Abstract:

Local projections are commonly used in empirical macroeconomics to estimate impulse response functions because of their robustness and semi-parametric nature. Yet, as they consist of a sequence of regressions that are performed horizon-by-horizon, they are inefficient and suffer from small-sample bias. This paper shows analytically that slope restrictions can reduce the small-sample bias by more than the increase in misspecification bias that arises from imposing such restrictions. Consequently, in finite samples, estimating the local projection model with occasional slope restrictions can be both bias and variance reducing. Without knowledge of the data generating process, at which horizons to impose such restrictions is unclear. To address this, I propose a data-driven Bayesian sequential clustering algorithm to sample slope-sharing restrictions that maintains the semi-parametric nature of traditional local projections, with improved small-sample performance.