MAR 3O0 218 February 2018 LIBRARIES @ Gregory Howard, MMXVIII

Essays on the Interactions of Local Economies and their Macroeconomic Implications

by Gregory Howard

B.S. Mathematics, with a second major in Economics, University of North Carolina at Chapel Hill (2010)

Submitted to the Department of Economics in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Economics MASSACHUSETTS INSTITUTE OF TECHNOLOGY at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY MAR 3O0 218 February 2018 LIBRARIES @ Gregory Howard, MMXVIII. All rights reserved. ARCIVE4 The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created.

Author...... C/ Vi Department of Economics -~ A October 14, 2017

Certified by ...... Ivin Werning Professor of Economics Thesis Supervisor Certified by...... Arnaud Costinot Professor of Economics , Thesis Supervisor

Accepted by ...... Ricardo Caballero Ford International Professor of Economics Chairman, Departmental Committee on Graduate Studies 77 Massachusetts Avenue Cambridge, MA 02139 MITLibraries http://Iibraries.mit.edu/ask

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The images contained in this document are of the best quality available. 2 Essays on the Interactions of Local Economies and their Macroeconomic Implications by Gregory Howard

Submitted to the Department of Economics on October 14, 2017, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics

Abstract This thesis consists of three chapters about the spatial aspects of macroeconomics. Chapter 1 argues that local labor demand shocks are amplified by migration. I document that within-U.S. migration causes a large reduction in the unemployment rate of the receiving city, over several years. To establish the causal effect of inmigration, I construct a plausibly exogenous shock by using the outmigration of other places and predicting its destination based on historical patterns. Next, I document that the increase in the demand for housing explains the boom, through two channels. The construction channel occurs because housing is a durable good: hence there is a surge in the number of new houses and construction jobs. The house price channel occurs because the migrants' housing demand drives up prices, leading to increased borrowing and higher non-tradable labor demand. Last, I estimate that these effects imply that endogenous migration amplifies other shocks by 20 percent. Chapter 2, which is joint with Jack Liebersohn, estimates that between 20 and 40 percent of the overall rise in real house prices during the 2000-2006 U.S. housing boom can be attributed to an increase in the relative desirability of inelastic-housing-supply areas. First, we show local housing demand is significantly driven by population changes and changing relative desirability. We develop a theory for why an increase in the relative desirability of inelastic areas would raise house prices nationally. Finally, we quantify the total effect by creating a new measure of housing supply elasticity that covers the entire United States. We show that the decline in manufacturing and the fall in interest rates both played an important role through this geography channel. Chapter 3 documents that shifts in the geographic distribution of economic activity are more frequent around recessions. This effect is more pronounced in professions with greater nominal wage rigidity. As a possible explanation, I develop a new mechanism for equilibrium switching during recessions in a model of agglomeration using downwardly sticky wages. In a dynamic setting, the model requires a sufficiently large shock to switch equilibria. Within the model, place-specific time-specific firm subsidies can be welfare enhancing.

Thesis Supervisor: Ivdn Werning Title: Professor of Economics

Thesis Supervisor: Arnaud Costinot Title: Professor of Economics

3 4 Acknowledgments

This thesis would not have been written without the guidance and help of so many. First, I would like to thank my advisors Ivan Werning, Arnaud Costinot, and David Autor. Each of these professors put in so many hours into helping me become a better researcher. I learned a lot by following their example, and I also learned a lot from them telling me how I needed to improve. With Ivhn, I have fond memories of outdoor reading groups, enjoying the Boston summer weather. I remember, less fondly, weekends in the office as he helped refine some of my ideas. And I am especially grateful that he took it upon himself to read up on an entire literature when my thesis turned from primarily theoretical to entirely empirical. Moving from Cambridge, I will also miss getting to play tennis with him. With Arnaud, I am grateful for the trade tea, his diligent reading of my work, and his willingness to help. He always was able to show me how to clearly think about things that befuddled me. With David, I am grateful for him taking me on as a student late in my graduate career, as I realized my interests were more empirical. He was excellent at making my writing more pithy and clear. And he had many good suggestions that came from a different perspective. In addition to these three, I am thankful to the entire MIT faculty for all their help and guidance over the last five years. MIT Economics is a special department, and every faculty member with whom I interacted contributed to that culture. I am especially grateful to Alp Simsek, David Atkin, Frank Schilbach, and Daron Acemoglu. I would like to thank my classmates. I benefited tremendously from being able to chat with them about my work, and I have formed some life-long friendships because of it. In particular, I'd like to acknowledge Matt Lowe, Arianna Ornaghi, Ludwig Straub, Vivek Bhattacharya, Sebastian Fanelli, Jack Liebersohn, Yu Shi, Ernest Liu, Ben Roth, Dan Green, Ben Yost, Matt Rognlie, Adrien Auclert, Rodrigo Adao, Dejanir Silva, Rachael Meager, Nick Hagerty, Peter Hull, Elizabeth Setren, Donghee Jo, Yuhei Miyauchi, John Firth, Tite Yokossi, and Scott Nelson. Of course, I also owe a great debt to those that helped me along the way, even before I came to MIT. So I would also like to thank my mentors over the years: Tarhan Feyzioglu at the IMF, Lisa Ryu at the FDIC, Sue Goodman in the math department at UNC, Richard Froyen in the economics department at UNC, Beth Anne Wilson at the Fed, Rob Martin at the Fed, and many others along the way. I would not be who I am today without these men and women. Of all the things I am thankful to my parents for, my academic success is only a fraction. But I certainly am thankful for the values and habits that they passed down to me. Even if she insists it was not intentional, my mom got me interested in economics from a young age. I admire her for her work, and if I ever need motivation for doing economics, I can remember how her expertise benefited the country and the world during some very scary times. I would also like to thank my sister Kim for her encouragement and for always being there for me. A few friends in particular helped me stay sane during graduate school, through hiking, playing tennis, watching UNC basketball or Downton Abbey, traveling, praying, and just living life in community. Thank you to Michael and Shannon Poor, Andy and Emily Stuntz, Eric Esch, Dan and Ellie Chamberlain-Stoltzfus, Jahan Mohiuddin, Dan Reich, Annelise Mesler, Chris and Laura Martin, Frederick Wagner, Laura Doherty, Bethany Wagner, Eric Toler and Lauren Teegarden, Wilson and Anna Boardman, Anna Wargula, Leif and Katie Jentoft, Ryan and Abigail Zhang, Zac and Joanna Brooks, Rosemary Boyle, Rick Downs, and Nathan Barczi. I am also blessed to have a wonderful woman in my life, who I am excited to be marrying soon. Thank you, Heather, for your support and love.

5 6 Contents

1 The Migration Accelerator: Labor Mobility, Housing, and Aggregate Demand 17 1.1 Introduction ...... 18 1.2 Framework ...... 20 1.2.1 H ousing ...... 21 1.3 Empirics I: The Expansionary Effect of Migration ...... 23 1.3.1 D ata ...... 23 1.3.2 Identifying Inmigration Shocks ...... 25 1.3.3 Econometric Specification ...... 27 1.3.4 The Effect on Unemployment ...... 28 1.3.5 Threats to Identification ...... 32 1.4 Empirics II: The Housing Channels ...... 34 1.4.1 Construction Channel ...... 34 1.4.2 House Price Channel ...... 35 1.4.3 Cross-Sectional Heterogeneity ...... 36 1.4.4 The Housing Channels during the Mariel Boatlift ...... 39 1.4.5 Other Channels ...... 41 1.5 Counterfactual: The Migration Accelerator ...... 43 1.5.1 Migration's Response to Labor Demand ...... 44 1.5.2 Accelerator ...... 45 1.6 Conclusion ...... 48

2 The Geography Channel of House Price Appreciation: Did the Decline in Man- ufacturing Cause the Housing Boom? 49 2.1 Introduction ...... 50 2.2 The Cross-Section of Local Housing Demand ...... 52 2.2.1 Population Growth and Housing Prices .... . 52 2.2.2 Rents and Prices ...... 53 2.2.3 Housing Demand or Loan Supply? ...... 56 2.3 Theory: The Geography Channel ...... 57 2.3.1 Setup ...... 58 2.3.2 The Role of Manufacturing ...... 60

7 2.3.3 The Role of Interest Rates ...... 60 2.4 The Magnitude of the Geography Channel ...... 61 2.4.1 Constructing a measure of elasticity ...... 61 2.4.2 The Geography Channel ...... 63 2.5 The Timing of the Housing Boom ...... 66 2.6 C onclusion ...... 67

3 Regional Depressions: Sticky Wages in a Model of Agglomeration 69 3.1 Introduction ...... 69 3.2 Motivating facts ...... 71 3.2.1 Economic activity changes over time . . . 71 3.2.2 Activity changes more during recessions. . 72 3.2.3 Relationship to sticky wages ...... 74 3.3 A simple model ...... 74 3.3.1 Setup ...... 75 3.3.2 Flexible-price equilibria ...... 76 3.3.3 Stability of equilibria ...... 77 3.3.4 Sticky wages ...... 78 3.4 A dynamic model ...... 81 3.4.1 A "race" between firm mobility and wage adjustment 84 3.5 Welfare and policy ...... 85 3.6 Conclusion ...... 86

A Appendix to Chapter 1 87 A .1 D ata ...... 87 A.2 Proof of Proposition 1.1 ...... 88 A.3 Investigating Complementarity ...... 88 A.4 Similarities between high-migration city pairs . . 90 A.5 Robustness ...... 92

B Appendix to Chapter 2 97 B.1 Proofs ...... 9 7 B.1.1 Proof of Lemma 2.1 ...... 9 7 B.1.2 Proof of Lemma 2.2 ...... 9 7 B.1.3 Proof of Proposition 2.1 ...... 9 8 B.1.4 Proof of Proposition 2.2 ...... 9 8 ...... 99 B.2 Calibration ...... B .2.1 e ...... 9 9

8 C Appendix to Chapter 3 101 C.1 Algorithm for Identifying Trend Reversals ...... 101 C .2 P roofs ...... 101 C.2.1 Proof of Proposition 3.1 ...... 101 C.2.2 Proof of Proposition 3.2 ...... 102 C.2.3 Proof of Proposition 3.3 ...... 103 C.2.4 Proof of Lemma 3.1 ...... 103 C.2.5 Proof of Lemma 3.2 ...... 103 C.2.6 Proof of Proposition 3.4 ...... 104

9 10 List of Figures

1-1 The migration response to the inmigration shock, with 95 percent confidence intervals. Standard errors clustered by state...... 28

1-2 The effect of an inmigration shock causing an increase of one percent of the MSA's population, with 95 percent confidence intervals. Errors clustered by state. Number of M SA s: 381...... 29

1-3 The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381. 30

1-4 The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381. 31

1-5 The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381...... 32

1-6 The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381. Number of CBSAs: 917...... 33 1-7 The effect of an inmigration shock equal to one percent of the MSA's population on unemployment benefits (left) and the raw CPS unemployment data (right), with 95 percent confidence intervals. Errors clustered at MSA level. Number of MSAs: 381, 242...... 34

1-8 The effect of an inmigration shock equal to one percent of an MSA's population on housing permits issued and construction employment, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 310, 381...... 35

1-9 The effect of an inmigration shock equal to one percent of an MSA's population on house prices, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381...... 36

1-10 The effect of an inmigration shock equal to one percent of an MSA's population on mortgage originations(left) and non-tradable employment (right), with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381...... 37

11 1-11 The effect of an inmigration shock equal to one percent of the MSA's population on house prices (left) and unemployment (right) interacted with Saiz (2010) housing supply elasticity, with 95 percent confidence intervals. Errors clustered by state. Number of M SAs: 253...... 38 1-12 The effect of an inmigration shock equal to one percent of the MSA's population on house prices (left) and unemployment (right) interacted with high January temperatures, with 95 percent confidence intervals. Errors clustered by state. Number of M SA s: 381...... 38 1-13 Log House Prices (top left), Construction Employment (top right), Retail Employ- ment (lower left), and Manufacturing (lower right). Index, 1979=0...... 40 1-14 The effect of an inmigration shock equal to one percent of an MSA's population on tradable goods employment (right), with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381...... 42 1-15 The cumulative distribution function of the distribution of interest income, by migration status. American Community Survey, 2000-2014...... 43 1-16 The effect on migration of a labor demand shock, with 95 percent confidence intervals. Standard errors clustered by state. Number of MSAs: 381...... 45 1-17 The response of unemployment to a Bartik shock, and the portion that is due to migration, along with 95 percent confidence intervals. Standard errors clustered by state...... 46

2-1 House Prices in the Midwest and the Rest of the U.S...... 51 2-2 Population Growth and Housing Units ...... 53 2-3 Population Growth and Housing Prices ...... 54 2-4 Housing Demand and Manufacturing Share ...... 54 2-5 Houses per capita and manufacturing, elasticity ...... 55 2-6 Building Quality and House Price Area, Lot Area ...... 55 2-7 Multifamily NOI and House Price Growth ...... 56 2-8 Repeat Rent Index (RRI) and House Price Growth ...... 57 2-9 Map of Estimated Elasticities ...... 62 2-10 Comparison of estimated elasticities with Saiz (2010) ...... 63 2-11 Estimated Elasticity and Manufacturing Share by CZ ...... 64 2-12 Inverse Rent versus Elasticity ...... 65 2-13 The year-by-year regression coefficient of house price, rent, and population growth on elasticity (left) and the regression coefficient of house price growth on manufacturing (rig ht) ...... 67

3-1 State shares of total U.S. GDP ...... 71 3-2 Standard Deviation of Growth across U.S. States ...... 72 3-3 Reversals in Trend of Share of GDP by State: Moving average ...... 73

12 3-4 Sticky Wages and Cyclicality of Geographic Reallocation ...... 75 3-5 fib and A ...... 78 3-6 il' and A when wages are downwardly rigid and g > -y - 1...... 79 3-7 'iv and Awhen wages are downwardly rigid and g < y - 1...... 80 3-8 'f and A when wages are downwardly rigid and g = 7 - 1...... 82 3-9 Equilibria in the Dynamic case...... 83

A-1 The correlation between Adjusted Gross Income and distance moved, conditional on m oving counties...... 89 A-2 The effect of a one percent migration shock on the distribution of wages. MSAs: 337. 90 A-3 The effect of a one percent migration shock on the unemployment rate, split by college share. Number of MSAs: 158/158 ...... 91 A-4 The effect of outmigration from Katrina hit areas in 2005, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381...... 93 A-5 The effect of inmigration shocks using the 1940 network, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381...... 94 A-6 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...... 95 A-7 The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381...... 96

B-1 Land Shares and House Prices ...... 99

C-1 Trend Reversals: blue dots are reversals down, red dots are reversals up ...... 102

13 14 List of Tables

1.1 Sum mary statistics ...... 25 1.2 Characteristics of Migrants induced by the two different shocks ...... 47

2.1 Loan Demand and Manufacturing ...... 58

A .1 M igration Network ...... 91

15 16 Chapter 1

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

Because people choose to move to relatively prosperous regions, economists have traditionally believed that migration mitigates the effects of local shocks. In the first part of this paper, I document that the opposite holds in the data: within-U.S. migration causes a large reduction in the unemployment rate of the receiving city, over several years. To establish the causal effect of inmigration, I construct a plausibly exogenous shock by using the outmigration of other places and predicting its destination based on historical patterns. In the second part of the paper, I document that the increase in the demand for housing explains the boom, through two channels. The construction channel occurs because housing is a durable good: hence there is a surge in the number of new houses and construction jobs. The house price channel occurs because the migrants' housing demand drives up prices, leading to increased borrowing and higher labor demand in non- tradable sectors. Together, these channels account for the size of the labor demand boom. This boom implies that the endogenous response of migration amplifies local labor demand shocks, an effect I label the "migration accelerator." In the final part of the paper, I estimate that migration amplifies these shocks by 20 percent. 1

I1 would like to thank my advisors, Ivin Werning, Arnaud Costinot, and David Autor for their guidance. I would like to thank Andrea Raffo for a comment that inspired the title. I would also like 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, Vivek Bhattacharya, Alex Bartik, and seminar and lunch participants at MIT, the Federal Reserve Board of Governors, the Federal Reserve Bank of Chicago, and the Federal Reserve Bank of Minneapolis. This material is based upon work supported by the National Science 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 necessarily reflect the views of the National Science Foundation.

17 1.1 Introduction

Typical models suggest that domestic migration mitigates demand shocks in local labor markets (e.g. Blanchard and Katz, 1992). This result forms the basis for the criteria of high labor mobility in optimal currency areas (Mundell, 1961). However, many of these models abstract from salient features of the housing market, which, in theory, have the potential to overturn the result. In this paper, I empirically show that because of these housing features, labor mobility amplifies the impact of local labor demand changes. There are two relevant empirical question. One is whether labor moves to booming markets. Many studies, most famously Blanchard and Katz (1992), answer this question affirmatively. But also central is the causal effect domestic migration has on the local labor market. Using an instrument similar to the push-share instrument from the international migration literature (Altonji and Card, 1991), I estimate that domestic inmigration to a U.S. city lowers the local unemployment rate substantially and for several years. 2 In total, a one percent increase in the population due to inmigration has a cumulative effect of -1.3 percentage-point-years on the unemployment rate. In a framework of heterogeneous agents and housing, I show there are two housing channels that play a role in migration's effect on unemployment. The first is a construction channel, which occurs because housing is a durable good and is produced using local labor. Hence, in the short-run, housing investment and construction employment respond more than proportionally to an increase in population. The second is a house price channel, which occurs because consumption responds to house price changes, a well-documented effect. 3 A back-of-the-envelope calibration suggests these two channels are large. In a sense, this sets up the empirics as a test of the applicability of these models to a question they were not originally designed to answer. Indeed, I find that the result on the unemployment rate is driven substantially by these two channels, providing confirmation to the predictions of the model. Specifically, I use the same instrument and show that its impact on house prices, housing construction, construction employment, mortgages, and non-tradable employment are consistent with predictions from the model. I also test two dimensions of cross-city heterogeneity: the effect is stronger in cities with inelastic housing supplies and in growing cities. 4 Finally, I show suggestive evidence that these housing channels

2I focus on inmigration for two reasons. First, I show the majority of the net migration response to labor demand shocks, as constructed in Bartik (1991), is through inmigration, not outmigration. This is consistent with Monras (2015a), which uses different shocks and data, and Coen-Pirani (2010), which notes that inmigration is much more volatile than outmigration. In a different setting, Long and Siu (2016) find that during the Dust Bowl era, the fall in net migration was also due to inmigration and not outmigration. So to better understand how migration changes the effects of these shocks, it is of primary interest to understand the effects of inmigration. 3 For example, Mian, Rao, and Sufi (2013), Campbell and Cocco (2007), Attanasio, Leicester, and Wakefield (2011), Agarwal, Amromin, Chomsisengphet, Piskorski, Seru, and Yao (2015), Str6bel and Vavra (2015), and Kaplan, Mitman, and Violante (2016). Berger, Guerrieri, Lorenzoni, and Vavra (2015) summarize the literature and suggest the average estimated elasticity is about 0.2. 4 Other theories could explain my main result( that the unemployment rate falls after an inmigration shock), including factor complementarity, increasing returns to scale, and love for variety. While they can explain the sign, they cannot explain the timing, magnitude, sectoral composition, and relation to housing supply elasticity. In contrast, the housing channels easily explain my headline results and each of these facts. I expand on this in Section 1.4.5.

18 were operative during the Mariel boatlift, the most famous of the natural experiments regarding the effects of migration. 5 In the final part of the paper, I quantify the economic impact of the previous results through a counterfactual exercise. I calculate the difference between the effect of a labor demand shock when migration endogenously responds and the counterfactual where migration is held constant. I label the difference the migration accelerator. I find that migration amplifies the effect on the unemployment rate by 20 percent locally. My empirical strategy and question are close to a literature on estimating the labor market effects of internationalmigration, but with several important differences in setting and methodology, and starkly different results. In particular, I use a similar empirical strategy to Altonji and Card (1991), Card (2001), Lewis (2005), Saiz (2007) and Hong and McLaren (2015), which combine the location of immigrant communities and immigrants coming from that country to construct an instrument. The literature, using this and other methodologies, has found a range of effects of international migration on labor market outcomes, typically wages, ranging from a modest positive effect (Ottaviano and Peri, 2006; Card, 2009) to a large negative effect from immigration (Borjas, 2003; Monras, 2015b). 6 Even different studies of the Mariel boatlift have divergent results. Card (1990) concluded that wages of comparable workers in Miami were largely unaffected, while Borjas (2015) found that they dropped dramatically. Other methodologies have also produced a range of results, as summarized by Dustmann, Sch6nberg, and Stuhler (2016). My results lie outside of the range of previous findings, documenting a substantial improvement in the local labor market in response to an increase in domestic inmigration. Another strand of the immigration literature looks specifically at housing, but primarily because a rise in housing costs is evidence that immigrants do not completely displace natives, and because changes in house prices are a transfer of wealth from immigrants to natives. Saiz (2003, 2007), Gonzalez and Ortega (2013), Greulich, Quigley, and Raphael (2004) and Ottaviano and Peri (2006) find positive effects of immigration on housing costs. 7 I find larger effects on house prices, and I focus on how rising house prices are a part of a housing-led demand boom. Many papers since Blanchard and Katz (1992) have looked at population adjustments in re-

5 Saiz (2003) investigates the effects of the Mariel boatlift on the housing market, finding a large increase in rental prices. However, he does not find an increase in house prices, in contrast to my findings. A key difference is that he looks at house price changes beginning in 1980Q3, after the boatlift, whereas I use a baseline of 1979. Lewis (2004) looks at changes in industry mix after the Mariel boatlift as well, but focuses exclusively on tradable goods. His hypothesis is that the composition of tradable goods changes according to the Rybczynski (1955) theorem. Hanson and Slaughter (2002) and Lewis (2005) also find evidence of industry composition effects within tradable goods, in other settings. These papers do not focus on the role of non-tradables or construction, the key industries driving my results. 6 Hong and McLaren (2015) report a sizable increase in the employment of cities that receive immigrants, finding that each immigrant creates 1.2 jobs in the receiving city. They also find a sizable increase in the number of natives in the labor force. For native workers, the number of jobs increases by 0.86, while the native labor force increases by 0.97, per migrant. If the native unemployment rate were below 10 percent initially, this would imply migration raised the unemployment rate. In 1990 and 2000, the unemployment rate in the U.S. averaged 5.6 and 4.7 percent. 7 Saiz finds positive effects on rents in both studies. Saiz (2003) finds a negative effect on house prices, while Saiz (2007) finds a positive effect. He suggests these opposite results are because natives prefer not to live near immigrants. The other listed papers find a positive effect.

19 sponse 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, 2015a). Charles, Hurst, and Notowidigdo (2017) find that the working-age population in MSAs with housing booms increased while MSAs with manufacturing declines experienced population decreases. All of these papers find evidence that labor mobility responds to the conditions of local labor markets. My results contribute to this literature by providing an explanation for why high rates of labor mobility do not close the gaps in labor market outcomes across space, similar to Amior and Manning (2016). There is also a large literature on how house prices change migration decisions (see Van Nieuwer- burgh and Weill, 2010; Notowidigdo, 2013; Davis, Fisher, and Veracierto, 2013; Head, Lloyd-Ellis, and Sun, 2014; Nenov, 2015). Several papers, including Struyven (2014) and Schulhofer-Wohl (2011), focus on housing lock, the idea that underwater mortgages 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. The rest of my paper is organized as follows. Section 1.2 presents a framework for understanding why a model with housing could allow for inmigration to be expansionary. Section 1.3 outlines my empirical strategy and shows that inmigration has an expansionary effect on local labor markets in the United States. Section 1.4 presents the evidence in favor of the construction and house price channels. Section 1.5 quantifies the size of the migration accelerator.

1.2 Framework

In this section, I present a model of a city. Capital letters are used for aggregate variables in the city, 8 and lower-case letters are used for individual agents, indexed by i. Time runs from t G {0, ... , T}. A subscript t denotes the variable in that time period, and a super-script denotes the entire sequence. Normalize the initial population, N, to unity. My framework is based on an Bewley (1986)-Huggett (1993)-Aiyagari (1994) model in which agents face idiosyncratic risk and borrowing constraints. They are limited to investing in a riskless bond at interest rate R. I assume the aggregate shocks can be linearized, so that agents base their consumption decisions on individual state variables and expectations of future aggregate variables.

Ct = JOEj[ct (aijt, W', Ut, Rt) ]di where Ct is aggregate consumption from period t onward, ct is individual consumption, which is a function of ai,t, their own assets at time t; Wt, the expectations of future wages; R', the expectation of future interest rates; and Ut, the expectations of future unemployment. 9 Assume E[cfl is weakly increasing in ai,t and decreasing in each element of Ut.

8 The finiteness of time plays no substantive role, but does simplify notation. 9 1n most search-and-matching models, agents care about labor market tightness, but this has a one-to-one relationship with unemployment.

20 Phillips Curve and Monetary Policy. Because it relates more directly to my empirical results, assume a Phillips curve that is flat, i.e. Wt = W. Also assume that monetary policy is unresponsive Rt = R because the city is part of a currency union. For simplicity, I will drop W and R from future notation. Labor Demand (without housing). Assume agents consume both tradable and non-tradable goods. Assume non-tradables are competitively produced with local labor and linear technology. If consumption is homogeneous over these two things, and wages and non-tradable prices are fixed, the relation becomes aCt + Dt = 1 - Ut where a is the share of non-tradables in consumption and D' is the exogenous demand for tradables. C is denoted in units of labor required to produce it. No-Housing Equilibrium. A no-housing equilibrium is a set of Ut, C' and c such that each c (ai,t, Ut) is a maximization of the agents' problem, C aggregates the c$'s, and Ut satisfies the labor demand equation.

Theorem 1.1. Consider a no-housing equilibrium. An increase in the number of agents N, if the new agents have wealth that is first-order stochastically dominated by existing agents, causes the unemployment rate to weakly increase in all future periods.

As I show in Section 1.4.5, during this time period, migrants' wealth is indeed first-order stochastically dominated by non-migrants, satisfying the additional assumption. The intuition behind this proposition is simple. Labor supply increases more than labor demand because people spend money on tradables outside the city. The assumption rules out the possibility that people are moving in and then spending down their wealth. The following equation summarizes the change: &Ct I + a 0, dUt = -ac' dN + (1 - Ut)dN where act is a matrix with the elements corresponding to L. That term is a Keynesian multiplier, multiplying the change in unemployment. The right-hand side is the effect migration has on labor demand and labor supply. The proof consists of showing that agents do not consume more than their income and that the Keynesian multiplier will not reverse the sign.

1.2.1 Housing

In Section 3, the data will sharply reject this proposition. One way to resolve this puzzle is by introducing housing to the model. This requires several additions to the baseline model, similar to the recent literature including Favilukis, Ludvigson, and Van Nieuwerburgh (2017), Berger, Guerrieri, Lorenzoni, and Vavra (2015), and Kaplan, Mitman, and Violante (2016). First, housing will be a state-variable for agents, and they will base consumption on current and future housing prices. N Ct Ei [ct (ai,t, hi,t , P', Ut }|di 0h

21 Second, housing is produced with local labor, and there must be enough to match housing demand.

Ht = (1 - 6)Ht-1 + H(Lh,t)

Ht = jiEi[ht(ai,t,hi,t, Ph, Ut)]di where H is concave. Third, assume housing production is competitive and that house prices are equal to construction costs.10

Ph,t = WH/(Lh,t)~1

Last, the labor demand equation now includes construction:

aCt+Dt +Lt 1 = 1-Ut

Housing Equilibrium. A housing equilibrium is a set of Ut, Ct, P , H', Lh and c , h such that households maximize, markets clear, and house prices are given by the marginal cost. Now the effect of immigration can be broken down into four terms:

I + a a dUt -actdN + (1 - Ut)dN - a MPCH dP' - H' dH Non-tradable Demand Labor Supply House Price Channel Construction Channel where MPCH, the marginal propensity to consume out of housing, is a T x T matrix in which the given by d . sr elementSr of MPCH is dPh,, In this equation, the first two terms are the same as from the no-housing equilibrium. But there are two additional terms that can overturn Proposition 1.1. The first is that the path of consumption may change in response to house prices. If the marginal propensity to consume from housing is positive, then a house price increase will lower the unemployment rate. Secondly, increased construction will employ workers, lowering the unemployment rate. The construction term is conceptually different than the labor demand term because housing is a durable good. Hence, housing investment increases more than proportionally.'1 If each agent's housing demand is inelastic (ht = 1), then this can be written simply:

act dU' 16* Pt I + a =-lact + (1 -Ut) - aMPCH _Pt - * h (1.1) alUt )dN "M 0- j W where a is the housing supply elasticity and 6* is a diagonal matrix with the first element equal to

1 0 Because housing is produced with decreasing returns to scale, assume any profits are given to absentee landown- ers.To the extent that this is a bad assumption, it would be an additional channel through which increases in housing production could lead to greater local labor demand. "The logic is similar to Baxter and King (1993), in which changes in permanent government spending have a big effect on investment. Similarly, Rognlie, Shleifer, and Simsek (2017) argue that an abundance of housing was a partial cause of the Great Recession. Kochin (1996) also makes this point in a variety of settings, including the cow market of 1630's New England.

22 1, and other elements on the diagonal equal to 6. There are two important things that come out of this equation. First is the role of (*, which highlights that the role of housing is much larger in the short-term. This is because housing is a durable good. Second, this equation provides a prediction about the role of u-: the house price channel should be stronger in areas with less elastic housing supply. There is reason to think that these house price forces should be large in the short-term, based on estimates from the literature. Moretti (2010) would suggest a large local multiplier: that a > . Many estimates of o- are around 2 (Poterba, 1984; Topel and Rosen, 1988). A "normal" house price to annual income ratio for the United States is 3.5 (Becketti, Yannopoulous, and Lacy, 2016), though it was above 4 during parts of this time period. ( for housing is quite small; the IRS accounting for rental property, ( = 0.036, is typically thought to be an overestimate for owner- occupied housing. Berger, Guerrieri, Lorenzoni, and Vavra (2015) summarizes the literature on consumption response to house prices, and suggest an elasticity (MPCH E")) of 0.2. Based on these numbers, either the house price channel or the construction channel ought to overwhelm the labor supply increase, leading to a decline in the unemployment rate in the first period.' 2 This model predicts that, in the short-run, inmigration causes an increase in house prices, housing construction, and employment in the construction and non-tradable sectors. I will show later that these things are true empirically. Furthermore, based on a rough calibration, these effects should be strong enough to overwhelm the increase in labor supply, leading to a short-run decline in the unemployment rate. This is a testable implication. Equation 1.1 also implies that the results should depend on housing supply elasticity, setting up another empirical test for the model.

1.3 Empirics I: The Expansionary Effect of Migration

In this section, I test the causal effects of inmigration on unemployment. I use previous migration patters and concurrent outmigration to construct a plausibly exogenous shock of inmigration. I find that inmigration causes unemployment to fall, rejecting Proposition 1.1 and confirming the prediction of the model with housing.

1.3.1 Data

I 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

12 In theory, agents could intertemporally substitute and mute these effects, a channel that would come through the left-hand side multiplier. However, these channels are very large and as documented by Kaplan, Violante, and Weidner (2014), many agents are constrained from doing this substitution.

23 dataset because it allows me to create a network of migration, which I use to construct the shock.' 3 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. In estimating the effect of migration, I aggregate to metropolitan statistical areas (MSAs) using the Missouri Census Data Center aggregation tables. I will note when I also use micropolitan statistical areas, which together with MSAs, are referred 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 Unemployment 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.14 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, Rao, and Sufi (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 1.1 as well as data coverage. There are more details in Appendix A.1.

1 3 There are a few drawbacks to this data. First of all, the address used to determine migration is the address from which the tax return is filed, meaning that the date of migration could be anytime before filing taxes. While much of the migration likely occurred in the previous calendar year, some will have occurred in the first few months of the next year. In 2015, 132 million returns were filed by May 28, out of 148 million filed by November 24, over 85 percent. Marlay and Mateyka (2011) report large seasonality of moves, with summer being the most common season to move during, even more so for people that cross state or county lines. Furthermore, the timing of filing taxes might be endogenous to moving, so the ratio of inmigration to non-migrants might be slightly mismeasured. Finally, the sample before 2011 does not include any people who filed after September. These people tend to be richer and have more complex taxes, and they are being missed from the data. So potentially, migrants are under-counted compared to non-migrants, and it might especially be true for rich migrants. Another potential issue is that the data is censored below, and only records data if there are more than 10 returns. Finally, the data covers only people who file taxes and their dependents. The elderly and the jobless are certainly under-counted. Despite all these drawbacks, the data is still very useful in determining patterns of migration, and any of these measurement errors are likely to be small compared to other available datasets. 4 1 Some of the estimate is imputed from demographically-adjusted state-wide estimates, which could imply mis- leading within-state correlations. However, the primary building blocks are establishment employment counts 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.

24 Table 1.1: Summary statistics

Variable Mean Std. Dev. Years N Unemployment Rate (Percent) 6.2 2.9 1990-2013 381 Employment (1000s) 299 700 1990-2013 381 Population (1000s) 628 1479 1990-2013 381 Inmigration Rate (Percent) 3.4 1.6 1990-2013 381 Outmigration Rate (Percent) 3.2 1.4 1990-2013 381 House Permits Issued per 1000 people 6.4 11.1 1995-2013 310* House Price Growth (Percent) 2.9 5.6 1991-2013 381* All Mortgage Originations per Capita ($s) 4.0 3.8 1990-2013 381 Second Lien Mortgage Originations per Capita ($s) 0.2 0.4 2004-2013 381 Non-tradable Employment to Population Ratio (Percent) 7.8 1.7 1998-2013 381 Construction Employment to Population Ratio (Percent) 3.3 1.5 1998-2013 381 Tradable Employment to Population Ratio (Percent) 4.9 3.2 1998-2013 381 Median Hourly Wage ($s) 14.1 2.1 2001-2013 337* *Unbalanced panel. Over 80 percent of MSAs report values in all years.

1.3.2 Identifying Inmigration Shocks

The goal of this section is to estimate the effect of inmigration to an MSA on the MSA's unemployment rate. Isolating the causal relationship requires plausibly exogenous shocks to inmigration because inmigration and unemployment are likely to be correlated for other reasons. One concern with using the migration rate itself is reverse causality: people choose to migrate to areas with lower unemployment. This would bias the OLS regression downward, because it induces a negative correlation between inmigration and unemployment. My other major concern is omitted variable bias: during my sample, an increase in housing prices lowered unemployment (Mian, Rao, and Sufi, 2013). If it also affected the inmigration rate because housing is less affordable, there would be omitted variable bias. This would bias the OLS upward, because it induces a positive correlation between inmigration and unemployment. These two concerns are not meant to be an exhaustive list, but are both likely to be major sources of bias. In this section, I identify shocks to inmigration as a strategy to address these concerns. I use the historical patterns of migration and the outmigration from far-away counties, to construct a shock to inmigration to an MSA. I only use the outmigration that goes to places far from the MSA as well, meaning that the shock is not directly related to the economic conditions of the MSA of interest. This is similar to the strategy used by Altonji and Card (1991) and many papers since, but tailored to suit the domestic migration setting. 15 Specifically, I use the first four years of the IRS data, covering movements from 1990-1994

1 5Beaudry, Green, and Sand (2014) use a similar idea to construct instruments based on the migration preferences of specific demographic groups within the United States. Their identification is based on changes in migration across demographic groups rather than counties of origin. They look for longer-term effects using Census data. In contrast, my instrument allows me to use high-frequency variation in order to capture short-term effects. Shimer (2001) and Foote (2007) also use demographics as an instrument for increases in population. A major difference of my instrument is that demographic trends may be more predictable than changes in outmigration of historically-connected counties, leading to a more gradual change in housing stock that mutes both of the channels I discuss in this paper.

25 to map the network of migration around the United States. Then, to construct the predicted inmigration 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 the concurrent year to places more than 100 miles from the MSA. Then I sum over all counties. In my baseline construction of predicted migration, 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,1 6 and by using a cutoff of 500 miles. In math, the formula for predicted inmigration is:

Zn,t = Mc+nto Mc-n,t cE-n Mc-+-n,to where -n is the set of all counties that are sufficiently far from n, to is the pre-period, and mcn is the migration from county c to area n. I normalize this measure by the city's population. As a concrete example, suppose I am constructing a prediction for inmigration to the Boston- Cambridge-Newton Metropolitan Statistical Area. To start, I would pick a county, say 'Montgomery County, Maryland. From 1990-1994, 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 predicted inmigration, 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 a prediction for inmigration to Boston in 2007. Because the patterns of migration are relatively stable, this measure is strongly correlated 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. The predicted inmigration to a county is autocorrelated. So I take a final step to isolate the innovation in the predicted inmigration. I assume i follows an AR(2) process.17

3 Zn,t =:- 1Zn,t-1 + 2En,t-2 + an + at + Zn,t where zn,t is the local innovation to the shock. I include a time fixed effect because there are trends that occur at the national level. I use the Arellano and Bond (1991) estimator to estimate /3 and 02. From this regression, I recover the zn,t's. The final step is to normalize z,,t, such that it predicts an increase in inmigration equal to one percent of the city's population. The identifying assumption behind these results is that the outmigration from historically-

6 1 For this measure, I also throw out any counties for which more than half of their outmigrants move to the MSA. Including those counties gives noisy and small outmigration shocks large influence over the shock's variation and makes the estimates much less precise. 1 7 This is robust to the choice of lags. Coefficients on lags greater than 2 were insignificant.

26 connected counties is unrelated to other factors that might cause a change in the unemployment rate. In my data, the most pronounced outmigration episodes are because of two hurricanes: Katrina and Irene. In Appendix A.5, I show similar results to my main regression using only the outmigration from Hurricane Katrina.1 8 One 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 1.3.5.

1.3.3 Econometric Specification

My specification is

Au",t E /35AZn,t- + aet + En,t s=-3 where un,t is the unemployment rate in MSA n in period t. The methodology used to construct shocks used up the first six years of migration data, so the sample period is from 1997-2013.19 I estimate a moving-average model in order to trace out the impulse response of the migration shock.2 0 The response of ut+s to the shock in period t is simply f3,. In addition to lags, I include leads of the shock as a placebo test to make sure migration is not "causing" changes in the unemployment rate before it occurs.21 I chose to use six lags because the effect dissipates after six years, implying that additional years are unlikely to be an important omitted variable. Three lags are used 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, Smith, and Wozniak, 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. Figure 1-1 shows the response of inmigration and outmigration to this shock. For this figure, I run the same specification, but with the migration rate on the left-hand side. I normalize z such that the total inmigration response over the six year period is equal to 1 percent of the original city's population. Hence, for future impulse responses, it can be interpreted as the response to a

18 1t is easier to study the effects of Katrina because it primarily hit eight counties, whereas the effects of Irene were more widespread. The exercise is quite similar to McIntosh (2008), which finds negative effects on wages and employment in Houston in the first-year after Katrina. Indeed, I also find a rise in the unemployment rate in the first year, but a large decline afterward. 190ne might be concerned this is a special time in U.S. history, especially since the housing boom and bust plays a prominent role throughout most of the time period. However, in Section 1.4, I argue that the relationship we see between housing construction and house prices match well with previous estimates from before the housing bubble (Poterba, 1984; Topel and Rosen, 1988). Results are robust to splitting the sample to before and after 2007. 20 See Hansen and Sargent (1981) or Plagborg-Moller (2015) for a discussion of moving average models. 2 1 A violation of parallel trends is not necessarily a violation of exogeneity, as there may be anticipatory effects from the inmigration. Nonetheless, an absence of parallel trends lends credence to the identifying assumption.

27 .2

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

Inmigration - Outmigration

Figure 1-1: The migration response to the inmigration shock, with 95 percent confidence intervals. Standard errors clustered by state. shock which will increase inmigration by 1 percent over the course of six years. Note there is not a response from outmigration initially. Whatever the cause of the outmigration from historically- connected counties, it is not common to the receiving city.

1.3.4 The Effect on Unemployment

Baseline Results

Figure 1-2 shows the effect of an inmigration shock on the unemployment rate. The blue line, with dashed confidence interval bands, is the estimated effect of the one-percent inmigration shock. 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 0.1 percentage points. In period t + 1, the unemployment rate falls more, to a total effect of 0.3 percentage points, which stays roughly constant through t +2 and t + 3, before gradually returning to zero by t + 6. In total, the inmigration lowers the unemployment rate by 1.3 percentage-point-years. The red line is produced in a similar way, but uses the residuals of actual inmigration, rather than the predicted inmigration outlined in the previous section. This is a similar exercise to comparing ordinary least squares and instrumental variables regressions. While qualitatively similar, the magnitude of the results is larger using the exogenous variation. As mentioned previously, this could be because the housing bubble during this time period played a major role in both limiting inmigration and boosting the economy. During this time period, high house prices were associated with both higher inmigration and lower unemployment rates.2 2 The result rejects Proposition 1.1, as well as the belief that migration is a mitigating force for local shocks. If, as I have shown here, migration has a negative effect on the unemployment rate, 22 If the sample is restricted to areas with high housing elasticity, the OLS estimate is larger than the IV estimate, suggesting that the housing bubble is biasing the regression in this direction.

28 0

C I

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

Respose to Migration Shock - Using Inmigration Residual

Figure 1-2: The effect of an inmigration shock causing an increase of one percent of the MSA's population, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381. then migration does not dampen local shocks. Rather, as people move to prosperous areas, it will amplify those shocks.

Robustness to Specification

One set of concerns over this regression is that the choice of specification is important. In Figure 1-3, I show that this is not the case. In my baseline specification, I used first-differences in case one of the variables was non-stationary. However, using fixed effects does not meaningfully change the results. I also run the regression in first-differences with a fixed effect, effectively allowing for a linear city-specific trend, to show that the result is not driven by differential trends in both migration and unemployment. Lastly, I also include two additional lags in migration, to show that my results are not sensitive to their inclusion.

Robustness to City Characteristics

Another set of concerns over this regression is that the constructed shock might be correlated to other city-time-specific characteristics. For example, one might be concerned that outmigration might be driven by the performance of specific industries, which are also present in the receiving city. Another concern might be that some national shocks could change both migration and unemployment differently in higher-educated cities. Figure 1-4 presents the robustness of the result to these concerns. I flexibly control for industry and education. To do this, I interact the shares of 2-digit SIC industries in 1990 with a year dummy to control for industry. For education, I interact shares of the 11 education codes in the 1990 Census with year dummies. I also present the results using an alternative shock. To construct this shock, I exclude using migration to or from cities that are similar to the receiving city, based

29 E a,

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t+7 t+8 years

- Baseline ---- Additional Lags " Fixed effects - --- Allowing for city trends

Figure 1-3: The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381.

on the correlation of Bartik shocks. The result is robust to all of these alternate specifications.

Robustness to Spatial Correlations

In Figure 1-5, I investigate a variety of robustness checks aimed at addressing concerns about the spatial structure of my regression. The concern here is that there may be an omitted variable that affects areas near the MSA, causing people to move, but which also directly affects the unemployment rate. Because my shock 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 Census Division each MSA is in, interacting each division with year fixed effects. These controls do not affect the results. In addition to these robustness checks, in Appendix A.5, I present a similar regression using a migration network based on the 1940 Census instead of my pre-period, finding similar results. I also show similar results when only using variation that is based on the outmigration following Hurricane Katrina.

Robustness to Alternate Measures of the Labor Market

A final robustness check is to make sure we can see this force in other measures of the labor market. In Figure 1-6, I show the effect on the employment-population ratio, for both MSAs and 23 In Section 1.5.1, I construct Bartik instruments for each MSA. I compute the correlation of these Bartik shocks over my entire sample, and I reconstruct my inmigration shock, excluding outmigration from the 250 MSAs that have the most highly correlated Bartik shocks.

30 .years

-0-Baseline - '-- Industry Controls -+--- Education Controls -U--- Instrument Excluding Similar Cities

Figure 1-4: The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381.

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 1-7, I also show that unemployment benefits fell, and I construct my own measure of unemployment for a subset of the sample. Unemployment benefits come from the BEA's personal current transfer receipts. To calculate the unemployment rate myself, I use the public use microdata CPS (Ruggles, Genadek, Goeken, Grover, and Sobek, 2015), and measure unemployment in counties which are large enough to be identified in the public data.

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.2 4 Ideally, I could distinguish individuals by where they lived previously, but that would require a large panel dataset that tracked both location and employment status. Nonetheless, by focusing on the unemployment rate, there is a natural bound on the direct effect coming from the employment status of migrants. If I assume each inmigrant has a job and each outmigrant is unemployed I can calculate a bound. In t +i 1, the shock has added about 0.63 percent of the population in inmigrants, and about 0.09 percent of the population has left. This implies a bound of 0.63 times the original unemployment rate plus 0.09 times one minus the unemployment rate, assuming the labor force participation rate is the same. The average unemployment rate in my sample is 6 percent, implying that the upper bound on this mechanical effect is 0.11 percentage points. In that time period, I estimate the

Itappears from the descriptive data that their adjusted gross incomes are not necessarily that much higher. See for example, Figure A-i in Appendix A.3.

31 E I I I i I I J" z

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t-6 years Baseline Instrument: no cutoff Instrument: 500 miles -+-- Census Division controls

Figure 1-5: The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381. unemployment rate has fallen by 0.32 percentage points, implying most of the effect must have been because of additional jobs for non-migrants, even under these extreme assumptions. The fall in the level of unemployment benefits (Figure 1-7) is also indicative that the effect is not driven purely by inmigrants being more likely to have jobs, as that would not change the level of benefits.

1.3.5 Threats to Identification

In this section, I consider a few threats to the exclusion restriction, and whether they could be driving the results.

Regional Shocks

One threat to identification is economic shocks that affect multiple cities at once. Such a correlation would violate the exclusion restriction if it changed the outmigration rate in one city and the unemployment rate in the other.2 5 For example, an oil boom would make Dallas more prosperous, and fewer people would migrate out. At the same time, it would lower the unemployment rate in Houston. This would bias my regression. I expect this bias to be small and positive, suggesting that my results are an upper-bound on inmigration's true effect on the unemployment rate. In Appendix A.4, I show that city pairs with high migration between them tend to be similar in location and industrial composition. In Section 1.5, I show that negative local shocks lead to an increase in outmigration. Taking these two facts together, the instrument, the outmigration rate of one city, and the outcome, the unemployment

25 It is because of such concerns that I exclude migration within 100 miles of the MSA, and I check for the robustness of the regression with industry and education controls. However, a skeptical reader might not believe these to be sufficient.

32 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 years

-4-MSAs --- CBSAs

Figure 1-6: The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381. Number of CBSAs: 917. rate of a connected city, are likely to be positively correlated if an economic shock hits both cities. Hence, they would bias my regression upward.

Substitution between Cities

Another threat to identification is that a low unemployment rate in one city would lower migration between other cities. For example, a boom in Boston might cause someone leaving Montgomery County to decide to move there instead of New York. Because I am using migration from Mont- gomery County to New York to construct my instrument, this would bias my regression. I again expect this bias to be small and positive. A boom in one city will cause the instrument to be slightly smaller, causing a positive correlation between the unemployment rate and the instrument.

Terms of Trade Effects

One might be concerned that two cities with high migration might compete against each other in the same industries. For example, many people move between Boston and San Francisco, both of which produce pharmaceuticals. If Boston pharmaceuticals were struggling, that might lead to higher outmigration from Boston, and a higher price of pharmaceuticals. The change in price would benefit San Francisco, and could cause the unemployment rate to fall. However, in Section 1.4.5, I show that the decline in the unemployment rate does not come from employment in industries that produced tradable goods. Rather, the benefits are concentrated in construction and non-tradable goods and services. So this bias does not seem to be driving the decline in the unemployment rate.

33 7 CN

. Lo E

E LO- . E 0)

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 Baseline ---- Raw CPS Data years

Figure 1-7: The effect of an inmigration shock equal to one percent of the MSA's population on unemployment benefits (left) and the raw CPS unemployment data (right), with 95 percent confidence intervals. Errors clustered at MSA level. Number of MSAs: 381, 242.

1.4 Empirics II: The Housing Channels

In Section 1.2, I argued that a standard model cannot explain the decline in the unemployment rate which I found in Section 1.3. I also showed housing could play that role. In this section, I show the empirical evidence in favor of this hypothesis. 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. Sec- ond was the house price channel, which was based on an increase in house 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. Throughout this section, I use the same specification as in Section 1.3.

6 E3Azn,t-s + O't + En,t n,,t s s=-3

where x is house permits, construction employment, house prices, mortgages, or non-tradable employment. To study the effect on employment composition, I use the employment categories from Mian, Rao, and Sufi (2013). Their decomposition assigns NAICS 4-digit categories to one of four sectors: construction, non-tradable, tradable, and other. They make up respectively 9 percent, 19 percent, 11 percent, and 61 percent of employment in my data. For house prices, which have a strong trend component, I also include a city fixed effect, effectively controlling for a linear trend.

1.4.1 Construction Channel

The construction channel requires a build-up of new housing, especially in the short-term. In Figure 1-8, I show that housing permits, from the Census, increase significantly after a migration shock.

34 4) CD

U))))

t-3 t-2 t-1 t + t+2 t+3 t+4 t+5 t+6 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years years

Figure 1-8: The effect of an inmigration shock equal to one percent of an MSA's population on housing permits issued and construction employment, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 310, 381.

The effect is quite large, a one percent migration shock causes a 10 percent increase in the number of permits per year. Over the course of six years, the number of houses goes up by approximately 40 percent of a typical year's permits. In my sample, the number of permits per year averaged 0.65 percent of an MSA's population, so the cumulative effect corresponds to about one new house for every four inmigrants. In the right half of Figure 1-8, we see an increase in the construction sector. For one percent inmigration, there is a corresponding increase in construction equal to 0.1 percent of the population for about three years. Recall from Figure 1-6 that the total employment-to-population ratio increased by about 0.2 percent in response to the shock, so the construction channel seems to be explaining about half of that. In Appendix A.5, I show the robustness of these results to many of the same checks I showed in Section 1.3.

1.4.2 House Price Channel

I now turn to the house price channel, which posits that house prices go up and cause increased non-tradable demand. In Figure 1-9, I show that house prices do increase, responding by roughly five 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 short-run housing supply elasticity of about 2. This is line with Poterba (1984), which estimates a housing supply elasticity of between 0.5 and 2.3; and Topel and Rosen (1988) which estimate a one-quarter-short-run elasticity of 1 and a long-run elasticity of 3 that occurs mostly within a year. Both estimate the elasticity off the time series of aggregate U.S. data.26

2 6 Finding an estimate within this range is important because it suggests the results are being driven by a change in construction, and is less likely to be special to the housing bubble.

35 0 a)

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

Figure 1-9: The effect of an inmigration shock equal to one percent of an MSA's population on house prices, with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381.

In Figure 1-10, I present some evidence that this housing price increase is leading to additional consumption. On the left is the rise in mortgage lending. Not surprisingly, there is a large increase in the amount of total mortgages. But the percentage increase in second-lien mortgages is much higher. 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.2 7 On the right is the rise in non-tradable employment, which increases by about .06 percentage points 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 five percent, and assuming a consumption- to-house-price elasticity of 0.2 (Berger, Guerrieri, Lorenzoni, and Vavra, 2015), we would expect non-tradable consumption to rise by 1 percent. The mean non-tradable-employment-to-population ratio is 8 percent in my data, which would predict a 0.08 percentage point increase in non-tradable employment, slightly higher than what we see in Figure 1-10. This increase is a bit less than half the total increase in the employment-to-population ratio. Together, the house price channel and the construction channel appear to explain most of the total labor market response. 28

1.4.3 Cross-Sectional Heterogeneity

Because migration affects unemployment through house prices, one hypothesis is that areas in which house prices are more responsive to demand might experience bigger changes in unemployment.

2 7 The majority of second-lien mortgages are home equity lines of credit (HELOCs). See Lee, Mayer, and Tracy (2012) for a further discussion of second liens in recent years. Of course, second liens are less than 10 percent of the mortgage market, so the increase is smaller in dollar terms. 28Given 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 1.4.5.

36 .2c .2

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years ______

Liens - All Mortgages t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 Second I years

Figure 1-10: The effect of an inmigration shock equal to one percent of an MSA's population on mortgage originations(left) and non-tradable employment (right), with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381.

In this section, I investigate heterogeneity across cities that differ in housing supply elasticity and population growth.

Heterogeneity by Housing Supply Elasticity

In response to an increase in housing demand, cities with lower housing supply elasticities should experience a larger increase in house prices. Potentially, this provides a channel through which the effects on unemployment vary by housing supply elasticity. I interact the inmigration shock with the housing supply elasticity from Saiz (2010).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. I run the following regression:

6 6 Z= SAzat_ x elasticity0 + #3Azn,t-s +at x elasticityn + 'Yt + En,t s=-3 s=-3 where x is house prices or the unemployment rate. As before, the house price regression includes a city fixed effect. 3*, the coefficient of interest, estimates the heterogeneous effect of migration by housing supply elasticity. Figure 1-11 shows that the effects do differ by housing supply elasticity. On the left, I show that house prices increase by less in more elastic areas, as expected. On the right, I show that the unemployment rate falls by less in those same areas.

Heterogeneity by Population Growth

The marginal effects of migration may differ by a city's population growth because a declining city has excess housing stock (Glaeser and Gyourko, 2005). With many vacancies, the marginal migrant

2 9 Saiz (2010) uses the previous vintage of MSAs. I am able to match 253 of them to current MSAs.

37 0'I

E // ------E

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years years

Figure 1-11: The effect of an inmigration shock equal to one percent of the MSA's population on house prices (left) and unemployment (right) interacted with Saiz (2010) housing supply elasticity, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 253.

A N... ~ ~-..

E o E

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years years

Figure 1-12: The effect of an inmigration shock equal to one percent of the MSA's population on house prices (left) and unemployment (right) interacted with high January temperatures, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381. can move into an empty house with minimal impact on either construction or house prices. Hence, one prediction is that the effect of migration on unemployment ought to be larger in growing cities. A notable pattern during this time period is that population increased more in areas of the country with warmer winters (Rappaport, 2007). So to test the prediction, I test if the marginal effects of migration are stronger in warmer climates. The regression is similar as for housing price elasticities:

6 6 AXnt =x*A n,t-s x Jan. Tempn + E #3Azn,t-, + at x Jan. Tempr + Yt + En,t s=-3 s=-3 where I use the average of the high of daily January temperatures from 1990 to 2013, available from the Center for Disease Control and Prevention.

38 The results are presented in Figure 1-12. In warmer MSAs, house prices increase more in response to migration and the unemployment rate falls more. These results are consistent with the fact that migration has large effects on unemployment through the housing market and that the housing market is more responsive in growing MSAs.

1.4.4 The Housing Channels during the Mariel Boatlift

In this section, I use a different source of variation to demonstrate the presence of these housing channels. Specifically, I use the famous example of the Mariel boatlift in Miami in 1980, where around 125,000 Cuban immigrants arrived in Miami. The goal of this exercise is not to ask whether the Mariel boatlift was stimulatory, but rather to see if there are similar patterns in house prices and employment across industries. One might expect that housing demand of a Cuban immigrant to Miami would be smaller than an American's, so the magnitudes of this channel might be correspondingly smaller. Because the boatlift was a one-time event, I will compare outcomes in Miami to those of a control group, based on similar cities in the United States at that time. There is significant debate over the appropriate group, so I will use the baseline group from Card (1990) and the baseline group from Borjas (2015). Card (1990) uses Atlanta, Houston, Los Angeles, and Tampa; while Borjas (2015) uses Anaheim, Rochester (New York), Nassau, and San Jose. Miami, from 1979-1980, does have a bigger increase in house prices than either control group, by 2 percent against Card, and 5 percent against Borjas (Figure 1-13), but it is relatively small compared to my previous results, and compared to the Card control group, it does not last. There are likely two reasons for this. One, Cuban migrants were less rich, were more likely to rent, and lived in smaller houses with more people (Greulich, Quigley, and Raphael, 2004). Secondly, the fact that they were immigrants may have lowered house prices by reducing demand from natives who did not want to live in proximity to them (Saiz, 2003).30 Turning to employment effects, I can only measure industries using SIC data at coarser levels, so using the decomposition from Mian, Rao, and Sufi (2013) is infeasible. Instead I will use manufacturing as a proxy for tradables, and retail trade as a proxy for non-tradables.3 ' Construction is measured using the SIC industry. I plot them in Figure 1-13. All of these plots show the same qualitative patterns as they do in response to migration shocks in the main body of my paper. In both construction and retail, there seems to be a temporary increase in the employment in that sector. In manufacturing, however, Miami's employment stays quite flat while the comparison cities are growing. Saiz (2003) plots new housing permits for Miami and several comparison groups over the same decade. In 1980, new permits in Miami increased from 1979, while in each of his comparison groups,

3 0 My results are slightly different than Saiz (2003), who, when studying the same event, finds a large increase in rents, but not in house prices. Critically, though, he indexes house price changes to 1980Q3, when many of the Marielitos had arrived, and any changes in house prices might have already occurred. 3 1 Bodvarsson, Van den Berg, and Lewer (2008) use a different methodology to consider the effect of the Mariel boatlift on the retail sector, and also find a large role of labor demand.

39 A p

>8 - ,-

0'- 78

3~7 /

1976 1978 1980 1982 1984 1 976 1978 1980 1982 1984 year year

--- Miami -- U-- Card (1990) Controls -+-- Miami - - - Card (1990) Controls - h--Boijas (2016) Controls - Borjas (2016) Controls

N - A / -u - A---- ~- U ~ ~ -a-- -U-- -~ CI - o- -- -8~~ .b~

'7 // U /

A1 1976 1978 1980 1982 1984 1976 1978 1980 1982 1984 year year

'- Miami - - * -- Card (1990) Controls Miami -- U -- Card (1990) Controls -- Borjas (2016) Controls - - Borjas (2016) Controls

Figure 1-13: Log House Prices (top left), Construction Employment (top right), Retail Employment (lower left), and Manufacturing (lower right). Index, 1979=0.

they decreased. He does not stress this, likely because there are quite significant differences in other time periods as well, but it is consistent with my finding that construction employment expanded.

In sum, the data are consistent with the two housing channels: the house price channel because we see an increase in house prices and retail employment; and the construction channel because we see an increase in permits and construction employment.

I want to conclude this section with a note about magnitudes. The Mariel boatlift was an approximately 7 percent expansion in the labor force (Card, 1990). This is significantly bigger than any shocks in my data, but the effects of these housing channels are nonetheless modest. When compared to the Borjas (2015) controls, the total jobs added in the construction sector and the retail sector are no more than 20,000, less than half of the 45,000 person increase in the labor force. Of course, retail is not an exhaustive list of non-tradable employment, so there could be bigger effects, but it is unlikely that this could drive a large decrease in the unemployment rate. Most likely, this is because there is less housing demand from each Mariel immigrant than from a domestic migrant in the United States.

40 1.4.5 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 and provide evidence against each: factor complementarity, agglomeration, and wealth heterogeneity. Previously, in Section 1.3.4, 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.

Factor Complementarity

One possibility is that migrants and non-migrants are complements, so that having more migrants lowers the unemployment rate of non-migrants. For example, if most migrants are high-skilled workers and most non-migrants are low-skilled, the incoming migrants could improve the productivity of non-migrants, making it easier for them to find jobs. Indeed, Molloy, Smith, and Wozniak (2011) show that migrants are more educated than non-migrants. Furthermore, I show in Appendix A.3 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 A.3). 3 2 Second, Ottaviano and Peri (2012) considers the effects of complementarity 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 A.3 includes the figures discussed in this paragraph and a lengthier discussion.

Agglomeration

A second possibility is that there are agglomeration effects. As migrants move in, knowledge spillovers (Audretsch and Feldman, 2004), the home market effect (Krugman, 1980), thick market externalities (Diamond, 1982), or other increasing returns forces increase employment. However, one might expect tradable goods to be most affected by agglomeration, or at least equally affected. Rather, I find that tradable goods employment declines, as seen in Figure 1-14. Second, many agglomeration stories would also imply a larger effect in the long-run than the short-run, and I find the opposite. Finally, the magnitude of my effects is much larger than these forces can 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 agglomeration effects, I am finding a decline in the unemployment rate of about 0.3 percentage points in response to a one percent increase in population, which is at least two orders of magnitude larger. 3 2 This assumes that there are not proportionately more college migrants being pushed to places with high college shares already, which I do not have data on.

41 0 E

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

Figure 1-14: The effect of an inmigration shock equal to one percent of an MSA's population on tradable goods employment (right), with 95 percent confidence interval. Errors clustered by state. Number of MSAs: 381.

A second possible agglomeration channel is thick-market effects, where an increase in unemployment levels might increase the job finding rates, lowering the unemployment rate. However, the magnitudes of my estimates imply a decrease in the level of unemployment.

Wealth Heterogeneity

A third possibility is that migrants are significantly wealthier than non-migrants. For 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 was ruled out by assumption in Proposition 1.1. To check whether this is an empirically plausible channel, I use the American Community Survey data, and look at the dividend, interest, and rental income of interstate migrants versus non-migrants and within-state migrants. The cumulative distribution function of this income is plotted in Figure 1-15. 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.3 3 More crucially, the distribution of interest income for non-migrants first-order stochastically dominates the interest income for migrants. Although the ACS does not measure wealth directly, this is suggestive evidence that non-migrants are wealthier than migrants. This is consistent with statistics from Molloy, Smith, and Wozniak (2011), which shows 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). These demographics would suggest that migrants are unlikely to be richer than non-migrants. In conclusion, none of these other channels, factor complementarity, agglomeration, or wealth heterogeneity, seems likely to be driving the results that I find in the data. But more importantly,

33 A very small fraction report negative interest income.

42 L)

C-

10 100 1000 10000 100000 Interest, Dividend, and Rental Income (Log Scale)

- Interstate Migrants - Same House/StayedWti tt

Figure 1-15: The cumulative distribution function of the distribution of interest income, by migration status. American Community Survey, 2000-2014.

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-supply elasticity areas. Hence, the evidence that I have shown is strongly supportive of housing causing the decrease in the unemployment rate.

1.5 Counterfactual: The Migration Accelerator

One implication of the result from Section 1.3 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.

To estimate this, I first estimate how much migration responds to increases in labor demand, a similar exercise to Blanchard and Katz (1992). 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, my previous estimates were based on a shock that implied a specific expected path for migration, which is different than the path in response to the labor demand shock. I need to make an assumption about migration's effect along this path. 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. Later, I show that migrants induced by either of these shocks are indeed comparable on two important observable dimensions.

43 1.5.1 Migration's Response to Labor Demand

The first step in calculating the accelerator is to estimate the effect that labor demand has on migration. There is an endogeneity problem of regressing migration on unemployment 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 an MSA and the growth rate of those industries in the rest of America to calculate an instrument for labor demand. I use 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

where Sj,n,t_1 is the employment share of industry j in MSA 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. As I did for inmigration, I then assume it is an AR(2) process, and use the residuals, z,, as my labor demand shock. One endogeneity concern is that nearby MSAs are likely experiencing similar labor demand shocks. If the economic conditions of those MSAs are affecting the decisions of potential migrants, it could bias the regression. To fix this, I control for the Bartik-shock 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

6 Amnt= S AZnt_, + (sAz (n),ts + at + En,t (1.2) s=-3 where g9,t is the growth rate of employment in CBSA n, z is the Bartik instrument in CBSA n, and zbc(n) is the average of the Bartik shocks 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. The timing of this regression is a bit different than the timing of the regressions I ran in Section 1.3. Because migration is measured at the time people file their taxes, while employment 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. The results for both inmigration and outmigration are shown in Figure 1-16. The effect on net migration can also be seen as the difference between the two lines. The effect for outmigration is smaller but significant. 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 0.25 percent after three years. 34

3 4 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. Monras (2015a) also finds that inmigration is the more reactive margin.

44 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years Inmigration - Outmigration

Figure 1-16: The effect on migration of a labor demand shock, with 95 percent confidence intervals. Standard errors clustered by state. Number of MSAs: 381.

1.5.2 Accelerator

To calculate the accelerator, I estimate the expected effect of the migration I found in Figure 1-16 on unemployment. I compare that to the total effect that Bartik shock has on unemployment. Using only my estimates from Section 1.3, I cannot estimate the effect of any sequence of inmigration, I can only do it for the sequence I observed in response to the inmigration shock. If Figure 1-16 looked exactly like the path of inmigration induced by this shock (Figure 1-1), I could directly use those estimates, but because its shape is different, I must make an assumption. The assumption I will use is that the effect of migration in year t on unemployment in t + s is differs only on s, but not when that migration is first anticipated. This may be a reasonable assumption because migration and expectations of the local unemployment rate may not be particularly salient to many people. 3 5 With this assumption, I can use my inmigration shock as an instrument for inmigration's effect on unemployment, and multiply the coefficients from the IV with the estimates from migration's response to the Bartik shock, to calculate the part of the unemployment effect that comes from migration.

He looks at different shocks more explicitly related to the Great Recession. 3 5 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. With rational expectations, the house price channel is driven by the unanticipated response of house prices. 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.

45 5)

E 0L -4}I

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years -- - -Total Effect Accelerator

Figure 1-17: The response of unemployment to a Bartik shock, and the portion that is due to migration, along with 95 percent confidence intervals. Standard errors clustered by state.

The instrumental variables specification is:

Aun,t E sAMn,t-s + t + En,t s=O 6

Amn,t-s 1 Kr,sAZn,t-r + Vt,s + rn,t,s r=O

I then combine the estimates of -ys with the estimates of Ob from equation (1.2), the effect of the Bartik shock on migration. Hence, the accelerator is

Accelerator, = E 3q'Yr q+r=s

I show the estimated Accelerator, along with the total effect of the Bartik shock on unemployment in Figure 1-17. As you can see, the effects from migration explain a small but significant portion of the unemployment rate's response. In the first year, the response is equal to 16 percent of the total effect, implying migration amplifies the effect of a Bartik shock by 20 percent. In subsequent years, it is an even larger fraction of the total effect. In the counterfactual world where migration did not respond to labor demand, the effect of the Bartik shock would have been smaller, equal to the difference between the two lines. While qualitatively similar, the effect would have been 16 percent more muted. One implication of this exercise is that migration increases the volatility of the local unemployment rate with respect to Bartik shocks. Hence, for non-movers, migration is amplifying the risk of shocks to local demand, by 20 percent. In addition, much of the persistence in the unemployment rate is driven by this migration as well. We can see this because, at later time periods, the accelerator component is an even larger fraction of the total change. Hence, migration can explain

46 Table 1.2: 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-Paap F-Statistic 64.8 13.7 64.8 13.7 CBSAs 917 917 917 917 Instruments Migration Labor Demand Migration Labor Demand Shocks Shocks Shocks Shocks Standard errors clustered at CBSA level. *** p<0.01, ** p<0.05, * p<0.1 a fraction of the persistent differences in regional outcomes.

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. 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. 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, AAGI migration ratet = /3Ami,t + at + Ei,t where the AGI migration rate is the total-income of all migrants into the CBSA, normalized by the CBSA'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. I use CBSAs for this exercise in order to have a powerful first-stage when using the Bartik instruments. The results are presented in Table 1.2. All the first-stage F-statistics are above ten, though not surprisingly, the migration shocks do a better job of predicting migration than the labor demand

47 shocks. 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.

1.6 Conclusion

In this paper, I document that inmigration shocks have a large positive effect on a local labor market. This effect is explained by two housing channels: an increase in construction and an increase in house prices, inducing non-tradable consumption. Because of the positive effect, migration amplifies the effects of other labor demand shocks, counter to the traditional view of migration as an equilibrating force. In fact, I quantify these effects to be large, amplifying labor demand shocks by 20 percent. There are two implications for policy. Currency unions do not benefit from migration in the way that many suppose from Mundell (1961). 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. 36 Rather than closing the differences between labor markets, migration amplifies their differences. This means that if the receiving MSA could control its own monetary policy, it would rather tighten by more than it would absent migration. Relative to a world without migration, differences in macro-stabilizing policies are larger. Second, migration's amplification of local shocks increases employment risk for people that do not move. However, this risk is smaller in cities with more elastic housing supplies. 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, reducing the amplification that I document in this paper.

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

48 Chapter 2

The Geography Channel of House Price Appreciation: Did the Decline in Manufacturing Cause the Housing Boom?

Changing locational preferences contributed significantly to the 2000-2006 housing boom in the United States. We estimate between 20 and 40 percent of the overall rise in real house prices can be attributed to an increase in the relative desirability of inelastic areas. The decline in manufacturing was a major contributor to this shift. In the first part of this paper, we show that local housing demand is significantly driven by population changes and changing relative desirability. We document patterns in population movements consistent with this claim and create a new local rent index from microdata to show that rents responded in the same way as house prices. We then develop a theory for why an increase in the relative desirability of inelastic areas would raise house prices nationally. Finally, we quantify the total effect by creating a new measure of housing supply elasticity that covers the entire United States. We then show that the decline in manufacturing and the fall in interest rates both played an important role in the house price increase through the geography channel.1

'This chapter is joint with Jack Liebersohn. We would like to thank Dan Greenwald, Alp Simsek, Ivan Werning, Arnaud Costinot, David Autor, and Antionette Schoar for their comments. Jack would like to the thank the Boston Federal Reserve Bank for their hospitality and the Becker Friedman Institute for financial support through the MFM Fellowship. Greg would like to thank the National Science Foundation for financial support through the Graduate Research Fellowship (Grant No. 2014136625). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. All errors are our own.

49 2.1 Introduction

House prices rose significantly in the early 2000s. The boom was spatially heterogenous, with some areas seeing house prices more than double, and some areas seeing almost no increase. Economists have largely focused on two theories: an increase in credit supply 2 or a shift in expectations of future house prices. 3 Often, these two theories are judged based on the extent they can match the cross-sectional facts. In this paper, we argue that the cross-sectional facts are not only a testing ground for different theories but are a crucial cause of the boom itself. For a variety of reasons, markets with inelastic housing supplies became desirable places to live. For example, there was a large decline in labor market outcomes in manufacturing, an industry highly concentrated in elastic areas (Liebersohn, 2017). In equilibrium, house prices rose nationally as people chose to move to inelastic areas. Figure 2-1 illustrates the forces we highlight in this paper. Around 2000, there was a marked decline in manufacturing (Charles, Hurst, and Notowidigdo, 2016; Autor, Dorn, and Hanson, 2013). As would be expected in most urban models, this opens up a large gap in house prices between high-manufacturing areas, like the Midwest, and the rest of the country. Because the Midwest has a high housing supply elasticity, were prices to fall there but remain constant everywhere else, there would be a net decline in aggregate housing supply. So in order to meet demand, aggregate house prices rose. This paper makes several contributions. First, we show that the cross-sectional facts about housing prices do seem to suggest a large role for people's choice of location. We show a tight relationship between the growth in total housing units and population growth, and that this feeds through to house prices. In contrast, low-manufacturing and low-elasticity areas, which had larger house price increases, did not experience an increase in the per capita amount of housing or the size of that housing. To further suggest the cross-sectional differences are primarily due to changes in locational preferences, we show in a new dataset that the patterns of changes in rents are quite similar. Second, we formalize a theory of why this shift would increase aggregate house prices. The key moment of the data is the covariance of the housing supply elasticity and the change in local housing prices. We also provide formulas for another channel that operates through the supply of construction materials. In particular, we highlight how two shocks of the time-the decline in manufacturing and the lowering of interest rates-would cause an increase in house prices through the geography channel. Third, we construct a new housing supply elasticity measure for commuting zones (CZs) and show this is strongly negatively correlated to house price increases. Using the formula from the

2 For example, several papers have argued that the increase in subprime mortgages was a key cause of the boom, e.g. Mian and Sufi (2009). Other papers have argued that falling interest rates are particularly important such as Mayer and Sinai (2009), while others have emphasized changes to borrowing constraints, such as Greenwald (2016). 3 For example, Glaeser and Nathanson (2017), DeFusco, Nathanson, and Zwick (2017), and Foote, Gerardi, and Willen (2012). Kaplan, Mitman, and Violante (2017) also suggest changing expectations play a large role in the boom-bust cycle of house prices in a quantitative model. They also suggest a large role for credit supply in explaining other phenomenon during the time period.

50 FHFA House Price Index Purchase-Only House Price Indices, 1990-2017 C0

YCa 0n 0m

effet mestht hrogh tiast Narkt CetariCnu Divditions We shwtAtlherUaiSwt manfatSin sharesusn innegnyrtree from FREDanexpeaanlbRetehaveofBthe efgraphy Lhaune.

Final Figy, 2-1 shwthtouster Preitse aidwessin bthm dRestng the tiU.S. h bo

This pa lgprointrbtes t0 seetands cn of the ttatreoo. ther rmeashusin of eatte daoe-o havety. Matotlreverted thares Heurst androtidwidh (2s6),ewilhtostabsises the aratle tmgftemanufacturing ro deaesine0 and exli aounglbof, whh gegah chanttngelyetefs

b ialyut so that ther theos aprly asa h eictrm huin banomauring ehie tim then thein boom.

OThr papers aontried to sevealtrayo the teraetr o the roltiet of housing sippty. Hsireh

and Moretti (2017) quantifies the effects that housing constraints have on aggregate productivity. Herkenhoff, Ohanian, and Prescott (2017) suggests the recent decline in trend growth can be attributed to higher land-use restrictions. This is consistent with evidence from Ganong and Shoag (2017). Here, we suggest that these restrictions played a major role in the cyclical aspect of the macroeconomy as well. Finally, there is a large overlap with papers that investigate the interaction between migration and housing. ? suggests that changing wages can explain a significant share of house price dispersion from 1975-2005. Glaeser and Gyourko (2005) suggests housing markets may explain sluggish population responses. Davis, Fisher, and Veracierto (2013) investigate this hypothesis and argue

51 other migration frictions are more important. These models have their bases in Rosen (1979) and Roback (1982), as does ours. By closing the model, we add an aggregate market-clearing condition on housing from which we can analyze the effects of relative location demand on aggregate house prices.

2.2 The Cross-Section of Local Housing Demand

This section presents evidence that changing patterns of regional demand for housing played an important role for explaining the cross-section of house price growth from 2000-2006. We begin in Section 2.2.1 by showing the strong relationship between population growth and housing demand. We also show that, cross-sectionally, house price growth is not well explained by cross-sectional changes in housing quality or size, and that population movements in turn are associated with exposure to the manufacturing sector. Section 2.2.2 presents evidence that similar patterns held for rents as for housing prices. This finding provides further evidence that cross-sectional house price changes reflected changes in relative demand. To show this, we create a new index of multifamily operating incomes using data from Commercial Mortgage-Backed Security (CMBS) records. Finally, in Section 2.2.3, we present evidence that allows us to reject an important alternative hypothesis - that regional patterns in house price changes are explained by regional changes in mortgage availability.

2.2.1 Population Growth and Housing Prices

This subsection presents evidence supporting the model's key mechanism - that cross-sectional variation in housing prices was caused by demand to live in particular areas. To provide evidence for this mechanism, we present three stylized facts. 1) Almost all of the cross-sectional changes in housing units is due to population change. 2) Low-manufacturing areas had the greatest population and price increases. 3) These areas did not have greater increases in either the number of houses per capita or the quality of housing. Figure 2-2 shows the relationship between population growth and housing unit growth from 2000 to 2006. The two variables are almost perfectly correlated: Population changes nearly one- for-one with housing units. Moreover, the R2 is this relationship is nearly 1 - after accounting for population growth, very little of housing unit growth remains unexplained. Moreover, population growth and housing price growth are positively correlated, shown in Figure 2-3. Next, we provide evidence that exposure to the manufacturing sector affected populations and prices in precisely the way one would expect from a regional demand shock. The relationship between manufacturing and population is shown in left half of Figure 2-4. From 2000-2006 there was an overall net migration from areas with high to areas with low manufacturing. On average, a 10 percent higher fraction of the population employed in manufacturing corresponded to lower population growth of 0.007 log-points. A similar pattern holds for price changes, shown in the right half of Figure 2-4. Low-manufacturing areas had greater price increases as well.

52 Log housing unit growth vs population growth, 2000-2006 Slope=0.97 (0.02)

- . CM

0.-

0-. .2 . Log population change

Figure 2-2: Population Growth and Housing Units

Cross-sectional housing demand does not seem to reflect differences in per capita housing growth.4 To see whether this is important, Figure 2-5 shows the relationship between manufacturing and the number of houses per capita across CZs. This relationship is near zero and not statistically significant. The general relationship between elasticity and housing units per capita growth is also near-zero and slightly negative (right side of Figure 2-5) .5 Finally, using data at the census division level from the Survey of Construction, we show that there is no strong relationship between the size of houses or lots and housing prices (Figure 2-6). This result is consistent with the finding by Albouy and Zabek (2016): most of the increase in housing values is due to changes in land values, not to major changes in the dispersion of the size or amenities of houses.

2.2.2 Rents and Prices

Because regional demand for housing is the model's key mechanism, the cross-sectional predictions for housing prices hold for rental prices as well. Here we present new evidence that rents and house prices co-moved cross-sectionally. To study the relationship between rents and housing prices, we use a new regional rental cost index using data from Commercial Mortgage Backed Securities. We have to create our own index because the CPI-Rents series is only available for a handful of cities and does not show high- frequency changes in rents. Other series that have been used as proxies for rents, such as fair market rents, attempt to measure something different. To create this index, we estimate annual

4 In a framework with no mobility, one would expect to find per-capita housing quantity or quality increases in high-elasticity and low-manufacturing areas. All agents would want more housing, and in elastic areas, they would get it, but in the inelastic areas they bid up house prices instead. Hence there would be a negative relationship between house prices and housing/capita. However, the stylized facts reject such a framework and instead support the view that demand for population movement is central for explaining housing prices. 5 See Section 2.4.1 for how we create the elasticity measure.

53 Log population growth vs house price growth, 2000-2006

0 J Cq 0

o. * 0 0 .. 00

0) * . -. -P 0 (CV & 0 -

-.2 0I .2 .4 Log population growth

Figure 2-3: Population Growth and Housing Prices -.

Log population growth vs manufacturing share, 2000-2006 Manufacturing share vs house price growth, 2000-2006 Slope=-0.21 (0.06) H igh-elasticity slope=0.00 (0.00); low-elasticity slope=0.00 (0.00)

0 0,o

M U, E) 2 C on 0 , 0 .~~~ C_ CL e 9 00 Lo *, .* a, ' =3 * o) OC) -I <90' 0 X _j

C',

0 .b 6 .2 .3 .4 .5 . .4o 2000 manufacturing employment share Manufacturing employment share

Figure 2-4: Housing Demand and Manufacturing Share

changes in property-level net operating incomes using the following specification:

Log(Income /Occupancy) = i3tYeart + -yiPropertyi+ cit

The year coefficients ft constitute the index. We estimate this specification separately for each CZ where at least 800 observations are available. This "repeat incomes" index is akin to a repeat-sales house price index. 6 This yields estimates of price changes for 98 CZ's from 1999-2015.

6 The repeat-NOI measure is informative for cross-regional variation in rents, but cannot be used to measure time series changes. The average estimated NOI growth from 2000-2005 is only 2 percent in the index, but this estimate is downward-biased because building quality declines as buildings age. As long as one focuses on cross- sectional differences in log NOI, this bias is not important under the assumption that aggregate depreciation is the same across regions. This is not unique to rents; downward bias caused by property depreciation is a well-known problem for repeat-sales indexes (Nagaraja, Brown, and Wachter, 2014) but this problem is more serious for rental properties than owner-occupied housing because of their faster depreciation rates (Shilling, Sirmans, and Dombrow, 1991). In a simple hedonic model, we estimate a 15 percent nominal increase in rents from 2000-2005 (and a 24

0. Log houses per capita vs manufacturing share, 2000-2006 Log housing/capita vs elasticity, 2000-2006 Slope=0.02 (0.01) Slope=0.000 (0.000)

CL 0 M * o*. ; --. Is o.- CL 0 .-. M 0 a) , .0 to :3W) oc: - C. .r- S; 0 ID tM o C 0 Mc, _J C> .2 0 0 0*-0 . . O* 0

0 .2 .4 .6 .8 0 .5 1 1.5 2 2.5 2000 manufacturing employment share Elasticity

Figure 2-5: Houses per capita and manufacturing, elasticity

Property Growth and Price Change Property Growth and Price Change Log changes, 2000-2006 Log changes, 2000-2006

* East South Central etast South Central

" New England i " 2 t- O Mountain * South Atlantic Soutt AManfir OVMountan West North Central Central Othest Soutn Centrat *East North Centra StMid-Atlantic

S Pacil *Mid-Ailantic OPacif *New. England .2 .4 .6 .8 .2 .4 .6 .8 Log price change Log price change

Figure 2-6: Building Quality and House Price Area, Lot Area

Figure 2-7 shows the relationship between price growth and rent growth from 2000-2006. The slope of the fit line is large and positive, supporting the claim that positive fundamental shocks affected both prices and rents in the same cities. Because the coefficient is greater than one, house prices moved more than one-for-one with property operating incomes in each city. Figure 2-8 verifies that prices and rents co-moved using the repeat-rent index constructed by Ambrose, Coulson, and Yoshida (2015). Unlike the repeat-NOI index, Ambrose, Coulson, and Yoshida (2015) measure rents directly. However, this index has the disadvantage that it is available at the CBSA-level and exists only for a handful of large CBSAs in the year 2000 because of data availability limitations (it is substantially expanded in later years). Nonetheless, it shows a similar relationship between prices and rents that we find using the NOI measure. percent increase from 1999-2005). Alternatively, prices can also be adjusted using existing estimates of depreciation rates. Jeffrey, Brent, Jerrold, and Webb (2005) suggest a 3.25 percent real appreciation rate per year. Assuming that cap rates are constant in building age, the 2 percent estimated rise in the repeat-NOI index implies a 21 percent depreciation-adjusted increase.

55 Log apt. income vs house price growth, 2000-2006 Slope=1.71 (0.21)

CL W0. 0

0* 0 o 0 0 00 4-J

00%

.3 -.2 -.1 0 .1 .2 Log Multifamily CRE NOI/Occupancy Growth

Figure 2-7: Multifamily NOI and House Price Growth

The relationship between rents and housing prices demonstrates that CZs with rising prices really did become more desirable to live in. This finding is important for distinguishing our model from models instead emphasizing changes to the possibility or desirability of home-ownership. If housing price changes were driven solely by changing characteristics of home-ownership, we would not expect such a relationship.

2.2.3 Housing Demand or Loan Supply?

Several theories of the housing boom argue that loan supply played an important role in explaining the housing boom. However, we argue that differential lending supply shocks cannot explain the cross-sectional price patterns. Areas with more manufacturing, or which had an elastic housing supply, had larger increases in loan application approval rates. Both of these patterns provide evidence that differences in mortgage demand, rather than mortgage supply, explains cross-sectional patterns. We study the relationship between prices and loan supply in Table 2.1. The estimates in both tables come from long-differences panel regressions estimating specifications of the following form:

Approved = Regioni(j) + LoanControlsj + 1(Yearj = 2006) x Manuf acturing(j,) Approved = Regioni(j) + LoanControls + 1(Yearj = 2006) x Elasticityi(j) where Manufacturingig() is the manufacturing share of the county the applicant is located in during the year 2000. The data is limited to loans from the years 2000 and 2006 in order to give this an interpretation as a long differences specification. The LoanControlsj variables are control variables measured at the loan (and not regional) level. In the first two columns of Table 2.1, the independent variable is manufacturing share, and in Columns 3-4, it is housing supply elasticity in

56 Log apt. income vs house price growth, 2000q3-2006q3 Slope=1.78 (0.29)

0)0 0 ' oo

C..) 0

-.1 0 .1 Log Repeat Rents Index

Figure 2-8: Repeat Rent Index (RRI) and House Price Growth

the CZ.7

We see that lower manufacturing and greater elasticity - which we have argued correspond to lower housing demand - are both associated with a lower approved fraction of loans. This finding allows two possible interpretations, both of which are consistent with our model. A natural one is that fundamental regional shocks (to amenities or jobs) are the main source of changes in housing and mortgage demand. A second possible explanation is that there is regional variation in the slope of the mortgage demand curve which is correlated with housing supply elasticity. A uniform, national shock in mortgage supply would then lead to both lower approval rates and higher prices in inelastic areas.

By contrast, we reject the interpretation that the relative housing boom in low-manufacturing areas was due to a relatively greater increase in loan supply in these regions. If this alternative explanation held, we would low manufacturing areas to have higher increases in loan approval rates from 2000-2006.

2.3 Theory: The Geography Channel

In this section, we explain how changes in the relative preferences for location have an impact on the national price level of housing. We also derive simple closed-form expressions for the effect of two prominent shocks during this time period, and how they would affect the national house price index through the geography channel.

7 See Section 2.4.1 for how the elasticity variable is created.

57 Table 2.1: Loan Demand and Manufacturing

(1) (2) (3) (4) Approval Frac. Approval Frac. Approval Frac. Approval Frac. YR=2006 -0.0133* -0.0135** -0.168*** -0.155*** (0.00683) (0.00628) (0.0114) (0.0103)

YR=2006 x Manuf. 0.401*** 0.374*** (0.0233) (0.0222)

YR=2006 x Elast. 0.188*** 0.173*** (0.00841) (0.00767)

County FE X X X X Individual Controls X X

N 1,427,379 1,356,189 1,449,814 1,377,386 R2 0.126 0.141 0.126 0.141 Source: Approval rates data are the fraction of loans that are approved in HMDA at the county level. Individual controls are for ventiles of DTI interacted with main applicant gender. Data is limited to 2000 and 2006.

2.3.1 Setup

Consider a spatial model with many cities indexed by i. Agents are mobile between cities. Agents consume a tradable good and a non-tradable good, with the price of the non-tradable good normalized to one. Housing is produced locally using local land, which is in fixed supply. Housing depreciates at a constant rate 6. Assume that agents each consume one unit of housing, regardless of location. While this assumption is obviously counterfactual, we showed in the previous section that local housing demand was strongly driven by population changes during this time period. By making this assumption, we are quantifying the increase in house prices purely due to changing locational demand. We are purposefully neglecting changes in demand relating to the size or quantity of housing, which has previously been the focus of the literature. An agent chooses a location i and has Cobb-Douglass utility over tradable and non-tradable goods: max c'c-a Catct n t such that wicnt + ct < wi - ri. This problem gives us the indirect utility function = wi-i Finally assume that amount of construction has no effect on intermediate inputs of housing production. We will relax this assumption later. Define a to be the local elasticity of housing supply and a -- E[a-3 to be the population-weighted average elasticity of housing supply.

Lemma 2.1. Consider any shock that changes the relative demand for location. Under the previous

58 assumptions, the change in the initial-population-weightedaggregate house price index is given by

log p , -i) d log p gh = - Cov(d

where the covariance is initial-population-weighted.

This equation illustrates that if prices in inelastic places rises compared to prices in elastic places, prices must rise on average. The equation is simply a rearrangement of the housing market- clearing condition and the definition of elasticity. The only assumptions it uses are that each agent consumes one unit of housing, and that housing markets clear. To set intuition, imagine a shift in population from a high-elasticity place to a low-elasticity place. In the high-elasticity place, there are fewer housing units needed, so prices go down, but not by much. In the low-elasticity place, there are more units needed, and prices rise by a lot. Prices rise by more in the low-elasticity area because it is relatively inelastic, and so, on average, they rise overall. Now we wish to relax the assumption that housing construction has no effect on the prices of intermediate goods. Here, we will impose additional structure in order to quantify these effects. Suppose there is a fixed amount of land within each city available to build new housing each period, and the housing production function is CES:

H, (Z, + AKK J)

where Ht is the number of new houses, Zi is the land used for construction, and Ki is the housing material input inputs. It can be shown that oi e (f/z) - 1). Hence the elasticity is decreasing in the density of the city.

Lemma 2.2. Under these assumptions, the effect on average house prices of a change in the relative demand for location is given by

E)] E Ki (oi +e) idlh dlogph Cov d~~~~~~(oi, d log p) p E[i(oi + o 7o o -E[i(ci +,e)] o-

where ki is an adjustment term for the capital-intensity of housing in the region. ki is proportional to (I + ) and Eki = 1.

This term is larger than the expression from Lemma 2.1. The intuition behind this lemma is similar. In the less elastic areas, housing requires more capital to be built, so if relative house prices increase in inelastic ares, the total demand for housing capital rises. Depending on the elasticity of this supply, it will drive up the price of this capital, increasing the total price of housing overall. Critically this formula relies on estimates of 'y and e.

59 2.3.2 The Role of Manufacturing

In this section, make the simplifying assumption that a -+ 1, implying that utility is a transformation of log wi - log p. Suppose a shock hits that affects the productivity of manufacturing, taking the following form:

d log wi =3 + Omi (2.1) where mi is the manufacturing concentration. 8 Then, because of the second assumption, d log pl =,' + #mi. Here, 0 is the same as the effect on wages, but /' need not be.

Theorem 2.1. If a -+ 1, -y -+ oc, and a shock takes the form of equation (2.1), then the change in house prices is given by: dlogph CO(mi, a-) where 0 is the coefficient from the regression of d log ph on mi.

In the next section, we show that this covariance is positive and large. Therefore, if productivity of manufacturing falls, lowering the price of housing in such areas, the national house price index rises. By assuming -y approaches infinity, we have shut down the channel that operates through intermediate housing materials. If 7 < oo, the effect would be larger. In fact, #mi could be directly substituted in for ph in the expression from Lemma 2.2. The assumption that a 1 was made primarily to simplify the algebra. With smaller a's, the term might be slightly smaller because wages and house prices in inelastic areas were higher to start with. However, this force is relatively small when taken to the data.

2.3.3 The Role of Interest Rates

In this section, we consider the effect of a permanent change in interest rates. We assume that the relationship between house prices and rents is given by the following:

h ri where ri is the rent in location i and R is the national interest rate. A one-for-one relationship between rents and housing prices is not implausible given our empirical finding that rents and prices co-move closely.

8 This form would fit the Autor, Dorn, and Hanson (2013) framework, or an exogenous shift in the relative productivity of manufacturing in any gravity model, combined with the assumption that 6 = 0, i.e. there is no mobility in equilibrium.

60 Theorem 2.2. If a = 0 and - -+ oo, then the effect of interest rates on house prices is given by

Cov ( i dlogph = -dlogR

In other models, changes in interest rates affect house prices because rents are pinned down, usually by an outside option. 9 This is not the case here, where house prices are pinned down by construction costs, and rents can move freely. This is clearly seen by considering the case where inverse-rent and elasticity are uncorrelated. In that case, interet rates have no effect on house prices at all. The fact that the level of rents matter is a natural explanation for why certain regions experienced larger growth during this time period. As interest rates fell, areas that were more expensive to start with became relatively more affordable, encouraging movement in that direction. Here, the assumption that a = 0 is not innocuous, if a -+ 1, this channel would not exist. One of the main predictions of this channel is discussed in Aladangady (2014), that in response to monetary policy, inelastic areas have bigger fluctuations in house prices than elastic areas. Again, that -y is zero is innocuous, a realistic calibration would have a larger effect on house prices, but the expression would be more convoluted.

2.4 The Magnitude of the Geography Channel

In this section, we put numbers on the expressions from the last section, arguing that the geography channel is large. First, we create a measure of elasticity that covers the entire country. We then use that measure of elasticity to compute the values of those expressions.

2.4.1 Constructing a measure of elasticity

In order to estimate the covariance between an economic shock affecting wages and the elasticity of housing supply, we must first have an estimate of housing supply elasticity. Existing measures of this elasticity are inadequate for our needs because they do not provide comprehensive coverage of the entire United States, mostly focusing exclusively on MSAs (e.g. Saiz, 2010). This is especially crucial because while the Saiz measures cover much of the population, it systematically undercovers areas that are high in manufacturing concentration. In this section, we construct a measure for each CZ in the country, providing full coverage for the United States. One way to do this would be simply to plug in the population density of each CZ into the formula from before. However, we do not wish to take the Z's literally as the amount of land in each CZ, recognizing that in the real world, there is variation in the suitability and availability of land for housing development. 10

9 1t is unclear to us why, in these models, the outside option is not similary affected by the interest rate. 1 0 For example, the formula from before would imply that the CZ with Manhattan in it would be less than one-one hundredth as elastic as the next most inelastic CZ.

61 El1.60 - 1.78 M 1.39 - 1.60 0 1.20 -1.39 M 0.04 - 1.20 EM No data

Figure 2-9: Map of Estimated Elasticities

Rather, we construct elasticities similar to the methodology of Saiz (2010) by directly estimating the effect of a change in house prices on a change in building permits, projecting this relationship onto two measures associated with land availability: land use regulations and population density. Specifically, we estimate following regression for the years 2000-2015:

d log Hi = d log pf x f(WRLURIs, log pop densityi) + Ec where WRLURI is the Wharton Residential Land Use Regulatory Index and pop density is the population of a CZ divided by the total square miles in it." f is estimated non-parametrically using cubic splines, with a dummy for areas without a WRLURI measure. Then for each CZ, we construct the elasticity by

-i = f(WRLURI, log pop densityi)

As noted in Saiz (2010), population density and land use regulation are fairly correlated. 0-i is negatively correlated to both WRLURI and population density, with a higher correlation to WRLURI. A map of the elasticities we estimate are presented in Figure 2-9. Compared to Saiz (2010), we estimate a smaller average elasticity,12 and a smaller range of elasticities as well. However, our measure is highly-correlated to his. In Figure 2-10, we present the comparison of estimated elasticities, for the areas of the country on which they overlap. Each dot represents a set of counties in the infemum of the MSA and CZ partitions, the largest partition that refines both.

"The WRLURI is calculated for places. We took a population-weighted average for all places within a CZ. Population density is the population-weighted average of county-level Census data. 12 This is consistent with Ganong and Shoag (2017), who document that land use regulation has increased over time.

62 0 0" 0

0 0 00 0 .00

U - 0

C - 0 5 1'0 15 Saiz (2010) Elasticity

Figure 2-10: Comparison of estimated elasticities with Saiz (2010)

2.4.2 The Geography Channel

We wish to see how much the geography channel contributed to the increase in house prices between 2000 and 2006. During this time period, real house prices increased 0.28 log-points. 13 Now that we have estimated elasticities for each CZ in the country, we can plug these values into the previous formulas. We use county-level house price data from the FHFA. In order to construct an index for each CZ, we take the population-weighted average increase by county. If a county does not have house price data, we do not include it in our averages. We look at total log-change between 2000 and 2006. In total, we have house price indices for 648 CZs, covering 99.8 percent of the total population. 14 The geography channel of house price appreciation, as calculated using the expression from Lemma 2.1, explains an aggregate increase of 0.052 log-points, about a fifth of the total increase in house prices. Taking into consideration the increase in demand for housing construction materials increases this number. In Appendix B.2, we calibrate at to 0.18. Obviously, it also depends significantly on -y. Unfortunately, we have not found a good way to discipline this parameter, so we present a range of estimates. As 7 -- o0, materials adds nothing to the previous estimate of 0.052 log-points. If, on the other hand, =.25, which seems plausible in the short-run, the number doubles to 0.104 log-points. To check the robustness of our results, we also use the Saiz (2010) elasticities instead of the ones created in Section 2.4. 1. For this to be correct, the assumption would have to be that no one moved in or out of the MSAs covered by this measure. Nonetheless, because this measure of elasticity existed and was popular before our paper, it serves as a reasonable check that these results are not

13We took the national FHFA data, and deflated by the CPI. 14In comparison, MSAs cover about 80 percent of the population.

63 due to the choices we made in constructing our measure. 15 In fact, using these elasticities would suggest a larger role for the geography channel. When -y -+ oc, the Saiz elasticities suggest an increase of 0.072 log-points.

The Role of Manufacturing

The decline of manufacturing played a large role in explaining this variation in house prices. To show this, we collect employment data from the QCEW to calculate manufacturing shares. Regressing the change in house prices on the manufacturing share gives an estimate of -1.57, with a confidence interval of [-1.91, -1.23].16 A one standard-deviation increase in manufacturing share, about 7.6 percentage points lowered local house prices by 0.118 log-points. The relationship between manufacturing and elasticity is shown in Figure 2-11. As can be seen, there is a strong relationship between the two. The covariance of manufacturing and elasticity divided by the average elasticity is 0.013, which means that manufacturing alone increased the national house price index by two percent. This is about 40 percent of the total geography channel contribution.

o . 00 %O

0 .5 1 1.5 2 2.5 Estimated Elasticity by CZ o Manufacturing Share, 2000 Fitted values

Figure 2-11: Estimated Elasticity and Manufacturing Share by CZ

We also do this exercise using the China shock from Autor, Dorn, and Hanson (2013). The correlation of this shock to elasticity is still significant, but accounts for only a 0.5 log-point increase, about a quarter of the effect we found for manufacturing overall. 17

5 ' The fact that, in general, Saiz (2010) measures larger elasticities, has little bearing, since a scaling transformation of the elasticity would have no effect on the expression in Lemma 2.1. "The regression is population-weighted and uses robust standard errors. 17 For some perspective, Autor, Dorn, and Hanson (2013) also claim that the China shock accounts for about a quarter of the total decline in manufacturing employment.

64 U') M~ 01

CD0

00 00

0 0 0 LOO

IC3 U' 00.5 1 .0 .

030 0

Estimated Elasticity by CZ 0 Inverse Rent Fitted values

Figure 2-12: Inverse Rent versus Elasticity

The Role of Interest Rates

Interest rates also played a substantial role in the geography channel. To calculate this, we use 30-year mortgage rates from Freddie Mac. The formula in Proposition 2.2 would allow us to use either rents or house prices. Our view is that rental rate levels are more comparably measured in the data, and so we take rents from the 5 percent Census sample Ruggles, Genadek, Goeken, Grover, and Sobek (2015). We translate PUMAs into CZs proportionally by population. The relationship between inverse rents and elasticity is shown in Figure 2-12. Not surprisingly, rents are higher in inelastic areas. The term multiplying the change in interest rates evaluates to -0.049, meaning that a decline in interest rates will cause an increase in house prices as higher-priced areas become more affordable. Using our prefered measure of R, the total effect on national house prices from Proposition 2.2 is .0154 log-points. This is of similar magnitude as the manufacturing shock from the last section. Note these are not directly comparable, since the two formulas make opposite assumptions about a. Taking a step-back, we have shown that the geography channel explains between 20 and 40 percent of the increase in national house prices, and that much of this variation is explained by the decline of manufacturing and lower interest rates. Of course, these two forces are not sufficient to cause the entire change. However, plenty of other explanations for the desirability of inelastic locations exist: including better amenities 18 or increased sorting. 19 Furthermore, evidence exists to suggest that other forces may be amplified by the migration itself (Howard, 2017).

1 8 Many papers, such as Albouy (2016) find coastal cities to have better amenities. 19 Diamond (2016) documents better-educated workers have sorted into specific cities, many of which are inelastic. The presence of these workers raises the amenities value. Gyourko, Mayer, and Sinai (2013) presents a model where sorting increases the skewness of house prices and incomes.

65 2.5 The Timing of the Housing Boom

Our theory makes precise predictions on the timing of the housing boom. Aggregate house prices should increase most when the cross-sectional covariance between local house price changes and elasticity is the most negative. In this section, we show that this covariance was most negative from 2000-2006, when the boom occurred. Furthermore, we estimate the size of this channel for a previous period, from 1994-2000, and show that the effect is economically insignificant. In the previous section, we showed that there was a significant negative correlation between local house price changes and elasticity from 2000-2006. This did not occur in the period beforehand. Using the same formula from Lemma 2.1 over the period of 1994-2000, there would have been an in house prices of about 0.005 log-points, less than 0.001 log-points per year.

The same point is illustrated with the blue line on the left side of Figure 2-13. In this figure, we regress changes in different local variables on house prices year-by-year. Hence, the point of the green line in the year 2000 represents the population-weighted regression coefficient of the the change in log house prices from 1999-2000 on housing supply elasticity. Before 2000, these coefficients were close to zero, but between 2000 and 2006 they are strongly negative. Interestingly, during the bust years, they are significantly positive, suggesting the geography channel contributed some to the bust as well.

Also pictured on the left side of Figure 2-13 are the cross-sectional relationships of rents and population with elasticity. Interestingly, the movement of people seems to lead changes in house prices. The biggest population shift toward inelastic areas occurs between the years 1996 and 2003. This may represent some sluggishness in house price changes.20 This is not a problem for our theory; if local house prices are sluggish to react to fundamental changes, our theory would simply predict that national house prices would be similarly sluggish. We include the rents data to show that it exhibits similar timing patterns, although unfortunately, our data extends only back to 2000. The timing of rents reverses before the downturn in the housing market, which may be further evidence of housing sluggishness.

The right side of Figure 2-13 does a similar exercise to assess whether the theory predicts similar timing for the contribution of the decline in manufacturing. Of couse, the location of manufacturing has not shifted significantly over time, but its effect on house prices has. Here, we run the regression of the change in local house prices on manufacturing share year-by-year, and plot each coefficient. From 2000-2006, the coefficients are significantly negative, and combined with the fact that manufacturing is concentrated in inelastic areas, this would predict rising house prices exactly during those years. Before 2000, there was even a postive relationship, though much less economically significant.

20 Interestingly, and in support of our theory, there was a similar movement of people towards inelastic areas before the 1980 housing boom. Consistent with the idea that housing supply has become more inelastic Ganong and Shoag (2017), there were larger changes in population and a smaller house price boom.

66 - House Prices (left axis) - Rents (left axis) - -o -- Population (right axis)

07 0 0) t

U)'I f

2006 2012 1994 2000 2006 2012 1994 2000

on Figure 2-13: The year-by-year regression coefficient of house price, rent, and population growth elasticity (left) and the regression coefficient of house price growth on manufacturing (right)

2.6 Conclusion

of Much of the literature on the housing boom has focused on why the demand for the quantity This housing or home-ownership increased, but little has focused on the location of that housing. the overall paper demonstrates that considering this geography can explain a significant fraction of boom. The result also questions the appropriateness of testing theories using the cross-section of hous- local ing without explicitly considering the role of mobility. At the very least, it demonstrates that housing markets cannot be viewed in isolation. Our results have abstracted from several important facts, including the dynamics of the boom. We believe our results on rents and house prices could be useful in calibrating a model of expectations that could help explain the overshooting and subsequent housing bust.

67 68 Chapter 3

Regional Depressions: Sticky Wages in a Model of Agglomeration

I document that shifts in the geographic distribution of economic activity are more frequent around recessions. This effect is more pronounced in professions with greater nominal wage rigidity. As a possible explanation, I develop a new mechanism for equilibrium switching during recessions in a model of agglomeration using downwardly sticky wages. In a dynamic setting, the model requires a sufficiently large shock to switch equilibria. Within the model, place-specific time-specific firm subsidies can be welfare enhancing. 1

3.1 Introduction

In every post-war U.S. recession, there has been large regional variation in economic outcomes. For many recessions, some areas of the country experienced dramatic falls in output and never fully recovered, implying a seemingly permanent shift in GDP compared to the rest of the country. Other areas of the country experienced milder recessions and rebounded faster, permanently gaining a larger share of U.S. GDP. A good example of this phenomenon is Hartford, Connecticut. In the 1980s, it was a manufacturing hub and produced lots of firearms. During the early 1990s recession, the area lost firms, and unemployment rose to 10 percent during a fairly mild recession for the rest of the country. Throughout the nineties, a decade of high growth and general prosperity in much of the U.S., Hartford was never able to regain much of the industry that it lost, and its population shrank by at least 10 percent. Much of the firearm industry moved to the South or overseas.2

11 would like to thank Ludwig Straub, Jack Leibersohn, Vivek Bhattacharya, Ivan Werning, Ricardo Caballero, Alp Simsek, Arnaud Costinot, and Ariel Burstein for their comments. This material is based upon work supported by the National Science 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 necessarily reflect the views of the National Science Foundation. 2 Today, Hartford has regained some economic strength due to the insurance industry, but its days as a manufacturing city are over.

69 In this paper, I develop a mechanism to explain this phenomenon based on models of multiple equilibria, similar to the economic geography literature, and wage stickiness, a common friction from the macro literature. I show how a model with both elements can lead to geographic reallocation during recessions.

The regional aspects of business cycles have long been of interest to economists. Blanchard and Katz (1992) model wage and worker location adjustment to regional shocks, focusing on convergence of wages and unemployment across states. More recently, Beraja, Hurst, and Ospina (2015) document regional variation in wage and employment outcomes during the Great Recession and use that relationship to estimate a Phillips curve. 3

The two key ingredients in my model are agglomeration externalities and downward nominal wage rigidity. Moretti (2012) discusses many of the possible forces for agglomeration, emphasizing the recent prominence of technology clusters. Delgado, Porter, and Stern (2010) estimate large regional effects from the presence of such clusters. Greenstone, Hornbeck, and Moretti (2010) use runner-up locations of big new plants to identify the effects of local agglomeration externalities. My model of downward nominal wage rigidity adopts the constraint from Schmitt-Groh6 and Uribe (2011), who also provide an overview of some of the empirical evidence. Kaur (2014) finds more direct evidence of such rigidities in India.

The two-city two-type-of-firm setup with multiple equilibria bears resemblance to the New Economic Geography literature that begins with Krugman (1991b). Mobile firms make the model somewhat resemble Forslid and Ottaviano (2003) in particular. A common result in this class of models is path-dependence, and in many such models it occurs over long time periods. For example, Krugman (1991a) uses the manufacturing belt in America as an example; Bleakley and Lin (2012) argue path-dependence is the reason for the modern existence of cities at portage locations; and Davis and Weinstein (2002) find mixed evidence for path-dependence looking at Japan over centuries. I have in mind path-dependence that is on a business-cycle time scale, much shorter than any of these papers.

The rest of the paper is organized as follows. In Section 3.2, I establish empirically that state GDP shifts in significant and persistent ways and that the timing of this is related to recessions. I also provide suggestive cross-profession evidence that wage stickiness is related to this phenomenon. In Section 3.3, I present a two-period model that highlights a new mechanism I have in mind to explain these facts. In Section 3.4, I present a dynamic continuous-time model to investigate the dynamic implications of such a mechanism. Proofs from Sections 3.3 and 3.4 are collected in Appendix C.2. In Section 3.5, I discuss the policy implications. Section 3.6 concludes.

3 I should note two things as they relate to Beraja, Hurst, and Ospina (2015). First, the stylized facts that I present are in tension with their model of idiosyncratic temporary shocks to specific regions. Secondly, any relocation, such as the type I consider in my model, will imply a difference between the regional Phillips curve and the aggregate Phillips curve.

70 3.2 Motivating facts

Three facts motivate this paper. First, the geographic distribution of economic activity changes over time. Second, these changes are related to the business cycle. Third, these changes are most related .to the business cycle in professions in which wages are most sticky.

3.2.1 Economic activity changes over time

Post-war, almost every state, during different periods, has grown faster and slower than the rest of America. This fact is strikingly apparent in Figure 3-1. For each state, I have plotted its share of national GDP in each quarter. I use quarterly state GDP data from the Bureau of Economic Analysis, and consider the share of total U.S. GDP by state. For example, in 2014Q1, California had a 20.5 percent share. In this time period, many states experience both long periods of relative growth and long periods of relative decline. IIRbesions

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-wrsnat-Flork -. G.orgh ma -.- ntas

--- Tinness -Mswri -mtart -Neaska -Nevada -New Ibnpttre -Newssey -New Mesico -NewYwrk -Ncrrh Croltia -Nnh Dkta -Oklahorna ~-Pemrwtvania oA'~c$ 4 q- A~ & - - Rhode Wand &~~g'~ -Ssih Caotia -South Dfaca -Toas 0.1 i -Vemont -uinia -Wmraton -West Vfii. -Wicosin

Figure 3-1: State shares of total U.S. GDP

Before seeing the data, one might wonder if shifts in the geographic concentration of output are permanent. But a quick glance at Figure 3-1 or any panel unit root test would establish that there is least some permanent component in whatever process is driving these shares. 4 This establishes

4There is debate over whether there are permanent shifts in GDP per capita by state. See Song and Yangru (1997) and Romero-Avila (2012). Even if GDP per capita is stationary, the patterns we see in population movement would

71 the first motivating fact: economic activity changes location in a very persistent way.

3.2.2 Activity changes more during recessions.

I wish to add a new element to this fact. State's trends shift during recessions. This fact is related to other better-known facts, such as that most job losses in manufacturing occur during a recession, highlighted in Jaimovich and Siu (2012). But I believe this is the first paper to suggest a cyclical relationship between GDP growth and changing trends in the location of economic activity. Figure 3-2 shows the standard deviation of growth rates in U.S. states. The higher this measure is, the more different is the distribution from one year ago. One striking feature of this graph is that many recessions have big spikes in this time series. If you believe all movements in states' share of GDP are permanent, then this series is evidence that the shifts are bigger during recessions.

0.020

Recessions

-Weighted standard deviakion of 4-quarter change in og stae GDP

0.015

0010

Figure 3-2: Standard Deviation of Growth across U.S. States

The assumption that all movements represent permanent shifts is a big one; it rules out temporary shocks affecting only some regions of the country, measurement error, and a number of other things. Since these things exist, the cyclicality of the standard deviation of growth is only suggestive. If there are both transitory and permanent shocks, this does not prove that permanent shocks happen more during recessions. The next time series aims to provide such evidence. be nonetheless interesting.

72 I first develop a methodology to identify when a state switches from above-average growth to below-average growth. I use a method similar to Bry and Boschan (1971), who develop a method for dating business cycles, henceforth referred to as the "BBQ" method.5 The BBQ method filters data to uncover the underlying trends, then looks for dates on which the trend switches direction. It throws out switches that occur too close to one another or too close to the end points, and finally goes back to the original data to pinpoint when the switch occurred. Because I am using the methodology for a different purpose than dating recessions, I use different parameters than the canonical paper. Details of how I implement this are in Appendix C.1. Having identified switching points for each state, I then create a count variable of how many switches, over all the states, occur in each quarter. Because there are only fifty states, and a quarter is a relatively short amount of time,6 I find it easier to visualize with a certain amount of smoothing. Presented in Figure 3-3, I plot the average rate of trend reversals per year in a rolling window of three years, centered on the x-axis date. I also split them up by trend reversals from a negative trend to a positive one, labeled "trend reversals up," and the opposite, labeled "trend reversals down."

0- 15

-2

-4-

Figure 3-3: Reversals in Trend of Share of GDP by State: Moving average

As you can see in Figure 3-3, there is a highly cyclical component to the count of trend reversals.

5 quarterly. 6 The "Q" stands for On average, significantly less than one state switches per quarter.

73 There does not seem to be a major difference in the timing for upwards versus downwards reversals. And they seem to occur most often in the years immediately preceding a recession, as growth begins to slow down. The biggest spike is during the Savings and Loans crisis on the eve of the early 1990s recession, but the pattern is similar for many recessions. The years immediately before a recession are typically associated with a "slowing down" of the economy and low growth. It appears from the graph that it is during this period of slowing down that trend reversals are most likely to occur. Correlations confirm that there is a negative relationship between the number of trend reversals and economic growth.

3.2.3 Relationship to sticky wages

Finally, the cyclical properties of geographic reallocation are strongest in professions that have the stickiest wages. The San Francisco Federal Reserve, see Daly and Hobijn (2015), calculates a measure of nominal wage rigidity for several professions, based on the percent of workers who have a constant wage over a twelve-month period. Figure 3-4 shows that this measure 7 is negatively correlated to the cyclicality of geographic reallocation for the period from January 2002 to February 2015.8 Hence, during the recent recession, the professions with the stickiest wages have had the most geographic reallocation as compared to their reallocation during normal times. My measure of within-profession geographic reallocation is calculated using a similar method as I used for Figure 3-2. Specifically, it is a weighted standard deviation of 12-month growth rates across states. Instead of state GDP, I use the employment of the profession, available from the Bureau of Labor Statistics Current Employment Statistics. For each profession, I take the time-series correlation with the 12-month growth in monthly U.S. real GDP, available from Macroeconomic Advisers, to construct my y-variable. The correlation coefficient is -. 5 and it is significantly different than zero at the 10 percent significance level. While the correlation is not evidence of causation, it is suggestive that wage stickiness may play an important role in explaining why geographic reallocation occurs during recessions.

3.3 A simple model

I develop a two-period model to highlight how wage stickiness in a model of agglomeration can lead to equilibrium switching during recessions. Sections 3.3.1, 3.3.2, and 3.3.3 describe a model that, because of firm agglomeration externalities, features multiple equilibria. Sections 3.3.4 then introduces downwardly sticky wages in the second period. Proposition 3.1 shows that as long as the economy is growing fast enough, sticky wages will not destabilize the old equilibrium. Proposition

7I take their measure from 2007, but the relative ordering of professions is highly stable over time. 8Data would have allowed the time frame to span from March 1992 onward, but wage rigidity data was not available before 2007. I thought post-2001 recession would be a good balance between having enough data and having validity of the wage stickiness measure. The negative correlation is robust to going back to 1992.

74 0.3 - DEducation

0.2 -

00 -1-

0 - Health Care and Social Assistance

-O.1 ormaon

-0.2 - Non-durables CArs and Entertainment

-03 Professional and Business Services

- - olesale trade Financial Activities

0 Retail trade -. Transponation and Utilities onstrction (3)A comodation and Food Service

-0.7 -Durables

-0.8

6 8 10 12 14 156A Fraction of workers with wages fixed for 12 months in 7

Figure 3-4: Sticky Wages and Cyclicality of Geographic Reallocation

3.2 shows that in recessions, sticky wages can do just that. Finally, proposition 3.3 shows that under certain parameter restrictions, a dramatic switch in agglomeration is the only stable equilibrium.

3.3.1 Setup

There are two periods, t = 1, 2, with aggregate productivity Zt in each. Denote the growth rate g - - - 1. In the first period, wages are perfectly flexible, but in the second period, they are subject to a downward wage constraint. There are two cities j E {1, 2}, each which has a unit mass of labor. There is a continuum of firms of measure 1, i E [0, 1], who choose which city to locate in and can move from the first period to the second. All firms are monopolistically competitive, but they come in two types. Firms with i < I are "agglomeration" firms which have a positive externality of co-locating with other firms. Firms with i > p are "plain" firms which do not give or receive such an externality. The production function for an agglomeration firm locating in city j at time t is

yi,j,t = ZtA( t)ti,, where f a is the mass of agglomeration firms located in city j, A : [0, P] -÷ R is a continuous, differentiable, non-decreasing function representing the agglomeration externality, and fi,Jt is the labor input for firm i. The production function for a plain firm is

Yjj,t = Ztfi,,

75 Final goods production is CES over all types of goods, with elasticity of substitution -.

Yt= y di

Labor, of mass 1 in each city, is supplied inelastically, and labor markets within city are competitive. Workers consume a separate good, whose price is normalized to 1.

3.3.2 Flexible-price equilibria

Plain firms choose to locate in the city with the lower wage. Agglomeration firms choose to locate in the city with a higher A(fj,1)/wji ratio. Solving the monopoly problem, labor market clearing implies that (3.1) ( K (fjiA(fj')- + ff) where K is some constant. Two conditions define equilibria: firms maximize profits and labor markets clear. I find equilibria by guessing a fa 1, solving for the wage and where plain firms choose to locate, and then verifying if our guess of fl1', is consistent with A(fj,1)/wj,1 in each city. If fa,1 E (0, p), which is the scenario I most wish to explore, then in must be that

A(fi,1 ) _ A(f 2,1 )

wi,i w2 ,1

This problem lends itself to being analyzed in three different regions of f1a 1. If

Ifa',A (f a),-l _ (IL - f a)A(/- - f, 1)"I ; 1 - then the economy is in a middle region where plain firms will distribute themselves between the two cities in such a way that wages equalize. To see this, note that this condition is the same as there existing a ff 1 in [0, 1 - p] such that

fja,1A(fja,1)1 + ff, - (p - f ,1 )A(p - f1 a,1)"- + - f,1 which, through the labor market clearing conditions, will imply equal wages in both cities. Denote f as the value at which IA(f)0- 1 - (p - f)A(p - f)"'- 1 - p. If fi,1 is bigger than f, all the plain firms will locate in city 2. Wages will be given by

(3.2) ,1 A(fa 1)or

(3.3) ( ) ((p - ff,1 )A(p - fl,1)G-l +1-p)

If fi,1 is smaller than p - f, all the plain firms will locate in city 1, and similar equations will

76 dictate wages. Denote the region I as , [0, y - f], region II as f1 ,1 E (p - f, f), and region III as f a,1 E [f, I'. In general, there will be at least three equilibria, one in each region. The one in region II occurs where fl, = ffa = i and f = f =- 1 . The wages will be the same in each region, as will the agglomeration term in the production function. Therefore, both types of firms can maximize profits by locating in either city, and so there is an equilibrium. The other two equilibria are symmetric, so without loss of generality, consider one in region

III, where fl', is big. At f, wi,1 W2 ,1 and A(f) > A(p - f). Define 0i1(fla,) = W, and W2,1 k(f, 1 ) = A(f a). Initially, at f,A > iv-. If they ever cross, that is an equilibrium, because profits are equal in each city. If they do not, then A > C for all f C [f, A], so fl, = pI is an equilibrium because all the agglomeration firms are locating in the city where their profits are higher. In general, I am more interested in cases where they cross. There will be another equilibrium in Region I by symmetry. There will be an interior asymmetric equilibrium under the condition that

(3.4) 1 - A(0) which I will adopt for the rest of the paper.

3.3.3 Stability of equilibria

I define an equilibrium, summarized by f', to be stable if there exists a neighborhood around fi', such that for any flat in the neighborhood, it must be that ff, > f * implies A(f-) A(f ) and by the labor market clearing conditions. 9 ff, < f '* fitW1,timplies > W2,t where W2,tw is determined In other words, if a few firms leave for the other city, that does not create the incentive for more firms to leave. Any other equilibrium I consider to be unstable. The symmetric equilibrium is always unstable. For fl,1 = -p-c,wages are still equalized across cities, but the agglomeration term is now larger in city 1. However, there is always a stable equilibrium in each of Regions I and III. If (3.4) holds, then there will be an equilibrium where the A crosses d from above, so that equilibrium will be stable. If (3.4) does not hold, then f 1,* = I will be a stable equilibrium. In Figure 3-5, I illustrate the three equilibria.' 0 The three regions correspond to the different areas in the relative wage function. Region II is the area where ?17I = 1 and is fiat. Region I is to the left of that and Region III is to the right. From the diagram, the three equilibria are clearly visible. The one in Region I is stable because locally to the right fv-1 is bigger than A, meaning the

9 0r in the next section, by the nominal rigidity. 1 0The parameters used for this figure and in subsequent figures are o = 2, p = .7, and A(f) a1 if f < 2 . The functional form says that firms get no externality unless they co-locate with exp(1.3(f(1 - ()) if f > " the majority of agglomeration firms, and after that they receive a constant proportional increase for each additional firm. The functional form of A greatly simplifies an expression coming in Section 3.3.4.

77 2 relative wages

-- -relative productivity

1.5 7

0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 3-5: Cv, and A relative wage exceeds the relative productivity, and firms would rather locate in city 2, whereas the opposite is true locally to the left. Since this is not true of the equilibrium in Region II, it is not a stable equilibrium.

3.3.4 Sticky wages

Period 2 has sticky wages, using the Schmitt-Groh6 and Uribe (2011) assumption. So the nominal rigidity for j = 1, 2 is

Wj,2 7Wj,1 for some y < 1

Since the rigidity is nominal, it is no longer innocuous to normalize the workers' consumption good's price. Rather, I assume that the central bank targets that price.11 Wage stickiness implies that the labor market clearing condition need not hold when the constraint binds. When it does, fj,t may be less than 1, which gives us a natural measure of employment:

Uj, 2 = rf: 2A(f 2 )'_1Z2 j,2

For any given wi,1 and w 2,1 , it is possible to solve for the equilibria. However, it is particularly interesting to focus on the situation where w1,1 and w2,1 come from a stable equilibrium in Section 3.3.3. In this case, there is always an equilibrium with the same distribution of firms as the previous

"This leads to the obvious policy implication that if the nominal rigidity is socially costly, the central bank should inflate it away. Since this is not the right model to consider the costs of inflation, and the policy implications are trivial, I will contain any discussion of central bank policy to this footnote.

78 period. But depending on the value of the growth rate g, the equilibrium may or may not be stable. Define ft'* to be the stable equilibrium distribution in Region III of agglomeration firms at t 1, with wi,1 and W2 ,1 given by (3.2) and (3.3). We know 'ti(fj'"*) = A(f'*) and that V'(f 1 *) ; A'(f= 'fj*).

Theorem 3.1. If g > - - 1, then f1,2 =f,'j* is a stable equilibrium. The idea behind Proposition 3.1 is that when the economy is growing, the wage constraint is not locally binding. Hence, both A and IV2 are locally the same as in the flexible-price scenario, and the equilibrium is stable. This intuition is illustrated in Figure 3-6. The relevant lines are the relative productivity line, which is unchanged from before, and the new relative wage schedule drawn as a dashed line. The flexible wage schedule is included for reference. The new wage schedule coincides with the flexible wage schedule in the area around the previous period's equilibrium. Outside of that neighborhood, it is flatter, but that property is unimportant for it being a stable equilibrium.

2 - ...... relative flexible wages - relative productivity relative sticky wages

1.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 3-6: D and A when wages are downwardly rigid and g > 7 - 1.

Theorem 3.2. If g <-y - 1 then, f1f,2 = f,'1* is an unstable equilibrium.

Under this condition, the wage constraint will bind for all f, 2 in a neighborhood around fa'. Therefore z-v is flat in that neighborhood. Proposition 3.2 is illustrated in Figure 3-7. The previously stable equilibrium is now unstable. There are still two stable equilibria, though. With these parameters, one occurs at f1,2 = 0, where firms fully agglomerate in city 2, and one occurs with in city 1, though in this case, not fl, 2 in between f', * and p, so there is even more agglomeration full agglomeration.

79 2 - -...... relative flexible wages relative productivity relative sticky wages

1.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 3-7: i-v and Awhen wages are downwardly rigid and g

An interesting knife-edge case occurs when g = y - 1. In that case, the wage constraint in city

2 binds for all fa,2 > f' 1 *, and the wage constraint in city 1 binds for all f,2 < fl,'i. Depending on how quickly wages rise in each of the cities, the equilibrium may be stable, unstable, or unstable in only one direction. We can break up the expression for log ibi into two parts:

1 log 1=- log(f 1 A(f 1 )'- ) - -log((p - f 1 )A(p - + 1 -

from city 1 from city 2

But in period 2, when the wage hits the constraint, the term from that city is replaced with the constraint. Hence, when g = -y - 1,

~ 2 log W1,1 - - log((P - fi, 2 )A(p - ff, 2 )1 1 - if f 2 <) f*a,,

I log(fM, 2A(fa,2 ) ) - g2,1 if f1, 2 - f,'2

This is continuous and piece-wise differentiable. But at f '* there is potentially a kink point. So it becomes important to order the following three slopes:

1. the slope of log A: A'(f *) A'(p - fa'*) A(f *) A(p -f'I*)

80 2. the slope of log fV 2 to the right:

i _ A'(fa,*) - ,* It AA(ffl<) f a'*)

3. the slope of log 172 to the left:

* A'(1-f'*)

a* 1 , A( lfi*) -1

The ordering of all of this will depend on the shape of the A function, y, and 0-.

Theorem 3.3. Consider the case when g = - 1. If the slope of log A is less than slope of log d3 to the left and to the right, then fa2 = fa'* will be a stable equilibrium. If the slope of log A is greater than the other two, then fl f1j'* is an unstable equilibrium. If it is between the two, then the equilibrium is unstable to just one side.

To be unstable to just one side means that if a small contingent of firms left for one of the city's in would provide incentives for more firms to leave. But if they left for the other city, it would provide incentives for firms to come back. Using the same parameters1 2 that have been used for all the figures, Figure 3-8 shows a scenario in which the equilibrium is unstable, but only to the left. In this case, there is only one stable equilibrium, which involves full agglomeration in city 2.

3.4 A dynamic model

It is an empirical fact that firms do not en masse relocate in short time periods. The stylized fact that came out of the BBQ method is that states' trends switch during recessions, not that there is an immediate jump in levels. Hence, this section presents a more realistic model with more realistic dynamics. Ergo I switch to a continuous time model, in which agglomeration firms receive Poisson Calvo-like shocks that allow them to move.1 3 Here, I will maintain the same assumptions on A and p to preserve the idea of partial agglomeration. However, since the model is now dynamic, I will from now on refer to the equilibria in Figure 3-5, as "steady-states." This setup allows for a myriad of rational expectations equilibria when interest rates are sufficiently low. There may be a global-games approach to pick a unique equilibria, but I prefer a less realistic but more tractable alternative for limiting the set of equilibria: that firms are myopic.

1 2 See previous footnote. In this case, the three slopes reduce to a, the exponential parameter in A(.); -( f a',+ a); and _ 1 These are relatively easy to order. 1 For tractability, I do not impose this on the plain firms. Alternatively, their optimal movement will be bounded, so I could set a rate which does not bind.

81 2 - ...... relative flexible wages -- relative productivity relative sticky wages

1.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 3-8: Cv and A when wages are downwardly rigid and g = -y - 1.

Under this assumption, solving for an equilibrium is entirely backwards looking. The relevant state variables are wages in the two cities and the distribution of firms. If firms receive the moving shock at rate K, then there exist bounds on the rate at which firms move:

-ft - dft '(I - fit)

Correspondingly, there are bounds on the wages:

dwj,t > (-y -1)wj,

for j = 1, 2. For any given fl and wit and W2,t, monopolists' labor demand will tell us employment, and the monopoly problem also tells us profits. If employment is less than 1, the wage will fall at the bounded rate. If profits are different across cities, firms will move to the more profitable city at the maximum rate. If there is full employment, and profits are equalized across cities, solving for equilibrium out-

comes has a similar flavor to the discrete case. For any given df1 within the moving bounds, we solve for dwj,t in both cities (subject to the wage constraint). This lets us look at the changes in

relative profits. If d7ri,t = d7r2,t, if the wages hit the upper bound for df 1 t and d7rit > d7r2 ,t, or if

wages hit the lower bound for df~a and d7rit < d7r2 ,t, then that dflat defines an equilibrium. Like in the discrete case, if there is full employment and profits are equalized, then it will always

= for j = 1, 2. In addition,be there an may equilibrium be up to four where df It = 0, and wj, t - Zt other equilibria, depending on the slope of A, w, and W2, and the growth rate of the economy. If

82 fv has a smaller slope than A, then there are equilibria where df '= - ff) and df1t =- So there are always three equilibria. If z-v has a larger slope than A, the number of equilibria may depend on the growth rate of the economy. I illustrate these in Figure 3-9. In Figure 3-9(a), dC is the relative wage schedule when there is sufficient growth such that the wage constraint does not bind for any value of dfle t. In this case, there is only one equilibrium, where dff, = 0 because wages respond more than productivity. In (a), dD' illustrates the relative wage schedule when !zt is a little bit bigger than y - 1. In this illustration, the wage constraint in city 1 binds for low values of df t. So there is an equilibrium where d7' and dA cross and an equilibrium at df , = -Kflt. While it is not the case in this figure, it could be that there are similar equilibria for positive values of df . In Figure 3-9(b), d" is the relative wage schedule when growth is slightly less than 7 - 1. Here there is a range of values around 0 for which the relative wage does not move. In this case, there are three equilibria. At df' t= 0, at df,= -ift, and for the positive value of dfa where the 1 lines intersect. Again, if w2 were steeper, the equilibria with a negative dfl might be interior.

ddi

di-v' -- dA div dwv

f a-fat) d xfa 0 K(t- flat) dt- 0

(a) (b)

Figure 3-9: Equilibria in the Dynamic case.

It is also a non-trivial problem when one city is not at full employment, but firms are indifferent between locations. In this case, dfla' = 0 is not an equilibrium except in the knife-edge case that ! = - 1. However, it will always be an equilibrium for firms to move to the city with unemployment at the highest possible rate. In addition, there exists a growth rate such that for any value of dfya the change in the relative wage will dominate, and the only equilibrium will be for firms to move to the unemployed city at the maximum rate. I now present two lemmas to give a better understanding of the economy and to set-up the key

83 result of in Proposition 3.4.

Lemma 3.1. For sufficiently high growth rates, if the economy starts at full employment, and

1, 2jy, then the economy will converge to either of the two stable steady-states from the discrete flexible-price case.

The exact condition for "sufficiently high" is in Appendix C.2. It is slightly higher than 1 - y to keep the wage constraint from beginning to bind because of moving firms. If productivity grows quickly enough and the economy starts at full employment, firms will converge to the steady-state where there is more agglomeration in the city which started with more firms. If fi,t=o = i, then the economy can converge to either of the stable steady-states under various assumptions on equilibrium selection, or it can remain there only if dfl, = 0 is always chosen. Even if the initial conditions do not include full employment, the economy will generally converge to one of the stable-steady states. The only concern is picking a wage and firm distribution combination such that the economy exactly hits the fla = i midpoint as the economy reaches full employment.

Lemma 3.2. Suppose that city 1 starts with e1,t=0 < 1 due to the binding wage constraint, that city starts with t2,t=O = 1, and that initially, firms are indifferent between the two cities. Then, for sufficiently high growth rates, the economy will converge to a steady-state with more firms in city 1 than it started with.

The conditions imply that initially, the firm distribution must be such that in the flexible wage setting, the relative wage would be higher than the relative productivity. The initial unemployment and falling wages are a draw for more firms to move to city 1. Then once the wage constraint stops binding, Lemma 3.1 applies.

3.4.1 A "race" between firm mobility and wage adjustment

In this section, I show that the model exhibits path-dependence in the following sense. If an economy starts in a steady-state, a recession is able to disrupt it, and firms may begin to relocate to the other city. If that happens, the depth of the recession and the strength of the recovery can determine whether the economy shifts to the other stable steady-state or returns to its original steady-state. Suppose the economy starts at the stable steady-state with most agglomeration firms in city 1. If firms leave at the fastest possible rate, the number of firms in a city will be given by ff t = f'*e'. So the city will have the minority of agglomeration firms for t > T* - log (2

Theorem 3.4. Suppose there exists an Trecession < T* such that ? <; 1 -1ifandonlyif t < Trecessio", as well as T ecove.y < T* such that there is sufficiently high growth in the sense of Lemma 3.2 for all t > T recover. Further suppose that initially, the equilibrium where dfr'to < 0 is chosen. Then there will exist a threshold Zcutoff : [TrcoYery,T*] -* R such that if Zt > Zc ctoff the

84 economy will return to its starting distribution of firms. But if not, it will converge to the other stable steady-state.

This proposition describes a recession during which firms begin to relocate to the other city. If the recovery is fast enough, the exodus of firms will stop before a critical mass of firms have left. In that case, the economy will return to the original steady-state. But if the recovery is too slow, the economy will eventually converge to the other stable steady-state. In this sense, the geographic concentration of economic activity displays path-dependence. It takes a sufficiently large and persistent shock to get the economy to switch steady-states.

3.5 Welfare and policy

If the government is allowed lump-sum taxes and transfers, any Pareto maximizing allocation will maximize production. One trivial result in this model is that unemployment is never welfare maximizing. If there is full employment, total production is proportional to

((A(f")"-1f + fP)i + (A(p - fa)7-l(p - fa) + 1 - p - f))i

This formula implies an optimal amount of agglomeration. If A(f)f is convex, some agglomeration will be optimal. There will never be an interior optimum which features firms of both types in both cities. In any output-maximizing firm distribution, all the plain firms will be in the same city, and there will be more agglomeration amongst the agglomeration firms than there is in the stable equilibria. The intuition is that without intervention, firms' externalities on other firms will always be larger in the bigger city as long as A(f)f is convex. In general, the model suggests policies that encourage agglomeration, such as a Pigouvian tax, are beneficial. These are standard and unsurprising for a model with externalities. Another policy that increases agglomeration is a minimum wage. Under certain parameters, the additional agglomeration outweighs the unemployment and leads to higher total output. Nonetheless, a minimum wage isl always dominated by policies like a place-specific subsidy that increase agglomeration without causing unemployment. Recessions lead to or exacerbate two inefficiencies. Firstly, they interact with the nominal wage stickiness to cause unemployment. Secondly, they can cause firms to relocate and lessen their positive externalities. If as in Proposition 3.4 the economy ends up switching steady-states, then during the transition there is a production loss from less agglomeration. The model also has room for location-specific, time-specific policies that aim to prevent mass relocation. Temporary subsidies to firms that are in a specific city can prevent geographic shifting, avoiding the welfare loss from relocation. Policy can even be made in the form of off-equilibrium threats, which can make a a non-stable equilibrium stable. For example, suppose dzt were sufficiently low such that dibt was zero for all possible values of df'at. The government could step in, though, and say that it would provide subsidies based on the value of dfi't: if firms moved to city 1, there would be subsidies to firms in city

85 2, and vice versa. If the subsidies were large enough to outweigh the benefits from agglomeration, the equilibrium dft = 0 would be the only equilibrium, and there would be no welfare loss from relocation. If there was a delay in policy, then the longer it took to implement a place-specific policy, the larger it would have to be to return the economy to its original steady-state. In a recession during which the relative wage does not adjust at all, if firms start moving to city 2, then city 2 becomes more and more relatively profitable. To get firms to move back to stop moving to city 2 and instead move back to city 1, there would need to be subsidies large enough to cover the gap that had already opened. Hence, if there is a large delay before policy gets implemented, it may be costly.14

3.6 Conclusion

In this paper, I document a newfact, namely that business cycles and reorganization of economic geography are linked. During recessions, the geography of economic activity is rearranged. Fur- thermore, during the recent recession, this effect was more pronounced in professions with stickier wages. I then explore a possible channel to explain these facts: during recessions, wage rigidities make the geographic equilibrium unstable, possibly leading firms to en masse move to other locations. I explore the dynamic implications and show that with moving frictions, it takes a sufficiently severe, in terms of depth and duration, recession to cause a shift to the other equilibrium. Finally, I explore policy, providing a rationale for place-specific time-specific subsidies. The model generally fits some of the stylized stories regarding some of the particularly hard-hit areas of the country during the recent recession. Sticky wages are often blamed for large falls in employment, and after long recessions during which wages have fallen significantly, economic activity has not necessarily returned to those areas. The dynamic model rationalizes place-specific time-specific subsidies to firms as a way to maintain a certain steady-state, and through that, avoid the welfare loss associated with geographic reallocation. The model part of this paper is a proof-of-concept, so it remains to explore whether this phenomenon is the primary cause of the stylized fact I present at the start, and to what extent it has had an impact on the recent economy. Nonetheless, the ingredients in the model, agglomeration externalities and wage stickiness, have been well-documented, so the possibility of such a mechanism is there.

1 4 It would not be costly in a welfare sense since lump-sum taxes and transfers are allowed, but costly in an accounting sense that the subsidies would be large.

86 Appendix A

Appendix to Chapter 1

A.1 Data

Migration data is obtained from the IRS Statistics of Income from 1990-2013. To clean the data, I adjust for county boundary and name changes, most crucially Miami-Dade county. I do not make any adjustment or imputation for data that is censored below at 10 tax returns. For 1940, migration data comes from the full Census. To convert county codes from ICPSR to FIPS, I take the five leading digits. Each moving respondent was asked which county they lived in five years prior. In several important ways, this is a different measure, and there is no censoring in this data. However, it is still highly predictive of movements in the IRS data 50 years later. Unemployment comes from the Bureau of Labor Statistics Local Area Unemployment Statistics. This is reported at the MSA level. To check robustness, I also use the public use microdata for the CPS, though not all counties are identifiable off of this. Nonetheless, counties are identifiable for a majority of respondents, which I aggregate to MSAs. I also use unemployment insurance payouts from the Bureau of Economic Analysis, which is available at the MSA level. Employment comes from the Quarterly Census of Employment and Wages, which is available for counties, which I aggregate to MSAs. Population is from the Census estimates. Again, I aggregate counties to MSAs. I use house prices from the Federal Housing Finance Authority, which reports local house price indexes for MSAs, going back to different points in time. By 2000, all but one MSA in my sample has a house price index. Permits come from the Census Building Permits Survey. Prior to 2003, the Census used a different definition of MSAs, which I converted to the new definitions using weights based on population in 2000. I then spliced those using the Census series for the new MSA definition, which is available after 2003. Mortgage data comes from Home Mortgage Disclosure Act, which is available on CD-ROMs for the earliest years. I matched Census tracts to MSAs. Second-lien mortgages were only available after 2004. I used the Mian, Rao, and Sufi (2013) definitions of tradable, non-tradable, and construction

87 employment, which I matched with the QCEW. The industry decomposition only matches after 1998. I use wage data from the Occupational Employment Survey, which reports average and median wages by MSA after 2005, and for a previous definition of MSAs before that. I again convert it using population weights from 2000. For the Mariel section of the paper, I use the FHFA and QCEW. To get estimates on the college education of the population, I use the Census 5 percent sample in 1990, and convert the Public Use Microdata Areas to MSAs based on population weighting. I estimate the share of college-education by dividing the number of respondents with 4 or more years of college by the total number of respondents. For the estimates of interest, dividend, and rental income, I use the American Community Survey from 2001-2014, which records migration status and income from these sources. I use the elasticities from Saiz (2010), which are computed for the old definition of MSAs. I convert these by hand. January temperatures are available by county and year from the Center for Disease Control. I take the average from 1990 to 2013, and aggregate to MSAs using 2000 population weights.

A.2 Proof of Proposition 1.1

Recall the equation from the text:

I + a dUt = -ac'dN +(1 -Ut)dN

It must be the case that aCt < 1 - Ut by the production of non-tradable goods. Since migrants have less wealth, it must be the case that actm aC' 1 - Ut as well. Hence the right-hand side of the equation is weakly positive. Define A = I+ a 2. Consumption in each period is a normal good. Hence &Cs 0 for all s, t. Then by the sum of all the agents' budget constraints, it must be the case that ET (1+1 , aO > S0T R)t-s a(lJt -1. Based on this, we can construct an M-matrix similar to A. Define B to be a diagonal matrix where Btt = (1+R)t. Then B- 1AB must be an M-matrix. A property of an M-matrix is that its inverse has all weakly positive elements (see Berman and Plemmons, 1979). Pre-multiplying by B, and post-multiplying by B- 1 preserves this property, so A- 1 must also have all elements weakly positive. Multiplying a weakly positive matrix by a weakly positive vector gives another weakly positive vector. So it must be the case that 4N is weakly positive. E

A.3 Investigating Complementarity

Much of the immigration literature focuses on whether migrants are substitutes or complements with native workers, with implications that substitutes' productivity will decline, while comple-

88 EO

o 1o 30 100 300 1000 Miles (log scale)

Figure A-i: The correlation between Adjusted Gross Income and distance moved, conditional on moving counties. ments' productivity increases. In contrast, in section 1.2, 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 A-i. 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 shock. Frorm Molloy, Smith, and Wozniak (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. 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 A-2. 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 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

89 14

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

10th Percentile - * -- 25th Percentile - -a- Median - -+ -- 75th Percentile - -~- 90th Percentile

Figure A-2: The effect of a one percent migration shock on the distribution of wages. MSAs: 337.

further the cutoff, the higher-skilled is the migrant. See Figure A-1. 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 A-3, 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 prediction on timing, such as Ottaviano and Peri (2012).

A.4 Similarities between high-migration city pairs

In this appendix, I show that migrants move between cities that are similar on two observable dimensions: location and industrial composition. To do this, I regress migration on measures of their similarity. The regression establishes that people do move between places that are similar, suggesting that places between which people move are likely to experience similar shocks. In column (1), I estimate a gravity-like relationship between migration on the distance between

90 CU4

E 0

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

---- High College Share MSA ' Low College Share MSA

Figure A-3: The effect of a one percent migration shock on the unemployment rate, split by college share. Number of MSAs: 158/158

Table A.1: 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 38,086 Origin and Destination Fixed Effects YES YES YES YES Flexible Distance Controls - YES YES Unit CBSA MSA CBSA MSA * p<.01, ** p<.05, * p<.1 Standard errors clustered by from and to MSAs/CBSAs. any two CBSAs using the specification below.1 In column (2), I show the same result for MSAs.

log minj,t, = flog distanceiai 7j+ +eij

Another piece of evidence is that migration is higher between 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 Similarityj - V 3 I||v i||v I||

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

91 where vi is the vector of employment by sector in MSA i, and f| is the Euclidean norm. The specification is

5 log mi+j,t0 = OIndustry Similarityij + P (log distanceij) + ai + 7 + %ij

There is a strongly positive relationship between industry similarity and migration, even conditional on distance.

A.5 Robustness

Hurricane Katrina

A major source of variation in my data is from Hurricane Katrina, where many people from New Orleans were displaced. This event has been used as a natural experiment to investigate the economic effects of migration on receiving cities, often Houston (see Gagnon and Lopez-Salido, 2014; McIntosh, 2008; De Silva, McComb, Moh, Schiller, and Vargas, 2010). Here, I show that my results are robust to using only this variation. Figure A-4 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 2005.2 The instrument for inflows to other cities is based on the 1990-1994 patterns used throughout the rest of the paper. In the top left of Figure A-4, I show that the instrument did a good job of predicting inflows. On the top right, I show this was associated with a decline in the unemployment rate. The bottom shows there was also an increase in house prices. The unemployment results are different in the first period, but then consistent with the rest of the paper. Initially, the unemployment rate rose, but then fell 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. Interestingly, the effects of migration due to Hurrican Katrina do not die out as other areas of the country did. There may be other forces at work or long-run trends in these particular MSAs.

1940 Migration Network

In Figure A-5, I construct the migration network using the 1940 Census rather than the pre-period of 1990-1993. I used the full 1940 Census, which asked migrants which county they lived in four years previous (see Ruggles, Genadek, Goeken, Grover, and Sobek, 2015). Besides the different pre-period, I construct the instrument in the same way and use the same regression. The effect on migration is shown in the top left. As you can see, the confidence intervals are a bit wider, as expected. Nonetheless, the effect on unemployment is robust to this pre-period. Indeed the

2 Only using this year necessitates only a two-year lead instead of three, because my data runs only through 2013.

92 I' I' I' I ~

Z- \ I' /1 \ I~ -- \ \ 2 \V. //! \ ~ -- E /1/; -- ~ ~\x C2 E

,, \~\ -, -

CI,4

t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years years

C) 5-I

CU - -

t-2 t-1 t +1 t+2 t+3 t+4 t+5 t+6 years

Figure A-4: The effect of outmigration from Katrina hit areas in 2005, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381.

93 /' I ~ \

1 N j N 0

/ N *.. / N E I N EM / N (, E .

t-3 t-2 t-1 t t-1 t2 t'3 +4 t15 VI6 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years years

N N 0

o0 N N -1 N N N N N

t-3 t-2 t-1 1 t+1 t+2 t+3 t+4 t+5 t+6 years

Figure A-5: The effect of inmigration shocks using the 1940 network, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381.

magnitude of the effect is larger, though it is also more short-lived. The increase in house prices is also larger.

This robustness check is suggestive that the results are not dependent on any specific shock that affected the pre-period migration patterns and the path of the unemployment rate, as such a shock would have had to delay its affect on unemployment for over 50 years.

Robustness of Employment Composition

In Figure A-6, I show the robustness of the employment composition effects, using similar controls as from section 1.3.4. 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.

94 8f

I-S

la E W

EN,

t-3 t-2 t-1 t t+1 1+2 1+3 1+4 t+5 t+6 Z t-3 t-2 tM 1 1+1 t+2 t+3 t+4 t+5 1+6 years years Baseline Industry and Education Controls Baseline Industry and Education Controls --- Fixed Effects -a---- Census Division Controls -+- Fixed Effects -a- Census Division Controls ---- Instrument: 500 miles Instrument 500 miles

r- 07

CL 0

E 91 CL E-7

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years

- Baseline - Industry and Education Controls - Fixed Effects - Census Division Controls -- +-- Instrument 500 miles

Figure A-6: 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.

Robustness of Housing Permits and Prices

Figure A-7 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 shocks suggests a larger elasticity because permits increase by more, and prices increase by less.

95 LO

0 LO (LO CD

0 C

-j U.) LO

t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 t+6 years years - Baseline Industry and Education Controls Baseline I Industry and Education Controls - Fixed Effects - Census Division Controls -+-- Fixed Effects .-.. - Census Division Controls - Instrument 500 miles *- Instrument: 500 miles

Figure A-7: The effect of an inmigration shock equal to one percent of the MSA's population, with 95 percent confidence intervals. Errors clustered by state. Number of MSAs: 381.

96 Appendix B

Appendix to Chapter 2

B.1 Proofs

B.1.1 Proof of Lemma 2.1

Agents demand one unit of housing, implies that the total amount of housing is fixed by the population. Therefore, NidlogH = 0

By the definition of housing supply elasticity, d log H = uid log p4, so

Ni i dlogp =0

The result is an algebraic rearrangement, solving for Ji :d logp .

B.1.2 Proof of Lemma 2.2

The two market-clearing conditions are that

ZNid log$h 0

1 kiddlogki = logrk

Under the CES housing supply assumption,

d log H = a (d log p - dlogrk) d log ki = (ui + a)(d log pi - d log rk

97 After simple algebra, the following two equations relate d log rk and d log ph

dlogrk = Cov (ai, d log pih) +dlogph

(y + a + E[niioi])d log rk = Cov(Ki(i + a), d logph) + (a + E[Kic-i])dlogph

where ti = K . Plugging in rk leads to

h Cov (ui, d log ph) ydlogp = +E[ _-(-+_a_o) & + Cov(i(o-i + a), d log p)

This can be decomposed into the original term and the contribution from additional

h Cov(o-i, d log pi) E[Kz(U- + a)] C i (-i + a) o-i ) ) dlog pi d log p = - + 'Y Cov _EK~r,

The last step is to show that ni satisfies the stated properties. Simply note that ,i c c

(,) and that E KN1 = K 1.

B.1.3 Proof of Proposition 2.1

Our assumptions imply that d logph = OM, + . Plugging this into Lemma 2.1 and factoring the # from the covariance gives the result.

B.1.4 Proof of Proposition 2.2

When wages are held constant, the following equation must hold for all i:

dlogu = d log+p + d log R)

It is still the case that Ej Ni-id logp= 0, and d log u is constant across cities. Doing algebra,

dlogu = dlogR Z Njoj Ni o-j

Plugging this in and solving for E> Nid log ph gives:

dlogpi =C , E

98 Land Share versus House Value, 2000 Slope=-0.81 (0.06)

(b 0

0r-

0o 0 0

0 V- o 0

C,-

11.5 12 12.5 13 13.5 Log House Value

Figure B-1: Land Shares and House Prices

B.2 Calibration

B.2.1 E

We made the assumption that housing was produced CES.

H,= Z E + AKK E

If everyone faces the same price of capital, it can be derived that

log(1 - Land Sharej) = + (E - 1) logph

To get a value for c, we used the Lincoln Land Institute's data from 2000 on Land Share and Home Value. The results are in Figure B-1. The regression gives a value of -. 81, implying E is approximately 0.19.

99 100 Appendix C

Appendix to Chapter 3

C.1 Algorithm for Identifying Trend Reversals

To look primarily at the underlying trends instead of business cycle fluctuations per se, I use an HP-filter with the standard parameter of 1600 for quarterly data. Once I have the HP-filtered series, I look for extrema in that series to determine the approximate dates of "trend reversals." To make sure they are indeed trends, I search for reversals that take place within five years of one another and throw them out. If a reversal occurs within five years of two different reversals, I throw it out along with the closer of the other two. Finally, because the date of the extrema in the trend series may differ dramatically from the date of the extrema in the underlying series, I take the corresponding local extrema in the full data within two years of the date of the extrema in the trend series. It is this date that I identify as the "trend reversal." In Figure C-1, I again plot each state's share of GDP, along with the dates I label as trend reversals. A visual inspection matches my qualitative identification of trend reversals with an almost perfect accuracy. With these dates, I create a variable for how prevalent trend reversals are across the United States. For each quarter, I count the number of states experiencing a trend reversal.

C.2 Proofs

C.2.1 Proof of Proposition 3.1

Proof. An equilibrium requires that either labor markets clear according to (3.1) or the wage constraint binds; and that both plain firms and agglomeration firms are locating in their preferred city, or if there are some in both cities, that they are indifferent between the two. Under the supposition, f1"_ describes an equilibrium such that the above conditions are met. We will guess and verify that it again describes at equilibrium at t. First, if wages increase such that -, an equal proportional change in each city, then (3.1) will continue to hold with the same distribution of firms. Wages are free to adjust in such a way because 1 + gt > y so the

101 3 -

2 -

___11

1943 1957 1971 1964 1996 2012 202 x11

Figure C-i: Trend Reversals: blue dots are reversals down, red dots are reversals up constraint will not bind. Second, since wages increased proportionally, the city with the higher wages will still have higher wages. So the same distribution of plain firms is still optimal. Last, since wages have increased proportionally, the relative wage has not changed. Therefore, the same distribution of agglomeration firms will leave agglomeration firms indifferent between the two cities. These three conditions establish that f = fe'>_ is an equilibrium. To show that it is a stable equilibrium, it suffices to show that for a range of ff, near f'* the wage constraint will not bind. Therefore, since in that neighborhood relative wages increased faster than relative productivity, it will be a stable equilibrium. There exists a neighborhood in which wages do not bind because wages are continuous in f by (3.1). Therefore, since at f_ wages adjust by 1+ gt which is strictly greater than y, there must be a neighborhood where wages adjust by an amount greater than -y.

C.2.2 Proof of Proposition 3.2

Proof. The argument that ff, = f ',*1 is an equilibrium is fundamentally the same. The one modification is that instead of (3.1) holding, the wage constraint binds. Now, wi,t = ywi,t_1 because of the constraint. Nonetheless, this still preserves the proportion gf, so firms still face the same profits in each city. By continuity, the wage constraint for both cities will bind in a neighborhood of f'*_1. There- fore, the relative wage is locally flat. Since A is non-decreasing, small increases in ff, will not lead to

102 city 1 becoming relatively less attractive and vice versa. Therefore the equilibrium is unstable. l

C.2.3 Proof of Proposition 3.3

Proof. The proof of this is mostly contained in the text of the paper. The argument that it is an equilibrium is identical to either of the two above. If log A is a less than the slope of log z to the left and the right, then for small changes in ff, it becomes more attractive to move back to the equilibrium. If log A is greater than either slope, then small changes in fa, mean that the productivity to wage ratio in the city toward which the change occurs increases faster than in the other city. This means the equilibrium is unstable. Finally, if the slope of log A is in between the other two slopes, then moving in the direction in which its slope is greater will lead to an increase in the relative profitability in that city, but moving in the other direction will lead to less relative profitability. Hence, the equilibrium is stable to only one side. L

C.2.4 Proof of Lemma 3.1

Proof. Without the wage constraint, wages would adjust

dZt 1 df t(A(f q) -1+ f (o - 1)A(f ,)a-2A'(f )) + df dlogwt = - + (C.1) Zt 0- A( f q )0-Iffy + fj t

Since df > is bounded by - rfja and K (p - fj,t), and df t is either 0 or exactly cancels out the entire

.(o-l)Af "A'(f ,t)) the wage term, then as long as -; - 1+ maxj=1,2 t constraint will not bind. As long as , is small and A is not too steep, this is only slightly greater than y - 1. Because the wage constraint never binds, at any time t, for fa, > ' and fat < f the stable steady-state in Region III, relative productivity will always exceed the relative wage. Therefore, firms will always move to city 1 at the maximum rate while in this region. In finite time, they will reach fa'* and stay there. Similarly, if fat > fla'*, then the relative wage will exceed relative productivity. Firms leave city 1 at the maximum rate and reach fla'* in finite time. By symmetry, fla < p will converge to the other stable equilibrium. l

C.2.5 Proof of Lemma 3.2

Proof. It must be the case that if wages were flexible, wages would be lower in city 1, and firms would

prefer to locate in city 1. Hence it must be the case that f ,_O0 is either in the range [0, A - f*'a) less than the lower stable steady-state, or in P, fj*'a), in between the unstable steady-state and the higher stable steady-state.

Because of the initial unemployment in city 1, wages will fall at rate = (- - 1). So if firms wet move toward city 1 at rate i(P~- f a, then city 1 will become more relatively productive and wages

103 will fall at the maximum rate. City 1 will become more profitable than city 2. Hence firms moving to city 1 is an equilibrium. Furthermore, if city 1 was already weakly preferred to city 2, then the same logic applies, so it is an equilibrium for firms to move to city 1 until the wage constraint no longer binds. For it to be a unique equilibrium, growth rates have to be sufficiently high such that city l's profits increases faster than city 2's profits for all possible df t. The evolution of d log W2,t is described by (C.1). Relative productivity evolves as dlog At = dfai + Hence growth needs to be sufficient to exceed

1 2 dZt ( A'(fa%) A'(f't) 1 (A(fat)O~ + fat(o- - 1)A(f 2at)- A'(fjat) > y - 1 + + + +ft Zt A (f( at) A (f2t) o-A( f( t)O-1 f at + fp2t

In that equilibrium, if the wage constraint stops binding at time t, then fli > f%_o. Consider the two cases in which fl_0 -p, Lemma 3.1 implies that the economy would converge to the upper stable steady-state. L

C.2.6 Proof of Proposition 3.4

Proof. As long as both wage constraints are binding, the initial movement to the left will make city 2 the more profitable city, and such movement will continue. Furthermore, the wage constraint will always stop binding in city 2 before it stops binding in city 1 because while it binds in both cities, the relative wage stays the same whereas the relative productivity increases in city 2 due to firm movement. Hence at the time of Trecession, there will be fewer firms in city 1 than there were initially, and the wage constraint will still bind. City 2 will also be strictly preferred to city 1. After Trecession, the situation where = -y - 1 and df6 = -fl continues until either firms are indifferent between the two cities or the wage constraint stops binding. Before T*, it will be that firms are indifferent between the two cities. To see this, imagine the opposite, that the wage constraint stopped binding. Then we are on the flexible relative wage curve, wh. But for t < T*, ft E (t, ff'*), so the relative wage curve is below the relative productivity curve, and city 1 is strictly preferred. By continuity, there must have been a previous time in which firms were indifferent. So if by time T*, firms are indifferent between the two cities, we can apply Lemma 3.2, and conclude that the firm will return to the original steady-state. If however, T* passes before firms are indifferent, two things can happen. Either the wage constraint will stop binding at a f i E (p - fla'*, 'p) or the economy will overshoot - fa,'* and firms will be indifferent between the two cities. In the first case, apply Lemma 3.1, and in the second case, apply Lemma 3.2. In both cases, the economy converges to the lower stable steady-state.

104 The only remaining part to show is that firm indifference between the two cities is achieved before T* for some Zcutoff. For indifference, it must be that city 2's wage constraint no longer binds; else the relative wage would still be at its original value. It must also be the case that city l's constraint does bind, as argued above. Hence wages are given by

Wit = WiOe(-Of

W2,t = Zt((p - f't)A(p -

Relative productivity is . Furthermore, fat = f '*e-,t. So firms will be indifferent if

Zcutoff _ w1,06 () - ff' e ) - fa* -tt)A( f 0*t-1)1/0 A(f '*e-t)

If this value is not reached by Tcutoff, the economy will converge to the lower steady-state. If it does hit this cut-off first, it will return to the original steady-state. l

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