Estimating Equation and Instrumental Variable

To investigate the effects of immigration on natives’ marriage, probability of having children, and family structure across U.S. cities, we stack the data for the three Census years between 1910 and 1930, and estimate

(1) $${y_{cst}} = {\gamma _c} + {\delta _{st}} + \beta Im{m_{cst}} + {u_{cst}}$$

where y _cst is the outcome for city c in state s in Census year t, and Imm _cst is the fraction of immigrants over the predicted city population.^{Footnote 13} In our baseline specification, we consider the stock of European immigrants who arrived in the United States in the previous decade, but results are robust to extending this definition to all immigrants, irrespective of their country of origin or their year of arrival. Since we always control for city and state by year fixed effects (γ _c and δ _st), β is estimated from changes in the fraction of immigrants within the same city over time, compared to other cities in the same state in a given year. Standard errors are clustered at the MSA level, and MSA boundaries are fixed to 1940 in order to keep geography constant.

When estimating the effects of immigration on natives’ fertility and marriage, we face a key empirical challenge: the location decision of immigrants might be endogenous to local, time-varying conditions. For instance, immigrants might be attracted to cities with stronger labor markets, where marriage prospects for natives are better. This would introduce a positive bias to OLS estimates of Equation (1). Alternatively, because of congestion costs, immigrants might be more likely to settle in otherwise declining cities, where marriage markets for natives are weaker. In this case, OLS estimates would be downward biased.

To deal with these and similar concerns, we closely follow Tabellini (Reference Tabellini2020) and construct a “leave-out” version of the shift-share instrument commonly adopted in the immigration literature (Altonji and Card Reference Altonji, Card, John and Richard1991; Card Reference Card2001). The instrument predicts the number of immigrants received by U.S. cities over time by interacting 1900 settlements of different ethnic groups with subsequent national migration flows from each sending region, excluding individuals that eventually settled in a given city’s MSA. Formally, Imm _cst in Equation (1) is instrumented with

(2) $${Z_{cst}} = {1 \over {\hat P}_{cst}}{{\sum}_j}{\alpha _{jc}}O_{jt}^{ - M}$$

where ${{\hat P}_{cst}}$ is predicted city population; α _jc is the share of individuals of ethnic group j living in city c in 1900 (relative to all immigrants from group j living in the United States in that year); and $O_{jt}^{ - M}$ is the number of immigrants from country j that migrated to the United States between t and t −1, net of those that eventually settled in city c’s MSA.Footnote ¹⁴

The instrument combines two sources of variation. The first one is the change in the total number of immigrants from any sending country migrating to the United States in a given decade ( $O_{jt}^{ - M}$ ). Two historical episodes contributed to the high variation in the share of immigrants from various European countries over this time period. First, WWI drastically decreased immigration from Europe, especially for countries more directly involved in the war and which did not belong to the Allies. Second, the Immigration Acts of 1921 and 1924 introduced country-specific quotas based on the 1890 immigrant population. The quotas were set to restrict immigration from Southern and Eastern Europe, while favoring that from older sending regions such as the United Kingdom, Germany, and Scandinavia.

The second source of variation exploited by the instrument comes from the geographic dispersion in the share of individuals from each ethnic group living in different U.S. cities in 1900 (α _jc). Such variation arose from the fact that, upon arrival in the United States, early settlers from different sending countries tended to locate in various U.S. cities, since the timing of outmigration varied widely across European countries, depending on local political and economic conditions (Hatton and Williamson Reference Hatton and Williamson1998). One important predictor of the geographic distribution of immigrants in the United States is the gradual expansion of railroads during the nineteenth century: as documented in Sequeira, Nunn, and Qian (Reference Sequeira, Nunn and Qian2020), places that gained access to the railroad just before an immigration boom received more immigrants in the following decade. As a consequence, before 1900, various U.S. cities were populated by different ethnic groups. For example, in 1900, while Italian communities were present in Boston, Philadelphia, and San Francisco, they were practically non-existent in Minneapolis. On the other hand, almost 4 percent of Swedes were settled in Minneapolis, but less than 1 percent of them were located in northeastern cities like Philadelphia or Boston (see also Abramitzky and Boustan Reference Abramitzky and Boustan2017). Online Appendix B presents a simple example to illustrate graphically how the instrument combines the time-series and cross-sectional variations.

Instrument Validity

Several recent papers discuss the conditions for the validity of shift-share instruments (Jaeger, Ruist, and Stuhler Reference Jaeger, Ruist and Stuhler2018; Adao, Kolesàr, and Morales Reference Adao, Kolesàr and Morales2019; Goldsmith-Pinkham, Sorkin, and Swift Reference Goldsmith-Pinkham, Sorkin and Swift2020; Borusyak, Hull, and Jaravel Reference Borusyak, Hull and Jaravel2022). In our setting, the key identifying assumption can be expressed as follows. Conditional on city and state by year fixed effects, city-specific factors that attracted immigrants from different European countries prior to 1900 must be uncorrelated both with post-1900 patterns of European immigration and with changes in socioeconomic conditions across U.S. cities.

This assumption may be violated if the city-specific characteristics that attracted immigrants from each specific sending country before 1900 had long-lasting effects both on migration patterns of individuals from that specific country and on natives’ marriage prospects. We provide evidence against this possibility in two ways. First, we document that the 1900–1910 change in outcomes is not correlated with the post-1910 change in immigration predicted by the instrument. Second, we allow cities to be on differential trends by interacting year dummies with several 1900 city characteristics—including the fraction of immigrants and proxies for manufacturing activity.Footnote ¹⁵

A second threat to identification is that local shocks hit U.S. cities while simultaneously attracting immigrants from countries that had sent more migrants to those same cities before 1900 (Borusyak, Hull, and Jaravel Reference Borusyak, Hull and Jaravel2022). The “trend-break” in immigration flows generated by WWI and the Immigration Acts mitigates this issue (Abramitzky et al. Reference Abramitzky, Ager, Boustan, Cohen and Hansen2023); it also assuages the concern of serial correlation highlighted by Jaeger, Ruist, and Stuhler (Reference Jaeger, Ruist and Stuhler2018). Tabellini (Reference Tabellini2020) presents further robustness checks in the same context as our paper, constructing alternative instruments that predict European immigration by exploiting only the WWI and quota shocks, as well as weather variation across countries in Europe. We describe all the robustness checks later, after presenting the main results.

First-Stage Results

First-stage results for the relationship between actual and predicted immigration are reported in Online Appendix Table A.4, after controlling for city and state by year fixed effects.Footnote ¹⁶ In Column (1), the dependent variable is the fraction of immigrants over actual city population, and the independent variable is the baseline instrument constructed in Equation (2). Columns (2) and (3) scale both the actual and the predicted number of immigrants by, respectively, 1900 and predicted population. In all cases, the F-stat is very high, and there is a strong and statistically significant relationship between the endogenous variable and the instrument.

Figure 1 plots the residual scatter plot of the regression reported in Column (3) and confirms visually the strong relationship between actual and predicted immigration.Footnote ¹⁷ From Column (3) onward, Online Appendix Table A.4 presents estimates for specifications where both the actual and the predicted number of immigrants are scaled by predicted city population, and explores the stability of the baseline specification to the inclusion of interactions between year dummies and 1900 city characteristics.

First, we augment the specification reported in Column (3) by interacting year dummies with the (log of) 1900 city total and immigrant population (Column (4)).Footnote ¹⁸ Next, in Columns (5) and (6), we include interactions between year dummies and, respectively, the 1904 (log of) value added by manufacture and the marriage rate of native women in 1900. Even though the F-stat falls relative to Column (1), it remains well above conventional levels. Also, and importantly, neither the economic nor the statistical significance of coefficients is affected.

Marriage Rates

In Table 2, we study the impact of immigration on natives’ marriages, focusing on the age groups with the highest marriage rates, that is, women aged 18–33 and men aged 20–35.Footnote ¹⁹ Panels A and B show results for native women and native men, respectively, estimating OLS (Column (1)) and 2SLS (Column (2)) regressions.Footnote ²⁰ Both OLS and 2SLS estimates suggest that immigration increased marriage rates for native women. These effects are not only statistically significant but also economically relevant. According to the coefficient in Column (2), a 5 percentage point (or, one standard deviation) increase in the fraction of immigrants raised marriage rates of native women aged 18–33 by 2.2 percent relative to the 1910 mean. Panel B documents that a similar pattern holds for native men aged 20–35: a 5 percentage point increase in immigration raised men’s marriage rates by 2.1 percent relative to their baseline mean.Footnote ²¹ Our findings are quantitatively close, with the opposite sign, to those obtained in Autor, Dorn, and Hanson (Reference Autor, Dorn and Hanson2019), who document that, over the last 30 years, a 1 percentage point increase in import competition from China lowered female marriage rates by 1.8 percent.

Table 2 IMMIGRATION AND MARRIAGE OF NATIVES

Notes: This table presents results of OLS and 2SLS for a balanced panel of the 180 U.S. cities with at least 30,000 residents in each Census year reported. For 1920, Sacramento (CA) and New Bedford (MA) had unreasonably low values for marriage, fertility, and the other demographic outcomes so we excluded them from the main analysis. The dependent variable is the fraction of women married in the age range 18–33 in Panel A and the fraction of men married in the age range 20–35 in Panel B. Fr. Immigrants refers to the fraction of immigrants arrived in the previous decade over predicted city population, and is instrumented using the baseline version of the instrument constructed in the Estimating Equation Section. The mean of dependent variables is shown at the bottom of the table. Column (3) is a falsification test (pre-trends). In Columns (4) and (5), we check the robustness of our results in Column (2), by augmenting our baseline specification interacting year dummies with the (log of) 1900 city and immigrants’ population and the 1900 marriage rates, respectively. Finally, in Column (6), we show the robustness of our results scaling both the actual and the predicted number of immigrants by 1900, rather than predicted, population. F-stat is the Kleibergen-Paap F stat for joint significance of instruments. All regressions include city and state by year fixed effects. Robust standard errors, clustered at the MSA level, in parentheses. *p<0.10, **p<0.05, ***p<0.01.

Source: Authors’ calculations using IPUMS data.

Subsequent columns of Table 2 explore the robustness of our baseline results. First, in Column (3), we test for pre-trends by regressing the 1900 to 1910 change in marriage rates on the post-1910 instrumented change in immigration. Reassuringly, in both Panel A and Panel B, the coefficient on immigration is statistically indistinguishable from zero and different from that reported in Column (2). Next, in Columns (4) and (5), we augment our baseline specification by interacting year dummies with the (log of) 1900 city total and immigrant population and the 1900 marriage rates, respectively. This exercise is performed to check that the results in Column (2) are not due to city-specific characteristics that may have simultaneously attracted more immigrants before 1900 and affected the evolution of natives’ marriage rates in subsequent decades. In all cases, the point estimate remains statistically significant and quantitatively close to that estimated in the baseline specification. Finally, in Column (6), we provide evidence that results are robust to scaling both the actual and the predicted number of immigrants by 1900, rather than predicted, population.Footnote ²²

As an additional robustness check, we examined whether our results are robust to interacting year dummies with the initial immigrant shares of groups that are particularly important for the variation exploited by the instrument. Following the approach suggested in Goldsmith-Pinkham, Sorkin, and Swift (Reference Goldsmith-Pinkham, Sorkin and Swift2020), we first calculate the Rotemberg weights associated with each of the 16 countries in our sample, and report the standard statistics in Online Appendix Table A.7. Reassuringly, out of the 16 countries (or groups of), only France, Switzerland, and Germany had a negative weight (which was nonetheless quantitatively small). Then, we isolate the five origin country-groups with the largest Rotemberg weights (Austria and Hungary; Portugal, Greece, and Spain; Russia; Italy; and Poland).Footnote ²³ We replicate the analysis by interacting year dummies with the initial shares of each of the five groups. Results are reported in Online Appendix Table A.8 for marriage rates of women and men (Panels A and B). In all cases, the estimates are in line with those from the baseline specification (reported in Column (1) to ease comparisons). Reassuringly, the size and the precision of coefficients also remain similar when including the interactions for the five countries simultaneously (Column (7)). These patterns indicate that our results are not driven by the potentially spurious correlation between the settlements of immigrant groups, which drive substantial variation in the instrument, and underlying changes in cities’ economic or demographic structure.

Up to now, we have reported results for the “marriage-relevant” age groups by gender. Figure 2 separately documents the effect of immigration on marriage rates of native men and women for different age groups. The effects estimated in Table 2 are driven by the youngest cohorts: a 5 percentage point increase in the fraction of immigrants raised marriage rates of native women aged 18–25 and men aged 20–27 by 3.4 percent and 4.0 percent, respectively, relative to their baseline means. The effect of immigration is not statistically significant for older cohorts. The point estimates and standard errors related to Figure 2 are reported in Online Appendix Table A.9, where we also consider the probability of being never married for the oldest cohorts (Column (5)). While immigration did not affect the probability of being never married for men, it lowered the likelihood that women aged 34–65 remained unmarried. These patterns thus suggest that, at least for native women, our estimates are not merely capturing an “anticipatory effect” in the timing of marriage.

Figure 2 THE IMPACT OF IMMIGRATION ON MARRIAGE RATES, BY GENDER AND AGE GROUPS

Notes: This graph shows the impact of a one standard deviation increase in the fraction of immigrants on the increase in marriage rates with respect to the mean value in 1910. We report the standardized coefficients by age group and for men and women separately.

Source: Authors’ calculations using IPUMS data.

Probability of Having Children

In Table 3, we study how immigration affected the probability of having children for native women. The first two columns focus on the children to women ratio, while in subsequent columns, we separately analyze the effect of immigration on the extensive and intensive margins. We define the former as the share of women with at least one child and the latter as the children to mothers ratio. In odd columns, the dependent variable is the total number of children in the household, while in even columns, the dependent variable is the number of children below the age of 5. Since full-count data allow us to match mothers with children only if they are living in the same household, we restrict the sample to women aged 18–33, whose children are likely to live with their parents.

Table 3 IMMIGRATION AND FERTILITY OF NATIVE WOMEN

Notes: This table presents results of 2SLS for a balanced panel of the 180 U.S. cities with at least 30,000 residents in each Census year reported. For 1920, Sacramento (CA) and New Bedford (MA) had unreasonably low values for marriage, fertility, and the other demographic outcomes so we excluded them from the main analysis. The dependent variable is: in Column (1) (Column (2)), the total number of children (toddlers) with a native mother in the age range 18–33 over the total number of women in the age range 18–33, in Column (3) (Column (4)) the fraction of women in the age range 18–33 who have children (toddlers) and in Column (5) (Column (6)) the average number of children (toddlers) per mother in the age range 18–33. Fr. Immigrants refers to the fraction of immigrants arrived in the previous decade over predicted city population, and is instrumented using the baseline version of the instrument constructed in the Estimating Equation Section. The mean of dependent variables is shown at the bottom of the table. F-stat is the Kleibergen-Paap F stat for joint significance of instruments. All regressions include city and state by year fixed effects. Robust standard errors, clustered at the MSA level, in parentheses. * p<0.10, ** p<0.05, *** p<0.01.

Source: Authors’ calculations using IPUMS data.

Both OLS and 2SLS results, reported in Panels A and B, respectively, document a positive and significant relationship between immigration and the probability of having children for native women. The point estimate in Column (1) of Panel B implies that a 5 percentage point increase in immigration raised the children to women ratio by 3.3 percent relative to its 1910 mean. Decomposing this effect along the extensive and the intensive margins, we note that immigration increased the number of women with children and the average number of children per woman by 2.4 percent and 1 percent, respectively. Said differently, for every ten new babies born to native women, seven were due to the extensive margin, while three were due to the intensive margin. The magnitude of the effect is similar when we restrict our attention to children below the age of 5.Footnote ²⁴

Between the late nineteenth century and the 1930s, the United States experienced a demographic transition, with a reversal of the positive relationship between income and economic growth (Galor and Weil Reference Galor and Weil2000). The fertility rate of the total white population declined substantially, with the birth rate moving from almost 50 per thousand people in 1850 to 20 per thousand in 1930 (Zelnik Reference Zelnik1959). The inclusion of state by year fixed effects takes care of these national trends, since the effect of immigration is estimated from changes in the fraction of immigrants within the same city over time compared to other cities in the same state in a given year. Moreover, as noted by Easterlin (Reference Easterlin1961), the decline in fertility was driven by rural areas; the fertility of the urban native (white) population remained stable during this time period.Footnote ²⁵

In Online Appendix Table A.10, we separately report the effect of immigration on fertility of native women by age groups. As for marriage, the effect is driven mainly by native women aged 18–25, especially on the extensive margin: a 5 percentage point increase in immigration raised the number of women in the younger age cohort with at least one child by 3.1 percent.

Household Formation and Homeownership

Table 4 provides evidence that immigration induced natives to leave their parental house earlier and set up their own independent family unit. In the first two columns, we focus on women aged 18–33, while in subsequent columns we report the effects of immigration on men aged 20–35.^{Footnote 26} Coefficients in Table 4 imply that a 5 percentage point increase in immigration raised the probability of living in an independent family unit by 2.4 percent for women and 2.2 percent for men relative to the mean in 1910. This effect is quantitatively close to that estimated for marriage rates, suggesting that the decisions to get married and leave the parental house were part of the same lifetime plan.^{Footnote 27} As shown in Online Appendix Figure A.2, these results are driven by women aged 18–25 and men aged 20–27: for these age groups, a 5 percentage point increase in immigration raised the probability of setting up their own household by more than 3 percent. Incidentally, these cohorts also experienced the largest increases in marriage and fertility because of immigration.

Table 4 IMMIGRATION AND LIVING CHOICES OF NATIVES

Notes: This table presents results of OLS and 2SLS for a balanced panel of the 180 U.S. cities with at least 30,000 residents in each Census year reported. For 1920, Sacramento (CA) and New Bedford (MA) had unreasonably low values for marriage, fertility, and the other demographic outcomes, so we excluded them from the main analysis. The dependent variables are listed in the top row of the table. Fr. Immigrants refers to the fraction of immigrants arrived in the previous decade over predicted city population, and is instrumented using the baseline version of the instrument constructed in the Estimating Equation Section. The mean of the dependent variables in 1910 is at the bottom of the table. F-stat is the Kleibergen-Paap F stat for joint significance of instruments. All regressions include city and state by year fixed effects. Robust standard errors, clustered at the MSA level, in parentheses. ***p < 0.01, **p < 0.05, p* < 0.10.

Source: Authors’ calculations using IPUMS data.

Consistent with the evidence provided thus far, Column (5) of Table 4 shows that immigration boosted homeownership rates for native men aged 20–35. The point estimate implies that a 5 percentage point increase in immigration raised homeownership rates for natives by 1.3 percentage points, or around 5 percent relative to the 1910 mean. Between 1910 and 1930, homeownership rates for natives in our sample increased, on average, by 10 percentage points, moving from 0.35 to 0.45. Our estimates suggest that the economic expansion induced by immigration can explain at least 10 percent of the increase in homeownership that took place in the cities in our sample from 1910 to 1930.

Stitching together the three sets of results presented in this section, our estimates paint a coherent picture of how immigration affected family formation, marriage rates, and fertility of native men and women in the urban early twentieth-century United States. The inflow of immigrants induced natives to marry more (and, possibly, earlier); this decision was accompanied by the choice to leave the parental house, buy a home, and set up an independent family unit. In a period in which oral contraception was not yet available (Bailey Reference Bailey2006), higher fertility was probably mechanically related to marriage and family formation decisions.

Natives’ Employment and the Supply of Marriageable Men

In two important contributions, Wilson (Reference Wilson1987, Reference Wilson1996) argues that the decline in marriage and the rise in the share of single-mother households in the United States since the 1970s have been, at least in part, due to deteriorating employment opportunities in manufacturing. Along these lines, exploiting exogenous variation in exposure to import competition from China across U.S. local labor markets, Autor, Dorn, and Hanson (Reference Autor, Dorn and Hanson2019) find that job losses in manufacturing caused a steep decline in marriage rates and a significant increase in the proportion of single-mother households. In this section, we investigate the possibility that a similar mechanism, with the opposite sign, was at play in our context. Specifically, we advance and empirically test the hypothesis that immigration had a positive effect on natives’ marriages by increasing employment and occupational standing of native men, in turn raising the supply of native “marriageable men.”

In Table 5, we study the effects of immigration on natives’ employment to population ratio, focusing on men in the “marriageable relevant” age range of 20–35. As in Table 2, Columns (1) and (2) estimate the baseline specification with OLS and 2SLS, respectively. In both cases, there is a strong and positive relationship between immigration and natives’ employment. The coefficient in Column (2), which is quantitatively very close to OLS results reported in Column (1), implies that a 5 percentage point increase in immigration raised natives’ employment to population ratio by 0.8 percent relative to its 1910 mean. As documented in Online Appendix Figure A.3, the effect of immigration is slightly larger for men in the age range 20–27, but remains positive and statistically significant for those aged 28–35. The point estimate is positive and quantitatively very similar, albeit not statistically significant, for older natives (aged 36–65).

Table 5 IMMIGRATION AND EMPLOYMENT OF NATIVE MEN

Notes: This table presents results of OLS and 2SLS for a balanced panel of the 180 U.S. cities with at least 30,000 residents in each Census year reported. The number of observations in Column (5) is 526 due to missing data on the (log of) 1904 value added by manufacture per establishment. For 1920, Sacramento (CA) and New Bedford (MA) had unreasonably low values for marriage, fertility, and the other demographic outcomes so we excluded them from the main analysis. The dependent variable is the natives’ employment to population ratio in the age range 20–35 for men. Fr. Immigrants refers to the fraction of immigrants arrived in the previous decade over predicted city population, and is instrumented using the baseline version of the instrument constructed in the Estimating Equation Section. Column (3) is a falsification test (pre-trends). In Columns (4) and (5), we check the robustness of our results in Column (2), by including the interaction between year dummies and, respectively: the (log of) 1900 city and immigrant population and the (log of) 1904 value added by manufacture per establishment. Finally, in Column (6), we show the robustness of our results scaling both the actual and the predicted number of immigrants by 1900, rather than predicted, population. The mean of the dependent variables is shown at the bottom of the table. F-stat is the Kleibergen-Paap F stat for joint significance of instruments. All regressions include city and state by year fixed effects. Robust standard errors, clustered at the MSA level, in parentheses. *p<0.10, ** p<0.05, *** p<0.01.

Source: Authors’ calculations using IPUMS data.

Figure 3 THE IMPACT OF IMMIGRATION ON MARRIAGE RATES, BY PARENTAGE

Notes: This graph shows the impact of a one standard deviation increase in the fraction of immigrants on the marriage rates of men and women by parentage with respect to the mean value in 1910. We report the standardized coefficients, separately by parentage and gender.

Source: Authors’ calculations using IPUMS data.

Subsequent columns of Table 5 test the robustness of these results. First, we verify that there are no pre-trends (Column (3)). Second, we show that results are robust to interacting year dummies with the 1900 log of city total and immigrant population (Column (4)) and log of value added in manufacturing (Column (5)). Third, we check that our estimates are unchanged when scaling both the actual and the predicted numbers of immigrants by 1900, rather than predicted, city population (Column (6)).Footnote ²⁸

Results in Table 5 are somewhat different from those obtained in Abramitzky et al. (Reference Abramitzky, Ager, Boustan, Cohen and Hansen2023), who find that the 1920s Immigration Acts did not have any impact on natives’ employment. We suspect that the different time period (1910–1930 vs. 1920–1930 only) and geography (cities vs. entire country) explain the discrepancy between our findings and those in Abramitzky et al. (Reference Abramitzky, Ager, Boustan, Cohen and Hansen2023). Our estimates are instead consistent with those in Ager and Hansen (Reference Ager and Hansen2017), Tabellini (Reference Tabellini2020), and Price, vom Lehn, and Wilson (2020). Most closely related to our paper, Tabellini (Reference Tabellini2020) shows that immigration induced natives to leave occupations that were more exposed to immigrants’ competition and to take up jobs where immigrants were prevented from entering, because of skill and language mismatch or because of discrimination. By linking individuals across Census years, Price, vom Lehn, and Wilson (2020) also find that such economic gains accrued to young native workers who in-migrated to cities that received more European immigrants, whereas older native workers who were likely displaced by the foreign-born moved elsewhere in the country. These heterogeneous effects do not alter either the validity or the interpretation of our results, since they are still consistent with the idea that, in this historical context, immigration increased the supply of native “marriageable men”—and this, in turn, increased marriage rates, the probability of having children, and family formation among natives.

In Online Appendix Table A.11, we provide additional evidence on the economic effects of immigration for native-born men in the marriageable age range (20–35). After re-stating the main result for employment (Column (1)), we document that immigration increased the share of native-born men holding a high-skilled job (Column (2)).Footnote ²⁹ Consistent with immigrants inducing natives to take on better jobs, we also find that immigration increased the occupational income score of native-born men (Columns (3) and (4)).Footnote ³⁰ Finally, we show that there is a positive relationship between immigration and the share of native-born women who were married to a native-born man who was employed (Column (5)) and held a high-skill job (Column (6)). Note, however, that the point estimate in Column (5) is not statistically significant.

Children, Schooling, and Economic Conditions of Families

The effects documented earlier suggest that immigration affected economic conditions of native families, with potentially long-lasting implications for younger generations. Consistent with this idea, Online Appendix Table A.12 shows that immigration lowered the share of children below the age of 10 born to native parents living in a household where the father was unskilled (Column (1)).Footnote ³¹ Similarly, even if the coefficient is not statistically significant at conventional levels, there is a positive relationship between immigration and the share of children of native parentage whose fathers were employed. These results suggest that, because of immigration, children of native parentage were likely to grow up in a better environment at home.

Next, in Online Appendix Table A.13, we show that immigration increased the fraction of sons with native parents aged 6–14 who were enrolled in school (Column (1)). Somewhat interestingly, though, we do not find a similar effect for daughters (Column (2)), even if the 1910 average enrollment was very similar for boys and girls. One possible explanation for this pattern is that families were credit constrained and, as more resources became available, parents chose to invest them first in sons rather than in daughters (Parish and Willis Reference Parish and Willis1993; Barcellos, Carvalho, and Lleras-Muney Reference Barcellos, Carvalho and Lleras-Muney2014).

Especially in an urban context, the employment boom generated by immigration might have increased job opportunities for male teens, leading them to drop out of school. In line with this idea, Column (3) of Online Appendix Table A.13 documents that immigration had a negative and statistically significant effect on school attendance for native males aged 15–18.Footnote ³² The 2SLS coefficient in Column (3) implies that a 5 percentage point increase in immigration lowered school enrollment rates for native males of age 15–18 by 0.7 percentage points, or 2 percent relative to the 1910 mean. The decline in school enrollment of native teens reported in Column (3) of Online Appendix Table A.13 is accompanied by a symmetrical increase in their employment probability (Column (4)). Specifically, a 5 percentage point increase in immigration raised the employment to population ratio for native males in the age range 15 to 18 by 1.5 percentage points, or 2.5 percent relative to the baseline mean. It is interesting to note that, for this age group, the percentage increase in employment implied by immigration is almost identical to the percentage decline in school enrollment, suggesting that these two patterns were closely related to each other.

Our interpretation is that, by increasing the opportunity cost of schooling, the economic expansion generated by immigration induced young (native) teens to drop out of school and enter the labor market earlier. As shown in Column (5) of Online Appendix Table A.13, most of the young males pulled into the labor force entered industries that were “not specified” in the U.S. Census, which were unlikely to provide workers with opportunities for skill or occupational upgrading.Footnote ³³ These findings resonate with those in Charles, Hurst, and Notowidigdo (Reference Charles, Hurst and Notowidigdo2019) and Cascio and Narayan (Reference Cascio and Narayan2022) for the contemporaneous period. They also suggest that, despite its average benefits for native workers and their families, the economic boom generated by immigration may have had long-lasting, negative consequences for native teens. By entering low-growth industries and by reducing their human capital accumulation, younger generations might have increased their exposure to future economic downturns.

Compositional Changes in the Native-Born Population

Price, vom Lehn, and Wilson (2020) documented that European immigration induced in- and out-migration of native-born men across U.S. cities in this historical context. If such migration response were concentrated within men 20–35, our estimates might partly capture compositional changes. While this would not invalidate our results, it would change their interpretation. In this section, we consider this mechanism using two complementary strategies.

First, we replicate the analysis by focusing on natives born within the same state.^{Footnote 34} We acknowledge that this is an admittedly imperfect proxy for non-movers, since it misses within-state migrants. Yet, it allows us to consider both men and women, since most standard linking algorithms are unable to follow women over time across U.S. Censuses (Abramitzky et al. Reference Abramitzky, Boustan, Eriksson, Feigenbaum and Perez2021). Moreover, by using data from the full-count Census, we do not need to deal with the potential concern of selection in the linking process, which may increase concerns about the generalizability of results as well as the validity of our estimates (Bailey et al. Reference Bailey, Cole, Henderson and Massey2020).

In Columns (1) to (5) of Online Appendix Table A.14, we consider the main outcomes for native-born men: marriage rates, share living with parents and in own house, home ownership, and employment. In Columns (6) to (8), we consider native-born women, presenting results for marriage rates and living choices. In Online Appendix Table A.15, we consider the six proxies for fertility used in Table 3. The estimates obtained for the sample of individuals born within the same state (Panel B) are remarkably similar to those from the main sample (Panel A), indicating that compositional changes induced by between-state migration are unlikely to influence our results. The only partial exception is the employment to population ratio: in Panel B, the point estimate is positive and statistically significant at the 10 percent level, but the magnitude is smaller. Note, however, that the 1910 mean of the employment to population ratio is also substantially larger for this sample compared to that of the baseline sample.

Second, we use the linked sample of (native-born) men taken from Abramitzky et al. (Reference Abramitzky, Boustan, Eriksson, Feigenbaum and Perez2021), restricting attention to individuals who lived in the same city during the previous decade. While this sample is not fully representative and does not include women (Bailey et al. Reference Bailey, Cole, Henderson and Massey2020), it allows us to consider both within and between state movers. We present results in Columns (1) to (5) of Online Appendix Table A.14, Panel C.^{Footnote 35} In all cases, results are in line with those presented in Panel A. As for Panel B, the only partial exception is the coefficient for employment to population ratio, which is precisely estimated but smaller than in both Panels A and B. It is worth noting that the 1910 mean of the employment to population ratio in the linked sample is 0.99, suggesting that this is a selected sample of men with higher attachment to the labor force and that there is limited scope for this variable to increase any further.

Taken together, the evidence in this section indicates that compositional changes among the native-born population cannot, alone, explain our results.

Changes in Sex Ratios

The literature has documented that sex ratios, that is, the relative number of men and women, can be an important determinant of marriage and family formation decisions (Angrist Reference Angrist2002; Abramitzky, Delavande, and Vasconcelos Reference Abramitzky, Delavande and Vasconcelos2011; Lafortune Reference Lafortune2013). Since more than 60 percent of immigrants entering the United States at the beginning of the twentieth century were young men, immigration likely altered sex ratios, possibly increasing the availability of potential mates for native women. However, we argue that this channel cannot explain a substantial fraction of our main results.

First, while changes in the relative number of men and women might have contributed to the increase in marriage rates and fertility of native women, they can hardly explain why immigration also raised marriage rates of native men.Footnote ³⁶ Second, as we show in Column (3) of Table 6 (Panel A), only 5 percent of native women had a foreign-born husband; likewise, Column (3) of Online Appendix Table A.16 documents that only 3 percent of native men had a foreign-born wife as of 1910. In addition, the increase in marriage rates for men and women was quantitatively similar (Table 2), suggesting that natives, in most cases, were marrying each other. These observations resonate with the idea that, at the time, marriage markets were highly segmented along ethnic lines (Angrist Reference Angrist2002).Footnote ³⁷

Table 6 IMMIGRATION, MARRIAGE RATES, AND FERTILITY OF NATIVE WOMEN AGED 18–33 (2SLS RESULTS)

Notes: This table presents results of 2SLS for a balanced panel of the 180 U.S. cities with at least 30,000 residents in each Census year reported. For 1920, Sacramento (CA) and New Bedford (MA) had unreasonably low values for marriage, fertility, and the other demographic outcomes, so we excluded them from the main analysis. In Panel A, the dependent variable is the marriage rate of women aged 18–33 by husband parentage. In Panel B, the dependent variable is the children to women ratio by father parentage. We consider only children of women aged 18–33. For example, in Column (2) of Panel B, the dependent variable is the number of children with a native mother aged 18–33 and a father with native parentage over the number of native women aged 18–33. Columns (4)–(6) focus on women who are second-generation immigrants. Fr. Immigrants refers to the fraction of immigrants arrived in the previous decade over predicted city population, and is instrumented using the baseline version of the instrument constructed in the Estimating Equation Section. The mean of the dependent variables is shown at the bottom of the table. F-stat is the Kleibergen-Paap F stat for joint significance of instruments. All regressions include city and state by year fixed effects. Robust standard errors, clustered at the MSA level, are in parentheses. *p < 0.10, **p< 0.05, ***p < 0.01.

Source: Authors’ calculations using IPUMS data.

Results reported in Panel A of Table 6 indicate that a 5 percentage point increase in immigration raised the probability of getting married to a husband of native parentage by around 6 percent for all native women, irrespective of their parentage (Columns (2) and (5)). The effect of immigration on the probability of having a foreign-born spouse for native women was indistinguishable from zero (Column (3)). For second-generation women, the impact of immigration on marriage is positive and statistically significant (Column (6)). However, since second-generation women who had a foreign-born husband represented less than 2.5 percent of all native women, focusing on females aged 18–33 implies a negligible effect of immigration on the overall marriage rates of native women.Footnote ³⁸ Panel B documents that these effects were mirrored by a corresponding increase in fertility precisely for couples with higher marriage rates, supporting the idea that immigration raised natives’ fertility by fostering marriage in an era when oral contraception was not yet available (Bailey Reference Bailey2006).

Having established that most of the effects of immigration were not driven by native women marrying foreign-born husbands, in the last part of this section, we study how the inflow of immigrants affected marriage prospects of second-generation men and women. Sex ratios can have important implications for the marriage market of second-generation immigrants, both directly and indirectly through the allocation of bargaining power within the couple. For example, in the same historical context of our paper, Angrist (Reference Angrist2002) finds that a higher relative number of men in their own ethnic group improved marriage prospects of second-generation females.

Figure 3 documents a pattern in line with this idea: because of immigration, marriage rates of second-generation women aged 18–25 increased twice as much as those of women of native parentage. On the other hand, while immigration had a positive and large effect on marriage rates for men of native parentage, it did not have any significant impact on second-generation men. This finding is consistent with the idea that immigration increased competition in the marriage market for second-generation men. In Online Appendix Table A.18, we separately report the effect of immigration on marriage rates of native men and women for different age groups and parentage, and document that all of the effect comes from the youngest cohorts represented in Figure 3 (i.e., women aged 18–25 and men aged 20–27).

To sum up, even though sex ratios were affected by immigration, they can hardly explain the increase in marriage rates of natives with native parentage, a group for which the relative number of men and women in the reference population was not significantly affected. Since U.S.-born individuals of native parentage were by far the largest group among natives, their decisions disproportionately affected natives’ marriage and fertility.

Preservation of “Natives”

Opposition to immigration was widespread during the Age of Mass Migration, with a heated aversion toward individuals coming from non-Anglo-Saxon and non-English-speaking countries (Higham Reference Higham2002; Leonard Reference Leonard2016). Since immigrants from Southern and Eastern Europe were linguistically and culturally far from natives (Hatton and Williamson Reference Hatton, Williamson, Foders and Rolf2006), it is possible that natives reacted to immigration by marrying more and having more children in order to preserve their own race and culture.

The role of culture in affecting marriage and fertility decisions has been stressed by, among others, Bisin and Verdier (Reference Bisin and Verdier2000) and Fernandez and Fogli (Reference Fernandez and Fogli2006), who study the transmission of cultural norms among second-generation immigrants in the United States. More broadly, social interactions can influence the diffusion of cultural norms and might have historically contributed to the convergence of fertility rates, both within and across countries (Spolaore and Wacziarg Reference Spolaore and Wacziarg2022). For instance, Daudin, Franck, and Rapoport (Reference Daudin, Franck and Rapoport2019) find that the demographic transition at the end of the nineteenth century in France was affected by the diffusion of low-fertility norms through internal migration.

To test if native men and women changed their family formation decisions to preserve their own culture, we analyze whether the effect on marriage rates and fertility was stronger when natives were exposed to linguistically farther individuals (which we take as a proxy for cultural distance). Specifically, we construct an index of immigrants’ linguistic distance from English, $L{D_{ct}} = {{\sum}_j} (sh_{ct}^j{L^j})$ , where $sh_{ct}^j$ is the share of ethnic group j among the foreign-born population of city c in year t, and L^j is the linguistic distance from English of country j, computed in Chiswick and Miller (Reference Chiswick and Miller2005).Footnote ³⁹ To ease the interpretation of results, which are reported in Online Appendix Table A.19, we standardize our measure of linguistic distance by subtracting its mean and dividing it by its standard deviation.

The coefficient on the fraction of immigrants remains positive and statistically significant, while that on the index of linguistic distance is close to zero and imprecisely estimated. Even though this evidence should be viewed as suggestive, it is not consistent with the idea that our results are driven by natives’ cultural reactions that might have induced them to marry more often in order to preserve their own race (Bisin and Verdier Reference Bisin and Verdier2000; Bisin and Tura Reference Bisin and Tura2019; Spolaore and Wacziarg Reference Spolaore and Wacziarg2022).

Increased Labor Market Competition for Women

From the end of the nineteenth century to the 1920s, female workers were mainly young, unmarried, and from low-income households (Goldin Reference Goldin2006). Most women were employed as pieceworkers in manufacturing, as private household workers or laundresses, or in clerical jobs. Upon getting married, women typically quit their jobs because of the stigma attached to wives working outside the home (Cherlin Reference Cherlin2014). Goldin (Reference Goldin1990) estimates that, before 1940, more than 80 percent of all married women exited the labor force upon marriage (see Goldin Reference Goldin1990, p. 7). As shown in Online Appendix Table A.20, in our sample of cities, the 1910 average labor force participation of native women aged 18–25 was 0.49, but was substantially lower for older women (0.33 and 0.25 for women aged 26–33 and 34–65, respectively).Footnote ⁴⁰

Studying the link between immigration, female labor force participation, and fertility, Furtado (Reference Furtado2016) shows that the availability of cheaper childcare opportunities brought about by immigration induced native women to have more children and work longer hours. In contrast to these results, at the beginning of the twentieth century, immigration may have increased competition in the labor market for women, which in turn induced them to first leave their jobs and then, as a consequence, to get married and have more children (Angrist and Evans Reference Angrist and Evans1998). While possible, this interpretation seems to be inconsistent with the historical context studied in our paper: at that time, as already discussed, women most frequently took care of their own children and tended to quit their jobs upon marriage. Moreover, even though immigrants provided a cheap and unskilled supply of labor, which in principle might have displaced women, during the Age of Mass Migration, the U.S. economy had large potential for economic expansion (Higgs Reference Higgs1971). Thus, the displacement of female workers due to immigration seems unlikely, even more so as immigrants were more closely substitutes for men than for women, and we showed earlier that immigration increased natives’ employment.

In line with this discussion, Online Appendix Table A.20 documents that immigration lowered labor force participation only for native women in the age group that experienced a significant increase in marriage rates (namely, women aged 18–25). The impact is indistinguishable from zero for all older age cohorts, including women between 26 and 33 years old, one-third of whom are in the labor force.Footnote ⁴¹ In Figure 4, we report the implied coefficients for the effect of a 5 percentage point increase in immigration, and show that female labor force participation in the age group 18–25 fell by 1.6 percent relative to its 1910 mean. Incidentally, this effect is only slightly smaller (in absolute value) than the increase in marriage induced by immigration for women in the same age group (Figure 2). Our interpretation of these results is that immigration first induced native women to marry and have children, and then, as a consequence of these two decisions, to leave the labor force.

Figure 4 THE IMPACT OF IMMIGRATION ON LABOR FORCE PARTICIPATION, BY AGE GROUPS OF WOMEN

Notes: This graph shows the impact of a 5 percentage point increase in the fraction of immigrants on the decrease in labor force participation of women with respect to the mean value in 1910. We report the standardized coefficients separately by age group.

Source: Authors’ calculations using IPUMS data.