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

A nonlinear regression framework is proposed for time series and panel data 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 correspond...