Fiscal Policy over the Real Business Cycle: A Positive Theory

Revised October 2008
Fiscal Policy over the Real Business Cycle: A Positive Theory∗
Abstract
This paper extends the political economy model of Battaglini and Coate (2008) to analyze the cyclical
behavior of fiscal policy. The theory predicts that, in the short run, fiscal policy can be pro-cyclical with
government debt spiking up upon entering a boom. However, in the long run, fiscal policy is counter-
cyclical with debt increasing in recessions and decreasing in booms. Government spending increases in
booms and decreases during recessions, while tax rates decrease during booms and increase in recessions.
In both booms and recessions, fiscal policies are set so that the marginal cost of public funds obeys a
submartingale. The correlations between fiscal policy variables and national income implied by the theory
are consistent with much of the existing evidence from the U.S. and other countries, and data on tax rates
from the G7 countries supports the submartingale prediction.
Marco Battaglini
Department of Economics
Princeton University
Princeton NJ 08544
mbattagl@princeton.edu
Stephen Coate
Department of Economics
Cornell University
Ithaca NY 14853
sc163@cornell.edu
∗We thank Andrea Civelli and Woong Yong Park for outstanding research assistance. For helpful comments, we
also thank Ulrich Muller, Christopher Sims, Aleh Tsyvinski, Ivan Werning and seminar participants at the 5th Banco
de Portugal Conference on Monetary Economics, University of Copenhagen, CORE, ECARES, Einaudi Institute for
Economics and Finance, Erasmus Universiteit Rotterdam, Georgetown, Johns Hopkins, ITAM, University of Miami,
NBER, Princeton, the LAEF conference at UCSB, Simon Fraser, the X Workshop in International Economics and
Finance at Universidad Torcuato Di Tella, and York University. Battaglini gratefully acknowledges the hospitality
of the Einaudi Institute for Economics and Finance while working on this paper.

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1
Introduction
Real business cycle theory develops the idea that business cycles can be generated by random
fluctuations in productivity. At the core of this research program, the fundamental issues are how
individuals react to productivity shocks and how these reactions affect the macro economy. While
the issue of reaction to shocks is typically studied at the individual level, it can also be raised at
the societal level. How do individuals, through their political institutions, collectively decide to
adjust fiscal policies in response to changes in productivity? Moreover, what is the role of changes
in fiscal policy in amplifying or dampening shocks? Though understanding individual responses to
shocks can be addressed with the tools of basic microeconomics, understanding societal responses
requires a study of how collective choices are made in complex dynamic environments.
In the last two decades, political economy has made important progress, both theoretically
and empirically, in understanding how governments function and the type of distortions that the
political process generates in an economy. This first generation of research, however, has largely
focused on static or two period models that are not well suited to answer the questions raised by
real business cycle theory. When longer time horizons are considered, other important elements of
the environment (such as shocks, rational forward looking agents, etc) are muted. Thus, the basic
question as to how governments react to business cycles is not well understood. Because of this,
empirical analysis on the cyclical behavior of fiscal policy remains largely guided by normative
models of policy making.
In Battaglini and Coate (2008), we proposed a dynamic political economy theory of fiscal
policy. Our framework begins with a tax smoothing model of fiscal policy of the form studied by
Barro (1979), Lucas and Stokey (1983), and Aiyagari et. al. (2002). The need for tax smoothing
is generated by shocks in the benefits of public spending created by events like wars and natural
disasters. Politics is introduced by assuming that policy choices are made by a legislature rather
than a benevolent planner. Moreover, the framework incorporates the friction that legislators can
redistribute tax dollars back to their districts via pork-barrel spending. The theory yields clean
predictions on how fiscal policy responds to public spending shocks and provides a sharp account
of how politics distorts economic policy-making.
In this paper we extend this framework to shed light on the cyclical behavior of fiscal pol-
icy. This involves making two changes to the underlying economic model. First, replacing public
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spending shocks with revenue shocks generated by random fluctuations in the economy’s produc-
tivity. Second, and more fundamentally, making these productivity shocks persistent as opposed
to independent and identically distributed. Persistent shocks are essential to capture the im-
plications of cyclical fluctuations. When an economy enters a boom or a recession, legislators’
expectations about future tax revenues will clearly be influenced and these changed expectations
will impact current taxing, spending, and borrowing decisions. For example, entering a boom will
result in more optimistic expectations about future revenue streams and legislators may increase
debt and spending in anticipation of this.
Specifically, the model we study assumes that a single good is produced using labor. This good
can be consumed or used to produce a public good. Labor productivity follows a two state, serially-
correlated Markov process. When productivity is high, the economy is in a “boom” and, when it
is low, a “recession”. While this is obviously not the most realistic assumption about the cyclical
evolution of productivity, it captures in a simple way the core idea that current shocks change
expectations about the future. Policy choices in each period are made by a legislature comprised
of representatives elected by single-member, geographically-defined districts. The legislature can
raise revenues by taxing labor income and by issuing one period risk-free bonds. Public revenues
are used to finance public good provision and pork-barrel spending. The legislature makes policy
decisions by majority (or super-majority) rule and legislative policy-making is modelled as non-
cooperative bargaining.
While the incorporation of persistent shocks certainly complicates the characterization of equi-
librium, the model remains tractable. Equilibrium fiscal policies converge to a stochastic steady
state in which they vary predictably over the business cycle. Upon entering a boom, public spend-
ing will increase, tax rates will fall, but the primary surplus will increase. Over the course of
the boom, public spending will continue to increase until it reaches a ceiling level, and tax rates
and the primary surplus will decrease until they reach floor levels. When the economy enters
a recession, public spending will decrease, tax rates will increase, but the primary surplus will
fall. As the recession progresses, public spending will continue to decrease, tax rates will continue
to increase, and the primary surplus will increase. The overall fiscal stance as measured by the
long run pattern of debt is counter-cyclical: government debt decreases in booms and increases in
recessions.1
1 There are a number of definitions of “counter-cyclical” fiscal policy in the literature. Consistent with a
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Perhaps the most interesting feature of the long run cyclical behavior of fiscal policy is that
debt falls when the economy enters a boom. Intuitively, one might have guessed just the opposite.
As argued above, a boom will increase the expectation of future tax revenues and this may lead
legislators to increase borrowing so they can appropriate these extra revenues for their districts.
Indeed, this is precisely the logic of the well-known “voracity effect” of Tornell and Lane (1999).
This initution is correct, but ignores the fact that any increase in debt will have permanent effects.
Thus, such a “voracity effect”-style debt expansion can arise in the short run when the economy
first moves from recession to boom, but, once this happens, the level of debt is too high for it to
occur again.
In addition, we identify an interesting implication of the theory concerning the dynamic evo-
lution of the so-called marginal cost of public funds (MCPF). The MCPF, a basic concept in
public finance, is the social marginal cost of raising an additional unit of tax revenue. It takes
into account the distortionary costs of taxation for the economy. In our model, it depends upon
the tax rate and the elasticity of labor supply. Our theory implies that, at each point in time and
over all phases of the cycle, the equilibrium choice of fiscal policies is such that the MCPF obeys
a submartingale.2 This means the expected MCPF next period is always at least as large as the
current MCPF and is sometimes strictly larger. This prediction contrasts with that emerging from
a planning model which implies that the MCPF obeys a martingale. Political distortions therefore
create a wedge between the current MCPF and the future MCPF. Moreover, this wedge is likely
to be greater the lower is the current MCPF, the lower is the level of government debt, and the
higher is the productivity of the economy. This submartingale result is true even in economies
without persistent shocks, though we did not realize it in our previous work.
The predictions of the theory appear consistent with much of the evidence from the U.S. and
Keynesian perspective, Kaminsky, Reinhart and Vegh (2004) and Talvi and Vegh (2005) define fiscal policy to be
counter-cyclical if government spending rises in recessions and tax rates fall. Adopting a neoclassical perspective,
Alesina, Campante, and Tabellini (2007) define as counter-cyclical “a policy that follows the tax smoothing principle
of holding constant tax rates and discretionary spending as a fraction of GDP over the cycle”. Our definition is
that fiscal policy is counter-cyclical if debt falls in booms and rises in recessions. Like Alesina, Campante, and
Tabellini, our definition is motivated by tax smoothing principles. However, it recognizes the fact that in a world
with incomplete markets and unanticipated productivity shocks, these principles do not imply constant tax rates or
government spending over the cycle. While reflecting a neoclassical perspective, our definition does not discriminate
between a neoclassical and Keynesian view of optimal fiscal policy over the cycle: in both cases, government debt
will rise in recessions and fall in booms. As suggested by Kaminsky, Reinhart and Vegh (2004), the way to
discriminate between these views is to look at the behavior of tax rates and public spending. We will discuss this
point in greater detail in Section 6.
2 In our model the assumptions of the standard submartingale convergence theorem are not satisfied, so the
MCPF does not converge to a constant or to infinity as t → ∞. Indeed, we show that in the long run the MCPF
will have a non degenerate stationary distribution.
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other countries. We find supporting evidence for the submartingale prediction in tax rate data
from the U.S. and the other G7 countries. The implication of the theory concerning the correlation
of debt with changes in GDP is consistent with evidence from the U.S. and that concerning the
correlation of spending with GDP is consistent with evidence from the U.S. states and many other
countries. The theory implies that the relationship between the primary surplus and changes
in GDP depends on the phase of the cycle and thus is theoretically ambiguous. This may help
explain the varied correlations that are found in the data. The theory also offers new predictions
on the cyclical behavior of the primary surplus, tax revenues, and pork-barrel spending that await
testing.
The organization of the remainder of the paper is as follows. Section 2 explains how our paper
relates to prior work on the theory of fiscal policy. Section 3 outlines the model and Section 4
establishes a benchmark by describing socially optimal fiscal policies. Section 5 defines political
equilibrium, develops a useful characterization of equilibrium, and establishes existence. Section
6 derives the submartingale result on the marginal cost of public funds and Section 7 explores the
cyclical properties of fiscal policy. Section 8 evaluates the empirical implications of the theory and
Section 9 concludes.
2
Related literature
The bulk of theoretical work on the cyclical behavior of fiscal policy has been normative. The the-
oretical framework that has guided empirical work is the tax smoothing theory of fiscal policy with
perfect foresight (Barro (1979)). Perfectly anticipated cyclical variation in the economy generates
fluctuations in tax revenues that create the need for tax smoothing. This theory implies that
the government should perfectly smooth both tax rates and government spending by borrowing
in recessions and repaying in booms (see, for example, Talvi and Vegh (2005)). The empirical
literature on cyclicality sees the evidence from developed countries as broadly in line with these
predictions, while that from developing countries is not. In particular, government spending is
strongly pro-cyclical in developing countries.3
This has led the literature to regard the perfect
foresight tax smoothing model as an adequate positive model for developed countries but not for
developing countries.
3 The empirical literature is reviewed in more detail in Section 8 below.
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A variety of theories have been advanced to explain the stronger pro-cyclical behavior of gov-
ernment spending in developing countries. In an early attempt to explain the phenomenon, Gavin
and Perotti (1997) note that pro-cyclical policies may be induced by tighter debt constraints in
recessions. Borrowing limits in recessions would force contractionary policies; as the limits are
relaxed in booms, we would observe expansionary policies. Other authors point to the dysfunc-
tional political systems that pervade developing countries. In a dynamic common pool framework
in which multiple groups compete for a share of the national pie, Lane and Tornell (1998) and
Tornell and Lane (1999) suggest that group competition can increase following a positive income
shock which may lead spending to increase more than proportionally to the increase in income
- the voracity effect. In the context of a perfect foresight tax smoothing model, Talvi and Vegh
(2005) show that if spending pressures increase with the size of the primary surplus, then opti-
mal fiscal policy will imply a pro-cyclical pattern of spending. In a political agency framework,
Alesina, Campante and Tabellini (2007) show that when faced with corrupt governments whose
debt and consumption choices are hard to observe, citizens may rationally demand higher public
spending in a boom.
We take issue with the literature’s view that the perfect foresight tax smoothing model is
adequate to explain the cyclical behavior of fiscal policy in developed economies. First, the
empirical evidence shows that government spending tends to be pro-cyclical even in developed
economies. Second, under the more palatable assumption that cyclical variations are not perfectly
foreseen, the tax smoothing approach has trouble explaining cyclical fiscal policy in the long
run. Specifically, in environments with incomplete markets, the approach often implies that the
government should self-insure, eventually accumulating sufficient assets to finance government
spending out of the interest earnings from these assets (Aiyagari et al (2002)).4
Thus, in the
long run, this model predicts no cyclical pattern in government spending or the primary surplus.
Third, while political systems are admittedly less dysfunctional in developed countries, policies
are determined by the voting decisions of elected representatives and these representatives are
interested in redistributing to their constituents. These political forces will lead policy to depart
from the normative ideal and it is important to understand how.
4 Different conclusions arise when there are complete markets and the government can issue state-contingent
debt. We focus on the incomplete markets assumption here because we feel that it is the most appropriate for
a positive analysis. We refer the reader to Chari, Christiano and Kehoe (1994) for a comprehensive analysis of
optimal fiscal policy in a real business cycle model with complete markets and to Marcet and Scott (2007) for an
interesting effort to empirically test between the complete and incomplete market assumptions.
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We see our theory as complementary to the political economy theories of Lane and Tornell
and Alesina, Campante and Tabellini. They are interested in modelling different, and much more
dysfunctional, political systems than us. As noted in the introduction, in the short run there may
be episodes of procyclical fiscal policy that may resemble the voracity effect identified by Lane and
Tornell. However, our analysis differs from their work in that our economy is subject to recurrent
cyclical shocks rather than a one time permanent shock that is either unforeseen or perfectly
anticipated at time zero. This accounts for our conclusions that the voracity effect can not
survive in the long run.
As explained in the introduction, the theory extends our earlier work on fiscal policy in
Battaglini and Coate (2008). More generally, our work is part of a second generation of research in
political economy attempting to develop models in more general dynamic environments of interest
to macroeconomists. Examples of this type of work include Acemoglu, Golosov and Tsyvinski
(2006), Azzimonti (2007), Hassler et al (2003), Hassler et al (2005), Krussel and Rios-Rull (1999),
Song, Zilibotti and Storesletten (2007), and Yared (2007).
Finally, we note that our theory is related to, but distinct from, the literature on the political
business cycle.5
This literature focuses on cyclical effects of expansionary fiscal policies gener-
ated by the attempts of incumbent politicians to win elections. These effects arise when voters
are myopic, or when there is asymmetric information about politicians’ abilities and incumbents
use spending as a signalling device. We assume rational forward-looking voters and complete
information, so the phenomena underlying political business cycles are not present in our model.
Our goal is to study how politicians react to shocks to the real economy rather than to present a
theory of how the political system generates cycles around elections.
3
The model
3.1
The economic environment
A continuum of infinitely-lived citizens live in n identical districts indexed by i = 1, ..., n. The
size of the population in each district is normalized to be one. There is a single (nonstorable)
consumption good, denoted by z, that is produced using a single factor, labor, denoted by l, with
the linear technology z = wl. There is also a public good, denoted by g, that can be produced
5 See Drazen (2000) and Persson and Tabellini (2000) for excellent reviews of the political business cycle
literature.
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from the consumption good according to the linear technology g = z/p.
Citizens consume the consumption good, benefit from the public good, and supply labor. Each
citizen’s per period utility function is
l(1+1/ε)
z + Agα −
,
(1)
ε + 1
where α ∈ (0, 1) and ε > 0. The parameter A measures the value of the public good to the citizens.
Citizens discount future per period utilities at rate δ.
The productivity of labor w varies across periods in a random way, reflecting the business
cycle.6
Specifically, the economy can either be in a boom or a recession. Labor productivity is
wH in a boom and wL in a recession, where wL < wH. The state of the economy follows a first
order Markov process, with transition matrix


 αLL αLH



αHL αHH .
Thus, conditional on the economy being in a recession, the probability of remaining in a recession
is αLL and the probability of transitioning to a boom is αLH. Similarly, conditional on being in
a boom, the probability of remaining in a boom is αHH and the probability of transitioning to a
recession is αHL. Though in many environments it is natural to assume that states are persistent,
this assumption is not necessary for our results. However, we do require that αHH exceeds αLH,
so that the economy is more likely to be in a boom if it was in a boom the previous period.7
There is a competitive labor market and competitive production of the public good. Thus, the
wage rate is equal to wH in a boom and wL in a recession and the price of the public good is p.
There is also a market in risk-free one period bonds. The assumption of a constant marginal utility
of consumption implies that the equilibrium interest rate on these bonds must be ρ = 1/δ − 1. At
this interest rate, citizens will be indifferent as to their allocation of consumption across time.
6 In Battaglini and Coate (2008), productivity is constant and the value of the public good A is random.
7 Our basic model assumes that in the “up-part” of the business cycle there is a single productivity level wH,
and in the “down-part” a single productivity level wL. Thus, within booms and recessions, there is no variation
in productivity. While this is a rather spartan conception of a business cycle, the model can be extended to
incorporate within state productivity shocks by assuming that productivity in state θ is given by wθ + ω where ω
is an i.i.d “shock” with mean zero, range [−ω, ω]. Though the introduction of i.i.d shocks makes the distinction
between booms and recessions less clear-cut, the equilibrium of the extended model has the same structure as the
equilibrium of the simpler model described in the text and produces the same predictions of the key correlation
between macro variables. A more complete analysis of this extension is available from the authors.
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3.2
Government policies
The public good is provided by the government. The government can raise revenue by levying
a proportional tax on labor income. It can also borrow and lend by selling and buying bonds.
Revenues can not only be used to finance the provision of the public good but can also be diverted
to finance targeted district-specific transfers which are interpreted as (non-distortionary) pork-
barrel spending.
Government policy in any period is described by an n + 3-tuple {r, g, x, s1, ...., sn}, where r
is the income tax rate, g is the amount of the public good provided, x is the amount of bonds
sold, and si is the proposed transfer to district i’s residents. When x is negative, the government
is buying bonds. In each period, the government must also repay any bonds that it sold in the
previous period. Thus, if it sold b bonds in the previous period, it must repay (1 + ρ)b in the
current period. The government’s initial debt level in period 1 is given exogenously and is denoted
by b0.
In a period in which government policy is {r, g, x, s1, ...., sn} and the state of the economy (i.e.,
boom or recession) is θ ∈ {L, H}, each citizen will supply an amount of labor
l(1+1/ε)
l∗θ(r) = arg max{wθ(1 − r)l −
}.
(2)
l
ε + 1
It is straightforward to show that l∗(r) = (εw
θ
θ(1 − r))ε, so that ε is the elasticity of labor supply.
A citizen in district i who simply consumes his net of tax earnings and his transfer will obtain a
per period utility of uθ(r, g) + si, where
εε(w
u
θ (1 − r))ε+1
θ(r, g) =
+ Agα.
(3)
ε + 1
Since citizens are indifferent as to their allocation of consumption across time, their lifetime
expected utility will equal the value of their initial bond holdings plus the payoff they would
obtain if they simply consumed their net earnings and transfers in each period.
Government policies must satisfy three feasibility constraints. The first is that revenues must
be sufficient to cover expenditures. To see what this implies, consider a period in which the initial
level of government debt is b, the policy choice is {r, g, x, s1, ...., sn}, and the state of the economy
is θ. Expenditure on public goods and debt repayment is pg + (1 + ρ)b, tax revenue is
Rθ(r) = nrwθl∗θ(r) = nrwθ(εwθ(1 − r))ε,
(4)
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and revenue from bond sales is x. Letting the net of transfer surplus (i.e., the difference between
revenues and spending on public goods and debt repayment) be denoted by
Bθ(r, g, x; b) = Rθ(r) − pg + x − (1 + ρ)b,
(5)
the constraint requires that Bθ(r, g, x; b) ≥
si.
i
The second constraint is that the district-specific transfers must be non-negative (i.e., si ≥ 0
for all i). This rules out financing public spending via district-specific lump sum taxes. With
lump sum taxes, there would be no need to impose the distortionary labor tax and hence no tax
smoothing problem.
The third and final constraint is that the amount of government borrowing must be feasible.
In particular, there is an upper limit x on the amount of bonds the government can sell. This
limit is motivated by the unwillingness of borrowers to hold bonds that they know will not be
repaid. If the government were borrowing an amount x such that the interest payments exceeded
the maximum possible tax revenues in a recession; i.e., ρx > maxr RL(r), then, if the economy
were in recession, it would be unable to repay the debt even if it provided no public goods or
transfers. Thus, the maximum level of debt is x = maxr RL(r)/ρ.
We avoid assuming that there is any “ad hoc” limit on the amount of bonds that the government
can purchase (see Aiyagari et al (2002)). In particular, the government is allowed to hold sufficient
bonds to permit it to always finance the Samuelson level of the public good from the interest
earnings. This level of bonds is given by x = −pgS/ρ, where gS is the level of the public good
that satisfies the Samuelson Rule.8
Since the government will never want to hold more bonds
than this, there is no loss of generality in constraining the choice of debt to the interval [x, x] and
we will do this below.9
We also assume that the initial level of government debt, b0, belongs to
the interval (x, x).
8 The Samuelson Rule is that the sum of marginal benefits equal the marginal cost, which means that gS satisfies
the first order condition that nαAgα−1 = p.
9 By assuming that the government can choose to borrow any amount in the interval [x, x], we are implicitly
assuming that labor productivity is sufficiently high that the amount spent on public goods is never higher than
national income. A sufficient condition for this is that nwL(εwL( ε ))ε > pg
1+ε
S (see Battaglini and Coate (2008)
for details).
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