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PozycjaDynamiczne stochastyczne modele równowagi ogolnej: Zarys metodologii badań empirycznych(Oficyna Wydawnicza AFM, 2007) Wróbel-Rotter, RenataThe paper presents general idea of construction and estimation of Dynamic Stochastic General Equilibrium Models. Models belonging to the class of DSGE combine in one specification the optimization behavior of consumers and producers with mechanisms that allow to model the nominal and real rigidities observed at the macroeconomic level. DSGE models are widely applied by financial institutions as a consequence of their ability to flexibly include and test alternative economic hypotheses and the existence of estimation methods. The article begins by reviewing main components of the theoretical model with discussion of the most important assumptions, which is followed by presentation of methods for solving rational expectation models and the Bayesian estimation of structural parameters. PozycjaFolia Oeconomica Cracoviensia, Vol. LII(Krakowska Akademia im. Andrzeja Frycza Modrzewskiego, Polska Akademia Nauk - Oddział w Krakowie - Komisja Nauk Ekonomicznych i Statystyki, 2011) Baster, Paweł; Pocztowska, Katarzyna; Malczyk, Krzysztof; Makieła, Kamil; Osiewalski, Jacek; Osiewalski, Krzysztof; Prusak, Anna; Stefanów, Piotr; Czarnecki, Lech; Iwasiewicz, Andrzej PozycjaFolia Oeconomica Cracoviensia, Vol. LIII(Krakowska Akademia im. Andrzeja Frycza Modrzewskiego, Polska Akademia Nauk - Oddział w Krakowie - Komisja Nauk Ekonomicznych i Statystyki, 2012) Marzec, Jerzy; Osiewalski, Jacek; Pipień, Mateusz; Prędki, Artur; Wróbel-Rotter, Renata; Iwasiewicz, Andrzej PozycjaFolia Oeconomica Cracoviensia, Vol. XLIX-L(Krakowska Akademia im. Andrzeja Frycza Modrzewskiego, Polska Akademia Nauk - Oddział w Krakowie - Komisja Nauk Ekonomicznych i Statystyki, 2009) Kosiorowski, Daniel; Gurgul, Henryk; Wójtowicz, Tomasz; Osiewalski, Jacek; Wróbel-Rotter, Renata; Iwasiewicz, Andrzej; Grabiński, Tadeusz; Kwiatkowski, Łukasz; Kwiatkowski, Jacek; Iwasiewicz, Andrzej PozycjaMarkov switching in stochastic variance. Bayesian comparison of two simple models(Oficyna Wydawnicza AFM, 2009) Kwiatkowski, ŁukaszIn the paper two particular Markov Switching Stochastic Volatility models (MSSV) are under consideration: one with a switching intercept in the Iog-volatility equation, and the other — with a regime-dependent autoregression parameter. While the former one is fairly common in the literature (as a tool of taking account for regimes of different mean volatility level), the latter has not been paid almost any attention so far. We note the fact, that state-varying mean volatility may arise from switches in the intercept or in the autoregression parameter. Hence, we aim to compare these two models in respect of goodness of fit to the data from the Polish financial market, employing Bayesian techniques of estimation and model comparison. Clear evidence of structural shifts in the volatility pattern is found. Two different regimes of the economy are characterized in terms of the mean volatility level and the variance of volatility. PozycjaModele hybrydowe MSV-MGARCH z trzema procesami ukrytymi w badaniu zmienności cen na różnych rynkach(Oficyna Wydawnicza AFM, 2011) Osiewalski, Jacek; Osiewalski, KrzysztofJ. Osiewalski and A.Pajor (2007, 2009) and J. Osiewalski (2009) introduced hybrid multivariate stochastic variance — GARCH (MSV-MGARCH) models, where the conditional covariance matrix is the product of a univariate latent process and a matrix with a simple MGARCH structure (Engle's DCC or scalar BEKK). The aim was to parsimoniously describe volatility of a large group of assets. The proposed hybrid specifications, similarly as other models from the MSV class, require the Bayesian approach equipped with MCMC simulation tools. In order to jointly describe volatility on two different markets (or of two different groups of assets), J. Osiewalski and K.Osiewalski (2011) consider more complicated hybrid models with two latent processes. These new specifications seem very promising due to their good fit and moderate computational requirements. This paper is devoted to hybrid specifications with three latent processes, even more complicated and located on the edge of possibilities of conducting exact Bayesian analysis. We present full Bayesian inference for such models and propose efficient MCMC simulation strategy. Our approach is used to jointly model volatility of six daily time series representing three different groups: two stock indices, prices of gold and silver, prices of oil and natural gas. We formally compare joint modelling to individual bivariate volatility modelling for each of three groups. PozycjaWybrane zagadnienia współczesnego modelowania strukturalnego, Część II: wnioskowanie w estymowanych modelach równowagi ogólnej(Oficyna Wydawnicza AFM, 2012) Wróbel-Rotter, RenataThe paper presents methods of estimation and evaluation of general equilibrium models, highlights problematic fields and challenges. After definition of preferences, technology and structural shocks model's equations, derived by solving microeconomic optimization problems, are loglinearised and the rational expectation solution is found. The next important step is the connection of theoretical variables with the observed counterparts tha t allows to construct the likelihood. Estimation, verification and numerical convergence plays crucial role in the overall goodness of the model. A general equilibrium model can also be used to construct hybrid vector autoregression that allows to test degree of its misspecification.