Wasserstein barycenter regression: application to the joint dynamics of regional GDP and life expectancy in Italy

We propose to investigate the joint dynamics of regional gross domestic product and life expectancy in Italy through Wasserstein barycenter regression derived from optimal transport theory. Wasserstein barycenter regression has the advantage of being flexible in modeling complex data distributions, given its ability to capture multimodal relationships, while maintaining the possibility of incorporating uncertainty and priors, other than yielding interpretable results. The main findings reveal that regional clusters tend to emerge, highlighting inequalities in Italian regions in economic and life expectancy terms. This suggests that targeted policy actions at a regional level fostering equitable development, especially from an economic viewpoint, might reduce regional inequality. Our results are validated by a robustness check on a human mobility dataset and by an illustrative forecasting exercise, which confirms the model's ability to estimate and predict joint distributions and produce novel empirical evidence.