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Derivative-Based Optimization with a Non-Smooth Simulated Criterion

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  • David T. Frazier
  • Dan Zhu

Abstract

Indirect inference requires simulating realizations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function is discontinuous and does not permit the use of derivative-based optimization routines. Using a specific class of measure changes, we propose a novel simulation algorithm that alleviates the underlying discontinuities inherent in the indirect inference criterion function, permitting the application of derivative-based optimization routines to estimate the unknown model parameters. Unlike competing approaches, this approach does not rely on kernel smoothing or bandwidth parameters. Several Monte Carlo examples that have featured in the literature on indirect inference with discontinuous outcomes illustrate the approach. These examples demonstrate that this new method gives superior performance over existing alternatives in terms of bias, variance and coverage.

Suggested Citation

  • David T. Frazier & Dan Zhu, 2017. "Derivative-Based Optimization with a Non-Smooth Simulated Criterion," Papers 1708.02365, arXiv.org.
  • Handle: RePEc:arx:papers:1708.02365
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    File URL: http://arxiv.org/pdf/1708.02365
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    References listed on IDEAS

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    1. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    2. Li, Tong, 2010. "Indirect inference in structural econometric models," Journal of Econometrics, Elsevier, vol. 157(1), pages 120-128, July.
    3. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    4. Joseph G. Altonji & Anthony A. Smith Jr. & Ivan Vidangos, 2013. "Modeling Earnings Dynamics," Econometrica, Econometric Society, vol. 81(4), pages 1395-1454, July.
    5. Vance L. Martin & Andrew R. Tremayne & Robert C. Jung, 2014. "Efficient Method Of Moments Estimators For Integer Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 491-516, November.
    6. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    7. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    8. Mark S. Joshi & Dan Zhu, 2016. "Optimal Partial Proxy Method for Computing Gammas of Financial Products with Discontinuous and Angular Payoffs," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(1), pages 22-56, March.
    9. Jiun Hong Chan and Mark Joshi, 2012. "Optimal Limit Methods for Computing Sensitivities of," Department of Economics - Working Papers Series 1142, The University of Melbourne.
    10. Di Iorio, Francesca & Calzolari, Giorgio, 2006. "Discontinuities in indirect estimation: An application to EAR models," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2124-2136, April.
    11. Dong Hwan Oh & Andrew J. Patton, 2013. "Simulated Method of Moments Estimation for Copula-Based Multivariate Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 689-700, June.
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