Block Kalman Filtering for Large-Scale DSGE Models

Abstract

In this paper block Kalman …lters for Dynamic Stochastic General Equilibrium models are presented and evaluated. Our approach is based on the simple idea of writing down the Kalman …lter recursions on block form and appropriately sequencing the operations of the prediction step of the algorithm. It is argued that block …ltering is the only viable serial algorithmic approach to signi…cantly reduce Kalman …ltering time in the context of large DSGE models. For the largest model we evaluate the block …lter reduces the computation time by roughly a factor 2. Block …ltering compares favourably with the more general method for faster Kalman …ltering outlined by Koopman and Durbin (2000) and, furthermore, the two approaches are largely complementary.We would like to thank Mattias Villani, Steve Lionel and Duncan Po. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as re ‡ecting the views of the Executive Board of Sveriges Riksbank. y

Using the “Chandrasekhar Recursions” for Likelihood Evaluation of DSGE Models

“…Strid and Walentin (2009) report that, for a large DSGE models, 60% of filtering time is spent on the operation T P t|t−1 T .…”

“…This is a crude comparison, but it gives a sense of the actual user experience running the algorithms. We compare three algorithms, the standard Kalman Filter, the Block Kalman Filter of Strid and Walentin (2009), and the Chandrasekhar Recursions. We implement all the algorithms in Intel Fortran 11.1 and Matlab 2010a.…”

“…We wrote code for the standard KF and the CR recursions, and used the code provided by Strid and Walentin (2009) for the Block Kalman Filter. This algorithm, specific for DSGE models, uses a priori knowledge of the structure of T -it has large matrix of zeros where the exogenous variables load onto the endogenous variables -and Z, which is often quite sparse, to build a fast Kalman filter.…”

“…So it becomes crucial to construct efficient algorithms for likelihood evaluation and state filtering. To wit, considerable effort has been expended constructing elaborate filters tailored to DSGE models-see, for example, Strid and Walentin (2009)…”

“…The method, which we will call the "Chandrasekhar Recursions" (CR), is simple to implement and can yield considerable speed improvements. This paper is closely related to Strid and Walentin (2009), who develop a "Block Kalman Filter" by exploiting the a priori known structure of the DSGE model to avoid some large matrix calculations. The algorithm must be applied on a case-by-case basis.…”