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DEWEY
ir\
o. <9
$-0*
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
Inflating the Beast:
Political Incentives
Ricardo
J.
Pierre
under Uncertainty
Caballero
Yared
Working Paper 08-07
January 15,2008
RoomE52-251
50 Memorial Drive
Cambridge,
02142
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paper can be downloaded without charge from the
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1
•
I
Inflating the Beast:
Political Incentives under Uncertainty
Ricardo
J.
Caballero and Pierre Yared*
January 2008
Abstract
High commodity prices and a sustained global expansion have brought about a
new
policy
dilemma
for
many
economies:
much wealth and what should be
the
Why
are governments accumulating so
response to this abundance?
fiscal
In this
paper we characterize how politicians' rent-seeking incentives and their interaction
with political and economic uncertainty
economy model
the standard political
affect the
management
of abundance.
of debt, the presence of political risk leads
current governments to over-borrow in order to starve the beast.
economic
risk is significant,
we show that the presence
gives rise to an option value of rent-seeking
.
relative to political risk, the standard result
incentive to over-save or inflate the beast.
also hedges less than
rules that
weaken
social welfare.
is
is
if
economic
risk is large
overturned and politicians have an
In the latter scenario, the government
we show that
and the option value
One implementation
However, when
of rent-seeking politicians
In this case,
socially optimal. Finally,
political risk
In
incentive compatible
of rent-seeking can
improve
of such rules takes the form of contingent tax
caps (lower during booms). In contrast, standard
fiscal rules
are suboptimal since
they do not address the central problem of high taxes.
JEL Codes:
Keywords:
E6, H2,
H6
Public funds, politicians, retained rents, starve the beast, inflate the
beast, option value of rent-seeking,
*MIT and NBER, and Columbia
commitment, hedging,
University, respectively.
We
fiscal rules,
tax-caps
are grateful to Stefania Albanesi
Patrick Bolton for comments and to Jose Tessada for research assistance. Caballero thanks the
financial support. First draft:
November
2007.
and
NSF
for
Introduction
1
Not long
ago, over-borrowing
was the typical
financial concern for sovereigns.
with the prolonged expansion of the world economy and sustained
prices, the
concern in
many
instances
on the other
is
rise in
side of the spectrum.
Today,
commodity
All around
the world, governments are creating "wealth funds," which, combined with central banks'
reserves,
add to around 8
trillion dollars
the beginning of the next decade
What
these large funds?
In this paper
characterize
we
how
is
(see, e.g.,
the optimal
fiscal
affect the
management
economy model
a rent-seeking government to save
However, this analysis
savers in the world
are governments creating
response to this period of abundance?
politicians' rent-seeking incentives
In the standard political
1
Why
Johnson 2007).
focus on a particular dimension of the answers to these questions:
and economic uncertainty
the beast.
today and could easily double this amount by
less
is
and
their interaction with political
of abundance.
of debt, the presence of political risk leads
than a benevolent government in order to starve
inconsistent with the fact that
economy can be categorized
some
of the biggest
as rent-seeking governments. This pattern
extends beyond a few special cases. For example, the
first
column of Table
1
categorizes
governments as high versus low rent-seeking based on three standard indicators of
tutional quality.
almost
2
2% more
shows that
It
of their
GDP
Table
1:
in 2006,
-.011
High Rent-Seeking
.007
Our model addresses
high rent-seeking governments on average saved
Average Surplus-GDP Ratio (200(
High Fiscal Uncertainty
(N =
(N =
89)
84)
this inconsistency
ative to political risk, the standard result
an incentive to over-save or
insti-
than low rent-seeking governments.
Average
Low Rent-Seeking
We
is
Low
Fiscal Uncertainty
=
(N =
.019
{N =
25)
-.023 (N
64)
.053
(N =
45)
-.046
39)
by showing that
if
economic
risk
is
large rel-
overturned and rent-seeking politicians have
inflate the beast relative to
a benevolent government. In our
framework, these excessive savings do not result from a standard precautionary motive
and are instead the
result of
an option value of rent-seeking, whereby politicians have
an increased incentive to postpone rent-extraction as economic
theoretical result
high levels of
^ee
2
is
fiscal
volatility increases.
in line with the observation that high rent-seeking
uncertainty save the most.
As an
illustration,
This
governments facing
Table
1
categorizes
Alesina and Perotti (1994) for a survey of the literature on the political economy of debt.
See Appendix for details on data construction.
countries as having high fiscal uncertainty
own
since governments often
The
they are significant exporters of
if
oil
or ore,
these resources and are exposed to their price volatility.
table shows that in the subset of countries facing low uncertainty, high rent-seeking
governments save
less
than low rent-seeking governments, which
tional understanding of the political
experiencing high
fiscal
economy
is
in line
with the conven-
However, in the subset of countries
of debt.
uncertainty, high rent-seeking governments save
more than low
rent-seeking governments. 3
Our main
by two
results are driven
and the intertemporal reallocation of
abundance of
forces: the current
fiscal
resources
rent-seeking. In our model, rent-seeking politicians
are partially benevolent since they are not only concerned about deadweight losses from
taxation, but they also value rent-extraction. If fiscal resources are very scarce, the benevolent
component
if fiscal
prevails,
and there
is
no concern with rent-seeking
resources are abundant, the questions of
to extract rents
become
With regards
how much
activities. In contrast,
and, most importantly,
when
central.
to the timing of rents, the calculations of the current government consid-
government. Since rent-extraction can induce a deadweight
ers the actions of the future
from taxation, the future government has a higher incentive to extract rents during
loss
booms than during
extract rents at
In fact,
recessions.
all (i.e., is left
if
the future government
with enough resources
for it),
booms, since otherwise rents could have been extracted
government always
prefers.
it
is
given the chance to
would only do so during
earlier in time,
This asymmetry introduces a
which the current
call option-like
element in the
payoff of the future government, which increases in value with an increase in aggregate
uncertainty.
By
postponing rent extraction and increasing public savings, the current gov-
ernment "purchases" more options and hence
if
political risk
which
is
is
likely to
raises
expected rent-extraction. However,
high, then the option value does not benefit the current
Thus, whether economic uncertainty leads to under- or
be replaced.
over-saving depends on the relative importance of political versus economic
Given the importance of low
inflate the beast scenario,
it
political risk
and high economic
follows that our result depends
sufficiently incomplete, since otherwise, effective
ative to political risk.
3
Our
example,
GDP
ratio,
1
a regression of surplus to
and
(iii)
risk in generating
ratio
an interaction term of the
on
(i)
economic uncertainty remains low
latter
the high rent-seeking
two variables, the
an
financial markets being
are not sensitive to our discontinuous definition of volatility.
GDP
dummy,
(ii)
fuel
rel-
we
For
exports to
coefficients are -.027, .006,
and
with the first and last terms significant at the 5% level. Our characterizations of Table
survive conditioning on terms of trade growth. It also survives defining institutional quality using only
.308, respectively,
1
on
risk.
In the cases in which the inflate the beast scenario prevails,
characterizations in Table
in
government
constraint on the executive (see Appendix).
show that
if
hedging markets exist but are expensive to use, then the government not only
has an incentive to over-save but also one to under-hedge.
By
hedging, the government
reduces the effective aggregate uncertainty faced by taxpayers (which
also reduces the option value of rent-seeking (which
then the latter
tle political risk,
In
summary, faced with
volatility
sufficient
and
economic
an incentive to over-save and under-hedge. In
it is
beneficial), yet
government faces
it
lit-
strong and the government opts for self-insurance
effect is
which both protects taxpayers from
costly). If the
is
is
raises the option value of rent-seeking. 4
risk, partially
benevolent governments have
this context the question arises of
possible to design a set of policy rules that shift the politicians' fiscal
decisions toward those of a benevolent government.
We
start
whether
and portfolio
from the premise that since
these rules are proposed and approved by politicians, they must be incentive compatible
to the government in power.
fashion
is
negligible.
We
show that a
rule that caps taxes in a state contingent
welfare improving as long as both political and economic uncertainty. are nonPoliticians are willing to cut rent-extraction
and taxes today,
if
in
exchange
they get a commitment for similar constraints on future politicians, in particular in the
form of a commitment to cut taxes during booms.
If
the rent-seeking government over-
saves in the absence of rules, the presence of rules can induce lower public savings and
increased hedging.
but not taxes
is
This paper
We
also
show that the
typically used rule of capping public deficits
suboptimal since politicians have an incentive to keep taxes too high.
is
related to the literature
on optimal
fiscal policy
and debt management
dating back to the classical work of Barro (1979) and Lucas and Stokey (1983). 5
We
depart from this work by relaxing the assumption of a benevolent government and by as-
suming that the economy
is
managed by
and who face potential replacement. In
erature on the political
economy
of debt,
politicians
this regard,
and
who
derive partial utility from rents
our paper
in
two important
respects.
First,
we allow
we
as in this work,
replacement can lead current governments to starve the beast.
for
is
6
related to the vast
highlight
We
how
lit-
potential
depart from this work
economic uncertainty which gives
rise to
the option value of rent-seeking, leading the current government to potentially inflate the
beast. Second,
we allow the government
to determine the effect of political
to hedge this uncertainty at a
economy on the government's
premium
in order
portfolio allocation de-
4
See, e.g. Caballero and Panageas (2007) and Borenzstein and Mauro (2004) for articles advocating
an increase in hedging by governments. From this perspective, our paper can be seen as a political
economy argument for why governments refuse to adopt modern risk management practices despite the
large economic advantages of doing so.
5
See also Aiyagari, and Marcet, Sargent, and Seppala (2002), Bohn (1990), and Chari and Kehoe
(1993a,1993b).
6
See for example Aghion and Bolton (1990), Alesina arid Perotti (1994), Alesina and Tabellini (1990),
Battaglini and Coate (2007), Lizzeri (1999), and Persson and Svensson (1989).
This costly hedging scenario also allows us to highlight the importance of market
cision.
incompleteness for the option value of rent-seeking mechanism. 7
Finally, our
paper
is
related to the literature in public finance which considers policy prescriptions that take
into account the potential non-benevolence of policy-makers. Specifically,
work
of Yared (2007)
economy
paper
is
of
who
it
builds on the
introduces non-benevolent politicians to the complete market
Lucas and Stokey (1983) and who evaluates policy prescriptions. 8 The current
different
from
this
work
in three
important respects.
First, in
our model,
politi-
cians are replaced in equilibrium, and this allows us to examine the interaction between
political
and economic uncertainty. 9 Second, we focus on the portfolio allocation decision
of governments in partially incomplete markets as opposed to complete markets. Third,
we provide a procedure
This introduction
is
for the evaluation of politically sustainable fiscal rules. 10
followed by five sections and an appendix.
the environment and a benchmark in which
government.
Section 2 describes
implemented by a benevolent
fiscal policy is
Section 3 introduces politicians and describes the main mechanisms. Section
4 introduces (costly) hedging instruments and studies the government's portfolio decision
and
its
interaction with the key
mechanisms
sub-optimal (but used in practice)
describes the data in Table
1
fiscal rules,
and includes
all
and
and Section 6 concludes. The Appendix
of the proofs.
Benchmark Model: Benevolent Government
2
Economic Environment
2.1
We
of our economy.
1.
Pr {y
In period
=
a}
1,
originally studied
effect of allowing for the partial
In period 0, the government raises tax revenue r
current exogenous level of assets Aq
7
economy
consider a two-period version of the incomplete market
Barro (1979). In Section 4 we examine the
to
in the model. Section 5 discusses optimal
^
to purchase assets
the government experiences an
= Pr{y = —a} =
1/2.
A\
^
completeness
and uses
its
at a price normalized
endowment shock y
The government must
>
by
= {— a, a}
for
which
finance public spending g
>
Battaglini and Coate (2007) allow for (unhedged) economic uncertainty though they do not describe
They focus on the long run equilibrium with permanent uncertainty in
which the benevolent government reaches the natural savings limit.
8
See Acemoglu, Golosov, and Tsyvinski (2007) for a similar application to a Mirleessian economy
without government debt or aggregate shocks.
9
A subtle difference which allows for this interaction is the partial benevolence of politicians in our
framework which directly exposes politicians to economic risk.
10
In this regard, our paper is related to the work of Kydland and Prescott (1977) which considers
the role of limited commitment and policy rules but that maintains the assumption of a benevolent
government which we relax.
the option value of rent-seeking.
which represents an increase
decline in commodity-reserves.
the increase in
liabilities
The government's
period
The government accommodates
by raising taxes t\
budget constraint
=.A 1
t
and
period
its
due to factors such as an aging population or
in liabilities
the
endowment shock and
and by using accumulated assets A\. u
>
is
-A
(1)
,
budget constraints under the high and low shock, respectively,
1
= g-Ax-a,
= g-A +
rf
t\
quadratic, so that social welfare
is
equal
(2)
(3)
For simplicity, this deadweight
loss.
to:
and
cj.
x
Raising revenue creates a deadweight
are:
loss is
12
(4)
Optimal Policy
2.2
To
fix ideas,
we
describe the benevolent government's policy which maximizes household
welfare (4) subject to (1), (2)
,
(3),
and To,rf rf >
,
ernment using assets to smooth the deadweight
deadweight
follows a
loss
is
random
equal to the tax
itself,
volatility
instance, taxes
loss of taxation,
which
is
t
\
" +
1 1
entails the gov-
and since the marginal
¥^
increasing in the volatility of the
In order to focus on interior solutions for taxes,
The
it
walk:
would be perfectly smooth with tq
Assumption
Specifically,
the optimal interior solution admits a tax which
to=
with a
0.
1 (Positive
^-^ >
Taxes)
(5)
endowment
a.
If
a
—
0, for
— t^^=t\.
we assume:
a.
following proposition characterizes the solution to the benevolent government's
All of our results can be extended to an infinite horizon
upon request.
standard, an open or closed economy
economy experiencing
a.
temporary endowment
shock. Details available
12
As
which households possess quasi-linear preferences and in
is associated with a convex deadweight loss function
of revenue generation. For expositional simplicity, we assume such a function to be quadratic.
is
which the government
is
in
constrained to linear taxes
We
problem. All proofs are in the Appendix.
ment with superscript
denote the policies of a benevolent govern-
b.
Proposition 1 The benevolent government chooses
=
r
Tj
g
b
Note that the
savings
It
is
'
—a =
— — and
-
'
A\
is
independent of a. This absence of precautionary
provides a useful benchmark for understanding
economic
3
satisfy:
a result of our assumption of a quadratic cost of taxation (certainty equivalence)
cians can alter the
in
2
level of savings
t1
which
+A
l
'
+a=
'
policies
way
in
is
independent of a precautionary motive.
Economy with Rent- Seeking
In the standard political
economy model
governments to over-borrow
significant,
we show
Politicians
of debt, the presence of political risk leads current
in order to starve the beast.
However, when economic
risk is
that the presence of rent-seeking politicians gives rise to an option
value of rent-seeking. In this case,
the standard result
incentives of rent-seeking politi-
which the savings decisions of governments respond to changes
manner which
risk in a
how the
is
when economic
risk is large relative to political risk,
overturned and politicians have an incentive to over-save or inflate
the beast.
3.1
Economic and
Political
Environment
In order to consider the impact of rent-seeking politicians,
benchmark economy
who
values social welfare, but
extracted in period
and
public spending, so that
1,
is
managed by a
also values rents
respectively.
(1), (2),
and
first
In particular, imagine
to allow for rent-seeking.
benevolent government, the economy
we must
instead of a
partially benevolent politician
>
x
if,
modify our
and
x\
>
These rents are financed
for j
= H,L
in the
who
which are
same fashion
as
the modified economy become, respectively:
(3) in
r
=
Ai -
t"
=
g
r\
=
g-A +a + x^.
A +
x
(6)
,
- A - o + x" and
x
x
,
(7)
(8)
Like households, politicians value social welfare
The
conditional on being in power.
q
€
he remains in power
(0, 1)
probability
1
—
q he is replaced
consumes the rents
and consumes rents x[
1
With
.
=
for j
probability
H, L, and with
1
who
instead
independent of and occurs together with the
is
Regime changes are not
realization of the shock to y.
—
values rents x
with an identical politician in period
Replacement
x\.
chooses t\ and x{ for j
politician in period
in period
However, they also value rents
(4).
H, L which maximize
The period
insurable.
1
politician
his welfare
JziL+fcj,
subject to (7) and (8) for 9
which parameterizes the
our introduction and Table
light of
olent,
>
(9)
1,
politician's desire for rents. In
one can think of 9
=
as representing a benev-
low rent-seeking government and a government with 9 >
as a high rent- seeking
government.
Given the behavior of the period
and A\ which maximize
1
politician chooses tq, Xq,
politician, the period
his welfare
E (- I
i'Y +9xo+q9xi
subject to
period
rents
1
The
(6),
where we have taken into account that the period
(i.e.,
utility
becomes the period
1
from rents captures the
is
Battaglini and Coate, 2007) since
consequences
for given taxes.
implies that politicians are
This
more
is
flexible
in period
.1
politician
period
1
this
environment
amounts to a transfer with no distortionary
it
an important assumption
13
loss
his choice of
of limited
our results
will
it
relative
Whoever
acquires power
in period 0. Consequently, the period
hold
A\
affects the incentives of the
commitment
for rent-seeking, since the
utility functions,
our setting since
13
limited commitment.
Note that the presence
Under more general
with the deadweight
request.
is
must take into consideration how
combined with the incentive
in
on the intertemporal reallocation of rents
cannot commit to particular policies
politician.
toward public spending relative
natural in distortionary taxation settings (see,
to the intertemporal reallocation of tax burdens.
Another feature of
politician receives
politician) with probability q.
politician's bias
to consumers' preferences. Its linearity
e.g.,
(10)
)
if
is
only relevant
benchmark economy
when
of Section
the curvature in the function associated
from taxes exceeds the curvature associated with
rents. Details available
upon
2
under a benevolent government
the order of events
specifically,
1.
The period
2.
Period
3.
1
absence of commitment. 14 More
in the
as follows:
x
,
and A\.
,
shocks are realized:
(a)
Economic shock: y
(b)
Period
=
{—a, a}.
politician replaced with probability 1
1
and
politician chooses T\
— q.
X\.
denote the policies of politicians with a superscript
by the period
policies chosen
Lemma
Let us characterize the
p.
1 politician.
Conditional on A\, the period
1
t{'
1
politician's strategy is
= max {5 —
p
xj'
forj
unchanged
politician chooses r
The period
We
is
is
p
y
—
A\, 6}
= max{O,0-s +
+
j/
and
,
(11)
j4 1 }
(12)
= H,L.
The marginal
deadweight
Remark
loss of taxes
p
1 rf'
The period
> t^ p
1
must
is
9.
Therefore,
also
be
9.
Alternatively,
politician always
rents are positive, the marginal
if
then rents are
0.
consumes weakly more rents when the economy
is
p
by (11) and zf'
experiencing a boom. This
rent-seeking
is
benefit of rents
>
if
taxes exceed
9,
L
x { v by
(12).
because the government's budget constraint
is
is
looser,
and
easier to achieve without additional increases in taxes. In principle, there
are three regions to consider:
Region
I:
Region
II:
Region
III:
A <
A G
A >
x
}
x
—a—9
[g - a - 9, g + o g + a - 9
g
Given the anticipated behavior of the period
remains in power in period
14
In Section
ment.
5,
we
consider
1,
1
government,
his continuation welfare
how much
9}
if
.
the period
politician
is
rents politicians are willing to sacrifice in exchange for commit-
2
V P (A )=
l
{
-ig-l Cg+^i)
-Y.+
If
+
If
(6
+ a-g + A
1)
WO-9 + Ai)
A\ < g — a — 9, the government
in period
use government resources for rents in period
[g
ie
1 is
Region
I
Region
II
Region
III
relatively poor, so that
it is
.
inefficient to
For intermediate values of Ai in the range
1.
— a — 9,~g + a — 9], rents are appropriated only under a favorable y shock
Ai > g + a — 9 rents are appropriated under both shocks in period 1.
If
the period
politician
is
thrown out of power
in period
1,
in period
1.
his continuation welfare
is
f
V N (A l )=l
[
- fr~Y +g2
Region
I
-l£- Iffii2=dil!
Region
II
-f
Region
III
,
where we take into account that he receives no benefit from the rents appropriated by the
period
1
politician.
Collecting terms,
we have that
max
the period
-^ + Oxq + qV p [A,) +
s.t.
It is
1
,
and t
,.t
(1
>
apparent from the objective that as long as q
we can disregard
date
(6)
region
politician to
III.
The date
consume
problem can be written
politician's
-
q)
V N (A
we
x )
0.
<
1,
which we assume throughout,
politician will never leave
enough resources
rents in both states of the world, for in such case
better for the current politician to consume with certainty a bit
the next sections
as:
more
it is
for the
strictly
rents at date
0.
In
characterize the solution to this problem in the remaining regions.
3.2
Starve or Inflate the Beast?
Figure
1:
Savings by Government Type
Benevolent Government
Figure
1
illustrates the choice of
level of political risk.
15
Rent-seeking Government
A\ as a function of economic uncertainty
There are two
sets of
important results in this
refers to the slope of politician's saving function
refers to the level of savings for different values of
discuss the
first set
The
figure
one
We
value of
focus on the level results.
shows that whether politicians save
ernment depends on the
first
economic uncertainty.
when explaining the option
of results in the next section,
we
The
with respect to economic uncertainty.
The second
rent-seeking, while here
figure:
a given
for
relative
less or
more than a benevolent gov-
importance of economic and
political uncertainty.
standard political economy model focuses on cases of low economic and high
uncertainty (low a and low
q),
which leads to the
classic
The
political
"starve the beast" result of
depressed savings (or higher debt) under politicians relative to a benevolent government.
However,
it is
clear
from the
takes place, the result
is
it
The
3
2
following proposition summarizes this discussion.
in
is
in
A >
g
—
the figures are (Ao^g^O.q)
10
29.
=
The
a situation of relative abundance,
politician chooses positive rents at
(Abundance)
The parameters chosen
the opposite configuration of uncertainty
ensures that the economy
in the sense that the period
Assumption
when
rather one of "inflate the beast", or higher savings relative to
a benevolent government.
assumption preceding
figure that
(15,80,40,
.9).
some
date.
Proposition 2 A\ > (<)A\
if
a > (<)0(2
-
g-A
q)
2
'
Importantly, the high savings in the politicians' equilibrium needs not represent good
news
are
for society, as these savings are
by future rent extraction. Figure
state at date
l.
16
rents at date 1)
not so
and during the high
For low levels of economic uncertainty, the economy
and an increase
the economy enters region
in uncertainty lowers savings
II (positive
in this uncertainty leads to
boom
driven by tax-stabilization as they
2 illustrates rents at date
extraction (to be explained in the next section)
to the
much
state in date
.
At higher
rents at date
1
is
in region
I
(no
and increases early rent
levels of
economic uncertainty
in the high state)
and an increase
an intertemporal reallocation of rent extraction from date
1.
Figure
2:
Rents by Government Type
15
25
20
30
Figure 3 illustrates the path of taxes behind these rents and savings. There are three
results that stand out: First,
on average, taxes are higher
Second (bottom panel), as economic uncertainty
rises,
in the presence of politicians.
high public savings by politicians do
protect taxpayers during recessions since, unlike the case for the benevolent government,
taxes increase less than one for one with uncertainty. Third, and most importantly (middle
panel), politicians
fail
to cut taxes during booms. Thus, for high economic uncertainty,
politicians extract a large
16
amount
of rents during
Recall that rents in the low state at date
1
booms (second panel
are always zero since q
11
<
1.
of Figure 2), as
they arrive to that state with high savings and unwilling to cut taxes.
Figure
Taxes by Government Type
3:
5
10
20
15
25
3.3
Option Value of Rent-seeking and
Let us
now
tainty,
which we describe
Corollary
Why
30
Political
Risk
return to the slope of the response of savings to changes in economic uncer-
1
A\
is
in the following corollary to Proposition
a for a > (<)9
increasing (decreasing) in
—
(1
2:
q) /2.
are public savings affected by economic uncertainty in the political equilibrium?
Or, what breaks the certainty equivalence result of the benevolent government? In a nutshell, it is
boom phase
the unwillingness to cut taxes during the
a sort of option value of rent-seeking which
rises
at date 1 that introduces
with economic uncertainty. This option
value increases the return to savings as long as political risk
is
low relative to economic
risk.
That
is,
while both the benevolent and rent-seeking government increase taxes during
recessions, only the former lowers
by saving more
it
protects the
boom. Going back
which taxes do not
economy during
to Figure 3,
rise
them during booms. Thus the government
we
recessions
see that there
is
is
it
increases rents during a
a range of economic uncertainty
during recessions when politicians are in power. This
example of the mechanism behind the option value
in uncertainty
and
accomodated with a one
economy from higher taxes during
for
recessions.
12
realizes that
is
in
an extreme
of rent-seeking. In this case, the rise
one increase in savings that insulates the
However, these higher savings also translate
one for one into additional rents during the high
state, since as the figure
shows politicians
do not cut taxes during booms.
The
when
increasing relation between public savings and economic uncertainty turns around
political risk
is
high relative to economic risk (the condition in the corollary) because
in such case the option value of rent-seeking
governments, in which case the
most
likely
goes not to the current but to rival
economic uncertainty exacerbates the incentive to
rise in
starve the beast.
More
formally, the marginal value of savings
from economic
risk
is:
^W + Tf).
(13)
In a model without rent-seeking, optimality requires that this value be equal to the marginal cost of saving which
from
is
(13) the cost of saving
r
In a
.
due to
model with rent-seeking,
politicians
must deduct
political risk:
-\{l-q)6.
(14)
Expression (14) takes into account that an additional unit of savings represents a
cation of rents from period
with probability
boom which
(1
—
q),
to period
and that
for
go to another government
margin these rents are worth 9
the region that concerns us the most
political uncertainty (region II)
is
at the
may
in the event of a
occurs with probability 1/2.
More importantly
political risk
that these rents
1,
reallo-
term
—the
role of political
—high economic and low
economy
is
not only to add the
(14) to the government's calculation, but also to alter
rf
in (13)
which
not only larger than under a benevolent government but also does not decline as the
size of the
risk
term
boom
(14),
rises.
it is
In
summary, while the value
of savings
is
reduced by the political
increased by the presence of economic risk in (13) as
a
increases.
Figure 4 illustrates these different effects in the benevolent and politicians' cases. The
two top panels describe the values of
(13)
and
considers the marginal cost of saving, which
is
17
(14) as a function of a.
equal to tq.
The bottom panel
ll
Note that this figure describes the equilibrium value of the different components of the marginal value
and cost of savings. The option value of rent seeking rises monotonically with economic uncertainty for
a given level of savings. However, in equilibrium (and hence in the figure) savings are not constant; they
fall early on and then rise throughout (see Figure 1).
13
Figure
4:
Decomposing Economic and
Political Risk
„
by Government Type
Rent-seeking Government
r
-
1
1
1
1
1
1
10
30
w
DC
S
"2
15
_
50
The Role
We
have thus
25
30
20
25
30
-
~1
1
15
3.4
20
of Political Institutions
far described the
manner by which economic
risk interacts
with the rent-
seeking motive of politicians to generate over-saving or under-saving by a rent-seeking
government
relative to a benevolent
government.
In this section,
we
disentangle the
rent-seeking motive of the government into the component associated with political risk
(q)
and the component associated with the marginal value
the
manner by which rent-seeking governments
differ
among themselves
facing the
of rent-seeking (9) to highlight
same
level of
economic
risk
may
in their savings behavior.
Corollary 2 The following comparative
statics apply to A^:
> (<)9
1.
It is
increasing (constant) in q for a
2.
It is
increasing (decreasing) in 9 for o
>
(<)
(1
—
q) /2,
A —
Figure 5 considers the same economy as Figure
g
1 for
+
and
9 (3
—
q).
different levels of q.
It
shows
that for any level of economic uncertainty, a reduction in political risk (an increase in q)
always weakly increases savings. The intuition for this
is
related to the conventional un-
derstanding of the political economy of debt whereby a reduction in political risk reduces
14
18
the incentive to starve the beast
Figure
Savings by Political Risk
5:
65
^02
60
55
;
s
/'
'*'
'*
y
50
S
/'
/
/'
40
v
•«
Figure
Figure
6,
/
i
6:
/
/
/
.'
45
''
^
/ //
'
s
s
s
/
/
/
/
i
i
i
i
i
10
15
20
25
30
Savings by Marginal Value of Rent-Seeking
which considers savings
for different levels of 9, reiterates the novel result
achieved in our framework. For low levels of economic volatility
that a high 9 government saves less than a low 9 government since
The economy with
q
=
1
technically represents the
there are multiple solutions associated with q
=
1.
15
economy
cr,
it
it is
always the case
has a greater incentive
as q approaches
1
from below, since
to starve the beast. Nevertheless, for a high
enough
more, since the option value or rent-seeking
is
level of
er,
a high 8 government saves
sufficiently high to
induce the government
to inflate the beast.
3.5
An
Welfare, Rents, and Uncertainty
increase in economic uncertainty lowers welfare in the benevolent planner's as well as
the politicians' equilibrium.
Figure 7 plots the gap between households' welfare under
and under the benevolent government. Since the presence of
politicians
cially costly, this difference is negative
worth highlighting.
First,
and
as in
when economic
risk
is
is
so-
throughout. Moreover, there are two related results
most of the
political risk (an increase in q) raises welfare for
literature,
politicians
political
many
economy
literature,
a decline in
parameters. However, unlike that
sufficiently high, the welfare
ranking inverts, and the low
q government provides higher welfare to households than the high q government. Second,
in the region
(region
a
II),
where public savings are increasing with respect to economic uncertainty
the welfare gap relative to the benevolent government initially decreases with
economic uncertainty but then starts increasing.
rise in
The reason
savings
is
for these
in turn increases
8,
results
public savings.
is
good but eventually the combination of low
uncertainty bloats too
Figure
two
much
public savings
(i.e.,
Initially,
an increase in public
political risk
and high economic
politicians inflate the beast),
and
this
expected rent extraction by politicians. The latter point can be seen in
which shows that the economic value of rent extraction, xq
once economic uncertainty becomes very
for society to face a
system with high
significant,
and
+ \x^
for this reason,
it
,
rises
sharply
may be
better
political risk, despite the incentive to starve the
16
beast that such governments experience.
Figure
Social Welfare
7:
Under Rent-Seeking Government
q="l
-400
-450
s
'-/
.
~
/
/
x 's.,
-500
.2
>
g
-550
y'
\
13
\
X3
\
<
-
-bUU
£
5
-
^
\
'
^
//
'
-
/
/
-
/
V— -""'" *
!
0)
-650
CO
o
(/>
-700
20
Figure
8:
25
Economic Value
30
of Rents
i
q-.»
q^.U
M
|
26
s
//
// /
24
° 22
<D
3
>
g
""'/
20
ivy
o
o
w
/
18
/
.
.
vl/
-
16
14
i
i
The next proposition summarizes our
Proposition 3
1.
i
i
welfare discussion.
The following comparative
statics apply
Social welfare weakly increases (decreases) in q
17
if
q
<
(>) {A
—
g
+
39
—
a) /6,
and
2.
The welfare gap increases (decreases) in a
if
a £ (g
1
)
[6
(1
—
q) /2,
A —g+
6 (3
—
q)\.
Economy with Hedging
4
The government's motivation
importance of
endogenous.
political
to starve versus inflate the beast depends
and economic
we model
In this section
hedge some of the economic
We
risk.
However,
risk.
and the hedging premium,
both economic risk
relative
in practice the latter risk is partially
by allowing the government to
this endogeneity
show that
on the
as long as political risk
politicians save
is
low relative to
more and hedge
less
than
benevolent governments. Nonetheless, as the hedging premium goes to zero this result
is
overturned, which highlights the importance of incomplete markets behind the inflate the
beast and under-hedge outcomes.
4.1
Hedging Opportunities
Let us assume that in addition to A\, the period
a >
at unit price
it
>
a if y = —a and
equal to
0.
In period
equal to
—a
1,
government can purchase insurance
the government receives an insurance payment
Budget constraints
otherwise.
(6)
— (8),
respectively,
become:
We
refer to
a
as the
r
=
Ax -
T^
=
g
r[
= g-
amount
A +
x
+
an,
- Ax - a + xf +
Ax
+
a
+
x[
-
(15)
a,
0, tt effectively
(16)
a.
(17)
of hedging purchased
insurance has an expected value of
and
by the government. Since
this
represents the hedging premium, and
the economy analyzed in the previous sections corresponds to a case in which the hedging
premium
is
arbitrarily large so that
an economy
in
which n
—
no government would ever choose to hedge. Note that
corresponds to the complete market economy of Lucas and
Stokey (1983).
The
welfare of households and politicians along with the order of events remains un-
changed, with the exception that the period
Ax and a in period
0.
18
politician
must now
allocate savings across
Optimal Policy
4.2
As a benchmark,
we know
=
sets x$
from Section
2,
us
let
describe the actions of a benevolent government, which as
first
=
x±
=
x\
and maximizes
random
taxes continue to follow a
now depends on
premium
the hedging
The
lower tax volatility.
Lower
7r:
social welfare.
in in
equation
(5)
walk, although the volatility of taxes
it's
policies of the benevolent
As
induce higher levels of hedging and
government are described
in the next
proposition.
Proposition 4
Proposition
1.
If
If
<
a
a >
7r
g~
7r
the benevolent
°
,
2
g~
°
TV
1-7T
g(l
^i
=
ab
=
+
for
+7T
1
policies as described by
policies
which
satisfy:
- AA + 7TCT
2 + 7T 2
.
2
) + Ao-7rcr
577"^
7T
2a-Tr(g- A
»
and
)
-
2
Thus,
-
L,b
Hfi
T-,'
h
.6
government chooses
the benevolent
,
2
government chooses
+ 7T
2
low enough levels of economic uncertainty, the benevolent government chooses
not to hedge. Eventually, however, as a rises the government uses some of
its
savings to
purchase hedging contracts.
Under- hedging
4.3
Now
7r
let
>
1
us consider the policies chosen by politicians.
—
q,
so that the hedging
premium
government, which means that the scope
Then, politicians hedge
2, for
less
high enough a and
The next
is
for
Our
central case
reducing exogenous economic risk
than a benevolent government. Moreover, as
q,
Ifir
= 0ifa<
1.
aP
2.
ap <
3.
A\>{<)A\
ot
if
>
1
—
q,
if
0,
a
is
limited.
in Proposition
the politician saves more than the benevolent government.
then
^g^ -9 + A
ab >
one in which
high relative to the time horizon of the
proposition summarizes these results:
Proposition 5
is
and ap >
and
>(<)9(2-q)-^.
19
if
a >
^^ ~g + A
,
The reason
for depressed
hedging
that postponed rent-extraction serves as a substi-
is
tute for hedging.
The statements
ogous to Figures
1
of the proposition are illustrated in Figures 9
and 2 with the exception that Figure 9 adds the
function of volatility o\
19
The high
Figure
9:
_ 50
<
Savings and Hedging
.
_
.
^
'
.
_
,
45
i
i
i
i
10
19
The parameters
hedging a as a
savings lower the value of hedging for politicians,
_
N--^-
which are anal-
level of
only start hedging at very high levels of economic uncertainty.
40
10,
apparent in them that as a increases, politicians backload
It is
rent-extraction and save more.
who
and
are chosen as before with
7T
=
.15.
20
i
i
Figure
To understand the under-hedging
economic
risk
result,
Rents
10:
note that the marginal value of hedging from
is:
(18)
since
an additional unit of insurance translates into a reduction
form of lower taxes
in a
downturn and higher taxes
an
politicians, optimality (at
cost of hedging which
is ttto.
(18) the benefit of hedging
in a
model with
be equal to the marginal
economy, politicians must add to
political
due to the reduction of
In a model without
boom.
interior) requires that this value
In a
in tax volatility in the
political risk:
1
(l-q)8.
(19)
Expression (19) takes into account that an additional unit of hedging (versus saving)
represents a reallocation of rents from the
may
boom
go to another government with probability
worth 8
in the event of a
boom which
Political
—
q),
and
at the
ties
boom
during a boom.
political risk
term
(19) to the government's cal-
culation (which increases the value of hedging), but also raises
ing, the latter effect
margin these rents are
the hands of the government during a
for rent-seeking
economy not only adds the
the value of hedging).
These rents
occurs with probability 1/2. Note that (19) takes
the opposite sign as (14) since hedging
whereas savings increases the scope
(1
in period 1 to period 0.
If political risk is sufficiently
rf
in (18)
(which reduces
low relative to the price of hedg-
outweighs the former, so that politicians under-hedge relative to the
21
benevolent government.
On
4.4
We
the Importance of Incomplete Markets
have highlighted thus
how
far
the presence of economic risk reverses the traditional
understanding of the political economy of debt.
Rather than under-saving, politicians
facing sufficient levels of economic risk over-save relative to a benevolent government.
costly hedging
is
available, this insight also manifests itself into lower
more uncontingent
for
In this section
we
(in
exchange
savings) by politicians relative to the social optimum.
how our
highlight
insights
financial markets. Specifically, consider
turns out that there
It
hedging
If
is
depend on the
what happens
a critical level
1
—
q,
sufficient
as the hedging
such that
if it
incompleteness of
premium
it
declines.
drops below this value, the
previous results are overturned and the traditional intuitions related to starve the beast
are upheld.
20
We
Proposition 6
1.
ap =
2.
a?
3.
A\ < A\.
If
If
it
0ifa<
>a
<
it
discuss this region next.
b
ifa p
—
1
q,
<
1
—
q,
then
7r§,
and a p >
>0
and 9
then xf' p
if
a >
<g - A
=
,
since
tt\,
and
it
cheaper for politicians to use the hedging
is
instrument as opposed to contingent rent-seeking in order to reduce the volatility of
taxes.
its
The
existence of politicians therefore implies a novel role for hedging.
usual purpose as a buffer for downturns
(i.e.,
allows the government to frontload whatever rents
and hence
it
also reduces political risk.
That
it
reduces economic risk), but
it
could acquire during a future
hedging
political risk (19)
20
main
There
differently,
also
boom
overaccumulation of savings when
hedging economic risk also serves as proxy-
for political risk.
If political risk is large
in the
Put
it
the possibility for hedging economic
is,
risk disentangles the dual role for savings driving the
markets are incomplete.
It serves
is
is
enough that the benefit from hedging due to the reduction
high, then a low hedging
text. In this case, politicians
premium overturns the
results
under-save and over-hedge.
a continuum of solutions at the boundary q
22
=
1
—
it.
in
we emphasize
Fiscal Rules
5
we
In the previous sections
ment
highlighted
policies to differ substantially
how
the presence of politicians can cause govern-
from those of a benevolent government. This policy-
gap clearly imposes welfare costs on households which could be reduced
somehow constrained
Why
would
politicians currently in
political risk. Recall
by
in the policies they
from Section
politicians in period
rules
allow
is
power ever accept such constraints? Because of
3 that
date
politicians
cannot control policies chosen
at date 1 (political risk). Therefore,
on the politician in period
it,
then the period
this policy
may be
this section
5.1
fail
We
also
willing to sacrifice
society can
if
impose
when economic
some
a different
fiscal
conditions
rents in exchange for
describe a set of welfare enhancing rules that
One implementation
are acceptable to current politicians.
simple contingent tax caps.
we
politician
if
to ensure that taxes are cut
1
politician
commitment. In
suboptimal since they
were
Consequently, taxes are not cut during a boom, although this
1.
power
in
politicians
can implement.
would have been the preferred policy outcome of the period
government
if
show that the
of such rules takes the
form of
typical fiscal rules used in practice are
to lower taxes during booms.
Optimal Rules
Let us define
W
p
politician in the absence of rules, as
as the welfare of the period
described in Sections 3 and
4.
Then the optimal
incentive compatible fiscal rules
we
consider are associated with the solution to the following problem:
max
to ,xq ,A i ,a,Ti ,rf ,xf ,xf
E (-^ - ^]
(20)
S.t.
E
(15)
The
solution to this
t2
f
-
r2
-f -^ + 9x
(17)
,
and r 0) x
+
,
program represents a
q9x 1
j
>
W,
rf r\ zf x\ >
,
,
,
set of policies
(21)
0.
(22)
which improve household
welfare while leaving politicians at least as well off as they would be in the absence of
fiscal rules.
We
denote the solution to (20)
Proposition 7 The solution
21
Note that much
to (20)
—
—
(22) with a superscript
r.
21
(22) satisfies the following properties:
like financial contracts, policies
under rules are not allowed to depend on the
ization of political uncertainty in our economy.
23
real-
1
-
=
T
(T^A)
1
^'
By
r
(TfA) /°
—
^0
H,r
'9^1
*^0
=
reducing Xj
restore the
,p
,
1
2
SOme
date
1
politicians
random walk property
^^O'
anrf
for
now
cut taxes during
of taxes exhibited
for the current
booms and along
government as long as
economy studied
Figure
Benevolent Government
11:
Rents
(it
=
in Section 3.
Fiscal Rules
40
20
20
15
22
This
is
20
a special case of the economy in Section 4 with n
24
way
25
=
1.
30
it
faces political
as well. Figures 11
22
1)
Rent-seeking Government
60
V
the
by the benevolent government. These
tax cuts and rent reduction at date
illustrate these effects in the
-
A-
tf,p
This gain creates space
and 12
-
Xl
changes represent a welfare gain
risk.
°
Figure
-
Benevolent Government
Taxes
12:
—
(ir
=
1)
Rent-seek
bU
40
30
1
i
'
10
5
)
15
20
25
30
20
25
30
i
"
a
50
V
10
5
()
15
a
60
H~
40
•
~
i
i
20
15
a
The counterpart
Figure
13.
These savings
uncertainty and
and the
of these tax
fall for
inflate the beast
Note that the presence
and rent cuts
rise relative to
high
levels.
is
the behavior of public savings,
shown
in
the rule-less economy for low levels of economic
That
is,
the rules partially alleviate both the starve
problems, as least in the extreme regions of economic uncertainty.
of incentive compatibility constraints implies that the general shape
of savings as a function of economic uncertainty shares
much
in
common with the
rule-less
economy.
One can
rules,
interpret our results in light of the discussion of Section 3.3.
Under
fiscal
on one hand an additional unit of savings continues to serve the purpose of
ducing economic risk
(13).
However, the cost of
political risk (14)
re-
no longer enters the
government's calculations since rules are chosen so as to constrain the period
1 politi-
cian into utilizing any additional units of savings (on the margin) for tax reduction in
downturns as well as in booms.
On
the one hand, the alleviation of political risk (14)
serves to increase the marginal value of savings to the government.
the implied reduction in
rf
in (13) relative to the rule-less
economy
On
serves to reduce the
marginal value of savings to the government. For low values of economic
force outweighs the latter,
and
economy, since they counteract
rules imply higher levels of savings
politicians'
the other hand,
risk,
the former
than in the
rule-less
tendency to starve the beast. For high values
of economic risk, the latter force outweighs the former, and rules imply lower levels of
25
savings, since they counteract politicians' tendency to inflate the beast.
Figure 13: Savings
Benevolent Government
-
(7r
—
1)
Rent-seeking Government
Fiscal Rules
/
/'
/
10
We
can see
with
in Figure 14 that the
25
30
+ ^x"
economic value of rents xq
declines substantially
intermediate levels of economic uncertainty. However, since the
rules, especially at
politician
20
15
must not be worse
off
under
increase in taxpayers welfare, which
is
rules, the
counterpart of this decline in rents
illustrated in Figure 15
_
_.
.
Rent seeking
26
„
=
1)
,
1
/
/
/
/
/
/
/
/
/
/
/'
/
/
/
/
/
r
/
-
f
\
y
-
/
.-'*
\
'
i
i
'
20
10
26
i
an
which depicts the welfare
gap with a benevolent government.
Figure 14: Economic Value of Rents (n
is
,
Figure
-250
E
.
1
=
Welfare (n
15: Social
—
1)
_
.
1
—I
1
1
1
-350
/
-450
1
.
t
/
1
I
/
s
\
\
\
-
\
1
1
1
I
i
I
10
Note that there
The reason
is
is
is
that in such case
no economic motive
no constraint on date
There
is
no gain from
no
is
rules
1
=
if
there
no economic uncertainty (a
is
rent extraction
all
for cutting taxes
is
frontloaded to date
1).
result,
=
0).
and there
during the boom, which means that there
governments that can increase the date
an entirely analogous
political risk [q
30
which we do not show here
politician's welfare.
for brevity,
government
In such case the date
is
is
when
there
also the date 1
government, and hence there are no concessions by future governments that can improve
the current government's welfare
period
(i.e.,
there
is
no time-inconsistency problem
for the
politician).
Figure 16 explores the implications of rules for the level of hedging in an economy
in
which (expensive) hedging opportunities are
available.
The main new
result
is
in
the second panel, which shows that under rules, the government starts hedging at lower
levels of
economic uncertainty than in the case without
compensates
high.
More
for the lower savings
specifically,
rules.
induced by the rule when economic uncertainty
the presence of rules reduces
rf
in
reducing political risk
on the margin. For high values of economic uncertainty, economic
(18) dominates, inducing the
government under rules to hedge more than
27
is
in (18) so as to increase the
economic benefit of hedging, but also makes the value of hedging
(19) less relevant
This increase in hedging
risk
in the rule-less
economy. 23
Figure
Savings and Hedging
16:
Benevolent Government
60
(1
-
q
<
tx
Rent-seeking Government
1
1
i
1
<
1)
Fiscal Rules
1
1
i
i
1
55
.-"".'-'"''
- 50
<
45
40
~--~-'
i
.
i
i
i
25
in Proposition 7, the question arises of what types of
Given the general characterization
rules
would the period
The next
politician accept
which could improve the welfare of households?
proposition shows that simple rules which constrain the size of taxes can induce
the optimal incentive compatible policy. Specifically, consider the following constraints:
Now
(24)
imagine
and
if
the period
Proposition 8 Under
(20)23
it
Furthermore, the period
constraints lead to the
to
TQ
(23)
r?
M
<
rS(l-A)
(24)
rf
<
r
r
(l
1 politician is free
ensure that these choices make
(25).
<
Furthermore, imagine
(25).
r
TO
in choosing
must
politician
as that
(25)
to choose any policy as long as
Ai and a, the period
possible for the period
same welfare
rules (23)
if
+ A)
1
it
satisfies
politician
must
politician to satisfy (24)
satisfy (23).
We
under the solution to
and
can show that these
(20)
—
(22).
(25), politician's strategies correspond to the solution
(22).
Recall that
if
the hedging
premium is very low, n < 1 — q, the economy with politicians frontloads
more than the benevolent government. In this region the optimal
rent extraction and hedges potentially
lowers hedging. We omit this case from the main text since our central concern
with relatively incomplete markets.
fiscal rule
is
28
in
the paper
Rules which constrain the size of taxes can serve to
well off
and household
strictly better off. If a fiscal constitution
households have an incentive
better
for
implementing
it
since
it
the period
is
politician as
possible, politicians
and
can make both parties strictly
off.
Suboptimal Rules (Used
5.2
make
in Practice)
bound on the government's
In practice, rules take a different form by imposing a lower
primary surplus:
-x
t
r^-xf-g
>
s
>
sf, and
(27)
s[.
(28)
r^-xf'-s >
The motivation
for
such rules
is
to provide incentives for governments to save in order
A
to ensure that they repay their debts.
improve
to
savings and potentially
rule does not put
issue at
hand
is
is
whether such rules can
not debt overhang but
In the context of our model, (27) and (28) provide motivation
by the period
for less savings
natural question
which the
efficiency in our context in
manage abundance.
(26)
,
politician,
whereas (26) provides motivation for more
more hedging. Whatever the
an upper bound on taxes, so that
the marginal product of rents
9.
direction of the overall effect, this
in equilibrium taxes
always exceed
Consequently, social welfare cannot reach the level under
24
the rules described in Proposition 8 in this circumstance.
The next
proposition states
these results.
Proposition 9 Under
rules (26)
do not correspond to the solution
Final
6
The
—
(28), politician's strategies induce
to (20)
—
To,T^,rf
(22).
is
that the combination of economic uncertainty and
rent-seeking behavior by politicians gives rise to an option value of rent-seeking
raises the expected future return
Whether
24
from public savings as uncertainty
this option value of rent-seeking leads to less or
benefits from
9 and
Remarks
building insight of this paper
which
>
its
return.
In our context, (26)
—
If
economic
risk is
mechanism
rises.
more savings depends on who
low relative to political
risk,
then the current
(28) are generally not incentive compatible since they only constrain the period
politician.
29
government expects other governments to benefit from
and starve
the beast. However,
if
economic
risk
is
it
and
is
inclined to cut savings
high relative to political risk then the
opposite happens and the current government raises savings above what a benevolent
government would do. That
is,
the government inflates the beast. This theoretical result
serves as a potential explanation for the pattern displayed in Table
1
whereby high
rent-
seeking governments over-save relative to low rent-seeking governments in the sample of
countries that are highly exposed to
Another widespread pattern
is
commodity
the government's strong bias toward
rather than hedging economic uncertainty.
of the inflate the beast result
is
expensive).
The reason
is
price shocks.
when markets
We
show that
this
is
self- insurance
simply the counterpart
are sufficiently incomplete
(i.e.,
when hedging
that the retained rents in public savings, while costly from the
point of view of high average taxes, have the side benefit of providing low cost insurance.
Finally, yet another increasingly prevalent practice
grated to the underlying stabilization funds.
is
likely to
be suboptimal, as
it
environment we describe, which
is
the adoption of
fiscal rules inte-
We argue that this widely praised mechanism
does not address one of the fundamental problems of the
is
that of high taxes during booms.
30
Appendix
7
Explanation of Data
We
describe in this section the data behind Table
calculated using statistics from the
sources since
it
Surplus to
1.
CIA World Factbook
GDP
(2007) which
is
ratio in
2006
is
preferred to other
maximizes the available cross-section of countries. In order to categorize
countries into high and low rent-seeking countries,
we use constraint on the executive
for
a given country in 2004 from the Polity IV dataset, the rule of law index in 2004, and the
control of corruption index in 2004, the last two variables being from
and Mastruzzi
A
(2005).
country
places the country in the
is
high rent-seeking
classified as
bottom 33rd
percentile of the sample.
we use
countries into high and low fiscal volatility countries,
GDP
and ore export data
If fuel
volatility
is
classified as experiencing
available, a
If
low
and ore export data
fuel
known
fuel exports as
a fraction of
a given country which are the averages for
country
is
is
neither of these conditions
There
fiscal volatility.
is
The data
oil.
is satisfied,
we
classify
fiscal volatility
is
if it is
fiscal
in the top
then the country
a small group of countries for
unavailable, and from these,
to be significant exporters of
high
classified as experiencing
the Republic of Congo, and Equatorial Guinea as high
are
In order to categorize
in the top 25th percentile in fuel exports or alternatively
if it is
25th percentile in ore exports.
which
for
any of these indicators
and are from the World Development Indicators (2007).
available years in 2000 to 2005
is
GDP
and ore exports as a fraction of
if
Kaufmann, Kraay,
summarized
OPEC countries,
countries since they
in
Appendix Table
Al.
Proof of Proposition
Let
fi
,
i//f
tively. First
,
and
1
\\i\ represent the
Lagrange multipliers on
(1), (2),
and
(3), respec-
order conditions yield:
TH
=
H — H
T _
Ti
Ti
To
:
l
T
/i
H-l
l
=
first
order conditions,
non- negativity constraint on taxes
Proof of
Lemma
is
we
'
Mi\ and
1
Combining these
,
h
1
r
achieve (5) which yields the solution.
satisfied
1
31
by Assumption
1.
Q.E.D.
The
If
the state
is
H, the period
politician chooses
1
rf and xf
maximize
to
rf =
9
if
otherwise which leads to the solution. Analogous arguments hold
if
the state
to (7)
>
and rf xf
,
First order conditions imply that
0.
Proof of Proposition
Combine
(6), (7),
and
f
T0,XQ,T
subject
and t^ > 8
Q.E.D.
L.
is
2
Lemma
together with
(8)
1
w»
1
1
2
--Tou - Trf - -Tj +
max
xf >
(9)
ri
4
2
,rf,xf,.Tf
x
„
8
1
4
1,
to rewrite the politician's problem:
Aw
-xf + -x
VV
/
x
+
q
1
(29)
2
2
s.t.
A -
g
+ T + -rf + -t[ -xq- -xf - -xf =
j
t{
this
program. Let
(32)
>
(33)
multipliers for constraints (30)
—
0,
xf
>
T
X
case then
\x
x
(39) since q
imply that
(37), (38),
=
<
it is
implies that
from
1.
and
(40)
Since t q ,t"\r\
9.
We
ip,
t/>
,
|</>f
,
Lemma 1
is
satisfied
and i^j represent the Lagrange
Mo
+ Ml,
=
V
M'0
~
Ml
+
+
Mi
(37)
V>
(38)
(39)
<?V
lH
=
qQ
+
<t>\
+ Mi =
<?#
+
^f-
Moreover,
1.
>
(36)
~
fl
(41),
not possible for Xo
r^ =
(35)
Mo
L
Lemma
and
0.
in all future proofs that
,
x
(34)
Ha-,
=
/z
from
/j,
,
—
To
r\
>
Q
and
(35), respectively. First order conditions yield:
TO
jLtj
0,
xf >
fj,
(31)
7?>0,
be apparent from the solution here and
by the solution to
(30)
- a - xf = Tf + a - xf
x
It will
0,
<b\
;
and
9
from
= xf =
0.
(36)
—
(41)
>
which implies that
(40)
and x\
=
fi
(39),
=
0.
If this is
not the
q9 but which contradicts
then Assumption 2 and (30)
From Lemma
1,
(36)
,
(37),
and
(39), this
characterize three cases and then perform comparative statics
with respect to A\.
Case
1:
x
>
and xf
=
0.
(36)
and
(39)
32
imply that t
=
9.
From
(31),
rf
= 9 + 2a,
=
which implies that A\
=
[i x
g
-
-
By Assumption
a.
a <
2a, so that (40) requires
0(1
-
and
(39)
A\ <
2,
A\.
From
From Assumption
q) /2.
(36)
0(1
2,
and
-
g)
(38),
/2
<
-g)-^.
0(2
Case
x >
2:
=
and xf >
0.
(36)
=
imply that r
0.
From
and
(36), (38),
- g), so that A? = + o" - (2 - g), which means that A\ > (<) A\ if
a > (<) 6 (2 — q) — ^y^. It is necessary that a > (1 — q) /2 since the alternative implies
that rf > 0+2cr which contradicts (31). Satisfaction of (33) requires o < A —g+6 (3 — q)
r{
(40),
6 (2
<?
given (30) and (31).
Case
3:
=
x
and xf >
(30)
and
that
A\ > (<) A\
>
(<)
implied value of tq exceeds
a >
into (30) that
Assumption
2, this
A —
(36)
^^ -
+
g
—
9 (3
0g.
and
for (36)
(40)
= 2r -6q. Combining
= (g + a + 2A + 9q) /3. This means
imply that t\
For this case to hold,
and
(39) to hold,
which exceeds 9
q)
(1
it
is
necessary that the
this implies
-
from substitution
/2 by Assumption
q)
^^ - 9q, so that A\> A\.
a >
implies that
Proof of Corollary
and
(38),
,
and xf implies that A\
(31) to solve for r
if ct
0.
By
2.
Q.E.D.
1
This follows from the solution described in the proof of Proposition
2.
Q.E.D.
2.
Q.E.D.
Proof of Corollary 2
This follows from the solution described in the proof of Proposition
Proof of Proposition 3
From
the proof of Proposition
9
-
r-P
{-g
+ a-A +
9
(
L
t v
=
{
\
{
It is clear
(A
—
g
+
(2(g
that for q
30
—
+
9q)/3
is
)
< (A —
if
q
<
1
if 1
-
2o-/0
if
g
q
and
-
2ct/0
<
> {A Q q
<
1
< (A + 30 - a)
q
g
g
+
30
-
a) /9
,
and
/9
- 2oj9
ifl-2a/9<q<{A -g + 39-a)/9.
9q) /3
+
a) /0, social welfare
q.
9
if
9(2-q)
+a-A -
decreasing in
=
2a
-(g +
which
p
'
rl
2,
39
—
if
q
> (A -
g
+
30
a) /9, social welfare
is
a) j9
increasing in
q.
If q
>
is
a-A
2
2
f/Q-(9q) /12-9 /4
(42)
In order to evaluate the welfare cost of political economy,
note that welfare under a benevolent government
33
is
equal to
—
(g
—
Aq)
— a 2 /2.
If
a <
—
9 (1
q) /2,
then social welfare under politicians
economy
welfare cost of political
is
increasing in a.
then social welfare under politicians
economy
declining in a.
is
a >
If
is
is
9 (1
If
-9 2 -9a -a 2
equal to
-
/2
q)
,
so that the
< a < A -g+9
(3
—
q),
independent of a, so that the welfare cost of political
A -
+
g
9 (3
-
q),
from (42) and Assumption
1,
the
Q.E.D.
welfare cost increases in a.
Proof of Proposition 4
Write the program as
The
Proof of Proposition
n represent the Lagrange multiplier
straints, letting
a.
in the
additional
order condition
first
a —
<
a
^~
"
a >
If
.
2
a > tt^-j^
requires
then
0,
Trite the
we
let
(5)
and
hand
a <
2.
a.
(44)
and t\
Imagine
if
a
r
(1
— a}
= x^ =
combined with
=
Lemma
1,
+ vr).
,
:
1:
x
(37),
>
=
7r/x
(38)
/ij
+
The
a.
k.
(44)
if
a >
can be substituted into
r
and
>
9
+
+
2r
x\
=
since
Lemma
by the proof of Proposition
(31), to achieve
7TT
(39), this implies that
and xf
=
—
7TCT
=
a — a—
T}
~r
'
0,
from (36) and (39) violates Assumptions
analogously to the proof of Proposition
Case
on
where
Substitution into (30) yields:
fact that
(36)
for the non-negativity constraint
This can only be true
0.
—
(36)
side of (31),
substituted in for y applies given that optimality requires
Ao — g
which by the
hand
as in the proof of Proposition 2 imply that
a,
xq
left
is
a
= {—a +
with modified budget constraints,
and 2a to the
side of (30)
order condition
The same arguments
(43) implies that
Q.E.D.
to be positive.
to the
first
and
5
k represent the Lagrange multiplier
with y
a
in the proof of Proposition 2
left
1
imply the solution by substitution, and this
(43)
program as
— air
additional
1
H
1
/
in order for the implied value of
Proof of Proposition
adding
non-negativity constraint on
then the solution corresponds to that under Proposition
0,
7r
for the
is
1
If
with the modified budget con-
1
0.
rf =
9.
We
1
and
2.
From
characterize the three cases
2.
Imagine
a >
if
substitution of (44) into (40) contradicts q
>
34
1
0.
Since r
— n. The
=
£i
solution
=
9
is
therefore identical to
from (36) and
(39),
that in case
Case
a =
of the proof of Proposition
1
and x^ >
>
x
2:
and that the solution
Case
=
xQ
3:
if
-
>
q6
t
^
6
3
(1
1 -g~+A
—
Q
that the economy
(36), (38)
(40),
,
The
0.
a >
-g+^^
A
1
and
=
imply that t
(44)
>a
b
if
b
a >
By some
0.
left
that
ab >
hand
0,
side of (45) increases in
n <
so that the
1
contradicts Assumptions
—
—
^=
^a
1
and 2 and the
a >
ap
and the
,
fact that r\'
>
t['
p
>
q) since q
9q
a <
if
1-vr, so
part of the proof.
first
+ tt) / (1 - vr),
(1
9+<r-A -eq(2+w)/(i-*)
so
Imagine
_
if
is
>
(45)
By Assumption
0.
fact that q
need only be checked
b
>
side of (45)
otherwise proved in the proof of Proposition
b
a =
c*
it is
this
=
and rf
n)
v
fc
since
7r
6 (2
,
-
(1
-
(3
occurs
(^)>^.
hand
left
9q/
a >
q)
(40), this occurs
would imply that
algebra, this
(- + *-*)
The
By
2 hold.
establishing the
0,
we achieve
that by substitution into (30) and (31),
ap
and
1
> A -g+6
then a
,
and a >
necessarily in case 3
is
solution coincides with that of case 3 in the
after substitution of the implied solution for t
instead
If
imply that
1
identical to that in case 2 of the proof of Proposition 2.
is
analogous arguments to cases
which
7r),
.
if
Analogous arguments to those of case
0.
and xf >
proof of Proposition 2
2.
1
maximized
—
To
n.
for case 3 for
a >
at
and the
1
=
rr
verify that
fact
but this
1,
A\ > A\
^J —g + A
,
if
since
This follows from (31), the fact that
2.
by Assumption 2 and since q >
1
—
n.
Q.E.D.
Proof of Proposition 6
Follow the same
initial steps as in
and
violates (36), (39), (40),
a =
If
the solution
0,
is
the proof of Proposition
identical to that in case
<
order for (44) to hold, this requires a
Ti
=
Ai
—g — 6 (1 + 7r/2). We
a >
9 (1
7r|,
Finally,
If
+
by Proposition
we
av =
verify that
but a
b
>
0,
2,
If
a >
p
0,
(30)
and from
a >
and
(36)
0,
If
dP
= a =
then this implies that
fact that
n <
1
it
(g
0,
(31) implies that
Proof of Proposition 7
35
1
This
0.
=
(39), t
- AQ
and
/2
)
< a <
Av <
2.
x
6.
In
a
=
a—
ir6/2
> a b when a p >
is
that 6
Since
0.
<
and
~g
—A
then this follows from Assumption
implies that
then this follows from Assumptions
and
xf >
then (38) and (44) imply that
the additional requirement for this to be true
b
if
of the proof of Proposition 2.
1
determine conditions under which a p
A\ < A\.
which together with the
If
7r|.
which by substitution into
7r),
>
Therefore, x Q
(44).
Imagine
5.
ty6/2, so that 9
A\ by Assumptions
Q.E.D.
>
1
g
.
2.
-A
and
2.
This program
constraint (32)
is
identical to that of the previous sections with the exception that
ignored and replaced with constraint (21). Let A represent the Lagrange
is
on constraint
multiplier
(21). First order conditions yield
to
+
(1
+.X)-rf-.=
(1
+
/i
X,
Mo
a
<
fi x
<
If
ap >
T*n
+
+
^
(f>
,
^t 1
'
/ij,
(48)
(49)
XqO
+
+
(47)
,
+ 0f
+
(50)
(j)\,
and
(52)
—
but this violates
p
+
|r
'
1
<
1.
and the
p
,
(31).
From
The second
fact that
and the
(48)
(50)
,
(51)
K.
< rf
follows from (30)
Tq
=
/i
Xq9
x
7T/i
=
-fM 1
> xf =
but this violates (49) since q
29
-n =
+ Mi =
fi
then (50) and (51) imply that x\
0,
implies that t\
ap =
A)rf
(46)
Mo-
part of the proposition follows from (46)
first
instead
A) T
H = \9 +
X
The
=
(1
From
0.
and
(51),
if
fact that
and
(47)
x\
>
0,
^
>
0.
If
(48), this
then
ji
l
=
0,
part of the proposition in the case that
from (46)
-
(48),
rr
+
\t
-1-
2
TX
where we have used the analyses of Propositions
,
\9
'1+A
2, 5,
and
<
6.
0, then the solution described in the proofs of Propositions 5 and 6 implies that
l_H,p, lL,P
a p n > 29 which follows from Assumptions 1 and 2, so that analogous
iT
+ Fi
2'1
reasoning holds. Q.E.D.
Proof of Proposition
There
exists a policy associated
can choose which
satisfies (23)
with different taxes.
solution to (20)
to (20)
8
— (22)
—
—
with the solution to (20)
Imagine
(25).
Then households would
(22) since taxes
the period
if
—
(22)
which the politician
the politician chose a different policy
necessarily be better off than under the
would be lower. Moreover, by definition of the solution
politician
would achieve a welfare
the politician does not choose different taxes.
strictly
below
W
p
.
Therefore,
Q.E.D.
Proof of Proposition 9
Lemma
1
applies here,
and
it is
the responsibility of the period
politician to ensure
that the policies induced by (11) and (12) satisfy (27) and (28). This
9
>
r1
'
r
and rf >
of Proposition
2.
9.
Moreover, t
>
9
>
means that rf >
t t by similar arguments to those in the proof
Q.E.D.
36
Appendix Table Al
Surplus' High Rent- High Fiscal
GDP
Country
Afghanistan
Albania
Seekmn
033
1
•0.053
1
•0
Algeria
Surplus/
Uncertainty
GDP
Country
Lao PDR
-0
Latvia
-0
Lebanon
-0
1
1
0.1 14
1
1
Antigua
Argenlrna
0.025
018
Armenra
-0.D15
1
Lithuania
006
574
-0 002
Australia
G 017
1
Luxembourg
0.001
Austrta
•0.013
Azerbaijan
•0
Bahanias
0.000
Bahrain
0.031
-0.039
Bangladesh
Barbados
Belarus
0001
Benin
Bnutan
•0
Bolivia
0.051
Bosnia and Herzegovina
CO40
Botswana
0.133
Madagasca'
1
Malawi
Malaysia
Maldives
1
1
093
Bulgaria
0.040
Surk-na Faso
-0.046
-0.1-8
-0
-0
1
1
003
039
044
-0 023
1
Morocco
Mozambique
Myanmar
-0.019
1
Namibia
Nepal
Netherlands
New Zealand
Nicaragua
0.026
1
1
-0.010
I
113
1
076
1
C.O05
034
Paraguay
0.006
Peru
Philipoines
025
-0 010
Poland
-0
Portugal
-G043
-0.007
-0
0.029
035
,0
Cuba
-0.047
1
Czechosiovakta
-0.053
Romania
Denmark
0.045
Russia
067
-0
-0.022
041
-0.016
Saudi Arabia
0.251
0.017
Serbia and
Momenegro
Senegal
1
-0.153
1
Estonia
0.045
G
Elhirjoia
-0.044
1
Fiji
-0.004
Solomon
Finland
0.039
South Africa
Slovakia
206
0-306
-0.029
Slovenia
-0.008
Islands
-0.027
0127
-0.055
1
Georgia
-0.033
1
Gennany
Ghana
-0.0 17
071
Sudan
-0
064
Sunname
I
1
Tanzania
-0
046
1
Hondu'as
Hong Kong
Hungary
0.016
Togc
Tonga
-O.090
Trinidad and
Iran
0069
Iraq
0.147
Italy
I
0465
06046
1
Uganda
-2
1
Ukraine
4J
-0
-0.06204
Kaza-Jislan
Kenva
001 164
-0 0255
KinbaTi
•0.05484
Yemen
Korea Rep.
000423
Zambia
Zimbabwe
I
1
Vanuatu
I
1
Venezuela.
Vietnam
1
1
I
1
1
37
1
1
01885
00755
007572
-0
Uzbekistan
0018974
RB
0.000267
-0.0 549
1
1
1
0.010883
-0 03054
-0.2O057
1
1
-0 029154
Uruguay
t
1
65E-02
00839
0.180512
United states
Jordan
G
•0.02 191
40135
00244
1
I
-0
-0
1
0003
1
Umled Arab Emirates
UnKed Kingdom
1
no
079
-0 028
-0 008
Turkey
Turkmenistan
Jamaica
Japan
Kuwait
Kyrgyz Republic
-0
1
I
-0.00884
-0
-0.029
Tobago
Tunisia
039
I
011
Thailand
•
U3077
Ireland
Israel
Syrian Arab Republic
014
0.063
1
1
•0.012
-0.012
1
1
-C.I28
-0
1
I
Haiti
Indonesia
1
•O.045
Guyana
Inula
1
Tajikistan
1
Switzerland
1
1
Taiwan
034
-0.036
-0.066
1
1
1
1
Sweden
065
-0
1
1
-O024
-0 026
022
002
-0 072
002
I
•0
-0.017
1
1
020
Lanka
Swaziland
a
1
069
-0
Sri
1
1
0.007
Greece
Grenada
Guatemala
Guinea
Iceiano
-0
Spam
France
Gabon
Gambia The
1
233
-0
Singapore
1
I
1
044
Leone
0.256
Eritrea
Sierra
1
-0.061
Equatorial Guinea
-0
-0
sevcnettes
1
1
1
100
Rwanda
Sao Tome and Pnnclpe
-0.008
1
-0.025
1
I
I
1
024
c
1
1
1
126
G-atai
I
-0.099
1
-0
Croatia
1
1
Panama
0312
1
044
Papua New Guinea
Congo. Rep
Cosla Rica
Cote dlvare
-O038
-0
-0.014
Pakistan
I
1
1
1
I
I
111
007
0.041
Oman
-0.006
1
1
1
244
0.053
0.013
-0 153
1
1
000
China
Colombia
Congo. Dem. Rep
Dominica
Dominican Republic
Ecuador
Egypt Arab Rep.
El Salvador
-0
Niqerm
•Norway
-0.039
Djibouti
001
Nigel
1
0.000
Chile
027
-0
1
1
-0.027
1
1
022
1
Mexico
Moldova
Mongolia
1
061
1
1
-0.045
1
-0.110
006
-0053
-0 037
-O039
Mauritius
I
1
1
-0
Mauritania
1
1
1
-0 011
Malta
1
t
1
-0 ISO
Mali
025
Brazil
Cambodia
Cameroon
Canada
Cape Verde
Chad
1
-0.018
-0.020
-0.05
FYR
1
-0.012
Belize
Burundi
1
Uncertainty
157
-0
Macedonia.
067
Belgium
Brunei
1
Seekina
116
153
Angola
Lesotho
Libera
Libya
High Rent High Fiscal
053
003
1
'
I
1
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