This paper investigates through Monte Carlo experiments both size and power properties of a bootstrapped trace statistic in two prototypical DGPs. The Monte Carlo results indicate that the ordinary bootstrap has similar size and power properties as inference procedures based on asymptotic critical values. Considering empirical size, the stationary bootstrap is found to provide a uniform improvement over the ordinary bootstrap if the dynamics is underspecified. The use of the stationary bootstrap as a diagnostic tool is suggested. In two illustrative examples this seems to work, and again it appears that the bootstrap incorporates the finite‐sample correction required for the asymptotic critical values to apply.

The Bartlett correction is derived for testing hypotheses about the autoregressive parameter ρ in the stable: (i) AR(1) model; (ii) AR(1) model with intercept; (iii) AR(1) model with intercept and linear trend. The correction is found explicitly as a function of ρ. In the models with deterministic terms, the correction factor is asymmetric in ρ. Furthermore, the Bartlett correction is monotonic increasing in ρ and tends to infinity when ρ approaches the stability boundary of 1. Simulation results indicate that the Bartlett corrections are useful in controlling the size of the LR statistic in small samples.

No abstract

This paper compares the first-order bias approximation for the autoregressive (AR) coefficients in stable AR models in the presence of deterministic terms. It is shown that the bias due to inclusion of an intercept and trend is twice as large as the bias due to an intercept. For the AR(1) model, the accuracy of this approximation is investigated by simulation.

Through Monte Carlo experiments the effects of a feedback mechanism on the accuracy in finite samples of ordinary and bootstrap inference procedures are examined in stable first‐ and second‐order autoregressive distributed‐lag models with non‐stationary weakly exogenous regressors. The Monte Carlo is designed to mimic situations that are relevant when a weakly exogenous policy variable affects (and is affected by) the outcome of agents’ behaviour. In the parameterizations we consider, it is found that small‐sample problems undermine ordinary first‐order asymptotic inference procedures irrespective of the presence and importance of a feedback mechanism. We examine several residual‐based bootstrap procedures, each of them designed to reduce one or several specific types of bootstrap approximation error. Surprisingly, the bootstrap procedure which only incorporates the conditional model overcomes the small sample problems reasonably well. Often (but not always) better results are obtained if the bootstrap also resamples the marginal model for the policymakers’ behaviour.