Theoretical Time Series

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 …

Conditional Inference in Nearly Cointegrated Vector Error-Correction Models with Small Signal-to-Noise

This paper studies inference in cointegrating regessions and vector error correction (VEC) models when the cointegrating errors are a nearly integrated process with a low signal-to-noise-ratio. This combination of persistent, yet low variance error …

Impulse response analysis for structural dynamic models with nonlinear regressors

We study the construction of nonlinear impulse responses in linear structural dynamic models that include nonlinearly transformed regressors. We derive the closed-form solution for the population impulse responses to a given shock and propose a …

Unit Roots, Cointegration and Pre-Testing in VAR Models

This article investigates the robustness of impulse response estimators to near unit roots and near cointegration in vector autoregressive (VAR) models. We compare estimators based on VAR specifications determined by pretests for unit roots and …

Sensitivity of Impulse Responses to Small Low Frequency Co-movements: Reconciling the Evidence on the Effects of Technology Shocks

This article clarifies the empirical source of the debate on the effect of technology shocks on hours worked. We find that the contrasting conclusions from levels and differenced vector autoregression specifications, documented in the literature, can …

Testing the Null of No Cointegration When Covariates Are Known to Have a Unit Root

A number of tests have been suggested for the test of the null of no cointegration. Under this null, correlations are spurious in the sense of Granger and Newbold (1974) and Phillips (1986). We examine a set of models local to the null of no …

Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

This paper provides a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that the methods proposed in Kilian [1999. …

Residuals-based Tests for the Null of No-Cointegration: An Analytical Comparison

This article studies the asymptotic distribution of five residuals‐based tests for the null of no‐cointegration under a local alternative when the tests are computed using both ordinary least squares (OLS) and generalized least squares …

Small-Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons

Existing methods for constructing confidence bands for multivariate impulse response functions may have poor coverage at long lead times when variables are highly persistent. The goal of this paper is to propose a simple method that is not pointwise …

Optimal Power for Testing Potential Cointegrating Vectors with Known Parameters for Nonstationarity

Theory often specifies a particular cointegrating vector among integrated variables, and testing for a unit root in the known cointegrating vector is often required. Although it is common to simply use a univariate test for a unit root for this test, …