New least-squares filter enhances sequence-space model econometrics

Sequence-space models are gaining prominence in macroeconomics, particularly for analyzing heterogeneous-agent models where entire agent distributions are state variables.

However, the econometric tools for these models have lagged behind traditional state-space methods.

This paper addresses this gap by introducing an efficient algorithm for filtering unobserved shocks in linear sequence-space models.

The proposed filter solves a least-squares optimization problem in closed form, providing the expectation of unobserved shocks conditional on observed data.

Its key advantages include efficiency, with processing times in milliseconds for medium-scale models, and flexibility.

The method can be adapted to handle complexities such as heteroskedasticity, missing observations, measurement error, and non-Gaussian shock distributions, making it a robust tool for economists.

The effectiveness of the new filtering method is demonstrated through its application to data simulated from an estimated medium-scale heterogeneous-agent New Keynesian (HANK) model.

This model incorporates heterogeneous households, idiosyncratic income risk, and standard DSGE elements.

The filter was tested under various conditions, including the presence of measurement error, heteroskedasticity, missing observations, and non-Gaussian shock distributions.

Results consistently show that the filter accurately recovers the underlying structural shocks, even when faced with severely fat-tailed distributions.

While missing data can impede performance, the filter still proves effective in identifying other shocks, underscoring its practical utility for economic analysis.