BOOTSTRAPPING THE TRACE STATISTIC IN VAR MODELS: MONTE CARLO RESULTS AND APPLICATIONS

ABSTRACT 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.     

Bartlett correction in the stable second‐order autoregressive model with intercept and trend

This paper derives the Bartlett factors that can be used to obtain higher‐order improvements for testing hypotheses about the autoregressive (AR) parameters in the stable AR(2) model with possible intercept and linear trend. The factors are obtained for testing hypotheses about individual parameters (φ₁ and φ₂) as well as their sum. Moreover, the effect of deterministic terms on the correction factors is found explicitly. All corrections are non‐decreasing in the AR parameters. Furthermore, the Bartlett corrections for φ₁ and φ₂ tend to infinity as φ₂ approaches 1, whereas the correction for φ₁ + φ₂ tends to infinity as φ₁ + φ₂ is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.     

BOOTSTRAPPING A STABLE AD MODEL: WEAK VS STRONG EXOGENEITY*

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.     

The cyclicality of R&D investment revisited

In Fabrizio and Tsolmon (Review of Economics and Statistics, 2014, 96(4), 662–675) and Barlevy (American Economic Review, 2007, 97(4), 1131–1164) it was concluded that R&D investments are procyclical. Fabrizio and Tsolmon utilized a model based on Barlevy, but it differed in some respects and allowed for more heterogeneity. However, we doubt whether their implied trends are intended. Fabrizio and Tsolmon also set missing values for R&D equal to zero, leading to unrealistic jumps in investment and its first differences. We reconcile and replicate both the Fabrizio and Tsolmon and Barlevy papers by considering extensions that encompass both models. Furthermore, we treat missing values more appropriately and consider some alternative specifications to check the robustness of the results. Procyclicality is confirmed, but we find much less heterogeneity than Fabrizio and Tsolmon did. In particular, obsolescence and patent effectiveness are no longer important but external financing is.