Semiparametric identification and estimation in multi-object, English auctions. (English) Zbl 1420.91111
Summary: Within the independent private-values paradigm, we derive the data-generating process of winning bids for two different objects sold sequentially at English auction, assuming the valuations across objects for a particular bidder are potentially dependent. We demonstrate that, within the Archimedean family of copulas, the model is identified using only observed winning bids, and then propose a semiparametric estimation strategy to recover the joint distribution of valuations. We implement our methods using data from fish auctions held in Denmark and estimate whether bundling is expected-revenue enhancing.
MSC:
| 91B26 | Auctions, bargaining, bidding and selling, and other market models |
| 62G05 | Nonparametric estimation |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62P20 | Applications of statistics to economics |
Keywords:
multi-object auctions; bundling; sequential; English auctions; fish auctions; Archimedean copulas; semiparametric identification; semiparametric estimationReferences:
| [1] | Athey, S.; Haile, P., Identification of standard auction models, Econometrica, 70, 2107-2140 (2002) · Zbl 1141.91390 |
| [2] | Bajari, P., 1997. The first price auction with asymmetric bidders: theory and applications. Ph.D. Dissertation, Department of Economics, University of Minnesota.; Bajari, P., 1997. The first price auction with asymmetric bidders: theory and applications. Ph.D. Dissertation, Department of Economics, University of Minnesota. |
| [3] | Bajari, P., Comparing competition and collusion: a numerical approach, Economic Theory, 18, 187-205 (2001) · Zbl 1049.91044 |
| [4] | Brendstrup, B., in press. Non-parametric estimation of sequential English auctions. Journal of Econometrics, doi:10.1016/j.jeconom.2006.10.004; Brendstrup, B., in press. Non-parametric estimation of sequential English auctions. Journal of Econometrics, doi:10.1016/j.jeconom.2006.10.004 · Zbl 1420.91109 |
| [5] | Brendstrup, B., Paarsch, H., 2004. Nonparametric estimation in models of multi-unit, sequential, Dutch auction with asymmetric bidders. Typescript, Department of Economics, University of Iowa.; Brendstrup, B., Paarsch, H., 2004. Nonparametric estimation in models of multi-unit, sequential, Dutch auction with asymmetric bidders. Typescript, Department of Economics, University of Iowa. |
| [6] | Brendstrup, B.; Paarsch, H., Identification and estimation in sequential, asymmetric English auctions, Journal of Econometrics, 134, 69-94 (2006) · Zbl 1420.91110 |
| [7] | Chakraborty, I., Bundling decisions for selling multiple objects, Economic Theory, 13, 723-733 (1999) · Zbl 0941.91034 |
| [8] | Chen, X.; Shen, X., Sieve extremum estimation for weakly dependent data, Econometrica, 66, 289-314 (1998) · Zbl 1055.62544 |
| [9] | Donald, S.; Paarsch, H., Piecewise pseudo-maximum likelihood estimation in empirical models of auctions, International Economic Review, 34, 121-148 (1993) · Zbl 0771.90020 |
| [10] | Donald, S.; Paarsch, H., Identification, estimation, and testing in parametric empirical models of auctions within the independent private values paradigm, Econometric Theory, 12, 517-567 (1996) |
| [11] | Donald, S.; Paarsch, H., Superconsistent estimation and inference in structural econometric models using extreme order statistics, Journal of Econometrics, 109, 305-340 (2002) · Zbl 1043.62103 |
| [12] | Donald, S., Paarsch, H., Robert, J., 2006. An empirical model of the multi-unit, sequential, clock auction. Journal of Applied Econometrics 21, 1221-1247.; Donald, S., Paarsch, H., Robert, J., 2006. An empirical model of the multi-unit, sequential, clock auction. Journal of Applied Econometrics 21, 1221-1247. |
| [13] | Embrechts, P.; Lindskog, F.; McNeil, A., Modelling dependence with copulas and applications to risk management (2001), Typescript, Department of Mathematics, ETHZ: Typescript, Department of Mathematics, ETHZ Switzerland |
| [14] | Genest, C., Frank’s family of bivariate distributions, Biometrika, 74, 549-555 (1987) · Zbl 0635.62038 |
| [15] | Genest, C.; MacKay, J., The joy of copulas: bivariate distributions with uniform marginals, The American Statistician, 40, 280-283 (1986) |
| [16] | Genest, C.; Ghoudi, K.; Rivest, L.-P., A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82, 543-552 (1995) · Zbl 0831.62030 |
| [17] | Guerre, E.; Perrigne, I.; Vuong, Q., Optimal nonparametric estimation of first-price auctions, Econometrica, 68, 525-574 (2000) · Zbl 1056.62512 |
| [18] | Haile, P.; Tamer, E., Inference with an incomplete model of English auctions, Journal of Political Economy, 111, 1-51 (2003) |
| [19] | Hortaçsu, A., Mechanism choice and strategic bidding in divisible good auctions: an empirical analysis of the Turkish treasury auction market (2002), Typescript, Department of Economics: Typescript, Department of Economics University of Chicago |
| [20] | Jofre-Bonet, M.; Pesendorfer, M., Estimation of a dynamic auction game, Econometrica, 71, 1443-1489 (2003) · Zbl 1154.91414 |
| [21] | Krishna, V., Auction Theory (2002), Academic Press: Academic Press San Diego |
| [22] | Laffont, J.-J.; Ossard, H.; Vuong, Q., Econometrics of first-price auctions, Econometrica, 63, 953-980 (1995) · Zbl 0836.90060 |
| [23] | Li, T., Econometrics of first-price auctions with entry and binding reservation prices, Journal of Econometrics, 126, 173-200 (2005) · Zbl 1334.91040 |
| [24] | Milgrom, P.; Weber, R., A theory of auctions and competitive bidding, Econometrica, 50, 1089-1122 (1982) · Zbl 0487.90017 |
| [25] | Nelsen, R., An Introduction to Copulas (1999), Springer: Springer New York · Zbl 0909.62052 |
| [26] | Paarsch, H., Deciding between the common and private value paradigms in empirical models of auctions, Journal of Econometrics, 51, 191-215 (1992) |
| [27] | Paarsch, H., Deriving an estimate of the optimal reserve price: an application to British Columbian timber sales, Journal of Econometrics, 78, 333-357 (1997) · Zbl 0900.62653 |
| [28] | Prakasa Rao, B. L.S., Identifiability in Stochastic Models: Characterization of Probability Distributions (1992), Academic Press: Academic Press San Diego · Zbl 0746.62008 |
| [29] | Rohatgi, V., An Introduction to Probability Theory and Mathematical Statistics (1976), Wiley: Wiley New York · Zbl 0354.62001 |
| [30] | Shih, J.; Louis, T., Inferences on the association parameter in copula models for bivariate survival data, Biometrics, 51, 1384-1399 (1995) · Zbl 0869.62083 |
| [31] | Weber, R., Multiple-object auctions, (Englebrecht-Wiggans, R.; Shubik, M.; Stark, R., Auctions, Bidding, and Contracting: Uses and Theory (1983), New York University Press: New York University Press New York), 165-191 |
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