Jean-Jacques Forneron, Liang Zhong
arXiv 27 Apr 2023 · Econometrics · 1 citations (OpenAlex)
arXiv:2304.14386 · PDF · DOI · OpenAlex · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Nocedal, J. and S. Wright (2006) Numerical Optimzation | 0.928 | 5 | 3 | 80% |
| 2 | Knittel, C. R. and K. Metaxoglou (2014) Estimation of random-coefficient demand models: two empiricists' perspective | 0.811 | 4 | 2 | 100% |
| 3 | Forneron, J.-J (2023) Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models self | 0.737 | 3 | 3 | 67% |
| 4 | Conlon, C. and J. Gortmaker (2020) Best practices for differentiated products demand estimation with pyblp | 0.693 | 5 | 1 | 100% |
| 5 | Nesterov, Y (2018) Lectures on convex optimization | 0.644 | 2 | 2 | 100% |
| 6 | Gourieroux, C. and A. Monfort (1996) Simulation-based econometric methods | 0.644 | 2 | 2 | 100% |
| 7 | Andrews, D. W (1997) A stopping rule for the computation of generalized method of moments estimators | 0.585 | 3 | 3 | 33% |
| 8 | Karimi, H., J. Nutini, and M. Schmidt (2016) Linear convergence of gradient and proximal-gradient methods under the polyak-ojasiewicz condition, in | 0.585 | 3 | 1 | 100% |
| 9 | Berry, S., J. Levinsohn, and A. Pakes (1995) Automobile Prices in Market Equilibrium | 0.511 | 2 | 2 | 50% |
| 10 | Dennis, J. E. and R. B. Schnabel (1996) Numerical methods for unconstrained optimization and nonlinear equations | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 48 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | SLIM: Stochastic Learning and Inference in Overidentified Models | 0.737 | 3 | 2 |
| 2 | Noisy, Non-Smooth, Non-Convex Estimation of Moment Condition Models | 0.644 | 2 | 2 |
| 3 | Occasionally Misspecified | 0.405 | 1 | 1 |