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.
翻译:时变参数(TVPs)模型常用于经济学中捕捉结构性变化。我强调一个未被充分利用的事实——这些模型实际上属于岭回归。这立即使得计算、调参和实现比状态空间范式更为简便。其中,解决等价的对偶岭问题即使在较高维度下计算速度也非常快,且关键的“时变程度”通过交叉验证进行调整。不断演变的波动性通过两步岭回归处理。我考虑了引入稀疏性(算法选择哪些参数变化,哪些不变)和降秩约束(变化与因子模型相关)的扩展。为展示该方法的有用性,我利用大规模时变局部投影研究了加拿大货币政策的变化。该应用需要估计约4600个时变参数,这一任务完全在新方法的适用范围之内。