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THE JOURNAL OF INDUSTRIAL ECONOMICS
Volume LV
June 2007
0022-1821
No. 2
PRODUCT MARKET COMPETITION AND AGENCY COSTS
Jen Baggsw
Jean-Etienne de Bettigniesz
We model the effects of competition on managerial efficiency and isolate
the agency effect of competition, present only in firms subject to agency
costs, from the direct pressure effect of competition, which is present in
all firms. Using a unique set of Canadian data that surveys both firms
and their employees, we then evaluate the empirical significance of these
two effects. We find that competition has a significant direct pressure
effect as well as a significant agency effect. Both effects increase the
importance firms place on quality improvements and cost reductions as
well as on contractual incentives and employee effort.
I. INTRODUCTION
ECONOMISTS HAVE A ‘VAGUE SUSPICION that competition is the enemy of sloth’
(Caves [1980] p. 88; cited in Nickell [1996]); yet the process through which
competition improves managerial effort is still not fully understood. There
are two primary ways to think about this process. Competition may put
direct pressure on firms to increase quality (or decrease costs)Ffor example
by increasing the marginal impact of such an increase on expected profitsFa
pressure that is passed on to agents through higher powered incentives. But
competition may also reduce agency costs, making it ‘cheaper’ for the
principal to elicit more effort from the agent.1 The purpose of this paper is
We thank two anonymous referees and the editor for very helpful comments. We are also
grateful to Statistics Canada, in particular the BLMA division, for giving us access to the data
used in this paper. We thank Richard Arnott, Jim Brander, Murray Frank, Keith Head,
Thomas Hellmann, John Ries, Tom Ross, Johannes Van Biesebroeck, Jim Vercammen and
Ralph Winter, as well as seminar participants at Queen’s University, the University of British
Columbia, the University of Florida, the University of Guelph, the University of Victoria, the
CEA meetings (Hamilton, 2005), the IIO conference (Atlanta, 2005), the FMA European
meetings (Siena, 2005), and the WFA meetings (Portland, 2005) for their suggestions and
advice. We gratefully acknowledge financial support from Social Sciences and Humanities
Research Council (SSHRC) MCRI grant 412-98-0025 and (Bettignies) from the Robert and
Carol Friesen Research Fellowship. All remaining errors are ours.
wAuthors’ affiliations: Faculty of Business, University of Victoria, PO Box 1700, STN CSC,
Victoria, British Columbia, V8W 2Y2, Canada.
e-mail: [email protected]
zSauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver,
British Columbia, V6T 1Z2, Canada.
e-mail: [email protected]
1
We thank an anonymous referee for suggesting this motivation.
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MA 02148, USA.
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
first to isolate theoretically the direct pressure effect from the agency effect
and then to measure the empirical impact of these effects on firms’ strategic
choices, contractual incentives and employee effort.
To that end, we propose a simple duopoly model where two firms compete
in quality and price. Within each firm, agency problems may arise from nonverifiable efforts and managerial wealth constraints. Competition is
measured by the degree of substitutability between products and has two
impacts in our model. First, by making demand more elastic, it increases the
impact of a quality improvement on the market share one can ‘steal’ from a
rival; we call this the increased business stealing effect. Second, it reduces
price-cost margins; we call this the rent reduction effect.
We show that the increased business stealing effect of competition, by
increasing the marginal impact of a quality increase on expected profits, puts
direct pressure on firms to provide more incentives and elicit higher agent
effort in order to improve quality. Rent reduction, on the other hand, works
the other way: it lowers the marginal product of quality, and hence puts
direct pressure on firms to reduce quality. The combination of these two
effects generates the direct pressure effect of competition (the increased
business stealing effect, net of rent reduction) and affects all firms.
In firms where agency costs are present, the increased business stealing
effect and the rent reduction effect also work through an additional channel:
they both reduce firms’ marginal cost of eliciting effort from agents. This
agency effect of competition has a positive impact on firms’ equilibrium
choice of product quality, the power of incentives, and employee effort.
Our theoretical analysis naturally calls for an empirical assessment of the
signs of the direct pressure effect and the agency effect. To address these
issues, we exploit a detailed set of linked employer-employee data that allows
us to observe simultaneously the presence (or absence) of agency costs in
firms, the intensity of competition firms face, the strategies they pursue, the
types of contracts and incentives offered to their employees, as well as
detailed information about individual employee effort. We isolate the
agency effect of competition from the direct pressure effect, and determine
their empirical significance. We find that, first, competition does have a
positive direct pressure effect. Even in firms in which agency costs are absent,
competition increases the importance firms place on quality improvements
and cost reductions, the intensity of contractual incentives, and individual
employee effort, suggesting that increased business stealing empirically
dominates rent reduction. Second, we find that competition also has an
agency effect. Indeed, the positive impact of competition on these variables
is even larger for firms that are subject to agency costs.
The theoretical literature on competition and incentives can be divided
into two broad categories depending on how agency problems are assumed
to arise. On the one hand, in hidden information models, inefficiencies arise
mainly because the agent has superior information, relative to the principal,
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about an important parameter such as the firm’s level of productivity. In
these frameworks, the effects of competition depend on the type of contract
designed in equilibrium, which in turn depends on managerial preferences.
In Hart [1983], preferences are such that a target profit for the manager is
optimal. Competition, by reducing the market price, induces managers to
increase their cost-reducing efforts, in an attempt still to meet profit targets.
In contrast, in Scharfstein [1988], managerial preferences require a statecontingent contract, and the impact of competition is shown to be negative.
On the other hand, in hidden action models, inefficiencies arise because
managerial effort is not verifiable. In Hermalin [1992], the main impact of
competition is an income effect. Since leisure is a normal good, his argument
suggests that competition, by reducing income, should lead the manager to
consume less leisure and work more. In Schmidt [1997], the increased threat
of liquidation associated with competition is what motivates the manager to
exert more effort. Finally, in Raith [2003], the effect of competition on
incentives and effort takes place through a change in the equilibrium number
of firms in the industry.
Our theoretical model makes two primary contributions to the literature.
First, using a Hotelling [1929] model of competition, we bring strategic
interactions between firms to the forefront of the model. Among other
things, this allows us to characterize the increased business stealing effect of
competition, which plays a key role in the derivation of our results. These
strategic interactions are absent in previous work.2 Indeed, Hart [1983] and
Scharfstein [1988], for example, use models of perfect competition in which
(increased) business stealing plays no role. In their models, an increase in
competition is measured by an increase in the proportion of ‘efficient’
entrepreneurial firms in the economy, which in turn leads to increased
aggregate supply and a fall in the market price.
Perhaps more importantly, although the effects of competition previously
identified in the literature emerge in the context of agency models, the link
between these effects and agency costs remains fuzzy. Indeed it is unclear
whether these effects are specifically related to agency problems and present
only in firms dealing with such issues, or whether they are unrelated to
agency problems and thus take place in all firms. Thus, the second key
contribution of our theoretical model is to disentangle these two types of
effects: we identify a positive agency effect that is distinct from the direct
pressure effect of competition. In doing so, we shed light on the precise
channels through which competition affects incentives, effort, and efficiency.
The empirical literature does seem to confirm a positive impact of
competition, measured in a variety of ways, on efficiency. Increased number
2
Raith [2003] is an exception. See also Bettignies [2006], which studies the impact of strategic
interactions on the boundaries of the firm in an incomplete contract framework.
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of competitors and lower levels of rents (Nickell [1996]) as well as lower
industry concentration (Haskel [1991]), for example, are shown to
significantly increase total factor productivity growth. Industry concentration has also been shown to reduce technical efficiency (Caves and Barton
[1990]; Green and Mayes [1991]; Caves et al. [1992]). As well, Syverson
[2004a, 2004b] recently showed that substitutability between products has a
positive impact on average productivity levels.
Much less work has been done, however, to analyze empirically howFi.e.,
through which processFcompetition affects efficiency. Several papers have
looked at pieces of this puzzle, including Burgess and Metcalfe [2000],
Santalo [2002], Cuñat and Guadalupe [2005], who find evidence of a link
between competition and managerial incentives, and Griffith [2001], who
shows that competition increases productivity and that this effect is larger in
firms where agency costs are present. Exploiting a more recent version of the
survey data used by Santalo [2002] which includes a richer set of variables to
choose from, we contribute to the empirical literature by providing a more
accurate picture of the precise channelsFdirect pressure and agency effectsF
through which competition affects not only efficiency and contractual
incentives, but also effort.
The paper is structured as follows. Section II presents our theoretical
model and results. We discuss the implications of the model, and their
empirical implementation, in section III. We describe the data in section IV
and our empirical results in section V. Section VI concludes.
II. THEORETICAL MODEL
II(i).
Basic Structure
Two firms, 1 and 2, are positioned at each end of a Hotelling [1929] line, with
locations x1 5 0 and x2 5 1, respectively. The two firms sell imperfectly
substitutable products and compete on quality q and price p. Marginal costs
of production for both firms are normalized to zero. Each firm is composed
of a principal and an agent, both of whom are risk-neutral. The principalagent relationship could be interpreted as the relationship between a board
of directors and the chief executive officer (CEO) of the firm, or between a
divisional manager and her subordinate, for example. For convenience, we
refer to the principal as female and to the agent as male.
A unique consumer, whose location is random and uniformly distributed
along the line, purchases one unit of the product from either firm 1 or firm 2.
Firms 1 and 2 know the location distribution of the consumer, but they do
not know the actual location on the line. At location x, the consumer incurs a
transport cost tx for travelling to firm 1 and a cost t(1 x) to visit firm 2. The
consumer enjoys conditional indirect utility U1 5 s þ q1 p1 tx from
product 1 and U2 5 s þ q2 p2 t(1 x) from product 2 (where s represents
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income) and simply chooses the product which gives the highest utility. The
timing of the game is as follows:
At date 0, principal i, i 5 1,2, makes a take-it-or-leave-it contractual offer
to agent i, who is wealth constrained with zero initial wealth and has a
reservation wage of zero. Offer i is only observable to agent i (and not to
agent j), a necessary assumption for the existence of equilibrium in our
model. This assumption is consistent with the fact that managers and
employees typically do not know the exact conditions stipulated in the
employment contract for the equivalent position in rival firms.
At date 1, agent i exerts effort ei at cost Kðei Þ ¼ 12e2i . Effort determines the
level of innovation undertaken by firm i and the product quality qi that results
from it. For simplicity we set qi 5 ei; hereafter, we refer to qi using agent effort
or product quality interchangeably. Note that all of the theoretical results of
the paper still hold if we assume that effort reduces the marginal cost of
production instead of increasing quality or that it affects both cost and
quality. This is confirmed empirically below, where we show that the results
are similar for quality-enhancing and cost-reducing investments.
At date 2, after observing qualities, principal i chooses price pi. The same
results apply if the pricing decision is given to the agent: this assumption is
made for clarity purposes and is without loss of generality.
At date 3, the consumer chooses one of the products and demands are
realized. Firm i realizes profits Pi which are split between the agent, who
receives payoff Wi according to the contract signed at date 0, and the
principal, who keeps Pi Wi.
Transport cost t, which measures the degree of horizontal product
differentiation, is an ideal parameter to represent toughness of competition
(or rather lack thereof ) in the industry, to use Sutton’s [1992, p. 9]
terminology. Throughout the paper, an increase in product market competitionis represented
by a decrease in t. We restrict our attention to values of
i
2
,
which
ensures
strict concavity of all maximization programs
t 2 4=3
;
9 9
throughout the paper and non-negative effort levels in both firms.
We assume that total revenues and hence profits are contractible. In
contrast, demands and prices are not verifiable and cannot be contracted
upon (although they are observable). This assumption, which helps us keep
the analysis simple by generating second-best equilibrium contracts that are
contingent only on profits, is not unreasonable. Indeed, in order for sales and
price of a product to be verifiable in a court of law, the nature of that product
must be described ex ante in a way that allows a judge to match products with
sales and prices. In practice, firms sell not one but a variety of products, the
nature of which changes enormously over time depending on contingencies
such as technological innovations or market conditions. We argue that these
products cannot be unambiguously described ex ante, and hence contracts
cannot be made contingent on associated sales or prices.
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For similar reasons, product quality (effort), though observable, may or
may not be verifiable: the multidimensionality of quality might make it
difficult to describe precisely in a contract ex ante (Hart and Holmström
[1987], p. 134). We analyze both possibilities. In subsections II(ii) and II(iii),
we characterize the subgame-perfect Nash equilibrium of the game (since in
our duopoly setting there are simultaneous moves at every stage by the two
rival firms) when quality is verifiable and not verifiable, respectively.
Depending on the verifiability of quality, the optimal contract may be
contingent on realized profits and/or product quality: Wi 5 Wi(Pi, qi). Three
conditions must hold for any contract to be feasible:
a) Incentive compatibility constraint: agent i exerts effort qbi , which
maximizes his expected gross payoff wi – which is a function of
expected profits pi(qi) and/or quality – minus his cost of effort:
ð1Þ
qbi 2 argmax½wi ðpi ðqi Þ; qi Þ Ki ðqi Þ:
b) Participation constraint: for the agent to participate, his expected
net payoff must be weakly larger than his (zero) reservation wage:
ð2Þ
wi ðpi ðqbi Þ; qbi Þ Ki ðqbi Þ*0:
c) Wealth constraint: the agent is wealth constrained with zero initial
wealth, and thus his realized payoff must be non-negative in all
states of the world:
ð3Þ
II(ii).
Wi ðPi ; qbi Þ*0 for all realized values of profits Pi :
Equilibrium with Verifiable Quality (First-Best)
In this subsection, we consider the case of firms that have verifiable qualities.
We determine the subgame-perfect Nash equilibrium and verify that the
first-best (FB) level of effortFi.e., the level that would be exerted if the
principal and the agent were one and the same personFcan be achieved.3
We then analyze how the equilibrium is affected by competition.
When quality is verifiable, principal i can elicit effort qi from agent i by
offering
wage
himthe following contract at date 0: the agent is to receive
Wi qi ¼ K qi ¼ 12q2
i at date 3 if quality is verified to be qi ¼ qi and Wi 5 0
otherwise. Note that the incentive compatibility constraint (1), the
participation constraint (2), and the wealth constraint (3) all hold under
the conditions of this offer. Therefore, the contract will be accepted by the
3
Note that the analysis in this section is not just a theoretical benchmark as in other papers: it
highlights equilibrium conditions for the subset of firms in which agency costs are either absent
(e.g., in cases where the owner and the employee are the same person), or can be circumvented
(e.g., when the agent’s effort can be verified). As shown in the empirical analysis below, this
subset represents a non-trivial fraction of the population of firms.
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agent and will induce him to exert the equilibrium effort qi chosen by the
principal. The equilibrium of the game can be determined by backward
induction as follows:
At date 3, principal i receives realized payoff Pi(qi, pi, qj, pj, t) Wi(qi).
At date 2, principal i chooses pi to maximize her expected payoff, taking
qualities as given:
ð4Þ
max pi ðqi ; pi ; qj ; pj ; tÞ Wi ðqi Þ;
pi
where expected profits pi(qi, pi, qj, pj, t) 5 pidi(qi, pi, qj, pj, t) are the product of
price and expected demand.4 Taking the first-order conditions with respect
to price for i 5 1,2 and solving the resulting system of two equations yields
the following equilibrium price:
ð5Þ
pi ¼ t þ
qi qj
:
3
Substituting equilibrium prices back into the expected demand, we obtain
an expression for expected profits as a function of qualities:
h
qi qj i 1 qi qj
þ
ð6Þ
pi ðqi ; qj ; tÞ ¼ pi ðqi ; qj ; tÞdi ðqi ; qj ; tÞ ¼ t þ
;
2
3
6t
q q where di ¼ 12 þ i 6t j is the expected demand for firm i.
At date 1, agent i exerts the effort level qi ¼ qi stipulated in the incentive
compatible initial contract.
At date 0, principal i simply chooses the level of effort qi to elicit from the
agent. This equilibrium level of effort maximizes the principal’s expected net
benefit, pi(qi, qj, t) wi(qi), which simplifies to NBFB
i ¼ pi ðqi ; qj ; tÞ Kðqi Þ.
corresponds
to
the
first-best
objective
function, which
Unsurprisingly, NBFB
i
would be maximized if the principal and the agent were one and the same
person and there were no agency costs. In other words, when quality is
verifiable, principal i can perfectly circumvent agency costs by contracting
directly on quality. Taking the first-order condition, she chooses qi ¼ qi
such that:
ð7Þ
@Ki @pi q ; qj ; t ¼
q ;
@qi i
@qi i
i.e., such that the marginal product of effort equals the agent’s marginal
cost of effort, as in the first-best. The first-order conditions for principals
4
A consumer located at x is indifferent between store 1 and 2 if and only if U1 5 U2, or
q1 p1 tx ¼ q2 p2 tð1 xÞ. Solving for x, we
easily derive the
expected demand
ðpj pi Þþðqi qj Þ
1
:
(purchase probability) for firm i: di qi ; pi ; qj ; pj ; t ¼ 2 þ
2t
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i and j form a system of two equations in two unknowns, which can be
readily solved. The unique solution is the symmetric first-best equilibrium
in which principals i and j elicit effort level qi ¼ qj ¼ 13 ¼ q from their
agent. Thus:
Lemma 1. With verifiable quality, the subgame-perfect Nash equilibrium
is the following. At date 0, both principals propose to pay their agents
W ðq Þ ¼ 12q2 at date 3 if first-best quality q ¼ 13 is verified and zero
otherwise. At date 1, agents exert first-best effort q . At date 2, prices are
chosen following (5), which yields pi ¼ pj ¼ t; and expected demands equal
di ¼ dj ¼ 12. Finally, demands and profits are realized, and the initial
contract is honored.
Proof.
Follows directly from above.
Effects of Product Market Competition. Competition affects equilibrium
effort to the extent that it affects principal i’s marginal benefit from eliciting
effort by her agent, net of her marginal cost of doing so. Indeed, starting
from an equilibrium situation where condition (7) holds, if for example an
increase in competition raises principal i’s marginal benefit from an effort
increase above the marginal cost, then her optimal response is to increase qi
(by strict concavity of her maximization program) until condition (7) holds
again. Principal j reacts in the same way, and a new equilibrium is reached.
As shown above, with verifiable quality, the principal’s marginal cost of
eliciting effort is simply the agent’s marginal cost of effort, @K@qðqi i Þ ¼ qi , which
is independent of t and unaffected by competition. In contrast, the
principal’s marginal benefit from inducing effort, which corresponds to
i
the marginal product of effort @p
@qi , is affected by competition. To see this,
note first that firm i’s marginal product of effort, given effort levels qi and qj,
can be obtained from (6) by differentiating expected profits with respect to qi:
@pi
@pi
@di
@qi ðqi ; qj ; tÞ ¼ @qi di ðqi ; qj ; tÞ þ @qi ðtÞpi ðqi ; qj ; tÞ. In equilibrium (when firms
choose identical strategies), this simplifies to:
@pi @pi @di
q ;q ;t ¼
d þ
ðtÞpi ðtÞ:
½8
@qi i j
@qi i @qi
The marginal product of effort can thus be expressed as the sum of two
factors. First, increasing effort/quality enables the firm to charge a higher
i
price to reflect the higher product quality: @p
@qi > 0; and the impact on expected
profits is the marginal change in price times equilibrium expected demand
@pi @qi di . Second, increasing effort/quality also allows firm i to gain a quality
i
advantage over its rival, and to ‘steal’ market share as a result: @d
@qi ðtÞ > 0. We
call this the business stealing impact of an effort/quality increase; and its
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impact on expected profits is the marginal change in expected demand times
i
the equilibrium price, @d
@qi ðtÞpi ðtÞ.
It is easily shown that competition does not affect the first factor. Indeed,
1
i
neither the marginal change in price @p
@qi ¼ 3, nor
equilibrium expected
i demand di ¼ 12, are functions of t, and hence @ @p
@qi di =@t ¼ 0. Therefore the
impact of competition on the marginal product of effort can be obtained by
differentiating the second factor with respect to t:
½9
@ 2 pi
@ 2 di @pi @di
:
¼
p þ
@qi @t @qi @t i
@t @qi
An increase in product market competitionFor, equivalently, a fall in
t – affects the marginal product of effort in two conflicting ways. First, by
making demand more elastic, competition increases the business stealing
@ 2 di
¼ 6t12 < 0. We call this the increased
impact of a quality improvement: @q
i @t
business stealing effect of competition. This effect of competition has a
@ 2 di positive impact on the marginal product of effort: @q
p < 0. Second,
i @t i
competition makes consumers more sensitive to prices and qualities, thus
@p
forcing firms to compete more fiercely and to lower their prices: @ti ¼ 1 > 0.
We call this the rent reduction effect of competition (in contrast to the
i
rent increase effect of quality @p
@qi in equation [8]). Since, as discussed above,
@di
@qi > 0,
effort:
rent reduction has a negative impact on the marginal product of
@pi @di
@t @qi > 0.
These results yield the following proposition:
Proposition 1: In the first-best, competition, through its increased business
stealing effect, raises the marginal product of effort. This has a positive
impact on principals’ net marginal benefit from an effort/quality increase,
and hence puts direct pressure on firms to elicit higher agent effort. However,
competition also has a rent reduction effect, which reduces the marginal
product of effort and hence works the other way. We define the direct
pressure effect of competition as the increased business stealing effect, net of
rent reduction.
Proof.
Follows directly from above.
The key implication of proposition 1 is that the sign of the direct pressure
effect of competition could in principle be positive or negative. If (and only
if ) increased business stealing dominates rent reduction, competition has a
positive impact on the principal’s (net) marginal benefit from an increase in
effort and puts direct pressure on firms to elicit higher effort/quality from
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their agents.5 To elicit this increase in effort, firms provide more incentive
to their agents; in the context of our first-best contract, this is achieved
by increasing the threshold level of quality q required
to
get positive
compensation, and the amount of that compensation Wi qi :
But does the increased business stealing effect dominate the rent reduction
effect? In the specific Hotelling framework considered here, the impact of
increased business stealing on the marginal product of effort, which
@ 2 di p ¼ 6t12 t ¼ 6t1 , is exactly offset by the impact of rent
simplifies to @q
i @t i
1
1
i @di
reduction, @p
@t @qi ¼ 16t ¼ 6t, and as a result, the direct pressure effect is null.
Vives [2004], on the other hand, shows that the direct pressure effect could be
positive or negative depending on the demand specification.6 The absence of
theoretical consensus on the direct pressure effect naturally calls for an
empirical assessment of sign of this effect. We address this question, and
other empirical implications of the model, in sections III-V.
II(iii).
Equilibrium with Non-Verifiable Quality (Second-Best)
If quality, though observable, is non-verifiable, it cannot be contracted upon
and contracts must be made contingent on profits.7 We focus on linear
contracts of the form W 5 aP þ b. In this subsection, we first characterize
the subgame-perfect Nash equilibrium, show that agency costs cannot be
circumvented, and then analyze the effects of competition on equilibrium
incentives and effort.
At date 3, principal i receives the following payoff: (1 ai)Pi(qi, pi, qj,
pj, t) bi.
At date 2, principal i chooses pi to maximize her expected payoff:
(1 ai)pi(qi, pi, qj, pj, t) bi, taking qualities as given. This maximization
yields the same equilibrium prices as the maximization described in (4), and
hence expected profits as a function of product qualities correspond to (6).
At date 1, agent i chooses qi so as to maximize his expected payoff
aipi(qi, qj, t) þ bi Ki(qi), taking qj as given. The agent chooses qi ¼ qbi such
5
The offsetting impacts of increased business stealing and rent reduction are not specific to
our Hotelling specification, and previous references to these effects can be found, for example,
in Anderson et al. [1992], p. 230, and in Raith [2003], in the context of logit framework, and
Salop [1979] circle, respectively.
6
To be precise, Vives [2004] finds a positive impact of competition with Shapley/Shubik
linear demands as well as in CES and constant expenditure models, but a negative impact with
Bowley linear demands. He does not explicitly isolate increased business stealing from rent
reduction.
7
This assumption of observable but non-verifiable quality is necessary for existence of
equilibrium. In Hermalin and Katz’s [1991] agency model with a risk-averse agent, this
assumption enables the principal to achieve the first-best through renegotiation after effort
exertion. This is not feasible in our model where both the principal and the agent are risk neutral
and there is no scope for renegotiation.
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that the incentive compatibility constraint holds:
@K
i
i
b
b
ð10Þ
ai @p
@qi qi ; qj ; t ¼ @qi ðqi Þ:
At date 0, principal i offers contract (ai, bi) to agent i. To determine the
optimal contract, the principal maximizes the following program:
ð11Þ
qi ; qj ; tÞ ðai pi ðb
qi ; qj ; tÞ þ bi Þ;
max pi ðb
q^i ;ai ;bi
subject to constraints ð2Þ; ð3Þ; and ð10Þ:
This optimization can be simplified as follows. First, ai must be strictly
positive, otherwise the agent, solving (10), would choose zero effort. And bi
must be non-negative: the wealth constraint (3)Fwhich can be expressed
here as aiPi þ biX0 for all Pi – simplifies to biX0 since it must hold even
when the consumer does not buy the product and realized profits Pi are zero.
Second, with ai 4 0 and biX0, the agent’s equilibrium expected payoff is
strictly positive since it can be no smaller than what he would get with zero
effort
he would choose zero effort), which itself is strictly positive:
(otherwise
ai pi qbi ; qj ; t þ bi Ki ðqbi Þ*ai pi ð0; qj ; tÞ þ bi > 0. Therefore, the participation constraint (2) is never binding and can be ignored. Note that this also
implies that the agent earns rents over and above his cost of effort; these rents
are the expression of the agency costs for the principal.
Third, since bi has a negative effect on the principal’s objective function
and does not affect incentive compatibility, it is optimal to set it as low as
possible, i.e., such that the wealth constraint binds: bi 5 0. The wealth
constraint can thus be replaced by bi 5 0 in the maximization program.
Finally, the incentive compatibility constraint
be expressed in
(10) can ^
q
q
ð
Þ
j
i
@K
@p
bi ; qj ; t ¼ @qii ðqbi Þ=@qii qbi ; qj ; t ¼ qbi = 13 þ 9t
;i.e., the value
terms of a
i q
bi ; qj ; t
of ai necessary to elicit an effort qbi from the agent. Substituting a
i q
into the objective function, the program simplifies to:8
ð12Þ
SB
max NBSB
qi ; qj ; tÞ a
qi ; qj ; tÞpi ðb
qi ; qj ; tÞ:
i with NBi ¼ pi ðb
i ðb
q^i
Taking the first-order condition, the principal chooses effort level
qbi ¼ q
i such that her marginal benefit from eliciting an increase in effort
8
Another way of solving this program is to solve (10) for qbi ðai ; qj Þ, to substitute qbi ðai ; qj Þ into
the objective function, and to maximize with respect to ai . While the two methods are formally
equivalent, here we use the former because it presents the second-best problem in terms of
optimal effort to be elicited from the agent, which can more easily be compared with the
optimal effort elicited in the first-best. In contrast, presenting the equilibrium results in terms
of optimal share of profits to be allocated to the agent is not conducive to comparisons between
first-best and second-best since in the first-best there are no a’s (the principal’s contract directly
on effort).
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
by the agent exactly equals her marginal cost of inducing such an increase:
ð13Þ
@pi @a pi
ðqi ; qj ; tÞ ¼ i ðq
i ; qj ; tÞ:
@b
qi
@b
qi
2 SB i
@ NB @ 2 NBSB
; 29 , which ensures
It can be shown that @q2 i þ @qi @qi j < 0 for all t 2 4=3
9
i
existence of a unique Nash equilibrium in effort (Vives [1999] pp. 47–48).
The symmetric equilibrium, provided it exists, therefore must be the unique
equilibrium of this game. Substituting q
i ¼ qj ¼ q into (13), we obtain
2
second-best
effort level q ¼ 3 3t, which is elicited by offering
a
q
;
q
;
t
¼ 3q to the agent. Thus:
i
i
j
Lemma 2. In the second-best, the subgame-perfect Nash equilibrium is as
follows. Both principals offer a fraction a ¼ 3q ¼ 2 9t of profits to
their respective agent. As a result, both agents choose effort q ¼ 23 3t.
Prices are chosen following (5), which yields p
i ¼ pj ¼ t; and expected
1
demands equal di ¼ dj ¼ 2. Finally, demands and profits are realized, and
the initial contract is honored.
Proof.
Follows directly from above.
Second-Best Versus First-Best Effort. A direct implication of lemmas
1 and 2 is that equilibrium
effort
i is lower in the second-best than in the first-
best: q < q for all t 2
4=3 2
9 ;9
. The intuition for this result is as follows.
When the principal can contract directly on effort/quality, her cost of
eliciting effort is simply the agent’s personal cost of effort, Ki ðqi Þ. In
contrast, when quality is not contractible, the only way the principal can
provide incentives is by giving up a fraction of profits to the agent; and
because of the agent’s wealth constraint, she cannot recoup this relinquished
share of profits through transfers. As a result, to the principal, the latter is a
more costly way of providing incentives. She must pay the agent not only his
cost of effort but also, as noted above, some additional rents, namely the
costs of agency. These agency costs translate into a higher marginal cost of
eliciting effort in the second best (everything else equal), leading to lower
effort in equilibrium.
To see this more formally, consider again equation (13), the principal’s
first-order condition in the second-best, which can be expressed as a function
of qi, qj, and t, as follows:9
9
a
i
@a
@Ki
@pi
@pi
i
i
Condition (13) can be expressed as: @p
@qi ¼ ai @qi þ @qi pi . To see why ai @qi ¼ @qi , recall that
@Ki @pi
@pi
¼ @qi =@qi . Substituting this into ai @qi gives the stated result.
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ð14Þ
301
@pi
@Ki
@a
ðqi ; qj ; tÞ ¼
ðqi Þ þ i ðqi ; qj ; tÞpi ðqi ; qj ; tÞ:
@qi
@qi
@qi
The principal’s marginal benefit from eliciting an increase in effort is the
i
marginal product of effort @p
@qi qi ; qj ; t , as in the first-best. But the marginal
cost of eliciting an increase in effort is different in the second-best: it is
i
the sum of the first-best marginal cost @K
@qi ðqi Þ, and another factor
@a
i
@qi ðqi ; qj ; tÞpi ðqi ; qj ; tÞ.
This second factor is the agency marginal cost of
inducing effort: it measures the increase in the fraction of profits that must be
paid out to the agent to induce him to increase effort.
To understand the difference between first and second best, consider the
behaviour of firms subject to agency costs, at the first-best equilibrium where
@a
qi ¼ qj ¼ q . The agency marginal cost @qi i pi , which is strictly positive in
equilibrium, implies that principal i’s marginal cost of eliciting an increase in
effort must be strictly larger than the marginal benefit at that point.10
Principal i therefore optimally responds by lowering qi down to the point
where (14) holds, taking rival effort as given. Principal j reacts in the same
way, and the second-best equilibrium is reached where the two principals
elicit lower agent efforts qi ¼ qj ¼ q .
Proposition 2. The presence of an agency marginal cost makes the
principal’s net marginal benefit from eliciting an increase in effort lower in
the second-best than in the first-best, everything else equal. As a result, in
equilibrium both principals elicit lower agent effort in the second-best.
Proof.
Follows directly from above.
This proposition verifies in a duopoly setting a result pioneered by
Sappington [1983] in a single firm model: agency costs associated with nonverifiable effort cannot be circumvented when the (risk-neutral) agent is
wealth constrained.
Note that the lower levels of effort in the second best are inextricably
associated with lower-powered incentives. Differences in compensation
schemes in the first and second best render difficult a comparison of
incentives across regimes. However, a first approximation of this difference
@a
where
It is easy to show that @qi i pi simplifies to 3t qj =2. At the first-best outcome
i
@a
2
qi ¼ qj ¼ q , we get @qi i pi ¼ 3t 13 =2, which is strictly positive for all t 2 4=3
9 ; 9 . Since the
@Ki @Ki
i
first-best equilibrium condition (7) requires @p
@qi qi ; qj ; t ¼ @qi qi , this implies that @qi þ
10
@a
@pi
i
@qi pi > @qi
when qi ¼ qj ¼ q . One can also verify that in the second-best equilibrium where
qi ¼ qj ¼ q , the agency marginal cost simplifies to 3t 13 > 0.
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can be obtained by comparing the power of incentives in second best,
a ¼ 2 9t, to the power that would have to be offered in the second best to
elicit the first best level of effort.
this is a ¼ 1, which is
Unsurprisingly
i
strictly superior to a for all t 2
4=3 2
9 ;9
.
Effects of Product Market Competition. It is immediately clear from
lemma 2 that in the second-best equilibrium, competition increases the
power of incentives a , and agent effort q . We now provide an intuition for
this result. From expression (14) we see that the direct pressure effect of
i
competition on the principal’s marginal benefit from eliciting effort ð@p
@qi Þ
must still be present here. However, competition also works through an
additional
channel in the second best, by reducing the agency marginal cost
@a
i
p
.
i
@qi
The agency marginal cost is the product of two
factorsFthe increase in
@a
incentives necessary to elicit higher agent effort @qi i , and expected profits piF
both of which are negatively affected by competition. The impact of
i
competition on expected profits is simply that rent reduction, @p
@t > 0, puts
downward pressure on prices, which in turn reduces expected profits. More
formally, looking back at (6), we see that in equilibrium when firms choose
@pi
1
i
identical strategies, @p
@t ¼ @t di ¼ 2 > 0.
To understand how competition affects the increase in incentives
@a
necessary to elicit higher agent effort @qi i , two points should be noted. First,
the size of this increase in incentives depends itself on the agent’s
responsiveness to incentives @@aq^ii . For example, if the agent’s responsiveness
to incentives is high, then only a small increase in a
i is necessary to generate
a given increase in effort. With lower responsiveness, a relatively larger
increase in incentives is necessary to achieve the same increase in effort.
Second, as shown in the appendix, responsiveness to incentives is a strictly
i
increasing function of @d
@qi , the business stealing associated with higher effort.
When responding to higher-powered incentives with higher effort, the agent
internalizes the impact of his response on the market share he can ‘steal’
from rivals: the larger this impact, the more responsive he 2is to incentives.
@ di
Competition, via its increased business stealing effect @q
< 0, increases
i @t
the market share the agent can steal with a marginal increase in effort. This
makes the agent more responsive to incentives, and in turn reduces the
@a
increase in incentives necessary to elicit higher agent effort @qi i . Together
these results yields the following proposition:
Proposition 3. In the second-best, the direct pressure effect of competition
i
on the principal’s marginal benefit from eliciting effort @p
@qi , is still present.
However, competition also works through an additional channel: increased
business stealing and rent reduction reinforce each other and jointly reduce
@a
the agency marginal cost @qi i pi , thus increasing the principal’s net benefit from
eliciting effort. We call this second factor the agency effect of competition.
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Proof.
See appendix 1.
This proposition characterizes an effect of competition that is present only
in firms subject to agency costs. In such firms, the principal’s marginal cost of
eliciting an increase in effort from the agent depends on the agent’s personal
marginal costs of exerting effort, and the agency marginal cost. Competition
reduces this agency marginal cost and hence makes it cheaper for the principal
to elicit a quality increase. This has a positive impact on principals’ net
marginal benefit from an effort/quality increase, and hence puts additional
pressure on firms to elicit higher agent effort with higher-powered incentives.
To obtain an expression for the impact of this agency effect on equilibrium
effort and on incentives, note that since the direct pressure effect is null in our
specific model, the agency effect equals the total effect of competition and
therefore can be obtained by differentiating equilibrium effort
and iincentives
with respect to t: @q@t ¼ 3 < 0, and @a@t ¼ 9 < 0 for all t 2
4=3 2
9 ;9
.
To our knowledge, our model is novel in identifying this agency effect of
competition. To highlight this effect, we explicitly disentangle the effects
of competition that are present in all firms from those that are present only
in firms subject to agency costs, unlike previous work that has focused on
the aggregate effect of competition in models of agency. Indeed, although
one may conjecture that the effects identified by Hermalin [1992], Schmidt
[1997], and Raith [2003] (see introduction) all belong to the direct pressure
category since they are likely to be present even in the absence of agency
costs, one cannot be sure whether the effect observed in the second best is a
direct pressure effect only, or in combination with some form of agency
effect. Conversely, the impact of competition in Hart [1983] may resemble an
agency effect, but it is unclear whether it would vanish in the first best.
We also depart from the previous work in two other ways. First, with our
Hotelling model of competition, we bring strategic interaction to the
forefront of the our analysis, and highlight the importance of the
relationship between increased business stealing and rent reduction. Second,
we use a simple model where agency arises due to the risk-neutral agent’s
wealth constraint (rather than risk aversion, as in the ‘classic’ principalagent model). The tractability of our agency model, together with a profitcontingent compensation scheme for the agent, play an important role in
deriving the agency effect and other results. Indeed, this may explain why
our agency effect is absent from Raith’s [2003] model, despite a competition
frameworkFa Salop [1979] circleFsimilar to ours. Unlike us he uses the
‘classic’ agency model with cost-reducing agent effort, and assumes that
agent compensation is cost-contingent rather than profit-contingent. Our
agency effect of competition is also absent in Schmidt’s [1997] model, even
though he uses an agency model with a risk-neutral but wealth-constrained
agent. This could be explained by the differences in modeling competition
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mentioned above and by the fact that in his binomial framework, the agent’s
compensation is contingent on the state of the world (good or bad) rather
than on realized profits.
III. EMPIRICAL IMPLICATIONS AND IMPLEMENTATION
Our model yields three key empirical implications. First, recall that our
discussion of proposition 1 led us to wonder about the empirical sign of the
direct pressure effect of competition on firms’ net benefit from a quality
increase, contractual incentives, and employee effort. If we observe
empirically that, in firms that are free of agency costs, competition increases
these variables, this will indicate that the direct pressure effect of competition is
positive, i.e. that increased business stealing dominates rent reduction.
Conversely a negative impact of competition will indicate that rent
reduction dominates increased business stealing.
The second key empirical implication results from proposition 3, which
states that in firms that are plagued by agency costs, there is, in addition to
the direct pressure effect, a positive agency effect of competition. This agency
effect of competition should have a positive impact on firms’ net marginal
benefit from a quality increase, and hence should put additional pressure on
firms to increase the power of incentives and employee effort. These two key
implications suggest that competition should have a differential impact
across firms. If the direct pressure effect of competition is positive, then the
agency effect should reinforce it, and the aggregate impact of competition
should be even more positive in firms subject to agency costs than in firms
that are not. On the other hand, if the direct pressure effect is negative, then
the agency effect should mitigate it, and the aggregate effect of competition
should be less negative in firms subject to agency costs.
Finally, the third empirical implication of our model, which results from
proposition 2, is the following. Agency costs should have a negative impact on
the net marginal benefit from a quality increase, and should put pressure on
firms to reduce the power of incentives and employee effort.
Our model describes a logical chain of events following a change in
exogenous variables such as competition or agency costs. For example, an
increase in the degree of competition raises firms’ net marginal benefit from
an increase in quality, and hence their quality target choice; to achieve this,
firms increase the power of incentives, and in turn, employee effort. Ideally,
we would be able to observe these events as they occur, recording a change in
competition at time t, the firms’ choice of quality in response to that change
at t þ 1, the contractual offer made to employees at t þ 2, and the effort those
employees exert in response to their new contract at time t þ 3. In practice,
however, t, t þ 1, t þ 2, and t þ 3 occur in rapid succession and, without daily
or weekly data, we are unable to observe these events in sequence, and
cannot model empirically the sequence of decisions implied by our theory.
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We do expect, however, that competition will have an impact on each
variable, namely the net marginal benefit from a quality increase, the power
of incentives, and employee effort; and we can test for that with annual
data. Naturally, we expect our empirical results to be consistent across
regressions. To test our theory, we propose the following empirical
specifications.
III(i). Importance of Quality Improvements
We start by examining firms’ net marginal benefit from a quality increase.
This theoretical concept can be interpreted as firms’ attitude towards a
quality increase, as a measure of the importance firms place on quality
improvements. Indeed, one would expect a firm’s long-term quality target to
be such that the net marginal benefit from a quality increase is zero. In the
short-term however, the net marginal benefit may be different from zero,
and the larger the net marginal benefit, the larger the quality increase
necessary to achieve the long-term goal (by strict concavity of the
maximization program). Consider the following linear regression:
ð15Þ
QUAL ¼ l0 þ l1 COMP þ l2 AGENCY þ l3 COMP AGENCY
þ l4 CONTROL þ e;
where QUAL represents the importance a firm places on quality improvements; COMP represents the degree of product market competition in terms
product substitutability (as in our theoretical model); AGENCY measures
agency costs and equals 1 when they are present in the firm, and to
0 otherwise; CONTROL is a vector of firm level control variables; and e is an
error term.
Equation (15) allows us to estimate the direct pressure effect of
competition, and the agency effect of competition, on firms’ attitudes
towards quality improvements. To see this, let us differentiate QUAL with
@QUAL
respect to COMP, which yields @COMP
¼ l1 þ l3 AGENCY.
An important implication of proposition 1 is that in firms that are not
subject to agency costs, the only impact of competition is the direct pressure
effect. This allows us to identify the direct pressure effect in our empirical
specification (15), since the impact of competition when AGENCY 5 0
@QUAL
simplifies to @COMP
¼ l1 . Indeed, l1 therefore econometrically captures the
direct pressure effect of competition on the importance firms place on
quality improvements. Our theoretical analysis suggests that the sign of l1 is
an open empirical question, since the direct pressure effect is the net of
two offsetting forces, increased business stealing and rent reduction.
A significantly positive l1 reflects increased business stealing dominance,
while a significantly negative l1 suggests rent reduction dominance.
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In firms that are subject to agency costs, as suggested in proposition
3, competition has both a direct pressure and an agency effect. In our
@QUAL
¼ l1 þ l3 when AGENCY 5 1. Since
specification, this is expressed as @COMP
l1 captures the direct pressure effect, we can identify l3 as the agency effect of
competition, which is predicted to be positive.
The impact of agency costs in equation (15) can be expressed as
@QUAL
@AGENCY ¼ l2 þ l3 COMP. It depends on l2, which can be interpreted as
the gross impact of agency costs on firms’ attitudes towards quality
improvements; and is also related to the agency effect of competition, l3 (if
the impact of competition is larger in firms subject to agency costs, then the
impact of agency costs is larger in more competitive industries). An
@QUAL
ought to be negative. Since
implication of proposition 2 is that @AGENCY
l3COMP is expected to be positive, we should find l2 to be negative;
sufficiently negative in fact for the net impact of agency costs l2 þ l3COMP
to be negative.
III(ii).
Incentives and Effort
Our model suggests that competitition affects the importance firms place on
quality improvements, contractual incentives, and employee effort in a
similar way, through a direct pressure effect and an agency effect. Thus, to
empirically examine the impact of competition on contractual incentives, we
propose a specification similar to (15):
ð16Þ
INCEN ¼ g0 þ g1 COMP þ g2 AGENCY þ g3 COMP
AGENCY þ g4 CONTROLEmp þ e;
where INCEN measures individual employee contractual incentives, and
CONTROLEmp is a vector of control variables which includes both firmlevel and employee level controls. In later specifications, our dependent
variable INCEN is replaced with EFFORT, a measure of individual
employee effort. We define the constant and the coefficients of COMP,
AGENCY, COMPAGENCY, and CONTROLEmp in the EFFORT regression as y0, y1, y2, y3, and y4, respectively.
With arguments similar to the ones used in our description of the
coefficients in the QUAL regression, it can easily be shown that g1 and y1
identify the direct pressure effect of competition on incentives and effort,
respectively. They should be of the same sign as l1, which could be positive or
negative. Coefficients g3 and y3 identify the agency effect of competition and
are predicted to be positive. Finally, g2 and y2 identify the impact of agency
costs on incentives and effort, and are expected to be significantly negative.
To test these empirical predictions, we have access to a unique dataset that
includes several measures of product market competition and of agency
costs, indications of firm attitudes towards quality improvements, the
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structure of employee contracts, and employee level measures of effort. We
now describe these variables in more detail.
IV. DATA
The Workplace and Employee Survey (WES)Fconducted by Statistics
Canada with the support of Human Resources Development Canada–is a
very rich longitudinal data set that consists of two components: 1) The
workplace survey of approximately 6,300 firms provides information on
work organization and organizational change, competitive environment,
business strategy, innovation, and firm performance; and 2) The employee
survey of approximately 25,000 employees in the same workplaces, which
contains information on compensation, human capital, training, work
hours and arrangements, and promotions. Taken together, these two
components generate approximately 1,000 firm and employee specific
variables and an unprecedented opportunity to examine the connection
between competition, contractual incentives and effort. To the best of our
knowledge, a comparable data set does not exist anywhere else. The WES
data is relatively new and to date has been predominantly used within
Statistics Canada and by a small group of labour economists, though its
potential for other applications is tremendous.
WES was first conducted in 1999 and has been readministered annually to
the selected cohort of firms over the following six years. WES is a linked
employer-employee file. Employers are sampled by physical locations, and
employees are then sampled from employer-provided lists within each
location. The survey covers all industries except farming, fishing, trapping,
and public administration and all regions of Canada with the exception of
the Arctic territories (the Yukon, Northwest Territories, and Nunavut).
Currently, data for 1999, 2000, and 2001 are available for analysis, and the
response rate for workplaces in each of these years is more than 95%. The
questions about firm strategy, which are used to construct our measures of
the emphasis firms place on quality improvements, were asked in 1999 and
2001 but not in 2000. In addition, our empirical model incorporates control
variables from t 1, eliminating the use of strategy responses from 1999 as
dependent variables. As a result, our main set of dependent variables is
derived from the 2001 WES, with independent variables drawn from both
2001 and 2000.
The process of sample selection for WES stratified businesses in Canada
into relatively homogeneous groups that were then used for sample
allocation and selection. Businesses were classified by fourteen industry
classifications, six regional classifications, and three employment size
categories, resulting in 252 possible strata. The strata were constructed so
as to maximize variation between strata and minimize variation within
strata. Firms are sampled using Neyman allocation, meaning firms are
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
sampled randomly from within each stratum; however, the choice of how
many firms to sample from each stratum depends not just on how many firms
are in the stratum (a stratum with 10% of the population does not
necessarily have 10% of the sample) but on how much variation there is
within the stratum. More firms are sampled from strata with higher
variances and fewer from strata with lower variances. To compensate for the
uneven numbers sampled, each sampled unit is assigned a sampling weight
based on its probability of selection. Using these strata and weighting
techniques, the survey was designed to render possible the estimation of
unbiased parameters that reflect the underlying population, despite the fact
that each workplace in Canada did not have an equal probability of
selection.11
All of our analysis is conducted with techniques expressly designed for
surveys. We control econometrically for selection as each observation did
not have an equal probability of being sampled. We control for clustering
since observations at the employee level were not sampled independently
from the population of Canadian workers; they were chosen from within the
surveyed firms. We also control for stratification; in our case firms were
sampled from 252 strata based on size, region, and industry, and sampling
within each stratum was random but unequal across strata. Statistics
Canada has calculated survey weights for each observation based on
probability of selection, sample clustering, and stratification; these weights
are used in all of our analyses. In addition, in all regressions, bootstrapping is
used to correct standard errors for the survey design.12
This paper uses survey data that have many advantages but suffer from
some lack of objectivity. While the considerable care and attention that went
into the construction and validation of WES has minimized many of the
problems faced by surveys conducted without the expertise and financial
backing of a national statistical agency, this may not have resolved all
possible forms of bias. A common criticism of this type of data is that firms’
self reports will be systematically biased, such as over reporting profits and
under reporting costs. While this may well be the case, we find no reason to
suggest that an upward bias in, for example, a firm’s self report of the
importance of quality improvements would be correlated with our measures
of competition. Another potential bias introduced by the use of survey data
11
See the Guide to the Analysis of the Workplace and Employment Survey for further details.
To compute the variances for estimates based on samples coming from finite populations,
it is important to account for the sample design. Estimation using only weights, without
accounting for design, results in the underestimation of the variance. This could have dire
consequences for hypothesis testing and for constructing confidence intervals. Accordingly, a
bootstrapping procedure is required. This technique is based on re-samplingFusing the
original sample, from which a simple random sample is selected with the replacement of as
many units as there were at the outset. This procedure is repeated many times to guarantee
consistency. We use these bootstrap weights in all analyses.
12
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occurs because the individuals completing the survey have different scaling
attitudes. Some tend to consistently use higher ratings and others lower
ratings; this increases the ‘noise’ in our data and likely inflates our standard
errors. Following Cooper and Emory [1995], we note that differences in
scaling attitudes do not introduce a systematic bias and, if anything, by
increasing standard errors, lead to more conservative results.
Importance of Quality Improvements (and of Cost Reductions). Variable
QUAL in regression (15) is meant to capture firms’ net marginal benefit from
a quality increase, which we interpret as the importance firms’ place on
quality improvements. The WES survey provides us with an excellent
measure of firms’ attitudes towards quality improvements, which we use as
our measure of QUAL: it asks firms to rank the relative importance of
improving product or service quality in their workplace’s general business
strategy. Firms rank the importance of quality as either 1 for ‘not applicable’
or describe the strategy’s importance on a scale of 2 to 6 where 2 is ‘not
important’ and 6 is ‘crucial.’
As noted in subsection II(i), our the model predicts the same effects of
competition for cost reduction as it does for quality improvement. The same
question asked with regards to the importance of quality is also asked
regarding the importance of cost reductions and we use these questions to
test both outcomes. In some of our specifications, QUAL is replaced by the
importance of cost reductions, denoted COST. The specific wording of
these, and all other questions used in this paper, can be found in appendix 2.
Product Market Competition. Recall from our theory section that in
markets with lower unit transport cost t, products are more substitutable,
indicating more intense competition. WES provides us with a measure of
competition that closely mirrors our theoretical structure. We measure
competition using firms’ self reports as to what extent different classifications of firms offer ‘significant’ competition (again on a scale of 2 to 6) to
their business. In this case, significant competition refers to ‘a situation
where other firms’ market products/services similar to your own which
might be purchased by your customers,’ a good proxy for the substitutability
of one’s products vis-à-vis competitors’. Firms are asked to rank the
significance of competition, as described above, from four types of firms:
i) locally owned, ii) Canadian owned, iii) American owned, and iv)
internationally owned firms. The value of COMP is set to one for firms
indicating they face no competition from other firms. For all other firms,
COMP is set to the maximum level of competition indicated from any type of
firm. Indeed, we are interested in the general level of competition faced by the
firm. If firms were asked the more general question: ‘to what extent do you
face significant competition to your business?’ we would expect them to
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
report the competition level they faced based on their most important
competitor(s), regardless of geography. Thus, if for example a firm indicates
no competition from American or internationally owned firms but indicates
that the competition created by Canadian owned firms is ‘important’ (4)
and that competition from locally owned firms is ‘crucially’ significant (6),
then that firm’s value of COMP is 6.13
One of the key difficulties in determining the effects of competition on firm
strategy or performance is that these effects may be endogenous to some
degree. In some cases the behaviour of firms, or other exogenous factors,
may have some effect on the amount of competition in the product market as
well as our dependent variables. We compensate for this issue and the
upward bias that it might create in our estimates, in several ways. First and
foremost, our measure of competition both theoretically and empirically
captures the degree of substitutability between products, not the competitive
behaviour of the firm. While the importance of quality improvements,
incentives, and effort may lead to a more or less aggressive competitive
behaviour among rivals, it is less clear that they will affect the degree of
substitutability between products. Second, we use one year lagged measures
of competition in all our regressions. While it is certainly possible that a
firm’s quality improvements in one year will affect the level of competition in
future periods, it is much less clear that quality in the current year affects
competition in the previous year. Third, we use industry and regional fixed
effects in all specifications. Fourth, our sample is composed primarily of
small firms operating in large markets. Small firms are less likely to have
significant market power, particularly in more competitive markets, and it is
accordingly less likely for the actions of these firms to significantly affect the
amount of competition in the product market.14
Agency Costs. The measurement of agency costs is notoriously difficult.
While recognizing that we do not have a perfect measure of agency costs, the
WES data set does provide us with some excellent proxies for the AGENCY
13
While competition is a categorical variable (equaling 1, 2, 3, 4, 5, or 6), it has been included
directly on the right hand side rather than as a set of dummy variables for ease of interpretation.
However, all specifications were re-estimated with dummy variables, and our results were
consistent with the slopes suggested by the direct inclusion of the categorical competition
variable. All of our specifications were also estimated with alternative measures of competition,
including the average and median level of competition faced by the firm across all markets and a
CR4 constructed with industry data. The results were consistent.
14
Some 40% of the firms in our sample have more than 20 competitors in their local market,
and 72% of firms report at least one ownership grouping of firms offering ‘important’
competition to their businesses. In addition, 43% of firms in our sample have less than 20
employees and 70% have less than 100 employees. To further confirm the robustness of our
results, we re-ran all of our specifications for the subsample of firms with less than 20 employees
and more than 20 firms in their local market; our findings were consistent.
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311
variable. Our primary measure equals 1 if the firm has more than one
employee and 0 if the firm has only one person working at the company. We
thus separate entrepreneurial firms where the owner and employee are one
and the same and agency costs are absent, from larger firms where decisions
are made by at least one person in addition to the owner and agency costs are
more likely to be present.15 This is consistent with our theoretical model
where agency costs are either present in or absent from the firm. In our
sample, 6% of firms (representing approximately 335 firms) have only one
employee, while the remainder have more than one employee.
Recognizing that agency costs are difficult to capture, we used an
alternative measure to evaluate the robustness of our criteria. Following
Jensen and Meckling [1976], increased equity ownership by insiders is
associated with lower agency costs. In the finance literature, a measure of
agency costs that has been used is the ratio of internal equity to external
equity (e.g., Capozza and Seguin [2003]). While our data does not directly
indicate the quantity of firm equity owned by employees (insiders), we do
know whether or not employees have stock purchase plans as part of their
compensation package. We assume that firms with such a package are more
likely to have a greater share of insider ownershipFand hence lower agency
costsFthan those that do not use equity in their compensation packages.
Accordingly, we develop an alternative measure of agency costs as a
categorical variable equaling 1 if employees do not have stock purchase
plans and 0 if they do. Seventeen per cent of firms in our sample have stock
purchase plans as a part of employee compensation.
When measuring agency costs using the existence of a stock purchase
plan, we compensate for the potential existence of a common factor affecting
a firm’s decision to improve quality or increase incentives, that might also
affect their decision to use stock purchases in compensation in the same year.
To do this, we re-estimate all of our regressions using data from 2001 for our
dependent variables, and restricting our sample to those firms that have
either offered a stock purchase plan in all of the previous three years or have
not offered such a plan in all three years. In this way, we only consider firms
15
All firms in our sample have at least one ‘employee,’ defined as at least one person
‘employed at this location.’ We cannot be certain that this one person is in fact the owner,
although we would expect this to be the case at most firms with only one person performing
tasks. Even if a small number of firms indicating one worker were in fact firms owned by an
individual who does not work in the business and the worker is an employee in the classical
sense, we would expect the employee’s effort to be verifiable (all outcomes are his/her doing), in
which case, as shown in the model, agency costs can be circumvented and the first-best can be
achieved. In contrast, in firms with two or more employees, everything else equal the separation
of ownership and control and the non-verifiability of effortFwhich create agency costs that
cannot be circumvented by contractFare more likely to be problematic. Griffith [2001] uses a
similar measure of agency costs: she distinguishes between managerial (multi-plant)
establishments, which are affected by agency costs, from entrepreneurial (single-plant)
establishments, which are not.
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
with persistentFand hence more exogenousFstock plans (or persistently
absent stock plans) and not those that introduce (or remove) these incentive
systems in our year of observation. The results are unaffected.
Incentives. We measure the incentives offered to agents as the share of
total remuneration each employee derives from variable sources. These
variable sources include commissions, tips, profit sharing, productivity
bonuses, and piecework.16 This measure captures the intensity of incentive
based pay in an employee’s total renumeration. It depends on both the
structure of the contract offered to the agent and the performance of the firm
and industry. Ideally, to correspond with our theoretical model, we would
have a measure of incentives that reflects only the intensity of incentives
offered to the agent in his or her contract rather than the realization of
incentives that is influenced by both the contract and other factors. This type
of measurement error is common in the incentives and compensation
literature (see e.g., Baker and Hall [2004]; and Bushman and Smith [2001]).
We compensate for the effect of firm and industry on realized incentives by
controlling for firm level performance (profits) and with industry fixed
effects.17
Effort. Any measure of the amount of effort an employee exerts in his or
her job is by nature somewhat subjective. We measure the effort exerted by
an agent using the most objective measure available to us: the employee’s self
report of the number of hours of unpaid overtime he or she usually worked
per week. Admittedly, effort and number of hours are not necessarily
equivalent. An employee does not need to work more hours to work harder;
however, we would expect considerable positive correlation between effort
and hours of unpaid overtime. Unpaid overtime is predominantly voluntary
and not contracted by the employer. Accordingly, we view the number of
hours of unpaid overtime worked as a reasonable proxy for effort. In our
sample, 24% of employees report some unpaid overtime, with the remainder
indicating no hours of unpaid overtime.18
16
When using employee stock purchase plans as our measure of agency costs, a potential
endogeneity exists between our measure of incentives (which includes profit sharing) and our
measure of agency costs. Accordingly, we re-estimated all of our incentive regressions with a variable pay measure that included only productivity bonuses, tips, commissions, piecework payments,
and any ‘other’ bonuses not related to stock ownership. The results were unaffected.
17
For robustness, we replaced the dependent variable with a dummy variable equaling 1 if
the employee reported any variable pay and 0 otherwise (estimation by probit). We also ran a
firm level regression where the dependent variable equals 1 if the firm offers any type of
incentive based-contracts and 0 otherwise. In all cases, the results for competition, agency
costs, and the interaction between competition and agency are of the same sign, significance,
and relative magnitude as those reported with our main measure.
18
For robustness, we repeated our estimation using only those employees who worked
unpaid overtime. We also replaced the dependent variable with a dummy variable equaling 1 if
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313
Control Variables. Firm level control variables are included to compensate for a number of alternative influences on the quality and cost choices of a
firm. We control for the size of the firm using the log of employees as we may
expect scale, for example, to be an important factor. Note that we use the
same underlying data source (number of employees) for our dummy variable
measure of agency costs. Indeed, we can exploit the same data to capture both
the threshold effect (existence or non-existence of agency costs) and the
continuous effect (economies of scale) separately. Firm profits from the
previous year are included, as the availability of cash may influence
investments in quality improvements or alter the urgency of cost reductions.
We also control for asymmetries in productivity by including ‘industry
leaders,’ a one year lagged variable defined as the one third of firms whose self
reports of productivity are ‘better’ or ‘much better’ than their competitors.
Employee-specific control variables are included to compensate individual characteristics that may influence effort or variable pay. We control for
an employee’s level of education, age, gender, marital status, and whether he
or she has dependent children. We also control for whether he or she
supervises other employees or is a member of a collective bargaining
agreement.
V. MAIN EMPIRICAL RESULTS
Some descriptive statistics for our main variables of interest can be found in
Table I. The table is self explanatory; note however that both the number of
employees and profits are highly skewed, resulting in our empirical use of the
log of these variables.
V(i).
Quality Improvements and Cost Reductions
We begin by estimating equation (15) by ordered probit, with each
observation weighted using the survey weights described in the previous
section to provide unbiased point estimates. Our main empirical results can
be found in Table II. Ordered probit is used since our dependent variable is
categorical, taking on values from 2 to 6; and ordinal, in that the importance
of quality improvements (or cost reductions) increases with higher numbers.
Columns 1 and 3 refer to specifications with the dependent variable’s
being the importance of quality improvements, while columns 2 and 4 use
the importance of cost reductions as the dependent variable. Columns 1 and
2 use our base measure of agency while columns 3 and 4 use the existence of
employee stock purchase plans.
the employee reported any unpaid overtime and 0 otherwise (estimation by probit); as well as
with the total number of hours an employee worked. Our results were consistent.
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
Table I
Descriptive Statistics
Firm Survey
Employee Survey
Mean
Median
COMP
QUAL
4.5
4.3
5
5
COST
4.2
4
Number of
Employees
Profits
125
29
$2,974,472
$137,568
Percentage of employees with any incentive based pay
Mean share of income derived from variable sources
(all employees)
Mean share of income derived from variable sources
(only employees with incentive pay)
Mean hours of unpaid overtime (all employees)
35%
20%
57%
2
Mean hours of unpaid overtime
(only employees working overtime)
7.4
Table II
Importance of Strategies: Quality Improvement and Cost Reduction
Dependent Variable
1
2
3
4
QUAL
COST
QUAL
COST
0.240
0.227
0.261
0.102
COMP (l1)
5 intensity of competition (scale of 1 to 6)
(0.084)
(0.077)
(0.085)
(0.022)
AGENCY (l2)
0.789 1.712
5 1 if firm has more than one employee, 0 otherwise
(0.296)
(0.588)
0.122
0.157
COMPAGENCY (l3)
5 level of competition agency cost
(0.060)
(0.046)
0.297 0.932
AGENCY (alternate measure: l2)
5 1 if stock purchase plan not available, 0 otherwise
(0.151)
(0.449)
COMPAGENCY (alt. measure: l3)
0.054
0.179
5 level of competition agency cost
(0.023)
(0.086)
Firm Size
0.208
0.133
0.196
0.148
5 ln(total employeest 1)
(0.031)
(0.035)
(0.030)
(0.031)
Profits
0.001
0.002
0.001
0.001
(0.001)
(0.001)
(0.0004) (0.001)
5 ln(revenuest 1 less expenditurest 1)
Industry Leader
0.395
0.044
0.390
0.040
5 1 if productivity in top third of firmst 1, 0 otherwise (0.076)
(0.086)
(0.075)
(0.086)
Industry and Region Fixed Effects
YES
YES
YES
YES
Number of Observations
4732
4541
4732
4541
5 significant at 1%.
5 significant at 5%. Standard errors in parentheses.
Effects of Competition. The sign of the direct pressure effect of
competition, l1 is positive and significant for all specifications: in firms
that are free of agency costs, competition increases the importance firms
place on quality improvements and cost reductions. Following proposition
1, this suggests that the increased business stealing effect of competition
empirically dominates the rent reduction effect.
The sign of l3 is positive and significant for all columns, verifying the
implication of proposition 3, that in firms where agency costs are present,
competition works through an additional channel, the agency effect of
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PRODUCT MARKET COMPETITION AND AGENCY COSTS
315
competition, which reinforces the direct pressure effect. Hence the impact of
competition on the importance firms place on quality improvements and
cost reduction is even larger in firms with agency costs than in those without.
Since both l1 and l3 are positive, the aggregate impact of competition
@QUAL
@COMP ¼ l1 þ l3 AGENCY is unambiguously positive (the same holds for
the derivative of COST with respect to COMP): although competition
affects the importance of quality improvements differentially in firms with
agency costs and firms without, this effect is positive for all firms.
Effects of Agency. Consistent with the implications of the model, l2, our
measure of the gross impact of agency on firms’ attitudes towards quality
improvements is negative and significant in all columns. In fact, l2 should be
@QUAL
sufficiently negative for the net impact of agency, @AGENCY
¼ l2 þ l3 COMP,
to be negative for all possible values of COMP (from 1 to 6). Looking back at
Table II, this prediction is consistent with the data in specifications 1 and 2:
l2 þ l3COMP o 0 for all possible values of COMP. In specifications 3 and
4, the total impact of agency is negative at low levels of competition but is not
significantly different from zero when COMP is high. In other words,
empirically, the agency effect of competition on QUAL, l3, is so strong that
at high levels of competition it may offset the negative impact of agency
costs, l2. Note that these results hold both when controlling for firm size and
when the log of employees is omitted from the right hand side (not reported).
Control Variables. In terms of control variables, lagged profits have a
positive impact on the importance firms place on quality improvements and
cost reductions, though this effect is significantly different from 0 at the 5%
level only in columns 2 and 3. Relative to weaker firms, the importance of
quality improvement in a firm’s business strategy is higher for industry
leaders. The same result holds if an industry leader is measured by sales or
profit performance instead of productivity.
V(ii).
Employee Incentives and Effort
We now estimate equation (16), where the dependent variable is either the
share of pay derived from variable sources (INCEN) or the number of hours
of unpaid overtime an employee worked (EFFORT). Estimation is by GLS,
with standard errors robust clustered at the firm level, again adjusted for
survey data. The results are found in Table III, which represents incentives in
columns 1 and 2, and effort in columns 3 and 4. Columns 1 and 3 use the base
measure of agency costs, and columns 2 and 4 use employee stock purchase.
Effects of Competition. When compared with the results in Table II, the
coefficients of our main variables of interest are consistent in sign and
significance in all 4 specifications. We confirm empirically that the impact of
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
Table III
Incentives & Effort: Share ofVariable Pay and Hours of Unpaid Overtime
1
Dependent Variable
INCEN
2
3
4
INCEN EFFORT EFFORT
0.038
0.021
0.113
0.719
COMP (g1 and y1)
5 intensity of competition (scale of 1 to 6)
(0.018)
(0.010)
(0.039) (0.305)
AGENCY (g2 and y2)
0.186
0.169
5 1 if firm has more than one employee, 0 otherwise
(0.053)
(0.079)
COMPAGENCY (g3 and y3)
0.025
0.081
5 level of competition agency cost
(0.012)
(0.036)
0.122
6.339
AGENCY (alternate measure: g2 and y2)
5 1 if stock purchase plan not available, 0 otherwise
(0.058)
(1.953)
0.035
1.109
COMPAGENCY (alt. measure: g3 and y3)
5 level of competition agency cost
(0.011)
(0.380)
Firm Size
0.002
0.006
0.107
0.875
5 ln(total employeest 1)
(0.007)
(0.007)
(0.063) (0.337)
Profits
0.001
0.001
0.001
0.001
5 revenuest 1 less expenditurest 1 in millions of dollars (0.0002) (0.0002) (0.001) (0.001)
Industry Leader
0.078
0.076
0.124
1.789
(0.019)
(0.019)
(0.157) (0.992)
5 1 if productivity in top third of firmst 1, 0 otherwise
Supervisor
0.004
0.004
1.754
1.693
5 1 if supervises other employees, 0 otherwise
(0.020)
(0.008)
(0.183) (0.180)
0.421
Education
0.005
0.004
0.404
5 employee’s highest educational attainment
(0.006)
(0.006)
(0.048) (0.048)
0.041
0.748 0.422
Unionized
0.045
5 1 if employee is member of collective barg. agreement (0.023)
(0.023)
(0.183) (0.048)
0.022
Age
0.001
0.001
0.015
5 age of employee in yearst 1
(0.001)
(0.001)
(0.006) (0.005)
Gender
0.003
0.001
0.546 0.618
5 1 if employee is female, 0 otherwise
(0.019)
(0.004)
(0.146) (0.137)
Industry & Region Fixed Effects
YES
YES
YES
YES
R2
0.03
0.03
0.09
0.12
Number of Observations
19147
19147
19147
19147
5 significant at 1%.
5 significant at 5%. Standard errors in parentheses.
competition on incentives, and on employee effort, is channeled through a
positive direct pressure effect of competition, which is present in all firms,
and a positive agency effect of competition which is present only in firms
subject to agency costs.
Effects of Agency. The effects of agency costs on incentives and effort are
also similar to their effects on quality improvements and cost reductions
depicted in table II, or even stronger. In all 4 specifications the gross impact
of agency costs (g2 for incentives and y2 for effort) is significantly negative.
Similarly, the net impact of agency costs (g2 þ g3COMP for incentives and
y2 þ y3COMP for effort) is negative for all levels of competition. This
confirms that contractual incentives and employee effort are lower in firms
that are subject to agency costs than in firms that are not.
Control Variables. Control variables in table III also suggest a number of
interesting implications. First, lagged firm profits and lagged relative
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productivity level of the firm have a significant positive effect on the share of
variable pay in total pay but an insignificant effect on unpaid overtime.
Second, firm size, measured by the natural log of total employees, is
insignificant in determining variable pay, consistent with Baker and Hall
[2004] who find that the CEO incentives are either unrelated or slightly
negatively related to size. We find a similar result looking at the intensity of
incentives for all types of employees. In contrast, firm size has a positive
impact on unpaid overtime, even though this effect is significant only in
column 4. Finally, incentives are positively affected by unionization and not
significantly related to education, age, gender, or supervisory roles. Unpaid
overtime significantly increases with age and education and is also higher for
employees who supervise others. However, it decreases if the employee is a
member of a collective bargaining agreement; or if the employee is female.
All the specifications in Table III were re-estimated using different control
variables, and variations in the dependent variables. We also re-ran all
regressions using only the subset of employees who were managers, as well as
the subset of managers and professionals. In all cases, the results for
competition, agency cost, and the interaction between competition and
agency, are of the same sign, significance, and relative magnitude as those
reported in Table III.
V(iii).
Discussion of Empirical Results
Consistent with our theory, our empirical results confirm the existence of
two distinct effects of competition: the direct pressure effect and the agency
cost effect. Combining these two, the aggregate effect of competition is
positive and significant for quality improvement, cost reduction, intensity of
incentives, and employee effort. In that sense, our results are consistent with
other theories that predict a positive or ambiguous aggregate effect of
competition (Hart [1983]; Hermalin [1992]; Schmidt [1997]; and Raith
[2003]).
Our empirical results are also consistent with previous empirical work.
For example, our results from table IIFthe overall positive impact of competition on the importance of quality improvements and cost reductionsF
are broadly consistent with the empirical literature on competition and
productivity discussed in the introduction; and on the related literature on
competition and innovation (Geroski [1990]; Bertschek [1995]; Blundell
et al. [1999]), with the exception of Aghion et al. [2005], who find an inverted
U relationship.
Similarly, our results on contractual incentives are consistent with, among
others, Cuñat and Guadalupe [2005], who find that competition increases
the steepness of performance pay contracts, and Burgess and Metcalfe
[2000], who find the likelihood of performance related pay increases with
competition. Burgess and Metcalfe [2000] use a British survey similar to
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JEN BAGGS AND JEAN-ETIENNE DE BETTIGNIES
WES and measure competition using a firm’s qualitative rating of the
‘degree of competition’ it faces, making their results directly comparable to,
and consistent with, ours.
Santalo [2002] finds a negative correlation between the number of
competitors and incentives; we pay particular attention to these results as he
also uses a portion of the WES data set. Our empirical methodology and
results differ sharply from his for several reasons. First, he uses the 1999
version of the WES data set, data we do not use because our dependent
variables are lagged to compensate for endogeneity; also, for our purposes,
later years offer a richer set of variables to choose from. Second, our measure
of competition, which is based on the degree of substitutability between
products, is quite different from his measure (number of competitors).
Substitutability between products has the advantage of being a better proxy
for our theoretical measure of competition, and less sensitive to assumptions
about barriers to entry.19 Finally, our empirical approach differs from
Santalo [2002], as well as from the papers cited above, in our use of a reliable
proxy for agency costs, which allows us to isolate empirically the agency
effect of competition from the direct pressure effect. To our knowledge, this
is one of the first empirical studies to isolate these factors. In that regard, our
paper is closer to Griffith [2001], who finds that competition has no impact
on efficiency in plants without agency costs and a positive impact in plants
with agency costs. Griffith [2001], however looks exclusively at productivity
and is silent about contractual incentives and effort.
VI. CONCLUSION
In this paper we shed light on the process through which product market
competition affects employee effort and firm efficiency. Our model predicts
that competition affects firms differentially, depending on whether or not
they are subject to agency costs. Indeed we identify an agency effect of
competition, which is present only in firms plagued by agency, and isolate it
from the direct pressure effect of competition, which is present in all firms.
Using a unique set of Canadian data that allows us to observe
simultaneously the characteristics of firms as well as their employees, we
then evaluate the empirical significance for these two effects. We find that
competition has a significant direct pressure effect, as well as a significant
agency effect. Both effects increase the importance firms place on quality
19
As a measure of competition, number of competitors is difficult to interpret. In markets
with free entry, as in Raith’s [2003] model that Santalo is testing, competition is usually
associated with a decrease in competitors. In contrast, it is associated with an increase in the
number of rivals in a market with barriers to entry (Vives, [2004]). Moreover, the number of
competitors is less likely to be exogenous, thus making the econometric specification more
vulnerable to endogeneity issues.
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PRODUCT MARKET COMPETITION AND AGENCY COSTS
319
improvements and cost reductions as well as contractual incentives and
employee effort.
Our results yield an interesting policy implication. Governments should
(continue to) focus their pro-competitive policy efforts on large corporations: presumably, in such firms agency problems are more prevalent, and as
shown theoretically and empirically in this paper, it is precisely in such
environments that the efficiency improving effects of competition are
strongest.
APPENDIX 1
PROOF OF PROPOSITION 3
The proofs of the effects of competition on @ pi/@ qi and on pi follow directly from
the
@a
discussion in the text, and are omitted here. The proof that competition reduces @qi i is as
follows:
First, applying the implicit function theorem to condition (10), we can express agent
i =@qi
qi ; qj ; ai ; tÞ ¼ @ 2 Ki =@q@p2 a
i’s responsiveness to incentives as @@aq^ii ð^
2 , which in equili2
i
i @ pi =@qi
@ ð@ q^i =@ai Þ
@di
brium simplifies to @@aq^ii q
i ; qj ; ai ; t ¼ 1= 3 2ai @qi ðtÞ . Clearly, @ ð@di =@qi Þ > 0. In
@i
words, the agent’s responsiveness to incentives, @a
, is strictly increasing in @ di/@ qi. This
i
2
@ di
< 0Þ, implies that in
result, together with the increased business stealing effect ð@q
i @t
equilibrium competition increases the agent’s responsiveness to incentives:
@a
@ ð@ q^i =@ai Þ
@ q^i =@ai Þ @ 2 di
@ q^i
i
we must have
¼ @@ ðð@d
< 0. Finally, since
@t
@qi ¼ 1= @ai ,
i =@qi Þ@qi @t
2
@ ð@ai =@qi Þ
@ ð@qi =@ai Þ @q
@a
i
¼
> 0. Thus, since competition reduces both @qi i and pi,
@t
@t
@ai
it must reduce
@a
i
@qi pi , the agency marginal cost.
&
APPENDIX 2
WORDING OF WES QUESTIONS USED TO CONSTRUCT OUR DEPENDENT AND
INDEPENDENT VARIABLES
Firm Strategy is measured using questions, each of which was ranked by the firm as:
1: Not Applic.; 2: Not Important; 3: Slightly Import.; 4: Import.; 5: Very Import.;
6: Crucial.
Please rate the following factors with respect to their relative importance in your
workplace’s general business strategy:
Improving product/service quality; Reducing labour costs; Reducing other operating
costs.
Competition was measured using these 4 questions, each of which was ranked by firms
as:
1: Not Applic.; 2: Not Important; 3: Slightly Import.; 4: Import.; 5: Very Import.;
6: Crucial.
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To what extent do these firms offer significant competition to your business? Significant
competition refers to a situation where other firms market products/services similar to
your own which might be purchased by your customers:
1. Locally-owned firms; 2. Canadian-owned firms;
3. American-owned firms; 4. Internationally-owned firms.
Firm size, and which firms had only one employee, was measured as follows:
In the last pay period of March this year, how many people were employed at this location?
Profits were measured as the difference between revenues and expenditures as derived
from these two questions: For this fiscal year, what was the gross operating revenue from
the sale or rental of all products and services for this location? What were the gross
operating expenditures for this location for the most recently completed fiscal year?
The existence of incentive based compensation at the firm level was measured using
the following 4 questions, each of which was answered ‘yes’ or ‘no’ by the firm. If a
firm answered ‘yes’ to any ONE question it was coded as having incentive based
compensation.
Does your compensation system include the following incentives?
1. Individual incentive systems (bonuses, piece rate, commissions and stock options).
2. Productivity/quality gain sharing and other group incentives (benefits to employees
for gains realized by increased productivity). Commonly, these benefits can be in the
form of money payments in the primary industries. 3. Profit sharing plan (any plan by
which employees receive a share of the profits from the workplace). 4. Merit pay and
skill based pay (a reward or honour given for superior qualities, great abilities or
expertness that comes from training, practice, etc.).
The share of incentive based bay in total pay at the employee level was constructed using
these four questions:
1. In your current job, what is your usual wage or salary before taxes and other deductions?
2. In the past twelve months did you earn any commissions, tips, bonuses, paid overtime or
any other types of variable pay such as profit sharing, productivity bonuses (gain sharing),
or piecework?
3. Were these commissions, tips, bonuses, paid overtime or other types of variable pay
included in the wage or salary reported in (question 1)?
4. What were your total earnings from commissions, tips, bonuses or variable pay in the
past 12 months?
The number of hours of unpaid overtime employees worked was measured using the
following question: How many hours of unpaid overtime do you usually work per week?
The following questions were used to measure the number of hours employees worked in
robustness checks:
1. Excluding all overtime, how many paid hours do you usually work per week at this job?
2. How many hours of paid overtime do you usually work per week?
3. Not counting overtime, how many paid hours on average do you work per week at this
job?
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4. Over the past 12 months, not counting overtime, what was the maximum number of paid
hours you worked per week at this job?
5. Over the past 12 months, not counting overtime, what was the minimum number of paid
hours you worked per week at this job (exclude the hours when you were on paid vacation
or sick leave)?
The following questions from the employee portion of the survey were used as controls
in the employee level regressions:
1. In what year were you born?
2. Gender (check box for male or female).
3. What is your current legal marital status?
1: Legally married (and not separated); 2: Legally married and separated;
3: Divorced; 4: Widowed; 5: Single (never married).
4. Are you currently living with a common-law partner? (yes/no)
5. Do you have any dependent children? (yes/no)
6. About how many people do you directly and indirectly supervise on a day to day basis?
7. Did you graduate from highs chool?
8. In your current job, are you a member of a union or covered by a collective bargaining
agreement?
9. Have you received any other education? What was that education?
1. Trade or vocational diploma or certificate;
2. Some college, CEGEP, Inst. of techn. or Nursing school; 3. Some University;
4. Teachers College; 5. University certificate or diploma below bachelor level;
6. Bachelor or undergraduate degree; 7. University certificate or diploma above
bachelor level;
8. Masters degree; 9. Degree in Medicine, Dentistry, Veterinary Medicine, Law,
Optometry or Theology or 1-year B.Ed after another bachelors degree;
10. Earned Doctorate.
Employee Stock Purchase Plan was measured using: In your current job are you included
in a stock purchase plan?
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