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Venice Summer Institute 2014
Venice Summer Institute
July 2014
THE ECONOMICS AND “POLITICAL ECONOMY”
OF ENERGY SUBSIDIES
Organiser: Jon Strand
Workshop to be held on 21 – 22 July 2014 on the island of San Servolo in the Bay of Venice, Italy
MODEL OF NON-CORRUPT VERSUS CORRUPT
GOVERNMENT IN DELIVERY OF TRANSPORT
SERVICES: THE IMPACT OF ENERGY SUBSIDIES
Jon Strand
CESifo GmbH • Poschingerstr. 5 • 81679 Munich, Germany
Tel.: +49 (0) 89 92 24 - 1410 • Fax: +49 (0) 89 92 24 - 1409
E-Mail: [email protected] • www.cesifo.org/venice
Model of Non-Corrupt Versus Corrupt Government in Delivery of Transport Services:
The Impact of Energy Subsidies1
By Jon Strand
Development Research Group, Environment and Energy Team (DECEE)
The World Bank
[email protected]
July 2014
NB: Very preliminary: Do not cite or quote
1. Introduction
This paper represents a follow-up to a World Bank Policy Research Working Paper, Strand
(2013). It relates closely to empirical work currently ongoing in the World Bank dealing with
energy subsidies and related themes. This general topic area of economic analysis has recently
attracted substantial interest, both in the World Bank and the IMF, with contributions found
among others in World Bank (2011); Commander (2011); Kojima (2012a, b); Vaglinasindi
(2012a, b); and IMF (2013). Some of the follow-up work has focused on building, estimating and
testing empirical models for fuel (gasoline, diesel and kerosene) pricing across countries over a
more than 20-year period, much of it based on an extensive data set for such pricing integrated
with various economic and political variables; see Strand (2011); Beers and Strand (2012); and
Kotsogiannis (2011). More recently other data, including for car ownership by country for a
large set of countries (matching many albeit not all of the countries for which we have fuel price
and consumption data), are being included to these data.2 The similar and recent work in the IMF
has focused on energy subsidy rates as shares of the overall economy, and thus also producing
useful data.
It is prudent to mention an earlier literature which discuss empirical political economy aspects of
fuel pricing, and which includes Hammar, Löfgren and Sterner (2004), and Fredriksson and
1
Viewpoints and opinions expressed in this paper are those of the author only, and do not necessarily represent
the World Bank, its directors, staff, or member countries.
2
Car stock data have, been subject to serious empirical scrutiny in previous research. See e g Dargay (1991; 2001;
2002), Fridstrøm (1998); Lescaroux and Rech (2008), Medlock and Soligo (2002) focusing on high-income
countries; and Dargay, Gately and Sommer (2007) and Storchmann (2005), where also lower-income countries are
included.
1
Millimet (2004) these papers are however based on more limited data sets than those we have
available. Most existing work has focused on high-income countries. Our improved data
situation also opens up for meaningful inclusion of additional political variables such as those
representing democratic or autocratic governments, length of regime or regime type tenure, and
democratic system (such as presidential versus parliamentarian).
As already noted the current paper represents an extension of Strand (2013), which attempted to
lie the analytical foundations for the political economy analysis of fuel (gasoline and kerosene)
subsidies and how these policies vary across countries. I there considered both economic and
political factors behind differences in subsidy policies across countries, with much of the focus
on differences in practices between democratic versus autocratic governments. I modeled a
political process where the promise of low fuel prices is used as a political tool: in democracies
to attract voters; and in autocracies to mobilize support among politically powerful support
groups. A key approach was that fuel subsidies are either easier to observe, commit to or deliver,
or better targeted at core groups, than other public goods or favors that can be offered or
promised by politicians. A main finding was that easier commitment and delivery, for the
“commodity” of low fuel prices as compared to regular public goods, can explain a high
prevalence of fuel policies in autocracies, and in young democracies where the capacity to
commit to or deliver complex public goods is incompletely developed.
This paper builds on and extends the framework in Strand (2013), mainly to also encompass the
inclusion of infrastructure investments in politicians’ choice sets, and thereby also including a
more explicitly dynamic formulation. We now focus much more explicitly on the trade-off
between the long run, here simply represented by the infrastructure (transport) investments, and
the short run, represented by the government’s energy pricing policy. We model a democracy
with multiple election periods; or alternatively a government under autocratic rule where leaders
rely on a “selectorate” to stay in power. Reelection of politicians in democracies (or staying in
power for an autocratic ruler) is in the basic model studied in section 2 assumed to be affected by
three factors; a) the quality of the infrastructure (provided by the politician in an initial
investment period); b) rate and amount of fuel subsidies or taxes; and c) the number of private
vehicles, which in turn determines the fraction of the public that has cars and thus gains from
motor fuel subsidies. We assume throughout that sitting governments are concerned only with
their net utility from governing (in excess of some outside reservation utility); and thus also with
their probabilities of remaining in power for future periods.
In sections 3-5 this basic model is extended in different directions. Section 3 considers additional
public-goods supplies which do not required up-front investments and may have benign effects
on growth. Section 4 considers the possible growth effects of energy subsidies themselves, which
may be negative; this factor may tend to further discourage such subsidies in particular for
governments who expect to remain in power for quite some time, and/or have growth concerns
high on the agenda. Section 5 studies a simple version of corruption in this context. We here
assume that politicians may accept bribes in return for providing energy subsidies favorable to
2
particular constituencies. We assume that politicians may be sacked when bribe taking is
revealed, but that the probability of this happen is a negative function of average bribe taking.
This may easily lead to multiple equilibria where very high and very low bribe taking are both
equilibrium solutions; the likelihood that the former occurs is higher when politicians place little
emphasis on future returns, and/or they in any case expect their reign to be short-lived. Section 6
concludes.
2. A Basic Model of Non-Corrupt Governments
We first consider a basic model where transport infrastructure investment, and transport-related
energy subsidies or taxes, are the only instruments of government that are explicitly analyzed.
We consider an infinite-period model where, in period 1, governments can provide an investment
T into a transport system, which can be interpreted alternatively as collective (such as train, bus
transit etc.) or road investment benefiting road vehicles (cars and trucks); or a combination of the
two. We assume that all voters are affected by this investment, but possibly to differing degrees
depending e g on whether they have cars. Fuels may be subsidized or taxed. Beneficiaries of net
fuel subsidies are only those with cars; the group of households which contain car owners are
also called the “middle class”. The investment T provides public goods only after an initial
(perhaps long) construction period; here defined as the unit period of the analysis. We assume
that some governments may have problems of credibility, in promising T to be actually delivered
and transformed into effective and operational infrastructure in the “next period”.
We consider in this section non-corrupt, and principally (but not exclusively) democratic
governments, and where delivery problems, and/or governments’ concern for and interest in the
public, may vary. Governments may be not fully democratic, and then rely on a so-called
“selectorate” (smaller constituencies than in standard democracies) for their political support.
Define the following objective function for the sitting government:
EW0  H ( B0 )  (T , s, N ) [G  U (T , s )  eV (T , N , s )  qC ( N , s )  H ( B)]
(1)
[(T , s, N )]2 
.  [(T , s, N )]3 
.  ...
 H ( B0 ) 
(T , s, N )
Z.
1  (T , s, N )
Z represents the argument of the politician’s periodic utility function while in power, defined by
(2)
Zt  Gt  U (T0 , st )  eV (T0 , Nt , st )  qC ( Nt , st )  H ( Bt ) ,
with individual terms explained further below. In (1), we have basically dropped subscripts and
assumed that recurring values, from period 1 on, are stationary, so that the summation formula
applied in the last line is valid.
3
We are assuming that the sitting government is in power for certain during the initial period 0,
and that only T is set in that period.
We have defined the following symbols:
T = transport infrastructure investment, determined in period 0. As noted, T can be considered as
investment in collective transport or road infrastructure.
N = number of private vehicles (defined for simplicity as the fraction of the public that has cars).
s = fuel subsidy rate, considering s as an excise tax (implying s < 0), or similar subsidy (s > 0).
S = total fuel subsidy amount = sN(s), where N’(s) > 0 (thus, assuming that the amount of
driving per car is a positive function of the fuel subsidy rate). This expresses the (negative) net
fiscal impacts of fuel subsidies.
C = carbon emissions per period.
G = utility to sitting government officials or politicians, due to being in power as such
(independent of other sources of utility embedded in (2)).
U = direct utility to government officials or politicians from transport infrastructure and fuel
subsidies. Note that U can also in principle reflect (fully or partly) the utility to the general
public; this depends on the degree of “societal concern” among politicians. We assume that the
partial derivatives UT and Us are both positive and decreasing in their arguments.
V = marginal externality cost in private transport in the country, assumed to be a negative
function of public infrastructure supply; and a positive function of the number of cars and the
fuel subsidy. For partial derivatives we assume VT < 0, VN > 0, and Vs > 0: externality costs of
transport increase in the number of cars and in fuel subsidies, but are reduced when transport
infrastructure improves (regardless of whether T represents public transport or road building).
e = the government-internalized costs related to externalities in private transport. A “responsible”
government will tend to emphasize efficiency in fiscal and externality policy, and put negative
weights on high and distortive energy subsidies, and have a high e value. e takes values from 0
(disinterested government) to 1 (fully internalizing fuel externalities).
q = carbon price facing the country, e g as a carbon tax or price under a c-a-t scheme; or a carbon
market offset price. For simplicity we assume that q is constant through time.
Φ = probability that the government remains in power until the following period. We consider
both democratic governments (with formal elections), and non-democratic ones. The process for
staying in power is likely to be different under autocracy, often with a “selectorate” determining
whether an autocratic government or ruler remains in power. In either case this probability is
affected positively by increases in both T and s. Effects of the number of car owners could go in
4
either direction, and may depend on T and s. When T is high (s low), those without cars are
likely tp vote for or support the politician; and an increase in N is likely to reduce this voting
propensity and thus Φ. When T is low (s high), we it could be opposite: households with cars are
likely to care less about public transport, and more about fuel subsidies.
δ = discount factor of government. This factor depends on length of the period (how many years
constitute an election period/cycle); on the time lag from investment in transport infrastructure,
T, to its effect on infrastructure quality; and on “subjective impatience” of government which
may vary by country and government type. It is related to, but not identical to, the standard
capital market discount rate, denoted r.
Bt = net budget balance in period t, where we only denote the initial period 0 (and otherwise do
not use time subscripts). Consider the following items entering into the budget balance:
(3)
Bt  Rt  rT0  St  Pt ,
where we have defined
Rt = total government revenue in period t, considered exogenous
rT0 = service payments to pay for the infrastructure investment done in period 0. We assume for
simplicity that the infrastructure investment is fully loan financed and that fixed payments (for
interest and principal) must be paid from period 0 and continuously thereafter.3
Pt = expenditure on “other public goods” in period t. We assume that these public goods do not
require investments, and thus only represent current expenditures. This would among other items
include health, education, social services, and other infrastructure. This is here for the moment
considered exogenous, but it can in reality be endogenous as perhaps being “squeezed” by the
two (endogenous) items S and rT. We will revert to an explicit analysis of such expenditures in
the next section below.
H(B) = utility to the sitting government from the current net budget surplus, where H(B) can be
positive or negative, and H’ > 0, H’’ < 0. We may think of H(B) as being positive if and only if
B is positive (thus in particular, H(B) = 0 for B = 0). Also, large budget deficits may be
considered as bad at the margin, in the sense here of making H’ large.
We assume, for simplicity of exposition and modeling, that all actions are taken in period 0 with
respect to transport infrastructure determined by the government, and determination of the
number of private vehicles by the private sector. The government also determines its fuel subsidy
level in period 1 and subsequent periods, sequentially. We however assume for simplicity that a
3
We here for simplicity assume that, even when some principal needs to be serviced, payments are required
forever (or as a minimum for the length of the incumbency of the current government).
5
steady-state level of S is found already in period 1 (but which may differ from the level in period
0). We also assume that S0 has no impact on following periods’ political and economic variables.
We assume that the sitting government derives utility from activities and events when being in
power, but we do not specify its utility from outcomes occurring when not in power. One way to
view this assumption is that the utility level is scaled such that out-of-power utility is set at zero.
The private sector determines the change in the vehicle stock, relative to the previous period, at
the start of any given period, on basis of the levels of T and s in the current period (s being, in
principle, variable over time):
(4)
N  N (T , s); NT '  0; Ns '  0; NTs ''  0.
We assume that the private sector acquires more additional motor vehicles when the fuel subsidy
rate is higher; and that it acquires fewer vehicles when the quality of public transport is higher.4
Also, with more public transport, we assume that the marginal effect of greater fuel subsidies on
the car stock falls. We will assume, for simplicity of our analysis, that cars are rented or leased,
period by period so there are no persistence or stock effects from a given car stock at the start of
the period.
The government is assumed to a) maximize its overall objective function with respect to its
period 0 infrastructure decision, T; b) maximize its period-by-period utility with respect to the
fuel subsidy rate s in periods 1, 2, .., for as long as the government stays in power. The latter
decision must take account of the relationships (3), and S = sN(s) determining the fiscal impact
of the fuel subsidy. We assume no persistence effects on future period outcomes from a current
fuel subsidy.
The maximization problem for T departs from the last expression in (1), which can be
maximized directly with respect to T (and where we recognize that all period Φ values are
affected in the same way by a given change in T in period 0). We first consider the effect on the
probability of staying in power, due to improved transport infrastructure, given by
(5)
d
 T   N NT  0 .
dT
Two components affect the reelection probability in response to improved public transport
infrastructure investments: a direct, positive political effect; but also an indirect effect on voting
as the number of drivers on the road is assumed to also affected by T. This latter effect may be
positive or negative. First, the derivative ФN can be positive or negative, depending on whether
the government, overall at the outset, considered “friendly” (“less friendly”) to drivers. This
derivative is more likely to be positive than otherwise when T is road investment; although this
4
Possibly, this effect could go the other way as better public transport also is likely to reduce motorists’ externality
costs of driving (in particular, less congestion). This effect may in principle spur the demand for cars.
6
depends only on this government’s voter reputations. Secondly, NT can be positive or negative: it
is much more likely positive when T is road investments, and likely negative when T is public
transport investments. Overall, in cases of both road and public transport investments, the last
main term in (5) is likely positive: in the former case both factors are positive, and in the latter
case they are negative. We can thus rather safely assume that the overall effect of better transport
infrastructure on the probability of reelection is positive.
The condition for optimal infrastructure investment T in period 0 is:
(6)
dEW0
1

1 

rH '( B) 
UT  eVT  (eVN  qCN ) NT   
 (T   N NT ) Z  0 .
dT
1  
1  
 1   
2
To interpret this condition, it is useful to write it on the following form:
(6a)
H '( B) 
 
El () ElN ()
Z

( T

NT ) 
UT  eVT  (eVN  qCN ) NT 
r 
1  
T
N

The El terms here represent elasticities of the Ф function with respect to the specified arguments.
The term on the left-hand side here expresses the marginal utility cost to the politician due the
infrastructure investment in period 0, evaluated at the equilibrium level of the budget surplus, B.
This means that the effective marginal cost is inversely related to B. In particular, when B is
highly negative, the marginal value to this government of budget improvements is likely to be
high.
This term is at the optimum for the government set equal to the marginal benefits of transport
infrastructure investments, represented by the two other main terms. Note that a (notional) cost
rT is incurred for the politician each period for as long as the politician stays in power, but no
longer (as the politician then no longer is “responsible for” this cost).
The first of the two major terms on the right-hand side of (6a) expresses the “direct marginal
utility value” for the government from having a higher level of transport infrastructure for as
long at the politician stays in power.5 Since VT < 0, both the two first utility elements going into
this term are positive. The last element is typically positive when T represents public transport
investment (as both VN and CN are positive, and in this case NT < 0); but negative when T
represents investment in roads, as the number of cars then increase which leads to greater
congestion and carbon emissions. Overall, the main bracketed is positive when T is public
transport investments, but more ambiguous when T is road investments.
The second main term expresses “political” impacts of increased transport infrastructure
investment, via changes in future reelection probabilities when infrastructure is improved by the
5
We here assume that politicians care about such utilities, even private ones, only as long as they stay in power.
7
current sitting government. This term tends to be large when 1/(1-δΦ) is large and thus δΦ large
(whereby current politicians put a lot of weight on future periods relative to the current
investment period; this occurs when the discount factor δ is close to unity, and the reelection
probability Φ is also high); and when ΦT is large (there is a large effect from the size of
transport infrastructure on the probability that the public continues to reelect this particular
politician, now and in future periods). The latter should be large when T is public transport and
voters care a lot for this; which is more likely when few initially have cars (greater supply of T
then should also discourage further car purchases, everything else equal). The last term depends
on the sign of ΦN which is determined by the propensity of voting for this politician when the
number of car owners increases. It is likely positive (negative) when the current government is
viewed as positive (negative) to the demands of car owners (including e g currently subsidizing
fuels). NT is likely positive when the T is “mainly” road infrastructure, but is likely negative
when T is “mainly” public transport infrastructure.
Both the second and third main terms are likely negative functions of T. Thus, factors that would
tend to make each of the terms large for any given T, would also tend to make the equilibrium
value of T large.
We next derive the optimal fuel subsidy rate s. Considering “starting” from period 1 (or
assuming that the country is now already in period 1, and the politician in power), we define the
following discounted expected utility function:
EW1  G  U (T , s1 )  eV (T , N ( s1 ), s1 )  qC ( N ( s1 ), s1 )
(7)
 H ( B1 ( s1 ) [(T , s, N ]Z 2  [(T , s, N )]2 Z 3  ...  Z1 
(2)
Z 2.
1  (2)
At a steady state, Z (the current periodic utility of a sitting government) is for simplicity taken to
be constant through time, and maximized period-by-period. Thus in period 1, Z1 is maximized
taking Z in future periods (with its stationary value denoted by Z2) as given; thus prompting the
last formulation in (7). Φ(i) is shorthand for the probability of political survival, for one more
period, being currently in period i. The point here is that setting s1 in period 1 affects Φ(1) and
Z1, but no other variables directly as there are no political persistence effects of a given policy
beyond the next following period (it is however rationally assumed that setting si in other periods
will then affect Zi similarly). Let us define
(8)
d
  s '  N ' N '( s),  s '  0, N '( s)  0.
ds
The sign of ΦN’ is here as before indeterminate, but we may reasonably assume that (6) is
positive. We now find
8
dEW1 dZ1 1
1
d


Z2
ds1
ds1  1  (2) ds
 U s  e(Vs  VN N s )  q (CN N s  Cs )  H '( B )(sN s  N )
(9)

1 1
( s   N N s ) Z 2  0,
 1  
where we have dropped subscripts to Φ, as is has a common value in steady-state. Also at a
steady-state, Z1 = Z2. The first main term on the right-hand side expresses effects via changes in
politicians’ utility function in period 1. This main term must be negative in equilibrium (so that
the first, positive, element is overtaken by the other, negative, elements). The second main term
expresses effects via changes in period 1 probability of staying in power. Only the latter
expresses “persistent” effects (for periods beyond the first). This term is positive, at least as long
as “populist” factors are at play.
Consider the role played by concern for budget balance, represented by H’(B), which is higher
when this concern is greater. A higher budget concern contributes to a less positive (or more
negative right-hand side expression in (9), thus reducing the subsidy (as such reduction drives H’
down).
To interpret (9), we may write it alternatively as
(9a)
dS
 U s  e[Vs  VN N '( s )]  q[C N N '( s )  Cs ]
ds
dZ
Z 2 Els () ElN ()
Z 2 Els () ElN ()

(

Ns )  S 
(

Ns )
1  
s
N
ds 1  
s
N
H '( B)
The left-hand side can be considered as the marginal cost of fuel subsidies, and the right-hand
side the overall marginal gain from paying additional subsidies. dZ-S/ds denotes any change in
politicians’ immediate welfare from increased s, when ignoring the direct subsidy cost (moved to
the left-hand side). dZ-S/ds could be positive or negative. It tends to be negative for a
“responsible” government which appropriately takes both the inefficiency cost and the excessive
carbon cost of fuel subsidies more into consideration. It can be positive when the direct utility to
politicians, from consumption of fuels of themselves or their associates, is high; more likely for a
non-representative government or one with a smaller, more tightly-knit selectorate. Less
ambiguously, dZ-S/ds is a decreasing function of s.
The second main term on the right-hand side expresses gains due to higher likelihood of staying
in power in the current period as a result of higher fuel subsidies today. There is no effect of
changes in s1 on the probability of staying in power in future periods, as s is set period-by-period
9
and there are no political persistence effects. There are still effects on future periods, since a
higher probability of staying in power now in itself makes it more likely to enjoy power in the
future. Also this main term is likely to be a decreasing function of s.
We can, based on the above discussion, identify factors which contribute to a high level of fuel
subsidy, as follows:
a) N low: This follows from the right-hand side of (9a) then being high. The fiscal costs of
subsidizing gasoline is small when relatively few have cars. This effect is however
countered by the fact that dΦ/ds is likely to be small when N is small (so that few voters
are affected by the gasoline subsidy); see point c) below; this leaves the factor overall
somewhat uncertain, although lower emphasis on points a and c may make point b
dominate more.
b) dZ-S/ds high at “moderate” s levels: This implies a high current utility level to the sitting
government, from paying out subsidies; and little emphasis among politicians on the
moderating factors (inefficiencies caused by subsidies; and excess carbon emissions).
Note that this derivative could easily be negative for all values of s; thus contributing to
less fuel subsidy in particular when factors a) and c) are small (as when N is small).
c) dΦ/ds high at “moderate” s levels: this implies a large political gain from additional fuel
subsidies. This could be the case in particular when the selectorate is small, or election
outcomes depend greatly on targeting particular groups sensitive to fuel subsidies.
d) U’(H) is small at “moderate” s levels: There is then small concern for additional budget
deficits created by fuel subsidies (either because such deficits are actually small, or the
government does not worry much about them).
3. Endogenizing additional public-good supplies
The model as studied so far ignores effects of growth on future reelection probabilities. It can
often be relevant to assume that such effects are present.
Consider a simple extension of the above model where growth effects are considered. We will
then assume that the government in question is “more active” in its determination of resources on
current expenditures on a range of public goods, P, to attract voters, and that may also affect
growth, at least in the longer run. We may here think of services such as education and health,
which are likely to have growth-enhancing effects in the long run; but which may still be
discouraged when a government takes mainly short-run positions. We will assume that P does
not require any up-front investments.
Assume that P enters into the government’s decision process in four separate ways:
10
a) As expenditure for the sitting government, via (3a).
b) As a potential utility element for government, entering into the utility function U (where
it may also represent altruistic valuation of the effect on the general public).
c) By affecting the voting propensity of voters who may be swayed by these expenditures.
d) By affecting the rate of growth of the economy. Considering in particular P as
educational expenditures, these are likely to raise the productive capacity of workers over
time. This effect could be small; but it could also be sizeable down the line.
These four pathways for effects are reflected in the following new formulation of the
government’s utility function:
EW1  G  U (T , P, s )  eV (T , N , s)  qC ( N , s)  H ( B)
(10)
(1  g ( P1 ))Z 2  (1  g ( P1 ))(1  g ) 2 3 Z 3  ...
 Z1  (1  g ( P1 ))Z  (1  g ( P1 ))
(1  g ) 2  2
Z
1   (1  g )
Here, we are here starting from period 1 as there are no up-front investments to consider in
period 0. The last equation in (10) indicates that P1 works via four channels in this case:
a) By affecting the immediate reelection probability Φ. This has repercussion effects by
affecting the level of the absolute value function also from period 2 on;
b) By affecting the level of Z1 through its effect on U
c) By affecting Z1 through its effect on H(B1), the government budget balance in period 1
d) By affecting the growth rate from period 1 to period 2 (thus appearing in period 2); this
also has repercussion effects in the same way as a).
Factors a, b and d are here positive, while c (the public sector cost of the service evaluated at the
current budget balance) is negative. The main effects of T and s are here little impacted by
introducing P. We however get an additional first-order condition with respect to P, as follows
(where we need to explicitly consider only P1, as decisions regarding P are sequential):
(11)
dEW1 1
P
1
 2

Z  gP
Z  U P  H '( B)  0 .
dP1
 1  (1  g )
 1  (1  g )
Effects on policy enter only as perceived by politicians; this also applies to the effect on growth;
although with rational expectations g would correspond to its true expected value. Politicians
may however be imperfectly informed about these effects. In particular, when considering a
utility maximizing and non-altruistic politician who may have UP close to zero, and perceive no
effect on growth (gP = 0), the only concern will be the effect on reelection (the first term in (9))
against the fiscal cost (the last term). Such a politician who may also feel a budget squeeze (high
H’), and little immediate political benefit from these types of public-goods supply (ΦP small),
may tend to opt for a low level of P.
11
Let us now consider, more formally, factors that might contribute to making P high, in the
context of the model. For this purpose we rewrite (9) as follows:
(11a)
 El ()

Z
.
H '( B)  U P   P
 g P 
 P1
 1  (1  g )
H’(B) here indicates the immediate marginal budgetary cost of P1. The terms on the right-hand
side represent marginal benefits of increasing P1. There are three such benefits (represented by
the three terms). These are:
a) The immediate utility to politicians (or the public when this factor reflects politicians’
altruistic concerns).
b) The impact of P1 on the immediate reelection probability. This has further effects in
subsequent future periods by increasing the probability of further staying in power.
c) Effects via the increased growth rate induced by higher P1. In our model, this effect works in
the way that positive growth effects, induced by growth-enhancing policies, are here favorable
by their own to politicians, by increasing the overall value of politician’s benefits for all periods
over which that politician is reelected (but, we assume, to for other periods). We see that this
effect becomes small if δ (politicians’ subjective discount factor) and/or Ф (the equilibrium
reelection probability in any future period) are small.
4. Growth impacts of energy subsidies
We will in this section consider a case where growth impacts could result also from energy
pricing as such. We may then conceptualize the idea of an “optimal fuel price” or a range for
such fuel prices, whereby one needs to add externality- and budget-constraint (Ramsey)motivated taxes to basic fuel costs; see e g Parry and Small (2005), or Parry and Strand (2012).
See also Mundaca (2014) presented at this workshop. By such arguments, fuel taxes below such
an optimal level could be detrimental to long-term economic growth. But on the other hand,
growth could also be hampered by “too high” fuel taxes. Indeed, much of the argument against
the imposition of carbon taxes is just that such taxes reduce growth in countries that impose
them. While much of that debate is likely politically motivated, there should be little basic
disagreement that charging fossil-fuel energy prices at a sufficiently high rate could reduce
overall economic output, in particular when alternative energy sources are expensive or not
available.
The discussion in this section is only indicative, with focus on the case where energy prices are
too low (due to energy subsidies). The avenues by which this effect works could then be several.
One is wasteful energy consumption as its price is too low; a second is distorted production
structure (with too capital- and energy-intensive industry creating too few jobs), for the same
reason; a third might be distorted investments by consumers and businesses, including reduced
12
energy-related R&D expenditures; and a fourth channel could be government spending
distortions, due to the fact that energy subsidies removes fiscal space, creating too little room for
spending on factors with long-term return productive potential such as education, health and
infrastructure. A fifth issue could be failure to correct negative production externalities of high
energy use.
To make this argument more compelling, assume that the optimal energy price, call it p*, is
comprised of four main elements:
(12)
p* = p0 + p1 + p2 + pF ,
where p0 is the basic or neutral (neither taxed nor subsidized) energy supply price (basic energy
cost, plus transport and distribution cost), p1 and p2 are production-related and consumptionrelated externality components respectively, while pF is a fiscal (Ramsey) component motivated
by the government’s pure need for fiscal revenue. We may (with slight abuse of terminology)
call the sum p1 + p2 + pF the “energy-related Pigou tax” for the economy in question.
One might here plausibly argue that at least p1 + pF, but perhaps not p2, are directly related to
output and growth. If so, the energy price that maximizes output and growth equals p** given by
(13)
p** = p0 + p1 + pF.
Thus when the fuel price is changed from an initial level p**, to either a lower or higher level,
growth is reduced. We may think of the curve as being quite flat in a range close to p** (and
perhaps rather flat up to or even above p*). It is however not likely to be flat, but more steeply
upward sloping in p, for lower p values (in particular when energy is subsidized so that p < p0).
An issue for the politician in this context is the timing of effects of possible fuel price changes or
reforms. The growth effect is likely to be most relevant for the long run, while very short-run
impacts could take other forms.
More generally, if this argument is adopted, one might define a function relating both the shortrun and the long-run effects on growth to the energy price.
We will not go into analytical details for this case. It is sufficient to point out that, when the
effect of subsidies on growth in future periods is simple (as in (10) only added an argument s to
the g function in the subsequent period), there will simply be an additional argument to disfavor
energy subsidies, but which has effect only for politicians that put weight on future reelection
probabilities and/or growth prospects. Its weight will then also depend on what weight voters put
on growth factors in elections. In consequence, this factor is more important for
13
5. Impacts of corruption
Corrupt activity can be modeled in a variety of ways in the context of this model. We will here
consider a simple case where bribes can be paid to government officials in charge of energy
pricing, in return for setting energy prices low. It may then be relevant to assume that a more
“focused” group of recipients or beneficiaries of energy subsidies makes such bribes more
viable.
We will also assume that corruption can be risky for politicians. One way to model this is to
assume that corruption, once discovered, can lead to the overthrow or the ousting of power of the
respective corrupt politician.
We are here particularly interested in studying how the benefits from corruption can depend on
parameters such as the fraction of the public that has cars.
To incorporate such effects, consider the following simpler version of the government budget
balance:
Bt  Rt  rT0  Nst  Pt .
(3a)
We now for simplicity assume that the fraction of households that have vehicles, N, is
exogenously given. This fraction could still however be important in determining the level of
corruption. Call the level of bribes paid Y, while the probability that a politician gets caught in
the following period as a consequence of receiving bribes, is called σ. We assume that the
politician’s utility function can now be written as
EW1  G  Y ( N , s1 )  U (T , s1 )  eV (T , N , s1 )  qC ( N , s1 )  H ( B1 ( s1 ))
(14)
(1   (Y ; YM )) [(T , s, N ]Z 2  [(T , s, N )]2 Z 3  ....
 Z1  (1   )
(2)
Z2
1  (2)
We here, for simplicity, take the magnitude of bribes paid as an exogenous function Y(N,s) of
the number of car owners, N, and the fuel subsidy rate, s. Lambda is here a scaling parameter
which makes it possible to compare bribes to budget allocations. Thus if λ > 1, a politician is
more concerned with bribes than with budgetary improvements. For corrupt politicians we could
have λ orders of magnitude greater than unity; and for non-corrupt politicians, λ could be close to
zero (or = 0 in the limit for a politician that is completely averse to corruption).
In the current period (1), bribes will here affect (increase) the politician’s utility only by raising
Z1 accordingly. For future periods, bribe taking has two effects: future values of Z (here for
simplicity represented by a stationary future value Z2) are all also increased accordingly, for as
long as the politician stays in power. But there is an offsetting effect from the fact that bribing
14
may be (successfully) reported and the politician sacked as a result, σ; in this case the politician
by assumption also forfeits his or her bribes.
The parameter σ is in turn assumed to be a function of two magnitudes: it is increasing in the
amount of bribes received by this politician, Y; and decreasing in the average amount of bribes
successfully received by all politicians in the economy, YM. When all bribers and all politicians
behave identically, YM = (1-σ)Y. If so, the equilibrium effect of simultaneous changes in bribing
propensities is given by (with subscript S denoting simultaneous changes in the overall
equilibrium bribing levels)
(15)
Y
 d 
,

 
 dY  S 1   YM Y
where all “general equilibrium” effects are taken into consideration, and where σY > 0 and σYM <
0 denote partial derivatives. The effect on the probability that a given politician is sacked due to
receiving bribes, σY, can be considered a negative function of average bribing, YM. Thus:
(16)
 d 

   Y (Y ; YM )
 dY  I
When optimizing (10a), any given politician will view YM as exogenously given and only
consider Y to be variable, and given as function of (here, the exogenous) N and (the endogenous)
s. We find in this case:
(17)
dEW1 d ( Z1  Y1 )
1  (1   )(1   )


 Ys 
( s   N N s )   s   Z 2  0

ds1
ds1
1    1  

Here Z1 – Y1 denotes period 1 non-bribe income (equivalent to the politician’s period 1 utility in
(7)); while δs is the marginal effect on the sacking probability from additional subsidies being
paid (which in turn induces the respective bribes). There are two new terms relative to (9),
namely λYs (the value of additional bribes paid to the politician resulting from higher fuel
subsidies), and the last term in the square bracket (the discounted utility loss due to the increased
probability of being fired when bribes are increased). The first term in the bracket is also
modified by the sacking probability (which itself reduces the future politician tenure). The
additional concerns, raised by the possibility of corruption. thus trades these terms off against
each other.
There are here several mechanisms by which the fuel subsidy rate can be affected by the
possibility of, or actual, bribing, which we consider in turn.
15
1) The value of lambda (the marginal utility value of bribes to the politician of receiving
them). A higher lambda raises the marginal value to the politician of paying fuel
subsidies. Thus s1 increases.
2) A given increase in fuel subsidies is rewarded more in terms of bribes, so that Ys
increases (independent of N). This has two offsetting effects on the subsidy rate: a
positive effect via an increased amount of bribes received; and a negative effect via an
increased probability of being fired due to corruption.
3) Higher N (more households have cars). This affects bribing revenue as the marginal value
of s in terms of Y increases. But there are two offsetting factors. First, also the budget
cost, (the negative of B) increases, which works in the opposite direction. Secondly, the
higher N also increases the detection probability σ for given subsidy rate. The overall
effect on corruption is unclear. Note however that this effect is generally less conducive
to bribe taking, as compared to a pure increase in Ys (as under point 2), due to the
moderating effect via the negative budget balance (when more households have cars and
must be subsidized).
4) A higher degree to which politicians are sacked due to corruption and bribing. This factor
reduces the long-run returns to the politician from increased subsidy payments.
5) A higher level of average bribing and corruption in society, YN. We here assume that this
leads to a reduced marginal effect of more bribing on the detection probability, so that σY,
and σs, are both reduced. This leads to more bribing by this particular politician.
We may also consider the effects of higher infrastructure investment T in period 0, on incentives
for corruption. Note that greater T affects little in the model except that it hurts the budget
balance B (interest payments on the associated loan are assumed to be paid in perpetuity), and
that the current utility of government is otherwise increased, and reelection probabilities
correspondingly increased. While it is not explicitly modeled, it is easy to think that increased T
may increase the public’s value of the transport infrastructure, and of their cars, and thereby
increase the incentives of the public (possibly represented by their lobbyists) to bribe politicians
into providing more fuel subsidies. (Note that motor fuel subsidies are worthless when there are
no roads; but have high value to motorists when the road system is good.) Thus politicians’
revenues from receiving bribes may increase. This may motivate extensions of our current model
to more complex situation where improvements in the transport infrastructure are made gradually
over time, and possibly subject to influence through bribing.6
6. Concluding remarks
In this paper we have studied a very stylized model of government behavior focusing on its
propensity to subsidize motor fuels. The model extend the analysis in Strand (2013), and serves
principally as a basis for follow-up empirical work on political determinants of fuel subsidies;
6
This may, in addition, raise the issue of possible corruption in infrastructure contract procurement, not pursued
further here.
16
see a start of such work in Beers and Strand (2013). The emphasis in our analysis is to serve as a
guide for empirical applications; to guide the choice of included variables in political-economy
analyses of energy subsidies; and to serve as a predictor of results from such analyses.
One basic new message, in addition to reiterating some of those from Strand (2013), concerns
tradeoffs between the short and the long run. The “long run” is here represented by factors that
affect politicians’ reelection probabilities, mainly through investments in transport infrastructure
in the initial period (but not in subsequent periods), and the returns from such investments. We
argue that increased government emphasis on long-term transport infrastructure investment is
often warranted for efficiency reasons, but is discouraged when government leaders take mainly
short-run positions, due to a combination of high discounting and low reengagement
probabilities. Improved infrastructure may sometimes increase the scope for corruption and bribe
taking by politicians, as fuel subsidies become more valuable to vehicle owners. Overall, taking
a long-run view by politicians tends to be welfare enhancing, but need not reduce the levels of
corruption.
Another message concerns the nature of corruption itself. We find that “corruption may breed
corruption” as rates at which given corruption is punished (corrupt politicians are sacked) may be
negatively related to overall corruption and bribing rates. This is not a new idea. Our discussion
however underlines the notion that multiple “bribing equilibria” (possibly, one with no bribing,
and one or more with positive or high bribing) may easily exist when the target for bribing is
politicians’ fuel subsidies.
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Symbols used in the paper
EWt = discounted utility of government starting in period t.
T = collective transport investment in period 0
N = number of private vehicles, number between 0 and 1 (= fraction of the public that has cars)
s = fuel subsidy rate
S = total fuel subsidies amount = sN(s), where N’(s) > 0
B = budget surplus
C = carbon emissions per period
G = (gross) utility to sitting government officials, due to being in power
Z = net flow utility to the sitting government
U = utility to government officials from transport infrastructure and fuel subsidies. (Can
incorporate fully or partly the utility to the general public.)
V = marginal externality cost in private transport in the country
q = carbon price
e = subjective disutility to government, related to the economic costs resulting from subsidizing
fuels, valued from 0 (disinterested government) to 1 (fully internalizing fuel externalities).
Φ = probability that the government remains in power until the next period
δ = discount factor of government
r = interest rate facing government
Y = bribes paid to politicians in return for setting low energy prices.
YM = average bribe taking level of politicians in the country.
σ = probability that a politician gets caught and is fired as a result of receiving bribes
λ = marginal utility of bribe money for politicians
19