Building a global sensitivity analysis to quantify the robustness of macro-economic models

Currently used macro-economic models are facing various defaults (see [Stiglitz, 2018]), especially in a complex economic environment involving a large number of calibrated / estimated parameters which leads to highly parameter-sensitive results (see [Grandjean and Giraud, 2017]). Moreover, in social sciences, where most data are approximations, the impact of inputs' uncertainties cannot be considered negligible, and questioning the robustness of our macro-economic models becomes more and more essential to conduct public policies in these fields [European Commision, 2009]. In this paper, the robustness of the [Grasselli and Costa Lima, 2012] model was tested in terms of sensitivity to parameters. After a review of the various sensitivity analysis methods (see also in appendix), a Global Sensitivity Analysis (GSA) with Sobol' indices estimated by the [Saltelli, 2002] method was selected according to the features of the models: nonlinearities, a small number of inputs, and modest computational costs. The process is based on two initial sampling matrices generated by Latin Hypercube Sampling (LHS). A review of literature shows that GSA has been also conducted on the DSGE, RBC, and DICE models [Nordhaus, 2008]. With this method, the sensitivity of an output in the [Grasselli and Costa Lima, 2012] model to its inputs is two to four times less important than the one in a DSGE [Ratto, 2008], RBC [Harenberg et al., 2017] or IAM (DICE) model [Nordhaus, 2008], [Miftakhova, 2019], [Butler et al., 2014] and [Anderson et al., 2014]. One can slightly improve the model's robustness by endogeneizing the main influential parameter. For instance, the [Grasselli and Costa Lima, 2012] model with a CES production function is slightly more robust than one with a Leontief production function.