DSGE Model Estimation on the Basis of Second-Order Approximation
This article compares the properties of different non-linear Kalman filters: the well-known Unscented Kalman filter (UKF), the Central Difference Kalman Filter (CDKF) and an unknown Quadratic Kalman filter (QKF). A small financial DSGE model is repeatedly estimated by several quasilikelihood methods with different filters for data generated by the model. Errors in parameters estimation are a measure of the filters’ quality. The result shows that the QKF has a reasonable advantage in terms of quality over the CDKF and the UKF, albeit with some loss in speed.
This paper presents a three-sector DSGE model for a small open economy under the intermediate exchange rate regime. The central bank balance sheet equations are added to allow introducing two different monetary policy rules in the model. The principal question is how many independent monetary policy rules do we need to describe Russian monetary policy in 2001–2012. To get an answer we perform Bayesian estimation of the DSGE model for four different combinations of monetary policy rules. The main finding of the paper is that describing dynamics of 14 observable variables requires using Taylor rule together with the exchange rate adjustment rule. Two rules do not make an overdeterminacy; they have original transmission channels and reflect two different stabilization principles: output and inflation stabilization (Taylor rule) vs. balance of payments stabilization (exchange rate-based rule).
This article suggests a new approach to an approximation of nonlinear DSGE models moments. This approach is fast and accurate enough to use it for an estimation of nonlinear DSGE models. A small financial DSGE model is repeatedly estimated by several modifications of suggested approach. Approximations of moments are close to the results of large sample Monte Carlo estimation. Quality of parameters estimation with suggested approach is close to the Central Difference Kalman Filter (the CDKF). At the same time suggested approach is much faster.
Optimization of coefficients in monetary policy rules is performed on the base of the DSGE-model with two independent monetary policy instruments estimated on the Russian data. It was found that welfare maximizing policy rules lead to inadequate result and pro-cyclical monetary policy. Optimal coefficients in Taylor rule and exchange rate rule allow decreasing about 20% of volatility estimated on Russian data of 2001–2012. The degree of exchange rate flexibility parameter was found to be lower than its current value. It means that Bank of Russia has to systematically smooth exchange rate dynamics when it will adopt inflation targeting in 2015.