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J u l y 2 0 0 5 N o t e N u m b e r 0 8
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Estimating the fiscal risks and costs
of output-based payments
An overview
By Glenn Boyle and Timothy Irwin
Output-based payments are an important tool of for efficiently encouraging investment in many cases.
government policy. Sometimes governments offer But if the payments are to encourage service providers
"output-based aid" to subsidize services sold to house- to make long-term investments, the government may
holds. Guatemala and Mozambique, for example, have to commit itself in advance to offering the pay-
subsidize new electricity connections, while Paraguay is ments for many years--perhaps for as long as the life of
piloting a program to subsidize new water connections. the assets used to provide the service. Even in this case,
At other times governments are the sole source of if the payment amounts are not subject to much risk
revenue for a private infrastructure firm. Many govern- (as in the case of many contracts with availability
ments enter into "public-private partnerships" in which payments), there may be little need for carefully mea-
they pay a private firm for making available such suring the fiscal risks the government is taking. But
facilities as roads, schools, prisons, or hospitals. Dozens when the subsidies represent long-term commitments
of developing countries buy wholesale electricity from of potentially large and uncertain amounts, the govern-
independent power providers under similar arrange- ment would be wise to understand the costs and risks
ments. A few countries, such as Portugal and the United associated with the decisions it is making.
Kingdom, pay "shadow tolls" to privately financed Output-based payments come in many forms, as do
roads. In all cases the government pays only when the the risks they present (table 1). The payment structure
firm delivers a service (such as when a connection is associated with output-based schemes also varies. In
made, a car uses a road, or power is made available). some schemes, such as connection subsidies, the
Because output-based payments are tied to the payment in any year depends only on output in that
delivery of outputs, they have an obvious advantage year; in others, such as access subsidies, the payment
over input-based payments. In agreeing to make such reflects not only this year's output but also the cumula-
payments, however, governments assume a liability not tive result of previous years' outputs. In addition,
unlike that created by taking on debt. Moreover, in subsidy expenditure can be capped or uncapped. Under
some cases the payment amounts are subject to consid- a capped scheme the government places a ceiling on
erable uncertainty. As a result governments may benefit the number of outputs it will subsidize. The cap can
from estimating both the costs of these commitments apply to either annual or cumulative output.
and the new fiscal risks they create--and comparing Measuring the risks and costs of output-based
these costs and risks with those of alternative policies. schemes is feasible but also, inevitably, mathematical.
(Output-based payments also create risk for the private Quantifying risk necessarily involves some knowledge
companies providing the outputs, including, in many
developing countries, the risk of the government's
failing to make required payments. See von Klaudy and Glenn Boyle is executive director of the New Zealand Institute for
Goswami 2004 for ways of reducing payment risk.) the Study of Competition and Regulation at Victoria University of
Wellington (glenn.boyle@vuw.ac.nz). Timothy Irwin is in the
When a government commits itself to making
Infrastructure Advisory Services group at the World Bank
payments for only a year, allowing itself the opportunity (tirwin@worldbank.org). This note is based on a companion paper
to decide at the end of the year whether to renew the by the authors, "Techniques for Estimating the Fiscal Costs and Risks
payments, the fiscal risks are likely to be small. This is of Output-Based Payments," OBA Working Paper No. 5 (GPOBA,
the safest option for governments and may be adequate Washington, D.C., 2005).
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Table 1. Output-based schemes
Type Applications Source of fiscal risk
Consumption subsidies Water, electricity Consumption per subsidized customer, number of eligible customers
Vouchers Education, health care Number of eligible customers, propensity to enroll
Connection subsidies Water, electricity, gas, Demand for new connections, supply of new connections, number of
telecommunications eligible customers
Access subsidies Water, electricity, gas, Propensity of customers to maintain access (as well as factors for
telecommunications connection subsidies)
Availability payments Wholesale water and electricity; Supply of capacity
roads; school, hospital, and
prison facilities
Shadow tolls Roads Traffic flows
and application of probability and statistics; estimating distribution, and the desired risk measure can then be
the cost of uncertain payments that occur at different calculated using a simple formula. In other cases,
points in time requires asset pricing techniques from particularly where payments depend on cumulative
modern finance theory. Nevertheless, most of the output or are capped, the distribution can be inferred
important issues are conceptual rather than technical. only from a numerical technique such as Monte Carlo
simulation. In simple terms, this technique works by
Measuring the risks using a random-number generator to create many
alternative realizations of output, each of which is
At its simplest, the risk associated with output-based consistent with historical information about the output
schemes can be thought of as the potential volatility of distribution. This approach makes it possible to build
required payments mandated by these schemes. But up a picture of the entire probability distribution of
surprises can be pleasant as well as unpleasant, and output and therefore of output-based payments. (With
volatility measures do not distinguish between the two. appropriate modification, each technique can be
Measures that explicitly focus on the potential for applied to portfolios of output-based schemes as well
unpleasant surprises, or so-called downside risk, are as to individual schemes.)
therefore more useful. One such measure, known as the
excess-payment probability, calculates the probability
of payments exceeding some prespecified level (table Figure 1. Estimated frequency distribution for a
2). Another measure, known as cash flow at risk, hypothetical output-based payment
estimates the maximum payment likely under normal
3,500
conditions. Both measures are particularly useful if a 3,151
government's fiscal position is threatened primarily by 3,000
particularly high payments. To get a full picture of the
2,500 2,376
fiscal risks of an output-based scheme, governments
can also estimate the probabilities that payments will 2,000 1,819
fall in each of several intervals (figure 1).
1,500 1,323
All risk measures require estimating some part of the
underlying probability distribution. The best procedure 1,000
657
for doing so will vary from case to case, and advice may
500 300
well be required from such experts as statisticians and
75 150
82
0 31 36
economic forecasters. In many cases the only realistic 0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 More
option is to assume that the future will look much like
the past and, accordingly, attempt to build up a picture Note: The bin on the far left, labeled 0, shows the estimated frequency out of
of the distribution implied by historical data. In some 10,000 of payments of 0 or less (0). The next, labeled 0.5, shows the
frequency of payments between 0 and 0.5 million (75). The bin on the far right,
cases there may be reasonable grounds for assuming labeled More, shows the frequency of payments greater than 5 million (36).
that the annual payment comes from a well-understood Source: Boyle and Irwin 2005.
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Table 2. Risk measures for output-based subsidy schemes
Measure Description Advantages Disadvantages
Volatility of Standard deviation of annual Provides a single number summarizing Doesn't distinguish between upside
payments change in payments the variability of payments and downside risk
Excess-payment Probability that subsidy Provides a single number that helps Doesn't offer much information on
probability payments exceed X determine whether risk to government's the probabilities of other payments
fiscal position is significant
Cash flow Maximum payment Provides a single number that helps Doesn't offer much information on
at risk with % probability determine whether risk to government's other possible payments; may be mis-
fiscal position is significant taken for maximum possible payment
Frequency Probability of payments Provides a picture of the entire range of Requires a graph or table to convey the
distribution of in each of several intervals possible payments information; is not succinct
payments
Valuing the obligations alternative approach that bypasses this problem
estimates the certainty-equivalent payment for each
A simple way of approximately valuing the obligations
year (the expected payment less a risk adjustment),
created by output-based schemes is to estimate the
discounts each of these at a riskless rate of interest, and
expected payments in each of the years for which the
then adds all the discounted payments together.
government has committed itself to making payments
and then to discount those expected payments at the For some schemes this alternative approach yields a
riskless rate of interest. This approach is good enough complicated-looking formula for cost that is in fact
for some purposes. But it ignores the price of bearing simply an application of the growing-annuity formula.
risk and may generate a poor estimate of the value of In most cases, however, no such formula exists, and
some obligations. For large, risky commitments the Monte Carlo simulation must be used to estimate the
government may want to use a valuation approach that certainty-equivalent payments before proceeding to the
incorporates the price of bearing risk. last two steps. The estimated cost should be fairly
accurate for a sufficiently large number of simulations
Such an approach raises complex issues. One
(given, of course, accurate input information about the
relates to the appropriate model for pricing risk. In
underlying distribution and the appropriate adjustment
general, a subsidy that mandates low payments when
for risk). Box 1 gives an overview of how a government
the government is flush and high payments when the
might go about estimating both the fiscal risks and the
government is constrained is costlier than one that
liability created by a particular long-term commitment
offers the opposite payment pattern. The standard
to make output-based payments.
approach for quantifying this insight, the capital asset
pricing model (CAPM), has at its core the result that So, quantifying the risks and costs of an output-
everyone (including governments) holds a perfectly based scheme is no simple task. But when the scheme
diversified portfolio, so what matters for the involves long-term commitments of large and uncertain
government's fiscal position is simply the return on the amounts, the effort is well worth it: making good
overall market of assets. To the extent that governments decisions about such commitments is difficult for a
hold imperfectly diversified portfolios, however, the government unless it understands the size of the liability
market return is only a proxy for the appropriate pricing and the nature of the risks.
factor.
A second valuation issue relates to the best way of References
incorporating risk pricing in the calculation of a
Boyle, Glenn, and Timothy Irwin. 2005. "Techniques
subsidy's cost. The standard approach estimates the
for Estimating the Fiscal Costs and Risks of Output-
expected payment for each year, discounts each of these
Based Payments." OBA Working Paper 5 GPOBA,
payments at a rate adjusted for risk (using, for example,
Washington, D.C.
the CAPM), and then adds all the discounted payments
together. However, the frequent complexity of output- von Klaudy, Stephan, and Umang Goswami. 2004.
based schemes means that the second step poses "Credit Enhancing Output-Based Aid." OBA
technical difficulties that render it infeasible. An Working Paper 3. GPOBA, Washington, D.C.
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Box 1 How a government might estimate the risks and costs of output-based payments
Suppose a government is planning a privately financed forecast payment in year 2, for example, is about $1.05
shadow toll road. It has forecast the initial volume of million ( 1,000,000 x exp(0.05 x 1) x $1). By year 15
traffic at 1 million vehicles a year and the growth in the forecast payment will hit the cap of $1.75 million
volume at 5 percent a year (continuously com- (1,000,000 x exp(0.05 x 14) 2,000,000).
pounded), with volatility of 10 percent a year. It plans To understand the fiscal risks of the scheme, the
to pay the private company a shadow toll whose level government could use Monte Carlo simulation to
depends on the volume of traffic as follows: estimate the frequency distribution of the payments it
For Xt 1.5, s1 = $1 will make in each year (as explained in Boyle and Irwin
For 1.5 < Xt < 2.0, s2 = $0.5 2005). From the frequency distribution it could extract
the risk measures discussed in the text. For example, it
For Xt 2, s3 = 0 could estimate the probability in each year of payments
where X1 is the volume of traffic in millions in year t, s1 greater than, say, $1.5 million (or another threshold of
is the shadow toll in the first band, s2 is the shadow toll interest to the government) and the cash flow at risk at,
in the second band, and s3 is the shadow toll in the say, the 95 percent level by year. It could also produce a
third band. That is, the shadow toll is $1 a vehicle for histogram of payments (such as that in figure 1) for
the first 1.5 million vehicles, 50 cents a vehicle for the each year.
next 500,000 vehicles, and zero thereafter. With this To estimate the total liability created by its commit-
schedule of shadow tolls, government expenditure on ment to pay shadow tolls, the government could use
the scheme is effectively capped at $1.75 million a year the Monte Carlo simulation to estimate the expected
( = 1.5(1) + (2 1.5)(0.5)). payments by year and then discount each expected
The government will commit itself to paying this payment at the riskless rate. But to take account of the
schedule of shadow tolls for 20 years in order to give price of risk, the government would have to use a
the privately financed toll road a reasonable chance of model of the price of risk bearing, such as the capital
recovering its costs, including the cost of capital. Given asset pricing model (CAPM). In particular, it could use
the initial traffic volume (1 million vehicles in year 1) the CAPM to estimate the certainty-equivalent pay-
and its forecast growth rate (5 percent), the govern- ments and then discount them at the riskless rate to get
ment can forecast the traffic volume in years 220 and an estimate of its liability (as explained in Boyle and
thus the shadow toll payments in those years. The Irwin 2005).
About OBApproaches
OBApproaches is a forum for discussing and The case studies have been chosen and presented
disseminating recent experiences and innovations for by the authors in agreement with the GPOBA
supporting the delivery of basic services to the poor. management team, and are not to be attributed to
The series will focus on the provision of water, GPOBA's donors, the World Bank or any other
energy, telecommunications, transport, health and affiliated organizations. Nor do any of the conclu-
education in developing countries, in particular sions represent official policy of the GPOBA, World
through output, or performance,-based approaches. Bank, or the countries they represent.
Global Partnership on
Output Based Aid
World Bank
Mailstop: H3-300
600 19th Street, NW
Washington, DC 20433, USA
To find out more, visit
www.gpoba.org The Global Partnership on Output-Based Aid
Supporting the delivery of basic services in developing countries