Tatiana Komarova

Binary choice models with discrete regressors: identification and misspecification

This paper explores the inferential question in semiparametric binary response models when the continuous support condition is not satisfied and all regressors have discrete support. I focus mainly on the models under the conditional median restriction, as in Manski (1985). I find sharp bounds on the components of the parameter of interest and outline several applications. The formulas for bounds obtained using a recursive procedure help analyze cases where one regressor’s support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I describe a relation between the maximum score estimation and support vector machines and propose several approaches to address the problem of empty identification sets when the model is misspecified.

Quantile Uncorrelation and Instrumental Regressions

Abstract We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a k-dimensional random vector X if and only if the slope from an LAD regression of Y on X is zero. Using this simple definition, we characterize properties of median uncorrelated random variables, and introduce a notion of multivariate median uncorrelation. We provide measures of median uncorrelation that are similar to the linear correlation coefficient and the coefficient of determination. We also extend this median uncorrelation to other loss functions. As two stage least squares exploits mean uncorrelation between an instrument vector and the error to derive consistent estimators for parameters in linear regressions with endogenous regressors, the main result of this paper shows how a median uncorrelation assumption between an instrument vector and the error can similarly be used to derive consistent estimators in these linear models with endogenous regressors. We also show how median uncorrelation can be used in linear panel models with quantile restrictions and in linear models with measurement errors.

Partial identification in asymmetric auctions in the absence of independence

This paper examines identification in second‐price and ascending auctions within the private‐values framework. The first part of the paper considers an arbitrary type of dependence of bidders’ values and analyses identification under several observational scenarios, in which the highest bid is never observed. In a basic scenario, only the winner’s identity and the winning price are observed. The most informative is the scenario in which all the identities and all the bids except for the highest bid are known. Using results from Athey and Haile (2002), the joint distribution of bidders’ values in these scenarios is not identified. The paper uses the information available in auctions’ outcomes to construct bounds on the joint distribution of values for any subset of bidders. The second part of the paper takes a different tack by showing how bounds can be improved under different types of positive dependence of bidders’ values.

Joint Analysis of the Discount Factor and Payoff Parameters in Dynamic Discrete Choice Models

Most empirical and theoretical econometric studies of dynamic discrete choice models assume the discount factor to be known. We show the knowledge of the discount factor is not necessary to identify parts, or all, of the payoff function. We show the discount factor can be generically identified jointly with the payoff parameters. It is known the payoff function cannot non-parametrically identified without any a priori restrictions. Our identification of the discount factor is robust to any normalization choice on the payoff parameters. In IO applications normalizations are usually made on switching costs, such as entry costs and scrap values. We also show that switching costs can be non-parametrically identified, in closed-form, independently of the discount factor and other parts of the payoff function. Our identification strategies are constructive. They lead to easy to compute estimands that are global solutions. We illustrate with a Monte Carlo study and the dataset from Ryan (2012).

On Monotone Strategy Equilibria in Simultaneous Auctions for Complementary Goods

We explore existence and properties of equilibrium when N>1 bidders compete for L>1 objects via simultaneous but separate auctions. Bidders have private combinatorial valuations over all sets of objects they could win, and objects are complements in the sense that these valuations are supermodular in the set of objects won. We provide a novel partial order on types under which best replies are monotone, and demonstrate that Bayesian Nash equilibria which are monotone with respect to this partial order exist on any finite bid lattice. We apply this result to show existence of monotone Bayesian Nash equilibria in continuous bid spaces when a single global bidder competes for L objects against many local bidders who bid for single objects only, highlighting the step in this extension which fails with multiple global bidders. We therefore instead consider an alternative equilibrium with endogenous tie-breaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that this exists in general. Finally, we explore efficiency in simultaneous auctions with symmetric bidders, establishing novel sufficient conditions under which inefficiency in expectation approaches zero as the number of bidders increases.

K-anonymity: A note on the trade-off between data utility and data security

Researchers often use data from multiple datasets to conduct credible econometric and statistical analysis. The most reliable way to link entries across such datasets is to exploit unique identifiers if those are available. Such linkage however may result in privacy violations revealing sensitive information about some individuals in a sample. Thus, a data curator with concerns for individual privacy may choose to remove certain individual information from the private dataset they plan on releasing to researchers. The extent of individual information the data curator keeps in the private dataset can still allow a researcher to link the datasets, most likely with some errors, and usually results in a researcher having several feasible combined datasets. One conceptual framework a data curator may rely on is k-anonymity, k>=2, which gained wide popularity in computer science and statistical community. To ensure k-anonymity, the data curator releases only the amount of identifying information in the private dataset that guarantees that every entry in it can be linked to at least k different entries in the publicly available datasets the researcher will use. In this paper, we look at the data combination task and the estimation task from both perspectives – from the perspective of the researcher estimating the model and from the perspective of a data curator who restricts identifying information in the private dataset to make sure that k-anonymity holds. We illustrate how to construct identifiers in practice and use them to combine some entries across two datasets. We also provide an empirical illustration on how a data curator can ensure k-anonymity and consequences it has on the estimation procedure. Naturally, the utility of the combined data gets smaller as k increases, which is also evident from our empirical illustration.

Preferences and Performance in Simultaneous First-Price Auctions: A Structural Analysis

Motivated by the empirical prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a structural model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have preferences over combinations. In this model, bidders have stochastic private valuations for each object and stable incremental preferences over combinations, nesting the standard separable model as the special case when incremental preferences over combinations are zero. We establish non-parametric identification of primitives in this model under standard exclusion restrictions, providing a basis for both estimation and testing of preferences over combinations. We then apply our model to data on Michigan Department of Transportation (MDOT) highway procurement auctions, quantifying the magnitude of cost synergies and evaluating the performance of the simultaneous first-price mechanism in the MDOT marketplace.Motivated by the empirical prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a structural model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have preferences over combinations. We begin by proposing a general theoretical model of bidding in simultaneous first price auctions, exploring properties of best responses and existence of equilibrium within this environment. We then specialize this model to an empirical framework in which bidders have stochastic private valuations for each object and stable incremental preferences over combinations; this immediately reduces to the standard separable model when incremental preferences over combinations are zero. We establish non-parametric identification of the resulting model under standard exclusion restrictions, thereby providing a basis for both testing on and estimation of preferences over combinations. We then apply our model to data on Michigan Department of Transportation highway procurement auctions, we quantify the magnitude of cost synergies and assess possible efficiency losses arising from simultaneous bidding in this market. ∗We are grateful to Philip Haile, Ken Hendricks, Paul Klemperer, and Balazs Szentes for their comments and insight. We also thank seminar participants at the University of Wisconsin (Madison), the University of Zurich, University of Leuven, Cardiff University, Oxford University, Cornell University, the University of East Anglia, and Universitie Paris 1 for helpful discussion. †London School of Economics, m.l.gentry@lse.ac.uk ‡London School of Economics, t.komarova@lse.ac.uk §London School of Economics and CEPR, p.schiraldi@lse.ac.uk