Global sensitivity analysis for macro-economic models

DSGE models are customarily built in the presence of uncertainties of various levels, such as the specification of behavioural equations of economic agents, the actual values of model parameters, and so on. When the degree of complexity of the model structure and its parameterization increases, it becomes not trivial if not impossible to know a priory the set of model coefficients assuring the stability of a model, or the mapping between structural parameters and the reduced form of a rational expectations model. Global sensitivity analysis techniques can be very useful in this context, helping to make the model structure and properties more transparent to the analyst. In this paper we will discuss two classes of methods: Monte Carlo Filtering techniques and functional/variance decomposition techniques. Monte Carlo filtering (MCF) techniques can be used to map the stability region of DSGE models and to detect parameters that mostly drive the violation of the rank condition. Such procedure is extremely useful for detecting critical regions in the model parameter space of DSGE models. In addition to stability, MCF techniques are also useful to map the fit of each singular series in complex multivariate systems, to answer the following types of questions: which parameters mostly drive the fit of GDP and which the fit of inflation? Is there any trade-off? The second class of sensitivity techniques is based on the so-called High-Dimensional Model Representation. Such a functional decomposition can be very effective in giving a non-parametric representation of the input-output mapping. For example, this approach can be used to map the relationship between structural parameters and the reduced form of rational expectation models. Applications to small DSGE models will complement the description of the methodologies.