Regressing on distributions in panel models: The nonlinear effect of temperature on regional economic growth

A framework is proposed for the situation where certain explanatory variables are available at a higher temporal resolution than the dependent variable. The main idea is to use the moments of the empirical distribution of these variables to construct regressors with the correct resolution. As the moments are likely to display nonlinear marginal and interaction effects, an artificial neural network regression function is proposed. The usefulness is demonstrated by analyzing the influence of daily temperatures in 260 European NUTS2 regions on the yearly growth of gross value added in these regions in the time period 2000 to 2021. In the particular example, the model allows for an appropriate assessment of regional economic impacts resulting from (future) changes in the regional temperature distribution (mean AND variance).