The Performance Pay Nobel

The Nobel Prize in economics goes to Oliver Hart and Bengt Holmstrom for contract theory, the design of incentives. See Tyler’s posts below for overviews. In our textbook, Modern Principles, Tyler and I have a chapter called Managing Incentives which covers some of this work, especially related to Holmstrom’s work on performance pay. Let’s give a simplified precis (fyi, the textbook doesn’t have the math).

Suppose that you are a principal monitoring an agent who produces output. The output depends on the agent’s effort but also on noise. It wouldn’t be a very efficient contract to just reward the agent based on output since then you would mostly be responding to noise—punishing hard-working agents when the noise factors were bad and rewarding lazy agents when the noise factors were good. Not only is that unfair–if you setup a contract like this the agents will a) demand that you pay them a lot of money in the good state because they will be taking on a lot of risk and b) the agents won’t put in much effort anyway since their effort will tend to be overwhelmed by the noise, either good or bad. Thus, rewarding output alone gets you the worst of all worlds, you have to pay a lot and you don’t get much effort.

But perhaps in addition to output, y, you have a signal of effort, call it s. Both y and s signal effort with noise but together they provide more information. First, lesson – use s! In fact, the informativeness principle says you should use any and all information that might signal the agent’s effort in developing your contract. But how should you combine the information from y and s? Suppose you write a contract where the agent is paid a wage, w=B0+By*y+Bs*s where Bo is the base wage, By is the beta on y, how much weight to put on output and Bs is the weight on the s signal–think of By as the performance bonus and Bs as a subjective evaluation bonus. Then it turns out (under some assumptions etc. Canice Prendergast has a good review paper) you should weight By and Bs according to the following formula:


that looks imposing but it’s really not.  σ^2s (sorry for the notation) is the variance of the s signal, σ^2y is the variance of the y signal. Now for the moment assume r is zero so the formula boils down to:


Ah, now that looks sensible because it’s an optimal information theorem. It says that you should put a high weight on y when the s signal is relatively noisy (notice that By goes to 1 as σ^2s increases) and a high weight on s when the y signal is relatively noisy. Notice also that the two betas sum to 1 which means that in this world you put all the risk on the agent. Ok, now let’s return to the first version and fill in the details. What’s r? r is a measure of risk aversion for the agent. If r is zero then the agent is risk neutral and we are in the second world where you put all the risk on the agent. If the agent is risk averse, however, then r>0 and so what happens? If r>0 then you don’t want to put all the risk on the agent because then the agent will demand too much so you take on some risk yourself and tamp down By and Bs (notice that the bigger is r the smaller are both By and Bs) and instead increase the base wage which acts as a kind of insurance against risk. So the first version combines an optimal information aggregation theorem with the economics of managing the risk-performance-pay tradeoff.

(c, by the way, is a measure of how costly effort is to the agent and so it also makes sense that the higher is c the less weight you put on performance incentives and the more on the base wage.)

Let’s also discuss some further work which is closely related to Holmstrom’s approach, tournament theory (Lazear and Rosen). When should you use absolute pay and when should you use relative pay? For example, sometimes we reward salespeople based on their sales and sometimes we reward based on which agent had the most sales, i.e. a tournament. Which is better? The great thing about relative pay is that it removes one type of noise. Suppose, for example, that sales depend on effort but also on the state of the economy. If you reward based on absolute sales then you are rewarding a lot of noise. Once again, that has two bad effects it means that you have to pay your agents a lot since you are imposing risk on them and it means that they won’t work that hard since they know they will be paid a lot when the economy is good and hardly at all when the economy is bad so in neither case do the agents have strong incentives to work hard. Suppose, however, that you have a relative pay scheme, a tournament. Now you have removed the noise coming from the state of the economy–since all the salespeople face the same economy and since there is always a first, second and third place the agent’s now have an incentive to work hard in good or bad times. Not only do they have an incentive to work hard you don’t have to pay them much of a risk premium since more of their pay is now based on their own effort rather than on noise.

But relative pay isn’t always better. If the sales agents come in different ability levels, for example, then relative pay means that neither the high ability nor the low ability agents will work hard. The high ability agents know that they don’t need to exert high effort to win and the low ability agents know that they won’t win even if they do exert high effort. Thus, if there is a lot of risk coming from agent ability then you don’t want to use tournaments. Or to put it differently, tournaments work best when agent ability is similar which is why in sports tournaments we often have divisions (over 50, under 30) or rounds.

FYI, in our textbook Tyler and I use this model to discuss when students should prefer an absolute grading scale and when they should prefer grading on a curve. Work it out!

Holmstrom’s work has lot of implications for structuring executive pay. In particular, executive pay often violates the informativeness principle. In rewarding the CEO of Ford for example, an obvious piece of information that should used in addition to the price of Ford stock is the price of GM, Toyota and Chrysler stock. If the stock of most of the automaker’s is up then you should reward the CEO of Ford less because most of the gain in Ford is probably due to the economy wide factor rather than to the efforts Ford’s CEO. For the same reasons, if GM, Toyota, and Chrysler are down but Ford is down less then you might give the Ford CEO a large bonus even though Ford’s stock price is down. Oddly, however, performance pay for executives rarely works like a tournament. As a result, CEOs are often paid based on noise.

The basic framework has since been applied in many different circumstances because principal-agent can be interpreted in many different ways employer-worker, teacher-student, regulator-banker and so forth. Thus the basic insights have been reflected in a wealth of applications each of which adds to the body of theory.


Any real world factual evidence that this performance pay "theory" is indeed correct in practice?

It does not need to be "correct in practice". A theory in microeconomics or IO is a way of linking behavioral assumptions to behavioral outcomes. Some theories are meant to describe "factual" behavior, and are often written together with econometric analyses and/or case studies. Other theories are normative and are meant as exercises of the sort "If we believe X, Y, Z, then the rational/optimal/equilibrium outcome is A, B, C". It is like philosophy, but more rigorous and the lack of "evidence" does not make them wrong per se.

Does the counterfeit Nobel generate counterfeit excitement?

The economics nobel might be counterfeit in the sense of not being authorized by Alfred Nobel's will. But in other respects it seems to be a pretty good mimic. The work rewarded tends to be foundational and broadly accepted, without many surprise winners or eccentric choices.

While there's no doubt the people that remind us about this every dang year as if we didn't know are silly, and worth teasing, I came across this bit at 538 which gives a pretty good reason WHY we may wish to remember that's it not a 'real Nobel':

But, technically, there is no Nobel Prize in economics. Instead, there is the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel. It was first awarded in 1969 and is named not after a person, but after the central bank of Sweden — the Sveriges Riksbank — which funds it. The Nobel Foundation doesn’t pay out the award or choose the winner (though the winner is chosen in accordance with the same principles used by the Nobel Foundation), but it does list the prize on its website along with the Nobels, tracks winners the same as Nobel laureates, and even promotes the prize alongside its own. Members of the Nobel family have spoken out against the award.

So why does it exist? Notre Dame historian Philip Mirowski has found evidence that the economics award grew out of Swedish domestic politics. According to Mirowski, in the 1960s, the Bank of Sweden was trying to free itself from government oversight and become independent. One way to do that was to frame economics as purely scientific, rather than political — in which case, government interference could only hurt the bank. Having a Nobel Prize boosted economics’ scientific street cred. And Mirowski isn’t the only academic who is skeptical of whether there should be a Nobel-associated economics prize. Friedrich von Hayek, who won the award in 1974, used his Nobel Banquet speech to critique the prize.3

“The Nobel Prize confers on an individual an authority which in economics no man ought to possess,” Hayek said. He worried that the prize would influence journalists, the public and politicians to accept certain theories as gospel — and enshrine them in law — without understanding that those ideas have a different level of uncertainty than, say, gravity or the mechanics of a human knee.

It's not just that this Nobel was tacked on later, it's that it can distort the field itself (as Hayek pointed out).

For all the talk of "can distort the field," these critics completely avoid explaining how. Mostly because the how makes no sense--the economics Nobel is extremely retrospective, possibly moreso than all the other scientific prizes, and usually lags the field's stance on its recipients. Most of the work cited in this Nobel is from the 70s and 80s!

Umm. We are governed by democracry. Paul Krugman can tell us that we need more bailouts and spending at all times. 10 million or more reliable voters believe him because they are dim and he has an unrelated Nobel.

Beyond that not at all being relevant to what I was talking about (the field of economics, not society), it's still a ridiculous point--do you really think Krugman is swaying 10 million marginal voters? Do you really even think that 1/30th of the US living population reads Krugman? Do you really think that the marginal effect is the name "Nobel," rather than just a position on the NYT?

Also, Hayek's point was not that a Nobel winner in economics would have undue political influence. It was that the field itself would tend to canonize the views and theories of any Nobel winner instead of treating their work as still testable and falsifiable. Basically it goes back to his philosophy that top-down expertise isn't worthy of blind faith.

"Oddly, however, performance pay for executives rarely works like a tournament. As a result, CEOs are often paid based on noise." Odd indeed. You'd almost suspect that it's cronies of the CEO who advise on such topics.

dearieme, you are exactly correct

Thanks for taking all the time to provide this information

1) On the risk aversion stuff, finance theory teaches us that only systematic, non-diversifiable risk should be rewarded. Yet, the theory here does not seem to distinguish between idiosyncratic and systematic noise, nor recognize that some risk can be offloaded in the financial markets. For example, the statement that agents will demand to be paid a lot to take on risk that they don't control doesn't necessarily apply to idiosyncratic noise unrelated to performance that could be diversified away through insurance or similar financial instruments. One might also think that the amount an agent needs to be paid to bear systematic noise risk, e.g., equity market beta risk, would somehow depend on the equity market risk premium rather than the individual agent's risk aversion.

2) "relative pay means that neither the high ability nor the low ability agents will work hard"
Does the employer care about effort or results? If base pay already reflects ability differences, then performance pay can be directed at effort. However, if everyone receives same base pay or if employer cannot distinguish between high ability and low ability agents a priori, then it seems like performance pay should reward ability as well as effort. Otherwise, the high ability agents will leave and the employer will attract and retain mostly low ability agents.

3) "CEOs are often paid based on noise"
Under this theory, that might explain why even poor performing CEOs are paid a lot: they are taking on a lot of risk beyond their control. (Again, though, I think one needs to incorporate market prices of risk from the financial markets.) This also suggests that better compensation schemes could result in lower CEO pay even while making the CEOs better off. They would be paid less but also bear less unwanted risk.

As described, relative performance pay could result in the Ford CEO receiving a large performance bonus even when the stock is down, but down less than other car companies' stocks. One difficulty with this is that, when Ford stock is down in absolute terms, the company may be in more financial distress, making it more difficult to pay the large bonus. Again, some of this might be addressable by hedging in the financial markets, e.g., company can short other car stocks. This seems to be a problem with performance pay in hedge funds and proprietary trading too. Ideally, one would like to pay bonuses based on performance relative to an appropriate benchmark. In practice, however, the cash available to pay bonuses often depends on absolute returns.

It is clear that BC is not capable of understanding the point. Which is not surprising given that someone had to explain it to Tyler first.

Troll. BC did a good post, even if not one point.

This is impressive work that deserves recognition. And it was, but not by a Nobel, as the title of this post mistakenly suggests. Hart and Holmstrom were actually awarded with the Sveriges Riksbank Prize, not a Nobel Prize.

And one more time:

This math seems but a trivial example from information theory, of the kind they use all the time in communications theory in electrical engineering. There's all kinds of formulae, the most fundamental being the Nyquist sampling theorem. Is this really worthy of a Nobel in economics? C'mon!

BTW, they DON'T do this sort of agent-principal compensation on Wall Street, with traders. Rather, they reward traders who succeed with oversized bets with big bonuses, and punish traders who fail with prosecution, aka the Société Générale scandal in France, or Barings Bank with Leeson. If this compensation scheme is so obvious, why aren't the quants on Wall Street being paid this way? I suspect it's because there's a 'bonus culture' akin to 'crony capitalism'. Now finding out why that inefficient saddle point has been reached and society is stuck on it would really be worthy of a Nobel anthropology.

"This thing I barely understand looks vaguely like something else I barely understand? It's definitely not Nobel-worthy!"

variance? So, we're talking about pay raises & annual performance. So we'll have a good idea of variance after 10-100 years or if the same job is being done by 20-100 individuals. Problem is, neither of those are likely to happen, regardless of job description, few jobs are static over decades and few organizations have the same job being done by so many. (depending on how sloppy you want to be with defining "same").

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