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Semi-nonparametric estimation of secret reserve prices in auctions

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  • Foster, Joshua

Abstract

This letter proposes an estimation method for the distribution of unobservable secret seller reserve prices in auctions. Within the symmetric affiliated private values model, I construct a density estimator using the semi-nonparametric quasi maximum likelihood approach developed by Gallant and Nychka (1987). I then use Monte Carlo experiments to demonstrate its performance in relatively small samples. A discussion on applying this method to structurally similar identification problems is provided.

Suggested Citation

  • Foster, Joshua, 2022. "Semi-nonparametric estimation of secret reserve prices in auctions," Economics Letters, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:ecolet:v:220:y:2022:i:c:s0165176522003172
    DOI: 10.1016/j.econlet.2022.110843
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    References listed on IDEAS

    as
    1. Tong Li & Isabelle Perrigne, 2003. "Timber Sale Auctions with Random Reserve Prices," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 189-200, February.
    2. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September.
    3. Levin, Dan & Smith, James L, 1996. "Optimal Reservation Prices in Auctions," Economic Journal, Royal Economic Society, vol. 106(438), pages 1271-1283, September.
    4. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, vol. 56(2), pages 433-447, March.
    5. Bernard Elyakime & Jean-Jacques Laffont & Patrice Loisel & Quang Vuong, 1994. "First-Price Sealed-Bid Auctions with Secret Reservation Prices," Annals of Economics and Statistics, GENES, issue 34, pages 71-114.
    6. Fenton, Victor M & Gallant, A Ronald, 1996. "Convergence Rates of SNP Density Estimators," Econometrica, Econometric Society, vol. 64(3), pages 719-727, May.
    7. Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
    8. Greblicki, Wlodzimierz & Pawlak, Miroslaw, 1985. "Pointwise consistency of the hermite series density estimate," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 65-69, April.
    9. Liu, Ming & Zhang, Harold H., 1998. "Overparameterization in the seminonparametric density estimation," Economics Letters, Elsevier, vol. 60(1), pages 11-18, July.
    10. Katkar Rama & Reiley David H, 2007. "Public versus Secret Reserve Prices in eBay Auctions: Results from a Pokémon Field Experiment," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 6(2), pages 1-25, January.
    11. Greblicki, W?odzimierz & Pawlak, Miros?aw, 1984. "Hermite series estimates of a probability density and its derivatives," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 174-182, October.
    12. Eklof, Matias & Lunander, Anders, 2003. "Open outcry auctions with secret reserve prices: an empirical application to executive auctions of tenant owner's apartments in Sweden," Journal of Econometrics, Elsevier, vol. 114(2), pages 243-260, June.
    13. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    14. E. Liebscher, 1990. "Hermite series estimators for probability densities," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 321-343, December.
    15. Zulehner, Christine, 2009. "Bidding behavior in sequential cattle auctions," International Journal of Industrial Organization, Elsevier, vol. 27(1), pages 33-42, January.
    16. Fenton, Victor M & Gallant, A Ronald, 1996. "Erratum [Convergence Rates of SNP Density Estimators]," Econometrica, Econometric Society, vol. 64(6), pages 1493-1493, November.
    17. repec:adr:anecst:y:1994:i:34:p:04 is not listed on IDEAS
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    More about this item

    Keywords

    Auctions; Sieve estimator; Secret reserve prices; Nonparametric estimation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L86 - Industrial Organization - - Industry Studies: Services - - - Information and Internet Services; Computer Software

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