Elsevier

Economics Letters

Volume 180, July 2019, Pages 71-75
Economics Letters

Estimating impulse response functions when the shock series is observed

https://doi.org/10.1016/j.econlet.2019.04.017Get rights and content

Highlights

  • There are many approaches to estimation of IRFs when the shock series is observed.

  • This letter investigates their finite sample performance in terms of RMSE.

  • Monte Carlo simulations reveal iterated approaches tend to perform well.

  • The inclusion of all relevant variables is not always desirable.

Abstract

We compare the finite sample performance of a variety of consistent approaches to estimating impulse response functions (IRFs) in a linear setup when the shock of interest is observed. Although there is no uniformly superior approach, iterated approaches turn out to perform well in terms of root mean-squared error (RMSE) in diverse environments and sample sizes. For smaller sample sizes, the inclusion of all ‘relevant’ variables is not always desirable.

Introduction

An important task in empirical economics is to track the effects of a shock on the variable(s) of interest (e.g., Kilian and Lütkepohl, 2017). Since shocks are rarely observed, much of the literature has been devoted to the issue of estimation and identification of shocks, usually within a vector autoregression (VAR) framework. If a shock can be measured, or is observed without error, however, then estimating IRFs is straightforward as noted by Kilian and Lütkepohl (2017, Chapter 7) and Stock and Watson (2017, p.63). In that case, many approaches are available to estimating IRFs, such as univariate distributed lag (DL) or iterated autoregressive distributed lag (ARDL) approaches, the local projection (LP) approach of Jordà (2005), and the asymptotically efficient VARX model. This paper focuses on the following three questions within the standard linear setup: (1) Do we need to care about which approach to use in practice? (2) Is it desirable to include all the relevant variables2 in estimating IRFs? and (3) Is there any approach that always dominates the others? Our answers, respectively, are: yes, not always, and no. We arrive at these answers by investigating the root mean-squared error (RMSE) of estimating individual IRF coefficients in a series of Monte Carlo (MC) experiments.3 We adopt a design with randomly generated coefficients as well as two additional designs calibrated to a quarterly international real output growth dataset and a U.S. macro dataset (relegated to the online Appendix).

We find a significant variation in the performance among various approaches under study, indicating that the choice of approach in empirical application can be consequential. Although there exists no uniformly superior approach, the iterated ARDL and vector ARDL (VARDL) approaches turn out to perform better in the simulation environments considered in our study. Moreover, parsimonious specifications outperform asymptotically efficient approaches when the time dimension is relatively small. These findings imply that one may not wish to include all ‘relevant’ variables for short samples even when the variables entering the true underlying model are identified.

Section snippets

Approaches to estimating IRFs when the shock is observed

Suppose that zt is an n×1 vector of variables generated from the following stationary VAR model, zt=Φzt1+ut,   fort=,0,1,2,,T,where Φ is an n×n matrix of coefficients and ut is an n×1 vector of reduced form shocks, which is partitioned as ut=rεt+ζt,where εt denotes the observed shock of interest which is uncorrelated with ζt. The observed shock (εt) might or might not have a structural interpretation. Not all variables in zt are necessarily observed as it might be the case in empirical work

Monte Carlo experiments

We conduct three sets of MC experiments. The first set is presented below and it features stochastically generated parameters. The remaining two sets are designed to match an international real output dataset and a U.S. macro dataset, which are relegated to the online Appendix. These experiments provide qualitatively similar results.

Conclusion

We find a substantial heterogeneity in the RMSE performance of various approaches to estimating IRFs in a linear setting when shocks are observed. Our simulation results suggest that iterated (ARDL/VARDL) approaches tend to outperform direct approaches. Moreover, the common practice of including all variables that are deemed to be part of the DGP is not always desirable. This paper does not address an equally important issue of inference about the impulse responses, which is left for future

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We would like to thank Georgios Georgiadis, Everett Grant, Oscar Jorda, Lutz Killian, Karel Mertens, and anonymous referee for helpful comments.

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The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Dallas or the Federal Reserve System.

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