Collaborative Research: Impulse Response Analysis for Nonlinear Structural VARs

Empirical studies that estimate the nonlinear response of economic variables to a shock often rely on local projections (LP) regressions. While existing papers show that local projections (LP) and Vector Autoregressions (VARs) have the same estimand in linear models (or when a linear VAR is used as a linear approximation of a nonlinear model), the validity of LP in nonlinear models has yet to be proven and there is little theoretical guidance as to what method is preferable in practice. For structural dynamic models with nonlinear regressors, Goncalvez et al. (2021) show that only a modified version of the LP estimator is consistent in the case where the policy variable, xt is i.i.d, but not in more general models. The goal of this project is to identify nonlinear structural impulse response functions and study the validity and performance of LP in a large class of nonlinear models. In doing so we will contribute to the literature on impulse response functions (IRFs) in nonlinear models by addressing four interrelated questions: (1) Under which conditions are LP estimators consistent in the widely use state- dependent SVAR? (2) How do LP and nonlinear VAR estimators for state dependent models perform in small samples and what recommendations can policy makers follow? (3) Can the results in Goncalvez et al. (2021) be generalized to a larger class of nonlinear models where the form of the nonlinearity is unknown? (4) How can nonlinear impulse response functions (IRFs) be extended to data rich environments such as factor augmented vector autoregressions (FAVAR).