Working Paper: CEPR ID: DP10143
Authors: Pierre Chaigneau; Alex Edmans; Daniel Gottlieb
Abstract: This paper shows that the informativeness principle does not automatically extend to settings with limited liability. Even if a signal is informative about effort, it may have no value for contracting. An agent with limited liability is paid zero for certain output realizations. Thus, even if these output realizations are accompanied by an unfavorable signal, the payment cannot fall further and so the principal cannot make use of the signal. Similarly, a principal with limited liability may be unable to increase payments after a favorable signal. We derive necessary and sufficient conditions for signals to have positive value. Under bilateral limited liability and a monotone likelihood ratio, the value of information is non-monotonic in output, and the principal is willing to pay more for information at intermediate output levels.
Keywords: contract theory; informativeness principle; limited liability; options; pay-for-luck; principal-agent model; relative performance evaluation
JEL Codes: D86; J33
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Informativeness principle under limited liability (D83) | Signal has zero value in contracting (D86) |
| Signal is informative about effort (D83) | Signal has zero value in contracting (D86) |
| Output is a sufficient statistic for effort (E23) | Signal has zero value in contracting (D86) |
| Limited liability (K13) | Principal cannot adjust payments downward upon receiving unfavorable signals (G19) |
| Limited liability (K13) | Signals are only valuable if they are informative about effort at output levels that maximize the likelihood ratio (D83) |