Abstract
In this study, we examine the price process of eBay online auctions. We pool sparse and unevenly spaced bidding histories of individual auctions, resulting in an unbalanced panel of bids. Since the price processes of online auctions are monotonically increasing within individual auctions and exhibit a substantial degree of heterogeneity, we propose a monotone series estimator for panel data with auction-specific slopes for a common relative price growth curve. We generalize Ramsay’s (1998, J R Stat Soc B 60(2):365–375) monotone series estimator to fit our panel model of the price process. We apply the proposed model and estimator to eBay auctions of a popular hand-held device (a Palm PDA). The results are shown to capture closely the overall pattern of observed price dynamics. In particular, the early bidding, mid-auction bidding drought, and end-auction bid sniping are well approximated by the estimated price curve.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ba S, Pavlou PA (2002) Evidence of the effect of trust building technology in electronic markets: price premiums and buyer behavior. MIS Q 26(3): 243–268
Bajari P, Hortacsu A (2003) The winner’s curse, reserve prices, and endogenous entry: empirical insights from eBay auctions. RAND J Econ 34(2): 329–355
Bajari P, Hortacsu A (2004) Economic insights from internet auctions. J Econ Lit 42(2): 457–486
Bapna R, Goes P, Gupta A (2004) User heterogeneity and its impact on electronic auction market design: an empirical exploration. MIS Q 28(1): 21–43
Box GEP, Cox DR (1964) An analysis of transformation (with discussion). J R Soc Stat B 26: 211–252
Brunk HD (1955) Maximum likelihood estimator of monotone parameters. Ann Math Stat 26: 606–616
Eubank RL (1999) Nonparametric regression and spline smoothing, 2nd edn. Marcel Dekker, New York
Henderson DJ, Parmeter CF (2009) Imposing economic constraints in nonparametric regression: survey, implementation and extension. Adv Econom 25: 433–469
Hyde V, Shmueli G, Jank A (2006) Investigating concurrency in online auctions through visualization. Am Stat 60: 241–250
Hyde V, Shmueli G, Jank A (2007) A family of growth models for representing the price process in online auctions. ACM International Conference Proceeding Series 58: 399–408
Jank W, Shmueli G (2006) Functional data analysis in electronic commerce research. Stat Sci 21: 155–166
Krishna V (2002) Auction theory. Academic Press, San Diego
Li Q, Racine JS (2007) Nonparametric econometrics: theory and practice. Princeton University Press, Princeton
Lucking-Reiley D, Bryan D, Prasad N, Reeves D (2000) Pennies from eBay: the determinants of price in online auctions. Working paper
Milgrom PR, Weber RJ (1982) A theory of auctions and competitive bidding. Econometrica 50(5): 1089–1122
Ockenfels A, Roth AE (2002) The timing of bids in internet auctions: market design, bidder behavior, and artificial agents. Papers Strateg Interact 23(3): 79–87
Paarsch HJ, Hong H (2006) An introduction to the structural econometrics of auction data. MIT Press, Cambridge, MA, USA
Racine JS, Parmeter CF, Du P (2009) Constrained nonparametric regression: estimation and inference. Working paper
Ramsay JO (1998) Estimating smooth monotone functions. J R Sat Soc B 60(2): 365–375
Roth AE, Ockenfels A (2002) Last-minute bidding and the rules for ending second-price auctions: evidence from ebay and amazon auctions on the internet. Am Econ Rev 92(4): 1093–1103
Shmueli G, Jank W (2005) Visualizing online auctions. J Comput Graph Stat 14: 299–319
Shmueli G, Jank W, Aris A, Plaisant C, Shneiderman B (2006) Exploring auction databases through interactive visualization. Decis Support Syst 42: 1521–1538
Shmueli G, Russo RP, Jank W (2007) The BARISTA: a model for bid arrivals in online auctions. Ann Appl Stat 1(2): 412–441
Wang S, Jank A, Shmueli G (2008) Explaining and forecasting online auction prices and their dynamics using functional data analysis. J Bus Econ Stat 26(2): 144–160
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, Y.Y., Gu, J. & Li, Q. Nonparametric panel estimation of online auction price processes. Empir Econ 40, 51–68 (2011). https://doi.org/10.1007/s00181-010-0374-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00181-010-0374-7