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Mr. Francis Vitek
This paper considers the problem of jointly decomposing a set of time series variables into cyclical and trend components, subject to sets of stochastic linear restrictions among these cyclical and trend components. We derive a closed form solution to an ordinary problem featuring homogeneous penalty term difference orders and static restrictions, as well as to a generalized problem featuring heterogeneous penalty term difference orders and dynamic restrictions. We use our Generalized Multivariate Linear Filter to jointly estimate potential output, the natural rate of unemployment and the natural rate of interest, conditional on selected equilibrium conditions from a calibrated New Keynesian model.
Mr. Francis Vitek and Ulric Eriksson von Allmen

. C. Robustness The dependence of our closed form multivariate linear filters on multiple parameters — entering into both the objective function that they minimize and the stochastic restrictions that they condition on — has advantages and disadvantages. This parametric flexibility provides considerable scope to adjust the relative volatility and theoretical congruence of the cyclical and appropriately differenced trend component estimates. The cost of this flexibility is the potential sensitivity of these estimates to parameter perturbations. Fortunately