Economic Shocks and Internal Migration

Transcription

1 DISCUSSION PAPER SERIES IZA DP No Economic Shocks and Interna Migration Joan Monras February 2015 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor

2 Economic Shocks and Interna Migration Joan Monras Sciences Po, LIEPP and IZA Discussion Paper No February 2015 IZA P.O. Box Bonn Germany Phone: Fax: E-mai: Any opinions expressed here are those of the author(s) and not those of IZA. Research pubished in this series may incude views on poicy, but the institute itsef takes no institutiona poicy positions. The IZA research network is committed to the IZA Guiding Principes of Research Integrity. The Institute for the Study of Labor (IZA) in Bonn is a oca and virtua internationa research center and a pace of communication between science, poitics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimuating research environment through its internationa network, workshops and conferences, data service, project support, research visits and doctora program. IZA engages in (i) origina and internationay competitive research in a fieds of abor economics, (ii) deveopment of poicy concepts, and (iii) dissemination of research resuts and concepts to the interested pubic. IZA Discussion Papers often represent preiminary work and are circuated to encourage discussion. Citation of such a paper shoud account for its provisiona character. A revised version may be avaiabe directy from the author.

3 IZA Discussion Paper No February 2015 ABSTRACT Economic Shocks and Interna Migration * Previous iterature shows that interna migration rates are strongy procycica. This woud seem to impy that geographic reocation does not hep mitigate negative oca economic shocks during recessions. This paper shows that this is not the case. I document that net inmigration rates decreased in areas more affected by the Great Recession. Using various IV strategies that rey on the importance of the construction sector and the indebtedness of househods before the crisis, I concude that interna migration might hep to aeviate up to one third of the effects of the crisis on wages in the most affected ocations. This is due to a disproportionate decrease in in-migration into those ocations rather than an increase in outmigration. More generay, I show that differences in popuation growth rates across ocations are mainy expained by differences in in-migration rates rather than in out-migration rates. I introduce a mode to guide the empirica anaysis and to quantify the spi-over effects caused by interna migration. JEL Cassification: J61, J20, J30, F22, J43, R23, R58 Keywords: interna migration, oca abor demand shocks Corresponding author: Joan Monras Economics Department and LIEPP Sciences Po 28, rue de Saint-Pères 75007, Paris France E-mai: joan.monras@sciencespo.fr * I woud ike to thank Don Davis, Eric Verhoogen and Bernard Saanié for guidance and encouragement and Jón Steinsson, Jesus Fernández-Huertas, Miche Serafinei, Brian Kovak and seminar participants at IIES for usefu comments and discussions. A errors are mine.

4 1 Introduction It is a common perception that Americans have historicay been an unusuay mobie peope, constanty seeking better economic conditions (Moretti, 2012). We woud, then, expect geographic reocation to be an important mechanism for American famiies to dea with periods of economic crisis. Is this the case? US interna migration rates are strongy pro-cycica (Saks and Wozniak, 2011). This coud impy that (most) interna migrants move to take advantage of opportunities created during good economic years. It is ess cear, however, whether interna migration aso heps in bad times. The fact that aggregate migration rates decine in downturns might suggest that US famiies do not respond to negative economic shocks by moving to other parts of the country and that instead, famiies remain in their current ocation unti the economy starts recovering. Is this true? Does this impy that spatia abor reaocation does not hep mitigate negative oca economic shocks in recessions? In this paper, I use the Great Recession to study how migration decisions are shaped by the effects of the crisis at the oca eve, i.e. across metropoitan areas. Contrary to previous iterature see Mian and Sufi (2013) and Mooy et a. (2011) I show that geographic reocation was important in mitigating negative oca economic shocks during the period In particuar, I show that the reocation mechanism is decreased in-migration rates into negativey hit ocations, rather than increased out-migration from them. To understand why reduced in-migration rates are important in mitigating the oca effects during recessions it is, first, important to reaize that whie in many metropoitan areas the average net migration rate is cose to 0, the gross fows are aways significanty higher since more than 3.5 percent of househods change metropoitan areas in any given year. 1 Second, the decreased migration rates during recessions are, party, a consequence of fewer peope moving towards negativey shocked oca abor markets. Third, this impies that the reevant counterfactua, i.e. what woud have happened had the Great Recession not occurred, needs to take into account that more peope woud have moved to the negativey hit ocations. This is crucia. In a cosey reated paper, Yagan (2014) shows how workers who suffered arger oca shocks in 2006 sti had worse outcomes through 2011, even if they reocated. He takes this as evidence that interna reocation does itte to mitigate the negative consequences of oca shocks. My resuts show that fewer workers moved into the ocations most affected by the Great Recession. Had they done so, the wage and empoyment effects woud have been even worse. 2 Adding this new eement gives a more positive picture of the 1 More generay, as computed in Mooy et a. (2011), around 1.5 percent of the popuation moves between Census regions, 1.3 percent move across states within these regions and around 3 percent move across counties within state. These numbers are obviousy consistent with the reported migration rates across metropoitan areas. 2 In Monras (2013) I show how the oca abor demand easticity is around -1, using the unexpected infow of Mexicans resuting from the Mexican Peso Crisis of This is important since reduced in-migration mitigates the wage effects of the Great Recession ony if the oca abor demand easticity is negative. 2

5 abiity of interna migration to smooth oca shocks. 3 In this paper, I show these resuts using two aternative strategies. My first strategy is to show that ocations which had arger construction sectors before the crisis (measured by the share of empoyment in construction in 2000) suffered arger oca economic shocks in These ocations, in turn, saw their in-migration rates decine disproportionatey. My second strategy buids on the work by Mian and Sufi (2013). They argue that the 2008 crisis owered the consumption capacity of highy indebted househods. This heps to expain the drop in consumption starting in Across the territory, the demand for tradabes dropped uniformy, whie the demand for non-tradabes dropped more in highy indebted ocations, precisey because non-tradabe goods can ony be consumed ocay. This transates, as Mian and Sufi (2013) show, into decines in non-tradabe empoyment in highy indebted ocations, whie it transates into uniform drops in empoyment in tradabe sectors. Thus, ocations that historicay had arger empoyment shares in non-tradabe empoyment and were highy indebted at the beginning saw sharper decines in per capita GDP and wages and higher increases in unempoyment rates. This paper shows that this is associated with arger drops in the in-migration rates. I find that a 1 percent decrease in wages eads to around a.30 percentage point decrease in the share of in-migrants at the oca eve. This heps to mitigate the shock that the crisis had on wages. If the easticity of the oca abor demand is equa to 1 (see Monras (2013) for an estimate of this order of magnitude) then the decrease in in-migration rates reduces the effect of the crisis on wages by around one third. This means that had these in-migrants moved into a city with an actua decrease of 1 percent in wages, the decrease woud have been around 1.3 percent. I show these resuts in detai using a dynamic mode of interna migration caibrated to the US economy. The mode is abe to capture not ony the short-run response of interna migration and wages during the Great Recession, but aso the fu adjustment due to interna migration across oca abor markets. These resuts impy that geographic reocation (i.e. net migration) took pace as a response to particuary strong negative oca economic shocks during the Great Recession. In other words, the popuations of more heaviy hit ocations grew ess than before the crisis. This was a consequence of ower in-migration rates rather than out-migration. Given these resuts, I then address the extent to which this mechanism can expain the growth and decine of cities or regions (Gabaix, 1999), (Eeckhout, 2004). To do so, I decompose the popuation growth rates of specific cohorts into in- and out- migration rates from a oca abor markets. 4 Using a number of different data sets and geographic definitions I obtain striking resuts. More than 90 percent of the variation in popuation growth rates across ocations is accounted 3 As emphasized in Tope (1986), the migrants that did not move to the negativey affected ocations are themseves abor suppy shocks that affect wages in ocations ess affected by the crisis. 4 By cohort, I refer here to a the peope that I observe in either the American Community Survey, Current Popuation Survey or US Census for whom I know both their current ocation and their ocation one or five years before the survey takes pace. 3

6 for by variation in in-migration rates. This means that the growth and decine of cities, states or regions is mainy due to persistenty high or ow in-migration rates with itte systematic differences in out-migration rates. Severa papers have ooked at the response of oca abor markets to negative oca abor demand shocks. In a semina contribution, Banchard and Katz (1992) argue that ocations affected by negative shocks experience permanent osses in empoyment, temporary increases in unempoyment rates and temporary decreases in oca wages. Their identification strategy does not distinguish between good and bad times, however. This has become an important issue because severa papers have argued that during this ast recession interna migration rates have not responded differenty across mutipe ocations. Mian and Sufi (2013) argue that, if anything, popuations increased (between 2007 and 2009) in highy indebted counties. This is obviousy very puzzing for the spatia economic iterature (see Gaeser (2008) or Moretti (2011)): with free mobiity, peope shoud eave decining ocations and move to rising ones. These puzzing findings are expained in this paper by the fact that highy indebted counties were attracting more peope than other counties before 2008 and stopped doing so as a consequence of the crisis. In a paper which is cosey reated to this one, Cadena and Kovak (2013) show that ocations more heaviy affected by the crisis (using either the construction sector or Mian and Sufi (2013) s insights as I do) saw decines in Mexican workers but ow interna migration responses amongst ow-skied native workers. They do not take into account, however, that the popuation trends of native ow-skied workers and Mexicans can be different. This is important. When I account for this, for exampe by directy examining migration rates, I find that natives and immigrants responded simiary to oca economic shocks. More broady, this paper cas into question the papers that interpret high moving costs as a imiting force for interna migration to mitigate economic shocks (Beaudry et a., 2014), (Kennan and Waker, 2011). Whie there are certainy migration costs, biatera fows across ocations are aways positive. Not moving to a ocation that has been hit by a negative shock is not costy and this is the main mechanism through which interna migration responds to negative shocks. As a resut, interna migration is shown to be an important force through which differences across oca abor markets are arbitraged away. Finay, this paper is reated to the iterature of spatia economics. Unike most papers in this iterature, I investigate short-term responses. It is we documented that paces where amenities or oca abor market conditions improve attract more peope (see Gaeser (2008) or more recenty Diamond (2013)) whie ocations with deteriorating oca conditions suffer from a shrinking popuation (see Hornbeck (2012), Hornbeck and Naidu (2012) or Autor et a. (Forthcoming)). It has aso been documented that peope respond to expectations of future positive prospects (Kennan and Waker, 2011). In ine with Gaeser and Gyourko (2005) or Notowidigdo (2013), I show that interna oca out-migration rates do not respond swifty to oca economic shocks. However, I aso 4

7 emphasize the importance of the response of in-migration rates into these paces. 2 Mode In this section, I introduce the mode that guides the empirica section and the evauation of the onger-run effects of the Great Recession across metropoitan areas. Two features of the mode stand out. First, oca abor demands in the various ocations are downward soping. This simpy means that if more workers move to a particuar ocation wages decrease on impact. Second, workers are constanty deciding where to ive in the foowing period. This creates a constant fow of workers across ocations that reacts to unexpected oca shocks in particuar paces. In principe, how these fows of workers react to oca shocks coud take various forms: increased out-fows or decreased in-fows (or a combination of both). This is an empirica question that is expicity tacked in the empirica section. The mode makes these two possibiities expicit. The mode has M regions which for most of the empirica part represent metropoitan areas. There is a singe fina consumption good that is freey traded across regions, at no cost. There is a fixed factor of production, caed and, which makes the oca abor demand downward soping. Workers ive for infinitey many periods, but they are myopic in that they ony care about the next period s ocation. 5 At each point in time they reside in a particuar ocation m. Unexpected permanent shocks that affect the oca abor market conditions in each ocation can occur. Workers can then decide whether to stay or move somewhere ese in the foowing period. Workers are sma reative to the abor market so they do not take into account the effect that they have on the abor market when reocating. 2.1 Timing The timing of the mode is the foowing. At the beginning of each period an unexpected permanent shock can happen in a ocation. Next, given the current distribution of workers across ocations, firms maximize profits and wages are determined. Lasty, given the wages in the economy, workers decide where to ive in the foowing period. 2.2 Production Function The production function in a regions is the same. Each region has a perfecty competitive representative firm producing according to: Q m = B m [θ m K ρ m + (1 θ m )N ρ m] 1/ρ (1) 5 See Kennan and Waker (2011) and Monras (2014) for a arger discussion on this point. In Monras (2014) I show that the mode can be extended to incorporate more future periods in the migration decision and that the resuts obtained in that mode are simiar to what I present here. 5

8 where N m is abor or popuation and K m is and. θ m represents the different weights or factor specific productivities of the two factors in the production function, whie ρ governs the easticity of substitution between these factors. B m is Tota Factor Productivity (TFP) of each ocation. 2.3 Labor market For simpicity, I assume that the abor market is perfecty competitive and workers ineasticay suppy a their abor. 6 Thus the abor market is determined by firms behavior: w m = p m (1 θ m )B σ 1 σ m Q 1 σ m N 1 σ m (2) where σ = 1/(1 ρ) is the easticity of substitution between abor and and. This defines the abor demand curve. We can normaize p m = 1. Free trade wi guarantee that prices are the same across regions. A simiar equation appies for and and its price r m. 2.4 Location Choice The indirect utiity of the workers is given by the oca wage w m, the amenities A m idiosyncratic draw they get for ocation m, given that they ive in m: and the v i m = n V m + ɛi m,m = n A m + n w m + ɛi m,m The intuition is straightforward. If an individua i moves to m, she wi receive wage w m and wi enjoy amenity eves A m. 7 Note that the indirect utiity has a common component to a workers n V m on variabes at destination and an idiosyncratic component ɛ i m,m current residence. Thus, workers maximize: that depends specific to each worker and her max {n V m m M + ɛi m,m } (3) The genera soution to this maximization probem gives the probabiity that an individua i residing in a ocation m moves to m, given current wages and vauations of amenities A, w in 6 It is easy to introduce search and matching frictions, which I do in the appendix. 7 It is easy to extend this equation to take unempoyment rates at destination into account. I do this in the appendix. 6

9 every ocation: 8 p i m,m = p m,m (A, w) (4) This shapes the fows of workers across ocations. By the aw of arge numbers we can then use equation (4) to obtain the fow of peope between m and m : P m,m = p i m,m N m for s s (5) where N m is the popuation residing in m. Note that this defines a matrix that represents the fows of peope between any two ocations in the economy. It is worth emphasizing that this determines the fows of workers, not the fina distribution in each ocation. This is new in the iterature of interna migration. It means that the mode presented here is dynamic and not static Dynamics By definition, the number of individuas in m at time t is the number of individuas who were iving in that ocation possiby times the natura growth rate n m which I assume to be 0 pus those who arrive minus those who eave: N m = N m + I m O m (6) Thus, interna reocation can take pace through either in-migration or through out-migration. We can use the definition of the fow of peope across ocations to define the in- and out-migration in each ocation: I m = j m P j,m (7) O m = j m P m,j (8) N m = j P j,s (9) This notation is usefu for the derivation of some of the resuts. 8 I use bod etters to denote the vector of a the ocations in the economy. Note that in genera, fows of workers between two ocations depend on the entire vector of amenities and wages in a the ocations. Later I make simpifying assumptions to obtain tractabe functiona forms. 9 See the discussion in section

10 2.6 Equiibrium The definition of the equiibrium has two parts. I start by defining the equiibrium in the short run. It satisfies two conditions. First, firms take as given the productivity B m, the productivity of each factor θ m and factor prices in each ocation to maximize profits. Second, abor markets cear in each ocation. This equates the suppy and the demand for abor and determines the wage in every oca abor market. More formay: Definition I. A short-run equiibrium is defined by the foowing decisions: Given {θ m, B m, K m, σ, w m, r m } m M firms maximize profits. Labor and and markets cear in each m M so that {w m, r m } is determined. Note that in the short run, the two factors of production are fixed. Thus, changes in technoogies or factor quantities directy affect prices. At the end of the period reocation takes pace which determines the distribution of workers across space in the foowing period. We can define the ong-run equiibrium by adding an extra condition to the short-run definition. In words, I say that the economy is in ong-run equiibrium when biatera fows of peope are equaized across regions. More specificay, Definition II. Given {θ m, B m, K m, σ, A m } m M, a ong-run equiibrium is defined as a short-run equiibrium with equaized biatera fows of popuation across ocations. This is: P m,m = P m,m, m, m M where the fows are determined by the ocation maximization probem introduced before. 2.7 Properties of the mode Mobiity Properties under a nested ogit ɛ To guide the empirica section I assume that the distribution of the idiosyncratic taste shocks is a nested ogit. At the individua eve, this means that the home ocation wi be more ikey to have a higher draw than any other destination. At the aggregate eve, it wi ook ike a representative worker that is deciding as foows: the first part of the decision is whether to stay in m or whether to move out from m. The second part is where to move, if the decision in part one was to move out (Anderson et a., 1992). This then transates into how the in-migration or the out-migration rate responds to shocks. I anayze this in what foows. Figure 1 shows this nested structure. [Figure 1 goes here] 8

11 This decision structure resuts in a cosed form soution for the probabiity of an individua moving from m to m. By mutipying by the number of individuas in each ocation, we can write the biatera fows as foows: V 1/λ m P m,m = N m η m j M V 1/λ j (10) where N m is the popuation in m, η m is the fraction of peope in m that (endogenousy) consider reocating and λ is the inverse of the easticity of substitution between different nodes in the second nest (when peope decide where to move). Lower vaues of λ make peope more sensitive to the oca economic conditions at destination. The expected vaue of reocating for someone iving in m is given by: n V m = λ n j M V 1/λ j where γ is the inverse of the easticity of substitution in the upper nest, i.e. between staying or eaving the origin. I assume that λ < γ, i.e. that the easticity of substitution within the ower nest is arger than that of the upper one. In this case, η m = V 1/γ m V 1/γ m + V 1/γ m This simpy says that if economic conditions esewhere (V m ) are good or economic conditions in m (V m ) are bad, a higher fraction of the popuation in m wi try to ook for a new destination. It is usefu to think what happens in the imiting cases when 1 γ 1 λ and 1 γ 0. When 1 γ 1 λ staying at the origin stops having a specia roe. In turn this impies that, in equiibrium, more peope wi be switching ocation at each point in time. Whie this is a possibiity, it is at odds with the empirica fact that ony a sma share of the popuation (around 3 or 3.5 percent) changes oca abor market in a given year. When 1 γ 0 then η m 1 2. This means that haf of the popuation in a given ocation decides each period whether they want to reocate and the other haf stays no matter what happens in the current ocation. This might be unreaistic, since we woud expect that, if things went bad, a higher share of the popuation woud eave the ocation in a given period. empirica question. It is, however, an It may aso be unreaistic because if haf of the popuation decides on the future ocation (and more or ess ocations are equa in terms of expected utiity) and there are M ocations, then, in equiibrium, ony a fraction 1 2 (1 + 1 M ) stay in the same ocation in each period. This is certainy above the empirica fact that around 3 to 3.5 percent of the popuation do stay where they are from one year to the next one. 9

12 A simpe assumption can dea with this issue. Assuming that the positive draw in the ocation of origin is η 1 times more ikey than any other ocation impies that: η m = V 1/γ s (η 1)V 1/γ m + V 1/γ s In terms of the decision tree described in Figure 1, this extra assumption simpy means that in the upper nest there are η branches. The first one is to reocate away from the origin, whie the other η 1 are to stay. In this case, when 1 γ 0 we have that η m 1 η so ony a fraction 1 η ooks for a new destination, or conversey, a fraction η 1 η aways decides to stay in the ocation of origin, no matter what the economic conditions in the various paces are. The fact that in equiibrium ony 3 to 3.5 percent reocate each year woud impy that 1 η is around 0.03, something I discuss in greater detai in the ast section. In what foows, I anayze how the popuation adapts to oca shocks. It is convenient to first anayze how the various biatera fows react when there is an unexpected shock in one of the oca abor markets. As wi be cear from the proofs, the imiting case of an arbitrariy arge number of ocations simpifies the agebra consideraby. Lemma 1. If ɛ i m,m (11) are i.i.d. and drawn from a nested ogit distribution with shape parameters λ and γ then, in the environment defined by the mode, we have that: n P j,m n w m 1 λ (12) n P m,m n w m 1 λ 1 γ (1 η m) (13) n P j,m n w j 1 γ (1 η j) (14) n P j,m n w m when the number of ocations is arbitrariy arge. Proof. See Appendix. 0 (15) Lemma 1 shows that there wi be a first order effect of shocks at destination that is governed by 1/λ. If a potentia destination m increases wages then a arger number of in-migrants from a the other ocations wi be attracted. Simiary, if wages improve in m, more workers who were iving in m wi decide to stay in m. Finay, given the structure of the idiosyncratic taste shocks, 10

13 economic shocks to a third ocation wi have a negigibe impact on the biatera fows between two ocations. The foowing proposition discusses how much a these responses of the biatera fows transate into popuation changes. Proposition 2. If ɛ i m,m are i.i.d. and drawn from a nested ogit distribution with shape parameters λ and γ then, in the environment defined by the mode, we have that: and n N m 1 n w m λ 1 P m,m γ P (1 η m ),m n N m 1 n w m m γ (1 η m ) when the number of ocations is arbitrariy arge. Proof. See Appendix. Intuitivey, proposition 2 says that a positive (resp. negative) shock wi increase (resp. decrease) the oca popuation substantiay and that it wi have spiovers to the rest of the oca abor markets that did not experience this shock. Thinking about popuation eves or changes in popuation eves in ight of the mode hides the fact that net in-migration may be a consequence of either changes in in-migration rates or changes in out-migration rates, or both. 10 I discuss this in the foowing proposition. Proposition 3. If ɛ i m,m are i.i.d. and drawn from a nested ogit distribution with shape parameters λ and γ then, in the environment defined by the mode, we have that: n I m n w m = 1 λ n O m n w m = 1 γ (1 η m) Proof. See Appendix This ast proposition can be re-expressed in terms of migration rates, which may be usefu for empirica appications Note that we can mode productivity evoutions to make the mode consistent with the city growth modes, see Eeckhout (2004). 11 In- and out-migration rates are usuay stationary series that are easier to anayze empiricay. 11

14 Coroary 4. If ɛ i m,m are i.i.d. and drawn from a nested ogit distribution with shape parameters λ and γ then, in the environment defined by the mode, we have that: (I m/n m) n w m (O m/n m) n w m = 1 I m λ N m = 1 γ (1 η m) Om N m Proof. See Appendix. Proposition 3 and Coroary 4 show that the responses of the in-migration rate and out-migration rate are governed by two different parameters The propagation of a oca shock We have seen that if there is a shock affecting the abor market conditions in one ocation, there wi be some adjustment. We have aso seen that this adjustment can come disproportionatey from changes in the in-migration rates or out-migration rates. Do these oca abor shocks spi over to non-affected ocations? If the oca abor demand is downward soping, changes in the distribution of peope across space wi indeed have consequences on wages. Fewer peope wi move to the shocked ocation or more wi eave. In either case, the abor suppy in that ocation decreases. This reduced in-migration or increased out-migration becomes an increase in the abor suppy in the non-affected ocations, which tends to equaize wages across ocations. For a this to happen, we need downward soping abor demands in the short run. In this mode, this is a consequence of the fixed factor of production. 12 Proposition 5. In the short run, oca abor demand is downward soping. Proof. See Appendix. If we know the abor demand easticity, it is straightforward to compute how the shock propagates, since we have estabished how much a shock changes popuation eves in the foowing period and how much this, in turn, affects wages. In the ast section I quantify this process. 12 Note that in spatia equiibrium it cannot be that average utiity in a city is (aways) increasing in popuation. If that was the case, more peope woud move in unti everyone in the country ived in the same city. It is usuay assumed that an important component of (indirect) utiity are wages, thus a simiar argument can be made with respect to wages. 12

15 2.7.3 Long-run properties of the mode In this section, I anayze the properties of the mode in the ong run, i.e. when biatera fows between regions are equaized. The foowing two propositions characterize wage eves in the crosssection in equiibrium. They share many of the properties of standard spatia equiibrium modes that are usuay meant to capture the ong-run distribution of peope across space, but add some nuances (Rosen, 1974), (Roback, 1982), Gaeser (2008). The first property that I discuss is whether there are mutipe ong-run equiibria or not. Proposition 6. There are mutipe ong-run equiibria. However, given an initia distribution of peope across space, there is a unique equiibrium. Proof. See Appendix. It is worth noting that this mode is in ine with the importance of ocation fundamentas or path dependence which woud hep to expain the initia distribution of peope and economic activity across space and with the random growth theories if technoogies or shocks are random (Davis and Weinstein, 2002). It woud not be hard to incude in the mode increasing returns to scae and transport costs. This is, however, eft outside of this paper. Coroary 7. In the ong run, the margina mover is indifferent between oca abor markets, and consequenty workers in particuar oca abor markets are fuy insured against oca shocks, which are absorbed nationay. This is the case even if out-migration rates hardy respond to oca shocks. It is worth noting that in absence of congestion costs in order to sustain the arger size, workers in big cities need to have higher equiibrium indirect utiities, on average. If this was not the case, biatera fows woud not be equaized. More specificay, the average indirect utiity of a worker that resides in m is A m w m whie in equiibrium condition says that A m w m /(η m N m ) λ is equaized across ocations. This impies that workers in arger cities N m have, on average, either higher wages or higher amenities that they directy vaue. There is a arge amount of iterature documenting that arger cities in fact pay higher wages Duranton and Puga (2004), Rosentha and Strange (2004) or, more recenty, Combes et a. (2012) 13. These are usuay justified as positive aggomeration externaities that make workers more productive in arger cities. 2.8 Mode Discussion This mode shows that it is at east theoreticay possibe that a decrease in in-migration rates without any change in out-migration rates can dissipate oca negative shocks across space. Whie 13 Traditionay, economists argued that this compensated the bad amenities of iving in the big cities. This view has been caed into question by recent papers (Abouy, 2013), (Gaeser and Gyourko, 2005). 13

16 this may seem natura with the mode presented, it is not how researchers have previousy anayzed interna migration. In genera, researchers have used static modes where the discrete ocation choice determines the fina distribution of peope across ocations, not the fows between ocations (see recent exampes ike Moretti (2011), Diamond (2013) or Notowidigdo (2013)). In those modes, there is no distinction between net and gross fows of workers. In fact, ony net fows can be obtained as the difference in the spatia distribution of peope across ocations at different points in time. To the best of my knowedge, ony Coen-Pirani (2010) is we aware of the importance of distinguishing between in- and out- migration rates. In fact, whie the mode he deveops is very different from the one in this paper, the empirica facts he reports are competey in ine with the mode and the empirica findings I show in what foows. Empiricay, Coen-Pirani (2010) reports that in the cross-section, in-migration rates have higher variance than out-migration rates. The intuition for this resut in the mode presented here is simpe. If we think that oca shocks happen randomy at different ocations, we shoud observe that in-migration rates tend to be more different across ocations than out-migration rates, at east in the cases where the atter do not respond strongy to oca economic shocks. Coen-Pirani (2010) aso emphasizes that net infow rates have a smaer variance than in-migration rates but higher than out-migration rates. This is simpy a possibiity that emerges when there is a positive correation between in- and out-migration rates, which in the context of the current mode, is a consequence of the convergence towards the ong-run equiibrium. At a theoretica eve, the resuts presented in this paper are more genera than in Coen-Pirani (2010). For instance in Coen-Pirani (2010), migration is totay directed towards the ocation that suffers a positive matching shock, whie in the mode presented above, the biatera fows are across any two ocations. Another cosey reated paper is Kennan and Waker (2011). 14. Contrary to what I argue in this paper, Kennan and Waker (2011) and other papers using their methodoogy suggest that migration costs need to be very high in order to be abe to expain the ow equiibrium interna migration. More precisey the variance of the idiosyncratic taste parameters needs to be sufficienty high so that oca conditions do not matter very much. In these circumstances, however, it has to be the case that in-migration rates are very unresponsive to oca shocks something that is competey in contradiction with the evidence that I present in what foows. Thus, when using ogit discrete choice modes there is a tension between the ow equiibrium interna migration rates and the high responsiveness of interna migration to oca shocks. By using a nested ogit structure, I introduce one extra parameter, and thus the sufficient fexibiity to aow both ow equiibrium interna migration and high responsiveness of interna migration to oca shocks. The key mechanism that the nested ogit captures is the asymmetry between the response of the out-migration rate and the in-migration rate. I document at ength this asymmetry in what foows. 14 And simiary, the iterature on abor reocation across sectors (Artuc et a., 2010) 14

17 3 Empirica Evidence: In- and out-migration rates 3.1 Data For this paper, I empoy four main data sources. I use the American Community Survey data from Rugges et a. (2008) to compute migration rates across US metropoitan areas, and in particuar information on the current and past residents ocations to construct in-migration rates, out-migrations and net migration rates during the Great Recession. I aso use the ACS data to compute unempoyment rates and average wages across metropoitan areas. My second source is the Bureau of Economic Anaysis, whose data aow me to obtain a measure of rea gross domestic product per capita. The third and fourth data sources are Census and Current Popuation Survey data, again from Rugges et a. (2008). I use these for the ong-run section. More concretey, I define the in-migration rate to metropoitan area m at time t as foows: In-migration rate m,t = I m,t L m,t (16) where I m,t denotes the number of individuas that ive in m at time t and were iving somewhere ese at time t Simiary, I define the out-migration rate from a metropoitan area m as: Out-migration rate m,t = O m,t L m,t (17) where, O m,t denotes the number of individuas that ive in m at time t 1 and were iving somewhere ese at time t. L m,t is simpy the popuation at m at time t. The net migration rate is simpy the in-migration rate minus the out-migration rate. If we imit the count of individuas to peope of a certain eve of education we obtain the inmigration, out-migration and net migration rates of individuas of education e. In particuar, I use a simpe distinction between high- and ow-skied workers. High-skied workers are defined as those who have attended coege (SC), graduated from coege (CG) or attended graduate schoo (GS). The ow-skied are high-schoo drop-outs (HSDO) and high-schoo graduates (HS) (see Katz and Murphy (1992), Autor and Katz (1999), Acemogu and Autor (2011) or Card (2009) for papers using simiar cassifications). One imitation of the data set is that I ony possess information on metropoitan areas of residence from 2005 unti Before that, ACS reports ony the state of residence and the state of residence in the previous year. Whie those coud be used to define oca abor markets, 15 I use the variabe metarea and migmet1 from Rugges et a. (2008). I do not use the observations where the metropoitan area is not identified. Aso, there are some metropoitan areas for which the variabe migmet1 was not constructed. I do not use these metropoitan areas. Equivaenty I use the anaogous variabes at the state or regiona eve in the onger-run section. 15

18 metropoitan areas are a much better approximation of a oca abor market. 16 An aternative woud have been to use CPS data, in which both state and metropoitan areas are reported. The use of CPS data, however, is imited by its sma sampe size. Furthermore, concerns have been raised about how the US Census Bureau deas with missing data, which further imit the number of observations avaiabe. 17 The sampe size is particuary important when studying yeary migration rates since these are usuay beow 4 percent. By using ACS data I can use more than 250 metropoitan areas, whereas it woud be hard to work with more than 50 metropoitan areas using CPS which expains why I use regions when using CPS data. For a detaied discussion of the data sources avaiabe to study interna migration, see Mooy et a. (2011). They argue that recent interna migration is best estimated using ACS data. When needed, I have merged these data sets by combining the metropoitan area definitions from the BEA and ACS. The pace-names usuay coincide perfecty. Sometimes the naming differs sighty but it is aways cear on inspection when two different names are referring to the same area. Very occasionay, the aggregation is sighty different across data sets. In those cases I needed to use the more aggregate definition of the two data sets. In tota, I obtained 250 metropoitan areas of various sizes and characteristics. 3.2 Summary Statistics Athough ife-ong migration rates are reativey high in the US, year-on-year migration rates are more modest (Mooy et a. (2011)). For a typica metropoitan area, around 3.5 percent of its residents ived in a different ocation the previous year. In fact, migration rates have decined in the ast 20 years or so, as documented in Mooy et a. (2011). This decine in migration rates continued in the 2000s, as can be seen in Tabe 1 when we compare migration rates before and after [Tabe 1 goes here] There is, however, some heterogeneity in how many peope in-migrate or out-migrate from various metropoitan areas. There are some extreme exampes, usuay in coege towns ike Boomington, Indiana and Bryan-Coege Station, Texas, which have in-migration rates consistenty above 15 percent. The buk of metropoitan areas, however, are not far from the average 3.5 percent. It is usuay the case that high in-migration metropoitan areas are aso high out-migration metropoitan 16 Autor and Dorn (2009) define oca abor markets by Commuting Zones in order to incude the entire territory of the US; this is one imitation of using metropoitan areas. In this case, I have imited my anaysis to the migration rates of the metropoitan areas. 17 Mooy et a. (2011) reports ower migration rates in CPS than in ACS, something that is expained in Kapan and Schuhofer-Woh (2012) as an undocumented error in the Census Bureau s imputation procedure for deaing with missing data in the Current Popuation Survey. 16

19 areas, again, for exampe, many of the coege towns in the US, as is aso documented in Coen-Pirani (2010). In the context of the mode presented before, this is simpy what you woud expect if the economy is not far from the ong-run spatia equiibrium. Unsurprisingy, net migration rates are not aways cose to 0. Some metropoitan areas are attracting more peope than the popuation they are osing to other metropoitan areas, contributing to their popuation growth. Figure 2 shows the distribution of net migration rates across metropoitan areas between 2005 and We see that around haf of the metropoitan areas have positive net migration rates, whie the other haf have negative net migration rates. It is aso the case that in every year there are some peope eaving and some peope moving into every metropoitan area. 18 As can be seen, gross migration fows are arger than net migration fows. 19 [Figure 2 goes here] In terms of per capita GDP, we observe in Tabe 1 that rea GDP per capita remained at around $44,350 per capita, both for the entire decade of and for the post-2008 years. This is mainy expained by the crisis. In 2008 and 2009, GDP per capita decreased on average in most metropoitan areas. It increased in a other years. Figure 3 shows the per capita GDP growth rates across metropoitan areas in 2008 and 2009 and a the other years. We can see that in most metropoitan areas GDP per capita decined in 2008 and 2009 whereas it grew in the other years. [Figure 3 goes here] GDP per capita is not the ony measure of oca eve economic activity that may be reevant for mobiity. Unempoyment rates and oca wages are aso very important. During the period, the share and the magnitude of wage reductions increased. The same is true for unempoyment rates. 20 [Figure 4 goes here] A three variabes per capita GDP, wages and unempoyment rates move very simiary. In fact if we ook at the easticities between GPD per capita, wages and unempoyment rates 18 The zero out-migration rates in Tabe 1 are due to sampe size, and are probaby not true zeros. 19 This is true both across ocations and aso industries Saks and Wozniak (2011), Artuc et a. (2010). It is aso the case that the average of the absoute vaue of net-migration rates is significanty arger than either in- or out-migration rates. 20 Not shown in the paper but avaiabe upon request. 17

20 (controing for metropoitan area fixed effects and time dummies), we see that the most responsive was the unempoyment rate, foowed by wages. Tabe 2 shows these resuts. In particuar, a 1 percent change in wages is associated with a.26 percentage change in per capita GDP. Simiary, an increase in unempoyment rates of 1 percentage point is associated with a decrease in per capita GDP of a bit more than 1.3 percent. These reationships can aso be seen when I compute, in the next section, the easticity of in- and out-migration with respect to a these variabes. [Tabe 2 goes here] It is worth emphasizing that whie wages may be nominay downward rigid (Day et a., 2012), this does not impy that they are downward rigid in rea terms across a US metropoitan areas. The average wage in metropoitan areas most affected by the crisis did indeed decrease, and moved in simiar ways to how unempoyment and GDP per capita did. 3.3 The short-run response of the in- and out- migration rates Empirica Strategy One of the main objectives of this paper is to estimate the (short-term) migration response to oca economic shocks. This can be estimated using the foowing specification: Migration rate m,t = βx m,t + δ m + δ t + ε e m,t (18) where Migration rate m,t is either the number of peope that move into metropoitan area m (divided by the popuation in that area), the number of peope that move out of metropoitan area m or the net in-migration to metropoitan m. δ m are metropoitan area (MSA) fixed effects, whie δ t are year fixed effects. I use the years , both incuded. X m,t is a measure of oca economic activity. I use the three aforementioned measures: (og) GPD per capita, average (og) wage and unempoyment rate First Stage: Loca economic variabes and the crisis As said in the introduction, I use two aternative strategies to estimate this easticity. Both rey on the unexpectedness of the current crisis. First, I use the importance of the construction sector and second, the eve of indebtedness of the househods. This atter measure is directy taken from Mian and Sufi (2013) and is defined as the debt to income ratio of househods in a number of US counties. To obtain a measure of indebtedness at the metropoitan area I simpy take the weighted 18

21 (by popuation) average of the different counties debt to income ratio whenever the metropoitan area has more than one county. In particuar, I run the foowing regression: X m,t = β shock t Z m,t + δ m + δ t + η m,t (19) where X m,t is either (og) per capita GDP, unempoyment rate or average (og) wage in metropoitan area m at time t, shock t is a dummy variabe that takes vaue 1 after 2008, and where Z m,t is either the number of workers in construction divided by the tota number of workers in metropoitan area m in 2000, the debt to income ratio in 2006, or the interaction of the debt to income ratio in 2006 with the share of workers in non-tradabe sectors in 2000, which is a measure of how important the drop in aggregate demand was in the metropoitan area 21. I ca these three aternative strategies, IV1, IV2 and IV3. δ m are metropoitan area fixed effects, whie δ t are year fixed effects. Tabe 3 shows the resuts of running these regressions. There are at east two remarkabe findings. First, a three measures that I use to see what the most affected metropoitan areas were when the crisis hit in 2008 are we correated with per capita GDP and unempoyment rates. Wages, in contrast, seem not to react so much to construction. Second, the measures reated to the indebtedness of the househods are much more cosey correated to decreases in GDP, increases in unempoyment and decreases in wages. If the aggregate demand channe is as important as Mian and Sufi (2013) argue, this is exacty what we woud expect to find. [Tabe 3 goes here] We can aso use the same strategies to investigate whether different ski groups are affected equay by the crisis across metropoitan areas. In Tabe 4 I compute the average (og) wage and the unempoyment rates for the ow- and high-skied separatey. 22 It shows that the shock affected the unempoyment rates of ow-skied workers reativey more than those of high-skied workers, whie it affected wages for high-skied workers reativey more than it did for ow-skied workers. These resuts thus suggest that the abor market might be more rigid for ow-skied workers than for high-skied ones so that adjustments take pace in quantities rather than in prices for the former group. [Tabe 4 goes here] 21 I foow Mian and Sufi (2013) to define non tradabe sectors. 22 Low-skied are defined as having finished high schoo or ess. High-skied are the rest of the popuation. 19

22 3.3.3 Second Stage: Interna migration rates and the crisis If we abstracted from the mode presented before, perhaps the most natura measure of oca economic activity woud be the GDP per capita in different metropoitan areas. Foowing the overa economy, most metropoitan areas saw decreases in per capita GDP in 2008, as previousy documented. Metropoitan areas more dependent on the construction sector and metropoitan areas whose househods were more indebted suffered the crisis disproportionatey. Previous iterature reports that, surprisingy, it seems that more peope seemed to move to these metropoitan areas (Mian and Sufi, 2013). When thinking about popuation changes it may be worth taking a wider perspective. Many cities grow over ong periods. A crisis in a given city might affect its trend without necessariy impying that the city wi necessariy ose popuation. First, as can be seen in the Tabe 5, ocations heaviy dependent on the construction sector and which were (to some extent, though much ess) more everaged were in fact attracting more peope than the average metropoitan area. This may be because the construction sector or the oca consumption boom attracted many peope ooking for jobs or simpy because, for other unreated reasons, these were metropoitan areas with higher in-migration rates. 23 What the crisis did was to decrease the rate at which these cities were attracting popuation. It coud we be the case, however, that these cities sti attracted more peope than other cities, despite the fact that they attracted ess peope than they used to. [Tabe 5 goes here] A direct way to ook at migration responses is to ook at migration rates. This has the advantage that we are ooking at the migration responses of exacty one cohort in each period, since I use the current residence and the residence in the previous year of the same individua. In this paper, I use the term cohort to refer to a the individuas that I observe in a given year and a given data set. In Tabe 6 I show the reation between net in-migration rates and the oca abor market economic variabes. The resuts are cear. Net in-migration rates decrease when per capita GDP decreases. A 1 percent decrease in GDP per capita eads to a percentage points decrease in the net in-migration rate, as can be seen in Tabe 6. Simiary a 1 pp increase in the unempoyment rate eads to a pp decrease in net in-migration whie a 1 percent decrease in the average wage eads to a.2-.3 pp decrease. [Tabe 6 goes here] 23 Note that in a other dimensions metropoitan areas do not differ significanty. 20

23 These responses of net migration rates are entirey due to the response of the in-migration rates, as shown in Tabe 7. A metropoitan area with a typica in-migration rate of around 3.5 percent woud see the in-migration rate drop to around percent as a resut of a 1 percent decrease in per capita GDP. In more concrete numbers, this represents.14 percent of the popuation of any given city. Thus, around 9,000 ess peope woud move into New York City if GDP per capita in New York were to drop by 1 percent. We aso see in Tabe 7 that the adjustment to the crisis takes pace through reductions in in-migration rates, rather than increases in out-migration rates. [Tabe 7 goes here] How genera is this resut? Why does this resut seem to contradict some other papers in the iterature? I investigate these questions in the foowing two sections Robustness: High- and ow-skied workers Wozniak (2010) emphasizes that high-skied workers are 5-15 percent more ikey to take advantage of good abor market opportunities. 24 Her anaysis, however, does not expain how sensitive the decision is of whether to move to particuar paces when they have been hit by a negative shock. An idea experiment to answer whether in-migration rates respond differenty to changes in oca abor market conditions woud be to have a shock that ony affects one type of workers. In this paper, the shock affected both high and ow-skied workers. Sti, one can compare what happens to changes in wages or unempoyment rates of specific groups and changes in interna migration of these groups. In this section I concentrate on in-migration rates, since a the action comes from this variabe. The resuts are shown in Tabes 8 and 9. [Tabe 8 goes here] Tabe 8 shows that the interna migration response of ow-skied workers is very simiar to that of the average popuation shown in Tabe 7. For exampe, the estimated easticity of in-migration rates to per capita GDP is between 9 and 16 percent for the average popuation whie it is from 10 to 17 percent for the ow-skied. Tabe 8 aso shows that this easticity does not change if we restrict the computation of in-migration rates to native workers. This seems to be in contradiction to the findings in Cadena and Kovak (2013), which I discuss beow. Tabe 9 shows that the estimates do not change significanty if we restrict attention to highskied workers. Again the easticities are simiar to the ones computed in Tabe Literature reviews about interna migration rates incude Greenwood (1997). 21

24 [Tabe 9 goes here] Robustness: Expaining some resuts in the iterature This section expains why both the evidence reported in Mian and Sufi (2013) and in Cadena and Kovak (2013) is not in contradiction with what I report here. It aso chaenges some of their concusions. Expaining Mian and Sufi (2013) Mian and Sufi (2013) argue that peope did not respond by reocating geographicay during the Great Recession. To ook at this, they regress the popuation growth rate between 2007 and 2009 on a measure of the debt to income ratio at the county eve. They find that popuation growth and debt to income ratios are not correated. This evidence eads to their concusion. To investigate this, I first show that their findings do not change when, instead of counties, we use metropoitan areas as the unit of anaysis. This can easiy be seen in Figure 5. We observe how the fitted vaues of the regression n pop c = α + βeconomic Impact c + ε c define a straight ine between 2006 and This is true independent of the different measures of economic impact discussed before. Figure 5 aso shows that the same regression between 2000 and 2006 gives a steep positive (and statisticay significant) sope. In other words, before the crisis, metropoitan areas that were hit harder during the Great Recession were growing more than the others and there was a cear sow down in their popuation growth rates. This is ceary suggestive that interna migration did respond during the Great Recession. [Figure 5 goes here] Expaining Cadena and Kovak (2013) To investigate how peope respond to oca shocks Cadena and Kovak (2013) regress the percentage change in native popuation between 2006 and 2010 on a measure of how hard the crisis hit across ocations. They then repeat the exercise for the percentage change in Mexican popuation on the same measure of oca economic shocks. They obtain a negative correation in the second regression and a zero (or even sighty positive) coefficient in the first one. This woud suggest that the native popuation is not responsive to negative shocks as concuded in Mian and Sufi (2013), whie immigrants, and in particuar Mexicans, do respond to negative shocks. Unike Mian and Sufi (2013), Cadena and Kovak (2013) concentrate on ow-skied workers. 22

25 This strategy misses the fact that popuation trends might be very different between natives and Mexicans, something that needs to be controed for. An easy way to ook at it is to repeat the same regression Cadena and Kovak (2013) use, but with the popuation change between 2000 and The change in trend between and is evident both for the Mexicans and for natives. This can be seen in Figure 6, which pots the fitted vaues of the regressions between 2000 and 2006 and between 2006 and 2010: [Figure 6 goes here] In particuar, Figure 6 shows that if we reate the growth rate of native popuation and the debt to income ratio computed in Mian and Sufi (2013), we observe that between 2000 and 2006 there is a strong positive reationship. This reationship becomes ess strong between 2006 and 2010, precisey when the crisis hits in high debt metropoitan areas. If we ook at Mexican immigrants aone, we observe that there was initiay a sighty negative reationship, that became even more negative between 2006 and This change in trend is very simiar between natives and immigrants. Knowing these different trends is crucia to interpreting whether ony ow-skied immigrants respond to oca shocks or whether natives aso do, despite the fact that the reationship between native popuation growth rates and debt to income ratio was not negative between 2006 and The onger-run Popuation growth and interna migration The resuts in the previous section show that the short-run response to a negative economic shock is a decrease in in-migration rates and itte changes in the out-migration rates. In this section, I investigate how genera this resut is by decomposing the popuation growth rates in different ocations between the in- and the out-migration rates in a number of standards data sets. More precisey, I decompose the popuation growth rate of a particuar cohort of workers as foows: N m,t N m 1,t = I m,t O m,t (20) N m,t 1 N m,t 1 N m 1,t where N m,t refers to the cohort of workers that at time t are between 18 and 65 years od in each metropoitan area m, and N m,t 1 refers to the exact same cohort but at their t 1 residence (either 5 or 1 years, depending on whether I use Census or CPS data). Equation 20 exacty decomposes the popuation growth rates in various metropoitan areas of particuar cohorts of workers. 25 I obtain simiar resuts for the aternative measures used in this paper of how hard the crisis hit across ocations. 23

26 Given that equation 20 is an exact decomposition, we can measure how much of the variance in popuation growth rates is expained by in-migration rates and how much by out-migration rates. In equations, we can run the foowing two regressions: I m,t N m 1,t = α 1 + β 1 N m,t N m 1,t N m 1,t + (+δ m + δ t ) + ε m,t (21) O m,t N m 1,t = α 2 β 2 N m,t N m 1,t N m 1,t + (+δ m + δ t ) + ɛ m,t (22) In this situation, it is necessariy the case that β 1 + β 2 = 1. β 1 is then the share of the variation expained by the variation in in-migration rates whie β 2 is the share expained by the variation in out-migration rates. Tabe 10 shows the resuts from using these decompositions. Across a number of specifications and data sets the message is cear. Most variation in popuation growth rates, generay above 70 percent (and many times even above 90 percent), is expained by variation in in-migration rates rather than variation in out-migration rates. In pane A, I show these decompositions at the metropoitan eve. We observe that cities grow (or decine) mainy because they have disproportionatey high (or ow) in-migration rates. This is true for each of the decades considered independenty, i.e to 2000, and it is aso true when pooing a the data together as in Tabe My preferred specification is the one shown in coumns (5) and (6) where I incude metropoitan area fixed effects which account for systematic differences in the eve of in- and out-migration rates across metropoitan areas and time fixed effects that account for possibe shocks to interna migration at the nationa eve in the given year ike different moments of the business cyce. This specification suggests that in-migration accounts for more than 70 percent of the variation of popuation growth rates across metropoitan areas. The fact that definitions of metropoitan areas vary sighty across decades, motivates the computation of the exact same decomposition but at the state eve. The benefit of this is that state borders do not change across decades, so in- and out- migration rates from states can be computed more reiaby and more consistenty across decades. This is shown in Pane B of the same Tabe 10. The picture is virtuay the same. Again, in my preferred specification, over 90 percent of the variation in popuation growth rates across states is accounted for by variation in in-migration rates. Pane C in Tabe 10 investigates whether these resuts are sensitive to the frequency of the data used. Athough the regressions using the Great Recession suggest than in-migration rates tend to respond more, this resut shoud aso be found using CPS data, and in a much arger time series 26 In fact, when considering every decade on a separate regression, the coefficients on in-migration are aways above.9. It is aso worth taking into account that there are some metropoitan areas for which out-migration rates cannot be computed and some that did not exist in the 1980 Census. I dropped these metropoitan areas, which eaves me with 158 metropoitan areas. 24

27 ( ). In this case, I present interna migration at the regiona eve. This is due to the fact that there are some sma states in the US for which the computation of migration rates is ess reiabe, due to the ack of individua eve observations. The resuts are, again, very simiar. In my preferred specification, we observe how more than 70 percent of the variation in popuation growth rates is accounted for by variation in in-migration rates. [Tabe 10 goes here] Popuation size and interna migration A natura consequence of the mode is that, in equiibrium, interna migration rates in the crosssection are necessariy smaer in bigger cities or regions. If this was not the case, biatera fows across ocations woud not be equaized, and thus the economy woud not be in spatia equiibrium as was defined in the first section of the paper. This is an easy prediction to test. In particuar, one can run the foowing regression: (n) Migrants mt = α + β(n) Popuation mt + (δ t ) + ε mt (23) To test if in-migration rates tend to be ower in arger ocations, we ony need check whether β < Tabe 11 shows the resuts of running this regression. It shows that both using metropoitan areas or states, it is aways the case that interna migration rates and popuation size are negativey correated. This is true both if we weight the observations by the size of the ocation (to account for measurement error) or if we don t and assume that measurement error is non-existent. The magnitudes suggest that if we doube the size of a ocation then its interna migration rate are around 7-20 percent smaer. [Tabe 11 goes here] It is worth noting that this resut, whie true in the mode presented, need not hod in other spatia equiibrium modes. In spatia equiibrium, popuation eves need to be constant. This impies zero net in-migration rates. These zero net in-migration rates coud be the resut of any combination of in- and out- migration rates. 27 Note that an aternative woud be to regress the (n) of the migration rates on the (n) popuation and test whether β < 0. This, obviousy, deivers the same resuts. 25

28 4 Speed of adjustment In the previous sections, I have shown that what determines which regions or cities gain or ose popuation is more reated to the in-migration into particuar ocations than to the out-migration from these ocations. I have aso shown that the reaction of the in-migration rates to oca shocks is a ot arger than that of out-migration rates. This expains how interna migration heps to dissipate oca shocks, even during recessions. In this section, I investigate quantitativey how these oca shocks propagate through the oca abor markets using a caibrated version of the mode with the parameters estimated in the empirica section. In particuar, I study the effects of interna migration in mitigating the negative consequences in the metropoitan areas that were most affected during the Great Recession in the US. This shows how important in-migration rate responses are in providing insurance against oca shocks. 4.1 Mode Caibration There are three key parameters in the mode that govern how oca shocks spread. The first two have been estimated in the empirica section. Those are the reaction of the in-migration rate (governed by λ) and the out-migration rate (governed by γ) to oca shocks. In the empirica section, we see that these are around 1/λ = 5 and 1/γ = The third key parameter is the oca abor demand easticity. I have not estimated this parameter in this paper, so I need to make some assumptions on it. Based on my previous research Monras (2013) a short-run oca abor demand easticity of 1 is a reasonabe parameter. It impies that the production function at the oca eve is Cobb-Dougas. Other easticities ony change the speed at which the oca shocks are transmitted. In any case, the ong-run oca demand easticity is cose to 0, in ine with the research on immigration by Atonji and Card (1991), Card (2001) and Card (2009). The rest of the parameters are caibrated to match the US data. In particuar, I obtain θ m by ooking at the share of output that is devoted to abor. I caibrate B m (the tota factor productivity of the city) and the contribution of and in what foows, I refer to the combination of these two as TFP as the difference between what is produced and the abor contribution. 29 The parameters that are a bit more chaenging for the caibration are the city-specific amenity eves. For these, I use the ong-run equiibrium condition. In simpe words, I assume that in 2005 the US economy was in ong-run spatia equiibrium. I observe the average wages and the popuation eves in a the ocations in the US and I infer the amenity eves as the vaues that 28 For 1/λ = 5 we ony need to use the coefficient of the regression of in-migration rates on wages, and mutipied by the equiibrium migration rate of between 3 and 3.5 percent. 1/λ = 5 is a ower bound on the responsiveness of in-migration rates. 29 More specificay I set ˆθ m = 1 wm Q m/n m and B mk θm m = Qm L m Lˆθ m m. 26

29 make the biatera fows of workers across ocations stabe. 30 For this I specificay use the equation 11 discussed in the theory section. More specificay, I chose the parameter η as the parameter that ensures that New York s average in-migration rate is at its empirica counterpart of a bit over 3 percent Interna migration during the Great Recession With a these parameters in hand, I can simuate the mode. The question is then how to think about the Great Recession in ight of the mode. A simpe way to do it is to assume that the Great Recession is a oss in the TFP of the cities of various magnitudes. This coud represent, for exampe, the functioning of the financia systems in these different ocaities, or the importance of particuar sectors more affected by the crisis. This change in TFP, however, is unobservabe. Instead, one can compare the wages in 2005 and those of 2008, assume that popuation eves are stabe through this period, and infer the TFP in 2008 that woud justify the observed wages in This is how I obtain the eves of TFP that cause certain cities to be more affected by the Great Recession in I can then feed these vaues into the mode and see the predictions of the mode with respect to wage and popuations eves and compare them with the data. It is worth emphasizing that the mode provides the effect of interna migration on wages and popuation eves across ocations if nothing ese was changing in the economy. In this respect, it isoates the contribution of interna migration to the mitigation of the wage decreases in the most affected ocations. From a short-run perspective, we can use the estimates we obtained, together with the assumed oca abor demand easticity, to anticipate the roe of decreased in-migration at the oca eve. The fact that a one percent decrease in wages is associated with a.3 percentage point decrease in the in-migration rate means that, if the oca demand easticity is 1, the potentia mitigation effect of reduced in-migration is around 1/3. This can be shown more graphicay (and more competey) with the hep of the caibrated mode. [Figure 7 goes here] The top pane of Figure 7 shows the evoution of wages in three seected cities: New York City, San Francisco and Ceveand. I normaize wages to 1 before the Great Recession hits, athough wage eves are not necessariy the same across ocations. The inferred change in TFP resuting 30 More expicity, I equate P m,m and P m,m for a m, m M and obtain the amenity eves with respect to a base ocation. The base ocation is the first metropoitan area in aphabetica terms. 31 Note that I coud use a different assumption of the year when the US is in ong-run spatia equiibrium, since 2005 is an arbitrary choice motivated by the fact that it is the eariest date where I can use ACS data. The resuts do not change substantiay if instead we were to assume another year (or average over some period) as the ong-run spatia equiibrium. 27

30 from the Great Recession is argest in Ceveand, foowed by New York and San Francisco (which in fact is doing sighty better than the nationa average). This can be appreciated in the wage evoution of the various cities. Ceveand sees a sharp decrease at time 0 that is mitigated in the foowing periods thanks to interna migration. The shock in New York is ess negative, whie in San Francisco the shock is roughy equa to the nationa shock. This means that wages in New York drop initiay, but not as much as in Ceveand, and they then sowy recover. In San Francisco they drop initiay, but since the city is ess affected than the others, wages do not recover (since the shock is no worse than the average shock in the whoe of US). The bottom part of Figure 7 shows how the evoution of wages shapes the evoution of popuation. We see that since Ceveand s wages drop more than the nationa average, fewer peope are attracted towards Ceveand. This decreases its popuation eve and partiay mitigates the negative consequences of the crisis. If we take the wage drop in San Francisco as the eve at which Ceveand shoud have been had it suffered the average negative shock during the Great Recession, we see that wages in Ceveand shoud have dropped by around 4.2 percent. Instead they drop by amost 7 percent. Once interna migration starts to act, we observe how wages in Ceveand recover a itte bit, to a oss of around 5.8 percent. This is a recovery of 1.2 percentage points, roughy one third of the difference between the 4.2 percent oss in San Francisco and the initia 7 percent oss in Ceveand. This happens quite fast, since most of the adjustment has aready taken pace within the first five years the first year being the one with the argest adjustment. The mechanism through which this is happening is, in this caibration, excusivey through reduced in-migration. This is shown in Figure 8. [Figure 8 goes here] In fact, there are a number of properties of the mode that become cear in Figure 8. First, we observe that equiibrium in-migration rates are higher in the smaer city (Ceveand) than in the arger ones. The effect of the Great Recession is a sharp decrease in in-migration rates toward Ceveand, a moderate decrease in New York City, and roughy no effect in San Francisco. This simpy refects the change in wages (reative to the nationa average) that the Great Recession caused in these three cities. 4.3 Comparing the mode and the data To test whether the mode captures the wage and popuation dynamics in the data we, we can compare the wage and popuation eves predicted by the mode and the ones observed in the data. To do so, I report the foowing regressions: 28

31 X mt = α + β ˆX mt + δ m + δ t + ε mt where X indicates either wages or popuation eves, and δ are time and metropoitan area fixed effects. The hat indicates that the variabe is the one predicted by the mode. [Tabe 12 goes here] The resuts are reported in Tabe 12. We see that the mode predictions are negativey correated with the actua wage evoution and positivey correated with the popuation evoution. An interpretation of this resut is that the Great Recession was not just a one period shock, but a arger shock to particuar metropoitan areas. This made wages in the data in the most negativey affected ocations decrease, whie in the mode they recover thanks to the effect of interna migration. This expains the negative correation. Another way to put it is that the mode is isoating the effect of interna migration on wages. At the same time, the evoution of popuation eves is in the direction of what is predicted by the mode, since affected areas, no matter if they are affected in one period or in mutipe, ose popuation. 5 Concusion Contrary to previous iterature, such as Mian and Sufi (2013), Mooy et a. (2011) and Yagan (2014), I show in this paper that interna migration rates responded to the crisis. Rather than observing popuations eaving the hard hit ocations, I have documented that fewer peope migrated into the ocations that suffered more from the crisis. This is important because it heps decrease the abor suppy in those metropoitan areas and it spreads the oca shocks spatiay. Furthermore, I show that this is found both when considering native workers aone, or together with immigrants. When distinguishing by ski, ow-skied workers are shown to be more responsive to unempoyment rates whie high-skied workers respond more to wage changes. This paper aso shows how differences in in-migration rates may be crucia for the understanding of city growth. Across a number of data sets and time periods, I show how most of the variance in popuation growth rates across cities is accounted for by variance in in-migration rates. In a, this paper shows that interna mobiity heps mitigate negative shocks at the oca eve. 29

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35 6 Figures Figure 1: Migration decision from an aggregate perspective Moves to 1 Worker i in m i moves from m, but where? Moves to j i stays in m Moves to m 33

36 Figure 2: Net migration rates across metropoitan areas Notes: Net migration is computed from the peope that move into and out of each metropoitan area. I have used data from 250 different metropoitan areas between 2006 and Source: ACS data from Rugges et a. (2008). 34

37 Figure 3: GDP per capita growth rates across metropoitan areas Notes: This figure shows the per capita rea GDP growth rates in a 250 metropoitan areas. Vertica ines distinguish positive from negative growth rates. Source: BEA. 35

38 Figure 4: Wage growth rates across metropoitan areas Notes: This figure shows average rea wage growth rates in a 250 metropoitan areas. Vertica ines distinguish positive from negative growth rates. Source: Rugges et a. (2008). 36