Minimax regret treatment choice with covariates or with limited validity of experiments

This paper continues the investigation of minimax regret treatment choice initiated by Manski (2004). Consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a sample. A certain scoring rule is known to achieve minimax regret in simple versions of this decision problem. I investigate its sensitivity to perturbations of the decision environment in realistic directions. They are as follows. (i) Treatment outcomes may be influenced by a covariate whose effect on outcome distributions is bounded (in one of numerous probability metrics). This is interesting because introduction of a covariate with unrestricted effects leads to a pathological result. (ii) The experiment may have limited validity because of selective noncompliance or because the sampling universe is a potentially selective subset of the treatment population. Thus, even large samples may generate misleading signals. These problems are formalized via a “bounds” approach that turns the problem into one of partial identification.In both scenarios, small but positive perturbations leave the minimax regret decision rule unchanged. Thus, minimax regret analysis is not knife-edge-dependent on ignoring certain aspects of realistic decision problems. Indeed, it recommends to entirely disregard covariates whose effect is believed to be positive but small, as well as small enough amounts of missing data or selective attrition. All findings are finite sample results derived by game theoretic analysis.     

Minimax-regret treatment choice with missing outcome data

I use the minimax-regret criterion to study choice between two treatments when some outcomes in the study population are unobservable and the distribution of missing data is unknown. I first assume that observable features of the study population are known and derive the treatment rule that minimizes maximum regret over all possible distributions of missing data. When no treatment is dominant, this rule allocates positive fractions of persons to both treatments. I then assume that the data are a random sample of the study population and show that in some instances, treatment rules that estimate certain point-identified population means by sample averages are finite-sample minimax regret.     

Identification of first-price auctions with non-separable unobserved heterogeneity

We propose a novel methodology for identification of first-price auctions, when bidders’ private valuations are independent conditional on one-dimensional unobserved heterogeneity. We extend the existing literature ( and ) by allowing the unobserved heterogeneity to be non-separable from bidders’ valuations. Our central identifying assumption is that the distribution of bidder values is increasing in the state. When the state-space is finite, such monotonicity implies the full-rank condition needed for identification. Further, we extend our approach to the conditionally independent private values model of Li et al. (2000), as well as to unobserved heterogeneity settings in which the implicit reserve price or the cost of bidding varies across auctions.     

The econometrics of auctions with asymmetric anonymous bidders

We consider standard auction models when bidders’ identities are not-or are only partially-observed by the econometrician. We first adapt the definition of identifiability to a framework with anonymous bids and explore the extent to which anonymity reduces the possibility of identifying private value auction models. Second, in the asymmetric independent private value model which is nonparametrically identified, we generalize Guerre, Perrigne and Vuong’s estimation procedure [Optimal nonparametric estimation of first-price auctions, Econometrica 68 (2000) 525-574] and consider the asymptotic properties of our multi-step kernel-based estimator. Monte Carlo simulations illustrate the practical relevance of our estimation procedure in small data sets.     

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.     

Stopping with anticipated regret

This paper analyzes a stopping problem where the decision maker is driven by anticipated ex-post regret. There are two sources of potential dynamic inconsistency, one is arrival of information and the other is changing choice opportunities over time—discarding the current stopping option may change how she stops the game in the future.First we consider a naive planner who prescribes a commitment solution, and illustrate the nature of the inconsistency problem. Then we consider a sophisticated planner who plays backward induction against her ‘successive selves’. The resolution of dynamic inconsistency does not in general allow the use of standard dynamic programming technique. We provide, however, a simple characterization of the backward induction strategy, which is given in a recursive formula.We also provide a behavioral implication, that larger indeterminacy of belief may lead to a more aggressive behavior, that is, continuing the gamble longer, which contrasts to the implication of ambiguity aversion.     

Identification of binary choice models with social interactions

This paper provides a set of results on the econometric identifiability of binary choice models with social interactions. Our analysis moves beyond parametric identification results that have been obtained in the literature to consider the identifiability of model parameters when the distribution of random payoff terms is unknown. Further, we consider how identification is affected by the presence of unobservable payoff terms of various types as well as identification in the presence of certain forms of endogenous group membership. Our results suggest that at least partial identification may be achieved under assumptions that in certain contexts may be plausible.     

IV models of ordered choice

This paper studies single equation instrumental variable models of ordered choice in which explanatory variables may be endogenous. The models are weakly restrictive, leaving unspecified the mechanism that generates endogenous variables. These incomplete models are set, not point, identifying for parametrically (e.g. ordered probit) or nonparametrically specified structural functions. The paper gives results on the properties of the identified set for the case in which potentially endogenous explanatory variables are discrete. The results are used as the basis for calculations showing the rate of shrinkage of identified sets as the number of classes in which the outcome is categorised increases.     

Beyond panel unit root tests: Using multiple testing to determine the nonstationarity properties of individual series in a panel

Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classification on the basis of n$n$ individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we suggest and demonstrate how to use the false discovery rate (FDR)$\left(FDR\right)$ in evaluating I(1)/I(0)$I\left(1\right)/I\left(0\right)$ classifications.     

Semiparametric estimation in models of first-price,sealed-bid auctions with affiliation

Within the affiliated private-values paradigm, we develop a tractable empirical model of equilibrium behaviour at first-price, sealed-bid auctions. The model is non-parametrically identified, but the rate of convergence in estimation is slow when the number of bidders is even moderately large, so we develop a semiparametric estimation strategy, focusing on the Archimedean family of copulae and implementing this framework using particular members—the Clayton, Frank, and Gumbel copulae. We apply our framework to data from low-price, sealed-bid auctions used by the Michigan Department of Transportation to procure road-resurfacing services, rejecting the hypothesis of independence and finding significant (and high) affiliation in cost signals.     

Estimation and inference in two-stage,semi-parametric models of production processes

Many papers have regressed non-parametric estimates of productive efficiency on environmental variables in two-stage procedures to account for exogenous factors that might affect firms’ performance. None of these have described a coherent data-generating process (DGP). Moreover, conventional approaches to inference employed in these papers are invalid due to complicated, unknown serial correlation among the estimated efficiencies. We first describe a sensible DGP for such models. We propose single and double bootstrap procedures; both permit valid inference, and the double bootstrap procedure improves statistical efficiency in the second-stage regression. We examine the statistical performance of our estimators using Monte Carlo experiments.     

Mixture models of choice under risk

This paper is concerned with estimating preference functionals for choice under risk from the choice behaviour of individuals. We note that there is heterogeneity in behaviour between individuals and within individuals. By ‘heterogeneity between individuals’ we mean that people are different, in terms of both their preference functionals and their parameters for these functionals. By ‘heterogeneity within individuals’ we mean that the behaviour may be different even by the same individual for the same choice problem. We propose methods of taking into account all forms of heterogeneity, concentrating particularly on using a Mixture Model to capture the heterogeneity of preference functionals.     

A Poisson mixture model of discrete choice

In this paper, we introduce a new Poisson mixture model for count panel data where the underlying Poisson process intensity is determined endogenously by consumer latent utility maximization over a set of choice alternatives. This formulation accommodates the choice and count in a single random utility framework with desirable theoretical properties. Individual heterogeneity is introduced through a random coefficient scheme with a flexible semiparametric distribution. We deal with the analytical intractability of the resulting mixture by recasting the model as an embedding of infinite sequences of scaled moments of the mixing distribution, and newly derive their cumulant representations along with bounds on their rate of numerical convergence. We further develop an efficient recursive algorithm for fast evaluation of the model likelihood within a Bayesian Gibbs sampling scheme. We apply our model to a recent household panel of supermarket visit counts. We estimate the nonparametric density of three key variables of interest-price, driving distance, and their interaction-while controlling for a range of consumer demographic characteristics. We use this econometric framework to assess the opportunity cost of time and analyze the interaction between store choice, trip frequency, search intensity, and household and store characteristics. We also conduct a counterfactual welfare experiment and compute the compensating variation for a 10%-30% increase in Walmart prices.     

Estimation of finite sequential games

I propose a new estimation method for finite sequential games that is efficient, computationally attractive, and applicable to a fairly general class of finite sequential games that is beyond the scope of existing studies. The major challenge is the computation of high-dimensional truncated integration whose domain is complicated by strategic interaction. This complication resolves when unobserved off-the-equilibrium-path strategies are controlled for. Separately evaluating the likelihood contribution of each subgame-perfect equilibrium that generates the observed outcome allows the use of the GHK simulator, a widely used importance-sampling probit simulator. Monte Carlo experiments demonstrate the performance and robustness of the proposed method.     

Sequential bargaining with common values

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own this object. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium outcome of this game which is unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent.     

Optimal selling mechanisms with countervailing positive externalities and an application to tradable retaliation in the WTO

We study revenue-maximizing mechanisms for a seller who sells an indivisible good to several buyers with positive, type-dependent and countervailing allocative externalities. To cope with the difficulty of types obtaining reservation utilities being endogenously determined, we first solve a minimax version of the seller’s problem by generalizing Myerson’s characterization techniques for the non-regular case. The solution is then shown to solve the seller’s original maximin problem as well in our setting. We find that the seller’s optimal mechanism normally features bunching even in the regular case and the type with the lowest expected payoff is typically not an extreme type. As an important illustration of our characterization procedures, we apply our results to the problem of selling retaliation rights in the WTO.     

Robust firm pricing with panel data

Firms often have imperfect information about demand for their products. We develop an integrated econometric and theoretical framework to model firm demand assessment and subsequent pricing decisions with limited information. We introduce a panel data discrete choice model whose realistic assumptions about consumer behavior deliver partially identified preferences and thus generate ambiguity in the firm pricing problem. We use the minimax-regret criterion as a decision-making rule for firms facing this ambiguity. We illustrate the framework’s benefits relative to the most common discrete choice analysis approach through simulations and empirical examples with field data.     

Are there common values in first-price auctions? A tail-index nonparametric test

We develop a consistent nonparametric test of common values in first-price auctions and apply it to British Columbia Timber Sales data. The test is based on the behavior of the CDF of bids near the reserve price. We show that the curvature of the CDF is drastically different under private values (PV) and common values (CV). We then show that the problem of discriminating between PV and CV is equivalent to estimating the lower tail index of the bid distribution. Our approach admits unobserved auction heterogeneity of an arbitrary form. We develop a Hill (1975)-type tail index estimator and find the presence of common values in BC Timber Sales.