Bayesian Nonlinear Regression using Sums of Simple Functions

TL;DR

This paper introduces a Bayesian nonlinear regression model that sums simple functions with logistic transitions, enabling efficient inference and accurate macroeconomic forecasting on large datasets.

Contribution

It presents a novel Bayesian model combining sums of simple functions with logistic transitions for flexible nonlinear regression in macroeconomics.

Findings

Accurate point and density forecasts in simulations

Effective modeling of nonlinear macroeconomic relationships

Fast inference enabled by conjugate priors

Abstract

This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined by a logistic function that depends on a single threshold variable and two hyperparameters. Each of these individual models only accounts for a minor portion of the variation in the endogenous variables. But many of them are capable of capturing arbitrary nonlinear conditional mean relations. Conjugate priors enable fast and efficient inference. In simulations, we show that our approach produces accurate point and density forecasts. In a real-data exercise, we forecast US macroeconomic aggregates and consider the nonlinear effects of financial shocks in a large-scale nonlinear VAR.