  Generalized and Simulated Method of Moments are often used to estimate
structural Economic models. Yet, it is commonly reported that optimization is
challenging because the corresponding objective function is non-convex. For
smooth problems, this paper shows that convexity is not required: under a
global rank condition involving the Jacobian of the sample moments, certain
algorithms are globally convergent. These include a gradient-descent and a
Gauss-Newton algorithm with appropriate choice of tuning parameters. The
results are robust to 1) non-convexity, 2) one-to-one non-linear
reparameterizations, and 3) moderate misspecification. In contrast,
Newton-Raphson and quasi-Newton methods can fail to converge for the same
estimation because of non-convexity. A simple example illustrates a non-convex
GMM estimation problem that satisfies the aforementioned rank condition.
Empirical applications to random coefficient demand estimation and impulse
response matching further illustrate the results.
