Testing Calibrated General Equilibrium Models

Abstract

This paper illustrates the philosophy which forms the basis of calibration exercises in general equilibrium macroeconomic models and the details of the procedure, the advantages and the disadvantages of the approach, with particular reference to the issue of testing "false" economic models. We provide an overview of the most recent simulation-based approaches to the testing problem and compare them to standard econometric methods used to test the fit of non-linear dynamic general equilibrium models. We illustrate how simulation-based techniques can be used to formally evaluate the fit of a calibrated model to the data and obtain ideas on how to improve the model design using a standard problem in the international real business cycle literature, i.e. whether a model with complete financial markets and no restrictions to capital mobility is able to reproduce the second order properties of aggregate saving and aggregate investment in an open economy.

The task of this chapter was to illustrate how simulation techniques can be used to evaluate the quality of a model's approximation to the data, where the basic theoretical model design is one which fits into what we call a calibration exercise. In section 2 we first provide a definition of what calibration is and then describe in detail the steps needed to generate time series from the model and to select relevant statistics of actual and simulated data. In section 3 we overview four different formal evaluation approaches recently suggested in the literature, comparing and contrasting them on the basis of what type of variability they use to judge the closeness of the model's approximation to the data. In section 4 we describe how to undertake policy analysis with models which have been calibrated and evaluated along the lines discussed in the previous two sections. Section 5 presents a concrete example, borrowed from Baxter and Crucini (1993), where we design four different simulation-based statistics which allow us to shed some light on the quality of the model approximation to the data, in particular, whether the model is able to reproduce the main features of the spectral density matrix of saving and investment for the US and Europe at business cycle frequencies. We show that, consistent with Baxter and Crucini's claims, the model qualitatively produces a high coherence of saving and investment at business cycle frequencies in the two continental blocks but it also has the tendency to generate a highly skewed simulated distribution for the coherence of the two variables. We also show that the model is less successful in accounting for the volatility features of US and European saving and investment at business cycle frequencies and that taking into account parameter uncertainty helps in certain cases to bring the properties of simulated data closer to those of the actual data.

Overall, the example shows that simulation based evaluation techniques are very useful to judge the quality of the approximation of fully specified general equilibrium models to the data and may uncover features of the model which are left hidden by more simple but more standard informal evaluation techniques.

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