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

TL;DR

This paper introduces a nonlinear regression framework using distribution moments and neural networks to analyze how high-frequency temperature data impacts regional economic growth, demonstrated with European data.

Contribution

It develops a novel nonlinear regression method that incorporates distribution moments and neural networks for high-resolution explanatory variables in panel data.

Findings

Temperature distribution moments significantly influence economic growth.

The model accurately captures nonlinear temperature effects on regional GDP.

It enables assessment of economic impacts from future temperature distribution changes.

Abstract

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 corresponding model operates within the traditional stochastic nonlinear least squares framework. In particular, a numerical Hessian is employed to calculate confidence intervals. The practical 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).