“The Power of Communication,” D. Rahman (2014)

(Before getting to Rahman’s paper, a quick note on today’s Clark Medal, which went to Roland Fryer, an economist at Harvard who is best known for his work on the economics of education. Fryer is no question a superstar, and is unusual in leaving academia temporarily while still quite young to work for the city of New York on improving their education policy. His work is a bit outside my interests, so I will leave more competent commentary to better informed writers.

The one caveat I have, however, is the same one I gave last year: the AEA is making a huge mistake in essentially changing this prize from “Best Economist Under 40” to “Best Applied Microeconomist Under 40”. Of the past seven winners, the only one who isn’t obviously an applied microeconomist is Levin, and yet even he describes himself as “an applied economist with interests in industrial organization, market design and the economics of technology.” It’s not that Saez, Duflo, Levin, Finkelstein, Chetty, Gentzkow and Fryer are doing bad work – their research is all of very high quality and by no means “cute-onomics” – but simply that the type of research they do is a very small subset of what economists work on. This style of work is particularly associated with the two Cambridge schools, and it’s no surprise that all of the past seven winners either did their PhD or postdoc in Cambridge. Where are the macroeconomists, when Europe is facing unemployment rates upwards of 30% in some regions? Where are the finance and monetary folks, when we just suffered the worst global recession since the 1930s? Where are the growth economists, when we have just seen 20 years of incredible economic growth in the third world? Where are the historians? Where are the theorists, microeconomic and econometric, on whose backs the applied work winning the prizes are built? Something needs to change.)

Enough bellyaching. Let’s take a look at Rahman’s clever paper, which might be thought as “when mediators are bad for society”; I’ll give you another paper shortly about “when mediators are good”. Rahman’s question is simple: can firms maintain collusion without observing what other firms produce? You might think this would be tricky if the realized price only imperfectly reflects total production. Let the market price p be a function of total industry production q plus an epsilon term. Optimally, we would jointly produce the monopoly quantity and split the rents. However, the epsilon term means that simply observing the market price doesn’t tell my firm whether the other firm cheated and produced too much.

What can be done? Green and Porter (1984), along with Abreu, Pearce and Stacchetti two years later, answered that collusion can be sustained: just let the equilibrium involve a price war if the market price drops below a threshold. Sannikov and Skrzypacz provided an important corollary, however: if prices can be monitored continuously, then collusion unravels. Essentially, if actions to increase production can be taken continuously, the price wars required to prevent cheating must be so frequent that join profit from sometimes colluding and sometimes fighting price wars is worse than joint profit than from just playing static Cournot.

Rahman’s trick saves collusion even when, as is surely realistic, cheaters can act in continuous time. Here is how it works. Let there be a mediator – an industry organization or similar – who can talk privately to each firm. Colluding firms alternate who is producing at any given time, with the one producing firm selling the monopoly level of output. The firms who are not supposed to produce at time t obviously have an incentive to cheat and produce a little bit anyway. Once in a while, however, the mediator tells the firm who is meant to produce in time t to produce a very large amount. If the price turns out high, the mediator gives the firm that was meant to produce a very large amount less time in the future to act as the monopolist, whereas if the price turns out low, the mediator gives that firm more monopolist time in the future. The latter condition is required to incentivize the producing firm to actually ramp up production when told to do so. Either a capacity constraint, or a condition on the demand function, is required to keep the producing firm from increasing production too much.

Note that if a nonproducing firm cheats and produce during periods you were meant to be producing 0, and the mediator happens to secretly ask the temporary monopolist firm to produce a large amount, you are just increasing the probability that the other firm gets to act as the monopolist in the future while you just get to produce zero. Even better, since the mediator only occasionally asks the producing firm to overproduce, and other firms don’t know when this time might be, the nonproducing firms are always wary of cheating. That is, the mediator’s ability to make private recommendations permits more scope for collusion than firms who only options are to punish based on continuously-changing public prices, because there are only rare yet unknown times when cheating could be detected. What’s worse for policymakers, the equilibrium here which involves occasional overproduction shows that such overproduction is being used to help maintain collusion, not to deviate from it; add overproduction to Green-Porter price wars as phenomena which look like collusion breaking down but are instead collusion being maintained.

Final working paper (RePEc IDEAS). Final version published in AER 2014. If you don’t care about proof details, the paper is actually a very quick read. Perhaps no surprise, but the results in this paper are very much related to those in Rahman’s excellent “Who will Monitor the Monitor?” which was discussed on this site four years ago.

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