When Do State-Dependent Local Projections Work?

Working Paper: CEPR ID: DP17265

Authors: Silvia Goncalves; Ana Maria Herrera; Lutz Kilian; Elena Pesavento

Abstract: Many empirical studies estimate impulse response functions that depend on the state of the economy. Most of these studies rely on a variant of the local projection (LP) approach to estimate the state-dependent impulse response functions. Despite its widespread application, the asymptotic validity of the LP approach to estimating state-dependent impulse responses has not been established to date. We formally derive this result for a structural state-dependent vector autoregressive process. The model only requires the structural shock of interest to be identified. A sufficient condition for the consistency of the state-dependent LP estimator of the response function is that the first- and second-order conditional moments of the structural shocks are independent of current and future states, given the information available at the time the shock is realized. This rules out models in which the state of the economy is a function of current or future realizations of theoutcome variable of interest, as is often the case in applied work. Even when the state is a function of past values of this variable only, consistency may hold only at short horizons.

Keywords: local projection; state-dependent impulse responses; threshold identification; nonlinear VAR

JEL Codes: C22; C32; C51

Causal Claims

Cause	Effect
LP estimator can recover the population impulse responses in multivariate models (C51)	Asymptotic validity of LP estimator (C51)
State indicator is a function of endogenous model variables (C20)	LP estimator is only valid for the impact response (C51)
State is endogenous (C32)	LP estimator may yield asymptotic biases (C51)
LP estimator's validity is contingent on the nature of the underlying data-generating process and the exogeneity of the state indicators (C51)	Asymptotic biases in LP estimator (C51)