Evaluating macro-economic models in the frequency domain: A note Peter McAdam ⁎, Ricardo Mestre Research Department, European Central Bank, Kaiserstr. 29, D-60311 Frankfurt am Main, Germany article info abstract Article history: Accepted 19 February 2008 We present a novel approach to the evaluation of macro-econometric models. Using the European Central Bank's “Area Wide Model”, we implement a Cholesky bootstrap whereby the model is stochastically-simulated using historically-consistent covariances. Using this generated data, and the standardized spectral density, we derive its implied frequency characteristics in terms of persistence, periodicity and spectral fit. We benchmark that against that of the historical data. The testing procedure is applicable to a large class of macro models and thus of general interest. © 2008 Published by Elsevier B.V. JEL classification: C10 C52 E32 E37 Keywords: Macro-model Spectral analysis Model evaluation 1. Introduction Assessing the “fit” and empirical relevance of economic models is a fundamental concern for model builders (e.g., Chow, 1982, Amano et al., 2000). However, the definition of “fit” can be highly user specific, reflecting the different uses and questions to which any particular model is addressed, as well as the environments and audiences to which it is exposed. For example, forecasting models will be judged primarily on their ability to capture short-run data characteristics with longer-run data features downplayed. By contrast, models used for policy analysis tend to emphasize theoretical coherence and the capturing of long-run volatilities and correlations. Notionally, these different approaches can be considered as corresponding to different points along the frequency domain spectrum. Viewed in that light, one might argue that familiar model evaluation metrics such as moments matching or forecasting exercises only take us so far in system evaluation. “Well-matching” models need not necessarily have any sensible structure or steady state. Reflecting the statistical weakness of matching methodology, an additional problem is that any number of maintained models may match data moments equally well. Likewise, short-run/forecasting models may generate implausible medium- to long-run paths for variables as a consequence of over-fitting high frequency characteristics. Given these tensions, it is surprising that little emphasis in the macro-modelling tradition has been given to analysing the full spectral characteristics of macro-economic models. That is the purposes of this paper. Although frequency domain methods have been used in past literatures (e.g., Watson, 1993, Diebold et al., 1997) these have also turned out to have fulfilled some quite limited purpose. First, for the most part, such methods have been used to calibrate models. 1 However, one might argue a much more realistic environment for model builders is to have existing models that are estimated (be they by Classical or Bayesian methods) and that they wish to evaluate on a regular basis. Second, despite the richness of the spectral approach, these methods themselves tend in practice to judge models on specific frequency characteristics. Economic Modelling 25 (2008) 1137–1143 ⁎ Corresponding author. Tel.: +49 69 13 44 6434; fax: +49 6913 44 6575. E-mail address: peter.mcadam@ecb.int (P. McAdam). 1 Calibration exercises using moment metrics also tend to be limited to compact structural models. Thus, a wide class of models in policy institutions and forecasting (which embody ad-hoc dynamics) falls outside this type of analysis. 0264-9993/$ – see front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.econmod.2008.02.005 Contents lists available at ScienceDirect Economic Modelling journal homepage: www.elsevier.com/locate/econbase