Estimating Nonlinear Business Cycle Mechanisms With Linear VARs: A Monte Carlo Study

Abstract

Recent macroeconomic research has revived the idea of nonlinear endogenous business and financial cycles. This paper investigates how well linear vector-autoregressions (VARs) identify endogenous cycle mechanisms and cycle frequencies when the underlying process is a nonlinear limit cycle. We conduct Monte Carlo simulations on five different nonlinear models in which cycles are driven by the interaction of two state variables. We find that while linear VARs quantitatively underestimate the strength of the interaction mechanism, they successfully identify the qualitative presence of a cycle mechanism in the majority of cases. Cycle detection rates range between 55% and almost 100%. The detection rate is higher (i) when the nonlinearity does not directly affect the interaction mechanism and (ii) the larger the strength of the interaction mechanism. Our results further suggest that linear VARs are relatively robust to false positives and are surprisingly successfully at estimating cycle frequencies of nonlinear processes. Overall, our findings suggest that linear VARs can be a useful tool to explore cyclical interactions even when the underlying process is nonlinear.

Keywords: vector-autoregression, limit cycles, endogenous cycles, business and financial cycles, cycle frequency

JEL Classification: C15, C32, E32