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Recently I am reading a paper by Ortner & Chassang (2018) on corruption control. It is a nice paper to read, and the idea is kinda cool.

The game is as follows. There are 3 players, a principle, a monitor, and an agent. The agent can choose to engage crime, and the principle offers a wage structure to the monitor in order to deter crime (for details, please refer to the paper if you are interested). One of the results says that, when the monitor's private cost of misreporting is strictly concave (convex) over the support, the agent is effectively risk-loving (risk-averse).

However, I do not quite understand the concept of being "effectively risk averse/loving" that they mentioned. I never saw this before. What does it mean? Does it simply mean that it is beneficial for the agent to be risk-loving?

Thanks for your clarification in advance. Please kindly provide some reference if there is any.

Lin Jing
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  • I think "effective" risk aversion means the agent's risk aversion is an equilibrium property, since "[the agent] obtains a higher payoff from a random wage schedule than from a deterministic one with the same expectation." In other words, in equilibrium the agent behaves as if she's risk averse. – Herr K. May 23 '20 at 04:39
  • Thanks for the comment. That's also my guess. But I can't find any formal definition of it or any reference about it. – Lin Jing May 23 '20 at 07:18

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"Effectively" has two definitions:

1: in such a manner as to achieve a desired result.

2: actually but not officially or explicitly.

O+C are using the second definition here. This is because the risk averse/loving behaviour that is being exhibited does not come from the concavity of the agent's utility function, but instead indirectly, from the concavity of the c.d.f of the random cost $\eta$ that the monitor will have to pay if they misreport information. So the agents are not "officially" risk averse/loving but as a result of the concavity/convexity of the monitor's cost cdf they will behave as a risk averse/loving agent would when the cdf is linear.

Hope this helps!

H Rogers
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    Thanks for the comment! You made it clear that it is not derived from the agent's utility function which is an important point. So, the as-if risk averse/loving behavior is actually induced by the environment under which being risk averse/loving is optimal, is this right? Any related reference the notion of "effective risk averse" would be great! Thanks again. – Lin Jing May 23 '20 at 13:37
  • That's correct! Since it's not really a formal term I don't think you'll be able to find much in the way of external references, in the same way there isn't really a strict definition of what it means to be "extremely risk averse". But if it helps, I can give a couple other examples of the word effective being used in a similar way: one might say a war is "effectively over" after fighting has stopped but before treaties have been signed. Or that a powerful advisor to a weak willed king is the "effective leader" of the kingdom. – H Rogers May 23 '20 at 13:48
  • Thanks a lot. The examples do help. – Lin Jing May 24 '20 at 01:54