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Research Summary

Overview of Research Interests

My research concerns a variety of topics in microeconomic theory and industrial organization.  Although most of my work is theoretical, a substantial portion focuses on empirical applications and econometric methods.  I am currently working in five main areas, with many papers spanning several of these topics: (1) Dynamic Games and Contracts, (2) Auctions, (3) Nonparametric Identification of Structural Econometric Models, (4) Economics of Organizations, and (5) Comparative Statics.  Most of my research is jointly authored with a variety of coauthors.

The research on dynamic games and contracts looks at the types of behavior that yields the highest possible payoffs for a group of agents who interact over time, when some or all players have private information about their costs and benefits of acting, and when these costs and benefits may change over time.  I ask questions about problems such as optimal collusion by a group of firms, the optimal degree of discretion for a privately informed monetary policy authority, and the ability of two agents to sustain efficient trade in each period of an ongoing relationship when both have private information.  I also prove a result establishing the existence of a payment scheme that induces truthful revelation of private information by agents in a very general class of dynamic games.

The work on auctions includes empirical work that tests theories about common value auctions and entry in auctions, as well as work that uses behavior in one type of auction (first-price) as a benchmark to assess the competitiveness of another type (ascending).  My research on auctions also includes theoretical analyses of existence of equilibrium and collusion at auctions.  I have also worked on econometric identification of auction models.

The study of econometric identification asks the following question: if we had a large dataset containing specified data elements (e.g. all bids from a series of first-price auctions), would it be possible to learn the economic primitives (e.g. the distributions from which bidders draw their valuations) from the data, given some assumptions about individual behavior.  I have analyzed econometric identification of a variety of models, including auctions, models of the impact of government policy on populations of individuals, models of organizational design, and models of consumer choice.

In the economics of organizations, I have explored in a couple of different papers questions about the role of hierarchies in both firms and in self-organizing "communities," showing how hierarchies can arise endogenously as a way to solve incentive problems.  I have also analyzed other topics, such as the diversity of organizations and affirmative action.

My work on comparative statics develops methods and tools for making predictions about how the optimal or equilibrium level of some economic variables (e.g. investment in information gathering) changes with exogenous parameters (such as the "informativeness" of a signal).  I have used the tools to prove existence of equilibrium in a large class of games of incomplete information; to analyze the value of information; and to study "increasing dominance" in oligopoly games where investments are strategic substitutes.

Dynamic Games and Contracts

In a series of papers, I developed a modeling framework for games where individuals interact over time, and each individual has hidden information about his costs and benefits of acting in each period that change over time (but potentially have some persistence).  I study cooperation and competition in such games.  Examples of such games are repeated auctions (as when a procurement agency holds a series of auctions over time), firms colluding in a market where the firms have privately observed costs, games where a small set of individuals (e.g. members of a family) trade "favors" over time, games where a privately informed policy-maker selects policies in the face of dynamic inconsistency problems (e.g. a central bank choosing monetary policy), and vote-trading games in political economy.  In most of the models I study, actions are publicly observed by all players and players can not use monetary transfers to provide incentives, due to legal constraints or other institutional considerations.

Consider the case of colluding firms.  In several papers (Collusion and Price Rigidity,Optimal Collusion with Private Information, Collusion with Persistent Cost Shocks), I ask questions such as: what is the profit-maximizing scheme for a cartel, and what is the best way to collude?  Should firms set high prices and share the market equally, or should they attempt to allocate market share efficiently, to the firm who happens to have the lowest cost that period?  If they attempt to do the latter, how do firms provide incentives for revealing a high cost draw, since revealing high cost requires the firm to forgo market share?  Is explicit communication necessary to achieve the cartel's objectives?  If firms can use bribes but risk detection by antitrust authorities, when will they choose to use them?  How do the answers to these questions depend on the extent to which a firm's cost shocks persist over time?  I show that under some conditions (limited observability, high persistence of shocks), "rigid-pricing" and stable market shares are optimal, while under other conditions, firms achieve efficient collusion by "trading favors" over time, so that a firm that admits to having high cost today gives up market share in the future.

In another paper (The Optimal Degree of Discretion in Monetary Policy), I analyze the question of how much discretion a monetary authority should have to respond to private information, when the monetary authority acts to maximize social welfare, but is privately informed about the best course of action for the economy.  The monetary authority faces a time-consistency problem, whereby it is tempted to claim that the economy unexpectedly requires more inflation.  If individuals in the economy anticipate this, the economy will be worse off, since higher inflation will result in every period.  However, limiting discretion entails social cost if the optimal monetary policy varies with the authority's private information.  Under reasonable conditions on the nature of the private information, the optimal policy is to set a simple inflation cap that limits the authority's discretion, and does not vary over time.  The simple policy is optimal despite the possibility that much more complex dynamic policies are possible. This result echoes a theme from the work on collusion: the shape of the distribution of private information determines whether or not it is optimal to use socially inefficient incentives (future inefficiency, such as future price wars or inefficient monetary policy in the future) to induce a privately informed player to make efficient use of his information in the present.  For "typical" distributions (log-concave), the tradeoff is always resolved by ignoring private information and bearing the associated inefficiency in decision-making.  The fact that a similar result arises in these two fairly different models suggests that there may be a more general principle at work.

I've also analyzed the problem of trade between a buyer and a seller who interact repeatedly (Efficiency in Repeated Trade with Hidden Valuations).  Can these players find a way to sustain efficient trade, even when both have private information?  In a static context, the answer is known to be "no."  I look for an "ex post" equilibrium in every period, where each player reports truthfully even if they know opponent reports with certainty, in order to capture the idea that it can be difficult to enforce exactly simultaneous communication in a decentralized, informal trading process.  I show that ex post incentives for efficient allocation are not compatible with budget balanced transfers among agents, but I derive a dynamic mechanism where players deposit and withdraw money from a joint account with bounds.  I provide conditions under which fairly patient players expect to attain exactly efficient payoffs from a dynamic mechanism, despite the fact that it is potentially challenging to provide incentives to the players to report truthfully near the bounds of the account.  For example, near the lower bound, there is little opportunity to withdraw funds to provide incentives, and in addition each withdrawal may not be as valuable to agents because they know it takes them closer to the bound, which may make them worse off.

In a more abstract pair of papers (An Efficient Dynamic Mechanism, Designing Efficient Mechanisms for Dynamic Bilateral Trading Games), I address an important open question in the theory of dynamic mechanism design: do there exist a set of monetary transfers that provide incentives for truthful revelation of private information in dynamic models?  I answer this question in the affirmative for a large class of games, where the players' information may be serially correlated, and interesting economic forces such as learning-by-doing, investment in information gathering, and experimentation are incorporated.  Since players learn about opponent information over time, their own beliefs change over time, and they also potentially have the incentive to manipulate the beliefs of opponents about their own current and future information.  In this environment, I construct transfers that are budget balanced (so that subsidies are not required and no money is wasted), incentive-compatible (so that players truthfully report their information in every period), and under some additional conditions satisfy participation constraints (so that players are willing to follow through on the transfers proscribed by the mechanism, rather than walking away).  This result can serve as a benchmark for equilibria of decentralized games without transfers, and for a restricted class of models I prove a "folk theorem"-like result: efficiency can be sustained in a decentralized, self-enforcing mechanism when players are sufficiently patient.

Auctions, Market Design, and Online Advertising (Theory, Empirical, and Econometrics)

My theoretical work on auctions includes analyses of the existence of equilibria in auction games (Single Crossing Properties and the Existence of Pure Strategy Equlibria in Games of Incomplete Information); collusion in repeated auctions, as described above; and competition in repeated auctions where bidders have persistent private information (Dynamic Auctions with Persistent Private Information).  Much of my work on auctions, however, concerns the empirics and econometrics of auctions.

In a series of papers, I have analyzed the role of market institutions in determining strategic behavior by bidders in one-shot auctions.  One paper (Information and Competition in U.S. Forest Service Timber Auctions) analyzes the strategic use of information by bidders in common value auctions (i.e., auctions where all bidders value the object equally, but each has a private signal about this value), with data from U.S. timber auctions.  I gather ex post data on the value of the timber tracts, thus allowing for an unusual opportunity to present direct evidence supporting the hypothesis that bidders are privately informed ex ante about the features of the tract.  I find that bidding behavior is consistent with the strategic use of private information, and that players follow subtle theoretical predictions about bidding in multi-dimensional auctions with scoring rules, an auction format commonly used by governments.

In another recent project (Comparing Open and Sealed Bid Auctions: Theory and Evidence from Timber Auctions), I analyze the effect of market design, in particular the auction format, on competition in auctions when entry is endogenous.  In timber auctions, potential bidders are heterogeneous, including both small logging operations and large mills.  I derive and test comparative statics predictions comparing entry and bidding behavior in oral ascending and first-price auctions, showing, for example, that weaker bidders participate more in first-price auctions.  I show that when comparing first-price and ascending auctions, the effect of auction format on participation is much larger than the effect of format on bidding conditional on participation.  In other words, how many bidders come is more important than how they bid once they get there.  In addition, using bidding behavior from first-price auctions as a benchmark, I provide evidence that suggests that bidders are not bidding competitively in ascending auctions.  Theory suggests that tacit collusion should be easier in ascending auctions. 

I have also analyzed the effects of small-business set-aside programs (Set-Asides and Subsidies in Auctions), showing that additional entry by small businesses can offset much of the potential revenue loss from excluding large bidders, and analyzing the efficiency of alternative policies to promote small businesses, such as subsidies.

My work on timber auctions extends to the policy arena as well.  For five years, I worked with the British Columbia Ministry Forests to design a major deregulation of the timber industry and a new auction-based method for pricing government timber, which comprises most timber in British Columbia and is responsible for about a quarter of the province's economic activity.  I have also advised other governments on auction policy, such as a project involving a combinatorial auction for government timber in Victoria, Australia.

In another line of work, I analyze conditions under which primitives of auction models can, in principle, be uncovered using a dataset containing bidding data from a series of many independent auctions (Identification in Standard Auction Models).  That is, I analyze the econometric identification of the distributions of bidder valuations.  With knowledge of these distributions, it is possible to ask questions about optimal auction design and policy.  I've also written two surveys of recent advances in the econometrics of auctions and their applications (Empirical Models of AuctionsNonparametric Approaches to Auctions).

Nonparametric Identification of Structural Econometric Models

I just described my research on the econometrics of auctions.  In Identification and Inference in Nonlinear Difference-in-Differences Models, I have also worked on non-parametric identification of a non-linear structural model that can be used to analyze data in a setting that is suited for "difference-in-difference" models: data is available for at least two groups and at least two time periods, with some groups being subjected to a "treatment" (e.g. a minimum wage change) in a later period.  My model allows for treatment effect to vary across individuals, and for the average effect of the treatment to vary across groups. Difference-in-difference models are widely used in applied economics, in order to control for the underlying time trend that would have occurred in the absence of a treatment and thereby isolate a "treatment effect."  My paper identifies key assumptions--assumptions that are interpretable in terms of economics--that are sufficient for identification of the treatment effect, showing that common functional form assumptions are not necessary.  This is useful because the traditional approach rules out important economic phenomena, such as a case where a state with higher average returns to a public program is the one that adopts it.

Another recent paper analyzes identification of a model of consumer preferences using discrete choice demand data (Discrete Choice Models with Multiple Unobserved Choice Characteristics).  Such models are widely used in industrial organization.

In earlier research I looked at the ability of an econometrician to test theories about whether different organizational design practices are complements (An Empirical Framework for Testing Theories About Complementarity in Organizational Design).

Economics of Organizations

One recent paper (A Theory of Community Formation and Social Hierarchy) studies the question of how trust can be sustained in environments where individuals have many possible trading partners, and institutions for enforcement of contracts are weak.  Examples include developing countries and online communities.  One commonly observed social institution is a "social hierarchy": more senior members of a group are more stable, more trustworthy, and are favored partners for trade and interaction.  More junior members may need to prove themselves. I analyze the role of social hierarchies in groups as a way to support cooperation.  The novel elements of the paper include the fact that groups are self-organizing and group size is endogenous, so that I may analyze the comparative statics of group size for both efficiency of trade and for sustaining cooperation.  In addition, I study how robust certain types of equilibria are to the entry of groups that fail to follow the same hierarchical structure and social conventions.  This is useful because phenomena that had received attention in past studies--such as specific investments required by groups in order to join--have the undesirable features that (i) individuals are not trusted merely to uphold social conventions, even when they are inherently trustworthy, and (ii) a particular group's specific investment helps sustain cooperation in other groups but confers no particular advantage to the group itself.  I construct equilibria that do not have these drawbacks.

I have also analyzed endogenous hierarchy in another paper about authority in organizations (Organizational Design: Decision Rights and Incentive Contracts).

Motivated by the observation that mentoring relationships in organizations (including academics) seem more likely to form among individuals who share some common demographic features, in Mentoring and Diversity I analyzed diversity and affirmative action in a dynamic model of a hierarchical organization that recognizes some productive advantage to mentoring among workers of the same type.  In a world with scarce talent, diverse organizations can better exploit the most talented workers from different groups, but homogenous organizations maximize the productivity of the dominant type.  I show that there can be both diverse and fully homogeneous steady states for an optimizing organization, and that firms may put in voluntary affirmative action policies to reach a preferred, diverse steady state more quickly.

Comparative Statics

I have analyzed the theory of comparative statics predictions in models with uncertainty (Monotone Comparative Statics Under Uncertainty, Characterizing Properties of Stochastic Objective Functions), and in dynamic models.  In Single Crossing Properties and the Existence of Pure Strategy Equlibria in Games of Incomplete Information I applied the tools of comparative statics to derive a general existence theorem for games with incomplete information, where players use strategies such that higher types choose higher actions.  I also analyzed different measures of the value of information in decision problems and games (The Value of Information in Monotone Decision Problems), using the tools of monotone comparative statics.  Another study (Investment and Market Dominance) looked at dynamic games with strategic substitutes, looking at conditions for "market dominance."

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