Mathematical modeling of the macroeconomic indicators dynamics on the basis of the dynamic stochastic general equilibrium model

The paper presents a small dynamical stochastic model of general equilibrium in Kazakhstan. A special feature of the approach is the Keynesian microeconomic foundation, which takes into account market failures such as imperfect competition, inflexible prices and wages. The second specific feature is the hypothesis of rational expectations.
The model is a system of equations describing the dynamics of the national income, inflation and interest rates relative to its equilibrium trajectories. Equilibrium is treated dynamically — stationary states are determined on the basis of the Hodrick–Prescott filter (for comparison, the results of determining the potential output based on the Cobb–Douglas production function with exogenous technological progress are given).
The system consists of three equations: the dynamic equation of the IS curve, the New keynesian Philipps curve, the Taylor equation. The first one relates the output gap and the real expected interest rate. The second one relates inflation with inflationary expectations and output (an analog of the aggregate supply equation). Finally, Taylor equation is used by central banks in inflation targeting to establish interest rates that smooth economic cycles.
To estimate the parameters of the model, a Bayesian approach was used that allows to take into account a priori information about the properties of the economy and statistical information. The latter is important in the context of short time series in the post-Soviet countries, as well as in the conditions of a change in monetary policy in connection with the transition to the policy of inflation targeting. The calculations were performed using the software package Dynare [1].
Using the constructed model, the effects on key macroeconomic indicators from demand shocks, prices shocks, and changes in the interest rate policy of the monetary regulator are estimated.
The results of modeling and calculations can be used by monetary authorities in the development of monetary policy.