Ukrainian econometricians often face a shortage o f observations necessary for providing precise answers to complex macroeconomic questions. Recent studies ha\’e shown that the Bayesian Estimation approach can solve this problem as it is partially based on nonsample information. In this paper the theoretical analysis and practical application o f using the Bayesian Estimation is presented. A bivariate VAR(2) model has been build to estimate quarterly GDP growth and CPIfor Ukraine using Gibbs sampling and a Minnesota prior. The empirical results show robust correlation betM’een the estimate and actual quarterly GDP and CPI figures, indicating the ability o f the Bayesian Estimation to provide a high level o f accuracy in macromodels o f Ukraine.