(0.00773)
(0.00775)
(0.00780)
Class of worker (base = employee for profit)
Employee of private non-profit
0.00573
0.00571
0.00567
(0.00770)
(0.00771)
(0.00768)
Employee of local government
0.0196
0.0196
0.0196
(0.0223)
(0.0223)
(0.0222)
Employee of state government
0.0113
0.0113
0.0114
(0.0217)
(0.0217)
(0.0218)
Employee of federal government
0.169***
0.169***
0.169***
(0.0180)
(0.0180)
(0.0180)
Self-employed, not incorporated business
-0.874***
-0.874***
-0.875***
(0.0302)
(0.0302)
(0.0303)
Self-employed, incorporated business
-0.0986***
-0.0986***
-0.0986***
(0.0159)
(0.0159)
(0.0159)
Language at home (base = another language)
Speaks only English at home
0.120***
0.120***
0.120***
(0.00958)
(0.00956)
(0.00950)
Disability (base = with disability)
No disability
0.136***
0.136***
0.136***
(0.00339)
(0.00339)
(0.00340)
Usual hours worked per week
0.00361***
0.00361***
0.00361***
(0.000337)
(0.000337)
(0.000337)
Constant
2.481***
(0.0510)
Observations
696,841
Note: Clustered standard errors at the state level are below each estimate. Regressions of log of real hourly
wages on the share of high-educated workers plus individual controls, MSA fixed-effects and year fixed-
effects. Column numbers match those of Table 3. *** p<0.01, ** p<0.05, * p<0.1.
25
Table 7. The effect of the concentration of high-educated workers on log wages of high-
educated workers. Fixed-effect models. Full set of coefficients for full-year full-time
workers
21
Dep. Variable:
OLS
Match
Synthetic
Log wages of workers with
college or more
[2]
[4]
[6]
Share of high-educated workers
0.225**
-0.0101
1.813*
(0.0885)
(0.201)
(0.935)
Population
1.38e-08
1.42e-08
1.09e-08
(9.61e-09)
(9.38e-09)
(1.17e-08)
Working population (%)
0.0318
0.0503
-0.0931
(0.0713)
(0.0831)
(0.0877)
Potential experience
0.00770***
0.00770***
0.00770***
(0.000232)
(0.000232)
(0.000232)
Schooling (base = Bachelor's degree)
Master's degree
0.196***
0.196***
0.196***
(0.00322)
(0.00323)
(0.00320)
Professional school degree
0.495***
0.495***
0.495***
(0.00876)
(0.00874)
(0.00874)
Doctorate degree
0.387***
0.387***
0.386***
(0.00631)
(0.00630)
(0.00628)
Gender (base = male)
Female
-0.193***
-0.193***
-0.193***
(0.00494)
(0.00494)
(0.00493)
Race (base = white)
Black or African American
-0.128***
-0.128***
-0.128***
(0.00457)
(0.00457)
(0.00461)
American Indian
-0.100***
-0.101***
-0.0992***
(0.0145)
(0.0145)
(0.0144)
Alaska Native
-0.161*
-0.161*
-0.161*
(0.0824)
(0.0824)
(0.0824)
A. Indian, Alaska Native - specified
-0.158***
-0.158***
-0.159***
(0.0326)
(0.0326)
(0.0327)
Asian
0.0365**
0.0366**
0.0363**
(0.0143)
(0.0143)
(0.0143)
Native Hawaiian (other Islands)
-0.0973***
-0.0973***
-0.0974***
(0.0310)
(0.0310)
(0.0308)
Other race
-0.165***
-0.165***
-0.166***
(0.0155)
(0.0155)
(0.0153)
Two or more races
-0.0816***
-0.0816***
-0.0814***
(0.00688)
(0.00688)
(0.00690)
Marital status (base = married)
Widowed
-0.178***
-0.178***
-0.178***
(0.00681)
(0.00682)
(0.00680)
Divorced
-0.0964***
-0.0964***
-0.0964***
(0.00325)
(0.00325)
(0.00325)
Separated
-0.127***
-0.127***
-0.126***
21
Results for ‘All’ workers (columns [1], [3], and [5] of Table 1) are suppressed to conserve space.
26
(0.00875)
(0.00873)
(0.00882)
Never married or under 15
-0.247***
-0.247***
-0.247***
(0.00469)
(0.00469)
(0.00469)
Nativity (base = native)
Foreign born
-0.131***
-0.131***
-0.131***
(0.0140)
(0.0140)
(0.0141)
Citizenship status (base = born in the U.S.)
Born in Puerto Rico, Guam…
-0.00920
-0.00920
-0.00924
(0.0225)
(0.0225)
(0.0223)
Born abroad of American parents
0.0181**
0.0182**
0.0179**
(0.00882)
(0.00880)
(0.00887)
US citizen, naturalized
0.106***
0.106***
0.106***
(0.0119)
(0.0119)
(0.0120)
Class of worker (base = employee for profit)
Employee of private non-profit
-0.182***
-0.182***
-0.182***
(0.00888)
(0.00887)
(0.00890)
Employee of local government
-0.185***
-0.185***
-0.185***
(0.0219)
(0.0219)
(0.0219)
Employee of state government
-0.169***
-0.169***
-0.168***
(0.0150)
(0.0150)
(0.0150)
Employee of federal government
0.0642***
0.0643***
0.0642***
(0.0152)
(0.0152)
(0.0153)
Self-employed, not incorporated
business
-1.169***
-1.169***
-1.169***
(0.0392)
(0.0392)
(0.0393)
Self-employed, incorporated business
-0.179***
-0.179***
-0.179***
(0.00919)
(0.00919)
(0.00920)
Language at home (base = another language)
Speaks only English at home
0.122***
0.122***
0.122***
(0.00401)
(0.00401)
(0.00400)
Disability (base = with disability)
No disability
0.175***
0.175***
0.175***
(0.00440)
(0.00439)
(0.00445)
Usual hours worked per week
0.00228***
0.00228***
0.00227***
(0.000445)
(0.000445)
(0.000444)
Constant
2.881***
(0.0551)
Observations
836,202
836,202
836,202
Note: Clustered standard errors at the state level are below each estimate. Regressions of log of real hourly
wages on the share of high-educated workers plus individual controls, MSA fixed-effects and year fixed-
effects. Column numbers match those of Table 3. *** p<0.01, ** p<0.05, * p<0.1.
27
Table 8. The effect of the concentration of high-educated workers on the wage gap. Full set
of coefficients for full-year full-time workers
22
Dep. Variable:
OLS
IV
Log of wage gap
Match
Synthetic
[1]
[2]
[3]
Share of high-educated workers
0.704***
1.307**
0.972***
(0.155)
(0.604)
(0.222)
Potential experience
0.00816***
0.00952***
0.00876***
(0.00182)
(0.00229)
(0.00180)
Years of schooling
0.0700***
0.0526***
0.0622***
(0.0159)
(0.0199)
(0.0162)
Share of women
-0.852***
-1.029***
-0.931***
(0.169)
(0.245)
(0.177)
Share of black
-0.175
-0.237*
-0.203
(0.129)
(0.139)
(0.125)
Share of married
0.413***
0.108
0.277*
(0.145)
(0.324)
(0.155)
Share of foreign-born
-0.412**
-0.490***
-0.447***
(0.170)
(0.164)
(0.165)
Usual hours worked per week
0.00471*
0.00364
0.00423*
(0.00261)
(0.00266)
(0.00252)
Constant
0.0779
-0.00259
0.0421
(0.0980)
(0.135)
(0.0966)
Observations
1,068
1,068
1,068
Note: Clustered standard errors at the MSA level are below each estimate. Each column is a regression of the
log-wage gap between high- and low-educated workers on the share of high-educated workers (workers with
college degree or more) plus controls. Dependent variable is the log of the hourly wage gap. All regressions
include state fixed effects. *** p<0.01, ** p<0.05, * p<0.1.
22
Results for different subsamples of workers (first, second, and third rows of Table 2) are suppressed to
conserve space.
28
Table 9. First stage statistics of the instruments used in Table 1
Match IV
Synthetic
Type of worker
All
Full Time
All
Full Time
[3]
[4]
[5]
[6]
High-School-
First stage F-statistic
26.094
25.324
5.993
5.823
Underidentification test
21.327
21.285
4.452
4.401
p-value
0.0000
0.0000
0.0349
0.0359
Overidentification test
1.233
1.391
--
--
p-value
0.2668
0.2382
--
--
Some college
First stage F-statistic
24.429
24.196
5.616
5.440
Underidentification test
19.807
19.865
3.975
3.916
p-value
0.0000
0.0000
0.0462
0.0478
Overidentification test
0.033
0.028
--
--
p-value
0.8565
0.8669
--
--
College+
First stage F-statistic
26.726
26.987
4.472
4.465
Underidentification test
16.739
17.012
3.197
3.177
p-value
0.0002
0.0002
0.0738
0.0747
Overidentification test
0.226
1.175
--
--
p-value
0.6343
0.2784
--
--
Note: First stage F-statistic is the Kleibergen-Paap rk Wald F statistic. Underidentification test uses the
Kleibergen-Paap rk LM statistic. Overidentification test corresponds to the Hansen J statistic. Column
numbers match the ones in Table 1.
29
Table 10. First stage statistics of the instruments used in Table 2
Match IV
Synth IV
Type of worker
[2]
[3]
All Workers
First stage F-statistic
27.568
288.257
Underidentification test
45.599
156.515
p-value
0.0000
0.0000
Overidentification test
4.458
--
p-value
0.0347
--
Working 50+ weeks
First stage F-statistic
28.490
290.396
Underidentification test
46.395
155.498
p-value
0.0000
0.0000
Overidentification test
3.901
--
p-value
0.0483
--
Working 50+ weeks, 30+ hours a week
First stage F-statistic
28.490
290.396
Underidentification test
46.395
155.498
p-value
0.0000
0.0000
Overidentification test
3.947
--
p-value
0.0469
--
Working 50+ weeks, 30-60 hours a week
First stage F-statistic
28.490
290.396
Underidentification test
46.395
155.498
p-value
0.0000
0.0000
Overidentification test
4.275
--
p-value
0.0387
--
Note: First stage F-statistic is the Kleibergen-Paap rk Wald F statistic. Underidentification test uses the
Kleibergen-Paap rk LM statistic. Overidentification test corresponds to the Hansen J statistic. Column
numbers match the ones in Table 2.
