Knowing that you know: incentive effects of relative performance disclosure

Abstract

This paper studies differential employee responses to the public disclosure of individual performance information throughout an organization. We argue that, to the extent that employees care about their colleagues’ perceptions of their productivity, public disclosure will increase motivation. Moreover, the effect should be stronger for employees whose colleagues expect them to have higher performance. We obtained data from a bank that transitioned from private to public disclosure of employee rankings and, consistent with our hypothesis, find heterogeneity in employee responses to public disclosure. Employees with a history of poor performance increase their output more than past good performers when rankings become public. Additionally, more highly educated employees react more strongly to the change. However, contrary to the literature that finds gender differences in competitive environments, we do not find systematic differences in the response to public disclosure on this dimension. Overall, the results suggest that public disclosure is an important dimension to consider when designing a compensation system.

Appendix

Proof of Propositions 1 and 2. The employee chooses the effort level to maximize her expected utility (notice that r depends on the realization of π, and hence is a random variable). If we denote the pdf of the posterior r by ϕ_r, then we can write:

$$ EU=\beta E\pi +{\gamma}_{-}{\int}_{-\infty}^{r_0}\left(r-{r}_0\right){\phi}_r(r) dr+{\gamma}_{+}{\int}_{r_0}^{+\infty}\left(r-{r}_0\right){\phi}_r(r) dr. $$

Because co-workers’ priors about the employee’s ability are normal and the signal they receive (output) is also normal, their posterior will be normally distributed and satisfies r − r₀ = μ(π − π^e), where π = θe + a + u, ${\pi}^e=\theta \hat{e}+{r}_0$, and $\hat{e}$ is the co-workers’ conjecture about the employee effort. Hence, r > r₀ if and only if $u>{r}_0-a+\theta \left(\hat{e}-e\right)$. From the employee’s perspective, as a is known, the uncertainty about her reputation is driven by u. If we let $\varGamma (e)={r}_0-a+\theta \left(\hat{e}-e\right)$ and ϕ_u be the pdf of a $N\left(0,{\sigma}_u^2\right)$, we have:

$$ EU=\beta \left(\theta e+a\right)+{\gamma}_{-}{\int}_{-\infty}^{\varGamma (e)}\mu \left(\theta e+a+x-\theta \hat{e}-{r}_0\right){\phi}_u(x) dx+{\gamma}_{+}{\int}_{\varGamma (e)}^{+\infty}\mu \left(\theta e+a+x-\theta \hat{e}-{r}_0\right){\phi}_u(x) dx. $$

By differentiating the expected utility using Leibniz’ rule, we get that the optimal choice satisfies:

$$ \beta \theta +\mu \theta \left[{\gamma}_{-}\Pr \left(r<{r}_0\right)+{\gamma}_{+}\Pr \left(r\ge {r}_0\right)\ \right]={c}^{\prime }(e)=e. $$

(1)

Proposition 1.a) follows immediately, as e^∗ is increasing in μ, γ₋, and γ₊. Notice also that, because Pr(r ≥ r₀) = 1 − Pr(r < r₀), we have ∂e^∗/∂a = μθ(γ₋ − γ₊)∂ Pr(r < r₀)/∂a, and similarly for ∂e^∗/∂r₀. Proposition 1.b) then follows from the fact that Pr(r < r₀) is decreasing in a and increasing in r₀. Finally, Proposition 2 follows from the fact that ∂²e^∗/∂θ∂a = μ(γ₋ − γ₊)∂ Pr(r < r₀)/∂a and ${\partial}^2{e}^{\ast }/\partial {\sigma}_a^2\partial a=\theta \left({\gamma}_{-}-{\gamma}_{+}\right)\left[\partial \Pr \left(r<{r}_0\right)/\partial a\right]\partial \mu /\partial {\sigma}_a^2$, with $\partial \mu /\partial {\sigma}_a^2>0$. ∎