Description
In investment, the bond credit rating assesses the credit worthiness of a corporation's or government debt issues. It is analogous to credit ratings for individuals.
Government’s Credit-Rating Concerns and the
Evaluation of Public Projects
+
Nadav Levy
IDC Herzliya
Ady Pauzner
Tel Aviv University
This version: September 2010
Abstract
Public projects typically generate both monetary revenue and social bene…ts that
cannot be monetized. Anticipated revenues from government-owned projects increase
the liklihood that the government will be able to repay its debt and thus improve its
credit rating and lower the …nancing costs of the debt. This should give monetary revenue
an added value relative to social bene…ts. However, informational problems – dynamic
inconsistency and adverse selection – push the government to an excessive emphasis on
social bene…ts, ignoring the external e¤ect of monetary revenue on debtholders. Since
the credit market anticipates this, the government’s credit rating is adversely a¤ected
and it is thus unable to extract the full potential of the projects. Finally, we show that
while privatization can sometimes alleviate these problems, there are cases in which the
government would be better o¤ if its hands were tied and it were not allowed to privatize.
Keywords: public projects, credit rating, social discount rate, privatization
We bene…tted from discussions with Alex Cukierman, Eddie Dekel, Daniel Ferreira, Elhanan Helpman,
Jose Scheinkman, Klaus Schmidt and Yossi Spiegel and from comments by seminar audiences at Bar-Ilan,
Ben-Gurion, Haifa, Hebrew and Tel-Aviv universities, IDC Herzliya, Banco de Mexico, the CEPR conference
on Government and Governance, Barcelona 2008 and the IFN conference on Privatization, Stockholm 2008.
1
1 Introduction
Governments on all levels – national, state and local – turn to credit markets to …nance a
signi…cant proportion of their activities. A government’s cost of borrowing is determined by its
credit rating, which re‡ects the credit market’s con…dence in its ability to repay its debt. This
can vary considerably between governments. For example, the yield spread between Italian
10-year euro-denominated bonds (rated A+ by S&P) and the equivalent German bonds (rated
AAA) has averaged about one percentage point over the last two years, and the yield spread
between 18-year general-obligation bonds issued by the State of California (rated Baa1 by
Moody’s) and those issued by the State of Georgia (rated Aaa) is currently
1
1.16%. The
e¤ect on a government’s cost of borrowing is substantial. For example, in the case of Italy,
with a debt-to-GDP ratio of over 100%, its lower credit rating is responsible for an additional
annual borrowing cost of more than one percent of GDP.
The impact on the government’s credit rating can be a major consideration in its decisions
regarding investment in public projects. The additional debt taken on to …nance a project
negatively a¤ects the credit rating. On the other hand, the addition of the project to the
asset side of the government’s balance sheet has a positive impact. Since these changes in the
credit rating a¤ect the cost of …nancing the government’s debt, they should be included in the
project’s cost-bene…t analysis. These considerations are important not only for large projects
with a major impact on the government’s credit rating, but also for projects that are small
relative to the size of the entire government debt. While their impact on the credit rating is
smaller, the associated change in the cost of …nancing the debt remains signi…cant relative to
their size.
While the e¤ect of a project’s …nancing cost on the credit rating is straightforward, un-
derstanding the e¤ect of its bene…ts is more subtle and requires a closer look at the nature of
public projects. Public projects typically generate both monetary revenue and social bene…ts
that cannot be monetized. For example, a new highway will yield both toll income and social
bene…ts in the form of driver surplus and reduced congestion on other roads. An oil …eld
generates sales revenue, but also carries environmental risks (in this case, a negative social
1
Sources: Yahoo! Finance, municipalbonds.com (September 2010).
2
bene…t). In Section 2 we develop a model that explains how the level of government debt
and the composition of its assets a¤ect the probability of default and the interest it pays on
its debt. Monetary revenue can be used to prevent default in cases of …nancial distress –
in contrast to social bene…ts that cannot be converted back into money. We derive a valu-
ation formula for public projects that takes into account their mix of monetary and social
bene…ts and serves as the main tool of the subsequent analysis. According to the formula,
monetary revenue has added value relative to social bene…ts, which can be decomposed into
two components: the option value of avoiding the penalties associated with default, and the
credit market value – the reduction in the cost of …nancing the government’s debt due to the
improved credit rating.
Crucially, this credit market value of the project depends on the credit market’s expec-
tations. Therefore, the information available to the market at the time the expectations are
formed plays a central role. While credit-rating considerations imply that the government
should place additional emphasis on a project’s monetary bene…ts relative to its social bene-
…ts, we argue that there are two important informational barriers that tend to prevent such
"credit market discipline" from materializing. When the government has private information
regarding a prospective project’s characteristics, its choice of projects is biased toward those
with high social bene…ts and low monetary revenue. And in cases where the mix of monetary
and social bene…ts is decided on only after the credit market has priced the government’s
debt, the government operates projects with an excessive emphasis on social bene…ts. Due to
these informational problems, the government is unable to harness the full revenue-generating
potential of its assets to improve its credit rating.
Section 3 looks at the …rst problem, i.e. private information regarding the project’s char-
acteristics. Consider, for example, a government that develops a new oil …eld. Future oil
revenue raises the probability that it will be able to repay its debt. An accurate prediction
of the …eld’s future output, however, is only available to the government, who has conducted
the geological survey. Since the credit market does not possess this information, the credit
rating will only re‡ect the expectations, based on publicly available information. Moreover,
whether the new …eld is economically viable cannot be inferred from the fact that the gov-
ernment found that developing the …eld is bene…cial, since the credit market does not know
the magnitude of non-monetary elements that in‡uenced the decision, such as job creation,
3
pressure from lobby groups, environmental risks, etc. Such private information gives rise to
adverse selection in the government’s decision whether or not to undertake a project. Relative
to the complete information benchmark, the government’s selection criterion is tilted in favor
of social bene…ts. Since the uninformed credit market treats every project as one with an
average income, the government is forced to forgo desirable income-intensive projects, whose
positive e¤ects on its credit worthiness are not fully appreciated. It also undertakes projects
with ample social bene…ts but negative true net value, taking advantage of the market’s in-
ability to observe their below-average monetary income. However, since the credit market
anticipates these choices, the revenue from projects undertaken in equilibrium is evaluated
correctly on average and the overall e¤ect on the government is, ex ante, negative.
In Section 4 we consider the second issue, i.e. the implementation decision in which the
government chooses a project’s mix of monetary revenue and social bene…ts. In the case of a
toll road, for example, the main tradeo¤ between future operating pro…ts and social bene…ts
is determined by the toll level. A higher toll increases revenue at the expense of reduced
driver surplus and increased congestion on alternative roads. During the construction stage,
the government would like to assure the credit market of an eventual stream of signi…cant toll
revenue, but once the road is operational, the government, now free of credit rating consid-
erations, has no reason to neglect social bene…ts and chooses a low toll. The credit market
foresees this at the construction stage and downgrades the credit rating accordingly. The
government thus faces a costly commitment problem, which takes the form of a dynamically
inconsistent toll policy.
As a natural application of our analysis we consider, in Section 5, the issue of privatization.
Privatization is commonly viewed as a tool for governments to capitalize the future monetary
income of public enterprises. In the case of a new project, the private operator shares the
setup cost in exchange for future revenue. For an existing enterprise, privatization generates
immediate revenue that can be used for other purposes. We show, however, that in the
absence of the informational limitations described in Sections 3 and 4 (and abstracting from
di¤erences in e¢ciency), privatization is exactly equivalent to the alternative of maintaining
ownership and raising the same amount of capital by issuing additional government debt.
That is, privatization simply lowers both sides of the government’s future balance sheet (debt
and revenue) by the same amount.
4
Privatization becomes non-neutral when these informational problems are present. It then
emerges as a way to overcome the adverse consequences of the government’s bias towards social
bene…ts. The dynamic inconsistency problem is solved since privatization delegates away the
government’s discretion over the implementation decision. However, unless the actions of the
pro…t-maximizing private operator can be su¢ciently restrained by a contract, it will utterly
disregard the social bene…ts and shift the implementation to the other extreme. Thus, the
government’s decision whether to privatize an asset involves a comparison between two regimes
– private versus government control – under which the respective modes of implementation are
shifted away from the desired outcome in opposite directions. The results of the comparison
are, in general, ambiguous.
Privatization can also change the nature of the adverse selection problem. A private entity
that bids for the project has the incentive to invest in verifying its revenue prospects. In this
way, it di¤ers from the holders of (non-dedicated) government debt who do not have su¢cient
incentive to perform a costly investigation of a speci…c project. While the fact that potential
private operators acquire full information may suggest that the adverse selection problem
should disappear, we show that such a result requires that operation by the government
not be superior to that by private operators for any project. In the general case, projects
heavily endowed with social bene…ts remain in government hands since the private operator’s
excessive focus on monetary revenue would be detrimental in this case. Revenue-rich projects
are provided by the private sector, which is better at extracting revenue from projects. The
ine¢ciency in project selection remains: the government has an incentive to privatize projects
with above-average monetary revenue and thereby gain the increment over the uninformed
credit market’s perceived value. This, however, negatively a¤ects the credit rating contribution
of those projects that the government decides to undertake on its own. The credit market
interprets the fact that the option to privatize was not exercised as a negative signal and infers
that the project has a below-average monetary income. Thus, while the option to privatize
projects must be bene…cial to the government ex post, an ex ante evaluation of this option is
complex. We show that there may be types of projects that the government would be better
o¤ by committing, ex ante, to never privatize.
The paper is related to the "social discount rate" literature (see, for example: Marglin
(1963), Harberger (1968), Sjaastad and Wisecarver (1977)), which is concerned with the ap-
5
propriate discount rate to be used by the government in its cost-bene…t analysis of prospective
public projects. Most of this literature focuses on an economy that is isolated from external
credit markets, and therefore government borrowing crowds out private investment. Our
framework di¤ers from the main stem of this literature in that the government can borrow in
global credit markets and is small relative to them (a notable exception is Edwards (1986);
we explore the relationship with that paper in Section 2.4). The contribution of our paper
to this literature is the focus on the composition of bene…ts from public projects and the
conclusion that the government should apply di¤erent discount rates to monetary and social
bene…ts. Moreover, we highlight the relevance of the credit markets’ expectations and the
e¤ect of informational asymmetries between the government and the credit market.
2 Credit rating and the valuation of public projects
In this section, we develop a minimalistic model that captures the e¤ect of a government’s
balance sheet on its credit rating. The model highlights the di¤erential e¤ect of monetary
revenue and social bene…ts from a government’s assets on its probability of default. This leads
to a valuation formula for public projects that is the basis for our subsequent analysis.
The basic premise of the model is that the government discounts the future at a higher
rate than the credit markets and therefore wishes to borrow. The …rst and main interpretation
of the model is of an open economy that is small relative to the global credit market. The
government mirrors a representative agent with a higher intertemporal substitution rate than
the rest of the "world". Under this interpretation, the model can be applied to governments
of subnational bodies such as municipalities and states, as well as national governments – as
long as the country is not large enough to signi…cantly a¤ect global interest rates. A second
interpretation of the model, which can also applied to large countries, is of a closed economy
in which the government discounts the future at a higher rate than its citizens and displays a
preference for supplying government goods over private consumption.
2
2
The heavier discounting by the government can be the result of, for example, the uncertainty as to whether
it will remain in power in the second period (as in Bulow and Rogo¤ (1989a)). A preference for supplying
public goods can be due to the positive e¤ect on the probability of being re-elected, to direct rents extracted
from running a large government (empire-building) and so on.
6
2.1 The basic model
There are two periods: In period 1, the government issues debt with face value d which it
promises to pay back to debtholders in period 2. The period 1 revenue from issuing the debt
(which depends on the credit market’s assessment of the risk of default) is 1. This revenue can
be used for consumption or for investment in public projects that will yield bene…ts in period
2. Period 1 utility, apart from the revenue from issuing debt 1 and investment expenses 1, is
normalized to 0:
n
1
= 1 ÷1.
The period 2 return on the public projects consists of a monetary component A and social
bene…ts 1 . Period 2 utility is the sum of A and 1 , plus a random income from other sources
: _ 0 (with cdf 1 and a continuous pdf ,), less the amount c _ d of debt that the government
decides to repay.
3
In the case of default (whether partial or total) on the debt, there is also a
utility loss of 1 1 for every dollar of default d ÷c.
4
Thus,
n
2
= A +1 +: ÷c ÷1 (d ÷c) .
Once it observes :. the government decides on c, subject to a monetary feasibility constraint:
max
e2[0;d]
n
2
:.t. A +: ÷c _ 0. (1)
Thus, while A and 1 are equivalent in terms of consumption value, only A can also be used
for debt repayment. For example, the government can use the revenue from an oil …eld (A) to
supply goods or to repay debt. In contrast, a nature preserve generates utility to its citizens
(1 ) that cannot be monetized to repay debt in case of …nancial distress.
3
For simplicity, we ignore the possibility of taxation and assume that s is exogenous. The e¤ects of allowing
taxation are discussed in Concluding Remark 6.2.
4
Under the open-economy interpretation, the loss L can represent the costs of direct trade sanctions or of
costly seizure of assets (see Bulow and Rogo¤ (1989a) for an in-depth discussion). L can also include the costs
of damage to reputation, which diminishes the ability to borrow in the future. In the case of a closed economy,
L can represent the costs to the government due to debtholders’ unrest, which may a¤ect their future voting
or even result in physical damage to government property.
7
The interest rate on riskless debt is normalized to 0. The government discounts the future
at a higher rate than does the credit market. Its intertemporal utility function is therefore:
l = n
1
+on
2
.
where n
1
and n
2
are the per-period utilities and o ¸ (0. 1) is the discount factor that applies to
the time between the two periods. This time spans from the project’s inception, through the
point at which it becomes operational, and until a "representative" point in the operational
phase (which is reduced in the model to a single point in time – period 2). Since this time
span tends to be of a magnitude of several years, o is considerably less than one.
2.2 The debt repayment decision
Since 1 1, the solution to the period 2 problem (1) is simply:
c
(d. A.
= min ¦d. A +:¦ . (2)
In other words, the government repays as much of its debt as it can and defaults (partially)
only when it doesn’t have enough funds to repay it all. This decision rule implies that the
government defaults whenever the realized income : is less than d ÷ A, which occurs with
probability 1 (d ÷A).
5
For convenience, we also denote 1
(d. A. = 1 (d ÷c
(d. A.).
5
There is a vast literature on sovereign debt, the risk of default and the mechanisms that enforce debt
repayment by sovereign borrowers. One strand of the literature, beginning with the seminal paper by Eaton
and Gersovitz (1981), considers the reputational e¤ects of default on the creditor’s future ability to borrow as
a deterrent to repudiating debt. The validity of this explanation has been questioned by Bulow and Rogo¤
(1989b). Another strand of the literature (see, for example, Bulow and Rogo¤ (1989a)) considers direct
sanctions that lenders can impose on creditor countries within their own borders (for example, trade sanctions
or seizure of assets) or through international bodies.
A main premise in the entire literature is that it is the country’s willingness, rather than its ability, to
repay its debt that determines the decision to default. The aim here is to develop a simple model of credit
rating, rather than a model that focuses solely on the default decision. Therefore, a simpli…ed framework
was chosen in which default on debt is solely the outcome of monetary constraints. While the model is a
simplistic description of the government’s default decision, it yields a very tractable formulation. The main
results developed in the rest of the paper regarding the e¤ects of credit rating on the valuation of public
projects should also follow from a more elaborate model of default and credit rating.
8
2.3 Determination of the debt level
We now analyze the government’s decision on the optimal debt level d, given its investment 1
and the anticipated returns on the investment A and 1 . We assume that credit markets are
risk-neutral. Since the interest rate on secure debt is normalized to 0, the period 1 revenue 1
from issuing debt with face value d is the expected payout:
1(d. A) = 1
s
[c
(d. A.] .
The government’s debt-determination problem in period 1 is:
l (A. 1. 1) = max
d
1(d. A) ÷1 +o (A +1 +1
s
[: ÷c
(d. A. ÷1
(d. A.]) . (3)
Substituting for 1(d. A) and taking the derivative with respect to d, we obtain the …rst-order
condition:
6
(1 ÷o)
J1
s
[c
]
Jd
= o
J1
s
[1
]
Jd
.
Note that the marginal dollar of debt augments c
(A. :. d) by 1 if eventually there is no
default – an event with probability 1÷1 (d ÷A) – and augments 1
(A. :. d) by 1 in the case
of default – an event with probability 1 (d ÷A). Thus:
J1
s
[c
(A. :. d)]
Jd
= 1 ÷1 (d ÷A)
and
J1
s
[1
(A. :. d)]
Jd
= 1 1 (d ÷A) .
Substituting these into the …rst-order condition yields:
(1 ÷o) (1 ÷1 (d ÷A)) = o1 1 (d ÷A) . (4)
The …rst-order condition is interpreted as follows: as the government issues more debt,
its credit rating deteriorates and the revenue from issuing an additional bond, J1,Jd =
J1(c
),Jd = 1 ÷1, decreases. At the margin, the probability of default 1 is so high that the
gains from trade which result from increasing the debt by one more dollar (LHS) equal the
discounted marginal loss in period 2 (RHS).
6
The derivations below show that the second-order condition is clearly satis…ed.
9
2.4 Evaluating the social and monetary bene…ts of projects
We now analyze the government’s evaluation of the marginal project. Suppose that the
government has already decided on a stock of projects with aggregate period 2 returns of A
and 1 (and has optimized the level of debt accordingly). It now contemplates undertaking one
more project, which will add r units to A and ¸ units to 1 , where r and ¸ are small relative
to the stock of government debt d.
7
In view of the credit-rating considerations analyzed in
the previous section, what is the period 1 value of the period 2 outcome (r. ¸)? That is, what
should the "social discount rate" be?
Theorem 1 below presents a simple valuation formula that forms the foundation of our
analysis in the following sections. Part 1 deals with the case where r is commonly known.
It shows that the government should employ two distinct social discount rates: One, which
equals the government discount rate o, to social bene…ts, and another, which equals the credit
market risk-free discount rate 1, to monetary bene…ts.
8
Part 2 deals with the case where the
credit market’s belief r
e
to di¤er from the true value r.
9
In this case, the valuation formula
includes a third term: the di¤erence r
e
÷r (which may be positive or negative) weighted by
the probability of default, 1.
7
For simplicity of exposition, it is assumed here that the project outcomes, x and y, are deterministic. All
our results would still follow if instead x and y were stochastic, as long as x is stochastically independent of
s. In this case, x and y would be interpreted as the expectations of the respective variables.
8
Note that even though the government has access to a perfectly elastic supply of credit, its discounting
of social bene…ts () is lower than the credit market’s discount rate (1). This di¤erence is possible because
default is costly and the cost is increasing in the level of government debt that is not backed by future
monetary revenues. Edwards (1986) also obtains a social discount rate for an open economy which is above
the international credit market rate. The mechanism by which his model yields an increasing marginal cost of
borrowing, however, is di¤erent from ours and is based on lenders and borrowers having a di¤erent perception
of the default probability.
9
More precisely, x
e
denotes the belief itself in the case that it is single-valued and the expectations of the
belief in the case that it puts weight on multiple values.
10
Theorem 1 Consider a small project that yields monetary bene…ts r and social bene…ts ¸.
1. In the case that r is commonly known, the …rst-order approximation of the project’s net
present value to the government is:
\ (r. ¸) = r +o¸. (5)
2. In the case that r is not commonly known, denote the expectations of the credit market’s
belief on r by r
e
and assume that the belief is independent of :, the period 2 income.
Then, the …rst-order approximation of the project’s value is:
\ (r. ¸; r
e
) = (1 ÷1) r +1 r
e
+o¸, (6)
or equivalently
\ (r. ¸; r
e
) = r +o¸ +1 (r
e
÷r) (7)
where 1 is the probability of default given the stocks of d and A.
Proof: Appendix.
While social bene…ts ¸ only has consumption value (which equals o per unit when dis-
counted to period 1 terms), monetary bene…ts r have an additional value, which comes from
two sources: its option value to repay debt and reduce direct default costs in cases of …nan-
cial distress, and its credit market value – the increase in the price of the debt issued by the
government due to the bondholders’ understanding that the additional r will help to repay
debt in case of default. Equation 5 states that the sum of the three components is 1 per unit.
Equation 6, deals with the case where the credit market’s belief r
e
may di¤er from the true
value r. It decomposes the total value of r to an internal value – the sum of the consumption
and option value – which equals 1 ÷1 and multiplies the true r, and the credit market value,
which applies to the belief r
e
, and equals 1.
10
The intuition behind the calculation of the internal and credit market values of r is as
follows: The internal value of each unit of r is a weighted average of 1 (the value in the case
10
There is also a third element that captures the bene…t to the government from re-optimizing the level of
debt d in response to the change in X. However, since the project is assumed to be small, this element is
negligible by the envelope theorem.
11
that there is no default and the added r is used for consumption) and 1 (the value in the case
of default in which the government uses the additional r to reduce the amount of the default).
The respective probabilities of the two events are 1 ÷ 1 and 1 (we can ignore the e¤ect of
r, which is relatively small, on the probability of default 1 (d ÷A) since it is of second-order
importance). Discounting the weighed average to re‡ect period 1 utility, the internal value
of r thus becomes o [(1 ÷1) 1 +1 1] per unit. By the …rst-order condition for the level of
debt (4), this is simply 1 ÷1.
As for the credit market value, recall that it is equal to the increase in the revenue 1
to the government from issuing the (same) debt d, due to undertaking the project. The
government’s creditors expect that an additional r
e
will be added to the debt repayment
whenever the government defaults – an event with probability 1. Thus, their expectations
of the payout on the entire debt d, and hence also the revenue 1, are augmented by r
e
1.
Hence, the credit market value of each unit of r
e
is 1.
Note that the internal value of r, i.e. 1 ÷1, is already larger than o, the value of ¸. Thus,
even when the credit market does not observe r, the government values r more than it values
¸. When the credit market does observe r, the government adds the credit market value, 1.
(We sometimes refer to this additional weight as the e¤ect of credit market discipline on the
government’s valuation of public projects.) The sum of these two values is simply 1.
11
We now turn to exploring two key situations in which the credit market does not observe
r before it prices the debt in period 1. Section 3 examines the case in which the government
has private information on r. Section 4 deals with the case in which the government chooses
r in period 2.
11
That the complete-information value of a unit of x equals 1 can also be deduced directly: The government
can increase its debt d by the same amount x, in which case, by (2), the payout e
will also increase by x,
independently of the income shock s. This leaves period 2 consumption unchanged and increases period 1
revenue R by x. Thus, because we assume that the government will always use any funds it has in period 2 to
repay debt and because the interest rate on secure debt is zero, every additional dollar that the government
has in period 2 – and which the market is aware of – is worth exactly one dollar in period 1 as well.
12
3 Project choice and adverse selection
In this section, we study the implications of informational asymmetry, whereby aspects of the
project are privately known to the government but not to the credit market. For example,
consider a discovery by Mexico of a new o¤shore oil …eld in its territorial waters in the gulf.
The expected oil output (r) is known only to the Mexican government which is in possession
of the geological survey. The development of the …eld also carries signi…cant environmental
risks, as exempli…ed in the recent oil spill from a BP well. The importance of these risks is
embodied in the geological data, but also depends on the Mexican government’s preferences
(such as the importance attributed to environmental concerns and the sensitivity to pressure
from the US which can also be a¤ected in case of a spill). These environmental risks, as well
as other externalities, such as job creation, determine ¸, which is thus also the government’s
private information. Assume that Mexico decides to invest in developing the oil …eld. Since
r is unknown to the credit market, its re-evaluation of the government’s credit rating can
respond only to its expectation, based on publicly available information. Moreover, even
the fact that the government decided that developing the …eld is bene…cial is not enough to
convince the market that r is large. Since the credit market does not know the magnitude of
¸, it will not be able to infer whether the project is expected to yield substantial monetary
bene…ts (which must be the case if the environmental risks are very high) or meager revenue
(which could be the case if the project creates many jobs).
We will show that the government’s informational advantage over the credit market can
lead to an adverse selection problem. Since the credit market responds similarly to all projects
of the same type, the government’s valuation and selection of projects is distorted. It under-
values projects rich in monetary income and overvalues projects poor in monetary income but
rich in social bene…ts. Thus, the set of projects it undertakes is not optimal in light of the
credit-market considerations.
Information structure and timeline
The government has the option to undertake a single project. The project has a setup
cost of 1 in period 1. The period 2 pair of monetary and social bene…ts, (r. ¸), is drawn
at the onset of period 1 from a …nite set H with a prior distribution G. We refer to pairs
(r. ¸) in H as "potential projects". (To be clear, one should interpret H not as a set of many
13
projects, but rather as the set of possible realizations of the attributes of one speci…c project
– for example, all the possible pairs of oil revenue r and environmental risks ¸ for a speci…c
oil …eld.)
The government privately learns which potential project was realized and decides whether
or not to undertake it. The credit market only knows the distribution G but not which
potential project was drawn from it.
12
Nonetheless, it observes the government’s decision
and takes it into consideration when it prices the government’s debt. That is, it prices the
government debt on the assumption that the project is an average one, conditional on the
fact that the government decided to undertake it.
13
In period 2, the project bears fruit (r. ¸).
Then, the period 2 income : is realized and the government’s debt-repayment decision is
made. We assume that the project is small relative to the government’s stock of debt (for any
(r. ¸) in H). Thus, the …rst-order approximations of a project’s valuation (Theorem 1) can
be applied.
3.1 The complete information benchmark
As a benchmark, we consider the case in which the realized project (r. ¸) is commonly known.
The government undertakes the project as long as its value exceeds its cost of 1 or, by Theorem
1, whenever:
\ (r. ¸) = r +o¸ _ 1.
The set of projects that the government will undertake under complete information is given
by:
GC\
CI
= ¦(r. ¸) : \ (r. ¸) _ 1¦ .
12
While small holders of the government’s debt clearly do not have su¢cient incentive to undertake an
expensive investigation of the project’s parameters, neither are there adequate incentives for credit rating
agencies (who rate the entire debt) to go beyond a crude estimate of the government’s assets and to perform
an in-depth analysis of each project. For instance, a credit rating agency will estimate the future output of a
new oil …eld according to historical precedents, rather than conduct its own geological survey.
13
We ignore possible signaling of the project’s characteristics through the re-adjustment of the level of debt.
This could be made formal by introducing some noise into the debt decision (either by assuming a small
amount of private information on the discount factor or in the market’s observation of the debt d), but this
is beyond the scope of the paper.
14
Figure 1 illustrates the set GC\
CI
. The line dividing between this region and that of rejected
projects (`C`) has the slope ÷1,o.
x
GOVCI
NON
y
Figure 1: Projects undertaken by the government - the complete information benchmark
The government’s ex ante utility is given by:
l
CI
=
(x;y)2GOV
CI
(\ (r. ¸) ÷1) G((r. ¸)) .
3.2 Asymmetric information
Under asymmetric information, the credit market only knows the distribution of projects G,
while the government knows the realization. Thus, when the government undertakes a project,
the (risk-neutral) credit market – unaware of the true monetary outcome of the project – takes
it to be that of an average project. More precisely, the price of government debt re‡ects the
expected monetary revenue from the project over all projects that the government undertakes
in equilibrium, denoted by r
e
, rather than the true r of the speci…c project.
Denote the set of possible projects that the government undertakes in equilibrium by:
GC\ = ¦(r. ¸) : \ (r. ¸; r
e
) _ 1¦
where r
e
= 1 [r[(r. ¸) ¸ GC\ ]
By Theorem 1, the government undertakes a project if:
r +o¸ +1 (r
e
÷r) _ 1.
This decision rule can be readily compared to its complete information counterpart (where
r
e
= r):
r +o¸ _ 1.
15
Thus, relative to the benchmark, the government adds the amount 1 (r
e
÷r) to the value
of the project. This term is positive for a project whose monetary bene…t r is below the
average r
e
and negative for projects with r r
e
. Consequently, the government undertakes
more projects with low r and high ¸ and fewer projects with high r and low ¸. Figure 2
illustrates the set of projects that the government would undertake. The boundary line is
‡atter than that for the complete information benchmark (a slope of (1 ÷1) ,o vs. a slope of
1,o). Thus, there are projects with negative net value under complete information that the
government undertakes under asymmetric information (the region denoted by +) and projects
with positive net value under complete information are rejected (the region denoted by ++).
x
GOV
y
Figure 2: Projects undertaken by government - asymmetric information
While the government’s decision rule is optimal ex post, given its knowledge of r, its ex
ante utility under asymmetric information is below that under complete information. The
credit market – whose expectations are rational – anticipates the government’s choices and
evaluates r
e
correctly, as the expectations of r over the actual set GC\ of projects that the
government undertakes. Thus the government "pays" for fooling the credit market. Its ex
ante utility is the sum of the complete information value of the projects this set, which di¤ers
from the set of all the projects with positive complete information value (GC\
CI
).
Denoting the government’s ex ante utility under asymmetric information by
l
AI
=
(x;y)2GOV
(\ (r. ¸; r
e
) ÷1) G((r. ¸)) ,
we thus obtain:
Theorem 2 If GC\ ,= GC\
CI
, then l
AI
< l
CI
.
16
Proof. Appendix.
In order to illustrate the results of this section, we consider two simple examples. In both,
a project is drawn from a distribution with two mass points with equal probabilities. In the
…rst, both projects have positive net value (and thus would be undertaken under complete
information), but under asymmetric information, the one with higher monetary revenue is
ine¢ciently rejected (i.e., located in region ++ in Figure 2). In the second example, only one
project has positive net value, but under asymmetric information, the second project, which
has negative value, is also undertaken – ine¢ciently (region +).
Example The government’s discount factor is o = 0.5 and the utility loss on each dollar
of defaulted debt is 1 = 4, so that, by (4), the probability of default is 1 = 0.2. A project
with setup cost 1 is drawn from a distribution with two points, c and /, each with equal prior
probability.
Case 1 c = (0.7. 0.65), / = (0.4. 1.25). Under complete information, \ (0.7. 0.65) = \ (0.4. 1.25) =
1.025 1 and therefore both projects would be undertaken. Under asymmetric information,
only / is undertaken in the unique equilibrium. To see why, observe that / must be under-
taken in any equilibrium since \ (0.4. 1.25; r
e
) _ \ (0.4. 1.25) for any 0.7 _ r
e
_ 0.4.
14
Next,
observe that c will not be taken in any equilibrium. Since / is undertaken with certainty,
r
e
is at most 0.5 0.4 + 0.5 0.7 = 0.55. But then \ (0.7. 0.65; r
e
) _ \ (0.7. 0.65; 0.55) =
1.025 + 0.2 (0.55 ÷0.7) = 0.995 < 1.
Case 2 c = (0.7. 0.65), / = (0.6. 0.79). Under complete information, \ (0.7. 0.65) = 1.025 1
and \ (0.6. 0.79) = 0.995 < 1 and therefore only c will be undertaken. Under asymmetric
information, the unique equilibrium is for both c and / to be undertaken. To see why, observe
that c must be undertaken in any equilibrium since \ (0.7. 0.65; r
e
) _ 1 for any 0.7 _ r
e
_ 0.6.
Next, observe that / will also be undertaken: Since c is undertaken with certainty, r
e
is at
least 0.5 0.7 + 0.5 0.6 = 0.65. But then \ (0.6. 0.79; r
e
) _ \ (0.6. 0.79; 0.65) = 0.995 + 0.2
(0.65 ÷0.6) = 1.005 1.
14
Formally, we assume that even out of equilibrium the belief x
e
is some convex combination of the two
possible values of x.
17
4 Project implementation and the government’s .
commitment problem
We now turn to analyzing a second type of informational asymmetry between the government
and the credit market whereby the government decides on a project’s mix of monetary and
social bene…ts after the credit market has priced its debt. Recall the toll road example, in
which increasing the toll yields higher income at the expense of reduced driver surplus and
higher congestion on alternative roads. Crucially, the decision on the mix of monetary and
social bene…ts is often taken long after the investment in the project.
To model the tradeo¤, we enrich the de…nition of a project in order to endogenize the choice
of the monetary to social bene…t mix (r. ¸). A project is now assumed to be a convex set of
feasible pairs (r. ¸) with a smooth e¢cient frontier from which the implementation point (r. ¸)
is chosen. The e¢cient frontier is represented by the function ¸ = /(r) which is decreasing,
smooth and concave and de…ned over the interval r ¸ [r
min
. r
max
]. We assume again that the
project is small relative to the total debt of the government, so that the valuation functions
derived in Theorem 1 can be applied. In order to simplify the exposition, we abstract from
the uncertainty studied in the previous section and assume that / is commonly known.
The timeline is as follows: In period 1, the decision to undertake the project is announced.
The credit market takes the project into consideration when pricing the government’s debt.
Importantly, the market prices the debt based on its (rational) expectations regarding the
implementation point (r. ¸). In period 2, the government chooses the mix (r. ¸). Then, : is
realized and the debt-repayment decision is made.
15
We will show that the informational asymmetry leads to a dynamic inconsistency problem:
In period 2, the government ignores credit rating implications and chooses an implementation
point that is skewed towards social bene…ts. Neglecting the monetary aspect, however, is
costly to the government since the credit market anticipates it. We start our analysis with a
benchmark case, in which the government does not face a commitment problem.
15
In reality, the operating phase (period 2) can be quite long. In that case, s is slowly revealed over time and
the implementation (e.g., the toll level) can change continuously over the operating period. Our reduced-form
model, in which the implementation decision is made before s is realized, can be viewed as a lower bound on
the timing of the implementation decision.
18
4.1 The full commitment benchmark
Assume that the government undertakes the project and commits to the implementation
scheme (r
c
. ¸
c
= /(r
c
)) before the credit market prices the debt. By Theorem 1, the govern-
ment’s maximization problem is:
max
x
\ (r. /(r)) = max
x
r +o/(r)
The …rst-order condition for r yields:
/
0
(r
c
) = ÷
1
o
.
The value of the project to the government is:
\ (r
c
. /(r
c
)) = r
c
+o/(r
c
) .
4.2 Government implementation absent commitment
Assume now that the government makes the implementation decision without commitment.
The valuation formula (Theorem 1) can be rewritten as:
\ (r. ¸; r
e
) = 1 r
e
+o
_
1 ÷1
o
r +¸
_
.
In period 1, the credit market prices the debt according to its expectation r
e
of the revenue
r that the government will choose in period 2. In period 2, the government takes r
e
as given,
and chooses r and ¸ = /(r) that maximize the expression in the square brackets:
max
x
1 ÷1
o
r +/(r).
Denoting the optimal solution by (r
gov
. ¸
gov
), the …rst-order condition is:
/
0
(r
gov
) = ÷
1 ÷1
o
. (8)
Thus, instead of choosing the point (r
c
. ¸
c
) on the e¢cient frontier, where its slope /
0
(r
c
) is
1
, the government now has no "credit market discipline", i.e. it ignores the credit market
value of r and chooses the point (r
gov
. ¸
gov
) where the slope is
1F
. Figure 3 illustrates the
relationship between the two points.
19
x
y
(x
c
,y
c
)
(x
gov
,y
gov
)
Figure 3: Government vs. commitment implementation
By rational expectations in the credit market, r
e
= r
gov
. We thus have:
\ (r
gov
. /(r
gov
) ; r
gov
) = \ (r
gov
. /(r
gov
)) = r
gov
+o/(r
gov
) .
By revealed preference, this is less than the full commitment outcome \ (r
c
. /(r
c
)) =
max
x
\ (r. /(r)).
The underlying intuition can be summarized as follows: The government ignores the ex-
ternality imposed on its debtholders when it chooses the type of implementation and thus
puts excessive weight on the social bene…ts ¸. However, debtholders foresee this and price
the debt accordingly. In a rational expectations equilibrium, the government pays exactly
for the negative externality. The government thus faces a dynamic inconsistency problem. It
would like to promise its creditors that it will shift implementation in favor of the monetary
component r, but such a promise would not be credible.
The above results are summarized in the following theorem:
Theorem 3
1. The full commitment outcome is (r
c
. ¸
c
), which is characterized by /
0
(r
c
) = ÷
1
.
2. A government with no ability to commit chooses the implementation (r
gov
. ¸
gov
), which
is characterized by /
0
(r
gov
) = ÷
1F
. Relative to (r
c
. ¸
c
), this implementation is tilted
towards higher social bene…ts and lower monetary bene…ts and yields lower ex ante value
for the project, i.e. \ (r
gov
. ¸
gov
) < \ (r
c
. ¸
c
).
20
5 Privatization
On October 15, 2004, the City of Chicago opened bids to operate the Chicago Skyway, a 7.8
mile toll bridge and road located on the City’s southeast side linking the Indiana Toll Road
(ITR) to the Dan Ryan Expressway. The winning bidder, the Cintra-Macquarie consortium,
agreed to make a $1.82 billion upfront payment (36 percent of Chicago’s budget) in exchange
for the right to operate and receive revenues for 99 years. Two years later, the State of Indiana
signed a 75-year lease agreement for the ITR with the same company. In return the State
received an upfront payment of $3.85 billion.
16
In both cases, the privatization had a favorable impact on credit rating. On February 2006,
Moody’s upgraded the city of Chicago’s overall bond rating from A1 to Aa3. In its report,
Moody’s cited one of the City’s credit strengths as “the vital infusion of $1.82 billion from the
lease of the Skyway."
17
The privatization also contributed to Standard & Poor’s upgrade of
Indiana’s credit rating from “AA” to “AA+”. Standard & Poor’s noted that the $3.85 billion
lease has contributed to the state’s improved credit standing.
18
Can our model shed light on the motivation for these privatizations? Can a reduction in
debt using the proceeds from privatization explain the improvement in credit rating?
In a world without informational asymmetries, the answer would be no. Thus, assuming
that the upfront payment from the highway privatizations equals the net present value of the
future revenue stream and that all proceeds of privatization were used to reduce debt,
19
priva-
tization leads to an equal reduction in both sides of the government balance sheet. However,
in our model the probability 1 of default on the marginal dollar of debt is simply a function
of the di¤erence d ÷A (since a government in …nancial distress uses all the future monetary
revenue A from projects it owns to pay its debt d). Thus, an equal reduction in debt and
revenue is neutral and does not a¤ect its credit rating.
The previous sections, however, showed that informational asymmetries cause the govern-
16
The account of these privatizations is based on Johnson, Luby and Kurbanov (2007).
17
Associated Press, February 10, 2006.
18
Standard & Poor’s Credit Pro…le for Indiana, January 24, 2006.
19
This is indeed the solution to the debt-determination condition (4).
21
ment to only partially internalize the credit market consequences of its decisions regarding
public projects and that it is thus unable to extract the full value of its assets. Speci…cally, the
results in Section 4 show that governments tend to operate public projects with an excessive
emphasis on social bene…ts. This is well illustrated by the ITR example. Johnson et al. (2007)
estimate the NPV of future cash ‡ow from ITR – had it remained under state control – at
$1.92 billion, far below the $3.85 billion lease. Not surprisingly, the high price paid for the
lease did not come for free. Under the contract with the private operator, the tolls immedi-
ately jumped from $4.65 to $8 for passenger vehicles and from $14.55 to $32 for trucks, with
a clause that allows for further increases of at least the change in nominal GDP per capita.
Had the State of Indiana operated the ITR with the same fees, its revenues would have been
much higher. However, in view of our results in Section 4, it could not commit to putting
so much weight on monetary revenue. Such a policy would be dynamically inconsistent since
social bene…ts such as driver surplus and reduced congestion on other roads would have always
remained a priority under state control.
In this section we explore the e¤ects of privatization. The model presented below combines
both the implementation issue exempli…ed in the ITR case above and the selection issue
discussed in Section 3 which is more relevant in the case of new projects.
In the context of implementation, we assume that under private operation there would be
less emphasis on social bene…ts, thus raising the project’s monetary revenue. By transferring
the project to a private operator, the government avoids the credit market’s predicament that
the project will be operated with a bias toward social bene…ts. However, unless the actions
of the pro…t-maximizing private operator can be su¢ciently limited by a contract, it will
utterly disregard the social bene…ts and reduce them further than is optimal, even taking into
account the credit-rating perspective. The comparison between the two regimes is, in general,
ambiguous.
In the context of project selection, we assume that a potential private owner who bids for
a project will learn its parameters – in contrast to the credit market which is composed of
small debtholders. While the fact that potential private operators acquire full information may
suggest that the adverse selection problemshould be solved, we showthat the problemdoes not
disappear. There are cases in which projects are privatized even though their implementation
by the government is more e¢cient. Moreover, there are examples in which the government
22
carries out projects with a negative net value and rejects projects with a positive net value,
while in the regime without the option to privatize it takes the e¢cient action.
20
5.1 The model
There is a …nite set of potential projects H. A project / ¸ H is a decreasing and concave
function, representing the e¢cient frontier ¸ = /(r) of all feasible implementation points. (To
focus on the credit rating dimension, we abstract from di¤erences between the e¢ciency of
the private operator and that of the government and assume that the frontier / is identical
irrespective of who undertakes the project.) At the onset of period 1, one project in H is
drawn according to a prior distribution G. The government privately learns its attributes and
decides whether to undertake it on its own, to privatize it or to reject it.
21
The credit market
observes this decision and takes it into consideration when it prices the government’s debt. In
20
There is a vast literature on privatization and its e¤ects. Vickers and Yarrow (1988) discuss the main
theoretical approaches and the experience with privatization programs in various countries. Megginson and
Netter (2001) survey the empirical studies on privatization. Two papers that have a more direct bearing on
our model are Hart, Shleifer and Vishny (1997) and Vickers and Yarrow (1991). Hart et al. demonstrates that
privatization can a¤ect the quality of the services provided. They argue that, under private control, managerial
e¤ort in both cost reduction and service improvement is greater than under public control. However, incentives
for cost reduction under privatization can be too large and thus have an adverse e¤ect on the quality of service
provided. The tendency of private operators to focus on the monetary aspects of the service (in this case, cost
reduction) and to ignore the bene…ts to the recipients is similar to what is postulated in our model. Vickers
and Yarrow (1991) argue that the raising of revenue is unlikely to be an important rationale for privatization
in developed countries. Selling bonds is likely to be a less costly way to raise revenue than selling equity due to
the direct costs of issuing equity (writing a prospectus, advertising, underwriting, etc.) and the more accurate
pricing of bonds. They argue, however, that the revenue motive may be relevant in less-developed countries
provided that the commitment not to expropriate equityholders is more credible than the commitment not to
expropriate bondholders. It may also be attractive to governments that are publicly committed to constraining
their borrowing levels. The arguments presented here show that a revenue motive may be important even in
the presence of a developed market for the country’s debt.
21
For purposes of exposition, the discussion relates to a new project. In the case of privatization of an
existing asset with the option to shut down, the analysis is the same except that the setup cost is taken to be
zero. Without this option, the government only has two options – retaining the project or privatizing it – but
the analysis that follows leads to similar insights.
23
period 2, the project (unless rejected) is operated by the government or the private operator.
Finally, the government’s income shock : is realized and its debt-repayment decision is made.
In the case that the government decides, in period 1, to privatize a project, it invites
potential private operators to bid for the right to …nance and operate the project and to collect
its future monetary bene…ts (bids can be negative, i.e., the private operator may demand a
subsidy). We assume that potential bidders know which project / was drawn.
22
We also
assume that there is competition among potential private operators and that they also have
access to the zero-interest credit market.
23
The project’s setup cost for a private operator is
1, which is the same as that for the government. In period 2, the private operator collects the
monetary revenue while the government enjoys the social bene…ts.
We analyze the game backwards: for any potential project /, we …nd the period-2 imple-
mentation schemes under government and private operation, denoted (r
gov
(/) . ¸
gov
(/)) and
(r
po
(/) . ¸
po
(/)), respectively (when no confusion arises we omit the (/) ). We then revert to
the project selection phase in period 1.
5.2 The value to the government of a privatized project
We begin by showing that the valuation formulas presented in Theorem 1 also apply to the case
of privatized projects. Since potential private operators have access to the zero-interest credit
market, the bids for the project equal its expected operating revenue, r
po
, minus the setup
cost of 1. In period 2, the government no longer receives monetary income from the project,
but does enjoy the social bene…t ¸
po
. The period 1 value to the government from privatizing
the project is thus r
po
÷1 +o¸
po
, i.e., exactly \ (r
po
. ¸
po
) ÷1. If the government had operated
the project on its own, the value would have been \ (r
gov
. ¸
gov
; r
e
)÷1 = \ (r
gov
. ¸
gov
)+1(r
e
÷
22
This assumption is justi…ed by the idea that, unlike the small holders of the government’s debt, potential
bidders for a project do have su¢cient incentive to invest resources in an expensive in-depth analysis of the
project’s attributes.
23
That a private operator can …nance the project at a riskless interest rate can be deduced from the following
assumptions: 1. The private operator maximizes pro…ts. 2. The credit market is aware that the private
operator knows h with certainty. 3. Bids are publicly observed. For brevity, we state this as an additional
assumption.
24
r
gov
) ÷1. This implies that if the implementations were identical (i.e., (r
po
. ¸
po
) = (r
gov
. ¸
gov
))
and if the credit market were fully informed about which project was drawn (and thus r
e
=
r
gov
), then the value of the project would be the same whether the government or the private
sector …nances the project. In other words, whether the government privatizes the project or
issues more debt and retains ownership and the right to future monetary revenue, then its
credit rating will remain unchanged. Any deviation from this neutrality must be due either
to a di¤erence in the modes of operation under the two regimes or to the credit market’s lack
of knowledge regarding the attributes of the project.
5.3 Implementation by the private operator
We distinguish between two possible situations: In the …rst, the private operator has full
discretion to choose the period-2 mode of operation. In the second, the project’s attributes
are such that the government is able, in period 1, to sign a binding contract with the operator
specifying how the project will be operated in period 2.
5.3.1 A private operator with full discretion
If the project is delegated to a private operator (PO) who is free to choose the implementation
scheme, it will ignore ¸ and choose the point that maximizes r:
(r
po
. ¸
po
) = (r
max
. /(r
max
)) .
The value of the privatized project to the government (before deducting the setup cost) is
\ (r
po
. ¸
po
), which is below the full commitment outcome \ (r
c
. ¸
c
). Recall (from Section 4)
that under government operation, the value of the project is \ (r
gov
. ¸
gov
), which is also below
\ (r
c
. ¸
c
). The comparison of \ (r
po
. ¸
po
) to \ (r
gov
. ¸
gov
) is in general ambiguous. These
two modes of implementation are shifted away from the commitment outcome in opposite
directions, as illustrated in Figure 4.
25
x
y
c
gov
po
Figure 4: Government vs. Private Operator implementation
5.3.2 Contracting with the private operator
Assume now that the government and the PO can write a binding contract (r. /(r) = ¸) that
speci…es the implementation scheme for the project. For example, the toll on a privatized
road can be contracted rather than left to the private operator’s discretion. In this case,
the government chooses r to maximize \ (r. /(r)). This is exactly the same maximization
problem as in the benchmark case (Section 4.1). The optimal contract is thus the same as
the full commitment outcome: (r
po
. ¸
po
) = (r
c
. /(r
c
)) and the value to the government is
\ (r
c
. /(r
c
)).
In this sense, one can view privatization as a commitment device: Whenever full contract-
ing with the private operator is feasible, a project should be delegated to the private sector,
thereby restoring the government’s …rst-best outcome.
Remark 1 An important insight is that the optimal ex ante contract will seem suboptimal
when viewed from an ex post perspective. For example, the toll on an existing toll road (as
contracted with the PO) might seem excessive when compared to that which generates the ex
post optimum (r
gov
. ¸
gov
). However, arguments that criticize the "excessive" toll might fail to
account for the ex ante considerations that put more weight on r as a result of credit market
discipline. In the ITR case, for example, there is an ongoing public outcry regarding the
diversions of tra¢c to already-congested state-owned routes as a result of the new aggressive
toll rate regime. A balanced evaluation of whether this privatization has bene…tted the people
of Indiana must also take into account the savings due to the improved credit rating in the
years since the privatization.
26
The results of this section are summarized in the following theorem:
Theorem 4 1. A private operator with full discretion chooses the implementation point
(r
po
. ¸
po
) = (r
max
. /(r
max
)). Relative to (r
c
. ¸
c
), this implementation is tilted towards
lower social bene…ts and higher monetary bene…ts and yields lower ex ante value for the
project, i.e. \ (r
po
. ¸
po
) < \ (r
c
. ¸
c
). If instead full contracting with the private operator
is feasible, then the outcome is (r
c
. ¸
c
).
2. \ (r
po
. ¸
po
) can be lower or higher than \ (r
gov
. ¸
gov
).
Remark 2 The analysis of the privatization scenario in this section (with or without contract-
ing) implicitly assumes that the government and the PO cannot renegotiate at the beginning
of period 2. Renegotiation in this case implies that the government will pay the PO to choose
(r
gov
. ¸
gov
) rather than the point it would have implemented otherwise (equivalently, the gov-
ernment could buy the project back from the PO). While there are gains to be made from such
trade at this stage, the credit market would foresee the period 2 renegotiation and monetary
transfer to the PO and would downgrade the government’s credit rating in period 1 to re‡ect
this, thus nullifying the gains from privatization.
Note, however, that while in many other dynamic applications the possibility of renego-
tiation is inherent and di¢cult to overcome, it is less likely in the context of privatization.
Here, various types of private information can be expected to break down the period-2 nego-
tiations. For example, the government may have private information regarding its relative
preference between r and ¸, re‡ecting factors such as the production functions for public and
government goods and politicians’ preferences (note that this information does not a¤ect the
period 1 negotiation if the PO does not expect to renegotiate). Another example would be if
the PO accumulates private information on parameters such as consumer demand, operating
costs, etc. during the construction and early stages of operation. Finally, even if renegotiation
were to change the outcome of implementation under privatization to make it identical to that
under government operation, privatization would still have a bene…cial e¤ect on the adverse
selection problem (see Theorem 5 below).
27
5.4 The decision whether to privatize
We now revert to analyzing the project-selection issue in period 1. Observe that if the credit
market had complete information on each project’s parameters, the government would pri-
vatize a project / whenever \ (r
po
(/) . ¸
po
(/)) max (\ (r
gov
(/) . ¸
gov
(/)) . 1) and operate
/ on its own whenever \ (r
gov
(/) . ¸
gov
(/)) max (\ (r
po
(/) . ¸
po
(/)) . 1). Clearly, in that
case the option to privatize can only be bene…cial. Projects that are transferred to private
operators generate higher values while those that remain under government ownership retain
the same value. In addition, some projects that would have been rejected due to their negative
value under government implementation may be pro…tably privatized.
Under incomplete information, this argument is no longer valid. The value of a project
under government operation is no longer independent of the equilibrium privatization de-
cision regarding other projects. In this case, the gross value of a self-operated project is
\ (r
gov
(/) . ¸
gov
(/) ; r
e
) rather than \ (r
gov
(/) . ¸
gov
(/)), where r
e
is the mean r of all projects
operated by the government in equilibrium. More formally, the space of projects is thus
partitioned into three subsets (some of which may be empty): projects undertaken by the
government (GC\ ), privatized projects (1C) and rejected projects (`C`), where:
GC\ = ¦/ ¸ H : \ (r
gov
(/) . ¸
gov
(/) ; r
e
) _ max (\ (r
po
(/) . ¸
po
(/)) . 1)¦
1C = ¦/ ¸ H : \ (r
po
(/) . ¸
po
(/)) _ max (\ (r
gov
(/) . ¸
gov
(/) ; r
e
) . 1)¦
where r
e
= 1 [r
gov
(/) [/ ¸ GC\ ] .
We start our analysis with the special case in which the complete information value of any
potential project under government ownership does not exceed that under private ownership.
That is, for any / ¸ H. \ (r
po
(/) . ¸
po
(/)) _ \ (r
gov
(/) . ¸
gov
(/)). This occurs if the distortion
due to the government’s dynamic inconsistency problem is more severe than that under private
operation. One notable case is when full contracting with the private operator over the
implementation of the project is feasible, thus making the PO’s implementation fully e¢cient
(see Section 5.3.2). Another interesting case, in which the condition holds with equality, is
that in which each potential project has only one feasible implementation point, i.e., any
/ ¸ H is a singleton (r
h
. ¸
h
). A concrete example is the oil …eld scenario discussed in Section
3, where even though there is substantial uncertainty regarding r and ¸, the only decision is
28
whether to develop the …eld, while no signi…cant tradeo¤ between the two is present in the
implementation.
Consider again the set of all projects that the government would have undertaken under
complete information. With the option to privatize, it is now de…ned as:
GC\
CI
= ¦/ ¸ H : \ (r
gov
(/) . ¸
gov
(/)) _ max (\ (r
po
(/) . ¸
po
(/)) . 1)¦ .
Note that this set may be empty (which would be the case, for example, if implementation by
a PO strictly dominates that by the government). If it is not empty, let r denote the minimal
revenue for a government-operated project under complete information:
r = min ¦r
gov
(/) : / ¸ GC\
CI
¦
The following theorem states that if implementation by a PO (weakly) dominates govern-
ment implementation, then PO’s will crowd out the government from undertaking projects.
The intuition behind this can be seen using an unraveling argument: For the realizations
of / that are most attractive from the credit market’s perspective (those with above-average
r
gov
(/)), the government prefers to privatize the project – otherwise, the credit markets would
take the project to be an average one. Understanding that, the credit market classi…es projects
that are not privatized as belonging to a set of inferior projects. Consequently, the govern-
ment is induced to also privatize the "better" projects in the new and smaller set, and so on.
The end result is that the government may only retain ownership of projects with minimal
monetary revenue or perhaps none at all.
Theorem 5 Assume that \ (r
po
(/) . ¸
po
(/)) _ \ (r
gov
(/) . ¸
gov
(/)) for all / ¸ H. Then,
the government does not undertake any project, except perhaps those with minimal revenue in
GC\
CI
, i.e. GC\ ¸ ¦/ ¸ H : / ¸ GC\
CI
and r
gov
(/) = r¦.
24
Proof. Appendix.
Note that if the set GC\ is non-empty, then r
e
= r, which implies that the government
obtains the complete information value \ (r
gov
(/) . ¸
gov
(/)) for every project / that it under-
takes. Thus, if the government decides to undertake a project, it must be that the value under
24
While our model assumes that the government and the PO face the same e¢cient frontier for each potential
project and can di¤er only in their choice of implementation point, the theorem clearly extends to the case in
which the e¢cient sets are di¤erent, as long as the PO still extracts a higher value from any potential project.
29
privatization \ (r
po
(/) . ¸
po
(/)) cannot strictly exceed \ (r
gov
(/) . ¸
gov
(/)). This argument
proves the following (weaker) corollary:
Corollary 6 If full contracting with the PO is feasible (so that \ (r
po
(/) . ¸
po
(/))
\ (r
gov
(/) . ¸
gov
(/)), for all / ¸ H) then the set GC\ is empty, i.e. the government does not
undertake any projects.
In the special case dealt with in Theorem 5, the project is implemented by whoever (either
the government or a PO) extracts a higher value under complete information (unless that value
is below the setup cost, in which case the project is rejected). Thus, there is no ine¢ciency
due to the credit market’s inferior information regarding the project’s attributes.
25
What is the ex ante bene…t of adding the option to privatize projects? In this special case
it is clearly positive. Not only does the value that the government extracts from the project
increase with privatization, but the introduction of privatization also corrects the distortion
in the selection of projects (undertaking projects with a negative value and rejecting positive-
value ones), which exists when the government is the only candidate for undertaking projects
(Section 3).
In general, however, the outcome need not be e¢cient. A project is sometimes implemented
by the entity that generates a lower complete-information value. In addition, as in the case
without privatization, the rejection criterion might be suboptimal. Remarkably, it might even
be the case that the government would have been better o¤, ex ante, if the option to privatize
projects did not exist at all. These potential ine¢ciencies are demonstrated in the following
examples:
Examples in which the option to privatize is disadvantageous
It is clear that when presented with a speci…c project, the government can only bene…t
from having the option to privatize. Why does this not imply that privatization is necessarily
bene…cial ex ante? Because the value of a project undertaken by the government depends on
the credit market’s assessment regarding its monetary revenue. This assessment changes if
the market knows that the government had the option to privatize the project but chose not
to exercise it.
25
This can formally be shown by a trivial extension of Theorem 2.
30
We present two examples that are constructed to highlight two separate e¤ects. In the
…rst, the same set of projects is undertaken with or without privatization. The source of
ine¢ciency in this example is suboptimal implementation under privatization. In the second,
the implementation of any project that is undertaken under both regimes is identical. However,
projects with positive net value that are undertaken by the government in the absence of the
privatization option are rejected when the option for privatization is added.
Each of the examples considers a di¤erent set of potential projects which are all transfor-
mations of the positive orthant of the unit circle. The transformation is de…ned by a pair of
positive scalars c
x
and c
y
, which "stretch" the unit circle in the r and ¸ directions, respec-
tively. For brevity, we refer to the potential project de…ned by c = (c
x
. c
y
) as "project c"
and to its e¢cient frontier as /
. We thus have:
¸ = /
(r) = c
y
_
1 ÷
r
2
c
2
x
for r ¸ [0. c
x
]
Figure 5 illustrates the Pareto frontier of the project for di¤erent values of c = (c
x
. c
y
):
x
y
x
y
x
y
?=(1,1) ?=(2,1) ?=(1,2)
1 2 1
1 1
2
Figure 5: Examples of potential projects
The project’s setup cost is 1 and the government’s discount factor is o = 1,3. The other
parameters of the model are chosen so that the probability of default is 1 = 1,3. Calculations
show that the government’s implementation is:
r
gov
(c) =
2c
2
x
_
4c
2
x
+c
2
y
; ¸
gov
(c) =
c
2
y
_
4c
2
x
+c
2
y
.
Under PO control, we have:
r
po
(c) = c
x
; ¸
po
(c) = 0.
31
In Example 1 below, there are two potential projects. Under complete information, both
have a higher value under government implementation than under private operation. (Note
that this is the opposite case to that analyzed in Theorem 5.) Under incomplete information,
the projects are misvalued by the credit market; nonetheless, the sum of misvaluations must
be null and the maximal ex ante value is obtained if both are kept under government control.
However, this is not an equilibrium if privatization were allowed since in that case the gov-
ernment would prefer to privatize the project with the higher monetary bene…t in order to
prevent it from being undervalued.
Example 1 There are two potential projects, (1. 1) and (1.21. 1), each assigned equal prior
probability.
The values of the projects under complete information exceed the setup cost of 1 and are
higher under government operation:
\ (r
gov
(1. 1) . ¸
gov
(1. 1)) = 1.043 \ (r
po
(1. 1) . ¸
po
(1. 1)) = 1
\ (r
gov
(1.21. 1) . ¸
gov
(1.21. 1)) = 1.245 \ (r
po
(1.21. 1) . ¸
po
(1.21. 1)) = 1.21
Thus, if the option to privatize does not exist, both projects are undertaken by the government.
If, however, the option to privatize does exist, this is no longer an equilibrium. To
see this, assume the opposite. We would then have r
e
= [r
gov
(1. 1) +r
gov
(1.21. 1)] ,2, im-
plying that \ (r
gov
(1.21. 1) . ¸
gov
(1.21. 1) ; r
e
) = 1.208. However this is slightly less than
\ (r
po
(1.21. 1) . ¸
po
(1.21. 1)) = 1.21. The government would thus prefer to transfer the project
into the hands of a PO – a contradiction.
Therefore, in the (unique) equilibrium, the project (1. 1) is undertaken by the government
and the project (1.21. 1) is delegated to a PO. The ex ante expected value to the government
under such an equilibrium is
1:043+1:21
2
, which is lower than in the case when privatization is
not allowed, i.e.
1:043+1:245
2
.
In Example 2, there are three potential projects. In the absence of privatization, all of
them are undertaken by the government. With the option of privatization, the one with very
high monetary bene…ts is transferred into private hands, even though its implementation un-
der government and PO ownership is identical. As in the previous example, the motive for
32
privatization is to avoid undervaluation. However, in this case there is a "market failure" with
regard to the remaining projects: adverse selection leads to the rejection of one of them, even
though it has a positive complete-information net value under government ownership. Essen-
tially, as long as the …rst project was part of the pool of government projects, it "subsidized"
the others and prevented market failure.
Example 2 There are three potential projects, (0. 3), (3. 0) and (7,8. 2), each of which is
assigned equal probability.
The …rst two projects are degenerate, i.e. each has a unique implementation point, (0. 3)
and (3. 0), respectively. Their values, if undertaken, are therefore independent of the regime
and equal to 1 and 3, respectively. The complete-information value of the third project is higher
than its cost of 1 only under government operation:
\ (r
gov
(7,8. 2) . ¸
gov
(7,8. 2)) = 1.078 \ (r
po
(7,8. 2) . ¸
po
(7,8. 2)) = 7,8.
If the option to privatize does not exist, the three projects are undertaken by the government.
(Since, in this case, r
e
= 1.192, the projects (0. 3) and (7,8. 2) are valued above their complete
information valuations and the value of the project (3. 0), which "subsidizes" the others, is
still well above its cost.)
If the government has the option to privatize, then the project (3. 0) is privatized so as not to
su¤er from undervaluation by the credit market since \ (3. 0; r
e
= 1.192) < \ (3. 0). However,
in that case, the project (7,8. 2), which has a positive net value, must be rejected. To see
this, assume that there is an equilibrium in which the government undertakes both remaining
projects (0. 3) and (7,8. 2). Then, r
e
= 0.288, and thus \ (r
gov
(7,8. 2) . ¸
gov
(7,8. 2) ; r
e
) =
0.982. Since this is less than the project’s cost of 1, the government would prefer to reject it
(7,8. 2) – a contradiction.
Note that in the absence of privatization, the cross-subsidy between the projects prevented a
market failure from arising. The cream-skimming e¤ect, by which the highest-revenue project
is privatized and thus no longer subsidizes the others, leads to market failure.
In conclusion, there are types of projects for which the option to privatize is bene…cial
for the government. In particular, privatization is unambiguously bene…cial if, at the imple-
mentation stage, the value of the project under private operation weakly exceeds that under
33
government operation (whether because there are no degrees of freedom in the implementa-
tion or because full contracting with the private operator is possible or because the distortion
due to the government’s dynamic inconsistency problem is more severe than that due to the
private operator’s exclusive focus on revenue for all possible realizations of the project). How-
ever, for types of projects for which the value is higher under government’s operation for some
realizations, it might be the case that the government would be better o¤ tying its own hands
and never privatize them.
6 Concluding comments
6.1 The magnitude of the model’s e¤ects
For the e¤ects demonstrated in this paper to have a sizable explanatory power in the real
world, it must be the case that the probability of (partial) default 1 is su¢ciently large. This
is because the severity of the dynamic inconsistency and adverse selection problems depends
on the weight 1 given to the credit market’s misassessment of monetary revenue (r
e
÷r) in
the valuation formula (7).
A cursory glance at bond prices might incorrectly suggest that the implied probability of
default is not very large. For example, even during the recent …nancial crisis, Italian 10-year
bonds has only yielded about 1% above the benchmark German bonds (perceived to be the
safest in the Euro zone). However, deriving the correct value of 1 in our model from these
bond yields involves three modi…cations that amplify the result signi…cantly.
First, actual spreads are expressed in annual terms, while the appropriate unit of time
in our model is a period of several years. It includes the time from the project’s inception
(period 1), through the point at which it becomes operational, and until a "middle" point in
the operational phase (period 2). Thus, the annual yields need to be multiplied by the total
number of years.
Second, note that in the event of default, the amount of debt that will not be repaid can
vary depending on the severity of economic distress in our model). Yield spreads in the
data re‡ect the expectations over that proportion of the total debt that will not be repaid.
34
In contrast, 1 in our model is the marginal probability of default, i.e. the probability that at
least one dollar of debt will not be repaid. It is thus much higher than the yield spread.
Third, even the benchmark German debt – with respect to which the above spread is
calculated – should not be considered immune to default in terms of our model. This is
because part of the debt may be de‡ated away by unexpected in‡ation, which would be
classi…ed as a partial default in our model. (Note that this risk component of German debt
is not even re‡ected in the price of Credit Default Swaps, since these instruments only cover
events of "declared" default.)
6.2 Taxation
Our model assumes that in the case of a severe income shock the government is obliged to
renege on some of its debt. The possibility of increasing taxes as an alternative to defaulting
is thus assumed away. Would our qualitative results change in a model that allows for taxes?
Assume that in period 2, a government that su¤ers an income shock (low and does not
have su¢cient funds to pay its debt has the option to increase taxes. It will choose this option
if the shadow cost of collecting the marginal dollar of taxes is below 1 – the loss from every
dollar of unpaid debt. There are, then, two possibilities:
1. Taxation is always preferred to default: Given the optimal level of debt, for all
possible realizations of the income shock :, the government prefers to meet all its obligations
by raising taxes. As in the model without taxes, the value of a project’s monetary bene…ts
equals 1 and that of social bene…ts equals o. That is, the government still prefers A to 1 .
The di¤erence 1÷o equals the (discounted) option value of A to reduce the cost of additional
taxation when : is low. However, in contrast to the model without taxes, where in the event
of default there is an external cost to creditors, in this case the entire cost associated with not
having su¢cient revenue to pay the debt – the cost of additional taxation – is internalized by
the government. Consequently, the credit market value of A is null and all the informational
problems discussed in this paper do not exist.
2. The government sometimes prefers to default: Given the optimal level of debt,
there are realizations of : for which the marginal cost of taxation is higher than that of
defaulting, and therefore the government prefers not to repay all its debt. In this case, our
35
qualitative results hold, with 1, the probability of default, representing those cases (i.e., the
event that : is below the level at which the government starts resorting to default). Since
there is an externality on creditors, A has a positive credit market value and the informational
problems are present in this case.
Which case better describes a speci…c real-world scenario? Note that whenever the yield
on a government bond is higher than the lowest yield in the market for a bond with the same
terms, it must be that the market attributes a positive probability to default. Then, case 2
is the more appropriate model and the insights of this paper are relevant. Moreover, even for
those governments whose bond yields are at the lowest tier, it may well be that the credit
market is still factoring in a possibility of default (see the previous remark).
6.3 In…nite horizon with debt rollover
Our modeling approach adopted the simplest framework which still captures the idea that
governments ignore the externality on debtholders and place insu¢cient weight on the mone-
tary revenue of public projects. One of our main simplifying assumptions has been that of only
two periods. In reality, there is never a …nal period and typically governments re…nance part
of their aggregate debt period by period. How dependent are the results on the two-period
setting? Could concerns regarding the terms of future debt rollover correct the government’s
incentives and restore the appropriate weight on A in its decisions? Or, in more formal terms,
would the equilibrium in such an in…nite horizon game include e¤ective enforcement strategies
on the part of the buyers of the new debt, which would deter the government from behaving
opportunistically?
We argue that our insights would remain qualitatively valid even in the in…nite horizon
setting. There are at least four reasons why e¤ective enforcement is not likely in our context.
First, in many circumstances the market only imperfectly monitors the government’s de-
cisions regarding projects. That is, over an extended period r might not be fully revealed
and only a noisy signal is obtained. This signal could be, for example, the aggregate …nancial
state at period 2 (A+: in our model) or, even worse, the binary variable of whether a default
has taken place. As shown in the vast literature on imperfect monitoring, it is often hard to
enforce non-opportunistic behavior in such environments.
36
Second, even if eventually the credit market accurately observes the project’s r, the pun-
ishment strategies needed to sustain cooperative behavior by the government will be ine¤ective
if its discounting of the future is severe. One could expect this to often be the case: recall
that the time horizon from project initiation to operation may be long, and that governments
may be myopic due to uncertain re-election prospects.
Third, punishment strategies, by which a deviation by the government from the "correct"
r is followed by the credit market charging a higher interest rate on the new debt, are limited,
in our context, to those in which the new interest rate re‡ects the true default probability.
Repeated game equilibria in which the credit market demands an interest rate that is higher
than the competitive equilibrium rate are not possible because each new small bondholder
would free-ride on the others’ punishment and buy more debt. Thus, e¤ective enforcement is
possible only if the continuation game has multiple rational expectations equilibria, each with
di¤erent government behavior and default probability, and the government’s past behavior
serves as a sunspot that determines which of the equilibria is selected.
Finally, note that even if such history-dependent equilibrium does exist, there always exists
another equilibrium in which the credit market ignores the history of government actions. In
such an equilibrium, the government necessarily acts in an opportunistic fashion. In other
words, the in…nite horizon model always has an equilibrium that replicates that of our two-
period model.
37
A Proofs
Theorem 1.
For clarity of exposition we present the proof for the case in which the market’s belief
r
e
is single valued. At the end, we explain how the proof can be modi…ed for the case of a
stochastic belief.
Assume that the initial stocks of monetary and social bene…ts are A and 1 , respectively.
By (3), the government’s utility after adding a small project (r. ¸; r
e
) is:
^
l (r. ¸; r
e
) = max
d
1(d. A +r
e
) ÷1 +o (A +r +1 +¸ +1
s
[: ÷c
(d. A +r. ÷1
(d. A +r.]) .
(Note that 1, period 1 revenue from issuing the debt, depends on the market’s perception r
e
,
while all period 2 values depend on the true r.) By the envelope theorem, the indirect e¤ect
due to debt reoptimization is negligible. Thus, the …rst-order approximation to the change in
the government’s utility,
^
l (r. ¸; r
e
) ÷
^
l (0. 0; 0) is:
\ (r. ¸; r
e
) = ¸
J
^
l (0. 0; 0)
J¸
+r
J
^
l (0. 0; 0)
Jr
+r
e
J
^
l (0. 0; 0)
Jr
e
Since
@
^
U(0;0;0)
@y
= o, the …rst summand is simply o¸. We now compute the second and third
summands. Note that:
J
^
l (0. 0; 0)
Jr
= o
_
1 ÷
J1
s
[c
(d. A.]
JA
÷
J1
s
[1
(d. A.]
JA
_
J
^
l (0. 0; 0)
Jr
e
=
J1(d
. A)
JA
=
J1
s
[c
(d. A.]
JA
,
and that:
J1
s
[1
(d. A.]
JA
=
J
JA
__
dX
s=0
1 (d ÷A ÷ , ) +
_
s
s=dX
0 ,)
_
= ÷1 0 , (d ÷A) ÷
_
dX
s=0
1 ,) + 0 , (d ÷A) = ÷1 (d ÷A) 1
J1
s
[c
(d. A.]
JA
=
J
JA
__
dX
s=0
(A + , ) +
_
s
s=dX
d ,)
_
= ÷d , (d ÷A) +
_
dX
s=0
,) +d , (d ÷A) = 1 (d ÷A) .
Thus, the second summand (the internal value of the project) is ro (1 ÷1 (d ÷A) +1 (d ÷A) 1).
By the …rst-order condition for the debt (4), this is simply r [1 ÷1 (d ÷A)]. The third sum-
mand (the credit market value) is r
e
1 (d ÷A). Summing the three elements yields Equation
6. Setting r = r
e
yields Equation 5.
38
In the case where r
e
is stochastic, and since the credit market is risk neutral, the revenue
from the debt d is 1(d. A +r
e
) = 1
s;x
e [c
(d. A +r
e
.]. Expanding the notion of "small
project" to imply that any value in the whole support of r
e
is small relative to the debt d,
and since r
e
is independent of :, we have 1
x
e
@Es[e
(d;X;s)]
@X
r
e
=
@Es[e
(d;X;s)]
@X
1
x
e [r
e
]. Abusing
notation and writing r
e
instead of 1 [r
e
], all the calculations above remain the same. QED.
Theorem 2.
The government’s ex ante utility under asymmetric information is:
l
AI
=
(x;y)2GOV
(\ (r. ¸; r
e
) ÷1) G((r. ¸))
=
(x;y)2GOV
(r +o¸ +1 (r
e
÷r) ÷1) G((r. ¸)) .
Since r
e
= 1 [r[(r. ¸) ¸ GC\ ], then
(x;y)2GOV
(r
e
÷r) G((r. ¸)) = 0. We thus have:
l
AI
=
(x;y)2GOV
(r +o¸ ÷1) G((r. ¸))
=
(x;y)2GOV
(\ (r. ¸) ÷1) G((r. ¸)) .
This is, of course, less than the government’s utility under symmetric information,
(x;y)2GOV
CI
(\ (r. ¸) ÷1) G((r. ¸)), which involves the same summand but summed exactly
over the set of points, GC\
CI
where it is positive. QED.
Theorem 5.
First note that in any equilibrium, all the projects / ¸ GC\ that the government un-
dertakes must generate the same monetary revenue r
gov
(/). Otherwise, there would exist a
project / ¸ GC\ with r
gov
(/) above the average r
e
. However, in that case, \ (r
po
(/) . ¸
po
(/)) _
\ (r
gov
(/) . ¸
gov
(/)) \ (r
gov
(/) . ¸
gov
(/) . r
e
), implying that the government would be bet-
ter o¤ privatizing it – a contradiction. Thus, in any equilibrium, GC\ is either empty or
there exists some r
1
such that for all / ¸ GC\ , r
gov
(/) = r
1
= r
e
.
Since r
1
= r
e
, there are no cross-subsidies between projects undertaken by the government:
\ (r
gov
(/) . ¸
gov
(/) . r
e
) = \ (r
gov
(/) . ¸
gov
(/)) for all / ¸ GC\ . Thus, / ¸ GC\ implies
/ ¸ GC\
CI
, i.e. GC\ ¸ GC\
CI
.
We next show that r
1
must equal r. By the de…nition of r, and since GC\ ¸ GC\
CI
, it
cannot be that r
1
< r. On the other hand, if it were the case that r
1
r, then for any project
39
/ ¸ GC\
CI
with r
gov
(/) = r we would have \ (r
po
(/) . ¸
po
(/)) = \ (r
gov
(/) . ¸
gov
(/)) <
\ (r
gov
(/) . ¸
gov
(/) . r
e
= r
1
), implying that the government would be better o¤ undertaking
it – a contradiction.
Clearly, if GC\
CI
is empty, then GC\ ¸ GC\
CI
is also empty. However, if GC\
CI
is
nonempty, it still can be the case that GC\ is empty. For example, if there exists a potential
project / with r
gov
(/) < r such that \ (r
gov
(/) . ¸
gov
(/)) < 1 and max ¦1. \ (r
po
(/) . ¸
po
(/))¦ <
\ (r
gov
(/) . ¸
gov
(/) . r
e
= r) then in any equilibrium in which GC\ is nonempty (and thus
r
e
= r), the government will prefer to undertake the project /. Note that to support an
equilibrium in which GC\ is empty, we must specify the market’s belief regarding r
gov
(/) in
the case that the government deviates and undertakes a project. Clearly, the belief that in
the case of a deviation r
gov
(/) is the minimal one over all projects / in the distribution would
do; in many cases other beliefs would also. QED
40
References
Bulow, J. and Rogo¤, K.: 1989a, A Constant Recontracting Model of Sovereign Debt, The
Journal of Political Economy 97(1), 155–178.
Bulow, J. and Rogo¤, K.: 1989b, Sovereign Debt: Is to Forgive to Forget?, American Economic
Review 79(1), 43–50.
Eaton, J. and Gersovitz, M.: 1981, Debt with potential repudiation: Theoretical and empirical
analysis, Review of Economic Studies 48(2), 289–309.
Edwards, S.: 1986, Country risk, foreign borrowing, and the social discount rate in an open
developing economy, Journal of International Money and Finance 5, S79–S96.
Harberger, A.: 1968, On measuring the social opportunity cost of public funds, Committee
on the Economics of Water Resources Development, Western Agricultural Economics
Research Council, Report no. 17 pp. 1–24.
Hart, O., Shleifer, A. and Vishny, R.: 1997, The Proper Scope of Government: Theory and
an Application to Prisons, The Quarterly Journal of Economics 112(4), 1127–1161.
Johnson, C., Luby, M. and Kurbanov, S.: 2007, Toll road privatization
transactions: The chicago skyway and indiana toll road, Available at
http://www.cviog.uga.edu/services/research/abfm/johnson.pdf .
Marglin, S.: 1963, The social rate of discount and the optimal rate of investment, The Quar-
terly Journal of Economics 77(1), 95–111.
Megginson, W. and Netter, J.: 2001, From State to Market: A Survey of Empirical Studies
on Privatization, Journal of Economic Literature 39(2).
Sjaastad, L. A. and Wisecarver, D. L.: 1977, The social cost of public …nance, The Journal
of Political Economy 85(3), 513–547.
Vickers, J. and Yarrow, G.: 1988, Privatization, MIT Press Cambridge, Mass.
Vickers, J. and Yarrow, G.: 1991, Economic Perspectives on Privatization, The Journal of
Economic Perspectives 5(2), 111–132.
41
doc_365719063.pdf
In investment, the bond credit rating assesses the credit worthiness of a corporation's or government debt issues. It is analogous to credit ratings for individuals.
Government’s Credit-Rating Concerns and the
Evaluation of Public Projects
+
Nadav Levy
IDC Herzliya
Ady Pauzner
Tel Aviv University
This version: September 2010
Abstract
Public projects typically generate both monetary revenue and social bene…ts that
cannot be monetized. Anticipated revenues from government-owned projects increase
the liklihood that the government will be able to repay its debt and thus improve its
credit rating and lower the …nancing costs of the debt. This should give monetary revenue
an added value relative to social bene…ts. However, informational problems – dynamic
inconsistency and adverse selection – push the government to an excessive emphasis on
social bene…ts, ignoring the external e¤ect of monetary revenue on debtholders. Since
the credit market anticipates this, the government’s credit rating is adversely a¤ected
and it is thus unable to extract the full potential of the projects. Finally, we show that
while privatization can sometimes alleviate these problems, there are cases in which the
government would be better o¤ if its hands were tied and it were not allowed to privatize.
Keywords: public projects, credit rating, social discount rate, privatization
We bene…tted from discussions with Alex Cukierman, Eddie Dekel, Daniel Ferreira, Elhanan Helpman,
Jose Scheinkman, Klaus Schmidt and Yossi Spiegel and from comments by seminar audiences at Bar-Ilan,
Ben-Gurion, Haifa, Hebrew and Tel-Aviv universities, IDC Herzliya, Banco de Mexico, the CEPR conference
on Government and Governance, Barcelona 2008 and the IFN conference on Privatization, Stockholm 2008.
1
1 Introduction
Governments on all levels – national, state and local – turn to credit markets to …nance a
signi…cant proportion of their activities. A government’s cost of borrowing is determined by its
credit rating, which re‡ects the credit market’s con…dence in its ability to repay its debt. This
can vary considerably between governments. For example, the yield spread between Italian
10-year euro-denominated bonds (rated A+ by S&P) and the equivalent German bonds (rated
AAA) has averaged about one percentage point over the last two years, and the yield spread
between 18-year general-obligation bonds issued by the State of California (rated Baa1 by
Moody’s) and those issued by the State of Georgia (rated Aaa) is currently
1
1.16%. The
e¤ect on a government’s cost of borrowing is substantial. For example, in the case of Italy,
with a debt-to-GDP ratio of over 100%, its lower credit rating is responsible for an additional
annual borrowing cost of more than one percent of GDP.
The impact on the government’s credit rating can be a major consideration in its decisions
regarding investment in public projects. The additional debt taken on to …nance a project
negatively a¤ects the credit rating. On the other hand, the addition of the project to the
asset side of the government’s balance sheet has a positive impact. Since these changes in the
credit rating a¤ect the cost of …nancing the government’s debt, they should be included in the
project’s cost-bene…t analysis. These considerations are important not only for large projects
with a major impact on the government’s credit rating, but also for projects that are small
relative to the size of the entire government debt. While their impact on the credit rating is
smaller, the associated change in the cost of …nancing the debt remains signi…cant relative to
their size.
While the e¤ect of a project’s …nancing cost on the credit rating is straightforward, un-
derstanding the e¤ect of its bene…ts is more subtle and requires a closer look at the nature of
public projects. Public projects typically generate both monetary revenue and social bene…ts
that cannot be monetized. For example, a new highway will yield both toll income and social
bene…ts in the form of driver surplus and reduced congestion on other roads. An oil …eld
generates sales revenue, but also carries environmental risks (in this case, a negative social
1
Sources: Yahoo! Finance, municipalbonds.com (September 2010).
2
bene…t). In Section 2 we develop a model that explains how the level of government debt
and the composition of its assets a¤ect the probability of default and the interest it pays on
its debt. Monetary revenue can be used to prevent default in cases of …nancial distress –
in contrast to social bene…ts that cannot be converted back into money. We derive a valu-
ation formula for public projects that takes into account their mix of monetary and social
bene…ts and serves as the main tool of the subsequent analysis. According to the formula,
monetary revenue has added value relative to social bene…ts, which can be decomposed into
two components: the option value of avoiding the penalties associated with default, and the
credit market value – the reduction in the cost of …nancing the government’s debt due to the
improved credit rating.
Crucially, this credit market value of the project depends on the credit market’s expec-
tations. Therefore, the information available to the market at the time the expectations are
formed plays a central role. While credit-rating considerations imply that the government
should place additional emphasis on a project’s monetary bene…ts relative to its social bene-
…ts, we argue that there are two important informational barriers that tend to prevent such
"credit market discipline" from materializing. When the government has private information
regarding a prospective project’s characteristics, its choice of projects is biased toward those
with high social bene…ts and low monetary revenue. And in cases where the mix of monetary
and social bene…ts is decided on only after the credit market has priced the government’s
debt, the government operates projects with an excessive emphasis on social bene…ts. Due to
these informational problems, the government is unable to harness the full revenue-generating
potential of its assets to improve its credit rating.
Section 3 looks at the …rst problem, i.e. private information regarding the project’s char-
acteristics. Consider, for example, a government that develops a new oil …eld. Future oil
revenue raises the probability that it will be able to repay its debt. An accurate prediction
of the …eld’s future output, however, is only available to the government, who has conducted
the geological survey. Since the credit market does not possess this information, the credit
rating will only re‡ect the expectations, based on publicly available information. Moreover,
whether the new …eld is economically viable cannot be inferred from the fact that the gov-
ernment found that developing the …eld is bene…cial, since the credit market does not know
the magnitude of non-monetary elements that in‡uenced the decision, such as job creation,
3
pressure from lobby groups, environmental risks, etc. Such private information gives rise to
adverse selection in the government’s decision whether or not to undertake a project. Relative
to the complete information benchmark, the government’s selection criterion is tilted in favor
of social bene…ts. Since the uninformed credit market treats every project as one with an
average income, the government is forced to forgo desirable income-intensive projects, whose
positive e¤ects on its credit worthiness are not fully appreciated. It also undertakes projects
with ample social bene…ts but negative true net value, taking advantage of the market’s in-
ability to observe their below-average monetary income. However, since the credit market
anticipates these choices, the revenue from projects undertaken in equilibrium is evaluated
correctly on average and the overall e¤ect on the government is, ex ante, negative.
In Section 4 we consider the second issue, i.e. the implementation decision in which the
government chooses a project’s mix of monetary revenue and social bene…ts. In the case of a
toll road, for example, the main tradeo¤ between future operating pro…ts and social bene…ts
is determined by the toll level. A higher toll increases revenue at the expense of reduced
driver surplus and increased congestion on alternative roads. During the construction stage,
the government would like to assure the credit market of an eventual stream of signi…cant toll
revenue, but once the road is operational, the government, now free of credit rating consid-
erations, has no reason to neglect social bene…ts and chooses a low toll. The credit market
foresees this at the construction stage and downgrades the credit rating accordingly. The
government thus faces a costly commitment problem, which takes the form of a dynamically
inconsistent toll policy.
As a natural application of our analysis we consider, in Section 5, the issue of privatization.
Privatization is commonly viewed as a tool for governments to capitalize the future monetary
income of public enterprises. In the case of a new project, the private operator shares the
setup cost in exchange for future revenue. For an existing enterprise, privatization generates
immediate revenue that can be used for other purposes. We show, however, that in the
absence of the informational limitations described in Sections 3 and 4 (and abstracting from
di¤erences in e¢ciency), privatization is exactly equivalent to the alternative of maintaining
ownership and raising the same amount of capital by issuing additional government debt.
That is, privatization simply lowers both sides of the government’s future balance sheet (debt
and revenue) by the same amount.
4
Privatization becomes non-neutral when these informational problems are present. It then
emerges as a way to overcome the adverse consequences of the government’s bias towards social
bene…ts. The dynamic inconsistency problem is solved since privatization delegates away the
government’s discretion over the implementation decision. However, unless the actions of the
pro…t-maximizing private operator can be su¢ciently restrained by a contract, it will utterly
disregard the social bene…ts and shift the implementation to the other extreme. Thus, the
government’s decision whether to privatize an asset involves a comparison between two regimes
– private versus government control – under which the respective modes of implementation are
shifted away from the desired outcome in opposite directions. The results of the comparison
are, in general, ambiguous.
Privatization can also change the nature of the adverse selection problem. A private entity
that bids for the project has the incentive to invest in verifying its revenue prospects. In this
way, it di¤ers from the holders of (non-dedicated) government debt who do not have su¢cient
incentive to perform a costly investigation of a speci…c project. While the fact that potential
private operators acquire full information may suggest that the adverse selection problem
should disappear, we show that such a result requires that operation by the government
not be superior to that by private operators for any project. In the general case, projects
heavily endowed with social bene…ts remain in government hands since the private operator’s
excessive focus on monetary revenue would be detrimental in this case. Revenue-rich projects
are provided by the private sector, which is better at extracting revenue from projects. The
ine¢ciency in project selection remains: the government has an incentive to privatize projects
with above-average monetary revenue and thereby gain the increment over the uninformed
credit market’s perceived value. This, however, negatively a¤ects the credit rating contribution
of those projects that the government decides to undertake on its own. The credit market
interprets the fact that the option to privatize was not exercised as a negative signal and infers
that the project has a below-average monetary income. Thus, while the option to privatize
projects must be bene…cial to the government ex post, an ex ante evaluation of this option is
complex. We show that there may be types of projects that the government would be better
o¤ by committing, ex ante, to never privatize.
The paper is related to the "social discount rate" literature (see, for example: Marglin
(1963), Harberger (1968), Sjaastad and Wisecarver (1977)), which is concerned with the ap-
5
propriate discount rate to be used by the government in its cost-bene…t analysis of prospective
public projects. Most of this literature focuses on an economy that is isolated from external
credit markets, and therefore government borrowing crowds out private investment. Our
framework di¤ers from the main stem of this literature in that the government can borrow in
global credit markets and is small relative to them (a notable exception is Edwards (1986);
we explore the relationship with that paper in Section 2.4). The contribution of our paper
to this literature is the focus on the composition of bene…ts from public projects and the
conclusion that the government should apply di¤erent discount rates to monetary and social
bene…ts. Moreover, we highlight the relevance of the credit markets’ expectations and the
e¤ect of informational asymmetries between the government and the credit market.
2 Credit rating and the valuation of public projects
In this section, we develop a minimalistic model that captures the e¤ect of a government’s
balance sheet on its credit rating. The model highlights the di¤erential e¤ect of monetary
revenue and social bene…ts from a government’s assets on its probability of default. This leads
to a valuation formula for public projects that is the basis for our subsequent analysis.
The basic premise of the model is that the government discounts the future at a higher
rate than the credit markets and therefore wishes to borrow. The …rst and main interpretation
of the model is of an open economy that is small relative to the global credit market. The
government mirrors a representative agent with a higher intertemporal substitution rate than
the rest of the "world". Under this interpretation, the model can be applied to governments
of subnational bodies such as municipalities and states, as well as national governments – as
long as the country is not large enough to signi…cantly a¤ect global interest rates. A second
interpretation of the model, which can also applied to large countries, is of a closed economy
in which the government discounts the future at a higher rate than its citizens and displays a
preference for supplying government goods over private consumption.
2
2
The heavier discounting by the government can be the result of, for example, the uncertainty as to whether
it will remain in power in the second period (as in Bulow and Rogo¤ (1989a)). A preference for supplying
public goods can be due to the positive e¤ect on the probability of being re-elected, to direct rents extracted
from running a large government (empire-building) and so on.
6
2.1 The basic model
There are two periods: In period 1, the government issues debt with face value d which it
promises to pay back to debtholders in period 2. The period 1 revenue from issuing the debt
(which depends on the credit market’s assessment of the risk of default) is 1. This revenue can
be used for consumption or for investment in public projects that will yield bene…ts in period
2. Period 1 utility, apart from the revenue from issuing debt 1 and investment expenses 1, is
normalized to 0:
n
1
= 1 ÷1.
The period 2 return on the public projects consists of a monetary component A and social
bene…ts 1 . Period 2 utility is the sum of A and 1 , plus a random income from other sources
: _ 0 (with cdf 1 and a continuous pdf ,), less the amount c _ d of debt that the government
decides to repay.
3
In the case of default (whether partial or total) on the debt, there is also a
utility loss of 1 1 for every dollar of default d ÷c.
4
Thus,
n
2
= A +1 +: ÷c ÷1 (d ÷c) .
Once it observes :. the government decides on c, subject to a monetary feasibility constraint:
max
e2[0;d]
n
2
:.t. A +: ÷c _ 0. (1)
Thus, while A and 1 are equivalent in terms of consumption value, only A can also be used
for debt repayment. For example, the government can use the revenue from an oil …eld (A) to
supply goods or to repay debt. In contrast, a nature preserve generates utility to its citizens
(1 ) that cannot be monetized to repay debt in case of …nancial distress.
3
For simplicity, we ignore the possibility of taxation and assume that s is exogenous. The e¤ects of allowing
taxation are discussed in Concluding Remark 6.2.
4
Under the open-economy interpretation, the loss L can represent the costs of direct trade sanctions or of
costly seizure of assets (see Bulow and Rogo¤ (1989a) for an in-depth discussion). L can also include the costs
of damage to reputation, which diminishes the ability to borrow in the future. In the case of a closed economy,
L can represent the costs to the government due to debtholders’ unrest, which may a¤ect their future voting
or even result in physical damage to government property.
7
The interest rate on riskless debt is normalized to 0. The government discounts the future
at a higher rate than does the credit market. Its intertemporal utility function is therefore:
l = n
1
+on
2
.
where n
1
and n
2
are the per-period utilities and o ¸ (0. 1) is the discount factor that applies to
the time between the two periods. This time spans from the project’s inception, through the
point at which it becomes operational, and until a "representative" point in the operational
phase (which is reduced in the model to a single point in time – period 2). Since this time
span tends to be of a magnitude of several years, o is considerably less than one.
2.2 The debt repayment decision
Since 1 1, the solution to the period 2 problem (1) is simply:
c
(d. A.
= min ¦d. A +:¦ . (2)In other words, the government repays as much of its debt as it can and defaults (partially)
only when it doesn’t have enough funds to repay it all. This decision rule implies that the
government defaults whenever the realized income : is less than d ÷ A, which occurs with
probability 1 (d ÷A).
5
For convenience, we also denote 1
(d. A.
= 1 (d ÷c(d. A.
).5
There is a vast literature on sovereign debt, the risk of default and the mechanisms that enforce debt
repayment by sovereign borrowers. One strand of the literature, beginning with the seminal paper by Eaton
and Gersovitz (1981), considers the reputational e¤ects of default on the creditor’s future ability to borrow as
a deterrent to repudiating debt. The validity of this explanation has been questioned by Bulow and Rogo¤
(1989b). Another strand of the literature (see, for example, Bulow and Rogo¤ (1989a)) considers direct
sanctions that lenders can impose on creditor countries within their own borders (for example, trade sanctions
or seizure of assets) or through international bodies.
A main premise in the entire literature is that it is the country’s willingness, rather than its ability, to
repay its debt that determines the decision to default. The aim here is to develop a simple model of credit
rating, rather than a model that focuses solely on the default decision. Therefore, a simpli…ed framework
was chosen in which default on debt is solely the outcome of monetary constraints. While the model is a
simplistic description of the government’s default decision, it yields a very tractable formulation. The main
results developed in the rest of the paper regarding the e¤ects of credit rating on the valuation of public
projects should also follow from a more elaborate model of default and credit rating.
8
2.3 Determination of the debt level
We now analyze the government’s decision on the optimal debt level d, given its investment 1
and the anticipated returns on the investment A and 1 . We assume that credit markets are
risk-neutral. Since the interest rate on secure debt is normalized to 0, the period 1 revenue 1
from issuing debt with face value d is the expected payout:
1(d. A) = 1
s
[c
(d. A.
] .The government’s debt-determination problem in period 1 is:
l (A. 1. 1) = max
d
1(d. A) ÷1 +o (A +1 +1
s
[: ÷c
(d. A.
÷1(d. A.
]) . (3)Substituting for 1(d. A) and taking the derivative with respect to d, we obtain the …rst-order
condition:
6
(1 ÷o)
J1
s
[c
]
Jd
= o
J1
s
[1
]
Jd
.
Note that the marginal dollar of debt augments c
(A. :. d) by 1 if eventually there is no
default – an event with probability 1÷1 (d ÷A) – and augments 1
(A. :. d) by 1 in the case
of default – an event with probability 1 (d ÷A). Thus:
J1
s
[c
(A. :. d)]
Jd
= 1 ÷1 (d ÷A)
and
J1
s
[1
(A. :. d)]
Jd
= 1 1 (d ÷A) .
Substituting these into the …rst-order condition yields:
(1 ÷o) (1 ÷1 (d ÷A)) = o1 1 (d ÷A) . (4)
The …rst-order condition is interpreted as follows: as the government issues more debt,
its credit rating deteriorates and the revenue from issuing an additional bond, J1,Jd =
J1(c
),Jd = 1 ÷1, decreases. At the margin, the probability of default 1 is so high that the
gains from trade which result from increasing the debt by one more dollar (LHS) equal the
discounted marginal loss in period 2 (RHS).
6
The derivations below show that the second-order condition is clearly satis…ed.
9
2.4 Evaluating the social and monetary bene…ts of projects
We now analyze the government’s evaluation of the marginal project. Suppose that the
government has already decided on a stock of projects with aggregate period 2 returns of A
and 1 (and has optimized the level of debt accordingly). It now contemplates undertaking one
more project, which will add r units to A and ¸ units to 1 , where r and ¸ are small relative
to the stock of government debt d.
7
In view of the credit-rating considerations analyzed in
the previous section, what is the period 1 value of the period 2 outcome (r. ¸)? That is, what
should the "social discount rate" be?
Theorem 1 below presents a simple valuation formula that forms the foundation of our
analysis in the following sections. Part 1 deals with the case where r is commonly known.
It shows that the government should employ two distinct social discount rates: One, which
equals the government discount rate o, to social bene…ts, and another, which equals the credit
market risk-free discount rate 1, to monetary bene…ts.
8
Part 2 deals with the case where the
credit market’s belief r
e
to di¤er from the true value r.
9
In this case, the valuation formula
includes a third term: the di¤erence r
e
÷r (which may be positive or negative) weighted by
the probability of default, 1.
7
For simplicity of exposition, it is assumed here that the project outcomes, x and y, are deterministic. All
our results would still follow if instead x and y were stochastic, as long as x is stochastically independent of
s. In this case, x and y would be interpreted as the expectations of the respective variables.
8
Note that even though the government has access to a perfectly elastic supply of credit, its discounting
of social bene…ts () is lower than the credit market’s discount rate (1). This di¤erence is possible because
default is costly and the cost is increasing in the level of government debt that is not backed by future
monetary revenues. Edwards (1986) also obtains a social discount rate for an open economy which is above
the international credit market rate. The mechanism by which his model yields an increasing marginal cost of
borrowing, however, is di¤erent from ours and is based on lenders and borrowers having a di¤erent perception
of the default probability.
9
More precisely, x
e
denotes the belief itself in the case that it is single-valued and the expectations of the
belief in the case that it puts weight on multiple values.
10
Theorem 1 Consider a small project that yields monetary bene…ts r and social bene…ts ¸.
1. In the case that r is commonly known, the …rst-order approximation of the project’s net
present value to the government is:
\ (r. ¸) = r +o¸. (5)
2. In the case that r is not commonly known, denote the expectations of the credit market’s
belief on r by r
e
and assume that the belief is independent of :, the period 2 income.
Then, the …rst-order approximation of the project’s value is:
\ (r. ¸; r
e
) = (1 ÷1) r +1 r
e
+o¸, (6)
or equivalently
\ (r. ¸; r
e
) = r +o¸ +1 (r
e
÷r) (7)
where 1 is the probability of default given the stocks of d and A.
Proof: Appendix.
While social bene…ts ¸ only has consumption value (which equals o per unit when dis-
counted to period 1 terms), monetary bene…ts r have an additional value, which comes from
two sources: its option value to repay debt and reduce direct default costs in cases of …nan-
cial distress, and its credit market value – the increase in the price of the debt issued by the
government due to the bondholders’ understanding that the additional r will help to repay
debt in case of default. Equation 5 states that the sum of the three components is 1 per unit.
Equation 6, deals with the case where the credit market’s belief r
e
may di¤er from the true
value r. It decomposes the total value of r to an internal value – the sum of the consumption
and option value – which equals 1 ÷1 and multiplies the true r, and the credit market value,
which applies to the belief r
e
, and equals 1.
10
The intuition behind the calculation of the internal and credit market values of r is as
follows: The internal value of each unit of r is a weighted average of 1 (the value in the case
10
There is also a third element that captures the bene…t to the government from re-optimizing the level of
debt d in response to the change in X. However, since the project is assumed to be small, this element is
negligible by the envelope theorem.
11
that there is no default and the added r is used for consumption) and 1 (the value in the case
of default in which the government uses the additional r to reduce the amount of the default).
The respective probabilities of the two events are 1 ÷ 1 and 1 (we can ignore the e¤ect of
r, which is relatively small, on the probability of default 1 (d ÷A) since it is of second-order
importance). Discounting the weighed average to re‡ect period 1 utility, the internal value
of r thus becomes o [(1 ÷1) 1 +1 1] per unit. By the …rst-order condition for the level of
debt (4), this is simply 1 ÷1.
As for the credit market value, recall that it is equal to the increase in the revenue 1
to the government from issuing the (same) debt d, due to undertaking the project. The
government’s creditors expect that an additional r
e
will be added to the debt repayment
whenever the government defaults – an event with probability 1. Thus, their expectations
of the payout on the entire debt d, and hence also the revenue 1, are augmented by r
e
1.
Hence, the credit market value of each unit of r
e
is 1.
Note that the internal value of r, i.e. 1 ÷1, is already larger than o, the value of ¸. Thus,
even when the credit market does not observe r, the government values r more than it values
¸. When the credit market does observe r, the government adds the credit market value, 1.
(We sometimes refer to this additional weight as the e¤ect of credit market discipline on the
government’s valuation of public projects.) The sum of these two values is simply 1.
11
We now turn to exploring two key situations in which the credit market does not observe
r before it prices the debt in period 1. Section 3 examines the case in which the government
has private information on r. Section 4 deals with the case in which the government chooses
r in period 2.
11
That the complete-information value of a unit of x equals 1 can also be deduced directly: The government
can increase its debt d by the same amount x, in which case, by (2), the payout e
will also increase by x,
independently of the income shock s. This leaves period 2 consumption unchanged and increases period 1
revenue R by x. Thus, because we assume that the government will always use any funds it has in period 2 to
repay debt and because the interest rate on secure debt is zero, every additional dollar that the government
has in period 2 – and which the market is aware of – is worth exactly one dollar in period 1 as well.
12
3 Project choice and adverse selection
In this section, we study the implications of informational asymmetry, whereby aspects of the
project are privately known to the government but not to the credit market. For example,
consider a discovery by Mexico of a new o¤shore oil …eld in its territorial waters in the gulf.
The expected oil output (r) is known only to the Mexican government which is in possession
of the geological survey. The development of the …eld also carries signi…cant environmental
risks, as exempli…ed in the recent oil spill from a BP well. The importance of these risks is
embodied in the geological data, but also depends on the Mexican government’s preferences
(such as the importance attributed to environmental concerns and the sensitivity to pressure
from the US which can also be a¤ected in case of a spill). These environmental risks, as well
as other externalities, such as job creation, determine ¸, which is thus also the government’s
private information. Assume that Mexico decides to invest in developing the oil …eld. Since
r is unknown to the credit market, its re-evaluation of the government’s credit rating can
respond only to its expectation, based on publicly available information. Moreover, even
the fact that the government decided that developing the …eld is bene…cial is not enough to
convince the market that r is large. Since the credit market does not know the magnitude of
¸, it will not be able to infer whether the project is expected to yield substantial monetary
bene…ts (which must be the case if the environmental risks are very high) or meager revenue
(which could be the case if the project creates many jobs).
We will show that the government’s informational advantage over the credit market can
lead to an adverse selection problem. Since the credit market responds similarly to all projects
of the same type, the government’s valuation and selection of projects is distorted. It under-
values projects rich in monetary income and overvalues projects poor in monetary income but
rich in social bene…ts. Thus, the set of projects it undertakes is not optimal in light of the
credit-market considerations.
Information structure and timeline
The government has the option to undertake a single project. The project has a setup
cost of 1 in period 1. The period 2 pair of monetary and social bene…ts, (r. ¸), is drawn
at the onset of period 1 from a …nite set H with a prior distribution G. We refer to pairs
(r. ¸) in H as "potential projects". (To be clear, one should interpret H not as a set of many
13
projects, but rather as the set of possible realizations of the attributes of one speci…c project
– for example, all the possible pairs of oil revenue r and environmental risks ¸ for a speci…c
oil …eld.)
The government privately learns which potential project was realized and decides whether
or not to undertake it. The credit market only knows the distribution G but not which
potential project was drawn from it.
12
Nonetheless, it observes the government’s decision
and takes it into consideration when it prices the government’s debt. That is, it prices the
government debt on the assumption that the project is an average one, conditional on the
fact that the government decided to undertake it.
13
In period 2, the project bears fruit (r. ¸).
Then, the period 2 income : is realized and the government’s debt-repayment decision is
made. We assume that the project is small relative to the government’s stock of debt (for any
(r. ¸) in H). Thus, the …rst-order approximations of a project’s valuation (Theorem 1) can
be applied.
3.1 The complete information benchmark
As a benchmark, we consider the case in which the realized project (r. ¸) is commonly known.
The government undertakes the project as long as its value exceeds its cost of 1 or, by Theorem
1, whenever:
\ (r. ¸) = r +o¸ _ 1.
The set of projects that the government will undertake under complete information is given
by:
GC\
CI
= ¦(r. ¸) : \ (r. ¸) _ 1¦ .
12
While small holders of the government’s debt clearly do not have su¢cient incentive to undertake an
expensive investigation of the project’s parameters, neither are there adequate incentives for credit rating
agencies (who rate the entire debt) to go beyond a crude estimate of the government’s assets and to perform
an in-depth analysis of each project. For instance, a credit rating agency will estimate the future output of a
new oil …eld according to historical precedents, rather than conduct its own geological survey.
13
We ignore possible signaling of the project’s characteristics through the re-adjustment of the level of debt.
This could be made formal by introducing some noise into the debt decision (either by assuming a small
amount of private information on the discount factor or in the market’s observation of the debt d), but this
is beyond the scope of the paper.
14
Figure 1 illustrates the set GC\
CI
. The line dividing between this region and that of rejected
projects (`C`) has the slope ÷1,o.
x
GOVCI
NON
y
Figure 1: Projects undertaken by the government - the complete information benchmark
The government’s ex ante utility is given by:
l
CI
=
(x;y)2GOV
CI
(\ (r. ¸) ÷1) G((r. ¸)) .
3.2 Asymmetric information
Under asymmetric information, the credit market only knows the distribution of projects G,
while the government knows the realization. Thus, when the government undertakes a project,
the (risk-neutral) credit market – unaware of the true monetary outcome of the project – takes
it to be that of an average project. More precisely, the price of government debt re‡ects the
expected monetary revenue from the project over all projects that the government undertakes
in equilibrium, denoted by r
e
, rather than the true r of the speci…c project.
Denote the set of possible projects that the government undertakes in equilibrium by:
GC\ = ¦(r. ¸) : \ (r. ¸; r
e
) _ 1¦
where r
e
= 1 [r[(r. ¸) ¸ GC\ ]
By Theorem 1, the government undertakes a project if:
r +o¸ +1 (r
e
÷r) _ 1.
This decision rule can be readily compared to its complete information counterpart (where
r
e
= r):
r +o¸ _ 1.
15
Thus, relative to the benchmark, the government adds the amount 1 (r
e
÷r) to the value
of the project. This term is positive for a project whose monetary bene…t r is below the
average r
e
and negative for projects with r r
e
. Consequently, the government undertakes
more projects with low r and high ¸ and fewer projects with high r and low ¸. Figure 2
illustrates the set of projects that the government would undertake. The boundary line is
‡atter than that for the complete information benchmark (a slope of (1 ÷1) ,o vs. a slope of
1,o). Thus, there are projects with negative net value under complete information that the
government undertakes under asymmetric information (the region denoted by +) and projects
with positive net value under complete information are rejected (the region denoted by ++).
x
GOV
y
Figure 2: Projects undertaken by government - asymmetric information
While the government’s decision rule is optimal ex post, given its knowledge of r, its ex
ante utility under asymmetric information is below that under complete information. The
credit market – whose expectations are rational – anticipates the government’s choices and
evaluates r
e
correctly, as the expectations of r over the actual set GC\ of projects that the
government undertakes. Thus the government "pays" for fooling the credit market. Its ex
ante utility is the sum of the complete information value of the projects this set, which di¤ers
from the set of all the projects with positive complete information value (GC\
CI
).
Denoting the government’s ex ante utility under asymmetric information by
l
AI
=
(x;y)2GOV
(\ (r. ¸; r
e
) ÷1) G((r. ¸)) ,
we thus obtain:
Theorem 2 If GC\ ,= GC\
CI
, then l
AI
< l
CI
.
16
Proof. Appendix.
In order to illustrate the results of this section, we consider two simple examples. In both,
a project is drawn from a distribution with two mass points with equal probabilities. In the
…rst, both projects have positive net value (and thus would be undertaken under complete
information), but under asymmetric information, the one with higher monetary revenue is
ine¢ciently rejected (i.e., located in region ++ in Figure 2). In the second example, only one
project has positive net value, but under asymmetric information, the second project, which
has negative value, is also undertaken – ine¢ciently (region +).
Example The government’s discount factor is o = 0.5 and the utility loss on each dollar
of defaulted debt is 1 = 4, so that, by (4), the probability of default is 1 = 0.2. A project
with setup cost 1 is drawn from a distribution with two points, c and /, each with equal prior
probability.
Case 1 c = (0.7. 0.65), / = (0.4. 1.25). Under complete information, \ (0.7. 0.65) = \ (0.4. 1.25) =
1.025 1 and therefore both projects would be undertaken. Under asymmetric information,
only / is undertaken in the unique equilibrium. To see why, observe that / must be under-
taken in any equilibrium since \ (0.4. 1.25; r
e
) _ \ (0.4. 1.25) for any 0.7 _ r
e
_ 0.4.
14
Next,
observe that c will not be taken in any equilibrium. Since / is undertaken with certainty,
r
e
is at most 0.5 0.4 + 0.5 0.7 = 0.55. But then \ (0.7. 0.65; r
e
) _ \ (0.7. 0.65; 0.55) =
1.025 + 0.2 (0.55 ÷0.7) = 0.995 < 1.
Case 2 c = (0.7. 0.65), / = (0.6. 0.79). Under complete information, \ (0.7. 0.65) = 1.025 1
and \ (0.6. 0.79) = 0.995 < 1 and therefore only c will be undertaken. Under asymmetric
information, the unique equilibrium is for both c and / to be undertaken. To see why, observe
that c must be undertaken in any equilibrium since \ (0.7. 0.65; r
e
) _ 1 for any 0.7 _ r
e
_ 0.6.
Next, observe that / will also be undertaken: Since c is undertaken with certainty, r
e
is at
least 0.5 0.7 + 0.5 0.6 = 0.65. But then \ (0.6. 0.79; r
e
) _ \ (0.6. 0.79; 0.65) = 0.995 + 0.2
(0.65 ÷0.6) = 1.005 1.
14
Formally, we assume that even out of equilibrium the belief x
e
is some convex combination of the two
possible values of x.
17
4 Project implementation and the government’s .
commitment problem
We now turn to analyzing a second type of informational asymmetry between the government
and the credit market whereby the government decides on a project’s mix of monetary and
social bene…ts after the credit market has priced its debt. Recall the toll road example, in
which increasing the toll yields higher income at the expense of reduced driver surplus and
higher congestion on alternative roads. Crucially, the decision on the mix of monetary and
social bene…ts is often taken long after the investment in the project.
To model the tradeo¤, we enrich the de…nition of a project in order to endogenize the choice
of the monetary to social bene…t mix (r. ¸). A project is now assumed to be a convex set of
feasible pairs (r. ¸) with a smooth e¢cient frontier from which the implementation point (r. ¸)
is chosen. The e¢cient frontier is represented by the function ¸ = /(r) which is decreasing,
smooth and concave and de…ned over the interval r ¸ [r
min
. r
max
]. We assume again that the
project is small relative to the total debt of the government, so that the valuation functions
derived in Theorem 1 can be applied. In order to simplify the exposition, we abstract from
the uncertainty studied in the previous section and assume that / is commonly known.
The timeline is as follows: In period 1, the decision to undertake the project is announced.
The credit market takes the project into consideration when pricing the government’s debt.
Importantly, the market prices the debt based on its (rational) expectations regarding the
implementation point (r. ¸). In period 2, the government chooses the mix (r. ¸). Then, : is
realized and the debt-repayment decision is made.
15
We will show that the informational asymmetry leads to a dynamic inconsistency problem:
In period 2, the government ignores credit rating implications and chooses an implementation
point that is skewed towards social bene…ts. Neglecting the monetary aspect, however, is
costly to the government since the credit market anticipates it. We start our analysis with a
benchmark case, in which the government does not face a commitment problem.
15
In reality, the operating phase (period 2) can be quite long. In that case, s is slowly revealed over time and
the implementation (e.g., the toll level) can change continuously over the operating period. Our reduced-form
model, in which the implementation decision is made before s is realized, can be viewed as a lower bound on
the timing of the implementation decision.
18
4.1 The full commitment benchmark
Assume that the government undertakes the project and commits to the implementation
scheme (r
c
. ¸
c
= /(r
c
)) before the credit market prices the debt. By Theorem 1, the govern-
ment’s maximization problem is:
max
x
\ (r. /(r)) = max
x
r +o/(r)
The …rst-order condition for r yields:
/
0
(r
c
) = ÷
1
o
.
The value of the project to the government is:
\ (r
c
. /(r
c
)) = r
c
+o/(r
c
) .
4.2 Government implementation absent commitment
Assume now that the government makes the implementation decision without commitment.
The valuation formula (Theorem 1) can be rewritten as:
\ (r. ¸; r
e
) = 1 r
e
+o
_
1 ÷1
o
r +¸
_
.
In period 1, the credit market prices the debt according to its expectation r
e
of the revenue
r that the government will choose in period 2. In period 2, the government takes r
e
as given,
and chooses r and ¸ = /(r) that maximize the expression in the square brackets:
max
x
1 ÷1
o
r +/(r).
Denoting the optimal solution by (r
gov
. ¸
gov
), the …rst-order condition is:
/
0
(r
gov
) = ÷
1 ÷1
o
. (8)
Thus, instead of choosing the point (r
c
. ¸
c
) on the e¢cient frontier, where its slope /
0
(r
c
) is
1
, the government now has no "credit market discipline", i.e. it ignores the credit market
value of r and chooses the point (r
gov
. ¸
gov
) where the slope is
1F
. Figure 3 illustrates the
relationship between the two points.
19
x
y
(x
c
,y
c
)
(x
gov
,y
gov
)
Figure 3: Government vs. commitment implementation
By rational expectations in the credit market, r
e
= r
gov
. We thus have:
\ (r
gov
. /(r
gov
) ; r
gov
) = \ (r
gov
. /(r
gov
)) = r
gov
+o/(r
gov
) .
By revealed preference, this is less than the full commitment outcome \ (r
c
. /(r
c
)) =
max
x
\ (r. /(r)).
The underlying intuition can be summarized as follows: The government ignores the ex-
ternality imposed on its debtholders when it chooses the type of implementation and thus
puts excessive weight on the social bene…ts ¸. However, debtholders foresee this and price
the debt accordingly. In a rational expectations equilibrium, the government pays exactly
for the negative externality. The government thus faces a dynamic inconsistency problem. It
would like to promise its creditors that it will shift implementation in favor of the monetary
component r, but such a promise would not be credible.
The above results are summarized in the following theorem:
Theorem 3
1. The full commitment outcome is (r
c
. ¸
c
), which is characterized by /
0
(r
c
) = ÷
1
.
2. A government with no ability to commit chooses the implementation (r
gov
. ¸
gov
), which
is characterized by /
0
(r
gov
) = ÷
1F
. Relative to (r
c
. ¸
c
), this implementation is tilted
towards higher social bene…ts and lower monetary bene…ts and yields lower ex ante value
for the project, i.e. \ (r
gov
. ¸
gov
) < \ (r
c
. ¸
c
).
20
5 Privatization
On October 15, 2004, the City of Chicago opened bids to operate the Chicago Skyway, a 7.8
mile toll bridge and road located on the City’s southeast side linking the Indiana Toll Road
(ITR) to the Dan Ryan Expressway. The winning bidder, the Cintra-Macquarie consortium,
agreed to make a $1.82 billion upfront payment (36 percent of Chicago’s budget) in exchange
for the right to operate and receive revenues for 99 years. Two years later, the State of Indiana
signed a 75-year lease agreement for the ITR with the same company. In return the State
received an upfront payment of $3.85 billion.
16
In both cases, the privatization had a favorable impact on credit rating. On February 2006,
Moody’s upgraded the city of Chicago’s overall bond rating from A1 to Aa3. In its report,
Moody’s cited one of the City’s credit strengths as “the vital infusion of $1.82 billion from the
lease of the Skyway."
17
The privatization also contributed to Standard & Poor’s upgrade of
Indiana’s credit rating from “AA” to “AA+”. Standard & Poor’s noted that the $3.85 billion
lease has contributed to the state’s improved credit standing.
18
Can our model shed light on the motivation for these privatizations? Can a reduction in
debt using the proceeds from privatization explain the improvement in credit rating?
In a world without informational asymmetries, the answer would be no. Thus, assuming
that the upfront payment from the highway privatizations equals the net present value of the
future revenue stream and that all proceeds of privatization were used to reduce debt,
19
priva-
tization leads to an equal reduction in both sides of the government balance sheet. However,
in our model the probability 1 of default on the marginal dollar of debt is simply a function
of the di¤erence d ÷A (since a government in …nancial distress uses all the future monetary
revenue A from projects it owns to pay its debt d). Thus, an equal reduction in debt and
revenue is neutral and does not a¤ect its credit rating.
The previous sections, however, showed that informational asymmetries cause the govern-
16
The account of these privatizations is based on Johnson, Luby and Kurbanov (2007).
17
Associated Press, February 10, 2006.
18
Standard & Poor’s Credit Pro…le for Indiana, January 24, 2006.
19
This is indeed the solution to the debt-determination condition (4).
21
ment to only partially internalize the credit market consequences of its decisions regarding
public projects and that it is thus unable to extract the full value of its assets. Speci…cally, the
results in Section 4 show that governments tend to operate public projects with an excessive
emphasis on social bene…ts. This is well illustrated by the ITR example. Johnson et al. (2007)
estimate the NPV of future cash ‡ow from ITR – had it remained under state control – at
$1.92 billion, far below the $3.85 billion lease. Not surprisingly, the high price paid for the
lease did not come for free. Under the contract with the private operator, the tolls immedi-
ately jumped from $4.65 to $8 for passenger vehicles and from $14.55 to $32 for trucks, with
a clause that allows for further increases of at least the change in nominal GDP per capita.
Had the State of Indiana operated the ITR with the same fees, its revenues would have been
much higher. However, in view of our results in Section 4, it could not commit to putting
so much weight on monetary revenue. Such a policy would be dynamically inconsistent since
social bene…ts such as driver surplus and reduced congestion on other roads would have always
remained a priority under state control.
In this section we explore the e¤ects of privatization. The model presented below combines
both the implementation issue exempli…ed in the ITR case above and the selection issue
discussed in Section 3 which is more relevant in the case of new projects.
In the context of implementation, we assume that under private operation there would be
less emphasis on social bene…ts, thus raising the project’s monetary revenue. By transferring
the project to a private operator, the government avoids the credit market’s predicament that
the project will be operated with a bias toward social bene…ts. However, unless the actions
of the pro…t-maximizing private operator can be su¢ciently limited by a contract, it will
utterly disregard the social bene…ts and reduce them further than is optimal, even taking into
account the credit-rating perspective. The comparison between the two regimes is, in general,
ambiguous.
In the context of project selection, we assume that a potential private owner who bids for
a project will learn its parameters – in contrast to the credit market which is composed of
small debtholders. While the fact that potential private operators acquire full information may
suggest that the adverse selection problemshould be solved, we showthat the problemdoes not
disappear. There are cases in which projects are privatized even though their implementation
by the government is more e¢cient. Moreover, there are examples in which the government
22
carries out projects with a negative net value and rejects projects with a positive net value,
while in the regime without the option to privatize it takes the e¢cient action.
20
5.1 The model
There is a …nite set of potential projects H. A project / ¸ H is a decreasing and concave
function, representing the e¢cient frontier ¸ = /(r) of all feasible implementation points. (To
focus on the credit rating dimension, we abstract from di¤erences between the e¢ciency of
the private operator and that of the government and assume that the frontier / is identical
irrespective of who undertakes the project.) At the onset of period 1, one project in H is
drawn according to a prior distribution G. The government privately learns its attributes and
decides whether to undertake it on its own, to privatize it or to reject it.
21
The credit market
observes this decision and takes it into consideration when it prices the government’s debt. In
20
There is a vast literature on privatization and its e¤ects. Vickers and Yarrow (1988) discuss the main
theoretical approaches and the experience with privatization programs in various countries. Megginson and
Netter (2001) survey the empirical studies on privatization. Two papers that have a more direct bearing on
our model are Hart, Shleifer and Vishny (1997) and Vickers and Yarrow (1991). Hart et al. demonstrates that
privatization can a¤ect the quality of the services provided. They argue that, under private control, managerial
e¤ort in both cost reduction and service improvement is greater than under public control. However, incentives
for cost reduction under privatization can be too large and thus have an adverse e¤ect on the quality of service
provided. The tendency of private operators to focus on the monetary aspects of the service (in this case, cost
reduction) and to ignore the bene…ts to the recipients is similar to what is postulated in our model. Vickers
and Yarrow (1991) argue that the raising of revenue is unlikely to be an important rationale for privatization
in developed countries. Selling bonds is likely to be a less costly way to raise revenue than selling equity due to
the direct costs of issuing equity (writing a prospectus, advertising, underwriting, etc.) and the more accurate
pricing of bonds. They argue, however, that the revenue motive may be relevant in less-developed countries
provided that the commitment not to expropriate equityholders is more credible than the commitment not to
expropriate bondholders. It may also be attractive to governments that are publicly committed to constraining
their borrowing levels. The arguments presented here show that a revenue motive may be important even in
the presence of a developed market for the country’s debt.
21
For purposes of exposition, the discussion relates to a new project. In the case of privatization of an
existing asset with the option to shut down, the analysis is the same except that the setup cost is taken to be
zero. Without this option, the government only has two options – retaining the project or privatizing it – but
the analysis that follows leads to similar insights.
23
period 2, the project (unless rejected) is operated by the government or the private operator.
Finally, the government’s income shock : is realized and its debt-repayment decision is made.
In the case that the government decides, in period 1, to privatize a project, it invites
potential private operators to bid for the right to …nance and operate the project and to collect
its future monetary bene…ts (bids can be negative, i.e., the private operator may demand a
subsidy). We assume that potential bidders know which project / was drawn.
22
We also
assume that there is competition among potential private operators and that they also have
access to the zero-interest credit market.
23
The project’s setup cost for a private operator is
1, which is the same as that for the government. In period 2, the private operator collects the
monetary revenue while the government enjoys the social bene…ts.
We analyze the game backwards: for any potential project /, we …nd the period-2 imple-
mentation schemes under government and private operation, denoted (r
gov
(/) . ¸
gov
(/)) and
(r
po
(/) . ¸
po
(/)), respectively (when no confusion arises we omit the (/) ). We then revert to
the project selection phase in period 1.
5.2 The value to the government of a privatized project
We begin by showing that the valuation formulas presented in Theorem 1 also apply to the case
of privatized projects. Since potential private operators have access to the zero-interest credit
market, the bids for the project equal its expected operating revenue, r
po
, minus the setup
cost of 1. In period 2, the government no longer receives monetary income from the project,
but does enjoy the social bene…t ¸
po
. The period 1 value to the government from privatizing
the project is thus r
po
÷1 +o¸
po
, i.e., exactly \ (r
po
. ¸
po
) ÷1. If the government had operated
the project on its own, the value would have been \ (r
gov
. ¸
gov
; r
e
)÷1 = \ (r
gov
. ¸
gov
)+1(r
e
÷
22
This assumption is justi…ed by the idea that, unlike the small holders of the government’s debt, potential
bidders for a project do have su¢cient incentive to invest resources in an expensive in-depth analysis of the
project’s attributes.
23
That a private operator can …nance the project at a riskless interest rate can be deduced from the following
assumptions: 1. The private operator maximizes pro…ts. 2. The credit market is aware that the private
operator knows h with certainty. 3. Bids are publicly observed. For brevity, we state this as an additional
assumption.
24
r
gov
) ÷1. This implies that if the implementations were identical (i.e., (r
po
. ¸
po
) = (r
gov
. ¸
gov
))
and if the credit market were fully informed about which project was drawn (and thus r
e
=
r
gov
), then the value of the project would be the same whether the government or the private
sector …nances the project. In other words, whether the government privatizes the project or
issues more debt and retains ownership and the right to future monetary revenue, then its
credit rating will remain unchanged. Any deviation from this neutrality must be due either
to a di¤erence in the modes of operation under the two regimes or to the credit market’s lack
of knowledge regarding the attributes of the project.
5.3 Implementation by the private operator
We distinguish between two possible situations: In the …rst, the private operator has full
discretion to choose the period-2 mode of operation. In the second, the project’s attributes
are such that the government is able, in period 1, to sign a binding contract with the operator
specifying how the project will be operated in period 2.
5.3.1 A private operator with full discretion
If the project is delegated to a private operator (PO) who is free to choose the implementation
scheme, it will ignore ¸ and choose the point that maximizes r:
(r
po
. ¸
po
) = (r
max
. /(r
max
)) .
The value of the privatized project to the government (before deducting the setup cost) is
\ (r
po
. ¸
po
), which is below the full commitment outcome \ (r
c
. ¸
c
). Recall (from Section 4)
that under government operation, the value of the project is \ (r
gov
. ¸
gov
), which is also below
\ (r
c
. ¸
c
). The comparison of \ (r
po
. ¸
po
) to \ (r
gov
. ¸
gov
) is in general ambiguous. These
two modes of implementation are shifted away from the commitment outcome in opposite
directions, as illustrated in Figure 4.
25
x
y
c
gov
po
Figure 4: Government vs. Private Operator implementation
5.3.2 Contracting with the private operator
Assume now that the government and the PO can write a binding contract (r. /(r) = ¸) that
speci…es the implementation scheme for the project. For example, the toll on a privatized
road can be contracted rather than left to the private operator’s discretion. In this case,
the government chooses r to maximize \ (r. /(r)). This is exactly the same maximization
problem as in the benchmark case (Section 4.1). The optimal contract is thus the same as
the full commitment outcome: (r
po
. ¸
po
) = (r
c
. /(r
c
)) and the value to the government is
\ (r
c
. /(r
c
)).
In this sense, one can view privatization as a commitment device: Whenever full contract-
ing with the private operator is feasible, a project should be delegated to the private sector,
thereby restoring the government’s …rst-best outcome.
Remark 1 An important insight is that the optimal ex ante contract will seem suboptimal
when viewed from an ex post perspective. For example, the toll on an existing toll road (as
contracted with the PO) might seem excessive when compared to that which generates the ex
post optimum (r
gov
. ¸
gov
). However, arguments that criticize the "excessive" toll might fail to
account for the ex ante considerations that put more weight on r as a result of credit market
discipline. In the ITR case, for example, there is an ongoing public outcry regarding the
diversions of tra¢c to already-congested state-owned routes as a result of the new aggressive
toll rate regime. A balanced evaluation of whether this privatization has bene…tted the people
of Indiana must also take into account the savings due to the improved credit rating in the
years since the privatization.
26
The results of this section are summarized in the following theorem:
Theorem 4 1. A private operator with full discretion chooses the implementation point
(r
po
. ¸
po
) = (r
max
. /(r
max
)). Relative to (r
c
. ¸
c
), this implementation is tilted towards
lower social bene…ts and higher monetary bene…ts and yields lower ex ante value for the
project, i.e. \ (r
po
. ¸
po
) < \ (r
c
. ¸
c
). If instead full contracting with the private operator
is feasible, then the outcome is (r
c
. ¸
c
).
2. \ (r
po
. ¸
po
) can be lower or higher than \ (r
gov
. ¸
gov
).
Remark 2 The analysis of the privatization scenario in this section (with or without contract-
ing) implicitly assumes that the government and the PO cannot renegotiate at the beginning
of period 2. Renegotiation in this case implies that the government will pay the PO to choose
(r
gov
. ¸
gov
) rather than the point it would have implemented otherwise (equivalently, the gov-
ernment could buy the project back from the PO). While there are gains to be made from such
trade at this stage, the credit market would foresee the period 2 renegotiation and monetary
transfer to the PO and would downgrade the government’s credit rating in period 1 to re‡ect
this, thus nullifying the gains from privatization.
Note, however, that while in many other dynamic applications the possibility of renego-
tiation is inherent and di¢cult to overcome, it is less likely in the context of privatization.
Here, various types of private information can be expected to break down the period-2 nego-
tiations. For example, the government may have private information regarding its relative
preference between r and ¸, re‡ecting factors such as the production functions for public and
government goods and politicians’ preferences (note that this information does not a¤ect the
period 1 negotiation if the PO does not expect to renegotiate). Another example would be if
the PO accumulates private information on parameters such as consumer demand, operating
costs, etc. during the construction and early stages of operation. Finally, even if renegotiation
were to change the outcome of implementation under privatization to make it identical to that
under government operation, privatization would still have a bene…cial e¤ect on the adverse
selection problem (see Theorem 5 below).
27
5.4 The decision whether to privatize
We now revert to analyzing the project-selection issue in period 1. Observe that if the credit
market had complete information on each project’s parameters, the government would pri-
vatize a project / whenever \ (r
po
(/) . ¸
po
(/)) max (\ (r
gov
(/) . ¸
gov
(/)) . 1) and operate
/ on its own whenever \ (r
gov
(/) . ¸
gov
(/)) max (\ (r
po
(/) . ¸
po
(/)) . 1). Clearly, in that
case the option to privatize can only be bene…cial. Projects that are transferred to private
operators generate higher values while those that remain under government ownership retain
the same value. In addition, some projects that would have been rejected due to their negative
value under government implementation may be pro…tably privatized.
Under incomplete information, this argument is no longer valid. The value of a project
under government operation is no longer independent of the equilibrium privatization de-
cision regarding other projects. In this case, the gross value of a self-operated project is
\ (r
gov
(/) . ¸
gov
(/) ; r
e
) rather than \ (r
gov
(/) . ¸
gov
(/)), where r
e
is the mean r of all projects
operated by the government in equilibrium. More formally, the space of projects is thus
partitioned into three subsets (some of which may be empty): projects undertaken by the
government (GC\ ), privatized projects (1C) and rejected projects (`C`), where:
GC\ = ¦/ ¸ H : \ (r
gov
(/) . ¸
gov
(/) ; r
e
) _ max (\ (r
po
(/) . ¸
po
(/)) . 1)¦
1C = ¦/ ¸ H : \ (r
po
(/) . ¸
po
(/)) _ max (\ (r
gov
(/) . ¸
gov
(/) ; r
e
) . 1)¦
where r
e
= 1 [r
gov
(/) [/ ¸ GC\ ] .
We start our analysis with the special case in which the complete information value of any
potential project under government ownership does not exceed that under private ownership.
That is, for any / ¸ H. \ (r
po
(/) . ¸
po
(/)) _ \ (r
gov
(/) . ¸
gov
(/)). This occurs if the distortion
due to the government’s dynamic inconsistency problem is more severe than that under private
operation. One notable case is when full contracting with the private operator over the
implementation of the project is feasible, thus making the PO’s implementation fully e¢cient
(see Section 5.3.2). Another interesting case, in which the condition holds with equality, is
that in which each potential project has only one feasible implementation point, i.e., any
/ ¸ H is a singleton (r
h
. ¸
h
). A concrete example is the oil …eld scenario discussed in Section
3, where even though there is substantial uncertainty regarding r and ¸, the only decision is
28
whether to develop the …eld, while no signi…cant tradeo¤ between the two is present in the
implementation.
Consider again the set of all projects that the government would have undertaken under
complete information. With the option to privatize, it is now de…ned as:
GC\
CI
= ¦/ ¸ H : \ (r
gov
(/) . ¸
gov
(/)) _ max (\ (r
po
(/) . ¸
po
(/)) . 1)¦ .
Note that this set may be empty (which would be the case, for example, if implementation by
a PO strictly dominates that by the government). If it is not empty, let r denote the minimal
revenue for a government-operated project under complete information:
r = min ¦r
gov
(/) : / ¸ GC\
CI
¦
The following theorem states that if implementation by a PO (weakly) dominates govern-
ment implementation, then PO’s will crowd out the government from undertaking projects.
The intuition behind this can be seen using an unraveling argument: For the realizations
of / that are most attractive from the credit market’s perspective (those with above-average
r
gov
(/)), the government prefers to privatize the project – otherwise, the credit markets would
take the project to be an average one. Understanding that, the credit market classi…es projects
that are not privatized as belonging to a set of inferior projects. Consequently, the govern-
ment is induced to also privatize the "better" projects in the new and smaller set, and so on.
The end result is that the government may only retain ownership of projects with minimal
monetary revenue or perhaps none at all.
Theorem 5 Assume that \ (r
po
(/) . ¸
po
(/)) _ \ (r
gov
(/) . ¸
gov
(/)) for all / ¸ H. Then,
the government does not undertake any project, except perhaps those with minimal revenue in
GC\
CI
, i.e. GC\ ¸ ¦/ ¸ H : / ¸ GC\
CI
and r
gov
(/) = r¦.
24
Proof. Appendix.
Note that if the set GC\ is non-empty, then r
e
= r, which implies that the government
obtains the complete information value \ (r
gov
(/) . ¸
gov
(/)) for every project / that it under-
takes. Thus, if the government decides to undertake a project, it must be that the value under
24
While our model assumes that the government and the PO face the same e¢cient frontier for each potential
project and can di¤er only in their choice of implementation point, the theorem clearly extends to the case in
which the e¢cient sets are di¤erent, as long as the PO still extracts a higher value from any potential project.
29
privatization \ (r
po
(/) . ¸
po
(/)) cannot strictly exceed \ (r
gov
(/) . ¸
gov
(/)). This argument
proves the following (weaker) corollary:
Corollary 6 If full contracting with the PO is feasible (so that \ (r
po
(/) . ¸
po
(/))
\ (r
gov
(/) . ¸
gov
(/)), for all / ¸ H) then the set GC\ is empty, i.e. the government does not
undertake any projects.
In the special case dealt with in Theorem 5, the project is implemented by whoever (either
the government or a PO) extracts a higher value under complete information (unless that value
is below the setup cost, in which case the project is rejected). Thus, there is no ine¢ciency
due to the credit market’s inferior information regarding the project’s attributes.
25
What is the ex ante bene…t of adding the option to privatize projects? In this special case
it is clearly positive. Not only does the value that the government extracts from the project
increase with privatization, but the introduction of privatization also corrects the distortion
in the selection of projects (undertaking projects with a negative value and rejecting positive-
value ones), which exists when the government is the only candidate for undertaking projects
(Section 3).
In general, however, the outcome need not be e¢cient. A project is sometimes implemented
by the entity that generates a lower complete-information value. In addition, as in the case
without privatization, the rejection criterion might be suboptimal. Remarkably, it might even
be the case that the government would have been better o¤, ex ante, if the option to privatize
projects did not exist at all. These potential ine¢ciencies are demonstrated in the following
examples:
Examples in which the option to privatize is disadvantageous
It is clear that when presented with a speci…c project, the government can only bene…t
from having the option to privatize. Why does this not imply that privatization is necessarily
bene…cial ex ante? Because the value of a project undertaken by the government depends on
the credit market’s assessment regarding its monetary revenue. This assessment changes if
the market knows that the government had the option to privatize the project but chose not
to exercise it.
25
This can formally be shown by a trivial extension of Theorem 2.
30
We present two examples that are constructed to highlight two separate e¤ects. In the
…rst, the same set of projects is undertaken with or without privatization. The source of
ine¢ciency in this example is suboptimal implementation under privatization. In the second,
the implementation of any project that is undertaken under both regimes is identical. However,
projects with positive net value that are undertaken by the government in the absence of the
privatization option are rejected when the option for privatization is added.
Each of the examples considers a di¤erent set of potential projects which are all transfor-
mations of the positive orthant of the unit circle. The transformation is de…ned by a pair of
positive scalars c
x
and c
y
, which "stretch" the unit circle in the r and ¸ directions, respec-
tively. For brevity, we refer to the potential project de…ned by c = (c
x
. c
y
) as "project c"
and to its e¢cient frontier as /
. We thus have:
¸ = /
(r) = c
y
_
1 ÷
r
2
c
2
x
for r ¸ [0. c
x
]
Figure 5 illustrates the Pareto frontier of the project for di¤erent values of c = (c
x
. c
y
):
x
y
x
y
x
y
?=(1,1) ?=(2,1) ?=(1,2)
1 2 1
1 1
2
Figure 5: Examples of potential projects
The project’s setup cost is 1 and the government’s discount factor is o = 1,3. The other
parameters of the model are chosen so that the probability of default is 1 = 1,3. Calculations
show that the government’s implementation is:
r
gov
(c) =
2c
2
x
_
4c
2
x
+c
2
y
; ¸
gov
(c) =
c
2
y
_
4c
2
x
+c
2
y
.
Under PO control, we have:
r
po
(c) = c
x
; ¸
po
(c) = 0.
31
In Example 1 below, there are two potential projects. Under complete information, both
have a higher value under government implementation than under private operation. (Note
that this is the opposite case to that analyzed in Theorem 5.) Under incomplete information,
the projects are misvalued by the credit market; nonetheless, the sum of misvaluations must
be null and the maximal ex ante value is obtained if both are kept under government control.
However, this is not an equilibrium if privatization were allowed since in that case the gov-
ernment would prefer to privatize the project with the higher monetary bene…t in order to
prevent it from being undervalued.
Example 1 There are two potential projects, (1. 1) and (1.21. 1), each assigned equal prior
probability.
The values of the projects under complete information exceed the setup cost of 1 and are
higher under government operation:
\ (r
gov
(1. 1) . ¸
gov
(1. 1)) = 1.043 \ (r
po
(1. 1) . ¸
po
(1. 1)) = 1
\ (r
gov
(1.21. 1) . ¸
gov
(1.21. 1)) = 1.245 \ (r
po
(1.21. 1) . ¸
po
(1.21. 1)) = 1.21
Thus, if the option to privatize does not exist, both projects are undertaken by the government.
If, however, the option to privatize does exist, this is no longer an equilibrium. To
see this, assume the opposite. We would then have r
e
= [r
gov
(1. 1) +r
gov
(1.21. 1)] ,2, im-
plying that \ (r
gov
(1.21. 1) . ¸
gov
(1.21. 1) ; r
e
) = 1.208. However this is slightly less than
\ (r
po
(1.21. 1) . ¸
po
(1.21. 1)) = 1.21. The government would thus prefer to transfer the project
into the hands of a PO – a contradiction.
Therefore, in the (unique) equilibrium, the project (1. 1) is undertaken by the government
and the project (1.21. 1) is delegated to a PO. The ex ante expected value to the government
under such an equilibrium is
1:043+1:21
2
, which is lower than in the case when privatization is
not allowed, i.e.
1:043+1:245
2
.
In Example 2, there are three potential projects. In the absence of privatization, all of
them are undertaken by the government. With the option of privatization, the one with very
high monetary bene…ts is transferred into private hands, even though its implementation un-
der government and PO ownership is identical. As in the previous example, the motive for
32
privatization is to avoid undervaluation. However, in this case there is a "market failure" with
regard to the remaining projects: adverse selection leads to the rejection of one of them, even
though it has a positive complete-information net value under government ownership. Essen-
tially, as long as the …rst project was part of the pool of government projects, it "subsidized"
the others and prevented market failure.
Example 2 There are three potential projects, (0. 3), (3. 0) and (7,8. 2), each of which is
assigned equal probability.
The …rst two projects are degenerate, i.e. each has a unique implementation point, (0. 3)
and (3. 0), respectively. Their values, if undertaken, are therefore independent of the regime
and equal to 1 and 3, respectively. The complete-information value of the third project is higher
than its cost of 1 only under government operation:
\ (r
gov
(7,8. 2) . ¸
gov
(7,8. 2)) = 1.078 \ (r
po
(7,8. 2) . ¸
po
(7,8. 2)) = 7,8.
If the option to privatize does not exist, the three projects are undertaken by the government.
(Since, in this case, r
e
= 1.192, the projects (0. 3) and (7,8. 2) are valued above their complete
information valuations and the value of the project (3. 0), which "subsidizes" the others, is
still well above its cost.)
If the government has the option to privatize, then the project (3. 0) is privatized so as not to
su¤er from undervaluation by the credit market since \ (3. 0; r
e
= 1.192) < \ (3. 0). However,
in that case, the project (7,8. 2), which has a positive net value, must be rejected. To see
this, assume that there is an equilibrium in which the government undertakes both remaining
projects (0. 3) and (7,8. 2). Then, r
e
= 0.288, and thus \ (r
gov
(7,8. 2) . ¸
gov
(7,8. 2) ; r
e
) =
0.982. Since this is less than the project’s cost of 1, the government would prefer to reject it
(7,8. 2) – a contradiction.
Note that in the absence of privatization, the cross-subsidy between the projects prevented a
market failure from arising. The cream-skimming e¤ect, by which the highest-revenue project
is privatized and thus no longer subsidizes the others, leads to market failure.
In conclusion, there are types of projects for which the option to privatize is bene…cial
for the government. In particular, privatization is unambiguously bene…cial if, at the imple-
mentation stage, the value of the project under private operation weakly exceeds that under
33
government operation (whether because there are no degrees of freedom in the implementa-
tion or because full contracting with the private operator is possible or because the distortion
due to the government’s dynamic inconsistency problem is more severe than that due to the
private operator’s exclusive focus on revenue for all possible realizations of the project). How-
ever, for types of projects for which the value is higher under government’s operation for some
realizations, it might be the case that the government would be better o¤ tying its own hands
and never privatize them.
6 Concluding comments
6.1 The magnitude of the model’s e¤ects
For the e¤ects demonstrated in this paper to have a sizable explanatory power in the real
world, it must be the case that the probability of (partial) default 1 is su¢ciently large. This
is because the severity of the dynamic inconsistency and adverse selection problems depends
on the weight 1 given to the credit market’s misassessment of monetary revenue (r
e
÷r) in
the valuation formula (7).
A cursory glance at bond prices might incorrectly suggest that the implied probability of
default is not very large. For example, even during the recent …nancial crisis, Italian 10-year
bonds has only yielded about 1% above the benchmark German bonds (perceived to be the
safest in the Euro zone). However, deriving the correct value of 1 in our model from these
bond yields involves three modi…cations that amplify the result signi…cantly.
First, actual spreads are expressed in annual terms, while the appropriate unit of time
in our model is a period of several years. It includes the time from the project’s inception
(period 1), through the point at which it becomes operational, and until a "middle" point in
the operational phase (period 2). Thus, the annual yields need to be multiplied by the total
number of years.
Second, note that in the event of default, the amount of debt that will not be repaid can
vary depending on the severity of economic distress
in our model). Yield spreads in thedata re‡ect the expectations over that proportion of the total debt that will not be repaid.
34
In contrast, 1 in our model is the marginal probability of default, i.e. the probability that at
least one dollar of debt will not be repaid. It is thus much higher than the yield spread.
Third, even the benchmark German debt – with respect to which the above spread is
calculated – should not be considered immune to default in terms of our model. This is
because part of the debt may be de‡ated away by unexpected in‡ation, which would be
classi…ed as a partial default in our model. (Note that this risk component of German debt
is not even re‡ected in the price of Credit Default Swaps, since these instruments only cover
events of "declared" default.)
6.2 Taxation
Our model assumes that in the case of a severe income shock the government is obliged to
renege on some of its debt. The possibility of increasing taxes as an alternative to defaulting
is thus assumed away. Would our qualitative results change in a model that allows for taxes?
Assume that in period 2, a government that su¤ers an income shock (low
and does nothave su¢cient funds to pay its debt has the option to increase taxes. It will choose this option
if the shadow cost of collecting the marginal dollar of taxes is below 1 – the loss from every
dollar of unpaid debt. There are, then, two possibilities:
1. Taxation is always preferred to default: Given the optimal level of debt, for all
possible realizations of the income shock :, the government prefers to meet all its obligations
by raising taxes. As in the model without taxes, the value of a project’s monetary bene…ts
equals 1 and that of social bene…ts equals o. That is, the government still prefers A to 1 .
The di¤erence 1÷o equals the (discounted) option value of A to reduce the cost of additional
taxation when : is low. However, in contrast to the model without taxes, where in the event
of default there is an external cost to creditors, in this case the entire cost associated with not
having su¢cient revenue to pay the debt – the cost of additional taxation – is internalized by
the government. Consequently, the credit market value of A is null and all the informational
problems discussed in this paper do not exist.
2. The government sometimes prefers to default: Given the optimal level of debt,
there are realizations of : for which the marginal cost of taxation is higher than that of
defaulting, and therefore the government prefers not to repay all its debt. In this case, our
35
qualitative results hold, with 1, the probability of default, representing those cases (i.e., the
event that : is below the level at which the government starts resorting to default). Since
there is an externality on creditors, A has a positive credit market value and the informational
problems are present in this case.
Which case better describes a speci…c real-world scenario? Note that whenever the yield
on a government bond is higher than the lowest yield in the market for a bond with the same
terms, it must be that the market attributes a positive probability to default. Then, case 2
is the more appropriate model and the insights of this paper are relevant. Moreover, even for
those governments whose bond yields are at the lowest tier, it may well be that the credit
market is still factoring in a possibility of default (see the previous remark).
6.3 In…nite horizon with debt rollover
Our modeling approach adopted the simplest framework which still captures the idea that
governments ignore the externality on debtholders and place insu¢cient weight on the mone-
tary revenue of public projects. One of our main simplifying assumptions has been that of only
two periods. In reality, there is never a …nal period and typically governments re…nance part
of their aggregate debt period by period. How dependent are the results on the two-period
setting? Could concerns regarding the terms of future debt rollover correct the government’s
incentives and restore the appropriate weight on A in its decisions? Or, in more formal terms,
would the equilibrium in such an in…nite horizon game include e¤ective enforcement strategies
on the part of the buyers of the new debt, which would deter the government from behaving
opportunistically?
We argue that our insights would remain qualitatively valid even in the in…nite horizon
setting. There are at least four reasons why e¤ective enforcement is not likely in our context.
First, in many circumstances the market only imperfectly monitors the government’s de-
cisions regarding projects. That is, over an extended period r might not be fully revealed
and only a noisy signal is obtained. This signal could be, for example, the aggregate …nancial
state at period 2 (A+: in our model) or, even worse, the binary variable of whether a default
has taken place. As shown in the vast literature on imperfect monitoring, it is often hard to
enforce non-opportunistic behavior in such environments.
36
Second, even if eventually the credit market accurately observes the project’s r, the pun-
ishment strategies needed to sustain cooperative behavior by the government will be ine¤ective
if its discounting of the future is severe. One could expect this to often be the case: recall
that the time horizon from project initiation to operation may be long, and that governments
may be myopic due to uncertain re-election prospects.
Third, punishment strategies, by which a deviation by the government from the "correct"
r is followed by the credit market charging a higher interest rate on the new debt, are limited,
in our context, to those in which the new interest rate re‡ects the true default probability.
Repeated game equilibria in which the credit market demands an interest rate that is higher
than the competitive equilibrium rate are not possible because each new small bondholder
would free-ride on the others’ punishment and buy more debt. Thus, e¤ective enforcement is
possible only if the continuation game has multiple rational expectations equilibria, each with
di¤erent government behavior and default probability, and the government’s past behavior
serves as a sunspot that determines which of the equilibria is selected.
Finally, note that even if such history-dependent equilibrium does exist, there always exists
another equilibrium in which the credit market ignores the history of government actions. In
such an equilibrium, the government necessarily acts in an opportunistic fashion. In other
words, the in…nite horizon model always has an equilibrium that replicates that of our two-
period model.
37
A Proofs
Theorem 1.
For clarity of exposition we present the proof for the case in which the market’s belief
r
e
is single valued. At the end, we explain how the proof can be modi…ed for the case of a
stochastic belief.
Assume that the initial stocks of monetary and social bene…ts are A and 1 , respectively.
By (3), the government’s utility after adding a small project (r. ¸; r
e
) is:
^
l (r. ¸; r
e
) = max
d
1(d. A +r
e
) ÷1 +o (A +r +1 +¸ +1
s
[: ÷c
(d. A +r.
÷1(d. A +r.
]) .(Note that 1, period 1 revenue from issuing the debt, depends on the market’s perception r
e
,
while all period 2 values depend on the true r.) By the envelope theorem, the indirect e¤ect
due to debt reoptimization is negligible. Thus, the …rst-order approximation to the change in
the government’s utility,
^
l (r. ¸; r
e
) ÷
^
l (0. 0; 0) is:
\ (r. ¸; r
e
) = ¸
J
^
l (0. 0; 0)
J¸
+r
J
^
l (0. 0; 0)
Jr
+r
e
J
^
l (0. 0; 0)
Jr
e
Since
@
^
U(0;0;0)
@y
= o, the …rst summand is simply o¸. We now compute the second and third
summands. Note that:
J
^
l (0. 0; 0)
Jr
= o
_
1 ÷
J1
s
[c
(d. A.
]JA
÷
J1
s
[1
(d. A.
]JA
_
J
^
l (0. 0; 0)
Jr
e
=
J1(d
. A)
JA
=
J1
s
[c
(d. A.
]JA
,
and that:
J1
s
[1
(d. A.
]JA
=
J
JA
__
dX
s=0
1 (d ÷A ÷
, ) +_
s
s=dX
0 ,
)_
= ÷1 0 , (d ÷A) ÷
_
dX
s=0
1 ,
) + 0 , (d ÷A) = ÷1 (d ÷A) 1J1
s
[c
(d. A.
]JA
=
J
JA
__
dX
s=0
(A +
, ) +_
s
s=dX
d ,
)_
= ÷d , (d ÷A) +
_
dX
s=0
,
) +d , (d ÷A) = 1 (d ÷A) .Thus, the second summand (the internal value of the project) is ro (1 ÷1 (d ÷A) +1 (d ÷A) 1).
By the …rst-order condition for the debt (4), this is simply r [1 ÷1 (d ÷A)]. The third sum-
mand (the credit market value) is r
e
1 (d ÷A). Summing the three elements yields Equation
6. Setting r = r
e
yields Equation 5.
38
In the case where r
e
is stochastic, and since the credit market is risk neutral, the revenue
from the debt d is 1(d. A +r
e
) = 1
s;x
e [c
(d. A +r
e
.
]. Expanding the notion of "smallproject" to imply that any value in the whole support of r
e
is small relative to the debt d,
and since r
e
is independent of :, we have 1
x
e
@Es[e
(d;X;s)]
@X
r
e
=
@Es[e
(d;X;s)]
@X
1
x
e [r
e
]. Abusing
notation and writing r
e
instead of 1 [r
e
], all the calculations above remain the same. QED.
Theorem 2.
The government’s ex ante utility under asymmetric information is:
l
AI
=
(x;y)2GOV
(\ (r. ¸; r
e
) ÷1) G((r. ¸))
=
(x;y)2GOV
(r +o¸ +1 (r
e
÷r) ÷1) G((r. ¸)) .
Since r
e
= 1 [r[(r. ¸) ¸ GC\ ], then
(x;y)2GOV
(r
e
÷r) G((r. ¸)) = 0. We thus have:
l
AI
=
(x;y)2GOV
(r +o¸ ÷1) G((r. ¸))
=
(x;y)2GOV
(\ (r. ¸) ÷1) G((r. ¸)) .
This is, of course, less than the government’s utility under symmetric information,
(x;y)2GOV
CI
(\ (r. ¸) ÷1) G((r. ¸)), which involves the same summand but summed exactly
over the set of points, GC\
CI
where it is positive. QED.
Theorem 5.
First note that in any equilibrium, all the projects / ¸ GC\ that the government un-
dertakes must generate the same monetary revenue r
gov
(/). Otherwise, there would exist a
project / ¸ GC\ with r
gov
(/) above the average r
e
. However, in that case, \ (r
po
(/) . ¸
po
(/)) _
\ (r
gov
(/) . ¸
gov
(/)) \ (r
gov
(/) . ¸
gov
(/) . r
e
), implying that the government would be bet-
ter o¤ privatizing it – a contradiction. Thus, in any equilibrium, GC\ is either empty or
there exists some r
1
such that for all / ¸ GC\ , r
gov
(/) = r
1
= r
e
.
Since r
1
= r
e
, there are no cross-subsidies between projects undertaken by the government:
\ (r
gov
(/) . ¸
gov
(/) . r
e
) = \ (r
gov
(/) . ¸
gov
(/)) for all / ¸ GC\ . Thus, / ¸ GC\ implies
/ ¸ GC\
CI
, i.e. GC\ ¸ GC\
CI
.
We next show that r
1
must equal r. By the de…nition of r, and since GC\ ¸ GC\
CI
, it
cannot be that r
1
< r. On the other hand, if it were the case that r
1
r, then for any project
39
/ ¸ GC\
CI
with r
gov
(/) = r we would have \ (r
po
(/) . ¸
po
(/)) = \ (r
gov
(/) . ¸
gov
(/)) <
\ (r
gov
(/) . ¸
gov
(/) . r
e
= r
1
), implying that the government would be better o¤ undertaking
it – a contradiction.
Clearly, if GC\
CI
is empty, then GC\ ¸ GC\
CI
is also empty. However, if GC\
CI
is
nonempty, it still can be the case that GC\ is empty. For example, if there exists a potential
project / with r
gov
(/) < r such that \ (r
gov
(/) . ¸
gov
(/)) < 1 and max ¦1. \ (r
po
(/) . ¸
po
(/))¦ <
\ (r
gov
(/) . ¸
gov
(/) . r
e
= r) then in any equilibrium in which GC\ is nonempty (and thus
r
e
= r), the government will prefer to undertake the project /. Note that to support an
equilibrium in which GC\ is empty, we must specify the market’s belief regarding r
gov
(/) in
the case that the government deviates and undertakes a project. Clearly, the belief that in
the case of a deviation r
gov
(/) is the minimal one over all projects / in the distribution would
do; in many cases other beliefs would also. QED
40
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