Seemingly Unrelated Regression Estimation for VAR Models with Explosive Roots*

Abstract

For VAR models with common explosive root, the OLS estimator of the autoregressive coefficient matrix is inconsistent (refer to Nielsen, 2009 and Phillips and Magdalinos, 2013). Although Phillips & Magdalinos (2013) proposed using the future observations as the instrumental variable for removing the endogeneity from VAR models, type I error occurs when testing for a common explosive root from the distinct explosive roots before the implementation of IV estimation. Such error creates bias and variance in the estimate and further causes incorrect inference in the structural analysis such as forecast error decomposition (FEVD). Hence, we propose using of seemingly unrelated regression (SUR) estimation for VAR models with explosive roots. Our SUR estimator is consistent in the case of both distinct explosive roots and common explosive root. We also consider models with drift in the system for generalization. Simulations show that the SUR estimate performs better than OLS and IV estimate in the case of both a common explosive root and distinct explosive roots case. In structural FEVD analysis, simulations show that SUR yields a different result from OLS and IV. We demonstrate the use of SUR in FEVD for agricultural commodity markets between 3 July 2010, and 29 January 2011.