The rise and fall of U.S. low-skilled immigration.

Hanson, Gordon ; Liu, Chen ; McIntosh, Craig 等

ABSTRACT From the 1970s to the early 2000s, the United States experienced an epochal wave of low-skilled immigration. Since the Great Recession, however, U.S. borders have become a far less active place when it comes to the net arrival of foreign workers. The number of undocumented immigrants has declined in absolute terms, while the overall population of low-skilled, foreign-born workers has remained stable. We examine how the scale and composition of low-skilled immigration in the United States have evolved over time, and how relative income growth and demographic shifts in the Western Hemisphere have contributed to the recent immigration slowdown. Because major source countries for U.S. immigration are now seeing and will continue to see weak growth of the labor supply relative to the United States, future immigration rates of young, low-skilled workers appear unlikely to rebound, whether or not U.S. immigration policies tighten further.

Immigration is a divisive issue in public discourse about U.S. economic policy. At the center of the debate is how to address inflows of undocumented immigrants. During previous decades, inflows of illegal aliens were substantial. The Pew Research Center estimates that between 1990 and 2007, the U.S. population of undocumented residents, which as of 2013 accounted for nearly two-thirds of the U.S. foreign-born adult population with 12 or fewer years of schooling, grew on net by an annual average of 510,000 individuals (Borjas 2016; Passel and Cohn 2016). These inflows contributed to a sizable increase in the U.S. supply of low-skilled, foreign-born workers (figure 1). During the 1990-2007 period, the number of working-age immigrants with 12 or fewer years of schooling more than doubled, rising from 8.5 million to 17.8 million. Since the Great Recession, however, U.S. borders have become a less active place when it comes to net inflows of low-skilled labor from abroad. The undocumented population declined in absolute terms between 2007 and 2014, falling on net by an annual average of 160,000 individuals, while the overall population of low-skilled immigrants of working age remained stable.

[FIGURE 1 OMITTED]

Viewed through the lens of the U.S. business cycle, the recent slowdown in low-skilled immigration hardly comes as a surprise (Villarreal 2014). Construction is the second-largest sector of employment for undocumented labor and the third-largest among all low-skilled immigrants (Passel and Cohn 2016). Because the collapse in the U.S. housing market helped precipitate the Great Recession (Mian and Sufi 2014), it follows logically that the downturn in home building after 2006 would have triggered a drop in new arrivals of low-skilled, foreign-born workers. Yet, there are good reasons to believe that the Great Recession may have merely advanced forward in time an inevitable reduction in low-skilled immigration. Today, about half of low-skilled immigrants are from Mexico and another one-quarter are from elsewhere in the Latin American and the Caribbean countries. Because these countries had marked declines in fertility after the late 1970s, they started to see slower growth in the size of cohorts coming of working age in the 2000s, thereby weakening a key demographic push factor for emigration (Hanson and Mcintosh 2010, 2012). Just as relatively strong growth in U.S. GDP and Latin American labor supplies a generation ago helped initiate the great U.S. immigration wave of the late 20th century, the reversal of these conditions may be launching the United States into an era of far more modest low-skilled labor inflows (Hanson and Mcintosh 2009, 2016).

The policy dilemma facing the United States is thus not so much how to arrest massive increases in the supply of foreign labor, but rather how to prepare for a lower-immigration future. The pertinent issues for economists to address include how the scale and composition of low-skilled labor inflows have changed over time, whether the drop in inflows is primarily a cyclical phenomenon or represents a secular decline, and how the U.S. economy would adjust to an environment with modest numbers of low-skilled, foreign-born workers entering the labor force each year. These questions guide the analysis in this paper.

We begin by summarizing trends in low-skilled immigration over the last several decades. As is well known, supplies of less-educated, foreign-born labor increased sharply after 1970, while their predominant national origins shifted from Europe to Latin America. Perhaps less appreciated, the demographic structure of this population has also changed, moving from younger, recent arrivals toward an older, more settled population. Which types of individuals select into immigration also appear to have changed, a pattern we examine in detail for the case of Mexico, given its outsize importance as a source country for U.S. immigrants. In 1990, those having recently migrated from Mexico to the United States--as captured by the population censuses of the two countries--were drawn more heavily from just above versus just below the mean of potential labor market earnings in Mexico (Chiquiar and Hanson 2005). This mild positive selection weakened during the 1990s and the 2000s, such that by 2010 the population of recent Mexican immigrants was close to a random draw of working-age individuals from Mexico, with a slight overrepresentation of individuals from the middle of the skill distribution. Although immigrant selection captured in census data may be subject to measurement error associated with undercounts of undocumented immigrants (Fernandez-Huertas Moraga 2011), selection patterns in these data are similar to those in the Mexican Family Life Survey, which appears less subject to missing information on undocumented migrants (Kaestner and Malamud 2014). The largely neutral selection of immigrants from Mexico in terms of skill implies that any future shock to Mexican immigration--such as a further tightening of U.S. borders--would target middle-income earners in Mexico, while affecting low-wage earners in the United States.

Recent changes in low-skilled immigration have occurred in a tumultuous environment for the U.S. labor market. Even before the economic turbulence that occurred after 2006, there were adverse changes in the demand for low-skilled labor associated with automation and increased import competition from low-wage countries (Autor and Dorn 2013; Autor, Dorn, and Hanson 2013; Pierce and Schott 2016; Cortes, Jaimovich, and Siu 2016). At the higher end of the labor market, demand for young, college-educated labor has also weakened (Beaudry, Green, and Sand 2016). Together, these changes have combined to create a period low wage growth since 2000 for all but the highest-earning U.S. workers (Valletta forthcoming).

To put recent changes in U.S. labor market conditions in a global context, we compare the level and volatility of U.S. income with that in major sending countries for low-skilled immigrants. The gap between the 25th percentile of the income distribution in the United States and the 50th percentile of the income distribution in Mexico--which approximates the expected gains in earnings for the typical Mexican migrant--was stable during the 1990s and early 2000s but shrank noticeably after 2007. Relative volatility in income growth has also changed. The Great Moderation heralded a period of steady U.S. GDP growth from the early 1980s to the mid-2000s (Bernanke 2004), a calm that was brought to an end by the Great Recession. In Mexico and other migrant-sending nations of the Western Hemisphere, the pattern is roughly the opposite. The 1980s and early 1990s were periods of high macroeconomic volatility, whereas the 2000s were a period of steady if not spectacular economic growth. Shrinking income gaps and reduced income volatility between the United States and major migrant-sending nations have eased pressures for net labor flows into the United States.

Another factor contributing to the decline in low-skilled immigration is changes in U.S. enforcement against illegal labor inflows (Roberts, Alden, and Whitley 2013). Between 2000 and 2010, the number of U.S. Border Patrol agents policing the U.S.--Mexico border doubled, from 8,600 to 17,500 officers, and has since remained at historically high levels. Concurrently, the U.S. government intensified immigration enforcement in the interior of the country, which led to an increase in deportations of noncriminal aliens--many of whom are apprehended through traffic stops or other routine law enforcement operations--from 116,000 individuals in 2001 to an average of 226,000 a year from 2007 to 2015. (1) Increases in border enforcement, which deter potential migrants from choosing to enter the United States (Gathmann 2008; Angelucci 2012), and in interior enforcement, which reduces the existing population of undocumented immigrants and may also deter future immigration, appear likely to continue under the administration of Donald Trump (Meckler 2017; Kulish and others 2017).

Looking toward the future of U.S. low-skilled immigration, forces are at work that are likely to soften pressures for labor inflows and that will remain in place for the next several decades. By the mid-1970s, the size of U.S. cohorts coming of working age was growing much more slowly than in Mexico and the rest of Latin America, creating steady pressure for migration to the United States. However, by the mid-2000s this demographic push factor had largely disappeared. Because the United States' neighbors to the south are today experiencing much slower growth in the labor supply, the future immigration of young low-skilled labor looks set to decline rapidly, whether or not more draconian policies to control U.S. immigration are implemented.

If changes in global macroeconomic conditions and U.S. enforcement policy have combined to weaken recent growth in the U.S. supply of low-skilled, foreign-born labor, what are the implications for U.S. labor markets? As a way of answering this question, we examine the net impact of immigration-induced changes in the labor supply on U.S. labor-market tightness. To perform this analysis, we apply the approach of Lawrence Katz and Kevin Murphy (1992) to data from the U.S. Current Population Survey (CPS), which involves modeling the relative hourly earnings of more- and less-skilled labor as a function of their relative supplies and a flexible time trend, meant to capture the evolution of labor demand. We estimate the model using earnings and employment data for the period 1976-2007 and then project relative earnings through 2015, using either actual labor supplies or labor supplies under counterfactual assumptions about low-skilled immigration. If, counterfactually, the low-skilled, foreign-born labor supply had grown at the same rate during the period 2008-15 as it did from 1994 to 2007, our simple model implies that the wage gap between more-skilled and less-skilled labor would have been 6 to 9 percentage points higher in 2015. This finding, though not a general equilibrium assessment of the wage effects of U.S. immigration, illustrates the magnitude of the immigration slowdown in terms of U.S. wage pressures. To the extent that slowing low-skilled immigration puts downward pressure on the skill premium, we would expect firms to invest more in automation and other changes in production techniques that reduce reliance on low-skilled labor (Card and Lewis 2007; Lewis 2011), effects that are likely to register most strongly in immigrant-intensive industries such as agriculture, construction, eating and drinking establishments, and nondurable manufacturing.

Our work complements the existing literature on immigration, much of which takes national changes in low-skilled foreign labor supply as given and examines its impact on the earnings of U.S. native-born workers. (2) As is well known, estimates of the wage effects of immigration vary widely across studies (Blau and Mackie 2016). Results depend on how one defines the geographic scope of labor markets, skill groups within these labor markets, and the interchangeability of native- and foreign-born workers on the job (Borjas 2003, 2013; Card 2001, 2009; Ottaviano and Peri 2012; Dustmann, Frattini, and Preston 2013). To explain instability in the wage effects of immigration, the literature has studied factors that may confound empirical analysis, including offsetting migration by native-born workers (Borjas 2006), the location choices of immigrant workers (Cadena and Kovak 2016), firm-level changes in technology (Lewis 2011), occupational downgrading by immigrant workers (Peri and Sparber 2009; Dustmann, Frattini, and Preston 2013), and measurement error in labor market earnings (Aydemir and Borjas 2011). Relative to existing work, we offer the inverse perspective of how and why the low-skilled immigrant labor supply has changed. Given the abundance of research on how immigration affects U.S. wages, the factors that govern the magnitude of low-skilled immigration are understudied. Our work helps address this gap in knowledge.

I. The Presence of Low-Skilled Immigrants in the U.S. Labor Force

We begin our analysis with an overview of the characteristics of low-skilled immigrants in the United States and then examine how selection into U.S. migration among individuals from Mexico has changed over time. For the analysis in this section and the next, we focus on individuals of working age, defined as those 18 to 64 years of age. We utilize data from the U.S. population censuses, the American Community Survey (ACS), and the CPS; and from Mexico's population census, available from the Integrated Public Use Microdata Series.

I.A. Characteristics of Low-Skilled Immigrants

A preliminary issue we must address is how to define low-skilled labor. When it comes to the analysis of immigration, the literature alternatively defines low-skilled workers as those with less than a high school education (Borjas 2003) or those with a high school education or less (Card 2001). (3) This difference matters, because those completing less than 12 years of schooling are an ever-smaller share of the U.S. native-born population but continue to account for a majority of adults in low- and middle-income countries. In the nations that send large numbers of low-skilled migrants to the United States--including Colombia, Cuba, the Dominican Republic, Ecuador, El Salvador, Guatemala, and Mexico--compulsory schooling is through grade 8 or 9, as opposed to being through age 16 in most U.S. states. The median worker in many sending countries thus has well less than the equivalent of a U.S. high school education (Clemens, Montenegro, and Pritchett 2008). Cross-national differences in compulsory education are manifest in the distribution of years of schooling among less-educated foreign- and native-born adults in the United States. In 1970, those not completing high school accounted for just over half of U.S. native-born adults with a high school education or less, a share that declined to 29.4 percent in 1990 and to 16.6 percent in 2015 (table 1). Among the U.S. foreign-born adult population with a high school education or less, the share with less than 12 years of schooling has also fallen but from a much higher base, beginning at 65.2 percent in 1970 and dropping to 55.0 percent in 1990 and to 44.7 percent in 2015. To ensure that our analysis is robust to the definition of skill, we utilize both education-based definitions of low-skilled labor. (4)

When viewed over the sweep of the last half century, the U.S. low-skilled, foreign-born population has transformed not just in terms of its size but also in its demographic structure. These evolutions are evident in tables 1 and 2, which present summary statistics on U.S. low-skilled foreign- and native-born individuals going back to 1970 using data from the U.S. census and ACS. In 1970, when the presence of the foreign born in the U.S. population was at a historic low, low-skilled immigrants, in comparison with the native born, were relatively old and likely to be female. This population came in its majority (52.9 percent) from Europe, was dominated by individuals who had arrived in the United States in 1960 or earlier (66.1 percent), and had a near majority (45.6 percent) with eight or fewer years of schooling.

As the incipient immigration wave gained momentum, the composition of low-skilled immigrants became younger, more likely to have come from Latin America, and more educated. These changes were most dramatic between 1970 and 1990. During this period, the fraction of foreign-born people age 18-33 rose from 28.6 to 43.2 percent, the fraction of males rose from 41.8 to 48.8 percent, and the fraction completing 12 years of education rose from 34.8 to 45.0 percent. In terms of origin countries, among immigrants with a high school education or less, the fraction born in Mexico rose from 11.6 to 34.0 percent, the fraction born elsewhere in Latin America (and the Caribbean) rose from 13.2 to 23.7 percent, and the fraction born in Asia rose from 5.7 to 16.2 percent. (5) The 1970 to 1990 increase in the shares of immigrants coming from Mexico and the rest of Latin America is even larger among those with less than a high school education, rising from 15.4 to 47.5 percent and from 12.6 to 21.2 percent, respectively. By 1990, nearly 7 in 10 (68.7 percent) of the least-skilled U.S. immigrants of working age came from other nations in the Western Hemisphere.

Jorge Durand, Douglas Massey, and Rene Zenteno (2001) describe this era of U.S. immigration as one marked by a preponderance of itinerant workers who came to the United States to take seasonal jobs, especially on farms in the Southwest, and often returned home during periods when labor demand was slack. During the two decades after 1970, the share of low-skilled immigrant workers employed in agriculture did rise, from 3.2 to 5.7 percent (as compared with a decline of 3.9 to 3.0 percent among the low-skilled, native-born workers of working age), and the fraction with 10 or fewer years of residence in the United States grew from 34.0 to 45.8 percent. (6) However, throughout the sample period, farm workers accounted for only a small share of low-skilled immigrant employment. During the first decades of the late-20th-century immigration wave, low-skilled immigrants spread themselves across a wide range of jobs, while concentrating more heavily, when compared with their native-born counterparts, in agriculture, construction, eating and drinking establishments, nondurable manufacturing, and personal services.

In subsequent decades, the low-skilled immigrant population has become more mature and more settled, at least when measured in terms of length of U.S. residence. By 2015, three-quarters (75.1 percent) of low-skilled immigrants had resided in the United States for 11 or more years, while the share of the population age 18-33 had dropped to 27.2 percent. Since 1990, the fraction of low-skilled immigrants from Mexico and the rest of Latin America has continued to rise, reaching 45.1 and 27.3 percent, respectively, in 2015. Among immigrants with less than a high school education, these shares are 59.3 and 24.9 percent, respectively, meaning that today, nearly 9 in 10 (85.2 percent) of the least-skilled, foreign-born workers are from Latin America and the Caribbean. It is particularly important that Mexico's dominance as a source country for low-skilled immigrants peaks in 2005, at 48.1 percent of those with a high school education or less and 64.0 percent of those with less than a high school education. The 4.7 percentage point drop in Mexico's share of the least-skilled immigrant population from 2005 to 2015 is largely offset by Central America's jump during the same period of 3.5 percentage points. As we discuss in section III, demographic push factors help account for Mexico's recent relative decline and Central America's continuing relative gain as source regions. After Latin America, Asia remains the next most important source region of low-skilled immigration, in 2015 accounting for 15.8 percent of all low-skilled immigrants and 10.8 percent of those with less than 12 years of schooling.

Over time, low-skilled immigrants have become more specialized in particular lines of work. The share employed in immigrant-intensive sectors in 2015 reached 14.8 percent in construction (up from 7.8 percent in 1990), 11.3 percent in eating and drinking establishments (up from 8.7 percent in 1990), 7.2 percent in personal services (up from 6.9 percent in 1990), and 6.9 percent in agriculture (up from 5.7 percent in 1990). The one immigrant-intensive sector registering a decline in its share of low-skilled immigrant employment is nondurable manufacturing--which includes apparel, footwear, furniture, and textiles--industries whose overall employment in the United States has fallen sharply in recent decades due to technological change and competition from China and other low-wage countries (Autor, Dorn, and Hanson 2013).

The transition of the U.S. low-skilled immigrant population from sojourners to settlers, first noted by Wayne Cornelius (1992) nearly three decades ago, today appears to be largely complete. Part of this shift is the natural result of a dynamic process of immigration in which early arrivals initially dominate the population, only to decline in importance as the existing stock grows and matures (Piore 1980). However, the shift is also the result of the pronounced slowdown in low-skilled immigration since the mid-2000s, as seen in figure 1.

Because the immigration levels portrayed in table 2 reflect changes in net immigration, they are uninformative about whether this slowdown is the result of reduced inflows of new immigrants, larger outflows of existing immigrants returning to their home countries, or some combination of the two. We next summarize evidence on changing inflows and outflows of immigrants over time. Figure 2 gives counts of immigrants by current age, age of arrival in the United States (inferred from years of U.S. residence), and census year for three source regions--Mexico, other countries in Latin America and the Caribbean, and Southeast Asia--which together account for the large majority of low-skilled immigration in the United States. To avoid concerns about tracking individuals who educate themselves out of the low-skilled category over time, we include all immigrants from these source regions, regardless of schooling.

Several patterns are apparent in the data. First, for most current-age groups and in most census years, the largest cohorts are those arriving between 15 and 24 years of age. That is, for a given current-age group, if we compare bars that have the same shading (thus comparing different arrival-age cohorts in the same census year for the same current-age group), those in the 15-24 arrival-age category are the largest in nearly all cases. Second, between 2000 and 2010, there are substantial declines in the sizes of given arrival-age or birth-year cohorts. For individuals from Mexico arriving in the United States between age 5 and 14, the number who are age 15-24 in 2000 is much larger than those who are age 25-34 in 2010. We see similar declines in the number of Mexican immigrants who are age 25-34 in 2000 and the number who are age 35-44 in 2010, both for the cohort arriving between age 5 and 14 and the cohort arriving between age 15 and 24. Similar patterns hold for immigrants from other countries in Latin America and from Southeast Asia. Declines in cohort size, as measured in the census, may result from mortality, return migration, or changes over time in the fraction of individuals in a cohort who are enumerated in the census. Given the youth of the cohorts considered, mortality seems unlikely to explain this decline. Moreover, given that we expect enumeration rates to increase with length of residence in the United States, declines in enumeration seem an unlikely explanation, which leaves return migration as the most likely cause for the decline in measured immigrant cohort sizes between 2000 and 2010.

The net impact of these changes is that the size of immigrant cohorts in 2010 is skewed heavily toward individuals who have more than 10 years of residence in the United States. For immigrants from Mexico in 2010 (indicated by the darkest shaded bars), those with fewer than 10 years of U.S. residence are the smallest cohort among all current age groups, a pattern that holds for other countries in Latin America and for Southeast Asia as well.

I.B. The Presence of Low-Skilled Immigrants in the U.S. Labor Force

To consider how the presence of low-skilled immigrants in the U.S. labor force has changed in recent years, we focus on movements at annual frequencies using data from the CPS. Because the CPS only begins asking questions about nativity in 1994, our use of these data is for that year forward. We use two measures of the working-age population: raw data on body counts; and these values expressed in terms of productivity-equivalent units (PEUs), following the weighting procedure used by David Autor, Lawrence Katz, and Melissa Kearney (2008).

Consistent with the post-1970 rise in low-skilled immigration seen in figure 1, figure 3 shows that the presence of low-skilled, foreign-born workers in the U.S. working-age population rose steadily from 1994 to 2007 but has been stable since. The left panel of figure 3 plots four measures of low-skilled immigration. The top line gives the share of the foreign born with a high school education or less among all working-age individuals in the United States. This fraction rose from 6.5 percent in 1994 to 9.1 percent in 2007, before stabilizing in subsequent years, settling at 8.8 percent in 2015. Just under half these foreign-born individuals were born in Mexico (43.1 percent in 1994; 47.3 percent in 2015). When, alternatively, we define low-skilled immigrants more narrowly as those with less than 12 years of schooling, we also see a growing immigrant presence in the U.S. working-age population, rising from 3.6 percent in 1994 to 4.5 percent in 2007, and showing little change thereafter. Individuals born in Mexico account for a high fraction of the foreign-born population with less than a high school education (61.1 percent in 1993, 64.4 percent in 2014).

[FIGURE 3 OMITTED]

Body counts of low-skilled immigrants overstate their presence in the U.S. labor force to the extent that these individuals have low labor productivity relative to the average U.S. person of working age. To measure the population in terms of PEUs, we apply the approach taken by Autor, Katz, and Kearney (2008), which involves reweighting individuals by their projected relative earnings. (7) Specifically, the weight attached to an individual is the ratio of the average weekly wage among full-time, full-year workers in his or her race, gender, education, and labor market experience cell to the average weekly wage for white, male, high school graduates with 8 to 12 years of potential work experience. (8) Population shares expressed in terms of PEUs appear in the right panel of figure 3. These shares are naturally smaller than in the left panel, owing to the fact that low-skilled immigrant workers have low earnings relative to other U.S. workers. Using the productivity-adjusted measure, foreign-born individuals with 12 or fewer years of schooling reach 6.5 percent of the U.S. working-age population in 2007, a share that declines slightly to 6.3 percent in 2015. (9)

Low-skilled immigrants tend to have high rates of labor force participation and employment when compared with similarly skilled native-born workers (Borjas 2016). Consequently, the population shares shown in figure 3 may give an incomplete characterization of the presence of the low-skilled, foreign-born workers in the effective U.S. labor supply. Figure 4 reports the shares of low-skilled immigrants in total hours worked, both using raw hours (left panel) and productivity-adjusted hours (right panel). The share of total hours worked by immigrants with 12 or fewer years of schooling rose from 5.2 percent in 1994 to 8.4 percent in 2007, before falling modestly to 8.0 percent in 2015. When expressed in PEUs, these shares are 3.6, 5.8, and 5.5 percent, respectively.

[FIGURE 4 OMITTED]

Because undocumented immigrants account for a large share of the low-skilled immigrant population, and because the large majority of these individuals come from Mexico and Central America, low-skilled, foreign-born labor accounts for a relatively high fraction of employment in the states along the U.S. border with Mexico. Figure 5 plots the share of low-skilled immigrants in hours worked for the four U.S. border states (Arizona, California, New Mexico, and Texas), again in terms of both raw hours and productivity-adjusted hours. Among these border states, the share of foreign-born workers with 12 or fewer years of education in total hours worked rose from 11.9 percent in 1994 to 16.2 percent in 2005 and then dropped to 14.1 percent in 2015.

Given the propensity of low-skilled immigrants to concentrate in particular sectors, it is not surprising that, in selected industries, they have come to account for a substantial fraction of total employment. As seen in table 3, in 2015 immigrants with 12 or fewer years of schooling account for 29.3 percent of total hours worked in agriculture (up from 3.9 percent in 1970), 21.8 percent in personal services (up from 6.4 percent in 1970), 20.3 percent in construction (up from 3.9 percent in 1970), 16.8 percent in eating and drinking establishments (up from 8.3 percent in 1970), and 13.5 percent in nondurable manufacturing (up from 5.9 percent in 1970), as compared with just 5.8 percent of employment in all other industries. For these immigrant-intensive industries, future changes in low-skilled immigration matter immensely.

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I.C. Who Chooses to Migrate to the United States?

Is the increase in low-skilled immigration in the United States the result of increasing immigration from countries that are relatively abundant in low-skilled labor or the result of low-skilled labor being relatively likely to select into international migration? One cannot answer this question by examining U.S. data alone. Differences in educational attainment across countries would make the average worker from, say, Mexico appear to be low skilled in the U.S. labor market, whereas at home he or she would fall in the middle of the earnings distribution.

In seminal research, George Borjas (1987) derived the conditions under which immigrants are negatively or positively selected in terms of skills. Conditions favoring negative selection--meaning that immigrants are drawn disproportionately from the bottom half of the skill distribution--are high returns to skills in the sending country relative to the receiving country, and migration costs that are proportional to worker productivity (for example, costs that have an iceberg form), which combine to give less-skilled workers a relatively strong incentive to migrate. Migration costs that are fixed in nature and a marginal utility of income that is not strongly decreasing favor positive selection of immigrants in terms of skills (Grogger and Hanson 2011), in which case immigrants are drawn more heavily from the top half of the skills distribution.

Whether immigrants are negatively or positively selected in terms of skills matters for how labor movements affect the distribution of income in sending and receiving countries and for the ease with which immigrants from low-income countries integrate themselves into the labor markets of high-income countries. If, for example, immigrants from Mexico are negatively selected in terms of skills, shocks that contribute to a positive net flow of labor from Mexico to the United States would tend to decrease Mexican wage inequality--by reducing Mexico's relative supply of low-wage workers--and to increase U.S. wage inequality--by expanding the U.S. relative supply of low-wage workers. Further, immigrants who are negatively selected in terms of skills may face greater challenges in assimilating economically in the U.S. labor market and may be more likely to be a net drain on public resources (Borjas 2016).

To examine the composition of low-skilled immigration in the United States from the sending country's perspective, we focus on the case of Mexico, which is by far the largest source country for U.S. labor inflows, accounting for nearly half of all U.S. low-skilled immigrants and nearly two-thirds of those with less than 12 years of schooling. We extend forward in time the analysis of Daniel Chiquiar and Gordon Hanson (2005), which utilizes the methodology of John DiNardo, Nicole Fortin, and Thomas Lemieux (1996) for constructing counterfactual wage distributions. (10) To examine differences in the distribution of skills between Mexican residents (that is, nonmigrants in Mexico) and Mexican immigrants, we compare the actual wage density in Mexico for Mexican residents with the counterfactual wage density that Mexican immigrants in the United States would obtain if they were paid according to Mexico's prevailing wage structure. This comparison reveals from where in Mexico's wage distribution migrants to the United States are drawn. Because this analysis projects U.S. immigrants onto Mexico's wage distribution based on workers' observable skills, it ignores the role of unobserved characteristics in migration and earnings. And because it takes Mexico's current wage distribution as given, the analysis is silent about the equilibrium impact of immigration on U.S. or Mexican wages.

Let [f.sup.i](w | x) be the density of wages w in country i, conditional on observed characteristics x, h(x|i - MX) be the density of observed characteristics among workers in Mexico, and h(x | i = US) be the density of observed characteristics among Mexican immigrants in the United States. The density of wages that would prevail for Mexican immigrants in the United States if they were to be paid according to the price of skills in Mexico is given by

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

This quantity corresponds to the counterfactual distribution of wages that arises from projecting the skill distribution of Mexican immigrants in the United States onto the current wage structure of Mexico. Although this distribution is unobserved, we can rewrite it as

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where Mexico's conditional wage distribution [f.sup.MX](w | x) and the skill distribution of its resident population h(x | i = MX) are observed, and where

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Hence, we can obtain the counterfactual wage density that we desire in equation 1 simply by applying the appropriate weight [theta] to the existing distribution of wages in Mexico. To compute this weight, we use Bayes's theorem to write

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Combining equations 4 and 5, we obtain an expression for [theta] that is the ratio of the conditional probability that a Mexican-born worker resides in the United States, Pr(i = US|x)/Pr(i = MX|x), to the unconditional probability that a Mexican-born worker resides in the United States, Pr(i = US)/Pr(i = MX). We estimate these probabilities via a logit model, use the estimates to calculate [theta], and apply the [theta] weights to estimate the counterfactual wage density in equation 2. (11)

We construct actual and counterfactual wage densities for males and females, separately, in the years 1990, 2000, and 2010. Earnings are annual labor income for individuals age 18-64. We estimate the logit regressions used to predict whether an individual born in Mexico resides in the United States separately for men and women as a function of education (seven categories, based on years of schooling: 0-4, 5-8, 9, 10-11, 12, 13-15, 16+) and age (46 categories, one for each year in the range 18-64). The population is all working-age individuals in Mexico and Mexican immigrants in the United States who have resided in the country for 10 or fewer years. Results are similar when we expand the analysis to include immigrants with 20 or fewer years of U.S. residence, who constitute the large majority of working-age Mexican immigrants in the United States. Wage densities are plotted relative to mean log earnings for workers in Mexico of a given gender in a given year, such that actual wage densities are centered on zero. Figure 6 presents the results, where in each plot the dashed line is the actual wage density for Mexico and the solid line is the counterfactual wage density in Mexico for current Mexican immigrants.

For the case of males, shown in the left-side panels of figure 6, we see that in each year, the actual and counterfactual densities are very similar to each other, suggesting that the observable skills of Mexican immigrants match closely those of individuals who have not migrated abroad. In 1990, the counterfactual wage density lies slightly to the right of the actual wage density, indicating that Mexican immigrants are mildly positively selected in terms of observable skills. This difference is more defined in figure 7, which plots the difference between counterfactual and actual wage densities. In 1990, this difference, as seen in the top-left panel, has a negative mass just below zero and a positive mass just above zero, indicating that male immigrants are underrepresented among those who would earn slightly less than mean earnings in Mexico and overrepresented among those who would earn slightly more than mean earnings in Mexico. The slight rightward shift in the counterfactual relative to the actual wage density is also present in 2000 and 2010. However, the difference between actual and counterfactual densities becomes less pronounced over time, such that in the top-left panel of figure 7, the negative hump below zero and the positive hump above zero are smaller in 2000 than in 1990 and smaller still in 2010 relative to 1990. These changes are also seen in the top-right panel of figure 7, which reports the double difference in densities: counterfactual relative to actual wage densities in 2010 relative to this difference in either 1990 or 2000. The double difference using 2010 and 1990 is larger than that for 2010 and 2000, indicating a lessening of positive selection over time. By the time that we arrive in 2010, working-age Mexican immigrants who reside in the United States appear to be close to a random draw on the population of working-age individuals in Mexico.

[FIGURE 7 OMITTED]

The three right-side panels of figure 6 repeat the analysis for women. Among women, we see evidence of stronger positive selection in 1990 and 2000 when compared with men. In each year, the rightward shift of the counterfactual wage density relative to the actual wage density is more pronounced than the corresponding density difference for males. As with males, the strength of positive selection diminishes over time, such that by 2010 the counterfactual and actual wage densities for women are very similar. We conclude that by 2010, the selection of immigrants from Mexico is close to neutral in terms of observable skills. As mentioned above, these results are silent about the pattern of immigrant selection in terms of unobservables.

One concern about the results shown in figures 6 and 7 is that we use census data to evaluate immigrant selection. Any undercount of the Mexico-born population in either Mexico or the United States that depends systematically on an individual's age or education could result in biased estimates either of the wage density for Mexico or of the counterfactual wage density that we construct for Mexican immigrants in the United States. There is a long-standing belief among demographers that the U.S. census undercounts undocumented immigrants in the United States (Warren and Passel 1987). To address this undercount issue, some studies evaluate immigrant selection using data exclusively from Mexico (Ibarraran and Lubotsky 2007). In noteworthy work, Jesus Fernandez-Huertas Moraga (2011) uses data from Mexico's national employment survey (Encuesta Nacional de Empleo, ENE), which follows households for five consecutive quarters and includes in the survey questions about whether household members have migrated to the United States during the period since the last survey was conducted. Distinct from Chiquiar and Hanson (2005), Fernandez-Huertas Moraga (2011) finds that Mexican immigrants are negatively selected in terms of skills, as captured by residuals from Mincerian wage regressions. The ENE, however, has measurement problems of its own. It suffers from high rates of attrition by households from the sample within the five-quarter survey window, which a recent study by the National Academies of Science, Engineering, and Medicine concludes makes it problematic as a data source for evaluating Mexican migration to the United States (Carriquiry and Majmundar 2013).

Fortunately, there is a source that provides longitudinal data on households in Mexico and that tracks information on individuals who migrate to the United States. The Mexican Family Life Survey (MxFLS) has been conducted in three waves -- 2002, 2006, and 2009 -- with a recontact rate of respondents between each wave of 90 percent. Of particular importance, the survey follows household members who migrate to the United States between waves. Robert Kaestner and Ofer Malamud (2014) use data from the first two MxFLS waves to analyze the selection of immigrants according to various measures of skills. Similar to what one sees in census data, migrants to the United States in the MxFLS are more likely to be young. In terms of education, both male and female migrants are more likely to have middle levels of schooling (4-9 years for men, 4-12 years for women) than to have low levels of schooling (0-3 years). For men, but not for women, migrants are less likely to have very high levels of schooling (more than 12 years) than to have very low levels (0-3 years). The MxFLS also provides a measure of cognitive ability in the form of a Raven's Progressive Matrices test score (Raven, Raven, and Court 2000). Although cognitive ability is a frequently discussed source of skill in the analysis of earnings (Heckman and Vytlacil 2001), few data sources provide evidence of how cognitive skills relate to migration decisions. Among both men and women, Kaestner and Malamud (2014) report no difference between migrants and nonmigrants in terms of their Raven scores, suggesting that the two populations have a similar distribution of observable cognitive abilities. Following Fernandez-Huertas Moraga (2011), Kaestner and Malamud (2014) also examine migrant selection in terms of observable and unobservable characteristics using Mincerian wage regressions. Their analysis shows that workers with the highest predicted earnings or the highest residual earnings in the first MxFLS wave--meaning those among the top quintile of predicted or residual wage earners--are less likely to migrate but that there is no pattern of selection among lower-wage individuals.

Despite problems with possible undercounts of undocumented migrants in census data, they provide a characterization of immigration selection that is comparable to that based on high-quality longitudinal micro data. Immigrants from Mexico to the United States are overrepresented among individuals whose skills place them in the middle of Mexico's wage distribution and mildly underrepresented among individuals who would be very low-wage or very high-wage earners in their home country. When we examine U.S. immigration from other source countries, evidence of positive selection in terms of observable skills such as education is even more pronounced (Grogger and Hanson 2011). In nearly all source countries for U.S. labor inflows, immigrants are relatively likely to come from among the more educated. (12)

I.D. Summary

The U.S. population of low-skilled immigrants has gone through an epochal half century of growth, transforming from a small cadre of older immigrants from Europe to a large population of immigrants from Latin America and Asia who are nearing middle age and who have now lived in the United States for an extended period of time. Immigrants from Mexico, who account for one-half to three-fifths of the low-skilled foreign born population, depending on the definition of skill, are preponderantly individuals who would be middle-income earners in their birth country. As the United States looks forward to an era of weakened incentives for low-skilled immigration due to changing labor demand and labor supply conditions at home and abroad, it will be shocks to middle-wage workers in migrant-sending countries that matter disproportionately for who migrates. Efforts to reduce the existing population of low-skilled immigrants, such as through increased deportations of undocumented immigrants, would target a population that appears to have a long tenure of residence in the United States.

II. Labor Demand, Labor Supply, and Low-Skilled Immigration

In this section and the next, we examine factors affecting the net flow of low-skilled immigrants into the United States. We begin in this section by describing recent changes in conditions surrounding low-skilled immigration, including income differences between the United States and major migrant-sending countries, U.S. immigration policy, and relative labor supply growth in the United States and major sending countries. We then analyze for the case of Mexico the contribution of labor demand and labor supply shocks to migration to the United States.

II.A. Income Differences between Countries

Perhaps the simplest manner in which to evaluate the incentive for immigration is to compare income between countries. Beginning with Larry Sjaastad (1962), economists have modeled immigration as an investment decision, in which the upfront cost of migration yields an income flow over time equal to the difference in earnings between the home and foreign economies. There may be considerable heterogeneity in the time horizon over which individuals consider migration (Dustmann 2003). Seasonal workers may focus on income differences between countries no more than a few months in advance, other individuals may be uncertain about their desire to relocate permanently and so put weight on the income differences they expect to be sustained over the next several years, and still others may treat migration as a long-term decision and therefore evaluate the expected discounted difference in income streams over their full working lives. To examine high-frequency changes in the incentive for immigration, we abstract away from such heterogeneity and consider point-in-time income differences between the United States and migrant-sending countries, an approach taken in the large body of literature that uses the gravity model to analyze bilateral migration flows (Karemera, Oguledo, and Davis 2000; Clark, Hatton, and Williamson 2007; Bertoli and Fernandez-Huertas Moraga 2013).

Even in making point-in-time income comparisons, one faces many choices for how to measure income. One approach is to evaluate earnings for individuals with similar observable skills who were born in the same country and now live in different countries. Using data from the U.S. and Mexican population censuses, Hanson (2006) reports that in 2000 the average hourly wage for a 28- to 32-year-old male with 9 to 11 years of education is $2.40 in Mexico and $8.70 among recent Mexican immigrants in the United States (these income values, like those we report below, are adjusted for purchasing power parity in terms of 2000 dollars). At a labor supply of 35 hours per week and 48 weeks per year, this would yield an annual income gain of $10,600. Combining data from Mexico's national survey of income and expenditures with data from the U.S. census, Michael Clemens, Claudio Montenegro, and Lant Pritchett (2008) obtain similar results, estimating that in 2000 the annual income gain to migration for a 35-year-old Mexican male with 9 to 12 years of education is $9,200.

Comparing migrants with nonmigrants is problematic if there are unobserved characteristics that affect both the migration decision and an individual's income-earning ability. An alternative approach is to use longitudinal data for the same individual, which allows comparisons of income before and after migration. Mark Rosenzweig (2007) uses data from the New Immigrant Survey to estimate the change in income for new U.S. permanent legal immigrants in 2003. He checks their current U.S. earnings against earnings in the last job they held in their country of origin. For a legal immigrant from Mexico with 9 to 12 years of education, the average gain in income is $15,900 (at 35 hours a week and 48 weeks a year). Comparing the same individual in two countries corrects for selection into the migration associated with unobserved, time-invariant individual characteristics but may introduce other complications. If, in preparing to migrate, individuals reduce their labor supply in a manner that diminishes income (or if negative shocks to income precipitate migration), this approach may overstate the income gains to migration. (13)

Evaluating how the incentive to migrate to the United States has changed across countries and over time is complicated by the fact that few countries produce annual household survey data, and census data are amassed infrequently. Our approach is to construct income differences between countries by combining annual data on average income from national accounts with data on the variance in income as inferred from summary statistics on income inequality. Although statistics on income inequality, such as the Gini coefficient, are often constructed at less than an annual frequency, they tend to change slowly from one year to the next (Solt 2016), which permits interpolation of their values to create an annual series. Under the assumption that income is log-normally distributed across households, which is approximately consistent with data for many countries (Pinkovskiy and Sala-i-Martin 2009), one can use the Gini coefficient to calculate the variance of income across individuals and then combine this value with average income to construct income at different percentiles of the distribution (Grogger and Hanson 2011). (14) Given the neutral selection of immigrants from Mexico in terms of observable skills, the 50th percentile (equal to $8,800 in 2000) is a natural choice for the reference income of a prospective Mexican migrant. To select the reference income in the United States for a typical immigrant from Mexico, we choose the percentile of the U.S. income distribution that yields an income gain to migration in 2000 that is approximately equal to the average income gain for migrants as described by Hanson (2006); Clemens, Montenegro, and Pritchett (2008); and Rosenzweig (2007). The 25th percentile of the U.S. income distribution ($20,100 in 2000) serves this purpose.

In the left panel of figure 8, we report the ratio of the 50th percentile of the Mexican income distribution to the 25th percentile of the U.S. income distribution, where we construct these values using Gini coefficients from UNU-WIDER's World Income Inequality Database, and per capita GDP, adjusted for purchasing power parity, from the World Bank's World Development Indicators. (15) This ratio is stable in the 1990s and early 2000s, averaging 0.44 between 1990 and 2007. During this period, a middle-income earner in Mexico who chooses to become a low-income earner in the United States would see his or her real earnings increase by a factor of 2.3. After the Great Recession, the U.S.--Mexico income difference compresses, with the ratio of the 50th percentile of Mexican income to the 25th percentile of U.S. income rising to an average of 0.53 between 2008 and 2015 and to 0.58 during the later period of 2011 to 2015. In the right panel of figure 8, we report the corresponding ratio of the 50th percentile of the sending country's income to 25th percentile of U.S. income for a composite of other countries in Latin America and the Caribbean. We choose the next-largest sending countries for which data on Gini coefficients are available--Colombia, the Dominican Republic, Ecuador, El Salvador, Guatemala, Honduras, and Jamaica--and we weight each country's income by its relative share of working-age, low-skilled immigrants in the United States in 2000. (16) The time path of relative income is similar to that for the U.S.--Mexico comparison, though the absolute income gap is larger. The income ratio is stable from 1990 to 2007, averaging 0.22, and then rises after the onset of the Great Recession, averaging 0.30 from 2008 to 2015. Since 2007, relatively slow U.S. income growth and rapid growth in neighboring countries have compressed the income gap between the United States and migrant-sending nations, presumably weakening incentives for immigration.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

In forming expectations about future income differences between countries, prospective migrants are likely to consider not just the level of income but also its variance. Over short time horizons, higher perceived variance in income in the sending country relative to the receiving country may add to the incentive for migration. At a monthly frequency, changes in attempted undocumented migration from Mexico to the United States, as captured by apprehensions at the U.S.--Mexico border, are strongly sensitive to changes in the dollar--peso real exchange rate, with attempted entry surging during periods following currency crises in Mexico (Hanson and Spilimbergo 1999; Monras 2015). When expanding data to include countries throughout the Western Hemisphere, emigration rates to the United States are larger for cohorts subject to a higher incidence of financial crises in their home country (Hanson and Mcintosh 2012).

To characterize changes in U.S. income volatility relative to that in migrant-sending economies, the left panel of figure 9 reports the standard deviation in quarterly real GDP growth in Mexico and the United States for rolling eight-quarter windows covering the period 1991:Q1-2016:Q1. Throughout this time span, volatility in GDP growth is higher in Mexico (average eight-quarter standard deviation of 3.7 percent) than in the United States (average eight-quarter standard deviation of 2.0 percent). However, there are evident changes in relative volatility over time. After the 1995 peso crisis, volatility spiked in Mexico while remaining low in the United States. During the ensuing 10 years, volatility remained uniformly higher in Mexico, though well below the elevated levels of crisis periods. With the onset of the global financial crisis of 2008-10, volatility jumps in both economies, declining thereafter to roughly equal levels. Reduced differences between Mexico and the United States in income volatility reflect the improved execution of monetary and fiscal policies in Mexico--which, as in much of Latin America, has helped lower inflation, reduce government debt, and stabilize GDP growth (Edwards 2009). In the right panel of figure 9, we compare volatility in quarter-to-quarter GDP growth in the United States with the same migrant-sending countries examined with regard to relative GDP levels in figure 8. Here again, we see that volatility in GDP growth in migrant-sending nations has decreased relative to the United States, which has presumably dampened pressures for cross-border labor flows.

II.B. U.S. Immigration Policy

Low-skilled immigrants enter the United States through three channels: with permanent legal residence visas (green cards), with temporary work visas, and as undocumented entrants. During the 2000s, the U.S. government engaged in a massive buildup in border enforcement efforts, with most newly committed resources allocated to the U.S. border with Mexico. To understand how changes in immigration policy may have affected incentives for low-skilled immigration, we review recent adjustments in U.S. policy mechanisms.

LEGAL IMMIGRATION The vast majority of low-skilled immigrants who obtain green cards do so through family sponsorship, for which visa eligibility derives from having a relative who is a U.S. citizen or legal resident, or as refugees or asylees (Rosenzweig 2007). The number of U.S. green cards and the policies governing their allocation have been stable since 1990. In that year, the Immigration Act set the annual number of family-sponsored visas at 480,000, the annual number of employer-sponsored visas (which go primarily to skilled workers) at 140,000, and the annual number of diversity visas (allocated via lottery to countries that have historically low migration to the United States) at 55,000. Visas available to immediate relatives of U.S. citizens are uncapped, though applications for these visas may be subject to processing delays. The number of green cards given to refugees and asylees, though having no set cap, shows no trend over time, having fallen from 114,000 per year in the 1990s to 83,000 per year in the 2000s, before rising to 109,000 per year during the 2010-15 period. (17) Any increase in low-skilled immigration via permanent legal visas thus cannot have occurred through expanded quotas for green cards. It must instead have occurred through increases in the number of low-skilled immigrants qualifying for, applying for, and receiving visas from the annual allocation of visas. (18)

Qualifying for a green card under family sponsorship requires having an immediate relative who is a U.S. citizen--which gives one access to visas that are not subject to numerical limit--or a more distant relative who is a U.S. citizen or legal resident--which allows one to apply for the fixed annual allocation of green cards. Because the number of new applications exceeds the annual cap on green cards, and has for many years, there is often a substantial lag between the time of application and the time of visa receipt, with waiting times of several years in length being common. The waiting time depends in part on one's visa preference category, which is a function of how closely related one is to a U.S. resident, and in part on the number of green card applicants from an individual's country of birth who are higher up in the visa queue.

Family sponsorship for green cards makes immigration a self-reinforcing process. As the number of permanent legal immigrants from a sending country increases, so too does the number of residents of that country who are eligible for a green card. For example, permanent visas awarded to residents of Mexico rose from 64,000 per year in the 1970s to 166,000 per year in the 1980s and to 225,000 per year in the 1990s, before dropping to 169,000 per year since 2000. (19) Visa growth from the 1970s to the 2000s partly reflects the growing population of Mexican residents who have family members who are legal U.S. residents, which has expanded the pool of eligible green card applicants. However, idiosyncratic changes in immigration policy are also at work. The 1990s blip in green cards awarded to residents of Mexico was partly a result of the legalization of undocumented immigrants under the Immigration Reform and Control Act of 1986, which delivered green cards to undocumented residents who met eligibility requirements on a one-time basis. The recent slowdown in low-skilled immigration is evident in green card allocations. Green cards awarded to Mexican residents declined from 175,000 per year during the 2001-05 period to 140,000 per year during the 2011-15 period. Because more residents of Mexico were eligible for green cards in 2010 than in 2000, the slowdown in green cards issued must be due to a decrease in demand for U.S. visas, which may be due to improved economic conditions in Mexico relative to the United States.

Another form of legal immigration available to low-skilled, foreign-born workers is a temporary work visa. These visas permit a non-U.S. resident to work in the United States for a period of less than one year. The H-2A program provides work permits to agricultural workers, while the H-2B program gives work permits to nonagricultural workers, often for seasonal jobs in construction or tourism. The number of H-2 visas has risen over time--H-2A visas from 46,000 in 2006 to 284,000 in 2015, and H-2B visas from 97,000 in 2006 to 120,000 in 2015. However, because these visas permit stays of less than one year and are nonrenewable, they account for no more than a small share (less than 3 percent) of the over 17 million low-skilled, working-age immigrants who resided in the United States as of the mid-2010s. (20)

UNDOCUMENTED IMMIGRATION The most significant recent changes in the United States' policy governing low-skilled immigration pertain to how the country monitors and enforces its borders and ports of entry. Undocumented immigrants gain entry to the United States either by overstaying their legal immigration visas or by crossing a U.S. border or entry point illegally. (21) The United States has substantially expanded the resources it devotes to preventing undocumented labor inflows (Roberts, Alden, and Whitley 2013). Figure 10 plots the number of U.S. Border Patrol agents stationed at the U.S.--Mexico border and other entry points. In 2016, 85.9 percent of agents were stationed in the Southwest, a share similar to that in 1992. The expansion in personnel at the border--which increased by a factor of 4.8 by 2016 -- encompasses only part of the buildup. There have also been substantial investments in infrastructure at the border and changes in how those caught attempting undocumented entry are treated.

[FIGURE 10 OMITTED]

To comprehend the dimensions of these changes, consider how the environment along the San Diego--Tijuana segment of the U.S.--Mexico border today compares with that in 1992, before the modern enforcement buildup began. In 1992, there were 1,009 Border Patrol agents assigned to the San Diego region, which stretches from the Pacific Ocean for about 60 miles east, among the 3,555 agents stationed along the entire U.S.--Mexico border. Barriers at the border itself were insubstantial, consisting in many areas, including those adjacent to the heart of urban Tijuana, of no more than a chain-link fence, in which large holes were frequently cut. In 1992, the Border Patrol apprehended 545,000 individuals in the San Diego sector, representing 542 apprehensions per agent. Across the entire U.S.--Mexico border, there were 1,134,000 apprehensions, representing 319 apprehensions per agent. Agents spent much of their time chasing down migrants as they attempted to run into the United States and find cover in San Diego neighborhoods. More than 95 percent of those apprehended were Mexican nationals, and nearly all were subject to "voluntary removal," under which they face no legal sanction for being apprehended. After capture, most were bused across the nearest border crossing, leaving them free to attempt entry again soon thereafter (Hanson 2007). Thus, as of the early 1990s, the U.S.--Mexico border was porous, the enforcement presence was unsophisticated and lightly resourced, and sanctions against migrants attempting illegal entry were weak.

Today, the San Diego--Tijuana border, as with much of the U.S.--Mexico border, is a much different place. The number of Border Patrol officers in San Diego has grown to 2,325, among the 17,026 stationed along the entire border. San Diego and Tijuana are now separated by multiple layers of border barriers, which include rows of closely spaced, vertically mounted steel beams that reach 18 feet in height. These barriers constitute part of the 650 miles of fencing along the U.S.--Mexico border, 600 miles of which were constructed between 2006 and 2010 (Roberts, Alden, and Whitley 2013), which cover nearly all the U.S-Mexico border that does not coincide with the Rio Grande, a river that spans the near entirety of Texas's border with Mexico. The San Diego--Tijuana border is patrolled by Border Patrol agents in SUVs, who traverse groomed roads constructed between each layer of border fencing, with manned and unmanned aircraft surveilling from above. Night-vision-capable video cameras posted every few hundred yards provide a continuous feed to Border Patrol stations nearby. In 2015, apprehensions in the San Diego sector were down to 26,000 (11 apprehensions per agent) and down to 337,000 for the U.S.--Mexico border as a whole (29 apprehensions per agent). Whereas, in the past, the Border Patrol spent much of its time physically apprehending migrants, today its job is to serve as a deterrent force against those who would consider illegal entry. In fiscal year 2017, the U.S. Department of Homeland Security spent an estimated $7 billion on salaries and benefits for Border Patrol agents and Customs and Border Protection officers (whose employment numbers are roughly equal); $3.6 billion on Coast Guard efforts to maintain the security of U.S. ports, waterways, and coastal areas; $2.9 billion on the detention and removal of deportable aliens; and $410 million to maintain infrastructure and purchase communications equipment related to border security (U.S. Department of Homeland Security 2016a).

Sanctions against undocumented immigration have also changed. The era of voluntary removal is over, replaced by a Consequence Delivery System (Argueta 2016). The disposition of those apprehended is conditional on their previous crossing activity and other circumstances. Since 2000, nearly all those apprehended at the border (meaning within 100 miles of a border and 14 days of entering the United States) have been finger-printed and recorded in a digital database. Consequences depend on whether the apprehension is the first ever or a repeat event. Since the early 2010s, the large majority of those apprehended (more than 85 percent) have been subject at a minimum to "expedited removal" (or "reinstatement of removal," if they have been removed before), which is a formal and immediate removal order that carries the considerable penalty of making the individual ineligible for legal U.S. immigration during the subsequent 10 years (enforceable via an individual's fingerprint record). Those with multiple prior apprehensions may be subject to a "warrant of arrest" and misdemeanor prosecution. Roughly one-third of those deported are now repatriated to a port of entry far from their attempted crossing point, which disrupts smuggling operations in which individuals pay smugglers for multiple attempts to cross the border (as a hedge against the risk of apprehension). (22) Since the enactment of the Consequence Delivery System, recidivism rates have dropped. During the 2005-07 period, 25 to 30 percent of those apprehended were caught within the same year. Recidivism began to decline in 2009, when the consequence program was rolled out, and in 2015 it stood at 15 percent.

The intensity of immigration enforcement has also increased in the U.S. interior. (23) U.S. Immigration and Customs Enforcement (ICE) is the government agency tasked with locating and removing "deportable aliens" in the U.S. interior, meaning all immigrants whose criminal activities--whether related to immigration or nonimmigration infractions--warrant deportation. By working more closely with local law enforcement agencies, ICE agents have expanded the deportations of individuals accused of minor infractions, including those driving without a license or driving under the influence of alcohol or other substances (Thompson and Cohen 2014). These changes in part account for the increase in the deportations of noncriminal aliens (that is, those whose nonimmigration crimes alone do not warrant deportation) from 112,000 per year during the first three years of the George W. Bush administration (2001-03) to 223,000 per year during the first three years of the Barack Obama administration (2009-11). Deportations of criminal aliens--those whose nonimmigration crimes do warrant deportation--has also increased, from 77,000 per year in 2001-03 to 164,000 per year in 2009-11, which may reflect a combination of an expanding population of criminal aliens and increased efforts by ICE to locate and remove these individuals when they finish their prison terms. The Department of Homeland Security's ICE budget in fiscal year 2017 was $6.2 billion (U.S. Department of Homeland Security 2016a).

What have these changes in policy meant for undocumented immigration? One indication of the impact of border enforcement is movements in the price for smuggling services. Most of those attempting to cross the U.S.--Mexico border hire a smuggler, known as a coyote, to serve as a guide through the desert and mountain regions of Arizona and Texas, where most undocumented immigrants now attempt to cross the border. Measures of coyote prices are available from the Border Patrol, which asks a subset of those apprehended whether they hired a coyote and the price paid; from the Mexican Migration Project (MMP), which surveys individuals in Mexico about their previous border-crossing experiences; and from the Survey of Migration on the Northern Border of Mexico (Encuesta sobre Migracion en la Frontera Norte de Mexico, EMIF Norte), which surveys migrants returning from the United States at bus stations and other transportation points in Mexico. (24) None of these sources are free of measurement problems. Border Patrol data are only available from those apprehended and questioned about their behavior, while the MMP and EMIF Norte are based on the selected sample of migrants who have returned to Mexico. Although average coyote prices differ across these sources, their time trends are similar (Roberts and others 2010). Border Patrol data show smuggler prices rising from $1,000 in 1999 to $1,600 in 2008 (in 2007 dollars). Using data from the MMP, Christina Gathmann (2008) estimates that a 10 percent borderwide increase in enforcement (measured in man-hours) increases the average smuggler price by 4.9 percent. Using this elasticity, the increase in Border Patrol manpower on the U.S.--Mexico border from 2007 to 2015 of 27.6 percent would have increased smuggler prices by 13.6 percent.

The cumulative effect of the U.S. enforcement buildup is hundreds of miles of new fencing, the rollout of technologically sophisticated border surveillance, a near quintupling of Border Patrol agents since the early 1990s, and the criminalization of illegal border crossings since the late 2000s. These changes combine with the recent compression in income differences between the United States and major sending nations to weaken incentives for low-skilled labor inflows.

II.C. Demographic Pressures far U.S. Immigration

In the 1970s, 1980s, and 1990s, macroeconomic shocks and relatively low incomes in Mexico and the rest of Latin America helped trigger labor flows to the United States. What sustained these flows over time was rapid growth in the relative labor supplies of these countries (Hanson and Mcintosh 2012). Whereas the U.S. baby boom came to a halt in the early 1960s, Latin America's baby boom did not abate until two decades later. Differences in the timing of the U.S. and Latin American demographic transitions mean that though the sizes of U.S. cohorts coming of working age began to slow in the early 1980s, they kept growing in Latin America until the 2000s, fueling pressures for emigration.

The relationship between labor supply growth and changes in U.S. migration appears in figure 11, which charts, for countries in Latin America and the Caribbean, the percent change in migration rates to the United States from 1980 to 2015 against the percent change in national birth cohort sizes over this interval. A strong positive relationship is evident, with the [R.sup.2] on the population-weighted linear fit equal to 0.45. As noted, the most important origin countries in terms of absolute number of current migrants residing in the United States are Mexico, El Salvador, Guatemala, the Dominican Republic, and Honduras. Mexico stands out in this group, with roughly 10 times the number of U.S. immigrants in the 15-40 age group as the next largest origin country in Latin America (figure 12). Mexico also stands out in terms of having the largest drop in migration between 2010 and 2015. Although most countries in Latin America see some decrease in the number of immigrants in this age group between 2010 and 2015, the number of Mexican-born individuals age 15-40 residing in the United States fell by more than 1.1 million over these five years. (25)

The durability of the decrease in migration from Mexico to the United States depends strongly on the reason it occurred. If the slowdown is due primarily to earlier shifts in population growth (Hatton and Williamson 2011), then given projected near constant U.S.--Mexico labor supply ratios, we may expect large-scale Mexican emigration to be a thing of the past. If the recent border enforcement buildup plays a significant role in the immigration slowdown (Gathmann 2008; Amuedo-Dorantes, Puttitanun, and Martinez-Donate 2013), then the pace of immigration from Mexico may be effectively in the control of the U.S. government. (26) Alternatively, if labor demand shocks are primarily responsible for the immigration slowdown (Villarreal 2014), the hiatus in high levels of immigration may end once the U.S. economy recuperates more fully.

To understand the causes of the decline in Mexican migration to the United States, we turn to data from the Mexican population census. We exploit variation in labor supply and per capita GDP across Mexican states to explain emigration. This analysis updates the work of Hanson and Craig Mcintosh (2010) to the 2000-10 period. (27) We count the base size of Mexican state-age-gender birth cohorts when they are first seen in the data, and use successive censuses to count the number of individuals remaining in Mexico each year. Because more than 95 percent of emigrants from Mexico go to the United States (Passel and Cohn 2009), and because we study young cohorts in which mortality is low, these numbers provide a usable estimate of net emigration to the United States from each Mexican state. To form our dependent variable, we aggregate individuals into three-year birth cohorts, and then calculate decadal changes in the percentage of the cohort that has emigrated, as measured by the change in its size. To investigate the role of labor supply in emigration, we include as a regressor the log ratio of the Mexican state birth cohort size to the U.S. birth cohort size. We restrict the analysis to individuals age 15-40, which is the age range during which most migration occurs. The regression specification is

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [dm.sub.icgt] is the change in the emigration rate for Mexican state i, birth cohort c, gender g, and census year t. To focus on low-skilled immigration, we take the log of the ratio of the Mexican state birth cohort size [N.sub.icgt] to the current U.S. native-born population with less than a high school education [N.sub.USgt]. Because we may be concerned that education decisions among U.S. natives are endogenous to Mexican immigration rates, we instrument for this ratio using the log ratio of the Mexican birth cohort to the entire respective U.S. birth cohort. Labor demand shocks are captured by the log ratio of GDP per capita in a Mexican state to the United States in the year that a cohort was age 16, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], as well as the log ratio of contemporary GDP per capita in a Mexican state to the United States, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], We select age 16 because it is a common year for entry into the labor market in Mexico; relative income in this year indicates prevailing economic conditions at a time when individuals first make choices about labor supply. To express labor demand factors in terms of deviations from trend changes in economic activity, we use residuals from a regression of the log ratio of Mexican state GDP per capita to U.S. GDP per capita on state-specific intercept and slope terms. To control for confounding shocks on migration, we include fixed effects for the Mexican state ([[alpha].sub.i]), gender ([[mu].sub.g]), birth cohort ([[eta].sub.c]), and census wave ([[rho].sub.t]).

The regression specification in equation 6 is motivated by the migration model of Borjas (2006), in which differences in relative labor supply combine with shocks to labor demand to create the incentive for the movement of labor between economies. Adjustment costs prevent migration from quickly equilibrating wages between regions, meaning that initial differences in labor supply--in particular, at the time a cohort enters the labor market--contribute to continuing pressure for migration in subsequent periods as a cohort ages. Hence, the migration rate is a function of initial labor supply and labor demand conditions, as well as subsequent innovations to labor demand.

The results of this analysis, presented in table 4, confirm a prominent role for labor supply in driving migration from Mexico to the United States. Column 1 shows the pooled results using all available census waves including 2010, column 2 excludes 2010, column 3 shows the results for males only, and column 4 shows the results for females only. In all cases, the log Mexico--U.S. labor supply ratio is positive and strongly statistically significant. The coefficient in the first column implies that a 10 percent increase in relative labor supply would translate into a 1.4 percentage point increase the decadal flow of net migration. The relationship is slightly weaker among women, with a coefficient approximately 70 percent as large as for men, but still very precisely estimated (t value of 9.1). The coefficient of 0.1441 in column 1 of table 4 combined with the doubling of the labor supply ratio between Mexico and the United States from 1970 to 2000 can more than explain the rise in the decadal net migration rate from 2.5 to 8.3 percent during this period. Now that U.S. cohorts are growing more rapidly than their Mexican counterparts, our results suggest that the drop in the average log labor supply ratio for a Mexican state to the United States, from -3.82 in 2000 to -3.73 in 2010, is responsible for more than four-fifths of the observed decrease in the decadal average net migration rate to the United States during that time interval (from 8.3 to 6.6 percent).

The effect of labor demand, as measured by the log ratio of GDP per capita for a Mexican state to the United States, is weaker and less stable. Contemporaneous GDP ratios are never significant and alternate in sign across specifications, while the GDP ratio at age 16 is consistently negative but significant only in the specifications that pool men and women. Surprisingly, it appears that this relationship becomes less pronounced during the Great Recession; when we exclude 2010, the fit becomes significant at the 1 percent level and the coefficient is almost four times as large in absolute value. (28) The relatively large swings in Mexican GDP during this period, as well as the fact that the recession occurred close to the end of the decade, may have dampened the sensitivity of migration to shocks during this interval. Nevertheless, positive income shocks to Mexican states (or negative income shocks to the United States) clearly have the overall effect of slowing migration.

How much of the migration slowdown can be attributed to the Great Recession? In trying to understand the labor demand effects of the Great Recession shock on migration, we conduct a simple simulation exercise. We use the marginal effect from the model estimated in column 2 of table 4--for the period preceding the Great Recession--to ask the out-of-sample question as to what would have happened to Mexico--U.S. migration if the United States had not experienced the Great Recession. We simulate the counterfactual log GDP ratios that would have occurred if the United States had remained on its long-term trend of GDP per capita. Because it is the GDP-at-age-16 variable through which income changes primarily affect migration, GDP shocks operate by altering the initial labor supply choices of individuals when they first enter the labor force: to seek work in Mexico or to move to the United States. The left panel of figure 13 shows the time series projection of U.S. GDP in the absence of the recession, and the right panel shows the actual and counterfactual log labor demand ratios that would have resulted. The right panel shows that the difference in log GDP ratios from actual versus predicted in 2010 opens up to about 0.06 = 1.25-1.19 log points, or 6 percentage points. This indicates that the total predicted effect on the migration rate for cohorts turning 16 after 2007 is 0.0042 = 0.06 x 0.07 log points, or roughly a half percentage point decrease in the decadal migration rate. Using the 2010 age cohort sizes and migration rates, there were 22 million Mexican-born individuals between the age of 15 and 25, and we would have expected 1.9 million of them to migrate to the United States. Adjusting the decadal migration rate downward by 0.5 percent for the decade that transpired between the Great Recession and the 2015 ACS, we would have expected a decrease in the total stock of migrants of 109,000 arising from the labor demand shock to those exposed to the Great Recession shock when 16 or younger. Given the results in the previous section illustrating that the stock of migrants in this age group fell by more than 1.1 million between 2010 and 2015, it would appear that labor demand shocks as captured by GDP per capita can explain only a modest portion of the reversal in migration flows.

[FIGURE 13 OMITTED]

To what extent are other factors, such as the ramp-up in enforcement at the border, responsible for the decreases in Mexico--U.S. migration between 2007 and 2015? We attempted to investigate the role of border enforcement using an instrumentation approach that first calculated the share of migrants from each Mexican state apprehended in each Border Patrol sector in the earliest available year, 1999. We then multiplied this sector- or state-specific enforcement incidence by an index of overall Border Patrol effort, the number of Border Patrol "linewatch" hours per year. The resulting instrument proved to be strongly positively correlated with Mexican state emigration rates, indicating that despite our effort to exogenize enforcement, it may be so strongly endogenous to migration that one cannot estimate a credible long-term impact of border enforcement on successful crossings. Our compromise, reduced-form approach described above omits direct measures of enforcement, whose effect on migration may therefore be absorbed by other covariates. How may the exclusion of enforcement affect our results? One possibility is that that enforcement responds endogenously to relative GDP ratios, in which case it is captured by the reduced-form relationship between GDP per capita and migration (Hanson and Spilimbergo 2001). A second possibility is that enforcement is orthogonal to our core explanatory variables, and hence remains in the residual. A third possibility is that omitted enforcement variation is incidentally correlated with changes in labor supply, in which case its effects load onto this variable. In any case, it appears clear that the push factors driving migration from Mexico to the United States have abated sharply during the past decade, and hence the marginal effectiveness of border enforcement spending in terms of prevented crossings is falling.

Taking our results at face value, the analysis suggests that labor supply shocks play a major role in driving low-skilled immigration flows in the United States. This fact, combined with the relatively predictable nature of future population growth, provides an opening for predictive analysis. We therefore turn next to a forecasting exercise using data from all the Latin American sending countries to assess U.S. immigration pressures decades into the future.

II.D. Summary

From the early 1980s to the mid-2000s, there were robust pressures for low-skilled immigration in the United States. U.S. incomes for low-skilled workers far exceeded those in migrant-sending nations; the U.S. macroeconomy was considerably more stable than Latin America's; and enforcement against illegal entry, though not entirely lax, permitted large inflows to occur. These conditions changed abruptly after the Great Recession. Gaps in the level and volatility of income between the United States and migrant-sending nations have compressed, while there has been an extensive buildup in U.S. immigration enforcement. Despite these recent changes in the pattern of relative income growth, it appears that changes in relative labor supply growth have mattered the most for current trends in U.S. immigration.

III. Low-Skilled Immigration in the Long Run

It may be tempting to view the period since the Great Recession as a temporary pause in the U.S. immigration wave that began in the 1970s. After all, U.S. incomes for low-wage labor are still roughly twice those in Mexico, and are even larger when compared with those of other sending nations in Latin America. Should not high levels of immigration resume once the U.S. economy returns to a period of normal growth? Such a perspective downplays both the recent increase in U.S. enforcement and the demographic determinant of recent U.S. labor inflows from the Western Hemisphere. Looking forward, demographic pressures for U.S. immigration are set to weaken significantly. In this section, we construct a model of long-run changes in U.S. immigration, which we use to project U.S. labor inflows in coming decades. We then characterize how changes in low-skilled immigration may affect labor market conditions in the United States.

III.A. A Predictive Analysis of Future Migration from Latin America to the United States

To evaluate the effects of future demographic change on U.S. immigration, we turn to the national level and incorporate the long-term population growth forecasts for countries in the Western Hemisphere provided by the United Nations' World Population Prospects. (29) We examine how immigration from Latin American countries may have changing effects on U.S. labor inflows in coming decades. Recognizing that future migration episodes will also be driven by unanticipated economic and political shocks, differential demographic growth estimates for the next 15 years provide one of the clearest lenses on the future that is available. Labor supply provides a uniquely forecastable component of migration pressures: The cohorts that will enter the labor force in the next 16 to 20 years have already been born, and changes in cohort sizes for the next two decades can be predicted relatively accurately using current trends in fertility. (30)

[FIGURE 14 OMITTED]

A simple visual perspective on the issue is given in figure 14, which plots observed and projected population relative to the United States for major sending countries from 1980 to 2050, where we normalize 1980 values to 1. The most striking demographic transition is in El Salvador; having reached a peak in relative labor supply in 2010, its population relative to the United States is projected to decline rapidly in the future, reaching 1980 levels again by 2050. (31) Mexico follows a similar temporal pattern, but with a slower future decline. Guatemala and Honduras have seen similarly steep increases in relative labor supply, reaching roughly 250 percent of their 1980 values by 2015. The future experiences of these two Central American countries diverge strongly, with Guatemala's relative labor supply continuing to grow almost linearly for another 25 years, whereas Honduras's supply begins to decline immediately. Continuing robust labor supply growth in Guatemala may allow it to partially replace diminished U.S. migrant inflows from other Latin American countries. However, given Guatemala's small size--its 2015 population was 16 million, compared with Mexico's population of 127 million--its migrant-sending capacity is limited.

To use population forecasts as the basis for a predictive model of future U.S. immigration, we first calculate five-year birth cohort ratios in the historical (census) and future (United Nations) data in the same manner, and project future GDP based on growth forecasts from the International Monetary Fund so as to be able to take log GDP per capita ratios. Using data for the 25 available countries in Latin America and the Caribbean, we estimate the model using observed migration rates from 1980 to 2015, and use the resulting parameters to project age-gender-country--specific migration rates through 2040. In order to capture the dramatic shift in immigration enforcement that occurred between 1990 and 2000, we estimate a trend-break model that fits piecewise linear time trends to the "low enforcement" era preceding 2000 and the "high enforcement" era starting in 2000. (32) Because we want to estimate effects for the full age distribution of immigrants in the United States, we use all available age cohorts and not just those of young workers. The estimating equation is

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Here, [m.sub.icgt] is the net migration rate to the United States for source country i, age cohort c, and gender g, at the time of census wave t. Regressors include the log ratio of the origin-country birth cohort to the U.S. birth cohort ([N.sub.icg]/[N.sub.UScg]) and the contemporaneous log GDP ratio of the origin-country's GDP per capita to U.S. GDP per capita ([GDP.sub.it]/[GDP.sub.USt]). We include fixed effects for the origin country ([[alpha].sub.i]), the age cohort ([[eta].sub.c]), and gender ([[mu].sub.8]). We let time trends (and trend breaks) be specific to the origin country by allowing each country to have separate intercept and time trend terms within the low-enforcement and high-enforcement eras. First, we interact the country fixed effect with a dummy variable indicating the year 2000 and later ([[delta].sub.2t]), then we interact the fixed effect with a 1980-90 trend ([t.sub.i]), and finally with a second term picking up the high-enforcement 2000-15 time trend ([t.sub.2]). We predict over the interval 2020-40, meaning that we forecast for the same number of periods as are used to estimate the post-enforcement trend. In using a broad set of age cohorts (age 2-67), we partition the regression to estimate separate coefficients for the young (age 2-37) and the old (age 42-67), given the divergent migration trajectories of these two groups.

The parameter estimates for the central parameters in the cross-country regression for Latin America and the Caribbean are given in table 5, where we suppress the large number of country-level intercept and slope interactions. The regression results contain several noteworthy features. First, the strong push factor of large cohort size is experienced entirely before age 40, after which there is no significant relationship between the log birth cohort ratio and net migration rates. Second, the effect of GDP ratios flips across ages; for the young cohorts, high income in the origin country has no effect on migration, whereas for the older cohorts, high origin-country income accelerates migration. This latter result is consistent with gravity model estimates of bilateral migration (Clark, Hatton, and Williamson 2007). It could be explained by migration costs being a greater constraint to migration across Latin America as a whole than in Mexico, with positive income shocks enabling migration by credit-constrained individuals (Mckenzie and Rapoport 2007).

[FIGURE 15 OMITTED]

Having estimated the model on decadal changes in the migration rate, we then predict the net migration rate for future decades, using the International Monetary Fund's GDP forecasts and UN population growth forecasts for future decades. We maintain the time trends estimated on data for 2000 and later, such that we presume the strong immigration enforcement regime stays in effect. The results are shown in figure 15. With this predicted future migration rate in hand, we multiply these by the UN-projected future birth cohort sizes to calculate predicted migrant counts for each cohort. These values are then summed up to obtain migration totals for each country in each year.

[FIGURE 16 OMITTED]

As seen in figure 15, this empirical structure predicts declining net migration rates from Mexico over the coming decades, with other major Latin American destinations seeing roughly constant rates. Figure 16 shows that Mexican-born migrant stocks in the key age 15-40 group are predicted to drop to less than half their current level by 2040. Rather than showing that the Great Recession has caused a temporary pause in an ongoing wave of immigration from Mexico, these long-term trends suggest that the 1990-2007 housing boom may have caused a temporary surge in migration, arresting a demographically driven long-run slowing. (33) Given the strong role that demographic factors play in our estimation model, convergence in fertility rates across the Americas removes a powerful factor pushing workers across borders. We find little support for the idea that Latin American immigration will surge again as the U.S. economy recovers.

Our focus on the declining population of migration-age individuals overlooks an important role that Mexican-born individuals will play in American demographics. In a manner even more pronounced than for Mexico itself--which has recently undergone a rapid demographic transition (Tuiran and others 2002)--the U.S. Mexican-born population will age very quickly. We can draw frequencies of Mexican-born individuals in our data, starting with the observed numbers in 1980 and 2015, and then plot the predicted values in 2040, as shown in figure 17. Whereas the modal Mexican-born resident in the United States was 20 years old in 1980 and 40 years old in 2015, he or she will be almost 60 years old by 2040. Rapid aging arises from the confluence of declining fertility in Mexico and the demographic amplifier of emigration, which pushes a larger share of larger cohorts into the United States and therefore accentuates the implications of Mexico's demographic transition for the age structure of the Mexico-born population on the U.S. side of the border. A large elderly population of undocumented immigrants is a policy challenge that the United States has hitherto not faced.

[FIGURE 17 OMITTED]

Stepping back to examine the age distribution of all Latin American immigrants, we see broad evidence of an aging population in the United States. Table 6 illustrates that the total Latin American--born population under 40 in the United States by 2040 will be only 56 percent of its current size (4.9 million versus 8.8 million), while the foreign-born population over 40 will be 235 percent of its current size (22.9 million versus 9.8 million). The model predicts a negative net migration rate for some counties of origin in 2040 (negative values are not possible in practice; but in our linear predictive model, they indicate a phenomenon that could be interpreted as net migration pressure out of the United States). (34) The main policy question posed by first-generation immigrants from Latin America and the Caribbean thus appears likely to shift from one of the labor market effects of large-scale labor inflows to one of the cost of social programs and health care for an elderly immigrant population with relatively low incomes (and relatively low rates of naturalization when compared with high-skilled immigrants).

III.B. Changes in Low-Skilled Immigration and U.S. Labor Market Tightness

We have seen that incentives for low-skilled immigration in the United States have changed markedly since the early 2000s, and have already manifested demographic pressures that are likely to compress migration inflows in coming decades. How will these developments affect the U.S. economy? A reduction in the relative supply of low-skilled labor, by putting upward pressure on wages for these workers, may operate directly by causing changes in the U.S. wage structure (Borjas 2003). Alternatively, wage pressures may induce firms to alter their production techniques in a manner that mitigates the wage effects of shocks to the relative labor supply by generating endogenous changes in labor demand (Lewis 2011). Whichever form labor market adjustments take, the magnitudes of these adjustments are likely to be determined by the implicit pressure of changes in immigration inflows on U.S. wages, which we analyze next.

As a final exercise, we consider how the United States' demand for and supply of labor have evolved over time and how the supply of low-skilled, foreign-born workers meshes with these changes. Our approach employs the methodology of Katz and Murphy (1992), as applied by Autor, Katz, and Kearney (2008), to examine the relative earnings of more- and less-skilled workers. The exercise we perform allows us to translate the recent slowdown in low-skilled immigration into implied pressures on the wage premium enjoyed by skilled workers.

Consider a production function with constant elasticity of substitution that takes as its arguments the employment of low-skilled and high-skilled workers, where within each skill group we treat native-born and foreign-born workers as perfect substitutes, as is consistent with recent evidence (Borjas, Grogger, and Hanson 2012). (35) From the first-order conditions for firm profit maximization, we obtain an expression for the relative wages of high-skilled and low-skilled labor,

(8) log([w.sub.ht]) - log([w.sub.lt]) = [[gamma].sub.0] + [[gamma].sub.1][log([N.sub.ht]) - log([N.sub.lt])] + [[gamma].sub.2][X.sub.t]+ [[epsilon].sub.t],

where log([w.sub.ht]) - log([w.sub.lt]) is the log U.S. wage for high-skilled workers relative to the log U.S. wage for low-skilled workers, log([N.sub.ht]) - log([N.sub.lt]) is the log U.S. supply of high-skilled workers relative to the log U.S. supply of low-skilled workers, and [X.sub.t] is a vector of controls that capture labor demand shocks. (16) Each skill group is made up of a combination of native-born and foreign-born labor. By taking the difference in earnings between skill groups in equation 8, we remove from the specification labor demand shocks that are common to high-skilled and low-skilled workers (for example, aggregate changes in labor demand associated with recessions, and growth in total factor productivity). Following Autor, Katz, and Kearney (2008), within each skill group we measure wages as average weekly earnings--holding constant the age, gender, and racial composition of workers--and we measure employment in terms of labor supplies expressed in PEUs. High-skilled workers are those with at least a college education, whereas low-skilled workers are those with a high school education or less. We estimate equation 6 with annual data from the CPS for the period 1963-2007, and we use the results to predict relative earnings for the period 1963-2015, which includes the out-of-sample range 2008-15.

In our baseline specification for equation 8, which includes a time trend as the only additional covariate, the coefficient estimate for [[gamma].sub.1] is -0.42 (with a t value of 9.9) when we define the low-skilled group to be workers with a high school education or less; and it is -0.18 (with a t value of 8.0) when we define the low-skilled group to be workers with strictly less than a high school education. Consistent with the theory underlying equation 8, increases in the relative supply of skilled labor drive down the wage premium for skill. These estimates change little when we expand the period from 1963 to 2015 or include the following additional covariates: a quadratic time trend, the aggregate unemployment rate, and the log real federal minimum wage. (37) The first coefficient--for the impact of relative labor supply on the wage gap between college- and high school--educated workers--compares in value with the estimates given by Autor, Katz, and Kearney (2008) of -0.40 to -0.62, depending on the covariates included, for the period 1963-2005, suggesting that our coefficient estimates are at the low end of those obtained in previous empirical work.

[FIGURE 18 OMITTED]

Figure 18, which presents the results, shows three series for relative earnings: the actual skill premium for the period 1963-2015; the projected skill premium for 1963-2015 based on equation 6, using coefficients estimated on data for 1963-2007; and a counterfactual projection of the skill premium, where we again use the estimation results for equation 8, but now replace the relative labor supplies we feed into the projection with a counterfactual series in which we assume that the number of low-skilled immigrant workers grows at the same rate from 2008 to 2015 as it does for 1994 to 2007. For the out-of-sample period 2008-15, the first projection is based on observed changes in the relative supply of skilled labor (which embody actual changes in both high-skilled and low-skilled immigration), whereas the second projection is based on the observed labor supply through 2007 and the counterfactual supply thereafter (which suppresses the slowdown in low-skilled immigration).

In constructing the counterfactual projection, it is worth noting that inflows of both low-skilled and high-skilled immigrants slowed after 2007. Our counterfactual labor supply series, by imposing continued growth for low-skilled but not for high-skilled immigration, thus understates the post-2007 growth in the relative supply of skilled labor. The resulting counterfactual projection of the skill premium therefore corresponds to an artificial setting, which we view as useful for describing the magnitude of the low-skilled immigration slowdown in terms of wage pressures but not for evaluating the impact of immigration on earnings during this period. (38)

For low-skilled workers defined to be those with less than a high school education (the left panel of figure 18), the actual skill premium is flat from the early 1960s to the late 1970s, rises steadily from the late 1970s to the mid-2000s, and is flat again thereafter. During the within-sample period 1963-2007, the predicted skill premium rises more slowly than the actual skill premium in the mid-1970s, suggesting that the relative demand for skill rises more slowly than the linear trend would indicate, and rises more rapidly than the actual skill premium from the late 1970s to the late 1990s, suggesting growth in the demand for skill that exceeds the linear trend during this interval.

Turning to the out-of-sample period 2008-15, the post-2007 slowdown in immigration tempers growth in the supply of low-skilled labor, causing the predicted skill premium to rise more slowly after 2007 than before. Replacing actual relative labor supplies with the counterfactual series that assumes sustained growth in low-skilled immigration (that is, a 2007-15 annual growth rate equal to the 1994-2007 annual growth rate), the projected path of the skill premium naturally lies above the projected path based on observed data. If low-skilled immigration had not slowed after 2007, the relative supply of skilled labor would have grown more slowly, which in turn would have mandated a larger increase in relative earnings for skilled labor. The difference between the two projected wage series in 2015 is 8.6 log points, which indicates that the magnitude of the slowdown in low-skilled immigration--holding all else equal, including high-skilled immigration--is consistent with a decrease in the skill premium of 1.1 percent a year during the 2007-15 period. To put this magnitude in context, the observed increase in the wage premium for college-educated workers versus workers with less than a high school education during the 1980-2007 period of rapidly rising wage inequality is 1.6 percent a year. Again, we do not take this value to be the true change in wages due to the immigration slowdown (because we are not addressing changes in high-skilled immigration), but rather as an indication of the magnitude of the immigration-induced change in the labor supply expressed in terms of wage pressures.

When we instead define low-skilled workers to be those with a high school education or less (right panel of figure 18), the broad patterns for the actual skill premium are similar, though the flattening in the premium during the 2000s is less pronounced and the absolute premium is smaller. For the out-of-sample period 2008-15, it is again the case that the projected skill premium based on actual labor supplies lies above the observed skill premium, indicating an increase in the demand for skill that is less than the linear trend. Comparing this projected skill premium with that which obtains when using counterfactual labor supplies (involving no post-2007 slowdown in immigration), the latter exceeds the former by 6.1 log points in 2015, or a difference of 0.8 percent a year during the period 2007-15. To put this magnitude in context, the observed increase in the wage premium for college-educated workers versus workers with a high school education or less for 1980-2007 is 1.1 percent a year. Because low-skilled immigrants are a smaller share of the skill group with a high school education or less than of the skill group with strictly less than a high school education, the implied wage pressures of the immigration slowdown are weaker when we move to this more expansive definition of being low-skilled. Similar patterns are observed when we restrict the sample from all industries (figure 18) to low-skill industries (figure 19).

III.C. Summary

The U.S. immigration wave of the late 20th century was enabled to a substantial extent by the rapid growth of the labor supply in Latin America and the Caribbean relative to the United States. Because labor supply growth in migrant-sending nations is slowing and will continue to slow, the demographic push for U.S. immigration is abating. Abetting these demographic forces is the substantial increase in U.S. immigration enforcement, which thus far has been maintained. Absent economic or political crises in the Western Hemisphere that reignite international migration, standard migration models predict that migration rates from major U.S.-sending nations will drop sharply in coming decades. Indeed, the weakening of these migration pressures began in the early 2000s, and may have been masked by the temporary labor demand boost provided by the U.S. housing boom. The resulting post-2007 slowdown in low-skilled immigration is of a magnitude consistent with a decrease in the wage gap between high-skilled and low-skilled U.S. labor of 6 to 9 percentage points. If, as predicted by demographic forces, low-skilled immigration continues to decline in future decades, U.S. firms--especially those located in U.S.--Mexico border states and in the immigrant-intensive industries of agriculture, construction, eating and drinking establishments, and nondurable manufacturing--are likely to face pressure to alter their production techniques in a manner that replaces low-skilled labor with other factors of production.

[FIGURE 19 OMITTED]

IV. Looking Forward

From the early 1970s to the early 2000s, the United States experienced an epochal wave of low-skilled immigration, which was the combined result of relatively high U.S. incomes, relatively stable U.S. GDP growth, relatively slow U.S. labor supply growth, and moderately permissive immigration enforcement. Since the mid-2000s, each of these drivers has attenuated. The U.S. macroeconomy is no longer so stable relative to migrant-sending countries; U.S. labor supply growth is now similar to that in much of the Western Hemisphere; and the U.S. borders, having been heavily fortified, are much harder to cross without a visa.

The future of low-skilled immigration thus appears to be less about streaming inflows of young workers from lower-income nations and more about the needs of an aging population of lower-income adults that is settled in the United States. Those within this group who are undocumented--somewhere between one-half and three-fifths--do not qualify for most federally funded welfare benefits, including Medicare and Medicaid. In recent decades, the primary fiscal effects of low-skilled immigration were the cost of primary and secondary education for the children of immigrants, and, to a lesser extent, for publicly funded health care for the subpopulation of this group that was born in the United States (Blau and Mackie 2016). Judith Treas and Zoya Gubernskaya (2015) document that 51 percent of the foreign-born population is covered by some form of public insurance, as compared with 35 percent of the native born, suggesting that the costs of caring for the foreign born are likely to fall disproportionately on publicly funded programs. Given our estimates of an increase of 13 million (134 percent) in the population of foreign-born immigrants over the age of 40 by the year 2040, there may be considerable growth in the demand for safety net programs as a result of past and future immigration. Under existing financing rules, U.S. states and localities would be the entities primarily responsible for shouldering these costs.

In light of the changing demographics of migrant-sending nations, and the apparent effects of the existing immigration enforcement surge, the current emphasis of the U.S. government on further intensifying immigration enforcement is puzzling. One interpretation of the planned enforcement buildup is that it is driven by politics. Having lived through the great immigration wave of the last 35 years, some native-born voters may be upset by the laxity of past enforcement and willing to reward politicians who are seen as atoning for these transgressions. Supporting stronger enforcement may be a way for politicians to signal their disapproval of earlier policy choices. Such signaling would come at a substantial cost, however, given that the U.S. immigration enforcement budget now exceeds $20 billion a year. Another interpretation is that intensifying enforcement is an effort to forestall future claims on public resources. The aging of the low-skilled, foreign-born population means that by increasing deportations today--when many low-skilled immigrants are approaching middle age--the United States may avoid demand for social spending in the future. If U.S. voters oppose providing public benefits to low-skilled immigrants--and if the U.S. government cannot credibly commit to deny benefits to low-income, elderly, foreign-born residents down the road--then expanding current deportations may reduce the expected drain on U.S. public coffers in later decades. (39) The cost of these extra deportations--beyond the incremental spending on enforcement--includes reducing the supply of workers who are in their prime earning years, who have accumulated substantial U.S. labor market experience, and who are well established in their communities.

Changes in U.S. immigration policy affect not just the U.S. economy but also the economies of migrant-sending nations. To the extent that immigration enforcement has played a dominant role in the recent slowdown in migration, improvements in the welfare of U.S. workers come in part at the cost of potential migrants who forgo higher wages, and their nonmigrant compatriots, who now face more crowded labor markets at home. Because the modal immigrant from Mexico would be a middle-income earner at home, expanding deportations and tightening border security would tend to expand labor supplies and depress earnings in the middle of Mexico's wage distribution (and from higher quantiles of the wage distributions in other sending countries for migrants). From the perspective of those born in sending countries, wages take a hit from immigration restrictions whether or not workers decide to migrate.

Mexico, by virtue of its status as a transit country for undocumented immigrants, is doubly exposed to changes in U.S. immigration enforcement. Many Central Americans planning to enter the United States traverse Mexico illegally on their way north. Stronger U.S. enforcement may have the indirect consequence of increasing the supply of undocumented Central Americans seeking to live and work in Mexico. Given that Guatemala is the one major U.S. migrant-sending nation in the Western Hemisphere that will continue to experience high rates of labor supply growth in coming decades, Mexico faces the real possibility that continued tightness in U.S. immigration policy would increase its supply of low-skilled, foreign-born residents.

Taking immigration controls as a means to improve the plight of low-skilled U.S.-born workers, how would we expect the incidence of benefits to stack up against alternative policies? An increase in minimum wages may benefit those with jobs that pay equilibrium wages above a higher wage floor, at a cost to consumers who purchase labor-intensive goods and services and to workers excluded from the labor market. Investments in skill development and retraining may target native-born workers more finely, but the effectiveness of such programs is in question (LaLonde 1995). The attractiveness of immigration restrictions relative to these alternative policies also depends on the extent to which we take the welfare of the foreign-born into account. Immigration controls therefore appear to be a prolabor instrument that comes at a high cost to consumers and foreign-born workers relative to alternative potential policies.

It may be premature to declare that the most recent episode of high U.S. immigration is over. Many factors could cause the population of low-skilled immigrants in the United States to begin growing again. Prime among these is increased economic or political instability in the Western Hemisphere. Indeed, heightened insecurity in Central America, due in large part to violence associated with organized crime, appears to have increased recent labor outflows from the region. Mexico, for its part, has not had a financial crisis since 1995. The reform of the country's electoral laws in 1997 created a political process that is competitive and free of the vote rigging that marred the Institutional Revolutionary Party's 70-year rule during the 20th century. However, the openness of Mexico's economy leaves it vulnerable to external shocks, in particular in the United States, which is the destination for more than 80 percent of its exports. At least in the short to medium runs, the U.S. government itself seems to be in a position to determine--whether through its trade or its immigration enforcement policies--the potential supply of low-skilled immigrants.

ACKNOWLEDGMENTS We thank Janice Eberly, Adriana Kugler, Edward Lazear, James Stock, and the participants in the Spring 2017 Brookings Panel on Economic Activity for helpful comments on a draft of this paper; Daniel Leff for excellent research assistance; and the Center on Global Transformation at the University of California, San Diego, for financial support.

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GORDON HANSON

University of California, San Diego

CHEN LIU

University of California, San Diego

CRAIG MCINTOSH

University of California, San Diego

Conflict of Interest Disclosure: The authors received financial support for this work from the Center on Global Transformation at the University of California, San Diego. With the exception of the aforementioned affiliations, the authors did not receive financial support from any firm or person for this paper or from any firm or person with a financial or political interest in this paper. They are currently not officers, directors, or board members of any organization with an interest in this paper.

(1.) Noncitizens (including legal immigrants) convicted of an aggravated felony, a drug crime, or multiple crimes involving moral turpitude are subject to deportation upon or before completion of their prison sentence. Deportations of criminal aliens also increased in the 2000s, from 73,000 in 2001 to an average of 156,000 per year over 2007 to 2015. See Gonzalez-Barrera and Lopez (2016).

(2.) Other literature on the effects of low-skilled immigration in the United States examines its consequences for local consumer prices (Cortes 2008), the labor supply of high-skilled, native-born women (Cortes and Tessada 2011), local housing prices (Saiz 2007), state GDP growth (Edwards and Ortega 2016), cultural diversity (Ottaviano and Peri 2005), and occupational employment and wages of native-born workers in local labor markets (Burstein and others 2017).

(3.) We define high school education to mean completing 12 years of school, whether or not a degree is granted, a convention we adopt because the meaning of a high school degree varies across countries. Throughout the paper, we use high school education and 12 years of schooling interchangeably.

(4.) Education is, of course, an imperfect definition of skill. Language barriers and occupational licensing present obstacles to foreign-born workers in integrating themselves into the U.S. labor force, which may induce some immigrants to downgrade occupationally by taking jobs for which, based on their observable skills, they would appear overqualified (Lazear 1999, 2007; Dustmann, Frattini, and Preston 2013).

(5.) Half of the 1970-90 increase in low-skilled immigration from Asia (55.1 percent) is from Southeast Asia, with much of this inflow associated with a substantial but temporary rise in U.S. refugee admissions from the region that occurred following the end of the Vietnam War.

(6.) The question for length of U.S. residence in the ACS reads, "When did this person come to live in the United States?" with the instruction, "If this person came to live in the United States more than once, print latest year."

(7.) When applying wage-based weights to the entire population, we assume that nonworking individuals would earn the same average wage as full-time workers who share their age, gender, race, education, and nativity profile. Because employment rates increase with potential earnings, this assumption may lead our productivity-adjusted shares of the low-skilled immigrant population to overstate the shares one would calculate based on "true" wage weights. This problem is partially ameliorated when we examine the share of low-skilled immigrants in total hours worked, as we do in figure 4.

(8.) We construct these weights as follows. First, we divide workers into labor market groups broken down by gender, two education categories (less than 12 years of education, exactly 12 years of education), and eight experience categories (0-4, 5-9, 10-14, 15-19, 20-20, 25-29, 30-34, and 35-39 years of potential labor market experience). Then, for each gender-education-experience group, we calculate the weight as average weekly earnings in each year (for full-time, full-year workers, defined to be those working at least 35 hours per week and 40 weeks a year) divided by average weekly earnings for white, male, high school graduates with 8 to 12 years of labor market experience.

(9.) The number of Mexican-born workers in the United States increased by more than 350,000 per year over the 20 years from 1980 to 2000. Negative net migration of 160,000 per year subsequent to 2007 therefore represents a drop of half a million people per year relative to the prior trend, enough to constitute a noticeable change in the foreign-born population when cumulated over a decade of low migration.

(10.) Also on the selection of immigrants from Mexico in terms of observable skill, see Feliciano (2001), Orrenius and Zavodny (2005), Mckenzie and Rapoport (2007, 2011), and Akee (2010).

(11.) This method for constructing weights ignores differences in labor force participation rates in the two countries. Whereas labor force participation among male residents of Mexico and male Mexican immigrants in the United States are similar, labor force participation is higher among immigrant Mexican women than among nonmigrant Mexican women. Not accounting for these differences would tend to overstate negative selection among immigrants. See Chiquiar and Hanson (2005) for details and for methods to account for cross-national differences in labor force participation.

(12.) One exception to this pattern is Puerto Rico, which as an unincorporated territory of the United States is not subject to the same barriers to U.S. immigration as foreign nations (Borjas 2008).

(13.) Since Rosenzweig (2007) examines legal immigrants, his figures are not directly comparable to those of Hanson (2006) or Clemens, Montenegro, and Pritchett (2008), whose samples include all immigrants.

(14.) Suppose log income is normally distributed with mean [mu] and variance [[sigma].sup.2]. Given an estimate of the Gini coefficient G, the standard deviation of log income is [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] The value of log income at the a quantile is then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [z.sub.[alpha]] is the [alpha]th percentile of N(0,1).

(15.) Because Gini coefficients are not available in all years, we interpolate values for missing years. The series on Gini coefficients ends in 2012 in some countries and in 2013 in others. We assume that Gini coefficients in later years equal those in the last year for which data are available.

(16.) In 2000, the share of U.S. low-skilled, working-age immigrants accounted for by these countries is 15.0 percent (4.1 percent for El Salvador, 2.8 percent for the Dominican Republic, 2.3 percent for Guatemala, 1.7 percent for Jamaica, 1.6 percent for Colombia, 1.3 percent for Honduras, and 1.1 percent for Ecuador). Gini coefficients are unavailable for Cuba and Haiti (2.5 and 1.5 percent of U.S. low-skilled immigrants in 2000, respectively), leading us to leave them out of figures 8 and 9. Significant sending nations for U.S. low-skilled immigrants outside the Western Hemisphere (and their shares of this population in 2000) include Vietnam (4.1 percent), the Philippines (2.2 percent), China (2.1 percent), South Korea (1.5 percent), Germany (1.4 percent), Italy (1.2 percent), Canada (1.2 percent), India (1.2 percent), and Poland (1.1).

(17.) A refugee is a foreign resident who is unable or unwilling to remain in his or her country of nationality because of fear of persecution based on race, religion, social group, or political opinion; an asylee is a foreign national who meets the conditions of a refugee and is already in the United States. A refugee is eligible to apply for a green card after one year of U.S. residence. At the beginning of each fiscal year, the president, in consultation with Congress, sets a worldwide ceiling on refugee admissions.

(18.) All data on legal immigration are from the U.S. Department of Homeland Security's Yearbook of Immigration Statistics (https://www.dhs.gov/immigration-statistics).

(19.) Regarding admission of permanent legal residents from nations in the rest of Latin America and the Caribbean, green cards issued have risen from 50,000 per year in the 1970s, to 180,000 per year in the 1980s, to 205,000 per year in the 1990s, and to 250,000 per year since 2000.

(20.) That is, if a current H-2 visa holder desires to return on an H-2 visa in the following year, he or she must return to his or her country of residence and seek admission out of the following year's visa allocation.

(21.) As of the mid-2000s, approximately 45 percent of undocumented immigrants in the United States appeared to be visa overstayers (many of whom do not remain in the United States in the longer term). See Pew Research Center (2006) and U.S. Department of Homeland Security (2016b) for estimates of annual overstay rates by country.

(22.) The Alien Transfer Exit Program repatriates Mexican nationals through geographic areas different from their attempted point of entry (Argueta 2016).

(23.) Changes in interior enforcement are important, in light of the fact that about two-fifths of undocumented immigrants may have entered the country on legal visas, which they subsequently overstayed (Passel and Cohn 2016). By increasing border and interior enforcement simultaneously, the Department of Homeland Security may reduce incentives for border crossers to become visa overstayers.

(24.) For the methodology of the Mexican Migration Project, see http://mmp.opr.princeton.edu/research/design-en.aspx; and for EMIF Norte, see http://www.colef.mx/emif/eng/bases_metodologicas.php.

(25.) Our data indicate that the total number of Mexican-born individuals in the United States of all ages fell by 272,000 from 2010 to 2015, roughly in line with the estimate from Gonzalez-Barrera (2015) using data from the Mexican National Survey of Demographic Dynamics (Encuesta Nacional de la Dinamica Demografica, ENADID) that the United States lost 141,000 Mexican-born individuals from 2009 to 2014. This muted change relative to the population age 15-40 indicates both that the young are more sensitive to changes in conditions than the old, and foreshadows the results later in this section that the population of older Mexicans will continue to grow even once the number of younger individuals starts to fall (Giorguli-Saucedo, Garcia-Guerrero, and Masferrer 2016). Due to how mortality increases with age, our measure of net migration (differences between migrant numbers and birth cohort size) becomes less reliable as cohorts become older.

(26.) Other factors driving migration from Mexico to the United States in recent decades include Mexican policy reforms in the 1990s that privatized land rights, which allowed rural residents to sell their land, or to leave for urban areas without fear of relinquishing their claim to communal land (de Janvry and others 2015).

(27.) Although the 2015 Mexican micro census Conteo de Poblacion y Vivienda should permit a similar exercise to be conducted, we found the resulting population estimates to be too noisy to use. Hence, the analysis uses data only through 2010.

(28.) Villarreal (2014) also finds declining trend migration and a weak discontinuous effect of Mexican and U.S. GDP on migration during the Great Recession. His analysis suggests that migration tracks U.S. employment rates quite closely during this time period, but due to endogeneity concerns we do not pursue this control for economic conditions.

(29.) To avoid circularity in studying how future population growth will drive migration from countries whose population will in turn be determined by migration, we use the UN's "no migration" population forecast, which ignores as-yet-unobserved future migration in its projected population estimates.

(30.) Many migration episodes, such as the recent surge of Syrians into Europe and the arrival of Vietnamese immigrants in the United States in the late 1970s, were driven by shocks other than labor supply. Some shifts in labor supply, such as the rapid fertility decreases in Catholic Southern Europe and Latin America, were not forecasted. Nonetheless, given our lack of ability to anticipate future income shocks, demographic differentials remain an attractive way of predicting medium-term migration trends.

(31.) Because the U.S. population is growing, declines in these relative population size ratios do not imply absolute declines in the populations of origin countries.

(32.) These trend breaks (which we allow to be country-specific) are consistent with the inclusion of time period fixed effects in the first-differenced model in equation 6. We move from first differences in equation 6 to levels in equation 7 to accommodate forecasting immigrant stocks.

(33.) Despite using a much longer panel and a different estimation structure than that used by Hanson and Mcintosh (2016), these results confirm these previous predictions that new inflows of working-age Mexicans will drop substantially by the middle of the 21st century.

(34.) Negative net migration rates are an artifact of the linear model used to forecast future flows. Our model predicts only 14 percent of the dyads to have negative net migration in 2020, but future decreases in population growth in sending countries drive the share of predicted negative dyads to 24 percent by 2040.

(35.) The fact that the CPS does not include measures of nativity until 1994 makes this assumption a necessity if we are to estimate equation 6 based on time series variation.

(36.) This estimation approach makes the strong assumption that labor is freely mobile across occupations. See Burstein and others (2017) for an analysis that uses a Roy (1951) model in the analysis of how immigration affects labor market outcomes at the occupation level.

(37.) The time trend carries a positive coefficient, indicating a positive trend in the relative demand for skilled labor; the unemployment rate carries a negative sign but is imprecisely estimated; and the minimum wage enters negatively, indicating that a higher minimum wage compresses the skill premium. The assumption that the time trend for relative labor demand is linear over the course of several decades is of course quite strong. Nevertheless, allowing for a quadratic time trend has minimal impact on the estimate of [[gamma].sub.1].

(38.) For analyses of the impact of immigration on earnings, see Card (2001); Borjas (2003); Ottaviano and Peri (2012); and Dustmann, Frattini, and Preston (2013).

(39.) This characterization of political support for immigration enforcement is roughly consistent with the framework used by Alesina, Baqir, and Easterly (1999), in which enthusiasm for public spending is diminished by increased ethnic and racial diversity in a jurisdiction. Table 1. Characteristics of Native-Born and Foreign-Born U.S. Working-Age Population with High School Education or Less, 1970-2015 (a) 1970 1980 1990 Native- Foreign- Native- Foreign- Native- born born born born born Sex Male 46.4 41.8 46.6 AAA 48.6 Female 71.6 75.8 63.9 69.1 59.1 Age 18-33 38.1 28.6 43.4 40.2 41.6 34-49 33.5 34.9 28.1 33.0 31.7 50-64 28.5 36.5 28.5 26.8 26.6 Years of schooling 0-8 23.5 45.6 14.3 39.2 8.6 9-11 27.2 19.6 24.5 19.0 20.8 12 49.2 34.8 61.2 41.7 70.6 Industry, share of labor force Agriculture 3.7 3.2 2.9 4.0 2.8 Construction 6.8 6.1 6.8 5.7 8.0 Eating and drinking establishments 2.9 5.8 3.8 6.8 4.8 Nondurable manufacturing 10.0 14.5 8.9 13.0 7.6 Personal services 4.8 7.0 3.2 5.8 3.3 Other industries 67.2 58.7 66.6 56.8 65.2 Unemployment rate 4.6 4.6 7.8 7.8 8.4 2000 2015 Foreign- Native- Foreign- Native- Foreign born born born born -born Sex Male 48.8 50.3 51.2 54.3 51.2 Female 64.1 56.8 63.9 46.2 60.5 Age 18-33 43.2 36.4 42.2 38.2 27.3 34-49 34.5 37.9 38.2 27.9 42.3 50-64 22.3 25.6 19.6 33.8 30.5 Years of schooling 0-8 38.2 4.9 33.7 4.0 29.6 9-11 16.8 15.8 16.5 12.6 15.1 12 45.0 79.3 49.8 83.4 55.3 Industry, share of labor force Agriculture 5.7 2.1 5.5 2.3 6.9 Construction 7.8 9.1 10.8 9.2 14.8 Eating and drinking establishments 8.7 5.3 9.2 7.6 11.3 Nondurable manufacturing 9.5 5.5 7.5 4.3 5.8 Personal services 6.9 2.9 6.3 2.9 7.2 Other industries 51.6 67.6 52.1 63.9 47.9 Unemployment rate 9.8 7.5 8.6 9.7 6.1 Sources: U.S. Census Bureau, decennial census, American Community Survey. (a.) All values are expressed as percentages. The sample is restricted to individuals age 18-64 with 12 years of education or less. Table 2. Summary Statistics for Foreign-Born U.S. Working-Age Population with High School Education or Less, 1970-2015 (a) 1970 1980 1990 2000 2005 2015 Years of residence in the United States 0-5 19.2 23.2 24.2 22.8 21.8 11.9 6-10 14.8 18.4 21.6 19.1 18.4 13.0 11 + 66.1 58.4 54.2 58.1 59.9 75.1 Age of arrival in the United States 0-14 22.1 13.6 14.7 19.1 18.1 20.2 15-25 28.0 34.8 42.4 47.5 47.3 45.0 26+ 44.0 51.4 43.0 33.4 34.3 34.4 Country or region of origin, less than high school education Mexico 15.4 33.3 47.5 60.6 64.0 59.3 Central America 1.6 3.5 8.7 10.8 12.4 15.9 Caribbean 8.4 10.7 9.2 7.2 5.7 6.0 South America 2.6 3.6 3.3 3.4 3.2 3.0 Southeast Asia 1.7 4.6 6.6 5.8 4.7 4.8 Other Asia 3.3 5.4 5.6 4.7 4.0 6.0 Africa 0.4 0.5 0.4 0.7 1.0 1.6 Middle East 1.6 1.5 1.2 0.9 0.8 0.9 Europe 51.6 25.9 11.4 5.0 3.5 2.0 Other 13.5 11.0 6.2 0.9 0.7 0.5 Country or region of origin, high school education or less Mexico 11.6 23.2 34.0 44.4 48.1 45.1 Central America 1.6 3.3 7.7 9.3 10.1 12.2 Caribbean 8.6 11.1 10.8 9.9 8.8 9.4 South America 3.0 4.4 5.3 5.8 6.1 5.7 Southeast Asia 1.7 4.9 7.5 7.8 6.9 6.9 Other Asia 4.0 7.1 8.7 7.7 7.0 8.9 Africa 0.5 0.8 0.9 1.7 2.2 3.0 Middle East 1.8 1.8 1.6 1.4 1.4 1.6 Europe 52.9 30.9 16.5 10.2 8.0 5.8 Other 14.4 12.5 7.2 1.8 1.6 1.3 Sources: U.S. Census Bureau, decennial census, American Community Survey. (a.) All values are expressed as percentages. The sample is restricted to individuals age 18-64 with 12 years of education or less. Table 3. Percentage of Foreign-Born Workers with a High School Education or Less, by Industry, 1970-2015 (a) Industry 1970 1980 1990 2000 2015 Agriculture 3.9 7.0 13.5 21.4 29.3 Construction 3.9 4.4 6.9 12.0 20.3 Eating and drinking establishments 8.3 8.5 11.4 15.6 16.8 Nondurable manufacturing 5.9 7.1 7.9 11.2 13.5 Personal services 6.4 8.9 12.5 17.7 21.8 Other industries 3.0 3.3 3.7 5.1 5.8 Sources: U.S. Census Bureau, decennial census, American Community Survey. (a.) All values are expressed as percentages. The sample is restricted to individuals with 12 years of education or less. Table 4. Analysis of Net Migration at the Mexican State Level (a) Decadal change in net migration (b) (1) (2) Excluding Independent variable (c) Pooled 2010 Labor supply with less than 0.1441 (***) 0.1643 (***) a high school education (d) (0.010) (0.011) Innovations to GDP per -0.0197 (*) -0.0735 (***) capita at age 16 (0.010) (0.016) Innovations to GDP per 0.022 -0.0472 capita in census year (0.020) (0.039) No. of observations 3,328 2,432 [R.sup.2] 0.122 0.175 (3) (4) Independent variable (c) Men Women Labor supply with less than 0 1733 (***) 0.1190 (***) a high school education (d) (0.015) (0.013) Innovations to GDP per -0.0262 -0.0134 capita at age 16 (0.017) (0.012) Innovations to GDP per 0.0234 0.0187 capita in census year (0.034) (0.024) No. of observations 1,664 1,664 [R.sup.2] 0.108 0.189 Sources: U.S. Census Bureau, decennial census; Instituto Nacional de Estadistica y Geografia, Mexican decennial census; authors' calculations. (a.) The units of analysis are three-year birth cohorts. The log of the ratio for Mexican state birth cohort size to the U.S. birth cohort size is used as an instrument for the log of the ratio for Mexican state birth cohort size to the U.S. labor supply with less than a high school education. Robust standard errors in parentheses are clustered by birth cohort and weighted by birth cohort size. Statistical significance is indicated at the (***) 1 percent, (**) 5 percent, and (*)10 percent levels. (b.) The mean decadal change in net migration for the pooled sample is 0.0619, holding the Mexican state cohort size fixed at its initial value. (c.) Each independent variable is the log of the ratio for the Mexican state to the United States. (d.) The native U.S. labor supply with less than a high school education is measured contemporaneously. Table 5. Results of the Prediction Regression (a) Independent variable Net migration rate Log birth cohort ratio for origin country to United States 0.7716 (0.760) Log birth cohort ratio x under 40 years old 3.9292 (***) (0.734) Log GDP ratio for origin county to United States 1.9581 (***) (0.518) Log GDP ratio x under 40 years old -1.4201 (*) (0.798) Female 0.3558 (***) (0.116) Female x under 40 years old -0.7988 (***) (0.116) Covariates (b) Yes No. of observations 3,310 [R.sup.2] 0.842 Sources: U.S. Census Bureau, American Community Survey; United Nations, World Population Prospects; International Monetary Fund; authors' calculations. (a.) The units of analysis are five-year birth cohorts. The analysis is conducted on 25 Latin American countries' net migration rates to the United States over the years 1980-2015. Robust standard errors in parentheses are clustered by birth cohort and weighted by birth cohort size. Statistical significance is indicated at the (***) 1 percent, (**) 5 percent, and (*) 10 percent levels. (b.) Covariates included but not reported are: (i) five-year age cohort dummies; (ii) country fixed effects; (iii) a country dummy for the year 2000 and later; (iv) a country-specific linear time trend for the low-enforcement era of 1980-90; (v) a country-specific time trend for the high-enforcement era of 2000-15; and (vi) the interactions between all these covariates and being under 40 years old. Table 6. Thousands of Foreign-Born Residents in the United States 1980 2015 2040 projected (a) Younger Older Younger Older Younger Older Country than 40 than 40 than 40 than 40 than 40 than 40 Antigua and Barbuda 2.8 0.8 4.4 10.9 6.8 8.9 Bahamas 7.8 4.0 13.7 18.5 4.5 47.1 Barbados 16.5 8.3 8.9 33.1 1.1 28.1 Belize 10.0 3.6 15.3 25.4 3.7 33.5 Bolivia 9.6 3.5 30.3 36.6 -61.4 86.7 Chile 24.5 10.3 32.2 54.4 -29.4 73.4 Colombia 101.5 40.2 253.0 374.6 -83.7 782.5 Costa Rica 101.5 40.2 37.3 40.0 -38.0 50.3 Dominican Republic 115.1 43.8 439.0 536.9 402.1 1,104.4 Ecuador 61.3 24.0 186.7 222.3 22.8 281.0 El Salvador 74.5 17.8 650.2 655.7 594.1 1,601.7 Grenada 4.6 2.2 5.5 19.1 0.2 19.5 Guatemala 49.3 12.6 557.1 346.1 813.5 1,102.3 Guyana 37.0 11.6 81.1 164.7 55.9 186.2 Haiti 63.0 25.2 256.0 349.9 205.0 967.7 Honduras 25.3 10.1 369.0 211.7 488.0 698.1 Jamaica 123.3 59.9 227.0 391.8 151.0 539.8 Mexico 1,574.7 452.3 5,299.0 5,663.8 2,707.0 14,146.0 Nicaragua 28.6 12.1 95.0 138.0 -69.7 336.2 Panama 39.4 16.6 25.5 60.2 -35.4 50.3 Paraguay 2.2 0.7 7.0 7.0 -167.8 45.3 Peru 38.8 15.6 157.4 248.5 -81.0 536.7 Trinidad and Tobago 46.9 17.1 73.8 131.6 22.8 150.1 Uruguay 8.8 4.7 13.7 23.3 -4.5 54.3 Total 2,485.5 805.1 8,838.1 9,764.1 4,907.7 22,930.1 Sources: U.S. Census Bureau, American Community Survey; United Nations, World Population Prospects; International Monetary Fund; authors' calculations. (a.) Negative values are an artifact of the linear model used to forecast future flows, and are not possible in practice. See the text for interpretation, specifically note 34.