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.