This paper reviews estimation and forecasting with Bayesian vector autoregressions (BVARs). In the first part of the paper, we propose a clear classification of the most frequently used prior distributions and we show how the parameters of posterior distributions can be computed for the priors we consider in the paper. A separate section describes the endogenous choice of prior hyperparameters that is currently a key step to estimate a BVAR in a data-rich environment.
The second part of this paper is devoted to forecasting with BVARs. We review both point and density forecasting.
We also developed a package bvarr for statistical environment R with the same notations as in this review. The bvarr package can be freely used for research and educational purposes.
This paper compares the forecasting performance of random walk, frequentist vector autoregression (VAR), and Bayesian vector autoregression with Minnesota prior (BVAR) models on quarterly Russian data sample running from 1995 to 2014. Maximal number of variables included in the model is equal to 14 that requires an endogenous search of optimal shrinkage hyperparameter. The search procedure follows [Bańbura et al., 2010] and [Bloor and Matheson, 2011]. According to the selection method the shrinkage hyperparameter equates the forecasting quality of the frequentist VAR and BVAR for the minimal considered dimension of the model (three variables). For any dimension of the BVAR model the optimal shrinkage hyperparameter is robust to considered functions of relative forecasting accuracy.
We show that the BVAR provides a more accurate forecast than the frequentist VAR on the studied sample. For key macro indicators (the industrial production index, consumer price index and the interbank interest rate), forecasting horizons, and all model sizes, the mean squared error of the BVAR is lower than that of the frequentist VAR. Moreover, the results show that the forecast made using the BVAR is more precise than the forecast made using random walk model for the CPI and using white noise model for the interbank rate. However, the BVAR cannot beat the random walk while forecasting the industrial production index.
The paper examines the structure, governance, and balance sheets of state-controlled banks in Russia, which accounted for over 55 percent of the total assets in the country's banking system in early 2012. The author offers a credible estimate of the size of the country's state banking sector by including banks that are indirectly owned by public organizations. Contrary to some predictions based on the theoretical literature on economic transition, he explains the relatively high profitability and efficiency of Russian state-controlled banks by pointing to their competitive position in such functions as acquisition and disposal of assets on behalf of the government. Also suggested in the paper is a different way of looking at market concentration in Russia (by consolidating the market shares of core state-controlled banks), which produces a picture of a more concentrated market than officially reported. Lastly, one of the author's interesting conclusions is that China provides a better benchmark than the formerly centrally planned economies of Central and Eastern Europe by which to assess the viability of state ownership of banks in Russia and to evaluate the country's banking sector.
The paper examines the principles for the supervision of financial conglomerates proposed by BCBS in the consultative document published in December 2011. Moreover, the article proposes a number of suggestions worked out by the authors within the HSE research team.