Multivariate sensitivity analysis with a very large CGE model

The purpose of this technical paper is to illustrate a computationally cheap approach of conducting the multivariate sensitivity analysis with a very large and complex non-linear model RHOMOLO. We evaluated model responses to the different combinations of the following input data a) elasticity parameters that define behavioural responses of RHOMOLO b) labour- and total factor productivity parameters that characterize technology and c) scenario perturbations that represent policy decisions with regard to fiscal transfers. Such selection of scenario perturbations is of particular importance in the context of the EU Cohesion policies that are evaluated with RHOMOLO: in accordance with a number of objectives, fiscal contributions enter the model being translated into the factor productivity shocks. In order to bypass the dimensionality curse we resorted to the deterministic approach, assigning three levels to each input parameter and implemented the exercise in two steps: One-at-a-time variation of fifteen elasticity parameters for the different combinations of three scenario shocks permitted to attribute the highest influence ranking to the elasticities that define possibilities of substitution between labour and capital, among the domestic and imported goods and to the wage curve elasticity. For the influence ranking we employed the standard elasticity index and the Hoffman&Gardner sensitivity index. All-at-a-time variation of the most influential elasticity parameters and scenario shocks demonstrated that the total factor productivity and labour productivity shocks are the main drivers of model results, showing strong individual and weak interaction effects. Quantification of the individual and interaction effects of multivariate scenario perturbations was based on a three-level factorial design approach. We developed the algorithms for the parallel execution of the multiple instances of RHOMOLO that permit all computations to be finished in five hours. Our approach can be applied to virtually any static or dynamic model that is programmed in GAMS requiring minor modifications in the model code. With a pedagogical purpose we provide the detailed explanations of algorithms and the full listings of computer codes that were developed to implement this multivariate sensitivity analysis exercise. The comprehensive sensitivity analysis of the individual and interactions effects allows prioritize the econometric estimations of the most influential parameters, thus increasing precision of policy impact assessment.