Convexity Not Required: Estimation of Smooth Moment Condition Models

Jean-Jacques Forneron and Liang Zhong

Papers from arXiv.org

Abstract: 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.

Date: 2023-04
New Economics Papers: this item is included in nep-dcm, nep-des and nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2304.14386 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2304.14386

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().