Impulse Response Estimation By Smooth Local Projections

Vector Autoregressions (VAR) and Local Projections (LP) are well established methodologies for the estimation of Impulse Responses (IR). These techniques have complementary features: The VAR approach is more efficient when the model is correctly specified whereas the LP approach is less efficient but more robust to model misspecification. We propose a novel IR estimation methodology -- Smooth Local Projections (SLP) -- to strike a balance between these approaches. SLP consists in estimating LP under the assumption that the IR is a smooth function of the forecast horizon. Inference is carried out using semi-parametric techniques based on Penalized B-splines, which are straightforward to implement in practice. SLP preserves the flexibility of standard LP and at the same time can increase precision substantially. A simulation study shows the large gains in IR estimation accuracy of SLP over LP. We show how SLP may be used with common identification schemes such as timing restrictions and instrumental variables to directly recover structural IRs. We illustrate our technique by studying the effects of monetary shocks.