Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models

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A practical challenge for structural estimations is the requirement to minimize a sample objective function which is often non-smooth, non-convex, or both. This paper proposes a simple algorithm designed to find accurate solutions without performing an exhaustive search. It augments each iteration from a new Gauss-Newton algorithm with a grid search step. A finite sample analysis derives its optimization and statistical properties simultaneously using only standard econometric assumptions. After a finite number of iterations, the algorithm transitions from global to fast local convergence, producing accurate estimates with high-probability. Simulated examples and an empirical application illustrate the properties and performance of the algorithm.