Modeling of Asymmetry between Gasoline and Crude Oil Prices: A Monte Carlo Comparison

Abstract

An Engle–Granger two-step procedure is commonly used to estimate cointegrating vectors and consequently asymmetric error-correction models. This study uses Monte Carlo methods and demonstrates that the Engle–Granger two-step method leads to biased estimates of asymmetric parameters and in some cases suggests symmetry in the asymmetric data generating process (DGP). The single equation error correction models (SEECM) based on ordinary least squares (OLS) and nonlinear least squares (NLS) are employed for simultaneous estimation of the cointegrating vector and the ECM. The SEECMs perform better than Engle–Granger two-step procedures in estimating the asymmetry and making inferences on its existence in various DGPs. We show that SEECM estimations are less biased and inferences are less likely to be misleading compared to the Engle–Granger two-step procedure. Unlike the asymmetric specifications based on Engle–Granger two-step approach, the asymmetric SEECMs do not refute the possibility of long-run asymmetry by allowing different cointegrating vectors for positive and negative regimes. Examining the model with real data also supports the Monte Carlo results. While the conventional approaches imply symmetry, the proposed asymmetric SEECM, which has been embedded in a Threshold Autoregressive model, uncovers asymmetry at the presence of different cointegrating vectors for positive and negative regimes.