When do state-dependent local projections work?

Joint work with Ana Herrera, Lutz Kilian and Elena Pesavento
The Erasmus University, Rotterdam Campus
Silvia Goncalves
Thursday 10 Mar 2022, 16:00 - 17:00
Spoken Language
Theil C2-3
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The Erasmus University, Rotterdam Campus

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 crucial condition for the consistency of the state-dependent LP estimator of the response function is that current and future states are conditionally mean independent of the structural shocks, 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 the endogenous model variables, as is often the case in applied work. Even when the state is a function of past values of these variables only, consistency may hold only at short horizons.

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