When the principal knows better than the agent: Subjective evaluations as an optimal disclosure mechanism

• Published date: 01 November 2019
• Author: Mengxi Zhang
• Date: 01 November 2019
• DOI: http://doi.org/10.1111/jems.12297

Received: 9 July 2017

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Revised: 15 July 2018

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Accepted: 6 November 2018

DOI: 10.1111/jems.12297

ORIGINAL ARTICLE

When the principal knows better than the agent: Subjective

evaluations as an optimal disclosure mechanism

Mengxi Zhang

Institute for Microeconomics, University

of Bonn, Bonn, Germany

Correspondence

Mengxi Zhang, Institute for

Microeconomics, University of Bonn,

Lennéstraße 37, Bonn 53113, Germany.

Email: mzhang@uni-bonn.de

Abstract

When the firm has some private and unverifiable information about an

employee’s ability, it can design a subjective evaluation mechanism, whereby

payments are tied to evaluations, to communicate such information. In this

paper, I investigate how to design an optimal disclosure mechanism for the

firm. I characterize the firm’s optimal disclosure policy as a function of the

worker’s ability distribution, with the hazard rate function playing a key role.

I also demonstrate that with some reasonable restrictions on the ability

distribution, the firm’s optimal strategy exhibits a particular pattern: it will

reward the best workers aggressively, fire the worst ones, and assign one central

rating to the rest. The predictions are consistent with the way firms utilize

subjective evaluations in reality.

KEYWORDS

ex‐ante contracting, feedback credibility, information revelation, mechanism design, subjective

evaluation

JEL CLASSIFICATION

D21, D82, M50, J30, J41

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INTRODUCTION

Consider a typical principal–agent problem in which a firm hires a worker to work on a project. In classic agency

theory, it is often assumed that the agent (he) has private information about his ability in performing the task. The

principal (she) is less informed and thus needs to design a screening contract to elicit such information from the agent.

In reality, however, there are many circumstances where the principal is in a better position to evaluate the agent’s job

specific ability. This is especially likely to be true for workers who are new to the industry, who just got assigned to new

jobs, and who work in large teams. For instance, an experienced manager is likely to form a better judgment of a new

J Econ Manage Strat. 2019;28:631–655. wileyonlinelibrary.com/journal/jems © 2018 Wiley Periodicals, Inc.

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This paper is based on Chapter 1 of my dissertation submitted to Boston University. I owe my greatest debt to my advisors, Bart Lipman, Jawwad

Noor, Kevin Lang, and Dilip Mookherjee for their advice, support and guidance during various stages of writing this paper. I would like to thank a Co‐

Editor and two anonymous referees of this journal for very insightful and detailed comments. I am also grateful to Eddie Dekel, George Georgiadis,

Albert Ma, Michael Manove, Andy Newman, Juan Ortner, Joel Sobel, Ran Spiegler, and the participants at Boston University Microeconomic Theory

Workshop, 2014 CIREQ Conference, 2014 SEA Annual Meeting, CUHK‐DSE Departmental Research Seminar, Spring 2015 Midwest Economic

Theory Meeting, UNSW Economic Theory Workshop for helpful conversations and comments. Funding by the Deutsche Forschungsgemeinschaft

(DFG, German Research Foundation) through CRC TR 224 and by the Hausdorff Center for Mathematics are gratefully acknowledged. All remaining

errors are my own.

worker’s potential at this particular job than the worker. A supervisor, by nature of her job, usually knows more about a

worker’s value to a large team project than any individual worker.

Suppose, as illustrated above, the principal has some private and unverifiable information about the agent’s job

specific ability.

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When the agent’s ability and effort are complementary inputs to production, the principal may be

willing to share some information to induce a better allocation of effort—a more able agent will work harder if his

ability is credibly revealed. Since the principal has an incentive to overstate the agent’s ability to boost his motivation,

no useful information can be credibly communicated via cheap talk. However, the principal can design a subjective

evaluation mechanism, whereby payments are linked to evaluations, to convey information to the employee.

Intuitively, she can offer to make a higher payment whenever she claims the agent has higher ability. Then on one

hand, the principal is still tempted to overreport the agent’s ability to induce more effort; on the other hand, she also

wants to underreport to cut the cost. The tradeoff between these two concerns may make credible communication

feasible.

In the paper, I study the principal’s optimal information disclosure strategy in such environments. I also

demonstrate that my results can help understand the way firms utilize subjective evaluations in reality, which is often

at odds with standard agency theory. To be precise, the predictions of my model are consistent with the following

empirical regularities. First, many firms conduct subjective evaluations of their employees and yet assign very coarse

ratings to them. Second, the commonly used evaluation scheme is not only coarse, but usually takes a very specific

form. Indeed, most firms tend to assign one or two central ratings to the vast majority, frequently more than 90% of

workers. Only very few workers get ratings outside the central categories. This phenomenon is commonly referred to as

“centrality bias.”In a typical example given by Medoff and Abraham (1980), a large US manufacturer rated 95% of its

employees as either “good”or “superior,”only 3.8% as “excellent”and 1.2% as “satisfactory.”

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Third, although

subjective evaluations are frequently linked with payments, the corresponding reward structure is often highly skewed.

The highest rated workers are rewarded aggressively, the lowest rated ones are more likely to get laid off, and the rest of

the workers receive little or no pay differentiation (Zenger, 1992).

The model proposed in this paper dovetails with the long‐standing view in the social psychology and human

resource management literature that firms use evaluations to provide feedback to workers. For instance, Cleveland,

Murphy and Williams (1989) surveyed 243 individuals who were employed at personnel departments or related

functions in private sector at the time of survey. They report that 53% of respondents perceived providing feedback to be

among the top three purposes of performance appraisals. The economic studies of subjective evaluations, in contrast,

predominantly focus on their direct incentive role (e.g., Baker, Gibbons & Murphy, 1994; Fuchs, 2007; Levin, 2003;

Macleod, 2003). The informational role of such evaluations, though also recognized (e.g., Milgrom & Roberts, 1992;

Prendergast, 2002), did not receive much attention in formal modeling until recently (Fuchs, 2015; Ray, 2007; Suvorov

& van de Ven, 2009; Zabojnik, 2014, etc.). Moreover, the study of optimal information disclosure in such circumstances

is largely missing from the literature.

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This paper consists of two major parts. In the first part, I examine the theoretical question of designing an optimal

disclosure mechanism for the principal. In the second part, I use calibration to demonstrate that my results resonate

well with the empirical regularities discussed above.

In the theoretical part, I first characterize the set of all implementable disclosure policies and show that revealing all

information is always implementable. Second, I investigate optimal disclosure policies for the principal. Sharing

information always increases expected productivity by inducing a better allocation of effort, but may not be cost‐

effective for the principal when the agent is protected by limited liability. I start by considering the case where both

parties have nonbinding outside options and then extend the model to incorporate binding options. With nonbinding

outside options, I characterize the principal’s optimal disclosure policy as a function of the agent’s ability distribution.

The key factor is the hazard rate function. The principal finds it optimal to withhold information in the region where

the distribution has an increasing hazard rate (IHR); she may or may not reveal information in the region where the

hazard rate is decreasing, depending on the exact conditions. However, she will certainly reveal top states if the rate

decreases to zero at the top. So if the agent’s ability distribution has a monotone IHR (uniform, logistic, etc.), as often

assumed in the screening literature, then the principal chooses to withhold all the information. On the other hand, if

the distribution has a sufficiently long right tail (e.g., lognormal, Pareto), the principal always has an incentive to

separate the best workers from others. With binding outside options, the principal may find it optimal to fire the worker

if his ability turns out to be too low and she may want to withhold information from some intermediate workers to

retain them. Otherwise, the optimal disclosure policy can be characterized in the same way as in the previous case.

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