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Convexity Not Required: Estimation of Smooth Moment Condition Models

Jean-Jacques Forneron, Liang Zhong

arXiv 27 Apr 2023 · Econometrics · 1 citations (OpenAlex)

arXiv:2304.14386 · PDF · DOI · OpenAlex · Extracted main text

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 conditions involving the Jacobian of the 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 moderately non-linear reparameterizations, and 3) moderate misspecification. The conditions preclude non-global optima. Numerical and empirical examples illustrate the condition, non-convexity, and convergence properties of different optimizers.

Citation extraction

48
references
76
in-text mentions
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Nocedal, J. and S. Wright (2006) Numerical Optimzation0.9285380%
2Knittel, C. R. and K. Metaxoglou (2014) Estimation of random-coefficient demand models: two empiricists' perspective0.81142100%
3Forneron, J.-J (2023) Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models self0.7373367%
4Conlon, C. and J. Gortmaker (2020) Best practices for differentiated products demand estimation with pyblp0.69351100%
5Nesterov, Y (2018) Lectures on convex optimization0.64422100%
6Gourieroux, C. and A. Monfort (1996) Simulation-based econometric methods0.64422100%
7Andrews, D. W (1997) A stopping rule for the computation of generalized method of moments estimators0.5853333%
8Karimi, H., J. Nutini, and M. Schmidt (2016) Linear convergence of gradient and proximal-gradient methods under the polyak-ojasiewicz condition, in0.58531100%
9Berry, S., J. Levinsohn, and A. Pakes (1995) Automobile Prices in Market Equilibrium0.5112250%
10Dennis, J. E. and R. B. Schnabel (1996) Numerical methods for unconstrained optimization and nonlinear equations0.5112250%

Showing the top 10 of 48 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1SLIM: Stochastic Learning and Inference in Overidentified Models0.73732
2Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models0.64422
3Occasionally Misspecified0.40511