Immigration and Spatial Equilibrium:
the Role of Expenditures in the Country of Origin
Christoph Albert1 and Joan Monras∗2
1
2

CEMFI

Universitat Pompeu Fabra, Barcelona GSE, and CEPR
September 30, 2019

Abstract
This paper investigates the spatial distribution of immigrants across US cities. We document that (a)immigrants concentrate in large, expensive cities, (b) the earnings gap between natives and immigrants
is larger in these cities, (c) these patterns are stronger when price levels in the country of origin are lower,and (d) immigrants consume less locally than natives. We develop a spatial equilibrium model in which
immigrants spend a fraction of their income in their countries of origin. Thus, immigrants care not only
about local prices but also about price levels in their home countries, which gives them a comparativeadvantage for living in more productive cities, where nominal earnings are higher and where they accept
lower wages than natives. We rely on arguably exogenous variation in real exchange rates to estimate themodel. Counterfactual simulations suggest that immigrants’ location choices reduce economic activity
in smaller, less productive cities, while they expand it in larger, more productive ones. Due to these
distributional effects, the model predicts that current levels of immigration lead to 1.3% higher worker
productivity and 0.6% higher welfare.
JEL Categories: F22, J31, J61, R11.
Keywords: Immigration, location choices, spatial equilibrium.

∗ Correspondence: jm3364@gmail.com. We are grateful to David Albouy, Paula Bustos, Donald Davis, Albrecht Glitz,
Stephan Heblich, Emeric Henry, Ethan Lewis, Melanie Morten, Florian Oswald, Fernando Parro, Diego Puga, and Jorge dela Roca for their insightful comments and to the audiences at the NBER SI ITI and URB/RE, CEPR-CURE and a numberof seminars and conferences for their useful questions, discussions, and encouragement. We also thank the insightful research
assistance of Micole De Vera and Ana Moreno. Monras thankfully acknowledges the funding received from the Fundación
Ramon Areces. All errors are ours. This paper previously circulated with the title “Immigrants’ Residential Choices and theirConsequences”.

1

1

Introduction

There are fundamentally two theories explaining immigrants’ location choices. First, it is well known
that immigrants tend to move to cities or regions that are thriving. One reading of this evidence isthat immigrants may be particularly important for “greasing the wheels” of the labor market since they
arbitrage away opportunities across locations – explored theoretically in Borjas (2001) and empiricallyin Cadena and Kovak (2016). This observation has had a profound influence on the literature that
estimates the effects of immigration on labor market outcomes. Many papers have compared high- to
low-immigration regions to try to infer the causal effect of immigration on outcomes of interest. However,
if immigrants’ primary motive for choosing particular cities or regions is that those areas are thriving,then there is a spurious correlation between labor market outcomes and immigrant settlement patterns.
Second, and in part as a solution to the aforementioned endogeneity concerns, many authors emphasizethat immigrants tend to move where previous immigrants settled (Munshi 2003). Former immigrants help
newer ones both in migrating and in finding jobs and suitable neighborhoods for their new life in the hostcountry. This idea has been the basis for the networks instrument, the most widely used instrument in
the migration literature (Altonji and Card 1991). Simply stated, past stocks of immigrants are usually agood predictor of future flows, which, in the absence of serially correlated outcomes, provides exogenous
regional variation in immigrant inflows. The widespread use of this instrument – despite numerous
criticisms (Borjas et al. 1996; Jaeger et al. 2018; Goldsmith-Pinkham et al. 2018; Adao et al. 2018;
Borusyak et al. 2018) – highlights the importance of understanding immigrant location choices within
host economies.
In this paper, we provide a completely new look at immigrants’ location choices, which we argue has
important implications for host economies and for our understanding of the incentives driving immigrants’settlement patterns. Migrants tend to spend large fractions of their income in their home country. Many
send remittances to their families, plan on returning, or simply spend their leisure time at home.1 Thismeans that they care not only about the prices in the location where they live but also about the prices
in their home countries. We argue that immigrants’ expenditure in the country of origin profoundly
shapes their residential choices and wages, which, in turn, affects the distribution of economic activity
across locations and the general equilibrium in the host economy.
In the first part of the paper, we use a number of different data sets to document four cross-sectional
empirical regularities using data on metropolitan statistical areas in the United States.2 First, we reportthat immigrants concentrate disproportionately in large and expensive cities, where, as it is well known
in the urban economics literature, nominal wages and productivity tend to be higher (Combes andGobillon 2014; Glaeser 2008). Second, the gap in earnings between natives and immigrants is larger inthese cities, even when we consider wage gaps within narrowly defined skill cells and when we control fornative-immigrant imperfect substitutability following Ottaviano and Peri (2012). Third, we show that
1 Dustmann and Mestres (2010) document that immigrants in Germany remit around 10% of their income. The literatureon temporary migrations, summarized in Dustmann and Gorlach (2016), takes into account that expenditures in the homecountry influences immigrants experience, but previous papers do not analyze how this shapes the spatial equilibrium in thehost country.
2 In particular we use data from the US Census, the American Community Survey (ACS), the Consumer Expenditure Survey,
the Matricula Consular, the New Immigrant Survey, and the World Bank’s International Comparison Program database.

2there is significant heterogeneity across immigrant groups both in location choices and relative wages.
We use cross-origin and arguably exogenous within-origin variation in real exchange rates to documentthat when real exchange rates are lower, immigrants’ concentration in expensive cities is stronger andthe gap in wages between natives and immigrants is higher. We then use data of state-to-state migration
flows from Mexico to the United States to show that Mexican immigrants from poorer states, where
presumably price levels are lower, tend to disproportionately migrate to the richest and most expensive
states in the United States. Using variation in years since arrival and plausibly exogenous variation inlegal status due to the Immigration Reform and Control Act of 1986, we also show that the patterns are
weaker for immigrants that are likely to be more attached to the US and, hence, more similar to natives.
Finally, we provide evidence that immigrants consume less locally than natives by comparing housing
and total expenditures of otherwise comparable native and immigrant households within locations.
In the second part of the paper, we explain these four strong empirical regularities with a spatial
equilibrium model, in which immigrants’ location choices are influenced by price differences between
host and origin country. When a part of immigrants’ consumption is related to their country of origin,
they have strong incentives to settle in locations with high nominal prices and wages. All else being equal,a native may be indifferent between one location and an alternative one that is twice as expensive as longas wages are also twice as high. However, immigrants’ smaller share of local consumption implies thatthey have incentives to live in the high-wage, high-price city. As a consequence, immigrants concentrate
in expensive cities and, if wages partly reflect the value of living in a city – which is the case in noncompetitive labor markets – the native-immigrant wage gap is higher in these locations.3 Some degreeof substitutability between home and local goods allows this mechanism to be stronger for immigrants
coming from cheaper countries, which is in line with the data both when we compare location and wage
patterns across countries of origin and when we relate them to real exchange rates.
To assess the economic importance of the role of expenditures in the home country, in the thirdpart of the paper we estimate the key parameters of our model using variation in immigrants’ origin
countries across metropolitan areas. Intuitively, the model estimates the share of total expenditures
immigrants spend on home country goods and the degree of substitution between consuming locally andat home that rationalizes the higher concentration of immigrants and the larger wage gap to natives
in expensive cities as well as the heterogeneity in these relationships across immigrants from different
origins. We complement these estimates with parameters from prior literature to perform quantitative
exercises. Specifically, we rely on Albouy (2016), Combes and Gobillon (2014), and Saiz (2010). Our
baseline estimates, which are obtained using only labor market data, imply that immigrants’ average
share of total expenditure in the home country is around 21% and the elasticity of substitution between
consuming locally and in the country of origin is around 1.61.4 We validate our estimation by showingthat the model performs well at predicting a range of non-targeted moments. In particular, we compare
3 In order to obtain this result, wage differences between workers cannot be competed away. This means that we depart fromstandard perfectly competitive models of the labor market and instead consider wage bargaining. See Becker (1957) and Black(1995).
4 We also analyze the sensitivity of this estimate to the parameters we borrow from the literature. Using a large number ofalternatives, we obtain a range of estimates for the average share of consumption in the origin country between 15% and 25%.
The range of estimates that we find in our sensitivity analysis for the elasticity of substitution between consuming locally andin the country of origin goes from 1.5 to 2.5.

3the model predictions on labor market outcomes and on consumption by origin country with the patterns
in the data.
We then use the estimated model to compute two counterfactuals that highlight the importance oftaking into account that immigrants spend part of their income in their countries of origin. Specifically,
we explore how a native-induced and an immigrant-induced population increase of 20% would change
the distribution of economic activity and aggregate outcomes in our model. We then compare these twosimulations to assess the role of immigration in shaping the spatial equilibrium. Our main finding isthat there is a significant redistribution of economic activity from small, unproductive cities to large,
productive ones as a consequence of immigration.5 We show that low-productivity cities are around
20% smaller, while those with high productivity are around 30% larger when the increase in population
is induced by immigrants as opposed to natives. This movement of economic activity towards moreproductive locations has aggregate implications as it leads to a rise in the average productivity of workers
by around 1.3%.
We conclude our analysis by exploring how immigrants’ consumption and location choices affectnative workers’ welfare. First, the expansion of the population in more productive locations induces anincrease in average productivity. Second, immigration affects local consumption of non-tradables throughtwo channels. On the one hand, given that part of what immigrants earn is spent in their countries oforigin, each immigrant household (relative to a similar-looking native household) tends to have a lower
demand for local non-tradable goods and, hence, increases their prices by less than natives, which is
positive for native workers’ welfare. On the other hand, immigrants disproportionally concentrate inhighly productive locations, where prices of non-tradables rise due to the higher aggregate demand.
Thus, natives are priced out into less productive locations. Combining all these forces, we estimate thatnative workers’ welfare is around 0.6% higher as a consequence of immigrants’ consumption behavior andlocation choices than in a counterfactual in which population growth is driven by natives.
This paper extends the seminal work of Borjas (2001), who argues that immigrants “grease the wheels”
of the labor market by moving into the most favorable local labor markets.6 Within a spatial equilibrium
framework, this means that they pick cities where wages are highest relative to living costs and amenity
levels. Thus, in this context, immigrants do not necessarily choose the most productive cities or those withthe highest nominal wages. Instead, in our model, migrants prefer high-nominal-income cities because
they care less than natives about local prices. This is a crucial difference that has important consequences
for both the distribution of economic activity across space and the general equilibrium. Moreover, thisinsight also has important implications for empirical studies that estimate the effect of immigration on thelabor market by comparing metropolitan statistical areas (Card 1990; Altonji and Card 1991; Borjas etal. 1997; Card 2005; Lewis 2012; Llull 2018a; Glitz 2012; Borjas and Monras 2017; Monras Forthcoming;
Dustmann et al. 2017; Jaeger et al. 2018).7 In particular, it provides an explanation for the positive
5 Large, expensive cities are so, in the context of our model, because they are more productive. See Albouy (2016). In related

work, Hsieh and Moretti (2017) show how housing constraints are responsible in part for the smaller than optimal size of themost productive cities. This paper shows that immigrant location choices reduce these constraints. On optimal city size see
also Eeckhout and Guner (2014).
6 There are other papers with models that help to make arguments similar to the one made in Borjas (2001), such as Bartel(1989) and Jaeger (2007).
7 Dustmann et al. (2016) provide a recent review of this literature. We discuss in more detail the literature on immigration4

correlation between wage levels and immigrant shares across cities, and, given the persistence in city size
rankings (Duranton 2007), it offers an alternative reason for why immigrants keep settling in the same
locations decade after decade.
This paper is also strongly related to a large body of recent work on quantitative spatial equilibrium models, including Redding and Sturm (2008), Ahlfeldt et al. (2015), Redding (2014), Albouy(2009), Fajgelbaum et al. (2016), Diamond (2015), Monras (2015), Caliendo et al. (2015), Caliendo et al.
(Forthcoming), Monte et al. (2015) and Bilal and Rossi-Hansberg (2019), among others, which explore
neighborhoods within cities, the spatial consequences of taxation, local shocks, endogenous amenities,
the dynamics of internal migration, international trade shocks, commuting patterns, and location choices
over the life cycle.8 In this literature, only Burstein et al. (2018), Caliendo et al. (2018), Piyapromdee(2017), and Monras (Forthcoming) use spatial equilibrium models to study immigration. In these papers,
immigrants are not characterized by how they consume but rather by differences in observable characteristics that may be important for the labor market but that are silent on the many empirical facts
uncovered in our paper. Our view on what fundamentally defines immigrants uncovers novel local andaggregate effects of immigration in the host economy that were unexplored until now. We explain thenovelty of our paper relative to the various papers that study the effect of immigration on host economies
in detail in section 4.1.
Finally, this paper also ties in with the literature that investigates the effects of migrants on housing
markets and local prices more generally. There is evidence suggesting that Hispanic migrants tend
to settle in expensive cities and that they exert pressure on housing price (Saiz 2003, 2007; Saiz and
Wachter 2011). Relative to these papers, we show that the effect of immigration on housing prices may
be very heterogeneous across cities, depending on the type of city. This heterogeneity, which explains
how immigration affects natives differently across locations, was not explored before. There is also somework showing that immigration may decrease the price of some non-tradables (Lach 2007; Cortes 2008).
This is usually explained by its impact on the cost of producing local goods. We abstract from thismechanism in this paper but we could integrate it in our model.
In what follows, we first describe our data in Section 2. Section 3 introduces a number of facts
on immigrants’ location choices, wages, and consumption patterns. We present a quantitative spatial
equilibrium model consistent with these facts in Section 4, which we estimate and use to study the effects
of immigration on the spatial equilibrium in Section 5. Finally, Section 6 concludes the paper.

2

Data

In the empirical part of this paper, we rely on various publicly available data sets for the United States.
For individual information on locations and labor market outcomes, we use the US Census and theAmerican Community Survey (ACS), both available on Ruggles et al. (2016) and widely used in previous
work. To document consumption patterns, we use the Consumer Expenditure Survey, Census and ACS
data. We use data from the World Bank to compute real exchange rates between the various countries
in Section 4.1.
8 Redding and Rossi-Hansberg (Forthcoming) provide a recent review of this literature.

5

of origin and the US dollar. Finally, we use Matricula Consular data to compute Mexican flows at thestate-to-state level. We describe these data sources below.

2.1

Census and American Community Survey data

Our main data set is the Census of population data for the years 1980, 1990, and 2000, and the American
Community Survey 2009-2011. In particular, we use information on the metropolitan statistical area
(MSA) of residence of surveyed individuals, the wage they received in the preceding year, the number
of weeks that they worked in the preceding year, and their country of birth. We only consider salary
workers aged between 25 and 59 who are not in school and report positive weeks and hours worked inour sample, and we define immigrants as individuals born outside the United States. To control for
potential demographic differences between natives and immigrants, we construct composition-adjusted
wages. That is, we use the residuals of a regression of weekly wages on sex, racial categories and marital
status categories for each year.
We use these composition-adjusted wages to compute the difference in wages between natives andimmigrants, which we refer to as the wage gap, at the city level. When workers are heterogeneous and canbe divided into different factor types, there are two potential problems when computing city-specific wage
gaps. First, it may be that immigrants and natives within narrowly defined skill groups are imperfect
substitutes, and hence immigrants might earn relatively less in locations where they are more highly
concentrated because of competition effects. Second, the skill sorting of natives and immigrants acrosscities might be different and could partly drive local wage gaps. Third, it could be that the gap in
earnings between natives and immigrants is larger among high-skilled workers than among low-skilledworkers. Then, the higher concentration of high-skilled workers in larger cities, i.e the sorting of skills
across cities, could generate higher average wage gaps in these locations.
To control for these factors, we combine the estimation equations of Card (2009) and Ottaviano
and Peri (2012). In particular, we estimate a model in which we relate the ratio between natives’ andimmigrants’ wages to the ratio of labor supplies in an MSA following Card (2009). Moreover, we group
workers in skills cells based on education and experience and calculate wage and employment ratios withinthose cells as in Ottaviano and Peri (2012). The inclusion of skill cell fixed effects absorbs any variationin wage gaps across cities due to different sorting along the education and experience dimensions. Moreconcretely, we estimate the following regression:ln(wI,k,c,t
LI,k,c,t) = φk + φc,t + γ ln() + εi,t ,wN,k,c,t
LN,k,c,t(2.1)

where k denotes the skill cell, which is defined by four education groups (high school dropout, highschool graduate, some college and college graduate) and eight experience intervals starting with one to
five years and ending with 36 to 40 years, and LI,k,c,t and LN,k,c,t are the total hours worked in skill cellk, city c and year t by immigrants and natives, respectively.9
This specification allows us to extract the city-time-specific component of the wage gaps as the city9 For the calculation of the experience, we follow Ottaviano and Peri (2012) in assuming that high school dropouts enter thelabor market at age 17, high school graduates at age 19, workers with some college at age 21, and college graduates at age 23.

6time fixed effects φc,t , which are adjusted for any effects due to spatial sorting or imperfect substitution
between natives and immigrants within education-experience cells.
We also use data from the Census and ACS to compute local price indices. We thereby follow Moretti(2013) and apply his code to our sample ranging to the year 2011. From this, we obtain a local priceindex for each of the MSAs in our sample that takes the variation in local housing cost into account.10
To give a sense of the metropolitan statistical areas in our analysis, Table 1 reports the MSAs withthe highest immigrant shares in the United States in 2000, together with some of the main economic
variables used in the analysis. As we can see in Table 1, most of the MSAs with high levels of immigration
are also large and expensive and pay high wages. The gap in earnings between natives and immigrants
is also large in these cities. In this general description, there are a few notable outliers, which are mostly
MSAs in California and Texas close to the border between the US and Mexico.

Table 1 goes around here

2.2

Current Population Survey data

To explore whether our results hold for higher frequency data, we rely on the Current Population Survey (CPS). In particular, we use the CPS March supplement to generate yearly cross-sectional data of
individuals including information on their demographic characteristics, labor market variables and location of residence. Although the CPS data are gathered monthly, only the March files contain detailed
information on yearly incomes, country of birth, and other variables that we need. In particular, we
use information on the current location – mainly MSAs – in which the surveyed individuals reside, thewage they received in the preceding year, the number of weeks that they worked in the preceding year,
and their country of birth. We only consider salary workers who are not in school and report positive
weeks and hours worked in our sample, and we define immigrants as individuals born outside the UnitedStates. This information is only available after 1994, which is why we only use CPS data for the period
1994-2011.

2.3

Consumer Expenditure Survey data

To document consumption patterns, we employ two different data sets. First, we use the Consumer Expenditure Survey, which is maintained by the Bureau of Labor Statistics and has been widely employed
to document consumption behavior in the United States. It is a representative sample of US households
and contains detailed information on consumption expenditure and household characteristics. Unfortunately, it contains no information on birthplace or citizen status, which is why it is impossible to directly
identify immigrants. Instead, we rely on one of the Hispanic categories that identifies households of
10 We use the version of Moretti’s price index that is calculated as the weighted sum of local housing cost and the cost of

non-housing consumption, which is assumed to be the same across areas. Local housing costs are measured as the average ofthe monthly cost of renting a two- or three-bedroom apartment in an MSA.

7

Mexican origin in the years 2003 to 2015.11 The data set contains around 30,000 households per year, of
which around 7% are of Mexican origin.
We also document consumption patterns using the Census and the ACS. Both the Census and the
ACS record the rent paid by households who are renting. This is the most important local expenditure
for many households and typically accounts for roughly 25% of household income.

2.4

Real exchange rate data

An important aspect of our empirical analysis is to document the variation by price levels of immigrants’countries of origin. To measure price levels at origin, we use real exchange rate data. The World Bank
provides real exchange rates with respect to the United States for a large number of countries in its
International Comparison Program database.12 These data expand the 89 countries of origin that we
use in our estimation exercise.13 In Table 2, we provide a list of the top and bottom 10 countries interms of the average real exchange rate with respect to the United States over the years 1990, 2000, 2010.
While price levels in countries like Norway or Japan are around 35% higher, the number of countries
with real exchange rates larger than one is relatively low. Australia, ranked 10th in the table, is only
7% more expensive than the United States. On the other end, prices in countries like Vietnam (withlarge immigrant communities in the United States) have prices that are only 20% of those in the UnitedStates.

Table 2 goes around here

2.5

Matricula Consular data

Mexican immigrants in the United States are encouraged to register in the local consulates, which issue
a card called the Consular ID. In order to obtain this card, Mexican immigrants need to show, essentially, their birth certificate or passport. In principle both immigrants legally admitted to the US andundocumented ones can obtain this card. The card is useful, among other things, to open bank accounts
in a number of financial institutions. These gives sufficient incentives to many Mexicans to register andobtain this ID card.
Among the information recorded with this registration process is the address of destination in the
US and the municipality of origin within Mexico. This enables to compute the flows of Mexicans in any
given year. In theory, these can be computed at the municipality level, although only state-to-state flows
are publicly available. Caballero et al. (2018) and Allen et al. (2019) show that these data matches well
11 Monras (Forthcoming) shows that the overlap between individuals identified as Hispanics of Mexican origin and Mexicanborn individuals is around 85% in Census data. This gives us confidence that, by using the Hispanic variable in Consumption
Expenditure data, we are capturing a large number of Mexican-born individuals.
12 The exact title of the series is “Price level ratio of PPP conversion factor (GDP) to market exchange rate.”
13 An alternative source of similar information is provided by the OECD and the Penn World Tables. The OECD also
estimates price levels of various countries. The number of countries that the OECD covers is smaller, which is why we report
estimates in the paper using the World Bank data, although estimates for OECD countries may be more reliable because they
cover richer, more developed, countries. We obtain similar estimates using OECD data. We also obtain similar estimates using
the GDP per capita in the country of origin, obtained from the Penn World Tables, to proxy for the price index.

8

representative data sets on stocks. In this paper, we use the state-to-state migration flows for the year
2016.

3

Empirical evidence

3.1

Immigration and cities

In this section, we document two very strong facts about the cross-sectional relationship between immigration and cities. First, we show that immigrants concentrate much more than natives in large andexpensive cities. Second, we document that the gap in wages between immigrants and natives is larger(i.e. more negative) in large and expensive cities.
To document the first fact, we define the “relative immigrant share” as the share of immigrants living
in city c divided by the share of natives living in city c (as fractions of the whole respective populationsin the US) and regress this measure (in logs) on the size or price level of city c. More specifically, we run
the following regression:lnImmc,t Natc,t/Immt Natt= βQ ln Pc,t + ψc + ψt + εc,t ,(3.1)

where Immc,t is the number of immigrants and Natc,t is the number of natives in city c at time t, andImmt and Natt is the overall number of immigrants and natives in the entire country.14 Pc,t is either
the total number of people in the city or its price level. An estimate βQ > 0 means that immigrants
concentrate more in large/expensive metropolitan areas than natives.
The second fact that we investigate is how the gap in wages between natives and immigrants is related
to city size and city prices. If wages reflect, at least in part, the value of living in a location – which is anatural result in non-competitive labor market models, see Section 4 – we should expect the relationshipbetween wage gaps and city size and city prices to be the mirror image of relative location choices. To
estimate the relationship between wage gaps and the city characteristics, we use the following regression:

φ̂c,t = βP ln Pc,t + ψc + ψt + εc,t .

(3.2)

where φ̂c,t is the gap in wages between natives and immigrants adjusted for both observable characteristics and heterogeneous labor, as explained in section 2.1, equation (2.1). In particular, φ̂c,t accounts
for the possibility that natives and immigrants are imperfect substitutes and that workers of different
educational background sort into different locations. An estimate of βP < 0 indicates that the adjusted
gap in wages between natives and immigrants is larger, i.e. more negative, in more populous or more
expensive cities.
We report the results of estimating equations (3.1) and (3.2) in Figure 1 and Table 3, and provide
a large number of robustness checks in Table 4. Figure 1 shows these relationships using only crosssectional data from the 2000 Census. In the left-hand panel of panel A, we observe that, even if there
14 We only use urban population for the entire analysis. Non-urban local labor markets are usually defined by commuting
zones (Autor et al. 2013). To define non-urban commuting zones we need information on county of residence, which is notprovided for ever year in CPS data. Urban commuting zones and MSAs are essentially the same.

9

is some variance in the relative immigrant share across metropolitan statistical areas, there is a positiveand statistically significant relationship between the distribution of immigrants and city population. The
marker sizes are proportional to the respective city price indices and indicate that the more populous
cities also tend to be more expensive. The relationship between the relative immigrant share and priceindices, shown in the right-hand side of panel A, is even stronger, and the linear fit is better.15 Here,marker sizes reflect city population levels. While there are some outliers, mainly along the US-Mexico
border, a city with a local price index that is 1% higher is associated with an 8% higher relative immigrantshare. In Appendix A.3, we show that this relationship also holds when using commuting zones insteadof MSAs.16 This evidence is in line with the contemporaneous paper by Albouy et al. (2018), who argues
that immigrants live in relatively high-nominal wage, high-amenity locations.

Figure 1 goes around here

Panel B of Figure 1 shows that the relationship between wage gaps and city size and price levels is
the mirror image of what we have seen for relative immigrants shares. As can be seen in the graph on
the left, there is a strong negative relationship between wage gaps and city size. This means that thedifference in the wages of immigrants and natives is larger in big than in small cities, i.e. immigrants
have relatively higher wages in small than in large cities. The graph on the right hand-side of panel B
shows that, again, the relationship is stronger between wage gaps and city price indices than it is withcity sizes.
We quantify these results in Table 3. In the first column, we show that, when pooling all the years
together, larger cities have a higher relative share of immigrants (panel A) and a larger wage gap (panel
B). This could be driven by variation across the years in the overall size or price level of cities. In column
2, we include year fixed effects, hence the estimates are the average cross-sectional relationships acrossthe four decades of our data. Both the coefficients in panel A and panel B remain similar. Column 3
includes MSA fixed effects. Hence, βQ and βP are identified from within-city variation over time. While
not the focus of the paper, since we are most interested in the cross-sectional variation, we also obtain
similar results in this column.

Table 3 goes around here

In columns 4 to 7 we investigate the relationships of relative immigrants shares and wage gaps withcity price indices, computed following Moretti (2013). Columns 4 and 5 are akin to columns 1 and 2
but using city level price indices instead of city size. We obtain the same results. In the cross-section,
immigrants concentrate in expensive cities where their wages relative to those of natives are lower. These
relationships may be driven by endogenous factors. Perhaps, immigrants make cities larger and more
expensive, and hence it is not that they prefer to live in expensive cities but rather they are the cause
15 This is also the case when we include both city price and city size in a bivariate regression.
16 Commuting zones are a partition of the US territory. Commuting zones can be divided between urban and rural commuting
zones. Urban commuting zones are equivalent to MSAs, whereas rural commuting zones are not captured by MSA information.

10

of these high prices. While this is unlikely to be the case given the persistence in city sizes rankings(Duranton 2007) and the current levels of immigration, we use an IV strategy in column 6 .
It is well documented that part of the variation in house prices across cities is driven by geographic
constraints, see for example Gyourko and Saiz (2006). Based on this idea, Saiz (2010) builds estimatesof housing supply elasticities that are based on the share of developable land around each city center.
This is a good predictor of high housing prices, which, in turn, is the most important aspect of local
price indices. Hence, we use the housing supply elasticities to predict the local price indices in the firststage regression of our IV specification.
The second stage regression is shown in column 6. Again, it is clear from this column that immigrants
choose to live in expensive cities, and that the gap of their wages with respect to those of natives is larger
in these cities. While not the focus of the paper, in column 7, we shows that we also obtain a similar
relationship when using only within city variation, although the magnitudes are smaller.
There are potentially different explanations for the results reported in Table 3. In particular, they
could be driven by particular subsamples of immigrants. We explore this in Table 4, in which we report
the regressions shown in columns 5 and 6 of Table 3 for various subsamples of immigrants.

Table 4 goes around here

Columns 1 and 2 of Table 4 show that when we restrict the sample of immigrants to those whoare likely documented or likely undocumented, we obtain very similar results. If anything, the results
are stronger for undocumented immigrants, maybe reflecting (as we argue in subsection 3.2.3) that
undocumented immigrants are less attached to the host country. We code likely documented or likely
undocumented immigrants following Borjas (Forthcoming), who uses, among others, variables indicating
the participation in welfare programs that require being legally in the country to identify documented
immigrants. In panel A and C we show the OLS results on relative immigrant shares and wage gaps,
respectively, while in panels B and D we show the same regressions using the IV strategy based on Saiz(2010).
Columns 3 to 6, panels A to D, show the results restricting the sample of immigrants and natives to
one of the four education groups. It is well documented that immigrants are concentrated in the bottom
and the top of the education distribution (Borjas 2003; Ottaviano and Peri 2012). If for whatever reason
very high- and very low-skilled workers had higher incentives to live in large cities (Eeckhout et al. 2014),
then it could be that the results in Table 3 are driven by this. However, columns 3 to 6 show that
there are higher concentrations of immigrants in expensive cities at each education level. We also obtain
similar wage results across education groups.
In the last column of the table we show that these results are not driven by Latin American immigrants
only. If we drop all immigrants from Latin American countries, we obtain results that are similar to ourbaseline specifications.
In this paper we argue that the patterns we uncover are driven by the comparative advantage that
immigrants have in living in expensive cities, which originates from the fact that part of their consumption
is not subject to local prices but rather prices in their countries of origin. In the following section 3.3 we11

corroborate this reading of the evidence by exploring in detail the heterogeneity by country of origin’s
price levels and exchange rate fluctuations.
As we argue in more detail in Section 3.4, our findings are not driven by sorting of immigrants across
US cities or imperfect substitution. All our regressions control for potential imperfect substitutability
between immigrants and natives following Ottaviano and Peri (2012), and hold even when we restrict our
regressions to particular education groups. Furthermore, we also investigate in Appendix A.2 whether
these relationships hold when we control for immigrant networks.

3.2

Immigrant Heterogeneity

In this section, we show that the results documented so far are stronger for immigrants whose consumption
share in the home country is likely to be higher, either because of lower prices in the home country or alower attachment to the US.

3.2.1

Heterogeneity across and within origin countries

To the extent that there is some degree of substitution between consuming locally or consuming in
the country of origin, the patterns documented so far should be stronger for immigrants coming fromcountries of origin with lower price levels relative to the United States or, in other words, lower realexchange rates with respect to the US. Moreover, it should also be the case that for each country oforigin the incentives to concentrate in more expensive cities are larger when it is cheaper to consume in
the home country.
To highlight that our results are not driven by particular countries of origin, we first show in a simple
graph the elasticities of relative locations and wage gaps of immigrants with respect to city size and pricelevels from different countries of origin as a function of the real exchange rate using data from the year
2000. For this, we estimate equation (3.1) at the city-origin level (i.e. we replace Imm by the immigrant
population from the respective origin, and we estimate origin-specific coefficients βQo , including origin
and MSA fixed effects in the regression).
We then estimate equation (2.1) at the skill-city-origin-time level and replace the city-time with cityorigin-time fixed effects.17 In the second step, we estimate origin-specific elasticities by the following
regression:

φ̂c,o,t = βo ln Pc + φt + φc + φo + εc,o .

(3.3)

One challenge of this exercise is that there are some countries of origin for which we observe immigrants
only in a subset of the MSAs in our sample, and hence there are some zeros when computing relative
immigrant shares at the MSA-origin level. Moreover, some skill-city-origin-time cells cannot be included
due to zero immigrant observations. To address this problem, we concentrate on the top 100 MSAs bysize and the top 89 sending countries, with which we can obtain non-missing wage gaps in around 60%
17 We still aggregate immigrant labor supply at the skill-city-time level as in (2.1). Results are virtually unchanged, if we also

disaggregate it at the origin level.

12

of all possible skill-city-origin-time combinations.18 Furthermore, in Table 5 we take into account thezeros by using a Poisson pseudo maximum likelihood (PPML) estimator.
Figure 2 shows the plots of the city price elasticities and city size elasticities of the relative immigrantshare against real exchange rates in panel A and the elasticities of the wage gap in panel B. All plotsshow statistically significant relationships that go in the expected direction. Panel A shows that theelasticity of the relative share of immigrants with respect to city size or city price from countries withlower real exchange rates is higher. This means that immigrants from cheaper countries concentrate morein larger and more expensive cities than immigrants from more expensive countries. The relationship ofthe elasticity of the wage gap with respect to city size or city price and real exchange rates is, again, themirror image of the relative location choices.19 As can be seen in panel B, the elasticity of the wage gap
is higher for immigrants from more expensive countries, meaning that the difference in wages between
natives and immigrants does not increase as much for them. Overall, these graphs show that there issubstantial variation across countries of origin, which is well aligned with the role that differences inprices should play in shaping the importance of home country expenditures for immigrants from different
countries of origin.20

Figure 2 goes around here

To document these relationships more systematically and to use arguably exogenous exchange ratevariation within countries of origin, we expand equations (3.1) and (3.2) by interacting the city variabledirectly with the real exchange rate (RER) and pool the Census years 1990 and 2000 and the combined
ACS 2009-2011 (real exchange rates are not available for 1980 in the World Bank data). In particular,
we estimate regressions of the following type:ln(Immc,o,t Natc,t/) = α1 ln Pc,o,t + α2 ln RERo,t + α3 ln Pc,t ∗ ln RERo,t + δt + δo + δc + εc,o,tImmo,t Natt

(3.4)

φ̂c,o,t = β1 ln Pc,t + β2 ln RERo,t + β3 ln Pc,t ∗ ln RERo,t + δt + δo + δc + εc,o,t , (3.5)
where as before ln Pc,t denotes the population or the price level of MSA c, and RERo,t is the realexchange rate of origin country o with respect to the United States at time t. We estimate the relative
share equation using a PPML regression model in order to deal with the incidence of zeros (Santos Silva
and Tenreyro 2006).
The estimates of interest are α3 and β3 . A negative estimate of α3 means that immigrants fromcheaper countries tend to concentrate more in larger or more expensive cities. Similarly, a positive
18 Different selections of MSAs lead to slightly different selections on the number of sending countries, which results in smallchanges in the estimates. Expanding the number of MSAs tends to introduce more measurement error, which attenuates theestimates of regressions with many fixed effects. Reducing the number of MSAs obviously reduces the number of observations,which has small consequences on the point estimates and confidence intervals.
19 Recall that the wage gap is defined as immigrant wage minus native wage. Therefore, a negative elasticity indicates anincreasing wage gap.
20 An alternative to this exercise is to see if the interaction of the immigrant dummy and city size or city price of equation(3.2) is higher at lower quantiles of the wage distribution. We show that this is indeed the case in Figure D.1 of the appendix.

13

estimate of β3 implies that the wage gap of immigrants from these countries of origin is larger in thesecities. When including origin and location fixed effects (δo and δc ), the identifying variation only comesfrom RER fluctuations across decades for each country of origin.
Table 5 goes around here
We present the results in Table 5. Panel A, reports the results on the relative immigrant share. In thefirst column, we only include the real exchange rate. A positive estimate means that the distribution of
immigrants from countries of origin with higher exchange rates tends to be more similar to the distributionof natives. The relationship is not very strong, however. In the second column, we include population,
which replicates the result we have shown before: The relative share of immigrants is increasing in city
size and city price. In column 3, we introduce the interaction between real exchange rates and city sizes.
A negative estimate suggests that the relative concentration of immigrants from high exchange rate
origins (e.g., Japan, Germany, or the United Kingdom) in larger cities is less strong than for immigrants
from low exchange rate origins (e.g. India or China). Including MSA fixed effects in column 4 leaves
the coefficient of the interaction term virtually unchanged. Columns 6 and 7 repeat the specification ofcolumns 3 and 4 but using city prices instead of city sizes. The estimate is, again, negative, suggestingthat immigrants from cheaper countries disproportionately locate in expensive cities.
In panel B of Table 5, we repeat the exercise of panel A using the wage gap as dependent variable. In
column 1, we include the real exchange rate, which shows that immigrants from expensive countries tend
to have higher relative wages than those from cheaper countries. This likely reflects that the possibilityof consumption at lower prices decreases the reservation wage of immigrants. Column 2 confirms theprevious result that the gap in immigrant’s earnings increases in city size. In column 3, we include theinteraction between city size and the real exchange rate. The positive coefficient indicates that the effectof city size on the wage gap is attenuated for origin countries with higher prices levels relative to the US.
The coefficient remains similar, when we include MSA fixed effects in column 4. In columns 5 to 7, we
replace city size with price level and find again significant effects with the expected signs. The city priceelasticity of the wage gap is stronger for immigrants from origins with lower real exchange rates.

3.2.2

Heterogeneity across Mexican immigrants

The country that sends the most migrants to the US is Mexico. Given the number of Mexicans in the US,
we can explore in more detail the heterogeneity among Mexican immigrants to see if we obtain results
consistent with the heterogeneity documented pooling all countries of origin.
One caveat of the results shown in Table 5 is that we can only use exchange rate variation over 10year gaps, when Census data is available. To complement this evidence, we also exploit fluctuations inreal exchange rates between the United States and Mexico at a higher, yearly frequency. Exchange rate
fluctuations are common and difficult to anticipate over short time horizons, offering arguably exogenous
variation.21 More concretely, we focus our analysis on Mexican immigrants who move to the United
21 In this paper, we complement the evidence shown in Nekoei (2013). Exchange rate fluctuations affect not only the intensive
margin of immigrant labor supply decisions (i.e. hours worked) but also, and very importantly, the extensive margin (i.e.
location choices).

14

States from abroad or who move within the United States across states in a given year to see where they
locate and the wages that they receive relative to natives as a function of the real exchange rate. For
this exercise, we can only compute city size elasticities and not city-price elasticities because CPS data
does not include the necessary information to compute city price levels as in Moretti (2013).
To obtain yearly elasticities of the relative immigrant shares with respect to city size we estimate
again (3.1) separately for each year.22 As the CPS contains a much lower number of observations thanthe Census and the immigrant sample is additionally reduced by only considering Mexican movers, wecannot calculate wages of immigrants at the skill-MSA-time level to estimate (2.1), i.e. we cannot
adjust for potential imperfect substitutability between natives and immigrants. Instead, we account forthe potential underlying individual level heterogeneity by estimating for each year standard Mincerian
wage regressions at the individual level (pooling natives and Mexican movers), including an immigrantindicator, a dummy variable for each skill cell (again defined by experience and education groups) andadditional controls for race, marital status and 82 occupation categories for this exercise. The dependent
variable is the weekly wage and the city size elasticity of the wage gap is identified by an interaction
between the immigrant dummy and MSA population.

Figure 3 goes around here

Figure 3 plots the estimated elasticities against the yearly average real exchange rate between the
Mexico and the US. The two plots show a linear fit that goes in the expected direction. The lower are theprices in Mexico relative to US prices, the more positive is the elasticity of the relative share of Mexican
immigrants and the more negative is the elasticity of the wage gap with respect to city size. In otherwords, Mexicans concentrate more in large cities and are paid lower wages in them relative to natives
when the Mexican Peso is relatively cheap.
To explore immigrant heterogeneity even further, we turn next, to analyze data on Mexican flows fromparticular states of origin in Mexico to particular states of destination in the United States.23 As before,
if there is some degree of substitution between consuming in Mexico and in the US, then immigrants fromcheaper origins in Mexico should disproportionately move towards expensive destinations in the UnitedStates. Unfortunately, we do not have local price index data for Mexican locations. Instead we use GDP
per capita at the state level to proxy for local price indices. There is a strong correlation between pricelevels, wages levels, and GDP per capita, which suggests that using GDP per capita is a good proxy.
More specifically, to investigate the heterogeneity in migration flows by Mexican state of origin we
use the following estimation equation:
Fij = β1 ln Pi + β2 ln Pj + β3 ln Pi ∗ ln Pj + (δi + δj ) + εij ,(3.6)

where Fij is either the fraction of all immigrants from Mexican state of origin i that move to US stateof destination j or the log of this fraction, ln Pi is the GDP per capita in i, and ln Pj is the GDP per
22 We do not take the log of the left-hand side of equation (3.1) to avoid losing MSAs without Mexican immigrant movers.
23 The publicly available Matricula Consular data is only available at the state level.

15

capita in j. In some specifications we also control for the level of population at origin and destination, or
include origin and destination fixed effects. Our main hypothesis is that β3 is negative. If β3 < 0, there
are relatively less flows to high GDP pc destinations from high GDP pc origin states.
Table 6 goes around here
Table 6 presents the results. In the first two columns we simply explain the flows of Mexican immigrants from origin i to destination j by the GDP per capita at origin and at destination. Mexicans of
all origins tend to disproportionately move to high GDP per capita states in the United States. Thiscan be read as further corroborating that immigrants prefer to move to high nominal income locations.
The positive coefficient GDP per capita in the origin shows that there are more migrants from highGDP per capita origin states. Selection or credit constraints when migrating can explain this result(Angelucci 2015). The next two columns control for the size of the origin and destination states. This is
an important control since larger origin states and larger destination states likely send and receive moremigrants, respectively. In the next two columns, we include state of origin and state of destination fixed
effects. These should control for unobservable characteristics of the states that go beyond size and GDP
per capita. The last two columns exclude California as a destination state. All the specifications show
the same result. There is a disproportionate flow of immigrants from low GDP per capita origin states
towards high GDP per capita destinations.

3.2.3

Heterogeneity by attachment to the United States

On top of the price differences or fluctuations, there are other reasons that may generate heterogeneity inthe importance of the host country for an immigrant. We explore in this section two such reasons. First,
we document that our results weaken for immigrants who have spent a long time in the US. Second, we
use variation due to the legalization of immigrants in the Immigration Reform and Control Act (IRCA)
of 1986 that gave legal status to immigrants who arrived to the US prior to 1982. We exploit the ideathat when gaining legal status immigrants may become more attached to the host economy and, hence,
reduce the importance that they give to consuming in the home country.
According to Dustmann and Mestres (2010), immigrants who do not intend to return to their countriesof origin remit a smaller share of their income. They are also less likely to spend time back home andthus are, in some way, more similar to natives. There is also a large body of literature starting with
Chiswick (1978) that estimates the speed of assimilation into the receiving country. This literature has
documented an early gap in wages between natives and immigrants that tends to disappear or attenuate
over time. This literature has interpreted this early gap as reflecting the lack of certain skills specific to
the receiving country that immigrants may not have upon arrival.
The literature on immigrant assimilation has not explored, however, how immigrant native wage gaps
and their relationship with either city size or city price levels, evolves with the length of immigrant stays.
If immigrants who have been longer in the US care less about consuming in the home country than
immigrants who have just arrived, then we should see that the gap in wages between immigrants andnatives in large relative to small cities is larger for the late arrivals than the early ones.

16

Figure 4 goes around here

To investigate this idea, we use the year of immigration available in the Census data and divide
immigrants into groups of 5-year intervals depending on their time spent in the United States. We thenestimate equation (3.3) but instead of the origin o, we disaggregate the wage gaps by the groups definedby time in the US and estimate β for each of these groups. We plot the different city size-wage gap
elasticities and city price-wage gap elasticities in Figure 4. The positive and strongly linear fits in bothplots indicate that the relationships between wage gaps and both city size and prices diminish with thelength of immigrants’ stay in the United States.
In the second exercise of this section, we exploit a sudden policy change that the Reagan Administration introduced in 1986. Among other things, the Immigration Reform and Control Act (IRCA) legalized
the working status of immigrants in the US that had arrived to the country before January 1st 1982.
Hence, immigrants who arrived in the US prior to this date are much more likely to be documented thanthose who arrived just after.
Hence, if gaining work permits makes immigrants have greater chances of staying in the US and hence,
makes them care less about their countries of origin, we should see that the gap in wages between natives
and immigrants in large and expensive relative to smaller and cheaper cities is larger for immigrants whoarrived just after 1982, relative to those who arrived just before 1982. In other words, the year 1982
should generate a discontinuity in the relationship between the wages of immigrants and city size andcity price levels. We explore this idea with the following regressions.
First, we compute whether the gap in wages of different groups (labeled by G in the equation) ofimmigrants with respect to natives increases more with city size and city price levels than for othergroups of immigrants.

GG
ln wi,c,t = α1t + α2 ImmG
i,c,t + β Immi,c,t ∗ ln Pc,t + γ ln Pc,t + φXi,c,t + εi,c,t ,(3.7)

where ln wi,c,t is the weekly wage in location c at time t of individual i, ImmG
i,c,t is a dummy variableindicating that individual i is an immigrant of group G, and where ln Pc,t is either the size or price index
of location c. The baseline regression is ran using low-skilled workers only, including immigrants of group
G and natives. We concentrate on low-skilled workers because we use the procedure suggested by Borjas(Forthcoming) to identify undocumented immigrants which Albert (2017) shows does a particularly goodjob for low-skilled immigrants.
In particular, we separately estimate β G for the immigrant group that arrived before 1982 and forthe group that arrived after 1982. For this exercise, we concentrate on immigrants who moved to the
US between 1976 and 1987. Immigrants who arrived before 1982 are (discontinuously) more likely tohave gained legal status, hence we expect |β Before 82 |< |β After 82 |, and both β Before 82 and β After 82 to be
negative since we expect that gap in wages between natives and immigrants to be larger in large andmore expensive cities for both groups of immigrants. In this regression, we control for the convergencein wages between natives and immigrants using a linear convergence rate following the assimilation rate.
We code the convergence rate variable as 35 minus the number of years that the immigrant has been in17

the US. This assumes that there is no gap in wages between immigrants who have been in the US for 35
years, and that the gap is larger for immigrants who arrived more recently.
We report the results in Table 7. The first column estimates |β Before 82 | and the second column
estimates |β After 82 | with respect to population levels, and columns 4 and 5 with respect to city prices.
It is clear from the table that in both cases |β Before 82 |< |β After 82 |. In Figure D.6 we show that the factthat |β Before 82 |< |β After 82 | comes from a discontinuity in 1982. In particular we plot the immigrant native wage gap elasticity with city prices for immigrants who arrived in each year between 1976 and1987 relative to the immigrant - native wage gap of the immigrants arriving to the US in 1981. The
graph shows that the gap in wages between natives an immigrants is larger (i.e. β G above more negative)
for immigrants arriving after 1982 which are likely to be more attached to their country of origin because
they are less likely to be legally residing in the US.
An alternative way to explore whether immigrants who are exogenously granted legal status seem to
be more attached to the host country is to directly compare the wages of immigrants who arrived before
1982 and those who arrived after 1982 and how they relate to city size and price levels. For this, we use
the following regression estimated using only data on immigrants who arrived between 1976 and 1987,
and where Before 82i,c,t is a dummy variable indicating whether immigrant i arrived to the US before
1982. An estimate of β > 0 means that wages of immigrants who arrived before 1982 increase more withcity size and city price levels than immigrants who arrived after 1982.

ln wi,c,t = δ1t + δ2 Before 82i,c,t + βBefore 82i,c,t ∗ ln Pc,t + γ ln Pc,t + φXi,c,t + εi,c,t(3.8)

Columns 3 and 6 in Table 7 show that β > 0. This is in line with columns 1, 2, and 4, 5, and with
the idea that immigrants who are less likely to have obtained legal status are less attached to the US
and thus their wage elasticities with respect to city population or prices are larger.

3.3

Immigrant consumption patterns

We have suggested that the previous results on relative wages and location of immigrants can be explainedby the fact that immigrants spend part of their income in their countries of origin. To the best of ourknowledge a data set that contains information on wages in the host economy and consumption in theorigin country does not exist. Instead, we rely on data on remittances and, especially, local consumption
to investigate the differential consumption patterns of immigrants relative to natives.
Dustmann and Mestres (2010) report that immigrants in Germany remit around 10% of their income.
While data of similar quality as in their study do not exist for the US, we can use the New Immigrant
Survey to get some notion of the remittance behavior of newly admitted immigrants in the US. For
instance, in Table F.3 of the Appendix, we report the likelihood, the average share of income sent asremittances, and the average share of income for those immigrants who remit, for a number of different
broad origins. There is quite some variation in the likelihood of remitting across origins. For example,
20% of immigrants from Mexico and as much as 32% of immigrants from other Latin American countries
seem to remit part of their income to their home countries. This number is significantly lower for
immigrants from European countries. For the entire population of immigrants, immigrant remittances18represent approximately between 2% and 3% of income. For those who remit, this number logicallyincreases to between 10% and 15%, which is closer to the estimate provided in Dustmann and Mestres(2010). All in all, the numbers for the US seem broadly consistent with this prior literature. The maindrawback of New Immigrant Survey data is that it does not include undocumented immigrants. Including
them would likely change the numbers significantly.
An alternative strategy is to look at data on local consumption of immigrants in the host economy(and compare it to natives), instead of trying to measure consumption in the country of origin. Measuring consumption is not an easy task as described in Attanasio and Pistaferri (2016), with difficulties
arising from measurement issues and from the treatment of durable goods. Our assumption is that total
consumption can be decomposed between local consumption (part of which can be measured), savings,
and remittances (or income spent in another country), and that the true overall consumption behaves
like the observable component. Hence, if we observe that immigrants spend less than natives locallyit must mean that they either save more (maybe thinking about a possible return to their country oforigin), or spend a significant fraction of their income on remittances. In any case, however, only a small
fraction of income is devoted to savings for the vast majority of households.24 Hence, by looking at local
consumption we can infer something about whether immigrants are likely to spend an important shareof their income in their countries of origin, as hypothesized.
More concretely, we investigate whether immigrants consume less locally than natives using twoalternative data sets: the Consumption Expenditure Survey data and Census data. The former allows us
to investigate overall consumption but only identifies Mexican immigrants, as explained in more detail in
Section 2. The latter allows us to identify immigrants from multiple countries of origin but contains only
expenditures on housing, which represent around 25% of total expenditures (Davis and Ortalo-Magne2011).
We start by investigating local consumption with Consumer Expenditure Survey data using thefollowing regression:ln Total Expenditurei = α + βMexicani +X

γj HH Income category j i + ηXi + δs + δt + εi

(3.9)

j

where “Total Expenditure” is the quarterly total expenditure at the household level.25 Consumer
Survey data identifies income only by category, hence we use income bracket dummies indexed by j.
“Mexican” identifies households of Mexican origin and δs and δt are state and time dummies, respectively. The coefficient of interest (β) measures the difference in total expenditures between Mexicans
and non-Mexicans conditional on observable characteristics, most importantly income categories. The
location fixed effects (δs ) ensure that the identification of β comes from within location comparisons. In
Consumption Expenditure Survey data the finest level of geographic disaggregation is state of residence.
24 As can be see in data from the St Louis Fed (https://fred.stlouisfed.org/series/PSAVERT), the aggregate personalsavings rate has fluctuated between 2 and 12% since 1980. See also Dynan et al. (2004) for a discussion on how savings varywith income.
25 More specifically, we use the variable “totexpcq” from the Consumer Expenditure Survey. This variable combines expenditures on all items.

19

The results are reported in panel A of Table 8, which suggests that, unconditionally, Mexicans consume
on average 33% less than non-Mexican households, and as much as 38% when we force within statecomparisons (column 2). In column 3 we include income controls, which reduce the estimate to around
15%. When we include all the controls in column 4, which include family size, race, and marital status,
our preferred estimate suggests that Mexican households consume around 22% less locally than nonMexicans. With close to zero savings rates (in the early 2000s the saving rate was around 2%), thisnumber also represents the share of income that is potentially devoted to consuming in the home country.

Table 8 goes around here

An important part of local expenditures is housing – something that we can measure both with theConsumption Expenditure Survey and with Census data. In Panel B of Table 8 we repeat the regressionsof Panel A but using the rents paid as dependent variable. The patterns are similar than what we observedin the Panel A, showing that an important part of the difference between how immigrants and natives
consume is likely related to the housing market. In particular, columns 3 and 4 suggest that Mexicans
consume around 10 to 18 percent less than similar looking non-Mexicans.
To explore in more detail how immigrants and natives consume housing we turn in Panel C to Census
data. In Census data we know both ownership status and the rents that renters pay. In Table F.4 in the
Appendix we show that immigrants are less likely to own the place where they live. Here we concentrate
on renters. With Census data we can run the following type of regressions:ln Housing Rentsi = α + βImmigranti + γ ln HH Incomei + ηXi + δc + δt + εi ,(3.10)

where δc are metropolitan area fixed effects, δt indicate year fixed effects, and Xi is a vector ofindividual characteristics including dummies for the number of persons present in the household, sex,
marital status, and age. Income is, in this case, a continuous variable. An alternative regression thatyields the same results is to use the share of income devoted to paying housing rents as dependent variable(either ins logs or levels), which we show in Table F.5 in the Appendix.
Like in Panel B of Table 8, we see in the first two columns of Panel C that immigrant households spend
around 7.5 to 15% less on rents than observationally similar natives within metropolitan areas, in linewith the results reported in Panel B. In column 3 we investigate whether immigrants pay relatively higher
rents in more expensive cities than in cheaper ones. While positive, the coefficient on the interaction
between the immigrant household dummy and (the log of) the city price level is not different than zero,suggesting little heterogeneity along this dimension. In column 4, we investigate instead, restricting
the sample to immigrant households, whether immigrants from more expensive countries of origin spend
more on housing than immigrants from cheaper origins, conditional on income, household characteristics,
and metropolitan area fixed effects. Consistent with the model that we later present, immigrants from
more expensive origins spend relatively more on housing in the host economy. One way to think about
the magnitude of the estimates is to realize that if immigrants spend between 15 to 22% less on housing
rents (as estimated in Panel A), and housing rents represent around 25% of income, then the share of20

income devoted to housing should be around 3 to 5 percent lower for immigrant households (.15 x .25),
broadly consistent with the direct estimates of this number provided in Panel B of Table F.5 in the
Appendix.26
Overall, these results suggest that immigrants spend less than natives on local goods, with only small
differences across metropolitan areas, and that immigrants that come from more expensive locations arelikely to consume less in their countries of origin and more in the host country. We return to this in
Section 5.2 when we compare the moments on consumption predicted by the model, which we estimate
solely on labor market data.

3.4

Discussion of additional mechanisms

For some of the evidence presented so far, one could think of alternative mechanisms as explanations.
In this section, we discuss several such alternative mechanisms that we have not discussed so far andcheck the robustness of the patterns we have uncovered by presenting additional empirical evidence which
we present more formally in Appendix A.2. As a remainder, in the main regressions we showed that
our results are not driven by imperfect substitutability between natives and immigrants, by differential
levels of human capital between natives and immigrants, nor by the fact that some immigrants are
undocumented, see Table 4.
One unaddressed potential concern is that there is a large literature documenting the role of immigrant networks in shaping immigrant location choices (Altonji and Card 1991; Munshi 2003). Immigrant
networks might be a potential explanation for some of the empirical patterns we described in previous sections, if immigrants initially settled in random locations and then these locations grew due to subsequent
immigration inflows as predicted by immigrant networks. This could have generated bigger gaps in wages
between natives and immigrants in these cities because newer immigrant inflows put disproportionate
pressure on wages of immigrants.
To address this concern, we extend our wage gap regressions with a control for the relative sizeof the immigrant community within the MSA for each of our countries of origin. As shown in moredetail in Appendix A.2 and Table F.2, including immigrant networks as a control does not change ourmain results. Furthermore, it is difficult to explain the country of origin immigrant heterogeneity. It
is unclear why immigrants from low-income countries would concentrate in large and expensive cities
in the earlier periods, or why cities in which immigrants from low-income countries concentrate growdisproportionately more than cities with more immigrants from high-income countries. In general, theevolution of city sizes is slow and the level of immigration in the United States not sufficiently large todramatically change city size rankings (Duranton 2007). In Appendix A.2, see Table F.1, we also showthat our results do not change if we measure city size using only native population or lagged city size.
Taken altogether, we believe that this additional evidence suggests that immigrants keep going to thesame large and expensive cities not just because former immigrants moved into them but also because
the same incentives that drove the earlier immigrants also shape location choices of more recent ones.
26 A direct comparison is not possible given that Consumer Survey data identifies Mexicans, while US Census data identifies

all immigrants.

21

A second concern is that immigrants might settle in larger cities because it is easier to find a job
there. However, this does not provide an explanation for why immigrants earn less relative to natives inthese cities. To further discard this explanation, we show in the Appendix A.2, Figure D.3, that there isno systematic relationship between city size and job finding rates or unemployment rates of immigrants.
Thus, labor market opportunities of immigrants in large cities do not seem to be systematically better
than in smaller ones.
A third unaddressed concern is that there might be differences in the distribution of jobs available inlarge cities. For instance, there could be more jobs in the lower part of the wage distribution, which may
be disproportionately held by immigrants. This would be in line with the extreme skill complementarity
hypothesis discussed in Eeckhout et al. (2014) and could generate a gap in wages between natives andimmigrants, especially in large cities. To address this concern, we show in Appendix A.2.4 that skewness
and kurtosis of the native wage distribution do not seem to be systematically related to city size or city
price levels.27 Also, we show in Table 4 that all our results hold within education groups. Finally, it
is not clear how differences in the distribution of wages in large and small locations would explain theobserved heterogeneity by country of origin.
A final concern is that the patterns might reflect that in larger cities there are more products that
immigrants value (Handbury 2011; Handbury and Weinstein 2015). For instance, tradable goods fromorigin countries may only make it to the largest locations in the United States if there is a fixed cost ofentering local product markets. It is difficult, however, to explain the observed immigrant heterogeneitywith tradable goods. For instance, it is unclear why there should be more products from the poorest
Mexican states of origin in the most expensive US states of destination, making these states disproportionately attractive to Mexicans from low-income countries of origin. Similarly, it is unclear why there
should be relatively more Mexican products in places like New York City, than, for example, German orCanadian products, being that New York City is a relatively high-income area and Germany and Canada
are countries specializing in relatively higher quality products.

4

A spatial equilibrium model with immigration

In this section, we introduce a quantitative spatial equilibrium model with immigrants that consume partof their income in their countries of origin. The model rationalizes the facts described so far. In Appendix
B, we present a more general version of this model with minimal assumptions that delivers the same
qualitative results than this quantitative model. We estimate the model and use it for counterfactual
analysis in Section 5.

4.1

Definition of immigration

Perhaps the first challenge in any model of the labor market with immigration is to precisely define inwhat ways an immigrant is different than a native. Prior work has emphasized several aspects and in
27 In fact, part of the wages observed and documented in prior literature in the tails of the overall wage distribution, particularlyin the lower tail, within cities is driven by immigrants.

22

fact one can argue that the way in which different researchers have thought about the distinctive featuresof immigrants relative to natives has shaped the type of questions that different strands of the literatureinvestigating the effects of immigration on labor markets have taken.28
A first way to think about immigration is to recognize that immigrants often arrive with an imperfectknowledge of country-specific skills; this deficit impedes workers’ ability to thrive in particular labormarkets (Chiswick 1978). Many authors have measured substantial gaps in wages between immigrants
and natives that tend to disappear over time.29 In this view, immigrants and natives are essentially thesame, except that it takes some time for immigrants to fully adapt to the host country. Papers in thisstrand of the literature include Borjas (2015, 1987); Hanson and Chiquiar (2005); Fernandez-Huertas(2012); Lessem and Sanders (2018); Abramitzky et al. (Forthcoming, 2014).
A second part of the literature – perhaps the largest in number of publications – views immigrants
simply as workers, and studies how immigrants affect natives or how immigrants themselves are influenced
by the migration experience. In the literature that studies the effect of immigration on native outcomes,
there is nothing particular from being an immigrant, but rather the distribution of immigrants over acertain characteristic defining a labor market, like education or location, is different than the distributionof natives. In this sense, immigration is a negative shock to the workers who share characteristics withimmigrants and a positive shock to all other factors of production. Hence, from this view, immigration
has mainly re-distributive consequences, which some papers estimate to be large and others to be small.
Papers that view immigrants as workers and hence can be included in this strand of the literatureinclude Borjas (2003); Llull (2018b); Dustmann et al. (2013, 2017, 2016); Card (1990, 2001, 2005); Borjas(Forthcoming); Monras (Forthcoming); Cadena and Kovak (2016); Caliendo et al. (2018); Cortes (2008);
Davis and Weinstein (2002); Glitz (2012); Friedberg (2001); Lach (2007); Lewis (2012); Burchardi et al.
(2019b); Allen et al. (2019); Morten and Bryan (Forthcoming); Bryan et al. (2014).
Finally, a third strand in the literature emphasizes that immigrants and natives are essentially different factors of production (Ottaviano and Peri 2012). This means that natives and immigrants areimperfect substitutes even conditional on observable skills. Papers that estimate or rely on imperfect
substitutability between natives and immigrants include Peri and Sparber (2009); Borjas et al. (2012);
Manacorda et al. (2012); Burstein et al. (2018); Card (2009); Piyapromdee (2017).30 According to thisview, the most important aspect is usually to understand how the arrival of immigrants re-shapes thepatterns of specialization of native workers across tasks, occupations, or sectors.
In this paper we take the view that immigrants and natives are identical except for the fact that
immigrants have an extra good in their utility function, which can only be consumed in their country oforigin. This extra good may represent the consumption by family members, thanks to the remittances; it
may also represent future consumption in the country of origin; or it may reflect that immigrants spend
a part of their time in their home country. Only a relatively small number of papers have effectively seen
28 We are omitting here work that has emphasized that immigrants bring a link to the home economy that may benefit thehost economy. A recent example of this type of research is Burchardi et al. (2019a).
29 There is some debate in this literature on the speed of convergence given the changing “quality” of cohort arrivals. See
Borjas (1985).
30 In this literature, Borjas et al. (2012) argue that the evidence in favor of imperfect native - immigrant substitutability is at
most weak.

23

immigration in this way, usually concentrating on studies of temporary and return migration, see a reviewof the literature in Dustmann and Gorlach (2016) and the recent paper Gorlach (2019). This previous
literature has not investigated, however, how temporary migration might affect the spatial equilibrium
in host economies.
In the model, we abstract from various aspects that previous work has emphasized, for instance thefact that natives and immigrants may be imperfect substitutes or may be distributed differently overcertain important characteristics for the labor market. We do so because our aim is to show how our
new mechanism affects host economies.

4.2

Location choices

The utility function in location c for an individual i from country of origin j is given by:T
ln Uijc = ρ + ln Ac + αt ln Cjc+ (1 − αt )

σ
ln
σ−1



σ−1
αf
αl
N T σ−1(Cjc) σ +(CjN T ) σ
αl + αfαl + αf+ εijcwhere αt denotes the share of consumption devoted to tradable goods, and where αl and αf denote
the weight of consumption in local non-tradable and foreign non-tradable goods, respectively. Tradable
goods are denoted by C T and the basket of non-tradable goods is denoted by C N T . Within non-tradable
goods, σ is the elasticity of substitution between local and foreign non-tradables. Note that there arealternative interpretations for what CjN T represents. It could include consumption in non-tradables in
the home country, remittances sent to relatives, or future consumption in the home country. We do
not explicitly model these different potential channels. We prefer to use a simpler formulation that
encapsulates all of them, rather than attempting to model the specificities that each of these channels
NTshould be thought, in the context of the model, as consumption of housing andmay exhibit.31 Cjc

other non-tradable goods available in location c. For simplicity, we will henceforth use the term “housing”
interchangeably with the term “non-tradable goods”.
Importantly, the α’s govern the shares of expenditure on the various types of goods. The difference
between natives and immigrants is that for natives αf is assumed to be zero, as stated more formallybelow. Besides this, ρ is a constant that ensures that there is no constant in the indirect utility function
to be derived in what follows, ε is an extreme-value distributed idiosyncratic taste parameter for living
in location c, and Ac denotes local amenities.
Individuals maximize their utility subject to a standard budget constraint given by:TNT
pT Cjc+ pc Cjc+ pj CjN T ≤ wjc
αfl
We assume αt + αl + αf = 1 and define the auxiliary parameters ᾱl = αlα
and ᾱf = αl +α
. We
+αf
f

assume that tradable goods are the numeraire, hence pT ≡ 1. By utility maximization, we then obtainthe following indirect utility of living in each location (derivation in Appendix C.1):
31 Moreover, it is very plausible that the importance of each of these channels differs from one type of immigrant to another.
For instance, remittances may be more relevant for low-skilled immigrants, while future consumption may be more relevant for
high-skilled immigrants. We do not attempt to address this heterogeneity in this paper.

24

ln Vijc = ln Vjc + εijc = ln Ac + ln(wjc ) − (1 − αt ) ln p̄jc (ᾱl , ᾱf ) + εijc ,

(4.1)

where
1

p̄jc (ᾱl , ᾱf ) = (ᾱlσ p1−σ
+ ᾱfσ p1−σ
) 1−σ .
cj
Given this indirect utility, workers decide where to live by selecting the location that delivers thehighest level of indirect utility given the realization of the taste parameter. Given the distribution of ε,the outcome of this maximization yields:
1/λVjc
πjc = P
=
1/λ
V
k jk



Vjc
Vj

1/λ

where λ is the parameter governing the variance of εijc , Vj = (

,

(4.2)

P
k

1/λ

Vjk )λ is the value of the economy

to workers from country of origin j, and πjc is the share of workers from j that decide to live in city
c as a function of indirect utilities. Note that indirect utility increases in wages and local amenities
and decreases in local prices. Thus, locations with higher wages, higher amenity levels, and lower priceindices will attract more people.

4.3

Production of tradable goods

Tradable goods are produced by one-worker firms using one unit of labor as the only input. Thus, theoutput value of tradables in city c is:

QTc = Bc Lc
where Lc =

P
j

(4.3)

Ljc is the sum of workers from all origins who live in c. Bc is the technological levelof city c for the production of tradables. If it depends on Lc , we have agglomeration externalities. In
particular, we can assume that Bc (Lc ) = Bc Lac with a ≥ 0.32 We will come back to this point in Section
5, but we ignore it in the presentation of the model to keep it simple. Note also that we are assumingthat natives and immigrants are perfect substitutes.33
The marginal revenue of hiring an extra worker is given by Bc . The cost of hiring an additional
worker, possibly from origin j, is the wage that the worker receives, which we denote by wjc . Thus, theextra profit generated by hiring an additional worker is given by Bc − wjc . The average cost of hiring
workers across all the cities is given by w̄. Note that we can choose to re-express the average amenity
level in the economy so that this average is relatively close to 1. Thus, using a Taylor expansion andFtaking logs, we have that (Bc − wjc ) ≈ Bc − 1 − ln wjc = ln B̃c − ln wjc = Sjc. This expression is thevalue of a new hire.
32 Note that agglomeration forces cannot be too strong to guarantee the existence of equilibrium.
33((

to introduce imperfect substitutability between natives and immigrants by assuming that Lc =PIt is not ρcomplicatedρI 1/ρ
j6=NLjc ) I + LN c )I, where LN c indicates natives in location c.

25

4.4

Labor market

We assume that labor markets are not competitive. Most of the literature on immigration has assumed
that labor markets are perfectly competitive. However, there is ample evidence that a number of phenomena are better understood with non-competitive labor markets. This includes, for example, thelong-lasting consequences of job loss or year of entry into the labor market (Davis and von Wachter 2011;
Oreopoulos et al. 2012; Jarosch 2016), the literature on discrimination in the labor market (Becker 1957;
Black 1995), and most of the literature investigating unemployment. In this paper, we argue that thefacts shown in our empirical section are explained quite naturally by assuming non-competitive labormarkets, although this assumption is not key for our results. What is crucial for our argument is thatwages reflect, at least in part, the value of living in a location for each worker.
Firms and workers meet, negotiate over the wage, and split the total surplus of the match. A worker’s
surplus in matching with a firm is given by:W
Sjc= ln Vjc

Hence, we make the simplifying assumption that once located in a city, the worker’s surplus no longer
depends on the initial taste shock drawn (which we assume is unobservable to the firm) and that his
outside option to working is receiving an indirect utility of zero.34 That is, a worker who chooses city cbenefits from the local indirect utility derived in that city.
The outcome of the negotiation between workers and firms is determined by Nash bargaining. Workers’ weight in the negotiation is given by β. Thus, a share β of the total surplus generated by a match
accrues to workers. Using this assumption, we can determine the wage levels of a worker from countryof origin j living in location c:ln wjc = −(1 − β) ln Ac + β ln B̃c + (1 − β)(1 − αt ) ln p̄jc

(4.4)

This equation shows standard results from the spatial economics literature. Higher wages in a cityreflect lower amenity levels, higher local productivity, or higher local price indices.
The firm profits are given byPcB̃c Lc −P P
cjwjc Lcj and are positive as long as Bc are sufficiently

large because of the non-competitive nature of the labor markets. We assume that they are distributed
to absentee firm owners, who only consume tradable goods (see other papers in the literature that makesimilar assumptions, like Eeckhout et al. (2014)).35

4.5

Housing market

For the sake of simplicity, we assume that housing is supplied by absentee landlords and that supply is
increasing in the local price of housing.36 A special case of this assumption is that there is a fixed supply
34 The basic results of this paper are not sensitive to the exact specification of the worker surplus as long as it depends
positively on local wages and amenities and negatively on local price levels.
35 Alternatively, we could assume that firm profits are distributed to workers who each hold a representative portfolio of thefirms in the economy. While this would have implications for welfare, it would not affect the main predictions of the model interms of location choices, wages, and local prices.
36 A number of papers in this literature assume absentee landlords. See, as an example, Eeckhout et al. (2014).

26

of housing in each location.
Demand for housing is, in this model, the demand for the non-tradable local goods introduced before.
The demand for housing is different between natives and immigrants because wages are different andbecause the weight of housing in total expenditures is also different.
More explicitly, we assume the supply of housing is given by Hc (pc ), an increasing function in housing
prices pc that reflects that at higher prices builders want to build more housing units. Local housing
prices are then defined by market clearing in each city:

Hc (pc ) =

X

NT
Cjc
= (1 − αt )(jX ᾱl σ σ−1
((

j6=N

pc

) p̄jc Ljc wjc ) +1
LN c wN c ),
pc

(4.5)

which can be transformed intopc =(1 − αt ) σ X p̄jc σ−1[ᾱl()
Ljc wjc + LN c wN c ].
Hc (pc )
pc

(4.6)

j6=N

This expression defines housing prices as a weighted average of the demand for housing of natives
and immigrants.37

4.6

Properties

Given these primitives of the model, in this subsection we derive a number of properties. These properties
are the basis for the structural estimation described in Section 5.1. The difference between natives andimmigrants is the weight they give to local and foreign price indices:
Assumption. Natives only care about local price indices so that αf = 0 and αl = α. Immigrants careabout local and foreign price indices so that αf 6= 0 and αl + αf = α.
Proposition 1. Under the assumptions made, there is a gap in wages between natives and immigrantsthat increases in the local price index and that is larger when pj is lower. The wage gap is given by thefollowing expression:

ln wN c − ln wjc = (1 − β)(1 − αt ) ln(pc /p̄jc )(4.7)

Proof. Appendix C.2

This expression highlights that there are no differences in the wage gap between natives and immigrants only in two extreme cases. First, if αt = 1, then all income is spent on tradable goods andtherefore the price difference in price indices of non-tradables is irrelevant. Second, when β = 1, workers
have all the bargaining power and always demand a wage equal to their output as can be seen from (4.4).
Thus, both local amenities and prices of non-tradables are not reflected in wages.
37 An alternative to this assumption is to assume that natives and immigrants consume one unit of housing as is done in manyother papers in urban economics, and that consumption of non-tradables reflects both this housing unit and other non-tradables.
This alternative results in a simpler relationship between city housing prices and native and immigrant population.

27

It is also worth noting that differences in the price index of the country of origin do not play a directrole only in the special case of σ = 1. In this case, the share of expenditure in home country goods isalways the same, irrespective of the prices. If instead σ > 1, then there is some degree of substitutability
between local and home consumption, which increases with σ.
In Section 3, we have also shown empirically that immigrants concentrate in higher proportions inlarger, more expensive cities. This can be summarized in the following proposition:
Proposition 2. Under the assumptions made, immigrants concentrate in expensive cities. The spatial
distribution of immigrants relative to natives is given by:βt λ
Ak B̃k /p1−α
πjc
1
k
ln
= β(1 − αt ) ln(pc /p̄jc ) + ln Pk
β
πN c
λ
t λ
Ak B̃k /p̄1−α
jk
k

P

(4.8)

Proof. Appendix C.2
As for the wages, there is no difference in the location choices between natives and immigrants if
αt = 1. However, the role of the bargaining power parameter for the distribution of immigrants relative
to natives is different. If β = 1, immigrants benefit most from locating in more expensive cities as they
enjoy the same wages as natives despite being less affected by the local price levels. If on the contrary
firms have all the bargaining power and thus β = 0, the wages offered to immigrants fully take into
account the prices they face, which implies that they do not benefit more than natives from living in
expensive cities. Hence, the spatial distribution of natives and immigrants would be the same.
Propositions 1 and 2 are directly linked to the facts that we report in Section 3. They show theconcentration of immigrants and that immigrants receive lower wages than natives in expensive cities.
We can use the allocation of workers across locations to obtain the equilibrium size of the city. In
particular, the following proposition characterizes the distribution of workers across cities given the total
native and immigrant populations (LN and Lj for each country of origin j).
Proposition 3. The equilibrium size of the city increases in local productivity and amenities accordingto:β

Lc = (Ac B̃c )

β
λ

X
j

(1−αt ) λβt λ(Ac B̃c /p1−α
)
c
+P
LN
P
(1−αt ) β1−αt βλ(Ak B̃k /p̄jk)(Ak B̃k /pk)λkk

Lj /p̄jc(4.9)

Proof. Appendix C.2
Note that this proposition also means that immigrants make large cities even larger. That is, because
they care less than natives about the cost of large cities (i.e., congestion), they enable big cities to becomelarger. Moreover, it shows that cities are large because they are either productive (Bc ) or pleasant tolive in (Ac ). Thus, conditional on amenity levels, immigration concentrates the population in moreproductive cities.
To see the aggregate effect of immigration on total output via immigrants’ location choices, we canobtain an expression of total output per capita depending on immigrant shares.

28

Proposition 4. Aggregate output per capita increases with the share of immigrants in the economy andis given by the expression:


q=

X

β

β+λ
β

(Ac B̃c

)

β
λ

c

X
j

(1−αt ) λ
Lj
/p̄jc
L
(1−α ) β(Ak B̃k /p̄jk t ) λ
k

P



β+λ

β

t λ
(A B̃ β /p1−α) LNc+ P c c1−αt β(Ak B̃k /p
)λ L

P

c

k

(4.10)k

Proof. Appendix C.2
In Section 4.4, we mentioned the possibility of allowing for agglomeration forces (external to firms),
which we model with an agglomeration parameter a > 0. When there are agglomeration forces, themovement of economic activity towards more productive locations makes these locations even moreproductive. This, in turn, creates even more incentives for immigrants and natives to be in these locations.
Hence, our results are stronger when a > 0 but qualitatively unchanged.
A final property of the model is that immigrants have a heterogeneous effect across locations on the
demand for housing. On the one hand, immigrants consume housing but spend a smaller fraction of
their income on housing than natives. This increases the demand for housing but less than it would if
immigrants consumed like natives. Hence, immigrants tend to reduce the per capita demand for housing
at the local level. Across cities, immigrants are drawn towards expensive cities. Hence, the increase in
the local aggregate demand for housing is larger in expensive than in cheaper cities. We show this more
explicitly in the estimated model.

5Model estimation and counterfactuals

5.1

Estimation

There are three key parameters in the model. First, we need to estimate αf , which governs the (average)
importance of home country in total expenditures. Second, we need to estimate σ, which measures theheterogeneity across immigrants from different countries of origin. And third, we need an estimate of λ,which governs how much of the immigrant-native differences are observed in wages versus locations.
To obtain the first two key parameters, we use the relationship between wage gaps and city prices
across countries of origin. We estimate the model combining 1990, 2000, and 2010 Census and ACS data
and World Bank real exchange rate data. We use the exact same data that we used for documenting
immigrant heterogeneity in Section 3.2.1, except that we limit the local price to include only the costof housing. In our empirical analysis, we have used local price levels that are a weighted average ofthe national consumer price index (including tradable goods) and the city-specific rental price indicesfollowing Moretti (2013). However, in the model, pc refers to the price of non-tradable goods only. For
the estimation and solution of the model, we therefore proxy pc with the rental price component of thelocal price index. While non-tradable goods might include other goods apart from housing, this is themost directly measurable component of the cost of living in a location. Moreover, to the extent that
other non-tradable goods require land, for example barbers or other local services, their prices should bestrongly correlated with local housing costs.

29

We first use the relationship between wage gaps and local price indices that the model generates atthe country of origin-MSA level given by equation (4.7) to estimate {ᾱf , σ}. More specifically, as can beseen from the proof of proposition 4 in the appendix, we obtain:w∂ ln wN,cj,c∂ ln pcw∂ ln wN,cj,c∂ ln pc ∂ ln pj= (1 − β)(1 − αt )(1 − Ωl )= (1 − β)(1 − αt )(1 − σ)Ωl (1 − Ωl )where Ωl = (ᾱlσ p1−σ)/(ᾱlσ p1−σ
+ ᾱfσ p1−σ
) is the share of consumption on local goods and a functionccjthat depends on the two parameters of interest, ᾱf and σ, and on the relative price index of foreign tolocal goods. We evaluate this term at the average city price level and real exchange rate in the year 2000
(to obtain a common Ωl ). In particular, we use the fact that on average origin country price levels are
52% of the price level in the United States.
To obtain the values of the above derivatives, we estimate the specification in column 6 of Table 5
but use the rental price component to measure the prices of non-tradable goods instead of the overallcity price index. The coefficient of the rental price is -0.168 and the coefficient of its interaction with thereal exchange rate is 0.067.38 Thus, we set the first derivative equal to former and the second derivativeequal to the latter value:39(1 − β)(1 − αt )(1 − Ωl ) = 0.168(1 − β)(1 − αt )(1 − σ)Ωl (1 − Ωl ) = −0.067
This is a (non-linear) system of two equations and four unknowns: {ᾱf , σ, β, αt }. We reduce thedimensionality of the parameter space by assuming that β = 0.2 and αt = 0.4. This means that weassume that the weight of workers when bargaining for wages is 20%, and that the share of consumptionthat goes to non-tradables is 60%.
There exist various estimates of the workers’ bargaining weight in the literature. Recent work suggeststhat an estimate of 20% is reasonable. For example, Lise et al. (2016) obtain an estimate of around 20%
for workers with, at most, a high school diploma, and 30% for college graduates. Since immigrants withlower education levels are relatively more prevalent in the United States, we opt for the lower estimate.40
Note that an estimate of 20% means that firms can extract quite some value from workers’ location
decisions.41 This implies that, in the context of our model, wages reflect to a large extent, the valueof living in each location. The tradable goods weight of 40% is based on the sum of the weights of
those goods in the BLS consumer price index (CPI-U) that are either tradable or difficult to substitutewith goods from the origin because they are mainly consumed locally. Specifically, these are Food and
38 Note that because we demean variables, the coefficient of the rental price indicates the effect on the wage gap at the mean
real exchange rate.
39 Because in the model we define the gap as native wage minus immigrant wage, we have to switch the signs of the coefficients.
40 All results are virtually unchanged when using a bargaining power of 0.3 (see Appendix D).
41 See also the survey article Manning (2011). In recent papers, the range of estimates moves from 5 to 34%.

30

beverages, Apparel, Transportation and Education and communication.42 In Appendix D, we test therobustness of the model predictions to setting the tradable share to 60%. This means that non-tradable
goods roughly have the same weight as the Housing component in the CPI-U. As non-tradable goods
usually include more than just housing, we view a tradable share of 60% as an upper bound of the actual
share of tradable consumption.
Once we have assumed specific values for αt and β, we are left with a system of two equations andtwo unknowns. We solve this system (numerically) and obtain the values ᾱf = 0.35 and σ = 1.61. These
parameter estimates have clear economic meaning. The fact that ᾱf is around 35% means that the
distribution of immigrants across locations and their wages is consistent with the fact that, on average,
immigrants consume around 35% of non-tradables in their country of origin. This represents around 21%of their total consumption (αf in the utility function defined above), since 60% of income is spent, on
average, on non-tradables. This number is close to the number estimated in column 4 of panel A of Table
8 using consumption data directly. The elasticity of substitution σ is identified from the heterogeneity
across countries of origin. An elasticity larger than one means that immigrants substitute consuming
locally for home country consumption. Thus, immigrants from cheaper countries consume relatively
more in their country of origin than immigrants from more expensive origins. Our estimate of σ = 1.61
captures quantitatively the extent to which immigrants substitute local and foreign consumption. In
Appendix D.1, we show how alternative assumptions on β and αt change our estimates of αf and σ.
Using a 30,000 point grid, we obtain a range of estimates for αf that goes from 0.15 to 0.25, and a range
for σ that goes from 1.5 to around 2.5.
To estimate λ, we use equation (4.8) and the estimates of β, αt , σ, and αf . From these we can obtain
the relevant price index for each country of origin and estimate equation (4.8) with PPML as we did in
Table 5. We obtain that λ1 β(1 − αt ) = 10.06 with a standard error of 1.30.43 From this we get λ ≈ 0.012.
The implied (internal) migration elasticity (which is 1/λ) is slightly higher than other estimates in theliterature, see Monras (2015) or Caliendo et al. (2015). However, the comparison is not straightforward
since the variation used in previous literature is quite different from what we use.
For the productivity levels, amenities, and housing-supply elasticities across cities, as well as local
agglomeration forces, we rely on prior literature. We use the productivity and amenity levels estimatedby Albouy (2016) for 168 (consolidated) MSAs, which are the ones we use to solve and simulate themodel. The Albouy model is similar to ours except for the fact that we take into account the role ofimmigrants. For the housing-supply elasticities, we rely on Saiz (2010).44 Finally, we use an estimate of
local agglomeration forces of 0.05, which is consistent with the consensus in the literature (Combes andGobillon 2014; Duranton and Puga 2004).
42 The remaining components of the CPI-U are Housing, Medical care, Recreation, and Other goods and services. Whilehousing is also consumed locally, unlike transportation or education, it can be partially substituted with home consumption, forexample by renting a low-quality apartment in the host country while sending remittances or saving to rent or buy an apartmentof higher quality in the home country. This notion is consistent with our findings on differences in housing expenditure between
natives and immigrants in Section 3.3.
43 Note that we remove the term ln(

Pt
Ak B̃k /p1−α
k

 βλ

P

)/(

t
Ak B̃k /p̄1−α
jk

 βλ

) from equation (4.8) using country oforigin fixed effects.
44 Saiz (2010) reports housing-supply elasticities at the primary metropolitan statistical area (PMSA), so we use Albouy(2016)’s crosswalk between PMSAs and consolidated metropolitan statistical areas (CMSAs).
k

31

k

In our baseline solution of the model with an immigrant worker share of around 18%, we use the rental
prices from the data as equilibrium housing prices p∗c . We then make use of the housing market equation(4.5) to back out the equilibrium housing supply Hc∗ . When we use the model to perform counterfactuals
by varying the share of immigrant workers in the economy, we apply the housing supply elasticities from
Saiz (2010) to obtain the counterfactual equilibrium housing supplies and prices for each city. Thus, weapproximate the housing supply equation by Hc (pc ) = (pc /p∗c )ηc Hc∗ , where ηc is the city-specific housing
supply elasticity estimated by Saiz (2010).45 Table 9 summarizes the value and source of our calibrationand estimated parameters.

Table 9 goes around here

5.2

Comparison of the model versus the data

5.2.1

Non-targeted moments I: Labor market data

Once we have all the parameters – those that we estimate ourselves and those that we borrow fromthe literature – we can compare the quantitative predictions of our model with the data. Using various
moments of the data should serve to show that our model can quantitatively match some of the key
features of MSA-level cross-sectional US data.
In Figure 5, we plot a number of variables against the estimate of city level productivity. Note that
our estimation of the model is at the city-origin level, while the moments in Figure 5 are at the MSA
level. The underlying productivities and amenities estimates taken from Albouy (2016) are the primitive
parameters that drive the results on both location and wages. Appendix Table F.6 gives an overview
over these parameters for the bottom 20 and the top 20 cities in terms of productivity.
The top-left graph in Figure 5, labeled as panel A, shows that the population distribution across US
cities generated by the model is very similar to the distribution in the data both in terms of steepness
and dispersion. The model only performs somewhat worse at the extremes of the distribution. It
underpredicts the size of the two largest cities, which are New York and Los Angeles, while it somewhat
overpredicts the size of the smallest cities. The model matches remarkably well the relationship between
wages (centered around the mean) and productivity as shown in panel B of Figure 5. In Appendix D.2
we show that this fit does not change substantially with alternative calibrations of β and αt .

Figure 5 goes around here

The model also does a fairly good job in explaining the immigrant population shares and nativeimmigrant wage gaps (aggregated at the city level). That is, the model predicts productivity to bepositively related to immigrant shares and negatively related to immigrants’ relative earnings, mimicking
the relationships in the data. Naturally, there is less dispersion in the model than in the data, as all
45 Results do not change substantially if we assume inelastic supply of housing instead.

32

differences between locations of similar productivity are only based on variation in amenities and nontradable prices, while in the real world there are many more sources of heterogeneity that drive immigrantshares and wage gaps.
It is interesting to see that there are some outliers in terms of immigrant shares. The smaller MSAs
with high shares of immigrants in the data are always close to the Mexican border. This is something thatthe model cannot match. Another outlier with respect to the prediction is the most productive city, San
Francisco, for which the model predicts an immigrant share of around 70% – almost twice as high as in
the data. San Francisco is a special case because it is at the extreme end of the distribution with respect
to all of its characteristics (see Table F.6). It is the most productive city and has the highest rental
price index by a large margin. Moreover, it has the second highest amenity value (after Santa Barbara)
and the second lowest housing supply elasticity (after San Diego). Naturally, for such a location, themodel predicts an extreme outcome in terms of the number of immigrants, who are attracted by thehigh nominal wage, which is driven by both the exceptionally high productivity and high non-tradable
price level. Because of the large discrepancy between data and model for this special case, we drop San
Francisco from the counterfactual analysis that we perform in the next section.

5.2.2

Non-targeted moments II: Consumption data

A second way to confront the model to non-targeted moments is to turn to consumption data. Note that
we estimate the model using exclusively labor market data. From this we obtain two key parameters for
consumption: the share of consumption that immigrants devote to home-country goods and the elasticity
of substitution between consuming in the home and host economies. We can thus compare our model tothese two moments.
As mentioned before, on average, the model predicts that immigrants (from all countries of origin)spend around 21 percent of their income in their countries of origin. We can compare this number tothe estimate provided in Table 8, Panel A, column 4. This estimate suggests that Mexicans – the only
immigrants that we can identify in the Consumption Expenditure Survey data – spend around 22 percent
less locally than similar looking natives, which is quite close to the 21 percent estimate implied by themodel. It is worth keeping in mind for this comparison that Mexicans are the largest immigrant group in
the US (and hence driving to a large extend the estimate implied by the model), and that if anything, we
would expect that the importance of the home country is larger for Mexicans than it is for immigrants
from other countries of origin given both the price level in Mexico and the proximity of Mexico to the
US.
The model also speaks to the heterogeneity in spending that exists across immigrants from different
countries of origin. Consumption Expenditure data does not allow us to identify immigrants from different
countries of origin. However, we used data on housing expenditures from the Census to document theexisting heterogeneity in local consumption by country of origin and how it relates to exchange ratechanges. Using these estimates, which were presented in Table 8, Panel C, column 4, we can predict how
much immigrants from the different countries of origin spend on local housing, which we can confront to
the model’s quantitative predictions.

33

We do this exercise in Figure 6. In panel A, we confront the share of rent expenses that we observe inthe data for immigrants of different countries of origin (each dot is the average for a different country),against the predicted share of local non-tradable consumption in the model. To be able to make thiscomparison we adjust the consumption data for observable immigrant characteristics that we evaluate at
the mean. It is apparent from Panel A of Figure 6 that there is a strong correlation between the model’s
predictions and the data.
Underlying the comparison shown in Panel A is the fact that there might be heterogeneity in housing
consumption across cities that is driven by mechanisms other than the one we highlight in this paper.
For instance, we have assumed for simplicity that there are no non-homotheticities in non-tradable local
consumption, something that may not be true in reality. Hence, to make the comparison tighter between
the model and the data, in Panel B of Figure 6 we control for city fixed effects, before aggregating ourconsumption data at the country of origin. Hence, in this figure the variables are measured as deviations
from the mean. Again, it is apparent from the graph that there is a tight relationship between the modeland the data, which lies reasonably close to a 45 degree line (displayed in the graph).
In sum, the predictions of the model – estimated exclusively using Census (hence labor market)
data – on consumption patterns of immigrants by country of origin do a remarkable job at predicting
consumption data. This gives further credibility to the quantitative merits of our model.

5.3

The impact of immigration on the spatial equilibrium

In this section we use our model to understand the quantitative importance of the fact that immigrants
consume a fraction of their income in their countries of origin. In particular, we perform two counterfactual exercises to investigate the changes in the equilibrium arising from immigration. First, startingfrom the actual number of immigrants and natives, we simulate an increase in the population equal to
the size of the actual immigrant share under the assumption that immigrants behave exactly like natives.
That is, the weight on home consumption αf is equal to zero both for natives and new incoming workers.
Second, we repeat this simulation assuming that the new arrivals’ αf is equal to its estimated value. By
comparing the predictions of these two simulations, we can quantify the importance of the mechanismthat we highlight throughout the paper.46
More concretely, we calculate the city-level percentage changes in four outcome variables predictedby the model when the number of immigrants increases to 20% of the overall population (holding theactual distribution over countries of origin as the one observed in the Census data). These four variables
are the overall population, the native population, the prices of non-tradable goods and native wages.
We perform this exercise both with and without agglomeration forces (i.e., with a = 0 and a = 0.05 inequation (4.3)).

Figure 7 goes around here
46 Note that an alternative way to isolate the effects of immigrants’ consumption choices would be to simulate an increase in

the share of immigrants while keeping total population constant and calculate the predicted changes in equilibrium outcomes.
The results using this alternative are almost identical to those we report here, which is why we do not even include them in an
appendix. Previous versions of this paper performed this alternative exercise.

34

The blue dots (each dot represents a city) in Figure 7 show the predicted equilibrium changes of thefirst simulation, which captures the effects of a pure increase in population. In this exercise, the variationin the predicted population growth rates across cities illustrated in panel A is driven by the city-specifichousing supply elasticity. If the housing supply elasticity was the same across cities, the populationin every city would just grow at the same rate as the overall population. In the data, the housing
supply elasticity tends to be higher in smaller cities, which implies that prices rise less strongly withthe population induced increase in the demand for housing. Hence, low-productivity cities can attract
relatively more workers than large cities, where housing prices rise more strongly, as seen in panel C.
Thus, the distribution of population shifts towards smaller, less productive cities and this decreases theaggregate worker productivity in the economy, which is the first main take-away from this simulation.
The higher living costs are only partially compensated by an increase in native wages, which is justaround half of the increase in price levels, as seen in panel D. Therefore, the second result is that thewelfare of native workers decreases, especially in cities with low housing supply elasticities.47
If we assume that there are positive agglomeration forces (red crosses in the graphs of each panel),population gains in a city also result in city-level productivity increases. Part of these productivity
increases translate into higher wages (Panel D), which in turn, increase the demand for housing. Lowproductivity cities see, with agglomeration forces, how their housing prices increase by more than when
we did not assume agglomeration forces. This is a result of two forces. First, low-productivity cities
tend to have higher elasticities of housing and, hence, can accommodate more workers without large
increases in housing prices. Second, agglomeration forces increase the income of workers in cities thatgrow the most, increasing the demand for housing. As a consequence, assuming positive agglomeration
forces reduces the variance in the effect of population growth on both wage changes and housing pricechanges across cities.

Figure 8 goes around here

Figure 8 shows the simulated changes in the equilibrium outcomes when the arriving immigrants
behave according to our estimates and, hence, consume a part of their income in their origin (i.e. thisexercise effectively estimates the effects of doubling of the immigrant population). Now, the effects are
drastically different. This is because the new immigrants, in addition to having incentives to settle in acity where they would exert low pressure on housing prices, have strong incentives to settle in cities where
nominal earnings are high. This implies that high-productivity cities can attract more of the additional
workers compared to the previous simulation. Therefore, as panel A shows, both high-productivity cities
and low-productivity cities with very high housing supply elasticities are the ones that grow the most,whereas most cities with intermediate productivity levels grow only by little. The growth rates of highproductivity cities are now up to 45%, whereas they were only between 10% and 20% previously. As
a result of immigrants’ strong incentives for cities with high nominal wages, the changes in price levels
47 Note that we do not explicitly model the production of non-tradable goods, i.e. housing. If native workers were owners of

housing, their welfare would increase due to the rise in prices.

35

are not anymore a mere mirror image of the changes in population but instead strongly increase inproductivity, which drives natives to move from more into less productive cities as shown in panel B.
Agglomeration forces do not have a smoothing effect on prices and wages in this simulation anymore
because the additional increase in demand for housing in high-productivity cities implies that the growth
in price levels increases even more steeply with productivity than in the previous simulation. While
prices and wages almost uniformly increase by 9% and 4.5%, respectively, in Figure 7, these increases
range from 5% to 12% for prices and from 2.5% to 6% for wages in Figure 8.
Overall, these two simulations suggest that immigrants’ location choices in combination with agglomeration forces can potentially account for a significant part of the increase in the dispersion of living
costs and nominal wages across metropolitan areas in the US, in line with evidence reported in Moretti(2013). In the context of the model, however, real-wage dispersion does not increase since price changes
are more pronounced than changes in nominal wages.

5.4

The impact of immigration on aggregate productivity and welfare

In Table 10, we present the effects of immigration on aggregate labor productivity (i.e., average tradable
output produced per worker), native workers’ welfare (measured as the common component of the indirect
utility of natives expressed in equation (4.1), Vc ), and house owners’ welfare.48 The latter is calculated
as the hypothetical change in welfare that arises due to a change in income caused by changes in housing
prices across cities.49
As mentioned before, when we assume that immigrants consume like natives (Counterfactual 1),
an increase in overall population implies relatively higher population growth in low-productivity cities,
where housing supply is on average more elastic. Given our estimated model, this results in a decreasein aggregate labor productivity of around 0.47% when we assume no agglomeration forces. Moreover,the higher housing prices lead to a decrease in natives’ welfare of around 0.84%. House price increases
are, on average, around 3.58%. We show these estimates in the first row of Table 10.
In contrast, when immigrants spend a part of their income in their origin country (Counterfactual 2),
aggregate labor productivity increases by 0.64%. This is because high-productivity cities grow relatively
more in this counterfactual. Native workers’ welfare decreases by only 0.21% as immigrants put lesspressure on housing prices when consuming a part of their income abroad. Home-owners’ welfare, which
is driven by housing price changes, increases by only 2.65% in this case. We show these estimates in thesecond row of Table 10.
By taking the difference between counterfactual 1 and counterfactual 2, we obtain an idea of theimportance of accounting for the fact that part of immigrants’ income is spent in the country of origin,which, in turn, can be considered the differential contribution of immigration to aggregate outcomes.
In the third row of Table 10, we show that immigrants enhance the effect of a population increase on
average labor productivity by around 1.1 and the effect on aggregate native workers’ welfare by around
48 Recall that we abstract from the welfare changes of firm owners, which are not modeled.
49 For simplicity, we assume that house owners are distributed across cities like natives, only own houses in the city the live inand earn income from supplying Hc units of housing at price pc before the population increase and the same quantity at new
prices p0c after the population increase.

36

0.63 percentage points. Instead, house owners lose on average 0.93 percentage points of their welfare
increase due to a smaller rise in housing demand.

Table 10 goes around here

If we assume that there are agglomeration forces, the effect of a population increase on labor productivity is positive (0.55%). This is because new workers increase endogeneously the productivity inthe cities they settle in. Hence, even if population increases concentrate in the least productive cities(where housing is supplied more elastically), on aggregate agglomeration forces dominate. Productivity
increases by 1.85% if the arriving workers choose where to live according to immigrant preferences. In
this case, on top of affecting local productivity, immigrant workers have incentives to live in the mostproductive cities, which are those that can sustain high house prices and wages. Despite the pressurethat immigration puts on house prices, aggregate native workers’ welfare does not decrease with thearrival of immigrants when we assume agglomeration forces. This is a result of the combined effectof higher productivity and house prices. When comparing counterfactual 1 and counterfactual 2 withagglomeration forces we obtain that immigration increases the welfare effect of a population increase byaround 0.6 percentage points. The differential aggregate effect on house owner’s welfare is also similar
in magnitude with and without agglomeration forces.
In Appendix D.2, we perform a range of robustness checks to show that the disaggregate and aggregate
predictions of the model do not change substantially with alternative calibrations of β and αt (i.e. withthe parameters on preferences that we do not estimate directly but instead take from the literature).
Overall we obtain similar results under these alternative calibrations, as can be seen in Figures D.8, D.9,

D.10, and D.11, and Table F.7. We estimate that aggregate productivity gains are in the order of 1 to
2.6 percentage points higher and native worker’s welfare in the order of 0.4 to 0.8 percentage points.
Overall, our model and estimates highlight the importance of taking into account that immigrants
spend an important fraction of their income in their countries of origin. The model-based counterfactualspresented in this section show that acknowledging this defining feature of immigrants changes substantially our understanding of how immigration affects the host economy, both on aggregate and acrosslocations.

6

Conclusion

In the first part of this paper, we document that immigrants concentrate in larger, more expensive cities
and that their earnings relative to natives are lower there. We show that these patterns are stronger
for immigrants coming from countries with low price levels and that immigrant household consume lesslocally than similar-looking native households.
Taking all this evidence together, we posit that these patterns emerge because a share of immigrants’consumption is not affected by local price indices but rather by prices in their country of origin. That is,given that immigrants send remittances home and are more likely to spend time and consume in theircountries of origin, they have a greater incentive than natives to live in high-nominal-income locations.

37

We build a quantitative spatial equilibrium model labor market with frictions to quantify the importance of this mechanism. We estimate the model and show that the differential location choices of immigrants relative to natives have important consequences: economic activity moves from low-productivity
to high-productivity cities. Model simulations suggest that, compared to a counterfactual in which incoming workers behave like natives, immigration has boosted overall worker productivity by around 1.3%
and increased native welfare by around 0.6% on average in US cities.
This paper extends some of the insights in the seminal contribution of Borjas (2001). Borjas’ mainargument is that immigrants choose the locations where demand for labor is higher, thus helping todissipate arbitrage opportunities across local labor markets. We show in this paper that immigrants not
only choose locations with higher demand for labor but specifically more productive locations, and wequantify how much these choices contribute to overall production in the United States.

38

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C. Ronnander, “Integrated Public Use Microdata Series: Version 4.0 [Machine-readable database].,”Minneapolis, MN: Minnesota Population Center [producer and distributor], 2016.
Saiz, A., “Room in the Kitchen for the Melting Pot: Immigration and Rental Prices,” Review of
Economics and Statistics, 2003, 85(3), 502–521.
, “Immigration and housing rents in American cities,” Journal of Urban Economics, 2007, 61(2),345–371.
, “The Geographic Determinants of Housing Supply,” Quartely Journal of Economics, 2010, 125(3),1253–1296.
and S. Wachter, “Immigration and the Neighborhood,” American Economic Journal: Economic
Policy, 2011, 3(2), 169–188.
Silva, J.M.R. Santos and S. Tenreyro, “The log of Gravity,” Review of Economics and Statistics,
2006, 88(4), 641–658.

45

7

FiguresFigure 1: Immigration and cities
Panel A: Relative immigrant share

Panel B: Wage gap

Notes: Panel A of this figure shows the relationship between the relative share of immigrants in an MSA and the MSA population(left) and price index (right). The relative share of immigrants is measured as the number of immigrants in the MSA relative
to all immigrants in the United States divided by the number of natives in the MSA relative to all natives in the United States.
Panel B of this figure plots the MSA-specific component of the wage gap against MSA population (left) and price index (right).
A negative number for the immigrant wage gap means that immigrants are paid less than natives in that metropolitan area.
The figure is based on the sample of prime-age workers (25-59) from the 2000 Census. The MSA price indices are computed
following Moretti (2013). Each dot represents one of 219 MSAs in the sample. Marker sizes reflect MSA price indices in theleft-hand plot and population level in the right-hand plot.

46

Figure 2: City size/price elasticity of relative immigrant share and wage gap by origin price level
Panel A: Relative immigrant share

Panel B: Wage gap

Notes: This figure uses data from the 2000 Census to show the elasticity between the relative immigrant shares (panel A) andthe native-immigrant wage gaps (panel B) with respect to the city size and city price, for each of the different countries of origin
as a function of the country of origin price level. The dots represents the origin-specific coefficients β obtained by estimating
equation (3.1) at the origin-level in case of panel A and equation (3.3) in case of panel B.

Figure 3: City size elasticity of relative immigrant share and wage gap of Mexicans

Notes: This figure uses data from the CPS 1994-2011 to show the relationships between the relative immigrant share andthe (composition-adjusted) wage gap of Mexican immigrants who changed location during the indicated year and the city size
elasticity. More specifically, we estimate the elasticity for each year and plot it against the average real exchange rate of the
Mexican peso to the US dollar during that year. Hence, each dot represents an estimate of the coefficient β for the particular
year based on equations (3.1) and (3.2). We can only compute city size elasticities because price indices can only be computed
using ACS and Census data, which is available only in selected years.

47

Figure 4: City size/price elasticity of wage gap by immigrants’ years in the country

Notes: This figure uses Census data to show the relationships between the city size and city price elasticity of the nativeimmigrant wage gap as a function of the time spent in the United States. Each dot represents an estimate of the coefficient β
for the indicated immigrant group based on a model similar to (3.3) but in which o denotes the groups defined by years spentin the US.

48

Figure 5: Non-targeted moments I: population and wages at the MSA-level
Panel A: Population

Panel B: Wages

Panel C: Immigrant Share

Panel D: Wage Gaps

Notes: This figure compares four untargeted moments in the data and the model. The model is estimated using country oforigin variation. From these estimates, we aggregate to the city level the data generated by the model to compute the four
moments shown in the figure. Each dot represents one of the 168 consolidated metropolitan statistical areas from Albouy(2016).

49

Figure 6: Non-targeted moments II: share of expenditures in non-tradable goods

Panel A: char. adj. comparison

Panel B: char. adj. conditional on city FE

Notes: The y-axis shows the share of expenditures in non-tradable goods predicted by the model for each country of origin
keeping wages constant and subtracting MSA means. The x-axis shows the share of expenditures in the data for each countryof origin adjusted for income and observable characteristics: familiy size, age, marital status and travel time to work.

50

Figure 7: Effects of immigration if new immigrants were like natives (i.e. with αf = 0)
Panel A: Population

Panel B: Native population

Panel C: Non-tradable/Housing prices

Panel D: Native wages

Notes: This figure compares the distribution of selected variables predicted by the model given a native-induced increase inpopulation equal to the size of the actual share of immigrants of 20%, both with and without agglomeration forces. Each dot
represents one of the 168 consolidated metropolitan statistical areas from Albouy (2016) and indicates the percentage difference
to the counterfactual.

51

Figure 8: Effects of immigration with new immigrants consuming in the country of origin (i.e. with αf = 0.21)
Panel A: Population

Panel B: Native population

Panel C: Non-tradable/Housing prices

Panel D: Native wages

Notes: This figure compares the distribution of selected variables predicted by the model given an immigrant-induced increasein the population equal to the size of the actual share of immigrants of 20%, both with and without agglomeration forces.
Each dot represents one of the 168 consolidated metropolitan statistical areas from Albouy (2016) and indicates the percentage
difference to the counterfactual.

52

8

TablesTable 1: List of top US cities by immigrant share in 2000

MSA
Miami-Hialeah, FL
Los Angeles-Long Beach, CA
McAllen-Edinburg-Pharr-Mission, TX
San Jose, CA
Salinas-Sea Side-Monterey, CA
El Paso, TX
Brownsville-Harlingen-San Benito, TX
New York, NY-Northeastern NJ
Visalia-Tulare-Porterville, CA
San Francisco-Oakland-Vallejo, CA
Fort Lauderdale-Hollywood-Pompano Beach, FL
Fresno, CA
San Diego, CA
Santa Barbara-Santa Maria-Lompoc, CA
Riverside-San Bernardino, CA
Ventura-Oxnard-Simi Valley, CA
Stockton, CA
Houston-Brazoria, TX
Honolulu, HI
Modesto, CA

Immig. (%)
64
48
44
44
40
40
38
36
33
33
33
30
29
29
28
28
27
26
26
25

Size rank
23
2
88
25
146
70
134
1
125
6
28
56
15
112
14
61
83
8
55
102

Population
1,056,504
6,003,886
229,812888,632
120,699
291,665
137,429
8,552,276
155,595
2,417,558
799,040
396,336
1,306,175
176,133
1,428,397
362,488
246,980
2,191,391
397,469
203,134

Weekly wage
332
395
258
563
355
300
275
454
306
494
393
327
411
390
388
460
386
427
393
372

Price index
1.13
1.20
0.88
1.52
1.22
0.92
0.90
1.22
0.95
1.38
1.17
0.98
1.19
1.25
1.07
1.23
1.04
1.04
1.23
1.03

Wage gap (%)
-20
-24
-16
-8
0
-14
-17
-19
-7
-10
-12
-8
-13
-8
-11
-17
-14
-18
-4
-3

Notes: This table shows a number of statistics for the sample of metropolitan statistical areas with the highest immigrant shares.
These statistics are based on the sample of prime-age workers (25-59) from the 2000 Census. Weekly wages are computed fromyearly wage income and weeks worked. Local price indices are computed following Moretti (2013). The wage gap is the gap
in wage earnings between natives and immigrants (a negative number means that natives’ wages are higher), controlling for
observable characteristics.

Table 2: Countries with the highest and the lowest real exchange rates
HighestNorwayJapan
BermudaDenmark
Switzerland
SwedenFinlandUnited Kingdom
FranceAustralia

1.36
1.34
1.34
1.30
1.29
1.25
1.22
1.10
1.07
1.07

LowestVietnam
Pakistan
Yemen
Egypt
Sierra Leone
Sri Lanka
Nepal
Indonesia
Tanzania
Nigeria

0.20
0.21
0.23
0.24
0.24
0.24
0.25
0.26
0.26
0.26

Notes: This table lists the top and bottom 10 countries with the highest and the lowest average real exchange rate over 1990,
2000 and 2010 with respect to the United States according to real exchange rate data from the World Bank.

53

Table 3: Immigration in large and expensive cities(1)OLS(ln) Population in MSA

0.531***(0.0540)

Panel A: Relative immigration share
(2)
(3)
(4)
(5)
OLS
FE
OLS
OLS
0.532***(0.0552)

(6)
IV

(7)
FE

0.769***(0.115)(ln) City price8.091***(0.683)8.360***(0.738)10.32***(0.937)1.021**(0.462)

Observations
R-squared
F-stat first stage

764
0.470

764
0.472

764
0.972

764
0.573

764
0.594

764
0.561
61.16

764
0.965

Year FEMSA FE

no
no

yes
no

yes
yes

no
no

yes
no

yes
no

yes
yes

Panel B: Wage gap
(2)
(3)
OLS
FE

(4)
OLS

(5)
OLS

(6)
IV

(7)
FE

-0.107***(0.00608)-0.605***(0.0645)-0.676***(0.0819)-0.124**(0.0564)(1)OLS(ln) Population in MSA-0.0435***(0.00445)-0.0419***(0.00460)-0.0283(0.0213)(ln) City priceObservations
R-squared
F-stat first stage

764
0.405

764
0.456

764
0.777

764
0.174

764
0.491

764
0.485
60.00

764
0.778

Year FEMSA FE

no
no

yes
no

yes
yes

no
no

yes
no

yes
no

yes
yes

Immc,t Natc,t/)), in panel A, and the gap in wages
Immt
Natt
between natives and immigrants adjusted for imperfect substitutability between natives and immigrants (φ̂c,t ), in panel B, on
the size of the city and the city price index. City price indices are computed following Moretti (2013). Column (6) instruments
the local price index by the housing supply elasticity estimated in Saiz (2010). This table uses data from the Census 1980-2000
and the combined 2009-2001 ACS. Robust standard errors clustered at the metropolitan area are reported. * significant at the0.10 level; ** significant at the 0.05 level; *** significant at the 0.01 level.
Notes: This table shows regressions of the relative share of immigrants (ln(54

Table 4: Immigration in large and expensive cities, robustness

Panel A: Rel. imm share, OLS
(3)
(4)
(5)

(1)

(2)

(6)

(7)

(ln) City price8.170***(0.664)9.370***(0.873)10.43***(1.188)10.03***(0.709)8.314***(0.602)

6.336***(0.513)8.360***(0.738)Observations
R-squared

764
0.612

763
0.538

763
0.486

764
0.637

764
0.675

764
0.658

764
0.594

(1)

(2)

Panel B: Rel. imm share, IV
(3)
(4)
(5)

(6)

(7)

(ln) City price10.43***(0.875)10.82***(1.164)13.08***(1.515)12.37***(0.936)

10.12***(0.772)7.815***(0.677)10.32***(0.937)

Observations
F-stat first-stage

764
60.02

763
57.86

763
58.01

764
55.68

764
59.66

764
64.16

764
61.16

(1)

(2)

Panel C: Wage gap, OLS
(3)
(4)
(5)

(6)

(7)

(ln) City price-0.601***(0.0573)-0.861***(0.115)-0.738***(0.106)-0.529***(0.0632)-0.392***(0.0493)-0.870***(0.119)-0.675***(0.0698)

Observations

764

561

745

755

748

753

764

(1)

(2)

(5)

(6)

(7)

(ln) City price-0.694***(0.0761)-0.935***(0.139)-0.996***(0.114)-0.575***(0.0866)-0.371***(0.0853)-1.101***(0.139)-0.746***(0.0887)

Observations
F-stat first-stage

764
59.17

561
58.67

745
60.13

755
59.58

748
59.73

753
59.64

764
57.46

SampleDocum.

Undocum.

<HS

HS

SC

C

No Lat. Am.

Panel D: Wage gap, IV(3)(4)

Notes: This table shows regressions of the relative share, in Panels A and B, and the gap in wages between natives andimmigrants adjusted for imperfect substitutability between natives and immigrants (φ̂c,t ), in Panels C and D, on the size of thecity and the city price index. City price indices are computed following Moretti (2013). Panel A and C show OLS regressions,while panel B and D instrument the local price index by the housing supply elasticity estimated in Saiz (2010). This table uses
data from the Census 1980-2000 and the combined 2009-2001 ACS. Column (1) only includes documented immigrants. Column(2) only includes undocumented immigrants. Column (3) restricts the sample to high-school dropouts. Column (4) restricts
the sample to high-school graduates. Column (5) restricts the sample to workers with some college. Column (6) restricts the
sample to workers with a college degree or more. Column (7) excludes immigrants from Latin American countries. Robust
standard errors clustered at the metropolitan area are reported. * significant at the 0.10 level; ** significant at the 0.05 level;*** significant at the 0.01 level.

55

Table 5: Immigration and heterogeneity: exchange rate variation by country of origin(1)(ln) RER

0.141*(0.0792)(ln) Population in MSA

Panel A: Rel. imm share, PPML
(2)
(3)
(4)
0.141*(0.0779)
0.465***(0.0727)(ln) Population in MSA x (ln) RER

0.153***(0.0445)0.314***(0.112)-0.214***(0.0679)

(5)

(6)

(7)

0.141*(0.0748)-0.101(0.0665)-0.0891*(0.0532)

2.119***(0.285)1.877***(0.347)-0.356***(0.122)-0.269*(0.154)-0.352***(0.102)

26,70026,70026,70026,700

(4)

(5)

(6)

(7)

0.0113(0.0163)
0.0215(0.0387)
0.0342***(0.00415)

0.135***(0.0101)

0.0306(0.0200)

0.0322(0.0198)-0.341***(0.0852)-0.332***(0.0827)
0.0781**(0.0305)-0.0134(0.119)0.0833***(0.0303)0.145***(0.0392)-0.0496(0.219)-0.207***(0.0508)(ln) City price(ln) City price x (ln) RER

Observations

26,700(1)(ln) RER

0.136***(0.0102)(ln) Population in MSA

26,70026,700Panel B: Wage gap, OLS(2)(3)
0.135***(0.01000)-0.0418***(0.00252)(ln) Population x (ln) RER

0.0125(0.0162)-0.0400***(0.00262)
0.0339***(0.00407)(ln) City price(ln) City price x (ln) RER

Observations
R-squared

16,621
0.058

16,621
0.075

16,621
0.154

16,621
0.166

16,621
0.069

16,621
0.146

16,621
0.164

Year FE
Origin FE
MSA FE

yes
no
no

yes
no
no

yes
yes
no

yes
yes
yes

yes
no
no

yes
yes
no

yes
yes
yes

Notes: This table shows regressions of relative immigrant shares and wages on population and city prices, real exchange rates(RER), and their interaction. The regressions are limited to the top 100 MSAs in size and 89 sending countries for the years
1990, 2000, and 2010. Standard errors clustered at the MSA-country of origin level are reported. We weight each observationby the number of individuals in a year-MSA-origin cell. * significant at the 0.10 level; ** significant at the 0.05 level; ***significant at the 0.01 level.

56

Table 6: Immigration and heterogeneity: Mexican Immigrant Flows by state of origin and destination(ln) GDP pc US x (ln) GDP pc Mex(ln) GDP pc US(ln) GDP pc Mex(1)
Rel. Flows(2)(ln) Rel. Flows(3)
Rel. Flows(4)(ln) Rel Flows(5)
Rel. Flows(6)(ln) Rel. Flows(7)
Rel. Flows(8)(ln) Rel. Flows-0.153**(0.0756)
1.995**(0.962)
1.766*(0.896)-0.300***(0.0791)
4.756***(0.905)2.869***(0.991)-0.153**(0.0756)
2.018*(1.020)1.769*(0.896)0.0117(0.00726)-0.0238(0.0889)-0.293***(0.0795)
2.598**(1.009)2.798***(0.994)0.126**(0.0580)
2.148***(0.515)-0.153*(0.0775)-0.224***(0.0669)-0.0685***(0.0147)-0.230***(0.0775)

1,581
0.158
no
no
yes

1,457
0.391
no
no
yes

1,581
0.159
no
no
yes

1,457
0.452
no
no
yes

1,581
0.469
yes
yes
yes

1,457
0.826
yes
yes
yes

1,550
0.407
yes
yes
no

1,426
0.813
yes
yes
no

(ln) Pop Mex(ln) Pop US

Observations
R-squared
Origin FE
Destination FE
Including California

57

Notes: This table shows the results of regressing the flows of immigrants from origin i to destination j relative to all migrants from Mexican state i on the GDP per capita at
destination (j), at origin (i), and the interaction between the two. We also control for total population at origin and destination. The data covers 31 sending Mexican states and
51 receiving US states. Columns (7) and (8) exclude the largest destination state (California) from the regression. Data from the Matricula Consular 2016. Robust standard
errors clustered at the destination level are reported. * significant at the 0.10 level; ** significant at the 0.05 level; *** significant at the 0.01 level.

Table 7: Immigrants’ wages before and after amnesty(ln) Population in MSA x Immigrant(1)(ln) Wage(2)(ln) Wage-0.0349***(0.0118)-0.0443***(0.0116)(ln) Population in MSA x Before 82(3)(ln) Wage(4)(ln) Wage(5)(ln) Wage-0.393**(0.168)-0.460***(0.161)(6)(ln) Wage

0.00954***(0.00318)(ln) City price x Immigrant(ln) City price x Before 82
Convergence rate (35 - years in US)-0.00299***(0.000900)-0.00378***(0.000977)-0.0163***(0.00169)-0.0102***(0.00332)-0.0108***(0.00272)

0.120***(0.0308)-0.0207***(0.00204)

Observations
R-squared
Xs
Sample1,196,666
0.235
yes
Before 82

1,191,573
0.238
yes
After 82

114,8170.145
yes
Immigrants

1,196,666
0.240
yes
Before 82

1,191,573
0.242
yes
After 82

114,8170.149
yes
Immigrants

Notes: These regressions use Census 1990 data. In columns 1 and 4, the comparison is between immigrants arrived prior to1982 and natives. In columns 2 and 5, the comparison is between immigrants arrived after 1982 and natives. Column 3 and6, compare immigrants arriving before and after 1982. Figure D.6 in the Appendix shows the regression in Column 6 for eachyear of arrival. Robust standard errors clustered at the metropolitan are level are reported. * significant at the 0.10 level; **significant at the 0.05 level; *** significant at the 0.01 level.

58

Table 8: Immigrants’ expenditure(1)(ln) Total Expenditure

Panel A: Consumer Expenditure Survey data(2)(3)(ln) Total Expenditure (ln) Total Expenditure(4)(ln) Total Expenditure

Mexican-0.325***(0.027)-0.382***(0.021)-0.149***(0.012)-0.226***(0.012)

Observations
R-squared
Year FE
State FE
IncomeCharacteristics

105,975
0.015
no
no
no
no

105,975
0.063
yes
yes
no
no

105,975
0.301
yes
yes
yes
no

105,975
0.312
yes
yes
yes
yes

(1)
(ln) Rents

Panel B: Consumer Expenditure Survey data(2)(3)(ln) Rents(ln) Rents(4)(ln) Rents

Mexican-0.222***(0.059)-0.299***(0.025)-0.097***(0.023)-0.182***(0.021)

Observations
R-squared
Year FE
State FE
IncomeCharacteristics

105,975
0.006
no
no
no
no

105,975
0.079
yes
yes
no
no

105,975
0.226
yes
yes
yes
no

105,975
0.244
yes
yes
yes
yes

(1)
(ln) Monthly rent
Immigrant-0.145***(0.0184)

Panel C: Census and ACS data(2)(3)(ln) Monthly rent(ln) Monthly rent
-0.0741***(0.0146)

Immigrant x (ln) City price-0.110***(0.0236)0.0383(0.0318)(ln) RER(ln) HH income

Observations
Year FEMSA FE
Sample903,825
yes
yes
all

(4)
(ln) Monthly rent

0.271***(0.00486)

0.270***(0.00549)

0.0711***(0.0155)
0.236***(0.00551)

903,825
yes
yes
all

903,825
yesnoall

204,276
yes
yes
Imm. only

Notes: Panel A shows regressions with log monthly gross rents as dependent variable using Census 1990-2000 and ACS 20052011 data of male household heads. Additional controls include dummies for the number of family members living in thehousehold, marital status and age. Panel B shows regressions with log total expenditure as dependent variable using data fromthe Consumer Expenditure Survey. The income controls included in column 3 are dummies for household income bins. The
characteristics added in column 4 include race, occupation, family size and marital status. Standard errors are clustered at
the MSA level in panel A and at the state level in panel B. * significant at the 0.10 level; ** significant at the 0.05 level; ***significant at the 0.01 level.

59

Table 9: Calibrated parameters and structural estimates of the model
Variable
Share of consumption on tradable goods (αt )Workers’ bargaining weight (β)
Share of home goods consumption (αf )Sensitivity to local conditions (λ)
Elasticity of substitution home-local goods (σ)
Amenity levels (Ac )Productivity levels (Bc )Housing supply elasticities (ηc )Local agglomeration forces (a)

Value
0.4
0.2
0.21
0.012
1.61

0.05

SourceComponents of CPI-U (see text)
Lise et al. (2016)
Estimated
Estimated
Estimated
Albouy (2016)
Albouy (2016)
Saiz (2010)
Combes and Gobillon (2014)

Notes: This table shows the estimates of the structural parameters of the model. The structural parameters of the model are
the set of parameters that minimize the distance between the model and the data. For this exercise we only use data on wages
and distributions of workers across locations at the country-of-origin level, taking as given the parameters borrowed from priorliterature.

Table 10: Predicted aggregate effects of immigration∆ Laborproductivity

Counterfactual 1: 20% increase in population
Counterfactual 2: 20% immigrant-induced increase in population
Difference:

-0.47
0.64
1.11

Counterfactual 1: 20% increase in population
Counterfactual 2: 20% immigrant-induced increase in population
Difference:

0.55
1.85
1.30

∆ Native workers’
welfare∆ House owners’
welfareNo agglomeration forces
-0.84
3.58
-0.21
2.65
0.63
-0.93
Agglomeration forces
-0.58
0.00
0.58

3.49
2.71
-0.78

Notes: This table shows the aggregate consequences of new immigration under two different counterfactuals. In Counterfactual
1 we assume that new immigrants consume like natives. In Counterfactual 2 we assume that new immigrants spend 21 percentof their income in their country of origin, as estimated. This table reports the aggregate consequences of these two counterfactuals on three outcomes: average labor productivity, average native worker’s welfare, and average house owner’s welfare. We
report results assuming no agglomeration forces and agglomeration forces of 5%. The difference between Counterfactual 1 andCounterfactual 2 is the effect of immigration on the three outcomes of interest.

60

A

Empirical Appendix

A.1

Return migration

A final and very important reason why immigrants care about price indices in their home country is thatmany of them likely plan to return home at some point during their lifetime (Dustmann and Gorlach
2016; Lessem 2018; Dustmann and Weiss 2007; Dustmann 2003, 1997).
To the best of our knowledge, there are no large, representative data sets directly documenting return
migration patterns. This would require observations in both the destination country and the homecountry over a certain period of time. While there are some data sets that make this possible, they are
generally not very comprehensive.
To obtain a better sense of general return migration patterns in the United States, we turn to Census
data. In particular, we can track the size of cohorts of immigrants and natives across Censuses anduse information on immigrants’ year of arrival to see how many of them are “missing” in the following
Census, and thus likely to have returned to their home countries.
The left-hand graph in Figure D.2 plots these survival rates by age cohort. We observe that morethan 98% of the natives aged between 25 and 30 in 2000 are still present in the 2010 ACS. This survival
rate declines with age. For example, for the population that in 2000 was between 45 and 50 years old, thesurvival rate decreases to around 94%. When we carry out the same exercise for immigrants who arrived
in the United States before 2000, the survival rates decline substantially with respect to natives.50

Figure D.2 goes around here

In the graph on the right-hand side, we estimate return migration rates by taking the difference insurvival rates between immigrants and natives. This is a good estimate if mortality rates for the sameage cohort are similar in both immigrants and natives. We observe that return migration is likely to bevery high for younger cohorts and converges to 0 for older cohorts, perhaps reflecting that as immigrants
grow old in the host country, their ties to the home country gradually diminish. The estimates show that
more than 10% of the immigrant population aged between 25 and 30 in 2000 are no longer in the UnitedStates by 2010. We begin the series at age 25, since these immigrants are already likely to be working in
the United States. Return migration rates are even higher for younger cohorts.
This means that for a large number of immigrants, future consumption takes place in a country otherthan the United States – possibly their home country. Thus, given that immigrants are likely to returnand to care about future consumption, return migration patterns give additional support to the ideathat immigrants partly take into account the price index in their country of origin when choosing theiroptimal location in the United States.
50 We use the years 2000 and 2010 because there are strong reasons to suspect that there is some undercount of immigrants
in Censuses prior to 2000. For example, the number of Mexican immigrants who claim to have arrived before 1990 in the 2000
Census is larger than the total number of Mexicans observed in the 1990 Census. See also Hanson (2006).

61

A.2

Robustness to alternative mechanisms

In this subsection, we investigate a number of alternative hypotheses that could potentially drive thepatterns we have documented so far. In particular, we show that endogenous population, immigrant
networks, human capital, imperfect substitutability to natives, legal status or job finding prospects inlarger cities are unlikely explanations for our findings.

A.2.1

Endogeneity of population levels

One concern about the results shown in the main text is that we use the total population in an MSA
as a running variable to explain our facts, which obviously includes immigrants (note that his concern
only applies to the results where we use population as dependent variable, not prices that we instrumentwith local housing supply elasticities). Hence, there might some endogeneity between relative outcomesof immigrants and a measure, in which immigrants are also included.
To show that this is not driving our results, we estimate equation (3.2), but with native population,
lagged total population and lagged native population instead of total population.

Table F.1 goes around here

Table F.1 shows that using native or lagged population instead results in similar relationships between
city size and native-immigrant wage gaps.

A.2.2

Immigrant networks

An alternative explanation for the relationship between immigrants’ earnings and city size could be that
immigrants earn less in large cities because of the presence of larger immigrant communities there. If
immigrants perceive communities of their country of origin as a positive amenity, they could potentiallyaccept lower wages in large, expensive cities because they are compensated through immigrant-network
amenities. If this were the only mechanism at play, we would expect the relationship between wage gaps
and city size to become stronger over time, which we do not see. On the other hand, Patel and Vella(2013) show that new immigrants tend to choose the same occupations as their compatriots who live inthe same region and that this has a positive effect on their earnings. Whichever is the direction of the
network effect on wages, it is worth investigating the importance of migrant networks in greater depth.
To do so, we estimate (2.1) again at the skill-city-origin-time level as described in section 3.2.1 but
additionally control for the immigrant network. Specifically, we estimate:ln(wI,k,o,c,t
LI,k,c,t) = φk + φo + φc,t + γ ln() + γ2 ImmigN etworko,c,t + εi,t ,wN,k,c,t
LN,k,c,t(A.1)

For each origin o, we construct the network as the MSA population share of immigrants from thatorigin: ImmigN etworkp,c,t =P opo,c,t. Thus, the newly estimated city-specific wage gap component φ̃c,t
P opc,t62

does not capture any variation in the wage gap across cities that might be due to variation in immigrant
networks.51

Table F.2 goes around here

Table F.2 shows the results of estimating (3.2) with φ̃c,t as dependent variable. Sign and significanceof the coefficients remain unchanged, while their magnitudes are somewhat smaller in columns (3) and(6) compared to those in Panel B of Table 3.

A.2.3

Unemployment and job finding rates

So far, we have only considered employed individuals earning a salary in our data samples. However,the location decisions of workers are not only affected by how much they can potentially earn, but also
by how long it takes to find a job. Job finding prospects might be even more important for immigrants
as their opportunity costs of working are often higher (e.g., they may not be able to rely on relatives orfriends during a period without income, and it is harder for them to claim unemployment benefits).52
Thus, immigrants might opt for locations where they have to spend less time searching for a job. Due tothe higher variety of jobs, this might attract immigrants to larger cities. If immigrants settling in thesecities are the ones with the higher opportunity cost of working, and if this induces them to accept lower
wages or worse job matches than natives, this could explain why the wage gap increases with city size.
If this mechanism is at play, we would expect immigrants to have relatively lower unemployment
rates in larger or more expensive cities. We investigate this in panel A of Figure D.3, in which we plot
the unemployment rates of immigrants, averaged from CPS monthly data over the period 1995-2005,
against city characteristics in the year 2000.53 For both city size and price index, the relationship is flat,
indicating that immigrants do not gain in terms of employment in larger or more expensive cities.
If the transition rates between employment and unemployment (i.e., both job finding and separation
rates) are higher in larger cities, this might result in immigrant unemployment rates of similar magnitude
as in smaller cities. However, if immigrants care more about finding a job than about the job’s duration(to establish an employment history, for instance), then they would still be drawn to larger cities. In
panel B, we therefore plot monthly immigrant job finding rates instead of unemployment rates againstcity characteristics.54 The plots show a slightly negative relationship, suggesting that unemployment
duration actually increases with city size or price index.
51 We find γ to be statistically significant and equal to -2.3. As argued by Borjas (2015), migrant networks may be detrimental
2
to immigrant wages. Our estimates suggest that a network that is 1% larger is associated with 2% lower wage of immigrants
relative to natives. This negative relationship can be interpreted as evidence that immigrant networks are detrimental toimmigrant assimilation into the labor market or as evidence to the fact that migrant networks may be a positive amenity for
immigrants; thus, when living in larger networks, immigrants may be willing to work for a lower wage.
52 This is especially the case for newly arrived immigrants who need to establish a history of employment first or for undocumented immigrants who are ineligible for unemployment benefits altogether.
53 As city prices are only available in 2000 or from 2005 onwards, we chose to average the CPS data during 11 years symmetrically around the year 2000 in order to get a sufficient number of observations of unemployed individuals per city. The results
are robust to considering different time periods.
54 The job finding rate is calculated as the fraction of all unemployed individuals in a given month that is employed in thefollowing month. In order to link individuals across months (whenever possible), we use the person identifier available fromIPUMS.

63

Figure D.3 goes around here

Altogether, the figures indicate that unemployment or job finding rates are unlikely drivers of thelocation choices and wage gaps of immigrants.

A.2.4

Skewness and kurtosis in larger cities

In this subsection we investigate whether city size or city prices are systematically related to fatter tailsof the wage distribution (kurtosis) or larger-than-expected left or right tails (skewness). Eeckhout etal. (2014) show that there seems to be a strong complementarity between high- and low-skilled workers,
which can explain fatter tails in larger cities relative to smaller ones in terms of skills. They show that
this is the case even when removing all immigrants from their exercise.
To investigate whether the evidence presented in this paper is affected by these fatter tails identified
in Eeckhout et al. (2014) we plot the skewness and kurtosis of the distribution of wages (not skills) of
natives in each location against city size and city price levels.

Figure D.4 goes around here

Figure D.4 shows that there does not seem to be a systematic relationship between skewness andkurtosis and city size.

A.3

Commuting zones

This section shows that the main relationship between location choices and relative wages between natives
and immigrants documented throughout the paper is independent of using MSA-level data or commuting
zone data. Commuting zones are equivalent to MSAs when we consider urban population. There are,however, many commuting zones that are rural areas, which are not covered in the MSA data. While inour context it seems quite natural to think about MSAs, some papers have emphasized the use of local
labor markets – typically measured by commuting zones – so that rural areas are also included.
The two graphs shown in Figure D.5 show that immigrants concentrate in large commuting zones andthat their wages relative to natives are lower there. All other results that we have checked are unchanged
when using commuting zones instead of MSAs.

Figure D.5 goes around here

A.4

Home ownership

If immigrants plan on returning to their countries of origin it is likely that ownership rates are lower
among them. Ownership rates vary considerably by income and other characteristics. Thus, it may
be useful to see if it is indeed the case that home ownership rates are lower among immigrants thansimilar-looking natives. This can be shown with the following regression:

64

Owneri = α + βImmigranti + γ ln Household Incomei + ηc Xi + εi

(A.2)

where “Owner” indicates whether the head of household i is a homeowner or not, Immigranti isa dummy indicating that household i has at least one immigrant, and Xi denote various household
characteristics, like the education level of the head of the household, marital status, the race of the headof the household, the size of the household, MSA fixed effects, occupation fixed effects, and time fixed
effects. Thus, β identifies whether immigrants tend to rent rather than own the house in which they live
relative to similar-looking natives.

Table F.4 goes around here

The results are shown in Table F.4, using Census and ACS data. It is apparent that immigrants arearound 10 percentage points less likely to own the house in which they reside.

65

B

A friction-less spatial equilibrium model

B.1

A standard Rosen-Roback spatial equilibrium model

In any free mobility spatial equilibrium model, natives decide on locations based only on indirect utility,
which, when abstracting from amenity levels, depends only on real wages. The free mobility condition
implies that real wages will be equalized across locations. We can denote the real wage in city c as
vc = wc /pc , where wc is the (nominal) wage in city c and pc is the price index in this city. Thus, inequilibrium we have:vc = wc /pc = wc0 /pc0 = vc0 for any c and c0 ∈ C.

(B.1)

In this context, a spatial equilibrium model is simply a theory that relates wages and prices (ormore generally, indirect utility) to population levels in each location: wc = wc (Lc ) and pc = pc (Lc ) (orvc = vc (Lc )). With this in hand, the free mobility condition determines the spatial distribution of people.
Denoting by Lc the amount of people in location c, we can implicitly define the distribution of people
across locations with the following C equations:wc (Lc )/pc (Lc ) = wc0 (Lc0 )/pc0 (Lc0 ) for any c and c’ , L =

X

Lc .

(B.2)

c

For an equilibrium to exist we need to make sure that vc0 (Lc ) < 0 (i.e., that real wages are declining
in population).55

B.2

A Rosen-Roback spatial equilibrium model with immigration

B.2.1

Basic set-up

What we propose in this paper is that immigrants have an extra good that determines the price index
that is relevant to them. To keep things simple, in this version we only consider immigrants from one
country of origin, with a price level given by pj . This means that an immigrant who lives in city cfaces a price index given by pjc = pI (pc , pj ), where pI (., .) is a function homogeneous of degree 1 thatcombines the local price index in c with the price index in the home country pj . We assume that pI (., .)is increasing in both pc and pj . Immigrants, like natives, choose their location by comparing real wages
across space. In equilibrium:
wjc /pI (pc , pj ) = wjc0 /pI (pc0 , pj ) for any c and c0 ∈ C,

(B.3)

where for the moment we allow immigrants to receive a wage in c different than the native wage
wc . With immigrants, the local price index and local wages are a function of native and immigrantcommunities. In this case, the standard spatial equilibrium model is modified slightly. In particular, we
can define a spatial equilibrium as follows.
55 With two cities, the proof is almost trivial. For an equilibrium to exist where population is spread across locations, we only
need the following: 1) vc (L) < vc0 (1 − L), ∀c, c0 , and vc0 (.) < 0. Then the existence of a distribution of people across locations
follows from a standard application of Bolzano’s theorem.

66

Definition I. Given C cities or locations, a spatial equilibrium is characterized by a mapping that
determines native wages in a city given its population, a mapping that determines local prices in a city
given its population, and a homogenous of degree 1 function pI (., .) that determines the immigrant priceindex given the local price index pc and the price index at origin pj , such that the following conditionshold:wc (Nc , Ic )w 0 (Nc0 , Ic0 )= c,∀c, c0 ∈ C
pc (Nc , Ic )pc0 (Nc0 , Ic0 )wjc0 (Nc0 , Ic0 )wjc (Nc , Ic )Immigrants free mobility: I= I,∀c, c0 ∈ C
p (pc (Nc , Ic ), pj )p (pc0 (Nc0 , Ic0 ), pj )Natives free mobility:

Natives clearing condition: N =

X

Nc

c

Immigrants clearing condition: I =

X

Ic

c

where Nc and Ic denote native and immigrant populations in location c.

This is a general model. In order to derive some properties we make a number of assumptions that
we argue are not strong and very often can be relaxed.
Assumption. Perfect substitutability. Natives and immigrants are perfect substitutes in production.
This assumption means that natives and immigrants can perform the exact same tasks. With perfectcompetition in the labor market, this necessarily implies that wages are the same (up to a constant)between natives and immigrants and given by: wc (Nc , Ic ) = wc (Nc + Ic ) = wc (Lc ) and wjc0 (Nc0 , Ic0 ) =wjc0 (Nc0 + Ic0 ) = wjc0 (Lc0 ), where Lc is the total population in c. In Section 4, we depart from perfectcompetition in the labor market, which allows wages of perfectly substitutable workers to be different inequilibrium.
Assumption. Common production technology. The production technology only differs across locations with a technological shifter (Bc > 0) that is orthogonal to wages. This is:
wc (Bc , Lc ) = Bc w(Lc ), and wjc (Bc , Lc ) = Bc wI (Lc )and w(.) and wI (.) are decreasing in their arguments, continuous and differentiable.
This assumption simply removes the potential heterogeneity coming from the c-specific functions
wc (.) and wjc (.). Similarly for price indices:
Assumption. Common production of housing The production technology for building housing is
identical across locations. This is:

pc (Nc , Ic ) = p(Nc , Ic )and p(., .) is increasing in their arguments, continuous and differentiable.

67

Note that there is a difference in what we assume for the labor and housing or local goods’ market.
Assuming that natives and immigrants are perfect substitutes means that the wages schedules only
depend on total population Lc . Assuming this for local prices is a bit more sensitive. Immigrants havean extra consumption good, and therefore less of their income is left to consume local goods. Hence, theeffect on local prices may be different than that of natives. To keep this possibility, we do not take astance, for the moment, on how p(., .) depends on its two arguments.

B.2.2

Immigrant locations and wage gaps

With these assumptions we can derive a number of results. For simplicity we concentrate on the case ofjust two cities, so that C = 2.
Proposition 5. All else equal, more productive cities (higher Bc ) are larger, pay higher wages, and are
more expensive.
Proof. Suppose Bc > Bc0 .
To show that c is larger than c0 , we need to look at the free mobility condition. From that we have that:
Bc w(Nc +Ic )p(Nc ,Ic )=Bc0 w(Nc0 +Ic0 )c +Ic ) w(Nc0 +Ic0 ), so that w(N/ p(N 0 ,I 0 )p(Nc0 ,Ic0 )p(Nc ,Ic )
c
c

B

B

= Bcc0 , but this is f (Nc , Ic )/f (Nc0 , Ic0 ) = Bcc0

where f (., .) is decreasing in Nc and Ic .
To see that larger cities pay higher wages, we only need to realize that natives’ wage are given by
wc = Bc w(Nc , Ic ) > Bc0 w(Nc0 , Ic0 ) if and only if Bc /Bc0 > w(Nc0 , Ic0 )/w(Nc , Ic ), which needs to be thecase since Nc is greater than Nc0 at equal levels of immigration.
Local prices are increasing in native and immigrant population whenever higher wages generate moredemand for local goods.

The intuition for this result is simple. When a location is more productive, wages can be higher andstill remain competitive. If wages are higher, more workers will choose this location. This will put somepressure on wages, but not enough to make wages lower than in other locations, since workers could
then move elsewhere. Similarly, with more workers in the location, local price indices increase. But thiseffect cannot be too large, since otherwise not so many workers would choose the location, and hence,the pressure on local prices would not be so strong. In other words, better underlying productivity ispartly reflected in quantities (i.e., amount of workers in the location) and partly on prices. The local
labor-demand elasticity and the local price-index elasticity to population determine how much underlying
productivity is reflected in quantities versus prices.
Next, we turn to our central claim. When immigrants have an extra consumption good that is
not included in the local price index, then they have a comparative advantage for living in productive
locations. If wages partly reflect the value of living in the location (i.e., if wage determination is suchthat wjc = w(vjc )), then part of the comparative advantage that immigrants have for living in productive
cities is reflected in wages.
Proposition 6. Under the assumptions stated above, it can be shown that:
1. Immigrants concentrate more than natives in highly productive cities

682. Immigrants’ wages are lower than natives’ wages in highly productive cities
And these results are stronger for low pj countries of origin if substitution effects dominate.
Proof. Assume C = 2 and suppose that B1 > B2 . With two cities, the definition of a spatial equilibrium
is given by the following set of equations.

Natives free mobility:
Immigrants free mobility:

B2 w(N2 + I2 )B1 w(N1 + I1 )=p(N1 , I1 )p(N2 , I2 )B1 wI (N1 + I1 )B2 wI (N2 + I2 )=pI (p(N1 + I1 ), pj )pI (p(N2 , I2 ), pj )Natives clearing condition: N = N1 + N2
Immigrants clearing condition: I = I1 + I2

From these equations we obtain that:w(N1 +I1 )p(N1 ,I1 )w(N2 +I2 )p(N2 ,I2 )=wI (N1 +I1 )pI (p(N1 +I1 ),pj )wI (N2 +I2 )pI (p(N2 ,I2 ),pj )=wI (N1 +I1 )p(N1 +I1 )pI (1,pj /p1 )wI (N2 +I2 )p(N2 ,I2 )pI (1,pj /p2 )Hence:wI (N1 +I1 )w(N1 + I1 )wI (N1 + I1 ) pI (1, pj /p2 )pI (1,pj /p1 )= wI (N +I ) = I22w(N2 + I2 )w (N2 + I2 ) pI (1, pj /p1 )I
p (1,pj /p2 )Which we can re-express as:wI (N1 + I1 ) 1/pI (1, pj /p1 )w(N1 + I1 )= I
w(N2 + I2 )w (N2 + I2 ) 1/pI (1, pj /p2 )Taking logs

ln w(N1 + I1 ) − ln w(N2 + I2 ) = (ln wI (N1 + I1 ) − pI (1, pj /p1 )) − (ln wI (N2 + I2 ) − ln pI (1, pj /p2 )And using Lc = Nc + Ic
ln w(L1 ) − ln w(L2 ) = (ln wI (L1 ) − ln pI (1, pj /p1 )) − (ln wI (L2 ) − ln pI (1, pj /p2 )Finally we have that:[ln w(L1 ) − ln wI (L1 )] − [ln w(L2 ) − ln wI (L2 )] = −[ln pI (1, pj /p1 )) − ln pI (1, pj /p2 )]Now, since B1 > B2 , then L1 > L2 . This expression says that, holding L1 and L2 constant, the gap
in wages between natives and immigrants in large locations relative to small locations is proportional tothe immigrant-specific price index of living in a large location relative to a small location. Given that the69

price index pI () is increasing in its arguments, this means that large cities have either larger immigrant
populations or higher wage gaps, and this is more pronounced the lower pj is.

To gain some intuition on these results, it is worth discussing some extreme cases. One such case isforcing immigrants and natives to receive the same wage in each location. In this case, immigrants wantto live in the most expensive city. That is, suppose pc > pc0 . Then an immigrant from j prefers to livein c over c0 if and only if:

wc /pI (pc , pj ) > wc0 /pI (pc0 , pj )which is true if and only if

1 > pI (1, pj /pc )/pI (1, pj /pc0 )and this holds since pI (., .) is homogeneous of degree one in their two arguments and because natives’
mobility condition imposes wc /pc = wc0 /pc0 . In turn, given that pI (., .) is increasing in both arguments,
this last inequality holds only when pc > pc0 .
Another extreme case takes place when wages of immigrants completely “exhaust” the comparativeadvantage that they have in a location. That is, immigrants do not have an incentive to choose c over c0
if the immigrant wage function wI (., .) is such thatwjc /pI (pc , pj ) = wjc0 /pI (pc0 , pj )The relative wages in the two locations are therefore

wjc /wjc0 = pI (pc , pj )/pI (pc0 , pj ) < wc /wc0
The last inequality follows from natives’ free mobility condition and pI (1, pj /pc )/pI (1, pj /pc0 ) < 1
when pc > pc0 . Thus, for a spatial equilibrium with immigrants not concentrating more than natives in
the highly productive cities to exist, we must have that immigrants’ nominal wages increase less withlocal price levels than natives’ wages.

B.2.3

Immigrants and local prices

The final result investigates the effect of immigration on local price indices across locations.
Proposition 7. The effect of immigration on local prices is ambiguous. On the one hand, immigrants
have higher incentives to live in large and expensive cities, putting pressure on local prices in these cities.
On the other hand, they consume a smaller fraction of their income locally, reducing the pressure on local
prices.
The intuition for this result is as follows. The demand for local goods by natives is driven by theshare of consumption that takes place locally. Hence, aggregate local demand by natives is given by
DcN = wc Nc , while aggregate demand for local goods from immigrants is given by DcI = (1 − ᾱf )wcI Ic ,70

where we made the simplifying assumptions that there are no tradable goods, and where ᾱf is the shareof immigrant consumption that is related to the home country. Total supply of local goods is given by
F (Lc ) since natives and immigrants are perfect substitutes. Hence goods market clearing implies that:wc Nc + (1 − ᾱf )wcI Ic = pc F (Lc )Totally differentiating this expression with respect to immigrants and assuming ᾱf is fixed – as it
would be with Cobb-Douglas preferences – we obtain:∂F (Lc )
∂wc
∂Nc
∂wI
∂pc
Nc + wc+ (1 − ᾱf ) c Ic + (1 − ᾱf )wcI =Fc (Lc ) + pc
∂Ic
∂Ic
∂Ic
∂Ic
∂Ic
We can further assume that immigrants do not affect wages, and hence obtain:∂Nc

I(1 − ᾱf )wc + wc ∂Ic − pc
∂pc
=
∂Ic
Fc (Lc )∂F (Lc )∂Ic

This equation shows that immigrants increase local price indices, if the increased local demand from
immigrants ((1 − ᾱf )wcI ) is not offset by the potential decrease in demand from natives leaving theclocation (wc ∂N) and the contribution of immigrants to new local production (pc ∂F∂I(Lc c ) ).
∂Ic

CTheory Appendix

C.1

Derivation of indirect utility

The utility in location c for an individual i from country of origin j can be written as:Tln Uijc = ρ + ln Ac + αt ln Cjc+ (1 − αt )σ−1σ
N T σ−1ln ᾱl (Cjc
) σ + ᾱf (CjN T ) σ
σ−1





+ εijcTNTs.t. Cjc+ pc Cjc+ pj CjN T ≤ wjc

We can solve the maximization problem in two stages:
NT ∗• Stage 1: Define an auxiliary variable E and find the optimal decisions Cjc(pc , pj , E) andCjN T ∗ (pc , pj , E) to the following maximization problem
max (1 − αt )σ−1σ
N T σ−1ln ᾱl (Cjc
) σ + ᾱf (CjN T ) σ
σ−1





NT
s.t. pc Cjc+ pj CjN T = E

LetṼ (pc , pj , E) = (1 − αt )σ−1σ
N T ∗ σ−1ln ᾱl (Cjc
) σ + ᾱf (CjN T ∗ ) σ
σ−1



71



• Stage 2: Solve for CjT ∗ (pc , pj , wjc ) and E ∗ (pc , pj , wjc ) of the maximization problemTmax ρ + ln Ac + αt ln Cjc+ Ṽ (pc , pj , E)T
s.t. Cjc+ E ≤ wjc

Stage 1max (1 − αt )σ−1σ
N T σ−1ln ᾱl (Cjc
) σ + ᾱf (CjN T ) σ
σ−1





NT
s.t. pc Cjc+ pj CjN T = E

The associated Lagrangian is
L = (1 − αt )σ−1σ
N T σ−1ln ᾱl (Cjc
) σ + ᾱf (CjN T ) σ
σ−1





NT
+ λ(E − pc Cjc− pj CjN T )First-order conditions are given by
−1

NT σ
)
(1 − αt )ᾱl (Cjc∂L:
σ−1
σ−1 − pc λ = 0
NT
NT
∂Cjc
) σ + ᾱf (CjN T ) σᾱl (Cjc−1(1 − αt )ᾱf (CjN T ) σ∂L:σ−1
σ−1 − pj λ = 0
NT
NT
∂Cj
ᾱl (Cjc) σ + ᾱf (CjN T ) σ
Dividing the two first-order conditions, we obtain the following relationship:
ᾱl
ᾱf



NT
Cjc
CjN T

 −1
σ
=

pc
NT
⇒ Cjc
=
pj



ᾱf pcᾱl pj−σ

CjN T

Using this relationship and the budget constraint, we find


NT
Cjc
=

pc



pc
ᾱl

−σ


CjN T =
pc



pc
ᾱl

pc
ᾱl

+ pj

pj
ᾱf

−σ

−σ


pj
ᾱf

−σ E

−σ

+ pj



pj
ᾱf

−σ E

Thus, the maximized objective function isṼ = (1 − αt )



 
σ
ln 
ᾱl 
σ−1 

= (1 − αt ) ln E + (1 − αt )


pc



pc
ᾱl

pc
ᾱl

−σ

1
ln
σ−1

+ pj

pc

 σ−1
σ

−σ





pc
ᾱl

pj
ᾱf


−σ E 

−σ


+ pj

= (1 − αt ) ln E − (1 − αt ) ln p̄(ᾱl , ᾱf )

72

pj
ᾱf


+ ᾱf 





−σ

!

pc



pc
ᾱl

pj
ᾱf

−σ


 σ−1
σ



 −σ E 

pj

−σ

+ pj

ᾱf

1

where p̄jc (ᾱl , ᾱf ) = (ᾱlσ p1−σ
+ ᾱfσ p1−σ
) 1−σ
c
j

Stage 2T
max ρ + ln Ac + αt ln Cjc+ (1 − αt ) ln E + (1 − αt )1ln p̄(ᾱl , ᾱf )σ−1Ts.t. Cjc+ E ≤ wjc

The associated Lagrangian isTT
L = ρ + ln Ac + αt ln Cjc+ (1 − αt ) ln E − (1 − αt ) ln p̄(ᾱl , ᾱf ) + λ(wjc − Cjc− E)

The first-order conditions are∂Lαt: T −λ=0T∂Cjc Cjc∂L (1 − αt )
:
−λ=0
∂E
E
Using these first-order conditions and budget constraints,

T
Cjc= αt wjc

E = (1 − αt )wjc
Thus, the optimal choices for consumption can be written asTCjc= αt wjc

ᾱlσ p−σc(1 − αt )wjc
σ 1−σᾱl pc + ᾱfσ p1−σjᾱfσ p−σj(1 − αt )wjc
CjN T = σ 1−σᾱl pc + ᾱfσ p1−σ
j

NT
Cjc
=

This solution can be shown to satisfy the first-order conditions of the original problem. If we let ρ
be a constant such that the indirect utility function has no constant, the indirect utility function can be
written asln Vijc = ln Vjc + εijc = ln Ac + ln wjc − (1 − αt ) ln p̄jc (ᾱl , ᾱf ) + εijc1with p̄jc (ᾱl , ᾱf ) = (ᾱlσ p1−σ
+ ᾱfσ pj1−σ ) 1−σ .
c

73

C.2

Proofs of propositions of the quantitivative model

Assumption Natives only care about local price indices so that αf = 0 and αl = α. Immigrants careabout local and foreign price indices so that αf 6= 0 and αl + αf = α.
Proof. Proposition 1• ln wjc = −(1 − β) ln Ac + β ln B̃c + (1 − β)(1 − αt ) ln p̄jc
• ln wN c = −(1 − β) ln Ac + β ln B̃c + (1 − β)(1 − αt ) ln pc
Taking the difference we get

ln wN c − ln wjc =(1 − β)(1 − αt ) ln pc − (1 − β)(1 − αt ) ln p̄jc .
.
Denote W = ln wN c − ln wjc . We are interested in the sign of ∂ ∂W
ln pc

W =(1 − β)(1 − αt ) ln pc − (1 − β)(1 − αt )1ln(ᾱlσ p1−σ
+ ᾱfσ p1−σ
)
c
j
1−σ

(1 − β)(1 − αt )ᾱlσ p−σ∂W (1 − β)(1 − αt )
c
=
−
∂pc
pc
ᾱlσ p1−σ+ ᾱfσ p1−σ
c
j
σ 1−σ

ᾱf pj∂W
pc =(1 − β)(1 − αt ) σ 1−σ∂pcᾱl pc + ᾱfσ p1−σjAs ∂ ln pc /∂pc = 1/pc , we have the wanted derivative, which is always positive:σ 1−σᾱf pj∂W=(1 − β)(1 − αt ) σ 1−σ>0∂ ln pc
ᾱl pc + ᾱfσ p1−σ
j
Also,
σ 1−σ

(ᾱl pc∂2W=(1 − β)(1 − αt )∂ ln pc ∂pj+ ᾱfσ p1−σ)(1 − σ)ᾱfσ p−σ− ᾱfσ p1−σ
(1 − σ)ᾱfσ p−σjjjj(ᾱlσ p1−σ
+ ᾱfσ p1−σ)2cjMultiplying both sides with pj and again using ∂ ln pj /∂pj = 1/pj we getᾱfσ p1−σᾱlσ p1−σ
∂2W
c
j
<0
=(1 − β)(1 − αt )(1 − σ) σ 1−σ∂ ln pc ∂ ln pj)2(ᾱl pc + ᾱfσ p1−σjThus, the gap in wages between natives and immigrants is increasing in the local price index. Furthermore, the effect of the local price index on the wage gap is larger for lower pj when σ > 1, i.e. when
consuming locally versus in the country of origin is imperfectly substitutable.

Proof. Proposition 2
We have that

74

1/λ

Vjc
πjc = P
=
1/λ
V
k jk



Vjc
Vj

1/λ

Thus,
ln πjc − ln πN c =11(ln Vjc − ln VN c ) − (ln Vj − ln VN )λλUsing the definition of ln Vjc and the expression for the wage gap obtained above, we haveln Vjc − ln VN c = ln wjc − ln wN c − (1 − αt ) (ln p̄jc − ln pc )= − (1 − β)(1 − αt ) ln pc + (1 − β)(1 − αt ) ln p̄jc − (1 − αt ) (ln p̄jc − ln pc )=β(1 − αt ) ln pc + β(1 − αt ) ln p̄jc
Note thatln Vjc = ln Ac + ln wjc − (1 − αt ) ln p̄jc

= ln Ac + −(1 − β) ln Ac + β ln B̃c + (1 − β)(1 − αt ) ln p̄jc − (1 − αt ) ln p̄jc
=β ln Ac + β ln B̃c − β(1 − αt ) ln p̄jc
Thus,
β(α −1)

Vjc = Aβc B̃cβ p̄jc t
Then,

Vj =

X

(α −1)
Ak B̃k p̄jk t

 βλ

!λ

 βλ

!λ

k

VN =

X

(α −1)
Ak B̃k pk tβ=

X  Ak B̃k  λkkAnd from this we have the expression we needed.

75

t
p1−α
c

!λ

Proof. Proposition 3
Note that
Ljc
πjc =
=
Lj



Vjc
Vj

 λ1

β(1−αt )Aβc B̃cβ /p̄jc
Vj

=

! λ1

Then, the total immigrant population in city c is

LIc =

X

X

Ljc =

j

j

X
Ljc
Lj
=
Lj
Lj
j

β(1−αt )Aβc B̃cβ /p̄jc
Vj

! λ1

Substituting the expression for Vj , we getβ

LIc = (Ac B̃c )βλ(1−αt ) λLj /p̄jc

X
j(1−αt ) βPk(Ak B̃k /p̄jk)λFor natives,ββ(Ac B̃c ) λLN c = P(1−αt ) λ(1−αt )k

(Ak B̃k /pk

LN /pcβ)λβ(Ac B̃c /Lcηc α ) λ
= P
LN
η α β
(Ak B̃k /Lkk ) λkAnd Lc = LIc + LN c .
Proof. Proposition 4
Noteq=

X Bc Lc
c

L

Thus,


q=

X
c

β

β+λ
β

(Ac B̃c

)

β
λ

X
j

(1−αt ) λ
Lj
/p̄jc
L
(1−α ) β(Ak B̃k /p̄jk t ) λ
k

P

76



β+λ

β

(A B̃ β /Lηc c α ) λ LN
+ P c cη α β(Ak B̃k /L k ) λ L

P

c

k

k

D

Alternative calibrations of the model

D.1

Effect of alternative calibrations of β and αt on αf and σ

In order to estimate αf and σ (and λ) we take estimates of β and αt from the literature. However, theliterature offers a range of estimates of these two parameters. First, there are alternative values for theworkers weight in bargaining. While Lise et al. (2016) suggest that an estimate of 0.2 is reasonable, theyalso consider estimates ranging from 0.1 to 0.3 or even slightly larger. Second, it is intrinsically hard tomeasure the share of consumption on tradable goods. A fraction of the inputs used in non-tradables arealso tradable, and hence, to some extent, some non-tradables are partially tradable. In the main text wetook the conservative estimate of αt = 0.4. However, this number could in principle be larger.
To investigate how much our estimates of αf and σ would change with alternative assumptions on
β and αt we construct a fine grid (incremental increases of 0.0025 and 0.005, for a total of 30,000
combinations of β and σ) over the interval [0.1, 0.35] x [0.30, 0.68]. This interval captures both low andhigh levels of both β and αt and, thus, offers an overview of estimates that we would have obtained byassuming reasonable alternative values of these two parameters.
The top-left graph of Figure D.7 shows the histogram of estimates of αf that we obtain from the
30,000-point grid described above. In a red vertical line we show the baseline estimate that we use in
the main text, which lies rather at the upper end but still well inside the range of potential estimates.
This graph suggests that αf is most likely between 0.15 and 0.25.

Figure D.7 goes around here

The graph on the right of Figure D.7 shows the histogram of estimates of σ. Our baseline estimate
lies at the mode of the distribution. The range of estimates suggests that σ is between 1.5 and 2.5, well
above 1, the limiting case in which there would not be any heterogeneity across countries of origin. The
bottom graph in Figure D.7 plots the area covered by our estimates of αf and σ. Overall, they are notvery sensitive to the assumed values of β and αt .
In the next subsection we set β and αt close to their upper bounds and show that the main resultsof the paper are robust to these alternative calibrations of β and αt .

D.2

Effect of alternative calibrations of β and αt on quantitative results

In this section, we check the robustness of the predictions of the counterfactual simulation to alternative
calibrations of the parameters β and αt and of the re-estimated parameters αf , σ, and λ.
First, we set β = 0.3, from which we obtain αf = 0.23, σ = 1.66, and λ = 0.02. Figure D.8 compares
the model and the data with this new parameterization and confirms that the model predictions arealmost identical to those shown in baseline Figure 5. Figure D.9 shows the predicted changes in thespatial equilibrium resulting from immigration, replicating Figure 8 with the new parameters. All plots
are very similar to the baseline figure. Only the changes in the overall population are slightly more
pronounced in Figure D.9 because workers are able to retain a higher share of the profit from production,

77

which means that their wages depend to a larger extent on productivity and to a lower extent on pricelevels. Hence, highly productive cities become even more attractive to immigrants than previously,
implying that cities with high productivity grow more while those with low productivity grow less.

Figures D.8 and D.9 go around here

Table F.7 presents the predicted changes in aggregate variables. As the more productive cities caneven attract more immigrants than in the baseline calibration, the positive effects on labor productivity
are stronger. In the case with agglomeration forces, productivity goes up by 2.12% due to immigration(compared to 1.85% previously). Also the difference to the counterfactual in which immigrants behave
like natives is somewhat larger (1.53 vs 1.30). On the other hand, the effect of immigration on native
workers’ welfare is smaller and now negative also with agglomeration forces (-0.23%). This is because
the larger bargaining power of workers implies that the weight on local price levels in the wages is lower.
As a consequence, workers are more affected by rising local prices since the compensation in their wages
is reduced. Therefore, a rise in prices due to population growth generally affects welfare more negatively
when β is higher. However, the difference between the two counterfactuals shown in the last row of F.7
is more pronounced, which is driven by the stronger increase in overall labor productivity.

Table F.7 goes around here

In the second robustness check, we set αt = 0.6, from which we obtain αf = 0.18, σ = 1.84 andλ = 0.011.56 Figure D.10 shows that also with these parameters, the model replicates well the data.
Compared to the baseline, this calibration matches somewhat better the population distribution andsomewhat worse the wage distribution across MSAs. Wages rise steeply with city productivity now
because the lower share of non-tradable consumption implies that wages depend to a lower extent on
non-tradable prices, which in turn are highly positively correlated with productivity.
The predicted changes in the equilibrium outcomes plotted in Figure D.11 are now attenuated, inparticular for native population, prices, and native wages. This is because the lower consumption shareof non-tradable goods implies that the increase in their demand and thus their prices is smaller, which inturn leads to a smaller increase in natives’ wages. Moreover, less natives relocate from more productive
to less productive cities because the price increase in the former relative to the latter is less pronounced
than in the baseline. Due to the lower weight of non-tradable consumption, the motive of immigrants
to choose cities with higher price elasticities of non-tradable supply is reduced. This is why cities at thelower end of the productivity distribution grow less in terms of population and thus the population shift
towards high-productivity cities is stronger.

Figures D.10 and D.11 go around here
56 Setting the share of tradable goods to 60% means that we assume non-tradables to consist only of housing, which has aweight of around 40% in the CPI-U.

78

Due to this stronger population shift towards high-productivity cities, also with this alternative
calibration the positive effects on overall labor productivity are stronger than in the baseline, which
can be seen in Table F.7. In the case with agglomeration forces, productivity goes up by 2.95% due toimmigration (vs 1.85% in the baseline) and the difference to the counterfactual with immigrants behaving
like natives is 2.59 ppt (vs 1.30 in the baseline). As non-tradable prices rise less due to their lower weightin the utility, effects on native workers’ welfare are more positive. As a result, both with and without
agglomeration forces, immigration increases welfare, whereas the difference to the counterfactual withimmigrants being identical to natives is somewhat smaller than in the baseline.
In sum, using different parameter values for β and αt within a reasonable range does not significantly
change the effects of immigrants on the distribution of population across cities and aggregate variables
predicted by the model. In fact, aggregate effects, in particular those on labor productivity, becomerather stronger when setting the parameters closer to their upper bounds.

79

E

Figures Appendix
Figure D.1: City size and native-immigrant wage gaps by quantiles

Notes: This graph plots the estimate of the interaction between an immigrant dummy and the (log) population size in thelocation for each quantile of the wage distribution. For this graph, we use a 20% random sample of the 2000 Census. The left
panel plots the city size-wage gap elasticity at each quantile, while the right panel plots the city price-wage gap elasticity.

Figure D.2: Return migration

Notes: This figure shows estimates of survival rates and return migration rates by age group. The graph on the left compares
the size of the cohort of natives and immigrants who arrived before 2000 in Census years 2000 and ACS 2010. The difference
between 2010 and 2000 in the size of the cohorts divided by the initial size of the cohort is an estimate of the cohort survival
rate. The graph on the right subtracts the native survival rates from immigrant survival rates to obtain estimates of return
migration rates by age group.

80Figure D.3: City size, price index, and immigrants’ unemployment and job finding
Panel A: Unemployment rates

Panel B: Job finding rates

Notes: This figure uses city size and price data from the 2000 Census and data of immigrant workers aged 25 to 59 from the
CPS basic monthly files. The rates are calculated for each city that can be matched to the Census data as averages over theperiod 1995-2005. The job finding rate is the monthly share of unemployed job searchers transitioning to employment.

81

Figure D.4: City size, price index, and skewness and kurtosis
Panel A: Skewness

Panel B: Kurtosis

Notes: This figure uses city size and price data from the 2000 Census and computes the within MSA wage skewness and kurtosis.

Figure D.5: Commuting zone size and immigrant distribution

Notes: The figure is based on the sample of prime-age workers (25-59) from the 2000 Census. Each dot represents a different
commuting zone. There are 191 different commuting zones in our sample. The red line is the fitted line of a linear regression.
The left panel shows the relationship between relative immigrant share and CZ size, while the right panel shows the relationshipbetween native-immigrant wage gaps and the CZ size.

82

Figure D.6: The effect of the legalization on immigrant wage elasticities to city price pre- and post 1982

Notes: This graph shows the differential wage elasticity for immigrants arrived in each of the years displayed in the x-axis, withrespect to city price, relative to the immigrants arriving in 1981. This follows Column 6 of Table 7. Dashed lines indicate 95%
confidence intervals.

83

Figure D.7: Robustness of estimates of αf and σ to different β and αt

Notes: This figures shows in red the estimates used in the main text (vertical line and red dot). The top left graph shows ahistogram of the estimates of αf that we obtain for a 30,000 point uniform grid for β x αt ∈ [0.1, 0.35] x [0.30, 0.68]. The top
right graph shows a similar histogram for estimates of σ. The bottom graph shows the area covered by these estimates.

84

Figure D.8: Population and wages at the MSA-level with β = 0.3
Panel A: Population

Panel B: Wages

Panel C: Immigrant Share

Panel D: Wage Gaps

Notes: This figure compares four untargeted moments in the data and the model. The model is estimated using country oforigin variation. From these estimates, we aggregate the data generated by the model at the city level to compute the four
moments shown in the figure. Each dot represents one of the 168 consolidated metropolitan statistical areas from Albouy(2016).

85

Figure D.9: Effects of immigration with new immigrants consuming in origin country with β = 0.3
Panel A: Population

Panel B: Native population

Panel C: Non-tradable/Housing prices

Panel D: Native wages

Notes: This figure compares the distribution of selected variables predicted by the model with the actual share of immigrants of
20% and the counterfactual distribution predicted if new immigrants consume like estimated, both with and without agglomeration forces. Each dot represents one of the 168 consolidated metropolitan statistical areas from Albouy (2016) and indicatesthe percentage difference to the counterfactual.

86

Figure D.10: Population and wages at the MSA-level with αt = 0.6
Panel A: Population

Panel B: Wages

Panel C: Immigrant Share

Panel D: Wage Gaps

Notes: This figure compares four untargeted moments in the data and the model. The model is estimated using country oforigin variation. From these estimates, we aggregate to the city level the data generated by the model to compute the four
moments shown in the figure. Each dot represents one of the 168 consolidated metropolitan statistical areas from Albouy(2016).

87

Figure D.11: Effects of immigration with new immigrants consuming in origin country with αt = 0.6
Panel A: Population

Panel B: Native population

Panel C: Non-tradable/Housing prices

Panel D: Native wages

Notes: This figure compares the distribution of selected variables predicted by the model with the actual share of immigrants
of 20% and the counterfactual distribution predicted if new immigrants consume as estimated, both with and without agglomeration forces. Each dot represents one of the 168 consolidated metropolitan statistical areas from Albouy (2016) and indicatesthe percentage difference to the counterfactual.

88

F

Tables Appendix
Table F.1: Wage gaps and city size measurement(1)Rel. Imm. Share(ln) Population in MSA(2)
Rel. Imm. Share(3)
Rel. Imm. Share

0.532***(0.0552)(ln) Native population in MSA

0.514***(0.0713)(ln) Population in MSA (t-10)

0.516***(0.0575)(ln) Native population in MSA (t-10)

Observations
R-squared
Year FE

0.501***(0.0718)
764
0.472
yes

764
0.383
yes

(1)
(ln) Wage Gap(ln) Population in MSA(2)(ln) Wage Gap

573
0.443
yes

573
0.369
yes

(3)
(ln) Wage Gap(4)(ln) Wage Gap-0.0328***(0.00431)(ln) Native population in MSA-0.0326***(0.00498)(ln) Population in MSA (t-10)-0.0336***(0.00435)(ln) Native population in MSA (t-10)

Observations
R-squared
Year FE(4)
Rel. Imm. Share-0.0338***(0.00501)
764
0.412
yes

764
0.376
yes

573
0.369
yes

573
0.337
yes

Notes: The regression uses data from the Census 1980-2000 and the combined 2009-2001 ACS. * significant at the 0.10 level;** significant at the 0.05 level; *** significant at the 0.01 level. Standard errors clustered at the metropolitan area level.

89

Table F.2: Immigrants’ wage gap and city characteristics controlling for immigrant networks(ln) Population in MSA(1)Wage gap
OLS(2)
Wage gap
OLS(3)
Wage gap
FE-0.0415***(0.00205)-0.0412***(0.00208)

0.000811(0.0274)(ln) City priceObservations
R-squared
Year FEMSA FE
widstat

16,621
0.545
nono16,621
0.549
yes
no

16,621
0.841
yes
yes

(4)
Wage gap
OLS(5)Wage gap
OLS(6)Wage gap
IV(7)
Wage gap
FE-0.0837***(0.0151)-0.336***(0.0796)-0.366***(0.0939)-0.0125(0.0765)

16,621
0.109
nono16,621
0.343
yes
no

15,979
0.345
yes
no
46.78

16,621
0.841
yes
yes

Notes: The dependent variable is the MSA-specific component of the wage gap estimated by equation (2.1) at the origin country
level and additionally controlling for immigrant networks (defined as MSA population share of immigrants from the same origin).
The regression uses a sample of prime-age workers (25-59) from the Census 1980-2000 and the combined 2009-2001 ACS. The
MSA price indices are computed following Moretti (2013). * significant at the 0.10 level; ** significant at the 0.05 level; ***significant at the 0.01 level. Standard errors clustered at the metropolitan area level.

Table F.3: Remittances
Origin region
Latin America
AfricaAsia
MexicoEuropeTotal

Likelihood (%)
32.54
30.31
25.31
20.55
12.93
24.73

Income share (%)
2.35
2.57
2.81
2.57
1.25
2.24

Income share for remit>0 (%)
8.86
12.17
12.80
14.02
10.73
10.98

Notes: This table uses data from the 2003 New Immigrant Survey (NIS). The NIS is a representative sample of newly admitted, legal permanent residents. Statistics are based on the subsample of immigrants with positive income (from wages,
self-employment, assets, or real estate) and with a close relative (parent, spouse, or child) living in the country of origin.
Income shares over 200% are dropped.

Table F.4: Immigrants’ homeownership rates

Immigrant(1)
Ownership(2)
Ownership(3)
Ownership-0.193***(0.00937)-0.116***(0.00993)
0.213***(0.00411)-0.137***(0.0178)0.215***(0.00431)

3,464,960
yes
yes
all

3,464,960
yes
no
all

(ln) HH income(ln) RER

Observations
Year FEMSA FE
Sample3,464,960
yes
yes
all

(4)
Ownership

0.231***(0.00686)-0.0135**(0.00573)
444,254
yes
yes
Imm. only

Notes: This table shows regressions with a dummy for home ownership as dependent variable using Census 1990-2000 and
ACS 2005-2011 data. Additional controls include dummies for the number of family members living in the household, marital
status and age. Standard errors clustered at the MSA level. * significant at the 0.10 level; ** significant at the 0.05 level; ***significant at the 0.01 level.

90

Table F.5: Immigrants’ expenditures on housing, alternative specifications(1)
ln (rent / HH Income)Panel A(2)ln (rent / HH Income)

0.118***(0.0130)-0.0741***(0.0146)

Immigrant
Immigrant x (ln) City price(3)ln (rent / HH Income)-0.110***(0.0236)0.0383(0.0318)(ln) RER-0.729***(0.00486)-0.730***(0.00549)

0.0711***(0.0155)-0.764***(0.00551)

903,825
yesnoall

204,276
yes
yes
Imm. only(1)(rent / HH Income)

903,825yes
yes
allPanel B(2)
(rent / HH Income)

0.0407***(0.00338)-0.0171***(0.00343)(ln) HH income

Observations
Year FEMSA FE
SampleImmigrant

903,825
yes
yes
all

Immigrant x (ln) City price(3)(rent / HH Income)(ln) HH income

903,825
yes
yes
all

(4)
(rent / HH Income)-0.0515***(0.00673)
0.0374***(0.00790)(ln) RER

Observations
Year FEMSA FE
Sample(4)ln (rent / HH Income)-0.220***(0.00411)-0.219***(0.00384)

0.0146***(0.00548)-0.251***(0.00567)

903,825
yes
yes
all

903,825
yesnoall

204,276
yes
yes
Imm. only

Notes: These regressions follow Table 8 with the dependent variable in levels. Standard errors are clustered at the MSA level.
* significant at the 0.10 level; ** significant at the 0.05 level; *** significant at the 0.01 level.

91

Table F.6: 20 least and most productive cities
20 cities with lowest productivity
Productivity Amenity Rent prices
-0.25
-0.01
0.85
-0.23
0.00
0.90
-0.23
-0.08
0.80
-0.22
0.00
0.94
-0.21
0.03
1.01
-0.21
-0.06
0.85
-0.19
-0.07
0.72
-0.19
-0.02
0.84
-0.19
0.01
0.92
-0.18
0.03
1.04
-0.17
-0.03
0.82
-0.17
-0.01
1.01
-0.17
-0.04
0.90
-0.16
-0.01
0.95
-0.16
0.01
0.93
-0.16
-0.04
0.82
-0.16
0.01
0.98
-0.16
-0.05
0.90
-0.15
0.01
0.95
-0.15
-0.04
0.86

HS elasticity
6.40
3.09
3.68
3.87
4.59
2.40
1.84
1.35
3.60
2.71
7.15
1.73
2.35
4.33
3.06
2.18
1.48
4.75
7.84
2.42

20 cities with highest productivity
City nameProductivity Amenity Rent prices
San Francisco
0.29
0.14
2.11
New York
0.22
0.03
1.63
Los Angeles
0.15
0.08
1.54
Monterey
0.14
0.14
1.64
Boston
0.13
0.05
1.67
Chicago
0.13
0.01
1.40
Washington-Baltimore
0.12
-0.01
1.50
Hartford
0.12
-0.02
1.29
Santa Barbara
0.12
0.18
1.71
Detroit
0.11
-0.05
1.22
San Diego
0.10
0.12
1.56
Philadelphia
0.10
-0.04
1.34
Seattle
0.09
0.06
1.45
Stockton
0.08
-0.00
1.19
Minneapolis
0.07
-0.02
1.33
Denver
0.07
0.05
1.40
Atlanta
0.06
-0.03
1.45
Las Vegas
0.05
-0.02
1.38
Modesto
0.05
-0.01
1.17
West Palm Beach
0.05
0.02
1.44

HS elasticity
0.70
0.77
0.67
1.10
0.86
0.82
1.47
1.50
0.89
1.33
0.67
1.63
0.98
2.07
1.45
1.57
2.55
1.39
2.17
0.83

City name
JoplinAbilene
McAllenWichita Falls
Killeen
BrownsvilleJohnstown
Johnson City
Springfield
Fayetteville
Alexandria
Ocala
El PasoLubbock
Billings
AltoonaPensacola
Longview
Columbia
SharonNotes: The first two variables are Trade Productivity and Quality of Life from Albouy (2016). Rent prices are calculated
following Moretti (2013) and refer to the year 2000. Housing supply elasticities are taken from Saiz (2010).

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Table F.7: Predicted aggregate effects of immigration, alternative parameter estimates

Parameters estimated with β = 0.3, αt = 0.4∆ Labor∆ Native workers’ ∆ House owners’
productivity
welfarewelfareCounterfactual 1: 20% increase in population
Counterfactual 2: 20% immigrant-induced increase in population
Difference:

-0.44
0.87
1.31

Counterfactual 1: 20% increase in population
Counterfactual 2: 20% immigrant-induced increase in population
Difference:

0.59
2.12
1.53

No agglomeration forces
-1.34
3.47
-0.53
2.28
0.81
-1.18
Agglomeration forces
-0.97
-0.23
0.74

3.40
2.39
-1.01

Parameters estimated with β = 0.2, αt = 0.6∆ Labor∆ Native workers’ ∆ House owners’
productivity
welfarewelfareCounterfactual 1: 20% increase in population
Counterfactual 2: 20% immigrant-induced increase in population
Difference:

No agglomeration forces
-0.59
-0.53
1.48
0.05
2.06
0.58

6.48
2.69
-3.79

Counterfactual 1: 20% increase in population
Counterfactual 2: 20% immigrant-induced increase in population
Difference:

Agglomeration forces
0.36
-0.23
2.95
0.21
2.59
0.44

6.18
3.09
-3.10

Notes: This table shows the aggregate consequences of immigration under two different counterfactuals. In Counterfactual 1
we assume that new immigrants consume like natives. In Counterfactual 2 we assume that new immigrants spend 21 percentof their income in their country of origin, as estimated. This table reports the aggregate consequences of these two counterfactuals on three outcomes: average labor productivity, average native worker’s welfare, and average house owner’s welfare. We
report results assuming no agglomeration forces and agglomeration forces of 5%. The difference between Counterfactual 1 andCounterfactual 2 is the effect of immigration on the three outcomes of interest.

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