## Abstract

This article assesses the connection between immigration and wage inequality in the United States. Departing from the focus on how the average wages of different native groups respond to immigration, we examine how immigrants shape the overall wage distribution. Despite evidence indicating that an increased presence of low-skilled immigrants is associated with losses at the lower end of wage distribution, we do not observe a similar result between high-skilled immigrants and natives at the upper end. Instead, the presence of foreign-born workers, whether high- or low-skilled, is associated with substantial gains for high-wage natives, particularly those at the very top. Consequently, increased immigration is associated with greater wage dispersion.

## Introduction

The wage consequence of immigration has been vigorously debated in the United States and other receiving countries. Proponents of more strict immigration policies emphasize the potential negative impacts of immigration on native workers: an increased supply of labor would heighten the competition in the labor market and reduce wages (Borjas 2003; Borjas et al. 2008). Given that many immigrants are low-skilled (Ruggles et al. 2015), the influx is likely to drive down the wages of low-skilled workers and result in higher inequality. Others have argued that the adverse effects are overstated. Although low-skilled native workers may face some competition, the actual impact of immigration is tangential (Card 2009b; Longhi et al. 2005; Mouw 2016).

In this study, we examine the connection between immigration and wage inequality in the United States between 1980 and 2015. Departing from the literature focusing on how the average wages of different native workers respond to immigration, we examine how immigration may promote wider dispersion of native wage distribution. The distinction is important because within-group heterogeneity has grown in recent decades, particularly among high-skilled workers. Not only did the top experience tremendous gain, but the wage variance among college-educated workers also increased substantially (Lemieux 2006, 2008).

Analytically, we separate immigrants into two skill groups and test how unconditional wage distribution responds to each flow of immigration. We find that an increased presence of low-skilled immigrants is associated with a small wage loss for natives at the bottom. Yet, the competition is more intense among low-skilled immigrants, who earn significantly lower wages as the number of their peers increases. A similar pattern is not present between high-skilled immigrants and natives. Rather, the presence of foreign-born workers, whether high- or low-skilled, is associated with substantial wage gains for natives at the upper end. Consequently, the influx of migrant labor is associated with a greater dispersion of native wages.

By exploring how the impact of immigration varies across the wage distribution, this study examines inequality related to population dynamics. It is well documented that contemporary wage inequality is driven by the concentration of income at the top (Piketty and Saez 2006). A focus on low-skilled workers may miss the link between immigration and rising inequality. Furthermore, studies have shown that the flows of goods and capital widen the distribution of income (Alderson and Nielsen 2002; Autor et al. 2013; Bandelj and Mahutga 2010; Beckfield 2006; Lee et al. 2007; Lin and Tomaskovic-Devey 2013). The flow of labor is less examined for this upward trend. We provide evidence suggesting that the current immigration system may not be distribution-neutral and is associated with the wage surges at the upper end.

## Immigration and Labor Market

The concern that immigrants could undermine the wages of native workers lends support from the competitive labor market theory, which predicts that an increased supply of workers must depress the price of labor (Borjas 2003). The wage erosion could take place through direct competition as well as the outflow of squeezed native workers into less competitive locations of the economy, which in turn suppresses the wages in other sectors. Given that many recent immigrants are low-skilled, similarly skilled natives are expected to experience the largest wage loss. Because competition is most plausible when immigrants and natives are otherwise substitutable, studies have often partitioned workers into different skill cells and examined how a within-cell increase of migrant labor alters labor market outcomes of natives.

Some studies have shown clear evidence for the adverse effect. For example, assuming that immigrants are perfect substitutes for natives with the same characteristics, Borjas (2003) found that between 1980 and 2000, immigrants reduced the average wage of native workers with similar education and work experience by 3 % to 4 %, and by 9 % for the least skilled. Extending this line of inquiry to Canada and Mexico, Aydemir and Borjas (2007) found a similar inverse relationship between immigration and native wages. A recent study on the impact of Cuban immigrants in Miami also showed that the supply shock significantly reduced the wages of the least-educated natives and that the effect size could be as large as 30 % (Borjas 2017). Taking an occupational approach, Kim and Sakamoto (2013) reported that immigration has an adverse effect on the wage of native workers who share the same occupation, and the effect is again greatest among low-skilled occupations.

Other studies questioned the degree to which immigrants compete with native workers. Card (2009a) argued that immigrants and natives are imperfect substitutes. As such, the influx of low-skilled immigrant labor explains little of the wage gap between high- and low-skilled natives across cities. Ottaviano and Peri (2012) showed that the wage impact of immigrant labor is limited when relaxing the assumption of perfect substitutability within skill groups and allowing the elasticity of substitution to vary across skill groups (see also D’Amuri et al. 2010; Manacorda et al. 2012). Using Longitudinal Employer Household Dynamics (LEHD) data, Mouw (2016) found that immigrants do depress native wages in the industry-skill cells, but the immediate consequence is much smaller than previous estimates: a 10 % increase in immigrant labor led to only a 1 % to 3 % decrease in wages. Pais (2013) reported that a larger presence of immigrants leads to a decline of wage growth but higher wages at the point of labor market entry, suggesting that young natives are able to avoid the competition from immigrants by pursuing more advantageous careers.

Although these studies disagreed on the magnitude, they generally considered the impact of immigration through the lens of competition (or the lack of) and focused on how migrant labor may or may not depress the wages of natives with a high school diploma and/or high school dropouts (cf. Blau and Kahn 2015). Although complementarity of immigrant labor has frequently been discussed in the literature (e.g., Ottaviano and Peri 2012), few studies have estimated how it may shape the overall distribution, particularly at the upper end. Moreover, these studies tended to use predetermined categories to partition workers, focusing on average group wages but not on within-group variance. Because the latter has increased substantially in past decades, especially among high-skilled workers, this approach may be insufficient in unpacking the connection between immigration and inequality.

This study moves beyond the focus on competition and investigates how immigrants may have shaped the wages of natives differently across the distributional spectrum. We hold that competitive market theory is most suitable for explaining the impact of low-skilled immigrants on similarly skilled natives but insufficient in understanding the distributional consequence of immigration. In the next section, we discuss how the current immigration system could be biased in favor of high-skilled natives. Specifically, we discuss the potential different-skill complementarity between immigrant and native workers as well as how capital inflow and regulation could moderate or even reverse the ramifications of high-skilled immigration.

## Immigration and Wage Inequality

Our main proposition is that the current immigration system has widened wage distribution in the United States. It has been argued that immigration provides general economic benefits, such as promoting economies of scale and expanding both the quantity and variety of demands (Greenwood and Hunt 1995), creating the “demographic dividend” (Bloom et al. 2003) and providing a flexible supply of labor (Hatton and Williamson 1998). We suspect that these benefits are not distribution-neutral but skill-biased, meaning that high-skilled natives receive a greater immigration bonus than their low-skilled counterparts.

Researchers have attempted to specifically examine the connection between immigration and wage inequality. Notably, Card (2009b) reported a strong correlation between the immigrant share of the workforce and the residual variance of wages across U.S. cities. However, assuming that immigrants affect only similarly skilled natives, Card found no association between immigrant share of workers and the wage gap between high school– and college-educated workers. Blau and Kahn (2015) examined whether immigrants contribute to inequality through their bifurcated skill composition and conclude that the compositional effect is small if not negligible.

On the other hand, Xu et al. (2016) showed a clear association between immigration and the Gini coefficient of income at the state level. Yet the aggregate-level analysis did not distinguish earned from unearned income (e.g., transfers) or the impacts on immigrants from those on natives. Examining the wage effect of immigration in the United Kingdom, Dustmann et al. (2013) found that immigrants depress native wages at the bottom quintile but lead to some wage gain for the rest of the distribution. Dustmann and colleagues suggested that immigrants may receive lower wages than their marginal productivity and that some native workers claim the gap through their higher bargaining power. Importantly, their findings indicate that immigrants are likely to have cross-skill effects on native wages.

We extend the distributional perspective and examine how low- and high-skilled immigrants compete with or complement different native workers. The inequality consequence of immigration is conceivable when considering cross-distribution complementarity, immigrant-driven capital inflow, and asymmetric regulations. If immigration provides inputs that retain economic activities or augment productivity, a large presence of immigrants is likely to advance labor market outcomes for differently skilled natives. Moreover, network-induced capital inflow and asymmetric regulation are likely to moderate, if not reverse, the effect of high-skilled immigrants on similarly skilled natives.

### Cross-Distributional Complementarity

Low-skilled immigrants often participate in labor market activities that natives are unwilling to engage, particularly those requiring manual labor (Light and Rosenstein 1995; Peri and Sparber 2009). In the absence of immigrants, one might argue that the compensation or working conditions of these jobs would be improved to attract native workers. Another likely scenario is that these economic activities would be gradually exported to countries with lower labor cost.

The retention of these production activities does not alter the concern that low-skilled immigrants may compete with low-wage natives and form networks and niches that prevent the entry of the latter (Waldinger 1997, 1999). Nevertheless, the retention does preserve industry-specific knowledge and secure job opportunities for highly skilled natives, who would otherwise compete with their counterparts in less-tradable industries or find employment abroad.

The different-skill complementarity of low-skilled immigrants is not limited to industries that are vulnerable to trade. The marginalized status of immigrants could lead to a substantial gap between their productivity and wages and a transfer of revenue to native workers, employers, or customers through exploitation (Bloomekatz 2007; Cranford 2005; Dustmann et al. 2013; Muñoz 2008; but see also Wilson and Portes 1980), a reduction in the price of goods and services, or the concurrence of both (Kang 2003).

Outside the agricultural and manufacturing sectors, low-skilled immigrants cluster in hospitality, landscaping, taxi, laundry, buildings and dwellings, and private household services (Hondagneu-Sotelo 2001). The main consumers of these products are highly paid workers who outsource these tasks to extend their paid work time (Costa 2000; Jacobs and Gerson 2005). For example, Cortes and Tessada (2011) found that low-skilled immigration is associated with substantial increases in the hours worked by highly educated women, and similar positive effects were reported in Italy and Singapore (Barone and Mocetti 2011; Hui 1997). Furtado (2016) showed that having access to affordable personal services is consequential to the extent that it drives up the fertility of college-educated married women in the United States, where public childcare support is limited. Certainly, these benefits are unlikely to be shared equally among natives. Many middle-class natives, even with college education, may not feel the need or could not afford to outsource these tasks. Thus, the complementarity is likely to be in proportion to natives’ opportunity costs: the higher a native’s wage, the more s/he may potentially gain from the influx of low-skilled immigrants.

The cross-distributional complementarity could also emerge between high-skilled immigrants and low-skilled natives when the former expand the demand for low-skilled labor. This could take place through production and consumption channels. In the case of production, if high-skilled immigrants promote certain economic activities (such as information technology), it could increase the demand for low-wage, supportive services. In the case of consumption, a net inflow of high-skilled workforce increases the aggregate consumption of nontradable goods and services, which improves the wage prospect of low-skilled service workers (Autor and Dorn 2009). In both cases, we expect that a large presence of high-skilled immigrants could lead to positive labor market outcomes for low-wage natives.

### Network-Induced Capital Inflow

Besides different-skill complementarity, network-induced capital inflow could moderate the inequality consequence of immigration. A key assumption in previous studies is that the supply of capital is either fixed or at least independent of immigration in the short run. This assumption is valid only when one considers immigrants as isolated individuals importing their human capital but not as agents embedded in transnational networks that export valuable information. Potential capital inflow arises when the social capital of immigrants is taken into consideration.

To further our argument, we distinguish three ways that immigration could relax capital constraints. The first is wage-induced capital inflow. In this case, immigration reduces local wages, which in the long run, draws capital investment. The second is the joint migration of labor and capital through business immigration programs. That is, immigrants enter the United States either as entrepreneurs (e.g., Tseng 2000) or employees of foreign subsidiaries. We do not pay particular attention to this possibility because the majority of immigrants in the United States entered as labor migrants, although there has been an uptake in capital migrants in most recent years (Simons et al. 2016).

We see evidence for a third type of capital inflow induced by transnational networks. Bandelj (2002) argued that migration facilitates the formation of cross-national ties and reduces information cost, which encourages foreign direct investment between the two countries (see also Leblang 2010). Examining the distribution of immigrants and foreign direct investment in the United States from 10 sending countries, Foad (2012) found that immigration leads the flow of investment from the sending country, and the amount of investment is positively associated with the skill of immigrants. These findings are not surprising considering that high-skilled immigrants have more immediate personal or business ties to investors in their homelands.

Hernandez (2014) argued that common nationality between immigrants and foreign firms could serve as a valuable conduit of knowledge and trust, which attracts capital investment. He reported that both the location choice and the survival of foreign subsidiaries in the United States are positively associated with the presence of immigrants from the same country. Further analyses have indicated that conational immigrant communities also influence the location choice of Korean investment in China (Li et al. 2015) and positively affect the profitability of foreign firms in Russia (Kulchina and Hernandez 2016). Like foreign direct investment, venture capital also faces great uncertainty and depends on private knowledge obtained through conational networks. Madhavan and Iriyama (2009) demonstrated that international venture funds often follow their high-skilled migrants to specific regions in the United States (see also Iriyama et al. 2010; Pandya and Leblang 2016).

If high-skilled immigrants attract net capital inflow, native workers of all skill levels are likely to experience upgrades in their labor market outcomes. However, the benefit is likely to be greater for high-skilled than low-skilled natives because most capital inflow is channeled to skill-intensive economic activities, which are relatively rare in their home countries. As such, the network-induced capital could either attenuate or even reverse the negative effect of high-skilled immigration on natives.

### Asymmetric Regulations

A third intervening factor is the asymmetric regulations governing the inflows of low- and high-skilled immigration. Many low-skilled immigrants enter through informal channels and face ambiguous and at times laissez faire policies. These immigrants find employment in the secondary labor market, where employers seek a low-wage alternative to native workers (Enchautegui 1998). The Immigration Reform and Control Act of 1986 attempted to close the informal channel through employer sanctions. However, the level of enforcement was weak (Brownell 2005; Fix 1991), and the penalty was trivial. Moreover, because subcontracting is exempted from the legislation, employers are incentivized to hire undocumented immigrants as independent contractors and offer even more precarious working conditions.

High-skilled immigrants, on the other hand, largely entered the United States through formal channels and find employment in the primary sector, in which filters and caps prevent foreign-born workers from adversely affecting the employment and wage prospects of similarly skilled natives. For instance, all applications for employment-based visas are required to demonstrate the intention to recruit natives and that the wages offered to immigrant workers have to meet or exceed the wages paid to natives performing similar tasks in the area (Code of Federal Regulations). As such, the supply of high-skilled labor is plausibly more driven by skill-specific needs than cost reduction, which promotes complementarity between high-skilled immigrant and native workers.

Previous studies have shown supportive evidence that the selectivity may lead to positive outcomes for similarly skilled natives. For example, Peri and Sparber (2011) showed that high-skilled immigrants cluster in occupations demanding quantitative and analytical skills, whereas high-skilled natives specialize in occupations that involve interactive and communication tasks. A subsequent study (Peri et al. 2015) found that an immigration-driven increase in STEM workers is associated with more wage gains for college-educated than less-skilled natives. Using firm-level data, Kerr et al. (2015) also reported that when firms employ more skilled immigrants, they also expand the overall employment of the skilled workforce.

The asymmetry in the immigration system indicates that low- and high-skilled immigrants may have divergent effects on the wage outcomes of similarly skilled natives. Although low-skilled immigrants are frequently employed to reduce labor costs, high-skilled immigrants tend to be selected into the United States based on skill scarcity and therefore have a lower propensity to compete with natives. This asymmetry, combined with network-induced capital inflow, might explain why previous studies have not found an adverse effect for the immigration of high-skilled workers on their native counterparts (Camarota 1998; Kim and Sakamoto 2013).

### Hypotheses

The preceding discussion expands the focus on competition and points out different mechanisms through which immigration could influence the economic prospects of natives across the wage distribution. We argue that in addition to substitution, immigrants may benefit different-skilled natives through the preservation of production activities, exploitation, and the provision of productivity-augmenting services. Stated formally, we expect the following:

• Hypothesis 1: The presence of low-skilled immigrants is positively associated with the wages of high-skilled natives.

• Hypothesis 2: The presence of high-skilled immigrants is positively associated with the wages of low-skilled natives.

Although the competitive market theory predicts that immigration would have adverse effects on the economic prospects of similarly skilled natives, we argue that the consequence of immigration is moderated by capital adjustment and the selection process. When high-skilled immigration attracts net capital inflow and is driven by skill scarcity, the adverse effect is likely to attenuate or even reverse. Stated formally, we expect the following:

• Hypothesis 3: The presence of high-skilled immigrants has either no association or a positive association with the wages of high-skilled natives.

If immigrants benefit differently skilled native workers (Hypothesis 1 and 2) and high-skilled immigrants promote the wages of high-skilled natives (Hypothesis 3), we expect the following:

• Hypothesis 4: Both the presence of low-skilled immigrants and that of high-skilled immigrants are associated with a wider wage distribution among native workers.

## Research Design

### Data

We use the 1980, 1990, and 2000 Integrated Public Use Microdata Samples (IPUMS) of the decennial U.S. Census and the American Community Survey (ACS) from 2001 to 2015 to examine the possible wage consequences of immigration (Ruggles et al. 2015). Our sample consists of full-year, private-sector workers aged 25–65 in the lower 48 states who earned at least \$5,000 (2016 dollars) in the previous year. We exclude part-year workers given the difficulty in calculating their hourly wages, as well as governmental workers because their wages are arguably less sensitive to immigration. These sample restrictions imply that our estimates will be conservative at the bottom of wage distribution, given that the most disadvantaged workers are not retained in the sample. In addition to individual-level data, we draw state-level data compiled from a variety of sources, such as the Bureau of Economic Analysis, the Bureau of Labor Statistics, the Tax Policy Center, and the Department of Labor. The main purpose is to account for the structural confounders that may cause spurious relationships between immigration and labor market outcomes.

### Variables

We define an immigrant as any individual who was born outside the United States and its outlying territories but not born to American parents, regardless of their citizenship and legal status. Throughout this article, we use the terms immigrant and foreign-born interchangeably. To assess the differential impacts of low- and high-skilled immigration, we follow the convention (Card 2009b) and classify low-skilled immigrants as those with a high school education or less and high-skilled immigrants as those with at least some college education. We then aggregate individuals to calculate the proportion of workers who are immigrants, low-skilled immigrants, or high-skilled immigrants at the state level. In a separate analysis (not shown), we divide immigrants by more detailed education level. The results are substantively similar to those reported here.

Between 1980 and 2015, the immigrant shares of workforce grew from 7 % to 19 %. The majority of these immigrants are commonly referred to as low-skilled (high school education or less), but an expanding portion of immigrants are equipped with at least some college education. The former group increased from 4.4 % of the workforce in 1980 to 10 % in 2015, and the latter increased from 2.6 % to 9 %.

The growth of immigrants is uneven. Figure 1 shows the percentage point growth of immigrants across the continental states. Most states had some increase in their immigrant workforce, but California led with the most dramatic growth: its immigrant shares of the workforce expanded by more than 22 percentage points. Nevada followed closely with a growth of 21.62 percentage points. Other states that had the largest gains include New Jersey (19.61 %), Texas (18.11 %), Maryland (16.82 %), Florida (15.6 %), and New York (14.72 %). The states with the least increase or no increase are Montana (–0.44 %), Maine (0.84 %), Vermont (0.88 %), and West Virginia (0.92 %).

Our outcome of interest is logged hourly wage, calculated as the pretax annual wage and salary earnings divided by annual work hours, adjusted to 2016 dollars. This includes cash bonuses, tips, and other monetary income received from the employer. Given that only employed respondents report wages, in section A of the online appendix, we examine the association between immigration and natives’ likelihood of being employed. The result indicates that the findings reported here are unlikely to be driven by selection into employment.

We consider an extensive set of confounding factors in our analysis. At the individual level, we control for the level of education; age and its squared term; race and ethnicity; part-time status; and the three-way interaction among sex, marital, and parental status, acknowledging that the effects of marriage and parenthood vary between men and women. Because the assignment of immigrants is nonrandom, we incorporate a series of state-level measures in an attempt to isolate the influence of immigration on the labor market dynamics from concurrent developments. These include logged GDP per capita, the proportion of workers who are college-educated, logged population size, the metropolitan share of the population, the statewide unemployment rate, the manufacturing share of employment, union density, and the inflation-adjusted minimum wage. We discuss these confounders and present descriptive statistics in the online appendix, section B.

### Analytical Strategy

We note two issues before introducing our analytical strategy. First, although our study attempts to assess the impact of immigration on wage distribution, the connection between the two is not straightforward. Both immigrants and natives have, however constrained, some degree of agency regarding where they reside. These decisions may be correlated with unobserved state characteristics that also produce more uneven wage distribution. One may even argue that immigrants are drawn to states with high inequality because these states provide niches for low-skilled, uncredentialed workers to find employment (Sassen 2001). Thus, the coevolution of immigration and inequality needs to be recognized, and any association between immigration and inequality should be interpreted with caution. We take extensive measures to mitigate omitted variable bias, knowing humbly that our analysis does not eliminate this issue.

Second, a common way to measure the impact of immigration on wages is to estimate a production function and then assess how the wages of a certain group of natives vary based on the increase or decline of a specific type of immigrants. Albeit useful, this approach requires the researchers to (1) presume the United States is a closed economy, (2) partition immigrant and native workers into predetermined groups, (3) make assumptions about the level of substitution or complementarity among groups, and (4) equate wages and marginal productivities. These decisions, as shown in the literature, are consequential to the estimates (Card 2009b; Ottaviano and Peri 2012).

While recognizing the scientific value of this common method, we take an alternative approach and allow the association between the presence of immigrants and native wages to vary across the distribution. Instead of making assumptions about how native workers should be partitioned and the relationships between groups, we take advantage of the recentered influence function regression (RIF; Firpo et al. 2009) to estimate how low- and high-skilled immigrants may shape various wage quantiles. The logic of the RIF function is based on the statistical concept of influence function: the relation between a data point and the statistics of interest. By recentering the influence function with statistics of interest and regressing each observation’s influence on the explanatory variables, one can estimate how these variables jointly associate with the unconditional statistics of interest.

We specify the first model as follows:
$RIFYQτ=α0+αj+αk+β1Fi,j,k+β2Ij,k+β3Fi,j,tIj,k+∑mMβmXm,i,j,k+∑nNβnSn,j,k+εi,j,k,$
1
where Y denotes the logged hourly wage, and Qτ denotes the τth wage quantile. We absorb the influences of time-constant, unobserved state characteristics with αj and year-specific national shocks with αk. Fi, j, k indicates the immigrant status of individual i, and Ij,k represents the share of immigrants in state j and year k. To separate the potential impact of immigration on natives from that on immigrants, we add an interaction term Fi, j, tIj, k to allow the coefficient to vary between immigrant and native wages. Xm and Sn account for the individual- and state-level confounders. The coefficient β1 in this equation denotes the deviation of immigrant wages from those of natives when there is approximately no immigrant in the state. The main coefficient of interest is β2, which captures the association of immigration with natives’ wages.
To differentiate the consequences of low- and high-skilled immigration, we specify the second equation as follows:
$RIFYQτ=α0+αj+αk+β1Fi,j,k+β2LIj,k+β3HIj,k+β4Fi,j,tLIj,k+β5Fi,j,tHIj,k+∑mMβmXm,i,j,k+∑nNβnSn,j,k+εi,j,k,$
2
where LIj, k and HIj, k represent the shares of population that are low- or high-skilled immigrants in state j and year k respectively. Similar to Eq. (1), we add two interaction terms between individual immigrant status and state immigrant density to differentiate the coefficients for immigrant and native wages. As such, β2 and β3 capture the associations of low-/high-skilled immigration and native wages.

Certainly, our spatial approach is not without issues. Many have argued that spatial analysis overlooks the adjustments made by native workers, and therefore underestimates the substitution effect of immigration (Borjas et al. 1996; Kim and Sakamoto 2013). That is, negatively impacted natives may choose to emigrate and therefore obscure the consequences of immigration. This bias tends to be greater when using small units (e.g., cities) than larger units (e.g., regions). Others have argued that cross-city analysis yields consistent results (Card 2009b) and that immigration-driven out-migration of the native population is limited (Card and DiNardo 2000).

Three reasons motivate our state-level analysis. First, although possible that natives emigrate due to the competition of immigrants, cross-state migration is more cost-prohibitive than within-state migration. Moreover, states with the most immigrant growth tend to be larger in their territories and on the margins of the continent (Fig. 1), which also favors within- over cross-state adjustment. In reality, the interstate migration rate declined during the period of analysis, and the natives who are the most vulnerable to immigration are the least likely to migrate across states because of a lack of resources (McFalls 2007). Second, the effects of complementarities as well as capital inflow are likely to be spatially bounded. It would be difficult to isolate the effect of immigration from those of other confounders with a national approach and limited degree of freedom. Last, other subnational units available in the data sets are inconsistent over the period of analysis, and most do not have national coverage because of privacy concerns in the census.1

Despite clear drawbacks, we hold that a cross-state framework is the best compromise that captures more residential and employment adjustment than smaller geographic units (such as cities or metropolitan areas) but also allows us to consider other economic contexts. To ensure that our results are not dependent on the geographic unit, we replicate our analysis with the 1980-1990-2000 Consistent Public Use Microdata Areas (ConsPUMA) developed by the IPUMS as a robustness test.

In any case, the spatial approach should provide more conservative estimates of the relationship between immigration and inequality than other approaches because it does not consider the geographical adjustments that workers make. To supplement our main analysis and address alternative explanations, we conduct a series of robustness tests with various estimators, a subsample, and an occupational analysis. The general results are consistent with our primary findings.

Unless otherwise specified, we report the coefficients of the proportion of immigration (between 0 and 1) rather than those of the percentage of immigration (between 0 and 100). State-clustered robust standard errors are used in all models to account for heteroscedasticity. The results are substantively similar to other specifications. Considering the large number of models and parameters, we present only the coefficients and standard errors of interest. Full estimates are available upon request.

## Main Results

Table 1 presents the estimates for β1, β2, and β3 in Eq. (1) at the 10th, 25th, 50th, 75th, and 90th percentiles of the wage distribution. The first coefficient (β1) shows that immigrants at the bottom or middle of the wage distribution tend to earn lower wages than natives. The gap expands from 9.6 % at the 10th percentile to 11.7 % at the 25th percentile, and then narrows to 5.2 % at the median. By contrast, immigrants at the upper end of the distribution receive higher wages. Those at the 75th percentile earn 3.8 % higher wages than their native counterparts, and those at the 90th percentile earn 8.2 %. This pattern is consistent with our argument that the selection process differs between low- and high-skilled immigrants. Many low-skilled immigrants are selected to reduce labor cost, and most high-skilled immigrants are selected for their skills.2

The second coefficient (β2) captures the association between immigration and native wages. Consistent with previous findings, we see that a large presence of immigrants in the state is linked to lower native wages at the bottom of the wage distribution. A 10 percentage point increase in the immigrant share of workforce (nationally, the share increased roughly 12 percentage points in the period of analysis) is associated with only a 0.46 % decrease in native wages at the 10th percentile (not statistically significant) and a 0.68 % decrease at the 25th percentile.3 The coefficient, however, reverses its direction at the middle and upper half of the distribution. At the median, a 10 percentage point increase in immigrant workforce is associated with a 2 % increase in native wages and a 10 % increase at the 90th percentile. These results support our proposition that the potential impact of immigration is skill-biased. Although some low-skilled natives face competition from immigrants, most native workers benefit from the presence of immigrants, and the highest-skilled natives receive the most bonus.

The third coefficient (β3) represents the difference in coefficients between immigrant and native wages. At the lower end of the distribution, we see that the wages of immigrants are much more sensitive to the presence of immigrants than those of natives. A 10 percentage point increase in immigrant workforce is associated with an additional 3.3 % decrease in wages at the 10th percentile and an additional 2.6 % decrease at the 25th percentile. The adverse effect is not limited to the bottom of the labor market: immigrant workers at the 50th and the 75th percentile also face wage losses as the presence of immigrants expands. Only highest-skilled immigrants (90th percentile) benefit from the inflow, but their bonus is significantly weaker (–0.609) than their native counterparts.

Thus far, we show that the level of immigration is positively associated with wage dispersion. A large presence of immigrants concurs with lower native wages at the bottom of the labor market but higher native wages at the upper end. Furthermore, the estimates indicate that the wages of immigrant workers are more sensitive to immigration than those of native workers. This result is consistent with the argument that the competition among immigrants is much greater than the competition between immigrants and natives (Card 2009b; Ottaviano and Peri 2012). However, the potential impacts of low- and high-skilled immigration are likely to differ. Although low-skilled immigrants compete with natives in the secondary labor market, high-skilled immigrants are most likely to seek employment in the primary or even high-paying sectors. To distinguish the two, we estimate Eq. (2) across the wage distribution, with 5 % intervals (19 sets of estimates).

Figure 2 presents the associations between skill-specific immigration and wages for both native and foreign-born (i.e., β2, β3, β2 + β4, and β3 + β5 in Eq. (2)). As expected, a large presence of low-skilled immigrants is associated with wage losses for natives in the lower part of the distribution. The negative association is particularly salient at the 10th and the 15th percentiles, where a 10 percentage point increase in immigrant workforce is linked to roughly a 2 % decrease in native wages. The link weakens above this point and turns positive for native workers at the middle and upper end. This result supports Hypothesis 1, which predicts that although competing with low-wage natives, low-skilled immigrants complement natives with different skills, particularly those with the highest wages.

Compared with natives’ wages, the wages of immigrants at the bottom of the labor market are much more negatively connected to the presence of low-skilled immigrants. At the 10th percentile of wage distribution, a 10 percentage point increase in the immigrant workforce is associated with an 11.5 % decrease in immigrant wages. The negative coefficient ripples through the middle segment, whereas a 10 percentage point increase in low-skilled immigrant labor leads to a 3 % decrease. The highest-skilled immigrants, in contrast, are not penalized by the presence of low-skilled immigrants.

The relation between high-skilled immigration and native wages differs in both pattern and magnitude. For native workers, an increased presence of high-skilled immigrants is associated with some wage increase (0.21) around the 10th percentile, suggesting that high-skilled immigrants do complement low-skilled native workers (Hypothesis 2). Yet the main beneficiaries are high-skilled natives, whose wages grow substantially as the proportion of high-skilled immigrants increases. At the 90th percentile, a 10 percentage point increase in high-skilled immigrant share of workforce is linked to a 15 % increase in native wages. The coefficient grows to 22 % at the 95th percentile. These findings suggest that unlike low-skilled immigrants, high-skilled immigrants do not compete with but instead advance their native counterparts (Hypothesis 3).

Low- and high-skilled immigrants also benefit from the presence of high-skilled immigrants. At the 10th percentile, a 10 percentage point increase is associated with a 6.6 % increase in immigrant wages. This estimate suggests that low-skilled immigrants benefit more (+2.1 %) from their native counterparts, which may result from the development of ethnic economy or the increased consumption of ethnic goods and services (Mazzolari and Neumark 2012; Waldinger et al. 1990). Similarly, the wages of high-skilled immigrants increase with the presence of their peers, a likely result of capital inflow. However, the bonus is smaller than that for high-skilled natives.

In sum, these estimates suggest that low-skilled immigrants compete with natives at the lower end of wage distribution but complement natives in the upper half. High-skilled immigrants, on the other hand, complement both low- and high-skilled natives, but the positive impact is much greater for the latter. As such, these results support Hypothesis 4, which predicts that both streams of immigration widen the distribution of wages.

## Robustness Tests

The preceding evidence supports our proposition that the current immigration system is biased in favor of high-skilled natives and conducive to higher wage inequality. In this section, we test the robustness of our findings with a series of alternative models. Specifically, we examine (1) whether the skill-biased finding of immigration is dependent on geographic unit; (2) whether the association between immigration and inequality is driven by the nonrandom assignment of immigrants; and (3) whether the positive association between high-skilled immigration and the wages of high-skilled natives is driven by an unobserved but growing demand for high-skilled labor.

### Alternative Geographic Unit

As discussed earlier, the proper unit of analysis is widely debated in the literature. Although we believe that a state-level analysis is the best compromise that allows for residential adjustment and enables us to control for a wide host of covariates, one may suspect that the states are too heterogeneous for comparison and that some large states consist of multiple (independent) labor markets. To address these issues, we use the 1980-1990-2000 ConsPUMA developed by the IPUMS as an alternative geographic unit to measure the presence of immigrants.

ConsPUMA identifies the 543 most detailed areas that can be consistently delineated using the geographic codes available in the Public Use Microdata Sample (PUMS) files.4 Using smaller areas yields more precise measures, but the downside is that moving between these small areas is more likely than relocating to another state. If natives migrate within state in response to the competition or complementarity of immigrants, we would expect both the negative and positive effects of immigration to be underestimated in this set of analyses.

Figure 3 presents the estimates using ConsPUMA. For this analysis, we estimate Eq. (2) but replace the state-level controls with ConsPUMA fixed effects. We see that the negative association between the presence of low-skilled immigrants and low-skilled native wages disappears, potentially a result of these natives migrating out of the area. We also see that the positive coefficient of immigration for high-wage natives attenuates, suggesting that other natives are drawn to areas with more immigrants. Despite these discrepancies, the general pattern in Fig. 3 remains supportive of our arguments that the impact of immigration is skill-biased. High-skilled natives benefit more from immigration than low-skilled natives.

### Nonrandom Assignment

A second challenge for our analysis is that immigrants are not randomly assigned to states. If immigrants are drawn to destinations with unobserved characteristics that widen the wage distribution, an artificial correlation would be introduced between immigration and inequality as a result of omitted variable bias. Our main analysis mitigates but does not eliminate this issue with an extensive set of state-level variables, such as GDP per capita, manufacturing share of employment, minimum wage, and unemployment, as well as state fixed effects.

In this section, we further test the connection between immigration and inequality with an instrumental variable approach. To obtain more conservative estimates, we restrict our samples to the observations between 2000 and 2015 and instrument immigrant density for each state-year with the distribution of immigrants in 1980, exploiting earlier settlement as a source of exogenous variation. Because the settlement pattern in 1980 is unlikely to be determined by the level of inequality or the associated factors 20 years after, we are confident that this approach drastically reduces the concerns related to nonrandom assignment. The trade-off, clearly, is that our estimates would be downwardly biased because of the extensive gap between our instrument and the period of analysis. To account for state-level variation and the national trend, we also include the dependent variable observed in 1980, the aforementioned state-level controls, and year fixed effects in these models.

Table 2 presents the estimates from state-level panel models predicting the 10th percentile, the 90th percentile, and the variance of the wage distribution between 2000 and 2015. All standard errors are clustered at the state level due to the presence of serial correlation. Given the substantial correlation between low- and high-skilled immigration (Fig. B1, online appendix) and the smaller sample size, we fit two separate sets of models for each variable. The estimates indicate that immigration in general leads to a marginal wage decline at the lower end (–0.029, nonsignificant), an increase at the upper end (0.303), and a larger variance (0.217) of the wage distribution, all of which are consistent with our previous findings. When examining low- and high-skilled immigration separately, we see neither the adverse association of low-skilled immigration nor the positive association of high-skilled immigration at the lower end. However, the estimates still show that both streams of migration are associated with higher wages at the top (0.516 and 0.556) and linked to wage dispersion (0.367 and 0.409).

To ensure these outcomes are not estimator-dependent, we also use generalized method of moments (GMM) and difference-in-differences (DID) estimators to assess the potential connection between immigration and inequality. The first procedure uses the first three lags (2000–2002) to instrument current immigration density; as such, only the 2003–2015 observations are analyzed. The second procedure first-differences all variables in the models to reduce the influence of changing state-level unobserved factors and address the issue of serial correlation. It therefore includes samples only for 2001–2015. Because the three sets of estimates use different samples and make different assumptions, their results are not necessarily comparable. Furthermore, the GMM and DID estimators may not be statistically appropriate considering the limited variability between 2000 and 2015. That said, all three estimators share consensus regarding the directions of almost all coefficients (only the association between high-skilled immigration and the 10th percentile wage differs), and all suggest that (low-skilled) immigration is linked to greater wage variance with statistical significance. The main disagreement regards the impact on low-skilled natives. Although the IV and GMM estimators find no significant negative association, the DID estimator indicates a large negative coefficient.

Another, and perhaps more straightforward, way to test the robustness of our finding and reduce the issue of endogeneity is removing the major destination states with high-paying industries (e.g., technology and finance) and global cities (Sassen 2001) to see whether the pattern holds for the remaining states or the “new destinations.” Specifically, we exclude California, Florida, Illinois, Massachusetts, New Jersey, New York, Texas, and Washington, which jointly account for 48 % of U.S. GDP in 2016, from the sample, and then we reestimate Eq. (2). The results, shown in Fig. 4, are similar to those presented in Fig. 2.

### High-Skilled Complementarity

In the main analysis, we show that high-skilled immigration is positively associated with the wages of high-skilled natives (Fig. 2) and consider it as supporting our arguments that high-skilled immigrants attract capital, and the selection of high-skilled immigrants is not as cost-driven. An alternative explanation for this result is that both high-skilled immigration and the wages of high-skilled natives reflect a growing demand for high-skilled labor that is not fully considered in our main models.

We examine this possibility with an occupational approach that tests how the impact of immigration may differ across occupations with varying levels of skill and demand. Specifically, we assign all workers into 316 occupations (based on the 1990 census classification) and four periods (1980, 1990, 2000, and 2011–2015). We then calculate three occupation-level variables. The immigrant share of an occupation is calculated as the number of foreign-born workers over total workers in the occupation, which varies over periods. The relative size of an occupation is calculated as the number of workers in the occupation over total workforce, which also varies over time and reflects the changing demand. The skill level of an occupation, assumed constant between 1990 and 2015, is calculated as the share of workers making above the median wage in 1990 (Hout 2012).5 All values are then scaled between 0 and 1 to facilitate the interpretation.

We estimate the following model for native wages:
$Yi,j,t=α0+αj+αt+β1∆Ij,t+β2∆Dj,t+β3Sj∆Ij,t+∑mMβmXm,i,j,t+εi,j,t,$
3
where αj and αt denote occupation and period fixed effects; ΔIj,t denotes the change in immigrant share from the previous period for occupation j; ΔDj,t denotes the change in employment size, which serves as a control for skill-specific demand growth; SjΔIj,t denotes the interaction between the level of skill and changing immigrant share; and Xm,i,j,t account for individual-level confounders. Sj is not included as a covariate by itself because its effect is already absorbed by αj. Note that the estimates in this model capture only within-occupation coefficients and are therefore not comparable to the estimates in Eqs. (1) and (2), which represent the ecological associations (for a review on this issue, see Dustmann et al. 2016).

Table 3 presents the estimates from the occupational model. The 1980 observations are excluded because immigrant share and demand are differenced. The results are consistent with the expectation. Immigrants compete with natives in low-skilled occupations (–1.580), and greater demand is associated with higher wages (0.845). More importantly, the interaction term shows that the adverse effect of immigrants attenuates as the level of skill increases (1.838). For high-skilled occupations, such as engineers, scientists, science technicians, and programmers, immigrants complement instead of competing with natives even within the same detailed occupation. This result suggests that high-skilled immigration may be associated with the inflow of capital that benefits native workers. Overall, the evidence presented in this section supports our argument that immigration could promote wage inequality by stretching both ends of the distribution.

## Discussion

This article investigates the distributional consequences of immigration in the United States between 1980 and 2015. Instead of focusing on the competition between immigrants and natives, we argue that immigration could promote the wages of native workers through cross-skill complementarity, capital inflow, and selection. We propose that the wage consequence of immigration varies across the wage distribution. High-wage natives benefit from both low- and high-skilled immigration, and low-wage natives experience either a small adverse or positive effect, depending on the skill levels of immigrants.

Our main findings indicate that an increased presence of low-skilled immigrants is associated with small wage losses for similarly skilled natives. However, the most intense competition is still among low-skilled immigrants themselves, who suffer much greater wage losses in states with a high density of their peers. Furthermore, we find that low-skilled immigration is associated with higher wages for high-skilled natives, likely by providing productivity-augmenting services or through exploitation. In contrast to our findings for low-skilled immigrants, we do not find an adverse relationship between high-skilled immigrants and high-skilled native wages. Instead, the presence of high-skilled immigrant workers is linked to some gain for low-wage natives and large increase for high-wage natives.

We test the robustness of our evidence with a more detailed geographic unit, various estimators, an alternative sample, and an occupational analysis that accounts for skill-specific demand. Together, these results suggest that the connection between immigration and inequality is not driven merely by the unit of analysis, the endogenous assignment of immigrants, or unobserved demand growth for high-skilled workers. Furthermore, additional analyses indicate that our results are not due to selection into employment (online appendix, section A).

Although the current immigration system may lead to wider wage dispersion, we do not claim that the connection between immigration and inequality is uniform or could be isolated from other socioeconomic contexts. In theory, high-skilled immigration is expected to have negative impacts on similarly skilled natives, but the skill-driven immigration policies and the influx of foreign capital seem to promote complementarity. The adverse effects of low-skilled immigrants on their peers and similarly skilled natives should also be attributed to ambiguous policies, business-friendly enforcement, and the transformation of employment relationship in the United States. This means that the link between inequality and immigration is contingent on labor market institutions and can vary substantially across national contexts (Blau and Kahn 2015).

Because of data limitations, we are unable to distinguish the wage consequences of documented and undocumented immigrants (Bean et al. 1988; Mouw 2016). If the ramifications of low-skilled immigrants are largely due to the arbitrage of legal status, we would expect both the positive and negative consequences of undocumented immigration to be stronger than those of documented. Future study may examine whether the consequence of immigration varies by legal status and by other within-skill-level heterogeneity, such as country of origin, duration in the United States, and English fluency.

Although this article focuses on the potential wage consequences of immigration, we do not hold that economic consequences should be the sole factor in determining immigration policies. Instead, our study underscores the necessity to integrate immigration and labor policies. An honest and comprehensive immigration reform should guide low-skill immigrants to sectors where native labor is truly cost-prohibitive and provide sufficient protection to immigrant workers from exploitation and destructive competition. Programs similar to the Trade Adjustment Assistance (TAA) Program for Workers should be in place to facilitate the transition of natives to other sectors.6

Overall, the concern over the wage consequence of the current immigration policy is misplaced. Although low-skilled immigrants might depress the wage prospect for similarly skilled natives, immigrants upgrade the wages of most natives, particularly those with the highest wages. However, the wage benefit of immigration is not distribution-neutral, and its contribution to inequality is nontrivial. In sum, the existing immigration system does not make native population worse off but may make the distribution of income less equal.

## Acknowledgments

We thank Yinon Cohen, Thomas DiPrete, Olivier Godechot, Gianluca Manzo, Etienne Ollion, David Pedulla, Kelly Raley, Eiko Strader, Stephen Trejo, the attendants of the PRC Brown Bag Series at the University of Texas-Austin, the attendants of Center for the Study of Wealth and Inequality seminar at the Columbia University, and the attendants of Paris Seminar on the Analysis of Social Processes and Structures for their comments on the earlier versions of this article. We also thank the editorial team at the Pennsylvania State University and the anonymous reviewers for their generous comments and suggestions. This research was supported by Grant P2CHD042849, awarded to the Population Research Center at The University of Texas at Austin by the Eunice Kennedy Shriver National Institute of Child Health and Human Development. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

## Notes

1

The census does not release detailed geographic information of the respondents in less populated areas, so no individual could be identified with the released information.

2

To be clear, we are not claiming that high-skilled immigrants do not face discrimination or that they have any advantages over natives in the U.S. labor market. Because our models do not consider industry and occupation, the immigrant premium at the upper end is likely driven by their clustering in high-paying industries and occupations.

3

These estimates are smaller than previous findings and are likely due to sample restrictions.

5

We use the share of workers with a college degree as a proxy of skill in a separate analysis, which yields similar results.

6

The TAA Program is a federal program developed in 1962 to weaken the impacts of free trade on workers. It consists of four subprograms, each of which addresses the needs of workers, farmers, firms, and communities. The TAA Program provides cash payment, training, and job-searching assistance for workers who lost their jobs as a result of increased imports.

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