Wage Mobility of Foreign-Born Workers in the United States

Wage Mobility of Foreign-Born Workers in the United States Seik Kim Department of Economics University of Washington seikkim@uw.edu http://faculty.washington.edu/seikkim/ February 2, 2010 Abstract This paper presents new evidence on whether foreign-born workers assimilate. While the existing literature focuses on the convergence/divergence of average wages, this study extends the analysis to the distribution of wages by looking at wage mobility. We measure the foreign-native gap in year-to-year transition probabilities from one decile group to another of a wage distribution, where the deciles are determined by a native sample. Our results, based on the matched Current Population Survey for 1996 to 2008, suggest that the majority of foreign-born workers fail to assimilate. Immigrants in middle and bottom decile groups, who are the majority of immigrants, tend to fall behind relative to natives in the same decile groups. Only those in top decile groups seem to keep up or improve relative to their native counterparts. The widening foreign-native gap in mean wages with the time spent in the U.S. is mostly driven by the middle and bottom decile group immigrants from Central and South America and the bottom decile group immigrants from Asia. We do not nd evidence that this is driven by di erences in occupations. Keywords: Economic Assimilation, Immigration, Wage Mobility JEL Classi cation Number: C13, C23, J31, J61 0 I have bene ted from helpful comments from Joseph Altonji, Yoram Barzel, Jennifer Hunt, Chang-Jin Kim, Fabian Lange, Shelly Lundberg, and participants in seminars at the annual meetings of the American Economic Association, University of Carlifornia-Davis, University of Washington, Washington State University, and the UW Center for Studies in Demography and Ecology (CSDE). I am grateful for support from the CSDE seed grant 549802. 1

1 Introduction The large and growing share of foreign-born workers in the United States has heightened interest in the economic impact of immigration. How immigrants fare as they accumulate experience in the U.S. labor market is the key to many of these e ects. 1 First and foremost, the earnings of immigrants will directly a ect the level and distribution of per capita income in the United States. Second, the better immigrants do on arrival and over time, the greater the extent to which their contributions as tax payers will outweigh their use of government services. Third, the greater the extent to which immigrants who enter the U.S. labor market in low-skill jobs quickly acquire country speci c skills and spread into higher skill jobs, the smaller any negative impact on less skilled natives is likely to be. This paper presents new evidence on whether foreign-born workers assimilate. Economic assimilation is de ned as the degree to which the wages of foreign-born workers approach those of native-born workers with additional time spent in the United States. 2 Assimilation rates are the net result of several o setting factors. Upon entry into the U.S. labor market, foreign-born persons may earn lower wages than their native counterparts to the extent that human capital is not perfectly transferable across economies and cultures and because employers are likely to have less knowledge about their productivity. On the other hand, some groups of foreign-born workers might outperform natives if they possess superior skill endowments, stronger work ethics, or more powerful incentives. As immigrants stay longer in the United States, their wages might converge to those of natives. A large literature studies whether an average foreign-born worker assimilate, focusing on the convergence/divergence of mean wages (Chiswick, 1978; Borjas, 1985, 1995; Jasso and Rosenzweig, 1988; Lubotsky, 2007; Kim, 2009b). However, a more informative question would be how foreignborn workers in di erent locations of wage distribution assimilate as they accumulate U.S. experience. This paper extends the literature of average wages to the distribution of wages by looking at wage mobility. We measure the foreign-native gap in year-to-year transition probabilities from one decile group to another in the wage distribution, where the deciles are determined by native samples. The estimation strategy draws on a rst-order Markov-switching model. We apply the method using the matched Current Population Survey (CPS) for 1996 to 2008. 1 In U.S. immigration law the term immigrant or permanent resident alien denotes a person admitted to this legal classi cation. For expositional convenience, we use the terms foreign-born person and immigrant interchangeably although our sample possibly includes aliens in an illegal status. 2 See Borjas (1999) and LaLonde and Topel (1997) for discussions of the e ect of immigrants on the labor market outcomes of natives. 2

The methodology is motivated by Buchinsky and Hunt (1999). They examine the wage mobility in the United States by estimating the probabilities of transition from one quintile to another and outside the distribution of wages. In this paper, instead of estimating the entire transition matrix, we reduce its dimension by estimating the probabilities of moving up to higher decile groups, moving down to lower decile groups, and staying in the same decile group. This reduction is useful since the immigrant sample size per group is small. This paper analyzes the foreign-native gap in the reduced transition probabilities rather than summarizing the gap into a single mobility measure. Our results suggest that there is little evidence of assimilation of foreign-born workers. 3 Immigrants in middle and bottom decile groups, who are the majority of immigrants, tend to fall behind relative to natives in the same decile groups. 4 Only those in top decile groups seem to keep up or improve relative to their native counterparts. We nd that age, marital status, and education as well as continent of origin play a signi cant role in explaining wage mobility and the foreign-native gap in wage mobility. Immigrants from Central and South America in middle and bottom decile groups tend to move down to lower decile groups than natives in the same groups. The top decile group immigrants from Central and South America do not outperform top decile group natives. Immigrants from Asia with wages below the native median are more likely to move down than below-median natives, whereas those with wages above the native median are more likely to move up than above-median natives. Immigrants from Europe are not very di erent from natives in terms of wage mobility. We conclude that the widening foreign-native gap in mean wages with the number of years spent in the United States is mostly driven by the middle and bottom decile group immigrants from Central and South America and the bottom decile group immigrants from Asia. 5 The paper proceeds as follows. Section 2 introduces the structure of the data set, presents summary statistics, and discusses unconditional foreign-native gap in mean wage growth. This gap roughly measures the dynamics in mean wages. Section 3 develops basic methodology and presents the observed wage mobility by years since migration, continent of origin, and education. Section 4 develops an estimation strategy based on a standard rst-order Markov-switching model. It presents and discusses empirical ndings. Section 5 o ers conclusions. 3 This is consistent with the ndings of the literature looking at the convergence/divergence of mean wages. Figure 2 in Section 2 illustrates the mean hourly wages of foreign-born and native-born workers of various age groups during 1994-2004. See Kim (2009b) for details. 4 While immigrants may fall behind natives, they may still do better than those who stay in their home countries. 5 This is because of the following two considerations. First the majority of immigrants are from Central and South America and from Asia. Second, most of them earn wages below native median. 3

Interview Months Non Interview Months Interview Months March 1994 April 1994 May 1994 June 1994 July 1994 August 1994 September 1994 October 1994 November 1994 December 1994 January 1995 February 1995 March 1995 April 1995 May 1995 June 1995 Outgoing Rotation Group Merged Outgoing Rotation Group (MORG) Outgoing Rotation Group Figure 1: Sample Design of the CPS and its Merged Outgoing Rotation Group 2 Data Description This section introduces the structure of the CPS samples and reports summary statistics. First, it highlights that the CPS cross-section is representative of the U.S. population and that the CPS panel is a nonrandom subset of the cross-section. Second, it presents the unconditional foreign-native gap in wage growth. An average male foreign-born worker exhibits slower wage growth over his life-time than an average male native-born worker. This fact motivates the current study to look at the distribution of the foreign-native gap in wage mobility. 2.1 The CPS: Cross-Section and Panel Samples The CPS is a monthly survey designed to collect information on demographic and labor force characteristics of the civilian non-institutionalized population 16 years of age and older. As of July 2005, approximately 72,000 assigned housing units from 824 sample areas are in the sample. A housing unit is interviewed for 4 consecutive months, dropped out of the sample for the next 8 months, interviewed again in the following 4 months, and then is retired from the sample. In all, a sample housing unit is interviewed eight times. Figure 1 demonstrates the sample design for a housing unit which, for instance, joins the survey in March 1994. This housing unit is interviewed from March 4

to June in 1994 and 1995. If the occupants of a dwelling unit move, the new occupants of the unit are interviewed. Nevertheless the CPS cross-section is representative of the target population at any point of the survey because the random sample of housing units is kept xed. The outgoing rotation groups, or the individuals in the fourth and the eighth interviews, are of interest because interviewees are asked their labor market outcomes, such as usual weekly earnings and usual weekly hours worked. By construction, an individual appears only once in a year, but may reappear in the following year. One may append data from the two interviews and get repeated observations on the same individuals. The appended sample is called the Merged Outgoing Rotation Group (MORG) or the matched CPS. The matched CPS is a collection of two-year panels. The 1996-1997 panel, for instance, contains the individuals in the households which enter the survey scheme between October 1995 and September 1996. Similarly, the 1997-1998 panel contains the individuals in the households which enter the survey scheme between October 1996 and September 1997. These two-year panels can mimic a regular longitudinal sample if combined properly. The matched CPS shares most of the advantages of usual panel data sets. First, the sample consists of multiple panels two years in length. Individual speci c permanent components can be controlled like in other usual panel data models. Second, the sample has the crucial advantage of being much larger than alternative panel data sets such as the Panel Study of Income Dynamics (PSID) or National Longitudinal Survey of Youth 1979 (NLSY79). Sample sizes matter in immigration studies because foreign-born persons, after all, are minorities. 6 Third, the CPS cross-section serves as a representative cross-section of the target population. This property is the key to correct for the attrition bias since the survey does not follow households who move. 7 2.2 Data and Summary Statistics Since 1994, the CPS includes information on international migration, such as year of entry into the United States and country of birth along with demographic and labor market information, such as age, schooling, marital status, earnings per hour or week, usual hours of work, and labor market 6 Even when the sample sizes are the same, a regular panel is only weakly preferred to a rotating panel. With a long panel, one can choose between rst-di erencing and dummy variable approaches. With short panels, rst-di erencing is the only option. Hence, estimates based on a regular panel is more e cient only if the dummy variable approach is the preferred method. The choice of estimation method, however, does not a ect consistency. We do nd signi cant point estimates in this paper although we apply rst-di erencing, the potentially less e cient method. 7 In the CPS, attrition is directly related to change in addresses. Sample attrition and population attrition rates for 1996 to 2008 are about 18-33% and 2-3% per year, respectively, and sample attrition has a larger impact on estimation results than population attrition does. 5

status. 8 The sample used in this analysis is drawn from the matched CPS between 1996 and 2008. We drop 1994 and 1995 because matching is not possible between June to December 1994 and 1995 and between January to August 1995 and 1996. We take a sample of foreign-born and native-born men of ages 24-60 for 1996 to 2008. 9 We de ne an individual as matched if the individual appears twice in the matched CPS. In order to examine di erences based on ethnic origin, we divide the foreign sample into four groups: immigrants from Central and South America, from Europe (including Australia, New Zealand, and Canada), from Asia, and from other countries. 10 The group of other countries consists of immigrants from Africa, Oceania, and unclassi ed ones. The last group is of little interest due to its small sample size and heterogeneity. Details on how the data are processed are explained in the Appendix. This section provides a general picture. Table 1 reports summary statistics for cross-section/matched samples. The matched sample consists of two year panels. The wage information in the CPS sample is mostly self-reported, but also involves imputed wages. 11 As the imputation rule does not account for the country of origin, the imputed wages of immigrant workers tend to be biased toward the wages of native workers. Consequently, our preferred way to handle the imputed wages is simply dropping them. 12 The persons in the matched sample are a nonrandom subset of the cross-section sample. About 21% of native interviewees and 29% of immigrant interviewees drop out of the sample in the second period. Table A1 in the Appendix reports native/immigrant matching rates by interview years. 8 Prior to 1994, CPS supplements on immigration were administered to all households participating in the survey in November 1979, April 1983, June 1986, June 1988, and June 1991. 9 The foreign sample includes foreign-born men who were not U.S. citizens at the time of birth. Following Warren and Peck (1980), our foreign sample consists of persons born outside the United States, the Commonwealth of Puerto Rico, and the outlying areas of the United States. Foreign-born persons may have acquired U.S. citizenship by naturalization or may be in illegal status. The reference group consists of native-born white men. The native sample includes persons born in the Unites States, but excludes persons born in the Puerto Rico and the outlying areas. 10 We combine Australia, New Zealand, and Canada with Europe because of sample size considerations and so that immigrants from countries that are predominantly white and are at a similar stage of political and economic development are grouped together. We refer to the group as Europe. The data do not identify mother tongue. The impact of language pro ciency has been studied in a large literature. LaLonde and Topel (1997) provide a survey. 11 When a person is working but does not report the wage, the Census Bureau assigns values for the missing wages using an allocation rule which is known as the cell hot deck match criteria. According to the imputation rule, a value of the wage is allocated based on the cell of same gender, age, race, education, occupation, hours worked and receipt of tips, commissions, or overtime. (The numbers of cells are 14976 in 1994-2002 and 11520 in 2003-2004.) 12 Hirsch and Schumacher (2004) nd that regression estimates including variables not used in imputation rules, such as union status, are biased. As country of origin is not used as imputation criteria, using the whole sample may bias the results. Bollinger and Hirsch (2006) propose a weighting scheme to correct for the bias. 6

Table 1. Summary Statistics Cross-Section Sample Matched Sample Natives Immigrants Natives Immigrants 1st year 2nd year 1st year 2nd year Age 40.9 39.0 41.4 42.4 39.5 40.5 (9.9) (9.4) (9.3) (9.3) (9.0) (9.0) Education 14.1 11.9 14.1 14.1 12.0 12.1 (2.2) (4.4) (2.2) (2.2) (4.4) (4.3) C.S.America 10.0 10.0 10.1 (4.1) (4.1) (4.1) Europe 14.5 14.5 14.6 (2.9) (2.9) (2.9) Asia 14.8 14.9 15.0 (3.1) (3.0) (3.0) Wage 16.9 13.3 17.2 17.5 14.1 14.3 (13.9) (12.2) (13.2) (12.7) (13.0) (12.6) C.S.America 9.8 10.2 10.4 (6.6) (6.6) (6.4) Europe 20.2 21.2 21.3 (17.7) (19.1) (18.0) Asia 18.0 18.9 19.3 (15.6) (16.2) (15.7) Hours 43.5 41.6 43.6 43.5 41.8 41.7 (8.9) (7.8) (8.4) (8.2) (7.5) (7.0) Marital Status 0.692 0.682 0.739 0.744 0.785 0.789 U.S. Citizen 1.000 0.367 1.000 0.413 0.413 C.S.America 0.583 0.566 Europe 0.130 0.144 Asia 0.234 0.242 Others 0.054 0.048 N 435721 71533 115968 115968 15721 15721 Standard deviations are reported in parentheses. N: sample size Wage: hourly rate of pay; Hours: usual hours worked per week Marital Status: 1 if married; U.S. Citizen: 1 if U.S. citizen; C.S.America: Central and South America; Europe: Europe, Australia, New Zealand, and Canada; Others: Africa, Oceania, and other countries 7

Years of education provides a rough measure of skill endowment. Foreign-born persons have lower mean and a much larger standard deviation of education. In the cross-section sample, the average education level is 14.1 years for native-born persons and is 11.9 years for foreign-born persons. Immigrants from Central and South America have 10.0 years of average education, those from Europe 14.5 years, and those from Asia 14.8 years. Estimates of years of education are virtually not di erent between the matched and the cross-section samples. In the cross-section sample, the average hourly wage of native-born workers is $16.9, in 1994 dollars, while the average foreign-born worker earns $13.3. Immigrants from Central and South America make $9.8 per hour, those from Europe $20.2, and those from Asia $18.0. Immigrant workers work 1.8-1.9 more hours per week than native workers. Although not reported in the table, 95.9% and 95.3% of the foreign-born and native-born populations are full-time workers, while 4.1% and 4.7% are part-time workers, respectively, among those who are employed. The proportions of full-time and part-time workers are relatively stable over the sampling period. Among immigrants, 56.6-58.3% are from Central and South America, 13.0-14.4% are from Europe, and 23.4-24.2% are from Asia. The estimates also indicate that foreign-born persons are about 2 years younger than native-born persons on average. An average native and an average is 40.9 years old and an average immigrant is 39.0 years old in the cross-section sample. Individuals in the matched sample are older than those in the cross-section sample. It implies that older individuals are more likely to be matched in the second year interview. A larger proportion of the foreign-born population is married. We nd substantial attrition. Table 1 reveals that persons in the matched samples, regardless of ethnic origins, tend to earn more and work longer than those in the cross-section samples. It implies that more successful workers are more likely to be matched than unsuccessful ones. Foreign-born persons from Central and South America tend to attrite more than those from Europe and Asia. The consequence of nonrandom attrition, however, has not been addressed in immigration studies using the matched CPS. 13 13 While many papers have used the matched CPS, only two that we are aware of focus on immigration: Duleep and Regets (1997a) and Bratsberg, Barth, and Raaum (2006). 8

Table 2. Mean Wage and Wage Growth Di erential by Year & Origin Natives All Immigrants C.S.America Europe Asia wage wage DD wage DD wage DD wage DD 1996 17.02 13.70 9.28 20.91 18.10 1997 17.97 14.58 0.07 9.84 0.38 21.75 0.10 19.44 0.39 [10842] [1165] (0.42) [624] (0.56) [182] (1.04) [304] (0.81) 1997 17.08 13.95 9.58 21.08 18.20 1998 16.64 13.31 0.20 9.86 0.71 18.10 2.53 17.05 0.70 [10571] [1200] (0.44) [649] (0.57) [194] (1.07) [326] (0.82) 1998 16.18 13.42 9.83 20.62 16.30 1999 16.98 13.70 0.51 10.12 0.51 21.31 0.10 16.82 0.27 [10123] [1224] (0.28) [702] (0.36) [196] (0.69) [287] (0.57) 1999 16.74 13.90 10.14 22.71 17.95 2000 17.30 14.32 0.13 10.46 0.25 22.77 0.50 18.95 0.43 [9435] [1211] (0.28) [698] (0.36) [172] (0.73) [283] (0.56) 2000 16.93 13.59 9.97 21.88 17.63 2001 17.62 14.19 0.09 10.25 0.41 23.05 0.47 18.48 0.16 [8740] [1286] (0.28) [751] (0.36) [179] (0.75) [286] (0.59) 2001 17.32 14.60 10.53 22.27 20.69 2002 17.92 14.88 0.32 10.55 0.57 23.66 0.78 21.12 0.16 [9368] [1249] (0.34) [723] (0.42) [166] (0.90) [288] (0.68) 2002 17.98 13.86 10.52 19.71 18.69 2003 17.34 13.62 0.39 10.40 0.51 19.45 0.37 18.02 0.02 [10043] [1350] (0.36) [778] (0.46) [191] (0.94) [317] (0.73) 2003 17.41 14.27 10.17 21.60 19.55 2004 17.72 14.52 0.06 10.57 0.09 21.08 0.82 19.76 0.10 [8957] [1304] (0.17) [742] (0.21) [197] (0.41) [309] (0.33) 2004 17.58 14.53 10.88 19.53 18.66 2005 17.86 14.81 0.00 10.94 0.22 19.92 0.10 19.17 0.21 [8149] [1181] (0.17) [619] (0.22) [193] (0.40) [301] (0.33) 2005 17.35 13.91 10.04 20.96 18.98 2006 17.58 14.34 0.20 10.28 0.00 21.81 0.62 19.72 0.51 [9964] [1412] (0.15) [794] (0.19) [202] (0.38) [337] (0.30) 2006 17.07 14.37 10.30 21.20 20.52 2007 17.53 14.74 0.08 10.64 0.12 21.76 0.10 20.85 0.12 [9749] [1598] (0.14) [934] (0.18) [204] (0.39) [374] (0.29) 2007 17.20 14.86 10.74 22.26 20.66 2008 17.45 14.79 0.32 10.63 0.34 21.76 0.73 20.84 0.06 [10027] [1541] (0.14) [891] (0.18) [193] (0.38) [385] (0.28) Average: 0.11 0.15 0.08 0.01 (0.08) (0.10) (0.21) (0.16) Mean Hourly Wages in 1994 dollar (sample sizes in square brackets and standard errors in parentheses) DD: di erence in di erence (the wage growth of an ethnic group relative to that of natives) 9

Table 2 presents the wage growth di erentials of foreign-born workers relative to native-born workers using the matched sample. For instance, in 1996-1997, the native mean wage increased by $0.95 (from $17.02 to $17.97) and the foreign mean wage increased by $0.88 (from $13.70 to $14.58). The column DD (di erence-in-di erence) reports the di erence between the wage increment of the two groups, $0.07. However, most of these estimates are noisy. In general, we nd no signi cant pattern with respect to which group is doing better than the other in terms of wage increments. 14 Overall, the summary statistics do not support the hypothesis of mean wage convergence for 1996-2008 because the estimates in the rst DD columns are usually negative although insigni cant. Figure 2 illustrates wage growth paths for average immigrant and native workers. The sample is drawn from the CPS. The gure depicts the mean hourly wages of foreign-born and native-born male workers of various age groups during 1994-2004. 15 The foreign-born workers in the gure are con ned to those who arrived between 1980 and 1991. For the time being, assume that selective return migration is negligibly small. The three thicker lines with larger symbols indicate the mean wages of native-born workers and the three thinner lines with smaller symbols indicate the mean wages of foreign-born workers. The solid lines with squares track the mean wages of those who were 20-24 years old in 1994. The dashed lines with triangles are the mean wages of those who were 30-34 years old in 1994. The dotted lines with circles correspond to the mean wages of those were 40-44 years old in 1994. We observe that the wage gap between the immigrants and the natives in the 20-24 in 1994 cohort widens as the foreign-born workers stay longer in the United States. Foreign-born workers who were 20-24 years old in 1994 fail to assimilate economically during the 1994-2004 period. The foreign-born workers in the 30-34 in 1994 cohort also fail to catch up over the 1994-2004 period the wage gap remains stable. The foreign-born workers in the 40-44 in 1994 cohort experience economic assimilation over the 1994-2004 period as the wage gap narrows. 14 Duleep and Regets (1997a) provide a similar table for 1987-1988. The mean wages of foreign-born workers are $9.51 in 1987 and $10.48 in 1988. The mean wages of native-born workers are $11.27 in 1987 and $11.88 in 1988. Consequently, their estimate of the wage growth of foreign-born workers exceeds that of native-born workers by $0.36 or 5.4% points. Hence their result supports the economic assimilation hypothesis for 1987-1988. 15 The native-born workers in this paper are whites, but there are several alternative ways of choosing a native sample. One may compare wages of foreign-born individuals with those of native-born individuals regardless of ethnic origins, with wages of their ethnically similar native-born counterparts, or compare wages between earlier and later arrivals within the foreign-born population. We use native-born white individuals because it gives the most conservative assimilation measure. Even with the most conservative de nition, we show that cross-section results imply faster wage growth for immigrants than natives, which is consistent with the results in previous literature, but longitudinal results are against economic assimilation. Another reason we use the white sample is that it is a solid reference group as the racial/ethnic composition of the native population has changed dramatically in recent years. 10

$20 $18 $16 $14 $12 $10 $8 $6 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 N 20 24 in1994 N 30 34 in1994 N 40 44 in1994 F 20 24 in1994 F 30 34 in1994 F 40 44 in1994 Figure 2: Average Wages (in 1994 Dollars) of Native-Born and Foreign-Born Workers 3 The Observed Wage Mobility: Unconditional Probabilities This section turns to the analysis of foreign-native di erence in transition probabilities. It explains the basic methodology and presents the unconditional transition probability estimates by years since migration, continent of origin, and education for each of the ten decile groups. The ten decile groups are determined by the CPS cross-sections, but the transition probabilities are estimated from the matched balanced CPS panels. To obtain consistent transition probability estimates, we assign weights to the individuals in the matched CPS using the attrition correcting method that accounts for sample attrition in the presence of unobserved population attrition. 3.1 Conceptual Framework Figure 3 presents the wage distributions of native-born and foreign-born workers in 1996 and 1997 using the 1996 and 1997 CPS cross-sections. Broken lines are the 1996 wage distributions and solid lines are the 1997 wage distributions. The native distributions are the ones with a mode around $10 (and are in red color). The immigrant distributions are the ones with a mode around $7 (and are in blue color). Vertical lines indicate the decile points for the 1996 native wage distribution. For example, native-born workers with hourly wages between $8.5-$9.9 in 1996 are in the 20-30th percentile group. The decile points for the 1997 native wage distribution are omitted, but are similar to those for the 1996 distribution. For example, to be in the 20-30th percentile group in 1997, 11

Foreign Native Figure 3: Wage Distribution of Natives and Immigrants the hourly wage has to be between $8.6-$10.2. We do not obtain decile points for immigrants. Instead, immigrants are assigned to the native decile groups. The wage distribution of natives is more dispersed and has higher mean than that of immigrants. The majority of foreign-born workers are located at the bottom decile of the native wage distribution. In principle, we can obtain the foreign-native gap in year-to-year transition probabilities from one decile group to another of a wage distribution, where the deciles are determined by the native sample. It requires us to estimate a ten-by-ten transition matrix for every two-year pair. For illustration purposes, take native-born and foreign-born workers who were in the 20-30th percentile of native wage distribution in 1996. First, take native-born workers in the 20-30th percentile group in 1996 and observe which proportion of workers move to each of the ten decile groups in 1997. Then repeat the exercise for foreign-born workers and analyze the foreign-native gap in the proportions for each of the ten decile groups in 1997. While it is not very di cult to estimate these matrices, a more parsimonious model would be estimating the probabilities of moving to higher decile groups, moving to lower decile groups, and staying in the same decile group. More precisely, for the workers in the 20-30th percentile group in 1996, one may observe which proportion moves to the 30-100th percentile group, which to the 0-20th percentile group, and which stay in the 20-30th percentile group in 1997. For the 1996-1997 sample, 12

Moving Up (36%) Moving Up (25%) Staying (43%) Staying (43%) Moving Down (21%) Moving Down (32%) Figure 4: Probability of Moving Up, Down, and Staying we nd that 36% of native-born workers moved up, 21% moved down, and 43% stayed. Among foreign-born workers, 25% moved up, 32% moved down, and 43% stayed. 16 The results are visualized in Figure 4. The horizontal axis depicts percentile values representing the decile groups. The 20-30th percentile groups lie between 20 and 30. The solid line corresponds to native-born workers and the dashed line is for foreign-born workers. The length of these lines represents the probability of staying. Since the staying probabilities of native-born and foreign-born workers are identical, the two lines in Figure 4 are of the same length. The vertical distance between 1 and the upper triangle indicates the probability of moving up. The triangle for foreign-born workers lies below of that of native-born workers, meaning that foreign-born workers between the 20-30th percentiles have a smaller probability of moving up than native-born workers. The vertical distance between 0 and the lower triangle indicates the probability of moving down. The inverse triangle for foreign-born workers lies above of that of native-born workers, meaning that foreign-born workers between the 20th-30th percentiles have a higher probability of moving down than native-born workers in the same group. 16 Since the matched CPS is a nonrandom subsample of the CPS cross-section, attrition-correcting weights are applied to obtain these estimates. The next section explains how to calculate the weights. 13

3.2 Sample Attrition in the Presence of (Unobserved) Population Attrition Attrition causes a serious problem for immigrant samples because we want to correct for both sample attrition and outmigration at the same time, yet the data does not tell us who emigrated from the United States. When a foreign-born respondent is missing in the second period, it is not possible to tell whether the person is in the United States or has gone back to his or her home country. When there is return migration, the second period population becomes a nonrandom subset of the rst period population. Since there is no representative cross-section for the second period, the sample attrition correcting method developed by Hirano, Imbens, Ridder, and Rubin (2001) and Bhattacharya (2008) cannot be applied. 17 This paper uses a method that accounts for sample attrition in the presence of unobserved population attrition proposed by Kim (2009a). The method assigns weights to persons in the matched sample. The resulting estimators are consistent. The key idea of attrition correction is generating a counterfactual cross-section where there is no outmigration prior to applying the existing sample attrition correcting scheme. For example, suppose that the two-year panel of 1996-1997 is of interest. The CPS provides 1996 and 1997 cross-sections, but the 1997 cross-section is not representative of the 1996 population due to population attrition. First, we use the 1996 cross-section as the basis for generating a representative counterfactual 1997 cross-section. The counterfactual sample is obtained by weighting the second period cross-section by one minus the probability of population attrition. The population attrition function can be identi ed when repeated cross-sections are available without knowing who emigrated from the United States. Then the two representative cross-sections (the 1996 actual and 1997 counterfactual cross-sections) are used as the basis for estimating attrition correcting weighting functions. In this step, an existing sample attrition correcting method can be applied. 18 Finally, we assign weights to the persons in the balanced part of the 1996-1997 panel. We estimate the weighting functions for the matched CPS between 1996-2008 year by year since residential mobility and return migration may vary by year. 19 A more formal discussion is presented in the Appendix. 17 In the absense of outmigration or population attrition, Hirano, Imbens, Ridder, and Rubin (2001) prove that the attrition process can be identi ed under fairly exible (additive non-ignorable) assumptions up to a known link function such as the logit or probit when a panel and representative cross-sections are available. The attrition correcting weighting function is given by the inverse of one minus the probability of sample attrition. As their attrition function is implicitly de ned by a set of nonlinear integral equations, Bhattacharya (2008) develops an estimation strategy. He shows that the identi cation condition by Hirano et al can be transformed into a set of conditional moment restrictions where the moments contain the attrition function as an unknown parameter. 18 See Hirano, Imbens, Ridder, and Rubin (2001) and Bhattacharya (2008) for details. 19 See Kim (2009a) for theory and application of this method. 14

3.3 Wage Mobility by Years Since Migration Figure 5: Wage Mobility by Years Since Migration 15

We apply the strategy to immigrants with di erent years of U.S. experience for 1996-2008. The six gures classify immigrants by years since migration: less than 6 years, 6 to less than 11 years,..., 21 to less than 26 years, and 26 years and above. We account for both sample attrition and population attrition in the two panel years to obtain these estimates. One can interpret the estimates as if there is no sample attrition and no population attrition in two year panels. No population attrition means that conditional on an immigrant is in the United States in the rst panel year, the immigrant is in the United States in the second panel year. For example, for those who have stayed in the United States for 5 years and are in the sample in the rst panel year, the counterfactual is that the immigrants are in the sample (and in the United States) in the second panel year. Overall, we nd some evidence of convergence, but it is unclear whether this is an outcome of assimilation or selection. The rst gure (top left) with immigrants with less than 6 years of U.S. experience shows the followings. Immigrants in bottom decile groups have a smaller probability of moving up and a larger probability of moving down than their native counterparts. Immigrants in middle decile groups have more or less the same probability of moving up as natives, but have a higher probability of moving down. Immigrants in top decile groups tend to move up relative to natives, although it is not very clear whether their probability of moving down is smaller than that of natives. In general, immigrants in top decile groups are more likely to keep up or improve relative to natives, while those in middle and bottom decile groups tend to fall behind. The only exception is the group of foreign-born workers who have stayed at least 26 years. For these people, however, it is unclear whether they have assimilated or if those who remain in the United States are similar to natives. Since most immigrants are located in the bottom decile groups, we conclude that the majority of foreign-born workers fails to assimilate into the U.S. labor market. 16

3.4 Wage Mobility by Continent of Origin Figure 6: Wage Mobility by Continent of Origin We conduct a similar analysis for immigrants from di erent continents. 20 First, immigrants from Central and South America tend to fall behind unless they are in the top two decile groups. Second, immigrants from Asia exhibit clear divergence. Asian immigrants with above-median wages have a higher chance of moving up and a lower chance of moving down than natives with abovemedian wages. For Asian immigrants with below-median wages, the exact opposite is true. Finally, immigrants from Europe are very similar to natives in terms of wage mobility. Our results suggest that the widening foreign-native gap in mean wages with U.S. experience is mostly driven by the middle and bottom decile group immigrants from Central and South America and the bottom decile group 20 In the United States, more than half of the foreign-born population is from Central and South America, about a quarter from Asia, and about one sixth from Europe. 17

immigrants from Asia. This is con rmed later when we present conditional transition probability estimates. 3.5 Wage Mobility by Education Figure 7: Wage Mobility by Education In this section, we conduct a similar analysis for natives and immigrants of di erent education levels. Individuals are assigned to four di erent groups of years of education: [0; 8), [8; 12), [12; 16), and [16; 1). The rst group with less than eight years of education includes 2% of natives and 19% of immigrants. Due to the small sample size of the native sample, native results (the solid lines) are relatively poorly estimated. Overall, immigrant workers with wages below median have higher chance of moving down and lower chance of moving up than their native counterparts. The second 18

group with [8; 12) years of education consists of 6% of natives and 12% of immigrants. Immigrant workers with below-median wages are more likely to move down than native workers in the same decile groups, but the chances of moving up are not di erent from those of natives. Among the above-median wage workers, the foreign-native di erences in the probabilities of moving up, moving down, and staying are small. The members in the third group have [12; 16) years of education. 60% of natives and 41% of immigrants are in this group. Below-median wage immigrant workers have a smaller probability of moving up than below-median wage native workers. Above-median wage immigrant workers have a greater (or similar) probability of moving up than above-median wage native workers. The probability of moving down is always larger for immigrants unless they are in the top two decile groups. Finally, the last group with 16 or more years of education includes 32% of natives and 28% of immigrants. In lower decile groups, immigrants have a lower probability of moving up and a higher probability of moving down. In middle decile groups, wage mobility is not very di erent between native and immigrant workers. In upper decile groups, immigrants have a higher probability of moving up and a lower probability of moving down. In other words, there is clear divergence among highly educated immigrant workers. Overall, the education results suggest that the below-median wage immigrant workers with less than 16 years of education can explain the widening foreign-native gap in mean wages. 4 Estimation of Wage Mobility: Conditional Probabilities This section develops an estimation strategy which modi es a standard rst-order Markov-switching model. This section estimates transition probabilities conditional on covariates for each of the ten decile groups. It presents and discusses empirical ndings. 4.1 Estimation of Wage Mobility Consider a rst-order Markov-switching variable S it that has ten states. The ten-state S it represents the ten decile groups, where i is individual and t is calendar year. A standard rst-order Markovswitching model de nes a transition probability from state s t 1 to state s t by Pr [S it = s t js i;t 1 = s t 1 ] ; (1) 19

for s t 1 ; s t 2 f1; 2; :::; 10g. In principle, the joint probability, Pr [S i;t 1 = s t 1 ; S it = s t ], can be estimated, but what we need for our analysis is the transition probabilities of moving up, moving down, and staying, which are even simpler than estimating the entire ten-by-ten transition matrix given by (1). The probability of moving up is given by p s;up = Pr [S it > sjs i;t 1 = s] ; for s = 1; 2; :::; 9 = 0; for s = 10; (2) and the probability of moving down by p s;down = Pr [S it < sjs i;t 1 = s] ; for s = 2; 3; :::; 10 = 0; for s = 1: (3) The probability of staying is simply the residual: p s;stay = 1 p s;up p s;down ; for s = 1; 2; :::; 10: (4) Now suppose that the probabilities (2)-(3) are functions of a vector of covariates, X, and are given in parametric forms. For any given state, S i;t 1 = s, let the vector of parameters be s. One may estimate the probabilities by maximum likelihood (ML) estimation. Conditional on S i;t 1 = s the ML estimator is given by the maximizer of L ( s ) = P n i=1 [1 fs it > sg log p s;up (X i ; s ) + 1 fs it < sg log p s;down (X i ; s ) + 1 fs it = sg log p s;stay (X i ; s )] : For each s = 1; 2; :::; 10, apply a separate maximum likelihood estimation procedure and obtain b s;ml. Then, the estimated probabilities are bp s;up (X i ) = p s;up X i ; b s;ml ; bp s;down (X i ) = p s;down X i ; b s;ml ; bp s;stay (X i ) = 1 bp s;up (X i ) bp s;down (X i ) : 20

4.2 Empirical Speci cation and Findings A maximum likelihood estimation procedure can be used to estimate equations (2)-(3) using a multinomial logit model. In our speci c model, partition the parameter vector s by s = 0 s; 0 0. s The probability of moving up is given by p s;up (X i ; s ) = = e x0 s ; for s = 1; 1 + e x0 s e x0 s ; for s = 2; :::; 9; 1 + e x0 s + e x0 s = 0; for s = 10; and the probability of moving down is given by p s;down (X i ; s ) = 0; for s = 1; = = e x0 s ; for s = 2; :::; 9; 1 + e x0 s + e x0 s e x0 s 1 + e x0 s ; for s = 10: The vector of covariates include a constant, age, age squared, education, a dummy for marital status, and all these variables interacted with a dummy for immigrant. In addition, years since migration, years since migration squared, country of birth, dummies for entry year, and calendar year dummies. Table 3 reports b s and b s. These estimates are not directly interpretable, but give the signs of the impact of corresponding covariates on the probabilities of moving up and down. Of the multinomial logit model estimates, b s and b s, in Table 3, the coe cients of age, education, and marriage variables are signi cant for some S t 1 = s. Overall, age is signi cant for the probability of moving down, but is not signi cant for the probability of moving up. Older individuals are less likely to move down than younger ones. The foreign-native di erence in the age coe cient estimates is not signi cant. The probabilities of moving up and moving down do not vary across immigrants with di erent years since migration, either. However, the coe cient estimates of age, age interacted with an immigrant dummy, and years since migration play a role when we evaluate the functions at di erent levels of age and years since migration. 21 Note that individual coe cients may not be signi cant, but combinations of them may be signi cant. 21 Later in the section the foreign-native di erence in the probabilities of moving up and moving down are evaluated at selected values of covariates. 21

Table 3A. Multinomial Logit Model Estimates: b s S i;t 1 : 1 2 3 4 5 6 7 8 9 Age.020.030.010.034.015.035.037.039.011 (.018) (.018) (.019) (.020) (.021) (.022) (.023) (.025) (.029) 1 100 Age2.043.058.006.028.009.035.032.032.009 (.023) (.023) (.023) (.024) (.025) (.026) (.028) (.029) (.033) Age imm.000.029.021.014.042.018.101.083.006 (.039) (.051) (.063) (.076) (.081) (.088) (.096) (.097) (.100) 1 100 Age2 imm.006.021.024.023.047.025.113.095.027 (.049) (.064) (.078) (.092) (.099) (.105) (.114) (.115) (.119) YSM.060.038.003.003.034.006.034.023.084 (.028) (.038) (.048) (.055) (.058) (.061) (.065) (.058) (.056) 1 100 YSM2.050.048.036.126.041.042.073.052.188 (.072) (.100) (.113) (.128) (.121) (.126) (.125) (.121) (.123) Educ.148.143.150.174.188.191.161.198.165 (.010) (.011) (.011) (.011) (.011) (.011) (.010) (.011) (.012) Educ imm.085.063.040.048.058.123.010.050.038 (.014) (.017) (.023) (.025) (.032) (.031) (.042) (.040) (.044) Married.550.306.226.275.171.226.250.191.239 (.045) (.045) (.047) (.048) (.049) (.052) (.054) (.057) (.065) Married imm.392.348.011.016.055.439.047.024.372 (.095) (.125) (.160) (.190) (.219) (.219) (.234) (.235) (.227) C.S.America.201.027 1.071.485.873 2.053 2.855.405 2.228 (.794) (1.052) (1.365) (1.601) (1.809) (1.944) (2.041) (2.142) (2.131) Europe.778.062.913 1.013 1.084 2.369 2.258.421 2.427 (.813) (1.068) (1.370) (1.605) (1.805) (1.961) (2.038) (2.140) (2.143) Asia.248.121.786.313 1.216 2.128 2.372.061 2.131 (.808) (1.064) (1.373) (1.605) (1.815) (1.963) (2.054) (2.138) (2.163) N 13061 13224 12973 13058 13081 13220 13309 13408 13725 Standard errors are reported in parentheses. N: sample size Variables with subscript imm are the variables interacted with an indicator variable of a foreign-born person. YSM: years since migration; Educ: years of schooling; Married: 1 if married Fixed E ects: birth country, arrival year, calendar year 22

Table 3B. Multinomial Logit Model Estimates: b s S i;t 1 : 2 3 4 5 6 7 8 9 10 Age.019.049.062.030.062.009.089.065.073 (.026) (.023) (.022) (.022) (.023) (.023) (.023) (.025) (.028) 1 100 Age2.019.051.076.033.066.003.095.077.074 (.033) (.028) (.027) (.027) (.027) (.027) (.027) (.028) (.031) Age imm.040.013.178.019.029.005.108.205.059 (.055) (.065) (.075) (.083) (.089) (.096) (.094) (.099) (.092) 1 100 Age2 imm.027.001.220.028.025.002.121.221.082 (.068) (.079) (.092) (.101) (.106) (.114) (.110) (.116) (.106) YSM.018.038.018.056.013.063.087.111.034 (.041) (.048) (.056) (.058) (.060) (.064) (.057) (.057) (.049) 1 100 YSM2.010.110.092.102.070.094.175.234.091 (.106) (.117) (.130) (.131) (.127) (.130) (.109) (.116) (.102) Educ.021.009.034.030.023.004.008.071.194 (.016) (.014) (.012) (.012) (.011) (.010) (.010) (.010) (.012) Educ imm.031.022.054.075.039.033.020.032.067 (.021) (.022) (.024) (.025) (.029) (.031) (.031) (.037) (.039) Married.037.079.001.019.046.076.112.066.103 (.063) (.057) (.054) (.053) (.053) (.053) (.054) (.054) (.060) Married imm.227.168.078.053.228.165.016.498.225 (.137) (.160) (.183) (.216) (.224) (.227) (.225) (.223) (.210) C.S.America.789 1.175 2.199 1.073.909 1.199.055 2.181 2.314 (1.146) (1.373) (1.568) (1.733) (1.913) (2.011) (2.034) (2.073) (2.037) Europe.801.688 2.283.528.459.354.779 2.589 1.679 (1.211) (1.398) (1.589) (1.733) (1.932) (2.028) (2.034) (2.072) (2.038) Asia.606.625 2.584.627.319.591.824 2.722 1.807 (1.155) (1.387) (1.580) (1.754) (1.934) (2.023) (2.035) (2.091) (2.045) N 13224 12973 13058 13081 13220 13309 13408 13725 12628 Standard errors are reported in parentheses. N: sample size Variables with subscript imm are the variables interacted with an indicator variable of a foreign-born person. YSM: years since migration; Educ: years of schooling; Married: 1 if married Fixed E ects: birth country, arrival year, calendar year 23

S t The e ects of education on the probabilities of moving up and moving down are interesting. For 1 = 1, the b s estimate of education is positive (=0.148) and signi cant at the 1% signi cance level. In general, more educated individuals have a greater probability of moving up than less educated ones for all S t 1 = s. More educated individuals, however, also have a greater probability of moving down for S t 1 = 4; 5; 6. For example, for S t 1 = 4, the b s estimate of education is negative (= 0.054) and signi cant at the 5% signi cance level. It means that the wages of more educated individuals in the middle decile groups have larger variance than the wages of less educated ones. More educated individuals have a smaller probability of moving down for S t 1 = 9; 10. For S t 1 = 9, the b s estimate is.071 and for S t 1 = 10, the b s estimate is 0.194. It implies that more educated individuals at the top decile groups have a greater tendency of staying in the top groups than less educated ones. Immigrants with higher education levels also have a greater probability of moving up than less educated natives for all S t 1 = s. For example, for S t 1 = 1, the sum of b s coe cients of education and education interacted with an immigrant dummy is 0.063 (=0.148 0.085) and is signi cant at the 1% signi cance level (not shown in Table 3). We also nd that the e ect of education on the probability of moving up for immigrants is not as great as the e ect of education for natives because many of the b s coe cients of education interacted with an immigrant dummy are negative and signi cant. For instance, for S t 1 = 1, the b s coe cient of education interacted with an immigrant dummy is negative (= 0.085) and signi cant at the 1% signi cance level. Di erent from higheducated natives, high-educated immigrants do not have a greater probability of moving down than less educated natives for all S t 1 = s. In general, foreign-born individuals do not bene t from higher education in terms of the moving up probability than native-born individuals, but at the same time they do not move down as their native counterparts do. Married individuals are more likely to move up than single ones. For S t 1 = 1, the coe cient estimate of a marriage dummy is positive (=0.550) and signi cant at the 1% signi cance level. For S t 1 = 2; :::; 9, the coe cient estimates are positive and signi cant at the 1% signi cance level. The positive e ect is not as strong among immigrants. The coe cient estimate of a marriage dummy interacted with an immigrant dummy is negative (= 0.392) and signi cant at the 1% signi cance level. For S t 1 = 2; :::; 9, the coe cient estimates are mostly negative, although they are mostly insigni cant even at the 10% signi cance level. Marital status is not signi cantly correlated with the probability of moving down, except for those who are located in lower decile groups. For example, in Table 3B when S t 1 = 1, the coe cient 24