The paper discusses fundamental problems concerning the construction and estimation of Dynamic Stochastic General Equilibrium (DSGE) models on the basis of an example taken from the literature. The DSGE models constitute at present the major tool for the monetary policy analysis as a consequence of the existence of estimation methods and considerable flexibility ot the models that allows to formulate and test a wide range of economic hypotheses. 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. The first part of the article contains the overview of the most important elements of the model with the discussion of utility and profits maximizations problems of producers and consumers that are solved in a decision making process. The second part of the text presents log-linearised structural equations, shortly discusses possible techniques of model solutions and subsequently sketches the Bayesian approach to the parameters estimation. The structural equations of any DSGE model are derived from the first order conditions of the agents' optimization problems, the resource constraints, policy rules, equations describing flows between countries and stochastic processes governing the exogenous variables and shocks. Nominal and real delays in adjustments of macroeconomic variables after a stochastic shock are modeled by introduction of the time intervals that restrict frequency of the optimization of prices and wages over time. The most widely used in practice in the Calvo mechanism of price and wage setting. The structural equations of the DSGE model form a nonlinear rational expectations system that can be solved using the nonlinear methods or after logarithmic linearization can be solved by the linear techniques . The possibility of the likelihood construction enables estimation of the structural parameters including the fundamental parameters characterizing the technology and preferences. The Bayesian methods additionally allow to include in the process of parameters estimation the prior information of the economy what is typically interpreted as an introduction of some evidence obtained from the microeconomic research. The estimated DSGE model can be used as a tool for the standard macroeconomic analysis concerning impulse responses, forecasting, shocks propagation and duration etc.
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