Holmstrom (1999) - Managerial Incentive Problems

Reference(s)

Holmstrom B., (1999) "Managerial Incentive Problems: A Dynamic Perspective," Review of Economic Studies, 66(1): 169-182 pdf

Abstract

The paper studies how a person's concern for a future career may influence his or her incentives to put in effort or make decisions on the job. In the model, the person's productive abilities are revealed over time through observations of performance. There are no explicit output-contingent contracts, but since the wage in each period is based on expected output and expected output depends on assessed ability, an "implicit contract" links today's performance to future wages. An incentive problem arises from the person's ability and desire to influence the learning process, and therefore the wage process, by taking unobserved actions that affect today's performance. The fundamental incongruity in preferences is between the individual's concern for human capital returns and the firm's concern for financial returns. The two need be only weakly related. It is shown that career motives can be beneficial as well as detrimental, depending on how well the two kinds of capital returns are aligned.

The Holmstrom Career Concerns Model

This model features:

• Moral Hazard
• Infinite periods
• Rational Expectation Equilibrium (i.e. Perfect Bayesian Nash)

Quick Summary

Holmstrom (1999/1983) models a claim from Fama (1980) that market forces will provide implicit incentives for agents to work (through their 'career concerns'), and that explicit incentives, through contracts, may not be needed.

The Holmstrom model assumes:

• Additively and time seperable utility
• No contracts (no way to link past performance to wages directly); wages are based on the prior period's output and paid in advance
• Private costs with Inada conditions
• Randomly drawn managerial ability is private, leads to asymmetric information
• Output is observed and is the sum of ability, effort and noise
• Infinately lived agents
• A competitive labour market

How to solve:

• Competitive labour market bids up to the expected output that a manager will provide
• In equilibrium the beliefs of the labour market are correct

Key results:

• The labour market acts as an indirect mechanism for linking past-performance to wages
• Career concerns generally do not provide first best incentives, they over and/or under shoot
• Career concerns (i.e. the incentive effects arising from career concerns) are strongest at the start of the career and weakest at the end

Set-up

Utility of the Manager is given by:

[math]U(w,a)=\sum_{t=1}^{\infty }\beta ^{t-1}[w_{t}-g(a_{t})]\,[/math]

where: [math]\beta\,[/math] is the discount factor, [math]w_{t}\,[/math] are wages, [math]g(\cdot)\,[/math] is the cost of effort, and [math]a_{t}\,[/math] is the effort.

Output is given by:

[math]y_{t}=\eta + a_{t} +\varepsilon_{t}\,[/math]

where [math]\varepsilon\,[/math] is noise and [math]\eta\,[/math] is the ability of the manager, such that [math]\varepsilon _{t}\sim N(0,\frac{1}{h_{\varepsilon }})\,[/math], and [math]\eta \sim N(m_{1},\frac{1}{h_{1}})\,[/math].

The market will set wages:

[math]w_{t}(y^{t-1})=\mathbb{E}[y_{t}|y^{t-1}]=\mathbb{E}[\eta |y^{t-1}]+a_{t}(y^{t-1})\,[/math]

The manager will best respond by choice an effort sequence:

[math]\underset{\{a_{t}(y^{t-1})\}_{t=1}^{\infty }}{\max }\;\sum_{t=1}^{\infty}\beta ^{t-1}[\mathbb{E}w_{t}(y^{t-1})-\mathbb{E}g(a_{t}(y^{t-1}))]\,[/math]

Two Period Model

Wages are paid in advance so in the second period the agent exerts no effort. In equilbrium [math]a_{1}^{*}\,[/math] is correctly anticipated.

The market observes [math]z_{1}\equiv \eta +\varepsilon _{1}=y_{1}-a_{1}^{*}\,[/math] and uses this to form its conditional expectation [math]\mathbb{E}[\eta|z_{1}]\,[/math]. Given the assumption of normality we can use the conditional normal equation to give:

[math][\eta |z_{1}]\sim N(m_{2},\frac{1}{h_{2}})\,[/math]

where

[math]m_{2}(z_{1})=\frac{h_{1}}{h_{1}+h_{\varepsilon }}\cdot m_{1}+\frac{h_{\varepsilon }}{h_{1}+h_{\varepsilon }}\cdot z_{1}\,[/math]

[math]h_{2}=h_{1}+h_{\varepsilon }\,[/math]