Quantile regression forecasts of inflation under model uncertainty

Introduction
Inflation is one of the often used monetary indicators in conducting monetary
policy. Even though money supply is an essential determinant of inflation, it
is not used in inflation modeling. Currently, output gap is considered as most
predicative variable. Bayesian Model Averaging (BMA) is a comprehensive approach that deals with the model uncertainty and thus solves the variable selection problem. The results of analysis confirmed that money supply includes more information of inflation than the output gap and thus should be used in inflation modeling. These outcomes are robust towards prior selection and high correlation of some variables
BMA is an application of Bayesian inference to the problems of model selection, combined estimation and prediction that produces a straightforward model choice criteria and less risky predictions. However, the application of BMA is not always straightforward, leading to diverse assumptions and situational choices on its different aspects. Despite the widespread application of BMA in the literature, there were not many accounts of these differences and trends besides a few landmark revisions in the late 1990s and early 000s, therefore not taking into account any advancements made in the last 15 years.
The article which we analyze proposes a new empirical procedure for implementing Bayesian model averaging, which allows different predictor variables to affect different quantiles of the dependent variable and the pluses of this flexible approach are evaluated using data for CPI inflation for the US and a quite large number of predictor variables. The results confirm that the quantile regression BMA approach indeed finds that different predictors are relevant for each quantile of inflation, and that by taking this feature into account predictive distributions are superior.
 
Aim and motivation of article

In Bayesian analysis a popular representation is that of a scale mixture of normals with scale parameter following the exponential distribution. But quantile regression is more appropriate for making inferences about predictive distributions and assessing forecast uncertainty, on other hand, quantile regression estimates are more robust against outliers in the variable of interest so the motivation is clear.
The aim of article is to show how to introduce Bayesian model averaging methods in quantile regressions.
The aim is also to allow the different predictors to affect different quantiles of the dependent variable. Author show that application of BMA in the quantile regression model allows to forecast each quantile of inflation using a different set of predictors. This interesting feature of model selection and averaging in quantile regression means another motivation to be able to approximate complex forms of the posterior predictive density of inflation, despite the fact that the quantile regression model author I specifies as inherently linear.