Strategic compromise, policy bundling and interest group power
2.3. MODEL effort of both players are lost. This success function is increasing and concave in the lobbying
effort ofG, while it is decreasing and convex in the effort of I.7 Such assumptions ensure a positive but diminishing marginal effect of each player’s effort on his own probability of winning the contest; moreover, they ensure that an increase in each player’s effort harms the other, making it strategically desirable for each player to induce a lower effort from the other. In such a setting, we will show that it is optimal forGto propose a reform(ea,eq)that is not necessarily equal to his desired reform bundle(a∗G, q∗G).
The expected payoffs ofGandI from the two-stage game are given by:
EUG=pUG(ea,q) + (1e −p)UG(0,0)−eG, EUI =pUI(ea,q) + (1e −p)UI(0,0)−eI.
Denote the stake of I by N(a, q) = UI(0,0)− UI(a, q) and the stake of G as UG(a, q)− UG(0,0) = UG(a, q) sinceG’s utility of the status quo is normalized to zero. The expected payoffs ofGandIcan then be expressed as:
EUG =pUG(ea,eq)−eG,
EUI =UI(0,0)−pN(ea,q)e −eI.
(2.2)
We consider subgame-perfect Nash equilibria consisting of reform proposals(˜a,q)˜ and effort levelse∗Gande∗Isuch that at every stage each player takes an action that maximizes his expected payoffs given the other’s behavior. Our interest is in comparingG’s resulting reform proposals in the presence of an interest group to his proposal without an interest group. In the absence ofI, the second stage legislative contest becomes trivial, andGwill win the contest with the smallest amount of effort.Gcan therefore propose his optimal reform(a∗G, q∗G). Indeed, we will be able to show that it pays forGto strategically bundle reforms together by proposing a positive amountea >0, for example, even if his desired point isa∗G = 0.
To analyze the case in whichI is present, we first look at the second-stage legislative contest.G andI maximize their expected payoffs in 2.2 with respect to their respective lobbying efforts.
Lemma 1
The equilibrium lobbying efforts ofGandIare given by:
e∗G=γN(ea,q)Ue G2(ea,eq) e∗I =γN2(ea,q)Ue G(ea,eq).
(2.3) withγ = αGαI
(αGUG(ea,eq)+αIN(ea,eq))2.
7Formally,∂p/∂eG>0,∂2p/∂e2G<0and∂p/∂eI <0,∂2p/∂e2I >0.
0.511.5eG*
0 .2 .4 .6 .8 1
eI*
UG/N=1.3 UG/N=.5
UG/N=1
Figure 2.2: Government’s best response Proof. See Appendix 2.A.1
Figure 2.2 illustratesG’s optimal effort,e∗G, givenI’s effort,e∗I, for different combinations of the relative stakes. At each level ofe∗I, the lower the stake ofGrelative toI, the less equilibrium effortGexerts.
Since equilibrium efforts e∗G and e∗I are functions ofG’s policy proposal (ea,q), comparativee static properties of the second stage contest can be characterized.
Lemma 2
Equilibrium effort of the interest group,e∗I, varies with the reform levelsaandqsuch that
∂e∗I
∂s =γN2
αIN −αGUG αGUG+αIN
∂UG
∂s + 2γN UG
αGUG αGUG+αIN
∂N
∂s (2.4)
wheres∈ {a, q}.
Proof. See Appendix 2.A.2
The first term in equation (2.4) represents how much the stake ofG changes with a change in a policys,s ∈ {a, q}. The second term on the other hand represents how much the stake ofI changes withs. The resulting sign of∂e∗I/∂stherefore depends on the signs of the two expressions in (2.4). Because the second term directly takes the sign of∂N/∂s, the ambiguity in the sign of∂e∗I/∂sarises from(αIN−αGUG)in the first term, which can be negative or positive depending on the effort productivities and stakes of bothI andG. In analyzing the first-stage reform decision of the government, Lemma 2 plays a crucial role because this ambiguity in the
2.3. MODEL sign of∂e∗I/∂svanishes when evaluated atG’s desired reform level(a∗G, qG∗).
To describe the underlying mechanism driving equation (2.4), Figure 2.3 draws the reaction curves ofGand I for the case in whichαI =αG = 1. For any increase in eitheraor q,G’s stake in the contestUGincreases, raisingG’s reaction curve fromG0toG1.
Suppose there is an increase ina. Assuming the case presented in Figure 2.1 in whichIprefers more ofaand less ofqthanG, the stake of the interest groupN(a, q)goes down, reducingI’s optimal effort for any level of effort byG. The reaction curve ofIthen shifts to the left fromI0 toI1, and the equilibrium point moves from point 0 to point 1 as illustrated in Figure 2.3a. With more of policya,G’s effort will rise andI’s effort will fall in equilibrium. Because the interest group is in favor ofa, moreawould induce them to exert less lobbying effort in equilibrium.
(a) Normal case (b) Extreme case
Figure 2.3: Reaction curves ofGandI withαI =αG= 1
Suppose instead that there is an increase in policyq. BecauseI prefers less ofq, moreqwould induceI to exert more lobbying effort for any level of effort byG. This would shiftI’s reaction curve to the right fromI0 toI2. The resulting equilibrium effort levels would then increase for bothGandI. However, there could also be situations in which an increase inqreducesthe effort ofI. Figure 2.3b illustrates such an example, where an increase inqaugments the stake ofGby so much that equilibriume∗Igoes down. Due to the non-linearities of the reaction curves, the response of equilibrium effort to increases in reforms will depend on the relative changes in the stakes of both players. The direction to whiche∗Ireacts to reforms is particularly important for G’s reform decision in the first stage.
In order to highlight strategic bundling of reforms, we assume without loss of generality that a∗G = 0, whileqG∗ 6= 0.8 In other words, without oppositionGwill propose a positive level of reforms for the policyqand the status quo for policya.
8The results will hold for anya∗G6= 0.
(aG*
,qG*
)
a q
(aI*
,qI*
) UG
cG
UI
cI
Figure 2.4: Example of(a∗I, qI∗)and(a∗G, qG∗).
We will explore two cases in the government’s first stage optimization. First, a simplified case in which the government can only propose on one policy dimension. In such a case,Gwill propose on theqdimension, since it prefersato remain at the status quo. Second, we will explore the case in whichGcan propose on both dimensionsqandaand show that ifI prefers less ofqand more ofathanG, even ifG’s ideal level ofais zero, he will bundle some positive level ofain equilibrium, to maximize his winning probability.
2.3.1 One policy
Let us first analyze the case in which reforms can only have one policy component. SinceG prefers the status quo ina, it will only propose in the policy dimensionq, which, as represented in Figure 2.4,I prefers less of thanG. That is, the preferences ofI are decreasing inqatG’s ideal pointqG∗.9 LetUI(q)andUG(q)beI’s andG’s preferences overq, respectively. Opposition toqmeans that0≤qI∗ < qG∗. For simplicity, we assume here thatq∗I = 0, the status quo.
The governmentGmaximizes his expected utility in (2.2) with respect toq, taking into account the preferences of the interest group and the level of lobbying effort given in Lemma 1.
Lemma 3
The government’s proposed policyqeis such that
∂EUG
∂q =p∂UG(q)
∂q − ∂e∗I
∂q UG
N = 0. (2.5)
9Formally,∂UI/∂q|q=q∗<0.
2.3. MODEL Proof. See Appendix 2.A.3
The first term in the above expression is the marginal utility gain from an increase inq, provided the policy is enacted. The second term represents the marginal cost ofqbrought about by the increase in the lobbying effort of the interest group.Gtherefore chooses to propose a levelqesuch that his marginal benefit from increased utility equals his marginal cost from a more aggressive opposition.
Lemma 3 introduces the tradeoff that emerges from taking account of the effort I exerts in opposing the reform, much in the spirit of Becker’s (1983) political influence model. This tradeoff allows us to relate the proposed policy leveleqwithG’s desired policy levelqG∗ .
Proposition 4
In the presence of an opposition, the proposed reformqewill be such thatq < qe G∗. Proof. See Appendix 2.A.4
In the face of an opposing interest group, it pays for the government to restrain his proposal of the reform to reduce the lobbying effort of the opposition, thereby increasing his winning probability. This result coincides with the strategic restraint result presented by Epstein and Nitzan (2004). Essentially, the level of eq proposed by the government serves two functions:
a policy reform that contributes to the utility of the government, and a “bargaining tool” that affects the incentive of the opposition to engage in lobbying efforts against the reform.
2.3.2 Two policies
Now let us assume instead that the government is free to propose a reform of two components, (a, q), and thatIprefers more ofaand less ofqthanG.10 That is, we can describe the preferences
of the interest group byUI(a, q), which is increasing ina and decreasing inqat G’s optimal point(a∗G, qG∗).11
Proposition 5
In the presence of an opposition, the proposed reforms(ea,q)e are such thatea > a∗Gandq < qe G∗. Proof. See Appendix 2.A.4
In seeking to maximize expected payoffs,Gmakes a strategic compromise by over-proposing in the policy component thatIfavors and under-proposing in the component thatIopposes. The
10See again the example in Figure 2.4.
11In other words, the utility functionUI(a, q)ofIsatisfies∂UI/∂a|a=a∗ > a∗Gand∂UI/∂q|q=q∗<0.
intuition behind the results is simple. In the face of opposition,Grecognizes that he is dealing with a group whose lobbying efforts are affected by the extent of his proposed reforms. As a result, although proposing anea > a∗G and aq < qe G∗ reduces his payoffs, doing so also reduces the stake ofI, thereby reducing their incentive to exert as much lobbying effort. In effect, G gets a higher probability of reform enactment. The critical point that drives this trade-off can be seen from looking at equation (2.4) of Lemma 2. Moving from any point on thea−qplane creates an ambiguous change in the direction ofI’s optimal effort due to the countervailing effects on the stakes ofGandI. This is true except at the point(a∗G, qG∗). Any movement away from(a∗G, qG∗), where the first order condition holds forUG, creates only a negligible second-order effect on the stake ofG, collapsing the first term of equation (2.4) to zero. That is, although moving from (a∗G, q∗G)to(ea,q)e causes a second-order reduction in the stake ofG, doing so creates a first-order increase in the stake ofI that induces an unambiguous reduction inI’s effort, thereby improving G’s chances of enacting the reform. At the point(a∗G, q∗G)therefore, the trade-off between lost utility and gained probability of winning favors the gain in probability, givingGan incentive to strategically compromise.
(b) Restraint in the proposal of quality reforms
Figure 2.5: Strategic compromise
Figure 2.5 illustrates these results graphically. In Figure 2.5a, the slope ofEUGat the govern-ment’s desired levela∗G is positive because the utility loss from increasingais smaller than the probability gain from reducingI’s effort. Thus,Gwill gain from moving his proposedeato the right ofa∗G up to the point where the slope ofEUG is zero. A similar argument holds for the opposed reformq in Figure 2.5b. The slope of EUG at the government’s desired level q∗G is negative because, at that level ofq, the loss in utility from reducing qis smaller than the gain in probability from makingI less aggressive. Thus,Ggains from moving back his proposedqe belowqG∗ until the point where the slope ofEUGis zero.
Corollary 1
In the presence of an opposition, the government will strategically bundle different policies in