Chicano Economics | Course Paper

The University of Chicago Graduate School of Business

Selected Paper 86

Marianne Bertrand

The University of Chicago

Graduate School of Business

Sendhil Mullainathan

Massachusetts Institute

of Technology

Are CEOs Rewarded for Luck?

The Ones without Principals Are

K5777

U of Chicago #34920 Assm: NS

Marianne Bertrand

and Sendhil Mullainathan

Marianne Bertrand is Associate Professor

at the University of Chicago Graduate

School of Business, Chicago, Illinois,

60637

(marianne.bertrand@gsb.uchicago.edu,

gsb.uchicago.edu/fac/marianne.bertrand).

Sendhil Mullainathan is Mark Hyman Jr.

Career Development Associate Professor

of Economics at Massachusetts

Institute of Technology, Cambridge,

Massachusetts, 02139

(mullain@mit.edu)

The results in this paper were previously

circulated as part of a larger working

paper entitled “Do CEOs Set Their Own

Pay? The Ones without Principals Do.”

For their very helpful comments, we are

extremely grateful to Daron Acemoglu,

Rajesh Aggarwal, George Baker, Patrick

Bolton, Peter Diamond, Robert Gibbons,

Denis Gromb, Brian Hall, Bengt

Holmstrom, Caroline Hoxby, Glenn

Hubbard, Lawrence Katz, Jörn-Steffen

Pischke, Nancy Rose, David Scharfstein,

Robert Shimer, Andrei Shleifer, Richard

Thaler, and seminar participants at

Berkeley, Columbia, Chicago, Harvard,

Massachusetts Institute of Technology,

Princeton, and the National Bureau of

Economic Research Corporate Finance

Summer Institute 1999. We thank

Kenneth Ayotte and Michael Mitton for

excellent research assistance, Michael

Haid for giving us access to his data set

of oil companies, and David Yermack for

giving us access to his data on execu-

tive compensation. Financial support was

provided by the Russell Sage Foundation,

the Princeton Industrial Relations

Section, and the Princeton Center for

Economic Policy Studies.

Marianne Bertrand and Sendhi

Mullainathan, “Are CEOs Rewarded for

Luck? The Ones without Principals Are,”

originally appeared in The Quarterly

Journal of Economics, 116:3 (August

Fellows of Harvard College and the

Massachusetts Institute Technology.

Reprinted with permission.

Publication of this Selected Paper

was supported by the Albert P. Weisman

Endowment.

07-03/13M/CN/02-149

Design: Sorensen London, Inc.

K5777

U of Chicago #34920 Assm: NS

Abstract

The contracting view of CEO pay assumes that shareholders use pay to solve

an agency problem. Simple models of the contradicting view predict that pay

should not be tied to luck, where luck is defined as observable shocks

to performance beyond the CEO’s control. Using several measures of luck,

we find that CEO pay in fact responds as much to a lucky dollar as to a

general dollar. A skimming model, where the CEO has captured the pay-

setting process, is consistent with this fact. Because some complications to

the contracting view could also generate pay for luck, we test for skimming

directly by examining the effect of governance. Consistent with skimming,

we find that better-governed firms pay their CEOs less for luck than for

performance.

Marianne Bertrand

and

Sendhil Mullainathan

Are CEOs Rewarded for Luck?

The Ones without Principals Are

Selected Paper Number 862

I. Introduction

CEO pay usually is viewed through the lens of principal agent models. Under this

contracting view, pay is used to reduce the moral hazard problem that arises because

CEOs often own very little of the firms they control. Shareholders (perhaps acting

through the board or the compensation committee) optimally design the pay pack-

age in order to increase the CEO’s incentive to maximize firm value.1Simple mod-

els of the contracting view generate one important prediction: shareholders will not

reward CEOs for observable luck. By luck, we mean changes in firm performance

that are beyond the CEO’s control. Tying pay to luck, therefore, cannot provide

better incentives and will only make the contract riskier (Holmstrom 1979).2

This paper starts using three measures of luck to examine whether CEOs are in

fact paid for luck.3First, we perform a case study of the oil industry, where large

movements in oil prices tend to affect firm performance on a regular basis. Second,

we use changes in industry-specific exchange rate for firms in the traded goods

sector. Third, we use year-to-year differences in mean industry performance

to proxy for the overall economic fortune of a sector. For all three measures, we

find that CEO pay responds significantly to luck.4In fact, we find that CEO pay is

as sensitive to a lucky dollar as to a general dollar. Moreover, these results hold

as well for discretionary components of pay—salary and bonus—as they do for

options grants.

These results are inconsistent with a simple contracting view. Motivated by

practitioners such as Crystal (1991), we propose an alternative, skimming, that can

explain these results (Bertrand and Mullainathan 2000a). The skimming view also

begins with the separation of ownership and control, but it argues that this separa-

tion allows CEOs to gain effective control of the pay-setting process itself. Both

because of entrenchment, such as packing the board with supporters, and because

of the complexity of the pay process, many CEOs de facto set their own pay, with lit-

tle oversight by shareholders. Their pay level then becomes constrained by an

unwillingness to draw shareholders’ attention. Pay for performance arises in the

skimming view because good performance may ease these constraints, in essence

creating slack for the CEO. In other words, when the firm is doing well, sharehold-

ers are less likely to notice a large pay package. To the extent that lucky dollars cre-

ate slack as readily as general dollars do, pay for luck arises.

Finding pay for luck, however, does not necessarily single out the skimming

model. Complications to the agency model can make it such that paying for luck is

in fact optimal. For example, suppose the value of a CEO’s human capital rises and

falls with industry fortunes. One would then find that pay correlates with luck

because the CEO’s outside wage moves with luck. Another possibility is that boards

may tie pay to luck in order to motivate CEOs to forecast or respond to luck shocks.

1. Murphy (1985, 1986)

is a forerunner of the

vast empirical literature

on the contracting view.

Murphy (1999) and

Abowd and Kaplan

(1999) summarize the

CEO pay literature.

Formal tests of the con-

tracting view can be

found in Gibbons and

Murphy (1990, 1992),

Garen (1994), Hubbard

and Palia (1994),

Bertrand and

Mullainathan (1999),

and Aggarwal and

Samwick (1999a,

1999b).

2. Note our emphasis

on observable luck. In

any model, given the

randomness of the

world, CEOs (and

almost everyone else)

will end up being

rewarded for unobserv-

able luck. Note also our

emphasis on the fact

that this prediction

holds in simple agency

models. As we will dis-

cuss shortly, complica-

tions to the agency

model can in principle

alter this result.

3. Blanchard, Lopez-

de-Silanes, and

Shleifer (1994) present

suggestive evidence on

pay for luck by showing

that windfall gains from

court rulings raise the

pay of CEOs. It is only

suggestive, because

court rulings may not

be luck but rather a

result of the CEO’s

work. In another

domain, Shea (1999)

independently per-

forms an exercise simi-

lar to ours for baseball

players.

Bertrand and Mullainathan 3

Section II.D discusses whether arguments such as these can truly explain the pay-

for-luck relationship.

To differentiate skimming from these explanations further, we empirically

examine a direct implication of the skimming model. Skimming should be less

prevalent in better-governed firms. Well-governed firms, such as those with a large

shareholder on the board, limit the CEO’s ability to capture the pay process. We test

this hypothesis using several measures of governance: presence of large sharehold-

ers (on the board and overall), CEO tenure (interacted with the presence of large

shareholders to better proxy for entrenchment), board size, and fraction of direc-

tors that are insiders. Consistent with skimming, we generally find that the better-

governed firms pay less for luck.5These effects are strongest for the presence of

large shareholders on the board. An additional large shareholder on the board

reduces pay for luck by 23% to 33%. Large shareholders are especially important

as CEO tenure increases, consistent with the idea that, unchecked, CEOs can

entrench themselves over time. If pay for luck was optimal, we would have expected

well-governed firms to pay for luck as much as (if not more than) poorly governed

firms do. For example, whether or not a large shareholder is present, the CEO

would have to be rewarded for a rise in the value of his human capital. These find-

ings suggest that at least some of the pay for luck in poorly governed firms is due

to skimming by CEOs.

II. Pay for Luck Test

II.A Theoretical Background

A simple theoretical model will make more precise what agency theory says about

the reward for observable luck. Consider a standard agency setup, where risk-neu-

tral shareholders try to induce a risk-averse top manager to maximize firm per-

formance. Since the actions of the CEO can be hard to observe, shareholders will be

unable to sign a contract that specifies these actions. Instead, shareholders will

offer the CEO a contract in which the compensation level will depend on the firm’s

performance. Let prepresent firm performance and athe CEO’s actions, which by

assumption are unobservable to the shareholders. Firm performance depends on

the actions of the CEO and on random factors. We split the random factors into two

components: those that can be observed by shareholders and those that cannot. For

an oil firm, the price of crude oil would be an observable random factor. Letting o

be the observable factor and ube the unobservable noise term, we assume that per-

formance can be written as paou.

Under some technical conditions (CARA utility and Brownian motion for

the performance process), Holmstrom and Milgrom (1987) calculate the optimal

incentive scheme for this model. Let sdenote this incentive scheme. Since

4. This last test very

much resembles the

approach followed in

the relative perform-

ance evaluation (RPE)

literature (Gibbons and

Murphy 1990,

Janakiraman, Lambert,

and Larcker 1992, and

Aggarwal and Samwick

1999a). Problems can

arise with RPE as a spe-

cial case of luck.

Filtering this specific

kind of luck may not be

optimal from an agency

theoretical point of

view. As Gibbons and

Murphy (1990) note,

relative performance

evaluation can distort

CEO incentives if they

can “take actions that

affect the average out-

put of the reference

group.” Aggarwal and

Samwick (1999b)

develop a formal model

along these lines. By

using other shocks to

performance that are

even more objectively

beyond managerial

influence, we circum-

vent these problems.

5. Whenever we refer to

“less pay for luck,” we

mean that there is less

pay for luck relative to

the amount of pay for

performance. Thus,

these results would not

be driven by well-gov-

erned firms simply giv-

ing less overall pay for

performance. In fact,

we find that governance

correlates very little

with pay for perform-

ance, only with pay for

luck.

Selected Paper Number 864

shareholders can observe only two variables, pand o, the incentive scheme could

depend at most on these two variables. In fact, shareholders will reward CEOs only

for performance net of the observable factor:

(1) s~po!~au!.

In other words, the optimal incentive scheme filters the observable luck from

performance. This is because leaving oin the incentive scheme provides no added

benefit to the principal as, by definition, the agent has no control over o.

Motivating the CEO on o has no incentive effects. Beyond providing no benefit,

tying pay to luck actually costs the principal because the variance of the incentive

scheme is higher, and the principal must increase mean pay to compensate the

risk-averse CEO.

In practice, explicit incentive contracts, such as options, rarely filter. For

example, options are rarely, if ever, indexed against market performance. This

need not be inconsistent with a lack of filtering, however. It may be that the discre-

tionary components of pay, such as salary and bonus, are the ones used to filter. In

theory, these other components could adjust enough to undo the effect of the

options value fluctuating with luck. Such adjustment could happen if a board were

to monitor luck and alter each year’s salary, bonus, and number of new options

granted so that the CEO’s overall pay package remained free of luck.

II.B Empirical Methodology

Within the agency framework, most of the empirical literature on CEO pay estimates

an equation of the form:

(2) yit*per fit gixtX*Xit eit

where yit is total CEO compensation in firm iat time t,per fit is a performance

measure, giare firm-fixed effects, xtare time-fixed effects, and Xit are firm- and

CEO-specific variables such as firm size and tenure. The coefficient captures the

strength of the pay for performance relationship.

Performance is typically measured as changes in either accounting returns or

stock market returns, and we will use both measures.6In measuring compensation,

yit, much of the literature focuses on the flow of new compensation. Ideally, the

compensation in a given year also would include changes in the value of unexer-

cised options granted in previous years (Hall and Liebman 1998). Such a calcula-

tion requires data on the accumulated stock of options held by the CEO each year,

whereas existing data sets, including ours, contain only information on new options

granted each year. Consequently, our compensation measure excludes this compo-

nent of the change in wealth. For our purposes, however, this exclusion does not

pose much of a problem. The change in wealth due to changing option values is

6. These are flow meas-

ures. In practice, given

the firm-fixed effects,

we will use market

value and level of

accounting returns as

measures of per fit.

Bertrand and Mullainathan 5

mechanically tied to luck because options are not indexed. Thus, even if these data

were available, focusing on the subjective components of pay would still be a natu-

ral strategy. We discuss this issue at greater length in section II.D.

To estimate the general sensitivity of pay to performance, we will follow the lit-

erature and estimate equation (2) using a standard ordinary least squares (OLS)

model. To estimate the sensitivity of pay to luck, we need to use a two-stage proce-

dure. In the first stage, we will predict performance using luck in order to isolate

changes in performance that are caused by luck. In the second stage, we will see

how sensitive pay is to these predictable changes in performance. This two-stage

procedure is essentially an instrumental variables (IV) estimation, where the luck

variable is the instrument for performance.7

Letting o be luck, the first equation we estimate is

per fit b*oit gictaX*Xit eit

where oit represents the luck measure (oil price, for example). From this equation

we predict a firm’s performance using only information about luck. We call this

predicted value per

^

fit. We then ask how pay responds to these predictable changes

in performance due to luck:

yit Luck *per

^

fit gixtaX*Xit eit

The estimated coefficient Luck indicates how sensitive pay is to changes in

7. One might wonder

why we should use

this procedure rather

than simply including

o directly into the pay

for performance

equation (2) and run-

ning OLS to estimate

yit*per fit f*o

gixtX*Xit 

eit. This equation is

hard to interpret, how-

ever. Even if there is no

pay for luck, the coeffi-

cient fwill equal not

, but rather ,

as we can see from

equation (1). Since we

do not estimate , the

estimated coefficient f

can be small either

because there is pay for

luck or simply because

is small. The first

equation in the IV pro-