The informativeness principle demonstrates qualitative benefits to increasing signal precision. However, it is difficult to quantify these benefits — and compare them against the costs of precision — since we typically cannot solve for the optimal contract and analyze how it changes with informativeness. We consider a standard agency model with risk-neutrality and limited liability, where the optimal contract is a call option. The direct effect of reducing signal volatility is a fall in the value of the option, benefiting the principal. The indirect effect is a change in the agent’s effort incentives. If the original option is sufficiently out-oft the-money, the agent can only beat the strike price if he exerts effort and there is a high noise realization. Thus, a fall in volatility reduces effort incentives. As the agency problem weakens, the gains from precision fall towards zero, potentially justifying pay-for-luck.
