Spatial Changes in the College Wage Premium
Joanne Lindley*and Stephen Machin**
August 2012
*
Department of Economics, University of Surrey
**
Department of Economics, University College London and Centre for Economic
Performance, London School of Economics
Abstract
We study spatial changes in the US college wage premium for states and cities using US
Census and American Community Survey data between 1980 and 2010. We report
evidence of significant and persistent spatial disparities in the college wage premium for
US states and MSAs. We use estimates of spatial relative demand and supply models to
calculate implied relative demand shifts for college graduates vis-à-vis high school
graduates and show that relative demand has shifted faster in places that have experienced
faster increases in R&D intensity and shifted slower in places where union decline has
been faster. Overall, our spatial analysis complements research findings from labour
economics on wage inequality trends and from urban economics on agglomeration effects
connected to education and technology.
JEL Keywords: College wage premium; Relative demand; Spatial changes.
JEL Classifications: J31; R11.
Corresponding author: Joanne Lindley: [email protected].
Acknowledgements
We would like to thank Gilles Duranton, Lowell Taylor and participants in the II
Workshop on Urban Economics in Barcelona for a number of helpful comments and
suggestions.
0
1. Introduction
Over the last twenty years, study of the evolution of the wage distribution over time has
become a major preoccupation of empirical economists. A widening of the wage
distribution showing rising wage inequality in a number of countries has been very clearly
documented in this work.1 Empirical studies in this area have highlighted the temporal
evolution of particular wage differentials linked to, for example, education or experience
emphasising increase in the college wage premium or the return to experience that have
gone hand-in-hand with rising wage inequality.
Despite there being a sizable urban economics literature studying the urban wage
premium2, work studying the spatial dimensions of rising wage inequality is more sparse.3
In part, this is because within/between type decompositions show that a significant part of
the increase in overall wage inequality, or in particular wage differentials, has been within,
rather than between, spatial units of observation like regions, states, cities or local labour
markets.
Nonetheless, at a given point in time there are very sizable spatial differences in
wages and in wage differentials between different groups of workers. In the past,
specifically in the first few decades in the post-war period, these spatial differences tended
to show persistence through time, with if anything there being regional and spatial
convergence in wage or income differences. It is interesting to note that, in the period
since wage inequality started to rise in the US (since the mid-to-late 1970s), this pattern
1
See Katz and Autor (1999) or Acemoglu and Autor (2010) for reviews of the large literature in labour
economics and Hornstein et al. (2005) for a review of the work in macroeconomics.
2
See Puga (2010) or Rosenthal and Strange (2004) for discussions of the literature on urban wage premia
and how they relate to agglomeration effects that raise productivity in cities.
3
Although less concerned with inequality rises over time, see the recent work on spatial wage differences
and sorting (e.g. Combes, Duranton and Gobillon, 2008 or Baum-Snow and Pavan, 2012) and on local wage
and skill distributions (Combes et al., 2012).
1
seems to have stopped. Since then mean reversion in spatial wage differences is absent as
wages have tended to rise faster in places with higher initial wages. Moretti (2010), for
example, shows plots of the wages of college graduates and high school graduates in 288
US Metropolitan Statistical Areas (MSAs) in 1980 and 2000 where wages grow faster in
MSAs with higher wage levels in 1980 for both groups of workers. We find the same
using data between 1980 and 2010 for 216 MSAs, as demonstrated in Figure 1. 4 Figure 1
very much shows there to be faster increasing higher wage levels for college and high
school workers between 1980 and 2010 in MSAs where wages were already higher in
1980.
In this paper, our interest is in relative wage differentials between college and high
school workers. We study changing patterns of spatial college wage premia in the context
of changing relative supply and demand of college educated versus high school educated
workers. We begin by documenting the nature of changes in education employment shares
and the college wage premium across different spatial units, looking at their evolution
over time at state and MSA level. To do so, we use US Census and American Community
Survey (ACS) data from 1980 through 2010. We uncover an interesting spatial dimension
where, despite very rapid increases in the supply of college workers, the college wage
premia has risen almost everywhere, but to varying degrees as the spatial variation in the
wage gap between college educated and high school educated workers has become more
persistent over time.
In the wage inequality literature, rising wage gaps between college and high school
workers have been connected to shifts in the relative demand and supply of these groups
of workers. Indeed, aggregate evidence shows that a key driver of rising wage college
4
The Figure is based on the 5 percent 1980, 1990 and 2000 Censuses and the 1 percent 2010 ACS which we
collapse to 216 consistently defined MSAs. The Figure replicates Moretti's (2010) Figure based on 1980 and
2000 Census data. Moretti (2010) reported slope coefficients (and associated standard errors) of 1.82 (0.89)
for high school graduates and 3.54 (0.11) for college graduates.
2
premia has been an increased relative demand for college educated workers (see Katz and
Murphy, 1992; Katz and Autor, 1999; Acemoglu and Angrist, 2010). The presence of
rising spatial college wage premia at different rates in the face of rapidly rising supply also
suggests there may be differential relative demand shifts occurring at the spatial level. We
thus modify the commonly used relative demand and supply model to calculate the extent
of spatial relative demand shifts and examine the variations in their evolution through
time. We also consider what factors have been correlated with the observed spatial shifts
in relative demand, exploring whether technology measures (like R&D intensity or
computer usage) and the reduced importance of labour market institutions (through union
decline) display spatial correlations with changes in relative demand.
Previewing our key results, we report evidence of significant spatial variations in
the college wage premium for US states and MSAs, and show that the pattern of shifts
through time has resulted in increased spatial persistence. Because relative supply of
college versus high school educated has also risen faster at the spatial level in places with
higher initial supply levels, we also report a strong persistence in spatial relative demand.
These relative demand increases are bigger in more technologically advanced states that
have experienced faster increases in R&D intensity and computer usage, and in states
where union decline has been fastest. Finally, we report evidence that the relationship
between cross-state migration and college education has stayed relatively constant
between 1980 and 2010.
The rest of the paper is structured as follows. Section 2 offers a descriptive
analysis of changes in college shares in employment and changing college/high school
wage differentials in the US at different levels of spatial aggregation. Section 3 then
considers these differentials in the context of a relative supply-demand framework,
showing spatial variations in the nature of relative demand shifts over time. Section 4
3
considers the relationship between state level relative demand shifts and some potential
drivers of the shifts. Section 5 studies cross-state migration differences by education,
whilst Section 6 concludes.
2. Spatial Employment Shares and Wage Differentials - Descriptive Analysis
To investigate spatial changes in the college wage premium we use data from the US
Census in 1980, 1990 and 2000, and the American Community Survey (ACS) of 2010.
We use the 5 percent Census samples and the 1 percent ACS to study the evolution of
wage differentials for the 48 contiguous US states (dropping Alaska, Hawaii and the
District of Columbia) and for 216 consistently defined MSAs. We focus on US born
individuals aged 26-55 throughout our analysis. 5
It has been widely documented that the employment shares of more educated
workers have increased over time in the US (see, inter alia, Acemoglu and Autor, 2010).
As with much of the work studying these changes, we consider changes in the relative
employment of two composite education groups, 'college equivalent' and 'high school
equivalent' workers. To form these composite groups, we first define five education
groups, namely high school drop outs (with less than twelve years of schooling), high
school graduates (with exactly twelve years of schooling), those with some college
(thirteen to fifteen years of schooling), college graduates (sixteen years of schooling) and
postgraduates (with over sixteen years of schooling). The college equivalent group then
comprises college graduates plus postgraduates and 30 percent of the some college group
(both weighted by their wage relative to college graduates).6 High school equivalent
5
See the Data Appendix for more detail on the data used throughout the paper.
The wage weights used are the average wage of the respective education group over all time periods. 30
percent of the some college group are assigned to the college equivalent group and 70 percent to the high
school equivalent group because the some college wage is closer to the high school wage than to the college
wage.
6
4
workers are defined analogously as high school graduates or high school dropouts plus 70
percent of some college workers (with the high school dropouts and some college workers
having efficiency weights defined as their wage relative to high school graduates).
Table 1 shows the average college equivalent hours share between 1980 and 2010
for the 48 states and 216 MSAs. It reports that, on average across the 48 states we look at,
the hours share of college equivalents rose by 11.6 percentage points between 1980 and
2010, going from a share of 29 percent in 1980 to just under 41 percent by 2010. The
comparable average increase is much the same in the MSAs, at 9.7 percentage points
(going from 30 to 40 percent).
However, what this Table of means does not show is the sizable spatial disparities
in this relative education supply variable. For example, for states, the lowest hours share
of college equivalents is 22 percent in Wyoming in 1980 and the highest is 55 percent in
Massachusetts in 2010. Figures 2a and 2b therefore plot the state and MSA values of the
college equivalent hours shares for the three periods 1980-90, 1990-2000 and 2000-2010.
The same scale is utilised (from 0.2 to 0.55 for states, 0.15 to 0.65 for MSAs) so as to
clearly show how the shares have moved through time over the three ten year intervals.
The pattern in the Figures is quite striking. First of all, in all time periods there is a
strong persistence in rankings of high and low college equivalent states/MSAs. 7 8 Second,
there is evidence of relative supply increases in all states through time, as the scatterplot
moves in a North Eastern direction when moving from the 1980-90 plot at the top, to the
2000-2010 plot at the bottom. But this movement is to varying degrees in different states
7
Spearman rank correlation coefficients are strongly significant for all three time periods. For states, they
are: 0.94 (p-value = 0.00) for 1980-90; 0.97 (p-value = 0.00) for 1990-2000; 0.94 (p-value = 0.00) for 200010. For MSAs, they are: 0.94 (p-value = 0.00) for 1980-90; 0.93 (p-value = 0.00) for 1990-200; 0.94 (pvalue = 0.00) for 2000-10.
8
Our focus is on relative education differences in labour supply and demand. Other papers show that
broader sets of skills are concentrated in particular cities. Some recent examples are Bacold, Blum and
Strange (2009) who place a focus on the distribution of a range of cognitive and non-cognitive skills in US
cities and Hendricks (2011) who considers city skill compositions looking at spatial complementarities
between business services and the skill structure of employment.
5
and MSAs. For example, for states over the whole 1980-2010 time period, the smallest
increase is in New Mexico with a 4 percentage points increase and the largest in
Massachusetts, which rises by 18 percentage points. Thus, the spread widens: in 1980 the
range was 16 percentage points, by 2010 it was 25. For MSAs, the spread rises from 36 to
45 percentage points between 1980 and 2010. Thirdly, the slopes on the Figures show that,
if anything, the college hours shares are diverging over time (as the coefficient of above
unity on the slopes in the Figures shows).
Thus, the relative supply of college workers has risen sharply, and with differential
spatial evolutions. What about the spatial college wage premium? Our analysis of the
Census/ACS data makes it evident that, at the same time as the hours shares of the college
educated have risen, so have their relative wage differentials. Table 2 presents mean
composition adjusted log weekly wage differentials for college graduates relative to high
school graduates across states and MSAs. 9 One can see the well known average pattern of
increasing wage payoffs to college graduates as the college/high school log wage premium
rises by 0.178 percentage points between 1980 and 2010 across states of residence and by
0.185 percentage points across MSAs.
Previous research by Black, Kolesnikova and Taylor (2009) has noted that, at a
point in time (in their case the cross-sections from the 1980, 1990 and 2000 US Census),
there are sizable spatial disparities in education related wage differentials. This is also the
case for our analysis, both in terms of the yearly variations across spatial units (thus
9
These wages are composition adjusted on the basis of estimating log weekly wage equations for full time
full year workers separately for each year, for three birth cohorts/ages and by gender in each year for the 48
states and 216 MSAs respectively. The equations include dummies for age and race. To derive the
educational wage differentials, education dummies are included for postgraduates (more than 16 years of
education), college only (16 years of education), some college (13 to 15 years of education) and high school
dropouts (less than 12 years of education) relative to the omitted group of high school graduates (12 years of
schooling). The college/high school graduate log wage differential is the estimated coefficient on the college
only variable, which we weight across the sub-groups for which we estimate using the average share of
hours worked for each of the groups over 1980 to 2010.
6
confirming the Black, Kolesnikova and Taylor findings) and in terms of the increase in the
college premium.
This can be shown in the same way as for our earlier analysis of relative education
supply, as Figures 3a and 3b show the spatial distributions of the college wage premium
for the three sub-periods, 1980-90, 1990-2000 and 2000-2010. There is very clear
evidence of wide variations in the college premium. The lowest college/high school wage
differential is 0.21 log points in Utah in 1980 and the highest is 0.61 log points in New
York in 2010. Within years there is a wide spread which widens over time, from 0.20 log
points in 1980, reaching 0.26 log points by 2010. A comparison of the three Panels in the
Figures also reveals, as was the case for the relative supplies, a significant North Eastern
movement over time. Thus, the college wage premium rises in all states, mirroring the
national pattern, but it goes up by more in some places. In terms of states, the smallest rise
is in Delaware (at 0.07 log points) and the largest in Illinois (at 0.27 log points).
This upward movement in spatial wage differentials is also characterised by
persistence over time, and a persistence that seems to get stronger. For the state level
analysis in Figure 3a, the estimated slope over the ten year interval rises from 0.75 in
1980-90 to 0.99 in 1990-2010 and 0.90 in 2000-2010. Thus, in the first decade there is
some evidence of catch up, or mean reversion in the wage premia, from the states that has
lower wage premia to begin with. However, this alters in 1990-2000 and 2000-2010 where
the slope steepens as the premia move in the North Eastern direction in the Figures and
become insignificantly different from unity. The same qualitative pattern of a steepening
slope also occurs in the MSA data in Figure 3b, although there is also more evidence of
mean reversion at this more disaggregated level (possibly due to more noise because of
smaller samples of individuals from the Census/ACS data at this level of aggregation).
7
This descriptive section of the paper has highlighted spatial disparities in education
supply and in the college wage premium in the US over the last thirty years. In the
remainder of the paper, we focus on reasons why these disparities are present and why
they are persistent. In the next section we consider spatial demand and supply models that
enable us to use these patterns of change in education supply and the college wage
premium to calculate spatial shifts in relative demand.
3. Relative Supply and Demand Models
The spatial dimensions of a rising supply of more educated workers and simultaneously
rising college wage premia suggests a need to consider how these empirical phenomena
map into a supply-demand model of spatial labour markets. Consequently, we now draw
upon the Katz and Murphy (1992) canonical model of relative supply and demand to see if
there are differential relative demand shifts by state and MSA.
The starting point is a Constant Elasticity of Substitution production function
where output in for state or MSA i in period t (Y it) is produced by two education groups
(E1it and E2it) with associated technical efficiency parameters (θ1it and θ2it) as follows:
ρ
ρ 1/ρ
Yit  [δ it (θ1it E )  (1  δ it )(θ 2it E ) ]
1it
2it
(1)
where δ indexes the share of work activities allocated to education group 1 and ρ = 1 –
1/σE, where σE is the elasticity of substitution between the two education groups.
Equating wages to marginal products for each education group, taking logs and
expressing as a ratio leads to a relative wage equation (or inverse relative demand
function) of the form
W  1 
 E 
log 1it  
D - log 1it 
 W  σ  it
E 
 E 2it 
 2it 
8
(2)

where Dit  σElog δit

θ 
  (σ E  1)log 1it  is

θ 
 (1  δit ) 
 2it 
an index of relative demand shifts that depends
upon the (skill-biased) technological change parameters and the reflects shifts in relative
demand.
This equation therefore relates the relative wage to relative demand and supply
factors, and this is why the approach is sometimes framed as a race between supply and
demand. 10 A critical parameter determining the extent to which increases in relative
supply affect relative wages is the elasticity of substitution between the education groups
of interest, σE. A by now quite large literature has, in various ways, attempted to estimate
σE.11 For our purposes, we would like an estimate of σE at the spatial level, so that we can
construct a measure of implied relative demand at the spatial level by rearranging equation
(2) as:
W 
E 


1it


Dit  log
 σ Elog 1it 
E 
W 
 2it 
 2it 
(3)
where spatial relative demand is the relative supply plus the product of the elasticity of
substitution and the relative wage.
There are two main routes to obtaining an estimate of σ E which will enable us to
put together the patterns of spatial college wage premia and spatial relative education
supplies we described in Section 2 of the paper to form this index of spatial relative
demand. First, we could use estimates that exist. However, there are only a few at state
level as most estimates are at the aggregate level. Moreover, the ones that do exist do not
match our samples and time period of study. Thus, we decided to follow the second route
and estimate σE ourselves. To check robustness, we do also benchmark our estimates to
10
This dates back to Tinbergen (1974).
For the traditional labour demand work, see Hamermesh (1993). For the wage inequality research, see
Acemoglu and Autor (2010).
11
9
other state level estimates of the substitution elasticity (albeit from different samples as in
Ciccone and Peri, 2005, or Fortin, 2006).
Probably the key issue estimating σE, and particularly at the sub-national level as
we wish to, are possible biases emerging from geographical migration or because of potential
endogeneity. In addition, when estimating at the spatial level there may be issues of
measurement error that can cause attenuation bias. Consequently, we adopt a Two Stage
Least Squares (2SLS) approach. To instrument relative labour supply, we draw upon the
paper by Ciccone and Peri (2005) who use data from Acemoglu and Angrist (2000) to
show that changes in state level compulsory attendance laws are correlated with the labour
supply of high school graduates relative to high school drop outs. For our purposes it was
necessary to update the data used in Acemoglu and Angrist (2000) to include state level
compulsory attendance laws up to 2002.12 We then use these laws as instruments for
changes in relative supply at the state and MSA level. 13
The instruments are set up as five dichotomous variables associated with each
individual in the Census/ACS sample and then aggregated to the appropriate spatial unit in
each year. The dummies CA8, CA9, CA10, CA11 and CA12 are equal to 1, and all other
compulsory attendance law dummies are equal to 0, if the state where the individual is
likely to have lived when aged 14 had compulsory attendance laws imposing a minimum
of 8, 9, 10, 11 and 12 plus years of schooling. The five dummies are used to calculate the
share of individuals for whom each of the five dummies is equal to 1 in each state and
MSA of residence. We omit the share for CA8 (as the variables add up to 1) and these are
used as instruments for the relative supply of college graduates. The data do not include
12
The Acemoglu and Angrist (2000) data run from 1915 to 1978 and are available from the authors on
request. We updated these data by obtaining compulsory schooling data up to 2002 from the digest of
education statistics, supplemented by looking up the laws themselves in the state statutes. We cross checked
our new data with that derived in Oreopoulos (2009) and found we had very similar measures.
13
Ciccone and Peri (2005) adopt a similar instrumentation approach when they estimate state level demand
and supply models for high school graduates relative to high school drop outs using 1950-1990 Census data.
10
precise information on where individuals lived when aged 14, we therefore assume (as do
others who use state compulsory school leaving laws as instruments in various contexts)
that at age 14 individuals still lived in the state where they were born.
On a practical level, to be able to estimate equation (2) we need to model the
demand shift term in some way. We specify that Dit is a function of state fixed effects and
time so that Dit  ai  f(t)  eit where f(t) is a function of time (e.g. proxied by a time trend in
the economy wide approaches of Katz and Murphy, 1992, Autor, Katz and Kearney, 2008,
and Card and Lemieux, 2001), ai are state level fixed effects which are captured using
state/MSA level dichotomous variables and eit is an error term. Thus the estimating
equation becomes:
W 
E 


log 1it   a i  f(t)  γ log 1it   eit
E 
W 
 2it 
 2it 
(4)
where γ = –1/σE.
We specify the f(t) function in its most general way, using a full set of time
dummy variables, so that the estimating equation expresses the relative wage as a function
of a time, state/MSA fixed effects and relative supply. As with our earlier descriptive
analysis our focus is upon the college only/high school wage differential and we consider
relative supply in terms of the definitions of college equivalent and high school equivalent
workers introduced earlier.
Estimates of Relative Demand and Supply Models
Table 3 reports the estimates from the first stage regressions of the relative supply
on the state of birth instruments. The estimates also include time and state/MSA fixed
effects. These estimated coefficients are mostly negative and significant (relative to the
omitted group CA8) showing relative boosts to high school equivalent supply (as would
11
be expected) from the raising of state compulsory school leaving ages). The F tests show
the instruments to be significant, though they are not that strong leaving some possible
weak instrument concerns. We deal with this issue below, by using our estimate of the
elasticity of substitution from our 2SLS models, but also showing what happens if we use
other estimates from the literature by making assumptions on the magnitude of σE in
plausible bounds.
Table 4 provides the 2SLS estimates of equation (4). Again, these include time and
geographical fixed effects. The estimate of the labour supply parameter γ is negative, as
expected, in all cases. At state level, the 2SLS estimate is -0.396, which provides an
estimated elasticity of substitution of 2.53. For the MSA level estimates, the estimate of γ
is smaller (in absolute magnitude) with an estimated elasticity of substitution of 3.91.
These estimates are in line with estimates in the aggregate literature, especially the state
level estimate: for example, Lindley and Machin (2011) derive an estimate of around 2.6
using aggregate CPS data from 1963 to 2010 which is in the same ballpark as Autor, Katz
and Kearney's (2008) estimate of 2.4, who also use the CPS data from 1963 to 2005.14
The estimated parameters on the time dummies in Table 4 also tell us something
about the relative demand shifts that have occurred on a decade by decade basis. Relative
to the 1980s the relative demand for college graduates has increased across all time
periods although these incremental changes get smaller over time. This supports the idea
of a quadratic relationship between relative labour demand and relative wages over the
thirty years we study.15
Implied Relative Demand Shifts
14
Like Ciccone and Peri (2005) we also considered other estimation methods that may be robust to issues of
potentially weak instruments. We used limited information maximum likelihood (LIML) estimation methods
to produce similar estimates that were not statistically different to the 2SLS ones. For example, for our state
level 2SLS estimate (and standard error) of γ = -0.396 (0.160) a comparable LIML estimate was γ = -0.465
(0.190), implying an elasticity of substitution of 2.15.
15
If a trend and trend squared were entered into the equation in place of the year dummies they confirm this.
12
We are now in a position to combine the spatial changes in wage differentials and
supply into an implied relative demand index using our estimates of σE. As noted above,
the
demand
index
for
Dit  log(E1it/E2it )  σElog(W1it/W2it )
spatial
unit
i
in
year
t
can
be
calculated
as
for any two particular education groups. We construct the
demand index based upon our relative supply measure of college equivalent (CE) versus
high school equivalent (HE) workers and our composition adjusted college/high school
wage differentials (WC/WH) as Dit  log(EitCE /EitHE )  σElog(WitC/WitH ) .
Given that our estimates of relative demand depend on our elasticities of
substitution (2.53 and 3.91 for state and MSA level analysis respectively), which in turn
depend on the validity of our instruments, for robustness purposes we also bound our
estimates by imposing two polar assumptions on the size of σE. Firstly, we assume that the
elasticity of substitution σE is equal to unity (as for a Cobb-Douglas production function),
which is just below the range of estimates in Ciccone and Peri's (2005) state level study. 16
Second, we assume a larger (upper bound) with an elasticity of substitution equal to 5
(which is close to Fortin's, 2006, more recent study which focuses only on younger age
cohorts).17
Table 5 compares the slopes for the different values of σE from regressions of the
spatial relative demand shifts on their ten year lag, for the time periods 1980-90, 19902000 and 2000-2010 at both state and MSA level. The first row shows these for our
estimated σE values and reveals that putting together the relative supply and relative wage
measures to compute this demand index in this way produces a pattern of highly persistent
relative demand shifts at the spatial level. The persistence also becomes more marked in
16
Ciccone and Peri (2005) present a range of estimates derived from different estimation approaches. Their
Panels B and C of their Table 2 report estimates between 1.20 and 1.50 for data from 1950 to 1980.
17
Fortin (2006) presents state level estimates for age 26-35 workers between 1979 and 2002. Her 2SLS
estimates from her Table 3 are in the range of 4.39 to 5.68.
13
the 1990-2000 and 2000-2010 period where, in statistical terms, the estimated persistence
parameter is unity or above. This represents a shift from 1980-90, where there was also
strong persistence, but also some convergence as the estimated coefficient on the 1980
level was below unity. The second row imposes the assumption σ E =1 and the third row
that σE =5. In both cases, for both states and MSAs, whilst the estimated parameters do
shift a little, the same qualitative pattern of persistence remains.
To see more clearly what is going on, Figures 4a and 4b show the spatial
distributions of the demand shift measure, using our estimated elasticities of substitution
for states and MSAs (i.e. the first row of Table 5).18 These show that demand has shifted
strongly in favour of the college educated. But these also allow us to eyeball which states
and MSAs have increased their relative demand for college graduates the most (and the
least) over the three decades we analyse. In Figure 4a we can see that the Eastern states
like Massachusetts, Connecticut and New York have increased their relative demand the
most and that this is consistent over time. More Southerly states like West Virginia,
Wyoming and Nevada have experienced much smaller relative demand shifts.
Similarly, Figure 4b identifies two MSAs that have demonstrated relatively large
and consistent increases in college graduate demand over time. These are 188 (Stamford,
Connecticut) and 170 (San Jose, California). It is well known that Stamford has a large
cluster of corporate headquarters for international companies19 (including banks like UBS
and RBS), whilst San Jose is the largest city in Silicon Valley. MSAs that stand out as
having relatively low demand shifts for college graduates (especially in the 1990s) are 107
(Lima, Ohio) and 66 (Flint, Michigan). Throughout the 1980s and 1990s Lima suffered
18
Figures A1a to A2b in the Appendix report the same Figures for demand shifts calculated under the
assumption of σE = 1 and σE = 5 to very clearly show that the picture of increasing relative demand for
college graduates is very robust to those derived using our estimated spatial elasticities of substitution shown
in Figures 4a and 4b.
19
See David and Henderson (2005) for a discussion of the notion that places, like Stamford, generate
significant agglomeration effects (including education and technology agglomeration).
14
economic decline as a consequence of many large company closures and Lima's plight and
its subsequent efforts to re-define itself were captured in the PBS documentary Lost in
Middle America. In a similar way to Lima, Flint is a large city that experienced severe
economic decline but specifically this decline was in the automobile industry and in
particular the closure of the General Motors headquarters. Flint’s economic and social
downfall has also been the subject a television documentary in Roger & Me by Michael
Moore, as well as featuring in the movies Bowling for Columbine and Fahrenheit 9/11.
4. Potential Drivers of Implied Relative Demand Shifts
We can relate our estimated spatial relative demand shifts to potential demand side drivers
of rising wage inequality that can be directly measured at the state level. We look at three
different potential drivers of spatial relative demand shifts at state level that have been
considered in some of the existing literature, but which are usually analysed at the
aggregate or industry level. These are expenditures on R&D (measured relative to state
GDP), computer use and union coverage. The latter two are measured in state level
proportions.
Table 6 reports results from undertaking this exercise. The first three columns
report the individual correlations between these potential drivers and relative demand
shifts between 1980, 1990, 2000 and 2010, whilst the fourth column includes all three
potential drivers together for a horse race between the three. The final two columns
provide a robustness check for column 4 by assuming our two polar extremes for an
elasticity of substitution equal to 1 and 5. All equations include state and year fixed
effects.
Table 6 clearly shows that state level R&D intensity and computer use are
positively correlated, whilst union coverage is negatively correlated with our implied
15
demand shifts. Entering all three together in one equation shows that only R&D intensity
and union coverage are still statistically significant, although it is likely that R&D and
computer use are to an extent multi-collinear. Hence, states with higher union coverage
have also experienced lower shifts in relative demand for college graduates.
The final two columns show that although the negative union effect remains robust
to the assumptions of the value for the elasticity of substitution between college and high
school graduates, the horse race between R&D intensity and computer use is not. If one
assumes that college graduates and high school graduates have a unit elasticity of
substitution, then computer use is significantly correlated with the spatial demand shifts. If
one assumes an elasticity of substitution of five, then it is R&D intensity (and not
computer use) that is significantly correlated with implied demand shifts. Therefore,
whilst it seems that the story that technology and union decline matter are robust, the
precise form of the technology impact may be sensitive to the size of σE.
Figure 5 plots the long run 1980-2010 demand shifts against all three of our
potential demand side drivers of inequality. Again, presenting these correlations in
graphical form shows us which states are the most and least correlated with the proximate
determinants. For example, Massachusetts demonstrates the largest long run increase in
R&D, followed by Washington, Connecticut and New Jersey and these all show
significant increases in relative demand. The interpretation for identifying the main states
driving the changes in computer use is less obvious, mainly because of the mass
implementation of general purpose computer technology (especially in more recent
decades) which probably makes computers a less good proxy for technical change.
Notice in the plot of the demand shifts against change in the proportion of union
covered workers there is union decline in all states. This reflects the overall long run
decline in union coverage. However, some of the largest declines occurred in Michigan,
16
Indiana, Pennsylvania, Ohio, Illinois and West Virginia. These are states that have been
much more affected by de-industrialisation, with sectoral shifts away from unionised large
scale manufacturing firms and towards non-unionised service sector firms who are also
likely to employ more graduates.
5. Cross-State Migration and College Education
The US is a highly mobile society and so it is possible that some of the reported results to
date could be attributed to increased sorting of more educated individuals to potentially
more prosperous states over time. In this Section we therefore consider cross-state
migration differences by education and we study possible differences in relative supply
and demand changes for individuals who remain in their state of birth as compared to
those who move to another state.20
We are able to consider cross-state migration since the Census/ACS data not only
asks individuals to report their state of residence at the time of the survey, it also asks in
which state that US born individuals were born.21 There is a lot of cross-state migration. In
the 1980, 1990 and 2000 Census and 2010 ACS the proportion of 26-55 year old US born
individuals respectively reported that 38 percent (in 1980, 1990 and 2000) and 37 percent
(in 2010) resided in a different state from the one in which they were born. This is
proportion is significantly higher for college educated individuals as compared to high
school educated individuals as is shown in Table 7.
For our purposes, it is noteworthy just how stable the college/high school
differences in inter-state migration are between 1980 and 2010, suggesting little change in
education gaps from spatial sorting. Controlling for age, race and gender, and for state of
20
For early work on mobility and education see Ladinsky (1975) and the review of Greenwood (1975).
More recent studies include Wozniak (2010) and Malamud and Wozniak (2011).
21
It also asks individuals where they lived five years before. We look at the longer run migration measure
in this paper.
17
birth fixed effects, makes little difference to this, as is shown in the statistical models of
cross-state migration reported in Table 8.
The other aspect of migration that is of relevance to our earlier analysis is whether
migrants to a state operate in the same labour markets as those born in the state. Put
differently, we would like to know whether migrants and indigenous individuals compete
for the same jobs and can be thought of as perfect substitutes in production. If this were
the case, then our earlier analysis of supply and demand which made no distinction
between movers and stayers would be robust to this. 22
In the context of the CES production function in Section 3 (equation (1) above),
we can add a second nest to the production function to allow for potential imperfect
substitutability of movers and stayers within education groups. To do so we define CES
sub-aggregates for the two education groups as E1it





j

η

β1jE 1jit


1/η
and E 2it





1/η
β 2jE η2jit 
j

,
where j denotes movers/stayers and η = 1 – 1/σM, with σM being the elasticity of
substitution between movers and stayers. If η = 1 (i.e. when σM is infinity due to perfect
substitution) this collapses back to the standard model as there is no need to nest.
In an analogous manner to earlier, by deriving wages and setting them equal to
marginal products, we obtain the following estimation equation, which is a generalised
version of the earlier model we estimated at the level of mover/stayer j in state i in year t
 

 W1jit 

  a  a  f(t)  γ log E1it   γ log E1jit   log E1it   v
log
j
1
jit
 E  2  E 
 E 
W  i
 2it 
 2it 
 2jit 
  2jit 
22
(5)
The analysis of 1990 Census data in Dahl (2002) is suggestive that correcting college returns for selfselected migration does not make that much difference to the state-specific college wage premia, at least in
the cross-section he considers.
18
where γ1 = -1/σE, γ2 = -1/σM and v is an error term.23 Thus a statistical test of whether γ2 =
0 is a test of whether or not the movers and stayers are perfect substitutes within the
college and high school groups of workers.
Estimates of equation (5) are reported in Table 8. The models are again estimated
by 2SLS and show that we cannot reject the null hypothesis that γ2 = 0. Thus an
assumption that, at state level, the hypothesis that movers and stayers act as perfect
substitutes is consistent with the data. This is reassuring as it offers confirmation of the
robustness of our earlier findings.
6. Concluding Comments
We study spatial changes in the US college wage premium for states and cities using US
Census and American Community Survey data between 1980 and 2010. We report
evidence of significant spatial variations in the college wage premium for US states and
MSAs. We use estimates of spatial relative demand and supply models to calculate
implied relative demand shifts for college graduates vis-à-vis high school graduates. These
also show significant spatial disparities. Considering potential drivers of the differential
spatial trends, we show that relative demand has increased faster in those states and cities
that have experienced faster increases in R&D intensity and computer use, and increased
slower in those states and cities where union decline has been more marked.
These findings complement findings from the more aggregated work in labour
economics on trends in wage inequality and on shifts in the relative demand and supply of
more and less educated workers. They are also in line with the work in urban economics
23
In practice, the equation from the two-level nested CES model is estimated as a two step procedure. First,
the coefficient γ1 can be estimated from regressions of the relative wages of movers and stayers to their
relative supplies to derive a first estimate of σM and a set of efficiency parameters (the β1j's and β2j's in the
CES sub-aggregates) can be obtained for each education group from a regression of wages on supply
including mover/stayer dummy with spatial and year fixed effects. Given these, one can then compute E 1t
and E2t to obtain a model based estimate of aggregate supply. See Card and Lemieux (2001) for more detail.
19
that emphasises agglomeration effects in locations that are strongly connected to education
and technology. Our analysis brings these two areas of work together to an extent, by
emphasising that the US has seen significant rises in the college wage premium despite
rapid increases in education supply, and that there have been important spatial aspects to
this and to the relative demand shifts by education that have occurred in the last thirty
years.
20
References
Acemoglu, D. and J. Angrist (2001) How Large are Human-Capital Externalities?
Evidence from Compulsory Schooling Laws, NBER Macroeconomics Annual, 15,
9-59.
Acemoglu, D. and D. Autor (2010) Skills, Tasks and Technologies: Implications for
Employment and Earnings, in Ashenfelter, O. and D. Card (eds.) Handbook of
Labor Economics Volume 4, Amsterdam: Elsevier.
Autor, D., L. Katz, and M. Kearney (2008) Trends in U.S. Wage Inequality: Re-Assessing
the Revisionists, Review of Economics and Statistics, 90, 300-323.
Bacolod, M., B. Blum and W. Strange (2009) Skills and the City, Journal of Urban
Economics, 67, 127-35.
Baum-Snow, N. and R. Pavan (2012) Understanding the City Size Wage Gap, Review of
Economic Studies, 79, 88-127.
Black, D., N. Kolesnikova and L. Taylor (2009) Earnings Functions When Wages and
Prices Vary by Location, Journal of Labor Ecomomics, 27, 21-47.
Card, D. and T. Lemieux (2001) Can Falling Supply Explain the Rising Return to College
for Younger Men? A Cohort-Based Analysis, Quarterly Journal of Economics,
116, 705-46.
Ciccone, A. and G. Peri (2005) Long Run Substitutability Between More and Less
Educated Workers: Evidence From US States 1950-1990, Review of Economics
and Statistics, 87, 652-63.
Combes, P., G. Duranton and L. Gobillon (2008) Spatial Wage Disparities: Sorting
Matters!, Journal of Urban Economics, 63, 253-66.
Combes, P., G. Duranton, L. Gobillon and S. Roux (2012) Sorting and Local Wage and
Skill Distributions in France, IZA Discussion Paper No. 6501.
Dahl, G. (2002) Mobility and the Return to Education: Testing a Roy Model with Multiple
Markets, Econometrica, 70, 2367-2420.
David, J. and V. Henderson (2005) The Agglomeration of Headquarters, Regional Science
and Urban Economics, 38, 445-60.
Fortin, N. (2006) Higher-Education Policies and the College Wage Premium: Cross-State
Evidence from the 1990s, American Economic Review, 96, 959-87.
Greenwood, M. (1975) Research on Internal Migration in the United States: A Survey,
Journal of Economic Literature, 13, 397-443.
Hamermesh, D. (1993) Labor Demand, Princeton, NJ: Princeton University Press..
21
Hendricks, L. (2011) The Skill Composition of US Cities, International Economic
Review, 52, 1-32.
Hirsch, B. and D. Macpherson (2003) Union Membership and Coverage Database from
the Current Population Survey, Industrial and Labor Relations Review, 56, 349-54.
Hornstein, A., P. Krusell and G. Violante (2005) The Effects of Technical Change on
Labour Market Inequalities, in P. Aghion and P. Howitt (eds.) Handbook of
Economic Growth, North Holland.
Jaeger, D. (1997) Reconciling the Old and New Census Bureau Education Questions:
Recommendations for Researchers, Journal of Business and Economic Statistics,
15, 300-309.
Katz, L. and D. Autor (1999) Changes in the Wage Structure and Earnings Inequality, in
O. Ashenfelter and D. Card (eds.) Handbook of Labor Economics, Volume 3,
North Holland.
Katz, L. and K. Murphy (1992) Changes in Relative Wages, 1963-87: Supply and Demand
Factors, Quarterly Journal of Economics, 107, 35-78.
Ladinksy, J. (1967) The Geographical Mobility of Professional and Technical Manpower,
Journal of Human Resources, 2, 475-94.
Lindley, J. and S. Machin (2011) Postgraduate Education and Rising Wage Inequality,
IZA Discussion Paper No. 5981.
Malamud, O. and A. Wozniak (2011) The Impact of College on Migration: Evidence from
the Vietnam Generation, Journal of Human Resources, forthcoming.
Moretti, E. (2010) Local Labor Markets, in Ashenfelter, O. and D. Card (eds.) Handbook
of Labor Economics Volume 4, Amsterdam: Elsevier.
Oreopoulos, P. (2009) Would More Compulsory Schooling Help Disadvantaged Youth?
Evidence from Recent Changes to School- Leaving Laws, in J. Gruber (ed) The
Problems of Disadvantaged Youth: An Economic Perspective, University of
Chicago Press.
Puga, D. (2010) The Magnitude and Causes of Agglomeration Economies, Journal of
Regional Science, 50, 203-19.
Rosenthal, S. and W. Strange (2004) Evidence on the Nature and Sources of
Agglomeration Economies, in V. Henderson and J-F. Thisse (eds.) Handbook of
Urban and Regional Economics, North Holland.
Tinbergen, J. (1974) Substitution of Graduate by Other Labour, Kyklos, 27, 217-26.
Wozniak, A. (2010) Are College Graduates More Responsive to Distant Labor Market
Opportunities, Journal of Human Resources, 45, 944-70.
22
600
800
1000
1200
Slope (SE) = 1.267 (0.228)
200
250
300
350
400
Wage of High School Graduates in 1980
450
1500
2000
2500
3000
Slope (SE) = 3.887 (0.267)
1000
Wage of College Graduates in 2010
Figure 1:
Change Over Time in the Average Log Weekly Wage of High School and College
Graduates by Metropolitan Area
300
400
500
600
Wage of College Graduates in 1980
700
Notes: Each panel plots the nominal wage in 1980 against the nominal wage in 2010 by metropolitan area.
The top panel is for high school graduates and the bottom panel is for college graduates. These are weighted
using the number of workers in the relevant metropolitan area and skill group in 1980. There are 216
metropolitan areas. The regression line is the predicted log wage in 2010 from a weighted OLS regression.
The slope is 1.267 (0.228) for high school graduates and 3.887 (0.267) for college graduates. Data are from
the Census of Population. The sample includes all full time US born workers age between 26 and 55 who
worked at least 40 weeks in the previous year.
23
Figure 2a:
State Level College Equivalent Hours Shares, 1980 to 2010
College Equivalent Hours Shares, 1980 and 1990
.55
.5
.45
.25
.3
.35
.4
MA
CN
CO
NJ MD
NY
VI CA
NH
WA
VT
UT
RI IL
KA
MN
NM OR
TXAZ
DE
MN
NE
ND
GE
PA
MI
MOFL
OK WY
ME
ID
OH
SD
WI
LO
NC
AL
TN IO
SCMS NV
IN
KY
AR
WV
.2
State College Equivalent Share, 1990
Slope (SE) = 1.057 (0.054)
.2
.25
.3
.35
.4
.45
State College Equivalent Share, 1980
.5
.55
College Equivalent Hours Shares, 1990 and 2000
.55
.5
MA
.3
.35
.4
.45
CO CN
MD
NJ
VI NY
.25
AR
WV
MN
ILWACA
VT
RI NH
KA
DEORUT
GENE
MN
AZ
PAND TX
NM
MI
MEMO
FL
NC
WI
SD
IO
OH
ID
WY
OK
TN
AL
SC
IN
LO
KY MS
NV
.2
State College Equivalent Share, 2000
Slope (SE) = 1.024 (0.029)
.2
.25
.3
.35
.4
.45
State College Equivalent Share, 1990
.5
.55
College Equivalent Hours Shares, 2000 and 2010
.55
.5
MA
NJCCN
O
VI MD
NY
.25
.3
.35
.4
.45
MN
NHIL
RI WA
KA
VT
CA
MN
SD ND
OR
NE
DE
MI PA GE
NC
MOAZUT
FL
WI
METX
SC OH
IO
TN
IN AL ID
NM
KY
OK
WY
MS LO
ARNV
WV
.2
State College Equivalent Share, 2010
Slope (SE) = 1.080 (0.034)
.2
.25
.3
.35
.4
.45
State College Equivalent Share, 2000
.5
.55
Notes: These are college equivalent hours shares for workers aged 26-55 in 48 states in the 1980, 1990 and 2000 Census
(where wages refer to the previous calendar years, 1979, 1989 and 1999 respectively) and the 2010 American
Community Survey. For definitions of college and high school equivalent see the main text and the Data Appendix.
Standard errors in parentheses for the reported slope coefficients.
24
Figure 2b:
MSA Level College Equivalent Hours Shares, 1980 to 2010
College Equivalent Hours Shares, 1980 and 1990
.65
.6
.55
10
.2
.25
.3
.35
.4
.45
.5
188
29152 72
170
169
115
36
16
196 189
106
82 177
5567
13 88
27 172
134
101
216
149
124
108
4 95
139
346
171
49
140
168
157
40
104
128
160
28
44
214
144
111
8162
5132
63
18
147
173
197
146 96
166
56
133
183
202
41
116
19
187
47
26
182
19121
25
138
121
109
42
113
156
145
123
23
43
212
184
33
167
215
130
200 100
31
141
198
199
35
210
52
30
86
1
155
51
120
38
57
74
165
73
68
122
201
195
143112
135
275
127
77
6148
181
193
194
80
599
174
119
180
70
142
8568164
48
89
31
7192
98
211
22114
24
76
78 129
59
39
81150
15
7571
64
60
110
208
207 1765
62
185
125
161
14186
159
154
1
58
151
92
12
205
69
34
163
66
153
720
54
11
153
103
219
19087
105
32
94
90
136
126
179
204
178
218
217
83
118
209
61
97
102
91
137
107203
93131
117
79
213
7
50
45
.15
MSA College Equivalent Share, 1990
Slope (SE) = 1.036 (0.026)
.15
.2
.25
.3
.35
.4
.45
.5
.55
MSA College Equivalent Share, 1980
.6
.65
College Equivalent Hours Shares, 1990 and 2000
.65
.25
.3
.35
.4
.45
.5
.55
.6
188
.2
50
170
45 29
115
169
15272
67
189
36
16
106
27177
196
55
134
108
124
172
183
13
31 5618
4440
3 149
82
132
140
168
4796
144
214
157
139216
147
26
88
46
160
104
49
123
187
173
4
146
171
162
130
128
210
42
111
38
23
202
99 86
33
185 37175
35
197
21
101
145
85
138
199
182
28
181
166
68
121
30
198
212
141
43
109
19163
57
120
80
215
113
58
35
21
73
74
25
112
19
167
95
184
122
152
133
208
143
148
193
156
81
41
12159
6127
165
75
59
89
100
51
15
77
155
200
78
76211
174
195
39
8142
65
119
129
186
192
48
6422
180
70
201 116
97
114
62
176
125
164
151
154
110
163
14
98194
150
92
179103
161
209
178
24
60
54
205
69
131
53
153
137218
71
87
105
94
219
11345158
79 91 126
213
20
190
32
90
102
17 207
118
107
217
7 93
61
13666
83
117
203 204
10
.15
MSA College Equivalent Share, 2000
Slope (SE) = 1.013 (0.031)
.15
.2
.25
.3
.35
.4
.45
.5
.55
MSA College Equivalent Share, 1990
.6
.65
College Equivalent Hours Shares, 2000 and 2010
.65
188
45170
29
11510
152
169
189
27
177
196
216 124
55 16 72
82 134 106
40
36
18
37
140
144
33113
21
147
47
157
168
132
46
96
214
160
44172
108
26
149
215 99
42146
38
187
159
56 183
123
2 57 86
33
111
185
88
130
49
104
202
23
128
68
181
112
210
191
212
162 139
135
43
101
35
145
51143
182
95
74
197
28
30
121
141
65
148
109
193
85
19
166
138
4
175
77
122
184
58
15
681
173
199
73
198
80
25
76
89
97129
116
195
78
167
155
113
120
63 171
176
142
133
62
52
92163
22
64839
12
174
151
131
179
114
156
14
201
70
186
200
48
75
1
59
192
91 34
161
125
24
178
205
100
41
60
218
154
71
54
103
208
194
119165
153
209
10779219
53
69
211
98 180
105
127
94
118
102
90 5158
93
164
136
7 207
83
190 87 150
117 61 126
110
11
20
137
66 1732
213
203
50
204 217
.2
.25
.3
.35
.4
.45
.5
.55
.6
67
.15
MSA College Equivalent Share, 2010
Slope (SE) = 1.055 (0.025)
.15
.2
.25
.3
.35
.4
.45
.5
.55
MSA College Equivalent Share, 2000
.6
.65
Notes: These are college equivalent hours shares for workers aged 26-55 in 219 MSAsin the 1980, 1990 and 2000
Census (where wages refer to the previous calendar years, 1979, 1989 and 1999 respectively) and the 2010 American
Community Survey. For definitions of college and high school equivalent see the main text and the Data Appendix.
Standard errors in parentheses for the reported slope coefficients.
25
Figure 3a:
State Level College/High School Log Wage Differentials, 1980 to 2010
College/High School Wage Differentials, 1980 and 1990
.5
.3
.4
TN
GE
TX VI NC
AL
FL NY
AR DE
PA
LO
AZ
MO
MD
OK
IL KY
NJ CN
OH
MIMS
CA SC
NE
NM
CO
KA
MA
MN
NH
IN WI
WV
RI
ND
ID
ME
OR NV SDIO
WA
UT
VT
MN
WY
.2
State Log Wage Differential, 1990
.6
Slope (SE) = 0.747 (0.081)
.2
.3
.4
.5
State Log Wage Differential, 1980
.6
College/High School Wage Differentials, 1990 and 2000
.4
.5
TX
GE
VI
NY
CA
AL
CN
NC
NJ
IL MD
TN
ARFL
PA
MN
MA
OH KY
DE
MI
MO
AZ
LO
OK
WV KA
MN
SC
NH
NM
OR RI CO
NE
WA
ID IN
ME
MS
IO
WI
UT
NV ND
VT
SD
.3
WY
.2
State Log Wage Differential, 2000
.6
Slope (SE) = 0.991 (0.100)
.2
.3
.4
.5
State Log Wage Differential, 1990
.6
College/High School Wage Differentials, 2000 and 2010
Slope (SE) = 0.900 (0.080)
.5
.4
SD
VI
GETX
.3
WY
.2
State Log Wage Differential, 2010
.6
NY
AL
CA
KY
IL
OH TNNC
MI
CN
NJ
MAAR
MD
MO PA
MN AZ
FL
OK
IN
WIMS
KA
WAOR
RI LO
IO CO NH
SC
NE
DE
WV
NM
ND
ID
NV
UT
ME
MNVT
.2
.3
.4
.5
State Log Wage Differential, 2000
.6
Notes: These are fixed hours weighted composition adjusted college only/high school log wage differentials for full time
full year workers aged 26-55 in 48 states in the 1980, 1990 and 2000 Census (where wages refer to the previous calendar
years, 1979, 1989 and 1999 respectively) and the 2010 American Community Survey. The composition adjustment is
described in the main text and in the Data Appendix. The estimated slope coefficients (and associated standard errors
reported in parentheses) are weighted by the inverse sampling variance of the state level wage differentials.
26
Figure 3b:
MSA Level College/High School Log Wage Differentials, 1980 to 2010
College/High School Wage Differentials, 1980 and 1990
.8
.7
.6
118
32
.2
.3
.4
.5
48 25
39
93 159200
99
136 188
50
5317193
83 167
97
73 204
60
92
26
120
133
122
125
210
146
245 198
109
77
5 1 98
194
196
100145
49
24
38
85
34153
142
184
141
121
3
152
201
170
78
217
13
42
7
112
19722
126
18
111
174
15
127
47
89213
129
27
20
16
68
57191
71
134
86
163
1
99
18712
144
79
183
215
143
80
140
59
19
113
130135
110
189
171
154
87
33
148
128
180
160
43
209
214
175
44
181
88
195
82
29
69
81
52
1123
16
54
138
205
151
168
106
137 64
440
6102
190
51
37
186
46
176
31
150
202
55
8155
72
28
165
96
162
23
104
107
218
156
169
511
670
157
147
216
182
95158
105
65
124
132
166
10
14
114
74117
164
149
30
62
211
185
161
219
17321
108
203
61103
94 67
66
178
115212
179 7535
192207
58
17736208172 131
6376
119 41
91 139 101
90
.1
MSA Log Wage Differential, 1990
.9
Slope (SE) = 0.540 (0.051)
.1
.2
.3
.4
.5
.6
.7
MSA Log Wage Differential, 1980
.8
.9
College/High School Wage Differentials, 1990 and 2000
.8
.7
188
118
32
.6
170
.2
.3
.4
.5
6013625
31
85
49
122
26
156137
146
196
167
65
193
48
111
175
109
13
8 205
152
1799
163
38
169
22
29
27
15
71
183
95
16
42
125
39
134
77
120
54
133
68
162
20
168
100
21073
46
198
56
128
18
110
180
87
202
113
21
5093
144
78
31141
6
34
98
145
2
172 35
114
80
89
43
47
204
96
86
159
191
143
187
57
112
40
140
4106
5 192
135
211
81
37
126
190
52
213
127
142
82
160
199
158
138
176
88
148
51
123
20314
216
147
214
215
7217
200
28
195
130
104
44
79174
157
165
5564
201
33
124
182
181
153 97
8390
132
209
72
219
155
218
53
23
69
171
149
30
74
5919724
10
154
19
102
76
94
166
131
177
117
164
62
103
11936
184
207
212
11
178
194
179
185105
61
70
12945
173
186189
91 63192
115
151
75
108
58 67
66
208
11612
41
139
161
150
101
107
21
.1
MSA Log Wage Differential, 2000
.9
Slope (SE) = 0.749 (0.056)
.1
.2
.3
.4
.5
.6
.7
MSA Log Wage Differential, 1990
.8
.9
College/High School Wage Differentials, 2000 and 2010
.9
Slope (SE) = 0.782 (0.071)
.8
32
.3
.4
.5
.6
.7
11
.2
21
31
27
170
207
119
59 79106 73 65
163
167
91 164 51
169
60
154
90 52 134
125
189
15
85
26
8
118
62 14 40
38
196
47
111
13
16
128
86
49 25
112
20
2121
44
42
142
17
123
92
200
168
29
217
152
48
130
187
145
88
138
82
190
46
101 151
146
43
57
69
100
122
188
144
141
171
143
33
193
202
96
180
157
133
216
126
76
78
158
95
35
120
74
18
179177
53
153
160
124
218
80
99205
83
135
87
162
172
97
209
155
104
98
24
64
219
150
56
107
148
89
161
182
191
197
198
165
114
68
175
195
110
39
10
34
3113
210
140
77
117
54
181
55
1
108
6
22
67
214
109
93
70
147
4
201
174
215
115 178
5
58
63
36
184
103
72 37
71
212
166
185
61
156
194
159
176
199
19132
105
28
81
12
75 173
149 213
94
136
23
137
139 192 131
102
204
7
41
208
116 45 30 203 50183
127
129
211
186
.1
MSA Log Wage Differential, 2010
66
.1
.2
.3
.4
.5
.6
.7
MSA Log Wage Differential, 2000
.8
.9
Notes: These are fixed hours weighted composition adjusted college only/high school log wage differentials for full time
full year workers aged 26-55 in 219 MSAs in the 1980, 1990 and 2000 Census (where wages refer to the previous
calendar years, 1979, 1989 and 1999 respectively) and the 2010 American Community Survey. The composition
adjustment is described in the main text and in the Data Appendix. The estimated slope coefficient s (and associated
standard errors reported in parentheses) are weighted by the inverse sampling variance of the MSA level wage
differentials.
27
Figure 4a:
Implied Relative Demand Shifts, State Level, 1980 to 2010
Relative Demand Shifts, 1980 and 1990
1.25
1
.75
.5
.25
0
-.25
VIMD
NY
MACN
NJ
CO
CA
TX
IL
GE
DE
AZ
NH
KA
FLRIMN
NM
PA
MO
TN
NE
NCOK
WA
ALMI
OR
LOVTUT
OH ND
MSWI
ID
SC
ME
MN
KY AR
IO
SD
IN
NV
WY
WV
-.5
State Relative Demand Shift, 1990
1.5
Slope (SE) = 0.884 (0.041)
-.5
-.25
0
.25
.5
.75
1
State Relative Demand Shift, 1980
1.25
1.5
Relative Demand Shifts, 1990 and 2000
1.25
.5
.75
1
MA
CN
VI
NY
NJMD
CA
GEILTX CO
.25
WV
MN
KA DE
WA
RI NH
NCPA
FL AZ
OR
NE
MO
MI
AL
VT TNNM
OH
UTOK
ME ND
IO M
ID
WI
LO
N
KYSC
AR
IN
SD MS
-.25
0
WY
NV
-.5
State Relative Demand Shift, 2000
1.5
Slope (SE) = 1.146 (0.042)
-.5
-.25
0
.25
.5
.75
1
State Relative Demand Shift, 1990
1.25
1.5
Relative Demand Shifts, 2000 and 2010
1.25
.25
.5
.75
1
IL
CA
MN GE
CO
MI NC
KA
TX
RI
NH
WA
PA
OHAL
OR
TN MO
AZ
KY
SD
NEFL DE
WI
N
D
IO
VT
IN MN
SC
AR OK
UT
MS
LOME NM
ID
WV
-.25
0
WY
NV
MA
NY
VI
NJCN
MD
-.5
State Relative Demand Shift, 2010
1.5
Slope (SE) = 0.986 (0.060)
-.5
-.25
0
.25
.5
.75
1
State Relative Demand Shift, 2000
1.25
1.5
Notes: The relative demand shifts are calculated as log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is
the log relative supply of college equivalent versus high school equivalent hours, σE (= 2.53) is the elasticity
of substitution between college and high school workers and log(WC/WH) is the fixed weighted composition
adjusted college/high school log wage differential. The estimated slope coefficient (and associated standard
error reported in parentheses) are weighted by the inverse sampling variance of the state level wage
differentials.
28
Figure 4b:
Implied Relative Demand Shifts, MSA Level, 1980 to 2010
Relative Demand Shifts, 1980 and 1990
3
2.5
50
0
.5
1
1.5
2
188
-1 -.5
MSA Relative Demand Shift, 1990
3.5
Slope (SE) = 0.786 (0.041)
-1
45
19610
170152
2529 72
16
200
13
49
27
167
134
3
146
82
118 32 189
133
169
106
26
85
88
99
109
55
48
145
73
197
140
18
120
11115
11168
171
210
121
128
394144
198
184
160
193
42
40
141
44
47122
214
159
216
191
38
2100
187
77
183
19
194
46
124
95
67
201113
104
28
60
149
157
215
116199
36
130
162
142
86
98
43
33
138
57
112
96
24
147
202
53
92
12790 31
125143
123
108
132
5268
65177
174
17
5
135
80
182
89
195
78
136
166
23
22
156
51
180
181
148
71
15
175
173
155
204
6
83
165172
129
59
153
97 34
93
110
21
37
8
81
30
64
12
154
74
70
65101
212
35
163
120
5087
63
139
151
186
205
217
126
69
114
41
176
164
54
211
158
190
14
58
11
62
209
185
161213
192
75
797219
76
218
207
119
66105102
94137
208
103
178
179 107
61 203
117
131
91
-.5
0
.5
1
1.5
2
2.5
MSA Relative Demand Shift, 1980
3
3.5
3
3.5
Relative Demand Shifts, 1990 and 2000
3
188
2.5
170
0
.5
1
1.5
2
152
169 29196
27 16
31
1325 10
26
134
49
183 85
106
72
146
172
3
168
18
56
111
144
46
55
38
40
45
175
47
122
140
99118
42
177
96
162
82
36124
109
167
210
156
44
216
202
193
115
88
68
187
160
147
214
32
4128
145
157
120
65
198
141
132
86
60
121
73
189
95
35
104
149
67
83715
123
113
48
43
133
80
130
2
1159
91
138
199
57
77
39
100
137 205
22
28
33
6181
135
112
171
197
89
163
143
78
1
182
23
108
125
215
81
52
180
148
142
110
114
127
30
211
54
51
166
71
165
136
200
98
174
74
173
195
185
19
212
87
155
92201
59
34
184
64
139
76 14176
20
97
517
119
63
154
158
209
62
24
153
213
164
69
190
58
126
218
12953
131 179
103
79
186
70
93
208
75
219
101
12
41
178
192
94
194
7105
116
20490
151 83
50217
11
102
207
203
161 150
91
61
21
117
66
107
-1 -.5
MSA Relative Demand Shift, 2000
3.5
Slope (SE) = 1.099 (0.040)
-1
-.5
0
.5
1
1.5
2
2.5
MSA Relative Demand Shift, 1990
Relative Demand Shifts, 2000 and 2010
3.5
3
170
2.5
27
31
169
106
29
152
13416196
66
32 47
40 10
67
26
65
13
82
177
51
216
38
73
44
124
168
115
42
144
111
46
167
86
2
146
163
187
128
1885
49
15
123
11
157
96
112
130
88
57
11959 52
55
160
33
121
7962
145
91207 101
43
202
72
140
3172
143
8104
138
99
25
36
125
141
147
122
154
142
60
193
14
35
56
45
37
214
108
95
92
74
162
135
171
215
76
68
151
78
191
90 164
200
181
133
48
210
182
80
120
197
132
118
148
97155
175
89
159
185
198
77
100
195
109
212
6
179
149
4
69
58
64
184166
113
180
39
218
153
6320
114
205
28
24
190
53
158
19
161 219
209
23
199
174
122
21
173
34
98
107
70
201
176
5481
126
165
139
17
87
156 183
178
103
71
150 83194
12
93
75
30
117 105
110
217
192
1315
116
61 10294
136
41
7 208
129
213
127137
186
203
211
204
50
188
0
.5
1
1.5
2
189
-1 -.5
MSA Relative Demand Shift, 2010
Slope (SE) = 1.044 (0.044)
-1
-.5
0
.5
1
1.5
2
2.5
MSA Relative Demand Shift, 2000
3
3.5
Notes: The relative demand shifts are calculated as log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is
the log relative supply of college equivalent versus high school equivalent hours, σE (= 3.91) is the elasticity
of substitution between college and high school workers and log(WC/WH) is the fixed weighted composition
adjusted college/high school log wage differential. The estimated slope coefficient (and associated standard
error reported in parentheses) are weighted by the inverse sampling variance of the MSA level wage
differentials.
29
Figure 5:
State Level Relative Demand Shifts and Changes in R&D Intensity
1.4
Slope (SE) = 2.803 (2.180)
IL
1.2
KY
OH GE
NY
VI
AL
SD
MO
KA WI
IO
SC
AZ
RI
AR
MD
NDNE
TX
MS
FL
ME
VT
1
.8
1980-2010
TN
MN
WV
.6
OK
LO NV
MA
MI
IN
PA
NC
MN
NH NJ
OR
CA
WA
CN
CO
UT
DE
ID
NM
.4
WY
0
.01
.02
.03
Change in R&D, 1977-2007
.04
.05
1.4
Slope = 1.198 (0.645)
IL
KY
OH GE
1.2
NYMI MA IN
PA
VI
SD NC
AL
MN NH
WAKA
WI
TN
OR
IO
AZ AR
RI
CN
MD
NE
ND
CO
NJ
1
CA
TX
FL
.8
1980-2010
MO
SC
MS
ME VT
MN
WV
OK
UT
NV DE
.6
LO
ID
NM
.4
WY
.25
.3
.35
Change in Computer Use, 1984-2003
.4
1.4
Slope = -1.016 (0.557)
IL
KY
OH
1.2
MIIN
PA
VI
AL
MN
NJ
MO
1
IO
WI
WA
MD
FL
MN
.8
1980-2010
TN
MS
GE
NY MA
SD
NH
NC
KA
OR
CA
AZ
RI AR
CN
NE
NDCO
TX
SC
ME
VT
WV
.6
UT DE
NV
OK
LO
ID
NM
.4
WY
-.2
-.15
-.1
-.05
Change in Union Coverage, 1980-2010
0
Notes: The estimated slope coefficient (and associated standard error reported in parentheses) are weighted
by the inverse sampling variance of the state level wage differentials.
30
Table 1:
Average State/MSA Hours Shares of College Equivalent Workers - 1980, 1990 and 2000 Census and 2010 ACS
Mean College Equivalent Hours Share
State of Residence
MSA of Residence
0.292
0.343
0.381
0.408
0.300
0.346
0.377
0.397
0.116
(0.010)
0.097
(0.008)
1980
1990
2000
2010
Change 2010-1980
Notes: Hours shares are for all workers aged 26-55. To construct the shares, college equivalent workers are defined as college or college plus workers plus 30 percent of some
college workers (where the college plus and some college workers have efficiency weights defined as their wage relative to college graduates). High school equivalent
workers are defined analogously as high school graduates or high school dropouts plus 70 percent of some college workers (with the high school dropouts and some college
workers having efficiency weights defined as their wage relative to high school graduates). The college equivalent hours share is then hours of college equivalent workers
divided by the sum of hours of college equivalent and high school equivalent workers. See the Data Appendix for more detail.
31
Table 2:
Composition Adjusted College Wage Premia - 1980, 1990 and 2000 Census and 2010 ACS
Mean College/High School Log Wage Differential
State of Residence
MSA of Residence
0.310
0.404
0.460
0.488
0.299
0.395
0.447
0.484
0.178
(0.012)
0.185
(0.008)
1980
1990
2000
2010
Change 2010-1980
Notes: The composition adjusted state of birth college plus/high school log wage differential are derived from estimated log wage equations estimated separately for each
year, age group (3) and gender for 48 states and 216 MSAs respectively (i.e. six equations per year for each state/MSA). The equations include dummies for age and race
Three education dummies are included for college plus (16 or more years of education), some college (13 to 15 years of education) and high school dropouts (less than 12
years of education) relative to the omitted group of high school graduates (12 years of schooling). The college graduate/high school graduate log wage differential is the
estimated coefficient on the college graduate variable. The wage sample consists of US born full time full year workers age 26-55. For the change 2010-1980 standard errors
are in parentheses.
32
Table 3:
First Stage 2SLS Regressions - 1980, 1990 and 2000 Census and 2010 ACS
(Relative Supply = College Equivalents/Non-College Equivalents).
State of Residence
MSA of Residence
Relative Supply
College
Equivalents
Non-College
Equivalents
Relative Supply
College
Equivalents
Non-College
Equivalents
-0.052 (0.091)
-0.167 (0.097)
0.047 (0.173)
-0.221 (0.128)
0.179 (0.114)
0.120 (0.122)
0.620 (0.218)
0.112 (0.161)
0.231 (0.138)
0.288 (0.147)
0.573 (0.263)
0.333 (0.194)
-0.065 (0.063)
-0.143 (0.066)
-0.100 (0.126)
-0.177 (0.084)
-0.068 (0.100)
-0.141 (0.104)
0.361 (0.198)
-0.274 (0.133)
-0.003 (0.110)
0.003 (0.115)
0.461 (0.219)
-0.097 (0.147)
F-Test
P-Value
2.07
0.08
2.20
0.07
1.71
0.15
2.36
0.05
3.51
0.01
1.81
0.12
Spatial Fixed Effects
Year Dummies
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Sample Size
192
192
192
864
864
864
CA9
CA10
CA11
CA12
Notes: Where CA9 is the proportion of individuals residing in a geographical area with 9 years Compulsory Schooling Attendance (CSA) in the state in which they were born,
when they were age 14. Similarly CA10 is the same but for CSA of ten years, CA11 for CSA of 11 years and CA12 for CSA of 12 years and over. College equivalents
contain the hours of college graduates and half of the hours for some college. Non-college equivalents include the hours for high school drop outs, high school graduates and
half of the hours for some college.
33
Table 4:
2SLS Estimates of Supply-Demand Models of College Plus/High School Wage Differentials - 1980, 1990 and 2000 Census and 2010 ACS
(Relative Supply = College Equivalents/Non-College Equivalents)
State of Residence
MSA of Residence
-0.396*
(0.160)
0.198*
(0.041)
0.333*
(0.067)
0.416*
(0.087)
-0.256*
(0.155)
0.159*
(0.040)
0.268*
(0.063)
0.340*
(0.081)
Spatial Fixed Effects
Yes
Yes
Sample Size
192
864
Log(Relative Supply)
Year = 1990
Year = 2000
Year= 2010
Notes: The dependent variable is the log of the fixed weighted composition adjusted college/high school wage differential. State Compulsory School Leaving Laws used as
instruments for Log(Relative Supply) - the first stages are in Table 3). Estimates are weighted by the inverse sampling variance of the state/MSA level wage differentials. Standard
errors in parentheses.
34
Table 5:
Spatial Persistence in Implied Relative Demand Shifts For Different σE Estimates
Estimates of ψ1 from:
Dit = ψ0 + ψ1Di,t-10 + uit
1980-1990
States
1990-2000
2000-2010
1980-1990
MSAs
1990-2000
2000-2010
Estimated σE = 2.53 (State), σE =3.91 (MSA)
0.884
(0.041)
1.146
(0.042)
0.986
(0.060)
0.786
(0.040)
1.099
(0.040)
1.044
(0.044)
σE = 1
0.932
(0.037)
1.039
(0.033)
1.103
(0.049)
0.977
(0.027)
1.056
(0.025)
1.077
(0.024)
σE = 5
0.819
(0.053)
1.207
(0.062)
0.953
(0.070)
0.725
(0.042)
1.078
(0.045)
1.020
(0.049)
Notes: The dependent variable is the implied relative demand shift log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is the log relative supply of college equivalent versus
high school equivalent hours, is the elasticity of substitution between college and high school workers and log(WC/WH) is the fixed weighted composition adjusted
college/high school log wage differential. Estimates are weighted by the inverse sampling variance of the state level wage differentials log(WC/WH). Standard errors in
parentheses.
35
Table 6:
State Level Demand Shifts, Technological Change and Union Coverage
Implied Relative Demand Shifts, log(LCE/LHE) + σE log(WC/WH),
1980, 1990 and 2000 Census and 2010 ACS
(1)
(2)
(3)
(4)
(5)
(6)
σE = 1
σE = 5
-0.960
(0.342)
2.172
(1.054)
0.571
(0.314)
-0.874
(0.338)
1.053
(0.792)
0.874
(0.236)
-0.646
(0.253)
3.983
(1.708)
0.080
(0.509)
-1.244
(0.547)
Estimated σE = 2.53
R&D/GDP
2.251
(1.089)
Computer Usage
0.684
(0.322)
Union Coverage
State Fixed Effects
Year Fixed Effects
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Sample Size
192
192
192
192
192
192
Notes: The dependent variable is the state level implied relative demand shift log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is the log relative supply of college
equivalent versus high school equivalent hours, is the elasticity of substitution between college and high school workers and log(WC/WH) is the fixed weighted composition
adjusted college/high school log wage differential. Estimates are weighted by the inverse sampling variance of the state level wage differentials log(W C/WH). Standard errors
in parentheses.
36
Table 7:
Cross-State Migration and Education in the Census and ACS Data, 1980 to 2010
Proportion Moving State
All
College
High School
Gap (Standard Error)
1980
0.378
0.472
0.326
1990
0.379
0.477
0.306
2000
0.378
0.465
0.298
2010
0.366
0.303
0.139
0.146
(0.001)
0.171
(0.001)
0.168
(0.001)
0.139
(0.001)
Notes: Individuals aged 26-55. Sample sizes are: 1980 - 3797299; 1990 - 4556006; 2000 - 5036408; 948062.
37
Table 8:
Cross-State Migration and College Education, 1980 to 2010
Pr(State of Residence ≠ State of Birth
1980
1990
2000
2010
0.159
(0.001)
0.177
(0.001)
0.168
(0.001)
0.141
(0.001)
Yes
No
Yes
No
Yes
No
Yes
No
3797299
4556006
5036408
948062
0.165
(0.001)
0.180
(0.001)
0.165
(0.001)
0.136
(0.001)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
3797299
4556006
5036408
948062
A. Without State of Birth Fixed Effects
College
Control Variables
State of Birth Fixed Effects
Sample Size
B. With State of Birth Fixed Effects
College
Control Variables
State of Birth Fixed Effects
Sample Size
Notes: Individuals aged 26-55.These are linear probability estimates where the dependent variable is a 0-1 dummy coded to 1 for movers and 0 for stayers. The control
variables are a full set of age dummies and dummies for gender and race. Standard errors in parentheses.
38
Table 9:
Test of Substitutability of Movers and Stayers
State of Residence
Log(State Relative Supply)
-0.307
(0.138)
0.050
(0.034)
0.029
(0.018)
0.176
(0.035)
0.295
(0.508)
0.367
(0.075)
Log(Mover/Stayer State Relative Supply) Log(State Relative Supply)
Mover
Year = 1990
Year = 2000
Year= 2010
State Fixed Effects
Yes
Sample Size
384
Notes: The dependent variable is the log of the fixed weighted composition adjusted college/high school wage differential. State Compulsory School Leaving Laws used as
instruments for Log(Relative Supply) - the first stages are in Table 3). Estimates are weighted by the inverse sampling variance of the state/MSA level wage differentials.
Standard errors in parentheses.
39
Appendix
Figure A1a: Implied Relative Demand Shifts by State, 1980 to 2010 (σE = 1)
Relative Demand Shifts, 1980 and 1990
.5
.25
0
-.75
-.5
-.25
IL
NH
WA
RIKATX
MN
AZDE
OR UT
GENE VTNM
PA
FL
MO
MI
NDOKMN
NC
TN LO ID
OH
AL
ME
WI
SD
MS IO
SC
WY
IN
KY
AR NV
WV
MA
CN
NYMD
CO
NJ
VI
CA
-1
MSA Relative Demand Shift, 1990
.75
Slope (SE) = 0.932 (0.037)
-1
-.75
-.5
-.25
0
.25
MSA Relative Demand Shift, 1980
.5
.75
Relative Demand Shifts, 1990 and 2000
.5
.25
NJ
MD
VI
NY
CO
MA
CN
-.75
-.5
-.25
0
IL CA
MN
WA
GE KA
RITXNH
DE
VT
PA
NEORAZ
NC MI
FL UT
MO
NM
ND
ME
OHMN
TN OK
IOWI
IDAL
SCSD LO
IN
KY
AR WY
WV NV MS
-1
MSA Relative Demand Shift, 2000
.75
Slope (SE) = 1.039 (0.033)
-1
-.75
-.5
-.25
0
.25
MSA Relative Demand Shift, 1990
.5
.75
Relative Demand Shifts, 2000 and 2010
.5
MA
-.75
-.5
-.25
0
.25
IL
MN
NH CA
RI
KA
GE
WA
MI
NCPA
OR
SD OH MONE
VT
TX
ND
MN AZ DE
WI
TN
AL FL
UT
KY SC IO
IN
ME
OK
NM
ID
AR
MS
LO
WY
NV
WV
VI
NY
NJCN
MD
CO
-1
MSA Relative Demand Shift, 2010
.75
Slope (SE) = 1.103 (0.049)
-1
-.75
-.5
-.25
0
.25
MSA Relative Demand Shift, 2000
.5
.75
Notes: The relative demand shifts are calculated as log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is the log
relative supply of college equivalent versus high school equivalent hours, σE (= 1) is the elasticity of substitution
between college and high school workers and log(WC/WH) is the fixed weighted composition adjusted college/high
school log wage differential. The estimated slope coefficient (and associated standard error reported in parentheses)
are weighted by the inverse sampling variance of the state level wage differentials.
40
Figure A1b: Implied Relative Demand Shifts by MSA, 1980 to 2010 (σE = 1)
Relative Demand Shifts, 1980 and 1990
1
-1
-.5
0
.5
188 10
50
29152
17072
196169
16
189
115
82
13
2755106
36
134
67
88
3495
177
216 12849
124
149
172
171
140
85
168
14626
40
25
160
108
111
18
46
44
144
157
104
197
133
214
101
28
162
200
132
167
109
147
183
96
47
121
187
139
19113
191
42
116
56
173
202
184
100
166
198
210
138
1145
141
182
120
43
63
215
123
33
130
73
199
156
23
99
38
122
86
21
31
193
57
201
2112
77
48
68
212
51
194
155
195
3552
30
12741
143
135
165
142
174
80
181
39
74
98
6
180
148
175
24
89
65
22 59
60
70
159
8 37 71
78
58
15
81
32125
150
211
110
92164
129
5114
64
119
192
53
17
154
118
186
34
12
151
76
75
90
62
158
176
14
205
185
161
163
69
207 153
136
54
20
204
87208
83
11
190
66
126
97219
105
217
103
94
93
209
218
102
17961
178
137
107 79
213
7117
203
91131
45
-1.5
MSA Relative Demand Shift, 1990
1.35
Slope (SE) = 0.977 (0.027)
-1.5
-1
-.5
0
.5
MSA Relative Demand Shift, 1980
1
1.35
Relative Demand Shifts, 1990 and 2000
1
188
10
-1
-.5
0
.5
170
29
169 152
45
16
196
27
72
115
106
36 189
67
177
134
31 183 172
55
13
124
3 82
26
18
40
56
168
140
44
108
144
49
47
216
132
46
96
214
147
157
149
146
88
160
85
111
162
38
42
187
104
128
210
99
4
123
202
130
139
145
37175
171
35
86
25
68122
199
138
109
33
121
197
23
198
173
28
141
182
120
181
43
167
191
113
80
73
185 159
95
193
257
166
156
30
135
215
133
212
143
1100
15
52
67
4112
77
101
148
81
865
89
63
19
39
78
142
48
165
51
200
58
127
22
174
59
195
155
21184
211
180
76
60
208
163
125
114
110
1264
41
75
119
201
176
98
137 9754205
129
186
14
92
154
62118
192
70
164
116
71
32
209
24
87
103
69
151
34
131 178
179
53
218 20153
5150 194
158
161
219
213 94
105
79
190
11136
126
9017
91
93217
7 102
83207
61
204
107 66
203
50117
-1.5
MSA Relative Demand Shift, 2000
1.35
Slope (SE) = 1.056 (0.025)
-1.5
-1
-.5
0
.5
MSA Relative Demand Shift, 1990
1
1.35
Relative Demand Shifts, 2000 and 2010
1.35
1
170
188
-1
-.5
0
.5
29
67 27 169
189
152
4510
115
196
106
16
177
31
134
216
124
40 55
82
47
13 72
18
144
168
26
46
36
157
44
140
96
38
3
146
42
37
147
160
187
111
86
25733
123
214
132
49
108
88
128
130
99
5165
215
112
56 172
202
21
149
104
73
101
159
43
145
85
143
15
121
68
185
162
35210
181
135
191
167
95
74
138
141
193
122
182
212
197
183
25
163
23
148
175
109
171
62
77
80
78
4
142
28
9776
652166
198
58
184
89
139
8
120
195
155
19
92
59
199
113
173
14
91 79 179
81133
151
119
63
30
125
200
176
60
48
154
64
39
22
116
114
174
100
201
70
12
1 156
66
24
205
161
218
32
153
34
118
129
90
69
164
54
178
131
209
75180
11
219
53
107 207
103
71
165
98
158
192
194
41
190
105
208
8393126
5 87186
94
150
20
117 7102136
127
110
17
211
61
137
213
217
203
50
204
-1.5
MSA Relative Demand Shift, 2010
Slope (SE) = 1.077 (0.024)
-1.5
-1
-.5
0
.5
MSA Relative Demand Shift, 2000
1
1.35
Notes: The relative demand shifts are calculated as log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is the log
relative supply of college equivalent versus high school equivalent hours, σ E (= 1) is the elasticity of substitution
between college and high school workers and log(WC/WH) is the fixed weighted composition adjusted college/high
school log wage differential. The estimated slope coefficient (and associated standard error reported in parentheses)
are weighted by the inverse sampling variance of the MSA level wage differentials.
41
Figure A2a: Implied Relative Demand Shifts by State, 1980 to 2010 (σE = 5)
Relative Demand Shifts, 1980 and 1990
2.5
2
1.5
WY
.5
1
IN
WV
NV
VI
NY
MDCN
TX NJMA
GE CO
DE
IL TNFL CA
AZ
NC
AL
PA
M
O OKMN
NH
KA
NM
LO
NE
MI
RI
OH
AR
OR
MS
SC
ND
KY WI
WA
UT VT
ID
ME
IO
SD
MN
.2
MSA Relative Demand Shift, 1990
3
Slope (SE) = 0.819 (0.053)
.2
.5
1
1.5
2
MSA Relative Demand Shift, 1980
2.5
3
Relative Demand Shifts, 1990 and 2000
2.5
VI
MA CNNY
NJ
TXMD
CAGE
IL
1.5
2
CO
PA
NCDE
KA
MN
NHALFL
AZ
RI
MI MO TN
WA
OROHNE
NM
OK
AR LO
KY
ME
U
VT
T SC
WV IO IDWIND
IN
MN
MS
1
NV SD
.5
WY
.2
MSA Relative Demand Shift, 2000
3
Slope (SE) = 1.207 (0.062)
.2
.5
1
1.5
2
MSA Relative Demand Shift, 1990
2.5
3
Relative Demand Shifts, 2000 and 2010
2
2.5
IL
1.5
SD
NV
.5
1
WY
MI MN
NC
OH AL
CO
KY
PA
TN
WA
MO
RI KA
NH
OR AZ
FL
WI AR
IN
DE
IO SC OKNE
MS ND LO
VT
MN
UT
IDME NM
WV
NYVI
MA
CN
NJ
CA
GE
MD
TX
.2
MSA Relative Demand Shift, 2010
3
Slope (SE) = 0.953 (0.070)
.2
.5
1
1.5
2
MSA Relative Demand Shift, 2000
2.5
3
Notes: The relative demand shifts are calculated as log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is the log
relative supply of college equivalent versus high school equivalent hours, σ E (= 5) is the elasticity of substitution
between college and high school workers and log(WC/WH) is the fixed weighted composition adjusted college/high
school log wage differential. The estimated slope coefficient (and associated standard error reported in parentheses) are
weighted by the inverse sampling variance of the state level wage differentials.
42
Figure A2b: Implied Relative Demand Shifts by MSA, 1980 to 2010 (σE = 5)
Relative Demand Shifts, 1980 and 1990
3
MSA Relative Demand Shift, 1990
4.2
Slope (SE) = 0.725 (0.042)
50
-.8
0
1
2
188
45
196
170
25 152
118
10
200
29
16
32
13
167
72
189
49
146
27
26133
3
99
48
85
82
109
73
106
1 134
120
145
39
169
210
88
159
100
197
1
11
193
18
122
55
121
140
198
171
184
141
144
42
128
2
7
7
38
160
47
4 19
194
40
191
21444
187
60
168 90
183
201
216
98
46
113
142
5
3
199
115
92
24
124
215
86
17
95
112
130
125
116
57
28
43
104
33
136
68
157
138
162
5132
149
174
96
202
147
123
78
52
143
89
135
22204
80
36 127 3167
56
93
195
97 34181
108
71
180
15
51
183
182
48
23
153
156
175
166
177
129
59
6
155
110
173
12
81
37 165
154
64172
8150
163
20151
70
30
21
217
74
126
212 65
69
205
186
5487
176
114
6335
101
164
139
190
158
211
209
41
11
14
7
102
62
213
79 192
58
161
105
137185
75
218
76
66
207107
219119103
94
208
179 178117
61 203
131
91
-.8
0
1
2
3
MSA Relative Demand Shift, 1980
4.2
Relative Demand Shifts, 1990 and 2000
MSA Relative Demand Shift, 2000
4.2
Slope (SE) = 1.078 (0.045)
188
3
170
-.8
0
1
2
152
169 29 196
31
2716
26
49
13 25
134
85
183 106
146
118
10
172
111
168
18
3
72
56
122
38
175
46
144
32
99167
40
47
42
109
162
140
55
156
96
193
210
128
82
60
124
65
202
68
120
216
187
44
145
36
198
73
95
88
4160
147
214
121
837177
86
157
15
133 45
113
137 35163
132
80
43
77
104
115
2141
123
191
3948
22
57
149
100
138
130
199
6182
159
205
112
89
135
78
143
28
125
67
33
1 189
197
180
136
171
81
52
215
181
110
23
5430
71
114
142
148
127
211
98
51
108
200
165
166
174
87
195
74
34 17
92
176
19184
20
155
173
201
64
59
14
212
76185
97524
158
139
213
209
154
119
190
126
153
69
93 53
62
164
63186
218
79
131 179
103
129
219
58
70
204
90
94
741
50
178
75
208
194
217
192
12
102
11101
151 83116
203 207105
91
61
117 161 150
21
66
107
-.8
0
1
2
3
MSA Relative Demand Shift, 1990
4.2
Relative Demand Shifts, 2000 and 2010
4.2
27
31
169
189 32106
29
13416196
152
6547
40 13
26
51 67 73
11
38
82
167
216
44
177
10
168
111
163
42
59
85
15
86
144
124
46
119
2
128
49
123
187
112
79
115
157
9618146
130
91207
88
52
57
145
33
8121
160
101 62
43
55
125
202
60
154
138
143
14 142
99
122
141
140
317225
72
35
95
36193
171
147
56
104
74
162
135
151901647692
200
108
214
118
37
48
78
133
68
215
191
120
80
182
181
210
197
148
97155
100
45
175
89
132
198
77
179
69
195
185
159
6149
64
180
4 109
212
20
190
113
58
153
218
184
39
158
205
53
24
114
166
63
22
209201
161 8370
17
219
98
107
126
128
174
34
19
199
87
165
54
173
23
176
81
103139 71
21150
156 183
178
12
217
194
110
117 105
75 93 5
192
30
131
61 116
94
136
102
41
208
7 213
137
129
127
20350
204
186
211
0
1
2
3
66
170
188
-.8
MSA Relative Demand Shift, 2010
Slope (SE) = 1.020 (0.049)
-.8
0
1
2
3
MSA Relative Demand Shift, 2000
4.2
Notes: The relative demand shifts are calculated as log(LCE/LHE) + σE log(WC/WH), where log(LCE/HHE) is the log
relative supply of college equivalent versus high school equivalent hours, σ E (= 5) is the elasticity of substitution
between college and high school workers and log(WC/WH) is the fixed weighted composition adjusted college/high
school log wage differential. The estimated slope coefficient (and associated standard error reported in parentheses) are
weighted by the inverse sampling variance of the MSA level wage differentials.
43
Data Appendix
1. Basic Processing of the Census and ACS Data
We use the 5 % PUMS 1980, 1990 and 2000 Decennial Census data, as well as the 1 %
2010 ACS. We drop Alaska, Hawaii and the District of Columbia from all of our analyses.
We consistently defined 216 MSAs between 1980 and 2010. Our basic sample consists of
all working individuals aged 26-55. Hours are measured using usual hours worked in the
previous year. Full-time weekly earnings are calculated as the logarithm of annual
earnings over weeks worked for full-time, full-year UK born workers. Weights are used
in all calculations. Full-time earnings are weighted by the product of the CPS sampling
weight and weeks worked. All wage and salary income was reported in a single variable,
which was top-coded at values between $75,000 in 1980 and $200,000 in 2010. Following
Katz and Murphy (1992), we multiply the top-coded earnings value by 1.5. Earnings
numbers are inflated into 2010 prices using the PCE deflator.
2. Coding of the Education Categories
We construct consistent educational categories using the method proposed by Jaeger
(1997). For the pre 1990 education question, we defined high school dropouts as those
with fewer than twelve years of completed schooling; high school graduates as those
having twelve years of completed schooling; some college attendees as those with any
schooling beyond twelve years (completed or not) and less than sixteen completed years;
college-only graduates as those with sixteen or seventeen years of completed schooling
and postgraduates with eighteen or more years of completed schooling. In samples coded
with the post Census 1990 revised education question, we define high school dropouts as
those with fewer than twelve years of completed schooling; high school graduates as those
with either twelve completed years of schooling and/or a high school diploma or G.E.D.;
some college as those attending some college or holding an associate’s degree; college
44
only as those with a bachelor degree; and postgraduate as a masters, professional or
doctorate degree.
3. Construction of the Relative Wage Series
We calculate composition-adjusted relative wages overall and by age cohorts using the
wage sample described above, excluding the self-employed. The data are sorted into
gender-education-age groups based on a breakdown of the data by gender, the five
education categories described above, and three age categories (26-35, 36-45 and 46–55).
We predict wages separately by sex and age groups. Hence, we estimate six separate
regressions for each state/MSA and year including education and age dummies (as well as
two dummies for race). The (composition-adjusted) mean log wage for each of the thirty
groups in a given state/MSA and year is the predicted log wage from these regressions for
each relevant education group. These wages are then weighted by the hours shares of each
group for the whole time period.
4. Construction of the Relative Supply Measures
We calculate relative supply measures using the sample above. We form a labour quantity
sample equal to total hours worked by all employed workers (including those in selfemployment) age 26 to 55 to form education cells in each state/MSA and year. Education
groups are high school dropout, high school graduate, some college, college graduate, and
postgraduate. This provides our efficiency units by education group.
The quantity data are merged to a corresponding price sample containing real
mean full-time weekly wages by state/MSA, year and education group (Wage data used
for the price sample correspond to the earnings samples described above). For each state
and year we calculate aggregate college equivalent labour supply as the total efficiency
units of labour supplied by postgraduates weighted by the postgraduate-college graduate
45
relative wage from the price sample, plus college graduate efficiency units, plus 30
percent of the efficiency units of labour supplied by workers with some college weighted
by the some college-college graduate relative wage. Similarly, aggregate high school
equivalent labour supply is the sum of efficiency units supplied by high school or lower
workers, plus 70 percent of the efficiency units supplied by workers with some college, all
weighted by respective relative high school graduate average wages. Hence, the collegeonly/high school log relative supply index is the natural logarithm of the ratio of collegeonly equivalent to non-college equivalent labour supply (in efficiency units) in each
state/MSA and year.
5. Compulsory School Attendance Laws
We update the data used in Acemoglu and Angrist (2001) which run from 1915 to 1978 to
include state level compulsory attendance laws up to 2002. We obtained compulsory
schooling law data up to 2002 from the Digest of Education Statistics, supplemented by
information from the state statutes. We cross checked our new data with that derived in
Oreopoulos (2009) and found we had very similar measures. This provides five variables
(CA8, CA9, CA10, CA11 and CA12) for 48 states and years between 1915 and 2002 the
capture compulsory years of schooling. For example CA8 equals one in the states that had
a minimum of 8 years of compulsory schooling for the relevant years and zero otherwise,
whereas CA12 equals one in the states that had over 12 years of compulsory schooling for
the relevant years and zero otherwise. We match these into the individual Census and ACS
data by state of birth and year aged 14.
6. R&D, Computer Use and Union Coverage Data
Our Research and Development (R&D) intensity measures are generated using R&D
expenditure divided by nominal GDP for 1977, 1987, 1997 and 2007. These are taken
46
from the National Industrial Productivity Accounts (NIPA) made available by the Bureau
of Economic Analysis. State level changes in R&D performance are measured using Total
(company, Federal and Other) funds for industrial R&D performance in millions of
dollars.
The computer use data are measured in proportions per state in each year. These
are taken from the October 1984, 1987, 1997 and 2003 CPS supplements and derived
from the question `Do you use a computer at work?’. Computer use is the proportion of
employed workers in the CPS that use computers at work.
The union coverage data are also in state level proportions per year and are taken
from the Union Membership and Coverage Database provided by Hirsch and Macpherson
(2003).24 These are generated using CPS data beginning in 1973 and are updated annually.
24
These data are available to download from http://www.unionstats.com/.
47