Analysis of price transmission and asymmetric adjustment using Bayesian econometric methodology

Abstract

Within the econometric models of asymmetric price transmission, different specifications which detect asymmetry at different rates or culminate in different inferences and conclusions have been developed. However, the goal of asymmetric price transmission modelling is to select a single model from a set of competing models that best captures the underlying asymmetric data generating process for derivation of policy conclusions. This leads to issues of model comparison and model selection, measuring the relative merits of alternative specifications and using the appropriate criteria to choose the most reliable method or model specification which best fits or explains a given set of data. The Bayesian theory which provides a flexible and conceptually simple framework for comparing competing models is theoretically introduced and demonstrated in the price transmission models. On the basis of Marginal Likelihood and Information-theoretic Selection Criteria, alternative methods of testing for asymmetry are evaluated when the true asymmetric data generating process is known. Using a Monte Carlo simulation of model selection, the performance of a range of model selection algorithms to clearly identify the true asymmetric data generating process is examined and the effects of the amount of noise in the model, the sample size and the difference in the asymmetric adjustment parameters on model selection are also simulated. The results of 1000 Monte Carlo simulation indicates that information criteria and the marginal likelihood provides a holistic and consistent approach to ranking and selecting among the competing models of asymmetric price transmission. Estimation results with all simulated data are accurate for the true model and the marginal likelihood and information criterion clearly identifies the correct model out of alternative competing models or on the average points to the true asymmetric data generating process. The Monte Carlo simulation results further indicates that the sample size, the difference in the asymmetric adjustment parameters, the number of asymmetric adjustment parameters (i.e. model complexity) and the amount of noise in the model are important in identifying the true asymmetric data generating process. Subsequently, the ability of the model selection procedures to recover the true asymmetry data generating process(i.e. Model Recovery Rates) increases with increases in the difference between the asymmetric adjustments parameters, increases in sample size , increases in number of asymmetric adjustment parameters (i.e. complexity of the true model) and decreases in the amount of noise in the model. Intuitively, the number of informative variables used to model an asymmetry may improve the recovery of the true data generating process. Importantly, model selection may have difficulty in identifying the true asymmetric model at higher noise levels or performance of the model selection methods in recovering the true model deteriorates at higher noise levels in the asymmetric price transmission modeling framework. Generally, larger sample sizes may improve the ability of the Bayesian criteria to make correct inferences about the asymmetric price transmission models. As expected, model fit declined with increases in stochastic variance in the asymmetric price transmission models analysed. Similarities exist between the performance of the marginal likelihood and its approximations (BIC) and (DIC). The marginal likelihood gives the same model ranking when compared with the Bayesian Information Criteria (BIC), suggesting that the BIC could be used as a complementary approach. The Monte Carlo simulation results indicate that a relatively new information criterion, Drapers's Information Criteria (DIC), which shares the features of the Bayesian Information Criteria, performs similarly to or better than the BIC in the price transmission modeling framework on the basis of the recovery rates of the true asymmetric data generating process. Importantly, the factors that affect the performance of the model selection methods in recovering the true asymmetric data generating process are also influential in the power test of asymmetry. Methodologically, the comparison provided contributes to knowledge and understanding of the empirical performance of the marginal likelihood and information criteria (i.e. Model Selection Methods) in an asymmetric price transmission modeling framework for which no studies have been undertaken. Researchers can apply the Bayesian criteria, knowing from this research that the Bayesian criteria on average do points to the true data generating process in the asymmetric price transmission modeling framework. The results of various Monte Carlo experiments reinforce the importance of design informativeness in an asymmetric price transmission modeling framework and suggest the conditions under which the ability of the model selection methods in identifying the true asymmetric model that governs a given data will improve. Similarly, the conditions which will improve the power of the test for asymmetry are also suggested. The model recovery simulations exemplified will serve as a useful tool for investigating model selection problems in other applications.