We study the identification and estimation of first-price auctions with independent private values if bidders face ambiguity about the valuation distribution and have maxmin expected utility. Using variation in the number of bidders we nonparametrically identify the true valuation distribution and the lower envelope of the set of prior beliefs. We also allow for CRRA and unobserved auction heterogeneity, and propose a Bayesian estimation method based on Bernstein polynomials. Monte Carlo experiments show that our estimator performs well, and incorrectly ignoring ambiguity induces bias and loss of revenue. We find evidence of ambiguity in timber auctions in the Pacific Northwest.
If managers maximize the payoffs of their shareholders rather than firm profits, then it may be anticompetitive for a shareholder to own competing firms. This is because a manager's objective function may place weight on profits of competitors who are held by the same shareholder. Recent research found evidence that common ownership by diversified institutional investors is anticompetitive by showing that prices in the airline and banking industries are related to generalized versions of the Herfindahl-Hirschman Index (HHI) that account for common ownership. In this paper we propose an alternative approach to estimating the competitive effects of common ownership that relates prices and quantities directly to the weights that such managers may be placing on the profits of their rivals. We argue that this approach has several advantages. First, the approach does not inherit the endogeneity problems of HHI regressions, which arise because HHI measures are functions of quantities. Second, because we treat quantities as outcomes we can look for competitive effects of common ownership on both prices and quantities. Third, while concentration measures vary only at the market-time level, the profit weights also vary at the firm level, which allows us to control for a richer set of unobservables. We apply this approach to data from the banking industry. Our empirical findings are mixed, though they're preliminary as we investigate irregularities in ownership data (Anderson and Brockman (2016)). The sign of the estimated effect is sensitive to the specification. Economically, estimated effects on prices and quantities are fairly small.
We extent the point-identification result in Guerre, Perrigne, and Vuong (2009) to environments with one-dimensional unobserved auction heterogeneity. In addition, we also show a robustness result for the case where the exclusion restriction used for point identification is violated: We provide conditions to ensure that the primitives recovered under the violated exclusion restriction still bound the true primitives in this case. We propose a new Sieve Maximum Likelihood Estimator, show its consistency and illustrate its finite sample performance in a Monte Carlo experiment. We investigate the bias in risk aversion estimates if unobserved auction heterogeneity is ignored and explain why the sign of the bias depends on the correlation between the number of bidders and the unobserved auction heterogeneity. In an application to USFS timber auctions we find that the bidders are risk neutral, but we would reject risk neutrality without accounting for unobserved auction heterogeneity. * We are very grateful to Amit Gandhi and Jack Porter for their advise and many helpful suggestions. We would also like to thank Andrés Aradillas-López, Bruce Hansen and Xiaoxia Shi for their helpful comments. Serafin Grundl: Federal Reserve Board of Governors, serafin.j.grundl@frb.gov. Yu Zhu: Department of Economics, University of Leicester, yz317@leicester.ac.uk. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the staff, by the Board of Governors, or by the Federal Reserve Banks.
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