Survey_CW_2003

Abstract

We conduct stochastic simulations of the model to obtain the stationary distributions of the endogenous variables under alternative monetary policy strategies. In preparation for these simulations, we first computed the structural residuals of the model based on Japanese, euro area and U.S. data from 1980:Q1 to 1998:Q4. The process of calculating the structural residuals would be straightforward if the model in question were a purely backward-looking model. For a rational expectations model, however, structural residuals can be computed only by simulating the full model and computing the time series of model-consistent expectations with respect to historical data. The structural shocks differ from the estimated residuals to the extent of agents’ forecast errors. We obtained the structural shocks by solving the model algebraically for the reduced form using the AIM implementation (Anderson and Moore, 1985, and Anderson, 1987) of the Blanchard and Kahn (1980) method for solving linear rational expectations models. We calculated the covariance matrix of those structural shocks and using this covariance matrix, we generated 100 sets of artificial normally-distributed shocks with 100 quarters of shocks in each set from which the first 20 twenty quarters of shocks were discarded in order to guarantee that the effect of the initial values die out. We then used the sets of retained shocks to conduct stochastic simulations under alternative values of the equilibrium nominal interest rate, while imposing the non-negativity constraint on nominal interest rates. If it were not for this nonlinearity, we could use the reduced form of the model to compute unconditional moments of the endogenous variables without having to resort to stochastic simulations.