Do Immigrants Assimilate More Slowly Today than in the Past?

Abstract

Using millions of historical census records and modern birth certificates, we document that immigrants assimilated into US society at similar rates in the past and present. We measure cultural assimilation as immigrants giving their children less foreign names after spending more time in the United States, and show that immigrants erase about one-half of the naming gap with natives after 20 years both historically and today. Immigrants from poorer countries choose more foreign names upon first arrival in both periods but are among the fastest to shift toward native-sounding names. We find substantial cultural assimilation for immigrants of all education levels.

The cultural assimilation of immigrants is a divisive political issue in the United States. Many politicians and voters hold the nostalgic view that European immigrants assimilated quickly in the past, in contrast to immigrants today.¹ However, this passionate debate about cultural assimilation is not new. Writing in 1891, Senator Henry Cabot Lodge asserted that immigration from Southern and Eastern Europe “is bringing to the country people whom it is very difficult to assimilate and who do not promise well for the standard of civilization in the United States” (Lodge 1891, p. 35). Progressive reformers sought to “Americanize” immigrants through compulsory schooling and English-only laws (Lleras-Muney and Shertzer 2015; Bandiera et al. 2019). Eventually, swayed by this growing coalition, Congress passed strict immigration quotas in the early 1920s, ending the Age of Mass Migration (Higham 1955, Goldin 1994, King 2009, and Abramitzky and Boustan 2017).

Our paper provides the first quantitative comparison of the cultural assimilation of immigrants in the past and the present. We focus on two waves of migration to the United States, the first mostly from Europe (1850–1913) and the second from Asia and Latin America (1965–present). Measuring cultural assimilation is challenging because information on cultural practices—things like food, dress, and accent—are not systematically collected.² The premise of this paper is that we can trace cultural assimilation by examining shifts in the names that immigrants give their children as they spend time in the United States. We draw on a rich literature in sociology and economics suggesting that names are signals of cultural identity.³ One benefit of name selection as a measure of cultural assimilation is that it is a pure choice, unlike intermarriage, which reflects both a choice (who you want to marry) and a constraint (who wants to marry you).⁴ Furthermore, name choices will capture assimilation that can take place within co-ethnic couples, as well as between couples of different backgrounds.

We construct “Foreignness Indices,” also referred to as the F-index, for each name in the past and present indicating the relative probability that a given name was held by immigrants versus the US-born. We then compare the name choices that immigrants selected for their children after they spent more time in the United States. For the past, we use the 1920 Population Census and for the present, we use California birth certificate records for 1989–2015 (California Department of Public Health 1989–2015). Using different data sources raises obvious comparability issues. The 1920 census covers the entire US population, records names as reported to the enumerator, and includes information about immigrants’ year of arrival to the United States. In contrast, the birth certificate records cover only the state of California, contain an infant’s legal name, and most importantly do not include direct information about years of arrival. We try to standardize the historical and modern data, and Section V further investigates sensitivity to these differences.

We find that the rate of name-based assimilation was similar in both periods. Although immigrants did not completely converge with the US-born in name choices in one generation either historically or today, immigrants reduce the naming gap with the US-born by about one-half after spending 20 years in the United States. Furthermore, we find that the rate of cultural assimilation varies substantially by country of origin, with groups that started with high foreign sounding names switching more rapidly to more American sounding names (Southern and Eastern Europeans in the past, Mexican and Vietnamese immigrants today). We find substantial cultural assimilation for both literate and illiterate immigrants in the past, and for immigrants at all education levels today.

Despite perceived economic returns to having a native-sounding name,⁵ immigrants may give their children ethnic names in order to retain their original cultural identity. The fact that parents do not fully adopt native naming patterns within the first generation highlights the value that immigrants place on maintaining their cultural identity, consistent with Akerlof and Kranton’s (2000) and Benabou and Tirole’s (2011) theories of the economics of identity and Bisin and Verdier’s (2000) model of cultural transmission within families. Shifting toward native-sounding names may reflect learning about US culture, a greater identification with US culture over time, or making a final decision to stay in the United States rather than return home.⁶

Our paper is also one of the first to document cultural assimilation for first generation immigrants. Many papers in economics and other social sciences show that the children of immigrants readily join US society. Second generation immigrants have similar fertility behavior, labor force participation, and political preferences to the children of the US-born, with only minor differences associated with their parents’ home country.⁷ However, it has been a challenge to find large longitudinal datasets that allow researchers to follow shifts in first generation immigrants’ behavior over time.

We emphasize that our paper has no normative implications. That is, we do not imply that immigrants should assimilate culturally into the US society. In fact, arguably part of what makes a society flourish is its openness to cultural diversity. Our paper simply documents what immigrants do in practice.

I. Data and Definitions

A. Datasets with Information on Names

For the past, we use the 1920 census to reconstruct the names and ages of children living in the household with immigrant and US-born mothers. We also observe mother’s current age, place of birth, and arrival year in the United States.⁸ Because modern census data does not reveal names, our modern sample is the universe of births occurring in the state of California between 1989 and 2015 (excluding 2011, which is incomplete).⁹ California housed one-third of the foreign-born population in 1990. Birth certificates report the names of children, their mothers, and often their fathers. California birth certificates do not contain information on age of arrival, which is a key limitation.

Our research design compares multiple births from the same mother. In the 1920 census, we directly observe all children living in the household. For the modern data, we instead link mothers across births occurring in California using mothers’ first name, maiden name, birth place, and exact birth date. Overall, we match 80 percent of US-born mothers who report having two or more children (as recorded in the parity measure). We match a lower share of foreign-born mothers (67 percent) because a larger proportion of their births occurred outside California. Online Appendix Figure 1 documents the match rate by year. The match rate is lower at the beginning of the sample because many reported births occurred before the dataset began. Panel A of online Appendix Table 1 compares the characteristics of matched and unmatched mothers. Matched mothers have higher levels of education than unmatched mothers. Panel B documents that these educational differences are driven primarily by the lower match rates for immigrants and mothers born outside of California, suggesting that the matching process itself does not select on the basis of educational attainment.

B. Measuring the Foreignness of Given Names

We construct an index of name foreignness for every given name, based on the relative probability that the name is held by someone born in the United States or abroad. The formula is given by

$$R_{name}=\frac{\frac{\#foreignersname}{total\#foreigners}}{\frac{\#nativesname}{total\#natives}}.$$

This measure has a natural interpretation: for example, R = 2 implies that a name is twice as likely to be used by foreigners as by natives.

The formula for relative probability is sensitive to outliers. We thus adopt the normalized index used by Fryer and Levitt (2004) to measure distinctly black names. In particular, the foreignness index or F-index is defined as

$$ForeignnessInde{x}_{name}=100\cdot \frac{\frac{\#foreigner{s}_{name}}{total\#foreigners}}{\frac{\#foreigner{s}_{name}}{total\#foreigners}+\frac{\#native{s}_{name}}{total\#natives}},$$

and ranges from zero to 100, with a value of zero reflecting distinctively native names and a value of 100 reflecting distinctively foreign names. Note that the F-index is a simple function of R, equivalent to R/(1 + R).¹⁰

Calculating the F-index is data intensive because it requires having counts of foreign- and US-born residents with each given name. This is straightforward in the historical data because the 1920 census contains information on the first name and birth country of every resident of the United States. However, in the modern birth records, we can only use the names of birth parents to compute the modern F-index. A further concern in the modern data is that birth certificates record the birth places (and thus foreign-born status) of mothers, but not of fathers. We impute birth places for men in the modern data by assuming that all foreign-born mothers were paired with foreign-born fathers, and likewise for US-born mothers.¹¹ The foreignness of a given name changes over time as names come into and out of fashion. We thus construct the F-index from individuals born soon before the children in the sample. To ensure that we have enough data to accurately reflect each name, we construct the F-index from ten birth cohorts in each period (1895–1905 for the past; parents born between 1985–1995 for the present).¹² Online Appendix Table 3 lists the most foreign, neutral, and native names for boys and girls for our main F-index in the past and present.

Section V presents results with alternative versions of the F-index. Our preferred historical index uses the names of the entire population (both parents and non-parents), but we show below that results are nearly identical when using the names of parents only (the correlation between the two indices is 0.954). For the historical data, we also present results using a birth cohort specific F-index to better capture naming trends calculated from cohorts born in t – 1 to t – 20 for a child born in t. We address measurement error in boys’ names in the modern data by calculating an F-index from the names of the children themselves, rather than from birth parents. In this case, we classify children of foreign-born mothers as “foreign” and children of US-born mothers as “native.”

II. Estimating the Relationship between Time in the United States and Name Choice

Conceptually, we are interested in comparing the two periods of mass migration in both the level of assimilation (gap) and the rate of assimilation (closing the gap) between the US-born and foreign-born. We start by describing our empirical exercise and then we discuss the identification assumptions required to compare both the level and rate of assimilation across the two periods.

We first consider the rate of assimilation. A natural approach to estimating the effect of years spent in the United States on name foreignness of children would be to consider the following specification for foreign-born mothers:

$$\begin{array}{l}ForeignnessInde{x}_{ijt}={\alpha }_j+{\beta }_1\sum _{m=1}^{20}1\left[YearsU{S}_{ijt}=m\right]\\ +{\beta }_2\sum _{k=1}^{K}1\left[Birthorder{}_{ijt}=k\right]+{\gamma }_{ijt}+{\epsilon }_{ijt}.\end{array}$$ (1)

The dependent variable is the foreignness index of child i’s name born to mother j at time t. The main right-hand-side variable is a set of dummy variables for the number of years a mother has spent in the United States at the child’s year of birth t. The omitted category is women who give birth in their year of arrival to the United States (YearsUS = 0). By including mother fixed effects (α_j), we identify the effect of time spent in the United States using name differences between siblings born in different years. We control for the child’s rank in the birth order with a set of dummy variables to account for traditions in some cultures to name oldest sons and daughters after relatives.¹³ Note that child’s birth year dummy variables would be collinear with mother’s years in the United States and the mother fixed effect, which absorbs mother’s year of arrival. We thus add child’s birth year (γ_ij) in five-year bins to absorb secular trends in naming.¹⁴ We later show that results are robust to using three-year bins instead.

We cannot use equation (1) for a past/present comparison because we do not observe mother’s arrival year in the CA birth records. In addition, equation (1) does not allow us to compare the name choices of US-born and foreign-born mothers. Instead, our main analysis uses mother’s age in birth year t as a proxy for mother’s time spent in the United States. This proxy relies on a demographic equation relating mother’s years spent in the United States by birth year t to her age in birth year t and in her year of arrival to the United States (mother’s years in United States by birth year t = mother’s age in birth year t – mother’s age at arrival in United States). For example, a mother who arrived in the United States at age 20 and had a child at age 30 would have been in the United States for 10 years by the time of birth. Controlling for a mother fixed effect absorbs a mother’s age at arrival in the United States, allowing us to use mother’s age at birth year t as a proxy for mother’s years in the United States (net of measurement error).¹⁵ The key assumption underlying our interpretation of this proxy is that mother’s age at birth does not directly affect the rate or level of assimilation.

For our past/present comparison, we thus estimate the relationship between name foreignness and mother’s age at the time of birth for mothers between the ages of 20 and 40:

$$\begin{array}{l}ForeignnessInde{x}_{ijt}={\alpha }_j+{\pi }_1\sum _{m=21}^{40}1\left[AgeMothe{r}_{ijt}=m\right]\\ +{\pi }_2\sum _{k=1}^{K}1\left[Birthorde{r}_{ijt}=k\right]+{\gamma }_{ijt}+{\epsilon }_{ijt}.\end{array}$$ (2)

The main right-hand-side variable here is a set of dummy variables for the mother’s age at the child’s year of birth t. The omitted category is mothers who were 20 years old at a child’s birth.

We provide two pieces of evidence to support the assumption that mother’s age at birth does not have a direct effect on name choice beyond its effect on years spent in the United States. First, we consider the name choice of US-born mothers as they age. Our assumption implies that there should be a decline in name foreignness with mother’s age at birth, which increments by one for each year she spends in the United States (= years in the United States) for foreign-born mothers due to cultural assimilation but not for US-born mothers, which is indeed what we find (see Figure 1). Second, we consider the names given to the children of immigrants who themselves were born abroad before their mothers moved to the United States. Before migrating to the United States, mothers may still select US-sounding names for their children prospectively if a move to the United States is already planned, but we expect such assimilation to be more muted. We indeed find a substantially smaller reduction in name foreignness with mother’s age for children born abroad than for children born in the United States (see online Appendix Figure 3). Note that we can only observe children born abroad in the historical data.

Figure 1. IMMIGRANTS SELECTED LESS FOREIGN NAMES AFTER SPENDING TIME IN UNITED STATES: PAST AND PRESENT.

Notes: Panels A and B show the foreignness index of names given to children of native and foreign-born mothers by the mother’s age when the child was born. These figures report the constant plus the estimated effect of the individual mother’s age at birth indicators from equation (2). Panel C shows the foreignness index of names given to children of foreign-born mothers by the mother’s years in the United States at the time of the child’s birth. Specifically, we report the constant plus the coefficients on indicators of mother’s years in United States when the child was born from equation (1). Regressions also include indicators for child’s rank in the birth order, birth year in five-year bands, and mother fixed effects. The complete-count 1920 census data includes white children aged 0–15 who were born in a non-Southern state and were living with their parents in 1920. All children have mothers who were less than 43 years old in 1920 so that we can observe a relatively complete birth order, and who were between 20–40 years old at the time of the child’s birth. N(foreign-born) = 4,219,213; N(native-born) = 9,337,285. The California birth certificates data includes all children born to a mother aged 20–40 in California from 1989–2015. N(native-born) = 2,957,731; N(foreign-born) = 2,082,142.

Unless assimilation proceeds at a constant pace for each year spent in the United States, we need to additionally assume that the spacing between the mother’s age at arrival in the United States and her age at first birth in the United States is the same in the past and in the present in order to compare the rates of assimilation across these two time periods. Imagine that immigrant mothers in the past had their first child after two years in the United States, whereas immigrant mothers today wait five years before having their first child. If the rate of cultural assimilation is fastest in the first few years in the country, then we would overstate assimilation in the past relative to the present. However, we find a very linear relationship between mother’s age and name foreignness in both periods, suggesting that differential spacing between age at arrival and first birth would not likely affect our conclusions.

Without information on age of arrival in the modern data, we must proceed with caution in making statements about the levels of the naming gap between foreign and native-born mothers upon first arrival or by years spent in the United States. Mothers arrive in the United States at somewhat older ages today (age 24 on average) than they did in the past (age 20 on average).¹⁶ Our estimation approach uses mother’s age at birth as a proxy for mother’s years in the United States, which implicitly considers age 20 to be the first year in the United States in both time periods. Thus, we potentially overstate the naming gap in levels between immigrant and native mothers in the modern data at any given number of years spent in the United States. For example, at age 40, mothers will have had only 16 years in the United States in which to assimilate (on average), but we will treat them as if they have been in the United States for 20 years. Given we find that immigrants erase about −0.5 F-index points per year in the United States, a back of an envelope calculation that accounts for differences in age of arrival suggests that we overstate the level of the naming gap in the modern data relative to the historical data by 2 points (= −0.5 × 4 years) after 20 years in the United States.¹⁷

III. The Name Choice of Immigrant Mothers: Past and Present

A. Core Results

Consistent with a process of cultural assimilation, we observe that immigrant mothers gave their children fewer foreign names as they spent more time in the United States in both the past and the present. Figure 1 graphs the implied F-index of US-born and foreign-born mothers by mother’s age at the time of birth for the past (panel A) and the present (panel B). In particular, we report the constant plus the estimated effect of the individual mother’s age at birth indicators from equation (2), allowing us to show both the initial level and rate of assimilation.¹⁸ Online Appendix Figure 4 instead compares the rate of assimilation in both periods by directly graphing the coefficients on each mother’s age at birth indicator relative to the omitted category of mothers who gave birth at age 20.

In the past, the children of recently-arrived immigrant mothers (mothers who are 20 years old at birth) were given names that averaged 55 points on the F-index, and children of US-born mothers who gave birth at age 20 were given names that averaged 34 points. This initial disparity amounted to a 21 point gap between young immigrant and US-born mothers. As mothers age, the US-born continued to give equally foreign sounding names, but foreign-born mothers reduced the average F-index by around 10 index points over 20 years, erasing half of the naming gap between immigrants and natives. At the end of 20 years, foreign-born mothers chose names that averaged 45 points on the F-index and US-born mothers chose names that averaged 35 points on the F-index, a difference of only 10 points. Similarly, in the modern period, the initial gap in F-index between young foreign- and US-born mothers was 24 points (48 points on the F-index for the foreign-born and 24 points for the US-born).¹⁹ After 20 years, the foreign-born mothers reduced the average F-index by a similar degree (around 10 index points), erasing just under half of the naming gap with the US-born. The foreign-native gap at the end of 20 years was 12 points (37 points in the F-index for the foreign-born and 25 points for the native-born). One notable difference between the two periods is that both immigrant and US-born young mothers chose less-foreign names today.²⁰

We return to the more natural specification for cultural assimilation that uses mother’s years in the United States, rather than mother’s age at birth, in Figure 1 (panel C). We can only implement this specification (equation (1)) in the historical data. Children born after their mother had spent 20 years in the United States scored 13 points lower on the F-index relative to their siblings born upon their parents’ first arrival.²¹

B. Heterogeneity by Country of Origin and Education

Immigrants from sending countries that are culturally distant from the United States or that face high levels of discrimination may enjoy the largest benefit from name-based assimilation, but they also may have experienced the highest costs of assimilation, in terms of abandoning elements of their cultural identity. Figure 2 documents that the speed of name-based assimilation differs by country of origin in both past (panel A) and present (panel B). For brevity, we report estimates from a modified version of equation (2) that replaces indicators for individual years of age with a linear effect of mother’s age in birth year.

Figure 2. EFFECT OF TIME IN UNITED STATES ON NAME FOREIGNNESS BY SENDING COUNTRY: PAST and PRESENT.

Notes: In this figure we estimate a regression of the foreignness index of a child’s name on a set of interactions between mother’s country of birth and a linear term for mother’s age at birth. We report 20 × the coefficient value of mother’s age at birth for each country of birth. Regressions also include indicators for child’s rank in the birth order, birth year in five-year bands, and mother fixed effects. Country labels also report the foreignness index of children born to mothers age 20 from each country. Panel A uses the complete-count 1920 Census. Panel B uses California birth certificates from 1989–2015. Sample details in note to Figure 1. All countries except Wales in the historical data and China in the modern data have coefficients that are significantly different from zero at the 5 percent level.

In the past, immigrants from Western European countries like England and Denmark gave their children less foreign-sounding names on average (F-index of 39–40, compared to 35 for the US-born) but exhibited little to no decline in name foreignness with time spent in the United States. In contrast, immigrants from countries like Portugal, Finland, Austria, and Russia gave their children highly-foreign names on average (F-index = 59) but also exhibited faster rates of name assimilation as they spent more years in the United States (declines of 8–12 F-index points after 20 years in the United States). This result is not simply due to “regression to the mean”; without concerted effort on the part of immigrants to adapt to US society, the names given by immigrant parents would not mechanically drift toward the native norm.²²

Today, Mexican immigrants give their children the most foreign-sounding names (F-index = 50), whereas other immigrants choose substantially less foreign names (average F-index = 26).²³ However, Mexican immigrants shift away from foreign-sounding names most quickly, reducing the F-index by 10 points after 20 years spent in the United States. Vietnamese immigrants and immigrants from other countries (“rest of world”) also demonstrate rapid assimilation (a reduction of 7 points after 20 years in the United States), whereas immigrants from China and the Philippines exhibit little name shifting.²⁴

Immigrants of all literacy and education levels shift away from foreign-sounding names with time spent in the United States. Table 1 compares the pace of cultural assimilation by mother’s country of origin and literacy status (panel A, historical data) or education (panel B, modern data); as above, we report the coefficient on a linear effect of mother’s age at birth year on name foreignness. Panel A reports these estimates for the six countries that have at least 2,000 mother-child observations in each category (literate/not); recall that the literacy rate for some countries was more than 95 percent, and so this comparison is only feasible in some cases. We find substantial assimilation in all cases, with no clear pattern by literacy status. Illiterate mothers from Finland, Germany, and Portugal assimilated more rapidly than their literate counterparts, whereas for mothers from Austria, Italy, and Russia this pattern was reversed.

Table 1—

EFFECT OF TIME IN UNITED STATES ON NAME FOREIGNNESS BY MOTHER’S CHARACTERISITICS: PAST AND PRESENT

Dependent variable = foreignness index
			Mother is…
			Literate	Not literate
Panel A. Historical data (1920 census)
Italy	Mom age at birth		−0.318 (0.033)	−0.215 (0.034)
	Observations		405,349	307,335
Austria	Mom age at birth		−0.697 (0.039)	−0.520 (0.062)
	Observations		259,011	83,297
Germany	Mom age at birth		−0.307 (0.040)	−0.714 (0.245)
	Observations		257,488	5,812
Russia	Mom age at birth		−0.909 (0.037)	−0.693 (0.060)
	Observations		447,652	132,141
Finland	Mom age at birth		−0.574 (0.107)	−1.049 (0.386)
	Observations		48,264	4,037
Portugal	Mom age at birth		−0.633 (0.187)	−0.724 (0.181)
	Observations		15,845	16,442
	Less than HS (1)	HS grad (2)	Some college (3)	College plus (4)
Panel B. Modern data (California birth certificates)
Vietnam	−0.389 (0.319)	−0.393 (0.166)	−0.328 (0.176)	−0.245 (0.138)
Observations	21,296	44,331	32,784	46,190
Mexico	−0.544 (0.035)	−0.455 (0.045)	−0.488 (0.067)	−0.486 (0.106)
Observations	1,397,249	625,503	270,753	121,395
China	−0.768 (0.682)	−0.018 (0.331)	−0.094 (0.067)	−0.072 (0.168)
Observations	10,582	25,109	25,717	98,319

Notes: This table reports coefficients from estimates of a modified version of equation (2), a regression of the foreignness index of a child’s name on a linear measure of mother’s age at the time of birth. Regressions include indicators for child’s rank in the birth order, birth year in five-year bands, and mother fixed effects, and are conducted separately by mother’s country of origin and literacy status. Panel A uses complete-count 1920 census data. Panel B uses California birth certificate data (1989–2015). Sample details in note to Figure 1. The six countries included in panel A exhibit assimilation in Figure 2 and have at least 2,000 mother-child observations in each category (literate/not).

Panel B subdivides mothers in the modern data by country of origin and highest degree obtained in the data. For mothers from Mexico and Vietnam, the two countries that exhibit substantial name-based assimilation, we find rapid assimilation in all educational categories. If anything, less educated mothers appear to assimilate most rapidly, but we cannot statistically distinguish the coefficients across education groups.

IV. Sensitivity and Data Limitations

A. Data Comparability Issues

Throughout the paper, we attempt to standardize the historical and modern data. However, there are still a few remaining differences that we investigate here. First, the historical data covers the entire United States, while the modern data is only for California. We replicate our historical analysis in online Appendix Table 4 (row 1) for the state of California only; we still find substantial assimilation but the pace was somewhat slower than in the national sample.²⁵ Alternatively, we try reweighting the modern data so that the immigrant mothers in our sample reflect the country-of-birth distribution of immigrant mothers nationwide. In doing so, the reduction in name foreignness with time spent in the United States attenuates somewhat (from −10 points to −8 points after 20 years in the United States; see online Appendix Figure 9), primarily because of the high share of Mexican-born mothers in California with high rates of name-based assimilation.

Second, the modern data records legal name as reported on a birth certificate, while the historical data were collected by census enumerators who may instead write down a different name that is used in social settings. Individuals may also change their names after birth in order to assimilate. This possibility introduces the potential role of measurement error in birth names in the 1920 census. In this case, particularly foreign names given by young mothers may be changed later on, thereby masking some of the actual assimilation that took place. Although we cannot fully address this issue, we restrict the historical data in online Appendix Table 4 (row 2) to children six years of age or younger who have not yet been to school, and thus would not have had the time or the pressure to change their birth name. Patterns are similar to the full sample. Third, the F-index for the modern birth certificate data is based on the names of parents only, while the historical census data uses the full population (parents and non-parents). We instead replicate the results using an F-index based on parents only in the 1920 census (online Appendix Figure 10) and results are entirely comparable.

B. Heterogeneity by Gender

Sociologists have documented that parents are more open to new or creative names for girls, while boys tend to receive a more traditional set of names, and so parents may be more willing to shift toward native-sounding names for daughters (Rossi 1965; Sue and Telles 2007). On the other hand, parents may be more concerned about the possible negative consequences of having an ethnic-sounding name in the labor market for sons than for daughters, especially in the past. Online Appendix Figure 11 shows that immigrants shift toward more native-sounding names somewhat more rapidly for daughters than for sons both in the past and the present (a disparity of five F-index points by gender after 20 years in the United States in both periods).

In the modern data, differential results by gender could be driven by measurement error in the F-index of boy names (see Section II). Online Appendix Figure 12 reproduces results by gender using an alternative F-index constructed from the names of the children of foreign-born versus US-born mothers; this index treats boys and girls names symmetrically. Using this metric, differential name choice by gender attenuates in the historical data and disappears in the modern data. It appears that parents shift their naming behavior with time spent in the United States at a roughly equal pace for sons and for daughters.

C. Alternative Measures of the F-index

Online Appendix Table 5 presents results from alternative F-indices that provide insight into the strategies that immigrant families used to assimilate through name choice. Row 2 replaces the overall F-index with a country-specific index. This measure asks whether immigrants shift away from common ethnic names with time spent in the United States. Estimates of name-based assimilation are similar in this case. Row 3 standardizes all names to their phonetic equivalents by using the NYSIIS algorithm instead of using raw names (for example, treating Roberto and Robert as the same name). Results are similar in the historical data but, in the modern data, the extent of name-based assimilation is cut in half. This pattern suggests that in California today, Anglicizing Spanish names is one strategy that immigrant parents use to assimilate. Indeed, inspecting common names at different percentiles of the F-index distribution reveals some names like Mary and Anna (low F-index) that have Spanish equivalents like Maria and Ana (high F-index).

V. Conclusion

We study the cultural assimilation of immigrants during two Ages of Mass Migration drawing on historical census data for the early twentieth century and California birth certificate records for today. Both then and now, immigrants chose less foreign names for their children as they spent more time in the United States, reducing the difference in name choice with the US-born by about one-half after 20 years in the United States. There are substantial differences in the pace of name-based assimilation by country of origin, with the immigrant groups most often accused of slow assimilation assimilating most rapidly.

Our findings suggest that immigrants’ identification with United States culture grows stronger with time spent in the country. The gradual adoption of American-sounding names appears to have been part of a process by which newcomers learned United States culture, made a commitment to build roots in their adoptive country, and came to identify as Americans. Naming patterns also highlight the trade-off that immigrant families face between maintaining their cultural identity and assimilating into society at large.

Overall though, lessons from the Age of Mass Migration suggest that fears that immigrants cannot or will not fit into American society are misplaced. It would be a mistake to determine immigration policy based on the belief that immigrants will remain foreigners, preserving their old ways of life and keeping themselves at arm’s length from the dominant culture.²⁶ The evidence suggests that over time immigrant populations come to resemble the US-born, and that new generations form distinct identities as Americans.