Factor-Driven Two-Regime Regression

Posted: 26 Nov 2018

See all articles by Sokbae Lee

Sokbae Lee

Columbia University; Institute for Fiscal Studies (IFS)

Yuan Liao

Rutgers, The State University of New Jersey - New Brunswick/Piscataway

Myung Hwan Seo

Seoul National University - School of Economics

Youngki Shin

University of Rochester - Department of Economics

Date Written: October 25, 2018

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

JEL Classification: C13, C51

Suggested Citation

Lee, Sokbae and Liao, Yuan and Seo, Myung Hwan and Shin, Youngki, Factor-Driven Two-Regime Regression (October 25, 2018). Available at SSRN: https://ssrn.com/abstract=3276285

Sokbae Lee

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Institute for Fiscal Studies (IFS) ( email )

7 Ridgmount Street
London, WC1E 7AE
United Kingdom

Yuan Liao

Rutgers, The State University of New Jersey - New Brunswick/Piscataway ( email )

94 Rockafeller Road
New Brunswick, NJ 08901
United States

HOME PAGE: http://rci.rutgers.edu/~yl1114

Myung Hwan Seo

Seoul National University - School of Economics ( email )

San 56-1, Silim-dong, Kwanak-ku
Seoul 151-742

Youngki Shin (Contact Author)

University of Rochester - Department of Economics ( email )

Harkness Hall
Rochester, NY 14627
United States

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