🤖 AI Summary
This paper addresses the challenge of estimating impulse response functions (IRFs) in structural nonlinear time series models. We propose a semiparametric sieve estimation framework that avoids prespecifying functional forms. The method employs a two-step iterative algorithm: first nonparametrically estimating the structural function, then constructing the IRF estimator via sieve approximation. We establish, for the first time, a theoretical foundation—guaranteeing consistency and uniform convergence—for structural nonlinear autoregressive models. The framework enables identification of heterogeneous responses to uncertainty shocks. Monte Carlo simulations demonstrate its finite-sample superiority over competing approaches. Empirical macroeconomic analysis reveals that, relative to linear benchmarks, the sieve-based IRF estimates exhibit a stronger pointwise negative GDP response to interest rate hikes and more pronounced output and inflation contractions following interest rate uncertainty shocks.
📝 Abstract
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 US monetary policy application, we find that 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 imply more substantial contractionary effects both on production and inflation.
