Time-varying parameters as ridge regressions

Time-varying parameter (TVP) 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 and TVP-VARs with demanding lag lengths. The applications require the estimation of up to 4600 TVPs, a task within the reach of the new method.