Functional Inference for Assimilation Effects: Evidence from Migrants’ Mental Health in Italy

We analyze the assimilation effect in migrants’ mental health using data from the Italian health surveillance system PASSI for the period 2010-2023. The large sample size enables a detailed investigation of duration-of-stay dynamics across areas of origin and socio-demographic profiles. Assimilation is defined as the difference in the probability of depressive symptoms between migrants and natives with the same observable socio-economic characteristics, evaluated as a function of length of stay. To assess convergence patterns over time, we estimate a sampling-weighted semi-parametric model and construct stratified bootstrap-based simultaneous confidence bands and related inverse set methods to control the family-wise error rate. Assimilation is interpreted as a dynamic process in which the migrant-native gap is initially negative and converges to zero. Preliminary results do not support a convergence pattern. Instead, after several years of arrival, migrants exhibit a higher probability of depressive symptoms than comparable natives, particularly among socio-economically vulnerable individuals.