When smaller families look contagious: a spatial look at the French fertility decline using an agent-based simulation model

"Despite some disagreements about specific timing, it is now widely accepted that France was the first country in Europe to experience a systematic fall in birth rates. At least two further features, however, make the French case particularly noteworthy: how long it took and how persis- tent internal heterogeneity was throughout. Fertility rates evolved following quite a distinctive geographical pattern, where two clear areas of low fertility (the Seine valley and the Aquitaine re- gion) appeared to spread their influence while two ‘islands’ of high fertility (Bretagne and the Mas- sif Central) kept shrinking until they more or less disappeared in the early 1900s. Standard quanti- tative analyses have shed light into some of the factors driving this dynamic, but to better under- stand the mechanisms underlying this apparent diffusion we need other tools. In an attempt to pro- vide a sensible explanation of this salient feature, we build an agent-based simulation model [Ax- elrod, 1997, 2005; Arthur, 2005; Hedström, 2005; Gilbert, 2008; Gilbert and Troitzsch, 2005; Tes- fatsion, 2005] which incorporates both historical data on population characteristics and spatial in- formation on the geography of France, and assess how different behavioural assumptions on social interaction might have affected variations in the patterns followed by fertility rates. In doing so we incorporate two components normally neglected in the literature. On the one hand, we introduce the role of social influence in fertility decisions [e.g. Kohler, 2001]. On the other, we assess the ef- fect of the French Revolution. Its simultaneity with the onset of the decline is quite suggestive al- ready, but an increasing literature is now pointing towards a more regular connection between so- cial upheavals and fertility decline [Binion, 2001; Caldwell, 2004; Bailey, 2006]. We build upon these studies and introduce the Revolution in the model as a heterogeneous, exogenous shock to the population. In the model, individuals living in more ‘progressive’ départements are more likely to be affected by a shock that make them want to have fewer children, and we use département level quantitative data on the Ecclesiastical Oath of loyalty to the Revolution of 1791 [Tackett, 1986] to proxy for the percentage of agents switching to this new status. Preliminary results suggest that both social influence and the revolution might partly explain the particular evolution of fertility rates in France. The model performs relatively well at micro level, suggesting our choice of the proxy for the ‘modernisation factor’ might have been a good one. Although failing to fully per- ceive the impact on those départements leading the decline, simulated fertility trends –and in many cases levels– follow actual patterns in intermediate areas, and in those that lagged behind in the demographic transition. Overall, the model provides new insights into an old problem and serves as a benchmark to assess alternative behavioural hypotheses."