Replacing Sample Trimming with Boundary Correction in Nonparametric Estimation of First‐Price Auctions

Hickman, Brent R.; Hubbard, Timothy P.

doi:10.1002/jae.2385

Cited by 40 publications

(20 citation statements)

References 26 publications

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“…I use the Epanechnikov kernel function. The same correction is applied to the nonparametric estimation of first-price auction models byHickman and Hubbard (2015).…”

mentioning

confidence: 99%

Bargaining With Asymmetric Information: An Empirical Study of Plea Negotiations

Silveira

2017

Econometrica

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This paper empirically investigates how sentences to be assigned at trial impact plea bargaining. The analysis is based on the model of bargaining with asymmetric information by Bebchuk, 1984. I provide conditions for the nonparametric identification of the model, propose a consistent nonparametric estimator, and implement it using data on criminal cases from North Carolina. Employing the estimated model, I evaluate how different sentencing reforms affect the outcome of criminal cases. My results indicate that lower mandatory minimum sentences could greatly reduce the total amount of incarceration time assigned by the courts, but may increase conviction rates. In contrast, the broader use of non‐incarceration sentences for less serious crimes reduces the number of incarceration convictions, but has a very small effect over the total assigned incarceration time. I also consider the effects of a ban on plea bargains. Depending on the case characteristics, over 20 percent of the defendants who currently receive incarceration sentences would be acquitted if plea bargains were forbidden.

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“…I use the Epanechnikov kernel function. The same correction is applied to the nonparametric estimation of first-price auction models byHickman and Hubbard (2015).…”

mentioning

confidence: 99%

Bargaining With Asymmetric Information: An Empirical Study of Plea Negotiations

Silveira

2017

Econometrica

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“…Indeed, it is observed that the R factor at the right tail of the bid distribution often has quite a large number, as it is generated by dividing a positive number by a number close to zero, tending to result in the inflated estimates of valuations. To overcome the boundary problem, Hickman and Hubbard (2015) applied the method of boundary correction to the structural asymmetric auction estimation framework. Accordingly, throughout this study, we apply the boundary correction methods for all estimates.…”

Section: Structural Estimation Methodsmentioning

confidence: 99%

How Accurately Do Structural Asymmetric First-Price Auction Estimates Represent True Valuations?

Chernomaz

Yoshimoto

2019

Journal of Econometric Methods

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Structural asymmetric first-price auction estimation methods have provided numerous empirical studies. However, due to the latent nature of underlying valuations, the accuracy of estimates is not feasibly testable with field data, a fact that could inhibit empirical auction market designs and applications based on structural estimates. To assess their accuracy, we provide an analysis of estimates derived from experimental asymmetric auction data, in which researchers observe valuations. We test the null of statistical equivalence between the estimated and true value distributions against the alternative of non-equivalence. When advanced models are used, the Modified Kolmogorov-Smirnov test fails to reject the distributional equivalence, supporting structural asymmetric auction estimations for auction market studies. In addition, recovered efficiencies have plus-minus 2.5 percent precision, compared to the true efficiencies.

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“…As noted by Hickman and Hubbard (2015), boundary correction can be important in the estimation of auction models, especially if the objective is to estimate the density of valuations. The reason is that the bid distribution (in Hickman and Hubbard (2015)) or the distribution of win probabilities (here) has compact support and it is well-known that, absent a boundary correction, most nonparametric density estimators are inconsistent at the boundaries. The situation is more favorable in our case since we know that probabilities vary from zero to one whereas the top of the bid distribution must be estimated, albeit that this can be done super-consistently.…”

Section: Smoothing Transformations and Boundary Correctionmentioning

confidence: 99%

Estimation of Auction Models with Shape Restrictions

Pinkse¹,

Schurter²

2019

Preprint

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We introduce several new estimation methods that leverage shape constraints in auction models to estimate various objects of interest, including the distribution of a bidder's valuations, the bidder's ex ante expected surplus, and the seller's counterfactual revenue. The basic approach applies broadly in that (unlike most of the literature) it works for a wide range of auction formats and allows for asymmetric bidders. Though our approach is not restrictive, we focus our analysis on first-price, sealed-bid auctions with independent private valuations. We highlight two nonparametric estimation strategies, one based on a least squares criterion and the other on a maximum likelihood criterion. We also provide the first direct estimator of the strategy function. We establish several theoretical properties of our methods to guide empirical analysis and inference. In addition to providing the asymptotic distributions of our estimators, we identify ways in which methodological choices should be tailored to the objects of their interest. For objects like the bidders' ex ante surplus and the seller's counterfactual expected revenue with an additional symmetric bidder, we show that our input-parameter-free estimators achieve the semiparametric efficiency bound. For objects like the bidders' inverse strategy function, we provide an easily implementable boundary-corrected kernel smoothing and transformation method in order to ensure the squared error is integrable over the entire support of the valuations. An extensive simulation study illustrates our analytical results and demonstrates the respective advantages of our least-squares and maximum likelihood estimators in finite samples.Compared to estimation strategies based on kernel density estimation, the simulations indicate that the smoothed versions of our estimators enjoy a relatively large degree of robustness to the choice of an input parameter.

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Replacing Sample Trimming with Boundary Correction in Nonparametric Estimation of First‐Price Auctions

Cited by 40 publications

References 26 publications

Bargaining With Asymmetric Information: An Empirical Study of Plea Negotiations

Bargaining With Asymmetric Information: An Empirical Study of Plea Negotiations

How Accurately Do Structural Asymmetric First-Price Auction Estimates Represent True Valuations?

Estimation of Auction Models with Shape Restrictions

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