Wages, Rents and Prices: the Effects of Immigration on U.S.
Natives
Gianmarco I.P. Ottaviano, (University Bologna and CEPR)
Giovanni Peri, (UC Davis and NBER)∗
November, 2006
Abstract
In this paper we document a strong positive association between immigration and average
wages and price of houses of native individuals across U.S. states and metropolitan areas over
the period 1970-2005. Most of the existing literature, focussed on relative wage effects of immigration, missed these strong correlations. By constructing an instrumental variable that proxies
the supply-driven component of immigration at the state level we show that the positive wage
and housing price effects seem genuinely caused by immigration and not by unobserved demand
shocks. Then, using parameters estimated on the aggregate U.S. economy and a simple model,
we are able to simulate quantitatively most of the estimated effects of immigration on wages
and housing prices, for the average native. We also calculate the distributional effects on highly,
medium and less educated natives and we find that all these groups in the average U.S. state
experienced increases in their total real income (wage plus housing income) as a consequence of
the 1990-2005 immigration. This is due to the combination of two facts: foreign-born workers
do not perfectly substitute natives in production and immigrants have lower house ownership
rates than natives, so that house price increases act as a transfer from immigrants to natives.
Key Words: Immigration, Wages, Housing Prices, U.S. States, Welfare effects.
JEL Classification Codes: F22, J61, R23.
∗
Gianmarco I.P. Ottaviano, Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna,
Italy. Email: ottavian@economia.unibo.it. Giovanni Peri, Department of Economics, UC Davis, One Shields Avenue,
Davis, CA 95616. Email: gperi@ucdavis.edu. We thank David Card, Joe Gyourko, Ethan Lewis, Albert Saiz and
participants to several seminars for useful commenst on previous versions of this paper.
1
1
Introduction
The literature on the economic impact of immigrants on U.S. natives has been, so far, overwhelmingly
dominated by a labor market and ”partial equilibrium” logic and approach. Others things equal,
economists have argued, an increase in the supply of foreign-born workers of a certain skill depresses
the wages of native workers of the same skill (Borjas, 2003, Borjas, 2006, Borjas and Katz, 2005).
More recently empirical evidence has suggested that the increased demand for housing caused by
more immigrants has significantly increased the rents for U.S. born individuals (Saiz, 2003, 2005).
The tendency has been to characterize both effects as harmful for U.S. natives, especially those with
the lowest levels of education and income. In an economy with workers of different skills, however,
where natives may respond to inflow of immigrants (by moving, upgrading their jobs and so on),
where there are complementarities between skills and service produced by natives and immigrants,
where house owners’ income is positively affected by an increase in the price of houses and where
some local amenities such as restaurants and personal services may be made more affordable by
immigrants those negative partial effects may have a positive counterpart and the aggregate general
equilibrium effect could be very different from the partial effect and positive for natives. We have
argued elsewhere (Ottaviano and Peri, 2006b) that considering labor market interactions between
workers of different education and experience, and accounting for imperfect substitutability between
foreign-born and U.S. born workers, the average effect of immigrants on wages of U.S. born workers
is positive and significant. We also showed that there is a distributional effect as well: more educated
workers receive the largest part of that positive average effect and the group of workers with no high
school diploma suffers a small wage decline. The analysis of wages, however, does not tell the whole
story. U.S. born individuals are also consumers who may benefit from the variety in consumption of
goods and services introduced by immigrants and are residential capital/land owners, mostly in the
form of house-owning (by far their largest asset of U.S. residents) so that an increase in the value of
housing caused by immigration may also be a bonus for them.
We first document in detail, using census data 1970-2005, that there has been a positive, stable
and economically very significant relation between the inflow of foreign-born and the change in
average wage and house prices for natives across U.S. states. These two positive average effects
are very robust to variable definitions, sample chosen and method of estimation. In particular we
construct a supply-driven shift of immigrants across U.S. states based on different tendencies to
2
migrate to the U.S. for the 1970-2005 period and we use it as instrument to show that the positive
and significant correlation is not driven by demand (pull) factors and survives the IV estimates. An
inflow of immigrants is associated in the long run with higher average wages and value of houses of
natives and with a small migration of natives out of the state.
To explain these facts we model the behavior of U.S. natives as workers, consumers of a tradable
good and a local service and consumers of housing services and we analyze the consequences of
migration on wages, consumption and housing prices of natives in general equilibrium. Importantly
we consider heterogeneous native and foreign-born individuals grouped in three schooling levels. This
allows us to capture the average as well as the relative changes in wages, rents and welfare for natives
of low, intermediate or high levels of schooling. The model considers the representative state in the
U.S. and simulates the effect of the 1990-2005 migration flow on wages, prices, house values and
total income of U.S. natives. Using parameter values from the aggregate U.S. economy the model
matches fairly well the response of average wages, house prices and migration of natives to the inflow
of international migrants. We also derive from the model empirical predictions on the impact of
immigration on each group’s wage, housing price and overall welfare. Again the simulated results
match quite closely the estimated elasticities except for the wage effects on highly educated that
are, in the data larger than in the simulation. This may be due to skill-biased external effects of
highly skilled immigrants. The remarkable result is that due to complementarities in production
of the tradeable and of the non-tradable, the overall production effects of immigrants on natives is
positive, on average. Moreover, as even in the lowest skill level, natives have much higher ownership
rates of houses than foreign-born, each group of natives receives a positive housing income effect
from immigrants both in the short and in the long run. In all reasonable simulations the wage plus
housing income effect for natives is larger than the local price effect and natives of each skill level
gain from immigration. While some natives migrate out of the state to ”cash” on their increased
housing prices and to take advantage of lower housing prices elsewhere, both non-movers and movers
are made better off by the combined effect of immigrants on house prices and wages.
The rest of the paper is organized as follows: Section 2 reviews the previous literature on the regional effects of immigration on wages and housing prices. Section 3 presents new empirical estimates
of the effects of immigration on wages, house price and internal migration of natives considering average effects as well as effects by education 9skill0group. Section 4 presents the model that describes
3
the effect of immigrants on wages, housing prices and location of natives. Section 5 parametrizes and
simulate the equilibrium of the model in particular we simulate the responses of wages, house prices
and location of natives to the immigration flows of a typical U.S. state during the 1990-2005 period.
We do this for the averages as well as for each skill group. Section 6 shows the welfare implications
and discusses some of the main results of the model relative to each group of natives. Section 7
concludes the paper.
2
Literature Review
Our paper provides a coherent approach to analyzing the most important market-effects of immigration on U.S. natives. We leave out the analysis of the impact of immigration on taxes and provision
of public goods as it deserves separate attention and . Our work brings together two different strands
of the literature. On one hand a long empirical tradition (Card 1990, Card 2001) has looked at
states or metropolitan area wages to see wether they were systematically affected by immigration
finding little evidence of that. Even when considering the migratory response of natives (Card and
Di Nardo, 2000) such “regional” approach did not detect relevant effect of immigrants on native
wages. George Borjas (Borjas, Freeman and Katz 1997, Borjas 2003) has criticized such an approach
and recently has illustrated how the migratory response of natives and small sample bias may reduce
the estimates of the effects of migrants on wages (Borjas 2006, Borjas and 2006). At the same time
Albert Saiz (Saiz 2003, 2006) and our previous work (Ottaviano and Peri, 2005) have shown that
the price of housing in metropolitan areas across the U.S. are systematically positively correlated
with immigration flows. Immigrants live prevalently in metropolitan areas, and as their inflow is not
fully adjusted by migration of natives they increase the demand and price of housing. In theory, in
the long run, this effect should simply lead to more construction of houses, in practice however land
regulation and scarcity of desirable locations generates in most typical immigrants destinations an
increase in the value of land and houses (this mechanism is illustrated in Gyourko et al. 2005). The
wage and housing price channels are both very important to understand the effects of immigration
on welfare of native individuals and it is clear that they need to be analyzed together. As Robak
(1982) showed, to analyze a spatial equilibrium in which individual equate consumption wages across
locations we need to consider wages and local prices. The response of natives to immigration in a
4
U.S. state depends on how wages change relative to local prices. The price of housing is the most
relevant in determining local prices. Hence, those two and the location response of natives need to
be analyze within the same equilibrium model. Moreover, the increasing wage dispersion of the last
decades (Autor, Katz and Kearny, 2005) has been accompanied by a similarly increasing housing
price dispersion across states and metropolitan areas (Gyourko, Meyer and Sinai 2005). This suggests
that an important adjustment mechanism of a local economy may involve house prices increasing or
decreasing with wages in response to immigration, keeping ”consumption” wages more stable across
locations with little response of migration. Finally we incorporate in our analysis a third ”price effects” of immigrants. This could be called ”consumption variety” effect. In local non-tradable services
such as restaurants and entertainment (accounting for a share between 15% and 20% of the average
U.S. individual expenses in 2005) presence of foreign-born and their variety adds to the diversity of
services and has a positive economic value. The benefits from increased variety in consumption (so
celebrated in the trade and growth literature) have been mentioned often by the migration literature
but never modeled and measured seriously. Our work provides a frame and a first step to quantify
them. A slightly different approach to measuring this effect has been taken by Cortes (2005). She
analyzes the effect of immigration on the price of some non tradable local services (housekeeping,
gardening and so on) heavily staffed by immigrants. In a sense we can think of immigrants increasing
the variety and availability of those services.
3
3.1
The Empirical Evidence
Aggregate Wages and Aggregate House Prices
The point of departure of our analysis are some striking empirical measures of the aggregate impact
of immigration on average wages and house prices of natives. Previous literature has focussed on the
issue of relative wages of natives, considering immigration as a shift in relative supply towards less
skilled workers (Borjas 2003, Card 2001) and some articles have somewhat discredited the regional
approach claiming that labor mobility of natives would attenuate drastically any effect on wages
(Borjas, Freeman and Katz 1997, Borjas 2006). To the contrary we begin considering average wages
of natives, average house values of natives and their association with immigration at the state level.
There are three reasons why these correlations are particularly interesting and contain a lot of infor5
mation on the ”production” and ”consumption” value of immigration for natives. First, contrarily
to what implied by the critics of the ”area approach” differences in productivity and wages across
states, produced by differences in immigration rates need not be eliminated by internal migration
of natives if they also cause corresponding changes in value and price of housing so that positive
(negative) productivity effects are offset by more (less) expensive houses leaving real wages hardly
affected. Second, in Ottaviano and Peri (2006b) we showed that there is a mechanism, represented
by the complementarities in production, through which immigrants may raise significantly the average wage of natives even when immigrants of each particular skill type still have a negative partial
effect (”ceteris paribus”) on wages of natives. Such positive ”complementarity” effects would be captured only by aggregate empirical evidence and could be lost in an approach ”by skill”. Finally, in
previous work (Peri Ottaviano 2005, 2006a) we documented the positive correlation between native
wages/house prices and immigration across U.S. metropolitan areas, similarly Saiz 2006 documents
such a correlation for house prices across U.S. cities. Here we want to show that the positive correlation is found across states, that it is very robust, that its quantitative estimate is precise. Moreover,
by constructing a supply-driven shift of immigration across U.S. states we want to show that such
positive correlations are genuine ”effects” of immigration and not the spurious result of unobservable
state-specific demand shocks.
3.1.1
OLS Correlations
The data used in all our empirical analysis are from the Integrated Public Use Microdata Samples
of the U.S. Census as collected and homogenized by Ruggles et al. (2006). We use the 1% Form 1
State Sample for 1970, the 5% State sample for 1980, 5% state sample for 1990, 5% census sample
for 2000 and the 1 in 100 random sample for the American Community Survey, 2000. The units
of observation are states. For all employment and wage data we select people in the 17 to 65 age
range who worked at least one week and received positive salary. For population data we selected all
individuals residing in a state in the 17 to 65 age range. For all housing data we selected individuals
who are head of households. The aggregate and average data are constructed by weighting each
individual by the sample weight (variable PERWT). In our empirical analysis we consider as foreignborn those individuals who are not born in the U.S. or its territories overseas and who were not
citizens at birth. The first way to show a significant positive correlation between immigration and
6
average wages of U.S. born at the state level is presented in the first row of Table 1 as well as in Figure
1. The coefficients in Table 1 represent the partial correlation between immigration and change in
wages obtained by estimating the parameter γ wage in the following regression:
∆wH
jt
= αt + γ wage
H
wjt
µ
∆Fjt
Fjt + Hjt
¶
+ β0
µ
∆Hjt
Fjt + Hjt
¶
+ εjt
(1)
us
where wH
jt is the average wage of U.S. (home)-born workers in state j and Census year t, ∆w jt
is its change over the period between census t and the following one, αt are period fixed effects, Fjt
is the total employment of foreign-born in state j and year t and ∆Fjt is the net change between
census t and the following one, similarly Hjt is total employment of U.S. natives and ∆Hjt its intercensus change. Finally εjt is a random zero-mean state-period shock. An OLS estimate of (1) can
be no more than a correlation as we are regressing wages on employment and mixing demand and
supply shifts. One important thing, however, is that we are already controlling for the change in
employment of native workers, hence demand shocks that generically attract workers to the state
would be captured by the coefficient β 0 (not reported, but often insignificant or negative) while γ wage
captures only the comovement of native wages with movements in immigrant employment, orthogonal
to native employment. γ wage can be interpreted as an elasticity: when immigration increases state
employment by 1% the wage of natives in that state would increase by γ wage %. Whether measuring
wage in yearly or weekly terms and whether using all workers or male only to calculate average wages,
the first row of Table 1 always shows very significant estimates of γ wage between 0.45 and 0.5.Figure
´
³
∆wH
∆Fjt
jt
1 that represents the partial correlation between wH and Fjt +Hjt ,exactly as estimated in row 1
jt
column 1 of Table 1 shows a clear upward regression line with no evidence of nonlinearity or outliers
driving the result. Row 4 of Table 3 shows the elasticity when we consider only the metropolitan
workers in each state (identified by the METRO variable) and the immigration in the corresponding
metropolitan areas. The complementarity effects and the housing price effects could be stronger
in metropolitan areas where productive interactions are intense and land is scarce. The coefficient
estimated on metropolitan workers only is significant and close to (possibly slightly higher than) the
one estimated using all workers. In general we performed a number of other checks (not reported and
available upon request) using sub-samples of states (e.g. excluding California, or the top 3 receivers
of immigration) and periods (1970-2000 only) confirming the remarkable robustness of this estimate.
Table 2 and Figure 2 report a similar analysis for the effect of immigration on the price of houses
7
of native individuals. The first row of Table 2 shows the partial correlation between immigration
and change in house prices (rents) obtained by estimating the parameter γ house price in the following
regression:
∆rH
jt
= αt + γ house price
H
rjt
µ
∆Fjt
Fjt + Hjt
¶
+ β1
µ
∆Hjt
Fjt + Hjt
¶
+ εjt
(2)
where rH
jt is the average rent (or house price) of U.S.-born individuals in state j and Census year
t and ∆rus
jt is its change over the period between census t. The other variables are as defined above,
except that now we measure Fjt and Hjt as foreign- and U.S.-born population rather than employment. We still control for native’s population change so that the correlation γ house price indicates
the association of house prices of natives to immigration changes orthogonal to changes in native
population. Row 1 of Table 2 and Figure 1 shows an elasticity of rents to immigration between 0.6
and 0.8 and very significant. Figure 2 shows visually the partial correlation estimated in column 2
row 1 and confirms that there is a discernible positive association, not apparently driven by outliers
or odd nonlinearities Row 4 of Table 2, restricted to metropolitan areas of each state shows similar
elasticity estimates for rents, however the elasticity of house prices are often more volatile and imprecisely estimated, still always positive and often around one. We perform estimation using median
and averages as we are concerned that the strict top-coding of the census for monthly rents and value
of housing may eliminate a large upper tail of the price distribution and bias the average estimates.
There seems to be no systematic difference, however, between the estimates using the median and
those using the average rent and house price.
3.1.2
Supply Shocks and Instrumental Variables estimates
The possibility that unobservable demand/productivity shocks in states may be correlated with
immigration of foreign born (and certainly with immigration of natives) induces possible correlation
between the variable
∆Fjt
Fjt +Hjt
and the residuals of equations (1) and (1) so that the elasticities γ
cannot be interpreted as the effect on wages and house prices of an exogenous change (supply shift)
in immigration. In order to identify the γ 0 s as measuring the impact of immigration on native wages
and rents we need to identify shifts in immigration across states and periods due to supply (push)
factors rather than demand (pull) factors. This is done in the literature (originally the idea is from
Card 2001, then used in Lewis 2005, Ottaviano and Peri 2005, 2006a and Saiz 2006) by using the fact
8
that immigrants tend to settle disproportionately where other people of the same nationality already
reside and different nationalities had very different immigration rates to the US during the 19702005 period. Technically we consider the composition of the foreign-born population by state and
country of origin in 1970 and attribute to each group the net immigration rate (by nationality and
period) for the whole U.S. over each inter-census period. This allows us to construct an ”imputed”
population for foreign born by country of origin and state in each subsequent census year (1980, 1990,
2000 and 2005). Aggregating across nationality in each state and year we obtain an imputed foreign
born population that we use as instrument for the actual foreign-born population. The intuition
for why this constructed ”supply of immigrants” works well as instrument, proxying state supply of
immigrants and orthogonal to state demand is as follows. A state as California, had for geographic and
historical reasons a large Mexican population in 1970, while a state like Minnesota had a large group
of Scandinavian-born. Due to country-specific forces immigration of Mexicans increased dramatically
between 1970 and 2005 and immigration of Scandinavian almost stopped. As immigrant groups settle
in prevalence near previous settlers from the same country, this shift of pattern of immigration by
country of origin implies very different migration rates across states: California would experience a
much larger increase in immigrants than Minnesota would. Such differences, are completely unrelated
to the specific demand conditions of California and Minnesota between 1970 and 2005, but are very
much correlated to the actual migration flows. Formally we proceed as follows. Let us call Fcjt the
population of foreign-born from country c in state j and year t. The total population of foreign-born
P
from country c in the whole U.S. in year t will be denoted simply as Fct = j Fcjt . Its change between
census of year t and census of year t + n will be denoted as ∆Fct,t+n and the growth rate of that
group at the national level, between t and t + n will be denoted as gct,t+n = ∆Fct,t+n /Fct . We identify
56 foreign countries of origin covering more than 99% of all U.S. immigrants during the 1970-2005
period. The imputed foreign-born population for state j in year 1970 + n, where n can be 10, 20, 30
and 35 is given by the following expression:
Fbjt+n =
56
X
Fcj1970 (1 + gc1970,1970+n )
(3)
c=1
We use the change in foreign-born calculated using the imputed data as instrument for the actual
change. Namely the variable
∆Fejt+n
Ftt+n +Hjt+n
is used as an instrument for
∆Fjt+n
.Rows
Ftt+n +Hjt+n
2 of Tables
1 and 2 show the Instrumental Variable estimates of the coefficients γ wage and γ house price and rows
9
3 show the first stage coefficient and F-test for the instrument. Similarly Rows 5 and 6 show IV
estimates and first stage coefficients when considering the metropolitan samples across states. All
IV regressions include period dummies, and exclude the potentially endogenous change in native
employment (population) as now the instrument should isolate only the supply-driven changes in
immigration. The imputed change of foreign-born turns out to be a good instrument at the state
level with a partial R2 around 0.4, and and F larger than 20. The point estimates for γ wage using the
IV technique range between 0.35 and 0.55, depending on sample, and wage definition, and are always
significantly positive. The IV estimates for γ house price obtained using rents range between 0.64 and
0.81. In the case of house prices the elasticity are imprecisely estimated, always positive and large
in some cases as large as 2.4. This may be due to the larger volatility of prices, that also depend on
expectation of future appreciation while rents, the cost of use, should only depend on fundamentals.
All in all the IV estimates confirm and reinforce the OLS estimates that there is a positive elasticity
of wages and house prices to immigrants, with elasticities in the 0.35 − 0.55 and 0.6 − 0.8 ranges
respectively. One further test that the instruments seem to be working in the expected direction is
shown in Table 3. The table shows the elasticity of native population or employment to immigrants.
Interestingly, while the OLS estimates (first column) are positive and significant, proving that natives
and immigrants’ populations both respond to common shocks by moving together into and out of
states, the response of natives to supply-driven immigration shocks is negative, however rather small
and not significantly different from 0. We can rule out, however, that the IV estimates are equal to the
OLS ones, implying that unobservable demand shocks are driving, in part, both types of immigration
to a state. However isolating the supply-driven part of immigration shows that natives only have a
mild out-migration response much smaller than one for one (that would imply a coefficient of one)
possibly as small as 0. This fact, along with the positive effect on average wage and house prices is
one of the crucial regularities that our simple model should explain.
3.2
Wage and House Prices by skill group
The average effect of immigration has received little attention in the past, as economists have been
focussing on its distributional (relative) effects and increasingly so as immigration has become skewed
towards less skilled workers and as native unskilled workers have fared rather poorly (in terms of
wages) in the U.S. economy (see Ottaviano and Peri 2006b). We extend here our empirical analysis
10
to identify the correlation between immigration and wages/rents for different groups of natives,
depending on their schooling. Imperfect substitutability in production between workers of different
schooling levels, implies changes in their relative wages if supply changes are not uniform across
them. Hence we analyze the effects of immigrants on wages and house prices of native population
considering different education groups. The most parsimonious and meaningful way of doing this is
to divide natives and immigrants in three education groups: low education(with no degree), Medium
education (with high school degree) and high education (with college degree). The presence and
inflow of immigrants, as shown in Figure 3 as well as in previous work (Ottaviano and Peri 2006b)
is proportionally larger in the Low and High education groups than in the Medium education group.
We need a three skills structure to capture this characteristic U-shape of immigration by skill. At
the same time, as skills correspond to income, we can think of the housing market as segmented
between the three groups. The location and type of houses bought and rented by the low education
group, within a state or a metropolitan area tend to be quite different than those purchased and
rented by medium or highly educated people. Moreover, several recent papers (Gyourko et al. 2005,
Van Nieuwerburgh and Weil, 2006) have shown an increasing tendency to housing segregation by
skill/income and have explained the increased dispersion in house prices and rents via sorting of
individual and increasing wage (income) dispersion. As a consequence the effect of immigration on
house prices may be different at different levels of the skill distribution.
3.2.1
Rent effects in a Segmented Housing Market
We begin analyzing the impact of immigration on housing prices separately by skill. Table 4, in particular reports the coefficients obtained by estimating rent regressions such as (2) separately for each
education group (we also performed a SUR estimation and a pooled estimation allowing separate
elasticity by skills with very similar results). All variables are defined as above, including the instrument, except that now we only consider people in the specific education group when constructing
the imputed immigration Column 1 report the results for the high school dropout group, Column 2
for the high school graduate group and Column 3 for the College Graduate group. The instrument
are constructed by using the initial (1970) foreign population in a state by schooling and country
of origin and equating its inter-census growth to the national immigration rate of that group. In
this case our instrument capture the fact that a state with initially many Mexicans would experience
11
large supply-driven growth of the low education group among foreign-born as most of the Mexican
migration involved high school dropouts. On the other hand a state hosting many Russians or Indians in 1970 would experience a supply-driven increase in the highly educated foreign-born as those
countries experienced large brain drain during the nineties. We report the estimates of γ house price
using OLS (and controlling for natives population changes) or IV methods and using housing price
and rent per room as dependent variable. The first four rows of Table 3 refer to the whole state
sample and the last four to the sample including only metropolitan areas. First, let’s notice that
the instruments are better predictor of the change in low skill immigration than of the changes in
other education groups (possibly due to the predominant role of Mexican and central American in
this first group, while highly educated workers are more distributed across nationalities). Second, in
all estimates the impact of immigrants on prices of low skill housing is small and insignificant, while
the impact on prices of medium and high skill housing is positive, large and significant. The average
elasticity of rents of native high school dropouts to immigrants in the same schooling group is 0.2
while for the other two groups is in the 1-1.2 range. Given the very large increase in less educated
foreign-born who crowded the market for this type of housing and given that the out-migration of
natives in this group has been very moderate and in line with the average migration (γ population for
high school dropout is estimated to be around -0.20 with a standard error of 0.3 using the IV method)
such a low price response seems to suggest elastic house supply for this group. As our elasticities
capture the long-run responses of prices a plausible explanation could be that the land for better
housing is constrained by geography and zoning laws in particular for high immigration states (see
Gyourko et al 2005), while the low quality housing is on the ”marginal land” whose supply could be
expanded.
3.2.2
Wage Effects by Education
It is well known that in relative terms immigration should be reducing the wages of the group of
workers with low education, relative to the intermediate education group given the large relative
inflow of immigrants with little education. If there is imperfect substitutability between natives and
immigrants, however, due to skills, occupational and job choice then the possibility of an overall
positive effect on natives may emerge with some groups gaining more and other gaining less or
potentially loosing (Ottaviano and Peri, 2006). It is therefore useful to analyze how the average
12
positive effect of immigrants (estimated above) can be decomposed into the effect of immigrants of
each group on wages of natives in each group. Let us emphasize, for the reader that will find our
estimated parameters odd that here we are estimating a reduced-form elasticity. The experiment does
not consist in changing the supply of immigrants of one skill group, keeping all the other constant,
and estimate their wage impact on natives of that group. That exercise which would identify a
relative elasticity of wage has been done in previous work (e.g. Borjas 2006). Here we identify the
total effect associated to a supply-driven change in immigration on wages of workers by education
group. As on average in a state that receives many unskilled immigrants also skilled immigrants flow
in higher number the impact on the wage of low skills in a mixture of the direct competition and
indirect complementarity effect, hence it need not be negative. Table 5 shows the IV estimates of
the following three equations:
using
µ
¡
¢
∆wHk
jt
= αt + γ wage k
Hk
wjt
k
∆Fejt
k +H k
Fjt
jt
¶
Ã
∆Fjtk
Fjtk + Hjtk
!
+ k + εkjt for k = Low, Medium, High
(4)
as instrument and calculating average wages of each group either on all indi-
viduals (first row) or on males only (second row). The index k refers to the schooling level. The
estimated coefficients in table 5 can be interpreted as follows: in response to the average exogenous
immigration shock over the 1970-2005 period the wages of native dropouts experienced a negative
non significant effect while the other two groups experienced positive significant effects. An increase
in the employment of the group by 10% because of immigrants would be associated to a 1% decrease
in wages of dropouts, a 2% increase in wages of high school graduates and a 5% increase in wages
of college graduates. The actual immigration flows, however, were not an homogeneous 10% in each
skill group. In the period 1990-2005, for instance total immigration caused an increase by 22% of
high school dropout employment, by 8.2% for high school graduate employment and by 11.3% of
college graduate employment for an average increase of employment of 11.1% (proportions across
skill groups were similar in previous decades). That would correspond to -2.2% change in wages
of low skills, +1.6% change in wages of medium skills and +4.4% increase in wages of high skills.
Averaging these effects by using the weights of each group in wages we obtain a positive average
effect of 2.3% confirming the positive aggregate effect on average wage of U.S. born workers. Reading
Table 5 as revealing the relative effect of immigration we can say that the positive average effect
13
estimated in the aggregate analysis is associated to a relative effect that penalizes the low education
group (significantly in relative terms, although not much in absolute terms) and rewards the other
two groups. The estimates are not precise enough to rule out equal positive effects on these two
groups. Interestingly, the above estimates are similar to those obtained in a recent paper by Kugler
and Yuksel (2006). They use the displacement effect generated by Hurricane Mitch in countries as
Honduras, Nicaragua, Guatemala and El Salvador as a ”push”-shock for immigration to the U.S. and
evaluate the effect on US wages by skill, finding essentially no effects on low skills and positive and
significant effects on wages of US workers with high school and college education.
4
The Model
We consider a small open economy, such as a U.S. state, with heterogeneous individuals who supply
labor, consume a tradable good a non tradable local service and non tradable housing services. The
heterogeneity of individuals, relevant for their production and consumption characteristics, has two
”dimensions”. The total number of individuals in the state, W, are differentiated both horizontally
in terms of origin (Home- and Foreign-born) and vertically in terms of skill (schooling) level (Low,
Medium, High). This gives rise to six categories:
Home Foreign Total
LH
LF
L
Medium skill MH
MF
M
High skill
SH
SF
S
Total
H
F
W
Low skill
Each worker inelastically supplies one unit of labor to the production of the homogeneous good Y
and one unit of labor to the production of a local composite good X. We think of Y as summarizing
most of the goods and services in the U.S. economy while X is a composite that combines those
local services that particularly benefit from ”ethno-cultural” diversity in their supply, examples are
restaurants, retail trade, entertainment. We will refer to X as the ”ethnic” good. Efficiency units of
labor may vary across skill levels and place of origin of workers in the production of Y . Efficiency
units vary only across place of origins in the production of X. Specifically, we call 1/(τ k τ kh ), with
14
k ∈ {L, M, S} and h ∈ {H, F }, the efficiency units of a worker of ethnicity h with skill level k in
non-ethnic production. Analogously, we call 1/τ Xh the efficiency units of a worker of ethnicity h in
ethnic production (1/τ Xh can be also interpreted as a quality parameter). The state economy has
land area equal to to T . This area is divided in three districts with areas Tk , k = L, M, H, each
skill group lives in the specific district, capturing the stratification of housing by income within a
state (and metropolitan areas). The land is owned by local landlords who rent it out for housing to
workers and spend their income locally. Each land owner consumes housing produced by the same
type of land she owns.
4.1
Preferences
Workers’ preference are defined over three goods: the tradable good Y , the ethnic composite good
X, and housing, simply represented as land consumption T. Hence, individuals of skill k have the
following utility:
Uk = Y α X β Tk1−α−β
with
X=
"µ
XH
τ XH
¶ γ−1
γ
+
µ
XF
τ XF
(5)
γ
# γ−1
¶ γ−1
γ
(6)
where Y is consumption of the tradable, Tk is consumption of housing, XH and XF are the quantities
consumed of home-born and foreign-born produced ethnic goods, while γ > 1 is their elasticity of
substitution.
4.2
Technology
On the supply side, all markets are perfectly competitive. Production of the tradable takes place
according to the following technology:
Y = SC
where S is a total factor productivity term and C is a CES composite labor input that combines
the three skills:
C=
"µ
CL
τL
¶ δ−1
δ
+
µ
CM
τM
15
¶ δ−1
δ
+
µ
CS
τS
δ
# δ−1
¶ δ−1
δ
CL =
CM =
"µ
"µ
CS =
LH
τ LH
MH
τ MH
"µ
SH
τ SH
¶ σL−1
σ
L
−1
¶ σM
σM
¶ σSσ −1
S
+
µ
+
µ
+
µ
¶ σLσ −1 # σLL−1
σ
LF
τ LF
L
MF
τ MF
σM
# σM
¶ σM−1
−1
σ
M
¶ σSσ −1 # σSS−1
σ
SF
τ SF
S
δ > 1 is the elasticity of substitution between skill levels, σ S > 1 is the elasticity of substitution
between low skill workers of home and foreign origins , σ M > 1 is the elasticity of substitution
between medium skill workers of home and foreign origins and σ > 1 is the elasticity of substitution
between high skill workers of home and foreign origins. The imperfect substitutability of workers
across skills is largely documented in the labor literature (Katz and Murphy 1992, Hamermesh 1993,
Ciccone and Peri 2005). The imperfect substitutability between home and U.S. born workers in
production, due to different skills, constraints and choices of jobs and occupations is documented in
Ottaviano and Peri (2006b).
The production of ethnic good Xh requires one unit of labor h per unit of output. Hence, XH = H
and XF = F i.e.
XH = LH + MH + SH
XF = LF + MF + SF
Analogously, housing requires one unit of land per unit of output. Lot size is normalized to unity.
Land in district k is used to produce housing of type k. We also assume that while the land for skill
group M and S is constant, the land for skill group L can be expanded as an increasing exogenous
function of population in that group. The reason is that this group lives and dwells on the marginal
land, whose supply can increase while the other two groups are located in more desirable land whose
supply for geographic and legal constraints is limited (see Gyourko et al.,2005 for an analysis of
residential segregation along these lines). We assume for simplicity and consistently with simple
models of land supply (e.g. Van Nieuwerburgh and Weil 2006) that supply of land in the low-skilled
16
district is the following function of population in that district: TL = BLψ , where ψ is the elasticity of
land supply to population. A worker of type k demands only housing type k for her needs. So workers
of different skills are assumed to be exogenously segregated in different districts. Each individual is
a land-owner of a share of the type of land in the district he/she lives in. The land is rented out
for housing (partly to themselves) and the income is spent where the owner lives. Each land owner
consumes housing produced by the same type of land she owns. The ownership of land is separate
from the physical location where the individual lives, in the sense that a person can move out of
the state, and still own the land and rent it to other tenants, receive the income and pay a rent in
another state.
4.3
Equilibrium
Let us define wkh as the wage per worker of origin h with skill level k, pY the price per unit of tradable
good Y , pXh the price per unit of ethnic good h, and rk the land rent in district k. If we call w the
vector of wkh ’s and E the associated vector of labor endowments as well as r the vector of rk ’s and T
the associated vector of land endowments, then aggregate income in the economy can be written as:
I = w0 E + r0 T + pXH XH + pXF XF
(7)
with workers of ethnicity h with skill level k accounting for a fraction
Ikh = wkh kh + pXh kh
(8)
and landowners of land k accounting for a fraction
IT kH = rk TkH
(9)
Utility maximization, profit maximization, and land market clearing imply:
r0 T = (1 − α − β) I
17
(10)
with, by (9)
rk Tk = (1 − α − β) (Ik + IT k )
and Ik =
(11)
P
h Ikh .
Utility maximization, profit maximization, and ethnic market clearing imply:
PX X = pXH XH + pXF XF = βI
(12)
Utility maximization, profit maximization, and homogeneous good market clearing imply:
pY Y = αI
(13)
Conditions (7), (10) and (12) together with (13) give:
I=
w0 E
α
(14)
pY Y = w0 E
r0 T =
(15)
1−α−β 0
wE
α
(16)
1−α−β
Ik
α+β
(17)
with
rk Tk =
Profit maximization also requires:
pY S = PC
where:
¡
¢ 1
1−δ
PC = φL PL1−δ + φM PM
+ φS PS1−δ 1−δ =
(18)
Ã
X
k
φk Pk1−δ
1
! 1−δ
1
# 1−σ
"
k
X
1
¤
£
Pk = φkH (wkH )1−σk + φkF (wkF )1−σk 1−σk =
φkh (wkh )1−σk
h
for all k ∈ {L, M, S} are the price indices associated with the quantity indices C and Ck /τ k respec-
18
tively, σ k is the ethnic elasticity of substitution within skill level k and
φL ≡ (τ L )1−δ
φLH ≡ (τ LH )1−σL
φLF ≡ (τ LF )1−σL
φM ≡ (τ M )1−δ φMH ≡ (τ MH )1−σM φMF ≡ (τ MF )1−σM
φS ≡ (τ S )1−δ
φSH ≡ (τ SH )1−σS
φSF ≡ (τ SF )1−σS
The exact aggregation properties of the above quantity and price indices ensure that PC C = w0 E,
P
P
k Pk Ck = PC C,
h wkh kh = Pk Ck . Exploiting these properties, profit maximization also implies:
Pk Ck = φk
wkh kh = φkh
µ
µ
Pk
PC
¶1−δ
wkh
Pk
PC C
¶1−σk
(19)
Pk Ck
(20)
for all k = {L, M, S} and h = {H, F }. These expressions can be easily manipulated to produce
respectively:
µ
Pk
PC
φkh
µ
φk
¶1−δ
wkh
Pk
1
δ
= φk
¶1−σk
µ
Ck
C
1
σk
= φkh
¶ δ−1
δ
=
µ
¶ σkσ−1
kh
Ck
δ−1
1
φkδ Ck δ
1
δ−1
δ−1
1
1
δ−1
(21)
δ
φLδ CL δ + φM
CMδ + φSδ CS δ
k
σ k −1
σk
1
σ
φkhk kh
=
1
σk
σ k −1
σk
φkH kH
1
σk
σ k −1
σk
(22)
+ φkF kF
Considering PC C = w0 E together (18) gives:
w0 E = pY SC
(23)
which, together with (14), (21) and (19), yields:
X
h
1
δ
wkh kh = φk
µ
Ck
C
¶ δ−1
δ
1
δ
αI = φk
µ
Ck
C
¶ δ−1
δ
pY SC
(24)
Finally, we have to characterize the equilibrium prices of the ethnic good. To do this, we observe
that we can exploit for the utility the same aggregation properties we used for non-ethnic production.
Specifically:
1
pXh h =
γ
h
φXh
1
γ
φXH
H
γ−1
γ
19
γ−1
γ
1
γ
+ φXF
F
γ−1
γ
βI
(25)
for h = {H, F } and φXh ≡ (τ Xh )1−γ . Since XH = H and XF = F , we can write:
γ
¸ γ−1
∙ 1
1
γ−1
γ−1
γ
γ
X = φXH H γ + φXH F γ
and thus:
X
pXh kh =
h
When substituted in Ik =
X
h
P
h Ikh
"
1
γ
φXh
µ
h
X
¶ γ−1
γ
(26)
#
kh
βI
h
(27)
together with (8), results (24) and (27) allow us to express the
equilibrium income of skill group k as functions of labor:
Ik =
X
h
4.4
1
δ
Ikh = φk
µ
Ck
C
¶ δ−1
δ
αI +
"
X
1
γ
φXh
h
µ
h
X
¶ γ−1
γ
#
kh
βI
h
(28)
Labor market
Here we characterized the equilibrium of the labor market in terms of demand and supply .
4.4.1
Labor demand
Demand for labor of skill level k and ethnic group h can be derived by considering (18), (19), (20),
(21), (22), together with PC C = w0 E. This gives:
1
σk
wkh kh = A · S · C · φkh
µ
kh
Ck
¶ σkσ−1
k
1
δ
· φk
µ
Ck
C
¶ δ−1
δ
where A ≡ pY is a constant. Simplifying we get:
1
1
σ
− σ1
wkh = A · S · C δ · φkhk (kh )
k
1
−
· φkδ (Ck )
σ k −δ
δσ k
(29)
where δ < min{σ L , σ M , σ S }.
Equation (29) is an (inverse) labor demand schedule showing the wage of skill level k in ethnic
group H as a downward sloping function of its quantity kH .Moreover, for given kH , the schedule shifts
down if kF , workers of same skill and different nativity increase because, due to closer substitutability
within rather than across skill groups, Ck has a negative exponent in (29). The schedule would shift
to the right if supply of workers with different skills or productivity S increase. In general the wage
20
of native workers of skill k is:
• positively affected by a proportionate inflow different skills (larger C) due to love of variety in
production
• negatively affected by a proportionate inflow of same skill (larger Ck ) as more same-skill workers
are combined with a given stock of different-skill workers (since δ < min{σ L , σ M , σ S })
Finally, note that for a given total stock of skill k the skill composite
⎤ σ σ−1
k
σ k −1
µ
¶
k
X
σk
skh
⎦
Ck = k ⎣
τ kh
⎡
h∈{H,F }
is maximized for balanced ethnic composition skh /τ kh = 1/2, where skh = kh /k, and the labor
composite
C =
X
k∈{L,M,S}
= W
X
"µ
Ck
τk
⎡
k∈{L,M,S}
δ
# δ−1
¶ δ−1
δ
⎢ δ−1
⎢s δ
⎣ k
δ
⎤ δ−1
⎛⎡
⎞ δ−1
⎤ σ σ−1
k
δ
σ
−1
µ
¶ k
k
skh σk ⎦
⎜⎣ X
⎟ ⎥
⎝
⎠ ⎥
⎦
τ kh
h∈{H,F }
is maximized for balanced ethnic compositions skh /τ kh = 1/2 and balanced skill composition sk =
1/3, where sk = k/W .
4.4.2
Labor supply
At a free-mobility spatial equilibrium a worker must be indifferent about location irrespective of its
ethnicity and skill level. This is the case if she achieves the same level of indirect utility V kh is all
cities. Given the utility function (5) this requires
wkh + pXh = V kh pαY PXβ rk1−α−β
where
£
¤ 1
PX = φXH (pXH )1−γ + φXF (pXF )1−γ 1−γ
21
(30)
is the exact price index associated with (6) such that PX X = βI. Thus, by (14) and (17), we have
wkh = V
µ
¸1−α−β
¶β ∙
I
1 − α − β Ik
β
− pXh
X
α + β Tk
α
kh pY
where by (14) and (23), (26), (28) and (25) respectively:
pY SC
w0 E
=
α
α
γ
¸ γ−1
∙ 1
1
γ−1
γ−1
γ
γ
X = φXH H γ + φXH F γ
#
"
µ ¶ δ−1
µ ¶ γ−1
1
X
δ
γ
1
k
C
h
k
h
γ
βI i.e. Ik = sIk I
Ik = φkδ
αI +
φXh
C
X
h
h
γ−1
µ
¶
1
h γ I
γ
β
pXh = φXh
X
h
I =
wkh + pXh =
=
=
=
¸1−α−β
1 − α − β sIk
V
I 1−α
α + β Tk
¶1−α−β
¡ I ¢1−α−β
I 1−α
1−α−β
α β
V kh py β
sk
1−α−β
α+β
(X)β (Tk )
µ
¶1−α−β ¡ pY SC ¢1−α
¡ I ¢1−α−β
1−α−β
α β
α
V kh py β
sk
1−α−β
α+β
(X)β (Tk )
µ
¶1−α−β µ ¶1−α
¡ I ¢1−α−β
(SC)1−α
1−α−β
1
β
V kh py β
sk
1−α−β
α+β
α
(X)β (Tk )
α
kh py
µ
β
X
µ
¶β ∙
"
(SC)1−α
1
δ
αφk
1−α−β
(X)β (Tk )
µ ¶ γ−1
1
h γ SC
β
γ
− pY φXh
α
X
h
wkh = V kh B
µ
Ck
C
¶ δ−1
δ
+β
X
1
γ
φXh
h
µ
h
X
¶ γ−1
γ
kh
h
#1−α−β
(31)
where B is a positive constant
B ≡ py β
β
µ
1−α−β
α+β
¶1−α−β µ ¶1−α
1
α
Given the definitions of the composites C, Ck and h, (31) depicts the (inverse) supply of ethnicity
h with skill level k as a positive relationship between wkh and kh . For given kh , the schedule shifts
22
down if C increase as well as if X decreases, the reason being that the wage required to keep workers
is:
• positively affected by a proportionate inflow of all skills and ethnicities (larger C) as more
workers imply higher rents
• negatively affected by an increase in supply of ethnicities (by (6), larger X) as more workers
imply lower ethnic prices
5
Parametrization and Simulation
Summarizing the equilibrium conditions of the model we have the following variables: wages for each
type of native worker wHL , wHM , wHS price of each type of housing (land) rL , rM , rS price of each type
of ethnic good pXH , pXF and supply of each type of native workers HL , HM , HS .Their equilibrium
values solve the market-clearing conditions for the labor market for each skill in the production of
Y (3 conditions), the market clearing conditions for land of each type (3 conditions), the market
clearing conditions of goods XH and XF (2 conditions) and the free mobility of natives of each type
who equate the consumption wage between the location and the rest of the U.S. (3 conditions). We
consider the supply of foreign-born workers, FL , FM , FS as exogenous implicitly assuming that, due
to information constraints or strong preferences, they do not leave the state where they first moved.
As their initial location is largely driven by preferences, presence of family and specific opportunities
our exercise considers it as exogenous. This set-up allows us to think of inflow of new immigrants
as a pure ”supply” shock to labor supply, which is close in spirit to what we do when we estimate
empirically elasticities of wages and and house prices using the IV. Our simulation strategy proceeds
as follow. We first calculate the equilibrium values of wages, rents, local service prices and supply of
native individuals in each skill group assuming the distribution of foreign-born as in the average U.S.
state in 1990. Consistently with the empirical analysis we consider as ”low skill” those workers with
no degree, we consider as ”medium skills” those workers with a high school degree and we consider
as ”high skills” those workers with college degree or higher. We standardize the initial overall size
of the population in the economy to 1 and we calibrate the initial consumption wages for native
workers in each skill group, V kh , in order to match the supply of natives in the average state HL ,
HM , HS as of 1990. The distribution of natives and foreign-born by skill as of 1990 was as follows:
23
HL = 0.10, HM = 0.54, HS = 0.25 so that H = 0.89, and FL = 0.035, FM = 0.044, FS = 0.027 so
that F = 0.106.Similarly, in order to simulate the effect of immigration on the price of land and the
related income we assume that the land of each type (skill group) is owned by U.S. and foreing born
individuals in the same proportion as house ownership in the group (data from the census). Hence,
as the ownership rate in each group is higher among natives than among immigrants (see figure 4)
the share of land in each group assigned to natives is larger than their fraction in the population.
This assumption implies that the ownership of houses rented in each skill group mirror the ownership
of the other houses. Low skilled natives and foreign-born own houses in the low-skilled district
and rent them out to other low-skilled and to new immigrants in that skill group when they first
come. Following these assumptions as of 1990, 11% of the the stock of existing houses for low skilled
belonged to foreign-born (and 89% to natives), , 5% of medium skill-houses belonged to foreign born
(and 95% to natives) and 8% of the high-skilled houses belonged to foreign-owned and the remaining
92% of natives.
The parameter values required to simulate the model are obtained either directly from the literature or from simple calculations relative to the aggregate U.S. economy. We also provide several
robustness checks of our simulation results using different values for these parameters. Table 7 shows
the choice of parameters and the simulated effects of foreign immigration on average wages, rents and
incomes as described in the remaining of this section. The parameters of the utility function have
been obtained using the share of household expenditures on non-tradable service and housing. The
Consumer Expenditure Survey, available at Bureau of Labor Statistics (2005) allows us to calculate
the share of income spent on housing services by the average US family which would pin down the
parameters (1− α −β). Similarly, considering X as local services of food outside the house and entertainment, which we conservatively interpret as those local services in which ethnic diversity matter
most, we can obtain an estimate of β from the share in expenditures. . The share of expenditures
in housing services for the 1999-2002 period was close to 0.15. We choose 1 − α − β = 0.15 as a
base-value. As for the share of expenditures on local service X, we include expenditures for food in
restaurants, food in specialty shops, and entertainment. This share ranges between 0.15 and 0.20 of
the expenditures of the average U.S. household. We choose β = 0.15 as base-value and check the
robustness of results to β = 0.2. Table 7 and 8 also report the simulations when we eliminate the
local non-traded public service from consumption (Column IV, β = 0) and allow only for consump-
24
tion of tradable and housing. We use the range of estimates of substitutability between home and
foreign-born workers in production of Y consistent with the estimates of those parameters obtained
in Ottaviano and Peri (2006). We also re-estimate them using state data and the IV approach of
relative wages on relative supply of workers with the same schooling and different nativity (U.S. or
foreign). Some of the estimates are reported in Table 6 and range between 6.6 and 10. A third set
of estimates for these parameters is obtained in Peri (2006), specifically for the state of California.
Those estimates are mostly in the range between 3.3and 6.6. Hence we use 6.6 or 5 as values compatible with the existing estimates relative to the whole US as well as to single states . As for the
substitutability between the non-tradable services provided by the U.S. and foreign born, we assume
that it would be similar to the substitutability of natives and foreign-born in production of Y . Hence
we mostly use the value of 6.6 . Recall that the median elasticity of substitution between goods
within five-digit SITC sectors has been estimated by Weinstein and Broda (2004) as 4.7, our values
certainly fall on the high side of those estimates.1 Our choice of using a high elasticity limits the
importance of ethnic diversity in making a location attractive. Finally we use an elasticity of supply
of land of type L to population in the group equal to 0.4 calibrated to produce the best best fit for
the effect of immigration on price of houses of district L.
In the production of the traded good (??) we assume an elasticity between skill groups of δ =
2 which is consistent with most of the literature2 . The relative efficiencies of the factors (1/τ k )
are chosen to match the average U.S. wage premia in 1990 between education groups, given their
relative supplies and the elasticity of substitution δ. Standardizing the efficiency of low skilled
³ ´
native workers workers (τ L = 1) we can obtain the other values by using the formula: ln ττ Lk =
h ³ ´
³ ´i
wk
Ek
δ
1
ln
+
, where wk is the average national wage for native workers of education
ln
δ−1
wL
δ
EL
k, and Ek is the total supply of native workers of education group k. The relative efficiency of the
foreign born to U.S.-born both in any skill group and in the production of local services has been set
equal to 1.
Once we calculated the initial equilibrium relative to year 1990 as described above we let the
supply of foreign-born of each skill increase in percentage terms to match the actual inflow of foreignborn as experienced by the average U.S. state in the period 1990-2005. Such inflow is described by
the following changes in the foreign-born employment in the average U.S. state: ∆F/(F + H) = 0.11,
1
2
For instance a narrow SITC-5 digits category such as “cheese” has an elasticity of 4.5 among its varieties.
E.g. Katz and Murphy (1992), Hamermesh (1993), Angrist (1995), Ciccone and Peri (2005).
25
∆LF /(LF + LH ) = 0.28, ∆MF /(MF + MH ) = 0.082, ∆SF /(SF + SH ) = 0.11. After the exogenous
immigration shock we calculate the new values of wages, rents and prices that clear the local markets.
At first we do not impose the no-migration condition, but keep the supply of natives constant as
to obtain the effects with no native migration response. These are what we call impact effects of
immigration in Table 7. We also calculate and report the effect on impact to consumption wages
and total real income of natives. Then we evaluate the new equilibrium, reached when the supply of
U.S.-born workers in the state is adjusted so that the utility they enjoy in the state is the same as they
would enjoy anywhere else and when the supply of houses of type L is allowed to adjust to increased
population. Under the small economy assumption, the utility levels for natives who reside elsewhere
are kept constant at their initial values (V HL , V HM , V HS ). This completes the parametrization of
the model. In the next section we describe the results of this simulation.
5.1
Average Effects
Table 7 and 8 summarize the results of the simulations, over a small range of parameters values,
compatible with the empirical estimates. We performed many more robustness checks for somewhat
different values of the parameters. We do not report their results (usually not very different) but
we refer to them in the text. Table 7 reports the effects of immigration on average state variables
(wages, rents, prices, incomes) while Table 8 reports the effects on variables relative to each skill
group. The upper part of table 7 shows the choice of the key parameters which we already described
in section 5 above. The following two sections of Table 7 (labeled ”Long-Run elasticities” and ”Impact elasticities”) report the simulated long-run and impact effects of immigration on average wages,
house prices, employment and real total income of natives, respectively, expressed as elasticities. The
experiment consist in feeding to our model, calibrated to the 1990 initial conditions, the foreign-born
increase produced by immigration of the period 1990-2005 and evaluate the percentage changes of
averages in response of immigration that raises aggregate employment by 1%. The following two
sections of Table 7 (labeled ”long-run % effects of Immigration” and ”Impact % effects of Immigration”) report the same responses expressed as actual percentage point changes produced by the
1990-2005 immigration. The last column of table 7 reports, for comparison, the range of estimated
elasticities or percentage variations from section 3.1 above. Those are only relative to the variables
that were measurable in the empirical section, and provides a reference to see how well the model
26
explains the estimated effects. As we use decennial data in the empirical analysis we consider the
estimated effects as relative to the long-run. Considering Column (I), that uses an elasticity of substitution of 5 between native and foreign-born, we obtain that in the long-run an increase of foreign
born by 1% of employment increases wages of natives by 0.24%, on average. This positive effect is
due to the working of complementarities in production. At the same time that inflow of immigrants
produces and increase of housing prices equal to 1.1%. These two effects, relative to the long run,
accrue with the following dynamics: as immigrants flow in the state, average productivity of workers
increases and house price increases as well, as house supply is fixed in the short-run. Given our
model, the short-run impact on house prices and wages produces a small increase in average real
wage of natives (equal to 0.03% for immigration equal to 1% of employment). If workers are free to
move and assuming that they were in equilibrium in 1990 on average they will flow into the state to
take advantage of higher consumption wages, and the supply of houses of low skill, that is elastic,
increases to accommodate larger demand. Hence the new equilibrium is reached with immigration
of natives and more houses of the low-skill type. While real wages return to the initial level, as a
consequence of internal migrations, real income of natives (wages plus house income) increases as
land is now worth more. Housing income accrue to home-owners who are in larger part natives and
this accounts for their higher income. Three things must be noted. First, the impact effect on the
cost of housing affects native through two channels: first it increases the cost of living in the state,
second increases their house income (rent paid), if they own the house. The first effects hurt the
real income of natives, the second helps it as natives own houses in much larger percentage than
foreign-born. The second thing to note is that the simultaneous effects on wages and house prices
generate a very small impact on real wages (elasticity of 0.03, among the ”impact elasticities”). This
imply that the incentive to migrate are not changed by much before and after the immigration, and
small costs of migration could prevent it from happening. Keep in mind that real (consumption)
wage is the relevant variable to determine incentives to migrate, not real income. In fact the location
of the workers is independent of its house ownership and a worker can move out of the state and earn
higher real wage and still earn the house income by renting the owned house in the state while living
in a rented house out of the state. The third important fact to notice is that total income of natives
in real terms increases both on impact (elasticity of 0.20) and after the adjustment (0.41), hence
both the natives in the state preceding immigration and the new comers all enjoy, on average, gains
27
from those immigrants. To quantify the percentage effect, relative to the 1990-2005 immigration, we
see that in the long-run the average native’s wage increases by 2.6% due to immigrants, the value of
the average house by 12.0% and overall real income (house+wage) increased by 4.5%. The change in
real wage produced on impact by foreign-born was a small 0.4% of average real wages, hence most
of the real wage adjustment from immigration took place via higher cost of housing rather than via
migration.
The results reported in Column (II) simulated the economy assuming the σ elasticities equal
to 6.6 rather than 5. The main changes implied by this higher substitutability between native and
foreign-born is a smaller effect on wages and value of houses in the long-run, accompanies by a
small out-migration, rather than immigration of natives to the state. Again on impact, average real
wages of natives did not change much (decrease by 0.1%) so only a small group moved out of the
state. Again, both in the short and in the long-run real income of natives (wage+housing income)
increases by 1.5 and 1.2% respectively. Column (III) uses different elasticity for different groups,
allowing foreign-born workers to be more complementary to natives in the same skill group for the
high- and low-skilled (σ = 5) than for the medium skilled (σ = 6.6).The effects of immigration on
the average wages, prices and incomes in this case are intermediate between case (I) and (II) and
this configuration of the parameters helps explain the distribution of effects across skills (see Table 8
and section 5.2 below). Finally specification (IV) shows that most of the effects are very similar even
eliminating the local service from the utility function. The impact of immigration on wages, house
prices and income levels operates in large part through the labor and housing markets, rather than
through the effect on local prices via the good X.
Comparing the simulated elasticities to the estimated ones we can say that our model does a good
job in explaining the effect of immigration on housing prices: the simulated elasticities, between 0.8
and 1.1, are even somewhat higher than the estimated ones, often between 0.6 and 0.8 when we
use rent (but larger when we use house prices). It explains between 50 and 70% of the average
wage effect implying that we can explain using this ”complementarity” story the bulk of the average
wage effects estimated in section 3.1 but not quite all of them. Finally the simulations produce
migration responses of natives that are around 0, and not large in absolute value, consistent with
the insignificant effects estimated on US state data. The impact effect of immigrants, while large on
wages and house values, is not large on real wages (increased by production complementarities, but
28
hurt by the increase in rents) and therefore does not seem to stimulate large migratory responses.
5.2
Effects by Skill
Table 8 decomposes the effects of immigration on wages, house prices and income of natives in
different skill groups. We report the long-run elasticity of wages and house prices to immigration
and the percentage effect on real income (wage + house income) as well as the short-run effects
on real wages and real income. The first six rows present elasticities that can be directly compared
to our estimated ones (whose range is reported in the last column of the table). Specifications (I)
to (IV) mirror those of Table 7 in that they use the same parameter combinations. While there is
some variation across specifications the main feature of the simulations are similar. In terms of wages
the simulation reproduces fairly well the elasticity of Low Skills and Medium Skills to immigrants of
their own group. The first is close to 0 and the second between 0.2 and 0.3. The elasticity of wages
of high skills is about half of what should be, although given the standard errors of the empirical
estimates one cannot reject a value around 0.2 for the empirical estimates (which is the simulated
value). On the other hand the house price elasticities are all within (or very close to) the ranges of the
empirical point estimates, usually in the ”high part” of the range. So the only imperfect match of the
model concerns the wage of highly skilled and that may also explain the somewhat smaller average
wage elasticity generated by the model (as see in Table 7). The increased supply of highly educated
immigrants (College and plus) seems to benefit productivity of natives more than our model, based
on pure complementarities, would imply. It is plausible that highly skilled immigrants may generate
productive externalities affecting technological adoption or innovation, and having a particularly large
beneficial effect on highly skilled native workers. One author has used immigration of highly educated
workers in a previous paper to estimate skill-biased externalities of human capital (Iranzo and Peri,
2006) that turned out to be quite large. Even somewhat understating the positive wage effects of
highly educated immigrants our model does a good job in matching the effects on wages and house
prices. Hence it is very interesting to see that the model implies that in the long run, natives of any
skill group experienced a significant increase in their total real income (house plus wage) as shown
in the section of Table 8 entitled ”Long-run % effects of Immigration”. We see that, considering
for instance the simulation reported in column I, each group has a positive increase in real income,
which is due to several effects. First complementarity of foreign-born increases productivity of each
29
group of native workers, second the increase in housing prices increases the local price level but also
the local income from housing. On impact (see the section of the table entitled ”Impact % effects
of immigration”) these changes decrease the real wages of low and high skills and increase the real
wage of Medium skills. This induces out-migration of the two extreme skill groups and immigration
of native in the intermediate group. This migration re-establish the equality of real wages for each
skill group with the rest of the country and increases the real income of the two extreme groups
further, as now their wages are higher (some workers moved out). Notice, however, that also for
the two groups who migrated out (low and high skills) the initial total effect of immigration on real
income was positive. This is because the increased value of their house and rent income compensated
for their lower real wage. Hence the fact that they move out of the state is not a sign that their
income has been ”hurt” by immigration but that immigrants by increasing the value/income of their
real estate gave them the opportunity of increasing utility further by moving to a low-cost state.
Very interestingly the simulation by skill shows that each single group’s total income is increased on
impact as well as after the adjustment because of immigrants. At the same time (see rows 10 to
12) even for the group whose real wage is mostly hurt on impact (mainly because of the effect on
house-prices) which is the low-skill group the real wage loss is never larger than 2.6% (except for
column IV, which would imply a very large out-migration of low skilled natives with elasticity of 0.6
incompatible with the much smaller estimates). This implies that each individual household would
have small incentives to migrate in order to cash their real wage increase and even if they did not
they would still enjoy the higher overall real income relative to the pre-migration equilibrium. On
impact the highest real gain is for the group of intermediate skills, while in the long run the low-skills
who stay experience the highest gain because of the outflow of some of them which would further
increase their productivity and moderate the cost of housing.
6
Welfare Analysis
While our simulation is essentially an exercise of comparative statics, between an equilibrium before
immigration, the short-run effect of immigration and its long-run effect, we believe that we can
draw at least three new and interesting implications from this analysis on the welfare of natives and
specifically on the group of least skilled (poorest) natives. This group has attracted most of the
30
attention in the analysis of immigration (Borjas 2003, Borjas 2006) and the negative (relative) wage
effects that it has experienced in the recent decades have often been attributed at least in part to
immigration. This analysis for the first time consider a much more complete aspect of the welfare
of individuals, accounting for the total income they receive from work and house ownership (by far
the largest form of asset ownership among Americans) and for the costs of living they face in the
state of residence. Immigration turns out to have three effects on those workers. 1) For reasonable
estimates of the complementarity between U.S. and foreign-born workers, immigrants have a small
(negative) effect on wages of unskilled natives. This results from a negative effect through the increase
in relative supply of unskilled workers partly compensated by the complementarities within skill due
to different jobs/occupations between immigrants and natives. 2) Unskilled immigrants increase the
demand for housing in the same types of neighborhoods as unskilled natives. This increases the cost
of housing for natives, and decreases their real wages 3) Among all skill groups, including the group
of low-skilled workers, house ownership rates are much higher for natives than for foreign-born. This
implies that the increased house value is much less of a cost for natives than for other immigrants.
Who owns houses experiences an increase in income, through higher equity value (rental services) of
their house, as well as through the possibility of renting/selling part of the house to foreign-born.
The three effects described above act together in the short run, and in the long run they also interact
with the migration decision of natives.
While confirming that the relative wages of low skilled are not helped by immigration, our model
shows that nominal wages of workers with no degree still rise in the long run in response to immigration, just not as much those of high school or college graduates. Second, their real income inclusive of
housing income is not decreased in the short run and is increased in the long-run by immigration. The
simulated long-run effects on real income of unskilled (around +5%) could be unrealistically high,
due to our house-ownership assumption. If unskilled natives do not own all the houses rented to
other unskilled then part of those gains should go to the other groups. It is however likely, that they
would stay among natives as our assumption on ownership of rented houses is overall conservative in
attributing only a share to natives, when it may be true that most of the rented houses are owned
by natives. Finally, even considering consumption wages only and focussing on the ”impact effect”
of immigration we see that the most reasonable estimates put the loss of unskilled workers around
2.5%, while high school graduates gain 1% of their real wage. These are small numbers and unlikely
31
to trigger any relevant internal migratory response. The model, in presence of small costs of moving
would explain why, even when concentrated among less skilled, immigration has not triggered any
relevant response of natives in the form of internal migration.
7
Conclusions
This paper revisits the so called ”area analysis” approach to immigration in a number of ways. First
it extends our considerations from the labor market only to the housing market and the migratory
response of natives. Second it proposes a general equilibrium integrated approach to understanding
the effects of immigrants on wages, prices and rents for the average individual as well as for individual
in each skill group. Third it allows a more accurate and enhanced welfare analysis of immigration on
US natives. Usually the simple wage effects are considered while this piece, by defining real wages
and total real income of individuals, accounts for the local price effects and house ownership on
individual income. Fourth we are careful to combine a regression approach that identifies empirically
a set of elasticities that characterize the impact of immigration on wages and prices and a simulation
approach that consider a simple model of rational native agents responding to changes in skill supplies
due to immigration and we analyze the predicted variations of wages and prices between equilibria
before and after immigration. The results that we obtain are new mainly in two aspects. First we
document empirically and explain theoretically the existence of a strong positive correlation between
immigration and average wages and housing prices for natives. These positive effects coexist with a
negative partial elasticity of native wages to immigration within each skill group (as estimated by
the standard labor literature). The positive effects are qualitatively and quantitatively accounted
for by a moderate degree of complementarity in production between immigrants and natives and by
the sensitivity of housing prices to local crowding and income. Second, we show with our model
that accounting for the wages and income effects not only the average native individual but each
group of natives (by skill) is better off after immigration both in the short and in the long run. This
is true also for the group of low skilled workers who experiences a small negative wage effect from
immigrants because the housing price effect is positive for them too and this, combined with the
higher house ownership rates of natives produces a ”transfer” from immigrants (who occupy rented
houses) to natives (who own the house they occupy). Clearly we have used average numbers and rates
32
to obtain these results. For those native individuals who have no education and do not own their
house or any equities in housing of their type, both wage and housing prices effect from the inflow of
immigrants will go in the negative direction, at least on impact. However, for each one of them there
are several more natives in the same unskilled group for which the housing effect would go in the
positive direction. Our article show that, far from being uninformative, state data on immigration,
wages and house rents could be combined to estimate the welfare effects of immigration on natives
comprehensively and precisely.
33
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34
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36
Figures and Tables
Figure 1
Changes in Average Wage of U.S. Natives and Immigration.
U.S. states, decade changes 1970-2000 and 2000-2005.
Change in real wages of Natives and immigration
% change of wage, U.S. born
.227086
Slope: 0.45 (0.10),
R2: 0.10
-.234835
-.073888
.123779
% change empl, immigrants
Notes: The units of observation are the 50 U.S. states and D.C. during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005 for a total
of 204 observations. The vertical axis measures the percentage change in average weekly wage in constant 2000 U.S. $, for U.S. born
males, 17 to 65 years of age, cleaned of a common period-specific average. The horizontal axis measures the change in foreign-born
employment as percentage of initial total employment cleaned of the common period-specific average.
37
Figure 2
Changes in the Median Rent of U.S. Natives and Immigration
U.S. states, decade changes 1970-2000 and 2000-2005.
Change in real wages of Natives and immigration
% change of wage, U.S. born
.227086
Slope: 0.80 (0.16),
R2=0.12
-.234835
.123779
-.073888
% change empl, immigrants
Notes: The units of observation are the 50 U.S. states and D.C. during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005 for a
total of 204 observations. The vertical axis measures the percentage change in rent per room in constant 2000 U.S. $, for U.S. born
head of households, cleaned of a common period-specific average. The horizontal axis measures the change in foreign-born
population as percentage of initial total employment cleaned of the common period-specific average.
38
Figure 3:
Net Immigration (1990-2005) as share of the 1990 population in the group: three education groups.
Immigration 1990-2005 by skill as share of group
0.350
High school dropouts
0.308
High School Graduates
0.300
College Graduates
0.250
0.224
0.214
share
0.200
0.156
0.150
0.134
0.123
0.156
0.126
0.111
0.098
0.100
0.070
0.060
0.050
0.000
USA
California
Texas
New Jersey
State
Notes: Each bar of the histogram represents the change in foreign-born workers by education group (net immigration) during the
1990-2005 period as percentage of the total employment in the group.
39
Figure 4:
Ownership of Residential Space, 1990
Share of families that own their house, 1990, native and foreign-born
0.8
US born
Foreign-born
0.7
percentage owned
0.6
0.5
0.4
0.3
0.2
0.1
0
High School Dropouts
High School Graduates
College Graduates
education of head of household
40
Table 1
Estimates of the elasticity of average wage of natives to immigration,
Panel of U.S. States plus D.C.: 1970-80, 1980-90, 1990-2000 and 2000-2005 changes
γwage
Specification
Samlple
1
Male Only
OLS, controlling for change in
native employment
IV, Imputed supply-driven
immigrants as instrument
First Stage Coefficient
and
F-test
0.45**
(0.10)
0.35**
(0.16)
0.47**
(0.09)
26.65
OLS, controlling for change in
native employment
IV, Imputed supply-driven
immigrants as instrument
First Stage Coefficient
and
F-test
Observation
0.53**
(0.11)
0.51**
(0.27)
0.18**
(0.03)
22.7
204
Weekly Wages
2
All Workers
Whole State
0.51**
(0.10)
0.34**
(0.16)
0.47**
(0.09)
26.65
Metropolitan Areas Only
0.56**
(0.12)
0.56**
(0.21)
0.16**
(0.03)
22.4
204
Yearly Wages
3
Male Only
4
All Workers
0.45**
(0.11)
0.43**
(0.10)
0.47**
(0.09)
26.65
0.49**
(0.09)
0.42**
(0.20)
0.47**
(0.09)
26.65
0.55**
(0.10)
0.44*
(0.19)
0.18**
(0.03)
22.7
204
0.57**
(0.11)
0.56**
(0.27)
0.16**
(0.03)
22.4
204
Notes: Units of observation: 50 U.S. states plus D.C during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005. Observations
are weighted for the employment of that cell in each regression. Dependent Variable: percentage change in the real (CPI deflated)
average wage of natives, between 17 and 65 years of age. Explanatory Variable: change of foreign-born employment as percentage
of initial employment in the state. All regressions include period fixed effects. The OLS estimates control for the change in native
employment as percentage of total initial employment. The IV estimates use as instruments the imputed change in foreign-born
population 17-65 as percentage of initial population in the age-range. Method to construct imputed foreign-born population changes
by state is described in the main text. The top three rows include workers in the whole state while those in the bottom three rows
include only workers in metropolitan areas of each state. Each coefficient results from a separate estimation. In Parenthesis we
report heteroskedasitcity-robust standard errors.
41
Table 2
Estimates of the elasticity of Rent/House Value of natives to immigration,
U.S. States plus D.C.: 1970-80, 1980-90, 1990-2000 and 2000-2005 changes
γhouse price
Specification
Measure of Dependent Variable:
OLS, controlling for change in native
population
IV, Imputed supply-driven immigrants
as instrument
First Stage Coefficient
and
F-test
OLS, controlling for change in native
population
IV, Imputed supply-driven immigrants
as instrument
First Stage Coefficient
and
F-test
Observation
Dependent Variable: Rent per room
1
Average
2
Median
Whole State
0.60**
0.80**
(0.18)
(0.16)
0.64**
0.67**
(0.15)
(0.11)
0.47**
0.47**
(0.09)
(0.09)
26.65
26.65
Metropolitan Areas Only
0.76**
0.70**
(0.18)
(0.14)
0.81*
0.75*
(0.24)
(0.19)
0.16**
0.16**
(0.03)
(0.03)
22.4
22.4
204
204
Dependent Variable:
Housing Price per room
3
4
Average
Median
0.82
(0.49)
0.65
(0.42)
0.47**
(0.09)
26.65
0.64
(0.44)
1.80
(1.02)
0.47**
(0.09)
26.65
1.5**
(0.42)
2.2*
(0.96)
0.16**
(0.03)
22.4
204
1.3*
(0.72)
2.4*
(1.2)
0.16**
(0.03)
22.4
204
Notes: Unit of observation: 50 U.S. states plus D.C during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005. Observations are
weighted for the employment in that cell in each regression. Dependent Variable: percentage change in the real (CPI deflated) median/average
rent per room or real median/average house price of native head of households, between 17 and 65 years of age. Explanatory Variable: change
of foreign-born population as percentage of initial population in the state (age 17-65). The OLS estimates control for the change in native
population as percentage of total initial population. The IV estimates use as instruments the imputed change in foreign-born population 17-65
as percentage of initial population in the age-range. Method to construct imputed foreign-born population changes by state is described in the
main text. The top three rows include workers in the whole state, those in the bottom three rows include only workers in metropolitan areas of
each state. Each coefficient results from a separate estimation. In Parenthesis we report heteroskedasitcity-robust standard errors.
42
Table 3
Estimates of the elasticity of U.S. born Population/Employment of natives to immigration
U.S. States plus D.C.: 1970-80, 1980-90, 1990-2000 and 2000-2005 changes
Specification
1
2
3
IV
1970-2005
-0.37
(0.26)
-0.39
(0.27)
0.50**
(0.10)
26.3
204
IV
1970-2000
-0.35
(0.24)
-0.38
(0.27)
0.55*
(0.09)
36
153
Whole State
Population
Employment
Fist stage IV,
Coefficient
F-test
Observations
OLS
1970-2005
0.57*
(0.44)
0.38*
(0.20)
Not applicable
204
Notes: Unit of observation: 50 U.S. states plus D.C during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005.
Observations are weighted for the employment in that cell in each regression. Dependent variable: Change in population
(employment) of natives between 17 and 65 years as percentage of initial total population (employment) in the state.
Explanatory Variable: change in population (employment) of foreign-born between 17 and 65 as percentage of initial
population (employment) in the state. The IV estimates use as instruments the imputed change in foreign-born population 1765 as percentage of initial population in the age-range. Method to construct imputed foreign-born population changes by state
is described in the main text. Each coefficient results from a separate estimation. In Parenthesis we report heteroskedasitcityrobust standard errors.
43
Table 4
Estimates of the elasticity of Rent/House Value of natives to immigration,
Separated by skill of residents
U.S. States plus D.C.: 1970-80, 1980-90, 1990-2000 and 2000-2005 changes
Specification
Group, by Education
Median Housing price per room
OLS
Median rent per room
OLS
Median rent per room
IV
First Stage
Coefficient and F-test
Median rent per room
OLS
Median Housing price per room
IV
Median rent per room
IV
First Stage
Coefficient and F-test
Observation
1
2
Low Education
Medium Education
(High School Dropouts)
(High School Graduates)
Metropolitan Areas Only
0.15
1.9*
(0.50)
(0.9)
0.30
0.90**
(0.20)
(0.30)
0.14
0.87
(0.37)
(0.66)
0.23**
0.09**
(0.04)
(0.01)
32
28
Whole State
0.24
0.52
(0.37)
(0.60)
0.29
1.55**
(0.29)
(0.96)
0.24
0.62*
(0.37)
(0.70)
0.63**
0.31**
(0.03)
(0.07)
351
19
204
204
3
High Education
(College Graduates)
1.2
(0.7)
0.87**
(0.44)
2.3**
(1.1)
0.15**
(0.7)
4.7
1.21**
(0.37)
1.87**
(0.69)
1.1**
(0.37)
0.70**
(0.27)
7.8
204
Notes: Unit of observation: 50 U.S. states plus D.C during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005. Observations are
weighted for the employment in that cell in each regression. Dependent Variable: yearly percentage change in the median real rent per room or
real median rent of native head of households, between 17 and 65 years of age, with schooling as in the column header. Explanatory Variable:
change of foreign-born population as percentage of initial population in the state and in the education group (age 17-65). The OLS estimates
control for the change in native population in the education group as percentage of total initial population in the group. The IV estimates use as
instruments the imputed change in foreign-born population 17-65 in the education group as percentage of initial population in the age-range.
Method to construct imputed foreign-born population changes by state is described in the main text. The top three rows include workers in the
whole state, those in the bottom three rows include only workers in metropolitan areas of each state. Each coefficient results from a separate
estimation. In Parenthesis we report heteroskedasitcity-robust standard errors.
44
Table 5
Estimates of the elasticity of Wages of natives to immigration,
Separated by skill of worker
U.S. States plus D.C.: 1970-80, 1980-90, 1990-2000 and 2000-2005 changes
Specification
Method:
IV, weekly wages All US born
workers
IV, weekly wages males, US born
workers
First Stage
Coefficient and F-test
Observation
1
Low Education
Whole State
-0.10
(0.11)
-0.08
(0.09)
0.64**
(0.18)
11
204
2
Medium Education
3
High Education
0.20**
(0.09)
0.23**
(0.11)
0.29**
(0.05)
25
204
0.50**
(0.20)
0.42**
(0.20)
0.67**
(0.15)
19
204
Notes: Unit of observation: 50 U.S. states plus D.C during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005. Observations
are weighted for the employment of that cell in each regression. Dependent Variable: yearly percentage change in the average wage
of natives, between 17 and 65 years of age, with schooling as in the column header. Explanatory Variable: change of foreign-born
employment as percentage of initial employment in the state and schooling group as in the header. All regressions include period
fixed effects. The IV estimates use as instruments the imputed change in foreign-born population 17-65 in a schooling group as
percentage of initial population in the education-state group. Method to construct imputed foreign-born population changes by state
is described in the main text. Each coefficient results from a separate estimation. In Parenthesis we report heteroskedasitcity-robust
standard errors.
45
Table 6
Estimates of Relative wage elasticity of U.S.- and Foreign-born workers,
(inverse of the elasticity of substitution)
U.S. states, 1960-2005
Estimates of 1/σ
1: Yearly Wages
2: Weekly wages
Ordinary Least Squares
Whole Sample
Omitting 2005
0.14**
0.14**
(0.02)
(0.02)
0.11**
0.10**
(0.02)
(0.02)
2 Stage Least Squares
Whole Sample
Omitting 2005
0.15**
0.15
(0.03)
(0.04)
0.12**
0.09**
(0.04)
(0.04)
Notes: Unit of observation: 50 U.S. states plus D.C during the periods 1970-80, 1980-90, 1990-2000 and 2000-2005.
Observations are weighted for the employment of that cell in each regression. Dependent Variable: logarithm of relative
wage of natives/foreign-born, between 17 and 65 years of age, in an education group. Explanatory Variable: logarithm of
relative employment foreign-born/natives. All regressions include state by year fixed effects. The IV estimates use as
instruments the imputed foreign-born population 17-65 in a schooling group. Method to construct imputed foreign-born
population changes by state is described in the main text. Each coefficient results from a separate estimation. In
Parenthesis we report heteroskedasitcity-robust standard errors clustered by state-year.
46
Table 7
Simulated Immediate and Long-Run Average Impact of Immigration:
Elasticity of Wages, Housing Values and population of natives
(I)
(II)
(III)
Parameter Values
0.15
0.15
0.15
0.15
0.15
0.15
(IV)
1-α- β (share spent in housing)
0.15
0
β (share spent in entertainmentfood)
6.6
6.6
6.6
γ (elasticity of substitution ethnic 6.6
goods)
2
2
2
2
δ (elasticity of substitution
education groups)
5
6.6
5
6.6
σL
5
6.6
6.6
6.6
σM
5
6.6
5
6.6
σS
Long-run Elasticities, (perfect migration of natives)
0.24
0.20
0.21
0.21
γwage natives
1.10
0.79
1.02
0.82
γhouse price natives
0.25
-0.06
0.15
-0.03
γ employment natives
0.41
0.11
0.`18
0.16
γ real income (workers + house owners)
Impact Elasticities, (no migration of natives)
0.22
0.15
0.18
0.16
γwage natives
1.24
1.14
1.19
1.14
γhouse price natives
0
0
0
0
γpopulation/employment natives
0.03
-0.02
0.02
-0.01
γreal wage: incentives to migrate
0.20
0.14
0.18
0.15
γreal income (workers + house owners)
long-run % effects of Immigration, 1990-2005 period
Average Wage of Natives
2.6%
2.2%
2.4%
2.3%
Average House Price, Natives
12.0%
8.7%
11.4%
9.1%
Total Employment, Natives
2.7%
-0.6%
1.7%
-0.3%
Average Real Income
4.5%
1.2%
2.0%
1.7%
(workers + house owners)
Impact % effects of Immigration, 1990-2005 period
Wage of Natives
2.4%
1.6%
2.1%
1.7%
House Price, Natives
13.7%
12.6%
13.2%
12.6%
Total Employment, Natives
0
0
0
0
Consumption Wage Natives
0.4%
-0.1%
0.26%
-0.05%
Average Real Income
2.2%
1.5%
2.0%
1.6%
(workers + house owners)
Range of the
point-Estimates
0.15-0.2
0.15-0.2
Around 6
Around 2
5 to 6.6
5 to 6.6
5 to 6.6
0.34 to 0.56
0.60 to 0.81
-0.35 to 0.38
N/A
N/A
N/A
N/A
N/A
N/A
3.7% to 6.2%
6.7% to 9%
-3.8 %to 4.2%
N/A
N/A
N/A
N/A
N/A
N/A
Note: Total immigration in the 1990-2005 period: ΔF/(F+H)=11.1%, distributed as ΔLF/(LF+LH)=28.1%,
ΔMF/(MF+MH)=8.2%, ΔSF/(SF+SH)=11.3%. Simulations are described in the Main text. The elasticities are relative
to the percentage change in the group due to immigration.
47
Table 8
Simulated Immediate and Long-Run Impact of Immigration by skill:
Elasticity of Wages, Housing Values and population of natives
(I)
(II)
(III)
(IV)
Parameter Values
Long-run Elasticities, (perfect migration of natives)
0.07
0.03
0.05
0.03
γwage natives Low Skills
0.28
0.21
0.24
0.22
γwage natives Medium Skills
0.23
0.17
0.20
0.17
γwage natives High Skills
0.45
0.31
0.39
0.45
γhouse price natives Low Skills
1.9
1.5
1.7
1.9
γhouse price natives Medium Skills
1.5
1.1
1.4
1.5
γhouse price natives High Skills
long-run % effects of Immigration, 1990-2005 period
4.72
5.35
5.04
4.92
Real Income Low Skills
Real Income Medium Skills
1.39
1.42
1.37
1.43
Real Income High Skills
1.94
2.02
1.98
2.01
Impact % effects of Immigration, 1990-2005 period
-1.89
-2.62
-2.20
-3.99
Real Wages Low Skills
Real Wages Medium Skills
0.94
0.47
0.75
0.62
Real Wages High Skills
-0.18
-0.75
-0.24
-0.77
2.17
1.71
2.02
0.00
Real Income Low Skills
Real Income Medium Skills
2.46
1.93
2.21
2.10
Real Income High Skills
1.81
1.18
1.76
1.17
Range of the
Point Estimates
-0.08 to -0.10
0.20 to 0.23**
0.42 to 0.50**
0.15 to 0.30
0.62 to 1.90**
0.87 to1.87**
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Note: Total immigration in the 1990-2005 period: ΔF/(F+H)=11.1%, distributed as ΔFL(FL+HL)=28.1%,
ΔFM(FM+HM)=8.2%, ΔFS(FS+HS)=11.3%. Simulations are described in the Main text.
48
49