UK and US fertility rates: Historical evolution and long run trends in the context of fractional integration

This study examines the dynamics of fertility rates in the UK and the US by analysing long time series, spanning from 1541 to 1820, respectively. We use fractional integration methods to examine the degree of persistence in the data and to determine the nature of transitory or permanent shocks. The empirical findings, based on linear and nonlinear models, evidence greater persistence in the US compared to UK fertility rates, a phenomenon that might be attributable to heterogeneity in socioeconomic factors and different public policy frameworks in the two countries. For the UK, a differencing parameter statistically significantly smaller than 1 is observed for the period 1541–2022. This implies that fertility shocks are transitory and that the series eventually returns to its mean trend. However, the most recent period from 1820 to 2022, it shows a significant increase with a value close to 1, indicating that the series has gained significant persistence over the last two centuries, with shocks now considered permanent. In the US, the differencing parameter is consistently greater than 1. This clearly indicates greater persistence in US fertility rates, where shocks have permanent effects, and the series do not tend to return to their original state without intervention.