Do inter-district spillovers affect pork-barrel expenditures? Theory

and evidence∗

Kevin Milligan†

October 27, 2003

Abstract

This paper develops a congressional bargaining model studying pork-barrel spending in thepresence of spillovers between electoral districts. As the political benefit of pork-barrel spendingbecomes more concentrated, pork-barrel spending crowds out other spending in the budget. Therelationship between spillovers and spending is made ambiguous, however, by competing sub-stitution and income effects. I take the question to a data set of US congressional districts overa period of five decades, finding that physically larger congressional districts enjoy higher levelsof federal employment and military presence, holding other factors constant. If size is a goodproxy for spillovers, then the evidence is consistent with the model. This inference survives in-strumental variables estimation exploiting the decennial reapportionment of congressional seatsacross states. The theory and evidence imply that electoral boundaries which concentrate thepolitical benefits of federal spending lead to inefficient spending decisions.

∗I thank David Green, Wojciech Kopczuk, Anindya Sen, Herman Vollebergh, and audience members at SimonFraser University, the University of Waterloo, and the International Institute for Public Finance meetings in Praguefor helpful comments, as well as Michael Smart for his encouragement at early stages of the project. Finally, I thankAndrea Wenham for excellent research assistance.

†Department of Economics, University of British Columbia, #997–1873 East Mall, Vancouver, BC, Canada, V6T1Z1. E-mail:kevin.milligan@ubc.ca

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1 Introduction

Representatives to a legislature have a strong incentive to vote for projects favoring their own

electoral district when the costs are shared across all districts. This well-known ‘common pool’

problem can affect the level and the composition of government spending.1 In particular, ‘pork-

barrel’ projects that do not pass cost-benefit tests can arise. The strength of the incentives may

change, however, if the ability of the legislature to target spending at a certain district is imperfect.

As an example, consider a local labor market and a federal government spending program

that provides local employment. If only one district spans the entire local labor market, then any

political benefits arising from the project would be gained by the local representative. On the other

hand, if the local labor market is subdivided into several districts then individual voters would be

less likely to live and work in the same district. In this case, the benefits to the project would be

dispersed across electoral districts, and with them the incentive of local representatives to vote in

favor of the spending project.

In this paper, I study a legislative bargaining game in which a winning coalition of represen-

tatives is maintained by choosing a spending mix between a national public good and pork-barrel

projects. I show that when the impact of pork-barrel spending is perfectly dispersed across all dis-

tricts, the political process recreates the socially efficient level of public good provision. However,

when the benefits of pork-barrel spending are concentrated, inefficient pork-barrel spending arises.

This suggests that district boundaries designed to disperse voters with a particular political inter-

est across districts may provide better political decisions than boundaries designed to concentrate

interested voters.

In addition, I investigate how the level of pork-barrel spending changes when a larger proportion

of spending stays in the targeted district. A larger proportion of the benefit staying in the targeted

district can be interpreted as a change in the relative price of using the pork-barrel channel versus

the public good channel for keeping coalition members onside. With the change in relative prices,

there are substitution and income effects that pull in opposite directions. Thus, districts that

contain more of the benefits of pork-barrel spending within their boundaries may receive more

spending or they may receive less spending, depending on the strength of the competing effects.

A larger proportion staying in the targeted district can be interpreted as a change in the relative

price of using the pork-barrel channel versus the public good channel for keeping coalition members

onside. With the change in relative prices, there are substitution and income effects that pull in

opposite directions.1See, for example, Persson (1998) or chapter 7 of Persson and Tabellini (2000).

2

I proceed to study this question empirically with a data set spanning five decades of the United

States Congress. Using three measures of federal government spending that have impact on local

factor markets, I provide empirical evidence indicating a strong positive relationship between the

geographical area of congressional districts and federal expenditures. If larger districts are more

likely to contain the benefits of a local project within the district, then the evidence is consistent

with the model. Furthermore, instrumental variables results exploiting decennial reapportionments

of congressional seats across states suggest that naıve estimates may understate the nature of the

effect, possibly owing to gerrymandering of district boundaries. Finally, I document the effects of

including district area in a common empirical specification used for testing the influence of Senate

representation on per-capita district spending. I find that including district area diminishes the

strength of the evidence in favor of the influence of Senate representation on spending.

Below, I first place this paper in the context of the existing research on distributive politics

and public spending. I next lay out the structure of the model and solve it, studying the effect of

increasing the own-district benefits of redistributions. I then provide a discussion of the empirical

implementation, followed by a description of the data set used for the analysis. The penultimate

section presents the estimation results and some sensitivity checks. The paper closes with brief

concluding comments.

2 Related Research

Previous research on distributive (pork-barrel) politics is broad and deep. Persson and Tabellini

(2000) offer a comprehensive review and treatment of the literature. Below, I outline the bodies of

research most relevant for my work.

Social scientists have studied pork-barrel politics in great detail, starting with the seminal work

by Ferejohn (1974) examining the politics of spending on river and harbor projects. Models of

legislative bargaining over local projects developed by Shepsle and Weingast (1981) and Baron

and Ferejohn (1989) feature payments to all legislators and just those in the winning coalition,

respectively. Both Lindbeck and Weibull (1987) and Dixit and Londregan (1996) study party-

based electoral competition, finding that parties will target pork-barrel spending at ‘swing’ voters.

Empirical work has focused on the influence on pork-barrel spending of parties and ideology (Levitt

and Snyder (1995), Sellers (1997), Bickers and Stein (2000)), legislative committees (Alvarez and

Saving (1997), Carsey and Rundquist (1999)), and local-central matching grants (Knight (2002),

Knight (2003), DelRossi and Inman (1999), Limosani and Navarra (2001)).

A key feature of the model I present is the spillover of benefits across electoral districts. Weingast

et al. (1981) study a legislative bargaining game and emphasize the geographic distribution of costs

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across districts when the benefits are concentrated in one district. Persson and Tabellini (2000)

(chapter 8) incorporate benefit spillovers within a model of party-based electoral competition. My

analysis is distinguished by its setting within a legislative environment more suitable for studying

the United States Congress.

The literature on fiscal federalism compares the provision of local public goods by a central

government versus provision by local governments. Both the original contribution by Oates (1972)

and the recent extensions by Lockwood (2002) and Besley and Coate (forthcoming) argue that

when inter-district externalities are large enough, provision by a central level of government is

more efficient. The model I present, in contrast, restricts attention to purely redistributive spending

projects rather than public goods which may provide externalities to neighboring districts. Local

governments would never provide the type of projects I consider on their own.

Recent work on comparative politics studies the equilibrium outcomes of alternative political

institutions. Theory by Persson et al. (2000) and Lizzeri and Persico (2001), as well as empirical

work by Milesi-Ferretti et al. (2002), features a central distinction between ‘global’ public goods

which benefit all in the society and ‘distributive’ pork-barrel spending. The model presented here

incorporates a similar distinction.

Finally, Baqir (2002) finds evidence in favor of a related hypothesis. The author finds that

having more representatives will increase the overall level of spending, as a higher number of

districts exacerbates the common pool problem. In contrast, my paper studies the allocation of

government spending between pure public goods and distributive projects, rather than the overall

level of public spending.

3 The Model

A society has N individuals. They live in districts j ∈ {1, . . . , J}, with n individuals in each

district.2 For convenience, I assume that there is an odd number of districts, and that n = 1. Each

individual is endowed with y dollars of income, and individuals are not mobile across districts.

Utility is derived from a private consumption good cj and a public good G. The cost of the private

good is normalized to be $1 per unit, while the public good costs γ per unit. The public good is

non-rival and non-excludable across all N individuals, no matter the district of residence.

Utility is derived by each household in region j according to the following function:

U(cj , G) = cj + a(G). (1)

2I assume the number of districts is made at a constitutional stage not considered in this model. See Buchananand Tullock (1962) or Hain and Mitra (2002)

4

This utility function is quasi-linear in private goods consumption, so income changes do not affect

the demand for the public good. Utility increases with the public good according to the function

a(G), which is assumed to be increasing and strictly concave.

A legislature consisting of one representative from each district convenes, charged with the

responsibility of deciding on government expenditures. As individuals within each district are

homogenous, the representative could be chosen at random or elected. Tax revenue T is assumed

to be fixed before the meeting of the legislature at a level sufficient to fund the socially optimal

level of public good provision, G. (I am more precise on the determination of G below.)

Public resources may be diverted from provision of the public good to fund pork-barrel projects

targeted toward certain districts. These projects could be spending on a local museum, tax credits

that benefit an identifiable group, the production of government services such as administration

or defence, or more generally any spending that has asymmetric impact across districts. I assume

that the benefits of the spending are completely rival in nature, but have homogenous impact on

individuals within a district. I model the projects as pure redistributions of income from the central

budget to local voters.3

Let the per resident redistribution targeted to district i be ρi, assumed to be non-negative. The

government budget constraint can therefore be written as

T = γG +∑

j

ρj . (2)

Given the fixed budget T , any increase in redistributions must come out of public goods spending.4

The targeting of redistributions to districts is assumed to be imperfect. Some fraction of a

redistribution targeted at district i may spill over into other districts. The redistribution is de-

composed across all districts according to the parameter πij , where πij ∈ [0, 1]. The parameter πij

describes what proportion of redistribution aimed at district i ends up in district j. As ρi is a pure

redistribution of resources, these proportions will sum to one:

∑

j

πij = 1 ∀i. (3)

3An alternative would be to explicitly make the projects inefficient by assuming the benefit is less than the cost.By assuming that the projects are pure redistributions, the model focuses attention on the inefficiency induced bythe political process.

4If legislators simultaneously choose taxes and public goods spending, they will always choose G. Therefore, thefixed budget assumption is necessary to obtain non-trivial results. Lizzeri and Persico (2001) assume the governmentappropriates the entire income endowment of each individual to fund public spending. An assumption similar totheirs could be imposed in order to limit the taxation ability of the government.

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I assume that πjj > πji ∀i 6= j, which means simply that a redistribution targeted at district j has

its largest impact on district j.

Consumption is funded by the endowment of income less the individual’s share of taxes, plus

the individual’s share of redistributions:

cj = y − T

N+

∑

i

πijρi. (4)

When consumption is substituted into the individual utility function I obtain :

U({ρi}, G) = y − T

N+

∑

i

πijρi + a(G). (5)

This allows utility to be expressed as a function of the political choice variables, {ρi} and G, as

well as the parameters of the model.

3.1 Welfare

I assess society’s welfare through a Benthamite social welfare function W , formed by summing

equation (5) over the the J districts:

W =∑

j

U({ρi}, G) = Ny − T +∑

j

∑

i

πijρi +∑

j

a(G). (6)

For the redistributions, I can exchange the summations over regions j and i in order to exploit

the condition in equation (3) that the summation of the πij terms equals one. In addition, the

valuation of the public good does not vary by region, so may be summed across regions. With

these changes, aggregate welfare may be rewritten

W = Ny − T +∑

i

ρi + Na(G). (7)

Finally, I substitute the total tax bill in equation (2) into equation (7). The redistributions cancel,

leaving

W = Ny − γG + Na(G). (8)

A social planner could maximize social welfare by choosing the level of public goods G that

maximizes W in equation (8). The first order condition for this maximization problem is:

a′(G) =γ

N. (9)

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This is the familiar Samuelson condition. The public good should be provided until the sum of the

marginal valuations Na′(G) meets the marginal cost γ, which occurs at G. Equation (9) will serve

as the benchmark against which political equilibria are compared.

4 Political Equilibrium

I examine the equilibrium levels of public goods expenditure and redistributive spending using a

standard model of legislative bargaining.5 I implement an agenda setter model borrowed from

Persson and Tabellini (2000, chapter 7), which was based on the model of Baron and Ferejohn

(1989) using the minimum winning coalition concept developed in Riker (1962).

Two alternative forms of legislative bargaining could be considered.6 First, the ‘universalism’

concept developed by Weingast (1979), Shepsle and Weingast (1981), and Weingast et al. (1981)

assumes that each representative simultaneously chooses his privately optimal level of redistribution,

holding the decisions of the other representatives constant. The second alternative is the bargaining

game studied in Lockwood (2002) in a fiscal federalism model. He assumes that the equilibrium

set of projects emerges as a Condorcet winner over all other policies in pair-wise voting. However,

in the absence of large externalities, no redistributive project would be passed by a majority vote

in pairwise comparisons.7 This renders impracticable a Condorcet-winner approach to legislative

bargaining for the study of redistributive spending.

A trivial solution to the model would arise in the case of J = 1. With one national election, a

representative facing the incentives in this model would behave as a social planner and the efficient

result from section 3.1 would obtain. This result would arise because the model does not incorporate

any scope for benefits from having fewer constituents per representative.8

4.1 Equilibrium with Agenda Setter Bargaining

The bargaining game has three stages. First, when the legislature meets, one representative is

chosen as the agenda setter. In the notation below, I label district 1 as the home district of the5An alternative to legislative bargaining is an electoral competition model such as those developed in Lindbeck

and Weibull (1987) or Dixit and Londregan (1996). The main motivation for a legislative bargaining approach drawsfrom observation. The electoral competition approach is set in a strong party framework; it assumes that partiesmake binding electoral commitments in a unified party-wide policy platform. In contrast, parties in the US Congressoperate in a much less cohesive environment. Diermeier and Feddersen (1998) relate the cohesiveness of parties ina legislature to the rules surrounding ‘confidence votes,’ which play a more important role in parliamentary systemsthan in the US Congress.

6See Coate (1997) for a comparison of legislative bargaining in political economy models.7This point was first made in the classic essay on logrolling by Tullock (1959).8Buchanan and Tullock (1962) argue (chapter 15) that having more representatives for a given population will lead

to voters’ interests being more adequately represented. Hain and Mitra (2002) show that information asymmetriesbetween representatives and voters push the optimal number of districts higher.

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representative chosen as agenda setter. Second, the agenda setter offers a take-it-or-leave-it, non-

amendable policy proposal consisting of a level of the public good and a set of redistributions,

P = (G, {ρi}). Because amendments are not considered, this is a closed agenda. Finally, the

proposal is put to a majority vote against a default alternative policy in the legislature. I assume

that the default policy is to spend all tax revenue to purchase the socially optimal amount of public

good and to spend nothing on redistributions, P0 = (G, {0}).Under agenda setter bargaining with a closed agenda, the agenda setter must assemble a pack-

age P that will defeat P0. To do so, representative 1 must ensure that at least K = J−12 other

representatives are better off with policy P than with P0. I refer to this constraint as the incen-

tive compatibility constraint for the coalition members k ∈ K. The policy must also satisfy the

government budget constraint.

Representative 1 solves the following problem:

max〈G,{ρi}〉

y − T

N+

∑

i

πi1ρi + a(G), (10)

subject to the set of individual coalition member incentive compatibility constraints,

y − T

N+ a(G) ≤ y − T

N+

∑

i

πikρi + a(G), ∀k ∈ K, (11)

and the government budget constraint

γG +∑

i

ρi ≤ T. (12)

I associate a multiplier θk with the incentive compatibility constraint on coalition member k, and

a multiplier λ with the government budget constraint. The agenda setter can be thought to be

maximizing the utility of a representative household in his or her district, as all individuals within

a district are identical.

The first order conditions for the solution are the following J+1 equations:

w.r.t. G : a′(G) +∑

k

θka′(G)− γλ = 0 (13)

w.r.t. ρi : πi1 +∑

k

θkπik − λ = 0, ∀i ∈ J. (14)

The first equation is found by taking the derivative with respect to G. An increase in G yields

direct benefits to the agenda setter of a′(G). The second and third terms in equation (13) show the

indirect benefit and cost to the agenda setter through the coalition members’ incentive compatibility

8

conditions. An extra increment of G helps to relax the incentive compatibility constraints, but this

comes at a cost of γ fewer dollars available for redistributions.

The J first order conditions in equation (14) are found by taking the derivative with respect to

each ρi. An increase in ρi benefits the agenda setter directly through πi1 and indirectly through the

effect of πik on the incentive compatibility constraints of coalition members. This must be balanced

with the budget cost of reduced public goods spending.

Rearranging equation (13) and equation (14) written for representative 1, the following expres-

sion can be derived:

a′(G) = γ(∑

k θkπ1k + π11)(1 +

∑k θk)

(15)

Using the K first order conditions of coalition members, I can solve equation (15) for a solution in

terms of the model parameters. In what follows, I focus on the J = 3 case for algebraic simplicity.

Representative 1 is the agenda setter, and I assume that his attempted coalition partner will be

representative 2. In this case, the solution reduces to

a′(G) = γ(θ2π12 + π11)

(1 + θ2). (16)

A marginal decrease in public good provision frees up γ dollars to redistribute through ρ1. This

brings direct benefits to the agenda setter through π11, and indirect benefits through the slackening

of the incentive compatibility constraint (reflected in the θ2π12 term). This must be balanced against

the need to compensate district 2 for their lost G, expressed through the (1 + θ2) term.

Further simplification of the equilibrium condition is possible. Equation (16) can be combined

with equation (14) written for members 1 and 2 in order to obtain an expression for the multiplier

θ2:

θ2 =π11 − π21

π22 − π12. (17)

Substituting equation (17) into equation (15), I obtain

a′(G∗) = γ(π11π22 − π12π21)

(π11 + π22 − π12 − π21)(18)

The marginal utility of public good consumption is strictly positive because of the assumption that

π11 > π12 and π22 > π21. The solution can now be compared to the efficient solution in equation

(9).

Proposition 1 In a legislature with agenda setter bargaining and a closed agenda, the equilibrium

level of the public good G∗ is less than the efficient level G.

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Corollary 1 As the share of redistribution directed to any district approaches equality, the equilib-

rium level of the public good approaches the efficient level. As πij → π = 1J , ∀i, j, G∗ → G.

Proof.

See Appendix A.

When the own-district benefit of a redistribution is greater than the benefit to other districts,

the provision of the public good is less than optimal. Redistributions make a more effective tool

in satisfying coalition members’ incentive compatibility constraints than public good provision.

This allows the agenda setter to substitute away from public good provision while still satisfying

incentive compatibility. When the share of redistribution becomes more dispersed, the advantage

of redistributions over public good provision shrinks until, with perfect dispersion, the efficient

solution is obtained.

This result has strong implications for the design of electoral districts. Those charged with

deciding on political boundaries are often accused of arranging high concentrations of similar voters

in a few districts in an attempt to maximize the probability of winning in the balance of the

districts. Proposition 1 suggests that the concentration of voters with a particular interest not only

has consequences for fairness but for efficiency as well.

4.2 Changing the effectiveness of redistributions

What happens to public good provision and redistribution when the effectiveness of redistributive

spending changes? There are two channels through which changes in the πij parameters can have

impact. First, the representatives invited to enter the coalition may change. As shown below,

the higher are within-coalition spillovers, the greater becomes the agenda setter’s welfare. This

provides an incentive for the agenda setter to invite into the coalition representatives from districts

featuring high within-coalition spillovers. The second channel is the effect of spillovers, holding

coalition membership constant. As spillovers change, the incentive compatibility conditions for

coalition members change. This alters the mix of public goods and redistributions used by the

agenda setter to keep the coalition together.

Before stating the propositions, I must first establish a lemma relating to the provision of public

goods.

Lemma 1 With πjj > πij, the equilibrium amount of public good is decreasing in within-coalition

spillovers: ∂G∗∂πij

< 0, For i, j ∈ {1, 2}.

Proof.:

10

See Appendix A.

Public good provision decreases when the effectiveness of redistributions increases.9 Less of the

benefit of redistributions is now leaking outside the coalition, so more of each dollar in redistri-

butions hits the desired mark. As public goods and redistributions are substitutes in satisfying

district 2’s incentive compatibility constraint, a more effective redistribution channel decreases the

need for public good provision. This can be thought of as a change in the relative price of using

redistributions and public goods to keep coalition members onside.

Given a choice of coalition partners, which partner will be invited by the agenda setter into the

coalition?

Proposition 2 Holding all else constant, districts featuring higher within-coalition spillovers (π22,

π12, or π12) will be invited into the coalition by the agenda setter so long as π12 < 1J .

Proof.:

See Appendix A

A district featuring higher within-coalition spillovers makes the agenda setter better off because

such a district is cheaper to keep in the coalition and because transfers to it may spill into the

agenda setter’s district. The condition π12 < 1J ensures that redistributions are more efficient than

public goods in keeping district 2 in the coalition.

The analysis changes if one considers an increase in within-coalition benefits among existing

coalition members. Specifically, what happens to the redistribution for coalition members if the

own-district benefit π22 increases? There are two effects, corresponding to income and substitution

effects. First, holding the level of public goods constant, an increase in π22 means that a lower

redistribution ρ2 will suffice to satisfy incentive compatibility as more of the ρ2 will stay within

district 2. This is the income effect. However, the higher π22 makes the redistribution channel

cheaper compared to the public good channel. A substitution toward the redistribution channel

leads to an increase in pork-barrel redistributions. Putting these together, the overall effect of a

change in π22 on ρ2 depends on the strength of the income and substitution effects.

This can be seen by deriving an expression for ρ2 using the government budget constraint and

the incentive compatibility constraint:

ρ2 =a(G)− a(G)− π12(T − γG)

π22 − π12, (19)

9As the πij terms sum to one over j, an increase in πij must be offset by a decrease in the πim, of some otherdistrict m 6= j. I assume here that the offset happens through district 3, outside the coalition. As the πij parametersfor district 3 have no bearing on the equilibrium, they can be ignored.

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which is non-negative by assumption. Differentiating ρ2 with respect to π22 gives

∂ρ2

∂π22= − ρ2

(π22 − π12)−

∂G∂π22

[a′(G)− γπ12](π22 − π12)

(20)

The first term is negative, since ρ2 ≥ 0. It shows the static effect if G were held constant when

π22 changes. The second term reflects the effect of smaller G on district 2’s incentive compatibility

constraint. The direct effect through a′(G) increases the redistribution through ρ2 that is required

to keep district 2 in the coalition. By rearranging equation (20), the following proposition can be

derived:

Proposition 3 If a(G) is concave enough, then redistributions to coalition members will be in-

creasing in own-district benefits: ∂ρ2

∂π22> 0.

Proof.: See Appendix A When G drops sharply enough with an increase in π22, the substitution

effect offsets the income effect. This leads to a positive response of ρ2 to an increase in π22.

4.3 Simulated examples

The effects of increasing π22 can be seen more clearly through some examples, displayed in table

1. Suppose that a(G) takes the form Gα. If y = 1, n = 1, γ = 3 and α = 0.75, then the Samuelson

condition in equation (9) implies that the optimal provision of the public good is G = 0.316.

Given that taxes are fixed to provide the optimal level of the public good, total tax revenue

comes in at 0.949. With no redistributions, the payoff to a person in any district is therefore

1− 0.949/3 + (0.316)0.75 = 1.105.

Simulation A in the table displays this case with assumed parameter values for the π1j terms.

Across the columns are displayed the results for increasing values of π22. In column (a) with

π22 = 0.600, the equilibrium level of the public good sits at G∗ = 0.192, derived from equation

(18). Given that level of public good, a redistribution of ρ2 = 0.143 is necessary to achieve incentive

compatibility. This leaves 0.231 for the redistribution to district 1. The total value of the payoff

achieved by residents of district 1 according to equation (5) is 1.126, which is greater than the 1.105

residents of district 1 received in the default case with no redistribution.

Across the four columns from (a) to (d), the only parameter changes are increases to π22, with

offsetting decreases in π23.10 The payoff to residents of district 1 in the bottom row increases as

π22 decreases. If the four columns represent four possible coalition partners, then the agenda setter10When π32 is not too large, payoffs to district 3 make no difference to the agenda setter, so changing π23 does

not change the outcomes. If π32 is large and π22 small, it may become more efficient to satisfy district 2’s incentivecompatibility constraint through payments to district 3, spillovers from which will help district 2.

12

would choose to form the coalition with the representative from the highest π22 district. This

accords with proposition 2.

The same table can be used to investigate the strength of the income and substitution effects.

From (a) to (b), the increase in π22 leads to an increase in ρ2, as the effect on the incentive

compatibility constraint of the drop in G∗ is greater than the static effect in equation (20). In

columns (c) and (d), however, ρ2 decreases as π22 increases. Here, the income effect dominates

the substitution effect on the incentive compatibility constraint. Simulation B repeats this exercise

using a more concave function for a(G), with α = 0.25. In the second last row, ρ2 is increasing

in π22 across the four columns. When a(G) is concave enough, the change in G∗ induced by an

increase in π22 is large enough to offset the income effect.

Taken together, the simulations suggest two channels through which a district’s πjj affects its

redistributions. First, districts with higher πjj are more likely to be invited into the coalition.

Second, for a given set of coalition members, higher πjj will lead to a higher level of spending ρj if

the substitution effect is stronger than the income effect. The ambiguity of the relative strengths

of the two effects must be resolved empirically.

5 Empirical Implementation

The model predicts that districts featuring high own-district benefits are more likely to be recipients

of redistributive spending, but only if the substitution effect is stronger than the income effect. I

take this question to data using several measures of federal spending in US congressional districts.

In order to implement the prediction empirically, I must find an empirical analogue to the πjj

parameters, as well as suitable measures of federal spending. I discuss my choices below, and

outline the empirical challenges they raise.

5.1 District Size

To proxy for the amount of spending benefit that stays within a district, I use the geographical

size of the district. Residents of smaller districts will have more neighboring districts within a

reasonable commute. If a spending project has benefits that decline with commuting distance,

then more benefits may flow outside the district targeted by a redistribution. This logic suggests

that bigger districts have higher πjj .

To provide support for this proxy, I examine data from the 1990 Census Public Use Microdata

Sample.11 The Public Use Microdata Sample is the only Census file that reports the place of work11I use the one in one thousand sample (ICPSR 6497), formed as two per cent of the five per cent Public Use

Microdata Sample. I select only those observations with a response to the place of work question, leaving 250,611

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and the place of residence for each respondent. Both the state and the Public Use Microdata Area

(PUMA) are reported. PUMAs are geographic units with at least 100,000 residents. Congressional

districts are larger units than PUMAs, but studying commuting patterns across PUMA borders

can still provide some indication of how population density is related to commuting.

I analyze the hypothesis that higher population density makes residents more likely to live and

work in different PUMAs. For each respondent, I create a variable that takes the value 1 if the

respondent lives and works in the same PUMA, and 0 otherwise. I then collapse this to a mean for

each state. This variable is compared with state population density in Figure 1. State population

density is calculated as the total 1990 population of the state divided by its land mass. The log of

state population density is on the horizontal axis of the figure and the proportion of respondents

who live and work in the same PUMA is on the vertical axis.

There is a clear negative slope to the data plot. The correlation between the two variables

is -0.528. California, at the bottom right of the plot, has a population density of 199.7 residents

per square mile, while Wyoming at the top left of the plot has only 4.83. Because of its density,

California’s 198 PUMAs spread over 155,951 square miles are small in physical size. Only 12.9

per cent of California residents live and work in the same PUMA. In contrast, the four PUMAs in

Wyoming spread over 97,104 square miles are physically large, with over 98 per cent of residents

living and working in the same PUMA.

The analysis indicates that population density and commuting across PUMA borders are neg-

atively related. There is a clear analogue to congressional districts. I infer that residents of

physically smaller (and therefore more dense) congressional districts are more likely to regularly

travel to neighboring congressional districts. For government spending that disperses its benefits

geographically, this suggests larger spillovers for physically smaller districts.

5.2 Federal Spending Measures

Finding a suitable measure for pork-barrel spending is controversial, owing to the difficulties of

separating pork-barrel spending from productive public investment. With this in mind, I follow

the literature and aim to find measures of federal spending that embody some degree of political

discretion.12 It is also necessary that the measures be observable and consistent over long time

periods in order to implement my empirical strategy exploiting decennial reapportionments.

The three measures of spending that I employ are federal employees, military personnel, and the

presence of a military installation. All three measures are inputs into the production of goods and

observations. I use the sample weights provided for all calculations.12For example, Levitt and Snyder (1995) compare spending that is plausibly more discretionary to that which is

less discretionary to see if political variables explain better the more discretionary spending.

14

services, and therefore would exert a demand increase on local factor markets; a demand increase

that could spill across district borders in smaller districts.13 As well, these measures of spending

are more plausibly under political discretion than is spending such as entitlement transfers.14

5.3 Empirical Challenges

Two challenges confront the empirical strategy outlined above. First, congressional district bound-

aries are determined by each of the state legislatures. This means that both congressional district

boundaries and the location of federal spending are choice variables, decided by politicians. This

raises the possibility that a simultaneity bias may confound my estimates. Representatives with

federal spending in their district have an incentive to arrange gerrymandering of their district

boundaries to capture as much of the benefit as possible.15

A gerrymandering bias could work in either direction. For example, imagine that a military

base is located near the edge of an urban area. Suppose further that the existing district includes a

portion of the urban area around the base as well as a large section of the surrounding rural area.

An attempt to capture the benefits of the military base might lead a gerrymanderer to shift the

district borders to include more of the urban area and less of the far-off rural part of her district.

In contrast, if the base were located in the rural part of the district, it might be optimal to drop

the far-off urban part of the district in favor of a new, larger section of rural land. Because of the

idiosyncratic patterns of gerrymandering, no clear prediction of the direction of the bias may be

made.

A solution to this empirical challenge can be found through the use of an exogenous instrumen-

tal variable. Below in section 8 I describe in greater detail an instrumental variables strategy that

exploits the decennial reapportionment of congressional seats across states. This solution can po-

tentially overcome the effect of gerrymandering if the instrument is plausibly unrelated to variation

in government spending, except through its effect on district size.

The second challenge comes from potentially confounding factors that also might influence

spending. Government spending could be attracted to (or repelled from) low-density districts for

reasons unobservable to an econometrician. For example, the activity undertaken may produce

harmful externalities that neighbors would prefer not to endure. Similarly, spending may be dis-13Weingast et al. (1981) examine how locally-sourced inputs brings political benefits to the local market.14Military expenditures appear to be particularly sensitive to local political concerns. The political sensitivity of

base closures can be ascertained from the public debates around the Base Realignment and Closure (BRAC) processof the Department of Defence. See, for example, Department of Defense (1998).

15Sherstyuk (1998) and Gilligan and Matsusaka (2000) study optimal strategies for gerrymandering by vote-maximizing politicians. Gelman and King (1994) present evidence that gerrymandering can enhance the respon-siveness of democracy.

15

tributed spatially to cover the land mass of the United States and therefore attracted necessarily

to low-density regions. On the other hand, the spending projects may require a critical mass of

available labor and therefore be attracted to more dense populations.

To address this concern I am careful to control for the urban or rural population of the district,

to the extent possible in the data. This approach ensures that inferences are not confounded

by city-countryside or urban-rural effects. However, these controls are ineffective if spending is

intrinsically drawn to low density districts for reasons other than political spillovers.

5.4 Estimating Equation

The data take the form of a set of districts d across Congresses c and states s. The data are not in

the form of a panel — district boundaries and the number of districts within a state change across

time. I estimate equations of the form

Spenddsc = β′0Areadsc + β′1Xdsc + β′2Congressc + β′3States + edsc, (21)

where Spenddsc represents one of the three measures of spending for a district d in state s in

Congress c. Areadsc represents the physical area of the district, Xdsc is a vector of observed district

characteristics, Congressc is a set of dummies for each Congress, States is a set of state dummies,

and edsc is a mean zero disturbance term. The parameters β0, β1, β2, and β3 are to be estimated.

6 The Data

The main source of data is the congressional district data set assembled by E. Scott Adler.16 There

are 435 congressional districts per Congress. For each district, the Adler data include Census and

physical characteristics for each Congress from the 78th (1943-1944) to the 105th (1997-1998). I

supplement this base with data from several other sources. From the U.S. Census Bureau, I gather

state population totals for each Census from 1950 to 1990. From the Bureau of Economic Analysis,

I take data on average incomes by state. Finally, from the Roster of Congressional Office Holders I

merge in variables describing party membership, length of service, and age for each elected member

of the House of Representatives. Details about these sources are found in Appendix B.

Two alternative sources for federal spending data are the Federal Assistance Awards Data

System and the Consolidated Federal Funds Reports, both compiled by the U.S. Census Bureau.

The upside of these alternatives is the detailed breakdown of federal spending by district. The16The data are described in Adler (1998). These data are assembled from the relevant Congressional District Data

Book, Census, and other sources.

16

downside is the relatively short time-span over which it is available – only from 1984 forward. Since

I require data over several decennial reapportionments, these alternatives are not appropriate.

I make several selection decisions before arriving at the final sample used in the analysis. Owing

to the decennial nature of the Census, many variables in the Adler data set are updated only every

ten years. For this reason, using data from every Congress would lead to several nearly identical

observations for a given congressional district, and lead to an understatement of the true standard

errors. I therefore use only one Congress per Census period, choosing the 84th, 89th, 94th, 99th,

and 104th Congresses.17 The total number of observation across the five Congresses numbers 2,175.

Of these, I drop fourteen districts from states where a member was elected at-large in addition or in

the place of single-member districts.18 Finally, four districts are dropped for missing information.

The final data set consists of 2,157 congressional districts.

6.1 Construction of Variables

I construct the three dependent variables using data from the Adler data set. The first is the share

of the population that works for the federal government. This is reported in the Adler data set

using information from the Census, although it is not available for Censuses prior to 1970. For

analysis of federal employees, therefore, I am limited to the 94th, 99th, and 104th Congresses. The

second and third dependent variables capture different aspects of military spending. The Adler

data report the share of the population in the military, taken from the Census. In addition, the

data set reports the number of military installations in the district. I use this information to form

a variable indicating the presence of a military installation in the district.19

The focus of the analysis is the relationship between district area and the dependent variables

described above. A district area variable is reported in square miles in the Adler data. Also reported

is district population density, which I use to form an alternative dependent variable in a sensitivity

check. In addition to the area variable, I create several other control variables. Full details on their

construction are provided in Appendix B. Some of the variables describe the physical characteristics

of the district. In this category, I include a coastal district indicator, a border district indicator,17There is a limited degree of intercensal variation. The data coming from non-census sources, such as the military

establishments variable, are updated at higher frequencies. As well, there was intercensal redistricting in the 1960sfollowing the Baker v. Carr ‘one man one vote’ Supreme Court case. Including these extra Congresses from the1960s increased the precision of the estimated coefficients, but did not have much impact on the magnitude of theestimates. As well, choosing other sets of five Congresses made little difference to the results.

18For example, in Texas for the 84th Congress, one member was elected at-large in addition to the 21 single memberdistricts. Similar situations arise in Connecticut, New Mexico (two members), North Dakota (two members), andWashington for the 84th Congress, and in Hawaii (two members), Maryland, Ohio, New Mexico (two members), andTexas for the 89th Congress.

19I also tried other ways of expressing the number of military installations. OLS and Tobit regressions on thenumber of military installations both gave positive, significant results.

17

an indicator for being within 100 miles of Washington DC, and an indicator for the presence of a

major city in the district.

A second set of control variables captures some demographic characteristics of the district. The

proportion of the population that is black, age 65 or older, and lives in urban or rural areas is

recorded. I also include the growth rate of state-wide income over the previous intercensal period

and the rate of home ownership in the state. Finally, I include a set of three political variables.

A variable for the Representative’s age, years of service, and whether he or she is a Democrat is

created for each Congress. In order to match the period of the rest of the data, I then take an

average of these variables over the five Congresses covered by each Census period.

I also control for the population of each congressional district. As discussed in section 1, re-

searchers have found evidence that variation in per-capita representation affects per-capita spend-

ing. Cross-sectionally, there is variation in population per district across states since the congres-

sional apportionment formula favors small states. Through time, there is a great deal of variation

before and after the Supreme Court rulings of the 1960s which enforced greater within-state ad-

herence to population equality across districts.

6.2 Descriptive Statistics

Table 2 displays descriptive statistics for the sample. The first column reports the means and

standard deviations for the full five decade sample. The second column restricts the sample to the

last three decades of Congresses, which will be the focus of the federal employee analysis.

The proportion of the population in the military and in the employ of the federal government

is quite small. For the military, the average proportion is 0.008, while for employees of the federal

government, the proportion in the population is 0.016. The proportion of districts that contain

a military installation is just under half, at 0.468. The average size of a district is 7,776 square

miles. This average changed substantially only when Alaska and Hawaii were made states. The

other physical and Census characteristics of the sample reveal no surprises. About one third of

the districts are on a coastline or in a large city, and around two percent are within 100 miles

of Washington D.C. The proportion of the population living in rural-farm areas is 0.067 over the

sample, but falls dramatically through time from 0.176 in the 84th Congress to 0.016 in the 104th.

The final three variables in the table describe the characteristics of elected Representatives. The

average Representative has 8.4 years of service, and is 51.8 years old. Fifty-eight percent of elected

Representatives in these Congresses were members of the Democratic Party.

Probing deeper into the dependent variables, Table 3 compares the dependent variables across

values of the control variables. The top panel breaks down the dependent variables by several

18

categorical controls. The first five columns show the values of the dependent variables across the

five Congresses in the sample. Over the years, the share of the population with a federal job was

constant. In contrast, the cycles in military spending through time are evident as defense needs wax

and wane. The share of the population in the military peaked in the 94th Congress in 1975-1976

at 0.010, then declined to 0.007 by the 104th Congress twenty years later. The share of districts

with a military installation follows a similar cyclical pattern.

The right-hand side of Panel A breaks down the dependent variables by three geographical

categories. There are no large differences in the proportion of military personnel and federal

employees in major cities. While big city districts are less likely to have a military installation,

it is noteworthy that over forty per cent still do — installations are not strictly rural. All three

measures of spending are higher close to Washington D.C., and the military measures are higher

in coastal districts. Both of these phenomena are clearly attributable to factors outside the model.

Panel B of the table breaks down the dependent variables for the continuous control variables. In

each case, I compare observations with high values of the control variable (at or above the median)

with low values (below the median). Both military measures appear to be positively associated with

district area. Federal employment, however, is not. Looking across the other variables, there are

few strong differences. Military expenditure is slightly greater in districts with higher population,

lower income, more blacks, fewer elderly, and a lower urban share. The lack of a strong difference

between urban and rural districts gives some confidence that spending is not intrinsically biased

toward rural districts.

7 Empirical Results

Using the assembled data, I run several regressions to explore the relationship between the physical

size of a congressional district and the three measures of federal government spending. The sections

below discuss in turn the main results and some sensitivity analysis. This is followed in the next

section by a discussion of simultaneity and the implementation of instrumental variables estimators.

7.1 Main Results

I begin by running regressions on different combinations of control variables. Table 4 displays

results from four ordinary least squares (OLS) regressions, each using the binary dependent variable

indicating the presence of a military installation. The first column reports a univariate regression

on the logarithm of district area. The coefficient of 0.05 indicates that a 10 per cent increase in

district area would lead to a 0.005 percentage point increase in the probability of having a military

19

installation. This elasticity, while not large, is statistically significant and of the sign predicted by

the theory.

In column (b), a set of state dummies and a set of Congress dummies are added. This has a

minimal impact on the estimated coefficient. The third column adds several geographic controls

along with the logarithm of district population. Being on a coast or border is predicted to increase

the probability of having a military installation. The population of a district appears to exert a

strong influence on the probability of having a military installation. The coefficient indicates that a

10 per cent increase in district population leads to a 3.8 percentage point increase in the probability

of having a military installation. This contrasts with the results of Ansolabehere et al. (2002) who

find that state districts with more residents receive less per-capita spending.20

The fourth column of Table 4 shows the results with the demographic variables included in the

regression. The inclusion of these variables nearly doubles the estimated impact of district area.

Of the demographic controls, it is the proportion urban and proportion rural-farm variables that

have the biggest impact on the coefficient on district area. This results from the strong, negative

correlation between district area and the proportion of the population in urban areas.

Table 5 displays results for the full specification for each of the three dependent variables. The

first column reports results for the logarithm of the proportion of federal employees in the district.

Because this variable is not available for the earlier Congresses, there are only 1,303 observations.

The impact of district area on federal employment is positive. The coefficient of 0.091 implies that

a 10 percent increase in district area will lead to a 0.91 percent increase in the proportion of federal

employees living in the district. The result is highly significant.

The second column of Table 5 shows results using the logarithm of the proportion of military

personnel in the population as the dependent variable. The estimated OLS coefficient of 0.372 on

district area implies that a 10 percent increase in district area leads to a 3.7 percent increase in the

proportion of military personnel in the population. Finally, the third column of Table 5 repeats the

results of the full specification in Table 4. The geographic and census control variables generally

have the same sign across the three dependent variables, although the magnitudes and significance

differ.

7.2 Sensitivity

I present some evidence using alternative specifications to assess the sensitivity of the results pre-

sented above to empirical assumptions made in the estimation. Table 6 displays results using the20This difference could be related to the types of spending studied in their paper. As well, they use changes in

districts caused by the 1960s supreme court rulings. Since the 1960s also saw advances in civil rights and registration,these other legal developments could confound their inferences.

20

same set of control variables as found in the regressions of Table 5, with some modifications.

Panel A in the table presents results with some variables describing the elected Representative

for the district. Of the three variables, only the Representative’s years of service is statistically

significant. Tested jointly, however, the three variables are significant. The coefficient on the years

of service suggests that more years of service increases the proportion of federal employees in the

district’s population. The results for the measures of military spending show the same pattern.

This evidence is consistent with work stressing the importance of political actors in determining

federal spending.21 The inclusion of the political variables in Panel A has little impact on the

estimated coefficients on the logarithm of district area.

In Panel B, I replace the district area variable with a measure of density — the population

per square mile in the district. This measure bundles together the effect of district population

and district area. The estimated coefficients across all specifications are negative and statistically

significant, which is consistent with the main results above. This reinforces the inferences made in

the main specifications.

8 Simultaneity

The potential simultaneity of congressional district size and government spending may confound

the OLS estimates, as discussed in Section 5.3. In this section, I lay out an instrumental variables

strategy that attempts to correct for simultaneity. I then discuss potential threats to the validity

of the instruments. Finally, I present and discuss results of the estimations.

Along the way, I analyze the effects of including state population in the regressions. Previous

research has studied the representation hypothesis, which suggests that jurisdictions with more

representatives per capita will receive higher spending per capita.22 In the Senate, each state has

two representatives. Therefore, the only determinant of representation is state population. Small

population states are ‘over-represented’ and large population states are ‘under-represented.’ As

congressional district size is negatively correlated with state population in my data set (-0.177),

the exclusion of district size in previous work may have biased the estimated impact of Senate

representation.23

21See, for example, Alvarez and Saving (1997) and Carsey and Rundquist (1999).22Atlas et al. (1995), Lee (1998), Horiuchi and Saito (2001), and Ansolabehere et al. (2002) find evidence suggesting

that government spending is biased toward districts with more representatives per voter, while Levitt and Snyder(1995) finds the opposite.

23Lee (1998) dismisses area-based criticisms as unpersuasive, reasoning that small population states can be large(Wyoming) or small (Rhode Island) in physical size. However, she does not submit the criticism to an empirical test.

21

8.1 Instrumental Variables Strategy

A strategy to overcome the potential simultaneity of district area and federal spending requires

a plausibly exogenous source of variation in district size in order to form suitable instrumental

variables. A source of variation in district area is post-censal congressional reapportionment.24

Every ten years, the 435 seats in the House of Representatives are re-allocated according to a

process that depends on state population.25 Given the fixed land mass of each state, a change in

the number of districts should be a good predictor of the land area of districts - more districts

within a state is predicted to lead to smaller district area.

Between the 84th Congress (1955-1956) and 104th Congress (1995-1996), there have been sub-

stantial reallocations across states. Table 9 displays the number of districts per state for each

decade over the five-decade period covered in my data. California moved from 30 districts to 52,

for a gain of 22 seats. Florida gained 15 to reach 23 seats. On the other side, New York and

Pennsylvania were the largest losers, with drops of 12 and 9 respectively.

The driving force behind the reapportionment procedure is state population. Therefore, using

the number of districts as an instrument requires consideration of the role of state population in the

empirical model. The relationship between state population and the number of seats is nonlinear,

which suggests that it may be possible to include state population as a control variable and devise

instruments exploiting the nonlinearity. However, the predictive power of the nonlinearities was

not strong enough to form useful instrumental variables.26

24An alternative source of variation in district size is the court-ordered reapportionments following the SupremeCourt cases of the 1960s such as Baker v. Carr. (See Altman (1998) for a summary of the Supreme Court’s involvementwith redistricting.) Following the rulings, there was a move toward equal populations for each district within states.Ansolabehere et al. (2002) use court-ordered reapportionment at the county-state level to study the representationhypothesis. Counties that received more seats are compared to those that lost representatives. The analogue to mycase would be to compare states that lost or gained representatives. However, the court-ordered reapportionments atthe federal-state level did not change the number of representatives per state, only the within-state district borders.Therefore, the approach used in Ansolabehere et al. (2002) is precluded. Attempts to exploit this source of variationin other ways were unsuccessful.

25The apportionment process works as follows. First, each state is assigned one district, for a total of fifty districts.Second, states are assigned ‘priority values’ for subsequent districts. The priority value is the product of the state’spopulation and 1√

n(n−1), where n is the number of seats a state would have if it gained a seat. The state with the

highest priority value receives the 51st district. This continues until the 435th district is assigned. For the mostrecent reapportionment using the 2000 Census, the 51st seat was assigned to California, the 52nd to Texas, and the435th to North Carolina.

26With state population as a control, using the number of seats as an instrument produced imprecise results. Ialso tried experimenting with instruments based on simulated ‘priority values’ for the apportionment formula. Theseinstruments also failed to have sufficient predictive power when state population was included as a control.

22

8.2 Potential Threats to Validity

The reliance on state population raises two potential threats to the validity of an instrumental

variables strategy based on reapportionment. I discuss each in turn.

First, state population flows may be driven by economic factors. If the economic factors that

determine population flows are related to those determining the location of federal government

spending, then the instrument may be invalid. I include in the regressions the rate of income growth

for each state in the previous census period. This control is meant to proxy for the attractiveness

of the state to potential migrants.

The second concern relates to the representation hypothesis. The exclusion of state population

from the second stage equation requires the identifying assumption that a state’s population affects

federal spending only through its affect on the physical size of the district. This assumes that the

Senate representation hypothesis has no predictive power. Is this justified? Levitt (1996) shows

that Senator ideology is the primary driver of voting decisions, although he does not specifically

study local spending decisions. Empirically, the exclusion restriction is not invalidated, as the

instruments pass standard tests for exclusion for all three dependent variables as reported in the

table below.

8.3 Regression Results

The regression results are reported below. I first explore different specifications for the first stage

regression. Following that, I investigate the implications of senate representation for my strategy.

Finally, I report the two stage least squares estimates.

The first stage regression results are reported in Table 7. The first column includes only the

logarithm of the number of districts. The estimated coefficient of -0.427 indicates that a 10 per

cent increase in the number of districts will decrease district area by 4.3 per cent, as the same

land mass is split more ways. The second column replaces the number of districts with the state

population. Again, there is a strong, negative, and significant effect of changes in state population

on district area. Finally, I include both state population and the number of districts, along with

their interaction. This specification attempts to capture the discrete nature of the relationship

between population and the number of districts. A ten per cent increase in the population of a

small-population state is less likely to lead to a change in its allocation of seats than an equal

population increase in a large-population state. The instruments are strongly jointly significant in

the first stage across all three specifications.

Before analyzing the instrumental variables results, I focus on regressions with and without state

population included as a control to investigate the Senate representation hypothesis. The three

23

panels of Table 8 correspond to the three dependent variables. Column (a) reproduces the results

from Table 5. Column (b) has results from the same specifications, but with the logarithm of state

population replacing the district area variable. The estimated coefficients for all three dependent

variables are large, negative, and significant. The coefficient of -0.238 for federal employees suggests

that a ten per cent decrease in the state’s population increases the proportion of federal employees

by 2.38 per cent. These estimates are consistent with the representation hypothesis.

The evidence in favor of the representation hypothesis weakens in column (c), however. When

both district area and state population are included as controls, the estimated coefficient on state

population drops for all three dependent variables. This casts some doubt on the robustness of the

results in Atlas et al. (1995) and Lee (1998) who study the representation hypothesis using state

population but do not control for district area.

Another important result in Table 8 can be seen in a comparison of column (a) with column

(c). The coefficient on district area reveals almost no change when state population is included and

excluded. This suggests that excluding state population has very little influence on the estimated

impact of district area, which is important for the interpretation of the instrumental variables

results.

The two-stage least squares (2SLS) results are reported in column (d) of table 8. The coefficient

for federal employees is significant at the 10 percent level. In contrast to the military results below,

there is little difference between the OLS and the 2SLS results — the estimated coefficient of 0.087

on district area is within the 95 per cent confidence interval of the OLS estimate. In panels B and

C, the 2SLS results for the military dependent variables exceed the OLS estimates. For military

installations, the estimated coefficient increases by a factor of almost three.

These 2SLS results suggest that simultaneity may bias down OLS estimates. This is consistent

with an hypothesis of gerrymandering. If gerrymanderers attempt to capture the political benefits

of a military installation by forming systematically smaller districts around the installations, then

OLS estimates will underestimate the true impact of district size on the location of military instal-

lations.27 Taken in total, the 2SLS regressions provide greater confidence in the inferences drawn

from the OLS estimates.27A smaller district may capture more effectively the political benefit if a sparsely populated section of the district

far from the installation were traded for a more densely populated section close to the installation in a neighboringdistrict.

24

9 Conclusion

This paper has explored a model of distributive politics featuring inter-district spillovers. When

the political benefit of redistributions is spread across districts, I find that political decisions can

replicate the socially optimal allocation. However, when the political benefit becomes concentrated,

pork-barrel spending will arise. The direction and magnitude of the response of pork-barrel projects

to changes in the own-district benefits of spending is sensitive to choice of model parameters.

In the data, I find evidence that districts covering a smaller physical area are less likely to

attract federal employment, military personnel, or military installations. This evidence is robust

to instrumental variables estimates exploiting the decennial reapportionments of districts. I also

document that the inclusion of a measure of district area casts doubt on previous findings of a

relationship between Senate representation and local spending by the federal government.

This work makes clear predictions about the design of electoral districts. As an example,

the redistricting of the three congressional districts in Utah in 2002 is informative. In the new

boundaries for the 108th Congress, Salt Lake City was split three ways. Each new district takes

some of the urban center and a portion of the outlying areas of the state. In contrast, the previous

alignment for the 107th Congress had one congressional district covering most of Salt Lake City,

with the outlying areas divided between the other two districts.28 The model suggests that the

new alignment will lead to a weaker incentive to obtain redistributive spending for Salt Lake City,

as the political benefit will be spread three ways instead of concentrated in one district.

28According to Janofsky (2001), the redistricting was an attempt by the Republican majority in the state legislatureto dilute the Democratic stronghold of Salt Lake City across the three districts.

25

A Proofs

A.1 Proposition 1

The first step is to evaluate the bounds on the bracketed term on the right-hand side of equation

(18). Define

σ =π11π22 − π12π21

π11 + π22 − π12 − π21. (22)

The upper bound for σ is reached at π11 = π22 = 1. In this case, a′(G∗) = 3(12) > 1. For the lower

bound on σ, a candidate for the lower bound could emerge when πij = π = 1J , ∀i, j. When πij = π,

σ is indeterminate. To find the limit, I first fix π22 at 1J . I then take the limit as π11 approaches 1

J .

By l’Hospital’s rule, limπ11→ 1J

σ = 1J . Looking at equation (18), when σ = 1

J , a′(G∗) = γ 1J = γ

N ,

which aligns the congressional bargaining solution G∗ with the efficient solution G in equation (9).

¤

A.2 Lemma 1

The proofs for π22, π11, π21, and π12 are very similar. I show the proof only for π22. Differentiating

(18) with respect to π22 gives:

∂(a′(G∗))∂π22

= γ[π11(π11 + π22 − π12 − π21)− π11π22 + π12π21]

(π11 + π22 − π12 − π21)2. (23)

The terms can be rearranged to find

= γ(π11 − π12)(π11 − π21)

(π11 + π22 − π12 − π21)2. (24)

By assumption, π11 > π12 and π11 > π21. Therefore,

∂(a′(G∗))∂π22

> 0. (25)

Since∂(a′(G∗))

∂π22= a′′(G∗)

∂G∗

∂π22, (26)

and a′′(G∗) < 0 by assumption, equation (25) therefore implies

∂G∗

∂π22< 0. (27)

¤

26

A.3 Proposition 2

The proofs for π22, π21, and π12 are very similar. I show the proof only for π22. Using the incentive

compatibility and government budget constraints in equations (11) and (12), the utility function

for residents of district 1 in equation (5) can be represented as a function of G:

U1(G) =(π11 + π22 − π12 − π21) a(G) + (π11π22 − π12π21) (T − γG)− (π11 − π21) a(G)

π22 − π12+ y − T

N. (28)

Define a maximum value function V = U(G∗). The derivative of V with respect to π22 yields:

∂V

∂π22=

(π11 − π21)[a(G)− a(G∗)− π12γ(G−G∗)

]

(π22 − π12)2 , (29)

through substitution for a′(G∗) using equation (18) and for T using γG (since taxes are set to raise

enough to fund provision of the efficient level of public goods).

The derivative ∂ρ2

∂π22will be positive if

a(G)− a(G∗) > π12γ(G−G∗). (30)

Given the assumed concavity of a(G) and that G > G∗, then

a(G)− a(G∗)G−G∗ > a′(G). (31)

So, if

a′(G) > π12γ (32)

then inequality (30) holds. Substituting the Samuelson condition in equation (9) into the left-hand

side and rearranging gives

π12 <1J

. (33)

Therefore, ∂V∂π22

> 0 if π12 < 1J . ¤

A.4 Proposition 3

From equation (20), it can be seen that the derivative ∂ρ2

∂π22will be positive if

∂G

∂π22

[a′(G)− γπ12

]< ρ2. (34)

Substituting for ∂G∂π22

using equation (26) and rearranging leads to

27

a′′(G∗) < −

(∂(a′(G∗))

∂π22

)[a′(G)− γπ12]

ρ2. (35)

The terms on the right-hand side can be expressed in terms of the model parameters using equations

(24) and (18) to give

a′′(G∗) < −γ

((π11−π12)(π11−π21)(π11+π22−π12−π21)2

)((π11π22−π12π21)

(π11+π22−π12−π21) − π12

)

ρ2. (36)

The equilibrium redistribution ρ2 is a function of the model parameters, so inequality (36) depends

only on the values of the parameters. Therefore, if a(G) is concave enough that inequality (36)

holds, then ∂ρ2

∂π22is positive. ¤

28

B Variable Definitions

The source for each variable is listed at the end of the description in parentheses.

Proportion of federal employees: Number of persons age 16+ employed by the federal govern-ment divided by district population, as reported in the Census. (Adler)

Proportion of military population: Military population divided by district population, as re-ported in the Census. (Adler)

Presence of military installation: Binary variable indicating presence of military installation indistrict. Based on count of military installations. (Adler)

District area: Size of district in square miles. (Adler)

Coastal District : Binary variable for districts located on a coast. (Adler)

Border District : Binary variable for districts located on an international border. (Congressionaldistrict data books)

Washington DC area: Binary variable for districts located within 100 miles of Washington,D.C. (Adler)

Major city : Binary variable for districts within one of the fifty largest central cities in theUnited States. (Adler)

District population: Population of district. (Adler)

Median income: Median family income in district, as reported in the Census. Scaled to 1990dollars using the consumer price index. (Adler)

Proportion black : Number of persons identifying race as African-American divided by districtpopulation, as reported in the Census. (Adler)

Proportion age 65 : Number of persons age 65 or greater divided by district population, asreported in the Census. (Adler)

Proportion urban: Population living in urban areas divided by district population, as reportedin the Census. (Adler)

Proportion rural-farm: Population living in rural farm areas divided by district population, asreported in the Census. (Adler)

Proportion home owners: Proportion of state population that own a home in the year of thecensus. (U.S. Census Bureau)

State income growth: Growth in real per capita income in state over previous censal period, asreported in Regional Accounts Data. (Bureau of Economic Analysis)

State population: State population, as reported in 1990 Population and Housing Unit Counts,Table 16. (U.S. Census Bureau)

Representative’s years of service: Roster of United States Congressional Officeholders and Bi-ographical Characteristics of Members of the United States Congress, 1789-1996: Merged Data.(ICPSR 7803)

Representative’s age: Roster of United States Congressional Officeholders and BiographicalCharacteristics of Members of the United States Congress, 1789-1996: Merged Data. (ICPSR7803)

Representative is a Democrat : Roster of United States Congressional Officeholders and Bio-graphical Characteristics of Members of the United States Congress, 1789-1996: Merged Data.(ICPSR 7803)

29

References

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Altman, Micah (1998) ‘Districting principles and democratic representation.’ Doctoral Thesis,California Institute of Technology

Alvarez, R. Michael, and Jason L. Saving (1997) ‘Congressional committees and the political econ-omy of federal outlays.’ Public Choice 92, 55–73

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31

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32

Figure 1: Proportion Who Live and Work in the Same PUMA versus State Population DensityLive and Work in Same PUMA

Log

of S

tate

Pop

ulat

ion

Den

sity

12

34

56

78

.25.5.751

AK

AL

AR

AZ

CA

CO

CT

DE

FL

GA

HI

IA

ID

ILIN

KS

KYLA

MA

MD

ME

MI

MN M

O

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OK

OR

PA

RI

SC

SD

TN

TX

UT

VA

VT W

AWI

WV

WY

33

Table 1: Simulations

Simulation A: � = 0.75

Simulated ResultsParameters (a) (b) (c) (d)�

11 = 0.600 �21 0.100 0.100 0.100 0.100

�12 = 0.200 �

22 0.600 0.700 0.800 0.900�

13 = 0.200 �23 0.300 0.200 0.100 0.000

a(G) = G� �

0.316 0.316 0.316 0.316T 0.949 0.949 0.949 0.949� = 0.750 G* 0.192 0.153 0.128 0.111� = 3 a(G*) 0.290 0.244 0.214 0.192

n = 1 � 1* 0.231 0.333 0.408 0.465

y = 1 � 2* 0.143 0.159 0.158 0.152�= 0.316 Total Payoff to 1 1.126 1.143 1.158 1.170

Simulation B: � = 0.25

Simulated ResultsParameters (a) (b) (c) (d)

11 = 0.600 21 0.100 0.100 0.100 0.100

12 = 0.200

22 0.600 0.700 0.800 0.900

13 = 0.200 23 0.300 0.200 0.100 0.000

a(G) = G � 0.157 0.157 0.157 0.157T 0.472 0.472 0.472 0.472� = 0.250 G* 0.133 0.124 0.116 0.111 = 3 a(G*) 0.604 0.593 0.584 0.577

n = 1 � 1* 0.045 0.068 0.088 0.104

y = 1 � 2* 0.028 0.034 0.035 0.036�= 0.157 Total Payoff to 1 1.476 1.480 1.483 1.486

34

Table 2: Sample Characteristics

Full Five- 94th, 99th, and Congress Sample 104th Congresses

Number of Observations 2157 1303

Proportion of federal employees -- 0.016(0.013)

Proportion of military population 0.008 0.008(0.017) (0.017)

Presence of military installation 0.468 0.447(0.499) (0.497)

District area (square miles) 7,776 8,098(27,854) (30,260)

Coastal District 0.326 0.324(0.469) (0.468)

Border District 0.068 0.070(0.251) (0.255)

Washington DC area 0.023 0.024(0.149) (0.152)

Major city 0.314 0.332(0.464) (0.471)

Population 466,118 521,989(100,255) (61,348)

Median income (1990 dollars) 28,172 33,436(9,902) (7,903)

Proportion black 0.109 0.114(0.143) (0.151)

Proportion age 65 or older 0.116 0.135(0.047) (0.050)

Proportion urban 0.681 0.701(0.264) (0.265)

Proportion rural-farm 0.067 0.027(0.105) (0.042)

Proportion home owners 0.619 0.640(0.079) (0.067)

State income growth 0.304 0.257(0.181) (0.117)

Representative's years of service 8.4 8.6(6.3) (6.4)

Representative's age 51.8 51.2(8.3) (8.3)

Representative is a Democrat 0.581 0.590(0.424) (0.419)

Notes: Variable descriptions are in Appendix A.

35

Table 3: Breakdown of Dependent Variables

Con

gres

sM

ajor

city

Nea

r D

CC

oast

al D

istr

ict

8489

9499

104

yes

noye

sno

yes

noP

anel

A:

Sum

mar

y st

atis

tics

by

cate

gori

cal v

aria

bles

n42

642

843

343

543

567

714

8049

2108

703

1454

Pro

port

ion

of0.

016

0.01

60.

016

0.01

70.

016

0.06

90.

015

0.01

50.

016

fede

ral e

mpl

oyee

s(0

.013

)(0

.013

)(0

.013

)(0

.008

)(0

.015

)(0

.039

)(0

.008

)(0

.010

)(0

.014

)

Pro

port

ion

of0.

006

0.00

90.

010

0.00

70.

007

0.00

70.

008

0.01

80.

008

0.01

20.

006

mili

tary

pop

ulat

ion

(0.0

14)

(0.0

18)

(0.0

20)

(0.0

16)

(0.0

14)

(0.0

16)

(0.0

17)

(0.0

19)

(0.0

17)

(0.0

23)

(0.0

12)

Pre

senc

e of

mili

tary

0.45

50.

547

0.43

60.

480

0.42

30.

405

0.49

70.

735

0.46

20.

501

0.45

3in

stal

latio

n(0

.499

)(0

.498

)(0

.497

)(0

.500

)(0

.495

)(0

.491

)(0

.500

)(0

.446

)(0

.499

)(0

.500

)(0

.498

)

Pan

el B

: S

umm

ary

stat

isti

cs f

or c

onti

nuou

s va

riab

les

Dis

tric

t D

istr

ict

Med

ian

Bla

ck p

opul

atio

nA

ge 6

5 po

pula

tion

Urb

an p

opul

atio

nar

eapo

pula

tion

inco

me

shar

esh

are

shar

eP

ropo

rtio

n of

fed

eral

em

ploy

ees

Hig

h0.

015

0.01

60.

016

0.01

80.

018

0.01

8(0

.009

)(0

.014

)(0

.016

)(0

.015

)(0

.015

)(0

.016

)L

ow0.

017

0.01

50.

016

0.01

40.

014

0.01

4(0

.016

)(0

.011

)(0

.009

)(0

.009

)(0

.009

)(0

.009

)P

ropo

rtio

n of

mili

tary

pop

ulat

ion

Hig

h0.

009

0.00

80.

007

0.00

90.

006

0.00

8(0

.017

)(0

.015

)(0

.016

)(0

.019

)(0

.013

)(0

.017

)L

ow0.

006

0.00

80.

009

0.00

60.

010

0.00

8(0

.016

)(0

.018

)(0

.017

)(0

.014

)(0

.020

)(0

.016

)P

rese

nce

of m

ilita

ry in

stal

latio

nH

igh

0.54

80.

475

0.42

40.

477

0.45

00.

436

(0.4

98)

(0.5

00)

(0.4

94)

(0.5

00)

(0.4

98)

(0.4

96)

Low

0.38

90.

461

0.51

20.

459

0.48

60.

501

(0.4

88)

(0.4

99)

(0.5

00)

(0.4

99)

(0.5

00)

(0.5

00)

Not

es:

Pre

sent

ed a

re th

e m

eans

and

sta

ndar

d de

viat

ions

of

the

thre

e sp

endi

ng v

aria

bles

. In

Pan

el B

, obs

erva

tions

at o

r ab

ove

the

med

ian

valu

e of

the

vari

able

are

incl

uded

in th

e 'h

igh'

cat

egor

y, w

hile

thos

e be

low

the

med

ian

valu

e of

the

vari

able

are

in th

e 'lo

w' c

ateg

ory.

36

Table 4: Regression results with different control variables

Dependent variable: Presence of a military installation

(a) (b) (c) (d)Number of observations 2157 2157 2157 2157R-squared 0.0466 0.1621 0.1838 0.1944

log (District area) 0.050 ** 0.044 ** 0.050 ** 0.091 **(0.005) (0.007) (0.008) (0.015)

Coast district 0.119 ** 0.118 **(0.030) (0.030)

Border district 0.061 0.018(0.054) (0.051)

Washington DC area 0.263 ** 0.277 **(0.090) (0.090)

Major city 0.003 -0.003(0.031) (0.031)

log (Population) 0.384 ** 0.325 **(0.070) (0.079)

log (Median income) -0.206 **(0.095)

Proportion black -0.075(0.119)

Proportion age 65 or older -0.579(0.574)

Proportion urban 0.434 **(0.119)

Proportion rural-farm -0.140(0.254)

Proportion home owners 0.038(0.340)

State income growth 0.143 *(0.073)

State dummies no yes yes yes

Congress dummies no yes yes yes

Notes: Variable construction is described in the text and in Appendix A.Reported beneath each estimate is the robust standard error with clustering on state-Congresscells. Coefficients significant at the 10 percent level of confidence are indicated with one star, and those significant at the 5 percent level are indicated with two stars.

37

Table 5: Main Results

log (Proportion of log (Proportion of Presence offederal employees) military population) military installation

OLS OLS OLSNumber of observations 1303 2157 2157R-squared 0.5260 0.3935 0.1944

log (District area) 0.088 ** 0.355 ** 0.091 **(0.017) (0.051) (0.015)

Coast district 0.092 ** 0.620 ** 0.118 **(0.039) (0.115) (0.030)

Border district 0.052 0.163 0.018(0.052) (0.144) (0.051)

Washington DC area 1.382 ** 1.662 ** 0.277 **(0.188) (0.299) (0.090)

Major city 0.101 ** 0.117 -0.003(0.032) (0.092) (0.031)

log (Population) 0.047 0.554 ** 0.325 **(0.121) (0.248) (0.079)

log (Median income) -0.136 -0.724 ** -0.206 **(0.130) (0.305) (0.095)

Proportion black 0.737 ** 0.386 -0.075(0.156) (0.376) (0.119)

Proportion age 65 or older -1.067 -7.104 ** -0.579(0.659) (1.276) (0.574)

Proportion urban 0.630 ** 1.580 ** 0.434 **(0.121) (0.424) (0.119)

Proportion rural-farm -1.596 ** -2.747 ** -0.140(0.477) (0.636) (0.254)

Proportion home owners -0.208 3.277 ** 0.038(0.511) (0.924) (0.340)

State income growth -0.217 ** -0.423 * 0.143 *(0.101) (0.232) (0.073)

State dummies yes yes yes

Congress dummies yes yes yes

Notes: Variable construction is described in the text and in Appendix A.Reported beneath each estimate is the robust standard error with clustering on state-Congresscells. Coefficients significant at the 10 percent level of confidence are indicated with one star, and those significant at the 5 percent level are indicated with two stars.

38

Table 6: Sensitivity Analysis

log (proportion of log (proportion of Presence of federal employees) military population) military installation

OLS OLS OLS

Panel A: Include political variables

R-squared 0.5297 0.3972 0.1988

log (District area) 0.090 ** 0.357 ** 0.093 **(0.017) (0.015) (0.015)

Representative's years of service 0.005 ** 0.010 * 0.005 **(0.002) (0.005) (0.002)

Representative's age -0.001 -0.004 -0.003 **(0.002) (0.003) (0.001)

Representative is a Democrat -0.015 -0.027 -0.022(0.023) (0.056) (0.023)

Panel B: Using Population Density

R-squared 0.5259 0.3879 0.183

log (Population per square mile) -0.088 ** -0.354 ** -0.091 **(0.017) (0.051) (0.015)

Notes: Variable construction is described in the text and in Appendix A.Reported beneath each estimate is the robust standard error with clustering on state-Congress cells.Coefficients significant at the 10 percent level of confidence are indicated with one star, and those significant at the 5 percent level are indicated with two stars.Included in each specification are the same control variables as in Table 4. In panel B,log (population) is excluded.

39

Table 7: First stage regression results

Dependent Variable: log (District Area)

(a) (b) (c )Number of observations 2157 2157 2157R-squared 0.8595 0.8597 0.8539

log (Number of Districts) -0.427 ** -1.435(0.144) (1.239)

log (State population) -0.526 * -1.25 **(0.150) (0.428)

log (Number of Districts) * log (State population) 0.122(0.077)

F -statistic on instruments 8.76 12.25 6.23p-value 0.003 0.001 0.000

Notes: Variable construction is described in the text and in Appendix A. Reported beneatheach estimate is the robust standard error with clustering on state-congress cells. Coefficientssignificant at the 10 percent level of confidence are indicated with one star, and those significantat the 5 percent level are indicated with two stars. The regressions also include the controlvariables appearing in Table 4.

40

Table 8: State population and 2SLS estimates

(a) (b) (c ) (d)OLS OLS OLS 2SLS

A: Dependent variable: log(federal employees)

log (District area) 0.088 ** -- 0.087 ** 0.098 **(0.017) (0.017) (0.049)

log (State population) -- -0.249 ** -0.157 * --(0.082) (0.085)

Chi-squared statistic on exclusion of intstruments (2 df) 2.174p - value 0.337

B: Dependent variable: log(military personnel)

log (District area) 0.355 ** -- 0.351 ** 0.644 **(0.051) (0.051) (0.243)

log (State population) -- -0.584 ** -0.399 ** --(0.170) (0.174)

Chi-squared statistic on exclusion of intstruments (2 df) 4.189p - value 0.123

C: Dependent variable: Presence of a military installation

log (District area) 0.091 ** -- 0.090 ** 0.279 **(0.015) (0.015) (0.116)

log (State population) -- -0.147 ** -0.100 --(0.070) (0.070)

Chi-squared statistic on exclusion of intstruments (2 df) 3.632p - value 0.163Notes: Variable construction is described in the text and in Appendix A.Reported beneath each estimate is the robust standard error with clustering on state-Congress cells.Coefficients significant at the 10 percent level of confidence are indicated with one star, and those significant at the 5 percent level are indicated with two stars.Also included but not reported is the same set of control variables appearing in Table 4.

41

Table 9: Congressional Representation from 1955 to 199584th 89th 94th 99th 104th Change1955 1965 1975 1985 1995 1955 to 1995

AK 1 1 1 1AL 9 8 7 7 7 -2AR 6 4 4 4 4 -2AZ 2 3 4 5 6 4CA 30 38 43 45 52 22CO 4 4 5 6 6 2CT 6 6 6 6 6 0DE 1 1 1 1 1 0FL 8 12 15 19 23 15GA 10 10 10 10 11 1HI 2 2 2 2IA 8 7 6 6 5 -3ID 2 2 2 2 2 0IL 25 24 24 22 20 -5IN 11 11 11 10 10 -1KS 6 5 5 5 4 -2KY 8 7 7 7 6 -2LA 8 8 8 8 7 -1MA 14 12 12 11 10 -4MD 7 8 8 8 8 1ME 3 2 2 2 2 -1MI 18 19 19 18 16 -2MN 9 8 8 8 8 -1MO 11 10 10 9 9 -2MS 6 5 5 5 5 -1MT 2 2 2 2 1 -1NC 12 11 11 11 12 0ND 2 2 1 1 1 -1NE 4 3 3 3 3 -1NH 2 2 2 2 2 0NJ 14 15 15 14 13 -1NM 2 2 2 3 3 1NV 1 1 1 2 2 1NY 43 41 39 34 31 -12OH 23 24 23 21 19 -4OK 6 6 6 6 6 0OR 4 4 4 5 5 1PA 30 27 25 23 21 -9RI 2 2 2 2 2 0SC 6 6 6 6 6 0SD 2 2 2 1 1 -1TN 9 9 8 9 9 0TX 22 23 24 27 30 8UT 2 2 2 3 3 1VA 10 10 10 10 11 1VT 1 1 1 1 1 0WA 7 7 7 8 9 2WI 10 10 9 9 9 -1WV 6 5 4 4 3 -3WY 1 1 1 1 1 0

42