Impulse Response Analysis of Structural Nonlinear Time Series Models

This paper proposes a semiparametric sieve approach to estimate impulse response functions of nonlinear time series within a general class of structural autoregressive models. We prove that a two-step procedure can flexibly accommodate nonlinear specifications while avoiding the need to choose fixed parametric forms. Sieve impulse responses are proven to be consistent by deriving uniform estimation guarantees, and an iterative algorithm makes it straightforward to compute them in practice. With simulations, we show that the proposed semiparametric approach proves effective against misspecification while suffering only from minor efficiency losses. In a U.S. monetary policy application, the pointwise sieve GDP response associated with an interest rate increase is larger than that of a linear model. Finally, in an analysis of interest rate uncertainty shocks, sieve responses indicate more substantial contractionary effects on production and inflation.