Explosive Roots in Level Vector Autoregressive Models and Vector Error Correction Models

Abstract

Level vector autoregressive (VAR) models and vector error correction models (VECMs) are used extensively in empirical macroeconomic research. However, estimated level VAR models and VECMs may contain explosive roots, which is at odds with the widespread consensus among macroeconomists that roots are at most unity. This paper investigates the frequency of explosive roots in estimated level VAR models and VECMs in the presence of stationary and nonstationary variables. Monte Carlo simulations based on datasets from the macroeconomic literature reveal that the frequency of explosive roots in level VAR models is very high: it exceeds 40% in the presence of unit roots and increases significantly, to as much as 100% when the estimated level VAR coefficients are corrected for small-sample bias. Simulation results show that the frequency of explosive roots reduces significantly to below 5% under most specifications in estimated VECMs. These results suggest that researchers estimating level VAR models encounter explosive roots very frequently, and they can substantially reduce this high frequency of explosive roots by estimating VECMs.