Category Archives: Theory of the Firm

Nobel Prize 2016 Part II: Oliver Hart

The Nobel Prize in Economics was given yesterday to two wonderful theorists, Bengt Holmstrom and Oliver Hart. I wrote a day ago about Holmstrom’s contributions, many of which are simply foundational to modern mechanism design and its applications. Oliver Hart’s contribution is more subtle and hence more of a challenge to describe to a nonspecialist; I am sure of this because no concept gives my undergraduate students more headaches than Hart’s “residual control right” theory of the firm. Even stranger, much of Hart’s recent work repudiates the importance of his most famous articles, a point that appears to have been entirely lost on every newspaper discussion of Hart that I’ve seen (including otherwise very nice discussions like Applebaum’s in the New York Times). A major reason he has changed his beliefs, and his research agenda, so radically is not simply the whims of age or the pressures of politics, but rather the impact of a devastatingly clever, and devastatingly esoteric, argument made by the Nobel winners Eric Maskin and Jean Tirole. To see exactly what’s going on in Hart’s work, and why there remains many very important unsolved questions in this area, let’s quickly survey what economists mean by “theory of the firm”.

The fundamental strangeness of firms goes back to Coase. Markets are amazing. We have wonderful theorems going back to Hurwicz about how competitive market prices coordinate activity efficiently even when individuals only have very limited information about how various things can be produced by an economy. A pencil somehow involves graphite being mined, forests being explored and exploited, rubber being harvested and produced, the raw materials brought to a factory where a machine puts the pencil together, ships and trains bringing the pencil to retail stores, and yet this decentralized activity produces a pencil costing ten cents. This is the case even though not a single individual anywhere in the world knows how all of those processes up the supply chain operate! Yet, as Coase pointed out, a huge amount of economic activity (including the majority of international trade) is not coordinated via the market, but rather through top-down Communist-style bureaucracies called firms. Why on Earth do these persistent organizations exist at all? When should firms merge and when should they divest themselves of their parts? These questions make up the theory of the firm.

Coase’s early answer is that something called transaction costs exist, and that they are particularly high outside the firm. That is, market transactions are not free. Firm size is determined at the point where the problems of bureaucracy within the firm overwhelm the benefits of reducing transaction costs from regular transactions. There are two major problems here. First, who knows what a “transaction cost” or a “bureaucratic cost” is, and why they differ across organizational forms: the explanation borders on tautology. Second, as the wonderful paper by Alchian and Demsetz in 1972 points out, there is no reason we should assume firms have some special ability to direct or punish their workers. If your supplier does something you don’t like, you can keep them on, or fire them, or renegotiate. If your in-house department does something you don’t like, you can keep them on, or fire them, or renegotiate. The problem of providing suitable incentives – the contracting problem – does not simply disappear because some activity is brought within the boundary of the firm.

Oliver Williamson, a recent Nobel winner joint with Elinor Ostrom, has a more formal transaction cost theory: some relationships generate joint rents higher than could be generated if we split ways, unforeseen things occur that make us want to renegotiate our contract, and the cost of that renegotiation may be lower if workers or suppliers are internal to a firm. “Unforeseen things” may include anything which cannot be measured ex-post by a court or other mediator, since that is ultimately who would enforce any contract. It is not that everyday activities have different transaction costs, but that the negotiations which produce contracts themselves are easier to handle in a more persistent relationship. As in Coase, the question of why firms do not simply grow to an enormous size is largely dealt with by off-hand references to “bureaucratic costs” whose nature was largely informal. Though informal, the idea that something like transaction costs might matter seemed intuitive and had some empirical support – firms are larger in the developing world because weaker legal systems means more “unforeseen things” will occur outside the scope of a contract, hence the differential costs of holdup or renegotiation inside and outside the firm are first order when deciding on firm size. That said, the Alchian-Demsetz critique, and the question of what a “bureaucratic cost” is, are worrying. And as Eric van den Steen points out in a 2010 AER, can anyone who has tried to order paper through their procurement office versus just popping in to Staples really believe that the reason firms exist is to lessen the cost of intrafirm activities?

Grossman and Hart (1986) argue that the distinction that really makes a firm a firm is that it owns assets. They retain the idea that contracts may be incomplete – at some point, I will disagree with my suppliers, or my workers, or my branch manager, about what should be done, either because a state of the world has arrived not covered by our contract, or because it is in our first-best mutual interest to renegotiate that contract. They retain the idea that there are relationship-specific rents, so I care about maintaining this particular relationship. But rather than rely on transaction costs, they simply point out that the owner of the asset is in a much better bargaining position when this disagreement occurs. Therefore, the owner of the asset will get a bigger percentage of rents after renegotiation. Hence the person who owns an asset should be the one whose incentive to improve the value of the asset is most sensitive to that future split of rents.

Baker and Hubbard (2004) provide a nice empirical example: when on-board computers to monitor how long-haul trucks were driven began to diffuse, ownership of those trucks shifted from owner-operators to trucking firms. Before the computer, if the trucking firm owns the truck, it is hard to contract on how hard the truck will be driven or how poorly it will be treated by the driver. If the driver owns the truck, it is hard to contract on how much effort the trucking firm dispatcher will exert ensuring the truck isn’t sitting empty for days, or following a particularly efficient route. The computer solves the first problem, meaning that only the trucking firm is taking actions relevant to the joint relationship which are highly likely to be affected by whether they own the truck or not. In Grossman and Hart’s “residual control rights” theory, then, the introduction of the computer should mean the truck ought, post-computer, be owned by the trucking firm. If these residual control rights are unimportant – there is no relationship-specific rent and no incompleteness in contracting – then the ability to shop around for the best relationship is more valuable than the control rights asset ownership provides. Hart and Moore (1990) extends this basic model to the case where there are many assets and many firms, suggesting critically that sole ownership of assets which are highly complementary in production is optimal. Asset ownership affects outside options when the contract is incomplete by changing bargaining power, and splitting ownership of complementary assets gives multiple agents weak bargaining power and hence little incentive to invest in maintaining the quality of, or improving, the assets. Hart, Schleifer and Vishny (1997) provide a great example of residual control rights applied to the question of why governments should run prisons but not garbage collection. (A brief aside: note the role that bargaining power plays in all of Hart’s theories. We do not have a “perfect” – in a sense that can be made formal – model of bargaining, and Hart tends to use bargaining solutions from cooperative game theory like the Shapley value. After Shapley’s prize alongside Roth a few years ago, this makes multiple prizes heavily influenced by cooperative games applied to unexpected problems. Perhaps the theory of cooperative games ought still be taught with vigor in PhD programs!)

There are, of course, many other theories of the firm. The idea that firms in some industries are big because there are large fixed costs to enter at the minimum efficient scale goes back to Marshall. The agency theory of the firm going back at least to Jensen and Meckling focuses on the problem of providing incentives for workers within a firm to actually profit maximize; as I noted yesterday, Holmstrom and Milgrom’s multitasking is a great example of this, with tasks being split across firms so as to allow some types of workers to be given high powered incentives and others flat salaries. More recent work by Bob Gibbons, Rebecca Henderson, Jon Levin and others on relational contracting discusses how the nexus of self-enforcing beliefs about how hard work today translates into rewards tomorrow can substitute for formal contracts, and how the credibility of these “relational contracts” can vary across firms and depend on their history.

Here’s the kicker, though. A striking blow was dealt to all theories which rely on the incompleteness or nonverifiability of contracts by a brilliant paper of Maskin and Tirole (1999) in the Review of Economic Studies. Theories relying on incomplete contracts generally just hand-waved that there are always events which are unforeseeable ex-ante or impossible to verify in court ex-post, and hence there will always scope for disagreement about what to do when those events occur. But, as Maskin and Tirole correctly point out, agent don’t care about anything in these unforeseeable/unverifiable states except for what the states imply about our mutual valuations from carrying on with a relationship. Therefore, every “incomplete contract” should just involve the parties deciding in advance that if a state of the world arrives where you value keeping our relationship in that state at 12 and I value it at 10, then we should split that joint value of 22 at whatever level induces optimal actions today. Do this same ex-ante contracting for all future profit levels, and we are done. Of course, there is still the problem of ensuring incentive compatibility – why would the agents tell the truth about their valuations when that unforeseen event occurs? I will omit the details here, but you should read the original paper where Maskin and Tirole show a (somewhat convoluted but still working) mechanism that induces truthful revelation of private value by each agent. Taking the model’s insight seriously but the exact mechanism less seriously, the paper basically suggests that incomplete contracts don’t matter if we can truthfully figure out ex-post who values our relationship at what amount, and there are many real-world institutions like mediators who do precisely that. If, as Maskin and Tirole prove (and Maskin described more simply in a short note), incomplete contracts aren’t a real problem, we are back to square one – why have persistent organizations called firms?

What should we do? Some theorists have tried to fight off Maskin and Tirole by suggesting that their precise mechanism is not terribly robust to, for instance, assumptions about higher-order beliefs (e.g., Aghion et al (2012) in the QJE). But these quibbles do not contradict the far more basic insight of Maskin and Tirole, that situations we think of empirically as “hard to describe” or “unlikely to occur or be foreseen”, are not sufficient to justify the relevance of incomplete contracts unless we also have some reason to think that all mechanisms which split rent on the basis of future profit, like a mediator, are unavailable. Note that real world contracts regularly include provisions that ex-ante describe how contractual disagreement ex-post should be handled.

Hart’s response, and this is both clear from his CV and from his recent papers and presentations, is to ditch incompleteness as the fundamental reason firms exist. Hart and Moore’s 2007 AER P&P and 2006 QJE are very clear:

Although the incomplete contracts literature has generated some useful insights about firm boundaries, it has some shortcomings. Three that seem particularly important to us are the following. First, the emphasis on noncontractible ex ante investments seems overplayed: although such investments are surely important, it is hard to believe that they are the sole drivers of organizational form. Second, and related, the approach is ill suited to studying the internal organization of firms, a topic of great interest and importance. The reason is that the Coasian renegotiation perspective suggests that the relevant parties will sit down together ex post and bargain to an efficient outcome using side payments: given this, it is hard to see why authority, hierarchy, delegation, or indeed anything apart from asset ownership matters. Finally, the approach has some foundational weaknesses [pointed out by Maskin and Tirole (1999)].

To my knowledge, Oliver Hart has written zero papers since Maskin-Tirole was published which attempt to explain any policy or empirical fact on the basis of residual control rights and their necessary incomplete contracts. Instead, he has been primarily working on theories which depend on reference points, a behavioral idea that when disagreements occur between parties, the ex-ante contracts are useful because they suggest “fair” divisions of rent, and induce shading and other destructive actions when those divisions are not given. These behavioral agents may very well disagree about what the ex-ante contract means for “fairness” ex-post. The primary result is that flexible contracts (e.g., contracts which deliberately leave lots of incompleteness) can adjust easily to changes in the world but will induce spiteful shading by at least one agent, while rigid contracts do not permit this shading but do cause parties to pursue suboptimal actions in some states of the world. This perspective has been applied by Hart to many questions over the past decade, such as why it can be credible to delegate decision making authority to agents; if you try to seize it back, the agent will feel aggrieved and will shade effort. These responses are hard, or perhaps impossible, to justify when agents are perfectly rational, and of course the Maskin-Tirole critique would apply if agents were purely rational.

So where does all this leave us concerning the initial problem of why firms exist in a sea of decentralized markets? In my view, we have many clever ideas, but still do not have the perfect theory. A perfect theory of the firm would need to be able to explain why firms are the size they are, why they own what they do, why they are organized as they are, why they persist over time, and why interfirm incentives look the way they do. It almost certainly would need its mechanisms to work if we assumed all agents were highly, or perfectly, rational. Since patterns of asset ownership are fundamental, it needs to go well beyond the type of hand-waving that makes up many “resource” type theories. (Firms exist because they create a corporate culture! Firms exist because some firms just are better at doing X and can’t be replicated! These are outcomes, not explanations.) I believe that there are reasons why the costs of maintaining relationships – transaction costs – endogenously differ within and outside firms, and that Hart is correct is focusing our attention on how asset ownership and decision making authority affects incentives to invest, but these theories even in their most endogenous form cannot do everything we wanted a theory of the firm to accomplish. I think that somehow reputation – and hence relational contracts – must play a fundamental role, and that the nexus of conflicting incentives among agents within an organization, as described by Holmstrom, must as well. But we still lack the precise insight to clear up this muddle, and give us a straightforward explanation for why we seem to need “little Communist bureaucracies” to assist our otherwise decentralized and almost magical market system.

Nobel Prize 2016 Part I: Bengt Holmstrom

The Nobel Prize in Economics has been announced, and what a deserving prize it is: Bengt Holmstrom and Oliver Hart have won for the theory of contracts. The name of this research weblog is “A Fine Theorem”, and it would be hard to find two economists whose work is more likely to elicit such a description! Both are incredibly deserving; more than five years ago on this site, I discussed how crazy it was that Holmstrom had yet to win!. The only shock is the combination: a more natural prize would have been Holmstrom with Paul Milgrom and Robert Wilson for modern applied mechanism design, and Oliver Hart with John Moore and Sandy Grossman for the theory of the firm. The contributions of Holmstrom and Hart are so vast that I’m splitting this post into two, so as to properly cover the incredible intellectual accomplishments of these two economists.

The Finnish economist Bengt Holmstrom did his PhD in operations research at Stanford, advised by Robert Wilson, and began his career at my alma mater, the tiny department of Managerial Economics and Decision Sciences at Northwestern’s Kellogg School. To say MEDS struck gold with their hires in this era is an extreme understatement: in 1978 and 1979 alone, they hired Holmstrom and his classmate Paul Milgrom (another Wilson student from Stanford), hired Nancy Stokey promoted Nobel laureate Roger Myerson to Associate Professor, and tenured an adviser of mine, Mark Satterthwaite. And this list doesn’t even include other faculty in the late 1970s and early 1980s like eminent contract theorist John Roberts, behavioralist Colin Camerer, mechanism designer John Ledyard or game theorist Ehud Kalai. This group was essentially put together by two senior economists at Kellogg, Nancy Schwartz and Stanley Reiter, who had the incredible foresight to realize both that applied game theory was finally showing promise of tackling first-order economic questions in a rigorous way, and that the folks with the proper mathematical background to tackle these questions were largely going unhired since they often did their graduate work in operations or mathematics departments rather than traditional economics departments. This market inefficiency, as it were, allowed Nancy and Stan to hire essentially every young scholar in what would become the field of mechanism design, and to develop a graduate program which combined operations, economics, and mathematics in a manner unlike any other place in the world.

From that fantastic group, Holmstrom’s contribution lies most centrally in the area of formal contract design. Imagine that you want someone – an employee, a child, a subordinate division, an aid contractor, or more generally an agent – to perform a task. How should you induce them to do this? If the task is “simple”, meaning the agent’s effort and knowledge about how to perform the task most efficiently is known and observable, you can simply pay a wage, cutting off payment if effort is not being exerted. When only the outcome of work can be observed, if there is no uncertainty in how effort is transformed into outcomes, knowing the outcome is equivalent to knowing effort, and hence optimal effort can be achieved via a bonus payment made on the basis of outcomes. All straightforward so far. The trickier situations, which Holmstrom and his coauthors analyzed at great length, are when neither effort nor outcomes are directly observable.

Consider paying a surgeon. You want to reward the doctor for competent, safe work. However, it is very difficult to observe perfectly what the surgeon is doing at all times, and basing pay on outcomes has a number of problems. First, the patient outcome depends on the effort of not just one surgeon, but on others in the operating room and prep table: team incentives must be provided. Second, the doctor has many ways to shift the balance of effort between reducing costs to the hospital, increasing patient comfort, increasing the quality of the medical outcome, and mentoring young assistant surgeons, so paying on the basis of one or two tasks may distort effort away from other harder-to-measure tasks: there is a multitasking problem. Third, the number of medical mistakes, or the cost of surgery, that a hospital ought expect from a competent surgeon depends on changes in training and technology that are hard to know, and hence a contract may want to adjust payments for its surgeons on the performance of surgeons elsewhere: contracts ought take advantage of relevant information when it is informative about the task being incentivized. Fourth, since surgeons will dislike risk in their salary, the fact that some negative patient outcomes are just bad luck means that you will need to pay the surgeon very high bonuses to overcome their risk aversion: when outcome measures involve uncertainty, optimal contracts will weigh “high-powered” bonuses against “low-powered” insurance against risk. Fifth, the surgeon can be incentivized either by payments today or by keeping their job tomorrow, and worse, these career concerns may cause the surgeon to waste the hospital’s money on tasks which matter to the surgeon’s career beyond the hospital.

Holmstrom wrote the canonical paper on each of these topics. His 1979 paper in the Bell Journal of Economics shows that any information which reduces the uncertainty about what an agent actually did should feature in a contract, since by reducing uncertainty, you reduce the risk premium needed to incentivize the agent to accept the contract. It might seem strange that contracts in many cases do not satisfy this “informativeness principle”. For instance, CEO bonuses are often not indexed to the performance of firms in the same industry. If oil prices rise, essentially all oil firms will be very profitable, and this is true whether or not a particular CEO is a good one. Bertrand and Mullainathan argue that this is because many firms with diverse shareholders are poorly governed!

The simplicity of contracts in the real world may have more prosaic explanations. Jointly with Paul Milgrom, the famous “multitasking” paper published in JLEO in 1991 notes that contracts shift incentives across different tasks in addition to serving as risk-sharing mechanisms and as methods for inducing effort. Since bonuses on task A will cause agents to shift effort away from hard-to-measure task B, it may be optimal to avoid strong incentives at all (just pay teachers a salary rather than a bonus based only on test performance) or to split job tasks (pay bonuses to teacher A who is told to focus only on math test scores, and pay salary to teacher B who is meant to serve as a mentor). That outcomes are generated by teams also motivates simpler contracts. Holmstrom’s 1982 article on incentives in teams, published in the Bell Journal, points out that if both my effort and yours is required to produce a good outcome, then the marginal product of our efforts are both equal to the entire value of what is produced, hence there is not enough output to pay each of us our marginal product. What can be done? Alchian and Demsetz had noticed this problem in 1972, arguing that firms exist to monitor the effort of individuals working in teams. With perfect knowledge of who does what, you can simply pay the workers a wage sufficient to make the optimal effort, then collect the residual as profit. Holmstrom notes that the monitoring isn’t the important bit: rather, even shareholder controlled firms where shareholders do no monitoring at all are useful. The reason is that shareholders can be residual claimants for profit, and hence there is no need to fully distribute profit to members of the team. Free-riding can therefore be eliminated by simply paying team members a wage of X if the team outcome is optimal, and 0 otherwise. Even a slight bit of shirking by a single agent drops their payment precipitously (which is impossible if all profits generated by the team are shared by the team), so the agents will not shirk. Of course, when there is uncertainty about how team effort transforms into outcomes, this harsh penalty will not work, and hence incentive problems may require team sizes to be smaller than that which is first-best efficient. A third justification for simple contracts is career concerns: agents work hard today to try to signal to the market that they are high quality, and do so even if they are paid a fixed wage. This argument had been made less formally by Fama, but Holmstrom (in a 1982 working paper finally published in 1999 in RESTUD) showed that this concern about the market only completely mitigates moral hazard if outcomes within a firm were fully observable to the market, or the future is not discounted at all, or there is no uncertainty about agent’s abilities. Indeed, career concerns can make effort provision worse; for example, agents may take actions to signal quality to the market which are negative for their current firm! A final explanation for simple contracts comes from Holmstrom’s 1987 paper with Milgrom in Econometrica. They argue that simple “linear” contracts, with a wage and a bonus based linearly on output, are more “robust” methods of solving moral hazard because they are less susceptible to manipulation by agents when the environment is not perfectly known. Michael Powell, a student of Holmstrom’s now at Northwestern, has a great set of PhD notes providing details of these models.

These ideas are reasonably intuitive, but the way Holmstrom answered them is not. Think about how an economist before the 1970s, like Adam Smith in his famous discussion of the inefficiency of sharecropping, might have dealt with these problems. These economists had few tools to deal with asymmetric information, so although economists like George Stigler analyzed the economic value of information, the question of how to elicit information useful to a contract could not be discussed in any systematic way. These economists would have been burdened by the fact that the number of contracts one could write are infinite, so beyond saying that under a contract of type X does not equate marginal cost to marginal revenue, the question of which “second-best” contract is optimal is extraordinarily difficult to answer in the absence of beautiful tricks like the revelation principle partially developed by Holmstrom himself. To develop those tricks, a theory of how individuals would respond to changes in their joint incentives over time was needed; the ideas of Bayesian equilibria and subgame perfection, developed by Harsanyi and Selten, were unknown before the 1960s. The accretion of tools developed by pure theory finally permitted, in the late 1970s and early 1980s, an absolute explosion of developments of great use to understanding the economic world. Consider, for example, the many results in antitrust provided by Nobel winner Jean Tirole, discussed here two years ago.

Holmstrom’s work has provided me with a great deal of understanding of why innovation management looks the way it does. For instance, why would a risk neutral firm not work enough on high-variance moonshot-type R&D projects, a question Holmstrom asks in his 1989 JEBO Agency Costs and Innovation? Four reasons. First, in Holmstrom and Milgrom’s 1987 linear contracts paper, optimal risk sharing leads to more distortion by agents the riskier the project being incentivized, so firms may choose lower expected value projects even if they themselves are risk neutral. Second, firms build reputation in capital markets just as workers do with career concerns, and high variance output projects are more costly in terms of the future value of that reputation when the interest rate on capital is lower (e.g., when firms are large and old). Third, when R&D workers can potentially pursue many different projects, multitasking suggests that workers should be given small and very specific tasks so as to lessen the potential for bonus payments to shift worker effort across projects. Smaller firms with fewer resources may naturally have limits on the types of research a worker could pursue, which surprisingly makes it easier to provide strong incentives for research effort on the remaining possible projects. Fourth, multitasking suggests agent’s tasks should be limited, and that high variance tasks should be assigned to the same agent, which provides a role for decentralizing research into large firms providing incremental, safe research, and small firms performing high-variance research. That many aspects of firm organization depend on the swirl of conflicting incentives the firm and the market provide is a topic Holmstrom has also discussed at length, especially in his beautiful paper “The Firm as an Incentive System”; I shall reserve discussion of that paper for a subsequent post on Oliver Hart.

Two final light notes on Holmstrom. First, he is the source of one of my favorite stories about Paul Samuelson, the greatest economic theorist of all time. Samuelson was known for having a steel trap of a mind. At a light trivia session during a house party for young faculty at MIT, Holmstrom snuck in a question, as a joke, asking for the name of the third President of independent Finland. Samuelson not only knew the name, but apparently was also able to digress on the man’s accomplishments! Second, I mentioned at the beginning of this post the illustrious roster of theorists who once sat at MEDS. Business school students are often very hesitant to deal with formal models, partially because they lack a technical background but also because there is a trend of “dumbing down” in business education whereby many schools (of course, not including my current department at The University of Toronto Rotman!) are more worried about student satisfaction than student learning. With perhaps Stanford GSB as an exception, it is inconceivable that any school today, Northwestern included, would gather such an incredible collection of minds working on abstract topics whose applicability to tangible business questions might lie years in the future. Indeed, I could name a number of so-called “top” business schools who have nobody on their faculty who has made any contribution of note to theory! There is a great opportunity for a Nancy Schwartz or Stan Reiter of today to build a business school whose students will have the ultimate reputation for rigorous analysis of social scientific questions.

Douglass North, An Economist’s Historian

Sad news today arrives, as we hear that Douglass North has passed away, living only just longer than his two great compatriots in Cliometrics (Robert Fogel) and New Institutional Economics (Ronald Coase). There will be many lovely pieces today, I’m sure, on North’s qualitative and empirical exploration of the rise of institutions as solutions to agency and transaction cost problems, a series of ideas that continues to be enormously influential. No economist today denies the importance of institutions. If economics is the study of the aggregation of rational choice under constraints, as it is sometimes thought to be, then North focused our mind on the origin of the constraints rather the choice or its aggregation. Why do states develop? Why do guilds, and trade laws, and merchant organizations, and courts, appear, and when? How does organizational persistence negatively affect the economy over time, a question pursued at great length by Daron Acemoglu and his coauthors? All important questions, and it is not clear that there are better answers than the ones North provided.

But North was not, first and foremost, a historian. His PhD is in economics, and even late in life he continued to apply the very most cutting edge economic tools to his studies of institutions. I want to discuss today a beautiful piece of his, “The Role of Institutions in the Revival of Trade”, written jointly with Barry Weingast and Paul Milgrom in 1990. This is one of the fundamental papers in “Analytic Narratives”, as it would later be called, a school which applied formal economic theory to historical questions; I have previously discussed here a series of papers by Avner Greif and his coauthors which are the canonical examples.

Here is the essential idea. In the late middle ages, long distance trade, particularly at “Fairs” held in specific places at specific times, arose again in Western Europe. Agency problems must have been severe: how do you keep people from cheating you, from stealing, from selling defective goods, or from reneging on granted credit? A harmonized body of rules, the Merchant Law, appeared across many parts of Western Europe, with local courts granting judgments on the basis of this Law. In the absence of nation-states, someone with a negative judgment could simply leave the local city where the verdict was given. The threat of not being able to sell in the future may have been sufficient to keep merchants fair, but if the threat of future lost business was the only credible punishment, then why were laws and courts needed at all? Surely merchants could simply let it be known that Johann or Giuseppe is a cheat, and that one shouldn’t deal with them? There is a puzzle here, then: it appears that the set of punishments the Merchant Law could give are identical to the set of “punishments” one receives for having a bad reputation, so why then did anybody bother with courts and formal rules? In terms of modern theory, if relational contracts and formal contracts can offer identical punishments for deviating from cooperation, and formal contracts are costly, then why doesn’t everyone simply rely on relational contracts?

Milgrom, North and Weingast consider a simple repeated Prisoner’s Dilemma. Two agents with a sufficiently high discount rate can sustain cooperation in a Prisoner’s Dilemma using tit-for-tat: if you cheat me today, I cheat you tomorrow. Of course, the Folk Theorem tells us that cooperation can be sustained using potentially more complex punishment strategies in infinitely repeated games with any number of players, although a fundamental idea in the repeated games literature is that it may be necessary to punish people who do not themselves punish when they are meant to do so. In a repeated prisoner’s dilemma with an arbitrary number of players who randomly match each period, cooperation can be sustained in a simple way: you cheat anyone you match with if they cheated their previous trading partner and their previous trading partner did not themselves cheat their partner two rounds ago, and otherwise cooperate.

The trick, though, is that you need to know the two-periods-back history of your current trading partner and their last trading partner. Particularly with long-distance trade, you might frequently encounter traders you don’t know even indirectly. Imagine that every period you trade with someone you have never met before, and who you will never meet again (the “Townsend turnpike”, with two infinite lines of traders moving in opposite directions), and imagine that you do not know the trading history of anyone you match with. In this incomplete information game, there is no punishment for cheating: you cheat the person you match with today, and no one you meet with tomorrow will ever directly or indirectly learn about this. Hence cooperation is not sustained.

What we need, then, is an institution that first collects a sufficient statistic for the honesty of traders you might deal with, that incentivizes merchants to bother to check this sufficient statistic and punish people who have cheated, and that encourages people to report if they have been cheated even if this reporting is personally costly. That is, “institutions must be designed both to keep the traders adequately informed of their responsibilities and to motivate them to do their duties.”

Consider an institution LM. When you are matched with a trading partner, you can query LM at cost Q to find out if there are any “unpaid judgments” against your trading partner, and this query is common knowledge to you and your partner. You and your partner then play a trading game which is a Prisoner’s Dilemma. After trading, and only if you paid the query cost Q, when you have been cheated you can pay another cost C to take your trading partner to trial. If your partner cheated you in the Prisoner’s Dilemma and you took them to trial, you win a judgment penalty of J which the cheater can either voluntarily pay you at cost c(J) or which the cheater can ignore. If the cheater doesn’t pay a judgment, LM lists them as having “unpaid judgments”.

Milgrom, North and Weingast show that, under certain conditions, the following is an equilibrium where everyone always cooperates: if you have no unpaid judgments, you always query LM. If no one queries LM, or if there are unpaid judgments against your trading partner, you defect in the Prisoner’s Dilemma, else you cooperate. If both parties queried LM and only one defects in the Prisoner’s Dilemma, the other trader pays cost C and takes the cheater to the LM for judgment. The conditions needed for this to be an equilibrium are that penalties for cheating are high enough, but not so high that cheaters prefer to retire to the countryside rather than pay them, and that the cost of querying LM is not too high. Note how the LM equilibrium encourages anyone to pay the personal cost of checking their trading partner’s history: if you don’t check, then you can’t go to LM for judgment if you are cheated, hence you will definitely be cheated. The LM also encourages people to pay the personal cost of putting a cheater on trial, because that is the only way to get a judgment decision, and that judgment is actually paid in equilibrium. Relying on reputation in the absence of an institution may not work if communicating reputation of someone who cheated you is personally costly: if you need to print up posters that Giuseppe cheated you, but can otherwise get no money back from Giuseppe, you are simply “throwing good money after bad” and won’t bother. The LM institution provides you an incentive to narc on the cheats.

Note also that in equilibrium, the only cost of the system is the cost of querying, since no one cheats. That is, in the sense of transactions costs, the Law Merchant may be a very low-cost institution: it generates cooperation even though only one piece of information, the existence of unpaid judgments, needs to be aggregated and communicated, and it generates cooperation among a large set of traders that never personally interact by using a single centralized “record-keeper”. Any system that induces cooperation must, at a minimum, inform a player whether their partner has cheated in the past. The Law Merchant system does this with no other costs in equilibrium, since in equilibrium, no one cheats, no one goes for judgment, and no resources are destroyed paying fines.

That historical institutions develop largely to limit transactions costs is a major theme in North’s work, and this paper is a beautiful, highly formal, explication of that broad Coasean idea. Our motivating puzzle – why use formal institutions when reputation provides precisely the same potential for punishment? – can be answered simply by noting that reputation requires information, and the cost-minimizing incentive-compatible way to aggregate and share that information may require an institution. The Law Merchant arises not because we need a way to punish offenders, since in the absence of the nation-state the Law Merchant offers no method for involuntary punishment beyond those that exist in its absence; and yet, in its role reducing costs in the aggregation of information, the Law proves indispensable. What a beautiful example of how theory can clarify our observations!

“The Role of Institutions in the Revival of Trade” appeared in Economics and Politics 1.2, March 1990, and extensions of these ideas to long distance trade with many centers are considered in the papers by Avner Greif and his coauthors linked at the beginning of this post. A broad philosophical defense of the importance of transaction costs to economic history is North’s 1984 essay in the Journal of Institutional and Theoretical Economics. Two other titans of economics have also recently passed away, I’m afraid. Herbert Scarf, the mathematician whose work is of fundamental importance to modern market design, was eulogized by Ricky Vohra and Al Roth. Nate Rosenberg, who with Zvi Griliches was the most important thinker on the economics of invention, was memorialized by Joshua Gans and Joel West.

Nobel Prize 2014: Jean Tirole

A Nobel Prize for applied theory – now this something I can get behind! Jean Tirole’s prize announcement credits him for his work on market power and regulation, and there is no question that he is among the leaders, if not the world leader, in the application of mechanism design theory to industrial organization; indeed, the idea of doing IO in the absence of this theoretical toolbox seems so strange to me that it’s hard to imagine anyone had ever done it! Economics is sometimes defined by a core principle that agents – people or firms – respond to incentives. Incentives are endogenous; how my bank or my payment processor or my lawyer wants to act depends on how other banks or other processors or other prosecutors act. Regulation is therefore a game. Optimal regulation is therefore a problem of mechanism design, and we now have mathematical tools that allow investigation across the entire space of potential regulating mechanisms, even those that our counterfactual. That is an incredibly powerful methodological advance, so powerful that there will be at least one more Nobel (Milgrom and Holmstrom?) based on this literature.

Because Tirole’s toolbox is theoretical, he has written an enormous amount of “high theory” on the implications of the types of models modern IO economists use. I want to focus in this post on a particular problem where Tirole has stood on both sides of the divide: that of the seemingly obscure question of what can be contracted on.

This literature goes back to a very simple question: what is a firm, and why do they exist? And when they exist, why don’t they grow so large that they become one giant firm a la Schumpeter’s belief in Capitalism, Socialism, and Democracy? One answer is that given by Coase and updated by Williamson, among many others: transaction costs. There are some costs of haggling or similar involved in getting things done with suppliers or independent contractors. When these costs are high, we integrate that factor into the firm. When they are low, we avoid the bureaucratic costs needed to manage all those factors.

For a theorist trained in mechanism design, this is a really strange idea. For one, what exactly are these haggling or transaction costs? Without specifying what precisely is meant, it is very tough to write a model incorporating them and exploring the implications of them. But worse, why would we think these costs are higher outside the firm than inside? A series of papers by Sandy Grossman, Oliver Hart and John Moore point out, quite rightly, that firms cannot make their employees do anything. They can tell them to do something, but the employees will respond to incentives like anyone else. Given that, why would we think the problem of incentivizing employees within an organization is any easier or harder than incentivizing them outside the organization? The solution they propose is the famous Property Rights Theory of the firm (which could fairly be considered the most important paper ever published in the illustrious JPE). This theory says that firms are defined by the assets they control. If we can contract on every future state of the world, then this control shouldn’t matter, but when unforeseen contingencies arise, the firm still has “residual control” of its capital. Therefore, efficiency depends on the allocation of scarce residual control rights, and hence the allocation of these rights inside or outside of a firm are important. Now that is a theory of the firm – one well-specified and based on incentives – that I can understand. (An interesting sidenote: when people think economists don’t really understand the economy because, hey, they’re not rich, we can at least point to Sandy Grossman. Sandy, a very good theorist, left academia to start his own firm, and as far as I know, he is now a billionaire!)

Now you may notice one problem with Grossman, Hart and Moore’s papers. As there was an assumption of nebulous transaction costs in Coase and his followers, there is a nebulous assumption of “incomplete contracts” in GHM. This seems reasonable at first glance: there is no way we could possibly write a contract that covers every possible contingency or future state of the world. I have to imagine everyone that has ever rented an apartment or leased a car or ran a small business has first-hand experience with the nature of residual control rights when some contingency arises. Here is where Tirole comes in. Throughout the 80s and 90s, Tirole wrote many papers using incomplete contracts: his 1994 paper with Aghion on contracts for R&D is right within this literature. In complete contracting, the courts can verify and enforce any contract that relies on observable information, though adverse selection (hidden information by agents) or moral hazard (unverifiable action by agents) may still exist. Incomplete contracting further restricts the set of contracts to a generally simple set of possibilities. In the late 1990s, however, Tirole, along with his fellow Nobel winner Eric Maskin, realized in an absolute blockbuster of a paper that there is a serious problem with these incomplete contracts as usually modeled.

Here is why: even if we can’t ex-ante describe all the future states of the world, we may still ex-post be able to elicit information about the payoffs we each get. As Tirole has noted, firms do not care about indescribable contingencies per se; they only care about how those contingencies affect their payoffs. That means that, at an absolute minimum, the optimal “incomplete contract” better be at least as good as the optimal contract which conditions on elicited payoffs. These payoffs may be stochastic realizations of all of our actions, of course, and hence this insight might not actually mean we can first-best efficiency when the future is really hard to describe. Maskin and Tirole’s 1999 paper shows, incredibly, that indescribability of states is irrelevant, and that even if we can’t write down a contract on states of the world, we can contract on payoff realizations in a way that is just as good as if we could actually write the complete contract.

How could this be? Imagine (here via a simple example of Maskin’s) two firms contracting for R&D. Firm 1 exerts effort e1 and produces a good with value v(e1). Firm 2 invests in some process that will lower the production cost of firm 1’s new good, investing e2 to make production cost equal to c(e2). Payoffs, then, are u1(p-c(e2)-e1) and u2(v(e1)-p-e2). If we knew u1 and u2 and could contract upon it, then the usual Nash implementation literature tells us how to generate efficient levels of e1 and e2 (call them e1*, e2*) by writing a contract: if the product doesn’t have the characteristics of v(e1*) and the production process doesn’t have the characteristics of c(e2*), then we fine the person who cheated. If effort generated stochastic values rather than absolute ones, the standard mechanism design literature tells us exactly when we can still get the first best.

Now, what if v and c are state-dependent, and there are huge number of states of the world? That is, efficient e1* and e2* are now functions of the state of the world realized after we write the initial contract. Incomplete contracting assumed that we cannot foresee all the possible v and c, and hence won’t write a contract incorporating all of them. But, aha!, we can still write a contract that says, look, whatever happens tomorrow, we are going to play a game tomorrow where I say what my v is and you say what your c is. It turns out that there exists such a game which generates truthful revelation of v and c (Maskin and Tirole do this using an idea similar to that of the subgame implementation literature, but the exact features are not terribly important for our purposes). Since the only part of the indescribable state I care about is the part that affects my payoffs, we are essentially done: no matter how many v and c’s there could be in the future, as long as I can write a contract specifying how we each get other to truthfully say what those parameters are, this indescribability doesn’t matter.

Whoa. That is a very, very, very clever insight. Frankly, it is convincing enough that the only role left for property rights theories of the firm are some kind of behavioral theory which restricts even contracts of the Maskin-Tirole sense – and since these contracts are quite a bit simpler in some way than the hundreds of pages of legalese which we see in a lot of real-world contracts on important issues, it’s not clear that bounded rationality or similar theories will get us far.

Where to go from here? Firms, and organizations more generally, exist. I am sure the reason has to do with incentives. But exactly why – well, we still have a lot of work to do in explaining why. And Tirole has played a major role in explaining why.

Tirole’s Walras-Bowley lecture, published in Econometrica in 1999, is a fairly accessible introduction to his current view of incomplete contracts. He has many other fantastic papers, across a wide variety of topics. I particularly like his behavioral theory written mainly with Roland Benabou; see, for instance, their 2003 ReStud on when monetary rewards are bad for incentives.

“Dynamic Commercialization Strategies for Disruptive Technologies: Evidence from the Speech Recognition Industry,” M. Marx, J. Gans & D. Hsu (2014)

Disruption. You can’t read a book about the tech industry without Clayton Christensen’s Innovator’s Dilemma coming up. Jobs loved it. Bezos loved it. Economists – well, they were a bit more confused. Here’s the story at its most elemental: in many industries, radical technologies are introduced. They perform very poorly initially, and so are ignored by the incumbent. These technologies rapidly improve, however, and the previously ignored entrants go on to dominate the industry. The lesson many tech industry folks take from this is that you ought to “disrupt yourself”. If there is a technology that can harm your most profitable business, then you should be the one to develop it; take Amazon’s “Lab126” Kindle skunkworks as an example.

There are a couple problems with this strategy, however (well, many problems actually, but I’ll save the rest for Jill Lepore’s harsh but lucid takedown of the disruption concept which recently made waves in the New Yorker). First, it simply isn’t true that all innovative industries are swept by “gales of creative destruction” – consider automobiles or pharma or oil, where the major players are essentially all quite old. Gans, Hsu and Scott Stern pointed out in a RAND article many years ago that if the market for ideas worked well, you would expect entrants with good ideas to just sell to incumbents, since the total surplus would be higher (less duplication of sales assets and the like) and since rents captured by the incumbent would be higher (less product market competition). That is, there’s no particular reason that highly innovative industries require constant churn of industry leaders.

The second problem concerns disrupting oneself or waiting to see which technologies will last. Imagine it is costly to investigate potentially disruptive technologies for the incumbent. For instance, selling mp3s in 2002 would have cannibalized existing CD sales at a retailer with a large existing CD business. Early on, the potentially disruptive technology isn’t “that good”, hence it is not in and of itself that profitable. Eventually, some of these potentially disruptive technologies will reveal themselves to actually be great improvements on the status quo. If that is the case, then, why not just let the entrant make these improvements/drive down costs/learn about market demand, and then buy them once they reveal that the potentially disruptive product is actually great? Presumably the incumbent even by this time still retains its initial advantage in logistics, sales, brand, etc. By waiting and buying instead of disrupting yourself, you can still earn those high profits on the CD business in 2002 even if mp3s had turned out to be a flash in the pan.

This is roughly the intuition in a new paper by Matt Marx – you may know his work on non-compete agreements – Gans and Hsu. Matt has also collected a great dataset from industry journals on every firm that ever operated in automated speech recognition. Using this data, the authors show that a policy by entrants of initial competition followed by licensing or acquisition is particularly common when the entrants come in with a “disruptive technology”. You should see these strategies, where the entrant proves the value of their technology and the incumbent waits to acquire, in industries where ideas are not terribly appropriable (why buy if you can steal?) and entry is not terribly expensive (in an area like biotech, clinical trials and the like are too expensive for very small firms). I would add that you also need complementary assets to be relatively hard to replicate; if they aren’t, the incumbent may well wind up being acquired rather than the entrant should the new technology prove successful!

Final July 2014 working paper (RePEc IDEAS). The paper is forthcoming in Management Science.

On Coase’s Two Famous Theorems

Sad news today that Ronald Coase has passed away; he was still working, often on the Chinese economy, at the incredible age of 102. Coase is best known to economists for two statements: that transaction costs explain many puzzles in the organization of society, and that pricing for durable goods presents a particular worry since even a monopolist selling a durable good needs to “compete” with its future and past selves. Both of these statements are horribly, horribly misunderstood, particularly the first.

Let’s talk first about transaction costs, as in “The Nature of the Firm” and “The Problem of Social Cost”, which are to my knowledge the most cited and the second most cited papers in economics. The Problem of Social Cost leads with its famous cattle versus crops example. A farmer wishes to grow crops, and a rancher wishes his cattle to roam where the crops grow. Should we make the rancher liable for damage to the crops (or restrain the rancher from letting his cattle roam at all!), or indeed ought we restrain the farmer from building a fence where the cattle wish to roam? Coase points out that in some sense both parties are causally responsible for the externality, that there is some socially efficient amount of cattle grazing and crop planting, and that if a bargain can be reached costlessly, then there is some set of side payments where the rancher and the farmer are both better off than having the crops eaten or the cattle fenced. Further, it doesn’t matter whether you give grazing rights to the cattle and force the farmer to pay for the “right” to fence and grow crops, or whether you give farming rights and force the rancher to pay for the right to roam his cattle.

This basic principle applies widely in law, where Coase had his largest impact. He cites a case where confectioner machines shake a doctor’s office, making it impossible for the doctor to perform certain examinations. The court restricts the ability of the confectioner to use the machine. But Coase points out that if the value of the machine to the confectioner exceeds the harm of shaking to the doctor, then there is scope for a mutually beneficial side payment whereby the machine is used (at some level) and one or the other is compensated. A very powerful idea indeed.

Powerful, but widely misunderstood. I deliberately did not mention property rights above. Coase is often misunderstood (and, to be fair, he does at points in the essay imply this misunderstanding) as saying that property rights are important, because once we have property rights, we have something that can “be priced” when bargaining. Hence property rights + externalities + no transaction costs should lead to no inefficiency if side payments can be made. Dan Usher famously argued that this is “either tautological, incoherent, or wrong”. Costless bargaining is efficient tautologically; if I assume people can agree on socially efficient bargains, then of course they will. The fact that side payments can be agreed upon is true even when there are no property rights at all. Coase says that “[i]t is necessary to know whether the damaging business is liable or not for damage since without the establishment of this initial delimitation of rights there can be no market transactions to transfer and recombine them.” Usher is correct: that statement is wrong. In the absence of property rights, a bargain establishes a contract between parties with novel rights that needn’t exist ex-ante.

But all is not lost for Coase. Because the real point of his paper begins with Section VI, not before, when he notes that the case without transaction costs isn’t the interesting one. The interesting case is when transaction costs make bargaining difficult. What you should take from Coase is that social efficiency can be enhanced by institutions (including the firm!) which allow socially efficient bargains to be reached by removing restrictive transaction costs, and particularly that the assignment of property rights to different parties can either help or hinder those institutions. One more thing to keep in mind about the Coase Theorem (which Samuelson famously argued was not a theorem at all…): Coase implicitly is referring to Pareto efficiency in his theorem, but since property rights are an endowment, we know from the Welfare Theorems that benefits exceeds costs is not sufficient for maximizing social welfare.

Let’s now consider the Coase Conjecture: this conjecture comes, I believe, from a very short 1972 paper, Durability and Monopoly. The idea is simple and clever. Let a monopolist own all of the land in the US. If there was a competitive market in land, the price per unit would be P and all Q units will be sold. Surely a monopolist will sell a reduced quantity Q2 less than Q at price P2 greater than P? But once those are sold, we are in trouble, since the monopolist still has Q-Q2 units of land. Unless the monopolist can commit to never sell that additional land, we all realize he will try to sell it sometime later, at a new maximizing price P3 which is greater than P but less than P2. He then still has some land left over, which he will sell even cheaper in the next period. Hence, why should anyone buy in the first period, knowing the price will fall (and note that the seller who discounts the future has the incentive to make the length between periods of price cutting arbitrarily short)? The monopolist with a durable good is thus unable to make rents. Now, Coase essentially never uses mathematical theorems in his papers, and you game theorists surely can see that there are many auxiliary assumptions about beliefs and the like running in the background here.

Luckily, given the importance of this conjecture to pricing strategies, antitrust, auctions, etc., there has been a ton of work on the problem since 1972. Nancy Stokey (article gated) has a famous paper written here at MEDS showing that the conjecture only holds strictly when the seller is capable of selling in continuous time and the buyers are updating beliefs continuously, though approximate versions of the conjecture hold when periods are discrete. Gul, Sonnenschein and Wilson flesh out the model more completely, generally showing the conjecture to hold in well-defined stationary equilibrium across various assumptions about the demand curve. McAfee and Wiseman show in a recent ReStud that even the tiniest amount of “capacity cost”, or a fee that must be paid in any period for X amount of capacity (i.e., the need to hire sales agents for the land), destroys the Coase reasoning. The idea is that in the final few periods, when I am selling to very few people, even a small capacity cost is large relative to the size of the market, so I won’t pay it; backward inducting, then, agents in previous periods know it is not necessarily worthwhile to wait, and hence they buy earlier at the higher price. It goes without saying that there are many more papers in the formal literature.

(Some final notes: Coase’s Nobel lecture is well worth reading, as it summarizes the most important thread in his work: “there [are] costs of using the pricing mechanism.” It is these costs that explain why, though markets in general have such amazing features, even in capitalist countries there are large firms run internally as something resembling a command state. McCloskey has a nice brief article which generally blames Stigler for the misunderstanding of Coase’s work. Also, while gathering some PDFs for this article, I was shocked to see that Ithaka, who run JSTOR, is now filing DMCA takedowns with Google against people who host some of these legendary papers (like “Problem of Social Cost”) on their academic websites. What ridiculousness from a non-profit that claims its mission is to “help the academic community use digital technologies to preserve the scholarly record.”)

“What Determines Productivity,” C. Syverson (2011)

Chad Syverson, along with Nick Bloom, John van Reenen, Pete Klenow and many others, has been at the forefront of a really interesting new strand of the economics literature: persistent differences in productivity. Syverson looked at productivity differences within 4-digit SIC industries in the US (quite narrow industries like “Greeting Cards” or “Industrial Sealants”) a number of years back, and found that in the average industry, the 90-10 ratio of total factor productivity plants was almost 2. That is, the top decile plant in the average industry produced twice as much output as the bottom decline plant, using exactly the same inputs! Hsieh and Klenow did a similar exercise in China and India and found even starker productivity differences, largely due a big left-tail of very low productivity firms. This basic result is robust to different measures of productivity, and to different techniques for identifying differences; you can make assumptions which let you recover a Solow residual directly, or run a regression (adjusting for differences in labor and capital quality, or not), or look at deviations like firms having higher marginal productivity of labor than the wage rate, etc. In the paper discussed in the post, Syverson summarizes the theoretical and empirical literature on persistent productivity differences.

Why aren’t low productivity firms swept from the market? We know from theory that if entry is allowed, potentially infinite and instantaneous, then no firm can remain which is less productive than the entrants. This suggests that persistence of inefficient firms must result from either limits on entry, limits on expansion by efficient firms, or non-immediate efficiency because of learning-by-doing or similar (a famous study by Benkard of a Lockwood airplane showed that a plant could produce a plane with half the labor hours after producing 30, and half again after producing 100). Why don’t inefficient firms already in the market adopt best practices? This is related to the long literature on diffusion, which Syverson doesn’t cover in much detail, but essentially it is not obvious to a firm whether a “good” management practice at another firm is actually good or not. Everett Rogers, in his famous “Diffusion of Innovations” book, refers to a great example of this from Peru in the 1950s. A public health consultant was sent for two years to a small village, and tried to convince the locals to boil their water before drinking it. The water was terribly polluted and the health consequences of not boiling were incredible. After two years, only five percent of the town adopted the “innovation” of boiling. Some didn’t adopt because it was too hard, many didn’t adopt because of a local belief system that suggested only the already-sick ought drink boiled water, some didn’t adopt because they didn’t trust the experience of the advisor, et cetera. Diffusion is difficult.

Ok, so given that we have inefficient firms, what is the source of the inefficiency? It is difficult to decompose all of the effects. Learning-by-doing is absolutely relevant in many industries – we have plenty of evidence on this count. Nick Bloom and coauthors seem to suggest that management practices play a huge role. They have shown clear correlation between “best practice” management and high TFP across firms, and a recent randomized field experiment in India (discussed before on this site) showed massive impacts on productivity from management improvements. Regulation and labor/capital distortions also appear to play quite a big role. On this topic, James Schmitz wrote a very interesting paper, published in 2005 in the JPE, on iron ore producers. TFP in Great Lakes ore had been more or less constant for many decades, with very little entry or foreign competition until the 1980s. Once Brazil began exporting ore to the US, labor productivity doubled within a handful of years, and capital and total factor productivity also soared. A main driver of the change was more flexible workplace rules.

Final version in 2011 JEP (IDEAS version). Syverson was at Kellogg recently presenting a new paper of his, with an all-star cast of coauthors, on the medical market. It’s well worth reading. Medical productivity is similarly heterogeneous, and since the medical sector is coming up on 20% of GDP, the sources of inefficiency in medicine are particularly important!

“Decentralization, Hierarchies and Incentives: A Mechanism Design Perspective,” D. Mookherjee (2006)

Lerner, Hayek, Lange and many others in the middle of the 20th century wrote exhaustively about the possibility for centralized systems like communism to perform better than decentralized systems like capitalism. The basic tradeoff is straightforward: in a centralized system, we can account for distributional concerns, negative externalities, etc., while a decentralized system can more effectively use local information. This type of abstract discussion about ideal worlds actually has great applications even to the noncommunist world: we often have to decide between centralization or decentralization within the firm, or within the set of regulators. I am continually amazed by how often the important Hayekian argument is misunderstood. The benefit of capitalism can’t have much to do with profit incentives per se, since (almost) every employee of a modern firm is a not an owner, and hence is incentivized to work hard only by her labor contract. A government agency could conceivably use precisely the same set of contracts and get precisely the same outcome as the private firm (the principle-agent problem is identical in the two cases). The big difference is thus not profit incentive but the use of dispersed information.

Mookherjee, in a recent JEL survey, considers decentralization from the perspective of mechanism design. What is interesting here is that, if the revelation principle applies, there is no reason to use any decentralized decisionmaking system over a centralized one where the boss tells everyone exactly what they should do. That is, any contract where I could subcontract to A who then subsubcontracts to B is weakly dominated by a contract where I get both A and B to truthfully reveal their types and then contract with each myself. The same logic applies, for example, to whether a firm should have middle management or not. This suggests that if we want to explain decentralization in firms, we have only two roads to go down: first, show conditions where decentralization is equally good to centralization, or second, investigate cases where the revelation principle does not apply. In the context of recent discussions on this site of what “good theory” is, I would suggest that this is a great example of a totally nonpredictive theorem (revelation) being quite useful (in narrowing down potential explanations of decentralization) to a specific set of users (applied economic theorists).

(I am assuming most readers of a site like this are familiar with the revelation principle, but if not, it is just a couple lines of math to prove. Assume agents have information or types a in a set A. If I write them a contract F, they will tell me their type is G(a)=a’ where G is just a function that, for all a in A, chooses a’ to maximize u(F(a’)), where u is the utility the agent gets from the contract F by reporting a’. The contract given to an agent of type a, then, leads to outcome F(G(a)). If this contract exists, then just let H be “the function concatenating F(G(.))”. H is now a “truthful” contract, since it is in each agent’s interest just to reveal their true type. That is, the revelation principle guarantees that any outcome from a mechanism, no matter how complicated or involving how many side payments or whatever, can be replicated by a contract where each agent just states what they know truthfully to the principal.)

First, when can we do just as well with decentralization and centralization even when the revelation principle applies? Consider choosing whether to (case 1) hire A who also subcontracts some work to B, or (case 2) just hiring both A and B directly. If A is the only one who knows B’s production costs, then A will need to get informational rents in case 1 unless A and B produce perfectly complementary goods: without such rents, A has an incentive to produce a larger share of production by reporting that B is a high cost producer. Indeed, A is essentially “extracting” information rents both from B and from the principal by virtue of holding information that the principal cannot access. A number of papers have shown that this problem can be eliminated if A is risk-neutral and has an absence of limited liability (so I can tax away ex-ante information rents), contracting is top-down (I contract with A before she learns B’s costs), and A’s production quantity is known (so I can optimally subsidize or tax this production).

More interesting is to consider when revelation fails. Mookherjee notes that the proof of the revelation principle requires 1) noncollusion among agents, 2) absence of communication costs, information processing costs, or contract complexity costs, and 3) no possibility of ex-post contract renegotiation by the principal. I note here that both the present paper, and the hierarchy literature in general, tends to shy away from ongoing relationships, but these are obviously relevant in many cases, and we know that in dynamic mechanism design, the revelation principle will not hold. The restricted message space literature is still rather limited, mainly because mechanism design theory at this point does not give any simple results like the revelation principle when the message space is restricted. It’s impossible to go over every result Mookherjee describes – this is a survey paper after all – but here is a brief summary. Limited message spaces are not a panacea since the restrictions required for limited message space to motivate decentralization, and particularly middle management, are quite strong. Collusion among agents does offer some promise, though. Imagine A and B are next to each other on an assembly line, and B can see A’s effort. The principal just sees whether the joint production is successful or not. For a large number of parameters, Baliga and Sjostrom (1998) proved that delegation is optimal: for example, pay B a wage conditional on output, and let him and A negotiate on the side how to divvy up that payment.

Much more work on the design of organizations is needed, that is for sure. (Final working paper – published in June 2006 JEL)

“Collaborating,” A. Bonatti & J. Horner (2011)

(Apologies for the long delay since the last post. I’ve been in that tiniest of Southeast Asian backwaters, East Timor, talking to UN and NGO folks about how the new democracy is coming along. The old rule of thumb is that you need 25 years of free and fair elections before society consolidates a democracy, but we still have a lot to learn about how that process takes place. I have some theoretical ideas about how to avoid cozy/corrupt links between government ministers and the private sector in these unconsolidated democracies, and I wanted to get some anecdotes which might guide that theory. And in case you’re wondering: I would give pretty high odds that, for a variety of reasons, the Timorese economy is going absolutely nowhere fast. Now back to the usual new research summaries…)

Teamwork is essential, you’re told from kindergarten on. But teamwork presents a massive moral hazard problem: how do I make sure the other guy does his share? In the static setting, Alchain-Demsetz (1972) and a series of papers by Holmstrom (May He Win His Deserved Nobel) have long ago discussed why people will free ride when their effort is hidden, and what contracts can be written to avoid this problem. Bonatti and Horner make the problem dynamic, and with a few pretty standard tricks from optimal control develop some truly counterintuitive results.

The problem is the following. N agents are engaged in working on a project which is “good” with probability p. Agents exert costly effort continuously over time. Depending on the effort exerted by agents at any given time, a breakthrough occurs with some probability if the project is good, but never occurs if the project is bad. Over time, given effort along the equilibrium path, agents become more and more pessimistic about the project being good if no breakthrough occurs. The future is discounted. Agents only observe their own effort choice (but have correct beliefs about the effort of others in equilibrium). This means that off-path, beliefs of effort exertion are not common knowledge: if I deviate and work harder now, and no breakthrough occurs, then I am more pessimistic than others about the goodness of the project since I know, and they don’t, that a higher level of effort was put in.

In this setting, not only do agents shirk (hoping the other agents will pick up the slack), but they also procrastinate. Imagine a two-period world. In a two period world, I can shift some effort to period 2, in the hope that the other agent’s period 1 effort will lead to a success. I don’t want to work extremely hard in period 1 when all that this leads to is wasted effort because my teammate has already solved the problem in that period. Note that this procrastination motive is not optimal when the team is of size 1: you need a coauthor to justify your slacking! Better monitoring here does not help, surprisingly. If I can see how much effort my opponent puts in each period, then what happens? If I decrease my period 1 effort, and this is observable by both agents, then my teammate will not be so pessimistic about the success of the project in period 2. Hence, she will work harder in period 2. Hence, each agent has an incentive to work less in period 1 vis-a-vis the hidden action case. (Of course, you may wonder why this is an equilibrium; that is, why doesn’t the teammate play grim trigger and punish me for shirking? It turns out there are a number of reasonable equilibria in the case with observable actions, some of which give higher welfare and some of which give lower welfare than under hidden action. The point is just that allowing observability doesn’t necessarily help things.)

So what have we learned? Three things in particular. First, work in teams gives extra incentive to procrastinate compared to solo work. Second, this means that setting binding deadlines can be welfare improving; the authors further show that the larger the team, the tighter the deadline necessary. Third, letting teams observe how hard the other is working is not necessarily optimal. Surely observability by a principal would be welfare-enhancing – the contract could be designed to look like dynamic Holmstrom – but observability between the agents is not necessarily so. Interesting stuff. (Final Cowles Foundation WP – paper published in April 2011 AER)

“Organizations as Information Processing Systems,” R. Daft & R. Lengel (1983)

I don’t believe this paper is well-known by economists, but it has been hugely influential for management and media studies. The theory in this paper is qualitative in the same way economic theory is, but is not mathematical. In this post, I’ll try to reinterpret the main ideas mathematically.

Firms face two primary types of uncertainty. First, the outside environment is uncertain. Second, the internal environment is uncertain. When speech is vague, a manager may misinterpret what the true state of the world is, or subordinates may misinterpret the goals of the organization. When speech is precise, it can be very costly to interpret. Indeed, precise speech about unclear goals is basically worthless: two subordinates may precisely state the answer to two different problems, both of which are different from what the manager wanted to know.

Choice of media, then, can vary. Sometimes speech within an organization is very formal: quantitative models, memos, etc. Sometimes it is informal: face-to-face meetings, informal legends, company lore. The informal speech is able to discuss a broader set of ideas, but with greater ambiguity. The formal speech can present specific ideas exactly, but nothing more. This tradeoff roughly implies the following: when the purpose of a discussion is equivocal or unclear, informal speech should be used to “get us on the same page”. When a discussion involves something routine, precise speech can be used. This has a number of implications: for example, informal communication will be most common at the goal setting stage, or when two different departments are beginning to work together on a task, but formal communication will be most common within a division or after goals have been agreed upon by all parties or when the external environment has less uncertainty.

Clearly, the intersection of language and economics is far more general. For example, equivocality is often introduced on purpose: people speak vaguely, for example, in order than common knowledge does not develop. An example, after a first date: “Would you like to come up to my apartment for some coffee?” Further, vague and precise speech are more than simply vague or precise, but rather are vague and precise in particular ways. Poetry is quoted rather than a meaningless stream of words, for example. Neither the authors or I have much to say on these extensions, but it is definitely an open field right now for some interested researcher.

How might you model the ideas of the present paper mathematically? (Of course, you might ask why these ideas should be modeled mathematically anyway, but I have discussed many times here why social science theory ought be formal, and to the extent that it’s formal, the tools of mathematical logic allow the cleanest possible transmission of ideas and derivation of unexpected consequences, so I won’t rehash those arguments here. Indeed, the whole “should we be formal” discussion seems a bit too meta in the context of this post…) Let the relevant true state be a number in [0,1]^n. Let transmission of the exact state be increasing in its dimension, perhaps linearly. Let transmission of imprecise information be increasing less than linearly, perhaps logarithmically. Imprecise states are interpreted by the receiver with error (something like the truncated exponential version of a normal distribution to ensure we stay in [0,1]^n). Loss functions of the final decision made by the receiver depend on distance from the true state. What should a manager do? Well, on simple decisions where the relevant state is only a point on the line segment [0,1], getting the exact state is cheap, so subordinates should send the manager fairly precise information like a statistical estimate in a memo. On complex decisions, where the relevant state is a point in the 100-dimension [0,1] hypercube, learning the true state will be very expensive (it may require the manager to read a 1000 page quantitative report, for instance), but learning an approximate state will be relatively cheap (it may involve some face-to-face conversations). Once the model is formalized like this, then we can answer questions like “Should management communicate via a hierarchy or not?” I have some plans for work along these lines, using some ideas about transmitting counterfactuals given a set of information partitions, and would definitely appreciate comments concerning how to model this type of media richness. (Working paper)

%d bloggers like this: