Immigrants Equilibrate Local Labor Markets: Evidence from the Great Recession

Abstract

This paper demonstrates that low-skilled Mexican-born immigrants’ location choices in the U.S. respond strongly to changes in local labor demand, and that this geographic elasticity helps equalize spatial differences in labor market outcomes for low-skilled native workers, who are much less responsive. We leverage the substantial geographic variation in employment losses that occurred during Great Recession, and our results confirm the standard finding that high-skilled populations are quite geographically responsive to employment opportunities while low-skilled populations are much less so. However, low-skilled immigrants, especially those from Mexico, respond even more strongly than high-skilled native-born workers. Moreover, we show that natives living in metro areas with a substantial Mexican-born population are insulated from the effects of local labor demand shocks compared to those in places with few Mexicans. The reallocation of the Mexican-born workforce reduced the incidence of local demand shocks on low-skilled natives’ employment outcomes by more than 50 percent.

1 Introduction

Over the past two decades, the labor market in the United States has shown signs of becoming less dynamic in a number of important ways. Job creation, job destruction, and job-to-job transitions have all fallen markedly (Davis, Faberman and Haltiwanger 2012, Hyatt and Spletzer 2013). Additionally, fewer people are making long-distance moves (Molloy, Smith and Wozniak 2011), which is concerning because geographic labor mobility is a primary means of equilibrating differences across local labor markets (Blanchard and Katz 1992). This declining dynamism is of particular concern for low-skilled workers during periods like the Great Recession, which featured mass unemployment and sharp differences across local markets. Not only are less educated workers disproportionately affected by job losses during downturns (Hoynes 2002, Hoynes, Miller and Schaller 2012), but a prominent literature finds that they are the least likely to move from depressed areas toward markets with better earnings prospects (Topel 1986, Bound and Holzer 2000, Wozniak 2010). The substantial geographic variation in labor market conditions during the Great Recession, combined with low levels of geographic mobility, created the potential for sharply disparate labor market outcomes across space, especially among workers without a college education.

In this paper, we examine mobility responses to geographic variation in the depth of the Great Recession, with the goal of determining how such mobility affects the incidence of local demand changes. The analysis reveals an important and novel finding: in sharp contrast to their native-born counterparts, low-skilled Mexican-born workers were quite likely to make earnings-sensitive location choices, and this population shifted markedly away from the hardest hit metro areas toward more favorable markets.¹ Importantly, this mobility occurred not only among new arrivals, but also among immigrants who were living in the US prior to the recession. Moreover, demand-sensitive migration by Mexican-born immigrants dramatically reduced the geographic variability of labor market outcomes faced by less-skilled natives. Natives in metro areas with a substantial Mexican-born population experienced a more than 50 percent weaker relationship between local demand shocks and local employment rates, compared to metro areas with relatively small Mexican-born populations.

Conducting this type of analysis requires identifiable changes in labor demand. During the Great Recession, as in previous downturns, the primary employer response to declining product demand was to cut employment rather than to reduce wages. This feature makes it possible to determine which metro areas faced larger and smaller demand shocks by observing relative changes in employment across those locations. We also instrument for local labor demand using the standard Bartik (1991) measure that relies on the pre-Recession industrial composition of local employment. The results confirm the previous literature's finding of a strong education gradient in geographic responsiveness to labor market conditions. For example, among highly skilled (some college or more) native men, a 10 percentage point larger decline in local employment from 2006 to 2010 led to a 4.6 percentage point relative decline in the local population, compared with no measurable supply response among less skilled (high school degree or less) natives. In sharp contrast, less skilled Mexican-born men responded even more strongly than highly skilled natives, with a 10 percentage point larger employment decline driving a 5.7 percentage point larger decline in population. Immigrants thus play a crucial and understudied role in increasing the overall geographic responsiveness of less skilled laborers in the U.S., and this result adds a new dimension to the existing literature that focuses on workers’ responsiveness to demand shocks based on education and demographics.²

Having established that less skilled Mexicans are highly geographically responsive to changes in labor market conditions while less skilled natives are not, we examine the implications of Mexican mobility for natives’ employment outcomes. We find that in metro areas where the Mexican-born comprised a substantial share of the low-skilled workforce prior to the recession, there was a much weaker relationship between labor demand shocks and native employment probabilities than in areas with relatively few Mexican workers. Natives living in metro areas with many similarly skilled Mexicans were thus insulated from local shocks, as the departure (arrival) of Mexican workers absorbed part of the relative demand decline (increase). Therefore, Mexican mobility serves to equalize labor market outcomes across the country, even among the less mobile native population.

Finally, we consider possible explanations for why the Mexican-born are more likely to make demand-sensitive long-distance moves. We begin by noting that a portion of the difference can be explained by larger overall mobility rates when including international migration. The remainder reflects differential sensitivity to changing labor market conditions, and we thus examine a number of reasons why the location decisions of the Mexican-born are more responsive. We consider differences in observable demographic characteristics such as age, education, family structure, and home ownership, but find that these do not account for the differential responsiveness. Instead, we conclude that a likely contributing factor is the fact that the Mexican-born are a self-selected group of people with high levels of labor force attachment and a greater willingness to move long distances to encounter more favorable labor market conditions. In addition, Mexican-born workers have access to a particularly robust network that reduces both the costs of acquiring information about distant labor markets and the financial costs of moving (Munshi 2003).

These findings have important implications for multiple literatures. First, as mentioned above, various papers find that the mobility of workers reduces geographic inequality (Bartik 1991, Blanchard and Katz 1992) and that differences in responsiveness across worker types determine the degree to which local shocks are realized in local outcomes for particular worker groups (Topel 1986, Bound and Holzer 2000). Prior work has focused on differences across education groups, and we confirm that native-born less skilled workers respond much less strongly to local market conditions than their higher skilled counterparts do. We further demonstrate an even larger difference in responsiveness within the less skilled market, between immigrants and natives. This distinction between less skilled immigrants and natives likely explains why we find an important role for equalizing migration, while other recent work focusing on citizens (Yagan 2014) or total population (Mian and Sufi 2014) finds a more limited role for migration during the Great Recession. We show that the presence of highly responsive immigrants increases the overall geographic elasticity of the less skilled labor force, and immigrants’ mobility serves as a form of labor market insurance by transferring employment probability from relatively strong markets to relatively weak ones. Importantly, immigrants’ mobility mitigates the very negative outcomes that natives otherwise would have faced in the most depressed local markets, which had been the primary concern of the earlier literature.

Second, demand-driven location choices by immigrants represent a central challenge in the literature measuring immigrants’ effects on natives’ labor market outcomes. To address this challenge, researchers have used instrumental variables based on the existing locations of immigrant enclaves (Card (2001), for example) or relied on national time-series identification rather than cross-geography comparisons (Borjas 2003).³ Our results confirm the hypothesis that immigrants’ location choices respond strongly to local economic conditions, and we show that during the Great Recession more than 75 percent of Mexican immigrants’ geographic response occurred through return migration or internal migration by previous immigrants, channels that are largely neglected in prior work.⁴ This finding demonstrates that geographic arbitrage can occur even without much new immigration, as long as the labor market has a large stock of immigrants whose location choices are highly sensitive to employment opportunities. Moreover, the fact that immigrants’ mobility reduces variability in labor market outcomes faced by natives is an important effect of immigration on the host country, and a complete welfare accounting should take it into consideration.⁵

Third, the most closely related prior work is Borjas's (2001) seminal paper, which introduced the possibility of spatial arbitrage through the arrival of new immigrants to states with high wage levels and simulated the potential geographic smoothing effect on natives’ wages. Although similar in examining geographic smoothing resulting from immigrants’ location choices, the current paper differs in important ways. Our unit of analysis is the metropolitan area rather than the state, allowing us to more closely approximate local labor markets. Importantly, we focus on responses to plausibly exogenous labor demand shocks rather than to unconditional wage levels or wage growth. As just mentioned, we examine the importance of return migration and internal migration rather than focusing only on newly arrived immigrants. Finally, we introduce a test to demonstrate empirically the geographic smoothing that Borjas investigated through simulation. Rather than assuming a particular degree of substitutability between immigrants and natives, we uncover a relationship in the data that would not exist if immigrants and natives did not compete for similar jobs. In this sense, our work provides strong empirical support for his hypothesis that immigration “greases the wheels of the labor market,” while expanding the finding to show that immigrants continue to fulfill this role even after arrival.

The remainder of the paper is organized as follows: the next section provides context for examining demand-sensitive location choices during the Great Recession. Section 3 provides the main results and multiple robustness checks of the Mexican/native-born differences in geographic responsiveness. Section 4 demonstrates that Mexican immigrants’ mobility smooths labor market outcomes for natives. Section 5 shows that similar mobility and smoothing results apply during the pre-Recession period. Section 6 decomposes the supply responses into various channels and discusses potential reasons why Mexican-born immigrants may be uniquely positioned to serve as an equilibrating force in the low-skilled labor market. Section 7 concludes.

2 Background and Conceptual Framework

2.1 Measuring Demand Shocks

Like many previous recessions, the Great Recession was characterized by large employment declines and much smaller wage cuts.⁶ Our initial identification strategy exploits the fact that employers adjusted primarily on the employment margin rather than the wage margin, which makes it possible to observe the relative size of demand declines across metro areas directly through employment changes. Note that for our purposes, it is unimportant why employers responded this way; rather, this approach simply requires the descriptive fact that the bulk of the response occurred through employment.⁷ We therefore initially measure each metro area's demand shock as the proportional decline in observed payroll employment, and then examine how local labor supply responded to this measure of the degree to which local conditions deteriorated. It is important to emphasize that this approach is appropriate only because of the particular features of the labor market during the Great Recession and would likely not be applicable in periods with low rates of unemployment, when employment changes are more likely to reflect shifts in both supply and demand.

Although the recessionary environment makes it plausible that changes in employment reflect only changes in demand, changes in the size of the local population may affect local labor demand through the consumer demand channel, creating a reverse causality problem. As we discuss in more detail in section 3.2, it is unlikely that the resulting bias will vary substantially across demographic groups, implying that the relative supply responses across groups remain informative. However, we further support this interpretation by conducting IV analysis using the Bartik (1991) measure as an instrument for changes in local employment. These results are very similar to those using OLS, and in most specifications, we fail to reject the null hypothesis that the two sets of estimates are equal, which supports the interpretation that measured employment changes reflect demand shocks.

2.2 Geographic Variation in Employment Changes

There was considerable geographic variation in the depth of the recession. The hardest-hit locations (e.g. Nevada, Michigan, Florida) lost more than ten percent of employment from 2006-2010, while a few places (including North and South Dakota and Texas) experienced modest employment growth over the same period.⁸ Our empirical specifications define a local labor market as a metropolitan area (we will use the word “city” interchangeably for ease of exposition), and there was even greater variation in employment changes at this level of geography.⁹

Several recent papers examine the sources of these differences. Mian and Sufi (2014) show that counties with higher average household debt-to-income ratios in 2006 experienced larger declines in household expenditure and hence larger employment declines, particularly in non-traded industries that depend on local consumer demand. Greenstone, Mas and Nguyen (2014) show that counties whose small businesses borrowed primarily from banks that cut lending following the financial crisis experienced larger employment declines, and Chodorow-Reich (2014) provides direct evidence that firms with greater exposure to such banks experienced greater employment losses. Fort, Haltiwanger, Jarmin and Miranda (2013) show that states facing larger housing price declines experienced declining employment among young small businesses who often rely on home equity financing. Further, certain industries (notably construction and manufacturing) experienced especially large losses in employment, and these industries comprised different shares of local demand for labor. We leverage the resulting geographic variation in the local depth of the recession to identify the effects of labor market strength on individuals’ location choices.

2.3 Geographic Mobility 2006-2010

Throughout our analysis, we consider locational supply responses separately by sex, skill, and nativity.¹⁰ Table 1 reports long-distance (cross-city or international) mobility rates for these demographic groups. Immigration and internal migration are measured using the ACS, while emigration to Mexico is measured in the 2010 Mexican Decennial Census. In all cases, the numbers reflect average annual mobility rates throughout our study period.¹¹ Notably, every demographic and skill group experienced substantial mobility over this time period, which suggests that there is scope for the reallocation of labor across markets in response to local shocks. In nearly all cases the more educated portion of each demographic group exhibits a higher mobility rate. Natives are generally more likely to have moved within the U.S., while the foreign-born are more likely to have moved from an international location.¹² As expected, emigration to Mexico is an important channel for Mexican-born population adjustment during this time period.¹³ Overall, less skilled Mexican-born individuals are substantially more likely to have moved during our sample period than are similarly skilled natives. For example, less skilled Mexican men's yearly migration rate was 7.0 percent, while the same rate for natives was 4.0 percent.

Table 1.

Average Yearly Mobility Rates

	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Immigration	0.2%	1.9%	1.8%	2.1%
Internal Migration	3.8%	3.3%	3.0%	3.6%
Emigration to Mexico		1.2%	2.3%
Total	4.0%	6.4%	7.0%	5.7%
Panel B: Men, Some college or more
Immigration	0.3%	2.8%	1.9%	2.9%
Internal Migration	4.6%	4.7%	3.3%	4.9%
Emigration to Mexico		0.1%	1.0%
Total	4.8%	7.7%	6.2%	7.8%
Panel C: Women, High-school or less
Immigration	0.1%	1.8%	1.2%	2.4%
Internal Migration	3.6%	2.9%	2.4%	3.2%
Emigration to Mexico		0.4%	1.0%
Total	3.7%	5.1%	4.5%	5.6%
Panel D: Women, Some college or more
Immigration	0.2%	2.8%	1.7%	2.9%
Internal Migration	4.4%	4.3%	3.1%	4.4%
Emigration to Mexico		0.1%	0.8%
Total	4.5%	7.2%	5.6%	7.3%

Sample: individuals aged 18-64, not enrolled in school, and not in group quarters at the time of the survey. “Immigration” and “Internal Migration” are calculated using the 1-year mobility question in the 2006-2010 ACS. “Immigration” reports (individuals arriving in MSAs from abroad) / (individuals living in an MSA in the survey year or prior year). “Internal Migration” reports (individuals moving across MSA boundaries within the U.S. who arrived in or left an MSA) / (individuals living in an MSA in the survey year or prior year). These are calculated for each ACS year and averaged across years. “Emigration to Mexico” is calculated using the 2010 Mexican Census and the 2005 ACS, and reports (individuals moving from the U.S. to Mexico between June 2005 and June 2010) / (individuals living in the U.S. in 2005), divided by 5 for the average yearly rate. The values are approximately zero for all but the Mexican-born.

We stratify our analysis by nativity not only because immigrants are more mobile in general, but also because they are likely more motivated by labor market conditions when selecting a location. In section 6.2, we discuss multiple pieces evidence that the Mexican-born are especially likely to move for economic rather than personal reasons. Thus, the differences across groups in supply responses that we document below reflect both differences in the unconditional probability of moving and differences in responsiveness to economic conditions among those who migrate.

3 Population Responses to Demand Shocks

3.1 Data Sources and Specifications

Our empirical strategy examines changes in a city's working age population (separately by sex, skill level, and nativity) as a function of the relevant demand shock, as reflected by changes in payroll employment. Our dependent variable is the change in the natural log of the relevant demographic group's population from 2006-2010, calculated from the American Community Survey (ACS).¹⁴ Note that the ACS sample includes both authorized and unauthorized immigrants.¹⁵ Our sample includes individuals ages 18-64, not currently enrolled in school, and not living in group quarters. Because we will examine tightly defined groups of workers, we limit our analysis to cities with a population of at least 100,000 adults meeting these sampling criteria. Additionally, we drop cities with fewer than 60 sampled Mexican-born individuals in 2006 and cities with any empty sample population cells (for any demographic group) in the 2006 or 2010 ACS. These city-level restrictions are imposed uniformly, resulting in a sample of 95 cities in each regression.¹⁶

Although we do not estimate a formal location choice model, both Borjas (2001) and Cadena (2013) provide theoretical (discrete-choice-based) justifications for using linear models to examine proportional changes in supply as a function of changes in expected earnings.¹⁷ Note that with only small changes in wages, the percentage change in expected earnings that a labor market offers (prior to any mobility) will be approximately equal to the percentage change in the number of jobs. We therefore use changes in the natural log of employment as our primary measure of local demand shocks, which we calculate using employment information from County Business Patterns (CBP) data.¹⁸ Throughout the discussion we use the notation ẋ to signify changes in logs: ẋ ≡ log(x₁)–log(x₀). Unless otherwise noted, this change refers to the 2006 to 2010 long difference. Our primary specification is thus

$${\stackrel{.}{N}}_c={\beta }_0+{\beta }_1{\stackrel{.}{L}}_c+{ϵ}_c,$$ (1)

where c indexes metro areas, Ṅ_c is the proportional change in working-age population, and L̇_c is the proportional change in employment from 2006-2010.

One concern with this basic specification is that overall employment changes understate the change in expected earnings for low-skilled and foreign-born workers, who were disproportionately represented in the hardest-hit industries.¹⁹ There was considerable variation in employment declines across industries, and Mexican-born workers (the largest single group among the low-skilled foreign-born) were more concentrated in the types of jobs that experienced the largest declines (see Appendix section A.2 for details). We therefore construct group-specific employment changes that account for these differing industrial compositions.²⁰ Note that the proportional change in city c's overall employment can be expressed as a weighted average of industry-specific (i) employment changes, with weights equal to the industry's share of total employment in the initial period.

$${\stackrel{.}{L}}_c=\sum _i{\phi }_{ic}^{t_0}{\stackrel{.}{L}}_{ic},\text{where}{\phi }_{ic}^{t_0}\equiv \frac{L_{ic}^{t_0}}{L_c^{t_0}}.$$ (2)

Based on this insight, we calculate the relevant change in employment for a given education and/or demographic group, g, using industry employment shares that are specific to each group, ${\phi }_{ic}^{g{t}_0}$, rather than shares for the local economy as a whole, such that ${\stackrel{.}{L}}_c^g\equiv {\sum }_i{\phi }_{ic}^{g{t}_0}{\stackrel{.}{L}}_{ic}$.²¹

The primary advantage of the CBP is that it obtains data from the universe of establishments in covered industries. Unfortunately, the CBP data do not cover employment in agricultural production, private household services, or the government. In our preferred specifications, therefore, we fill in the missing changes in employment using (city x industry) calculations from the ACS.²² The only remaining concern, therefore, is the informal sector. If the employment losses in the informal sector are similar (in proportional terms) to losses in the formal sector, the results will be unaffected. It is nevertheless possible that foreign-born workers face larger employment declinesthan our measure indicates. Given the substantial difference in the responsiveness of native and foreign-born individuals, however, this issue seems unlikely to drive the results.

Our preferred specification also weights each city to account for the heteroskedasticity inherent in measuring proportional population changes across labor markets of various sizes. We construct efficient weights based on the sampling distribution of population counts, accounting for individuals’ ACS sampling weights.²³ In practice, nearly all of the cross-city variation in the optimal weights derives from differences in the 2006 population, and results from population-weighted specifications are quite similar. Additionally, unweighted specifications produce qualitatively similar results in most specifications, particularly for the native-born and Mexican-born low-skilled workers that we focus on.²⁴

Finally, we note that although employment changes represent the bulk of employers’ responses to demand changes, there is a small positive correlation between wage changes and employment changes across metro areas.²⁵ Thus the elasticity of population with respect to payroll employment slightly overstates the supply elasticity with respect to expected earnings. However, our primary interest is the difference in elasticities across demographic groups rather than the level of the effect per se, and we do not expect wages to adjust differently across nativity groups. In fact, we have examined the time series of wages separately for native-born and Mexican-born workers, and we find no appreciable difference in the degree to which wages adjusted rather than employment.

3.2 Geographic Labor Supply Elasticities by Demographic Group

Figure 1 shows scatter plots based on equation (1) for low-skilled native-born and Mexican-born men. Each circle represents a metro area, with its size proportional to the weight it receives in the regression.²⁶ The x-axis shows the change in log employment, constructed using industry shares specific to each worker type, and the y-axis shows the change in log population for the relevant group.²⁷ The figure clearly demonstrates our central finding regarding the labor supply responses of less-skilled workers: Mexican-born workers respond much more strongly to local labor demand shocks than do natives, with Mexican-born population shifting away from the hardest-hit cities and toward those with relatively mild downturns, while native populations respond much less.

Figure 1.

Population Responses to Employment Shocks: Native-born and Mexican-born Low-Skilled Men

Source: Authors’ calculations from American Community Survey and County Business Patterns. Changes calculated as the long difference in logs from 2006 to 2010. Individual sample, 95 city sample, and construction of group-specific employment changes described in the text. Weighted to account for heteroskedasticity (details in appendix).

Table 2 reports similar elasticities for a variety of groups defined by skill, sex, and nativity, with each coefficient in the table coming from a separate regression. For example, the Native-born and Mexican-born coefficients for less skilled men in Panel A correspond to the scatter plots in Figure 1. Comparing Panels A and C to B and D, respectively, we find the well-established empirical regularity that, in general, workers with at least some college education are much more responsive than are workers with at most a high school degree. There are also substantial differences among skill groups by nativity, with the foreign-born consistently more responsive than the native-born. For less skilled workers, the strongest mobility responses appear among Mexican-born immigrants, in sharp contrast to the very small and statistically insignificant estimates for natives.²⁸ The fact that less-skilled Mexican-born immigrants respond so strongly to labor demand shocks is, to our knowledge, a novel finding. We therefore spend the remainder of the paper examining this result and its economic implications.

Table 2.

Population Response to Labor Demand Shocks

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.163*** (0.061)	0.041 (0.072)	0.388** (0.169)	0.569*** (0.202)	−0.087 (0.264)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.498*** (0.090)	0.463*** (0.092)	0.605*** (0.206)	0.171 (0.316)	0.717*** (0.209)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.408*** (0.115)	0.196 (0.156)	0.616*** (0.186)	0.652*** (0.192)	0.505 (0.332)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.475*** (0.126)	0.440*** (0.118)	0.826*** (0.271)	0.218 (0.505)	0.898*** (0.268)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) from 2006-2010 on the change in log(group-specific employment) from County Business Patterns data over the same time period, using the demographic group's industry mix. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

To rule out the possibility that the Mexican mobility result is driven by changes in other determinants of location choice that may be correlated with local changes in demand, we introduce a variety of controls. We control for the Mexican-born share of each city's population in 2000, which accounts for the potential decline in the value of traditional enclaves discussed by Card and Lewis (2007). We also add indicators for cities in states that enacted anti-immigrant employment legislation or new 287(g) agreements allowing local officials to enforce federal immigration law, based on the immigration policy database in Bohn and Santillano (2012). Table 3 presents population elasticities analogous to Table 2, with the addition of these controls.²⁹ The pattern of elasticities remains essentially unchanged.³⁰

Table 3.

Population Response to Labor Demand Shocks - With Enclave and Policy Controls

	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.150** (0.063)	0.040 (0.071)	0.292** (0.141)	0.475*** (0.172)	−0.084 (0.281)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.479*** (0.074)	0.435*** (0.082)	0.631*** (0.187)	0.014 (0.285)	0.742*** (0.204)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.395*** (0.121)	0.166 (0.157)	0.631*** (0.179)	0.743*** (0.202)	0.444 (0.348)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.473*** (0.095)	0.423*** (0.102)	0.841*** (0.243)	0.315 (0.597)	0.939*** (0.248)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (2006-2010, using the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data over the same time period, using the demographic group's industry mix. These specifications include the enclave and policy controls in Column (4) of Table A-1. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Although the pattern of elasticities is robust to the controls just mentioned, there remains the possibility of reverse causality, in which unmeasured factors drive population changes, and these population changes result in changes in employment, either through decreasing consumer demand or by mechanically reducing the number of workers. We address this issue in two ways. First, we note that this mechanism would apply to all demographic and nativity groups. Thus, this alternative interpretation cannot explain the lack of a relationship between native population changes and employment changes, which exists despite substantial cross-city mobility (see Table 1). Moreover, since Mexicans often remit a substantial portion of their income rather than spending it locally, reverse causality through the demand channel would be stronger for natives and would bias the difference in elasticities in the opposite direction of the observed gap.

Second, we use the standard “Bartik instrument” (Bartik 1991), which predicts changes in local labor demand by assuming that national employment changes in each industry are allocated proportionately across cities, based on each city's initial industry composition of employment.³¹ This measure is plausibly exogenous to counterfactual population growth and strongly relates to changes in local employment. We calculate the instrument as ${\psi }_c={\sum }_i{\phi }_{ic}^{t_0}{\stackrel{.}{L}}_i$, where ${\phi }_{ic}^{t_0}$ is the fraction of city c employment in industry i in 2006, and L̇_i is the proportional change in national employment in industry i.

The results when using ψ_c as an instrument for the local employment decline are presented in Table 4; these specifications also include the controls introduced in Table 3.³² For each specification, we report the IV elasticity estimates, the p-value of a test that the OLS and IV coefficients are equal, the first-stage coefficients on the instrument, and partial F Statistics for the instrument in the first stage.³³ Although the instrument is identical in all cases, the first-stage coefficients differ based on how the Bartik measure relates to each group-specific employment decline. With the exception of highly skilled native women, we do not appear to face a weak instrument problem, and the first stage coefficients are similar in magnitude to those in the prior literature.³⁴ The IV elasticity estimates for men are similar to the OLS results and exhibit an even larger difference in responsiveness between less skilled natives and Mexicans, though the estimates are less precise. In spite of a few negative point estimates for other immigrants and highly skilled workers, our conclusions regarding the strong responsiveness of less skilled Mexican immigrants and essentially no response among less skilled natives are supported when using this standard method of isolating demand shocks.³⁵ The coefficient estimate of 0.922 for low-skilled Mexican-born men implies that a city facing a 10 percentage point larger employment decline experienced a 9.92 percentage point larger decline in Mexican-born population. Compare this strong response to the very precisely estimated zero coefficient for low-skilled native men.

Table 4.

Population Response to Labor Demand Shocks: Bartik (1991) IV Estimates

	Dependent Variable: Change in log Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
IV Estimate
Change in log of Group-Specific Employment	0.223 (0.166)	0.007 (0.090)	0.402 (0.409)	0.992** (0.468)	−0.675** (0.278)
P-value testing shock exogeneity	0.541	0.764	0.606	0.029	0.072
First Stage
Predicted Change in log Employment	4.196*** (0.702)	4.038*** (0.672)	4.590*** (0.912)	5.108*** (1.478)	4.717*** (0.699)
Partial F Statistic	35.74	36.13	25.31	11.94	45.60
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.270* (0.157)	0.411** (0.192)	−0.237 (0.264)	−0.475 (0.387)	−0.161 (0.329)
P-value testing shock exogeneity	0.316	0.935	0.017	0.331	0.081
First Stage
Predicted Change in log Employment	2.651*** (0.542)	2.662*** (0.569)	2.985*** (0.486)	5.337*** (0.947)	2.727*** (0.449)
Partial F Statistic	23.89	21.91	37.76	31.79	36.89
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.145 (0.168)	−0.405 (0.287)	0.273 (0.504)	1.811*** (0.665)	−0.979* (0.556)
P-value testing shock exogeneity	0.169	0.040	0.315	0.047	0.022
First Stage
Predicted Change in log Employment	2.067*** (0.387)	2.068*** (0.405)	2.167*** (0.419)	2.502*** (0.675)	1.983*** (0.317)
Partial F Statistic	28.59	26.09	26.76	13.73	39.17
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	−0.066 (0.378)	−0.054 (0.420)	−0.754 (0.716)	0.438 (0.919)	−1.092 (0.738)
P-value testing shock exogeneity	0.209	0.368	0.010	0.886	0.056
First Stage
Predicted Change in log Employment	1.081** (0.447)	1.061** (0.449)	1.580*** (0.439)	2.915*** (0.558)	1.364*** (0.377)
Partial F Statistic	5.854	5.578	12.97	27.33	13.12

Each listed coefficient represents a separate instrumental variables regression of the change in log(population) for the relevant group (2006-2010, using the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data over the same time period, using the demographic group's industry mix. All regressions include an intercept term, 94 city observations, and the enclave and policy controls in Column (4) of Table A-1. These specifications omit Brazoria, TX, which is a substantial outlier in the first stage; see appendix section A.9 for details. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

The excluded instrument is the predicted change in log(employment), based on Bartik (1991) and described in the text. The listed “p-value testing shock exogeneity” is from a test of the null hypothesis that the OLS and IV slope coefficients are equal to each other. The first-stage coefficient on the instrument and the partial F statistic are reported below the corresponding IV estimate.

Finally, we use a false experiment approach to rule out the possibility that persistent unobserved factors drove the observed mobility responses. We regress pre-recession (2000-2006) population changes on the demand shocks from 2006-2010. Other than the change in the timing for the dependent variable, these specifications are identical to the main analysis. Figure 2 shows this falsification test for low-skilled Mexican-born and native-born men.³⁶ For both groups, we find a negative relationship. Thus, if anything, the large population responses among the Mexican-born in the latter half of the decade represent a reversal of pre-recession trends. Note that cities facing larger employment declines during the Great Recession on average experienced larger employment increases during the pre-recession period, and additional analysis in section 5 directly supports the interpretation that population changes in the earlier period also reflect earnings-maximizing behavior.³⁷

Figure 2.

Falsification Test: Population Change 2000-06 vs. Group-Specific Employment Change 2006-10

Source: Authors’ calculations from American Community Survey and County Business Patterns. Falsification test with changes in log(population) from 2000 to 2006 and changes in log(payroll employment) from 2006 to 2010. Individual sample, 95 city sample, and construction of group-specific employment changes described in the text. Weighted to account for heteroskedasticity (details in appendix).

Overall, this section documents sharp differences in the responsiveness of less skilled natives and Mexican immigrants to local labor demand shocks. This finding is robust to controlling for other determinants of immigrants’ location choices and to alternative approaches for identifying local labor demand shocks, and it was not driven by pre-existing migration patterns.³⁸

4 Mexican Mobility Smooths Employment Outcomes

The previous section provides robust evidence that Mexican-born workers leave labor markets ex periencing larger labor demand declines in favor of markets facing smaller declines. Here we show that natives living in cities with substantial Mexican populations are insulated from the employment effects of local labor demand shocks.

4.1 Approach to Measuring Smoothing

We define smoothing as the degree to which workers’ employment probabilities are equalized across space rather than tied to local demand.³⁹ Assuming that the employment probability is given by the ratio of employment to working-age population, L_c/N_c, one can measure the degree of smoothing based on the observed relationship between local changes in the employment rate (d ln(L_c/N_c)) and the local demand shock (d ln L_c). In the absence of any equalizing migration response, the local change in employment probability would be proportional to the labor demand decline in each city. In contrast, if earnings-sensitive migration was sufficient to equilibrate employment probabilities across cities, then the local change in employment probability would be uncorrelated with the local demand shock.

To formalize this intuition, consider the relationship between the local change in the employment rate and the local demand shock:

$$\frac{d\ln (L_c∕N_c)}{d\ln L_c}=1-\frac{d\ln N_c}{d\ln L_c}.$$ (3)

Labor demand shocks have a proportional direct effect on local changes in employment probability, but the observed effect may be mitigated by equalizing migration, reflected in a positive relationship between d ln L_c and d ln N_c. We therefore quantify smoothing by running the following regression:

$$({\stackrel{.}{L}}_c∕N_c)={\gamma }_0+{\gamma }_1{\stackrel{.}{L}}_c+{ϵ}_c$$ (4)

The dependent variable is the change in the log of the employment to working-age population ratio calculated from ACS data.⁴⁰ The independent variable is the change in the log of payroll employment, calculated from CBP data. Recall from Section 3.1 that we calculate proportional changes in city level payroll employment using a weighted average of proportional changes in city level industry employment. For this smoothing analysis, we initially use weights based on the pre-recession industry shares among all low-skilled workers in each city and calculate employment rates among the entire low skilled population.

A slope coefficient of one in this regression would imply that local employment changes depend entirely on local shocks, whereas a coefficient of zero would indicate that local outcomes are unrelated to local shocks, with only the aggregate national shock determining the realized change in employment rates. Because we only approximate the employment losses incident on low-skilled workers, however, we expect some attenuation of the estimated coefficient due to measurement error. We therefore focus on relative differences in coefficients across different cities rather than their absolute levels when evaluating the degree of smoothing.⁴¹

In particular, we measure the smoothing influence of Mexican mobility by dividing our sample of cities into those above and below the median Mexican-born share of the low-skilled population.⁴² Cities with few Mexican immigrants have little scope for outmigration in response to a larger-than-average demand decline. Further, when selecting a new location, Mexican movers (including new arrivals from abroad) tend to choose cities with higher Mexican-born populations, either because these populations themselves are a direct amenity or because they proxy for unobserved amenities especially valued by the Mexican-born. As a result, less-skilled workers’ employment probabilities in cities with many Mexicans should be less strongly related to local labor demand shocks than are those in cities with few Mexicans, which do not have access to equalizing Mexican mobility. We therefore estimate versions of (4) separately for cities with above- and below-median Mexican-born population shares, expecting to observe weaker relationships between employment probabilities and labor demand shocks in cities with many Mexican-born workers.

4.2 Smoothing Results

4.2.1 Smoothing in the Overall Less-Skilled Market

We first examine the smoothing effects of Mexican mobility for the low-skilled labor force as a whole. Figure 3 provides a visual representation of the results.⁴³ As expected, there is a much weaker relationship between employment probabilities and demand shocks in cities with large Mexican populations than in cities with smaller Mexican populations.⁴⁴ Table 5 panel (a) confirms this pattern using the Bartik (1991) instrument for local employment changes. In fact, the relationship is more than 50 percent weaker in cities with high concentrations of Mexican-born workers. By increasing the average mobility of the less-skilled population, Mexicans smooth average employment probabilities across space for less-skilled workers.

Figure 3.

Mexican Mobility Smooths Employment Outcomes: Change in Male Low-Skilled Emp/Pop Ratio vs. Change in Low-Skilled Employment

Source: Authors’ calculations from 2006-2010 American Community Survey and County Business Patterns. Changes in log(employment) and log(employment to population ratio) are calculated from 2006 to 2010 for low-skilled men (without regard to nativity). Construction of group-specific employment changes and weights described in the text and the appendix. Fitted lines are from a weighted regression using efficiency weights based on the entire low-skilled male population in each city. See Table A-31 for slope estimates.

Table 5.

Mexican Mobility Smooths Employment Outcomes: Bartik (1991) IV Estimates

dependent variable: change in log employment/population (ACS)
	City's Mexican population share
	below-median	above-median	difference
(a) dependent variable sample: less-skilled men
change in log employment for less-skilled men (CBP)	0.685*** (0.119)	0.305*** (0.071)	−0.380*** (0.138)
(b) dependent variable sample: native less-skilled men
change in log employment for less-skilled men (CBP)	0.731*** (0.138)	0.283*** (0.072)	−0.448*** (0.155)
(c) dependent variable sample: native less-skilled men
change in log employment for less-skilled native men (CBP)	0.736*** (0.131)	0.305*** (0.077)	−0.431*** (0.152)
(d) dependent variable sample: native high-skilled men
change in log employment for high-skilled native men (CBP)	0.293*** (0.112)	0.214** (0.102)	−0.079 (0.151)

Examines the relationship between labor market outcomes (changes in employment probability) and labor demand shocks (changes in payroll employment) separately for cities with above- and below-median Mexican population share to demonstrate the smoothing effect of Mexican mobility. Smaller coefficients indicate more smoothing. We use the predicted change in log(employment), based on Bartik (1991) and described in the text, as an instrument for the change in log(group-specific employment). Panel (a) examines the relationship between low-skilled employment shocks and low-skilled men's employment probability. Panel (b) examines the relationship between low-skilled employment shocks and low-skilled native men's employment probability. Panel (c) examines the relationship between low-skilled native employment shocks and low-skilled native men's employment. Panel (d) examines the relationship between high-skilled native employment shocks and high-skilled native men's employment. These specifications omit Brazoria, TX, which is a substantial outlier in the first stage; see appendix section A.9 for details.

This finding is a direct consequence of the mobility results in Section 3. Consider the following decomposition of the change in the less-skilled employment to population ratio (L_c/N_c) in a particular city.

$$\frac{d\ln (L_c∕N_c)}{d\ln L_c}=1-\left((1-{\eta }_c)\frac{d\ln N_c^n}{d\ln L_c}+{\eta }_c\frac{d\ln N_c^m}{d\ln L_c}\right),$$ (5)

where superscripts m and n refer to Mexicans and natives respectively, and η_c is the Mexican population share. Section 3 reveals that Mexican populations are more responsive to changes in demand than are native populations ($\frac{d\ln N_c^m}{d\ln L_c}>\frac{d\ln N_c^n}{d\ln L_c}$), so cities with larger Mexican population shares exhibit a weaker (less positive) relationship between local shocks and local employment probabilities. Hence, the mobility results directly imply that Mexican mobility smooths average employment probabilities for the aggregate low-skilled workforce.

4.2.2 Smoothing in the Native Less-Skilled Market

The results presented thus far leave open the possibility that Mexican mobility equalizes overall less-skilled employment probabilities simply by equalizing employment rates among Mexicans without having any effect on the employment rates for less-mobile natives. We now determine whether native labor market outcomes are less related to local shocks in locations with larger Mexican population shares, by estimating versions of equation (4) in which the dependent variable is calculated using employment to population ratios for low-skilled native men ($L_c^n∕N_c^n$). Importantly, results using this approach are not mechanically driven by the preceding mobility results because changes in Mexican population do not appear in the denominator. Instead, Mexican mobility can affect the native employment to population ratio only by affecting native employment in the numerator.

Panel (b) of Table 5 shows the results. Changes in employment probabilities for natives living in cities with large Mexican populations are much less related to local demand conditions than are changes in cities with few Mexicans. The relationship in above-median cities is 61 percent weaker than in below-median cities. Thus, native employment probabilities were insulated from local shocks in the presence of substantial numbers of Mexican-born workers, with improved native outcomes in the hardest hit cities and diminished ones in more favorable markets.

To understand the scale of the smoothing result, consider a city that faced a relatively severe employment decline but that had few low skilled Mexican-born workers, such as Orlando, FL.⁴⁵ Orlando experienced a decline in the native employment to population ratio from 78.6 to 66.0 percent from 2006 to 2010. If the labor market were characterized by full smoothing, with all cities experiencing the average decline in employment rates, Orlando's rate would have declined to only 73.6 percent in 2010. The smoothing estimates in panel (b) of Table 5 imply that if Orlando had a larger Mexican-born population comparable to that of Phoenix, AZ, which faced a similar employment shock, its native employment to population ratio would have fallen to 68.7, which is substantially closer to the full smoothing level than is 66.0.⁴⁶ Thus, the employment to population ratio in Orlando was 2.7 percentage points lower than it might have been had a substantial Mexican-born population been present to absorb some of the local shock through equalizing migration. It is important to emphasize that the same smoothing results imply opposite effects for cities experiencing relatively positive shocks. In that case, cities with low Mexican-born populations experienced more positive employment growth than would have occurred in the presence of equalizing migration.

The findings in Panel (b) of Table 5 are precisely what one would expect if the presence of Mexicans in a local market weakened the effects of a decline in labor demand on natives’ employment probabilities. However, there are two potential alternative explanations that we consider. In both cases the evidence supports interpreting the differential slopes as resulting from larger Mexican population shares.

First, suppose that less skilled Mexican immigrants and natives worked in completely different types of jobs, i.e. that the labor market were perfectly segmented by nativity. In this case, a measure of the local decline in total low skilled employment would not necessarily capture the demand declines facing the native portion of the market. The weaker relationship between shocks and employment rates could derive, in part, from measuring the relevant decline in demand for native workers more accurately in cities with fewer Mexican-born workers.⁴⁷ To address this possibility, in panel (c) of Table 5 we adjust the independent variable and calculate proportional job losses using the city-specific industry distribution of native less skilled workers rather than the industry distribution of all less skilled workers in the city as in panel (b). The gap between high and low Mexican share cities decreases only slightly; the shock-outcome relationship is still 59 percent weaker in below-median cities, and the difference remains statistically significant. While this adjustment does not rule out segmentation by occupation within industry, the very modest change

$$\frac{(1-\varphi )\mathrm{var}\left({\stackrel{.}{L}}^n\right)+\varphi \mathrm{cov}({\stackrel{.}{L}}^n,{\stackrel{.}{L}}^m)}{{(1-\varphi )}^2\mathrm{var}\left({\stackrel{.}{L}}^n\right)+{\varphi }^2\mathrm{var}\left({\stackrel{.}{L}}^m\right)+2(1-\varphi )\varphi \mathrm{cov}({\stackrel{.}{L}}^n,{\stackrel{.}{L}}^m)},$$

where ϕ is the Mexican share of employment, var(L̇ⁿ) and var(L̇^m) are the variance in labor demand shocks in the native and Mexican segments of the labor market, and cov(L̇ⁿ, L̇^m) is their covariance. in observed smoothing when accounting for the substantial differences in natives’ and Mexicans’ industry distributions (see Appendix Figure A-6) suggests that labor market segmentation is an unlikely explanation for the differences between these two sets of cities.

Figure A-6.

Employment Shares by Industry Among Low-Skilled Men, Native- and Mexican-Born, 2006

Sources: Authors’ calculations from the 2006 American Community Survey. See text for individual sample restrictions. This figure reports information for men with no more than a high school education. See Figure A-5 for industry employment changes used to sort categories.

As a second alternative, we consider the possibility that some other unobserved factor causes some local labor markets to adjust to shocks more easily and that this other factor is correlated with the Mexican share of the low-skilled population. Perhaps Mexicans are attracted to local economies that are more flexible on a number of other dimensions including differences in local regulations and capital flexibility. Under this alternative, natives’ outcomes would have been smoother in these cities even in the absence of a large Mexican population. We address this hypothesis by repeating the smoothing analysis for highly skilled native-born men. Because we do not expect low-skilled Mexican mobility to affect outcomes for higher skilled workers, any differential incidence of local shocks among this skill group would suggest the presence of such an unobserved factor.

Panel (d) of Table 5 reports the relationship between changes in highly skilled native employment rates and labor demand shocks, calculated using highly skilled native men's industry employment distribution. We maintain the same classification of cities into above- and below-median Mexican population share (among low-skilled workers) used in the previous panels. There is no evidence that the incidence of employment shocks is any different for highly skilled workers in the two groups of cities. Thus, there is no support for the hypothesis that the labor markets with higher Mexican population share are more able to absorb labor demand shocks in general.⁴⁸

This set of results therefore implies that the presence of substantial Mexican-born population insulates less skilled natives from the effects of local labor demand shocks. This is an important finding, as it indicates very different outcomes for natives living in cities facing similar labor demand shocks but with different Mexican population shares. Importantly, the smoothing result applies both to relatively positive and relatively negative shocks, with the presence of Mexicans improving outcomes for natives in the hardest hit markets and depressing outcomes for natives in the most positively affected locations.

4.2.3 Migration as the Smoothing Mechanism

The preceding results show that cities with a large Mexican population experienced smoother labor market outcomes among native low-skilled workers. We now discuss whether this smoothing is likely the consequence of equalizing migration or whether larger Mexican populations affect the incidence of labor demand shocks and native employment through some other mechanism. Consider the following identity demonstrating how the Mexican employment share, ϕ_c, influences the relationship between native employment probability, $L_c^n∕L_c^n$, and the local employment shock.⁴⁹

$$\frac{d\ln (L_c^n∕N_c^n)}{d\ln L_c}=1+{\varphi }_c\left(\frac{d\ln L_c^n}{d\ln L_c}-\frac{d\ln L_c^m}{d\ln L_c}\right)-\frac{d\ln N_c^n}{d\ln L_c}$$ (6)

The last term on the right hand side is the native population response, which the results in Section 3 show is approximately zero on average.⁵⁰ The term in parentheses captures the differential equilibrium incidence of local job losses on native and Mexican workers, and it must be negative to be consistent with a weaker relationship between changes in natives’ employment probabilities and local employment shocks in cities with larger Mexican shares. Thus, in equilibrium, following job losses, turnover, and any migration responses, local employment declines are disproportionately reflected in declining local employment of Mexican-born workers.

This is precisely what one would expect if Mexican mobility had a direct effect on natives’ employment probability. By leaving (or failing to enter) the most depressed local markets, Mexican workers absorb a disproportionate share of the local employment decline, and natives’ share of employment rises as a result. To reinforce this interpretation, we show that it implies a degree of smoothing that is comparable to that observed in the data. Suppose that less skilled natives and Mexicans are perfect substitutes, in the sense that they are indistinguishable to employers. In this case, a given decline in overall employment will decrease equilibrium employment probabilities identically for both nativity groups, and differential employment changes will be driven by differ ential population changes.⁵¹ Under this interpretation, one can predict the amount of smoothing using employment shares and mobility responses. Indexing cities with Mexican population shares above and below the median by a and b respectively, plugging the estimated mobility responses into (6), and differencing across the two groups of cities yields the following expression:

$${\left(\frac{d\ln (L_c^n∕N_c^n)}{d\ln L_c}\right)}^a-{\left(\frac{d\ln (L_c^n∕N_c^n)}{d\ln L_c}\right)}^b=({\varphi }_c^a-{\varphi }_c^b)\left(\frac{d\ln {\widehat{N}}_c^n}{d\ln L_c}-\frac{d\ln {\widehat{N}}_c^m}{d\ln L_c}\right)$$ (7)

Implementing this calculation yields a predicted gap of −0.29, which is similar in scale to the difference in slopes reported in panel (c) Table 5.⁵² Thus, the observed scale of smoothing is consistent with the prediction of a simple model of differential mobility and labor market competition between less skilled native-born and Mexican born workers.⁵³

Taken as a whole, the results in the section imply that Mexican immigrants’ willingness to move away from the hardest hit cities and toward the least affected cities substantially reduced geographic inequality during the Great Recession. Further, their mobility exerted an equilibrating influence on the employment rates of native-born workers in addition to smoothing outcomes among the Mexican low-skilled population. Mexican mobility therefore provides an implicit form of insurance to native workers by transferring native employment probability from cities with relatively strong demand to cities experiencing the largest negative shocks.

5 Pre-Recession Analysis

In this section, we examine whether the differential population responses and associated smoothing that occurred during the Great Recession were similarly operative during the preceding boom (2000-2006). As discussed previously, OLS regressions of population changes on employment changes are likely appropriate only in an environment like the Great Recession, where adjustment to demand shocks occurred primarily through employment rather than wages. As this feature was not present during the boom, Table 6 presents Bartik IV specifications for 2000-2006, following Table 4.⁵⁴ In this earlier time period, high-skilled workers of both genders are more responsive than were low-skilled workers, at least among the native-born. There is not as clear of a pattern among other groups, and the elasticities are, on the whole, estimated less precisely. Importantly, however, the strong positive elasticity among low-skilled Mexican-born men remains. Recall that the set of cities that experienced large demand increases during the boom period tended to have larger declines in the bust. Thus, this additional analysis directly supports interpreting the reversal of trends among the Mexican-born shown in Figures 1 and 2 as reflecting a substantial and rapid population response to local demand conditions in both time periods.

Table 6.

Population Response to Labor Demand Shocks 2000-2006: Bartik (1991) IV Estimates

	Dependent Variable: Change in log Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
IV Estimate
Change in log of Group-Specific Employment	0.322** (0.145)	0.127 (0.139)	0.050 (0.584)	0.872*** (0.221)	−0.142 (0.775)
P-value testing shock exogeneity	0.026	0.029	0.005	0.638	0.004
First Stage
Predicted Change in log Employment	3.856*** (0.984)	4.005*** (0.856)	3.467*** (1.277)	4.207*** (1.129)	3.101** (1.447)
Partial F Statistic	15.37	21.92	7.368	13.87	4.590
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.356** (0.139)	0.296* (0.165)	0.040 (0.421)	1.495* (0.767)	−0.090 (0.454)
P-value testing shock exogeneity	0.998	0.965	0.003	0.330	0.001
First Stage
Predicted Change in log Employment	3.485*** (1.084)	3.447*** (1.018)	3.777*** (1.377)	3.165*** (1.049)	3.865*** (1.433)
Partial F Statistic	10.33	11.47	7.523	9.109	7.272
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.367 (0.227)	0.232 (0.234)	−0.266 (0.707)	0.561 (0.382)	−0.076 (0.707)
P-value testing shock exogeneity	0.051	0.139	0.001	0.466	0.007
First Stage
Predicted Change in log Employment	2.759*** (0.812)	2.837*** (0.756)	2.961*** (0.892)	3.648*** (0.742)	2.623** (1.080)
Partial F Statistic	11.55	14.07	11.02	24.15	5.898
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.492** (0.240)	0.422* (0.244)	−0.142 (0.665)	0.455 (0.842)	−0.240 (0.695)
P-value testing shock exogeneity	0.453	0.637	0.018	0.598	0.016
First Stage
Predicted Change in log Employment	2.603** (1.291)	2.662** (1.279)	2.637* (1.366)	2.076** (0.855)	2.737* (1.438)
Partial F Statistic	4.065	4.335	3.724	5.897	3.624

Each listed coefficient represents a separate instrumental variables regression of the change in log(population) from 2000 to 2006 for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data over the same period, using the demographic group's industry mix. All regressions include an intercept term, 95 city observations, and the enclave control listed in Column (2) of Table A-1. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

We use the predicted change in log(employment), based on Bartik (1991) and described in the text, as an instrument for the change in log(group-specific employment). The listed “p-value testing shock exogeneity” is from a test of the null hypothesis that the OLS and IV slope coefficients are equal to each other. The first-stage coefficient on the instrument and the partial F statistic are reported below the corresponding IV estimate.

Table 7 presents smoothing results for the pre-Recession period, splitting the city sample into those above and below median Mexican-born population share, as in Table 5. Again, we use the Bartik instrument to predict changes in local employment. In panels (a)-(c), the results continue to show that less-skilled men's local outcomes are less tied to local shocks in cities with greater access to Mexican-born workers, although the differences are not statistically significantly different from zero in the latter two panels. Importantly, the results in panel (d) continue to show no substantial difference in smoothing in the high-skilled labor market based on Mexican-born population share. Thus, the phenomena of large population responses among the Mexican-born and the resulting smoothing occur to some extent regardless of whether the economy is growing or shrinking, although it is reasonable to conclude that the smoothing effect may be especially operative during downturns.

Table 7.

Mexican Mobility Smooths Employment Outcomes 2000-2006: Bartik (1991) IV Estimates

dependent variable: change in log employment/population (ACS)
	City's Mexican population share
	below-median	above-median	difference
(a) dependent variable sample: less-skilled men
change in log employment for less-skilled men (CBP)	0.526** (0.241)	−0.108 (0.215)	−0.634** (0.323)
(b) dependent variable sample: native less-skilled men
change in log employment for less-skilled men (CBP)	0.285*** (0.078)	0.175 (0.128)	−0.111 (0.150)
(c) dependent variable sample: native less-skilled men
change in log employment for less-skilled native men (CBP)	0.289*** (0.079)	0.190 (0.142)	−0.099 (0.162)
(d) dependent variable sample: native high-skilled men
change in log employment for high-skilled native men (CBP)	0.140** (0.063)	0.105* (0.063)	−0.035 (0.089)

Examines the relationship between labor market outcomes (changes in employment probability) and changes in payroll employment separately for cities with above- and below-median Mexican population share to demonstrate the smoothing effect of Mexican mobility. This table reports the results of specifications run using data from 2000-2006 for both the dependent and independent variables. Smaller coefficients indicate more smoothing. We use the predicted change in log(employment), based on Bartik (1991) and described in the text, as an instrument for the change in log(group-specific employment). Panel (a) examines the relationship between low-skilled employment shocks and low-skilled men's employment probability. Panel (b) examines the relationship between low-skilled employment shocks and low-skilled native men's employment probability. Panel (c) examines the relationship between low-skilled native employment shocks and low-skilled native men's employment. Panel (d) examines the relationship between high-skilled native employment shocks and high-skilled native men's employment.

6 Extensions and Discussion

In this section we study the mechanisms through which the less skilled Mexican-born population adjusted to labor demand shocks and investigate some hypotheses for why Mexicans respond so much more strongly than similarly skilled natives.

6.1 Channels of Population Adjustment

A city's Mexican-born working-age population, $N_c^m$, can change between 2006 and 2010 through five channels: 1) arrivals from abroad after 2006, 2) migration between cities within the U.S., 3) departures from the U.S., 4) aging in or out of the sample, and 5) entering or leaving the sample due to changing schooling status. Here, we measure the importance of each channel in driving the strong population responses among less skilled Mexican-born men. Channels 1 and 4 are directly observable, as the ACS records immigrants’ age and year of arrival. Channel 5 likely makes a very small contribution, particularly among the less skilled working-age immigrants in our sample. Channels 2 and 3 are more difficult to separate in the data; we return to this below.

We begin by examining changes in the number of Mexican-born individuals who arrived in the U.S. before and after 2007. Thus, we partition a city's change in Mexican population as (suppressing city subscripts):

$$N^{m,2010}-N^{m,2006}=N_{new}^{m,2010}+(N_{pre-2007}^{m,2010}-N_{pre-2007}^{m,2006}).$$ (8)

In words, the change in the Mexican-born population consists of the number of immigrants who arrived in 2007 or later ($N_{new}^m$) plus the change in the number of immigrants who arrived in the U.S. in 2006 or earlier ($N_{pre-2007}^m$). Notice that $N_{pre-2007}^{m,2006}$ is simply the resident Mexican population in 2006. Dividing both sides of (8) by N^m,2006, one can decompose the proportional change in Mexican population into components resulting from new arrivals (channel 1) and from reallocation of existing residents (channels 2-5).

We therefore estimate slightly modified versions of Equation (1) for less skilled Mexican men, using the proportional change in the population ($\frac{N^{m,2010}-N^{m,2006}}{N^{m,2006}}$) and each component thereof as dependent variables, rather than the change in log population. The results are presented in Table 8. Column (1) reproduces the overall elasticity for low-skilled Mexican men shown in Figure 1; column (2) shows the slight change in the magnitude from the change in the dependent variable. The next two columns additively decompose that estimate into components coming from new arrivals and movement of existing residents. The coefficient in column (3) implies that 22 percent of the reallocation occurred through differential inflows of new immigrants in response to differential demand shocks. Note that fewer than 22 percent of Mexican-born immigrants living in the US in 2010 arrived during the preceding five years; thus these new arrivals account for more than their “fair share” of the reallocation.⁵⁵ It is likely that during periods with larger immigration inflows, this channel would account for a larger share of overall adjustment, but net migration inflows approached zero by the end of the decade (Passel, Cohn and Gonzalez-Barrera 2012). The remaining 78 percent of the reallocation occurred among existing residents (channels 2-5), and this aggregate effect is reflected in the coefficient in column (4). Column (5) provides a direct estimate of the contribution of net aging in (channel 4); as expected the contribution of this channel is negligible.⁵⁶

Table 8.

Channels of Population Response: Male Low-Skilled Mexican-Born Population

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Total Elasticity (Chg. In log Pop..)	Total Elasticity (Prop. Chg. In Pop..)	New Arrival Sorting	Change in Pre-2007 Arrivals	Net Aging In	Internal Inflows	Internal Outflows
Change in log Employment	0.569*** (0.202)	0.528*** (0.177)	0.115*** (0.024)	0.413** (0.174)	−0.025 (0.019)	0.025 (0.060)	0.087** (0.034)
Constant	0.028 (0.035)	0.034 (0.033)	0.072*** (0.007)	−0.039 (0.031)	0.005 (0.007)	0.090*** (0.018)	−0.066*** (0.007)
Share of Total Elasticity	N/A	100.0%	21.8%	78.2%	−4.8%	4.7%	16.5%
Share of Pre-2007 Elasticity	N/A	N/A	N/A	100.0%	−6.1%	6.1%	21.1%
R-squared	0.203	0.178	0.132	0.142	0.013	0.001	0.055

Column (1) reproduces the corresponding estimate from Table 2. Column (2) replaces the change in log(population) with the proportional change in population. As described in the text, Columns (3)-(7) decompose the overall response in column (2) into different migration components. All other specification details are identical to Table 2. The dependent variable in column (7) is the growth in the local population due to internal outflows, i.e. the negative of the proportional change in population due to outflows. A test of the null hypothesis that the sum of the coefficients in columns (6) and (7) is zero returns a p-value of 0.108.

Most of the reallocation therefore occurred through migration by those already resident by 2006. The large share of reallocation among existing immigrants is an important finding, as the majority of the previous literature focuses only on location choices among newly arriving immigrants. Decomposing this channel further is difficult, however, because there are no available data sources that allow reliable measurement of return migration flows to Mexico separately by US city during this time period.⁵⁷ In addition, the ACS asks respondents only about internal movement over the past year; the five year mobility question, standard in prior decennial censuses, does not appear in the ACS. Thus, it is not possible to precisely decompose pre-2007 arrivals observed in the 2010 ACS into those who lived in the same city in 2006 and those who lived in another US location. Nevertheless, one can construct imperfect estimates of internal migration by aggregating internal inflows and outflows from each successive annual ACS survey. The regressions in columns (6) and (7) are based on this technique, and they reveal that, together, measured internal migration can explain roughly 20 percent of the overall reallocation, with internal outflows relatively more important. Given the lack of a direct measure of return migration and the fairly wide confidence intervals on each of the other components, it is difficult to precisely estimate the relative contribution of return migration. It is clear, though, that both migration internal to the US and return migration to Mexico were important components of the overall local supply elasticity, consistent with the descriptive migration rates for Mexican-born individuals reported in Table 1.

6.2 Why are the Mexican-Born More Responsive?

We now consider potential explanations for the sharp differences in population elasticity between native-born and Mexican-born less skilled workers. Recall from Table 1 that, although the less skilled Mexican-born are less likely than similarly skilled natives to migrate within the U.S., their much higher rate of international mobility implies a substantially larger overall probability of migrating. This difference may simply reflect a process of self-selection in which the immigrant pool consists primarily of highly mobile individuals.

Thus, to some extent, immigrants’ demographics and other observable characteristics may account for their increased responsiveness compared to natives. To investigate this possibility, we first estimate probit regressions in which we predict Mexican-born status based on either age, marital status, detailed educational attainment, home ownership, or all of these factors together.⁵⁸ We then use the resulting propensity score weights to calculate city-level populations and industry shares (to calculate the relevant employment changes) using native workers whose observable characteristics, on average, match those of the Mexican-born. We then repeat our main mobility analysis for this reweighted group of natives. The results are shown in columns (3)-(7) of Table 9, with the baseline results for less skilled Mexican-born and native-born men provided for reference in columns (1) and (2). Even after making these adjustments, we find no evidence that natives move toward cities with better job prospects.

Table 9.

Propensity Score Reweighting of Less Skilled Native Men to Match Less Skilled Mexican-Born Men's Observables

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
	No Reweighting		Reweighted Natives Based on Listed Covariates
	Mexican-Born	Native-Born	Skill Only	Age Only	Rent vs. Own Only	Family Structure Only	All Prior Covariates	Outside Birth State	Outside Birth State and Other Covariates
Proportional Change in Group-Specific Employment	0.569*** (0.202)	0.041 (0.072)	−0.028 (0.101)	0.119 (0.084)	−0.047 (0.094)	0.047 (0.067)	0.014 (0.122)	0.211* (0.119)	0.385 (0.282)
Constant	0.569*** (0.202)	−0.013 (0.010)	−0.022 (0.015)	−0.022** (0.011)	0.010 (0.012)	−0.017 (0.011)	−0.002 (0.022)	−0.026 (0.020)	−0.018 (0.054)
R-squared	0.203	0.005	0.001	0.028	0.004	0.005	0.000	0.031	0.023

Columns (1) and (2) reproduce corresponding estimates from Table 2 for Mexican-born and native-born less skilled men. Columns (3)-(7)present population responses for natives, reweighted to match Mexican-born individuals’ based on the listed characteristics. Column (8)provides population responses among natives living outside of their state of birth, and in column (9) these populations are further reweighted to match the same set of covariates as in column (7). All other specification details are identical to Table 2. See text and appendix for details.

We then consider the possibility that natives who have previously made long-distance moves may be similarly more responsive. Column (8) presents the results of a version of column (2), but with population changes and city-level employment changes calculated based on the subset of low-skilled natives who are living outside of their state of birth. The estimated elasticity in this group is substantially larger than the elasticity among all natives, and the coefficient is marginally statistically significant. In column (9), we further reweight the population used in column (8) to reflect all of the covariates included in column (7). This specification yields the largest point estimate among any native population, although it is imprecisely estimated. Thus, it appears that part of the strong mobility responses among the Mexican-born derives from self-selection, although the differences do not appear to be entirely driven by differences in demographics.

Additionally, Mexican immigrants may be more responsive to labor market conditions for a variety of other reasons. First, they are less likely to be eligible for Unemployment Insurance (UI) and other social safety net programs, the existence of which reduces geographic differences in total income (Tatsiramos 2009). More than half of Mexican-born immigrants are in the US without authorization (Passel 2005) and are thus ineligible for UI benefits. Empirically, foreign-born individuals are substantially less likely to receive UI benefits compared to natives (see Appendix Section A.16), which makes immigrants’ total incomes more dependent on their labor market earnings.⁵⁹

Moreover, many Mexican immigrants report moving to the U.S. intending a relatively short stay, often planning to save a particular amount of money to invest back in Mexico or with the objective of remitting a particular amount at regular intervals (Massey, Durand and Malone 2003).⁶⁰ Additionally, Massey et al. (2003) report that some individuals migrate to the U.S. from Mexico as part of a larger household's diversification of human capital across labor markets. Workers with either of these types of motivations will find extended periods of unemployment especially costly and may therefore be more willing to relocate in order to find new employment more quickly.

These factors suggest that Mexican-born immigrants are especially likely to make an earnings-improving move because they have strong attachment to the labor market. Mexican-born workers’ unemployment durations are, on average, 33 percent shorter than than those of natives (see Appendix Figure A-14), and among movers, the Mexican-born are especially likely to report moving to look for work or because they lost a previous job (see Appendix Table A-36). In fact, among all possible answers, this category is the most common response among the Mexican-born (23.8 percent). This descriptive evidence is consistent with the idea that Mexican immigrants are more likely to consider the strength of a local labor market when making a location decision.

Figure A-14.

Unemployment Duration (Among Unemployed) by Nativity 2000-2012

Source: Authors’ calculations from Current Population Survey data. Sample includes men ages 18-64, not in school, not in group quarters, with at most a high school degree. Average duration calculated among those who are unemployed in the reference month.

Table A-36.

Stated Reasons for Moving Among Cross-County Movers, 2001-2010

	Native-Born	Mexican-Born	Other Immigrant
Attend/leave college	1.7%	1.1%	1.7%
Change in marital status	6.6%	3.2%	5.1%
Change of climate	1.3%	0.2%	1.1%
For cheaper housing	5.2%	4.3%	4.0%
For easier commute	4.5%	4.3%	4.4%
Health reasons	1.9%	0.7%	0.4%
Natural disaster	0.3%	0.2%	0.1%
New job or job transfer	16.3%	17.1%	15.1%
Other family reason	16.7%	12.4%	16.3%
Other housing reason	6.9%	4.8%	6.5%
Other job-related reason	3.4%	4.7%	4.4%
Other reasons	4.5%	2.1%	8.0%
Retired	0.7%	0.0%	0.2%
To establish own household	7.0%	5.0%	5.0%
To look for work or lost job	5.3%	23.8%	10.3%
Wanted better neighborhood	3.3%	3.6%	2.9%
Wanted new or better housing	8.9%	9.6%	9.0%
Wanted to own home, not rent	5.7%	2.9%	5.5%

Source: Authors’ calculations from March CPS data, 2000-2010. Sample includes men ages 18-64, not in school, not in group quarters, with at most a high school degree who are living in a different county in the survey year than in the previous year.

Finally, the Mexican-born have access to particularly robust networks and a diffuse set of enclaves. There are nontrivial Mexican-born populations in many more of the nation's labor markets than there are for any other immigrant source country. Mexican immigrants comprise at least one percent of the population of more than half of US metro areas, whereas no other source country is similarly represented in more than ten percent of cities.⁶¹ Several studies have found that immigrants tend to locate in markets with previous migrants from the same source country, and that the Mexican-born population has continued to spread out geographically over the previous two decades.⁶² Further, networks provide information about local labor market conditions and lower moving costs, thereby increasing the probability that a move across labor markets will result in a favorable employment outcome (Munshi 2003).

A natural remaining question is what factors motivate less skilled natives’ cross-city moves and why labor market conditions are of relatively little importance. One prime candidate is the substantial home bias that has been identified in prior work (Kennan and Walker 2011, Diamond 2015). In fact, over our study period, 47 percent of all cross-city moves by low-skilled natives had the mover's state of birth as the destination. This substantial likelihood of selecting a city in one's home state does not simply reflect a generally higher prevalence of within state moves; of those beginning in a state other than their state of birth, only one third moved to a different city within the same state. Among those beginning from a city in their home state, in contrast, roughly two thirds chose another city in the same state.⁶³ Although not conclusive, these calculations suggest that much of the substantial cross-city mobility occurs for reasons related to family or other amenities of one's home state rather than for employment conditions.

In sum, while we are unable to explain with certainty all of the sources of the higher responsiveness among the less skilled Mexican-born, the available evidence suggests that they are so responsive because they are a self-selected group of highly mobile individuals, they have particularly strong labor market motivations, and they have the informational and informal financial resources necessary to make demand-sensitive location choices. Relative to natives, they also have lower access to programs such as unemployment insurance that make remaining in a weak labor market less costly.

7 Conclusion

This paper has demonstrated that low-skilled Mexican-born workers’ location choices responded very strongly to geographic variation in labor demand during the Great Recession (and during the preceding boom). This behavior is in sharp contrast to low-skilled native-born workers who show little response. Further, the reallocation of Mexican immigrants reduced spatial variation in employment outcomes for natives living in cities with substantial Mexican-born share. This novel empirical finding represents economically significant behavior, and it is quite robust to a number of alternative interpretations.

The high degree of mobility among low-skilled Mexican-born individuals has a number of important implications. First, Mexican immigrants comprise an increasing share of the less skilled labor force, and their growing presence has raised this group's average geographic supply elasticity substantially. The rising share of the Mexican-born among the low-skilled therefore partially mitigates concerns that the relative lack of mobility among less skilled workers leads to large disparities in these workers’ earnings across local labor markets (Bound and Holzer 2000). As U.S. policy makers seek ways to normalize the status of unauthorized workers and put in place legal channels for less skilled temporary migrant workers, they should consider the geographic flexibility immigrants provide labor markets when they are free to change locations and employers in response to changing demand conditions.

Second, this paper provides evidence that immigration inflows respond to demand conditions, and it further shows that immigrants continue to alter their locations in response to labor demand after residing in the country for some time. Although precisely disentangling the contributions of internal migration and return migration to Mexico is difficult, the evidence shows that both channels are important and that a substantial share of the geographic reallocation occurred among previously resident immigrants. This additional layer of responsiveness is an understudied phenomenon, and it deserves continued research.

Finally, these findings support previous evidence showing that immigrants’ location choices respond to exogenous changes in labor market conditions (Cadena 2013, Cadena 2014). This endogenous supply response potentially confounds research designs relying on geographic variation in immigration inflows to identify immigrants’ effects on natives. A further examination of the methods used to overcome this empirical challenge is likely warranted given the growing body of evidence favoring endogenous immigrant inflows.

Table A-6.

Population Response to Labor Demand Shocks - General Shocks

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.163*** (0.061)	0.0172 (0.067)	0.443** (0.182)	0.699*** (0.244)	−0.037 (0.271)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.498*** (0.090)	0.455*** (0.093)	0.698*** (0.196)	0.274 (0.441)	0.756*** (0.200)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.408*** (0.115)	0.216 (0.161)	0.708*** (0.179)	0.824*** (0.192)	0.496 (0.351)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.475*** (0.126)	0.444*** (0.118)	0.804*** (0.266)	0.130 (0.507)	0.897*** (0.261)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the general (not group-specific) change in log(employment) from County Business Patterns data. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Table A-7.

Population Response to Labor Demand Shocks - General Shocks with Enclave and Policy Controls

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.150** (0.063)	0.019 (0.066)	0.346** (0.155)	0.590*** (0.202)	−0.048 (0.279)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.479*** (0.074)	0.433*** (0.082)	0.701*** (0.183)	0.176 (0.422)	0.785*** (0.195)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.395*** (0.121)	0.191 (0.162)	0.717*** (0.182)	0.893*** (0.207)	0.400 (0.365)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.473*** (0.095)	0.432*** (0.100)	0.820*** (0.241)	0.219 (0.588)	0.942*** (0.243)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the general (not group-specific) change in log(employment) from County Business Patterns data, with the full set of enclave and policy controls discussed in the paper. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Table A-8.

Population Response to Labor Demand Shocks - Omitting Industries with Incomplete CBP Coverage

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.132** (0.056)	0.024 (0.068)	0.303** (0.152)	0.410** (0.186)	−0.100 (0.242)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.431*** (0.101)	0.406*** (0.099)	0.507** (0.215)	0.099 (0.305)	0.630*** (0.222)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.345*** (0.117)	0.169 (0.160)	0.601*** (0.191)	0.661*** (0.197)	0.415 (0.352)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.420*** (0.132)	0.406*** (0.115)	0.692** (0.291)	0.123 (0.495)	0.765*** (0.290)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data, using the demographic group's industry mix. Industries with incomplete coverage in CBP are omitted from the employment changes. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Table A-9.

Population Response to Labor Demand Shocks - Omitting Industries with Incomplete CBP Coverage, with Enclave and Policy Controls

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.115** (0.058)	0.024 (0.067)	0.206 (0.127)	0.323** (0.147)	−0.100 (0.259)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.428*** (0.080)	0.396*** (0.084)	0.535*** (0.195)	−0.033 (0.280)	0.649*** (0.215)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.334*** (0.120)	0.141 (0.161)	0.575*** (0.203)	0.739*** (0.233)	0.345 (0.378)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.435*** (0.0993)	0.406*** (0.0977)	0.712*** (0.261)	0.202 (0.569)	0.800*** (0.274)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix), with the full set of enclave and policy controls discussed in the paper. Industries with incomplete coverage in CBP are omitted from the employment changes. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Table A-10.

Population Response to Labor Demand Shocks - Shocks Calculated from ACS

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.258*** (0.072)	0.0467 (0.092)	0.733*** (0.184)	1.006*** (0.177)	0.148 (0.264)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.730*** (0.074)	0.686*** (0.078)	0.943*** (0.186)	0.514 (0.468)	0.990*** (0.179)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.584*** (0.107)	0.337** (0.146)	1.081*** (0.176)	1.096*** (0.198)	1.032*** (0.238)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.684*** (0.080)	0.637*** (0.090)	1.031*** (0.232)	0.503 (0.701)	1.062*** (0.235)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group on the change in log(group-specific employment) (both calculated using the American Community Survey). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Table A-11.

Population Response to Labor Demand Shocks - Shocks Calculated from ACS, with Enclave and Policy Controls

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.247*** (0.074)	0.047 (0.089)	0.647*** (0.142)	0.956*** (0.177)	0.156 (0.263)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.701*** (0.072)	0.650*** (0.078)	0.977*** (0.192)	0.212 (0.466)	1.049*** (0.189)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.577*** (0.114)	0.320** (0.145)	1.064*** (0.121)	1.116*** (0.177)	0.906*** (0.242)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.654*** (0.076)	0.604*** (0.090)	1.041*** (0.241)	0.561 (0.741)	1.103*** (0.242)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group on the change in log(group-specific employment) (both calculated using the American Community Survey), with the full set of enclave and policy controls discussed in the paper. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Table A-12.

Population Response to Labor Demand Shocks - Population Changes from 3-year ACS

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.130* (0.073)	0.031 (0.080)	0.302** (0.150)	0.484*** (0.173)	−0.163 (0.228)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.453*** (0.076)	0.434*** (0.065)	0.497** (0.222)	0.428** (0.172)	0.525** (0.243)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.433*** (0.0987)	0.291*** (0.107)	0.529*** (0.197)	0.588*** (0.204)	0.360 (0.347)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.475*** (0.113)	0.472*** (0.100)	0.730*** (0.277)	0.465* (0.261)	0.703** (0.286)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the 3-year samples of the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-13.

Population Response to Labor Demand Shocks - Population Changes from 3-year ACS, with Enclave and Policy Controls

	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.110 (0.073)	0.011 (0.078)	0.210* (0.117)	0.399*** (0.109)	−0.154 (0.254)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.436*** (0.062)	0.410*** (0.057)	0.523** (0.200)	0.374** (0.173)	0.551** (0.229)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.412*** (0.105)	0.253** (0.112)	0.538*** (0.193)	0.722*** (0.218)	0.329 (0.347)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.473*** (0.0786)	0.454*** (0.0821)	0.753*** (0.254)	0.487 (0.327)	0.725** (0.284)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the 3-year samples of the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix), with the full set of enclave and policy controls discussed in the paper. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-14.

Population Response to Labor Demand Shocks - Weighted by 2006 Population

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.162*** (0.061)	0.049 (0.073)	0.400** (0.181)	0.588*** (0.212)	−0.071 (0.248)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.497*** (0.090)	0.465*** (0.090)	0.599*** (0.204)	0.281 (0.340)	0.708*** (0.204)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.417*** (0.118)	0.192 (0.158)	0.625*** (0.174)	0.645*** (0.179)	0.552* (0.310)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.472*** (0.126)	0.431*** (0.117)	0.822*** (0.270)	0.195 (0.506)	0.910*** (0.274)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the group-specific 2006 population. Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-15.

Population Response to Labor Demand Shocks - Weighted by 2006 Population, with Enclave and Policy Controls

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.147** (0.062)	0.047 (0.073)	0.293** (0.140)	0.488*** (0.176)	−0.0661 (0.266)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.475*** (0.073)	0.433*** (0.080)	0.624*** (0.184)	0.026 (0.330)	0.736*** (0.198)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.399*** (0.123)	0.163 (0.158)	0.642*** (0.176)	0.726*** (0.192)	0.521 (0.328)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.464*** (0.095)	0.410*** (0.100)	0.836*** (0.241)	0.158 (0.562)	0.947*** (0.256)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix), with the full set of enclave and policy controls discussed in the paper. All regressions include an intercept term and 95 city observations. Observations are weighted by the group-specific 2006 population. Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

Table A-16.

Population Response to Labor Demand Shocks - Unweighted

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.243*** (0.059)	0.111 (0.079)	0.506*** (0.081)	0.788*** (0.147)	0.531 (0.350)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.511*** (0.099)	0.545*** (0.120)	0.437 (0.266)	0.733 (0.758)	0.618 (0.467)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.323*** (0.112)	0.202 (0.126)	0.223 (0.243)	0.120 (0.296)	−0.242 (0.593)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.517*** (0.149)	0.453*** (0.141)	0.903** (0.357)	−0.768 (1.048)	0.931* (0.518)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are equally weighted. Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-17.

Population Response to Labor Demand Shocks - Unweighted, with Enclave and Policy Controls

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.230*** (0.061)	0.095 (0.084)	0.518*** (0.082)	0.797*** (0.162)	0.494 (0.335)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.452*** (0.100)	0.492*** (0.120)	0.400 (0.267)	0.448 (0.811)	0.553 (0.387)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.249** (0.118)	0.148 (0.132)	0.477* (0.247)	0.410 (0.321)	0.370 (0.610)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.430*** (0.156)	0.382** (0.156)	0.824** (0.379)	−0.968 (1.039)	0.545 (0.535)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix), with the full set of enclave and policy controls discussed in the paper. All regressions include an intercept term and 95 city observations. Observations are equally weighted. Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-19.

Population Response to Labor Demand Shocks

	Dependent Variable: Change in log of Population
	Native-Born					Foreign-Born
	White Non-Hispanic	Black Non-Hispanic	Asian Non-Hispanic	Hispanic	Other Non-Hispanic	Mexican	Other W. Hemis.	Asian	Other
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.118 (0.074)	−0.164 (0.186)	1.547 (0.971)	−0.359** (0.146)	−0.295 (0.492)	0.569*** (0.202)	−0.203 (0.302)	−0.083 (0.455)	0.145 (0.318)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.383*** (0.070)	0.589* (0.319)	1.117 (0.792)	0.202 (0.215)	−0.170 (0.599)	0.171 (0.316)	0.869** (0.346)	0.695*** (0.205)	0.651* (0.335)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.146 (0.177)	0.120 (0.456)	2.759* (1.413)	−0.425 (0.268)	1.728** (0.817)	0.652*** (0.192)	0.122 (0.645)	0.336 (0.315)	1.511*** (0.497)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.465*** (0.106)	0.263 (0.271)	0.818 (0.768)	−0.041 (0.315)	−0.111 (0.935)	0.218 (0.505)	−0.595 (0.480)	0.958*** (0.297)	2.151*** (0.486)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-20.

Population Response to Labor Demand Shocks - With Enclave and Policy Controls

	Dependent Variable: Change in log of Population
	Native-Born					Foreign-Born
	White Non-Hispanic	Black Non-Hispanic	Asian Non-Hispanic	Hispanic	Other Non-Hispanic	Mexican	Other W. Hemis.	Asian	Other
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.129* (0.075)	−0.158 (0.212)	1.461 (1.053)	−0.277* (0.165)	−0.277 (0.484)	0.475*** (0.172)	−0.198 (0.311)	−0.256 (0.519)	0.293 (0.349)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.389*** (0.073)	0.561** (0.272)	1.213 (0.776)	0.192 (0.228)	−0.218 (0.596)	0.014 (0.285)	0.887** (0.339)	0.723*** (0.212)	0.649* (0.358)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.189 (0.162)	0.250 (0.494)	2.594* (1.477)	−0.342 (0.317)	1.652** (0.792)	0.743*** (0.202)	0.067 (0.622)	0.175 (0.353)	1.571*** (0.494)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.466*** (0.113)	0.450* (0.265)	0.682 (0.757)	−0.071 (0.341)	−0.217 (0.927)	0.315 (0.597)	−0.574 (0.488)	0.957*** (0.291)	2.186*** (0.491)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix), with the enclave and policy controls in Column (4) of Table 3. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-21.

Population Response to Labor Demand Shocks - Falsification Test: Population Change 2000-06 vs. Group-Specific Employment Change 2006-10

	Dependent Variable: Change in log of Population
	Native-Born					Foreign-Born
	White Non-Hispanic	Black Non-Hispanic	Asian Non-Hispanic	Hispanic	Other Non-Hispanic	Mexican	Other W. Hemis.	Asian	Other
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	−0.253** (0.127)	−0.367 (0.369)	−2.244** (1.016)	−0.585** (0.271)	0.038 (0.380)	−0.481*** (0.169)	−1.249*** (0.438)	−0.248 (0.379)	−0.709 (0.505)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	−0.066 (0.115)	−0.295 (0.292)	−0.136 (0.638)	−0.465* (0.260)	0.416 (0.521)	−0.216 (0.376)	−1.716*** (0.636)	−0.207 (0.327)	−0.373 (0.281)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.167 (0.187)	0.038 (0.569)	−1.709 (1.217)	−0.504 (0.395)	−0.358 (0.732)	−0.021 (0.470)	−1.169 (1.097)	0.149 (0.443)	−0.236 (0.708)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.376** (0.146)	0.369 (0.370)	0.282 (0.754)	−0.393 (0.328)	0.534 (0.626)	0.790 (0.561)	−0.695 (1.008)	−0.044 (0.309)	−0.295 (0.411)

Each listed coefficient represents a separate regression of the pre-Recession change in log(population) from 2000-06 for the relevant group (from the American Community Survey) on the Recession period change in log(group-specific employment) from 2006-10 from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

A Appendix

A.1 Employment and Wage Changes During the Great Recession

As discussed in section 2.1, there is substantial evidence that during the Great Recession employers responded to decreases in product demand through cutting payroll employment rather than by cutting wages. Figures A-1 and A-2 document this descriptive fact. Figure A-1 shows the national employment to population ratio among prime age workers (25-54) from 1979 to 2013. This ratio fell sharply between late 2007 and late 2009, declining by five percentage points. Compared to the pre-recession trend, it is clear that employment growth stalled by 2007, so we consider 2006 as the pre-recession baseline period and 2010 as the post-recession period throughout our analysis.

Figure A-1.

Time Series of National Employment to Population Ratio, Ages 25-54, 1979-2013

Sources: Bureau of Labor Statistics and National Bureau of Economic Research.

Figure A-2.

Time Series of Wages and Employment, 2006-2010

Sources: Authors’ calculations from Bureau of Labor Statistics data; Rothstein (2012).

Figure A-2 compares employment and wage changes over this time period. This figure combines the employment to population ratio from Figure A-1 with calculations from Rothstein (2012) of changes in wage rates over the same time period.⁶⁴ All values represent proportional changes compared to the same month in the previous year. Average wages are roughly constant over this time period, although they rise in real terms in 2008, which reflects a combination of approximately flat nominal wages and price deflation. Additionally, the lack of downward wage changes was not due to compositional effects. Using the panel dimension of the CPS, the “Within-Worker Wages” series exhibits mildly rising wages for workers observed in the reference month and in the preceding year. As a whole, these results show no evidence of falling wages, even when employment was falling by more than four percent per year in mid-2009.

A.2 Employment Changes in the Great Recession

This section presents summary statistics on employment changes that occurred during the Great Recession. Figure A-3 shows changes in log(employment) by state, as measured in County Business Patterns data. Figure A-4 provides time series information on employment for the metro areas with the largest decline, largest increase, and the median change in employment over this same time period, showing substantial variation across cities. Figure A-5 shows that there was considerable variation in employment declines across industries, and Figure A-6 shows that Mexican-born workers (the largest single group among the low-skilled foreign-born) were more concentrated in the types of jobs that experienced the largest declines.

Figure A-3.

Changes in Employment 2006-2010, US States

Source: County Business Patterns.

Figure A-4.

Employment 2006-2010, Selected Metro Areas

Source: Authors’ calculations from Current Employment Statistics, metro area total non-farm employment. Normalized to 1 in July 2006.

Figure A-5.

Employment Changes by Industry 2006-2010

Sources: Authors’ calculations from County Business Patterns (CBP) and the American Community Survey (ACS). CBP employment changes shown for all industries except those without without full coverage in the CBP: Agriculture, Other Services, and Government. ACS employment changes shown in those cases.

A.3 Details of the Multinomial Logit Estimation of Industry Shares

In constructing employment declines faced by each (skill × sex × nativity) group in each city, we need information on each group's city-level industry shares. We calculate these shares based on multinomial logit estimates. In earlier versions, we calculated shares by directly measuring the within-city share of the group working in each industry in the ACS. This approach is potentially problematic because the cell sizes can be quite small for particular industries. The remainder of this section describes the implementation of the approach we use, although we emphasize that none of these decisions are pivotal. In fact, the results are remarkably similar to those obtained using the simpler sample-based shares approach.

We predict the probability that an individual of type j living in city c works in industry i as a function of his/her type and location. Our explanatory variables are a full set of worker type dummies and city dummies, and we run separate models for each (skill sex) group. Note that if we included dummies at the (type × city) level, the predicted probabilities × would simply be the sample shares. Our method therefore imposes the assumption that the influence of worker type and city on the industry distribution of employment are separable in determining an individual's likelihood of working in a given industry.⁶⁵

For further richness, we also account for the different composition of the native and foreign-born workforce across cities. For natives, we allow a worker's industry to depend on his/her racial and ethnic composition, with separate coefficients for non-Hispanic whites, non-Hispanic blacks, non-Hispanic Asians, native-born Hispanics, and other non-Hispanics. Among the “other immigrants” category, we allow for a separate industry mix based on groupings of source countries including Western Hemisphere immigrants, Asian immigrants, and other immigrants.

After running these models, we predict individual-level probabilities of working in each industry. We then aggregate these predicted probabilities to the city level for the broader groups considered in the regressions (native-born, foreign-born, Mexican-born, other foreign-born).⁶⁶ We use these shares to create the employment shocks based on CBP data at the city-industry level.

A.4 Heteroskedasticity Weights

The population growth measures we use as dependent variables are estimates derived from underlying micro data, and hence are likely to result in heteroskedasticity. Along with reporting heteroskedasticity-robust standard errors, we weight by the inverse of the sampling variance of the population growth estimates. This section describes how we construct these variance estimates.

A.4.1 Proportional Growth

In previous versions of this paper, we used the proportional growth in population as the dependent variable. Under the specification, for a particular city c, our dependent variable is

$$\frac{{\widehat{p}}_c^{2010}-{\widehat{p}}_c^{2006}}{{\widehat{p}}_c^{2006}}=\frac{{\widehat{p}}_c^{2010}}{{\widehat{p}}_c^{2006}}-1$$ (9)

where ${\widehat{p}}_c^t$is the estimated city population in year t. The variance of the dependent variable is thus

$$var\left(\frac{{\widehat{p}}_c^{2010}}{{\widehat{p}}_c^{2006}}-1\right)=var\left(\frac{{\widehat{p}}_c^{2010}}{{\widehat{p}}_c^{2006}}\right)$$ (10)

Since this represents the variance of a nonlinear combination of random variables, we must use the delta method to approximate the variance of the overall expression based on the variances of the individual random variables. Applying the delta method to the ratio of random variables, we have

$$var\left[\frac{{\widehat{p}}_c^{2010}}{{\widehat{p}}_c^{2006}}\right]\approx {\left(\frac{E\left[{\widehat{p}}_c^{2010}\right]}{E\left[{\widehat{p}}_c^{2006}\right]}\right)}^2\left(\frac{var\left[{\widehat{p}}_c^{2006}\right]}{E{\left[{\widehat{p}}_c^{2006}\right]}^2}+\frac{var\left[{\widehat{p}}_c^{2010}\right]}{E{\left[{\widehat{p}}_c^{2010}\right]}^2}-2\frac{cov\left[{\widehat{p}}_c^{2006},{\widehat{p}}_c^{2010}\right]}{E\left[{\widehat{p}}_c^{2006}\right]E\left[{\widehat{p}}_c^{2010}\right]}\right)$$ (11)

Assuming independent sampling across [parenleftBig] years, the covariance term goes to zero. Then plug in the sample estimates for the means ($\widehat{E}\left[{\widehat{p}}_c^t\right]={\widehat{p}}_c^t$) and variances to yield a feasible estimate of the variance of the dependent variable.

$$v\widehat{a}r\left[\frac{{\widehat{p}}_c^{2010}}{{\widehat{p}}_c^{2006}}\right]\approx {\left(\frac{{\widehat{p}}_c^{2010}}{{\widehat{p}}_c^{2006}}\right)}^2\left(\frac{v\widehat{a}r\left[{\widehat{p}}_c^{2006}\right]}{{\left({\widehat{p}}_c^{2006}\right)}^2}+\frac{v\widehat{a}r\left[{\widehat{p}}_c^{2010}\right]}{{\left({\widehat{p}}_c^{2010}\right)}^2}\right)$$ (12)

In our data, sampling probabilities are not equal for all observations, so we must account for that in calculating the variance of the city population estimates. By definition, ${\widehat{p}}_c^t$ is simply an estimate of the population total of an indicator ${\iota }_{ic}$ taking the value 1 if individual i lives in city c. Letting w_i be the inverse of individual i's probability of appearing in the sample, we calculate the city population estimate as

$${\widehat{p}}_c^t=\sum _{i=1}^{n_t}{w}_i{t}_{ic}$$ (13)

Given that ${\widehat{p}}_c^t$ estimates the population total of ${\iota }_{ic}$, we can follow Deaton equation (1.24) by estimating var $\left[{\widehat{p}}_c^t\right]$ as

$$v\widehat{a}r\left[{\widehat{p}}_c^t\right]=\frac{n^t}{n^t-1}\sum _{i=1}^{n^t}{(z_i-\overline{z})}^2,$$ (14)

where $z_i\equiv w_i{\iota }_{ic}$.⁶⁷ Combining these results, we have the following estimator for the variance of the proportional change in population.

$$v\widehat{a}r\left[\frac{{\widehat{p}}_c^{2010}-{\widehat{p}}_c^{2006}}{{\widehat{p}}_c^{2006}}\right]\approx {\left(\frac{{\widehat{p}}_c^{2010}}{{\widehat{p}}_c^{2006}}\right)}^2\left(\frac{v\widehat{a}r\left[{\widehat{p}}_c^{2006}\right]}{{\left({\widehat{p}}_c^{2006}\right)}^2}+\frac{v\widehat{a}r\left[{\widehat{p}}_c^{2010}\right]}{{\left({\widehat{p}}_c^{2010}\right)}^2}\right)$$ (15)

where $v\widehat{a}r\left[{\widehat{p}}_c^t\right]$ is given by (14).

$$w{N}^t\left[\frac{n_c^t}{n^t}\left(1-\frac{n_c^t}{n^t}\right)\right]$$

A.4.2 Change in log Population

In the present version of the paper, the dependent variable is

$$\ln \left({\widehat{p}}_c^{2010}\right)-\ln \left({\widehat{p}}_c^{2006}\right).$$ (16)

Applying the delta method, plugging in feasible estimates for the means and variances, and imposing zero covariance across years yields the variance of the change in log population,

$$var\left[\ln \left({\widehat{p}}_c^{2010}\right)-\ln \left({\widehat{p}}_c^{2006}\right)\right]\approx \frac{v\widehat{a}r\left[{\widehat{p}}_c^{2006}\right]}{{\left({\widehat{p}}_c^{2006}\right)}^2}+\frac{v\widehat{a}r\left[{\widehat{p}}_c^{2010}\right]}{{\left({\widehat{p}}_c^{2010}\right)}^2}$$ (17)

where $v\widehat{a}r\left[{\widehat{p}}_c^t\right]$ is given by (14).

A.4.3 Summary

We use three-year ACS samples to calculate these variance estimates to avoid wildly inaccurate estimates for demographic groups with only a few individuals in a given city (this only appreciably affected the weights in a few cities for the “other foreign-born” group). In practice, these weights turn out to be very closely related to the 2006 population, with a correlation coefficient of 0.987 when considering observations for all demographic groups in all cities. For completeness, later in this appendix we present versions of Tables 2 and 3 weighting by 2006 population, with no substantive changes to the main results.

Calculating the variance of the dependent variable for the employment rate and wage regressions is simpler because these dependent variables are changes in sample means from one survey year to another. Continuing to impose the assumption of independent sampling across years, the variance of the difference is simply the sum of the variances of the components. We estimate each of these year-specific variances using a regression of the underlying microdata on city-level fixed effects, which we run separately for each sex-skill-nativity group in each year. We then use the square of the resulting standard errors on the fixed effects as estimates of the sampling variance of the city-level means in order to calculate the estimated variance of the dependent variable.

A.5 Enclave and Policy Controls

In Table A-1, we investigate the population response of low-skilled Mexican-born men as we sequentially add controls for determinants of location choice that may be correlated with local changes in demand. Column (1) reproduces the baseline response of low-skilled Mexican-born men in Table 2. In Column (2) we control for the Mexican-born share of each city's population in 2000 to account for the potential decline in the value of traditional enclaves discussed by Card and Lewis (2007). Since the dependent variable is measured as the within-city change, this control allows for differential growth trends based on a city's traditional enclave status. Columns (3) and (4) add indicators for cities in states that enacted anti-immigrant employment legislation or new 287(g) agreements allowing local officials to enforce federal immigration law, based on the immigration policy database in Bohn and Santillano (2012).⁶⁸ In Column (4), all of these controls enter with a negative sign, as expected.

Table A-1.

Population Response to Labor Demand Shocks: Low-Skilled Mexican-Born Men With Enclave and Policy Controls

	Dependent Variable: Change in log Population - Mexican-born Men, High-school or less
	(1)	(2)	(3)	(4)
Change in log Employment	0.569*** (0.202)	0.564*** (0.205)	0.506*** (0.186)	0.475*** (0.172)
Enclave Measure (Mexican-born Share of City Population)		0.058 (0.152)	0.009 (0.159)	−0.041 (0.166)
New State Immigrant Employment Legislation			−0.057 (0.060)	−0.016 (0.032)
New State 287g Policy				−0.119** (0.051)
Constant	0.028 (0.035)	0.019 (0.047)	0.025 (0.046)	0.032 (0.045)
R-squared	0.206	0.207	0.223	0.264

Each column represents a separate regression of the change in log(population) among low-skilled Mexican-born men (2006-2010, using the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data over the same time period, using that demographic group's industry mix. All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

* 10%.

A.6 Wage and Employment Changes

As discussed in section 3.1, the elasticity of population with respect to employment will overstate the supply elasticity with respect to expected earnings when wage changes and changes in the employment probability are positively correlated. Figure A-7 shows the relationship between nominal changes in log wages and payroll employment shocks for low-skilled native-born men from 2006-2010. The wage data come from the ACS questions on annual earnings, usual hours worked, and annual weeks worked. The figure reveals a positive relationship between changes in log wages and changes in log employment. With the exception of the outlier cities in the SW corner of the figure, however, the range of average wage changes is relatively narrow. The hardest hit cities experienced close to zero nominal wage growth while cities with relatively stronger labor demand changes saw wage growth in line with inflation. The change in CPI-U from 2006 to 2010 was roughly eight percent, which is close to the largest predicted value from the smoothed conditional expectation line. These results are consistent with the large body of literature showing that employers respond to demand decreases through layo s and that workers often continue to receive small raises even when employers are cutting payrolls.

Figure A-7.

Wage Changes and Employment Changes 2006-2010

Source: Authors’ calculations from ACS and CBP data. The wage data are calculated as annual earnings divided by (usual weekly hours * annual weeks worked). The wage sample includes native men with a high school degree or less. The employment changes are calculated using the industry weights for this population. The fitted line is the fit from an epanechnikov kernel (bw=0.04) calculated at each city's value of the employment shock. These conditional means are weighted using city weights. The outliers in the SW corner are Naples, FL and Fort Meyers-Cape Coral, FL.

A.7 Population Sizes of Demographic Groups

Table A-2 provides the estimated population sizes for each of the sex-skill-nativity groups considered in the main analysis. Note that roughly 90 percent of Mexican-born immigrants have no more than a high school degree. Also, splitting the immigrant population into Mexican and non-Mexican portions among the lower skilled results in roughly equal cell sizes. Among higher-skilled immigrants, however, the cell sizes for the Mexican-born are substantially smaller than for the other foreign-born.

Table A-2.

Population Sizes for Demographic Groups used in Population Response Regressions (2005)

	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Estimated Sample Population	21,243,571	14,427,983	6,815,588	3,704,846	3,110,742
Share of Group with Education Level	0.496	0.452	0.626	0.893	0.462
Panel B: Men, Some college or more
Estimated Sample Population	21,559,797	17,492,647	4,067,150	444,215	3,622,935
Share of Group with Education Level	0.504	0.548	0.374	0.107	0.538
Panel C: Women, High-school or less
Estimated Sample Population	20,641,339	14,504,441	6,136,898	2,820,215	3,316,683
Share of Group with Education Level	0.483	0.445	0.605	0.883	0.477
Panel D: Women, Some college or more
Estimated Sample Population	22,079,281	18,068,539	4,010,742	374,327	3,636,415
Share of Group with Education Level	0.517	0.555	0.395	0.117	0.523

Estimated total populations are the sum of person weights for sample observations meeting the overall sampling criteria discussed in the text, calculated separately for each demographic group using the American Community Survey. All statistics are based on a consistent sample of 95 city observations. Listed shares add to 1 for each nativity-sex cell.

A.8 Descriptive Statistics for Population Elasticity Regressions

Table A-3 provides the mean and standard deviation for the change in log(population) and change in log(group-specific employment) measures used as the dependent and independent variables (respectively) in the main population elasticity regressions (2006-2010). Table A-4 provides similar statistics for the change in log(population) for 2000-2006. Table A-5 provides the mean and standard deviation for each of the controls used in Tables A-1 and 3 as well as for the Bartik and leverage instruments used in Tables 4 and A-27 respectively.

Table A-3.

Descriptive Statistics for Population Response Regressions

	All		Native-Born		Foreign-Born		Mexican-Born		Other Foreign-Born
Panel A: Men, High-school or less	mean	std. dev.	mean	std. dev.	mean	std. dev.	mean	std. dev.	mean	std. dev.
Change in ln Population	−0.019	0.045	−0.018	0.047	−0.022	0.110	−0.069	0.146	0.029	0.145
Change in ln Group-Specific Employment	−0.142	0.087	−0.134	0.081	−0.154	0.100	−0.171	0.115	−0.131	0.079
Panel B: Men, Some college or more
Change in ln Population	0.058	0.053	0.055	0.054	0.066	0.102	0.151	0.33	0.056	0.102
Change in ln Group-Specific Employment	−0.077	0.058	−0.074	0.059	−0.088	0.058	−0.123	0.095	−0.083	0.053
Panel C: Women, High-school or less
Change in ln Population	−0.026	0.050	−0.060	0.058	0.045	0.090	0.043	0.127	0.045	0.119
Change in ln Group-Specific Employment	−0.046	0.048	−0.045	0.048	−0.049	0.051	−0.055	0.062	−0.045	0.042
Panel D: Women, Some college or more
Change in ln Population	0.096	0.045	0.085	0.046	0.140	0.082	0.232	0.278	0.130	0.083
Change in ln Group-Specific Employment	−0.013	0.041	−0.010	0.042	−0.027	0.039	−0.018	0.054	−0.028	0.037

Each panel provides the mean and standard deviation of change in log(population) (from the American Community Survey) and the change in log(employment) from County Business Patterns data, using the demographic group's industry mix, for a different demographic group of workers (by sex and education level). All statistics are based on a consistent sample of 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable.

Table A-4.

Descriptive Statistics for Population Response Regressions False Experiment 2000-2006

	All		Native-Born		Foreign-Born		Mexican-Born		Other Foreign-Born
Panel A: Men, High-school or less	mean	std. dev.	mean	std. dev.	mean	std. dev.	mean	std. dev.	mean	std. dev.
Change in ln Population	−0.019	0.045	−0.019	0.047	−0.024	0.109	−0.074	0.145	0.025	0.141
Panel B: Men, Some college or more
Change in ln Population	0.057	0.052	0.055	0.054	0.063	0.099	0.144	0.331	0.053	0.100
Panel C: Women, High-school or less
Change in ln Population	−0.027	0.050	−0.061	0.058	0.043	0.088	0.039	0.122	0.042	0.117
Panel D: Women, Some college or more
Change in ln Population	0.095	0.044	0.084	0.046	0.137	0.079	0.228	0.270	0.127	0.081

Each panel provides the mean and standard deviation of change in log(population) (from the American Community Survey) for a different demographic group of workers (by sex and education level). All statistics are based on a consistent sample of 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable.

Table A-5.

Descriptive Statistics for Population Response Regressions Controls and Instrumental Variables

	mean	std. dev.
Controls
Enclave Measrure (Mexican-born Share of City Population)	0.150	0.087
New State Immigrant Employment Legislation	0.159	0.366
New State 287g Policy	0.093	0.290
Instrumental Variables
Bartik (1991) Predicted Change in log Employmenta	−0.076	0.010
Mian and Sufi (2012) Household Leverage	1.944	0.588

Statistics are based on a sample of 95 city observations, and observations are weighted using heteroskedasticity efficiency weights for low skilled mexican men's population changes.

^a94 metro area observations, omitting Brazoria, TX; see appendix section A.9 for details.

Table A-27.

Population Response to Labor Demand Shocks: Household Leverage IV Estimates

	Dependent Variable: Change in log Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
IV Estimate
Change in log of Group-Specific Employment	0.078 (0.102)	−0.092 (0.107)	0.312 (0.216)	0.546** (0.252)	−0.216 (0.401)
P-value testing shock exogeneity	0.439	0.184	0.890	0.650	0.681
First Stage
Household Leverage	−0.116** (0.017)	−0.105** (0.016)	−0.128** (0.019)	−0.141** (0.022)	−0.109** (0.023)
Partial F Statistic	48.03	41.34	44.71	41.78	21.98
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.509** (0.155)	0.507** (0.193)	0.604* (0.344)	−0.367 (0.415)	0.958** (0.422)
P-value testing shock exogeneity	0.831	0.693	0.929	0.302	0.611
First Stage
Household Leverage	−0.060** (0.016)	−0.058** (0.017)	−0.064** (0.015)	−0.119** (0.016)	−0.056** (0.017)
Partial F Statistic	13.56	11.55	18.75	56.19	11.09
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.108 (0.169)	0.053 (0.214)	0.745** (0.316)	1.104** (0.318)	−0.065 (0.808)
P-value testing shock exogeneity	0.061	0.548	0.674	0.203	0.440
First Stage
Household Leverage	−0.062** (0.011)	−0.063** (0.011)	−0.059** (0.011)	−0.070** (0.011)	−0.042** (0.016)
Partial F Statistic	34.11	34.52	29.60	41.46	7.174
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.552** (0.178)	0.676** (0.218)	0.607 (0.481)	0.916 (0.708)	0.383 (0.628)
P-value testing shock exogeneity	0.600	0.167	0.485	0.299	0.387
First Stage
Household Leverage	−0.048** (0.011)	−0.047** (0.012)	−0.046** (0.011)	−0.069** (0.009)	−0.041** (0.013)
Partial F Statistic	17.26	15.51	17.76	55.74	10.28

Each listed coefficient represents a separate instrumental variables regression of the change in log(population) for the relevant group (2006-2010, using the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data over the same time period, using the demographic group's industry mix. All regressions include an intercept term, 95 city observations, and the enclave and policy controls in Column (4) of Table A-1. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^**significant at the 1% level

^**5%

^*10%.

The excluded instrument is average household leverage, calculated using household debt data from Equifax and household income data from the IRS (see text for details). The listed “p-value testing shock exogeneity” is from a test of the null hypothesis that the OLS and IV slope coefficients are equal to each other. The first-stage coefficient on the instrument and the partial F statistic are reported below the corresponding IV estimate.

A.9 Outlier in Bartik IV Analysis

The analysis using the Bartik IV drops Brazoria, TX from all specifications because it is a severe outlier in both the first-stage and the reduced form. Its outlier status derives, in part, from the fact that the Bartik shock value for Brazoria is 4.01 standard deviations below the mean while the next lowest shock is only 1.81 standard deviations below the mean. Despite this very large negative value of predicted employment loss based on the instrument, employment rose slightly in Brazoria over this time period, which occurred in only a handful of the 95 analysis cities. This employment increase appears both in the ACS and CBP data. The most likely explanation appears to be that Brazoria's labor market benefitted from its ties to the energy extraction sector, which allowed it to deviate substantially from national trends. Although Brazoria was highly dependent on the manufacturing sector, manufacturing jobs declined only slightly from 2006-2010. Across the country, manufacturing employment fell by about 22 percent; in Brazoria, it fell by only 6 percent.

This combination leads Brazoria to have extreme leverage in the smoothing analysis in particular. Figure A-8 provides a scatter plot of data points showing the relationship between changes in the male low-skilled employment rate and the Bartik instrument. Given Brazoria's clear status as an outlier with extreme leverage, we have omitted it from all of the analysis using the Bartik instrument in the 2006-2010 time period.

Figure A-8.

Brazoria, TX is an Outlier with Extreme Leverage in Bartik IV

Source: Authors’ calculations from 2006-2010 American Community Survey and County Business Patterns. Changes in log(employment to population ratio) are calculated from 2006 to 2010 for low-skilled men (without regard to nativity). Construction of the Bartik instrument described in the text.

A.10 Population Elasticity Specification Checks

We have conducted several specification checks for the main elasticity results as discussed in the main text. These include using employment declines that are not specific to each demographic group, various ways of addressing the CBP's non-covered industries, using the three-year samples of ACS data to calculate population changes, and alternative weighting schemes (including un-weighted results). We include versions of Table 2 (population elasticities without controls) and Table 4 (elasticities with controls) for each of the specification alternatives. As discussed in the text, all of these alternatives are consistent with the primary finding that native-born low-skilled individuals respond very little to demand shocks while Mexican-born low-skilled immigrants are highly responsive.

A.10.1 Demand Shocks that are not Group-Specific

In the main results, we calculate demand shocks based on local employment changes that take account of each demographic group's industry mix. The following two tables provide results using shocks that are calculated only by skill level and sex. As expected, these shocks show an even larger gap between natives and the Mexican-born, as low-skilled employment losses fall disproportionately on the latter.

A.10.2 Treatment of Industries Not Covered by CBP

As mentioned in the text, the CBP does not cover employment in agricultural production, private households, or government. In our main results, we fill in employment changes in these industries using calculations from the ACS at the city x year level. We completed two additional robustness checks of this way of constructing demand shocks. First, we re-calculate the demand shocks treating the CBP data as missing in taking share-weighted averages of job losses by covered industry. Those results are in the following tables.

Additionally, we calculated all employment changes using the ACS (rather than CBP) at the (city x year) level. The results using those shocks are are provided below.

A.10.3 Three Year ACS Samples for Population Changes

Although the ACS is a one percent sample of the entire country, it has relatively small sample sizes for some (sex × skill × demographic) cells. The ACS also makes available three-year samples that are based on a reference year and the years immediately preceding and following. For robustness, we ran versions of our main results using population changes measured with three-year samples centered at 2006 and 2010, and our preferred shock measures. As expected, the results are slightly muted, likely because some movement is already occurring in 2007 and it is not complete by 2009.

A.10.4 Alternative Weighting Schemes

As discussed in the paper and in Appendix Section A.4, our preferred weighting scheme uses a feasible version of the inverse of the analytical sampling variance of the dependent variable. For completeness, we provide results here for two alternatives: population weighting and equal weighting. As mentioned in the paper, the efficient weights are very closely related to the group-specific population in 2006. The first set of tables contains results using these group sizes as weights.

Finally, we provide results where each city is given equal weight. We also calculated the p-value for a test of the null that the squared residuals are unrelated to the group's population size. In nearly all cases, this null is rejected. Comparing these tables to the main results in Tables 2 and 4, whenever the null of homoskedasticity is rejected, the efficient-weighted results produce estimates with smaller standard errors, which suggests that the weighted specification is, in fact, more efficient. In most cases, the unweighted results are very similar to the main results. The one exception is the point estimate among the other foreign-born, which is substantially more positive in the unweighted versions. Some additional investigation reveals that this point estimate is being driven by a few very small population cities that are outliers. In addition, the size of the coefficient falls by nearly half when adding controls (for men). Nevertheless, we note that the results for the other foreign-born are much more dependent on specification than are the results for natives and for Mexican-born immigrants, which form the core of our analysis.

A.10.5 Falsification Results for All Groups

Figure 2 provided the results for the pre-trend falsification test for low-skilled men (native- and Mexican-born). For reference, Table A-18 provides analogous results for all (sex x skill x nativity) groups.

Table A-18.

Falsification Test: 2000-2006 Population Change vs. 2006-2010 Labor Demand Shocks

	Dependent Variable: Change in log of Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	−0.310 (0.199)	−0.168 (0.183)	−0.664*** (0.214)	−0.481*** (0.169)	−0.986*** (0.332)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	−0.090 (0.133)	−0.022 (0.118)	−0.599* (0.357)	−0.216 (0.376)	−0.640* (0.372)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.176 (0.301)	0.199 (0.268)	−0.125 (0.490)	−0.021 (0.470)	−0.248 (0.619)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.235 (0.156)	0.346** (0.146)	0.096 (0.373)	0.790 (0.561)	−0.215 (0.371)

Identical specification to Table 2, with the exception that the changes in log(population) are calculated for 2000-2006.

A.10.6 Detailed Race/Ethnicity or Source Country

In the main text, we examine mobility responses of natives-born, Mexican-born, and other foreign-born individuals. Here we examine mobility responses of less aggregate groups. While we are able to calculate robust mobility estimates for the larger groups discussed in the main text, the results for these smaller groups are often imprecisely estimated and vary across specifications. Hence, we focus on the more aggregate groups in the main text and present the less aggregate results here for completeness.

The following table replicates Table 2 for these more detailed population groups.

Among less-skilled native workers, white and Asian populations respond most strongly to labor demand shocks. Hispanic natives exhibit a surprising negative response, apparently moving toward the most negatively affected locations. As we will see below, this counterintuitive result is not robust to changes in specification, and may reflect ongoing trends for this group. Among less-skilled foreign-born individuals, Mexican men and women, and women from “Other” countries are the only groups exhibiting strong relocation toward more favorable markets.

The following table adds controls, as in Table 4 in the main text. The results are similar to those without controls, but the surprising negative response for less-skilled Hispanic natives is no longer statistically significant at the five percent level. (The Mexican enclave control absorbs much of the variation in this specification, an interesting result warranting study in future work.)

We now consider the pre-recession false experiment in which we relate the 2000-2006 population change to the 2006-2010 employment decline. As discussed in the main text, the strong positive response of Mexican-born immigrants in the main analysis represents a reversal of the existing trend. It is also clear that the strange negative results for Hispanic natives partly reflect the continuation of an ongoing trend, which changed in the expected direction during the recession period. Similar findings for immigrants from the Other Western Hemisphere and Other locations suggest that the surprising negative (though insignificant) point estimates for these groups may also partly reflect preexisting trends.

In general, the analysis shows that our approach reveals quite robust findings for larger demographic groups such as natives overall or Mexican-born immigrants, but has trouble identifying consistent results for smaller groups. While this does not affect the conclusions of the main analysis, it does make it difficult to determine with certainty how population responses among larger groups compare to smaller groups’ responses.

A.11 Robustness and Heterogeneity of Population Response Results

In this section, we return to our primary specification of Table 2 and Table 3 to conduct additional robustness checks, and examine potential heterogeneity.

A.11.1 Dropping California

In order to investigate whether metro areas in California were driving the population responses, Table A-22 replicates Table 3, with the exception of omitting California. Notably, the important contrast between low-skilled Mexican-born men and low-skilled native-born men remains.

Table A-22.

Population Response to Labor Demand Shocks - Including Policy and Enclave Controls and Omitting California

	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
Change in log of Group-Specific Employment	0.103 (0.0754)	−0.0285 (0.0889)	0.257 (0.175)	0.613*** (0.166)	−0.168 (0.305)
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.504*** (0.0771)	0.459*** (0.0902)	0.730*** (0.236)	0.982* (0.542)	0.684** (0.263)
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.324 (0.199)	0.0455 (0.236)	0.475 (0.302)	0.0953 (0.279)	0.613 (0.482)
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.499*** (0.130)	0.437*** (0.153)	0.981*** (0.291)	−0.133 (1.135)	1.140*** (0.309)

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix), with the enclave and policy controls in Column (4) of Table 3. All regressions include an intercept term and 73 city observations, omitting those in California. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

A.11.2 Heterogenous Responses

We next consider potentially heterogeneous population responses based on three separate characteristics of cities that are either fixed or measured prior to the start of the recession. We consider this potential heterogeneity for both the Mexican-born and native-born populations.

Column (1) of Table A-23 replicates column (4) of Table A-1. Column (2) adds a level effect control for the road distance to the border.⁶⁹ Columns (3) through (6) investigate interaction effects. We first use the enclave measure for Mexican immigrants. As shown in column (3), the population responses are somewhat weaker in cities that have historically attracted many Mexican-born immigrants.⁷⁰ The negative interaction could reflect the fact that employment prospects are less of a determining factor in location choices for the types of immigrants who are attracted to larger enclaves. We fail to reject the null, however, that population elasticities are the same regardless of a city's enclave size.

Table A-23.

Investigation of Heterogeneous Low-Skilled Mexican-Born Male Population Response to Labor Demand Shocks

Dependent Variable: Change in log Population - Mexican-born Men, High-school or less
	(1)	(2)	(3)	(4)	(5)	(6)
Change in log Employment	0.475*** (0.172)	0.436** (0.179)	0.471** (0.231)	0.300 (0.231)	0.964*** (0.248)	0.950*** (0.248)
Interaction: Change in log Employment × Enclave Measure			−0.242 (1.618)
Interaction:Change in log Employment × Road Distance to the Border				0.207 (0.165)
Interaction:Change in log Employment × Above Median Mexican-Born Share					−0.442 (0.339)	−0.513 (0.313)
Enclave Measure (Mexican-born Share of City Population)	−0.041 (0.166)	0.262 (0.224)	0.237 (0.305)	0.265 (0.236)
New State Immigrant Employment Legislation	−0.016 (0.032)	−0.035 (0.030)	−0.035 (0.030)	−0.036 (0.030)		0.016 (0.046)
New State 287g Policy	−0.119** (0.051)	−0.091* (0.049)	−0.090* (0.049)	−0.096* (0.051)		−0.153*** (0.053)
Road Distance to the Border (1000 km)		0.043** (0.021)	0.044** (0.020)	0.077** (0.035)		−0.017 (0.022)
Indicator: Above Median Mexican-Born Population Share					−0.149** (0.065)	−0.204** (0.079)
Constant	0.032 (0.045)	−0.054 (0.069)	−0.051 (0.073)	−0.077 (0.074)	0.158*** (0.053)	0.217*** (0.077)
R-squared	0.262	0.289	0.289	0.303	0.248	0.323

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

We also consider the possibility that population responses may be more elastic for locations that are closer to the Mexican border. In column (4), we interact the change in employment with the shortest road distance to a major border crossing. Contrary to this hypothesis, the point estimate suggests that populations are somewhat more elastic in locations farther from the border, although we again fail to reject the null that the interaction term is zero.

Finally, in columns (5) and (6), we interact the labor demand shock with a dummy variable for having larger than the median Mexican-born population share. Column (5) omits the road distance control while column (6) includes it. The motivation for this column is conceptually similar to that of column (3), although this column's results allow for a direct comparison of elasticities within the groups of cities considered separately throughout the smoothing analysis (e.g. in Table A-31). Consistent with the results in column (3), we find weak evidence that populations are less elastic in response to shocks in cities with relatively many Mexican-born residents, although, again, there is not sufficient statistical evidence to rule out the null hypothesis that responses are equal in both types of cities.

Table A-31.

Mexican Mobility Smooths Employment Outcomes: Change in Low-Skilled Emp/Pop Ratio vs. Change in Payroll Employment

dependent variable: change in log employment/population (ACS)
	City's Mexican population share
	below-median	above-median	difference
(a) dependent variable sample: less-skilled men
change in log employment for less-skilled men (CBP)	0.503*** (0.048)	0.299*** (0.043)	−0.204*** (0.064)
(b) dependent variable sample: native less-skilled men
change in log employment for less-skilled men (CBP)	0.524*** (0.056)	0.309*** (0.043)	−0.215*** (0.070)
(c) dependent variable sample: native less-skilled men
change in log employment for less-skilled native men (CBP)	0.546*** (0.059)	0.342*** (0.047)	−0.204*** (0.075)
(d) dependent variable sample: native high-skilled men
change in log employment for high-skilled native men (CBP)	0.238*** (0.048)	0.246*** (0.046)	0.008 (0.066)

Examines the relationship between labor market outcomes (changes in employment probability) and labor demand shocks (changes in payroll employment) separately for cities with above- and below-median Mexican population share to demonstrate the smoothing effect of Mexican mobility. Smaller coefficients indicate more smoothing. Changes measured as the long difference from 2006-2010. Panel (a) examines the relationship between low-skilled employment shocks and low-skilled men's employment probability. Panel (b) examines the relationship between low-skilled employment shocks and low-skilled native men's employment probability. Panel (c) examines the relationship between low-skilled native employment shocks and low-skilled native men's employment. Panel (d) examines the relationship between high-skilled native employment shocks and high-skilled native men's employment.

Table A-24 provides a parallel set of results examining heterogeneity in population responses among low-skilled native-born men. Again, there is no evidence of meaningful heterogeneity in population responses. Notably, natives are no more elastic in places with fewer Mexicans where the incidence of local shocks is higher due to relatively lower access to the more mobile factor.

Table A-24.

Investigation of Heterogeneous Low-Skilled Native-Born Male Population Response to Labor Demand Shocks

Dependent Variable: Change in log Population - Native-born Men, High-school or less
	(1)	(2)	(3)	(4)	(5)	(6)
Change in log Employment	0.040 (0.071)	0.039 (0.074)	−0.070 (0.127)	0.017 (0.113)	−0.005 (0.114)	0.015 (0.115)
Interaction: Change in log Employment × Enclave Measure			1.231 (0.939)
Interaction:Change in log Employment × Road Distance to the Border				0.017 (0.077)
Interaction:Change in log Employment × Above Median Mexican-Born Share					0.052 (0.148)	0.043 (0.148)
Enclave Measure (Mexican-born Share of City Population)	0.037 (0.084)	−0.245* (0.125)	−0.134 (0.124)	−0.249* (0.129)
New State Immigrant Employment Legislation	0.003 (0.024)	0.007 (0.018)	0.011 (0.018)	0.007 (0.018)		0.010 (0.020)
New State 287g Policy	0.004 (0.021)	−0.017 (0.017)	−0.019 (0.018)	−0.017 (0.017)		−0.008 (0.019)
Road Distance to the Border (1000 km)		−0.026*** (0.008)	−0.029*** (0.008)	−0.024** (0.010)		−0.017** (0.008)
Indicator: Above Median Mexican-Born Population Share					0.021 (0.021)	−0.009 (0.026)
Constant	−0.017 (0.011)	0.048** (0.023)	0.040* (0.023)	0.047** (0.023)	−0.025* (0.015)	0.016 (0.027)
R-squared	0.010	0.120	0.146	0.121	0.028	0.075

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Tables A-25 and A-26 provide a parallel set of results instrumenting for the change in log(employment) with the Bartik IV and for each interaction term with the interaction of the instrument and the corresponding independent variable. Again, this set of results reveals so systematic heterogeneity in population responses by any of the included city characteristics.

Table A-25.

Investigation of Heterogeneous Low-Skilled Mexican-Born Male Population Response to Labor Demand Shocks: Bartik IV Estimates

Dependent Variable: Change in log Population - Mexican-born Men, High-school or less
	(1)	(2)	(3)	(4)	(5)	(6)
Change in log Employment	0.992** (0.468)	0.825** (0.417)	0.623 (0.436)	0.801 (0.512)	0.832** (0.361)	0.943** (0.403)
Interaction: Change in log Employment × Enclave Measure			1.355 (3.487)
Interaction:Change in log Employment × Road Distance to the Border				0.034 (0.220)
Interaction:Change in log Employment × Above Median Mexican-Born Share					0.108 (0.610)	−0.078 (0.547)
Enclave Measure (Mexican-born Share of City Population)	−0.047 (0.147)	0.183 (0.211)	0.325 (0.399)	0.184 (0.212)
New State Immigrant Employment Legislation	0.031 (0.061)	0.004 (0.056)	0.002 (0.055)	0.004 (0.056)		0.073 (0.083)
New State 287g Policy	−0.093* (0.052)	−0.079 (0.051)	−0.087* (0.049)	−0.080 (0.053)		−0.150*** (0.046)
Road Distance to the Border (1000 km)		0.032 (0.021)	0.027 (0.023)	0.038 (0.040)		−0.032 (0.025)
Indicator: Above Median Mexican-Born Population Share					−0.051 (0.095)	−0.156 (0.098)
Constant	0.111 (0.068)	0.025 (0.082)	0.007 (0.074)	0.021 (0.094)	0.130** (0.065)	0.239** (0.102)
First-stage partial F statistic	26.98	24.06	6.510	11.87	15.05	15.16
P-value testing shock exogeneity	0.0290	0.114	0.213	0.0843	0.140	0.140

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

Table A-26.

Investigation of Heterogeneous Low-Skilled Native-Born Male Population Response to Labor Demand Shocks: Bartik IV Estimates

Dependent Variable: Change in log Population - Native-born Men, High-school or less
	(1)	(2)	(3)	(4)	(5)	(6)
Change in log Employment	0.007 (0.090)	0.184* (0.099)	−0.028 (0.145)	0.203 (0.157)	−0.021 (0.099)	0.147 (0.127)
Interaction: Change in log Employment × Enclave Measure			2.021** (0.795)
Interaction:Change in log Employment × Road Distance to the Border				−0.015 (0.074)
Interaction:Change in log Employment × Above Median Mexican-Born Share					0.121 (0.163)	−0.019 (0.169)
Enclave Measure (Mexican-born Share of City Population)	0.042 (0.081)	−0.272** (0.118)	−0.086 (0.105)	−0.270** (0.120)
New State Immigrant Employment Legislation	0.002 (0.023)	0.012 (0.019)	0.017 (0.019)	0.012 (0.019)		0.015 (0.021)
New State 287g Policy	0.003 (0.020)	−0.016 (0.017)	−0.019 (0.018)	−0.015 (0.017)		−0.010 (0.018)
Road Distance to the Border (1000 km)		−0.027*** (0.008)	−0.031*** (0.008)	−0.029*** (0.010)		−0.020** (0.008)
Indicator: Above Median Mexican-Born Population Share					0.030 (0.025)	−0.025 (0.031)
Constant	−0.021 (0.013)	0.070** (0.028)	0.052* (0.028)	0.072** (0.030)	−0.027* (0.014)	0.042 (0.034)
First-stage partial F statistic	28.93	38.39	21.04	19.14	17.17	16.65
P-value testing shock exogeneity	0.764	0.201	0.368	0.467	0.927	0.564

Each listed coefficient represents a separate regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term and 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

A.12 Additional IV Results

In Table 4, we use a Bartik (1991) style instrument for local employment growth. In this section, we present another instrumental variable approach based on Mian and Sufi (2014), who find that counties with more highly leveraged households experienced larger employment losses during the Great Recession. Importantly, they find that these employment losses were concentrated in industries providing goods and services locally, suggesting that the tightening of credit during the financial crisis led to a decline in consumer demand and that this decline was largest among households that were more indebted. Mian and Sufi (2011) identify several mechanisms through which household leverage drove declining demand. Indebted households became less able to roll over their debt and were thus forced to spend a greater share of their incomes on debt service rather than consumption. Households in cities with higher average leverage had a large share of their debts in mortgages, and many may have treated the annual increase in home value as “income,” which disappeared during the crisis. Finally, some households may have decided that their previous levels of consumption were unsustainable and decided to find a new equilibrium spending path. We construct the household leverage ratio analogously to Mian and Sufi (2014), aggregating MSA-level variables from county-level information provided by Equifax (total household debt) and the Internal Revenue Service (total income). Mian and Sufi (2014) provide more detail on the data sources. The Equifax data are available through the Federal Reserve Bank of New York. Our restriction to large MSAs avoids the concern that only a portion of the counties used in the original paper are publicly available, as the restricted data are for counties with small populations.

Table A-27, which is otherwise identical in format to Table 4, presents the results of these specifications, which include the same set of controls as in Table 3. On the whole, the results are quite consistent with the OLS results in Table 3, and, in fact, none of the population elasticity estimates using this instrument is statistically significantly different than the OLS version at the five percent level. The pattern of elasticities continues to show strong differences by skill level, and among the low-skilled, only the Mexican-born population responds significantly to changes in local labor demand.

Note that the Mian and Sufi measure may fail to satisfy the IV exclusion restriction by influencing migration through channels other than local labor market conditions, especially because Hispanic households held a disproportionate share of subprime mortgages prior to the credit crisis. For example, foreclosures, which led people to move out of their homes, may also trigger out-migration if, for example former homeowners moved into the local rental market and drove up rental prices. Recall, however, that our primary interest is in determining the relative responsiveness of different groups to local demand conditions. While these concerns suggest that the IV estimates may be somewhat more positively biased among Mexican immigrants, it seems unlikely that they are sufficient to explain the entirety of the differential population responses, especially because the native-born point estimates remain indistinguishable from zero.

We have presented two sets of exactly identified IV population elasticity results (Tables 4 and A-27) rather than including both instruments simultaneously. We do so because the Local Average Treatment Effects of these two instruments may be different, and it is potentially useful to examine the results separately. A candidate explanation for potential heterogeneity is a difference in the permanence of the demand shocks represented by the Bartik and leverage instruments. If, for example, demand shocks due to household leverage were expected to be shorter lived, then it would not be surprising to find weaker population responses to this instrument. Nevertheless, for completeness, Table A-28 provides overidentified IV versions of the population elasticity results of Table 2 using both instruments simultaneously.

Table A-28.

Test of Overidentifying Restrictions for Bartik and Leverage IVs Population Response Regressions 2006-2010

	Dependent Variable: Change in log Population
	All	Native-Born	Foreign-Born	Mexican-Born	Other Foreign-Born
Panel A: Men, High-school or less
IV Estimate
Change in log of Group-Specific Employment	0.127 (0.096)	−0.052 (0.080)	0.333 (0.238)	0.596** (0.248)	−0.454 (0.316)
P-value testing shock exogeneity	0.790	0.245	0.776	0.421	0.128
P-value testing instrument exogeneity	0.225	0.492	0.653	0.062	0.323
First Stage
Predicted Change in log Employment	2.778*** (0.643)	2.910*** (0.643)	2.515*** (0.825)	1.629 (1.188)	3.489*** (0.685)
Household Leverage	−0.096*** (0.017)	−0.087*** (0.016)	−0.105*** (0.019)	−0.127*** (0.019)	−0.079*** (0.020)
Partial F Statistic	34.62	35.01	24.34	23.79	62.09
Panel B: Men, Some college or more
Change in log of Group-Specific Employment	0.392*** (0.126)	0.455*** (0.148)	0.176 (0.248)	−0.423 (0.364)	0.351 (0.338)
P-value testing shock exogeneity	0.506	0.867	0.035	0.149	0.276
P-value testing instrument exogeneity	0.348	0.774	0.120	0.911	0.097
First Stage
Predicted Change in log Employment	2.104*** (0.639)	2.188*** (0.660)	2.131*** (0.685)	2.273*** (0.783)	2.104*** (0.638)
Household Leverage	−0.050*** (0.017)	−0.048*** (0.017)	−0.046** (0.019)	−0.096*** (0.016)	−0.041** (0.020)
Partial F Statistic	23.87	22.37	27.76	36.48	23.67
Panel C: Women, High-school or less
Change in log of Group-Specific Employment	0.122 (0.127)	−0.079 (0.195)	0.606* (0.361)	1.151*** (0.323)	−0.611 (0.579)
P-value testing shock exogeneity	0.021	0.127	0.919	0.147	0.018
P-value testing instrument exogeneity	0.893	0.134	0.244	0.176	0.384
First Stage
Predicted Change in log Employment	1.286*** (0.397)	1.395*** (0.397)	1.118** (0.555)	0.425 (0.717)	1.536*** (0.531)
Household Leverage	−0.052*** (0.012)	−0.054*** (0.012)	−0.048*** (0.016)	−0.066*** (0.015)	−0.028 (0.020)
Partial F Statistic	47.64	42.95	34.89	25.32	23.67
Panel D: Women, Some college or more
Change in log of Group-Specific Employment	0.463*** (0.172)	0.568*** (0.190)	0.242 (0.515)	0.832 (0.702)	−0.052 (0.634)
P-value testing shock exogeneity	0.960	0.353	0.069	0.339	0.150
P-value testing instrument exogeneity	0.158	0.188	0.046	0.629	0.142
First Stage
Predicted Change in log Employment	0.591 (0.475)	0.634 (0.475)	0.845 (0.550)	0.922* (0.533)	0.828 (0.517)
Household Leverage	−0.044*** (0.012)	−0.043*** (0.012)	−0.038*** (0.014)	−0.059*** (0.011)	−0.034** (0.016)
Partial F Statistic	11.97	11.62	12.11	32.24	9.065

Each listed coefficient represents a separate instrumental variables regression of the change in log(population) for the relevant group (from the American Community Survey) on the change in log(group-specific employment) from County Business Patterns data (using the demographic group's industry mix). All regressions include an intercept term, 94 city observations, and the enclave and policy controls in Column (4) of Table A-1. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable (see appendix for details). Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

^**5%

^*10%.

We use the predicted employment change (based on Bartik (1991)) and average household leverage as instruments for the change in log(group-specific employment). The first-stage coefficient on the instrument and the partial F statistic are reported below the corresponding IV estimate.

In addition to reporting the IV slope coefficients, the table includes the results of two additional hypothesis tests for each regression. The first p-value listed (“shock exogeneity”), is from a test of the null that the OLS and IV coefficients are the same. For the most part, we fail to reject these null hypotheses, although three of the twenty listed p-values are less than 0.05. Notably, none of these significant p-values occurs in the low-skilled native-born or Mexican-born population groups that we focus on. The second p-value listed (“instrument exogeneity”) is from a test of the null that the IV coefficients are the same when using each IV separately. This null hypothesis is commonly referred to as a test of instrument exogeneity, although, as discussed above, this interpretation relies on the assumption of equal local average treatment effects from each instrument. Only one of the twenty reported p-values is below 0.05, which means that we cannot rule out the null hypothesis that differences in slope coefficients between Tables 4 and A-27 are due to sampling error alone.

A.13 Descriptive Statistics for Smoothing Regressions

Table A-29 provides the mean and standard deviation for the dependent variable used in the smoothing analysis: the change in log(employment/population). Notably, these distributions are remarkably similar for the two sets of cities with above-median and below-median Mexican-born population share.

Table A-29.

Descriptive Statistics for Smoothing Regressions

Change in log Employment to Population Ratio
City's Mexican Population Share:	below-median		above-median
	mean	std. dev.	mean	std. dev.
Sample:
Less-skilled Men	−0.101	0.048	−0.092	0.043
Native Less-skilled Men	−0.122	0.048	−0.116	0.053
Native High-skilled Men	−0.036	0.023	−0.040	0.023

Each panel provides the mean and standard deviation of change in log(employment to population ratio) (from the American Community Survey) and the change in log(employment) from County Business Patterns data (using the demographic group's industry mix) for a different demographic group of workers (by sex and education level). All statistics are based on a consistent sample of 95 city observations. Observations are weighted by the inverse of the estimated sampling variance of the dependent variable.

A.14 Additional Smoothing Results

As discussed in footnote 44, we investigated whether the above-/below-median split of the cities in the smoothing results (throughout section 4) was too coarse. Table A-30 shows the results of running analogous specifications splitting the cities into quartiles of Mexican-born population share. Panels (a)-(c) consistently show that the relationship between local shocks and local outcomes becomes weaker moving from the first to third quartiles. This pattern then levels off when comparing the third to the fourth quartile. The coefficients in panel (d) are all relatively similar to each other with no apparent pattern across quartiles. These results are consistent with the interpretation that the presence of Mexican immigrants smooths outcomes substantially as long as there is a critical mass of potential workers in the local labor market.

Table A-30.

Mexican Mobility Smooths Employment Outcomes: Change in Low-Skilled Emp/Pop Ratio vs. Change in Payroll Employment

dependent variable: change in log employment/population (ACS)
	City's Mexican population share quartile
	1 (lowest)	2	3	4 (highest)
(a) dependent variable sample: less-skilled men
change in log employment for less-skilled men (CBP)	0.677*** (0.137)	0.454*** (0.064)	0.297*** (0.046)	0.341*** (0.070)
(b) dependent variable sample: native less-skilled men
change in log employment for less-skilled men (CBP)	0.678*** (0.147)	0.459*** (0.063)	0.308*** (0.046)	0.354*** (0.084)
(c) dependent variable sample: native less-skilled men
change in log employment for less-skilled native men (CBP)	0.664*** (0.147)	0.488*** (0.066)	0.329*** (0.051)	0.406*** (0.089)
(d) dependent variable sample: native high-skilled men
change in log employment for high-skilled native men (CBP)	0.248*** (0.041)	0.194* (0.106)	0.290*** (0.036)	0.213** (0.094)

Examines the relationship between labor market outcomes (changes in employment probability) and labor demand shocks (changes in payroll employment) separately for cities based on quartiles of Mexican population share to demonstrate the smoothing effect of Mexican mobility. Smaller coefficients indicate more smoothing. Panel (a) examines the relationship between low-skilled employment shocks and low-skilled men's employment probability. Panel (b) examines the relationship between low-skilled employment shocks and low-skilled native men's employment probability. Panel (c) examines the relationship between low-skilled native employment shocks and low-skilled native men's employment. Panel (d) examines the relationship between high-skilled native employment shocks and high-skilled native men's employment.

Further, we have run a version of the smoothing results in table 5 using OLS rather than the Bartik IV. The results of this specification, which are quite similar to those in Table 5, are presented in Table A-31.

In addition, we have run a version of Table A-31 that omits cities in California; these results are in Table A-32. The qualitative results are unchanged, which suggests that California alone was not driving the main results.

Table A-32.

Mexican Mobility Smooths Employment Outcomes: Change in Low-Skilled Emp/Pop Ratio vs. Change in Payroll Employment Omitting California

dependent variable: change in log employment/population (ACS)
	City's Mexican population share
	below-median	above-median	difference
(a) dependent variable sample: less-skilled men
change in log employment for less-skilled men (CBP)	0.499*** (0.0511)	0.316*** (0.0428)	−0.183*** (0.0666)
(b) dependent variable sample: native less-skilled men
change in log employment for less-skilled men (CBP)	0.517*** (0.0587)	0.281*** (0.0486)	−0.235*** (0.0762)
(c) dependent variable sample: native less-skilled men
change in log employment for less-skilled native men (CBP)	0.536*** (0.0617)	0.317*** (0.0539)	−0.219*** (0.0818)
(d) dependent variable sample: native high-skilled men
change in log employment for high-skilled native men (CBP)	0.218*** (0.0481)	0.243*** (0.0255)	0.0254 (0.0546)

Examines the relationship between labor market outcomes (changes in employment probability) and labor demand shocks (changes in payroll employment) separately for cities with above- and below-median Mexican population share to demonstrate the smoothing effect of Mexican mobility. Cities in California are omitted from the analysis. Smaller coefficients indicate more smoothing. Panel (a) examines the relationship between low-skilled employment shocks and low-skilled men's employment probability. Panel (b) examines the relationship between low-skilled employment shocks and low-skilled native men's employment probability. Panel (c) examines the relationship between low-skilled native employment shocks and low-skilled native men's employment. Panel (d) examines the relationship between high-skilled native employment shocks and high-skilled native men's employment.

Finally, as discussed in footnote 48, a potential concern with the smoothing analysis is that cities with a larger Mexican-born populations may have less rigid wage structures. Recall that under this hypothesis, wage changes should be more strongly correlated with employment changes in cities with greater Mexican concentrations. Table A-33 shows that, in fact, the opposite is true. Instead, the pattern is consistent with the interpretation that Mexican mobility smoothed both employment and wage outcomes for natives. Note, however, that the difference in slopes for the two sets of cities is not statistically significantly different from zero, which implies that the smoothing in employment rates documented in the main text is the primary effect.

Table A-33.

Mexican Mobility Smooths Employment Outcomes: Change in Low-Skilled Wages vs. Change in Payroll Employment

dependent variable:change in mean log wage (ACS)
	City's Mexican population share
	below-median	above-median	difference
(a) dependent variable sample: less-skilled men
change in log employment for less-skilled men (CBP)	0.377*** (0.121)	0.216*** (0.053)	−0.161 (0.132)
(b) dependent variable sample: native less-skilled men
change in log employment for less-skilled men (CBP)	0.425*** (0.128)	0.297*** (0.086)	−0.127 (0.154)
(c) dependent variable sample: native less-skilled men
change in log employment for less-skilled native men (CBP)	0.442*** (0.131)	0.306*** (0.097)	−0.137 (0.162)
(d) dependent variable sample: native high-skilled men
change in log employment for high-skilled native men (CBP)	0.296*** (0.092)	0.148* (0.083)	−0.149 (0.124)

Examines the relationship between changes in average log(wage) and labor demand shocks (changes in payroll employment) separately for cities with above- and below-median Mexican population share. Smaller coefficients indicate more smoothing. Panel (a) examines the relationship between low-skilled employment shocks and low-skilled men's wages. Panel (b) examines the relationship between low-skilled employment shocks and low-skilled native men's wages. Panel (c) examines the relationship between low-skilled native employment shocks and low-skilled native men's wages. Panel (d) examines the relationship between high-skilled native employment shocks and high-skilled native men's wages.

A.15 Propensity Score Reweighting

Table A-34 provides the results of the probit specifications used to reweight the native population for the results described in section 6.2. Recall that these are probit specifications predicting whether an individual observation is a Mexican-born immigrant, with the sample limited to native-born and Mexican-born men with at most a high school degree. The specification in column (1) includes a dummy variable for whether the individual completed less than a high school degree. Column (2) includes a series of dummy variables, one for each age. Column (3) includes a dummy variable for renting one's home rather than owning it. Column (4) includes dummies for 20 family status types, one for each combination of a dummy for “married, spouse present” and dummies for the number of children (one each for every category from zero to “9+″). Column (5) includes all covariates together. The weights based on columns (1)-(5) are then used to run the regressions reported in columns (3)-(7), respectively, of Table 9.

Table A-34.

Probit Regressions Predicting Mexican Nativity (2006)

dependent variable: indicator for Mexican nativity
	(1)	(2)	(3)	(4)	(5)
High school dropout indicator	1.196*** (0.010)				1.165*** (0.011)
Age indicators		X			X
Renter indicator			0.530*** (0.009)		0.428*** (0.011)
Interactions of married spouse present indicator and number of children indicators				X	X

Results are coefficient estimates of a probit regression predicting whether an observation is a Mexican-born immigrant. The sample includes native-born and Mexican-born men observed in the 2006 ACS with at most a high school degree who meet individual sampling criteria and live in the 95 cities used throughout the results. The coefficients marked with an “X” are displayed in subsequent tables. Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

** 5%

* 10%.

Column (1) reveals that those without a high school degree more likely to be Mexican-born. Similarly, column (3) shows that renters are more likely to be Mexican-born. The coefficients for the age dummies and family type (from column (5)) are shown in Figures A-9 and A-10 respectively. Conditional on skill and home ownership, younger men (roughly those under the age of 40) are more likely to be Mexican-born while older men are more likely to be native-born. Larger family sizes typically predict a greater likelihood of being Mexican-born, although the coefficients become fairly imprecise in the smaller cell sizes representing families with seven or more children.

Figure A-9.

Probit Coefficients Predicting Mexican Nativity (2006)

This figure shows coefficient estimates (solid line) and the associated 95 percent confidence interval for age dummies (one for each year) from the probit regression reported in column (5) of Table A-34. The reference category is 18 year olds, which is denoted in the figure with a coefficient of zero without a standard error. The sample includes native-born and Mexican-born men observed in the 2006 ACS with at most a high school degree who meet individual sampling criteria and live in the 95 cities used throughout the results.

Figure A-10.

Probit Coefficients Predicting Mexican Nativity (2006)

This figure shows coefficient estimates (solid lines) and the associated 95 percent confidence interval for dummies for the number of children interacted with a dummy variable for being married with a spouse present from the probit regression reported in column (5) of Table A-34. The omitted category is men without a spouse present with no children in the household, which is denoted in the figure with a coefficient of zero without a standard error. The gray line shows coefficients for men without a spouse present, but with children in the household; the black line shows analogous results for men with spouses present. The regression was run without a “main effect” for marital status. Thus each coefficient compares the denoted group to the omitted category. The sample includes native-born and Mexican-born men observed in the 2006 ACS with at most a high school degree who meet individual sampling criteria and live in the 95 cities used throughout the results.

Table A-35 and Figures A-11 and A-12 provide analogous results for similar probit regressions limited to Mexican-born immigrants and native-born men living outside of their state of birth. The results reveal qualitatively similar relationships between the covariates and the likelihood that an observation is Mexican-born.

Table A-35.

Probit Regressions Predicting Mexican Nativity (2006) Natives Not Living in State of Birth

dependent variable: indicator for Mexican nativity
	(1)	(2)	(3)	(4)	(5)
High school dropout indicator	1.287*** (0.013)				1.275*** (0.014)
Age indicators		X			X
Renter indicator			0.493*** (0.012)		0.309*** (0.014)
Interactions of married spouse present indicator and number of children indicators				X	X

Results are coefficient estimates of a probit regression predicting whether an observation is a Mexican-born immigrant. The sample includes native-born living outside their state of birth and Mexican-born men observed in the 2006 ACS with at most a high school degree who meet individual sampling criteria and live in the 95 cities used throughout the results. The coefficients marked with an “X” are displayed in subsequent tables. Heteroskedasticity-robust standard errors in parentheses

^***significant at the 1% level

** 5%

* 10%.

Figure A-11.

Probit Coefficients Predicting Mexican Nativity (2006) Natives Not Living in State of Birth

This figure shows coefficient estimates (solid line) and the associated 95 percent confidence interval for age dummies (one for each year) from the probit regression reported in column (5) of Table A-34. The reference category is 18 year olds, which is denoted in the figure with a coefficient of zero without a standard error. The sample includes native-born living outside their state of birth and Mexican-born men observed in the 2006 ACS with at most a high school degree who meet individual sampling criteria and live in the 95 cities used throughout the results.

Figure A-12.

Probit Coefficients Predicting Mexican Nativity (2006) Natives Not Living in State of Birth

This figure shows coefficient estimates (solid lines) and the associated 95 percent confidence interval for dummies for the number of children interacted with a dummy variable for being married with a spouse present from the probit regression reported in column (5) of Table A-35. The omitted category is men without a spouse present with no children in the household, which is denoted in the figure with a coefficient of zero without a standard error. The gray line shows coefficients for men without a spouse present, but with children in the household; the black line shows analogous results for men with spouses present. The regression was run without a “main effect” for marital status. Thus each coefficient compares the denoted group to the omitted category. The sample includes native-born men living outside their state of birth and Mexican-born men observed in the 2006 ACS with at most a high school degree who meet individual sampling criteria and live in the 95 cities used throughout the results.

A.16 CPS descriptives

The following section uses Current Population Survey data that we reference in Section 6 when examining why the less-skilled Mexican-born respond so much more strongly than similarly skilled natives.

Figure A-13 shows UI participation rates by nativity groups for low-skilled men among those who had a spell of unemployment in the previous year. The patterns across groups for high-skilled men are broadly similar, although the high-skilled are less likely to claim benefits in general.

Figure A-13.

Unemployment Benefit Receipt by Nativity 2000-2011

Source: Authors’ calculations from Current Population Survey data. Sample includes men ages 18-64, not in school, not in group quarters, with at most a high school degree.

Figure A-14 shows average unemployment duration among those who are unemployed in the reference month, separately by nativity. The results show that Mexican-born workers have markedly shorter unemployment durations than natives.

Table A-36 is based on a question from the March supplement to the Current Population Survey asking recent movers why they moved. We report summary statistics for less skilled men who moved across county lines or internationally in the past year. The Mexican-born are especially likely to report moving to look for work or because they lost a previous job. In fact, among all possible answers, this category is the most common response among the Mexican-born (23.8 percent). Note that these numbers include individuals arriving from abroad. Nearly two thirds of Mexican-born arrivals from abroad report one of the job related reasons. Among internal migrants, the Mexican-born are still twice as likely to report moving to look for work or because of a lost job as are natives or other immigrants.