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Gerrit De Geest on Incentives - Dictionary of Arguments

Parisi I 439
Incentives/carrots/sticks/Dari-Mattiacci/De Geest: incentives can be generated by either carrots—promises to reward, such as with prizes or bonuses—or sticks—threats to punish, such as with fines or damages.* Carrots and sticks are prima facie equivalent, because any behavioral change induced by promising compliers a $100 reward can also be obtained by threatening violators with a $100 punishment.
Asymmetry: Yet, while carrots and sticks seem to produce the same effects, they are not chosen at random; some general patterns can be observed across legal systems. Incentives for careful driving are generally created by holding negligent drivers liable under tort law, rather than by rewarding careful drivers.
Prisi I 440
Nonetheless there can be cases in which a carrot and a stick of the same magnitude have different incentive effects. The most obvious case is when money has decreasing marginal utility for the agent, and a monetary carrot is used to induce a non-monetary effort. Since repeated carrots further increase the agent’s wealth, carrots may even have a saturation effect: there may be a wealth level at which a carrot can no longer incentivize an agent to make a significant effort.
e = the effort cost of an individual agent (e* is the level of enforcement);
c = the reward (carrot);
s = the punishment (stick);
Parisi I 441
n = the number of agents in the population; F(e) = the distribution of the cost of effort.
Assume that monitoring occurs with probability equal to one and that the ruler can perfectly and costlessly verify if an agent has exerted effort. Note that the ruler cannot verify the individual’s cost of effort and cannot use individualized carrots and sticks.
If the ruler uses carrots, an individual earns c–e upon compliance and 0 upon violation; thus, an individual will comply if his effort cost is e ≤ c. Similarly, if the ruler uses sticks, an individual pays e upon compliance and s upon violation; thus, he will comply if e ≤ s. Carrots and sticks are equivalent in terms of incentives (…).
(1) c = s = e*
Probabilistic monitoring: The ruler might monitor the behavior of individuals with a probability less than one, so that
pc = the monitoring probability with carrots;
ps = the monitoring probability with sticks.
Again, carrots and sticks are equivalent with respect to incentives (…)
(2) pcc = pcs = e*
(3) c = s = e* / p
Parisi I 442
Enforcement errors: (…) the ruler might make two types of errors. Even though an individual exerted effort, the ruler might erroneously believe that the individual exerted no effort (a type-I error). Similarly, even though an individual exerted no effort, the ruler might erroneously believe that the individual exerted effort (a type-II error):9 εI = probability of type-I error; εII = probability of type-II error. Then we will get for different probabilities:
(4) pcc = pcs = e*/ 1-epsilonI – epsilonII
For equal probability:
(5) c = s = e*/ p(1-epsilonI – epsilonII)
Parisi I 450
Population effect: If F(e) is a probability distribution of the effort costs in the population, then nF(e*) is the expected number of compliers. If instead F(e) describes the real distribution of effort costs in the population—that is, if F(e) is the ratio of the number of individuals with effort costs equal to or less than e and the total number of individuals—then nF(e*) is the real number of compliers. The ruler knows more in the second scenario than in the first, although in both scenarios she does not know the effort costs of an individual.
Parisi I 451
If the ruler knows the real distribution, then she can predict with certainty how many individuals will be rewarded. The same reasoning does not apply to sticks. The reason is that with sticks the ruler needs to be able to punish all individuals, not only the violators, or the threat of punishment would not be credible.
Sanctions: To see this point in the sharpest way, consider a ruler who enforces a rule e* on an individual with effort cost e ≤ e*. The individual complies. If the constraint were determined only by violators, a ruler with no budget would be able to do the job. But this cannot be the case, since a ruler with no budget cannot credibly threaten the application of (costly) sanctions.
>Transaction costs/Dari-Mattiacci/De Geest.
Population effect: If the ruler knows the population, carrots have to be available to reward only actual compliers, while sticks have to be available to punish all potential violators (not only the actual violators).

* A carrot can be defined as a payment from the principal to the agent upon compliance of the agent. A stick is then a payment from the agent to the principal upon violation by the agent. While a carrot can sometimes be rewritten as a mathematically identical stick through the use of entry fees, this is not the case when enforcement is probabilistic. See De Geest and Dari-Mattiacci (2013)(1).

1. De Geest, Gerrit and Giuseppe Dari-Mattiacci (2013). “The Rise of Carrots and the Decline of Sticks.” University of Chicago Law Review 80: 341–392.

Giuseppe Dari-Mattiacci and Gerrit de Geest. “Carrots vs. Sticks”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
De Geest, Gerrit
Parisi I
Francesco Parisi (Ed)
The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017

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