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Semi-nonparametric estimation of independently and identically repeated first-price auctions via an integrated simulated moments method

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  • Bierens, Herman J.
  • Song, Hosin

Abstract

In this paper we propose to estimate the value distribution of independently and identically repeated first-price auctions directly via a semi-nonparametric integrated simulated moments sieve approach. Given a candidate value distribution function in a sieve space, we simulate bids according to the equilibrium bid function involved. We take the difference of the empirical characteristic functions of the actual and simulated bids as the moment function. The objective function is then the integral of the squared moment function over an interval. Minimizing this integral to the distribution functions in the sieve space involved and letting the sieve order increase to infinity with the sample size then yields a uniformly consistent semi-nonparametric estimator of the actual value distribution. Also, we propose an integrated moment test for the validity of the first-price auction model, and an data-driven method for the choice of the sieve order. Finally, we conduct a few numerical experiments to check the performance of our approach.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 168 (2012)
Issue (Month): 1 ()
Pages: 108-119

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Handle: RePEc:eee:econom:v:168:y:2012:i:1:p:108-119

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: First-price auctions; Semi-nonparametric estimation; Sieve estimation; Empirical characteristic functions; Simulated moments; Legendre polynomials; Integrated moment test;

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References

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  1. Laffont, J.J. & Vuong, Q., 1992. "Structural Econometrics Analysis of Descending Auctions," Papers 92.272, Toulouse - GREMAQ.
  2. Donald, Stephen G. & Paarsch, Harry J., 1996. "Identification, Estimation, and Testing in Parametric Empirical Models of Auctions within the Independent Private Values Paradigm," Econometric Theory, Cambridge University Press, vol. 12(03), pages 517-567, August.
  3. Susan Athey & Philip A. Haile, 2002. "Identification of Standard Auction Models," Econometrica, Econometric Society, vol. 70(6), pages 2107-2140, November.
  4. Laffont, Jean-Jacques & Ossard, Herve & Vuong, Quang, 1995. "Econometrics of First-Price Auctions," Econometrica, Econometric Society, vol. 63(4), pages 953-80, July.
  5. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  6. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  7. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  8. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
  9. Susan Athey & Philip A. Haile, 2006. "Empirical Models of Auctions," Cowles Foundation Discussion Papers 1562, Cowles Foundation for Research in Economics, Yale University.
  10. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  11. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  12. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
  13. Bierens, Herman J., 2008. "Semi-Nonparametric Interval-Censored Mixed Proportional Hazard Models: Identification And Consistency Results," Econometric Theory, Cambridge University Press, vol. 24(03), pages 749-794, June.
  14. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60 Elsevier.
  15. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
  16. Tong Li, 2005. "Econometrics of first-price auctions with entry and binding reservation prices," Journal of Econometrics, Elsevier, vol. 126(1), pages 173-200, May.
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