Tatiana Komarova - Academia.edu (original) (raw)

Papers by Tatiana Komarova

The Review of Economic Studies

Motivated by the prevalence of simultaneous bidding across a wide range of auction markets, we de... more Motivated by the prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have non-additive preferences over combinations. 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.

SSRN Electronic Journal

We introduce multivariate ordered discrete response models that exhibit non-lattice structures. F... more We introduce multivariate ordered discrete response models that exhibit non-lattice structures. From the perspective of behavioral economics, these models correspond to broad bracketing in decision making, whereas lattice models, which researchers typically estimate in practice, correspond to narrow bracketing. There is also a class of hierarchical models, which nests lattice models and is a special case of non-lattice models. Hierarchical models correspond to sequential decision making and can be represented by binary decision trees. In each of these cases, we specify latent processes as a sum of an index of covariates and an unobserved error, with unobservables for different latent processes potentially correlated. This additional dependence further complicates the identification of model parameters in non-lattice models. We give conditions sufficient to guarantee identification under the independence of errors and covariates, compare these conditions to what is required to attain identification in lattice models and outline an estimation approach. Finally, we provide simulations and empirical examples, through which we discuss the case when unobservables follow a distribution from a known parametric family, focusing on popular probit specifications.

Essays on Identification in Econometric Models Tatiana Komarova This dissertation consists of thr... more Essays on Identification in Econometric Models Tatiana Komarova This dissertation consists of three essays on the identification analysis of econometric models.

Abstract. We introduce a notion of median uncorrelation that is a natural extension of mean (line... more 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...

∗ We thank the seminar participants at the London School of Economics, the University College Lon... more ∗ We thank the seminar participants at the London School of Economics, the University College London and the University of Toronto for their comments. We also appreciate feedback from the participants of the Canadian Econometric Study Group and the participants of the all UC Econometrics Conference.

This paper provides a novel evidence (based on a new dataset) on bidding and subcontracting behav... more This paper provides a novel evidence (based on a new dataset) on bidding and subcontracting behavior of primary contractors participating in California highway procurement market. We develop a model of procurement auction with subcontracting stage which is capable of rationalizing the patterns documented in the data. Next, we use this framework to assess the implications of ex-ante subcontracting rule which is frequently imposed in government procurement.

arXiv: Methodology, 2019

We describe and examine a test for a general class of shape constraints, such as constraints on t... more We describe and examine a test for a general class of shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity, log-convexity, rrr-convexity, among others, in a nonparametric framework using partial sums empirical processes. We show that, after a suitable transformation, its asymptotic distribution is a functional of the standard Brownian motion, so that critical values are available. However, due to the possible poor approximation of the asymptotic critical values to the finite sample ones, we also describe a valid bootstrap algorithm.

SSRN Electronic Journal, 2021

The econometric literature on program-evaluation and optimal treatment-choice takes functionals o... more The econometric literature on program-evaluation and optimal treatment-choice takes functionals of outcome-distributions as target welfare, and ignores programimpacts on unobserved utilities, including utilities of those whose outcomes may be unaffected by the intervention. We show that in the practically important setting of discrete-choice, under general preference-heterogeneity and income-effects, the distribution of indirect-utility is nonparametrically identified from average demand. This enables cost-benefit analysis and treatment-targeting based on social welfare and planners' distributional preferences, while also allowing for general unobserved heterogeneity in individual preferences. We demonstrate theoretical connections between utilitarian social welfare and Hicksian compensation. An empirical application illustrates our results.

SSRN Electronic Journal, 2020

Empirical economic research crucially relies on highly sensitive individual datasets. At the same... more Empirical economic research crucially relies on highly sensitive individual datasets. At the same time, increasing availability of public individual-level data that comes from social networks, public government records and directories makes it possible for adversaries to potentially de-identify anonymized records in sensitive research datasets. Most commonly accepted formal definition of an individual non-disclosure guarantee is referred to as differential privacy. With differential privacy in place the researcher interacts with the data by issuing queries that evaluate the functions of the data. Differential privacy guarantee is achieved by replacing the actual outcome of the query with a randomized outcome with the amount of randomness determined by the sensitivity of the outcome to individual observations in the data. While differential privacy does provide formal non-disclosure guarantees, its impact on the identification of empirical economic models as well as its impact on the performance of estimators in nonlinear empirical Econometric models has not been sufficiently studied. Since privacy protection mechanisms are inherently finite-sample procedures, we define the notion of identifiability of the parameter of interest under differential privacy as a property of the limit of experiments. It is naturally characterized by the concepts from the random sets theory and is linked to the asymptotic behavior in measure of differentially private estimators. We demonstrate that particular instances of regression discontinuity design may be problematic for inference with differential privacy. Those parameters turn out to be neither point nor partially identified. The set of differentially private estimators converges weakly to a random set. This result is clearly supported by our simulation evidence. Our analysis suggests that many other estimators that rely on nuisance parameters may have similar properties with the requirement of differential privacy. Identification becomes possible if the target parameter can be deterministically localized within the random set. In that case, a full exploration of the random set of the weak limits of differentially private estimators can allow the data curator to select a sequence of instances of differentially private estimators that is guaranteed to converge to the target parameter in probability. We provide a decision-theoretic approach to this selection.

This paper proposes an approach to proving nonparametric identication for distributions of bidder... more This paper proposes an approach to proving nonparametric identication for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the only available data pertain to the winner's identity and the transaction price. My proof of identication is constructive and is based on establishing the existence and uniqueness of a solution to the system of non-linear dierential equations that describes relationships between unknown distribution functions and observable functions. The proof is conducted in two logical steps. First, I prove the existence and uniqueness of a local solution. Then I describe a method that extends this local solution to the whole support. This paper delivers other interesting results. I show how this approach can be applied to obtain identication in more general auction settings, for instance, in auctions with stochastic number of bidders or weaker support conditions. Furthermore, I demonstrate that my results can be extended to generalized competing risks models. Moreover, contrary to results in classical competing risks (Roy model), I show that in this generalized class of models it is possible to obtain implications that can be used to check whether the risks in a model are dependent. Finally, I provide a sieve minimum distance estimator and show that it consistently estimates the underlying valuation distribution of interest.

The paper considers nonparametric estimation of absolutely continuous distribution functions of l... more The paper considers nonparametric estimation of absolutely continuous distribution functions of lifetimes of non-identical components in k-out-of-n systems from the observed "autopsy" data. In economics, ascending "button" or "clock" auctions with n heterogeneous bidders present 2-out-of-n systems. Classical competing risks models are examples of n-out-of-n systems. Under weak conditions on the underlying distributions the estimation problem is shown to be well-posed and the suggested extremum sieve estimator is proven to be consistent. The paper illustrates the suggested estimation method by using sieve spaces of Bernstein polynomials which allow an easy implementation of constraints on the monotonicity of estimated distribution functions.

SSRN Electronic Journal, 2017

Most empirical and theoretical econometric studies of dynamic discrete choice models assume the d... more 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 even all, of the payoff function. We show the discount factor can be generically identified jointly with the payoff parameters. On the other hand, it is known the payoff function cannot be nonparametrically 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 nonparametrically 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 used in Ryan (2012).

SSRN Electronic Journal, 2017

A note on the trade-off between data utility and data security Researchers often use data from mu... more 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, 2 k ³ , 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.

SSRN Electronic Journal, 2015

We explore existence and properties of equilibrium when N ≥ 2 bidders compete for L ≥ 2 objects v... more We explore existence and properties of equilibrium when N ≥ 2 bidders compete for L ≥ 2 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. We then consider monotone equilibrium with endogenous tiebreaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that these exist in general. These existence results apply to many auction formats, including first-price, second-price, and all-pay.

SSRN Electronic Journal, 2014

Motivated by the empirical prevalence of simultaneous bidding across a wide range of auction mark... more 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 nonparametric 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, with structural estimates suggesting that winning multiple projects substantially increases bidder costs. ⇤ We are grateful to Philip Haile for helpful discussions.

1. Reportedly, many businesses indeed rely on the combined data. See, for example, Wright (2010) ... more 1. Reportedly, many businesses indeed rely on the combined data. See, for example, Wright (2010) and Bradley et al. (2010), among others.

SSRN Electronic Journal, 2014

Businesses routinely rely on econometric models to analyze and predict consumer behavior. Estimat... more Businesses routinely rely on econometric models to analyze and predict consumer behavior. Estimation of such models may require combining a firm's internal data with external datasets to take into account sample selection, missing observations, omitted variables and errors in measurement within the existing data source. In this paper we point out that these data problems can be addressed when estimating econometric models from combined data using the data mining techniques under mild assumptions regarding the data distribution. However, data combination leads to serious threats to security of consumer data: we demonstrate that point identification of an econometric model from combined data is incompatible with restrictions on the risk of individual disclosure. Consequently, if a consumer model is point identified, the firm would (implicitly or explicitly) reveal the identity of at least some of consumers in its internal data. More importantly, we provide an argument that unless the firm places a restriction on the individual disclosure risk when combining data, even if the raw combined dataset is not shared with a third party, an adversary or a competitor can gather confidential information regarding some individuals from the estimated model.

Journal of Econometric Methods, 2012

for their comments. We also appreciate feedback from the participants of the Canadian Econometric... more for their comments. We also appreciate feedback from the participants of the Canadian Econometric Study Group and the participants of the all UC Econometrics Conference.

Quantitative Economics, 2013

A new approach to identifying generalized competing risks models with application to second-price... more A new approach to identifying generalized competing risks models with application to second-price auctions. Quantitative Economics, 4 (2). pp. 269-328.

Journal of Econometrics, 2013

In semiparametric binary response models, support conditions on the regressors are required to gu... more In semiparametric binary response models, support conditions on the regressors are required to guarantee point identification of the parameter of interest. For example, one regressor is usually assumed to have continuous support conditional on the other regressors. In some instances, such conditions have precluded the use of these models; in others, practitioners have failed to consider whether the conditions are satisfied in their data. This paper explores the inferential question in these semiparametric models when the continuous support condition is not satisfied and all regressors have discrete support. I suggest a recursive procedure that finds sharp bounds on the parameter of interest and outline several applications. After deriving closed-form bounds on the parameter, I show how these formulas can help analyze cases where one regressor's support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I also propose three approaches to address the problem of empty identification sets when a model is misspecified. Finally, I present a Monte Carlo experiment and an empirical illustration to compare several estimation techniques.

The Review of Economic Studies

Motivated by the prevalence of simultaneous bidding across a wide range of auction markets, we de... more Motivated by the prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have non-additive preferences over combinations. 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.

SSRN Electronic Journal

We introduce multivariate ordered discrete response models that exhibit non-lattice structures. F... more We introduce multivariate ordered discrete response models that exhibit non-lattice structures. From the perspective of behavioral economics, these models correspond to broad bracketing in decision making, whereas lattice models, which researchers typically estimate in practice, correspond to narrow bracketing. There is also a class of hierarchical models, which nests lattice models and is a special case of non-lattice models. Hierarchical models correspond to sequential decision making and can be represented by binary decision trees. In each of these cases, we specify latent processes as a sum of an index of covariates and an unobserved error, with unobservables for different latent processes potentially correlated. This additional dependence further complicates the identification of model parameters in non-lattice models. We give conditions sufficient to guarantee identification under the independence of errors and covariates, compare these conditions to what is required to attain identification in lattice models and outline an estimation approach. Finally, we provide simulations and empirical examples, through which we discuss the case when unobservables follow a distribution from a known parametric family, focusing on popular probit specifications.

Essays on Identification in Econometric Models Tatiana Komarova This dissertation consists of thr... more Essays on Identification in Econometric Models Tatiana Komarova This dissertation consists of three essays on the identification analysis of econometric models.

Abstract. We introduce a notion of median uncorrelation that is a natural extension of mean (line... more 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...

∗ We thank the seminar participants at the London School of Economics, the University College Lon... more ∗ We thank the seminar participants at the London School of Economics, the University College London and the University of Toronto for their comments. We also appreciate feedback from the participants of the Canadian Econometric Study Group and the participants of the all UC Econometrics Conference.

This paper provides a novel evidence (based on a new dataset) on bidding and subcontracting behav... more This paper provides a novel evidence (based on a new dataset) on bidding and subcontracting behavior of primary contractors participating in California highway procurement market. We develop a model of procurement auction with subcontracting stage which is capable of rationalizing the patterns documented in the data. Next, we use this framework to assess the implications of ex-ante subcontracting rule which is frequently imposed in government procurement.

arXiv: Methodology, 2019

We describe and examine a test for a general class of shape constraints, such as constraints on t... more We describe and examine a test for a general class of shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity, log-convexity, rrr-convexity, among others, in a nonparametric framework using partial sums empirical processes. We show that, after a suitable transformation, its asymptotic distribution is a functional of the standard Brownian motion, so that critical values are available. However, due to the possible poor approximation of the asymptotic critical values to the finite sample ones, we also describe a valid bootstrap algorithm.

SSRN Electronic Journal, 2021

The econometric literature on program-evaluation and optimal treatment-choice takes functionals o... more The econometric literature on program-evaluation and optimal treatment-choice takes functionals of outcome-distributions as target welfare, and ignores programimpacts on unobserved utilities, including utilities of those whose outcomes may be unaffected by the intervention. We show that in the practically important setting of discrete-choice, under general preference-heterogeneity and income-effects, the distribution of indirect-utility is nonparametrically identified from average demand. This enables cost-benefit analysis and treatment-targeting based on social welfare and planners' distributional preferences, while also allowing for general unobserved heterogeneity in individual preferences. We demonstrate theoretical connections between utilitarian social welfare and Hicksian compensation. An empirical application illustrates our results.

SSRN Electronic Journal, 2020

Empirical economic research crucially relies on highly sensitive individual datasets. At the same... more Empirical economic research crucially relies on highly sensitive individual datasets. At the same time, increasing availability of public individual-level data that comes from social networks, public government records and directories makes it possible for adversaries to potentially de-identify anonymized records in sensitive research datasets. Most commonly accepted formal definition of an individual non-disclosure guarantee is referred to as differential privacy. With differential privacy in place the researcher interacts with the data by issuing queries that evaluate the functions of the data. Differential privacy guarantee is achieved by replacing the actual outcome of the query with a randomized outcome with the amount of randomness determined by the sensitivity of the outcome to individual observations in the data. While differential privacy does provide formal non-disclosure guarantees, its impact on the identification of empirical economic models as well as its impact on the performance of estimators in nonlinear empirical Econometric models has not been sufficiently studied. Since privacy protection mechanisms are inherently finite-sample procedures, we define the notion of identifiability of the parameter of interest under differential privacy as a property of the limit of experiments. It is naturally characterized by the concepts from the random sets theory and is linked to the asymptotic behavior in measure of differentially private estimators. We demonstrate that particular instances of regression discontinuity design may be problematic for inference with differential privacy. Those parameters turn out to be neither point nor partially identified. The set of differentially private estimators converges weakly to a random set. This result is clearly supported by our simulation evidence. Our analysis suggests that many other estimators that rely on nuisance parameters may have similar properties with the requirement of differential privacy. Identification becomes possible if the target parameter can be deterministically localized within the random set. In that case, a full exploration of the random set of the weak limits of differentially private estimators can allow the data curator to select a sequence of instances of differentially private estimators that is guaranteed to converge to the target parameter in probability. We provide a decision-theoretic approach to this selection.

This paper proposes an approach to proving nonparametric identication for distributions of bidder... more This paper proposes an approach to proving nonparametric identication for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the only available data pertain to the winner's identity and the transaction price. My proof of identication is constructive and is based on establishing the existence and uniqueness of a solution to the system of non-linear dierential equations that describes relationships between unknown distribution functions and observable functions. The proof is conducted in two logical steps. First, I prove the existence and uniqueness of a local solution. Then I describe a method that extends this local solution to the whole support. This paper delivers other interesting results. I show how this approach can be applied to obtain identication in more general auction settings, for instance, in auctions with stochastic number of bidders or weaker support conditions. Furthermore, I demonstrate that my results can be extended to generalized competing risks models. Moreover, contrary to results in classical competing risks (Roy model), I show that in this generalized class of models it is possible to obtain implications that can be used to check whether the risks in a model are dependent. Finally, I provide a sieve minimum distance estimator and show that it consistently estimates the underlying valuation distribution of interest.

The paper considers nonparametric estimation of absolutely continuous distribution functions of l... more The paper considers nonparametric estimation of absolutely continuous distribution functions of lifetimes of non-identical components in k-out-of-n systems from the observed "autopsy" data. In economics, ascending "button" or "clock" auctions with n heterogeneous bidders present 2-out-of-n systems. Classical competing risks models are examples of n-out-of-n systems. Under weak conditions on the underlying distributions the estimation problem is shown to be well-posed and the suggested extremum sieve estimator is proven to be consistent. The paper illustrates the suggested estimation method by using sieve spaces of Bernstein polynomials which allow an easy implementation of constraints on the monotonicity of estimated distribution functions.

SSRN Electronic Journal, 2017

Most empirical and theoretical econometric studies of dynamic discrete choice models assume the d... more 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 even all, of the payoff function. We show the discount factor can be generically identified jointly with the payoff parameters. On the other hand, it is known the payoff function cannot be nonparametrically 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 nonparametrically 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 used in Ryan (2012).

SSRN Electronic Journal, 2017

A note on the trade-off between data utility and data security Researchers often use data from mu... more 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, 2 k ³ , 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.

SSRN Electronic Journal, 2015

We explore existence and properties of equilibrium when N ≥ 2 bidders compete for L ≥ 2 objects v... more We explore existence and properties of equilibrium when N ≥ 2 bidders compete for L ≥ 2 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. We then consider monotone equilibrium with endogenous tiebreaking building on Jackson, Simon, Swinkels and Zame (2002), and demonstrate that these exist in general. These existence results apply to many auction formats, including first-price, second-price, and all-pay.

SSRN Electronic Journal, 2014

Motivated by the empirical prevalence of simultaneous bidding across a wide range of auction mark... more 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 nonparametric 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, with structural estimates suggesting that winning multiple projects substantially increases bidder costs. ⇤ We are grateful to Philip Haile for helpful discussions.

1. Reportedly, many businesses indeed rely on the combined data. See, for example, Wright (2010) ... more 1. Reportedly, many businesses indeed rely on the combined data. See, for example, Wright (2010) and Bradley et al. (2010), among others.

SSRN Electronic Journal, 2014

Businesses routinely rely on econometric models to analyze and predict consumer behavior. Estimat... more Businesses routinely rely on econometric models to analyze and predict consumer behavior. Estimation of such models may require combining a firm's internal data with external datasets to take into account sample selection, missing observations, omitted variables and errors in measurement within the existing data source. In this paper we point out that these data problems can be addressed when estimating econometric models from combined data using the data mining techniques under mild assumptions regarding the data distribution. However, data combination leads to serious threats to security of consumer data: we demonstrate that point identification of an econometric model from combined data is incompatible with restrictions on the risk of individual disclosure. Consequently, if a consumer model is point identified, the firm would (implicitly or explicitly) reveal the identity of at least some of consumers in its internal data. More importantly, we provide an argument that unless the firm places a restriction on the individual disclosure risk when combining data, even if the raw combined dataset is not shared with a third party, an adversary or a competitor can gather confidential information regarding some individuals from the estimated model.

Journal of Econometric Methods, 2012

for their comments. We also appreciate feedback from the participants of the Canadian Econometric... more for their comments. We also appreciate feedback from the participants of the Canadian Econometric Study Group and the participants of the all UC Econometrics Conference.

Quantitative Economics, 2013

A new approach to identifying generalized competing risks models with application to second-price... more A new approach to identifying generalized competing risks models with application to second-price auctions. Quantitative Economics, 4 (2). pp. 269-328.

Journal of Econometrics, 2013

In semiparametric binary response models, support conditions on the regressors are required to gu... more In semiparametric binary response models, support conditions on the regressors are required to guarantee point identification of the parameter of interest. For example, one regressor is usually assumed to have continuous support conditional on the other regressors. In some instances, such conditions have precluded the use of these models; in others, practitioners have failed to consider whether the conditions are satisfied in their data. This paper explores the inferential question in these semiparametric models when the continuous support condition is not satisfied and all regressors have discrete support. I suggest a recursive procedure that finds sharp bounds on the parameter of interest and outline several applications. After deriving closed-form bounds on the parameter, I show how these formulas can help analyze cases where one regressor's support becomes increasingly dense. Furthermore, I investigate asymptotic properties of estimators of the identification set. I also propose three approaches to address the problem of empty identification sets when a model is misspecified. Finally, I present a Monte Carlo experiment and an empirical illustration to compare several estimation techniques.