[​数量经济学研讨会​]Nonparametric Tests for Monotonicity of Bidding Strategy in First-price Auctions



Title: Nonparametric Tests for Monotonicity of Bidding Strategy in First-price Auctions

This paper develops nonparametric tests for monotonicity of bidding strategy in first price auctions. As shown by Guerre, Perrigne, and Vuong (2000), monotonicity of bidding strategy is the essential restriction imposed by the (theoretical) symmetric first price auctions on the distribution of bids. Based on the equivalence between monotonicity of bidding strategy and convexity of integrated value quantile function, we propose a test statistic measuring a distance of the integrated value quantile function from convexity. It only involves in an estimation of bid quantile function, and hence avoids smoothing estimation of bid density. Our test with (rescaled) bootstrap critical values is shown to have the correct size asymptotically, to be consistent against all fixed alternatives and to have non-trivial power against root-n local alternatives. We also establish the uniformity of our test by providing a tight upper bound of our test statistic under the null hypothesis. Monte Carlo experiments show that our testing procedure works well in finite samples.
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