A Nonparametric GMM Series Approach to Solving Multi-equation Asset Pricing Models with Recursive Preferences

In an exchange economy with recursive preferences (Epstein and Zin, 1989), we propose a novel nonparametric generalized method of moment (GMM) series approach to estimate unknown policy functions which are recursively specified in a system of nonlinear conditional expectation models simultaneously as opposed to sequentially, thereby avoiding accumulation of approximation errors. Unlike current numerical solution methods, this new method does not require the imposition of tight auxiliary assumptions on the conditional distributions or matching moments of state variables and thus avoids spurious model conclusions due to mis-specification errors on state dynamics. Because there is an infinite number of moments and parameters due to series approximations, we propose a series continuously updated estimator (CUE) and establish a new result on consistency and asymptotic normality, which further helps facilitate rigorous inference on general equilibrium models in the presence of misspecified state variables or those with unknown dynamics. Three simulation studies are considered, and our new method has been proven to perform reasonably well in the finite sample in comparison with popular numerical solution methods