Time-Varying Parameters as Ridge Regressions

• URL: http://arxiv.org/abs/2009.00401v4
• Date: Thu, 14 Nov 2024 23:15:27 GMT
• Title: Time-Varying Parameters as Ridge Regressions
• Authors: Philippe Goulet Coulombe,
• Abstract summary: 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. I use it to study the evolution of monetary policy in Canada using large time-varying local projections.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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