The Effect of Age at Arrival on the Alignment Between Immigrant and Native-Born Gender Norms: A Distributional Approach

This paper examines how age at migration affects cultural assimilation by studying convergence in gender role attitudes between immigrants and the UK-born population. Although cultural values are central to policy debates about integration and social cohesion, most work on migration timing focuses on economic outcomes, leaving effects on values and beliefs far less explored. We address this gap by combining a sibling design with a distributional framework for measuring attitude convergence. Using the UK Household Longitudinal Study, we compare siblings within the same family who arrived in the UK at different ages, exploiting within-family variation to identify the causal effect of childhood exposure to host-country norms. To measure convergence, we compare the full distributions of ordinal survey responses to questions on gender norms for immigrants and locals. Our distance metric is the Total Variation (TV) distance between response distributions. TV has a clear policy-relevant interpretation: it equals the worst-case difference in mean responses over all bounded scoring rules. We then use our estimates to construct two measures of how migration timing changes this distance. The first asks how large the immigrant-UK-born TV distance would be if every immigrant had arrived at birth, and compares it to the observed distance. The second is a marginal measure that asks how the distance changes under a small uniform shift in arrival ages. Our results show that if all immigrants had arrived at birth, the cultural distance between immigrants and locals would decrease substantially, and that marginal increases in migration age incrementally widen this gap. Overall, the findings highlight the importance of early-life exposure in shaping cultural beliefs and provide a robust, broadly applicable framework for quantifying convergence in survey responses.