Nonparametric Identification of Risk Aversion in First‐Price Auctions Under Exclusion Restrictions

This paper studies the nonparametric identification of the first‐price auction model with risk averse bidders within the private value paradigm. First, we show that the benchmark model is nonindentified from observed bids. We also derive the restrictions imposed by the model on observables and show that these restrictions are weak. Second, we establish the nonparametric identification of the bidders' utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders' participation, leading to a latent distribution of private values that is independent of the number of bidders. The key idea is to exploit the property that the bid distribution varies with the number of bidders while the private value distribution does not. We then extend these results to endogenous bidders' participation when the exclusion restriction takes the form of instruments that do not affect the bidders' private value distribution. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values, and asymmetric bidders. Last, possible estimation methods are proposed.     

The Affiliation Effect in First‐Price Auctions

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in affiliated private‐value models of first‐price sealed‐bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the effect of a change in n on the bid level into a competition effect and an affiliation effect. The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the affiliation effect can occur in both private‐ and common‐value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.     

On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First‐Price Auctions

We establish the existence of pure strategy equilibria in monotone bidding functions in first‐price auctions with asymmetric bidders, interdependent values, and affiliated one‐dimensional signals. By extending a monotonicity result due to Milgrom and Weber (1982), we show that single crossing can fail only when ties occur at winning bids or when bids are individually irrational. We avoid these problems by considering limits of ever finer finite bid sets such that no two bidders have a common serious bid, and by recalling that single crossing is needed only at individually rational bids. Two examples suggest that our results cannot be extended to multidimensional signals or to second‐price auctions.     

Valuing Dealers' Informational Advantage: A Study of Canadian Treasury Auctions

In many financial markets, dealers have the advantage of observing the orders of their customers. To quantify the economic benefit that dealers derive from this advantage, we study detailed data from Canadian Treasury auctions, where dealers observe customer bids while preparing their own bids. In this setting, dealers can use information on customer bids to learn about (i) competition, that is, the distribution of competing bids in the auction, and (ii) fundamentals, that is, the ex post value of the security being auctioned. We devise formal hypothesis tests for both sources of informational advantage. In our data, we do not find evidence that dealers are learning about fundamentals. We find that the “information about competition” contained in customer bids accounts for 13–27% of dealers' expected profits.     

Keyword Auctions,Unit‐Price Contracts,and the Role of Commitment

Motivated by the enormous growth of keyword advertising, this paper explores the design of performance‐based unit‐price contract auctions, in which bidders bid their unit prices and the winner is chosen based on both their bids and performance levels. The previous literature on unit‐price contract auctions usually considers a static case where bidders' performance levels are fixed. This paper studies a dynamic setting in which bidders with a low performance level can improve their performance at a certain cost. We examine the effect of the performance‐based allocation on overall bidder performance, auction efficiency, and the auctioneer's revenue, and derive the revenue‐maximizing and efficient policies accordingly. Moreover, the possible upgrade in bidders' performance level gives the auctioneer an incentive to modify the auction rules over time, as is confirmed by the practice of Yahoo! and Google. We thus compare the auctioneer's revenue‐maximizing policies when she is fully committed to the auction rule and when she is not, and show that the auctioneer should give less preferential treatment to low‐performance bidders when she is fully committed.     

Constructing Optimal Instruments by First‐Stage Prediction Averaging

This paper considers model averaging as a way to construct optimal instruments for the two‐stage least squares (2SLS), limited information maximum likelihood (LIML), and Fuller estimators in the presence of many instruments. We propose averaging across least squares predictions of the endogenous variables obtained from many different choices of instruments and then use the average predicted value of the endogenous variables in the estimation stage. The weights for averaging are chosen to minimize the asymptotic mean squared error of the model averaging version of the 2SLS, LIML, or Fuller estimator. This can be done by solving a standard quadratic programming problem.     

An Analysis of Scoring and Buyer‐Determined Procurement Auctions

In procurement auctions, the object for sale is a contract, bidders are suppliers, and the bid taker is a buyer. The suppliers bidding for the contract are usually the current supplier (the incumbent) and a group of potential new suppliers (the entrants). As the buyer has an ongoing relationship with the incumbent, he needs to adjust the bids of the entrants to include non‐price attributes, such as the switching costs. The buyer can run a scoring auction, in which suppliers compete on the adjusted bids or scores, or, he can run a buyer‐determined auction, in which suppliers compete on the price, and the buyer adjusts a certain number of the bids with the non‐price attributes after the auction to determine the winner. Unless the incumbent has a significant cost advantage over the entrants, I find that the scoring auction yields a lower average cost for the buyer, if the non‐price attributes are available. If the non‐price attributes are difficult or expensive to obtain, the buyer could run a buyer‐determined auction adjusting only the lowest price bid.     

Nonparametric Identification and Estimation of Nonadditive Hedonic Models

This paper studies the identification and estimation of preferences and technologies in equilibrium hedonic models. In it, we identify nonparametric structural relationships with nonadditive heterogeneity. We determine what features of hedonic models can be identified from equilibrium observations in a single market under weak assumptions about the available information. We then consider use of additional information about structural functions and heterogeneity distributions. Separability conditions facilitate identification of consumer marginal utility and firm marginal product functions. We also consider how identification is facilitated using multimarket data.     

Semi‐Nonparametric IV Estimation of Shape‐Invariant Engel Curves

This paper studies a shape‐invariant Engel curve system with endogenous total expenditure, in which the shape‐invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions, allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support. Root‐n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of “low‐level” sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves.     

Optimal Reserve Prices in Name‐Your‐Own‐Price Auctions with Bidding and Channel Options

Few papers have explored the optimal reserve prices in the name‐your‐own‐price (NYOP) channel with bidding options in a multiple channel environment. In this paper, we investigate a double‐bid business model in which the consumers can bid twice in the NYOP channel, and compare it with the single‐bid case. We also study the impact of adding a retailer‐own list‐price channel on the optimal reserve prices. This paper focuses on achieving some basic understanding on the potential gain of adding a second bid option to a single‐bid system and on the potential benefits of adding a list‐price channel by the NYOP retailer. We show that a double‐bid scenario can outperform a single‐bid scenario in both single‐channel and dual‐channel situations. The optimal reserve price in the double‐bid scenario is no less than that in the single‐bid case. Furthermore, the addition of a retailer‐own list‐price channel could push up the reserve prices in both single‐bid and double‐bid scenarios.     

Behavior in Multi‐Unit Demand Auctions: Experiments with Uniform Price and Dynamic Vickrey Auctions

We experimentally investigate the sensitivity of bidders demanding multiple units of a homogeneous commodity to the demand reduction incentives inherent in uniform price auctions. There is substantial demand reduction in both sealed bid and ascending price clock auctions with feedback regarding rivals' drop‐out prices. Although both auctions have the same normal form representation, bidding is much closer to equilibrium in the ascending price auctions. We explore the behavioral process underlying these differences along with dynamic Vickrey auctions designed to eliminate the inefficiencies resulting from demand reduction in the uniform price auctions.     

Efficient Semiparametric Estimation of the Fama–French Model and Extensions

This paper develops a new estimation procedure for characteristic‐based factor models of stock returns. We treat the factor model as a weighted additive nonparametric regression model, with the factor returns serving as time‐varying weights and a set of univariate nonparametric functions relating security characteristic to the associated factor betas. We use a time‐series and cross‐sectional pooled weighted additive nonparametric regression methodology to simultaneously estimate the factor returns and characteristic‐beta functions. By avoiding the curse of dimensionality, our methodology allows for a larger number of factors than existing semiparametric methods. We apply the technique to the three‐factor Fama–French model, Carhart's four‐factor extension of it that adds a momentum factor, and a five‐factor extension that adds an own‐volatility factor. We find that momentum and own‐volatility factors are at least as important, if not more important, than size and value in explaining equity return comovements. We test the multifactor beta pricing theory against a general alternative using a new nonparametric test.     

First‐Price Auctions With General Information Structures: Implications for Bidding and Revenue

We explore the impact of private information in sealed‐bid first‐price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning‐bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative auction mechanisms.     

The 2007 Subprime Market Crisis Through the Lens of European Central Bank Auctions for Short‐Term Funds

We study European banks' demand for short‐term funds (liquidity) during the summer 2007 subprime market crisis. We use bidding data from the European Central Bank's auctions for one‐week loans, their main channel of monetary policy implementation. Our analysis provides a high‐frequency, disaggregated perspective on the 2007 crisis, which was previously studied through comparisons of collateralized and uncollateralized interbank money market rates which do not capture the heterogeneous impact of the crisis on individual banks. Through a model of bidding, we show that banks' bids reflect their cost of obtaining short‐term funds elsewhere (e.g., in the interbank market) as well as a strategic response to other bidders. The strategic response is empirically important: while a naïve interpretation of the raw bidding data may suggest that virtually all banks suffered an increase in the cost of short‐term funding, we find that, for about one third of the banks, the change in bidding behavior was simply a strategic response. We also find considerable heterogeneity in the short‐term funding costs among banks: for over one third of the bidders, funding costs increased by more than 20 basis points, and funding costs vary widely with respect to the country‐of‐origin. The funding costs we estimate using bidding data are also predictive of market‐ and accounting‐based measures of bank performance, reinforcing the usefulness of “revealed preference” information contained in bids.     

Identification and Inference in Nonlinear Difference‐in‐Differences Models

This paper develops a generalization of the widely used difference‐in‐differences method for evaluating the effects of policy changes. We propose a model that allows the control and treatment groups to have different average benefits from the treatment. The assumptions of the proposed model are invariant to the scaling of the outcome. We provide conditions under which the model is nonparametrically identified and propose an estimator that can be applied using either repeated cross section or panel data. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean–variance trade‐off. We also propose methods for inference, showing that our estimator for the average treatment effect is root‐N consistent and asymptotically normal. We consider extensions to allow for covariates, discrete dependent variables, and multiple groups and time periods.     

A Bayesian Semiparametric Model for Radiation Dose‐Response Estimation

In evaluating the risk of exposure to health hazards, characterizing the dose‐response relationship and estimating acceptable exposure levels are the primary goals. In analyses of health risks associated with exposure to ionizing radiation, while there is a clear agreement that moderate to high radiation doses cause harmful effects in humans, little has been known about the possible biological effects at low doses, for example, below 0.1 Gy, which is the dose range relevant to most radiation exposures of concern today. A conventional approach to radiation dose‐response estimation based on simple parametric forms, such as the linear nonthreshold model, can be misleading in evaluating the risk and, in particular, its uncertainty at low doses. As an alternative approach, we consider a Bayesian semiparametric model that has a connected piece‐wise‐linear dose‐response function with prior distributions having an autoregressive structure among the random slope coefficients defined over closely spaced dose categories. With a simulation study and application to analysis of cancer incidence data among Japanese atomic bomb survivors, we show that this approach can produce smooth and flexible dose‐response estimation while reasonably handling the risk uncertainty at low doses and elsewhere. With relatively few assumptions and modeling options to be made by the analyst, the method can be particularly useful in assessing risks associated with low‐dose radiation exposures.     

Lower Risk Bounds and Properties of Confidence Sets for Ill‐Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation,Unit Roots,and Estimation of Long Memory Parameters

Important estimation problems in econometrics like estimating the value of a spectral density at frequency zero, which appears in the econometrics literature in the guises of heteroskedasticity and autocorrelation consistent variance estimation and long run variance estimation, are shown to be “ill‐posed” estimation problems. A prototypical result obtained in the paper is that the minimax risk for estimating the value of the spectral density at frequency zero is infinite regardless of sample size, and that confidence sets are close to being uninformative. In this result the maximum risk is over commonly used specifications for the set of feasible data generating processes. The consequences for inference on unit roots and cointegration are discussed. Similar results for persistence estimation and estimation of the long memory parameter are given. All these results are obtained as special cases of a more general theory developed for abstract estimation problems, which readily also allows for the treatment of other ill‐posed estimation problems such as, e.g., nonparametric regression or density estimation.     

Distributionally Robust Optimization of Two‐Stage Lot‐Sizing Problems

This paper studies two‐stage lot‐sizing problems with uncertain demand, where lost sales, backlogging and no backlogging are all considered. To handle the ambiguity in the probability distribution of demand, distributionally robust models are established only based on mean‐covariance information about the distribution. Based on shortest path reformulations of lot‐sizing problems, we prove that robust solutions can be obtained by solving mixed 0‐1 conic quadratic programs (CQPs) with mean‐risk objective functions. An exact parametric optimization method is proposed by further reformulating the mixed 0‐1 CQPs as single‐parameter quadratic shortest path problems. Rather than enumerating all potential values of the parameter, which may be the super‐polynomial in the number of decision variables, we propose a branch‐and‐bound‐based interval search method to find the optimal parameter value. Polynomial time algorithms for parametric subproblems with both uncorrelated and partially correlated demand distributions are proposed. Computational results show that the proposed models greatly reduce the system cost variation at the cost of a relative smaller increase in expected system cost, and the proposed parametric optimization method is much more efficient than the CPLEX solver.     

Long‐Term Debt and Optimal Policy in the Fiscal Theory of the Price Level

The fiscal theory says that the price level is determined by the ratio of nominal debt to the present value of real primary surpluses. I analyze long‐term debt and optimal policy in the fiscal theory. I find that the maturity structure of the debt matters. For example, it determines whether news of future deficits implies current inflation or future inflation. When long‐term debt is present, the government can trade current inflation for future inflation by debt operations; this tradeoff is not present if the government rolls over short‐term debt. The maturity structure of outstanding debt acts as a “budget constraint” determining which periods' price levels the government can affect by debt variation alone. In addition, debt policy—the expected pattern of future state‐contingent debt sales, repurchases and redemptions—matters crucially for the effects of a debt operation. I solve for optimal debt policies to minimize the variance of inflation. I find cases in which long‐term debt helps to stabilize inflation. I also find that the optimal policy produces time series that are similar to U.S. surplus and debt time series. To understand the data, I must assume that debt policy offsets the inflationary impact of cyclical surplus shocks, rather than causing price level disturbances by policy‐induced shocks. Shifting the objective from price level variance to inflation variance, the optimal policy produces much less volatile inflation at the cost of a unit root in the price level; this is consistent with the stabilization of U.S. inflation after the gold standard was abandoned.     

Model Selection and Estimation with Quantal‐Response Data in Benchmark Risk Assessment

This article describes several approaches for estimating the benchmark dose (BMD) in a risk assessment study with quantal dose‐response data and when there are competing model classes for the dose‐response function. Strategies involving a two‐step approach, a model‐averaging approach, a focused‐inference approach, and a nonparametric approach based on a PAVA‐based estimator of the dose‐response function are described and compared. Attention is raised to the perils involved in data “double‐dipping” and the need to adjust for the model‐selection stage in the estimation procedure. Simulation results are presented comparing the performance of five model selectors and eight BMD estimators. An illustration using a real quantal‐response data set from a carcinogenecity study is provided.