This paper addresses the issue of obtaining maximum likelihood estimates of parameters for structural VAR models with a mixture of distributions. Hence the problem does not have a closed form solution, numerical optimization procedures need to be used. A Monte Carlo experiment is designed to compare the performance of four maximization algorithms and two estimation strategies. It is shown that the EM algorithm outperforms the general maximization algorithms such as BFGS, NEWTON and BHHH. Moreover, simplification of the problem introduced in the two steps quasi ML method does not worsen small sample properties of the estimators and therefore may be recommended in the empirical analysis.

We estimated a structural vector autoregressive (SVAR) model describing the links between a banking sector and a real economy. We proposed a new method to verify robustness of impulse-response functions to the ordering of variables in an SVAR model. This method applies permutations of orderings of variables and uses the Cholesky decomposition of the error covariance matrix to identify parameters. Impulse response functions are computed and combined for all permutations. We explored the method in practice by analyzing the macro-financial linkages in the Polish economy. Our results indicate that the combined impulse response functions are more uncertain than those from a single model specification with a given ordering of variables, but some findings remain robust. It is evident that macroeconomic aggregate shocks and interest rate shocks have a significant impact on banking variables.

The model considered in the paper is defined as VAR with the prior distribution for parameters generated by the dynamic stochastic general equilibrium (DSGE) model. The degree of economic restrictions in the DSGE-VAR model is controlled by the weighting parameter. In the paper there is investigated the impact of the weighting parameter prior specifications for the posterior shape of impulse response functions (IRFs). In case of conditional models the paths of IRFs highly depend on the value of the weighting parameter that is set arbitrary. When considering full estimation with different prior types, means and gradual change in the dispersion the posterior time paths of IRFs are similar in models with high values of the marginal data density.