This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze the conditions under which the nested pseudo-likelihood (NPL) algorithm achieves convergence and derive its convergence rate. We find that the NPL algorithm may not necessarily converge when the fixed point mapping does not have a local contraction property. To address the issue of non-convergence, we propose alternative sequential estimation procedures that can achieve convergence even when the NPL algorithm does not. Upon convergence, some of our proposed estimation algorithms produce more efficient estimators than the NPL estimator.
Contraction dynamic games nested pseudo likelihood recursive projection method