Susan Athey

Single Crossing Properties And The Existence Of Pure Strategy Equilibria In Games Of Incomplete Information

This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of pure strategy Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC), roughly described as follows: whenever each opponent uses a nondecreasing strategy (in the sense that higher types choose higher actions), a players best response strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite-action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite-action games that converges to a PSNE of the continuum-action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first-price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first-price, multi-unit, and all-pay auctions; pricing games with incomplete information about costs; and noisy signaling games.

Optimal Collusion with Private Information

We analyze collusion in an infinitely repeated Bertrand game, where prices are publicly observed and each firm receives a privately observed, i.i.d. cost shock in each period. Productive efficiency is possible only if high-cost firms relinquish market share. In the most profitable collusive schemes, firms implement productive efficiency, and high-cost firms are favored with higher expected market share in future periods. If types are discrete, there exists a discount factor strictly less than one above which first-best profits can be attained using history-dependent reallocation of market share between equally efficient firms. We also analyze the role of communication and side-payments.

Monotone Comparative Statics under Uncertainty

This paper analyzes monotone comparative statics predictions in several classes of stochastic optimization problems. The main results characterize necessary and sufficient conditions for comparative statics predictions to hold based on properties of primitive functions, that is, utility functions and probability distributions. The results apply when the primitives satisfy one of the following two properties: (i) a single-crossing property, which arises in applications such as portfolio investment problems and auctions, or (ii) log-supermodularity, which arises in the analysis of demand functions, affiliated random variables, stochastic orders, and orders over risk aversion.

IDENTIFICATION OF STANDARD AUCTION MODELS

This paper presents new identification results for models of first-price, second-price, ascending (English), and descending (Dutch) auctions. We consider a general specification of the latent demand and information structure, nesting both private values and common values models, and allowing correlated types as well as ex ante asymmetry. We address identification of a series of nested models and derive testable restrictions enabling discrimination between models on the basis of observed data. The simplest model--symmetric independent private values--is nonparametrically identified even if only the transaction price from each auction is observed. For richer models, identification and testable restrictions may be obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders; (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidder-specific covariates. While many private values (PV) models are nonparametrically identified and testable with commonly available data, identification of common values (CV) models requires stringent assumptions. Nonetheless, the PV model can be tested against the CV alternative, even when neither model is identified. Copyright The Econometric Society 2002.

Product and Process Flexibility in an Innovative Environment

This article studies several attributes of a firms long-run decisions about organizational structure, attributes that affect the firms short-run innovative activity. We focus on flexibility, which lowers the future costs of implementing innovations, and research capabilities, which improve the future opportunities for innovation. We consider two dimentsions of innovation: demand-enhancing (product) and cost-reducing (process). These two types of innovation are complementary in terms of increasing the firms net revenue in the short run. The complementarities between the firms short-run decision variables then lead to complementarities between its long-run decisions about product and process flexibility and research capabilities.

Information and Competition in U.S. Forest Service Timber Auctions

This paper analyzes the role of private information in U.S. Forest Service timber auctions. In these auctions, firms bid a per unit price for each timber species. Total bids are computed by multiplying these prices by Forest Service volume estimates, but payments depend on actual volumes harvested. We develop an equilibrium theory for these auctions. We then relate (ex post) data about volume to (ex ante) bids. We show that bidders have private information about volumes of species and use it as predicted by theory. Differences in bidder estimates appear to affect the allocation of tracts, but competition limits information rents.

Organizational Design: Decision Rights and Incentive Contracts

We explore the interaction between the allocation of decision rights over investment opportunities and the design of incentive contracts to induce unobservable effort in a multiagent, multitasking agency framework. These are linked in our model because the only available performance measures confound the two: the returns to investments are not directly observed by the principal, but instead affect the means of the signals on effort. In our model, the optimal effort-inducing incentives give very bad incentives for selecting investments, while providing incentives to make the right investment decisions is costly in terms of inducing effort. In this set-up, hierarchy can emerge endogenously, with one agent being given authority to decide about implementing projects developed by another. The agents then get very different incentive contracts. Other solutions may involve each agent being empowered to adopt projects he has developed or both having to agree before a project is accepted. Bringing in a third agent to make investment decisions may also be optimal.

Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions

We study entry and bidding patterns in sealed bid and open auctions with heterogeneous bidders. Using data from U.S. Forest Service timber auctions, we document a set of systematic effects of auction format: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. We propose a model, which extends the theory of private value auctions with heterogeneous bidders to capture participation decisions, that can account for these qualitative effects of auction format. We then calibrate the model using parameters estimated from the data and show that the model can explain the quantitative effects as well. Finally, we use the model to provide an assessment of bidder competitiveness, which has important consequences for auction choice.

Recursive partitioning for heterogeneous causal effects

In this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population. We provide a data-driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects. The approach enables the construction of valid confidence intervals for treatment effects, even with many covariates relative to the sample size, and without “sparsity” assumptions. We propose an “honest” approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation. Our approach builds on regression tree methods, modified to optimize for goodness of fit in treatment effects and to account for honest estimation. Our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation. We address the challenge that the “ground truth” for a causal effect is not observed for any individual unit, so that standard approaches to cross-validation must be modified. Through a simulation study, we show that for our preferred method honest estimation results in nominal coverage for 90% confidence intervals, whereas coverage ranges between 74% and 84% for nonhonest approaches. Honest estimation requires estimating the model with a smaller sample size; the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7–22%.

Estimation and Inference of Heterogeneous Treatment Effects using Random Forests

ABSTRACT Many scientific and engineering challenges—ranging from personalized medicine to customized marketing recommendations—require an understanding of treatment effect heterogeneity. In this article, we develop a nonparametric causal forest for estimating heterogeneous treatment effects that extends Breiman’s widely used random forest algorithm. In the potential outcomes framework with unconfoundedness, we show that causal forests are pointwise consistent for the true treatment effect and have an asymptotically Gaussian and centered sampling distribution. We also discuss a practical method for constructing asymptotic confidence intervals for the true treatment effect that are centered at the causal forest estimates. Our theoretical results rely on a generic Gaussian theory for a large family of random forest algorithms. To our knowledge, this is the first set of results that allows any type of random forest, including classification and regression forests, to be used for provably valid statistical inference. In experiments, we find causal forests to be substantially more powerful than classical methods based on nearest-neighbor matching, especially in the presence of irrelevant covariates.