The Cultural Diffusion of the Fertility Transition: Evidence from Internal Migration in 19th Century France

France experienced the demographic transition before richer and more educated countries. This paper offers a novel explanation for this puzzle that emphasizes the diffusion of culture and information through internal migration. It tests how migration affected fertility by building a decennial bilateral migration matrix between French regions for 1861-1911. The identification strategy uses exogenous variation in transportation costs resulting from the construction of railways. The results suggest the convergence towards low birth rates can be explained by the diffusion of low-fertility norms by migrants, especially by migrants to and from Paris.


Introduction
France is usually viewed as an anomaly in studies dealing with the role of fertility decline in the transition from "Malthusian" to modern economic growth (see, e.g., Lee, 2003, Galor and Weil, 2000, Galor, 2005a, Galor, 2005b, Galor, 2012. This is because French birth rates already declined in the late 18 th century, and the differences in the fertility rates across French regions disappeared in the course of the 19 th century to reach a uniformly low level throughout the country before WWI (Cummins, 2013, Guinnane, 2011, Weir, 1994). Yet, France was a relative economic laggard vis-à-vis countries like England or the Netherlands in the 18 th century and grew at a slower rate than England or Germany during the 19 th century (Maddison 2001).
The factors which drove the rapid convergence towards low fertility rates across French regions during the 19 th century are still debated. 1 There were, of course, changes in economic conditions, e.g., the rise in the demand for human capital which occurred during the second Industrial Revolution, the decline in child mortality or increased life expectancy. However studies on the demographic transition in France (e.g., Weir, 1994, Murphy, 2015 all suggest that such changes were probably not substantial and rapid enough to explain, on their own, the demographic transition. 2 It is however possible that increased social interactions, which spread information and cultural norms, contributed to the convergence in fertility rates (Gonzalez-Baillon, 2008, Murphy, 2015, Spolaore and Wacziarg, 2014. 3 In this respect, two 1 An unsubstantiated explanation is that lower birth rates might have stemmed from the quick diffusion of contraceptive techniques which was criticized by the moralists of the day. On this issue, see Bergues et al. (1960) and Murphy (2015). Relatedly, Boyer and Williamson (1989) suggest that the fertility transition in England between 1851 and 1911 could be partly attributed to the diffusion of contraceptive techniques. 2 On infant and child mortality, see e.g., Dupâquier and Poussou (1988), Eckstein et al. (1999) and Doepke (2005) for a different view. On the demand for human capital, see e.g., Galor and Weil (2000), Galor and Moav (2002), Becker et al. (2010Becker et al. ( , 2012 and Klemp and Weisdorf (2012). On increased life expectancy, see Galor (2012) as well as Hazan (2009) for a different view. See also de la Croix and Perrin (2016) for a rational choice model of education and fertility in 19 th c. France. 3 Cultural norms are defined as preferences and beliefs that impact current economic behavior although they were developed at a different time and place (Fernandez 2007). Relatedly, Fernandez and Fogli (2006) and Blau et al. (2011) show that the social norms of the source countries keep affecting the behaviour of second-generation immigrants, notably in matters of fertility. See also David and observations are noteworthy. First, it was in the course of the 19 th century that France progressively developed a national culture, as reflected by the spread of French at the expense of regional languages (Weber, 1976). 4 Second, the French did not migrate to the New World during the 19 th century but instead moved within France. 5 These two observations suggest that migration may have contributed to cultural harmonization within France, a conjecture which we directly address in this study by focusing on the decline in fertility.
Indeed, this paper investigates whether the progressive regional convergence of fertility rates in France during the second half of the 19 th century was fostered by the rise in internal migration which conveyed economic and cultural information. 6 For this purpose, it focuses on the specific patterns of internal migration between 1861 and 1911 between the French departments, i.e., the administrative divisions of the French territory which were established in 1790. 7 Our study relies on the French Census and on the Enquête des 3000 familles (Survey of the 3000 Families), which provides information based on parish registers Sanderson (1987), Fargues (2007), Bertoli and Marchetta (2015), Munshi and Myaux (2006), and specifically La Ferrara et al. (2012) on the role of norms in the fertility transition currently taking place in developing countries. See also Beine et al. (2013) who examine a cross-section of developing and developed countries during the 20 th century and suggest that fertility choices in migrant-sending countries are influenced by diaspora networks that transfer of fertility norms prevailing in the host countries. 4 Before the 19 th century, a substantial share of the population did not speak French in regions like Brittany (in the West) or Provence (in the South) and this language barrier reflected further cultural and behavioural differences, including in matters of fertility (see also Braudel, 1986, vol. 1, pp. 88-94). 5 See Hatton (2010), as well as Abramitzky et al. (2013Abramitzky et al. ( , 2014 Docquier et al. (2016), Mercier and Chauvet (2014) and Barsbai et al. (2016) on political preferences. Instead, research on the impact of migration movements in 19 th century France focused on the role of migrant networks on marriages (e.g. Bonneuil et al., 2008) or wealth transmission (e.g., Bourdieu et al., 2000) but did not analyze the possibility that internal migration may have contributed to the convergence in the fertility rates by conveying cultural norms. 7 Departments were designed so that it would take at most one day by horse travel to reach the administrative center of the department from any location in the department. They were thus organized independently of fertility patterns and migratory movements in the 18 th century. on the places of birth and death of all the individuals whose last name starts by the three letters "T", "R" and "A". These two datasets enable us to build a bilateral matrix of inter-regional migrations for the period 1861-1911 (Bourdelais, 2004, Bourdieu et al., 2004, Dupâquier, 2004 which we combine with the data on departmental fertility computed by Bonneuil (1997). We then assess the migrants' contribution to the demographic transition across France by constructing, for each department, the fertility norms of immigrants and emigrants as weighted averages of the fertility rates in the migrants' origin and destination department, in line with the approach of Spilimbergo (2007Spilimbergo ( , 2009).
Our identification strategy relies on exogenous variations in the bilateral travel costs between the French departments that entailed a time-varying decrease in travel costs and had a positive effect on migration. 8 The choice of this instrumental variable is motivated by the historical development of the railroad network which the central government designed to connect Paris, the capital, to the main economic centers of France (Caron, 1997). There is indeed substantial anecdotal evidence, which is confirmed by our falsification tests, that the railroad network was developed independently from fertility patterns and migration choices.
Our results show that fertility declined more in areas that (i) had more emigration and (ii) whose migrants migrated towards low-fertility regions, especially Paris. These results are robust to accounting for the potential confounding effects of factors such as declining child mortality, increased life expectancy, rising education levels, industrialization and religiosity. Our interpretation is that emigrants who moved from high-to low-fertility areas transmitted cultural and economic information about fertility norms and the cost of raising children in the regions where they had settled to the inhabitants of the regions where they came from. This information might have been then taken into account by actual and would-be emigrants, thus explaining why we find that departments with a larger share of emigrants experienced a larger drop in fertility. This interpretation is supported by our counterfactual analysis which shows 8 The development of the railroad networks might have fostered long-term and permanent migration, but also short-term migration. However it is not clear whether patterns of fertility decline can be attributed to short-term migration which had existed in France since the end of the Middle Ages and was motivated by the need for a temporary workforce during harvests. In fact, Châtelain (1976) documents that short-term migration began to decline in the second half of the 19 th century, when longterm and permanent migration became more common. that emigration to Paris, which accounted for 26.33% of the total number of French internal emigrants between 1861 and 1911, explains half of the national decline in fertility, in line with the economic, political and cultural importance of Paris within France. Finally, we note that child mortality is the only socio-economic variable which has a significant, albeit quantitatively limited, effect on the fertility decline while our robustness checks establish that other potential factors of information diffusion and cultural change, such as newspapers, the age at marriage or the number of children born out of wedlock, do not weaken the impact of migration on the decline in fertility.
The remainder of this article is as follows. Section 2 presents the data. Section 3 discusses the estimation strategy. Section 4 presents our main results and our robustness checks. Section 5 analyzes the channels for the informational transmission of the fertility decline. Section 6 concludes. Table A1 in the Supplementary Appendix provides descriptive statistics for our variables which are measured at the departmental level and cover the 1861-1911 period. Because of changes in the borders in the wake of the 1870-1871 French-Prussian war, France had 90 departments in 1861 and 87 after 1871. However, we restrict, for simplicity, our analysis to the departments which were part of France throughout the whole period.

Fertility rates
We measure fertility rates in each French department for every decade between 1861 and 1911. Specifically we use data from Bonneuil (1997) Bonneuil (1997) shows that, at the start of the 19 th century, there were substantial differences in the fertility rates of the various departments that, presumably, reflected cultural and linguistic diversity within France (Weber, 1976, Braudel, 1986 Italy, is confirmed by the standard unconditional convergence regressions (Barro and Sala-i-Martin, 1992) which we report in Supplementary Appendix.

Migration in 19 th century France
Our data on emigrants from, and immigrants to each French department between 1861 and 1911 stem from the TRA dataset, also known as the Enquête des 3000 familles (Survey of the 3000 Families) between 1861 and 1881. There may be concerns with the representativeness of the TRA dataset since it only provides information on the place of birth and death of all individuals whose surnames start by the three letters "T", "R" and "A" (Blanchet and Kessler, 1992, Bourdelais, 2004, Dupâquier, 2004

Figure 2: Main bilateral migration corridors -1891 Census data
Notes: • For the sake of readability, this map does not report all the 7,832 observations (=89*88, as there are 89 départements) of the migrant stocks but only those which are larger than 10% of the largest stock, i.e., the 128 stocks larger than 9,000 (as the largest stock was formed by the 90,000 inhabitants of the Seine département born in the neighbouring Seine-et-Oise département).
• In the legend, the first two numbers represent the bounds of the bracket for the stock of migrants; N represents the number of links between départements in each bracket.
The data enable us to compute bilateral migration stocks which are defined as the number of people born in department i and living in department j in year t. They show that migrants moved from rural to urban areas as can be seen in Figure 2, where we 12 Abramitzky et al. (2011) show that the TRA dataset is representative of the whole French population in their assessment of nuptiality patterns. graph the migration patterns in France in 1891. 13 Many migrants moved to the closest industrial city, e.g., Lille in the North of France or Marseille in the South. However, Paris attracted migrants from all over the country. Overall, the descriptive statistics Table A1 indicate that 17.3% of the French population emigrated from their department of origin over the 1861-1911 period.
It must be noted that our study does not account for international migration for two reasons. First, as we mentioned above, the French did not migrate to high land to labor ratio (and therefore high-fertility) destinations such as the USA and other European offshoots, unlike the inhabitants of other European countries (e.g., Great Britain, Ireland, Sweden or Norway). The annual mean French gross emigration rate from 1860 to 1913 was only 0.18 international emigrants per 1000 inhabitants (including to French colonies and in particular to Algeria), compared to 9.25 for Italy, 4.61 for Great-Britain and 1.5 for Germany (Hatton and Williamson, 1998). Instead, most French migration during the 19 th century took place within France. 14 Second, there was some foreign immigration to France, but it was limited, only amounting to 2.9% of the total population in 1911 (Dupâquier and Poussou, 1988). In any case, international migration did not prevent the decline and convergence of fertility rates in France.
Rather, the importance of internal migrations in France and of external migrations in other European countries may explain the specific effect of migration on fertility in France for at least two reasons. First, the implied patterns in terms of self-selection on fertility behavior are different. Second, the potential transmission of fertility norms from destination-to-origin regions would work in opposite directions, because the urban and industrial destinations of French internal migrants were predominantly lowfertility places, in contrast to the countries in the New World where high land-tolabour ratios favored large families in rural areas. Indeed, as Livi-Bacci 2012, pp 54-55) writes: "International rural-to-rural migration required stable families with large numbers of children. Families of that sort were well suited to the destination countries where land was abundant and so a large family of workers an advantage. Similarly 13 A similar pattern was documented by, e.g., Cairncross (1949) and Baines and Woods (2004), for Great Britain. 14 Given the low numbers of French emigrants abroad, it does not seem relevant to investigate which emigrants moved within the country and which emigrants left the country, as might be the case for emigration studies for countries like Sweden or Great Britain. advantageous were the traditional social and family values of those migrants.
Migration from the countryside to cities and industrial regions, where workers were employed primarily as wage workers in manufacturing and construction, favored instead a different profile, namely, individuals whose family ties were looser, nuclear families able to carefully plan births."

Economic and social characteristics of the departments
In our empirical analysis, we control for the socio-economic factors which might have contributed to the convergence in fertility rates in France in the second half of the 19 th century.

Life expectancy and child mortality
We use Bonneuil (1997)'s computations of life expectancy at age 15 for the individuals living in each department during the 1806-1906 period which we extend to 1911 by using data from the French census. We also rely on the successive issues of the French census to compute infant mortality, which we define as the share of children who died before age one.

Education and religiosity
The regressions account for the confounding effects of education on fertility. For this purpose, we compute the shares of the male and female population age five to 19 enrolled in primary and secondary schools. 15 Moreover, education may be correlated with religiosity. Therefore, to assess the confounding effects of religious observance on fertility we collect data from the French census to compute the share of male and female children enrolled in Catholic (i.e., private) primary and secondary schools, as opposed to those studying in secular state-funded primary and secondary schools. 16 2.3.3 Workforce and urbanization 15 In 1881 and 1882, laws were passed to make primary school attendance until the age of 13 mandatory and to make state-funded schools tuition-free and secular. Therefore, to get a better sense of educational achievement in France during the period, we also consider secondary school attendance until age 19. 16 Since data on actual church attendance is unavailable for the 1861-1911 period, we use a measure of school choice, which is very often motivated by religious observance (e.g., Cohen-Zada, 2006). However, it is not a priori clear whether the decline in religiosity was connected to the decline in fertility in France. Departments such as Côtes du Nord and Nord experienced a decline in fertility during the 19 th century but remained staunchly Catholic until WWI and notably elected representatives who opposed the separation of Church and State in 1905 (Franck, 2010).
Our regressions account for the confounding effects of changes in the workforce in the 19 th century, characterized by the decline in the agricultural sector and the growth of the industry, as well as of urbanization, on fertility. For this purpose, we compute the shares of the workforce in the industrial and service sectors (the control group is the workforce in the agricultural sector) as well as the share of the population living in urban areas (the control group is the population in the rural areas).

Empirical methodology
Baseline model 3.1.
To assess the impact of migration on fertility, we estimate the following equation: where , is the fertility rate in department i in year t, X i,t is a vector of socio- where IBRN is the immigrants' birthplace fertility norm.
In addition, we define the share of emigrants, "# , , in proportion of the population of department i "# , ∑ 1 2, 23 5 , 4 and the share of immigrants, # , , among inhabitants of department i as where 1 2, is the number of people born in department i living in department j at time t and 5 , is the total population of department i at time t.
To estimate Equation (2), we follow the methodological approach of Brown and Guinnane (2007) and Guinnane (2011) in their analysis of the European fertility decline (Coale and Watkins, 1986). We include interaction terms between the fertility norms and the shares of emigrants/immigrants to check whether the intensity of the diffusion is larger where there are more migrants. We also include department and time fixed effects to exploit within-department variations across periods and correct for unobserved heterogeneity between departments. However, it is a priori unclear whether we should specify Equation (2) in growth rates or in levels, and whether we should include a lagged dependent variable and/or lagged explanatory variables to account for the potential delayed effects of economic changes. Our additional regressions, which are available upon request, suggest that it is preferable to use a specification in level without lagged variables.

Identification strategy 3.2.
To estimate Equation (2), we use changes in travel costs via the railroad network within France as an instrumental variable. This identification strategy is motivated by the fact that travel costs were time-varying during the 19 th century, as the railroad network was gradually built throughout the country. A decrease in travel costs should therefore lower the costs of migration and increase the stock of migrants. Indeed, transport costs were substantial enough to matter. Even in 1901, the cheapest train ticket (in third class) between Paris and Lyon (approximately 450 km) cost three days of a Parisian worker's wages and five days of a provincial one. A coach ticket was three times as expensive. In 1872, these numbers would have been six and 10.5 days (France -Statistique des salaires, 1901). 17 Our first stage regression estimates a panel gravity model with the standard Poisson Pseudo Maximum Likelihood that solves for heteroskedasticity and for the existence of zero migrant stocks (Silva and Tenreyro, 2006): log 1 2, *. log 6 789 6 : 8 8 ; < :. log 6 789 6 : 8 8 ;$< β . β > β ? 0 17 For the sake of comparison, the cheapest ticket was worth five hours of the net minimum wage in 2012.
where 1 2, are the migrant stocks while β t , β o and β d are the year-, origin-department and destination-department fixed effects. We use 20 and 30-year lagged transport costs because the mean migrant age was, according to the TRA dataset, 38 years old in 1861, 40 in 1872, 41 in 1881, 43 in 1891, 45 in 1901 and 50 in 1911, i.e. between 20 and 30 years after migration. These transport costs are computed in a four-step procedure. First, we use Caron (1997)'s rail network map to determine the available travel (railroad, road, sea) links between adjacent departments. Second, we compute the great-circle distance between the administrative centres (chef-lieu) of adjacent departments. Third, since rail prices were regulated by the State (Toutain, 1967, p. 277), there was a constant road or rail price per kilometer throughout France and this strategy provides the travel cost between adjacent departments. Fourth, we apply a short-route finding algorithm taken from the UCINET network analysis program (Borgatti et al., 2006) to compute the cheapest route and hence the travel costs between each department.
To be a valid instrument, transport costs must not only correctly predict bilateral migration but they should also neither entail reverse causality nor violate the exclusion restriction by affecting the cultural diffusion of fertility norms through other channels than migration. This will lead us to provide a series of robustness checks in Section 4.2. At this point, however, it is worth noting that reverse causality may only be an issue if migrants are self-selected on preferences for fertility and choose their destination accordingly. 18 Individuals living in a low-(respectively, high-) fertility department who have preferences for large (small) families may have found it beneficial to migrate to a high-(low-) fertility department where their own preferences are more in line with the prevailing norms in terms of family size.
However, this would have not contributed to a convergence but to a divergence in the fertility rate across departments. As such, reverse causality and the self-selection of emigrants would imply that our OLS coefficients underestimate the actual effect of migration on the fertility decline.
As for the exclusion restriction, the historical account on the development of the French railroad network suggests that it took place independently of fertility patterns, or of the demand and supply for migration (Caron, 1997). Indeed, from the 1840s 18 Home fertility is well recognized as a push factor of international migration but fertility at destination is not thought to be a significant pull factor (Mayda, 2010). onwards, the French government designed the railroad network to connect Paris to the main economic centres of the country and by the mid-1880s, the railroad network connected all the main administrative towns (chef-lieu) of each department. 19 To illustrate our point, we graph in the Supplementary Appendix the Coale fertility index of each department between 1811 and 1911 and a vertical line that indicates when the department was linked to Paris via the railroad. These graphs show that the introduction of the railroad was not linked to the decline in fertility. Table 1 reports the regression results of the first-stage regression in Equation (7) where we assess the relationship between our IV transport costs and migrant stocks.
Column 1 considers all migrants while Columns 2 and 3 distinguish between male and female migrants. 20 The first-stage regression results show that migrant stocks decline with increasing travel costs, as could be expected. In other words, migrations increased as travel costs decreased. In particular, our results in Column 1 suggest that the elasticity between 20-year lagged transport costs and migrant stocks is -0.9 while that between 30-year lagged transport costs and migrant stocks is -0.6. Given that the median decrease in bilateral transports costs until 1891 is equal to 13%, these figures suggest that the median increase in bilateral migrant stocks every decade after 1861 predicted by transport costs is 19.5%. Given that the actual figure is 20%, this finding corroborates the validity of our first-stage results. An intuition for these results is that the decline in bilateral transport costs at time t predicts more or less accurately the increase in bilateral migrant costs at time t+30 years. Finally, we note that the first stage regression results reported in Columns 2 and 3 suggest that there is no specific effect for men or women, either in terms of size or magnitude.
A potential concern with our identification strategy is that transport costs and migration may be correlated with other factors which also influence fertility rates. We discuss this issue in Section 4.2 and provide several robustness checks for the size, significance and validity of our results.

Results
The effect of migration on the decline in fertility 4.1. Table 2 analyses the impact of migration of men and women on the convergence in the fertility rates of the French departments. Columns 1 and 2 report OLS estimates while Column 3 show IV estimates. Column 1 only includes the fertility norms of emigrants and immigrants, the shares of migrants and the interaction variables while Columns 2 and 3 also includes our set of control variables. It appears that none of these controls has a significant effect on fertility, except for infant mortality.
The results in Table 2 suggest that immigrants and emigrants did not have the same effect on the fertility convergence between 1861 and 1911. At first glance, immigrants seem to have no systematic effect on fertility while emigrants do. Indeed, the positive and significant coefficient of Emigrants' Residence Norm suggests that departments whose emigrants moved to destinations with strongly declining fertility experienced a larger decline in their own fertility. Moreover, the negative and significant coefficient of Share of Emigrants suggests that departments with the largest increase in the share of emigrants experienced the largest drop in fertility.
However, we cannot interpret the coefficients of the interacted variables by themselves. We note that the interaction variable Emigrants' Residence Norm * Share of Emigrants has a negative and significant sign. 21 This suggests two possible interpretations. On the one hand, the interaction variable mitigates the effect of the two variables Emigrants' Residence Norm and Share of Emigrants taken separately because individuals who remained in departments with an increasing share of emigrants moving to low-fertility areas were more likely to have a high number of children. On the other hand, the interaction variable suggests that the effect of the Emigrants' Residence Norm is lower at high levels of emigration. This is suggestive of diminishing returns to migration in terms of informational transmission, in line with the rest of the literature (e.g., Spilimbergo (2008) and Beine et al. (2013)). In any event, our counterfactual analysis in Section 5.2 provides a quantitative discussion of how these different effects balance out. However, we first provide a series of robustness checks in the next subsection. 21 In the studies of Spilimbergo (2008) and Beine et al. (2013) whose specification is very similar to ours, this interaction term is not significant.

Robustness checks 4.2.
Some concerns pertaining to our analysis may be related to the endogenous relationship between migration and fertility. While reverse causality and the selfselection of migrants are unlikely to bias our estimates as we discussed in Section 3.2, our identification strategy is meant to address potential omitted variable bias and ensure the validity of the exclusion restriction in our regressions. Specifically, it could be argued that lower transport costs could ease the diffusion of norms of low fertility, not just through migration, but also through other channels, notably the diffusion of newspapers and books. 22 More generally, one may also be concerned that transport costs in the second half of the 19 th century are associated with other forces that could have shaped the joint evolution of migration and fertility. However, it is worth noting that in 19 th century France, there were internal tariffs, known as octrois, which constituted an impediment to the circulation of many goods (Franck et al., 2014).
To mitigate these concerns, we run three series of robustness checks. First, we test whether there is a relationship between migrant stocks between 1861 and 1911, whether instrumented by the fall in transport costs or not, and the fertility decline between 1811 and 1861. It is reassuring to find in Table 3 that there is not such a relationship.
Second, we include a series of "bad controls" (Angrist and Pischke, 2009) which are potentially endogenous to migration and fertility in the regressions in Table 2.
These include other potential vectors of cultural diffusion, such as the total number of periodicals published in each year and each department. These also include demographic variables that could be correlated with both migration and fertility 23 , such as the share of births out of wedlock, the share of illegitimate births as a share of out-of-wedlock births, as well as the shares of married men and women for the 20-24, 25-29, 30-34 and 35-39 age groups. Except for the total number of periodicals which we collect from the successive issues of the Bibliographie de la France ou Journal général de l'imprimerie as well as from Avenel (1895Avenel ( , 1901 and Mermet (1880-22 Newspapers and books are high value-to-weight whose dissemination across France between 1851 and 1911 was more likely to be influenced by changes in the availability of transport rather than by changes in transportation costs. On the diffusion of newspapers and, in particular, on the importance of regional newspapers outside Paris, see, e.g., Manevy (1955), Bellanger (1969) and Albert (1972). 23 Since these variables are likely endogenous, they are not included in our baseline regressions. 1901), all these other variables are collected from the successive issues of the French census. The results are reported in Table 4. We find that none of these "bad controls" has a consistent effect on the coefficients of our variables of interest, either in terms of size or significance level.
Third, there might be some concern that our results are driven by spatial autocorrelation, given the nature of our data and empirical strategy (see also Murphy (2015)). It is therefore reassuring to find in Table 5 that our main regression results are robust to accounting for the inclusion of spatial autocorrelation.

Channels of the fertility decline: a counterfactual analysis
In this section, we discuss possible channels through which emigration affected fertility. Specifically we carry out a counterfactual analysis to examine potential differences between the migration of men and of women, as well as the role of migration from and to Paris.
Tables 6 and 7 present regression results on a sample that only includes male and female migrants, respectively. Moreover, the sample in the regressions shown in Table 8 excludes all migrants, i.e., both men and women, to and from Paris, which made up most of the Seine department.
In Tables 6 and 7, the significance and the size of the coefficients associated with Emigrants' Residence Norm, Share of Emigrants and Emigrants' Residence Norm * Share of Emigrants are roughly similar to those in Table 2. These results suggest that male and female emigrants contributed equally to the fertility decline. They are thus in line with the historical evidence that long-term migrations, which our study analyses to capture the decline in fertility, were often joint migrations of men and women, unlike short-term migrations which were overwhelmingly undertaken by men alone (Châtelain, 1976). 24 24 We note that in Table 7 the Share of (Female) Immigrants and the interaction variable (Female) Immigrants' Residence Norm * Share of (Female) Immigrants have positive and significant coefficients. This effect is however not found for male immigrants. While these results confirm our remark in Section 4.1 that immigrants had overall no effect on the decline in fertility, it nonetheless suggests that female immigrants did not immediately adopt the lower norms of their department of destination. It is likely that they had more children than the women in their destination department but fewer children than in their origin department. As such their behaviour did not prevent the convergence in fertility rates.
In Table 8, we report regression results on a sample that excludes male and female migration from and to the Seine department (which comprised Paris). They are different from those in Table 2 since the coefficients associated with Emigrants' Residence Norm, Share of Emigrants and Emigrants' Residence Norm * Share of Emigrants are smaller in Table 8 and not systematically statistically significant across the OLS and IV regressions. They actually suggest that migration to Paris played a major role in the decline in fertility in France, even though our data indicate that only 26.33% of migrants lived in Paris throughout the period. 25 We develop this intuition in our counterfactual analysis below.
We then compute the counterfactual values of the fertility rate in each department under the assumption that the size, bilateral structure, and fertility of emigrants and immigrants would have remained at their 1861 level. For this purpose, we use the OLS and IV regression results in Columns 2 and 4 (with the control variables) of Tables 2, 6, 7 and 8 (i.e., on the samples of all migrants, only male migrants, only female migrants, as well as of all migrants excluding Seine as destination and origin).
In Table 9, we report these counterfactual values at the national level along with the actual fertility data between 1861 and 1911. We assess the fit of each model with the Pearson χ 2 statistic as in Buchinsky et al. (2014). 26 Overall, the Pearson χ 2 statistic shows that our regressions capture the impact of migration on fertility decline.
To illustrate our analysis, we report two graphs based on the counterfactual values obtained with the IV regressions reported in Column 4 of Tables 2, 6, 7 and 8 and reported in Table 9. First, Figure 3 shows the evolution of the actual and counterfactual values for the IV regressions of the unweighted average fertility rate at the national level between 1861 and 1911 under the assumption that no changes in fertility norms and in the shares of migrants had occurred after 1861. Second, Figure 4 shows these same values in the form of histograms, thus highlighting the decline in the standard error of fertility rates over time, and the progressive convergence of fertility rates across France. 25 Only 5.25% of the total emigrants were born in the Seine department throughout the period. 26 The Pearson χ 2 statistic is computed as χ 2 ∑ 56"@ : "@ − B*8"6C"@ D 56"@ : "@ ⁄ Note: This figure graphs the evolution of the actual, IV-predicted and counterfactual IV-predicted of the fertility rate for the whole of France using the IV regression results with the control variables in Column 4 of Tables 2, 5, 6 and 7 and as reported in Note: This figure provides histograms for the counterfactual values of the fertility rate in the French departments using the IV regression results with the control variables in Column 4 of Tables 2, 5, 6 and 7 and as reported in Table 9. 22 Third, Table 9 suggests that Paris played a major role in the decline in fertility rates throughout the period. 27 As can be seen in Panel B of Figures 3 and 4 All in all, these observations thus suggest that emigrants to the Seine department mattered more than other emigrants, and this is in line with the cultural, economic and political importance of Paris within France. We may think that would-be emigrants sought to move to Paris, even if they eventually migrated to the closest regional industrial center, and chose to have few children because they learnt from emigrants from their regions that individuals who were already living in Paris had few children.
This might have been a cultural element of Parisian life, and there is evidence that the political and economic elites living in Paris already had few children by the end of the 18 th century (Livi-Bacci 1986). But this feature of Parisian life might also have been grounded in an economic rationale: Parisians had few children because raising many children in Paris was costly and difficult. In fact, it was customary for Parisians to send new-borns to foster care in the countryside, even though this was expensive and infant mortality rates were high (Rollet-Echalier, 1990). 28 28 The poorer the French couples were, the further away they would have to send their children from Paris. In the second half of the 19 th century, well-to-do families would employ a wet nurse at home to take care of their children (Faÿ-Sallois, 1980). See also Rapoport and Vidal (2007) for additional anecdotal evidence and an interpretation in terms of endogenous parental altruism formation.
which pertains to the diffusion via migrants of an information which combined a cultural component and an economic rationale related to the cost of child rearing in Paris.

Conclusion
In this study, we investigate the impact of migration on the fertility transition. We focus on the convergence in fertility rates within France between 1861 and 1911 by taking advantage of the fact that internal migration was much more prevalent than international migration over that period (in contrast to most other European countries). Using various historical data sources, we build a bilateral migration matrix between French departments, with observations every ten years. We then assess the effects of the changing fertility norms of emigrants and immigrants in their birthplace and residence departments. We address the endogeneity of migration choices by using time-varying bilateral travel costs resulting from the gradual development of the railroad network as an instrumental variable.
Our results suggest that the transmission of information via migration explained most the convergence of fertility rates across France while socio-economic variables had, at best, a limited impact. In particular, emigrants sent back information to their region of origin regarding the decreasing fertility norms of their region of destination.
It is therefore plausible that emigrants sent information to those who stayed behind,  Note: Robust standard errors clustered at the origin-department. & destination-department are reported in brackets. *** indicates significance at the 1%-level, ** indicates significance at the 5%-level, * indicates significance at the 10%-level.   Table 3. All the variables are in logarithms. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level.  Table 4. All the variables are in logarithms. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level. Note: This table reports spatial autoregressive regressions with fixed effects using the xsmle Stata command (Belotti et al., 2013) for the regressions in Table 2. All the variables are in logarithms. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level. Note: All the variables are in logarithms. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level. Note: All the variables are in logarithms. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level. Note: All the variables are in logarithms. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level. Note: This table reports the mean an standard deviation at the national level for the actual, predicted and counterfactual values under the assumption that no changes in fertility norms and in the shares of migrants had occurred after 1861 at the national level using the OLS and IV regression results with the control variables in Columns 2 and 4 of Tables 2, 5, 6 and 7. The counterfactual values obtained from the IV regression results are graphed in Figure 3.

For Online Publication --Supplementary Appendix
Supplementary Appendix A.

Supplementary Appendix C. Unconditional convergence test of fertility decline
Following our discussion in Section 2, where we discuss the convergence in the fertility levels across the French departments, we run a series of unconditional convergence regressions that follow (Barro and Sala-i-Martin 1992)'s approach: log K L M,NOPQ L M,N R = . log , + #" S"@ " ": 8 + 0 The results of this regression are reported in Table C Our third stage is to transform the TRA dataset so as to obtain a matrix which is defined by the margins coming from the census and the odds ratios (the ratio between, for example, the odds of an immigrant in département A to be an emigrant from département B instead of being from C and the odds of an immigrant in département D to be an emigrant from département B instead of being from C) coming from the TRA (See (Smith 1976), p. 672-3). For this purpose, we apply a marginal standardization algorithm known as the RAS technique (see (Smith 1976) and (Cox 2006 29 This assumption is based on computations of thecourse an approximation. Using net positive migration rates by age using data from (Bonneuil 1997), we computed that the mean age at migration was 19.4 years in 1861, 18.6 in 1872, 22.5 in 1881 and, 21.4 in 1891. 30 For simplicity we ignore emigration to foreign countries -which was anyway small -and the small number of emigrants from Alsace-Lorraine (which was seized by Germany after 1871) by assuming they were a fixed proportion of emigrants in each département throughout the country. 31 This procedure is also known as biproportional matrices, iterative proportional fitting or raking.

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These transformed TRA data then become our main measure of bilateral migration. A similar procedure is used to compute male and female migration, except that the gender differentiated margins for 1891 have to be extrapolated from the 1881 and the 1901 census. Note: In the legend, the first two numbers represent the bounds of the bracket for the stock of migrants; N represents the number of links between départements in each bracket. Life Expectancy Age 15 (t) -0.  Note: All the variables are in logarithms. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level. Note: All the variables are in logarithms. The control variables and the constant term are not reported. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level. Note: This table reports the elasticities of the coefficients evaluated at the mean. Robust standard errors clustered at the department-level are reported in brackets. *** indicates significance at the 1% level, ** at the 5%-level, * at the 10%-level.