Impulse Response Functions for Self-Exciting Nonlinear Models

We calculate impulse response functions from regime-switching models where the driving variable can respond to the shock. Two methods used to estimate the impulse responses in these models are generalized impulse response functions and local projections. Local projections depend on the observed switches in the data, while generalized impulse response functions rely on correctly specifying regime process. Using Monte Carlos with different misspecifications, we determine under what conditions either method is preferred. We then extend model-average impulse responses to this nonlinear environment and show that they generally perform better than either generalized impulse response functions and local projections. Finally, we apply these findings to the empirical estimation of regime-dependent fiscal multipliers and find multipliers less than one and generally small differences across different states of slack.