A least-squares filter for sequence-space models

Sequence-space models are becoming increasingly popular in macroeconomics, especially in the heterogeneous-agent literature. However, the econometric toolkit for users of these models remains less developed than that available for traditional state-space methods. This note introduces an algorithm for efficiently filtering unobserved shocks in linear sequence-space models. The proposed filter solves a least-squares optimization problem in closed form and returns the expectation of unobserved shocks conditional on observed data. It handles heteroskedasticity, missing observations, measurement error, and non- Gaussian shock distributions. To illustrate its properties, I apply it to data simulated from a medium-scale heterogeneous-agent New Keynesian model and show that it accurately recovers the underlying structural shocks. JEL Classification: C32, E27, E32, E37