working papers

- Bootstrapping Stochastic Time-Varying Coefficient Models.

Abstract: We propose a novel local pairs bootstrap (LPB) in the context of autoregressive models with stochastic time-varying coefficients. Asymptotic validity is established under general forms of (conditional and unconditional) heteroskedasticity. In the process, we also show asymptotic validity of a fixed-regressor wild bootstrap (FWB) and compare the finite sample properties of the two methods, in the spirit of Gonçalves and Kilian (2004). We introduce a dynamic bandwidth to allow for local adaptive smoothing and provide two data-driven procedures for calibration. Extensive Monte Carlo simulations show that both bootstrap methods outperform the standard asymptotic estimator and that the LPB is generally preferable. Finally, we implement our theoretical findings to investigate the empirical issue of the evolution of inflation and expected inflation persistence.

- Parameters on the Boundary in Predictive Regression (with Giuseppe Cavaliere and Iliyan Georgiev).

Abstract: We consider bootstrap inference in predictive (or Granger-causality) regressions when the parameter of interest may lie on the boundary of the parameter space, here defined by means of a smooth inequality constraint. For instance, this situation occurs when the definition of the parameter space only allows for the cases of either no predictability or sign-restricted predictability. We show that in this context constrained estimation gives rise to bootstrap statistics whose limit distribution is, in general, random, and thus distinct from the limit null distribution of the original statistics of interest. This is due to both (i) the possible location of the true parameter vector on the boundary of the parameter space, and (ii) the possible non-stationarity of the posited predicting (resp. Granger-causing) variable. We discuss a modification of the standard fixed-regressor wild bootstrap scheme where the bootstrap parameter space is shifted by a data-dependent function, thus allowing us to eliminate the boundary as a source of limiting bootstrap randomness. Under possible non-stationarity of the predicting variable as the only remaining source of limiting bootstrap randomness, we prove validity of the associated bootstrap inference in the cases where the posited predicting variable is either I(1) or I(0). Our approach, which is initially presented in a simple location model, has bearing on inference in parameter-on-the-boundary situations beyond the predictive regression problem.

PAPERS IN PROGRESS

- Bootstrap Inference for Regression Discontinuity Designs (with Giuseppe Cavaliere, Sílvia Gonçalves & and Morten Ørregaard Nielsen).

- Bootstrapping Exogeneity Tests in Linear Models with Possibly Weak Instruments (with Prosper Dovonon and Nikolay Gospodinov).

- When did the Phillips Curve Become Flat? A time-varying estimate of structural parameters (with Antonio Marsi).