# Inducing Sparsity and Shrinkage in Time-Varying Parameter Models

## TL;DR

This paper introduces simple methods to induce sparsity and shrinkage in time-varying parameter models, enhancing forecast accuracy and reducing uncertainty, especially in macroeconomic applications.

## Contribution

It develops a shrink-then-sparsify approach for TVP models that improves estimation and forecasting over traditional shrinkage methods.

## Key findings

- Shrink-then-sparsify improves forecast accuracy.
- Method reduces estimation uncertainty.
- Enhanced performance in macroeconomic forecasts.

## Abstract

Time-varying parameter (TVP) models have the potential to be over-parameterized, particularly when the number of variables in the model is large. Global-local priors are increasingly used to induce shrinkage in such models. But the estimates produced by these priors can still have appreciable uncertainty. Sparsification has the potential to reduce this uncertainty and improve forecasts. In this paper, we develop computationally simple methods which both shrink and sparsify TVP models. In a simulated data exercise we show the benefits of our shrink-then-sparsify approach in a variety of sparse and dense TVP regressions. In a macroeconomic forecasting exercise, we find our approach to substantially improve forecast performance relative to shrinkage alone.