The Migration Accelerator:Labor Mobility, Housing, and Aggregate Demand

Greg Howard ∗

MITJob Market Paper

October 24, 2016

Abstract

Labor mobility affects how local shocks affect labor markets because people moveto more prosperous areas. The traditional view, associated with Blanchard and Katz(1992), argues that migration mitigates these shocks, and relies on the assumptionthat inmigration makes local labor markets slack. In this paper, I empirically test thatassumption by constructing an instrument for domestic inmigration based on previousmigration patterns and current outmigration in other places. I document that withinU.S.-migration causes a large local labor market boom, the opposite prediction of thetraditional view. The effect is large: a migration shock equal to one percent of theMSA’s population causes a fall in the unemployment rate of half a percent. Thisis a surprising result in theory, but I show increased housing demand leads to twoadditional channels which can explain this finding. First, housing is a durable good,so the labor demand for construction is front-loaded. Second, a house price increaseinduces additional consumption by non-migrants. I show these channels are presentin the data and account for the total effect. Finally, I use these estimates to concludethat migration amplifies local labor demand shocks by 15 percent.

∗ghoward@mit.edu. I would like to thank my advisors, Ivan Werning, Arnaud Costinot, and David Autorfor their input. I would like to thank Andrea Raffo for a comment that inspired the title. I would alsolike to thank Alp Simsek, David Atkin, Daron Acemoglu, Frank Schilbach, Emi Nakamura, Isaiah Andrews,Ludwig Straub, Jack Liebersohn, John Firth, Arianna Ornaghi, Rachael Meager, Sebastian Fanelli, Yu Shi,and Vivek Bhattacharya for useful discussion. This material is based upon work supported by the NationalScience Foundation Graduate Research Fellowship under Grant No. 2014136625. Any opinions, findings,and conclusions or recommendations expressed in this material are those of the author and do not necessarilyreflect the views of the National Science Foundation.

1

1 Introduction

America has a high rate of labor mobility, with an average of more than 3 percent of Amer-

icans moving to a new MSA every year. This mobility changes how local shocks1 affect

local labor markets, with implications for the aggregate effects of these shocks, the ability

of migration to provide insurance, the appropriateness of a unified monetary policy, and the

magnitude and duration of regional inequalities.

The traditional view is that migration mitigates local shocks as people move into more

prosperous areas. This means that local shocks are spread across regions, that migration

provides insurance even for non-movers, and that labor mobility is helpful for a monetary

union. This view is most closely associated with Blanchard and Katz (1992), which showed

that population responded positively to employment shocks, meaning that the employment

level never returned to trend, even though the unemployment rate did.

The traditional view relies on a key assumption, which is present in many standard

models: that migration causes slack in the receiving labor market.2 Certainly, when migrants

move into a MSA, the total labor supply increases, and if demand is unchanged, a natural

implication is that the labor market becomes more slack. Combining the empirical results

of Blanchard and Katz (1992) with this assumption implies migration mitigates differences

in local labor markets.

In this paper, I empirically test this key assumption by estimating the effect of domestic

migrants on the labor market of the receiving MSA. To get a causal effect, I construct an

inmigration instrument using the pre-period migration network and current outmigration

from connected MSAs. I find that the key assumption is false: within-U.S. migration from

1995 to 2013 causes a large local labor market boom in the receiving MSA. An inmigration

shock the size of one percent of the MSA’s population causes a decrease in the unemployment

rate of more than half a percent.

I focus on inmigration for two reasons. First I show the majority of the net migration re-

sponse to demand shocks is through inmigration, not outmigration.3 A local bust drives only

a few people away, but does discourage many people from coming in. So to better understand

how migration changes the effects of these shocks, it is of primary interest to understand the

1Many shocks are local, and many shocks that we think of as national have significant regional differences.(see Greenstone, Mas, and Nguyen, 2014; Autor, Dorn, and Hanson, 2013; Mian, Rao, and Sufi, 2013;Nakamura and Steinsson, 2014).

2Monras (2015) puts it this way: “For this [mitigating effect] to be true, the short-run local labor demandelasticity needs to be negative” (p. 2). Later, “I am not aware of evidence for the entire population thatcan be readily used in this setting” (p. 26).

3This is consistent with Monras (2015), which uses different shocks and data, and Coen-Pirani (2010)which notes that inmigration is much more volatile than outmigration.

2

effects of inmigration. Second, because outmigration is less correlated with local economic

conditions, its fluctuations are an appealing instrument for inmigration elsewhere.4

In a sense, the primary exercise of my paper is the reverse of the empirical exercise in

Blanchard and Katz (1992). They show a positive response of net migration to labor demand

shocks. I show a positive response of labor demand to inmigration shocks. The combination

of these results is what implies an accelerator, that migration amplifies the effects of labor

demand shocks.

The intuition behind the traditional view is strong and is present in many standard

models, including the model from Blanchard and Katz (1992). Inmigration increases the

labor supply, so if labor demand curves are downward sloping, the wage will fall. If wages

are sticky, the unemployment rate will rise instead. Migrants also move with their labor

demand, as stressed in Farhi and Werning (2014), but if they consume non-local goods,

their labor supply will usually exceed their labor demand. So in order to make sense of this

result, I focus on two previously unexplored channels, both stemming from increased housing

demand.

The first channel I label the construction channel. Housing is durable and requires local

labor. When migrants move in, the demand for housing rises. In the long-run, the steady-

state housing stock will increase and require more construction labor. But since housing

is a durable good, its short-run production must increase by more in order to reach that

steady-state. The logic is similar to how Baxter and King (1993) think of the response of

capital to government spending. Similarly, Rognlie, Shleifer, and Simsek (2015) consider a

model with too much initial housing stock relative to steady-state, causing a recession, the

opposite case of a migration shock.

The second channel I label the house price channel. Housing is a considerable fraction

of wealth and a major determinant of a borrower’s credit. The increased housing demand

causes house prices to rise, which has been documented to have a large effect on consump-

tion, including the consumption of goods produced by local labor. The Great Recession

encouraged research into this effect, with many papers, most notably Mian et al. (2013),

finding a large elasticity of consumption to house prices.5

4One could imagine using a similar network and concurrent inmigration as an instrument for outmigration,essentially the reverse of what I do in this paper. However, the predictive power is much weaker, raisingconcerns about weak instruments. Furthermore, because inmigration is driven by labor market conditions,concerns about the exclusion restriction are larger.

5Other papers that estimate the response of consumption to house prices include Campbell and Cocco(2007), Attanasio, Leicester, and Wakefield (2011), Agarwal, Amromin, Chomsisengphet, Piskorski, Seru,and Yao (2015), Strobel and Vavra (2015), and Kaplan, Mitman, and Violante (2016b). Berger, Guerrieri,Lorenzoni, and Vavra (2015) summarize the literature and suggest the average estimated elasticity is about0.2.

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I document the evidence of these two channels in my data. I show the same inmigration

shock leads to a sharp increase in housing permits and construction jobs, evidence of the

construction channel. I also show that house prices increase, that second-lien mortgage

originations rise, and that employment in non-tradable sectors rise as well, evidence of the

house price channel.

In addition, I show the results conditioning on the housing supply elasticity of the MSA

from Saiz (2010). For MSAs with lower elasticities, house prices do increase more and the

unemployment rate declines more in response to the shock. The theory is ambiguous on

this point: while the house price channel should be larger in more inelastic MSAs, the

construction channel could go either way depending on housing demand. So even though

this is not a formal test of a prediction of the model, it is consistent with the two channels

I outline and would be hard to explain by channels without housing as a key component.

The implication of this result is that migration amplifies local shocks as people move to

better labor markets, the exact opposite of the traditional view. To estimate the size of this

accelerator, I combine my estimates on the effect of migration on labor demand and the

effect of labor demand on migration. I then compare the effect of a labor demand shock on

employment, allowing or not allowing migration to respond to the shock. I find that with

migration, the effect on the employment-population ratio is amplified by 15 percent locally.

The result informs the common wisdom that labor mobility is a desirable property for

currency unions. Mundell (1961) first proposed labor mobility as an important criteria for

an optimal currency area, and it is widely accepted by academics and policymakers today.

As recently as 2012, the head of the European Central Bank said “For the euro area, too,

increased labour mobility across borders is crucial” (Draghi, 2012). My results, however,

suggest that within a currency union, migration may cause changes in aggregate demand

that exacerbates regional differences and hurts non-movers in depressed areas.6

Many papers since Blanchard and Katz (1992) have looked at population adjustments

in response to local economic shocks in different settings or time periods (see Decressin and

Fatas, 1995; Jimeno and Bentolila, 1998; Bound and Holzer, 2000; Cadena and Kovak, 2016;

Monras, 2015). All of these papers find evidence that economic conditions do affect mobility.

There is also a large literature on how house prices change migration decisions, usually

finding that the cost of housing plays a small role (see Head, Lloyd-Ellis, and Sun, 2014;

Davis, Fisher, and Veracierto, 2013; Nenov, 2015). Several papers, including Struyven (2014)

and Schulhofer-Wohl (2011), focus on housing lock, the idea that underwater mortgages

6Another reason labor mobility is important in currency unions is because it provides insurance for themigrants themselves. Insurance is more important in currency unions because monetary policy cannot playthat role. My results have little to say about this role. However, Yagan (2014) shows that migration providedlittle insurance during the Great Recession.

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prevent migration. In contrast to all these papers, I highlight a different role for housing:

how increased housing demand can have strong effects on local labor demand. Because labor

demand is a draw for migrants, it might explain why they find a small role of house prices

in migration decisions. Furthermore, none of these papers use a similar empirical strategy

to allow them to identify the effects of migration directly.

My work is closely related to the structural literature looking at spatial equilibria and how

shocks are propogated throughout the economy (see Caliendo, Parro, Rossi-Hansberg, and

Sarte, 2014; Kline and Moretti, 2014; Allen and Arkolakis, 2014; Diamond, 2016; Redding

and Rossi-Hansberg, 2016). My accelerator results are closely related because I also wish

to consider how local shocks interact with migration in equilibrium. In fact, many of these

papers allow for migration to improve labor markets through increasing returns to scale,

or through trade costs similar to Krugman (1980). But in contrast to these papers, my

empirical results suggest that housing is the key determinant of the improving labor market.

My empirical strategy and question are quite close to a literature on estimating the

effects of international migration (for example, Card, 1990; Borjas, 2016). In particular, I

use a similar empirical strategy to Card (2001), which combines the location of immigrant

communities and immigrants coming from that country to create a similar instrument. My

papers differ from these in two specific ways. First, I focus on internal migration; internal

and international migrants are different in several ways, likely including housing demand.

Second, I focus on the two channels associated with housing demand. This motivates a focus

on the short-run, and hence I estimate the effects year-by-year.

Saiz (2003, 2007) finds positive effects of immigration on house prices and rents. Much of

this literature is interested in the effect on house prices for a different reason, though: rising

house prices are evidence that immigrants have not completely displaced native workers.

In contrast, I focus on how rising house prices are a part of a housing-led demand boom.

While I am not aware of any work that focuses on these channels in response to international

migration, and I hope to extend the methodology in this paper to international migrants in

a future paper.

Much of the immigration literature focuses on skill complementarity, something I abstract

from in the main body of this paper. If migrants and non-migrants are complements, the

unemployment rate might fall because the non-migrants become more productive, and not

because of increased housing demand. Similarly, other papers suggest love of variety might

imply immigration is beneficial to natives (see Hong and McLaren, 2015). Many of the spatial

equilibria papers mentioned above allow for increasing returns to scale, as well. However, the

timing, magnitude, industrial composition, and relation to housing supply elasticity lead me

to believe a housing story is explaining my headline result. I discuss this further in Section

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4.4.

The rest of my paper is organized as follows: in Section 2, I present a theoretical model

that frames the discussison, and show that housing is a critical feature to explain my empirical

results. In Section 3, I outline my empirical strategy and show that inmigration has an

expansionary effect on local labor markets in the United States. Section 4 shows the evidence

in favor of the construction and house price channels. Section 5 estimates the effect that

employment has on migration, and combines that with the results from Section 3 to calculate

the size of the migration accelerator.

2 Theoretical Framework

In this section, I present a model of an MSA that includes migration. I consider the effects

of inmigration on the equilibrium, and especially its effect on the unemployment rate. I

highlight the construction channel and the house price channel, showing that without them,

migration is unable to cause a decline in the unemployment rate. In a special case of the

model, where I consider log-utility so as to not keep track of the wealth distribution of agents,

I show that if the preference parameter on housing consumption is high enough, these two

channels will cause a decline in the unemployment rate.

There will be two main shocks to the economy. The first is to the utility of living

elsewhere, what I call a “migration shock.” The second will a labor demand shock. Each of

these shocks has an empirical counterpart.

For notation, I will use capital letters as aggregate quantities within the MSA, and lower-

case letters as per-capita terms. Prices will also be lower-case. I will use lower subscripts for

indexing of people i and time periods t. When there is no time component to an equation,

I may omit the lower t subscript.

2.1 Setup

2.1.1 The agent’s problem

Denote Γ as the aggregate state of the economy, which is the previous period’s population

of the MSA, N , the wealth distribution of all agents, the housing owned by each agent,

and the two shocks: the outside option G(·) for potential migrants, and tradable demand,

DX . The agents use these state variables to forecast future prices. Agents, indexed by i,

value their consumption of housing, h; tradables, cT ; and non-tradables, cNT . They own

one-period bonds a and housing h, and e denotes their employment status. The discount the

next period’s utility by β. With probability ρ, they leave the MSA, and receive continuation

6

utility V ∗.7

V (Γ, ai, hi, ei) = maxcNTi ,cTi ,h

′i,a′i

u(cNTi , cTi , h′i) + β

((1− ρ)E[V (Γ′, a′i, h

′i, e′i)] + ρV ∗(a′i + phh′i)

)and are subject to a budget constraint:

cTi + pcNTi + phh′i +1

1 +Ra′i ≤ ph(1− δ)hi + ai + wei

I normalize the price of tradables to one, so p is the price of non-tradable goods, w is the

wage, and ph is the price of housing. δ is the depreciation rate for housing. The agent is also

subject to a collateral constraint:

(1− δ)h′iph′ ≤ φa′i

Assume a unit mass of potential migrants considers moving in. If they do move in, their

value function is:

V (Γ, ai, 0, e) ≡ Ee[V (Γ, ai, 0, ei)]

The expectation is over whether or not they get a job when they first move in. The potential

migrants also have an outside option, V ∗i . There is a joint distribution over the outside

option and assets, which is stochastic.

(V ∗i , ai) ∼ G(·, ·)

Define Ga as the marginal distribution of a, and GV |a as the partial distribution of V for a

given a. Hence g(V , a) = ga(a)gV |a(V ).

Hence the population N is

N = (1− ρ)N−1 +m (1)

where

m =

∫G−1V |a (Ee[V (Γ, a, 0, e)]) dGa(a) (2)

Implicit in this notation is a timing assumption: potential migrants first choose whether to

move in, then either receive or do not receive a job, and then make spending decisions.

7I choose to model outmigration as exogenously determined because it is relatively unresponsive to mi-gration and labor demand shocks, as I show empirically in Section 3.5 and Section 5.1.

7

2.1.2 Land and Housing

The MSA has a fixed amount of land, L, upon which housing is built. Each period, a fraction

δ of the housing depreciates, leaving δL available for development. Although it is not key to

the model, it is easiest to assume that the land from depreciated houses is lump-sum taxed

by the government, who then sells it to house-producers and keeps the profits.8 Housing is

produced competitively using that land, as well as labor and imported goods. The price of

housing is flexible and the production function H is constant returns to scale.

H ′ = (1− δ)H +H(Dh, TH , δL)

The price of housing is then pinned down by a marginal cost function:

ph = ph(H ′ − (1− δ)H,w) (3)

where ph is increasing in both arguments. The labor demand from housing is determined by

the same things:

Dh = Dh(H′ − (1− δ)H,w) (4)

Dh is increasing in the first argument and decreasing in the second argument.

2.1.3 Tradables and Non-tradables

Production of non-tradable goods is linear in labor. I normalize productivity to 1. Hence,

labor demand for the production of non-tradables is

YNT = Dc (5)

Assume further that the market is competitive and that prices are not sticky beyond any

stickiness in wages.

w = p (6)

Assume Dx(w), the labor demand from the production of tradable goods, is stochastic and

exogenously given.

8A reasonable alternative assumption is that homeowners keep the land. Because the price of land andthe price of houses are monotonically related, Proposition 1 is not affected by this assumption. However,the equations in Appendix B become more complex.

8

2.1.4 Aggregate demand

Aggregate demand, expressed in labor units, is the sum of labor demand for non-tradable

goods, tradable goods, and housing.9

D = Dc +Dx +Dh (7)

2.1.5 Philips Curve

Assume wages, and hence prices, are perfectly sticky.

w′ = w (8)

While this is extreme, it helps to highlight my mechanism.

Labor is allocated randomly between agents.

P (ei = 1) = e =D

N(9)

2.2 Equilibrium

Agents solve their maximization problem:

cNTi = cNTi (Γ, ai, hi, ei) (10)

cTi = cTi (Γ, ai, hi, ei) (11)

hi = hi (Γ, ai, hi, ei) (12)

Assume that these are all twice continuously-differentiable.

The market clearing conditions are

Ht =

∫hidi (13)

YNT =

∫cNTi di (14)

For any shocks G and Dx and state Γ, an equilibrium is the new population N , the

migration m; prices, w, p, and ph; employment, ei; consumption, cNTi , cTi , and hi; and

aggregate variables H, YNT , Dc, Dh, and D; such that equations (1)-(14) hold.

9This equation looks a lot like the Y = C + I + G + X −M equation from introductory macro. In mynotation, Dc is equal to consumption minus imports, the only investment is in housing, and, in my baselinemodel, I am abstracting from government spending.

9

2.3 A one-period model

To set ideas, it is useful to think of the equilibrium when β = 0. In this case, assume that

ai is given exogenously, rather than chosen by the agents the period before.10 Furthermore,

assume agents must consume 1 unit of housing to live in the MSA, and are satiated by that

housing.

In this case, the only relevant aggregate variable to the agent is ph, so the value function

is simplified:

V (ph, ai, ei)

A useful way to think about the equilibrium is the interaction between e and m. For a

given e, the value function for a migrant is

V (ph, am − ph, e)

Recall that ph(m) is increasing in m. Hence, migration solves the equation

m =

∫G−1V |am

(V (ph(m), am − ph(m), e)

)dGa(am) (BK)

For a given e, migrants move and house prices rise until the marginal migrant is indifferent.

The cost of housing outweighs the benefits of additional borrowing capabilities. Hence,

equation (BK) defines a positive relationship between e and m.

Similarly, consider how e responds to m.

e =Dx +

∫cNT (ph, aj, e)dj +

∫cNT (ph, ai, ei)di+Dh(m)

(1− ρ)N +m(E)

where j indexes migrants and i indexes non-migrants. For a given m, the numerator is

the number of jobs, added up across tradable goods, non-tradable goods demanded by non-

migrants and migrants, and housing demand which is increasing in the number of migrants.

The denominator is the labor supply.

In the traditional view, this curve defines a negative relationship between e and m.

Without housing, the intuition for this is clear because equation E reduces to

e((1− ρ)N +m) = Dx +

∫cNT (ai, ei)di+

∫cNT (am, e)dm

If the wealth distribution of migrants is first-order stochastically dominated by the wealth

10The main problem this assumption fixes is that the migrants would not have the money to purchase ahouse.

10

m

e

BK

E

Figure 1: A graphical representation of the traditional-view equilibrium in the one-periodcase.

distribution of non-migrants, this will be a decreasing relationship between e and m.11 In-

tuitively, labor supply increases by a bigger percentage than labor demand.

This equilibrium is graphed in Figure 1. Empirically, each of these lines can be identified,

M by exogenous changes in labor demand which moves E around, and E by exogenous

changes in the outside option, which moves M around.

With housing, the slope of E is less clear. An increase in the number of migrants increases

housing prices, allowing non-tradable consumption to increase for non-migrants. And the

housing production for these migrants employs more workers. Each non-migrant requires

δ new houses, while each migrant requires a whole new house. If these forces are strong

enough, the slope may be increasing.

Figure 2 presents a case where E is increasing. This figure allows me to illustrate the

accelerator. Suppose E shifts to E ′ due to an exogenous increase in tradable demand. The

equilibrium shifts up and to the right. The bracketed dashed lines indicate the size of the

migration response, the initial size of the demand shock, and the “accelerator,” the extra

increase in e due to the equilibrium migration response.

2.4 The effect of migration on aggregate demand per capita

When β > 0, the current price of housing and the employment rate are no longer sufficient

statistics for Γ, the aggregate state space. Because Γ is so large, it is intractable to solve this

model with aggregate shocks. Rather, I will linearize around a deterministic steady-state,

11This assumption is sufficient such that the agents will consume less non-tradables on average. SeeTheorem 1.

11

m

e

M

E

E ′

demand shock

accelerator

migration response

Figure 2: A graphical representation of the housing equilibrium in the one-period case.

where the variance of the outside option and the demand for tradable goods approaches zero.

Without these aggregate shocks, agents can perfectly forecast ph and e, which are the only

aggregate variables that matter for their migration and consumption decisions.

The value function can then be written as follows

V ({phs , es}s≥t, ai, hi, ei)

and the consumption functions of agents can similarly replace Γ with {phs , es}s≥t.One of the key questions this paper seeks to answer is what is the effect of a migration

shock on the employment rate (and also the unemployment rate). Based on our decomposi-

tion above, we can break down detdM

.

Ntdetdm

= −et(1− ρ)t︸ ︷︷ ︸Labor supply increase

+ cNTm,t(1− ρ)t︸ ︷︷ ︸Migrant demand

+∞∑s=0

∫∂cNTi,t∂es

didesdm︸ ︷︷ ︸

Non-tradable Keynesian multiplier

+∞∑s=0

∫∂cNTi,t∂phs

didphsdm︸ ︷︷ ︸

House price channel

+dDH,t

dHt

(dHt

dm− (1− δ)dHt−1

dm

)︸ ︷︷ ︸

Construction channel

The first two terms are the direct effects of migrants: they increase the labor supply, lead-

ing to lower employment rates; and they consume non-tradable goods, requiring labor and

increasing employment. The third term is a Keynesian multiplier, amplifying the effects of

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the other terms because with more employment, agents consume more non-tradables.

The fourth and fifth terms are new, and highlight the two channels. The fourth term

is the effect that house prices have on non-tradable consumption. With the increase in

housing demand, house prices increase, and non-tradable consumption increases because of

that. Berger et al. (2015) break down the effect of house prices into four: a wealth effect,

a substitution effect, a collateral effect, and an income effect. They also argue on empirical

and theoretical grounds that the total effect is sizable. My model includes all four effects,

though not the assumptions to imply that the income, substitution, and collateral effect

exactly cancel out.

The fifth term is the construction channel. With the housing demand increase, the

number of houses will increase. The change in construction demand is proportional to the

change in the number of houses in period t, but is negatively affected by the number of new

houses in period t−1, because there is already a stock of housing that does not require labor

to be built. Hence, there is a front-loading effect as the stock of housing is built up.

Note the demand for non-tradable goods does not change because we hold prices fixed.

Of course, housing and house prices are determined in equilibrium. The change is the

solution to the following system of equations. But more importantly, we can also estimate

these in the data. Hence, the equation above is a useful guide to the empirical exercise even

without solving out for dph

dmand dH

dm.

dHt

dm= dhtm(1− ρ)t +

∞∑s=0

∫∂hi∂es

didesdm

+∞∑s=0

∫∂hi,t∂phs

didphsdm

dphtdm

=∂pht∂Ht

(dHt

dm− (1− δ)dHt−1

dm

)This decomposition allows me to a proposition about the traditional view, in the spirit

of Farhi and Werning (2014).

Proposition 1 (The Traditional View). Suppose there were no housing, Ht = 0. If migrants

are less wealthy than non-migrants, i.e. the wealth distribution of migrants is first-order

stochastically dominated by the wealth distribution including housing of non-migrants, then

the employment rate weakly decreases (the unemployment rate weakly increases) in every

subsequent period.

The assumption that migrants are less wealthy is reasonable. From Molloy, Smith, and

Wozniak (2014), we know that most migrants tend to be younger than the general pop-

ulation, and so have had less time to build up wealth. In Section 4.4, I show that the

interest, dividend, and rental income of migrants is first-order stochastically dominated by

13

non-migrants in ACS data.

The important part of the proof is that the labor supply goes up by more than the labor

demand. Because the migrants are less wealthy, they spend less money on non-tradable goods

than non-migrants. Hence the demand for non-tradables goes up by a smaller percentage

than the labor supply increase. Combined with the fact that the Keynesian multiplier term

simply amplifies other effects, the employment rate must decrease.

The key insight of this paper is that the logic of Proposition 1 breaks down when housing

is incorporated into the model. One way in which it breaks down is that housing is through

the construction channel. With non-tradables, the key assumption is that changes in non-

tradable demand and changes in labor demand are contemporaneous. But the additional

labor demand from housing isdDH,t

dHt

(dHt

dm− (1− δ)dHt−1

dm

), which is not contemporaneous.

Dh,t depends on both Ht (positively) and Ht−1 (negatively). For example, if dHt

dmis constant

for all t ≥ 0, the additional labor demand is much higher in the first period and only slightly

larger in all subsequent periods. Hence, for even small increases in the amount of housing

demand, the amount of initial labor demand can be quite large.

The other reason housing breaks the logic of Proposition 1 is that the consumption

of homeowners increases when house prices appreciate. For one thing, the wealth W0, i

increases when house prices go up. In addition, borrowing limits are relaxed, leading to a

collateral channel. These may be mitigated by an income effect because it is more expensive

to own housing, and the substitution effect of housing has ambiguous effects on employment.

But empirical estimates have shown that increases in house prices generally lead to higher

consumption.

In Appendix B, I show that for a model with log-utility and Cobb-Douglass housing

production, it is quite possible for the unemployment rate to fall in response to migration.

This is true when agents place a high value on the utility of housing, leading them to own

more of it and to employ more construction workers. For sufficiently high values, the increase

in wealth and construction outweighs the increase in labor supply.

3 The Expansionary Effect of Migration

Under the traditional view, migration causes an increase in the unemployment rate. In this

section, I construct an instrument to test this assumption, using previous migratory patterns

and outflows from other MSAs to study the effects of plausibly exogenous inmigration. I

find that the unemployment rate falls, the opposite of the traditional view.

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3.1 Data

I will use two main sources of data. The first is the Internal Revenue Service’s Statistics of

Income U.S. Population Migration Data. The sample covers the entire United States from

1990-2014, and records migration flows from county to county on a yearly basis. The data

records the number of returns filed, as well as any exemptions they claim, proxying for the

total number of people in the household. It also includes the adjusted gross income of the

migrants. This is a uniquely useful dataset because it allows me to create a network of

migration, which I use to construct the instrument.12 Datasets from the ACS only record

the state from which someone moved, and matched Census data is not at a high enough

frequency to capture the effects I am interested in.

In general, a county is smaller than a labor or housing market. So in estimating the effect

of migration, I mostly aggregate to metropolitain statistical areas (MSAs). I will note when

I also use micropolitain statistical areas, which together with MSAs, are refered to as core-

based statistical areas (CBSAs). A metropolitan statistical area is a collection of counties

with an urban area of at least 50,000 people, while a micropolitan area only requires an

urban area of 10,000. I choose MSAs instead of commuting zones because certain housing

data is more readily available this way, especially Saiz elasticities. My dataset consists of

381 MSAs and 917 CBSAs.

The second data set comes from the Bureau of Labor Statistics’s Local Area Unem-

ployment Statistics (LAUS). I use annual unemployment rates. The LAUS uses a variety of

sources to calculate local area unemployment rates, including the Current Population Survey,

the Quarterly Census of Employment and Wages, and unemployment insurance claims.13

12There are a few drawbacks to this data. First of all, the address used to determine migration is theaddress from which the tax return is filed, meaning that the date of migration could be anytime before filingtaxes. While much of the migration likely occured in the previous calendar year, some will have occured inthe first few months of the next year. In 2015, 132 million returns were filed by May 28, out of 148 millionfiled by November 24, over 85 percent. Marlay and Mateyka (2011) report large seasonality of moves, withsummer being the most common season to move during, even more so for people that cross state or countylines. Furthermore, the timing of filing taxes might be endogenous to moving, so the ratio of inmigration tonon-migrants might be slightly mismeasured. Finally, the sample before 2011 does not include any peoplewho filed after September. These people tend to be richer and have more complex taxes, and they are beingmissed from the data. So potentially, migrants are undercounted compared to non-migrants, and it mightespecially be true for rich migrants. Another potential issue is that the data is censored below, and onlyrecords data if there are more than 10 returns. Finally, the data covers only people who file taxes and theirdependents. The elderly and the jobless are certainly undercounted. Despite all these drawbacks, the datais still very useful in determining patterns of migration, and any of these measurement errors are likely tobe small compared to other available datasets.

13Some of the estimate is imputed from demographically-adjusted state-wide estimates, which could implymisleading within-state correlations. However, the primary building blocks are establishment employmentcounts and unemployment insurance claims, which are area-specific. Adjustments for commuting are made,so I focus on MSAs when using this data because MSAs are constructed to cover popular commuting patterns.

15

For robustness and to explore the housing channel, I also use data from a variety of

other sources. Wage and industry employment data comes from the Quarterly Census of

Employment and Wages. I sort these into categories based on the decomposition of Mian

et al. (2013). House price data comes from the Federal Housing Finance Agency. Housing

starts comes from the Census Building Permits Survey. Mortgage data comes from the Home

Mortgage Disclosure Act data. Population data comes from the Census. Wage data comes

from the BLS Occupational Employment Statistics. Estimates of housing elasticity come

from Saiz (2010). The location of counties is taken from the Census Censtats database.

I report means and standard deviations of key variables in Table 1. Each variable is

available for 381 MSAs, and N < 7620 reflects that variable is not available in all years.

Table 1: Summary statistics

Variable Mean Std. Dev. NUnemployment Rate (Percent) 6.1 2.8 7620Employment (1000s) 306.1 712.5 7620Population (1000s) 643.0 1505.3 7620Inmigration Rate (Percent) 3.3 1.6 7620Outmigration Rate (Percent) 3.2 1.4 7620House Permits Issued per 1000 people 6.4 11.2 5714House Price Growth (Percent) 2.9 5.9 7592All Mortgage Originations per Capita ($s) 4.5 3.9 7620Second Lien Mortgage Originations per Capita ($s) 0.2 0.4 3810Non-tradable Employment to Population Ratio (Percent) 7.8 1.7 6096Construction Employment to Population Ratio (Percent) 3.3 1.5 6096Tradable Employment to Population Ratio (Percent) 4.9 3.2 6096Average Weekly Earnings per worker ($s) 636.4 158.1 7449

3.2 Econometric Specification

I wish to estimate the effect of migration on a MSA’s unemployment rate. There are several

econometric challenges in estimating the effect. Primarily, the concern is that migration is

endogenous, and that the unemployment rate and migration are correlated because of reverse

causality. In fact, as I show in Section 5.1, people move more to areas that experience positive

labor demand shocks.

16

My specification is

∆un,t =4∑

s=−3

βs∆mn,t−s + αt + εn,t

∆mn,t−s =4∑

r=−3

δr,s∆zn,t−r + γr,s + ηn,r,s

where un,t is the unemployment rate in MSA n in period t, m is the migration rate, and z is

the instrument which I discuss in the next section.

I estimate a moving-average of migration because migration is autocorrelated, so omitting

leads and lags would bias my results.14 Further, a moving average allows me to read-off the

impulse response of unemployment to migration. The response of ut+s to inmigration in

period t is simply βs. In addition to lags, I include leads of the instrument to test the

assumption of parallel trends.15 I chose to use four lags because the effect dissipates after

four years, implying that additional years are unlikely to be an important omitted variable.

Three lags is appropriate to show a lack of a trend.

I include a year-fixed effect to control for aggregate economic conditions, since it is well-

known that gross migration is correlated to economic conditions (See Molloy et al., 2014).

I also estimate the equation in first-differences due to concerns that migration or the

unemployment rate may be non-stationary. As I show in robustness checks, estimating the

equation using MSA fixed effects leads to almost exactly the same results.

I cluster my standard errors at the MSA level due to the persistence of the unemployment

rate, as suggested in Bertrand, Duflo, and Mullainathan (2004).

3.3 Instrument

Because migration is not randomly assigned, I use an instrument to identify the causal effect

migration has on an MSA. I use the historical patterns of migration and the outmigration

from far-away counties, to construct an instrument for inmigration to a MSA. I only use the

outmigration that goes to places far from the MSA as well, meaning that the migration is

not directly related to the economic conditions of the MSA of interest.

Specifically, I use the first four years of the IRS data, covering movements from 1990-

14See Hansen and Sargent (1981) or Plagborg-Møller et al. (2015) for a discussion of moving averagemodels. The following papers have also used a similar econometric set-up, often to answer more aggregatequestions: Ramey (2015), Jorda (2005), Angrist, Jorda, and Kuersteiner (2013).

15A violation of parallel trends is not necessarily a violation of exogeneity, as there may be anticipatoryeffects from the inmigration. Nonetheless, an absence of parallel trends lends credence to the identifyingassumption.

17

1994 to map the network of migration around the United States. Then, to construct the

instrument for a particular MSA in a particular year, for each county more than 100 miles

away, I take the share of people moving into that MSA in the historical network, and multiply

by the outmigration of the origin county in that year to places more than 100 miles from

the MSA. Then I sum over all counties.

Because the patterns of migration are relatively stable, this instrument is strongly corre-

lated to the actual inmigration of that MSA. There are many possible explanations over why

the patterns are stable, perhaps because of ethnic similarities or family ties (Bartel, 1989).

Other determinants, such as distance or the similarity of climate, are quite stable over time

as well.

In my baseline construction of the instrument, I throw out all flows that are to or from

a county within 100 miles of the MSA. I check the robustness and exogeneity of this cutoff

by using all counties outside the MSA,16 and by using a cutoff of 500 miles.

As a concrete example, suppose I am constructing an instrument for inmigration to

the Boston-Cambridge-Newton Metropolitain Statistical Area. To start, I would pick a

county, say Montgomery County, Maryland. Historically, 1.0 percent of the outmigrants

from Montgomery County move to the Boston MSA, and 98.6 percent move at least 100

miles away from Boston. In 2007, 42,032 people moved from Montgomery County to other

places 100 miles or more away from Boston. To calculate the instrument, I would multiply

those 42,032 by 1 percent and divide by 98.6 percent to predict that 426.3 people moved to

Boston. I would then sum over all counties in America that are at least 100 miles away from

Boston, which would give me an instrument for inmigration to Boston in 2007.

In math, the formula for my instrument is:

zn,t =∑c∈−n

mc→n,T

mc→−n,Tmc→−n,t

where −n is the set of all counties that are sufficiently far from n, T is the pre-period, and

mc→n is the migration from county c to area n.

The identifying assumption behind these results is that the outmigration from historically-

connected counties is unrelated to other factors that might cause a change in the unemploy-

ment rate, that η is perpendicular to ε. In my data, the most pronounced outmigration

episodes are because of two hurricanes: Katrina and Irene. In Appendix D, I show similar

results to my main regression using only the outmigration from Hurricane Katrina.17 One

16For this instrument, I also throw out any counties for which more than half of their outmigrants moveto the MSA. Including those counties gives noisy and small outmigration shocks large influence over theinstrument’s variation and makes the estimates much less precise.

17It is easier to study the effects of Katrina because it primarily hit eight counties, whereas the effects of

18

concern for identification is that areas with high mobility between them might experience

similar shocks. However, if the shocks go in the same direction, and if positive shocks induce

people to stay, then the bias from this story will attenuate my results, suggesting my results

might be a lower bound for how expansionary inmigration is. I discuss this bias in more

detail in Section 3.6.

Table 2: First stage(1) (2) (3) (4) (5) (6) (7) (8)

Inmigration Inmigration Inmigration Inmigration Inmigration Inmigration Inmigration InmigrationVARIABLES t+3 t+2 t+1 t t-1 t-2 t-3 t-4

Instrument, t+3 1.166*** -0.003 0.305*** 0.001 -0.168*** -0.188*** -0.110** -0.262***(0.129) (0.073) (0.055) (0.051) (0.059) (0.049) (0.054) (0.047)

Instrument, t+2 0.015 1.682*** -0.193* 0.074 -0.124** -0.074 -0.130* -0.284***(0.123) (0.178) (0.098) (0.094) (0.049) (0.080) (0.073) (0.061)

Instrument, t+1 0.222** -0.060 1.795*** -0.209** 0.044 -0.210*** -0.081 -0.228***(0.102) (0.131) (0.180) (0.105) (0.099) (0.054) (0.084) (0.062)

Instrument, t 0.037 0.029 0.080 1.899*** -0.341*** -0.077 -0.252*** -0.090(0.076) (0.072) (0.105) (0.197) (0.123) (0.101) (0.069) (0.083)

Instrument, t-1 -0.116 0.119 0.005 0.027 1.795*** -0.336*** -0.068 -0.231***(0.085) (0.075) (0.071) (0.113) (0.197) (0.124) (0.104) (0.070)

Instrument, t-2 -0.028 0.067 0.018 -0.058 0.034 1.824*** -0.331*** -0.067(0.078) (0.069) (0.086) (0.080) (0.127) (0.198) (0.116) (0.092)

Instrument, t-3 -0.335*** 0.073 0.006 -0.028 -0.001 0.078 1.864*** -0.377***(0.076) (0.077) (0.067) (0.088) (0.083) (0.134) (0.190) (0.120)

Instrument, t-4 -0.158** -0.259*** -0.002 -0.022 0.091 0.077 0.120 1.800***(0.077) (0.063) (0.065) (0.066) (0.107) (0.083) (0.121) (0.167)

First Differenced YES YES YES YES YES YES YES YESYear FE YES YES YES YES YES YES YES YESSanderson WindmeijerF-stat 203.5 216.3 259.7 184.9 175.5 204.5 196.0 193.2R-squared 0.429 0.328 0.341 0.312 0.293 0.284 0.272 0.277

N 4572 4572 4572 4572 4572 4572 4572 4572MSAs 381 381 381 381 381 381 381 381

*** p<.01, ** p<.05, * p<.1Instrument and Inmigration measured as a percent of MSA population.

Standard errors clustered at the MSA level.The Kleibergen-Paap F-statistic is 11.46.

Table 2 shows the first-stage results. The first thing to note is that the coefficients

are about what you would expect. Along the diagonal of the table, the coefficients are

large, positive, and statistically significant, showing that the instrument does predict the

contemporaneous inmigration well. The fact that the coefficients are larger than one is a

result of the fact that migration to MSAs is more variable than migration to other places.

Perhaps, when a local push causes many people to leave, they are more likely to move to big

cities, than when they have to move for personal reasons. Off the diagonal, the coefficients

are much smaller. Some are significant, which is not surprising since the reasons to leave a

MSA are likely to be temporally correlated. In addition, someone that leaves a MSA in one

period cannot then leave in the next period, leading to a possible negative correlation. The

Irene were more widespread.

19

off-diagonal significance does emphasize the need for the moving average specification, but

is not a concern for the exogeneity of the instrument.

I would also note that the F-tests are large. Unfortunately, there is not yet a widely-

accepted rule-of-thumb on an appropriate weak instruments test with this many endogenous

regressors.18 Because of this, I will report the Anderson-Rubin Wald test p-values for my

headline result, which is a joint test of all the regressors in an equation, and is robust to

weak instruments.

3.4 The Effect on Unemployment

Figure 3 shows the effect of an inmigration shock on the unemployment rate. It is the effect

of the inmigration of an additional one percent of current residents in a MSA. In periods

t − 3 to t − 1, the coefficients are not significantly different from zero, giving no evidence

of a pre-trend. In period t, the period of the shock, the unemployment rate falls by 0.4

percentage points. In period t+ 1, the unemployment rate falls more, to a total effect of 0.6

percentage points. In periods t+ 2 and t+ 3, the effect begins to diminish, before returning

to zero in t+ 4.19

The result is the opposite of the assumption inherent to the traditional view. If, as I

have shown here, migration has a negative effect on the unemployment rate, then migration

does not dampen local shocks. Rather, as people move to prosperous areas, it will amplify

those shocks.

Figures 4 and 5 demonstrate the robustness of this result. In each figure, the same

baseline impulse response from 3 is shown in blue with shaded confidence intervals. A variety

of robustness checks are superimposed on them, all with the same qualitative pattern.

In Figure 4, the first robustness check is using fixed effects instead of first-differences.

The one difference is that there is a significantly positive effect in t + 4, which would make

sense with the transitory nature of a housing shock which then reverses itself, as the stock

of housing rises and savings decrease. Allowing for MSA trends does not have a meaningful

difference. Nor does including education and industry controls.20

18Sanderson and Windmeijer (2016) have a test for multiple endogenous regressors, but the test is foreach first-stage, and one might worry about multiple testing. Kleibergen and Paap (2006) provide aheteroskedasticity-robust joint test of all the instruments, which uses critical values from Stock and Yogo(2005), but they do not provide critical values for this many endogenous regressors.

19A natural comparison is to the OLS regression, also shown in Figure 3. While qualitatively similar,the magnitude of the results is larger in the IV. This could be caused by measurement error because of theIRS Migration Data’s censoring process. Another possible reason would be that the housing bubble duringthis time period played a major role in both limiting inmigration and boosting the economy. During thistime period, high house prices were associated with both higher inmigration and lower unemployment rates.However, they do not seem to be correlated to outmigration.

20I interact the shares of 2-digit SIC industries in 1990 with a year dummy to control for industry. For

20

Figure 3: The effect of an inmigration shock equal to one percente of the MSA’s population,with 95 percent confidence intervals. Errors clustered at the MSA level. Number of MSAs:381. Anderson-Rubin test: F (8, 380)-statistic: 9.49, p = 0.000

In Figure 5, I investigate a variety of robustness checks aimed at addressing concerns

about the spatial structure of my regression. Because my instrument relies on the cutoff

of 100 miles, I investigate the robustness to that by using no cutoff, and using a cutoff of

500 miles. The results are similar, though for no cutoff, the coefficient in period t is much

smaller. This could be evidence of bias if a cut-off is not used because the area around the

MSA could be doing poorly, causing people to move out. Reassuringly, the estimate for 500

miles is almost right on top of the baseline specification. The last robustness check is that I

control for the economic conditions of nearby MSAs by including a fourth-order polynomial

in latitude and longitude by year control. My specification is

∆un,t =4∑

s=−3

βs∆mn,t−s + P 4t (latituden, longituden) + εn,t (15)

∆mn,t−s =4∑

r=−3

δr,s∆zn,t−r + P 4r,s(latituden, longituden) + ηn,r,s (16)

where P 4 is a fourth-order polynomial including all the interaction terms. For this specifi-

cation, I drop the MSAs in Alaska and Hawaii (four total), rather than include higher order

polynomials. This exercise shows that it is not driven by a small set of regions which had

uniform migration and unemployment paths.

In addition to these robustness checks, in Appendix D, I present a similar regression

education, I interact shares of the 11 education codes in the 1990 Census with year dummies.

21

Figure 4: The effect of an inmigration shock equal to one percent of the MSA’s population,with 95 percent confidence interval. Errors clustered at the MSA level. Number of MSAs:381.

using a migration network based on the 1940 Census instead of my pre-period, finding

similar results, but noisier because the Census does not use the county of origin, only the

state.

A final robustness check is to make sure we can see this force in other measures of

employment. In Figure 6, I show the effect on the employment-population ratio, for both

MSAs and the broader category of CBSAs. Here I construct the employment-population

ratio by dividing employment in the Quarterly Census of Employment and Wages by the

population estimates of the U.S. Census. Estimates are consistent with the effects on the

unemployment rate, with the employment-population ratio rising.

In Figure 7, I also show that earnings went up and that unemployment benefits fell.

Earnings also comes from the QCEW, as measured by the annual average weekly wage,

while unemployment benefits come from the BEA’s personal current transfer receipts.

I allow for a city trend when estimating earnings. Earnings, along with several other

variables I later will consider, have different trends around the country, which are correlated

to the level of migration. Migration as a whole has trended downward throughout my

data, as documented by Molloy, Smith, and Wozniak (2011). Correspondingly, areas with

higher initial rates of migration have seen steeper trend declines over the time period.21 The

correlation between these two things is categorically different than the short-term variation

driving my unemployment results.22 I control for a linear trend by adding a fixed effect to

21Another similar method to solving this problem is to control for the migration rate in the pre-periodinteracted with a linear time trend. The results are quite similar.

22I do not find any evidence of systematic trends in unemployment, or any relation between that and

22

Figure 5: The effect of an inmigration shock equal to one percent of the MSA’s population,with 95 percent confidence intervals. Errors clustered at the MSA level. Number of MSAs:381 (377 for “latitute and longitude controls”).

the first-difference specification. Note that the regressions I run later on house prices also

have this feature. The first-stage and the F-statistics are quite similar.

My regression becomes

∆wn,t =4∑

s=−3

βs∆mn,t−s + αt + αn + εn,t (17)

∆mn,t−s =4∑

r=−3

δr,s∆zn,t−r + γr,s + γn,s + ηn,r,s (18)

where w is the log weekly wage. The only difference in this specification is that there is an

αn and a γn,s, which, with first-differences, captures the trend.

3.5 Effect on non-migrants

A natural question is whether the effects on the unemployment rate could be driven purely

by migrants being more likely to have jobs. It appears from the descriptive data that their

adjusted gross incomes are not necessarily that much higher.23 Nonetheless, by focusing on

the unemployment rate, we have a natural bound on the direct effect of the migrants’ jobs.

It first needs to be established that inmigration does not have a large effect on the

outmigration rate. I show this in Figure 8. Therefore, if the migrants participate in the

migration levels.23See for example, Figure 17 in Appendix C.

23

Figure 6: The effect of an inmigration shock equal to one percent of the MSA’s population,with 95 percent confidence interval. Errors clustered at the MSA or CBSA level. Numberof MSAs: 381. Number of CBSAs: 917.

labor force at the same rate as natives, even if they all have jobs, the direct effect of this is

bounded by the unemployment rate itself, which in my sample, averages 0.06. Even if we

take the upper limit of the outmigration rate confidence interval and assume none of them

have jobs, the total effect would be less than 0.25, which is significantly less than the initial

impact of a migration shock, around 0.5. Even with these relatively extreme assumptions,

the estimates are too big to explain by a higher likelihood to have a job for migrants.24

3.6 Bias

A worry of using this instrument is that there might be an omitted variable driving both the

outmigration from other places and the unemployment rate. Specifically, if local demand

shocks are correlated between places with high historical mobility, those shocks might drive

outmigration and the unemployment rate, biasing my regression.

Because of this concern, I exclude migration within 100 miles of the MSA, and I check

for the robustness of the regression with industry and education controls. In this section, I

argue that any plausible bias would likely lead to me finding a more positive effect on the

unemployment rate, compared to the true effect. Hence, my result should be taken as an

upper bound on the effect of migration on unemployment, and this bias is not a threat to

the claim that migration lowers the unemployment rate.

24With the additional extreme assumption that inmigrants and outmigrants are all in the labor force, it ispossible to get numbers of approximately the same magnitude as the estimates. Nonetheless, a story alongthese lines would not have the same predictions that I outline in the next several sections.

24

Figure 7: The effect of an inmigration shock equal to one percent of the MSA’s populationon unemployment benefits (left) and earnings (right), with 95 percent confidence intervals.Errors clustered at MSA level. Number of MSAs: 381.

In Section 5, I demonstrate that outmigration does decline in response to positive labor

demand shocks, although the effect is small, suggesting this bias is also likely small. So if

historically people were moving between places that now have positively correlated shocks,

this bias will be in the opposite direction of my results.

In Table 3, I explore whether historically-connected CBSAs are likely to experience similar

shocks on two observable dimensions: distance and industry similarity. In column (1), I run

a regression of log migration on the distance between any two CBSAs.25 In column (2), I

show the same result for MSAs. Another piece of evidence is that they move to MSAs with

similar industries. In columns (3) and (4), I control for a quintic in log-distance, and run

the regression on an industry similary index, using 2-digit SIC codes from 1990. I construct

the vector of employment in each of those industries, and use the following formula:

Industry Similarity =vi · vj||vi||||vj||

where vi is the employment vector in industry i, and || · || is the Euclidean norm. There is

a strongly positive relationship between industry similarity and migration, even conditional

on distance.

In sum, bias is likely to come from the fact that MSAs between which people move have

similar industries and are likely to experience similar shocks. However, this bias is likely

small because outmigration does not respond strongly to labor demand shocks, and it would

25There is definitely some misspecification here because the data is censored below by requiring ten taxreturns. In fact, CBSAs that are further away are much more likely to be censored, suggesting the truerelationship is even stronger than this relationship suggests.

25

Figure 8: The effect of an inmigration shock equal to one percent of the MSA’s populationon the outmigration rate, with 95 percent confidence intervals. Errors clustered at CBSAlevel. Number of CBSAs: 917.

Table 3: Migration Network(1) (2) (3) (4)

VARIABLES Log Migration Log Migration Log Migration Log Migration

Log Distance -1.684*** -1.627***(0.032) (0.037)

Industry Similarity 2.508*** 3.215***(0.267) (0.430)

Observations 57,401 38,086 57,401 38,086Origin and Destination Fixed Effects YES YES YES YESFlexible Distance Controls – – YES YESUnit CBSA MSA CBSA MSA

*** p<.01, ** p<.05, * p<.1Standard errors clustered by from and to MSAs/CBSAs.

go against my results because people tend to move between similar areas.

4 The Housing Channel

In section 2, I argued that a standard model would need an extra ingredient to explain the

decline in the unemployment rate which I found in Section 3. I suggested that housing could

play that role. In this section, I show the empirical evidence in favor of such a view.

Recall the key equation from Section 2, which outlined two channels. One was the

construction channel, which was based on a boom in new houses as the economy adjusted to

higher housing demand. Of key importance was new housing, and the increase in construction

employment. Second was the house price channel, which was based on an increase in house

26

prices that induce higher consumption. I show evidence in favor of each of these channels,

and then show that the unemployment rate’s response to migration is dependent on housing

price elasticities. The robustness of the results throughout this section are presented in

Appendix D.

4.1 Construction Channel

The construction channel requires a build-up of new housing, especially in the short-term.

In Figure 9, I show that housing permits, from the Census, increase significantly in the first

three years after a migration shock.26

The specification for this regression is the same as for unemployment, but using the first-

difference in log house permits on the left-hand side of the equation. The effect is quite large,

a one percent migration shock causes a 20 percent increase in the number of permits per

year. While it might seem extraordinary at first, this increase would be consistent with a 1

percent increase in the housing stock if the depreciation rate were 2.5 percent. For reference,

the IRS allows rental property to be depreciated at about 3.6 percent. Alpanda and Zubairy

(2016) calibrates a depreciation rate closer to 1 percent.

Figure 9: The effect of an inmigration shock equal to one percent of a MSA’s population onhousing permits issued and construction employment, with 95 percent confidence interval.Errors clustered at the MSA level. Number of MSAs: 381.

To study the effect on construction employment, I use the employment categories from

Mian et al. (2013). Their decomposition assigns NAICS 4-digit categories to one of four sec-

tors: construction, non-tradable, tradable, and other. They make up respectively 9 percent,

19 percent, 11 percent, and 61 percent of employment in my data.

26Ideally, I could measure the stock of housing as well, but unfortunately, the local housing stock onlybegan to be measured by the Census in 2010.

27

In the right half of Figure 9, we see an increase in the construction sector. For one

percent inmigration, there is a corresponding increase in construction equal to 0.2 percent of

the population. On average, construction employment is about 3.4 percent of the population,

so this measure is slightly smaller than the effect found on house permits. One potential

reason for this is that Mian et al. (2013) are very broad in their definition of construction,

as they aim to show a null result; that construction was not a major cause of the Great

Recession, and include industries as diverse as logging and real estate agents. Hence, 3.4

percent may be an overestimate of the share of the population working in construction.

4.2 House Price Channel

The other non-standard channel is the house price channel, which posits that house prices

go up and cause increased non-tradable demand.

In Figure 10, I show that house prices do increase, responding by roughly ten percent in

response to one percent inmigration. Housing prices come from the Federal Housing Finance

Agency, and is based on both sales prices and appraisals. Based on the increase in housing

permits, it would suggest a housing supply elasticity of about 2, in line with other estimates

(Saiz, 2010).

Figure 10: The effect of an inmigration shock equal to one percent of a MSA’s populationon house prices, with 95 percent confidence interval. Errors clustered at the MSA level.Number of MSAs: 381.

In Figure 11, I present some evidence that this housing price increase is leading to ad-

ditional consumption. On the left is the rise in second-lien mortgages. Not surprisingly,

there is a large increase in the amount of total mortgage lending, shown for comparison.

But the percentage increase in second-lien mortgages is much higher. Of course, second liens

28

are less than 10 percent of the mortgage market, so the increase is smaller in dollar terms.

Second-lien mortgages are often taken to finance consumer spending, and as such, are good

evidence that people are responding to their increased housing wealth.27

Figure 11: The effect of an inmigration shock equal to one percent of a MSA’s population onmortgage originations(left) and non-tradable employment (right), with 95 percent confidenceinterval. Errors clustered at the MSA level. Number of MSAs: 381.

On the right is the rise in non-tradable employment, which increases by about one-tenth of

a percentage point for four years. In the context of the model, non-tradable employment can

change because of house prices, but also because of differences in demand between migrants

and non-migrants, or a Keynesian multiplier. Given a house price rise of about ten percent,

and assuming a consumption-to-house-price elasticity of 0.2 (Berger et al., 2015), we would

expect non-tradable consumption to rise by 2 percent. The mean non-tradable-employment-

to-population ratio is 7.8 percent in my data, which would predict a 0.15 percentage point

increase in non-tradable employment.

Together these two channels appear to explain most of the response in the employment-

to-population ratio calculated earlier. Given that there are also non-tradable components to

many parts of the “other” category, it may require a decline in the tradable-employment-to-

population ratio, which I will find in Section 4.4.

4.3 Housing Supply Elasticities

Because migration is affecting unemployment through house prices, areas in which house

prices are more responsive might experience bigger effects. To investigate, I split my cities

by above and below the median housing supply elasticity, as measured by Saiz (2010).28

27The majority of second-lien mortgages are home equity lines of credit (HELOCs). See Lee, Mayer, andTracy (2012) for a further discussion of second liens in recent years.

28Saiz (2010) uses the previous vintage of MSAs. I am able to match 253 of them to current MSAs.

29

This allows me to see whether the effects of a migration shock are different in areas where

we might expect house prices to react more.

Figure 12 shows that the effects do differ by housing supply elasticity. On the left, I show

that house prices do increase by more in low elasticity areas, as expected. On the right, I

show that the unemployment rate moves by much more in those same areas. In fact, there

seems to be almost no migration effect on areas with high housing supply elasticities.

The differences between the two lines are significant at the 10 percent level in the second

and third years. In the appendix, I present an alternate specification, which uses a continuous

version of the Saiz elasticity, rather than below or above the median. The interaction term

between the Saiz elasticity and the inmigration is significant at the five percent level in the

first, second, and third years, for both house prices and unemployment.

Figure 12: The effect of an inmigration shock equal to one percent of the MSA’s populationon house prices (left) and unemployment (right), with 95 percent confidence intervals. Errorsclustered at the MSA level. Number of MSAs: 126/127.

In my theoretical framework, a lower housing supply elasticity undoubtedly makes the

house price channel stronger.29 However, for the construction channel, the effect is ambigu-

ous. In Appendix B, a model with log-utility over housing would have a smaller construction

channel in low-elasticity MSAs. But if I augment the one-period model from Section 2.3,

where the intensive margin of housing demand is inelastic, with Cobb-Douglass production

of housing, the construction channel would be larger in low-elasticity MSAs. In the data, I

find very little difference in construction employment for high and low elasticity cities (not

shown).

29Consistent with this, I do find migration’s effect on second lien mortgages is higher in low-elasticityareas.

30

4.4 Other Channels

Besides housing, there are other theories about why inmigration might lead to a decline in

the unemployment rate. In this section, I discuss three: complementarity, agglomeration,

and wealth heterogeneity. Previously, in Section 3.5, I discussed how a selection story, where

migrants have a lower unemployment rate than non-migrants, could lead to a small effect,

but could not explain the bulk of the finding.

One possibility is that migrants and non-migrants are complements, so that having more

migrants lowers the unemployment rate of non-migrants. Indeed, Molloy et al. (2011) show

that migrants are more educated than non-migrants. Furthermore, I show in Appendix C

that the 10th percentile of wages increases, while there is no significant effect on the 25th,

50th, 75th, or 90th percentile. All of this evidence is consistent with a complementarity

story. However, a prediction of the complementarity story is that areas with fewer college

educated workers would benefit more from inmigration, but I find the opposite in the data

(see Appendix C).30 Second, Ottaviano and Peri (2012) considers the effects of complemen-

tarity in the short and long run, and finds immigration to be more beneficial in the long-run

because capital has had time to adjust; the timing of my results is the opposite. And the

10th percentile of wages could also be driven by the fact that many of those workers work in

the food preparation and serving or sales, which would be consistent with a housing story.

Appendix C includes the figures discussed in this paragraph and a lengthier discussion.

A second possibility is that there are agglomeration effects. As migrants move in, knowl-

edge spillovers, the home market effect, thick market externalities, or other increasing returns

forces increase employment. For example, Moretti (2012) suggests ideas exchange could lead

to productivity increases in industry clusters. Other papers mentioned in the introduction

have other stories as well. One problem with this story is that the magnitude of my effects

is much larger than these forces typically explain. Across MSAs in my sample, the biggest

cities have, on average, about 0.3 percentage points lower unemployment than the smallest

MSAs, despite having populations about 50 times as large. Even if this were all agglom-

eration effects, I am finding a decline in the unemployment rate of about 0.5 percentage

points in response to a one percent increase in population, which is at least two orders of

magnitude larger. A second problem is that one might expect tradable goods to be most

affected by agglomeration, or at least equally affected. Rather, I find that tradable goods

decline, as seen in Figure 13. Many agglomeration stories would also imply a larger effect in

the long-run than the short-run, and I find the opposite.

A third possibility is that migrants are significantly wealthier than non-migrants. For

30This assumes that there are not proportionately more college migrants being pushed to places with highcollege shares already, which I do not have data on.

31

Figure 13: The effect of an inmigration shock equal to one percent of a MSA’s populationon tradable goods employment (right), with 95 percent confidence interval. Errors clusteredat the MSA level. Number of MSAs: 381.

example, if a retiree moves to Florida, and spends down his savings, he is adding to labor

demand but not labor supply. In fact, this force is possible in the model from Section 2.

However, from Molloy et al. (2011), the interstate migration rate is highest for ages 18-24 (4.2

percent), second highest for ages 25-44 (3.0 percent), and lowest for ages 65+ (0.9 percent).

Renters also have a higher migration rate (4.7 percent) than homeowners (1.3 percent). This

would suggest that migrants are unlikely to be richer than non-migrants.

To provide further evidence on the relative wealth of migrants, I use the American Com-

munity Survey data, and look at the dividend, interest, and rental income of interstate

migrants versus non-migrants and within-state migrants. The cumulative distribution func-

tion of this income is plotted in Figure 14. The first thing to note from this plot is that

more than 80 percent of people, migrants and non-migrants, do not report interest income.31

However, it does appear that the distribution of interest income for non-migrants does first-

order stochastically dominate the interest income for migrants. Although the ACS does not

measure wealth directly, this is suggestive evidence that non-migrants are wealthier than

migrants.

In conclusion, none of these other channels, complementarity, agglomeration, or wealth

heterogeneity, seems likely to be driving the results that I find in the data. But more

importantly, none of these channels make the prediction that non-tradables and construction

employment would increase while tradable goods employment would fall. Nor would any of

these channels have predictions on whether the effect would be stronger in high housing-

31A very small fraction report negative interest income.

32

Figure 14: The cumulative distribution function of the distribution of interest income, bymigration status. American Community Survey, 2000-2014.

supply elasticity areas. Hence, the evidence that I have shown is strongly supportive of

housing causing the decrease in the unemployment rate.

5 Accelerator

One implication of the result from Section 3 is that there exists a “migration accelerator,”

an amplification of local labor demand shocks due to migration. When an MSA experiences

an increase in labor demand, people move there. Because that migration is expansionary,

labor demand increases by even more.

In this section, I estimate how much migration responds to increases in labor demand,

a similar exercise to Blanchard and Katz (1992). In general, I find this effect to be smaller

and measured with more noise than the regressions from Section 3. Therefore, I exclusively

focus on CBSAs when calculating the accelerator. I then combine that with my estimates

of the expansionary effect of migration in order to calculate the accelerator, but with two

important caveats. First, I interpret my previous results as the effect of an unexpected

inflow of migration. To the extent that migration in response to increases in labor demand

is expected, the effect of the accelerator would be more front-loaded: bigger initially and

smaller in later periods, when compared to the accelerator presented here. Second, I assume

the effect from migrants who move in response to higher labor demand are similar to the

effect of migrants who move in because of a push-factor from other cities. At the end of this

section, I show that migrants induced by either of these shocks are indeed comparable on

two important observable dimensions.

33

5.1 Migration’s Response to Labor Demand

The first step in calculating the accelerator is to estimate the effect that labor demand has on

migration. Again, there is an endogeneity problem of regressing migration on employment

because, as I have shown in this paper, reverse causality is a major concern.

To solve this, I use a Bartik (1991)-style instrument, using the share of industries in

a CBSA and the growth rate of those industries in the rest of America to calculate an

instrument for labor demand. I use a two-digit SIC, before 1998, and three-digit NAICS

codes, after 1998, to construct the instrument in each year. The formula for the instrument

is

zbn,t =∑j

sj,n,t−1gj,−n,t

where sj,n,t−1 is the employment share of industry j in CBSA n in year t − 1, and gj,−n,t

is the growth rate of employment in industry j in the rest of the U.S. besides n in year t.

One endogeneity concern is that nearby CBSAs are likely experiencing similar labor demand

shocks. If the economic conditions of those CBSAs are affecting the decisions of potential

migrants, it could bias the regression. To fix this, I control for the Bartik-instrument in

those other cities. I create this control by weighting cities based on the migration patterns

from the pre-period.

I specify the regression as follows

∆mn,t =4∑

s=−3

βs∆gn,t−s + ζs∆zbc(n),t−s + αt + εn,t

∆gn,t−s =4∑

r=−3

δr,s∆zbn,t−r + ζt,s∆z

bc(n),t−r + γr,s + ηn,r,s

where gn,t is the growth rate of employment in CBSA n, zbn is the Bartik instrument in CBSA

n, and zbc(n) is the average of the Bartik instrument over all MSAs from which people move to

n or to which people move from n. This is a very similar specification to the main regressions

run in this paper. While it might feel unnatural to difference the employment level twice, it

uncovers the parameter that is the effect of a labor demand shock on outmigration.

The timing of this regression is a bit different than the timing of the regressions I ran

in Section 3. Because migration is measured at the time people file their taxes, while em-

ployment is measured quarterly throughout the year, naively running this regression would

show a pre-treatment effect. Therefore, I estimate this equation using the previous year’s

migration. I note this prominently because it matters for calculating the accelerator.

In Table 4, I present the first-stage of the regression. The results are as expected: large

34

and statistically significant on the diagonal. The Sanderson-Windmeijer F-statistics are

large for each first-stage regression. The Kleibergen-Paap F-statistic is perhaps smaller than

prefered, but Stock and Yogo (2005) do not report critical values with this many endogenous

regressors.

Table 4: First-stage: Bartik instruments regressed on labor demand(1) (2) (3) (4) (5) (6) (7) (8)

Employment Employment Employment Employment Employment Employment Employment EmploymentVARIABLES Log-Diff, t+3 Log-Diff, t+2 Log-Diff, t+1 Log-Diff, t Log-Diff, t-1 Log-Diff, t-2 Log-Diff, t-3 Log-Diff, t-4

Instrument, t+3 1.235*** -0.051 -0.093 0.150 -0.011 -0.060 0.170 -0.161(0.248) (0.213) (0.140) (0.114) (0.111) (0.140) (0.115) (0.100)

Instrument, t+2 0.265** 1.089*** -0.109 0.039 0.092 -0.002 0.041 0.064(0.116) (0.178) (0.174) (0.136) (0.115) (0.097) (0.100) (0.114)

Instrument, t+1 0.129 0.169 1.087*** -0.030 0.006 0.085 0.109 -0.105(0.110) (0.107) (0.175) (0.166) (0.129) (0.103) (0.101) (0.098)

Instrument, t -0.034 0.023 0.247** 1.118*** -0.124 0.020 0.252** -0.124(0.132) (0.108) (0.108) (0.187) (0.205) (0.141) (0.111) (0.095)

Instrument, t-1 -0.176 -0.196 0.116 0.312** 0.958*** -0.008 0.096 0.031(0.160) (0.119) (0.105) (0.121) (0.176) (0.158) (0.135) (0.127)

Instrument, t-2 0.111 -0.311* -0.153 0.168 0.474*** 0.647*** 0.204 -0.081(0.094) (0.174) (0.117) (0.126) (0.136) (0.156) (0.135) (0.129)

Instrument, t-3 -0.135 -0.020 -0.380** 0.136 0.200 0.218* 0.797*** 0.066(0.141) (0.116) (0.176) (0.129) (0.122) (0.118) (0.132) (0.133)

Instrument, t-4 0.200 -0.218* -0.053 -0.194 0.236 0.006 0.220 0.694***(0.167) (0.117) (0.174) (0.234) (0.188) (0.158) (0.137) (0.136)

First Differenced YES YES YES YES YES YES YES YESYear FE YES YES YES YES YES YES YES YESSanderson WindmeijerF-stat 42.61 160.95 162.10 114.32 150.98 57.01 76.34 12.30MSAs 917 917 917 917 917 917 917 917

*** p<.01, ** p<.05, * p<.1Standard errors clustered at the MSA level.

Kleibergen-Paap F-statistic: 0.426

The results for both inmigration and outmigration are shown in Figure 15. The effect

on net migration can also be seen as the difference between the two lines. The effect for

outmigration is close to zero, but significantly negative for one period. In contrast, the

effect on inmigration is relatively large, about twice the size, and lasting for three years.

The cumulative effect of a one percent labor demand shock on net inmigration is about 0.2

percent after three years.

This result justifies the focus of this paper on inmigration. Inmigration is the relevant

margin to focus on because it responds more strongly to labor demand.32 The fact that

outmigration responds so little also suggests that the bias for my main regressions which I

discussed in Section 3.6, is likely small.

32Monras (2015) also finds that inmigration is the more reactive margin. He looks at different shocks moreexplicitly related to the Great Recession.

35

Figure 15: The effect on migration of a labor demand shock, with 95 percent confidenceintervals. Standard errors clustered at CBSA level. Number of CBSAs: 917. Anderson-Rubin test for Outmigration: F (8, 916)-statistic: 3.12, p = 0.002; Inmigration, F (8, 916)-statistic: 5.73, p = 0.000

5.2 Accelerator

Recall from Section 2.3 that the accelerator is the additional response of the employment-

population ratio when labor demand shifts, taking into account the equilibrium migration

response. In a simple one period model, the formula is fairly simple, and depends on the slope

of the two lines. Recall that E defines the partial equilibrium response of the employment

rate to migration, and that BK is the opposite response: migration to the employment rate.

Accelerator =slope of E

slope of BK− slope of E

In this section, I extent this to multiple periods.

Define the matrix Dme to be the matrix of responses of the employment rate to migration.

Element ij is det+i

dmt+j. Similarly, the ij element of Dem is dmt+i

det+j.

Proposition 2. The migration accelerator is equal to the top row of

(I − (Dme)(Dem))−1 − I

In Sections 3 and 5.1, I estimated many of these responses. For example, det+i

dmtis the

βi coefficient from a regression similar to Section 3, where on the left side you put the

employment rate. Similarly, dmt+i

detis the βi+1 coefficient from the regression in Section 5.1.

Note the shift in timing because of when in the year migration and employment are measured.

36

Unfortunately, it is much harder to empirically measure other rows of Dme or Dem,

because they are the response of the employment rate to an expected change in the migration

rate, or vice versa. Although nothing about the instruments necessarily requires it to be a

surprise, I interpret my results as the effect of an unanticipated change. Nonetheless, in order

to calculate the accelerator, I make the assumption thatdmt+i+j

det+j= dmt+i

detand

det+i+j

dmt+j= det+i

dmt.

I revisit the likely effects of this assumption in the next section.

Figure 16: The additional effect due to migration of a one log point labor demand shock, with95 percent confidence interval. Standard errors clustered at the CBSA level and calculatedusing the delta method. Number of CBSAs: 917.

I make several small changes to previous regressions in order to calculate the accelerator.

First, I only use the lags, assuming that the leads in the regression are zero. This improves

power, and since the purpose of the leads was to check parallel trends, they are not useful to

calculating the accelerator. Second, I use the first-difference of the log of the employment-

population ratio and the migration rate as my endogenous variables, so that I can use the

Bartik and migration instruments. I estimate the equations jointly because estimating the

cross-correlation in the regressions is necessary to calculate standard errors. I continue to

cluster by CBSA. I then use the above proposition to calculate the accelerator, using the

delta method to calculate the standard errors. The results are shown in Figure 16. Migration

amplifies labor demand shocks by 15 percent contemporaneously, and the effect grows to 20

percent over the next several years.

5.3 Anticipated Changes in Migration or Employment

In the previous section, I made the assumption thatdmt+i+j

det+j= dmt+i

det. This may be a reason-

able assumption because migration and expectations of the local unemployment rate may

37

not be particularly salient to many people.33 In this section, I suggest how with rational

expectations, the accelerator would be shaped slightly differently, implying that 15 percent

may be a lower bound in the short-term.

First, let’s consider how the effects of migration might be different if that migration is

anticipated. Regardless of when the new migrants move in, the economy transitions to a

new steady-state in terms of the housing stock. If it is known in advance, the construction

of new houses will begin before the inmigration because non-migrants will anticipate the rise

in house prices. So there is no change in the total number of additional construction jobs,

only in the time period in which they occur.

In the estimates from Section 4.1, construction employment and new housing permits

increase for three years in response to unanticipated migration. The equilibrium response

to anticipated migration would spread out the construction over the time period before the

migration as well. For example, if the anticipated migration is one year ahead of time, the

construction boom might lead to increasing the number of jobs by about three-fourths over

four years instead of three.

With rational expectations, the house price channel is driven by the unanticipated re-

sponse of house prices. If construction follows the path outlined above, house prices would

likely only rise by about three-fourths of its original amount. Hence, the house price channel

would likely be smaller, but it would also begin in the period in which the migration becomes

known, not when the migration actually happens.

Hence, the total effect of anticipated migration is positive before the migration occurs,

decreasing as the migration is further and further out, and is weaker in the periods after the

migration than it would have been were it a surprise.

The opposite effect is straightforward. Anticipated increases in employment increase the

value of living in a city, and would encourage migrants to move in anticipation of improving

labor markets.

Combined, these arguments imply that if migration and employment responses are antic-

ipated, then the accelerator is likely more front-loaded; bigger in the first period, but smaller

in subsequent years. Hence, the immediate impact which I estimate, of 15 percent, is likely

33One way to write down a model with this flavor is to assume that agents make decisions using onlytwo state variables, the current price of housing and the current employment rate, rather than forecastingthem into the future. Often, more structural papers will make this assumption for tractability, and arguethat it approximates the true policy rule (see Krusell and Smith, 1998; Iacoviello and Pavan, 2013; Kaplan,Mitman, and Violante, 2016a). One drawback is that if you want to consider the counterfactual of a worldwithout migration, as I do here, the response of consumption to the limited set of state variables might bequite different with and without migration. Hence it would be appropriate to think of the accelerator asa comparison between a world with and without migration, but in which agents believe that migration ishappening.

38

a lower bound for the true effect.

5.4 Characteristics of Marginal Migrants

A key assumption for this to be a valid exercise is that the migrants have the same housing

and non-tradable demand whether they come because of the migration shock or because of

the labor demand shock. A more empirical way to think about this assumption is in terms

of treatment effects. I am using the effect of migrants that move because of the migration

shock as an approximation for the effect of migrants that move because of the increased

labor demand. Within the model, the two important statistics for this exercise were the

consumption of non-tradables and housing of these two groups.

The IRS Migration Statistics do not measure consumption of non-tradables or housing,

but does include the adjusted gross income and the number of returns. These two statistics

might be reasonable proxies for housing and non-tradable demand. Certainly, the number of

returns per exemption will be related to family size, and the adjusted gross income is probably

a good proxy for how rich the migrants are, two important determinants of demand.

I only see the totals for county-to-county flows, similar to exemptions. So I can only

estimate the effect on the means of these variables. To find the average income of these

migrants, I run the following regression,

∆AGI migration ratei,t = β∆mi,t + αt + εi,t

where the AGI migration rate is the total income of all migrants into the MSA, normalized by

the MSA’s population. I then instrument for the migration rate using lags of my migration

instrument, or lags of my labor demand instrument. I can do a similar thing for the average

returns-to-exemptions ratio.

The results are presented in Table 5. All the first-stage F-statistics are above ten, though

not surprisingly, the migration instruments do a better job of predicting migration than the

labor demand instruments. The incomes of migrants induced by the two shocks are almost

identical. There does seem to be a small effect on the returns, implying migrants induced by

labor demand shocks have slightly smaller families, which might mean they have less housing

demand. While statistically significant, this effect is economically small, but it does suggest

my accelerator estimates could be overstated.

39

Table 5: Characteristics of Migrants induced by the two different shocks(1) (2) (3) (4)

VARIABLES AGI ($1000s) AGI ($1000s) Returns Returns

Migration 26.00*** 26.91*** 0.494*** 0.525***(2.123) (3.224) (0.0103) (0.0198)

Kleibergen-PaapF-Statistic 64.8 13.7 64.8 13.7CBSAs 917 917 917 917Instruments Migration Labor Demand Migration Labor Demand

Instruments Instruments Instruments InstrumentsStandard errors clustered at CBSA level.

*** p<0.01, ** p<0.05, * p<0.1

6 Conclusion

I document that inmigration shocks have a large positive effect on a local economy, primarily

through a housing channel. Because migration leads to such a large labor demand effect,

migration amplifies the effects of other labor demand shocks. This is counter to the idea

that migration is an equilibrating force.

There are two implications for policy. It may be that policy makers would rather migra-

tion mitigate local shocks, or at least that it did not amplify these shocks. A large part of the

elasticity of housing supply is endogenous to local zoning laws and other housing regulations

(see Gyourko, Saiz, and Summers, 2008; Saiz, 2010). My estimates suggest that increasing

the housing supply elasticity would reduce the effects of migration on the unemployment

rate.

Another policy implication is that currency unions do not benefit from migration in

the way that many suppose. Rather than closing the differences between labor markets,

migration amplifies their differences. This means that the receiving MSA would rather

tighten monetary policy by more than it would absent migration, if it had control over it.

Relative to a world without migration, differences in macro-stabilizing policies are larger.

40

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45

A Proofs

A.1 Proof of Theorem 1

Proof. Without the housing term,

Ntdetdm

= −et(1− ρ)t + cNTm,t(1− ρ)t +∞∑s=0

∫∂cNTi,t∂es

didesdm

where Ntet =∫cNTi,t + Dx. Consumption in any period is increasing in a0 for a given ei.

Because the probability of employment is the same for all agents, migrants and non-migrants,

it must be the case that cNTm,t <1Nt

∫cNTi,t given the assumption that the wealth distribution

of non-migrants dominates that of migrants. Dx must be greater than or equal to zero, so

then it must be the case that

cNTm,t < et

Hence, the sum of the first two terms on the right-hand side are negative.

Consider the T × T matrix AT where AT,ij = − 1Nt

∫ ∂cNTi,t

∂esdi if i 6= j and AT,ii = 1 −

1Nt

∫ ∂cNTi,t

∂esdi. Note that it must be the case that

∑Ts=0

1(1+R)t−s

∂cNTi,t

∂es≤ 1 because of the

budget constraint.

Hence B−1T ATBT is a M-matrix where BT is a diagonal matrix and BT,tt is 1(1+R)t

. This

implies that all the elements of A−1T are weakly positive, because the inverse of M -matrices

have this property (see Berman and Plemmons, 1979).

Now consider AT [(et−cNTm,t)(1−ρ)t]Tt=1. The elements of this vector are all strictly negative

because of the argument above. Therefore, the product is weakly negative. Now consider

the lim infT→∞AT [(et − cNTm,t)(1− ρ)t]Tt=1 which must also be weakly negative.

Furthermore, this must be monotonic in T . To see this, consider CT = IT − B−1T ATBT

which is weakly positive everywhere. So (B−1T ATBT )−1 = limr→∞(CT )r. Because it is weakly

positive, for every i ≤ T and j ≤ T , it must be true that (CT )rij ≤ (CT+1)rij. Hence AT,ij must

also be increasing in T . Hence AT [(et−cNTm,t)(1−ρ)t]Tt=1 is also increasing in T . Therefore the

limit exists, and is equal to detdm

. Because the liminf was negative, detdm

must be negative.

A.2 Proof of Proposition 2

Proof. In the linearized model, the equilibrium must satisfy:[de

dm

]=

[0 Dme

Dem 0

][de

dm

]+

[εe

εm

]

46

The inverse of

[I −Dme

−Dem I

]is (1−DemDme)

−1

[I Dem

Dme I

]. The response of employment-

to-population to labor demand shocks is the row in the top left corner of this matrix, so it

is the first row of (1−DemDme)−1. The accelerator is the difference between this and when

Dem = 0, which is I.

B Simple Model

In this section, I consider a specific version of this model in which the intuitions are more

clear. The linearized version can be solved analytically, it serves as a proof-of-concept that

housing can cause a boom, and it illuminates the role of the housing supply elasticity.

Assumption B.1. Housing production is Cobb-Douglass:

Ht = (1− δ)Ht−1 + A(δL)αDγh,tT

1−α−γt .

Note that α is positively related to the housing supply elasticity because land is avaliable

in fixed supply, while labor and tradable goods have a set price.

Assumption B.2. Suppose utility were log:

U(h, cNT , cT ) = φ log h+ ψ log cNT + (1− φ− ψ) log cT

and that there is no collateral constraint except for the natural borrowing limit.

In this model, agents consume proportionally to their total wealth, including their house,

any asset holdings, and discounted future earnings. In response to a migration shock, the

increase in house prices will have an effect on their wealth, which will increase spending in

constant proportions forever. In Berger et al. (2015), the consumption effects of house prices

changes are equal to the wealth effects when utility is log. That is the case here as well,

although these assumptions imply a low MPC because of the permanent-income nature of

these agents.

Assumption B.3. All agents are identical except for their choice of location. Furthermore,

ρ = 0 and there is no gross migration in steady-state.

This assumption simplifies the analysis by assuming that the new migrants consume

housing and non-tradable goods in the same amount as the original workers. It also simplifies

the expression for the effect on labor supply, because everyone earns the same y.

47

Assumption B.4. The economy is at the deterministic steady-state.

Note that another assumption, required for this to be true, is that β(1 +R) = 1.

With these four assumptions, the effect of a migration shock, dydm

, can be worked out

analytically.

A couple definitions are helpful: Define ht = ht− (1− δ)ht−1 and Ht = Ht− (1− δ)ht−1.Define W = ph0h−1(1− δ) +

∑∞t=0 β

tyt and rht = pht − 11+R

(1− δ)pht+1.

Housing demand is given by:

hsrhs = φ

R

1 +RW

which implies h0ph0 = 1+R

R+δφRW . The change in housing demand is given by

d log hs = −d log rhs + d logW

Log-linearizing r and h, we get the following equations, which characterize the path of

housing construction and rents.

d log rht =1 +R

R + δ

α

1− α

(d log Ht −

1− δ1 +R

d log Ht+1

)(19)

for all t, and

d log Ht = −1

δ

(d log rht − (1− δ)d log rht−1

)+ d logW + dm (20)

for all t > 0. When t = 0,

d log H0 = −1

δd log rh0 +

1

δ(d logW + dm) (21)

The solution to these three equations is algebraic, but messy, so I’ll introduce some

notation:

d log Ht = (AB−t + 1)(1− α)(dm+ d logW )

The solution can be verified to have this form, and A and B are solutions to a messy quadratic

equation. Note that there is an increase in both the steady-state and along the transition

path, as the stock of housing rises to the new steady-state. Note that Cobb-Douglass implies

that the increase in labor demand for housing is simply (AB−t+ 1)(dm+d logW ). Similary,

since cNT = ψ R1+R

W , the increase in labor demand for non-tradable employment is dm +

d logW for all t.

The effect on e can be broken down into three simple terms:

48

d log et =Dh

weAB−t(dm+ d logW )︸ ︷︷ ︸

construction boom

+Dh +Dc

we(dm+ d logW )︸ ︷︷ ︸

increased steady-state demand

− dm︸︷︷︸labor supply increase

where A and B are functions of α, δ, and R that represent the size and duration of the

construction boom, and W is permanent wealth. As you can see, the key determinants of

the sign of d log e are the size of the construction and non-tradable sectors, and the effect of

migration on permanent wealth. The construction boom is temporary in this model, as the

stock of housing converges to its new steady-state. But there is also a steady-state increase

in labor demand which might dominate the increase in labor supply because of the effect on

housing wealth.

The effect of migration on d logW can also be worked out analytically.

d logW =(1− δ)phh

Wα(A+ 1)(dm+ d logW )︸ ︷︷ ︸

house price appreciation

+wDh

W

(A(1 +R)

1 +R−B

)(dm+ d logW )︸ ︷︷ ︸

extra transition income

+1 +R

R

w(Dh +Dc)

W(dm+ d logW )︸ ︷︷ ︸

extra steady-state income

− 1 +R

R

y

Wdm︸ ︷︷ ︸

labor supply increase

Intuitively, there are four forces for how migration effects permanent wealth. The first is the

effect on house prices, the second is the extra construction income from the initial period,

the third is the change in steady-state income, which could be positive or negative, and the

fourth is the negative effect from extra labor supply.

Proposition 3. Under assumptions B.1 to B.4, if δ > 0, there exists a φ∗ such that for all

φ > φ∗, a migration shock causes an increase in the employment rate, d log e0dm

> 0.

Proof. All the terms of the equation above can be rewritten in terms of paramaters.

d logW = (1− δ)1 +R

R + δφRα(A+ 1)(dm+ d logW )︸ ︷︷ ︸

house price appreciation

+ γRδ

R + δφ

(A(1 +R)

1 +R−B

)(dm+ d logW )︸ ︷︷ ︸

extra transition income

+

(ψ + γ

(1 +R)δ

R + δφ

)(dm+ d logW )︸ ︷︷ ︸

extra steady-state income

−(

1− 1 +R

R + δφR

)dm︸ ︷︷ ︸

labor supply increase

As φ grows, the coefficients on the first three terms grow, while the last one shrinks. Hence,

d logW grows without bound.

49

It is also possible to express d log et as a function of parameters which are increasing in

φ. and d logW . Hence, d log et must also grow with φ and also without bound. Therefore,

there exists some cutoff such that for φ > φ∗, d log etdm

is positive.

This proposition simply states that, under these assumptions, if you like housing enough,

then migration will improve the labor market. It is an important proof of concept, that

with housing, it is possible to have an increase in labor market conditions in response to

migration. However, this is not proof that housing is enough to have this increase; that

remains an empirical question.

Proposition 4. Under assumptions B.1 to B.4, if γ = 0, then d log etdm

is decreasing in α.

Proof. In this case Dh = 0, so it suffices to show that d logW is decreasing in α. Specifically

it must be shown that A is decreasing in α. A and B solve the following equations (along

with C):

δA+ C = 1

δA+ C − C

B= δ

C =1 +R

R + δ

α

1− α

(A− 1− δ

1 +RAB

)Consider α∗ > α and let A∗, B∗, and C∗ solve that equation. Suppose A∗ ≥ A. By the

first equation C∗ ≤ C. Subtracting equation 1 from equation 2 implies B∗ ≤ B. But then

the right hand side of the third equation is strictly larger while the left hand side is strictly

smaller. This is a contradiction. Therefore, A∗ < A.

This proposition abstracts from the construction channel to focus purely on the house

price channel. It states that places with less elastic housing supplies (higher α’s) have a

stronger housing price channel.

In this model specifically, the strength of the construction channel is decreasing in α.

The reason for this is because of the log-specification. There are two forces at work: a higher

α implies that each additional housing unit requires more workers because you have to sub-

stitute from land to other inputs. However, a higher α also means that house prices increase

by more, lowering demand for housing. In the log-model, the demand force dominates, but

this would not be true in a model in which housing demand was less elastic.

So while the effect of α on the construction channel is ambiguous, the effect on the house

price channel is unambigously positive. It is an empirical question how much the elasticity

changes.

50

C Investigating Complementarity

Much of the immigration literature focuses on whether migrants are substitutes or com-

plements with native workers, with implications that substitutes’ productivity will decline,

while complements’ productivity increases. In contrast, in section 2, I assume everyone is a

perfect substitute. In this appendix, I investigate whether a complementarity story might

be explaining some of the results.

The first step is to determine how skilled migrants are. A reasonable proxy might be

income, which I plotted in Figure 17. Most people who move over 100 miles make, on average,

700 dollars more per year than those who stay in the same MSA. The 100 miles cutoff is

relevant because that is what I use to construct my instrument. From Molloy et al. (2011),

we also know they also tend to be younger and more educated. Therefore, a complementarity

story would suggest that higher-skilled workers’ labor markets would get worse, while the

lower-skilled workers would benefit.

Figure 17: The correlation between Adjusted Gross Income and distance moved, conditionalon moving counties.

One way to investigate this is to use the occupational employment statistics dataset on

the wage distribution. This data starts in 2001, so does not cover my complete dataset.

It also uses a different definition of MSA for the first few years of data. I run the same

regressions as I do throughout the rest of the paper, but using the 10th, 25th, 50th, 75th,

and 90th percentiles of the hourly wage distribution as my independent variable. I plot the

results in Figure 18.

The migration shock increases the 10th percentile of workers’ hourly wages, consistent

with a complementarity story. However, there is no negative effect on high wage earners.

Perhaps it is only because it does not come through in the noisy data.

Even with the result on the 10th percentile, I do not believe that skill-complementarity

51

Figure 18: The effect of a one percent migration shock on the distribution of wages

is driving my results. Although my theory does not speak directly to this, I should note

that many of the 10th percentile workers work in non-tradable sectors, specifically “food

preparation and serving-related occupations” or “sales and related occupations.” The median

wage in these occupations closely tracks the aggregate 10th percentile wage. So perhaps

the increase in non-tradable demand, rather than skill-complementarity is driving the wage

result.

My results do not depend on the cut-off that I use to construct my instrument. In

general, the further the cutoff, the higher-skilled is the migrant. See Figure 17. So under

a complementarity story, you might expect the further cut-offs to have larger effects. But

there are none.

In addition, the temporary nature of the effects suggests skill-complementarity is not the

main force. It would last for a longer amount of time, whereas the channels I highlight,

especially the construction channel, are much more temporary in nature.

Furthermore, a natural implication of this model is that the benefits would accrue more in

less highly-skilled communities, assuming migrants are roughly the same skill mix. In Figure

19, I show the opposite is the case; MSAs with a higher percentage of college-educated people

(as measured by the ACS in 1990, where I consider anyone with 4 or more years of college to

be college-educated) have a larger effect from migration than those without. This result is

robust to using any years of college education rather than requiring four. One thing to note

is that the college share is negatively correlated to the housing supply elasticity. Controlling

for that reduces the difference between the two lines.

The complementarity story does not have a natural prediction for tradable versus non-

tradable goods, high and low elasticity of housing, and would likely make the opposite

52

Figure 19: The effect of a one percent migration shock on the unemployment rate, split bycollege share. Number of MSAs: 158/158

prediction on timing, such as Ottaviano and Peri (2012).

D Robustness

Figure 20 uses only outflows from the eight counties hit hardest by Katrina: Cameron,

Plaquemines, Jefferson, St. Bernard, and Orleans in Louisiana; and Hancock and Harrison

in Mississippi. I also only use the outflows from 2005. The instrument for inflows to other

cities is based on the 1990-1993 patterns used throughout the rest of the paper. The results

are different in the first period, but then consistent with the rest of the paper. Initially, the

unemployment rate is predicted to rise, but then falls in the next year, and remains low. The

initial rise is inconsistent but not surprising: the displaced migrants might be less prepared

to find work than an average migrant, and so mechanically raise the unemployment rate; or

perhaps 100 miles is not sufficient to rule out direct effects of the hurricane on these other

MSAs.

In Figure 21, I construct the migration network using the 1940 Census rather than the

pre-period of 1990-1993.34 The main downside to this approach is that the Census only

records the state from which you migrated, and not the county. Hence, the instrument for

inmigration becomes a significantly worse predictor. Rather than using a cut-off of 100 miles

or 500 miles, I only use migration flows between other states, or non-contiguous states. If a

MSA spans multiple states, I do not use any of those states (or contiguous ones). The results

34I accessed this data from the Integrated Public Use Microdata Series, (see Ruggles, Genadek, Goeken,Grover, and Sobek, 2015).

53

Figure 20: The effect of an inmigration shock equal to one percent of the MSA’s population,with 95 percent confidence intervals. Errors clustered at the MSA level. Number of MSAs:381.

for the effect on unemployment are largely similar, although using all other states finds no

effect in the contemporaneous period. I suspect this could be due to similar reasons as not

using a cutoff at all finds a smaller contemporaneous effect.

In Figure 22, I show the robustness of the employment composition effects, using similar

controls as from section 3.4. The same general patterns emerge as in the main body of the

paper: sizable increases in construction and non-tradable employment, with a decrease or no

effect on tradable employment. The results are least robust to controlling for the industry

and educational controls, but the point-estimates follow the same general patterns.

Figure 23 shows the robustness of the increase in house prices and permits. The results

are largely the same, with house prices and permits increasing, except for using industry

and education controls, in which case the permits are not statistically different from zero.

Interestingly, using the 500 mile instruments suggests a larger elasticity because permits

increase by more, and prices increase by less.

In Figure 24, I present an alternative specification to investigate the interaction of mi-

gration and house price elasticities. Rather than splitting simply by the median elasticity,

as I do in the paper, I allow the elasticity to have a linear effect. The regression I run is the

54

Figure 21: The effect of an inmigration shock equal to one percent of the MSA’s population,with 95 percent confidence intervals. Errors clustered at the MSA level. Number of MSAs:381.

following:

∆un,t =4∑

s=−3

βs∆mn,t−s +4∑

s=−3

β∗s∆mn,t−s × σn + αt + εn,t

∆mn,t−s =4∑

r=−3

δr,s∆zn,t−r +4∑

s=−3

δ∗r,s∆zn,t−r × σn + γr,s + νn,t,s

∆mn,t−s × σn =4∑

r=−3

δr,s∆zn,t−r +4∑

s=−3

δ∗r,s∆zn,t−r × σn + γr,s + νn,t,s

and I am primarily interested in the β∗’s. I normalize the Saiz elasticities to have standard

deviation one.

In the top row of Figure 24, I show the effect on house prices. On the left is the speci-

fication from the main paper with only the sample of MSAs for which Saiz (2010) reports

elasticities. On the right are the β∗’s from this regression. As you can see, cities with more

elastic housing supplies have significantly less of an increase in housing prices. Each standard

deviation is of approximately similar magnitude to the average effect.

In the bottom row, I show the same thing for the unemployment rate. Here, the more

elastic cities experience less of a decline in the unemployment rate. Similar to the house

price graphic, an increase of one standard deviation is of the same magnitude as the average

effect.

55

Figure 22: The effect of an inmigration shock equal to one percent of the CBSA’s population,with 95 percent confidence intervals. Errors clustered at the CBSA level. Number of CBSAs:911.

Figure 23: The effect of an inmigration shock equal to one percent of the MSA’s population,with 95 percent confidence intervals. Errors clustered at the MSA level. Number of MSAs:381.

56

Figure 24: The effect of an inmigration shock equal to one percent of the MSA’s popula-tion (left) and the interaction of that shock with Saiz (2010) elasticities, with 95 percentconfidence intervals. Errors clustered at the MSA level. Number of MSAs: 381.

57