SOLVING LARGE INCOMPLETE MARKETS MODELS BY USING PERTURBATIVE EXPANSIONS

It has been shown in the econometric literature that consistent estimates of consumption-saving models with incomplete markets can be obtained from cross-section data if the model is solved and the observed agents' choices are compared to those predicted by the policy rules.Estimating this class of models by using numerical dynamic programming to compute policy functions is computationally unfeasible for three reasons: the state space is large, agents are heterogeneous and since the values of the structural parameters are not known a priori the model has to be solved many times. In this paper perturbative expansions are used to solve the model instead of numerical dynamic programming. This approach reduces the high computational cost of computing decision rules by several orders of magnitude, making the above econometric approach feasible. As an application the perturbation technique is used to study the role of aggregation and borrowing constraints in the statistical rejection of some dynamic aggregate incomplete markets models. It is also used to show that the common "time dummy" strategy to estimate models with incomplete markets gives inconsistent estimates of the structural parameters.