Time-Varying Parameters as Ridge Regressions
This method simplifies and speeds up time-varying parameter estimation for economists, though it is incremental as it reframes existing models rather than introducing a new paradigm.
The paper tackles the computational complexity of time-varying parameter models in economics by showing they are equivalent to ridge regressions, enabling fast estimation and tuning via cross-validation, and demonstrates its utility by estimating about 4600 parameters in a monetary policy study.
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.