A Monte Carlo comparison of minimum description length model selection criteria for asymmetric price transmission models

Abstract

The Minimum Description Length (MDL) provides an attractive basis for statistical inference and model selection. However, little is known about the relative performance of its different formulations in Asymmetric Price Transmission (APT) modelling framework. To explore these issues, the study investigates different formulations of the MDL against commonly used alternatives (AIC and BIC) in terms of their ability to recover the true asymmetric data generating process (DGP) under various models, error sizes, asymmetric adjustment parameters and sample size conditions. Monte Carlo simulations results indicate that the performance of model selection method depend on sample size, level of asymmetry, noise levels and model complexity. The results further indicate that the different formulation of MDL, AIC and BIC all points to the true data generating process and clearly identifies the true model. In larger samples, rMDL is comparable to BIC and outperforms gMDL, nMDL, eMDL and AIC. At higher noise levels, AIC is comparable to eMDL and outperforms gMDL, nMDL, rMDL and BIC. AIC is comparable to nMDL and outperforms rMDL, gMDL, eMDL and BIC at strong levels of asymmetry. Empirically, application of a more complex model or increase in the number of asymmetric adjustment parameters improves the recovery of the true data generating process by the model selection methods. These results suggest that MDLs are very reliable and useful criteria in Asymmetric Price Transmission modelling. To achieve optimal APT linear models, one should always aim at stronger levels of asymmetry, lower noise and moderate to large samples