2016 was in many respects a happy year for me. Two of my favorite economists, Bengt Holmström and Oliver Hart, won the Nobel Prize “for their contributions to contract theory.” Perhaps even better: My girlfriend, who is a civil servant, earned a bonus the size of a monthly salary.
While we were celebrating all this over a dinner at a Michelin star restaurant, my thoughts drifted away and I could not help wondering: why exactly did my girlfriend get a bonus? So, I asked her: “What did you do to earn the bonus?” Guess what she said: “Nothing special.” I paused. Perhaps she was just being modest. “What do you mean, nothing special?” “I mean I did my best and all, but there was not a particular achievement that resulted in the bonus. This is all at the discretion of my boss.”
I almost choked on the 40-day-old fillet of ruby-red beef cooked over coals. Why would her boss (1) have the discretion to award bonuses, and (2) why award one at all if the main criterion appears to be as vague as ‘doing one’s best’? Another question popped up: “Is there any limit to the bonus?” “Yes. It is at most a monthly salary.”
The smoked bone marrow started to taste funny. Was she teasing me? Everything my girlfriend was saying was completely in conflict with standard contract theory. How to make sense of this?
I took a sip of my red wine, a 2010 Brunello di Montalcino Podere Santa Maria.
Standard contract theory relies on a model with a principal and an agent. The principal cannot observe how much effort the agent puts into her job, but he can observe the agent’s output. The principal’s payoffs depend on the agent’s output. This principal-agent model seems a good analogy of the relation between a farmer and a fruit picker. The farmer sends the fruit picker into his apple orchard. The farmer has other obligations, so he cannot stand behind the fruit picker to observe whether she actually picks fruit. However, at the end of the day, he can observe how many apples the fruit picker has harvested. He benefits from this because he can sell the apples on the market.
The key question in contract theory is: How can the principal write a contract with the agent to ensure that the agent’s interests are aligned with his? A fixed salary won’t do the job. The agent wouldn’t exert as much effort as the principal would like because effort is costly for the agent. A fruit picker would spend most of the day at the apple farm lying in the sun chatting with the other fruit pickers. It turns out that the optimal contract pays the agent an amount for each unit of output equal to the marginal benefit for the principal. That is, for every apple that the fruit picker harvests, she should get the price at which the principal sells the apple in the market. In other words, it is optimal for the principal ‘to sell the firm to the agent.’
But how could this be optimal for the principal? The contract forces him to pay every cent that he earns to the agent! Well, the principal earns money because the agent has to pay the principal to work for him. The contract is optimal because the agent obtains the exact amount of incentive to optimally trade off the benefits of the principal (output sold in the market) and her own effort costs. In other words, the contract maximizes the size of the pie. The principal then gets a share of the pie because the agent pays him a nice amount for the right to work for him. Such contracts are not only of theoretical interest: Think about taxi drivers that pay a lump sum to a taxi company while keeping the money earned from transporting passengers.
The Mugwort panna cotta with blowtorched berries, whipped cream, roasted peach ice cream, and honeycomb was served. I asked my girlfriend a couple of other questions.
“How would you define your ‘output’?”
“That is hard to tell. In the end, some of my policy proposals become part of government legislation.”
“Any idea what your past year’s output was worth?”
“I helped draft a policy proposal that is estimated to save society hundreds of millions of euros.”
“So, why was your bonus not in the order of hundreds of millions of euros?”
“Ha! You’re hinting at the ‘selling-the-firm-to-the-agent’ result from standard contract theory.”
My girlfriend is an economist, too.
“Well, first of all, I’m risk averse. Standard contract theory would require me to pay the government quite a lot of money. If I can get a bonus of hundreds of millions of euros, I would have to pay an amount in the same order of magnitude. I find that a bit risky: What if my policy proposal was not implemented in the end? The government would have to compensate me with a substantial risk premium for me to be willing to accept such a contract.”
Wait a minute, this line of reasoning is exactly one of the main contributions to contract theory by the 2016 Nobel Prize laureates. In fact, my girlfriend appears to know their work quite well.
“What’s more, in my job it is not so clear what my individual contribution is to government policy, at least for an outsider.”
“So, your boss can tell?”
“To some extent, yes.”
“Fine. But why would he award you a bonus then?”
“Both my boss and I know that I performed well. If he does not pay me the bonus, I won’t do my best next year. So, we both have a reason to stick to the implicit contract, even though it cannot be enforced by the courts.”
“But why is the bonus limited to a monthly salary?”
“If it was any higher, my boss would have too great an incentive not to pay it. Remember that, according to my actual contract, he does not have to pay me a bonus. He would rather save the money for the bonus than see me work hard in the future. So, the implicit contract would no longer be credible.”
We drank a cup of jasmine pearl tea and went home with the satisfactory feeling that the Nobel Prize had been quite deservedly awarded to Bengt Holmström and Oliver Hart for their contributions to contract theory.