Time-Varying Parameters as Ridge Regressions

TL;DR

This paper shows that time-varying parameters models are equivalent to ridge regressions, simplifying computation and tuning, and demonstrates the approach with large-scale monetary policy analysis in Canada.

Contribution

It introduces a ridge regression perspective for TVP models, enabling efficient estimation of high-dimensional parameters and extensions like sparsity and reduced-rank restrictions.

Findings

Efficient estimation of approximately 4600 TVPs in a real-world application.

Ridge regression approach simplifies computation compared to traditional state-space methods.

Extensions incorporate sparsity and factor-based restrictions for flexible modeling.

Abstract

Time-varying parameters (TVPs) models are frequently used in economics to capture structural change. I highlight a rather underutilized fact -- that these are actually ridge regressions. Instantly, this makes computations, tuning, and implementation much easier than in the state-space paradigm. Among other things, solving the equivalent dual ridge problem is computationally very fast even in high dimensions, and the crucial "amount of time variation" is tuned by cross-validation. Evolving volatility is dealt with using a two-step ridge regression. I consider extensions that incorporate sparsity (the algorithm selects which parameters vary and which do not) and reduced-rank restrictions (variation is tied to a factor model). To demonstrate the usefulness of the approach, I use it to study the evolution of monetary policy in Canada using large time-varying local projections. The application requires the estimation of about 4600 TVPs, a task well within the reach of the new method.