Survey_AOSWW_2005

Abstract

We compute the unique stationary rational expectations solution of linear versions of our model using the Anderson and Moore (1985) implementation of the Blanchard and Kahn (1980) method, modified to take advantage of sparse matrix functions. The algorithm is discussed in more detail in Anderson (1997). We use this method for three different purposes in our paper. First, in preparation for our quantitative analysis, we computed the structural residuals of the model based on U.S. data from 1980 to 2000. 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 solving 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. In computing the structural historical shocks we assumed that monetary policy is set according to an estimated linear policy rule. We then computed the covariance matrix of those structural shocks for further use in the quantitative analysis. Secondly, we used the Anderson/Moore algorithm for deterministic and stochastic simulations of disinflations under linear policy rules. Thirdly, we derived unconditional moments of output and inflation given the historical covariance of shocks and alternative linear rules. The unconditional variances were computed using the doubling algorithm described in Hansen and Sargent (1997), also modified to take advantage of sparse matrix functions. The methodology for optimizing the coefficients of linear policy rules that we used to obtain the benchmark linear rule in our paper is described in further detail in Levin, Wieland and Williams (1999). A quantitative analysis of the opportunistic approach to disinflation in a model with rational expectations requires methods that can deal with nonlinearity. Because of the large number of state variables in our models (which include all lags and shocks) we have used a simulation-based approach to assess the implications of opportunism. Using the covariance matrix, we generated 1000 sets of artificial normally-distributed shocks with 100 quarters of shocks in each set.