Second-Order Sensitivity in Applied General Equilibrium

In most policy applications of general equilibrium modeling, cost functions are calibrated to benchmark data. Modelers often choose the functional form for cost functions based on suitability for numerical solution of the model. The data (including elasticities of substitution) determine first and second order derivatives (local behavior) of the cost functions at the benchmark. The functional form implicitly defines third and higher order derivatives (global behavior). In the absence of substantial analytic and computational effort, it is hard to assess the extent to which results of a particular model depend on third and higher order derivatives. Assuming that a modeler has no (or weak) empirical foundation for her choice of functional form in a model, it is therefore a priori unclear to what extent her results are driven by this choice. I present a method for performing second-order sensitivity analysis of modeling results with respect to functional form. As an illustration of this method I examine three general equilibrium models from the literature and demonstrate the extent to which results depend on functional form. The outcomes suggest that modeling results typically do not depend on the functional form for comparative static policy experiments in models with constant returns to scale. This is in contrast to an example with increasing returns to scale and an endogenous steady-state capital stock. Here results move far from benchmark equilibrium and significantly depend on the choice of functional form.sensitivity analysis, out-of-sample behavior, CGE models, flexible functional forms

Second-Order Sensitivity in Applied General Equilibrium

In most policy applications of general equilibrium modeling, cost functions are calibrated to benchmark data. Modelers often choose the functional form for cost functions based on suitability for numerical solution of the model. The data (including elasticities of substitution) determine first and second order derivatives (local behavior) of the cost functions at the benchmark. The functional form implicitly defines third and higher order derivatives (global behavior). In the absence of substantial analytic and computational effort, it is hard to assess the extent to which results of a particular model depend on third and higher order derivatives. Assuming that a modeler has no (or weak) empirical foundation for her choice of functional form in a model, it is therefore a priori unclear to what extent her results are driven by this choice. I present a method for performing second-order sensitivity analysis of modeling results with respect to functional form. As an illustration of this method I examine three general equilibrium models from the literature and demonstrate the extent to which results depend on functional form. The outcomes suggest that modeling results typically do not depend on the functional form for comparative static policy experiments in models with constant returns to scale. This is in contrast to an example with increasing returns to scale and an endogenous steady-state capital stock. Here results move far from benchmark equilibrium and significantly depend on the choice of functional for

Derivative-based global sensitivity measures: general links with Sobol' indices and numerical tests

The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the Derivative-based Global Sensitivity Measures (DGSM), defined as the integral of the squared derivatives of the model output, showing that it can help to solve the problem of dimensionality in some cases. We provide a general inequality link between DGSM and total Sobol' indices for input variables belonging to the class of Boltzmann probability measures, thus extending the previous results of Sobol and Kucherenko for uniform and normal measures. The special case of log-concave measures is also described. This link provides a DGSM-based maximal bound for the total Sobol indices. Numerical tests show the performance of the bound and its usefulness in practice

Derivative based global sensitivity measures

The method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol' sensitivity indices. This paper presents a survey of recent advances in DGSM concerning lower and upper bounds on the values of Sobol' total sensitivity indices $S\_{i}^{tot}$. Using these bounds it is possible in most cases to get a good practical estimation of the values of $S\_{i}^{tot}$. Several examples are used to illustrate an application of DGSM

Computing derivative-based global sensitivity measures using polynomial chaos expansions

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The {\em derivative-based global sensitivity measures} (DGSM) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis

Characterization of process-oriented hydrologic model behavior with temporal sensitivity analysis for flash floods in Mediterranean catchments

This paper presents a detailed analysis of 10 flash flood events in the Mediterranean region using the distributed hydrological model MARINE. Characterizing catchment response during flash flood events may provide new and valuable insight into the dynamics involved for extreme catchment response and their dependency on physiographic properties and flood severity. The main objective of this study is to analyze flash-flood-dedicated hydrologic model sensitivity with a new approach in hydrology, allowing model outputs variance decomposition for temporal patterns of parameter sensitivity analysis. Such approaches enable ranking of uncertainty sources for nonlinear and nonmonotonic mappings with a low computational cost. Hydrologic model and sensitivity analysis are used as learning tools on a large flash flood dataset. With Nash performances above 0.73 on average for this extended set of 10 validation events, the five sensitive parameters of MARINE process-oriented distributed model are analyzed. This contribution shows that soil depth explains more than 80% of model output variance when most hydrographs are peaking. Moreover, the lateral subsurface transfer is responsible for 80% of model variance for some catchment-flood events’ hydrographs during slow-declining limbs. The unexplained variance of model output representing interactions between parameters reveals to be very low during modeled flood peaks and informs that model parsimonious parameterization is appropriate to tackle the problem of flash floods. Interactions observed after model initialization or rainfall intensity peaks incite to improve water partition representation between flow components and initialization itself. This paper gives a practical framework for application of this method to other models, landscapes and climatic conditions, potentially helping to improve processes understanding and representation