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A Scrambled Method of Moments

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  • Jean-Jacques Forneron

Abstract

Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in more accurate estimates. This paper explores these methods in a simulation-based estimation setting with an emphasis on the scramble of Owen (1995). For cross-sections and short-panels, the resulting Scrambled Method of Moments simply replaces the random number generator with the scramble (available in most softwares) to reduce simulation noise. Scrambled Indirect Inference estimation is also considered. For time series, qMC may not apply directly because of a curse of dimensionality on the time dimension. A simple algorithm and a class of moments which circumvent this issue are described. Asymptotic results are given for each algorithm. Monte-Carlo examples illustrate these results in finite samples, including an income process with "lots of heterogeneity."

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  • Jean-Jacques Forneron, 2019. "A Scrambled Method of Moments," Papers 1911.09128, arXiv.org.
    • Handle: RePEc:arx:papers:1911.09128
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    References listed on IDEAS

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    1. Forneron, Jean-Jacques & Ng, Serena, 2018. "The ABC of simulation estimation with auxiliary statistics," Journal of Econometrics, Elsevier, vol. 205(1), pages 112-139.
    2. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1353-1381.
    3. Chris J. Oates & Mark Girolami & Nicolas Chopin, 2017. "Control functionals for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 695-718, June.
    4. Frazier, David T. & Oka, Tatsushi & Zhu, Dan, 2019. "Indirect inference with a non-smooth criterion function," Journal of Econometrics, Elsevier, vol. 212(2), pages 623-645.
    5. 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.
    6. Simon N. Wood, 2010. "Statistical inference for noisy nonlinear ecological dynamic systems," Nature, Nature, vol. 466(7310), pages 1102-1104, August.
    7. Alexander Buchholz & Nicolas CHOPIN, 2017. "Improving approximate Bayesian computation via quasi Monte Carlo," Working Papers 2017-37, Center for Research in Economics and Statistics.
    8. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    9. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    10. 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.
    11. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    12. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    13. Bruins, Marianne & Duffy, James A. & Keane, Michael P. & Smith, Anthony A., 2018. "Generalized indirect inference for discrete choice models," Journal of Econometrics, Elsevier, vol. 205(1), pages 177-203.
    14. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    15. repec:fip:fedreq:y:2011:i:3q:p:255-326:n:vol.97no.3 is not listed on IDEAS
    16. repec:dau:papers:123456789/5724 is not listed on IDEAS
    17. Mathieu Gerber & Nicolas Chopin, 2015. "Sequential quasi Monte Carlo," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(3), pages 509-579, June.
    18. Fatih Guvenen, 2011. "Macroeconomics with hetereogeneity : a practical guide," Economic Quarterly, Federal Reserve Bank of Richmond, vol. 97(3Q), pages 255-326.
    19. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
    20. Jean-Jacques Forneron, 2019. "Detecting Identification Failure in Moment Condition Models," Papers 1907.13093, arXiv.org, revised Oct 2023.
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