Evidence of strategic lobbying in the U.S. House of Representatives. Carlos R. Lever,∗ Banco de M´exico† February 14, 2011

Abstract I find evidence that Political Action Committees act strategically when giving campaign contributions in the US. House of Representatives. They do so by targeting legislators with a higher probability of being pivotal for a vote. I find that increasing the pivotality of a legislator by one standard deviation increases her contributions by 39,000 dollars. (10.8% of the average contributions.) I also show that pivotality is not related to distance to the median voter when there is uncertainty on how legislators vote, although the distribution of pivot probabilities has a similar spatial property: it’s single-peaked. Finally, my estimations show that Republicans disproportionately gained pivotality after the Republican takeover of 1994 and continued to increase it while they were in control of the House.

1

Introduction.

Empirical studies of contributions by Political Action Committees (PACs) in Congress have not settled whether they are strategic or ideological when deciding how to spend nor how much influence they have over legislators. The standard approach has been to estimate the effect of PAC contributions on legislators’ votes. The bulk of the work has tried to solve the reverse causality problem: do legislators vote in a PAC’s preferred direction because of it’s contributions, or do PACs contribute more to legislators who would vote in their preferred direction regardless of their contributions? The results seem to be decidedly mixed.1 In this paper I test a different prediction made by models of strategic spending: strategic PACs should spend more on legislators who have a higher probability of being pivotal. A legislator is ex-post pivotal for a bill if changing her vote changes the outcome of the election. Ex-ante, when there is uncertainty on how legislators will vote, PACs have to calculate the probability each legislator will be pivotal. Testing whether PACs spend on pivotal legislators is a good test for strategic lobbying because of three reasons. First, it’s a conclusion that holds under very general assumptions, so if we reject the hypothesis we can be sure we’re not rejecting the specific auxiliary assumptions of any given model of strategic spending. The main assumptions required are: (A) PACs optimize when they spend resources; (B) PACs only wish to ∗ I am very grateful to James Fowler; Ketih Poole and Howard Rosenthal; Charlie Stewart and the Center for Responsive Politics for making their data available online. Luis Enrique Candelaria provided excellent research assistance. I thank Liran Einav, Alex Hirsch and Zac Peskowitz for very useful comments. Tom´ as Rodr´ıguez provided a crucial reminder on first-order conditions. † Direcci´ on General de Investigaci´ on Econ´ omica: [email protected]. 1 See Snyder (1992).

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achieve their desired outcome (passing or preventing a bill) but do not care by how many votes; and (C) PACs have uncertainty on how legislators will vote. The second reason this is a good test is that the prediction is very demanding. Pivot probabilities are complicated objects that depend on the voting probability of all legislators in a chamber. (As we shall see in detail below.) The theory is very strict: a legislator is ex-post pivotal only if she casts a “yay” vote on a bill that passes by exactly one vote, or if she casts a “nay” vote on a bill that fails by exactly one vote. By definition, many legislators are simultaneously pivotal ex-post, but ex-ante they have different probabilities of being pivotal. To find these probabilities, a PAC must calculate the probability of all possible realizations of votes under which a legislator is pivotal. For a legislature the size of the US House of Representatives there is an astronomical number of potential realizations, so these calculations are very complicated. Furthermore, each realization has a very low probability of happening. The final reason this is a good test is that we do not need to know much information about the PACs’ objectives to test the prediction. This makes the test easier than directly estimating the effect of contributions on a legislator’s vote, since to do so we have to limit ourselves to bills and PACs in which we are confident we know what the PAC wants. For example, we don’t need to know if a PAC wants to promote or stop the bill, because the same legislators who are pivotal to pass a bill are pivotal to prevent it. We also don’t need to know how much the PAC benefits from promoting (or preventing) the bill and we don’t need to know its cost of raising resources, because these only determine the total contributions a PAC gives, while pivotality determines the distribution of contributions across legislators. A strategic PAC gives more to pivotal legislators, regardless of the total amount it spends. When testing this prediction, it’s important to understand that pivot probabilities are not related to distance to the median voter when there is uncertainty on how legislators vote. I show this in the paper through a simple counterexample with three voters. Pivotality is often confused with distance to the median voter because the median legislator will always have the highest pivot probability in a one-dimensional spatial model with full certainty on policy preferences. This is not true when there is uncertainty on how legislators will vote. Instead, pivot probabilities are complicated functions of the voting probability of all legislators in the chamber. In spite of this, I prove a new theorem that shows that pivot probabilities have a similar property to the median voter logic: pivot probabilities are “single-peaked” in the voting probabilities of the legislators. This means that if you order legislators according to their probability of voting for a bill, the pivot probabilities will monotonically increase until they reach a “peak” legislator who has the highest pivot probability and will then monotonically decrease. This holds whether the voting probabilities come from a spatial model or not. To measure pivotality in the data I use a popular structural model that predicts the legislators’ voting behavior: the DW-Nominate scores. The DW-Nominate model assumes that each legislator’s behavior can be described through an ideological parameter (her score) in a two-dimensional spatial model. Using the DWNominate scores I estimate the voting probability for each legislator on each bill and then run a simulation where I repeat the vote on each bill 100,000 times to calculate the legislators’ pivot probabilities. In the data, the “peak pivotal legislator” is 146 places away from the median legislator and is usually on the side of the aisle of the party that holds the majority. A total of 88% of bills in the sample had peak pivotal legislators who belonged to the majority party.2 For example, after the Republican takeover of 1994 2 A caveat: The theorem shows that there can be at most two peak pivotal legislators, but empirically it’s hard to estimate exactly who the peak is, because it involves estimating very small probabilities. To be able to identify the peak pivotal legislator

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the pivotality disproportionately swung toward the Republican camp. Before 1994 the median peak pivotal legislator was 160 positions to the left of the median voter and after she was 144 positions to the right. This disproportionate swing in pivotality might have happened because the bills on the agenda changed substantially. I then test the prediction by regressing the campaign contributions of each legislator on her pivotality. When I run an OLS regression, pivotality is not statistically significant and the magnitude of the effect is biased downward. This happens because OLS is not the appropriate specification to test this prediction. To understand why, it’s important to understand why strategic lobbies target pivotal legislators. Pivotality matters because pivotal legislators have the highest marginal benefit for the PAC and PACs that optimize adjust their spending to equate the marginal benefit of a legislator’s vote to the marginal cost of changing it, but this is only true for interior solutions. When a PAC gives zero contributions to a legislator it faces a corner solution and the relationship between pivotality and contributions breaks down. At a corner solution, PACs would like to spend less on legislators with small pivot probabilities, but they can’t because they’re constrained. The average PAC in the sample only contributed to about 9% of the legislators in the House, so 91% of the data are corner solutions.3 Thus, corner solutions contain a lot of information about the PACs’ decision making and must be dealt with in the specification. To do so, I run a tobit specification with legislator random effects to control for biases from unobserved characteristics of the legislators. After I correct this problem, I find that pivotality is a statistically significant predictor of campaign contributions by business and labor PACs. (p < 0.001) The magnitude of the effect is also substantively significant. My regression predicts that increasing the pivotality of the average legislator by one standard deviation increases her contributions by 39,000 dollars, which is 10.8% of the average contributions per legislator. Pivotality is one of the variables with the largest predictive power relative to it’s standard deviation. For example, the effect of becoming the House Speaker multiplied by it’s standard deviation is 44,000 dollars and the effect per standard deviation of joining the powerful Ways and Means committee is 45,000 dollars. For both variables, the difference with respect to pivotality is not statistically significant. Becoming the Speaker has a huge direct effect on the contributions of an individual legislator (it increases them by 909,000 dollars!) but it happens to so few legislators that it doesn’t explain much variation in the data. The estimated pivot probabilities show a trend toward making the Republicans relatively more pivotal toward the end of the sample. One of the most dramatics shift in the data occurred during the Republican takeover of 1994. Before 1994, Democrats were much more likely to be pivotal for a bill to pass. Because of this, the average Democratic Representative received 6,100 dollars above the average Republican. After the takeover, the change in pivotality made the average Republican receive 20,800 dollars above the average Democrat. The net change due to the swing in pivotality was 26,900 dollars in favor of the Republicans (6.6% of the average contributions). Understanding the role of pivotality is important because it shows how lobbying works to affect policy. An alternative theory states that lobbies are ideological in their contributions and target legislators who are most sympathetic to their positions. Understanding the motives behind the lobbyists’ actions is crucial to I had to smooth the pivot probabilities in my estimation, so I can only identify a “peak plateau” where several legislators have the same peak probability. For 59% of the bills in the sample, the legislators in the peak plateau belong exclusively to the party who had the majority is Congress. A further 29% of bills have peak plateaus that contain legislators from both parties. 3 A second corner happens at the top, because PACs have contribution limit of 10,000 dollars per electoral cycle. This only affects 0.06% of the observations.

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understand how they shape policy. For example, the work in Ansolabehere & Snyder (2003) persuasively argues that PAC contributions are extremely low relative to the high benefits of legislation. The authors suggest that lobbies therefore do not spend to influence legislation and that PAC contributions are a form of consumption. Another possibility (which the authors acknowledge) is that lobbies spend little because they can change little. As I show below, the probability a legislator is pivotal is very small. About 87% of bills that got voted on in the years I study had a zero probability of being decided by a pivotal vote, so the the value of buying a legislator’s vote was zero. For the rest of the bills, the average probability of observing a pivotal vote is less than 6%. The low probabilities involved in pivotal calculations generate a low expected marginal benefit from spending on a legislator. Regardless of the total amount each lobby spends, the optimal way to assign resources across legislators is by targeting pivotal voters. Lobbies might not be spending much, but my results indicate they target their resources in a way that gives them the largest “bang for their buck”. This can only happen if they spend to influence votes on bills. The rest of the paper is structured as follows: Section 2 develops a simple theoretical model of strategic spending to highlight the assumptions behind the prediction; Section 3 describes the data; Section 4 presents the regression strategy and the empirical results; Section 5 uses the results to analyze the 1994 Republican takeover of congress; Section 6 concludes. In Appendix A, I check if my results are sensitive to the structural assumptions behind the pivotality measure by repeating the estimation using a different method, the Heckman-Snyder scores. In Appendix B I report the results of applying the same exercise to the U.S. Senate, but due to the nature of the data, fewer legislators which are reelected infrequently and in a staggered fashion, it’s hard to get statistical power.

2

The Model.

I will set-up a simple model of strategic spending to highlight the assumptions under which lobbies target pivotal legislators. I will then show that the median voter need not have the highest pivot probability, but pivot probabilities possess a similar property to the median voter logic: pivot probabilities are “singlepeaked” in the order of the voting probabilities. This means there is always a “peak” pivotal legislator such that the pivotality of the other legislators decreases monotonically the farther away they are from her. This property had not been shown before. The rest of the section proceeds as follows. In subsection 2.1, I explain how I model the legislators’ voting behavior, I define pivot probabilities and show they are single-peaked. The reader who is less interested in the technical details of the proofs can read the first part to get the definitions on pivotality and skip to subsection 2.2, where I give a simple example to show that the peak pivotal legislator is not the median legislator. In subsection 2.3, I show that lobbies that spend strategically target pivotal legislators.

2.1

Pivotal voters.

There are N legislators who must make a decision on how to vote on a bill. Legislators cannot refrain from voting and the turnout is known. A bill requires M > N/2 votes to pass. I allow for supermajority rules in the theory section of the paper because the theoretical predictions remain basically the same: lobbies target pivotal legislators. The pivot probabilities, obviously, depend on the voting rule. Supermajority rules play 4

an important role for decision making in committees in Congress, but in the empirical section I will only focus on bills that are presented on the floor. I assume that from the lobbies’ perspective, legislators chose stochastically. This uncertainty might come from several sources: from fundamental uncertainty about events that shape a legislator’s vote, for example, the release of unemployment figures in a legislator’s district right before a vote; from private information by the legislator on her voting intention and her willingness to swing her vote; or from strategic uncertainty generated by the actions of other lobbies. I stress that voting doesn’t have to be stochastic from the point of view of the legislator, it only matters that it’s uncertain from the point of view of the lobby at the time it has to decide how to spend it’s resources. Adding uncertainty to the model is important for two reasons. It is a realistic feature of the political process and it allows us to talk to the data. Stochastic voting is the foundation behind most empirical models of legislative voting. For example, the DW-Nominate scores assume there are legislator specific random shocks that change their voting behavior. This uncertainty is used to fit a spatial to the data. In my empirical specification I will use the DW-Nominate scores to measure pivotality, so I’m being consistent by assuming there is uncertainty on how legislators vote. The probability a legislator votes in favor of a bill is denoted by: 0 < p1 < p2 < . . . < pN < 1 I assume the voting probabilities are strictly between 0 and 1 and strictly different to simplify the proofs, but these assumptions are not substantial. I assume that conditional on the pi ’s, the realization of each vote is independent. In a standard spatial model with legislator specific utility shocks, the voting probabilities would be determined by the legislators’ ideal point and by the positions of the bill and of the status quo in the policy space. For now, I am not assuming the voting probabilities necessarily come from a spatial model. Conditional on the voting probabilities, we can define the probability a voter is pivotal. Definition 1 (Pivotal voters and pivot probabilities.). A voter is pivotal for the election if once the votes are cast, changing her vote would change the outcome of the election. Voter i’s probability of being pivotal, or more succinctly her pivot probability, is given by qi =

X

Y

S⊂N \i j∈S |S|=M −1

pj

Y

1 − pk




k∈S / k6=i

Clearly many legislators must be ex post pivotal simultaneously, but that does not mean that everybody is pivotal at the same time. A legislator is pivotal if she casts a “yay” vote and the bill passes with exactly M votes, or if she casts a “nay” vote and the bill fails with exactly M − 1 votes. Since votes are stochastic, many different minimal prevailing coalitions are possible, with some more likely than others. This gives legislators different probabilities of being pivotal. I will now show that the pivot probabilities are single-peaked. This means that the pivot probabilities monotonically increase until they reach a peak legislator and then decrease monotonically. The median legislator is not necessarily the peak pivotal legislator.4 4 Technically, the proof below only shows there can be at most two “peak” pivotal legislators. I have been unable to produce a single example with two peak pivotal legislators, and I am confident that if such example exists, it only holds for a knife-edged set of parameters.

5

Let δi ∈ {0, 1} represent the realized vote of legislator i. I will first give some useful formal definitions, then I show a lemma and finally I prove the main proposition.

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Definition 2 (Single-peakedness). The pivot probabilities are single-peaked if for any three voters i, j, k with pi < pj < pk we have the following two conditions.

qk > qj ⇒ qj > qi

(1)

qi > qj ⇒ qj > qk

(2)

Condition (1) refers to the increasing section of the distribution and condition (2) to the decreasing section. Definition 3 (Single-crossing). Take n and N 0 such that 0 6 n 6 N 0 + 1 and 1 6 N 0 6 N . Define ∆(n; N 0 ), the marginal difference function at n, as X  X  ∆(n; N 0 ) ≡ P rob δi = n − P rob δi = n − 1 Where the probabilities are calculated using (p1 , . . . , pN 0 ). The marginal difference function, ∆(·; N 0 ), has the single-crossing property if, for all pairs (n, n0 ) with n < n0 , we have ∆(n0 ; N 0 ) > 0 ⇒ ∆(n; N 0 ) > 0 In words, the ∆ function has the single-crossing property if it begins positive, crosses zero at most once, and then becomes negative. Lemma 4. ∆ always has the single-crossing property. Proof. Take n < n0 . Since ∆(0, N ) is always positive and ∆(N + 1, N ) is always negative, we only have to show the single-crossing condition for n > 1 and n0 6 N . The proof works by induction on N . For N = 1 this is trivially true. Now assume ∆(·; N − 1) has the single-crossing condition. We can rewrite ∆(n; N ) as

∆(n; N ) =pN ∗ P rob

N −1 X

! δi = n − 1

+ (1 − pN ) ∗ P rob

i=1

" − pN ∗ P rob

N −1 X

! δi = n

i=1 N −1 X

! δi = n − 2

+ (1 − pN ) ∗ P rob

i=1

N −1 X

!# δi = n − 1

i=1

=pN ∆(n − 1; N − 1) + (1 − pN )∆(n; N − 1)

(*)

Suppose ∆(n0 ; N ) > 0. We want to show ∆(n; N ) is positive.

∆(n0 ; N ) > 0 ⇒ ∆(n0 − 1; N − 1) > 0

(By * and the single-crossing condition)

⇒ ∆(n; N − 1), ∆(n − 1; N − 1) > 0 ⇒ ∆(n, N ) > 0

(Again by the single-crossing condition) (By *)

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Proposition 5. The pivot probabilities are always single-peaked. Proof. Fix three voters i, j, k such that pi < pj < pk . I will show that qk > qj ⇒ qj > qi . Below is some useful notation for the proof. 1. Let A be the probability of getting M − 3 votes from N \ {i, j, k}. 2. Let B be the probability of getting M − 2 votes from N \ {i, j, k}. 3. Let C be the probability of getting M − 1 votes from N \ {i, j, k}. 4. With a slight abuse of notation I will use ∆(M − 2) for B − A and ∆(M − 1) for C − B.

We can write qj as qj = pi pk A + pk (1 − pi )B + (1 − pk )pi B + (1 − pk )(1 − pi )C From here we can write qj − qi as qj − qi

=


pk (pi − pj )A + pk (1 − pi ) − (1 − pj ) B


+(1 − pk )(pi − pj )B + (1 − pk ) (1 − pi ) − (1 − pj ) C   = (pj − pi ) pk (B − A) + (1 − pk )(C − B)   = (pj − pi ) pk ∆(M − 2) + (1 − pk )∆(M − 1) Analogously we can write qk − qj as   qk − qj = (pk − pj ) pi ∆(M − 2) + (1 − pi )∆(M − 1) We are now ready to rumble. qk − qj > 0 ⇒ pi ∆(M − 2) + (1 − pi )∆(M − 1) > 0 ⇒ ∆(M − 2) > 0

(By pk > pj )

(By the single-crossing condition.)

⇒ pk ∆(M − 2) + (1 − pk )∆(M − 1) > 0 ⇒ qj − qi > 0

The proof for qi > qj ⇒ qj > qk is symmetrical.

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(By pk > pi )

2.2

The median voter is not necessarily the peak pivotal voter.

Assume there are three voters with p1 = p2 = p and p3 ≈ 1.5 Assume a bill needs a simple majority to pass. Voters 1 and 2 are always the median voter. If we calculate the pivot probability we get the following: - For voters 1 and 2: p(1 − p3 ) + (1 − p)p3 = p3 − (2p3 − 1)p. - For voters 3: 2p(1 − p). Figure 1 shows what happens to the pivot probabilities as we change p. A voter is pivotal only if the other two split their vote. Since p3 is very likely to vote in favor of the bill, voters 1 and 2 have a higher probability of being pivotal for smaller values of p. As seen above, this relationship is linear in p. Voter 3, on the other hand, maximizes her probability of being pivotal with p = 1/2, which maximizes the probability voters 1 and 2 will split their vote. All voters have the same probability of being pivotal when p = 1/2 or p = p3 . Voter 3 is the peak pivotal voter for any intermediate value of p.

Figure 1: The figure shows the probability of being pivotal for three voters with p1 = p2 = p and p3 = 0.8. The median voter will always be either voter 1 or 2, yet voter 3 has a higher probability of being pivotal when p is between 0.5 and 0.8. 5 Yes, I know, I’m cheating here by allowing two voters to have equal voting probabilities. But I assure you it’s for the greater good.

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2.3

Strategic spending.

I will first set up the spending problem of a single lobby and then comment on what changes when multiple lobbies spend at the same time. A lobby L wishes to spend money to persuade legislators to vote in favor (against) a bill she wishes to pass (to fail). Let yi be the amount of money L spends on legislator i to increase (decrease) her probability of voting for the bill. I will assume that spending money changes voting probabilities in a smooth way. Assumption 1. The derivative of pi with respect to yi exists and is strictly positive if the lobby wants the bill to pass, and strictly negative if she wants it to fail. p0i (yi ) > 0; ∀yi ∈ [0, ∞), when the lobby wants the bill to pass. p0i (yi ) < 0; ∀yi ∈ [0, ∞), when the lobby wants the bill to fail. I am not assuming that pi (·) is the same for all legislators. Different legislators might be harder or easier to persuade. Also note that by writing pi as a function of yi , I am implicitly assuming that the expenditures on one legislator have no effect on the voting probabilities of the other legislators. To be explicit: Assumption 2. Spending on a legislator does not change the voting probabilities of the other legislators. ∂pi = 0; ∀j 6= i ∂yj

Finally, I assume that lobbying has decreasing returns. Assumption 3. The derivative of pi is strictly decreasing if the lobby wants the bill to pass and strictly increasing if she wants it to fail. p00i (yi ) < 0 when the lobby wants the bill to pass. p00i (yi ) > 0 when the lobby wants the bill to fail. It is useful to think of the ratio 1/|p0i | as the marginal cost of changing the voting probability of a legislator. If |p0i | is small, a large number of resources are required to persuade legislator i, so the marginal cost is high. If |p0i | is high, the marginal cost is low. In all cases I am assuming that the lobby faces an increasing marginal cost to persuade the legislator in her preferred direction. P
Let C yi be the lobby’s cost of raising resources. Assume C is convex and differentiable. Let V > 0 be the value a lobby receives if it gets it’s desired outcome.

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A lobby that wishes a bill to pass solves the following problem.

X  X   X  X Y Y max V ∗ P rob δi ≥ M − C pi (yi ) 1 − pj (yj ) − C yi = max V ∗ yi

y1 ,...,yN

y1 ,...,yN

S⊂N i∈S |S|≥M

j ∈S /

s.t. yi > 0; ∀i If L wishes the bill to fail she solves the following problem.

X   X   X Y Y X
 pi (yi ) 1−pj (yj ) −C δi ≥ M −C yi ∼ max −V ∗ yi max V ∗ 1−P rob y1 ,...,yN

y1 ,...,yN

S⊂N i∈S |S|≥M

j ∈S /

s.t. yi > 0; ∀i From here we can see that the objectives of a lobby that wishes a bill will pass are deeply related to the objectives of a lobby that wishes a bill will fail. In fact, one problem is the dual of the other. This implies lobbies on both side of the issue will target the same legislators (adjusting for the fact that they might have different marginal costs of changing the voting probabilities). To see this note that the first order conditions for both problems are P C 0 ( yi∗ ) ; if yi∗ > 0 V P C 0 ( yi∗ ) qi |p0i (yi∗ )| 6 ; if yi∗ = 0 V qi |p0i (yi∗ )| =

(3) (4)

Where yi∗ represents the optimal lobbying spending. This implies that for whichever two legislators a lobby decides to spend on we have p0j qi 1/p0i = 0 = ; if yi∗ , yj∗ > 0 qj pi 1/p0j Therefore, at an optimum, lobbies equate the ratio of the pivot probabilities to the ratio of the marginal costs. The value V and the cost C do not directly influence the optimal allocation across legislators. They do influence it indirectly by influencing the total amount of resources spent, but conditional on this they have no further effect. This is an important fact that will allow us to pool the information from many different lobbies to test if lobbies target pivotal legislators. To do so, we do not need to know how much a lobby values passing or preventing a bill. We don’t even need to know if it wants a bill to pass or to fail. And we don’t need to know L’s costs of raising resources. Suppose we observe lobbying expenditures on two bills where only the pivot probability of legislator i P ∗ changes such that qˆi > qi while yi and all other pivot probabilities remain constant. Assume also that the legislator was initially receiving a positive contribution such that yi∗ > 0. In the data we do not observe 11

changes in V or in C, but this doesn’t matter because they only influence the total lobbying expenditures P ∗ and here we are assume yi did not change. From (3) we have qˆi > qi ⇒ |p0i (ˆ yi∗ )| < |p0i (yi∗ )| ⇒ yˆi∗ > yi∗ From here we conclude that the lobbying expenditures on a given legislator must be positively correlated with her pivotality across different bills. We would also get the same relationship in a cross-section of legislators after we control for differences in the marginal cost of changing their voting probabilities. From equation (4) in the FOCs we can also see that the correlation only holds when lobbies are spending a positive amount on a legislator. For legislators at a corner solution, changes in the pivotality need not translate into changes in expenditures. If there are several lobbies spending simultaneously, the results are similar, but lobbies must take into account how the spending of the other lobbies changes the pivot probabilities and the marginal cost of persuading each legislator. For example, if a rival lobby spends a lot of resources on legislator i, this could increase the marginal cost of changing i’s vote or make her vote irrelevant because she no longer will be pivotal. In a pure-strategy nash equilibrium, every lobby knows how much the other lobbies spend and every lobby verifies her first-order conditions taking the strategy of the other lobbies as fixed. Adjusting for differences in the marginal cost of persuading a legislator, lobbies on opposing sides of the issue spend on the same legislators, because legislators who are pivotal to pass a bill are also pivotal to prevent it.6 If we have several lobbies spending on the same bill and on the same side of the issue, the key assumption is that lobbies spend their resources in an uncoordinated fashion. That way every lobby individually meets it’s FOCs. The marginal dollar spent by every lobby goes to the same legislator. I will discuss more about what assumptions I need to run my empirical specification in Section 4. For now, let me note that pivot probabilities are endogenous to the lobbying expenditures. Every time a lobby changes the voting probability of a legislator, the pivot probability of all other legislators changes in complicated ways. Keeping track on how pivot probabilities change is hard, fortunately at an optimum (or an equilibrium) lobbies target legislators who are pivotal after all the effects of lobbying are taken into account. Assuming lobbies have correct expectations of the effects of their lobbying, we can test the theory by estimating which legislators were likely to be pivotal after the lobbies spent their resources.

3 3.1

The Data. The lobbying expenditures.

To measure lobbying expenditures I use the campaign contributions by Political Action Committees (PACs) toward members of the US House of Representatives. I have data from the Federal Elections Committee (FEC) for 9 electoral cycles from 1990 to 2006. I downloaded the data from the Center for Responsive Politics.7 6 A literature on strategic spending called the Colonel Blotto games has given the incorrect impression that only mixedstrategy equilibria are possible in lobbying competitions. Pure-strategy equilibria are possible with one key assumption: the marginal cost of persuading a legislator increases fast enough when lobbies increase their spending on the legislator. Under some conditions, this property even guarantees that there is unique equilibrium of the game. See Shubik and Weber (1981); Snyder (1989); Lever (2010) for this result and Roberson (2006) for an overview of Colonel Blotto games. 7 http://www.opensecrets.org. Data downloaded September 2009.

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I have 929 legislators in my sample. Representatives run for reelection every 2 years and stay in Congress a long time. The average Representative in my sample had been 11 years in Congress. To be able to run a regression of campaign contributions on pivotality I had to match the FEC data with the ICPSR codes. This forced me drop some legislators due to problems matching the codes. On average I observe 425 Representatives each electoral year, so I didn’t lose too many observations.8 There were initially 7,171 PACs in my data. Most PACs give to very few legislators, 17.2 percent of PACs only gave to one legislator in any electoral year and 27.5 percent gave to two or less. Strategic spending will have very little power to discriminate spending across legislators when lobbies spend on very few of them. For this and for computational reasons, I had to chose a subset of PACs. To make the best case for the theory, I focus on the PACs that gave to at least 8 legislators in at least one electoral year. This corresponds to roughly 50 percent of the PACs in the data. I also focus on PACs classified as business or labor PACs by the FEC. This mostly means I left out the party, candidate and ideological PACs. At the end I was left with 2,385 PACs, of which 135 are labor PACs and 2,250 are business PACs.9 To be conservative, my results can be interpreted as only representative of this sub-population of PACs. These PACs account for about 83 percent of the total contributions by PACs in these electoral years and 98 percent of the contributions by business and labor PACs. Therefore, explaining their behavior goes a long way in explaining the PAC contributions in the House.

3.2

Measuring pivotality.

The model takes the voting probabilities as a primitive (or rather, the lobbies’ beliefs about them) but we cannot observe them directly. To be able to identify them I will assume that lobbies have correct expectations, so I can use the realized votes to estimate the lobbies’ beliefs. Inferring the voting probabilities for a given bill from a single realization of the vote would, of course, be impossible. Instead, I will make structural assumptions on how legislators vote to be able to leverage the information of votes across many bills. For my structural model I will use the DW-Nominate scores.10 As a robustness check, in Appendix A I repeat the analysis using a different structural model, the Heckman-Snyder scores. The results on campaign contributions are identical, but the analysis adds some qualifications about the differences in pivotality across parties. The DW-Nominate scores fit a two-dimensional spatial model to rationalize votes on bills within and across legislatures. The model assumes that the voting probability for each legislator is generated by an ideology parameter (the scores) plus idiosyncratic disturbances that are normally distributed (just as in a probit model). The main identifying assumption is that the voting probability of legislator j is correlated with the voting probability of legislator i in a way that is constant across bills within the same legislature.11 The ideological score for each legislator is adjusted to get the best fit of all the correlations while imposing a 2-dimensional spatial model. Once the scores are estimated, we can infer the associated voting probabilities for each bill through the 8I

have a data appendix detailing these problems which is available upon request. PACs are considered highly partisan, so it’s fair to ask if business PACs are more strategic. As a robustness check I ran a regression with an interaction between pivotality and a labor PAC dummy, but I found no significant effect. 10 See Poole and Rosenthal (2000, 1985). The data is available through http://www.voteview.com. 11 This relationship is allowed to change across legislatures, but only through a linear time trend. Poole & Rosenthal report that higher-order time polynomials do not significantly change the estimated scores. 9 Labor

13

maximum likelihood function that underlies the construction of the scores. Since the number of legislators is fixed and we observe each bill only once, these voting probabilities are not a consistent estimator of the true voting probabilities in any meaningful sense. Nevertheless, these voting probabilities are still the best estimation possible that is consistent with the assumptions of the DW-Nominate model. Calculating them is essential to calculate the likelihood function. It’s hard (and probably inappropriate) to interpret the units of the DW-Nominate scores directly. These units are constructs that only make sense through their relationship to the voting probabilities. Their interpretation crucially depends on the assumption about the distribution of the error term, the same way the interpretation of the coefficients from a probit or logit regression crucially depends on the likelihood function, without it we cannot calculate the marginal effects. Instead of interpreting the scores directly, we can use them to calculate relative voting probabilities between two legislators. That is, if we know the voting probability of legislator i we can use the scores to predict the voting probability of legislator j. For example, if we observe the voting probability of legislator i increase from one bill to the next, we can use the DW-Nominate scores to predict the increase (or decrease) in the voting probability of legislator j. Once we estimate the voting probabilities, another problem arises. Given the size of the House, calculating the exact pivot probabilities is impossible. Doing so would involve calculating the probability of all possible combinations of pivotal coalitions. For a chamber of 435 legislators, the number of possible coalitions with exactly 218 votes is approximately 3.3884 times 10129 , an unfathomable number. Of course, calculating the probability of all possible coalitions would be quite inefficient, since most have a probability near zero. Instead, I used the DW-Nominate voting probabilities to simulate the vote on each bill 100, 000 times and counted how many times each legislator was pivotal. The simulation ran in two steps. First I simulated a vote on each bill 5, 000 times. Then I deleted all bills where I did not observe a single pivotal vote. These bills have no predictive power to distinguish spending across legislators. I was left with about 13% of the bills for each legislature.12 On average, these bills had a 0.057 probability of passing or failing by a pivotal vote. I then ran a simulation of 100, 000 votes on each of these bills to calculate the pivot probabilities. See Table 1 for some summary statistics. Bills with a positive pivot probability were always bills were the actual votes cast were narrowly split. Figure 2 plots the frequency distribution of pivotal and non-pivotal bills grouped by their observed vote split. As can be seen in the figure, the distributions are very different between these two types of bills. The vast majority of pivotal bills (96%) have a vote split between 45% and 55%. Pivotality, though, is not simply a measure of close vote splits. Of all the bills that had a vote split between 45% and 55%, only 48% had a positive probability of getting a pivotal vote. Who are the peak pivotal legislators? Tables 1 and 2 contain some descriptive statistics. On the leftright political spectrum, the peak pivotal legislators are deep into the side of the aisle that corresponds to the party that had the majority. Due to the small probabilities involved in the estimation, peak plateaus rather than single peaks are prevalent in the estimated pivot probabilities.13 Of the peak plateaus, 59% were 12 About 75% of the bills did not have a single pivotal vote after 5,000 simulations. I also deleted a further 12% of bills which had a probability smaller than 0.001 of having a pivotal vote, because with such small probabilities it’s very hard to get estimates that are good enough to distinguish the pivot probabilities across legislators. As a benchmark I ran a simulation with 3 voters to see how long it took to get within 0.001 of the true pivot probabilities. Even with 3 voters it took about 450,000 iterations to get estimates within the tolerance. 13 This happened because I smoothed the pivot probabilities by building a grid on the voting probability space and averaging the pivot probability for legislators inside the same interval. In the regressions I used the unsmoothed pivot probabilities.

14

solely conformed by legislators from the party with the majority while 29% of bills had legislators from both parties. The average midpoint of the plateau was 146 positions away from the median legislator. (To the left or to the right depending on who controlled the chamber.) These are even more extreme positions than the median legislator of the majority party.14,15 After we calculate the pivot probabilities we face an additional challenge. We do not know which bill the lobbies are trying to influence.16 Because of this I will measure the pivotality of a legislator by her average pivot probability across all bills presented in an electoral year, so for legislator i, qi,t represents the average pivotality over all bills she voted on during Congress t. This averaging will generate measurement error in my explanatory variable, biasing the results against strategic spending. Since the objective of this paper is to show evidence that lobbies are indeed strategic, this does not change my results. The magnitude of the effect, though, has to be taken with caution.

4

The Regression.

4.1

Interpreting the data through the model.

I assume that in every electoral cycle where a PAC is active there is a single bill the PAC wants to influence. I assume each PAC has an estimate on the voting probabilities for the bill, knows which other PACs want to influence the bill and knows the marginal cost of changing the voting probability of each legislator. The PACs use their estimated voting probabilities to calculate which legislators are more likely to be pivotal and spend accordingly. To optimize their spending, PACs must take into account how their spending and the spending by other PACs change the pivot probabilities. At an equilibrium they have correct expectations about this. In principle, PACs might have a different value V and a different cost of raising resources C for every electoral year. This would add variation to the total contributions, but PACs would still target pivotal voters. I am not assuming that PACs use the DW-Nominate scores to estimate the voting probabilities. Presumably PACs construct their voting probabilities using more detailed information about the content of the bill and the preferences of the legislators. I am assuming that, on average, the DW-Nominate model is a good proxy to measure pivotality. As an outside observer, my best hope is that my pivotality measure is good enough to be able to explain the average behavior over many different PACs on many different bills. To measure PAC contributions I use the total contributions from each PAC to each legislator at any point during the electoral cycle. In doing so, I am ignoring the timing at which such transaction was registered at the FEC. For example, yk,i,104 is the observation in my sample that corresponds to PAC k, legislator i, and the electoral cycle for the 104th Congress. This means yk,i,104 is the sum of all the contributions from k to i that were registered in 1995 and 1996. In principle I could try to use the timing of the contributions to identify which bills each PAC was trying to influence. I don’t do so because it’s very hard to determine what is the right time frame for giving contributions. For example, campaign resources might mainly be used to gain access to a legislator so the the PAC can reveal verifiable information that will influence her vote. Strategic PACs would still focus their 14 The

positions were calculated using the first dimension of the DW-Nominate scores. we measure pivotality through the HS scores, the peak pivotal legislators tend to be much closer to the median legislator and the difference in pivotality between the two parties is smaller. See Appendix A. 16 And should we ask them, they would probably be loath to tell us. 15 When

15

resources on legislators’ who are pivotal, but PACs might need to give contributions early to have time to present the evidence. I am also including contributions that happen after a bill is voted on. In doing so I am assuming that PACs might “place their checks in the mail” before a bill, so contributions might be related to bills that were voted on before the contributions gets registered. Substantively, I am assuming that PACs cannot condition their contributions on the realized vote. In theory, PACs might want to offer each legislator a conditional contract where they only give a contribution if the legislator votes a certain way. PACs might even want to write a contracts that only pay in the event a legislator’s vote is ex post pivotal. Sustaining this strategy is difficult because these long-term contracts are illegal and therefore cannot be enforced by a court. Furthermore, since the probability a legislator is pivotal is small and there is an upper bound on the contributions, it might be impossible to provide incentives by conditioning contributions on the event that a legislator’s vote was ex post pivotal. By ignoring the information on the timing of contributions, I am adding an extraneous source of variation to my left-side variable. This should increase my standard errors, but not bias my results. The alternative is taking a stance on the right timeframe, but my results would be biased if I’m wrong.

4.2

The specification.

As we saw in the model, changes in pivotality should only be correlated with spending on legislators that receive a positive amount (interior solutions). Corner solutions are pervasive in the data, because most PACs give to few legislators. Even though I am focusing on PACs that contribute to 8 or more legislators in at least one electoral cycle, the average each PAC in my sample only contributed to 9.3% of the chamber, or about 39 legislators. This means 90.7% of the observations are left censored. A second corner solution happens because PACs have a limit of 10,000 dollars on the amount they can contribute to a candidate per electoral cycle. This censoring problem is much much less important, as it only affects 0.06% of the observations. To account for both types of censoring, I will run a tobit regression of campaign contributions on the pivot probability of each legislator while controlling for confounds. The unit of observations is the contributions from a specific PAC to a given legislator in a given electoral year expressed in 2006 dollars. The specification is as follows. For each PAC k, legislator i and electoral year t, there is a latent variable ∗∗ for contributions denoted by yk,i,t with the following specification:

∗∗ ˜ yk,i,t = αi + βq qi,t + βX ˜ Xi,t + ek,i,t,

(5)

The observed contributions are yk,i,t .  ∗∗ yk,i,t = max 0, min{yk,i,t , y¯t } Where y¯t expresses the 10,000 dollar legal limit on campaign contributions in 2006 dollars. The errors ek,i,t, are assumed to be mean-zero Normal and independent across legislators, but I will allow correlation within each legislator by using clustered standard errors.

16

˜ i,t is group of control variables that includes: The matrix X • Leadership dummies for the Speaker of the House, the Majority Leader, the Minority Leader and their respective whips. • Committee dummies for “prestige” committees: Appropriations; Ways and Means; House Rules; Energy and Commerce; and Banking and Finance. • Party and Majority dummies. Being in the party with a majority in congress is a significant predictor of campaign contributions, as found in Cox and Magar (1999). Since being in the majority is also correlated with being a pivotal voter, it’s important to control for this effect. • Seniority. Measured from the first time a legislator entered the House. • Year level dummies. These dummies help control the year to year variations in V and C. They also control for variations in the total number of pivotal bills presented in a year. A concern in the regression is that my explanatory variables might be correlated with unobservable characteristics of the legislators. For example, legislators who are pivotal might also be better negotiators. Even if PACs do not care about pivotality, they might target pivotal legislators because of their negotiation skills. Unobserved characteristics can especially bias the estimate of the leadership dummies. It’s very likely that a legislator who becomes her party’s leader has an above-average “ability” to pass legislation, to form coalitions or to raise campaign funds. Therefore her contributions might have been high even if she hadn’t occupied the leadership position. I will use the fact that I observe each legislator many times over different electoral years to control for any time-invariant characteristics. I do so by running a Chamberlain style random-effects specification.17 Every legislator will have a random effect αi that is drawn from a Normal distribution. The assumption on the distribution allows me to the incorporate random effects into the tobit specification. It’s important to note that the unobserved characteristics of a legislator only bias the coefficients of interest if they are correlated with the corresponding variables. Therefore I will allow the αi to be correlated with the characteristics of the legislator. I assume that the αi are distributed as follows. ¯ i + ηi αi = γX X ¯ is the average of the explanatory variables (including pivotality) per legislator across electoral Where X years and ηi is distributed N ormal(0, σα ). From here I rewrite my specification as follows.

∗∗ ˜ ˜ ¯ yk,i,t = αi + βq qi,t + βX ˜ Xi,t + ek,i,t = βq qi,t + βX ˜ Xi,t + γX Xi + ηi + ek,i,t .

(6)

The coefficient βx identifies the effect of variable x by using the variation across electoral years in the explanatory variables. 17 See

Wooldridge (2002).

17

4.3

The results.

Table 3 compares the outcome of an OLS over legislators (with fixed effects) with the marginal effect at the mean of my tobit specification. The probability of being pivotal is not significant under OLS, but pivotality is highly significant in the tobit (p = 0.000). The magnitude is also substantially larger. The coefficients for all other variables come out as expected. The largest effects come from the leadership dummies. Becoming the Speaker increases contributions by 909,000 dollars! The majority dummy predicts an increase of 24,000 dollars, which is not statistically different to the magnitude reported in Cox and Magar (1999) (36,000 dollars). Since it’s difficult to compare the magnitude of the coefficients for variables measured in very different units, Table 4 multiplies the marginal effect by the standard deviation of each variable. Doing this gives us a sense of how variation can be explained by each variable. Through this, the effect of leadership positions seems smaller. Becoming the Speaker has a huge impact on the campaign contributions of an individual legislator, but it happens to so few legislators that it does little to explain the variation in contributions in the data. Pivotality has one of the largest effects per unit of standard deviation. Increasing the pivotality of the average legislator by one standard deviation increases her campaign contributions by 39,000 dollars (10.8% of the average contributions), while becoming the Speaker increases them in 44,000 dollars (12.1% of the mean contributions) and joining the powerful Ways and Mean Committee increases them by 45,000 dollars (12.4%). The differences in the effects are not statistically different. The effect of pivotality is significantly larger (p < 0.001) than the effect of becoming the Majority Leader (15,000 dollars). An important fact that comes out of Table 4 is the channel through which pivotality increases contributions. We can decompose increase in contributions into two effects: the percentage increase in contributions from PACs that are contributing a positive amount and the percentage increase in the probability any PACs will give contribute. ∆%E(y|X) = ∆%E(y|y > 0, X) + ∆%P rob(y > 0|X) From Table 4 we see that the percentage increase in the contributions of PACs that are already donating to a legislator is small relative to the total increase on contributions. (1.8% vs. 10.8%). This means that most of the effect of increasing pivotality comes from the increase in the number of PACs that donate.

5

After 1994, pivotality shifts toward the Republicans.

During the Republican takeover of 1994 (congress 104), the Republicans took control of both chambers and kept it for the rest of the sample. This gave them a large boost in their campaign contributions. Table 5 shows the difference in pivotality between the average Democrat and the average Republican in each electoral cycle, as well as how it changed from one cycle to the next. When Democrats were in control of the House (legislatures 101, 102, 103) their average pivotality was higher than the Republicans’. Bill Clinton’s first midterm election changed this. The net swing in pivotality from Congress 103 to 104 gave the average Republican a net increase in their contributions of 26,900 dollars relative to the Democrats. This is 57% of the direct effect of losing the majority (47,400 dollars). After the Republican takeover, the Democrats continued to become less pivotal. Figures 3, 4 and 5 plot

18

the pivotality of each legislator against their ideological score. Pivotality clearly seems lopsided toward the party in the majority. The graphs are indicative of an asymmetry of pivotality with respect to the median legislator. Legislators from both parties who are on the minority side of the median legislator (to the right if Democrats hold the majority and to the left of Republicans do) have a smaller probability of being pivotal. This might occur because bills which have a positive probability of passing by a pivotal vote are those where the centrist members of the party in the majority are likely to break the party line. The difference in pivotality across parties should be taken with caution. The difference is only statistically significant for the 106, 107 and 18th legislatures. When the analysis is repeated using the Heckman-Snyder (see Appendix A) the estimated difference in pivotality between parties becomes smaller and is no longer statistically significant. The plots of pivotality against ideological scores look qualitatively similar, but shift in pivotality toward Republicans is less pronounced. (See Figures 6, 7 and 8.)

6

Conclusion.

I find evidence that PACs act strategically when giving campaign contributions to legislators in the US. House of Representatives. Theoretical models of strategic lobbying predict that PACs should target legislators with a higher probability of being pivotal. In my estimation, pivotality is a statistically significant predictor of campaign contributions. My estimation implies that increasing the pivotality of a legislator by one standard deviation increases her campaign contributions by 39,000 dollars, which corresponds to 10.8% of the average contributions. This effect is similar to the effect per unit of standard deviation of becoming the Speaker of the House (44,000 dollars) and of joining the Ways and Means Committee (45,000 dollars). An important step to test this prediction is using a censored regression (tobit) instead of an OLS regression, because most PACs give contributions to very few legislators. The average PAC in my sample only donated to 9.3% of the legislators. Theoretical models of strategic lobbying predict that differences in pivotality should translate into differences in contributions only for legislators that are receiving a positive contribution. This follows because pivotality measures the marginal benefit of spending on a legislator and at an interior solution (positive contributions) PACs equate the marginal benefit to the marginal cost. At a corner solution (zero contributions) this relationship breaks downs, so pivotality should have no predictive power. Another contribution of this paper is to show that pivotality is not related to distance to the median voter when there is uncertainty on how legislators will vote. Instead, PACs have to calculate the probability each legislator will be pivotal, which is a complicated calculation that depends on the voting probability of all legislators in the chamber. In spite of this, I show that pivot probabilities have a similar spatial property to the median voter logic: they are “single-peaked” in the order of the voting probabilities. This means that if you order legislators according to their probability of voting in favor of a bill, the associated pivot probabilities will be strictly increasing until they reach a peak legislator and will be strictly decreasing afterwards. To estimate the pivot probabilities I used the voting probabilities from the DW-Nominate model. The estimated pivot probabilities show that legislators in the majority party have a higher average probability of being pivotal. After the Republican takeover of 1994, pivotality disproportionately swung in favor of the Republicans and started a trend where Republicans would increase their average pivotality relative to the Democrats.

19

My work shows that pivotality can explain the average behavior of a very heterogenous set of PACs, with very different objectives and very different means to persuade legislators. Future work could increase our understanding by separating the PACs into more homogenous subgroups to see which PACs are more strategic in their behavior and which PACs are more ideological. I also had very little to say about the bills that where pivotal. My estimations show that pivotal votes are low probability events, with 87% of the bills having a zero probability of getting a pivotal vote. The bills that have a positive probability of a pivotal vote in my estimation are always bills where the realized vote split was very close, between 45% and 55%, but not all bills with a close vote split are pivotal. Out of all bills that had a close vote split, only 48% had a positive probability of getting a pivotal vote. More work should be devoted to understanding what determines if a bill is likely to have a pivotal vote or not.

References Cox, G. W. and E. Magar (1999): “How Much is Majority Status in the US Congress Worth?” The American Political Science Review, 93, 299–309. Fowler, J. H. (2006a): “Connecting the Congress: A Study of Cosponsorship Networks,” Political Analysis, 456–487. ——— (2006b): “Legislative Cosponsorship Networks in the U.S. House and Senate,” Social Networks, 28 (4), 454–465. Gopoian, J. D., H. Smith, and W. Smith (1984): “What makes PACs tick? An analysis of the allocation patterns of economic interest groups.” American Journal of Political Science, 28, 259–281. Grier, K. B., M. C. Munger, and B. E. Roberts (1994): “The determinants of industry political activity, 1978-1986.” American Political Science Review, 88, 911–926. Hirsch, A. V. (2009): “Theory Driven Bias in Ideal Point Estimates - A Monte Carlo Study,” Mimeo. Lever, C. R. (2010): “Strategic spending in voting competitions with social networks.” Banco de M´exico Working Papers, 2010-16. Nelson, G. (07-29-2010): “Committees in the U.S. Congress, 1947-1992. House of Representatives.” . Poole, K. T. (2007): “Changing Minds? Not in Congress!” Public Choice, 131, 435–451. Poole, K. T., T. Romer, and H. Rosenthal (1987): “The revealed preferences of political action committees.” The American Economic Review, 77, 298–302. Poole, K. T. and H. Rosenthal (1985): “A spatial model for legislative roll call analysis.” American Journal of Political Science, 29, 357–384. ——— (2000): Congress: A political-economy history of roll call voting, Oxford University Press. Roberson, B. (2006): “The colonel blotto game,” Economic Theory, 29, 1–24. Romer, T. and J. Snyder (1994): “An empirical investigation of the dynamics of PAC contributions.” American Journal of Political Science, 38, 745–769. 20

Shubik, M. and R. J. Weber (1981): “Systems Defense Games: Colonel Blotto, Command and Control,” Naval Research Logistics Quarterly, 28, 2, 281–287. Snyder, J. M. (1989): “Election goals and the allocation of campaign resources,” Econometrica, 637–660. ——— (1992): “Long-term investing in politicians; or, give early, give often.” Journal of Law and Economics, 35, 15–43. Snyder, J. M. and T. Groseclose (2000): “Estimating party influence in congressional roll-call voting,” American Journal of Political Science, 44, 193–211. Stewart III, C. and J. Woon (07-29-2010): “Congressional Committee Assingments, 103rd to 111th Congresses, 1993-2009. House of Representatives.” . Wawro, G. (2001): “A panel probit analysis of campaign contributions and roll-call votes,” American Journal of Political Science, 45, 563–579. Wooldridge, J. M. (2002): Econometric Analysis of Cross Section and Panel Data, The MIT Press. Wright, J. R. (1985): “PACs, contributions, and roll calls: An organizational perspective.” The American Political Science Review, 400–414.

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Appendix A

Are the results sensitive to the pivotality measure?

To test the robustness of my results I repeat the analysis using an alternative method to estimate pivot probabilities: the HS scores. This linear probability model was proposed by Heckman & Snyder (1997). The HS scores also fit a spatial model to rationalize the voting patterns in Congress, but the HS scores differ from the DW-Nominate scores in that they assume a uniform distribution for the legislator-specific voting errors. The HS model has several advantages over the DW-Nominate model. First, Heckman and Snyder show that these scores can be consistently estimated, while the DW-Nominate scores cannot. Second, regardless of the correct distribution of the errors, the HS scores can always be interpreted as the best lower-dimensional linear approximation to the voting probabilities.18 Finally, HS propose a rigorous statistical test to determine the number of dimensions required to describe the data, finding that anywhere between 5 and 8 dimensions might be necessary. In practice, though, the first two dimensions of the HS scores tend to be very highly correlated with the DW-Nominate scores and can account for most of the variance in the observed votes.19 For our purposes, it’s not obvious how this translates into pivot probabilities, since the two models make very different assumptions on the error term and pivot probabilities are highly non-linear function of the voting probabilities. Therefore it is necessary to repeat the whole estimation to see if the predictions survive. A problem with the using the HS scores, as with any linear probability model, is that one can get predicted probabilities that are outside of the [0, 1] interval. More than 30% of the predicted voting probabilities for my sample lie outside the interval.20 Since there is no easy way to correct this while keeping the linear probability assumption, I simply truncate the predicted voting probabilities so that negative values are set to 0 and large values are set to 1. For some legislatures, Heckman and Snyder statistically reject that model with less than eight dimensions can be used to describe the data. Because of this I ran simulations with two models, one with two dimensions and one with eight dimensions. For each model I ran 50,000 iterations on each bill.21 The two procedures differed somewhat on which bills they deemed pivotal. They mostly disagreed on bills that had a low probability of having a pivotal vote. In spite of this, the correlation of the pivot probabilities over the bills they both agreed were pivotal is above 0.999 for every legislature. The correlation in the average pivot probability for each legislator was similar, even when I include bills they disagree are pivotal. Using more than two dimensions does not seem to matter to measure pivotality. Therefore, for the rest of the analysis I only use the predictions from the two-dimensional model. Do the HS and the DW-Nominate scores agree on which bills are pivotal? They do agree on 70% percent of the bills.22 The correlation in the average pivotality per legislator between the two methods is 0.75. This correlation is strong but not necessarily enough to give the same results in the regression. As seen in Table 6, the estimated effects in the tobit regression are identical using both methods. Both 18 In the sense that the approximation minimizes the sum of squared deviations from the covariance matrix of the legislators’ votes across the bills in a legislature. 19 See Poole (2007). 20 This problem eventually disappears if one uses an HS model with enough dimensions. To reduce the percentage of wrong predictions in my sample to single digits, I would need to use more than 400 dimensions. 21 Just as before, I first ran 5,000 simulated votes, deleted the bills that had less than a 0.001 chance of getting a pivotal vote and then ran the rest of the iterations on the remaining bills. 22 That is, of the total number of bills that had a positive pivot probability using either model, 70% has a positive probability under both methods.

22

measures of pivotality are significant with p < 0.001. The difference in magnitude between the coefficients is less than one percent. We can conclude that the results do not crucially depend on the auxiliary assumptions used to estimate the pivot probabilities. Of course, the difference in the two measures might matter more when analyzing the pivot probabilities of any specific bill. An important difference between the methods comes when comparing the trend of pivotality toward the Republicans. Pivotality measured by the DW-Nominate model shows a very clear shift toward making the Republicans relatively more pivotal after the Republican takeover of 1994. (The Republicans would remain in control of the House for the remainder of the sample.) Qualitatively, the HS model seems to show a similar shift (see Figures 6, 7 and 8) but the change is much less pronounced (compare with Figures 3, 4 and 5). The difference in pivotality between the average Democrat and the average Republican is not statistically significant for any electoral year.

Appendix B

What about the Senate?

I tried to find similar results for the Senate, but working with the data is much more challenging than working with the House. The Senate has four times less legislators (101 vs. 435), who serve longer terms (6 years vs. 2 years) and who get reelected in a staggered way. As can be seen in Tables 7 and 8, most of the coefficients lack statistical power, even those that intuitively should matter a lot, like the dummies for leadership positions. Just as with the House, I only work with contributions from business and labor PACs and drop PACs that gave to few legislators on any electoral cycle. To be in my sample, a PAC had to contribute to at least four Senators in at least one electoral year, which corresponds to roughly 50% of all PACs that contributed. (These PACs account for a 90% of the contributions by business and labor PACs.) Even after dropping these PACs, the average PAC in my sample only contributed to 10 legislators in a given electoral year, a little less than 10% of the members of the chamber. The average legislator received contributions from 149 PACs per electoral year. An important difference with voting procedures in the US Senate is the use of the filibuster, which allows debates on a bill to continue unless 60 legislators vote to invoke the cloture rule. Therefore for some bills, Senators who are pivotal to break the filibuster might be more important than Senators who are pivotal for the actual vote on the bill. I calculated the pivot probability for both procedures by using the voting probabilities associated with the dw-nominate scores. The effect of filibuster probability in the regressions initially seems smaller, but the errors in the regression are so large that’s it’s impossible to distinguish the magnitude of both effects. Senators receive their contributions very unevenly throughout their terms. An observation in my sample corresponds to a two-year electoral cycle, and each Senator serves for three cycles before running for reelection. On average, Senators receive about 70% of their contributions in their third cycle, with the remaining 30% being equally divided between the first and second cycle. It’s not obvious how the effect of pivotality (and of the other variables) should change during electoral years. Since two thirds of the Senators are not running for reelection in any given cycle, PACs always have to allocate resources across legislators who are and who are not running for reelection. One alternative is to aggregate the contributions to include the full electoral cycle of each Senator, but this forces me to drop a lot of observations. To run an estimation with random-effects, I need to observe to observe at least two

23

full cycles for a Senator. This would only leave me with 67 (40%) out of the 166 Senators in my already low sample. I did run the regression, but nothing came out significant. I also tried running regressions with several interactions, but they had similar problems. At the end I settled for a parsimonious regression with only interactions between the year level dummies and “seekingreelection” dummy. The latent variable specification is a follows.

f ∗∗ m ˜ + βX yk,i,t = αi + βqm qi,t + βqf qi,t ˜ Xi,t + ek,i,t, .

Where qim represents the probability legislator i will be pivotal in a majority vote and qif is the probability the legislator will be pivotal for a cloture vote. (To break the filibuster.) Just as before, the random effects αi are assumed to be distributed Normal and correlated with the per-legislator mean-value of all variables. ˜ i,t includes year level dummies and the interaction of year level dummies with The matrix of controls X the dummy for senators who ran for reelection during that year. It also includes dummies for: being in the majority; switching parties; being the Majority leader, the Minority leader, the Majority Whip or the Minority Whip; and for belonging to the following committees, Appropriations; Finance; Armed Forces; Foreign Affairs; or Banking, Housing and Urban Affairs. The effect βx should be interpreted as the average effect between electoral and non-electoral years of variable x. As can be seen in Tables 7 and 8, the regression doesn’t have much statistical power. We cannot rule out that the effect of pivotality, whether majority pivotality or filibuster pivotality, is zero, but we also cannot rule out that the size of the effect is the same as in the House. (Compare Column 2 of tables 4 and 8.) Even variables that should matter, like becoming the majority and minority leader, are not significant. This strongly suggests that the regression is not adequate, rather than saying that the effect of pivotality is different in the Senate. This exercise does serve to highlight the limits to running my parsimonious specification. I am not controlling for differences in the cost of persuading a legislator, I’m using the average pivot probability instead of identifying the bills PACs wish to influence and I’m pooling the information of a large number of PACs with very different motives. The large number of observations in the House allow me to estimate the average effect, but the same exercise does not carry through to the Senate.

24

0.35

0.3

Fraction of bills

0.25

0.2

0.15

0.1

0.05

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Vote splits Figure 2: The plot shows the frequency distribution of bills by their observed vote splits. The red solid line is the distribution of pivotal bills. The blue dashed lines is the distribution of all other bills. Most pivotal bills (96%) had a vote split between .45 and .55.

25

Average pivot probability

Figure 3: DW-Nominate: Pivotality vs. Ideology. (101-103rd Congress. Dem. majority.) 2.8

2.6

2.4

Median legislator

103 Congress

101 Congress 102 Congress

2.2

2

1.8 ï1

ï0.8

ï0.6

ï0.4

ï0.2

0

0.2

0.4

0.6

0.8

1

First dimension dw nominate score

Figure 4: DW-Nominate: Pivotality vs. Ideology. (104-106rd Congress. Rep. majority.) Median legislator

Average pivot probability

3.8 3.6 3.4 3.2

106 Congress

3 2.8 2.6 2.4

104 Congress 105 Congress

2.2 ï1

ï0.8

ï0.6

ï0.4

ï0.2

0

0.2

0.4

0.6

0.8

1

First dimension dw nominate score

Figure 5: DW-Nominate: Pivotality vs. Ideology. (107-109rd Congress. Rep. majority.)

Average pivot probability

3.8

Median legislator

3.6 3.4 3.2

108 Congress

3 2.8 2.6

107 Congress 109 Congress

2.4 2.2 ï1

ï0.8

ï0.6

ï0.4

ï0.2

0

0.2

0.4

First dimension dw nominate score

26

0.6

0.8

1

Figure 6: Heckman-Snyder: Pivotality vs. Ideology. (101-103rd Congress. Dem. majority.)

Average pivot probability

2.5

Median legislator

103 Congress

2.4 2.3 2.2

102 Congress 101 Congress

2.1 2 1.9 1.8 ï1

ï0.8

ï0.6

ï0.4

ï0.2

0

0.2

0.4

0.6

0.8

1

First dimension ideological scores

Figure 7: Heckman-Snyder: Pivotality vs. Ideology. (104-106rd Congress. Rep. majority.)

Average pivot probability

3.8 3.6

Median legislator 106 Congress

3.4 3.2 3 2.8

105 Congress 104 Congress

2.6 2.4 2.2 ï1

ï0.8

ï0.6

ï0.4

ï0.2

0

0.2

0.4

0.6

0.8

1

First dimension ideological scores

Average pivot probability

Figure 8: Heckman-Snyder: Pivotality vs. Ideology. (107-109rd Congress. Rep. majority.) Median legislator

3.4 3.2 3

108 Congress 109 Congress

2.8 2.6 2.4

107 Congress

2.2 ï1

ï0.8

ï0.6

ï0.4

ï0.2

0

0.2

0.4

First dimension ideological scores

27

0.6

0.8

1

Summary statistics of pivotal bills. Congress 101 102 103 104 105 106 107 108 109 Average

(1) Pivot Bills 88 98 118 138 144 153 89 116 104 116

(2) Percent of Total Bills 11.7% 12.6% 12.2% 11.7% 15.2% 17.5% 13.1% 13.8% 11.6% 13.3%

(3) Average prob. a bill is pivotal 0.050 0.045 0.055 0.051 0.051 0.071 0.064 0.069 0.059 0.057

(4) Dem Peak Plateau 68% 49% 34% 20% 11% 8% 3% 6% 7% 23%

(5) Rep Peak Plateau 19% 24% 19% 49% 59% 54% 61% 77% 76% 49%

(6) Mixed Peak Plateau 13% 27% 47% 31% 30% 38% 36% 17% 17% 28%

Table 1: The table analyzes the pivotal bills and their corresponding peak pivotal legislators. Because determining the exact identity of peak pivotal legislator is difficult, Columns (4), (5) and (6) instead calculate the peak pivotal plateau for legislators who have a similar probability of voting for a bill. (Within .05 of each other). Column (4) shows how many peak plateaus had only Democrats, Column (5) shows how many had only Republicans, and Column (6) shows how many had legislators on both sides of the aisle. Note that the peak plateaus shift to the right after the Republican takeover in congress 104.

Description of peak pivotal legislators. Congress 101 102 103 104 105 106 107 108 109

Rank (L to R) 50 56 59 368 358 340 343 359 381

Rank (R to L) 391 382 379 78 85 100 99 82 58

Positions to median -171 -163.5 -160.5 144.5 136 119.5 121.5 138 161

DW-Nominate1 of midpoint -0.482 -0.481 -0.502 0.491 0.486 0.466 0.497 0.557 0.642

Table 2: The table describes the median peak pivotal legislator. For each congress, I first calculated the peak pivotal plateau for each bill, then I found the midpoint (median) legislator inside the plateau and finally I calculated the median across all these legislators. Note that the median midpoint legislator is always deep inside the party who holds the majority. (Democrats for 101, 102 and 103, and Republicans for there after.) All ranks where calculated using the first dimension of the DW-Nominate scores.

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Contributions by business and labor PACs in the U.S. House. Marginal effect per legislator at mean. (1) (2) VARIABLES OLS-FE Tobit-RE per Legislator per PAC Pivot Probability 23,000 71,000*** (Times 100)

(20,000)

(16,000)

49,000***

24,000**

(13,000)

(10,000)

Party Change dummy

-248,000***

-223,000***

(Rep=1 and Dem= -1)

(32,000)

(19,000)

1,126,000***

909,000***

(112,000)

(111,000)

604,000***

316,000***

(178,000)

(103,000)

655,000***

365,000***

(92,000)

(60,000)

550,000***

287,000***

(40,000)

(76,000)

498,000***

277,000***

(56,000)

(44,000)

Majority dummy

House Speaker Majority Leader Minority Leader Majority Whip Minority Whip Appropriations Cmte. Ways and Means Cmte. House Rules Cmte. Energy and Commerce Cmte. Banking Cmte. Seniority Observations R2 Number of Legislators

1,000

31,000*

(22,000)

(18,000)

165,000***

175,000***

(34,000)

(32,000)

-50,000

5,000

(60,000)

(35,000)

45,000

77,000***

(28,000)

(22,000)

41,000

47,000**

(26,000)

(20,000)

-4,500***

-400

(1,500)

(3,200)

3,751 0.157 919

5,969,426 919

Legislator-clustered standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 3: The table runs two regressions of campaign contributions over pivotality with controls. The first regression is an OLS with legislator fixed effects using data aggregated at the legislator level; the second regression is a tobit with random effects per legislator and uses data disaggregated into PAC-Legislator pairs. Pivotality is not statistically significant under OLS. Once the data is disaggregated and the corner solutions are taken into account, the pivotality coefficient considerably increases it’s magnitude.

29

Comparing the effects per unit of standard deviation in the U.S. House. VARIABLES

Pivot Probability Majority dummy House Speaker Majority Leader Ways and Means Observations

(1) MFX on E(y) per Std. Dev.

(2) As Percent of E(y)

(3) MFX on E(y|y > 0) per Std. Dev.

39,000

10.8%

70,000

1.8%

(9,000)

(2.5%)

(16,000)

(0.4%)

12,000

3.3%

21,000

0.5%

(5,000)

(1.4%)

(9,000)

(0.2%)

44,000

12.1%

55,000

1.4%

(5,000)

(1.4%)

(5,000)

(0.1%)

15,000

4.1%

23,000

0.6%

(5,000)

(1.4%)

(6,000)

(0.2%)

45,000

12.4%

72,000

1.9%

(8,000)

(2.2%)

(12,000)

(0.3%)

5,969,426

(4) As Percent of E((y|y > 0)

5,969,426

Legislator-clustered standard errors in parentheses

Table 4: The table calculates the marginal effects per unit of standard deviation to compare the magnitude of variables measured in different units. Dummies are treated as discrete variables. Column (1) calculates the marginal effect on the total expected contributions per legislator. Column (3) calculates it only counting PACs that were already giving a positive amount. Columns (2) and (4) express the marginal effects as a percentage. Note that the percentage increase in E(y) can be decomposed as the sum of the percentage increase in E(y|y > 0) plus the percentage increase in P r(y > 0).

Difference in pivotality: Democrats vs. Republicans. Congress 101 102 103 104 105 106 107 108 109

(1) Diff across parties. 0.126 0.053 0.086 -0.293 -0.366 −0.609∗∗∗ −0.846∗∗∗ −0.718∗∗∗ -0.358

(2) In USD 8,900 3,800 6,100 -20,800 -26,000 -43,200 -60,100 -51,000 -25,400

(3) As percent 2.2% 0.9% 1.5% -5.1% -6.4% -10.6% -14.7% -12.5% -6.2%

(4) Diff in Diff -0.073 0.033 -0.379 -0.073 -0.243 -0.237 0.129 0.360

(5) In USD -5,200 2,400 -26,900 -5,200 -17,300 -16,900 9,100 25,600

(6) As percent -1.3% 0.6% -6.6% -1.3% -4.2% -4.1% 2.2% 6.3%

*** p<0.01, ** p<0.05, * p<0.1

Table 5: The table compares the pivotality between parties across different legislatures. Column (1), Diff, shows the pivotality of the average democrat minus the pivotality of average republican; Column (2) expresses the difference in dollars using the marginal effect at the mean for the whole sample; and Column (3) express Diff as a percentage of the average contributions. Column (4), Diff in Diff, shows the difference in Diff from one year with respect to the last, with Columns (5) and (6) expressing it in dollars and as a percentage just like columns (2) and (3). The Republican takeover happened in Congress 104.

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HS vs DW-Nominate scores Marginal effect per legislator at mean. (1) (2) VARIABLES DW-Nominate Heckman-Snyder Pivot Probability 70,600*** 71,000*** (Times 100)

(15,900)

(22,300)

24,000**

40,000***

(10,000)

(9,000)

-223,000***

-222,000***

(19,000)

(23,000)

909,000***

681,000***

(111,000)

(55,000)

316,000***

324,000***

(103,000)

(120,000)

365,000***

378,000***

(60,000)

(72,000)

287,000***

289,000***

(76,000)

(79,000)

277,000***

258,000***

(44,000)

(33,000)

Majority dummy Party Change dummy (Rep=1 and Dem= -1)

House Speaker Majority Leader Minority Leader Majority Whip Minority Whip Appropriations Cmte. Ways and Means Cmte.

31,000*

27,000

(18,000)

(18,000)

175,000***

170,000***

(32,000)

(33,000)

House Rules Cmte. Energy and Commerce Cmte. Banking Cmte. Seniority Observations

5,000

3,000

(35,000)

(35,000)

77,000***

74,000***

(22,000)

(22,000)

47,000**

49,000**

(20,000)

(19,000)

-400

1,200

(3,200)

(3,200)

5,969,426

5,924,320

Legislator-clustered standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 6: Using data for the House of Representatives, the table uses two different measures of pivotality to run a tobit regression with legislator random effects. The first column is based on the DW-Nominate scores, while the second is based on a two dimensional Heckman-Snyder model. The effect of pivotality has less than a 1% difference in magnitude.

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Contributions by business and labor PACs in the U.S. Senate. Marginal effect per Senator at mean.

VARIABLES Majority Pivot Probability (Times 100)

Filibuster Pivot Probability (Times 100)

Majority dummy

(1) OLS-FE per Senator 7,000

(2) Tobit-RE per PAC 13,000

(50,000)

(40,000)

7,000

-1,000

(54,000)

(42,000)

44,000

25,000

(63,000)

(51,000)

Party Change dummy

-25,000

23,000

(Rep=1 and Dem=-1)

(100,000)

(115,000)

Majority leader

-195,000

-126,000

(196,000)

(122,000)

Minority leader Majority whip Minority whip Appropiations Cmte. Finance Cmte. Armed Forces Cmte. Banking, Housing and Urban Affairs Cmte. Foreign Affairs Cmte. Seniority Observations R2 Number of Senators

231,000

51,000

(217,000)

(172,000)

402,000***

627,000***

(72,000)

(218,000)

274,000*

247,000

(154,000)

(185,000)

195,000**

112,000

(94,000)

(81,000)

188,000**

167,000**

(83,000)

(80,000)

201,000*

139,000*

(87,000)

(78,000)

-51,000

-31,000

(79,000)

(50,000)

186,000*

163,000

(104,000)

(111,000)

-26,000**

-16,000

(11,000)

(16,000)

1,132,686 0.043 166

1,132,686 166

Senator-clustered standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 7: The table calculates the effects of pivotality on PAC contributions in the Senate using an OLS with fixed-effects and a Tobit with random effects. Working with the Senate data is much more challenging than working with the House, as can be seen by the lack of statistical power in most of the coefficients, including those for prestige committees and leadership positions. The Senate has four times less legislators, which serve 3 times longer terms and are reelected in a staggered way.

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Marginal effect per unit of standard deviation in the U.S. Senate. VARIABLES

(1) MFX on E(y) per Std. Dev.

(2) As Percent of E(y)

(3) MFX on E(y|y > 0) per Std. Dev.

(4) As Percent of E(y|y > 0)

Majority Pivot Probability

24,000

5.3%

35,000

0.8%

(Times 100)

(71,000)

(15.6%)

(104,000)

(2.5%)

-400

-0.09%

-500

-0.01%

(26,000)

(5.7%)

(39,000)

(0.9%)

Filibuster Pivot Probability (Times 100)

Majority dummy Majority leader Minority leader Appropiations Cmte. Finance Cmte.

Observations

12,000

2.6%

18,000

0.4%

(25,000)

(5.5%)

(37,000)

(0.9%)

-11,000

-2.4%

-18,000

-0.4%

(10,000)

(2.2%)

(20,000)

(0.5%)

5,000

1.1%

7,000

0.2%

(18,000)

(3.9%)

(24,000)

(0.6%)

51,000

11.2%

71,000

1.7%

(37,000)

(8.1)

(48,000)

(1.1%)

66,000

14.5%

89,000

2.1%

(32,000)

(7.0%)

(39,000)

(0.9%)

1,132,686

1,132,686

1,132,686

1,132,686

Senator-clustered standard errors in parentheses

Table 8: The table compares the marginal effect across multiple variable by scaling them with their standard deviation. Majority pivotality refers to the probability of being pivotal for a majority vote, while filibuster pivotality refers to the probability of being pivotal in a cloture vote. Filibuster pivotality has the wrong sign but the dollar amount is quite low and the standard errors are quite large. Even though the effect of pivotality as a percentage of average campaign contributions is smaller in the Senate than in the House, the difference is not statistically different. This is true whether one compares majority pivotality of filibuster pivotality.

33