The IMF Working Papers series is designed to make IMF staff research available to a wide audience. Almost 300 Working Papers are released each year, covering a wide range of theoretical and analytical topics, including balance of payments, monetary and fiscal issues, global liquidity, and national and international economic developments.
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.