BRIBE or LOBBY?
(it’s a matter of development)
Bård Harstad∗ and Jakob Svensson†
1 June 2005
FIRST DRAFT - WORK IN PROGRESS
Abstract
Corruption and lobbying are to some extent substitutes. Through lobbying a firm
may be able to "change the rules" to the firm’s advantage. Alternatively, a firm may
bribe a bureaucrat to "bend the rules" and thus avoid the cost of compliance. But
there are important differences. While a change in the rules is more permanent, the
bureaucrat can hardly commit not to ask for bribes also in the future. Based on this
simple assumption, and a simple growth model, we show that (i) an equilibrium with
corruption discourages firms to invest, (ii) firms bribe if the level of development is
low, but (iii) they switch to lobbying if the level of development is sufficiently high.
Combined, the economy might evolve from a bribing to a lobbying equilibrium, but
too large bribes may discourage the necessary investments for lobbying eventually
to become an equilibrium. The outcome is a poverty trap with pervasive corruption.
This poverty trap may be more likely if there is a lot of regulation and large penalties
on corruption - these policies should optimally increase in the level of development.
Keywords: Corruption, lobbying, development
JEL classification: O16, O17
∗
†
MEDS, Kellogg School of Management. Email: harstad@northwestern.edu
IIES, Stockholm University and DECRG, World Bank. Email: jakob.svensson@iies.su.se
1. Introduction
There is by now a fairly large literature on both corruption and lobbying. Somewhat
surprisingly, however, these two phenomena have either been studied separately or viewed
as basically being the same thing.1 The question why firms choose to lobby or bribe, and
the consequences of this choice, remains largely unanswered. In this paper we try to shed
some light on this issue.
We define lobbying, taking the form of campaign contributions or influence-buying
through other means, as an activity that aims at changing existing rules or policies. We
view bribing, on the other hand, as an attempt to get around existing rules or policies.2
While there is no comprehensive data on the extent of corruption and lobbying across
countries, a common perception is that firms in developing countries are more likely to
be forced to pay bribes to get around regulatory constraints while firms in developed
countries are more prone to lobby the government to change rules that adversely affect
them.3 What can account for this difference between developed and developing countries?
Should we expect an evolution from bribing to lobbying, or can countries get trapped in
a bribing equilibrium forever?
We present a simple growth model where firms initially are subject to a regulation.
For example, an import licence is required to import essential inputs or the inputs are
subject to a tariff. Instead of complying to the regulation, a firm can either bribe the
official to "bend the rules" and be exempt from the regulation, or lobby the government
to relax the requirements. We assume the firms coordinate their lobbying activities.4
We show that as countries grow, firms are more likely to switch from bribing to lobbying. Intuitively, lobbying takes place only when the amount of capital accumulated is
large enough, because then the hold-up problem is so severe (bribes are so large) that it
is better to lobby for a permanent change in the rules. However, the evolution from a
bribing to a lobbying equilibria is not predetermined. Under certain conditions, countries
may get stuck in a poverty-trap with extensive bribing forever.
We also study optimal policies related to corruption. While tough penalties on corruption makes the firms more likely to lobby instead of bribe, conditional on the stage
of development, they also increase the bribes a firm has to pay, and the incentives to in1
For example Coate and Morris (1999), building on Grossman and Helpman’s (1994) lobbying model,
interpret lobbying (or the political gift offered by a firm) as a bribe. Schulze and Ursprung (2001)
argue that the weighting factor in the same model, i.e. the weight the government places on political
contributions versus aggregate welfare, measures the level of corruption in the political system.
2
As we discuss below, these rules may have been put in place to collect bribes (Djankov et al., 2003).
Corruption also appears in response to benevolent rules when individuals pays bribe to avoid penalties
for harmful conduct or when monitoring of rules is incomplete — as in the case of theft.
3
This is also true in a historical perspective in many developed countries.
4
There are two reasons for this choice. The first is clarity. Assuming that firms can coordinate their
actions highlights the effects of the commitment problem. The second reason is that it seems reasonable
that firms over time, as a result of repeated interactions, will at least partly overcome the free-rider
problem. Since we here focus on the long-run evolution from bribing to lobbying, we therefore assume
that firms can coordinate their behavior.
2
vest are accordingly reduces. We show that both optimal regulation and penalties should
increase in the level of development.
Modern research on the economics of corruption began with Rose-Ackerman (1975,
1978). Following Becker and Stigler (1974), the early literature studied corruption primarily within a principal (government) agent (public official) framework. In this paper, on
the contrary, we follow Shleifer and Vishny (1993) and take the principal-agent problem
as given and instead focus on the consequences of corruption for resource allocation. As
in Choi and Thum (1999), we study the effects of repeated extortion. However, our focus
is primarily on the firms’ behavior, rather than the bureaucrats’. More important, we
focus on the choice between bribing and lobbying and the long-run consequences of this
choice.5 The literature on lobbying is extensive. Starting with the issue of interest group
formation (Olson, 1965), recent contributions have studied how and if lobbying influences
policy choices in an environment with competing interests.6 Lobbying, either taken the
form of strategic provision of information and advertising campaigns or through campaign
contributions, can either influence policy makers’ positions and actions or help preferred
candidates to win election. As argued in Grossman and Helpman (1994), the degree to
which an organized industry can influence policy depends on the strength of its political
organization and various industry characteristics. We take these results as a staring point
and initially assume there is an exogenous cost of (successful) lobbying. Later on, we
relax this assumption thus making the cost of lobbying endogenous. Unlike the lobbying
literature, where firms (or special interests) cannot influence the implementing agency
(through bribery), we explicitly study the choice between lobbying and bribery and the
long-run consequences of this choice.
This paper is also related to the political economy literature on policy reform and
policy persistence. Fernandez and Rodrik (1991) and Alesina and Drazen (1991) argue
that informational asymmetries between winners and losers of the reform can explain why
reforms are not undertaken (or are delayed). Branard and Verdier (1994) and Coate and
Morris (1999) instead stress the reaction of interest groups (for example an industry) to
the introduction of a policy. When a policy is introduced, the beneficiaries will undertake
costly actions to benefit from it and these actions will increase their willingness to lobby for
the policy in the future. For example, trade protection may cause the benefiting industry
to undertake less adjustment, increasing their willingness to pay for even more protection
in the future. Our argument for policy persistence differ in important ways from these
models. Specifically the policy in place (for example an import licensing requirement)
is assumed to be costly for the firms. Thus, when firms lobby they do it to change the
policy. Similar to the Branard and Verdier (1994) and Coate and Morris (1999) models
adjustment is a key variable in our analysis. However, in our model, if firms undertake
less adjustment or invest too little, because the discount or depreciation rates are high,
they may never build up a sufficiently large stock of capital to make lobbying worthwhile.
The economy will then be stuck in an equilibrium with policy persistence and bribing.
Finally, it is possible to view the model as a formalization of the human capital theories of institutions. The human capital theories argue that growth in human capital and
5
The literature on corruption is reviewed in Bardhan (1997) and Svensson (2005).
The literature is reviewed in Austen-Smith (1997) and Grossman and Helpman (2002). Pionering
work in this area includes Stigler (1971), Peltzman (1976) and Becker (1983).
6
3
income cause institutional development (Lipset, 1960; and more recently Glaeser et al.,
2004). Interpreting the rule as a composite measure of property rights protection, we provide a model with exactly this prediction. As income grow, the hold-up problem becomes
so severe (too much must be paid in bribes) that firm owners have strong incentives to
lobby for improved protection of property rights.
The paper is organized as follows. The next section presents a simple model of investments, bribing and lobbying. The model is solved in the following section. Section 3.1
finds the equilibrium bribes and Section 3.2. derives the equilibrium investments levels.
Section 3.3 then shows that the firms are more likely to lobby later in the development
process. Combined the results imply that firms bribes early in the development process,
while they later might - depening on the environment - switch to an equilibrium with
lobbying. In this simple model, we abstract from the government and the cost of lobbying is exogeneous. These assumptions are relaxes in Section 4, where we also derive
the government’s optimal choice of policies. Section 5 discusses how the analysis can be
extended in various ways, while Section 6 concludes.
2. The Simple Model: Bribing, Lobbying and Growth
A representative firm has the linear production function f (k) = rk, where r is a productivity parameter. To simplify, suppose that there is a continuum of such (identical)
firms, i ∈ [0, 1], so k measures both the aggregate and the firm-specific capital stock. The
(representative) firm faces some regulation, or red tape, which it has to overcome. If it
complies with the regulation, it costs c per unit of capital. The cost of compliance is
increasing in k because the regulation somehow constrains the production, which is proportional to k. Alternatively, the firm may negotiate with a bureaucrat that can "bend
the rules" and let the firm proceed without complying to the regulation. Doing this,
however, costs the bureaucrat θxk. The parameter x measures the expected penalty of
being corrupt; θ measures the bureaucrat’s personal stigma or individual type associated
with bribery; and this is multiplied with k to reflect that the size or the probability for
paying the penalty is proportional to the size of the crime (k). Thus, if θx < c, the firm
and the bureaucrat may prefer bribery instead of complying. The bureaucrats’ θ are iid
distributed on [0, 1]; different firms are dealing with different bureaucrats; and these may
vary over time. The firm observes the type of the bureaucrat and they negotiate over the
bribe, B. We will let the generalized Nash bargaining solution characterize the outcome
of the negotiations, and the firm’s relative bargaining power is α. Assume that c < x,
such that at least some firms (or bureaucrats) choose to comply instead of bribe.
As a third alternative, the firms may collectively lobby the government, at the cost
L, to change the rules more permanently. Assume the firms then lobby the government
to relax the regulation and set c = 0, thus eliminating the bureaucrat’s future bargaining
power. The cost L may include both the firms’ cost of collective action as well as the cost
associated with changing the rules in the government.
A change of the rules may be governed by time-consuming procedural rules and it may
also require the commission of reports to study impact and may need to be referred for
consideration at various authorities and courts. Frequent changes in for example the tariff
4
structure may also have an impact on a country’s relation to its trading partners. All
these factors suggest that it is costly to change the law frequently. The cost L of lobbying
can be shared arbitrarily among the firms, and we let the firms negotiate how the cost of
lobbying should be shared. We let the Nash bargaining solution characterizes the outcome
of these negotiations (as if the number of firms were finite), which implies that the costs
of lobbying are shared such that each firm benefits equally much on lobbying.
In a static framework, the model above would imply that the firms bribe if B < L,
while they would lobby if B > L. Our key distinction between lobbying and bribing
needs a dynamic framework, however: While the bureaucrat cannot commit not to ask
for bribes also in the next period, a change of the law is more long-lasting. For simplicity,
we assume that if the government changes the rules to relax the regulation, it will stay
like this permanently.7
In the dynamic framework, the capital depreciates at the rate d, but each firm may
increase its stock of capital by investing it at cost zi2t /2. Letting time be continuous, this
means:
·
kt = it − dkt .
(2.1)
The discount rate is δ, and let k0 = 0. The subscript t is frequently supressed for
convenience.
At each point in time, firms decide how much to invest and whether to lobby together.
If they do not lobby, each firm observes the type of the buraucrat it is dealing with this
time, and it decides whether to comply or negotiate with the bureaucrat. If a switch to
lobbying has taken place, the only decision is how much to invest.
While the parameters L, c, x and α are treated as exogeneous in this section, Section
4 introduces the government in order to endogenize the cost of lobbying and to derive the
government’s optimal choice of c, x and α.
The parameters z, d, and δ capture different aspects of the (economic, political, and
institutional) environment in the country. The capital good k in the model can be interpreted as a compostie good of human and physical capital. High adjustment costs z
could then, for example, reflect an inefficient education system (it takes time and costs to
aquire human capital). It could also reflect different forms of transaction and transportation costs. The depreciation rate d partly reflect the state of the public sector, specifically
the extent to which complementary public goods are provided. δ can be interpreted as the
sum of the pure time preference discount rate and the probability that the stock of capital
will be (partly) lost due to war, a negative shock or expropriation by the government.
3. The Solution
We solve the model in three steps. First, we solve for the bribes and the firms’ expected
profit and net rate of return to investment. Based on this, the second subsection derives
7
All results continue to hold qualitatively if we instead assume that at each point in time there is
some probability (strictly less than one) that the government changes the law again, making a new round
of lobbying necessary. The main difference would be that lobbying would be less attractive, and bribing
more likely, for the same parameter set.
5
the investment levels, depending on whether the firms bribe or lobby. In the third subsection, we investigate whether the firms actually prefer to lobby instead of to bribe, and
how this choice depends on the level of development. Combining these results implies
that while the firms lobby early in the development process, there may (and may not) be
an evolution where the firms switch to lobbying later in the development process. If that
happens, the growth rate increases.
3.1. Bribing
If c > θx, the firm and the bureaucrat can both be better off if the firm pay some bribe
B to the bureaucrat in order to get around the regulation. The amount of the bribe,
B, is determined by negotiations between the firm and the bureaucrat. Relying on the
generalized Nash bargaining solution, where α represents the firms bargaining power:
max (ckt − B)α (B − θxkt )1−α ⇒
B
B = (1 − α) ckt + αxθkt
If the firm’s stock of capital kt is large, the bribe is large for two reasons. First, a large
kt implies that the firm’s cost of the regulation is large, and it is thus willing to pay more
to get around it.8 Second, the bureaucrat’s cost of providing the input (θxkt ) is larger if
the firm is large because it is more likely that a large firm will be investigated, or because
the penalty of such a large crime is larger.
Since θ is uniformly distributed on [0, 1], the probability that a firm bribes is c/x,
while it otherwise (1 − c/x) complies. This is quite intuitive: The larger is the cost of
compliance relative to the expected penalty of corruption, the more firms prefer to bribe
instead of comply. Conditional on θ < c/x, the expectation of θx is c/2, so the expected
bribe (conditional on bribery) is EB = (1 − α/2)ckt . Thus, before learning the identity
of the bureaucrat, the firm’s (expected) profit is:
rk − min {ck, B} = rk − (c/x)EB − (1 − c/x)ck = ak, where
a ≡ r − c (1 − αc/2x)
(3.1)
Since we assume that c > x (such that some firms comply, and other bribe), a is decreasing
in c and x but increasing in α.
3.2. Investments
In order to solve for the equilibrium, consider, first, an equilibrium where bribing takes
place forever. In such a steady state, each firm will at time t plan its investments in order
8
This is consistent with the findings in Svensson (2003). Instrumenting for the firm’s profitability, he
finds in a cross-section of firms in Uganda that firms that invest more and make higher profits also pay
higher bribes.
6
to solve:
Z∞ ³
z 2 ´ −δτ
max
akτ − iτ e dτ s.t. kt and (2.1).
iτ
2
(3.2)
t
If the firms decide to lobby, they negotiate over the allocation of lobby contribution,
where the default is to continue to comply or bribe. Applying the Nash bargaining
solution, the firms then share equally the net value of lobbying instead of bribing. Thus,
each firm receives its default payoff, i.e. the payoff from continued bribing, plus the average
value of switching to lobby (and this term is exogeneous for a single firm). Therefore,
even if the firms anticipate lobbying at time T > t, they plan their investment decisions
at t according to (3.2).
If lobbying has taken place, however, such that the regulation is permanently relaxed,
the firm’s maximization problem is similar to (3.2) if just a is replaced with r.
Proposition 1: (i) In a bribing equilibrium, investments (3.3) are larger if α is large
while c and x are small. (ii) Investments are larger in a lobbying equilibrium. (iii) In
either case, investments are larger if r is large while d, δ and z are small.
i=
r − c (1 − αc/2x)
z (d + δ)
(3.3)
Proof: (3.2) is an optimal control theory problem, with the following current-value
Hamilton function:
z
H = ak − i2 + p (i − dk) ,
2
where p is shadow value of capital. Subscripts denoting time are eliminated for simplicity.
The first-order conditions are:
·
p − δp = −
∂H
= −a + dp
∂k
(3.4)
∂H
= −zi + p = 0
∂i
This gives differential equations with only one stable solution, which can be found straighforwardly by solving (3.4):
a
(d + δ)
a
i =
z (d + δ)
p =
Substituting for a from (3.1) completes the proof. QED
When the firms may bribe, they face a return of investments that is decreasing in the
bribes. And, since the size of the bribes increases in x but decreases in α, investments
do the opposite. Thus, a harsh penalty on corruption reduces growth in a bribing equilibrium, because the bureaucrats then require higher bribes. If c is larger, both the cost
7
of compliance and the bribes are larger, and investments decrease for both reasons. The
bribes constitute a hold-up problem which discourages investments, since the bureaucrat
cannot commit to not ask for higher bribes in the future. The more the firm invests, the
higher the bribes will be. When the regulation is relaxed, the firm can appropriate the full
marginal product of capital r. As a result, investments are higher after lobbying has taken
place. The result in (iii) may be less surprising: As expected, investments increase in the
rate of return (r) but decrease in the marginal cost of investment (z), the depreciates rate
(d), and the discount rate (δ).
3.3. Lobbying
Instead of complying or bribing, the firms may spend resources on lobbying the government for a more permanent relaxation of the regulation. The cost of such lobbying, L,
includes both the firms’ organizational cost as well as the cost for the government to
change its legislation. Given these costs, we assume that the firms’ collective action problem is solved and their decision is simply whether to bribe or (collectively) lobby, and
when to switch from one to the other. We will now show that, typically, the firms bribe
early in the development process, while they at a later stage (for a larger k) may switch
to lobbying.
Proposition 2: The firms prefer lobbying instead of bribing if k is sufficiently large,
such that (3.5) holds. For a given k, the firms are thus more likely to lobby than bribe if
c and x are large, while α, L, d, δ and z are small.
∙
¸2
1 c (1 − αc/2x)
kc (1 − αc/2x) +
≥ δL
(3.5)
2z
d+δ
Proof: If bribing would take place forever, the evolution of k follows from (2.1). Treating i as fixed and solving this differential equation gives:
kτ =
¢
i¡
1 − e−d(τ −t) + kt e−d(τ −t)
d
(3.6)
The present value of the firm (its profit), at time t, would be (after substituting for i):
Z∞ ³
a2
z ´
akt
akτ − i2 e−δ(τ −T ) dτ =
+
V (kt , a) =
2
d + δ 2zδ (d + δ)2
t
If lobbying would take place, however, the firm’s present value would be V (k, r). Thus,
if lobbying is going to take place at time T > t, the firms’ present value at time t is
ZT ³
z ´
akτ − i2 e−δ(τ −t) dτ + [V (kT , r) − L] e−δ(T −t)
2
t
8
Maximizing over T , the first-order condition becomes
∙
¸
³
¡
¢
z 2 ´ −δ(T −t)
∂V (kT , r) ∂kT
∂L −δ(T −t)
akT − i e
+
+ [V (kT , r) − L] −δe−δ(T −t) = 0
−
e
2
∂kT
∂T
∂T
(3.7)
−δ(T −t)
, substituting for i and setting ∂kT /∂T = i − dkT and
Eliminating the term e
∂L/∂T = 0, this becomes:
Ã
¶¸ ∙
¸
µ
¶2 ! ∙
µ
r
rkT
z
a
a
r2
akT −
+
−L =0
− dkT −δ
+
2 z (d + δ)
d + δ z (d + δ)
d + δ 2zδ (d + δ)2
Collecting the terms give:
−(r − a)kT +
−a2 + 2ra − r2
+ δL = 0, which is
2z (d + δ)2
(r − a)kT +
(r − a)2
= δL
2z (d + δ)2
(3.8)
The second-order equation is trivially fulfilled. By substituting for a from (3.1), Proposition 2 follows. QED
Lobbying is costly, so it is tempting for the firms to delay this, but the bureaucrat
continues to ask for larger and larger bribes as k grows. When k is sufficiently large,
the firms switch from bribing to lobbying. Moreover, lobbying is more an investment
than bribing (since its effect last longer), and it is thus more attractive if the long-run
importance of more investments is large (i.e. if d, δ and z are small). Straighforwardly,
lobbying is more attractive if L is small and the bribes large (which is the case if α is
small but c and x are large).
Combining Proposition 1 and 2 leads to the main result of the paper: While Proposition
2 says that the firms are more inclined to lobby instead of bribing when k is large,
Proposition 1 states that the growth rate of k depends on whether the firms actually
lobby or bribe. Thus, there may be an evolution where the firms bribe for low k, but
when time passes and k increases, the firms eventually reaches a stage where they switch
to lobbying. However, the hold-up problem between the bureaucrat and the firm implies
that investments are lower under the bribing than under the lobbying equilibrium. It is
thus possible that the investment level is so low, that the firms never switch from bribing
to lobbying. Then, the economy is stuck in a "poverty trap" with bribing forever: The
bribes are so large that the firms are discouraged to invest, and the capital stock never
reaches the level necessary to switch to lobbying.
Proposition 3: The firms will eventually switch from bribing to lobbying if and only
if (3.9) holds. Then, the time T of the switch is given by (3.10). That is, if r is large while
L, d, δ and z are small, lobbying is more likely to eventually take place, and if it does, it
does so at an earlier point in time. The effect of a (and thus α, c and x) is ambigious.
(r − a)2
a(r − a)
+
> δL
zd (d + δ) 2z (d + δ)2
9
(3.9)
¡
¢ δLzd (d + δ)
d(r − a)
−
1 − e−dT =
a(r − a)
2a (d + δ)
(3.10)
Proof: In order to find the time of lobbying, substitute (3.6) in (3.8). The latter becomes:
(r − a)
Substituting for i:
(r − a)
¢
i¡
(r − a)2
1 − e−dT +
= δL
d
2z (d + δ)2
¡
¢
(r − a)2
a
= δL
1 − e−dT +
dz (d + δ)
2z (d + δ)2
Solve T as a function of the rest:
¢ δLzd (d + δ)
¡
d(r − a)
−
,
1 − e−dT =
a(r − a)
2a (d + δ)
which is (3.10). The left-hand side is increasing in T . For lobbying eventually to take
place, it is necessary that this expression holds for some positive T . That is, it is necessary
that the left-hand side is larger than the right-hand side for T → ∞. This requires:
a(r − a)
(r − a)2
> δL
+
zd (d + δ) 2z (d + δ)2
Substituting for a completes the proof. QED
The result follows from Propositions 1 and 2. Investments are larger if r is large but
d, δ and z are small, and the level of development will then sooner reach the critical stage
where the firms switch to lobbying. The effect of c, x, and α are ambigiuos, however.
Define the firm’s expected cost of the regulation as b = r − a = c (1 − αc/2x) . While a
larger b makes the firms more tempted to lobby for a given k, it reduces i (and thus k)
at all stages, making the firms more likely to bribe. By further exploring the effect of
b, it turns out that a "moderate" b makes the switch to lobbying faster and more likely.
Roughly, the intuition is as follows. While the benefit of lobbying is approximately kb, the
capital stock is proportional to (r − b). Thus, when b is small, an increase in b increases
the incentives to lobby more than it reduces the capital stock, and overall, lobbying occurs
faster. But if b is large, the benefit of lobbying is already large, while the capital stock is
small. Then, a larger b reduces the capital stock so much that lobbying takes place later
and less likely.
Proposition 4: Define b = c (1 − αc/2x), which is increasing in c and x but decreasing
in α. (i) If b < b, given by (3.11), a larger b makes the switch to lobbying earlier and
more likely. If b > b, a smaller b makes the switch to lobbying earlier and more likely.
This means that c, α, and x, must be moderate to make lobbying likely and quick. (ii)
The threshold b increases in r but decreases in L, d, δ, and z.
10
q
b ≡ g/r − (g/r)2 − g, where
(3.11)
2
g ≡ δLz (d + δ)
Proof: (i) Solve T as a function of b:
¢ δLzd (d + δ)
¡
db
−
1 − e−dT =
b (r − b)
2 (r − b) (d + δ)
Differentiate the right-hand side w.r.t. b:
δLzd (d + δ) (2b − r) 2d (r − b) (d + δ) + 2db (d + δ)
−
[b (r − b)]2
[2 (r − b) (d + δ)]2
T increases in b if this is positive:
δLz (d + δ) (2b − r) (r − b) + b
> 0 , gives
−
b2
(d + δ)
δLz (d + δ)2 (2b − r) > rb2 , which requires
b ∈ (b, b) where
q
b = g/r − (g/r)2 − g
q
b = g/r + (g/r)2 − g
g = δLz (d + δ)2
For the square root to be positive, g/r2 > 1. Then, b > r, so upper boundary not
binding.
(ii) Differentiating b gives
sign
∂b
∂b
= −sign
, and
∂r
∂(1/r)
#
"
∂b
2g 2 /r
g
<0
= g− q
=g 1− p
2 − gr 2
∂(1/r)
2
g
2 (g/r) − g
#
"
h p
i
∂b
1
1
2g/r2 − 1
2g − r2
1
p
=
2g g 2 − gr2 − 2g 2 + gr2
=
− q
1− p
=
∂g
r
r
2 g 2 − gr2
2rg g2 − gr2
2 (g/r)2 − g
h
i2
p
1
p
= −
g − g 2 − gr2 < 0
r2g g2 − gr2
QED
11
4. Regulation, Regimes and Politics
The model above completely abstracts from the government, political regimes and optimal
policies. It is a nice property of the model that while the issues above can be studied
separated from politics, it is also easy to add the government in a simple extension. This
section will (i) formalize the government’s preferences and thus endogenize the cost of
lobbying, and (ii) study the government’s optimal choice of regulation, penalties and
bureaucratic power, and investigate how these depend on the level of development.
4.1. The Type of Regulation and Government
The government may have several concerns. To various extent, it may care about (i)
the firm’s activity, production or output, perhaps due to some externality e related to the
firms’ economic activity (which may be negative if the firms pollute), (ii) the fraction of the
production or firms that complies with the existing regulation. This value of compliance,
vc, is assumed to be proportional to the extent of the regulation (c). (iii) The government
may also implicitly benefit from corruption, since some of the rents (a fraction h, say)
may be allocated back to the government (e.g. because the government can lower the
bureaucrat’s wage if he is likely to receive a lot of bribes).9 In addition, the extent to
which the government is influenced by lobbying is normalized to 1. If p measures the
fraction of firms that bribe, the government’s utility function is:
uG = ek + (1 − p)vck + p(1 − α/2)hck + L
(4.1)
To induce the government to change the rules, the firms must compensate the government for the change a lobbying equilibrium will have on the government’s present
discounted utility. In addition, there might be some fixed cost associated with lobbying,
l, just as argued above. Since the parameters e, v and h determine the government’s
preferences, they will also influence whether the firms eventually switch from bribing to
lobbying, and when such a switch will happen.
Proposition 5: Lobbying replaces bribing more likely and sooner if e is large while
v and h are small.
Proof: In a bribing equilibrium, p = c/x, and the present discounted value of the
9
As argued by De Soto (1989) and Shleifer and Vishny (1993), regulations are partly instituted to
provide public officials the power, or the property rights, to demand and collect bribes. Evidence of
this is provided in Wade’s (1982) vivid account of corruption in the canal irrigation department in a
South Indian state. Wade describes how some irrigation engineers raise vast amounts in bribes from
the distribution of water and contracts, and redistribute part to superior officers and politicians. The
system of corruption is institutionalized and there is even a second-hand market for posts that provide the
holder an opportunity to extract bribes. This has two implications. First, politicians and senior officers
are able to obtain for themselves part of the engineers income from corruption by auctioning available
posts. Second, those specializing in corruption and thereby able to earn many times their annual official
income though bribes, will be able to outbid other contenders less able or less inclined to exploit their
official powers to extract bribes.
12
government’s utility function is
(e + vc(1 − c/x) + h(c/x)(1 − α/2)c)K(k, a), where
K(k, a) =
Z∞
t
−δτ
kτ e
µ
¶
a
a
kt
1
a
dτ =
+
kt −
=
2 +
zdδ (d + δ) (d + δ)
zd (d + δ)
(d + δ)
zδ (d + δ)
If the government "gives in" after lobbying, c = 0, and a becomes r. To compensate the
government for the change in its utility, the lobby contribution must be
L(k) = (e + vc(1 − c/x) + h(c/x)(1 − α/2)c)K(k, a) − eK(k, r) + l
na − e(r − a)
nk
=
+ l, where
2 +
(d + δ)
zδ (d + δ)
n ≡ vc(1 − c/x) + h(c/x)(1 − α/2)c
(4.2)
(4.3)
Unlike before, L is now a function of k. This should obviously be recognized when
the firms are chosing the optimal time for lobbying. Substituting for L(k) into the earlier
first-order condition (3.7), gives our new first-order condition for T :
¸
∙
³
¡
¢
∂L(kT ) ∂kT −δ(T −t)
z 2 ´ −δ(T −t) ∂V (kT , r) ∂kT
akT − i e
−
e
+
+[V (kT , r) − L(kT )] −δe−δ(T −t) = 0
2
∂kT
∂T
∂kT ∂T
Eliminating the term e−δ(T −t) , substituting for i and setting ∂kT /∂T = i − dkT and
∂L/∂k = n/ (d + δ), this becomes:
Ã
¶¸ ∙
¸
µ
¶2 ! ∙µ
¶µ
r
rkT
z
a
n
a
r2
+
−L =0
−
− dkT −δ
+
akT −
2 z (d + δ)
d+δ d+δ
z (d + δ)
d + δ 2zδ (d + δ)2
Substituting for L(k) from (4.2) and collecting the terms give:
−kT [r − a − n] +
−a2 + 2(r − n)a − r2 + 2 [na − e(r − a)]
+ δl = 0
2z (d + δ)2
which is:
kT [r − a − n] +
(r − a)2 + 2e(r − a)
= δl
2z (d + δ)2
Substituting for a and n from (3.1) and (4.3) gives Proposition 5. QED
Proposition 5 implies that if the regulation is beneficial for the government, whether
it is because it likes compliance (large v) or revenues from the bribes (large h), then
the cost of lobbying is higher and it is less likely that the firms will ever lobby the
government to relax the regulation, and if they do, they do so at a later point in time. If,
however, the government puts a lot of (positive) weight on the firm’s activity (large e),
then the government is more sympatetic to solving the hold-up problem which discourages
investments, the cost of lobbying is smaller, and the firms lobby more likely and at an
earlier point in time.
13
4.2. Short-term Policies
So far, we have treated the parameters c, x, and α as fixed. To some extent, however,
these may be the outcome of a deliberate choice by the government. Since we have defined
the government’s utility function, we can easily study its optimal choice of these political
variables.
The next subsection investigates the government’s optimal choice of policy in the
long run. For now, we let the government have a short-term perspective, as if it cannot
commit to future policies. For simplicity, assume that in every period, the firm makes its
investment decision before the government sets its policies. Then, the policy at t (which
only lasts for that period) will not affect any investment decision.
By changing c or x, the government affects the fraction of firms (c/x) that bribe
instead of comply. As noticed by the subsection above, the government may benefit from
both compliance and corruption, but these are clearly in conflict when the government
can influence c/x. If the value of the regulation is sufficiently large, such that
v > h(1 − α/2),
(4.4)
then the government prefers firms to comply (small p in (4.1)) even if it receives revenues
from bribes. If, instead, v is relatively small, and h large (such that (4.4) does not hold),
then the government benefits more from the firms that pay to avoid the regulation, than
from the firms that comply. We may call the case where (4.4) holds for "good regulation",
while it otherwise is merely "red tape".
From the government’s utility function (4.1), we immediately find:
Proposition 6: Without committing to the future, the government prefers to (i)
empower the bureaucrat (by setting α low), (ii) if the regulation is "red tape", it prefers
low penalties (x) and much regulation (c), but (iii) if the regulation is "good", it prefers
high penalties and regulation according to:
c=
vx
2 [v − h(1 − α/2)]
(4.5)
Proof: From differentiating (4.1):
∂uG
∂n
=
k = vk − 2c [v − h(1 − α/2)] k/x
∂c
∂c
∂uG
∂n
=
k = −c2 k [v − h(1 − α/2)]
∂(1/x)
∂(1/x)
∂uG
= −hc2 k/x < 0
∂α
If (4.4) holds, setting ∂uG /∂c = 0 gives (4.5), and its second-order condition holds.
Then, ∂uG /∂(1/x) < 0 and the government prefers to set x as large as possible. If (4.4)
does not hold, ∂uG /∂c > 0 and ∂uG /∂(1/x) > 0, and the government prefers to set c and
x as large as possible. In either case, ∂uG /∂α < 0 so the government prefers α to be as
small as possible. Natural boundaries to these variables complete the proof. QED
14
These results are quite intuitive. In the "red tape" case, the government prefers bribes
instead of compliance. By decreasing x and increasing c, more firms bribe, and the bribes
are larger. In the "good regulation" case, the government prefers firms to comply, so it
prefers to set x as large as possible. The choice over c involves a trade-off, since a large
c makes few firms comply, but it increases the amount of good regulation. The solution
of this trade-off is given by (4.5): If h is large, bribes are nice as well, and it is not that
important that most firms comply, so c can increase even if this makes more firms bribe.
The opposite is the case if v is large, since this makes bribes, relative to compliance, less
beneficial. Finally, if the firm has a lot of bargaining power, such that α is large, then
bribes are small and not very beneficial, and it is better to select a smaller c to encourage
more firms to comply. In either case, the government prefers to give most bargaining
power to the bureaucrat (small α), because this increases the bribes without affecting
anything else.
4.3. Long-term Policies and Development
Above, the government had a short-term perspective since its policies at time t did not
affect the firms’ investment decision. The investments, however, are depending on the
expectation over future policies. Thus, the government would be better off if it somehow
could commit to its policies. To the extent that policies are sticky (just as a change of
the rules is assumed to be permanent), the government is indeed able to commit. Thus,
suppose that the government at time t can set its policies and these will be in place forever
(ideally, the government would prefer to commit to time-dependent policies, but these are
probably even harder to commit to, as they will hinge on future parameters that may not
be verifiable).
Taking into account the long-term consequences of its policies, the government realizes that c, x, and α affects the investment levels of the firms. To the extent that the
government benefits from economic growth or a higher level of development (k), it may
want to modify c, x, and increase α, since each of these changes increases growth.
Proposition 7: If the government can commit to its policies, the optimal choice of
regulation c, penalty x, and bureaucrat’s power (1 − α) are lower than the short-term
optimal policies, but these are increasing in k, r, d and δ and decreasing in e.
Proof: In a bribing equilibrium, the present discounted value of the government’s
utility function is
(e + n)K(k, a).
15
Differentiating w.r.t. c, x, and α gives:
∙
¸
∂K
∂n r − c (1 − αc/2x)
(αc/x − 1)
kt
∂n
K(k, a) + (e + n)
=
− (e + n)
+
2
∂c
∂c
∂c
(d + δ)
zδ (d + δ)
zδ (d + δ)2
∙
¸
∂n
kt
∂K
∂n
r − c (1 − αc/2x)
αc2
+
K(k, a) + (e + n)
=
+
(e
+
n)
∂(1/x)
∂(1/x)
∂(1/x)
(d + δ)
zδ (d + δ)2
2zδ (d + δ)2
∙
¸
∂n
∂K
∂n r − c (1 − αc/2x)
c2
kt
K(k, a) + (e + n)
=
+ (e + n)
+
∂α
∂α
∂α
(d + δ)
zδ (d + δ)2
2xzδ (d + δ)2
In addition to the multiplicative effect (the square brackets), the dynamic concerns adds
the last term in each equation. Thus, the dynamic concern is an argument for lower c and
x, and a larger α, than the short-term optimum. Clearly, this effect is more important
(i) the lower is the term in the brackets, i.e. if k is low and r is low, and (ii) the larger is
the last term, i.e. if e is large and d and δ are small (if (d + δ) decreases, the last term
increases faster than the term within the brackets). QED
If k is small, such that the economy is not yet developed, then the dynamic effects are
very important. In order to encourage growth, the government prefers little regulation
and small penalties for corruption (harsh penalties increase the bribes and thus reduce
investments). As k grows, however, the dynamic effects are less important and the static,
or short-sighted, concerns more so. Then, the optimal c and x increase (if the regulation
is "good"), and α decreases to the extent the government can affect these variables.
Similarly, if r is large, there is less need to encourage further investments, and the optimal
c and x are larger. If e is large but d and δ are small, the future development of k is more
important, and the dynamic concerns moderates c, x and (1 − α).
5. Extensions: Market Structure
The model above is simple and could be extended in various ways. Time is assumed to be
continuous, although we talk about "period t" as if time were discrete. A discrete-time
model might be easier to interprete, particularly since the firm and the bureaucrat then
do not need to negotiate instantly, but only once every period. For this reason, we might
later change to a discrete-time model, although it would be slightly more cumbersome to
deal with.
Another simplifying assumption was to let a "change of the rules" be completely
permanent. This is unattractive, since then the lobby-equilibrium consist of one instant
with lobbying, and thereafter no action (except for the investments). A more general
model would allow the rules to stay in place a certain number of periods, or let the rules
change back to the original form with some positive probability every period. As long as
this probability were less than one, the results above would continue to hold. New results
would emerge, however: The more stable the rules were, the larger the investments would
be, and the more likely it is that the firms eventually will lobby.
A less innocent assumption was to let firms be identical and ignore the market structure. In fact, we believe that the market structure should be an important ingredient
16
for firms’ decision over whether to lobby or bribe. This might be particularly true if the
market is open to entry. If relatively few firms have entered the market, they might rationally anticipate that many more firms will enter if they lobby the government to relax
the rules permanently. This may intensify the competition and reduce the firms’ profit.
Thus, the firms currently in place may avoid lobbying, and instead bribe, just to keep
potential firms out of the market. Thus, the bribing equilibrium may remain in place
since it functions as a barrier to entry. Later in the development process, however, many
more firms may already be present in the market, and the threat of further entry might
be relatively smaller. Then, the firms find it more attractive to lobby for a permanent
change of the rules, even if this may increase entry somewhat. While it is beyond the
scope of this paper to investigate these issues, we find them sufficiently important to work
on in a companying paper.
6. Concluding Remarks
Corruption and lobbying are to some extent substitutes. Through lobbying a firm may
be able to change existing rules to the firm’s advantage. Through bribery a firm may get
the the bureaucrat to bend the rules and thus avoid the full cost of a policy. We believe
that one important difference between these two strategies is that the effect of lobbying is
more permanent than bribing, simply because the burecrat cannot commit to not asks for
bribes in future periods. Based on this simple assumption, we find that the firms prefer
bribing to lobbying early in the development process. At later stages, when firms have
invested more, their bargaining power relative to the bureaucrat is smaller and the bribes
therefore larger. Then, the firms are more likely to lobby the government. However, since
the corruption equilibrium discourages investments, the economy may be trapped in a
bribing equilibrium with so little investments that the firms never switch from bribing to
lobbying.
The results of the paper show how this evolution hinges upon parameters related to
the economy and the political environment. Tough penalties on corruption, for example,
may not be a good thing, since they lead to larger bribes and thus lower investments.
We also analyzed the government’s optimal policies, whether the regulation is in place to
raise money or to regulate the market. Generally, we find that the optimal penalty and
amount of regulation increase in the stage of development.
This paper is only a first attempt to compare bribing and lobbying as alternative rentseeking activities. Future research should further explore how the equilibrium regime
depends on the market structure and the environment more generally. This is necessary
not only to understand large cross-country variations in rent-seeking activities, but also
in order to derive good policies that mitigates bad rent-seeking activities.
17
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