Susan Athey's Research: A (Somewhat) Less Technical Introduction

Professor Susan Athey, Harvard University

 

This document provides a somewhat chatty discussion of selected research papers that may be accessible to a broader audience.  It starts with a discussion of different styles of research in economics, to try to better explain how some of my "basic research" fits in and how it might be used by other economists, and why it might be important even if it doesn't directly relate to policy.  The document then provides more in-depth discussion of a few selected papers in different areas of economics.

At the end of each extended description of a paper or set of papers, I have included an "executive summary" that boils the ideas down to a few sentences.

Contents

I.  Research Styles in Economics: How My Work Fits In

    I.A  Applied versus Basic Research in Economics

    II.B Comparative Statics Under Uncertainty

    I.C How have I ended up working at so many parts of the basic-to-applied continuum?

II.  Economics of Organizations

    II.A Diversity in Organizations

III.  Auctions and Market Design: Empirics, Econometrics, and Policy

    III.A Skewed Bidding

    III.B Comparing Auction Formats

    III.C Policy Questions

IV. Collusion

    IV.A Collusion and Price Rigidity

    IV.B Sophisticated Collusion

V. Nonparametric Identification of Structural Econometric Models

    V.A Difference-in-Difference Models

    V.B Testing Theories about Complementarity

 

 

I.  Research Styles in Economics: How My Work Fits In

I.A  Applied versus Basic Research in Economics

    I am often asked to describe common themes in my work, and to explain how I came to work on such a wide range of topics.  One way to explain this is in terms of the distinction between "applied" and "basic" or "fundamental" research.  Most academic economists work somewhere in the middle of this continuum, and one thing that makes me relatively unusual is that I have worked on both extremes.  

    Economists are ultimately trying to make predictions and evaluate alternative public policies.  The most applied part of economics research consists of analyses that are of direct use to policy-makers.  One example is advice that I give to governments about how to design auctions for public resources (such as timber), which is informed by theory and empirical research.  Another example is a paper I wrote on evaluating the impact of enhanced 911 systems on health care outcomes.  Although the paper was interesting to academic economists for other reasons, the results could be directly applied to help a policy-maker decide whether enhanced 911 was worth the investment.

    In the middle part of the basic-to-applied continuum, some applied theory research papers are designed to provide insight towards real-world problems, but on their own they would not be used as the sole basis for making a business or public policy decision.  For example, my research on mentoring and diversity in organizations (discussed in more detail below) identifies one set of forces that a firm might consider when setting its hiring and promotion policies; and it added a fresh element to the debate about the costs and benefits of affirmative action.  But my coauthors and I intentionally crafted a model that abstracted from numerous real-world concerns.  A well-designed applied theory model isolates the effects of particular forces, much as a scientist in a laboratory might try an experiment in a petri dish that has been sterilized and thus eliminates many microorganisms that are present in nature.  Applied theory models ideally provide qualitative predictions that can be tested with data, or they may form the basis of a statistical model used to calibrate parameters of the theoretical model using real-world data.

    Other kinds of papers in the middle of the continuum include empirical papers (that is, papers that analyze real-world data) that are of interest because they make a broader point, validate a more general class of theories, or estimate a parameter that is important for many economic applications (such as a parameter that describes risk preferences for a particular population).  I analyze historical data from U.S. Forest Service timber auctions, and economists are interested because many of the conclusions shed light on what behavior we might expect (qualitatively) in other auction markets.  For example, my research on "skewed bidding" (see below) documents that subtle predictions of game theoretic models are borne out in the data, and it highlights unintended consequences of auction rules that are used in a wide variety of government procurement auctions.  My work comparing open and sealed bids highlights the fact that the rules of an auction  can have quantitatively important consequences for the set of bidders who participate (large or small bidders), and how competitive the bidding process is.

    At the "basic research" end of the continuum are tools and methods that economists use to conduct research. This work is several steps removed from real policy questions, yet it can have a fairly broad impact, because it influences the way in which many different studies might be conducted.  Microeconomic theory may be relevant to researchers who develop applied theory models, while Econometric theory provides tools and methods for analyzing data. Econometrics often combines economic theory with statistical theory. Fairly unusual among present-day economists, I have done significant "basic research" in both microeconomic theory and econometric theory. 

I.B  Comparative Statics Under Uncertainty   

    In several cases, the goal of my basic research has been to design methods that focus the attention of the modeler on the essential economic assumptions, and allow the modeler to dispense with simplifying assumptions that are used only to make a model tractable.  When building an applied theory model, a researcher might assume that an agent faces uncertainty that follows a normal distribution. I developed methods that allow the modeler to consider arbitrary  (and unspecified) distributions, and my results help identity exactly what assumptions are required about the  distribution of uncertainty to make a desired prediction.  Removing unnecessary assumptions (the specific functional form of a normal distribution, for example) allows the researcher to truly understand the content of the remaining assumptions. It can make models more elegant, more transparent, and thus more insightful.

    My research on "comparative statics" under uncertainty falls into this category of basic research.  Comparative statics is the study of how economic variables change when something in the environment changes.  How do investors respond to an increase in uncertainty?  How do bidders respond to information about the amount of oil in the ground?  My research identifies the crucial economic assumptions on risk preferences and the nature of risk that allow the researcher to draw conclusions, such as the conclusion that investment decreases in response to an increase in uncertainty.

    I applied these tools myself in several other "basic research" problems.  For example, I showed that in a class of games such as auctions, if a bidder always places a higher bid when she has a higher valuation for winning, then we can be assured that a "pure strategy Nash equilibrium" exists.  A Nash equilibrium has the property that if one bidder knows the opponent's strategy (their "bidding plan" that specifies the bid they would place for each possible valuation), then the bidder does not want to alter her own strategy.  In a pure strategy Nash equilibrium, the player does not "toss a coin" to determine her bid after seeing her own valuation.  Knowing that such an equilibrium exists is a crucial first step towards analyzing outcomes in the auction, both theoretically and empirically. 

    I have also developed basic research tools to analyze informativeness of statistical information an economic agent might receive.

   These tools are necessarily abstract, and they have little use for, say, financial analysts on Wall Street.  They are designed to help academic economists craft more elegant and insightful theories with a minimum of distracting, extraneous assumptions.

I.C How have I ended up working at so many parts of the basic-to-applied continuum?

    Many (but certainly not all) economists focus their research on one  part of the basic-to-applied-research continuum.  How did I end up working (together with my coauthors) in so many different parts of it, and what are some common themes?  In several different instances, ideas for research have developed as a result of more applied research.  For example, my first papers were applied theory models of organizations, including research on diversity and affirmative action, and through that work I became exposed to empirical work on organizations.  In another example, I was working on an empirical paper about 911 systems that employed difference-in-difference methods (see below for more explanation of what these are).  In each case, my desire to understand the problems lead me to "basic research."  I noticed common themes in a wide range of papers, but was  dissatisfied with the conceptual frameworks and methods from the existing literature.   I then went on to write more abstract papers that developed new  tools and methods that could be used not only for my original applications, but also other applications as well.

    Since the methods arose in direct response to my own applications, I could be sure that they would be useful.  I was also able to exploit common themes across classes of problems: from my work on comparative statics to my work on statistical models, I have seen that monotonicity--the property that one variable always increases with another--plays a central role. 

    One reason I have liked working on the economics of auctions is that it is possible to study auctions from pretty much every point on the basic-to-applied continuum.  Auction design policy questions arise all the time, and I have been fortunate to have a role in designing real-world auctions.  I have also developed applied theory models and used them to guide empirical work.  Finally, I have done "basic research" on the statistical analysis of auction data, as well as on theoretical questions such as whether an equilibrium to the game between bidders even exists at all, and if so how the equilibrium can be computed.  Since auctions have had so many high-profile applications in recent years (see below for more discussion of these), it seems likely that they will continue to be an active area for all types of research in the future.

II.  Economics of Organizations

II.A Diversity in Organizations

    When I was starting out in graduate school, I noticed that some of my former students seemed to have particularly chummy relationships with some of the faculty.  Before long, I learned that there was a regular basketball game.  Now, I knew a fair bit about basketball, having graduated from Duke University, and I had played on co-ed intramural teams in college.  However, I soon learned that women were not welcome.  Nor, for that matter, were small or unathletic men.  When summer rolled around, some of those same students who were playing basketball had landed prime RAships with the faculty in the group.

    The debate in the media about affirmative action and diversity seemed almost entirely focused on fairness, and somewhat on role modeling.  Although I agreed that having a great role model would be a big help, that wasn't the only problem.  Being different seemed to make a difference to my productivity.  Yet, it also seemed to me that it didn't have to be that way.  For example, the guys in the economics department of my year (there was only one woman) were interested not just in basketball, but in weightlifting.  Though weightlifting wouldn't have been my first choice as a hobby, I could certainly participate fully, and so I did.  And thus I wasn't left out of the networking and informal conversations that can sometimes lead to collaborations.  After these experiences, I was left puzzling over what economic theory would have to say about these experiences.  What was missing from standard models that would account for these real effects of being a minority?

    Together with two classmates, Chris Avery and Peter Zemsky, I crafted an "applied theory" model of diversity in organizations that captured the idea that similarities among workers of different "types"--gender or race, for example--make mentoring more productive.  At the same time, the model incorporates a cost to homogeneity: talent is scarce, and if an organization restricts itself to hiring and promoting workers of just one type, they miss out on the best and brightest of the other type.  (This model requires that labor markets are somewhat thin--workers have preferences about the companies they work for, due to location or firm idiosyncracies--and talent specific to a particular firms' needs is scarce too.  These assumptions apply well to highly skilled labor markets like academics.)

    We analyzed the optimal promotion for firms in this setting, when firms have limited "senior" positions in a hierarchy and select among lower-level employees who have experienced mentoring during their "junior" phase.  A lack of diversity among senior workers will imply that junior workers of the minority type acquire less human capital.  The problem is inherently dynamic because "biasing" promotions--by considering type as well as ability in promotions--is a long-term investment that pays off when the firm achieves the the optimal ratio of different types from the perspective of mentoring.  We show that when there are diminishing returns to having more same-type mentors, the initial conditions of a firm can matter: a firm that starts out homogeneous may actively bias promotions in favor of the majority, since only a handful of minority junior candidates can ever hope to overcome the disadvantage of less effective mentoring.  Having a few minority senior agents isn't worth it, since the candidates they mentor never get promoted anyway.  On the other hand, if by chance or initial conditions, a firm achieves critical mass of the minority type in the senior ranks, the firm implements a "voluntary affirmative action" policy, investing in tipping the balance towards full diversity. 

    These types of phenomena can have long-term effects on the educational investment of workers.  If individuals anticipate future opportunities for promotion may be limited by type-biased mentoring, and there are not sufficient firms in the economy that cater to minorities, investments in education may be suboptimal.  Society may then prefer a more diverse set of firms.  On the other hand, firms that are prevented by law from implementing voluntary affirmative action problems may experience long delays in reaching their preferred (and more profitable/productive) level of diversity.

    This paper was my first economics paper (it was published later due to publication delays).  It taught me about the power of formal models to help make clear and logically consistent arguments that contributed to a policy debate.

    Executive summary of the mentoring and diversity paper: The paper considers promotion policies for firms when mentoring is more effective between senior and junior workers of the same type, and when talent is scarce.  Firms face a tradeoff between maximizing the mentoring that goes to the majority type--where type-biased mentoring implies that majorities are more likely to be promoted--and implementing voluntary affirmative action programs that lead the firm more quickly to full diversity, which allows the firm to provide intermediate amounts of mentoring to the best and brightest workers of both groups.

III.  Auctions and Market Design: Empirics, Econometrics, and Policy

Auctions are used in a wide variety of settings.  eBay auctions may be the most familiar to today's young people.  High-stakes auctions for spectrum (to be used for mobile phones and related technologies) have made headlines by raising billions of dollars at a time around the world.  One of my thesis advisors, Paul Milgrom, helped design the simultaneous ascending auction implemented by the FCC in 1994.  This auction simultaneously allocated licenses in hundreds of cities around the country.  Even before these "modern" examples, however, auctions have been used for large amounts of economic activity, including government procurement of goods and services, government allocation of natural resources such as oil and timber, and in the private sector for items as diverse as art, antiques, real estate, used cars, fresh fish, and fresh flowers.  Auctions have been documented from biblical times.

Auctions are an example of markets where individuals, firms, or governments play an active role in specifying and enforcing the "rules of the game."  In contrast, markets for many products are more "organic," in that firms and consumers interact without direct intervention from a central agent (except within broad legal constraints).  The field of "market design," which is fairly old in some ways but has only recently been popularized under that title, studies markets that are, or can be, actively designed.  Examples outside of auction markets included matching markets, such as the mechanisms that assign children to public schools in New York and Boston, medical residencies to newly minted M.D.'s, roommates to rooms, kidney donors to recipients, or prospective members to sororities.  My colleague Al Roth has studied many of these examples extensively.

The field of market design tends to focus on questions about how the rules of the game matter for efficiency, for distribution (what kinds of players win and lose with different rules), and in some cases for revenue (e.g. for auctioneers) and profits (for bidders).  In some cases, economists are asked to design entirely new market institutions, in which case they typically do theoretical analyses of the properties of new mechanisms as well as experiments to test their performance with real players.  Market design is a field where economists have been fairly successful in influencing policy: in many prominent examples (e.g. the FCC auctions for spectrum designed by my thesis advisor Paul Milgrom and his advisor, Bob Wilson), leading academic researchers have determined the main elements of new, high-stakes markets.  I am part of a firm called "Market Design" that provides advice to governments around the world on auction design. 

Personally, I got my start in auctions when I worked for a company that sold computers to the government through procurement auctions.  I wrote an undergraduate thesis about the procurement process for computers under the direction of Professor Bob Marshall (now at Penn State).  Bob went on to do research (of the "applied theory" variety) about the topic, and seeing him testify in front of Congress about his research inspired me about the ability of economic theory to influence public policy.

On Bob's suggestion, I went on to study timber auctions.  This turned into a long-standing area of research for me.  Timber auctions in the U.S. Forest Service provide a rich laboratory to test fairly nuanced predictions of game theory about strategic behavior in games where players have private information.  In addition, they provide the opportunity to show how the rules of the auction--the "market design"--matter for outcomes.

III.A Skewed Bidding

 In joint work with Jonathan Levin, I analyze 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.  In these auctions, bidding is multi-dimensional. 

 In the "scale sale" auction format used by the U.S. Forest Service (FS), a sale begins with the FS estimating the proportion of each species on a tract. These estimates are publicly announced, at which point potential bidders may conduct their own estimates. Firms bid a per-unit price for each species of timber. The winner is the firm with the highest "average" bid, computed by multiplying the unit prices by the proportions announced by the FS. The winner then has a number of years to remove all designated timber. The FS measures timber as it is removed, and the winner pays for the timber as it is removed at the rates specified in the bid. Thus, there may be a significant gap between the average bid, weighted by FS estimates, and the average payment, weighted by the true quantities. Such a gap is typical: on tracts with two main species of timber, the FS estimate of the proportion of timber that is the primary species is within 5% of the actual proportion removed on only half of the sales.

In a scale sale, if a firm has private information about the composition of the tract, it can structure its bid so that in expectation, its average payment is less than its average bid. This can be done by "skewing" one's bid onto the species the bidder believes has been over-estimated by the FS. To see this, suppose there are two species, Douglas Fir and Western Hemlock, and the FS estimates they are present in equal proportions. Suppose that based on its own cruise and the FS announcement, a firm estimates that 60% of the timber is Douglas Fir. The two bid vectors ($100,$100) and ($50,$150) yield the same average bid, $100. However, the firm expects to make an average payment of $100 under the first bid and only $90=.6*$50+.4*$150 under the second. Similarly, a bidder who believes that 65% of the timber is Douglas Fir will expect to pay an average of only $85 under the second bid.

Our paper first derives an equilibrium model of bidding in scale sale auctions.  Then, we gather ex post data on the actual amount of timber harvested from a set of timber tracts, thus allowing for an unusual opportunity to present direct evidence supporting the hypothesis that bidders are privately informed ex ante (at the time they place bids) about the composition of the tract.  We find that bidding behavior is consistent with the strategic use of private information, and that players follow the subtle predictions of the theory.

In particular, on average, bidders bid more aggressively on species where it turns out less timber is harvested than the FS estimated.  Thus, the revenue collected by the FS is systematically lower than what the FS estimated at the time of bidding.  We also find that it is the bidders who skew the most aggressively that tend to win auctions, as predicted by theory.    Even though firms could choose to insure themselves by bidding the same profit margin on each species of timber, doing so would be a handicap in competitive bidding.  Other firms can bid more, but expect to pay less, by skewing.

At times, skewing can be extreme, with bidders bidding several times more the selling value (gross of harvesting costs) for some species of trees.  Occasionally, a large gamble like this goes wrong for bidders, and they actually have to pay the (very unprofitable) price per tree on a large volume of timber.  Thus, one unintended consequence of the rules of the auction is that bidders must contend with bad results from risky bidding strategies.

While scale auctions may appear peculiar to the FS, similar mechanisms are employed widely in procurement. For instance, "unit-price" construction contracts specify per-unit prices for different items, and payment is made based on realized quantities. In contract auctions, bids are scored using pre-announced quantity estimates. In these contexts, "unbalanced bidding" is common.  In some cases, contracts explicitly protect against extreme skewing by stating that a unit price may be renegotiated if the realized quantities differ from the initial estimates by more than some fixed amount. Many government procurement contracts also have a similar "unit-price" structure.  The Government Purchasing Office (GPO) recently included new provisions to address unbalanced bidding, reserving the right to reject "materially unbalanced" bids.

III.B Comparing Auction Formats

In another recent project with Jonathan Levin and Enrique Seira, 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 two different types of auction formats.  One is the open ascending auction, where bidders meet in a room, and bidders raise one anothers' bids in an unstructured way until only one bidder remains.  In the first-price, sealed-bid auction, bidders submit sealed bids, which are opened simultaneously.  The highest bid wins, and the winner pays their own bid.

 We show that weaker bidders participate more in first-price auctions.  We further 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, we provide evidence that suggests that bidders are not bidding competitively in ascending auctions.  Theory suggests that tacit collusion should be easier in ascending auctions, and our results confirm this prediction. 

Jonathan Levin and I have also analyzed the effects of small-business set-aside programs, 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.

III.C Policy Questions

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. 

IV.  Collusion in Auctions and Dynamic Pricing Games

    Collusion among firms is a central problem in the economics of industrial organization.  Anti-competitive prices may harm consumers, and further, colluding firms may sacrifice productive efficiency by failing to allocate market share to the firms with the lowest production costs. 

    My research looks as questions such as the following: How can we understand the use of fairly simple-minded collusive schemes (such as firms setting equal prices while maintaining stable market shares over time) when such schemes clearly sacrifice a lot of the potential profit from tailoring market shares to changes in relative productivity, inventories, input costs, and other factors over time?  How does the ability to communicate influence prices and productive efficiency?  And what would change if firms were able as well to make direct side-payments to one another (perhaps at some cost, if side-payments are illegal but detection occurs with modest probability)?   Do predictions about collusive behavior have any macroeconomic implications, for example for how prices change with the business cycle?

    In a series of papers with Kyle Bagwell, I address these questions in an "applied theory" model of firm behavior that has the following central features: (i) firms interact repeatedly over time; (ii) monetary transfers among firms are restricted or prohibited; and (iii) the firms have private information about time-varying cost or local demand conditions.  Private information about cost may arise due to confidential labor or supply contracts; incremental process innovations; or changing inventory levels.  Collusive profits are highest if the firms can implement a self-enforcing collusive scheme whereby prices are close to monopoly levels and productive efficiency is attained.  Productive efficiency--allocating production to the most efficient firm-- requires that private information is truthfully “revealed” through market conduct, as when firms with lower cost levels charge lower prices and thus receive greater market share.  One theme of our analysis is that colluding firms tend to sacrifice productive efficiency instead of lowering prices, and some types of anti-trust enforcement may lead firms to decrease productive efficiency without significantly affecting prices.

    This research program also has some "basic research" components.  Collusion among firms entails subtle strategic incentives in a dynamic game, and when firms are privately informed, there is another layer of complexity in the strategies.  The key challenge is how to provide incentives for firms to reveal their private information, so that the information can be used to maximize profits for the cartel, when all firms have the incentive to pretend to be low-cost in order to gain more market share. 

    We were among the first to develop models of dynamic games with hidden information, and further the approach we took in our analysis is applicable to a much broader set of problems than collusion, some of which I have explored myself in other work.  We showed how tools from one area of basic research in microeconomic theory--"mechanism design"--could be fruitfully combined with tools from another area--"repeated games"--to yield elegant and tractable analyses of the way in which agents in a dynamic game provide incentives for revelation of private information and for cooperative behavior.  Our earlier papers started with games that were stationary--the environment is stable, and firms receive new realizations of private information each period that are independent over time--and later we went on to analyze games where firms have private information that is serially correlated over time, so that play in one period can reveal information relevant to future periods.

 IV.A Collusion and Price Rigidity

    In joint work with Kyle Bagwell and Chris Sanchirico, we address some "stylized facts" about collusion: prices are often more rigid, and market shares more stable, in concentrated industries.  In addition, there are many examples of real-world cartels that followed simple "rules-of-thumb," such as requiring all firms to charge the same price (which might be indexed to some commonly observable cost variable.)  When firms collude in this manner, the collusive price is independent of the private cost positions (beyond the wholesale price) of the member firms, and productive efficiency is not achieved.  We formalize the idea that price rigidity is prevalent because of the costs of private information: in order to dissuade a high-cost firm from pricing as if it had low cost, price wars and pricing distortions are required.  There is a tradeoff between high prices and efficiency in production, and we show that under some conditions, the tradeoff is always resolved in the same direction.  This theme arises in other applications I have studied as well: in some cases, it just isn't worth it to provide incentives for agents to reveal their private information.

    Our analysis of this model focuses on the case where firms have limited observability of one anothers' behavior: market-wide prices are observable, but not individual firm behavior.  As a result, price wars take place at an industry-wide level, and firms can not effectively tailor rewards and punishments to individual firms. 

    We identify a tradeoff that is associated with collusive pricing schemes in which each firm’s price is strictly increasing in its cost level: such “fully-sorting” schemes use prices to allocate market share to the lowest-cost firm, but they also imply an informational cost, since a higher-cost firm must be deterred from charging a low price and claiming that its costs are low.  The informational costs of collusion may be manifested in two ways. First, the prices of lower-cost firms may be distorted to low levels.  Second, following the selection of lower prices, the collusive scheme may sometimes call for an equilibrium-path price war in future periods.

    In the alternative we focus on, the rigid-pricing scheme, each firm selects the same price in each period, regardless of its current cost position.  Getting firms to reveal private information is not necessary in this scheme, because productive efficiency is sacrificed. We show that when demand is inelastic, the best collusive equilibrium for firms has the following properties: (a) there are no price wars in equilibrium, and (b) if firms are sufficiently patient and the distribution of costs satisfies weak regularity conditions (in particular, it is log-concave), firms use a rigid-pricing scheme.

    The first finding contrasts strikingly with the previously existing literature on collusion where firms do not have private information about costs, but rather firms can engage in secret price-cutting (Green-Porter (1984)).  In the secret-price-cutting literature, price wars are an integral component of collusion (they are the only instrument to deter secret price cuts).  The second finding offers an equilibrium interpretation of the empirical association between rigid pricing and industry concentration.  In broad terms, when firms are able to effect transfers only with inefficient instruments (i.e., industry price wars), then incentive-compatible productive efficiency is more trouble than it is worth.  Instead, the firms settle on a rigid price and accept inefficient allocation of production.

    We also study an extension of the model where there are i.i.d. demand shocks in each period.  In a high-demand state, the future looks unattractive relative to the present, and thus firms are more tempted to undercut the collusive price, serve the entire market today, and suffer the future price war.

    If firms are fairly impatient, when a firm draws a lower-cost type, the temptation to undercut the assigned price is severe, since the resulting market-share gain is then especially appealing.  For impatient firms, a collusive scheme thus must ensure that lower-cost types receive sufficient market share and select sufficiently low prices in equilibrium, so that the gains from cheating are not too great.  If firms are not sufficiently patient to go along with the rigid-pricing scheme, they may still support a partially-rigid collusive scheme, in which lower-cost types price substantially below higher-cost types, reducing the gain from an off-schedule deviation.  This amounts to an escape clause for low-cost firms: equilibrium collusion enables a firm that has especially low costs an "escape valve" as an alternative to deviating from the agreement and sending the industry into a price war.  Instead undercutting the collusive price just a little bit, which all firms would like to do (and thus would trigger a price war), the escape valve requires a deep price cut.  All firms know that only a very low-cost firm (or a firm with excessive inventories) would gain from such a price cut, and so a temporary price cut of this sort does not induce retaliation.

    The need for escape valves is especially great when firms see today's opportunities to grab market share as great relative to expected future profits from collusion.  Thus, symmetric collusion between impatient firms may be marked by occasional (and perhaps substantial) price reductions by individual firms. Such departures are most likely to occur when today’s demand shock is high, so that the future looks bleak relative to the present, and when one firm receives a favorable cost shock.  Although we might interpret this price reduction as a sort of price war, note that it does not induce retaliation: the price decrease represents a permitted “escape clause” (i.e., an opportunity to cut prices and increase market share) within the collusive scheme.

IV.B Sophisticated Collusion

    The research on price rigidity focuses on models in which collusion between firms proceeds in a symmetric fashion, in the sense that each firm’s expected value is the same at the beginning of each period, before any uncertainty is realized.  Collusion among firms can be more successful when firms can use asymmetric rewards and punishments. 

    Kyle Bagwell and I consider a model similar to the "Collusion and Price Rigidity" model outlined above, but with the following features: (i) firms can “communicate” with regard to current cost conditions; (ii) firms can use “market-share favors,” which requires that the identities of individual firms can be followed over time, and whereby individual firms can be treated asymmetrically as a reward or punishment for past behavior; (iii) firms can not make explicit monetary transfers (use “bribes”). After studying this model in some detail, we will analyze the way in which optimal collusion changes as restrictions (i) and (iii) are imposed or removed.  In a subsequent paper, we allow for firm costs to be correlated over time.

    Our first main result is that firms can achieve the highest possible level of profits--monopoly prices and efficient production--by exchanging "market share favors."  First consider how "inefficient" market-share favors might work.  One day, each firm announces a cost.  If firm 1 is low-cost and firm 2 is high-cost, firm 1 serves the market today, but in the next period, no matter what happens firm 2 takes a turn.  (I often illustrate this idea in class with an example about two roommates negotiating over dish-washing duty--one roommate claims to have a big problem set due, but promises to wash the dishes tomorrow.)  This gets efficient allocation of production in the first period, but in the second period, it might be inefficient.    

    Now consider "efficient market share favors."  In the first period of the game, if firm 1 has low cost and firm 2 has high cost, firm 1 serves the entire market; but, in the second period, firm 2 receives more than half the market in the event that the two firms have the same cost type, while otherwise the firms are efficient again.  The prospect of tomorrow's gain induces firm 2 to admit having high costs; but the reward is still efficient.  In this case, future market-share favors have no efficiency loss.  We show that when firms are sufficiently patient, first-best profits can be attained using efficient market-share favors.  The finding of exact efficiency depends on a model with only two possible cost types, but the qualitative results can be extended.

    When firms are less patient, "perfect collusion" with efficient market share favors may no longer be possible.  We show that in a profit-maximizing collusive scheme, firms tend to give up on trying to induce full productive efficiency, and instead share the market among low- and high- cost firms, rather than attempt to provide incentives using instruments like low prices in the present, price wars in the future, or inefficient production in the future.  Efficient market-share favors allowed firms to provide incentives to reveal private information "for free"--market share was transferred from one firm in the cartel to another, but there was no loss in total profits to the cartel.  Once incentives require things like low prices, that hurt the cartel as a whole, the cartel quickly abandons the goal of productive efficiency.  Intuitively, productive inefficiency entails a loss of total profits, but at least the inefficient members of the cartel stand to gain from it, rather than consumers.

    Consider next the role of communication.  Standard collusion folklore holds that collusive firms frequent “smoke-filled” rooms; but the theoretical literature addressing the role of communication is sparse.  In our model, communication among firms can offer benefits as well as costs.  The benefit is that, when firms communicate their costs to one another, they can allocate market shares in a smooth, state-contingent fashion.  On the downside, communication can make it especially temping to undercut the collusive price in a given period.  Firm 1 may be especially tempted to undercut its assigned price if it learns that firm 2 has low costs and the collusive scheme assigns firm 2 larger market share; such a firm has less incentive to undercut if it is unsure of firm 2’s cost, as it harbors some hope of serving the market without cheating.

    Weighing these costs and benefits, we find that for firms of moderate patience, the optimal collusive equilibria will entail communication in some periods and none in others. 

    Further, an anti-trust policy restricting communication reduces the collusive profits of moderately patient firms, potentially lowering productive efficiency but without affecting prices.  The idea is that firms that cannot communicate end up allocating production less efficiently; but they choose inefficient production rather than low prices.

    On the other hand, if firms are sufficiently patient, they are still able to achieve first-best profits in every period without communication. 

    In more recent research about this class of models, we ask how the results change when costs are correlated over time.  This introduces a whole new host of incentive problems, since information a firm reveals in one period can be used against it in the future.  Part of this analysis is "basic research": how can we even analyze such a complicated dynamic game?  After developing some tractable approaches for analysis, we provide two main insights.  First, when costs are highly correlated over time relative to the patience of firms, "price rigidity" is optimal and firms sacrifice efficient production, but when firms are relatively patient, a more complex version of efficient market-share favors (described above) can be used to achieve perfect collusion. 

    Second, when firms are less patient relative to persistence and when cost distributions are "irregular" (e.g. low and high costs are more likely than intermediate costs), optimal collusion may involve an initial "signaling" phase, where one firm charges a very low price for a period of time in order to credibly reveal that it has low costs today and expects to remain low cost in the future; and then, firms return to monopoly prices, but the low-cost firm gets more market share.  We can interpret this behavior as a form of "bargaining" over market share.  All of the firms would like to claim that they should get more than an even share of the market; but the initial signalling behavior of extremely aggressive pricing provides a credible signal that earns a truly low-cost firm greater market share in the future.  Higher cost firms would not find the initial signaling as worthwhile.  Elements of this type of behavior have been observed in some real-world high-stakes cartels.

Executive Summary of These Papers:  Privately informed colluding firms can achieve perfect collusion--with production allocated to the most efficient firm, and prices at monopoly levels--by using efficient market share favors.  High-cost firms are induced to admit high costs (and accept low market shares in the present) by the promise of getting extra market share in future periods when the firms have similar costs.  However, if costs are highly correlated over time, today's high-cost firm will also be high-cost in the future, and such schemes will not work as well.  Then, price rigidity may be optimal.  In addition, "signaling" behavior can emerge, whereby a low-cost firm initiates very low prices for a period of time, in order to capture an unequal share of the market at monopoly prices in the future.  Communication can help firms allocate more efficiently, and banning it may end up reducing productive efficiency without lowering prices.

V. Nonparametric Identification of Structural Econometric 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.

V.A Difference in Difference Models

I have also worked (together with Guido Imbens) 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 a large group of individuals in 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, and other groups (the "control groups") not subject to the change.  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; the goal is to isolate a "treatment effect."  Our 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.  Our model allows for treatment effect to vary across individuals, and for the average effect of the treatment to vary across groups. 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.

V.B Testing Theories About Complementarity

    A fairly large literature at the intersection of economics, strategy, and management is concerned with the question of how different organizational design practices--such as training programs, job security, job rotation, information technology adoption--interact in affecting firm performance.  Milgrom and Roberts' (1990) study of modern manufacturing focused attention on complementarity among different organizational design practices, and a number of empirical papers began documenting correlations among these practices.  In joint work with Scott Stern, I provide a formal model that shows how a whole battery of tests for complementarity that were proposed in the literature could be confounded by unobserved heterogeneity--that is, unobserved factors that might affect the costs and benefits of adopting different practices, that might themselves be correlated.  Although economists have long understood the importance of unobserved heterogeneity in empirical work, this paper provides a rigorous analysis of the direction of biases that might arise, and how the same underlying model of unobserved heterogeneity can lead to a consistent, and thus especially misleading, pattern of results across a battery of different tests for complementarity that have been proposed in the literature.