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Capital-Intensive Projects Induce More E¤ort
Central governments often subsidize capital spending by local gov-
ernments, instead of subsidizing operating expenses or labor-intensiveprojects. This paper o¤ers one explanation, focusing on the incentivee¤ects for local o¢ cials— a local o¢ cial can more easily shift the cost ofoptimizing a project to his successor on a labor-intensive project than ona capital-intensive project.
Keywords: federalism, capital subsidies, transit subsidies
Central governments often subsidize the capital costs of local projects but notthe operating costs. In transportation, for example, the federal governmentsubsidizes construction of roads, but not their maintenance; and it subsidizesthe purchase of buses but not operating costs. Why? One argument is theconcern with commitment and with durability. But it is not obvious that thefederal government would have a greater incentive to build durable projects thanwould a local government.
Relatedly, voters who currently in‡uence the central government may fear
So though the central government may promise an
operating subsidy, the local citizens may fear that the central government’spreferences will change, canceling the subsidy or imposing stricter conditions onit. The local voters may therefore prefer a capital-intensive project.
In some countries, local governments have only a limited tax base, making
it di¢ cult for them to adopt capital-intensive projects; the central governmentmay then want to subsidize such projects. In other countries the opposite mayhold. For example, in the United States local governments can issue tax-freebonds at low interest rates.
This paper takes a di¤erent approach, looking at the incentives of a local
o¢ cial, say the mayor, to exert e¤ort. We shall show that a mayor may workharder if he is responsible for a capital-intensive project than if he is responsiblefor a labor-intensive project. For on a project having low capital intensity, afree-rider problem can appear. The mayor in each period may want to leaveto a future mayor the task of optimizing the project. In contrast, a capitalproject can be optimized only when it is adopted, and so the mayor in o¢ cewhen the project is adopted may be induced to exert e¤ort in optimizing acapital-intensive project.
We …rst review other possible explanations for a bias toward capital-intensive
projects. We next present the assumptions and use a simple model to illustratethe bias in the management of di¤erent projects. We conclude with a discussionof capital subsidies as a remedy.
Several political factors can explain the adoption of ine¢ cient policies. (1) Whenthe policy makes transfers to special interests, the e¢ cient direct transfers maybe politically costly. In contrast, transfers resulting from a program that is notostensibly aimed at redistribution may fool the public, and so may face weak op-position. Tullock (1983) terms such programs “disguised" transfers. Coate andMorris (1995) formalize the argument, seeing cash as a direct transfer, whereasa public project may be undertaken either because the incumbent aims to makea transfer to some group, or because the incumbent believes the project has
social bene…ts. Cash transfers reveal that the politician is of a type who catersto special interests; for public projects the politician’s type remains uncertain.
(2) Ine¢ cient policies may commit future governments. Glazer (1989) shows
that a current government unsure about a future government’s support for aprogram will favor durable projects. Attempts to shape future preferences canlead to similar results. Acemoglu and Robinson (2001) argue that the currentmajority may favor policies that increase its size, or increase its future politicalpower, even if those policies are ine¢ cient when viewed as a¤ecting only currentincomes.
(3) Politicians can reduce future spending by committing to ine¢ cient poli-
cies; for example if spending is a¤ected by pressure group politics, then taxeswhich cause much deadweight loss will result in low spending (see Rodrik 1986,Wilson 1990, and Becker and Mulligan 1998).
(4) Relatedly, a government may increase its bargaining power over a special
interest by constraining itself to ine¢ cient programs that reduce the bene…t aspecial interest could obtain (see Drazen and Limao 2003).
Other work examines how uncertainty can induce delay. Applying the standardanalysis of option value shows the conditions under which an executive whoexpects to get more information soon should postpone any irreversible, costly,action.1
Other work relates to our assumption that a leader cares about outcomes afterhe yields power, and may take actions now to a¤ect future outcomes. Glazerand Kannianen (2007) consider a public o¢ cial’s incentive to incur the cost ofsearching for a good subordinate when the o¢ cial can shift that cost to hissuccessor.
In some countries, the tax base of local governments is small, making it di¢ cultfor them to …nance capital-intensive projects, and so inducing the central gov-ernment to subsidize capital. But conditions vary by country. In the U.S., localgovernments can issue bonds with only a small interest cost di¤erential. Al-ternatively, the federal government can give a state guarantee and then capitalsubsidies are not necessary.
1 See Arrow and Fisher 1974, Pindyck 1991, and Dixit 1992.
We make two central assumptions. First, the incumbent political leader (wewill call him the mayor) bene…ts from the project after he leaves o¢ ce. He maycare because he continues to live in the city he governed, a¤ected by decisionslike other residents are. Or perhaps the incumbent cares about future perfor-mance because he owns real property, with an optimized project generatingbetter public services and therefore higher property values. 2 Of course, oftenexternalities (negative or positive spillovers) to other jurisdictions appear. Suchexternalities can justify a central government’s concern with local performance.
But since the externalities can hold whatever the project’s capital intensity, weignore them here.
A second assumption is that a capital-intensive project can be optimized only
when it is adopted, whereas a labor-intensive project can be optimized in anyperiod. Take the example of urban transit, where a light-rail project requires…xing the routes for the tracks before the project is even completed, whereasthe less capital-intensive bus routes can be changed any time. This asymmetryin timing means that a mayor cannot impose on a later mayor the cost ofoptimizing a capital-intensive project. But a mayor who does not optimize alabor-intensive project may expect a later mayor to incur the cost of optimizingthe project.
We compare the behavior of a mayor when faced with two types of projects.
One is a capital-intensive project, which can be optimized only when the projectis adopted. A labor-intensive project has no design of capital. But its operationcan be optimized in any period; optimizing a project in one period generatese¢ cient operation in all future periods, and allows for no further improvement.
An optimized project (whether capital-intensive or labor-intensive) yields
bene…t VH in each period; a non-optimized project (whether capital-intensiveor labor-intensive) yields bene…t VL, with vH > vL. We normalize the bene…ts,with vL = 0. A mayor who optimizes a project bears a cost F . A mayordiscounts future bene…ts by the discount rate r.
Consider …rst a capital-intensive project, which can be optimized only by themayor when the project was adopted. The bene…ts when he works on optimizingare
2 Relatedly, Alesina and Tabellini (2004) argue that when a bureaucrat’s utility increases
with his perceived competence, career concerns can motivate bureaucrats.
A current mayor who does not optimize has 0 bene…ts. So the mayor opti-
Consider next optimizing a labor-intensive project. As before, a mayor who
optimizes a project has expected discounted bene…ts of H(1+r)
as with optimizing a capital-intensive project.
Recall that a mayor who does not optimize a project bene…ts from optimiza-
tion made by a successor, but saves the cost of the e¤ort F , as this is individ-ualized e¤ort, not outsourced project preparation. Then a current mayor whodoes not optimize the project whereas his successor does enjoys bene…ts
The mayor therefore optimizes the project if F < vH . Notice that this conditionis more stringent than the condition for optimizing a capital-intensive project,which was F < 1+r (v
The interesting case has the inequality F < vH
violated, so that no Nash equilibrium has a pure strategy, in which the mayorin any period optimizes a labor-intensive project with probability 1.
The Nash equilibrium will instead have mixed strategies.3 Let the probabil-
ity that any one future mayor optimizes the project be s. If the current mayordoes not optimize the project, then with probability s his successor in the nextperiod will; with probability (1
s)s his successor in two periods will, and so on.
The current mayor’s expected bene…ts when he does not optimize the projectare thus
In an equilibrium with mixed strategies, a mayor is indi¤erent between optimiz-ing the project or not, so that
We must check that this value of s lies in [0; 1] when F < 1+r (v
is, when the mayor would not optimize the project. Using (6) we …nd indeed
3 Though we discuss mixed strategies, similar results can appear with correlated equilibria.
For example, s could be the probability that the next mayor will be a Democrat, and theequilibrium could have a Democrat optimize a labor-intensive project, whereas a Republicanwould not.
Figure 1 Equilibrium optimisation effort probabilities s for
given project characteristics F/v and interest rates r
Range of projects whereoptimisation is worthwhilefor capital type projectsWhen r=0.05
that s = 0 for F = 1+r . The incumbent would optimize neither a capital-
intensive nor a labor-intensive project. We will …nd that s = 1 for F = 1.
This means that for a whole range of projects with 1 < F < 1+r a mayor
is indi¤erent between a labor-intensive project and a capital-intensive project.
In each of these problems, the mayor optimizes a labor-intensive project onlywith probability s < 1. If, instead, the mayor had a capital-intensive project,he would have optimized it.
We illustrate in Figure 1 the probability s that a mayor optimizes a labor-
intensive project that had not already been optimized. The …gure is limited tovalues of F within the range 1 < F < 1+r ; it considers two discount rates
(5% and 20%). At a low discount rate, up to F = 1+r = 21), the mayor
would optimize a labor-intensive-project. For high values of F , we see that
the probability s decreases. In the whole range of F values considered. Recall
that a value of s < 1 means that a mayor may not optimize a labor-intensiveproject, resulting in ine¢ ciency.
Consider next a higher discount rate for the mayor (20%). We see that
the mayor would optimize a capital-intensive project if ( F = 1+r
How important is the lack of optimizing a labor-intensive project? In the rangeof projects with 1 < F
< 1+r ; the mayor enjoys the same utility under a
capital-intensive project he optimizes as under a labor-intensive project he does
not. But because the mayor does not consider the e¤ort F shifted onto hissuccessors, a mayor’s utility can di¤er from social welfare.
Welfare under a capital-intensive project is
labor-intensive project optimized by a mayor with probability s (consideringthe e¤ort of the mayor and his successors) is
The welfare loss L under a labor-intensive project compared to a capital-
so that for small values of s the e¢ ciency loss approaches 100%. This makessense, as low values of s mean that any mayor is unlikely to optimize a labor-intensive project, though such optimization increases aggregate welfare. Buts itself declines with r (see Figure 1), so after substitution by the equilibriumvalue of s (6), we obtain the welfare loss as a function of the discount rate r.
So in our example of Figure 1, the welfare loss is approximately 5% for r = 5%,and 17% for r = 20%.
The intuition is that higher discount rates reduce the probability of optimiz-
ing a labor-intensive project. For a capital-intensive project, the future bene…tsof optimizing it also decrease. But, in the range of values considered, the mayoralways optimizes a capital-intensive project. In contrast, the probability of op-timizing a labor-intensive project declines with the discount rate, and so thewelfare loss rises with the discount rate.
Of course, the absolute welfare loss AL is a function of the net bene…t of
optimizing a project. This absolute loss declines with F and with the discount
So higher discount rates reduce what is at stake when the mayor optimizes
a project, absolute losses decline but relative losses increase. The value F is
the relative cost of optimizing a project compared to the bene…ts, and so a highcost of optimizing a project makes low probabilities of optimizing result in asmall loss of welfare.
If the mayor uses a di¤erent discount rate r from the social discount rate (i),
the expressions for absolute and relative welfare loss change. If the parameterscontinue to be such that it is socially optimal to optimize a project the loss is
This loss increases with the discount rate used by the mayor. A mayor with
a short time horizon will not optimize a labor-intensive project, generating ahigh e¢ ciency loss.
How to correct the welfare loss under labor-intensive projects? We can think ofregulatory, institutional, and incentive policies. In assessing policies we shouldconsider the limited information that the central government may have aboutlocal conditions, and to consider possible distortions that these policies generate.
A starting point may be for the central government to forbid, or to refuse to
fund, labor-intensive projects when a capital-intensive project o¤ers the sameservices at the same cost of optimizing a project. Such a blunt policy would,however, reduce opportunities for creativity at the local level. A more intel-ligent federal oversight may be to rely on yardstick competition, so that thechoice of ine¢ cient labor-intensive projects could be detected. But this type ofoversight may be di¢ cult in a mixed-strategy equilibrium: one may sometimesobserve serious optimization e¤orts and sometimes not at all. Large variationin the quality of a labor-intensive project remains a good signal to detect theine¢ ciency we describe.
A more institutional approach would extend the term limits of the politi-
cians. An extension of the term limit implies that a mayor will see higherrewards for optimizing a labor-intensive project. Extending term limits hasobvious drawbacks when the politician in o¢ ce is ine¢ cient or pursues othergoals.
A more straightforward, approach is to subsidize a capital-intensive project.
But such a subsidy also has drawbacks. The subsidies may induce a local gov-ernment to adopt too many projects, and to favor capital-intensive projectswhen labor-intensive projects would be more e¢ cient.
A fourth type of policy would be to reduce the costs of e¤ort for the lo-
cal policy maker. But as these are individualized and can consist of politicalopportunity costs, this is di¢ cult to operationalize.
This paper claimed that capital-intensive projects induce greater e¤ort by publico¢ cials than do labor-intensive projects. It is di¢ cult to observe e¤ort, and evenmore di¢ cult to test the hypothesis. Yet some evidence supports the hypothesis.
Obeng and Sakano (2000) contrast how total factor productivity in the pub-
lic transit industry responds to operating subsidies and to capital subsidies.
Our model would predict that local o¢ cials put more e¤ort into using capitale¢ ciently than into improving ongoing operations, and therefore that capitalsubsidies enhance productivity growth more than do operating subsidies. Theauthors …nd that.
When the e¤ects we discuss apply, voters will favor capital subsidies over op-
erating subsidies. That is the common pattern in the United States. Of course,some operating policies have little political appeal; we rarely see a politiciancelebrating the good maintenance of an old sewer line. But neither do politi-cians seek publicity over the construction of a new, technologically sophisticated,
sewer. So we must ask why voters may prefer that the federal government sub-sidize building but not maintaining sewer lines; the model presented above givesone answer.
The bias by the U.S. federal government toward subsidizing construction,
but providing no assistance for maintenance or other operating expense, is welldocumented by Cromwell (1989). For example, in 1988 the federal governmentprovided grants to states to complete, rehabilitate, and reconstruct the inter-state highway system at a 90 percent matching rate. Discretionary grants fromthe Urban Mass Transit Administration (UMTA) subsidized construction of ma-jor rail and subway systems with up to a 75 percent matching rate. Formulagrants from UMTA paid 80 percent of the cost of regular transit vehicle replace-ment. No corresponding subsidies, however, are provided for maintenance. Thispattern is con…rmed by Taylor and Kelly (2002) in their discussion of Federalpublic transit policy.
The bias toward capital-intensive projects will vary with conditions. For ex-
ample, term limits will increase the bias— an incumbent who does not addressmaintenance problems or ine¢ cient operations knows that his successor may.
Though we have no data to test for this e¤ect, our approach o¤ers a predictionopposite to most models of term limits, namely that short terms of o¢ ce leadpoliticians to focus on short-term problems, rather than on how best to imple-ment a new construction project. The length of the time horizon can a¤ect notonly the level of e¤ort by a public o¢ cial, but also the distribution of e¤ort.
vH Bene…t from project in each period from an optimized project
i Intertemporal discount rate of the mayor if it di¤ers from r
s Probability an o¢ cial optimizes a project if his predecessor had not
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Copyright 2008 @ the author(s). Discussion papers are in draft form. This discussion paper
is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author.
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