Dealing with trends in DSGE models. An application to the Japanese economy

In this paper we present a methodology to deal with trends in DSGE models. This type of models have consequences for long run growth as well as for cyclical dynamics and it would be desirable to deal with both aspects in an unified frame-work. Two different problems need to be addressed. The first ones concerns a rigorous local approximation of a balanced growth model. This is solved by the usual practice of stationarizing the model first, and using trends directly in(log-)linear form. The second issues deals with the estimation in the level of the data. When the data are not stationary, it is necessary to use a diffuse Kalman filter as the one proposed for example by Koopman and Durbin (2003).In this paper, we propose a modification of this filter in order to better deal with cointegrated variables. As an illustration, we develop a medium size New Keynesian model with consumption habits, adjustment costs and nominal rigidities in the goods and labor markets. This model is estimated on Japanese data. In order to take into account the zero nominal interest rate bound to which the Japanese monetary policy was confronted in the recent period, we experiment with modeling the log of the interest rate rather than the interest rate itself. This workaround is far from perfect, but it permits the use of local approximation without having a model generating negative values for the nominal interest rate.