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Factor-Driven Two-Regime Regression

Sokbae (Simon) Lee (), Yuan Liao (), Myung Hwan Seo and Youngki Shin ()

Department of Economics Working Papers from McMaster University

Abstract: We propose a novel two-regime regression model where the switching between the regimes is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a much larger panel data set. Our approach enriches conventional threshold models in that a vector of factors may represent economy-wide shocks more realistically than a scalar observed random variable. Estimating our model brings new challenges as well as opportunities in terms of both computation and asymptotic theory. We show that the optimization problem can be reformulated as mixed integer optimization and present two alternative computational algorithms. We derive the asymptotic distributions of the resulting estimators under the scheme that the threshold effect shrinks to zero. In particular, with latent factors, not only do we establish the conditions on factor estimation for a strong oracle property, which are different from those for smooth factor augmented models, but we also identify semi-strong and weak oracle cases and 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 a consistent factor selection procedure with a penalty term on the number of factors and present a complementary bootstrap testing procedure for linearity with the aid of efficient computational algorithms. Finally, we illustrate our methods via Monte Carlo experiments and by applying them to factor-driven threshold autoregressive models of US macro data.

Keywords: threshold regression; factors; mixed integer optimization; panel data; phase transition; oracle properties; l0-penalization. (search for similar items in EconPapers)
JEL-codes: C13 C51 (search for similar items in EconPapers)
Pages: 135 pages
Date: 2018-10
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Working Paper: Factor-Driven Two-Regime Regression (2020) Downloads
Working Paper: Factor-Driven Two-Regime Regression (2019) Downloads
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