Large quarterly Bayesian vector autoregression model for the modern Russian economy

It is often difficult to choose the necessary variables when we are forecasting the economic dynamics. On the one hand, vector autoregression (VAR) models can solve this problem by taking into account a sufficiently large number of variables. However, on the other hand, excessive parametrization of such models is not always justified, because it is often possible to choose such a small combination of variables the predictive power of which will be no worse than unlimited VARs with a large number of variables and lags. Bayesian methods help to solve this problem by introducing a priori restrictions on the VAR coefficients. The main goal of this work is to build a Large quarterly Bayesian vector autoregression (QBVAR) for the modern Russian economy. The hypotheses of the study: 1) BVAR(p) models reveal their maximum potential with a small number of variables, but with a large number of lags, 2) The Minnesota prior distribution is not always the best option for the modern Russian economy in the BVAR(p) model. As a result of the analysis, it turned out that for a number of the most important macroeconomic variables (GDP, inflation, key rate, unemployment, wages), Normal-Flat / Wishart-type priors turned out to be the optimal. In case of 29 input variables and two lags, the predictive power of the QBVAR(2) model is worse than the equivalent frequency VAR(2) or VECM(2). However, when it was possible to find the optimal combinations of variables, QBVAR(p) turned to be several times more accurate than its analogous frequency VAR(p) for all important macro indicators. In addition, the stiffness parameters of the considered a priori distributions decreases with increasing lags entering the model, i. e. the higher the order of the model with the minimum optimal set of variables, the tighter the distribution is necessary to obtain more accurate predictions. For the Russian realities, it is necessary to use very tight priors, 6–8 variables and 9–12 lags in a quarterly representation.