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Working Paper
State-Dependent Local Projections
Do state-dependent local projections asymptotically recover the population responses of macroeconomic aggregates to structural shocks? The answer to this question depends on how the state of the economy is determined and on the magnitude of the shocks. When the state is exogenous, the local projection estimator recovers the population response regardless of the shock size. When the state depends on macroeconomic shocks, as is common in empirical work, local projections only recover the conditional response to an infinitesimal shock, but not the responses to larger shocks of interest in many ...
Working Paper
Impulse Response Analysis for Structural Dynamic Models with Nonlinear Regressors
We study the construction of nonlinear impulse responses in structural dynamic models that include nonlinearly transformed regressors. Such models have played an important role in recent years in capturing asymmetries, thresholds and other nonlinearities in the responses of macroeconomic variables to exogenous shocks. The conventional approach to estimating nonlinear responses is by Monte Carlo integration. We show that the population impulse responses in this class of models may instead be derived analytically from the structural model. We use this insight to study under what conditions ...
Working Paper
When Do State-Dependent Local Projections Work?
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 ...