Factor-Driven Two-Regime Regression

TL;DR

This paper introduces a two-regime regression model driven by unobservable factors, estimating them via principal component analysis, and develops algorithms and inference methods for the model.

Contribution

It presents a novel factor-driven regime switching model, reformulates the estimation as mixed integer optimization, and derives asymptotic properties including phase transition effects.

Findings

Estimation algorithms for the model are effective in simulations.

Asymptotic distribution derived under shrinking threshold effect.

Bootstrap methods provide reliable inference in numerical studies.

Abstract

We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies.