pproaches J u l y 2 0 0 5 N o t e N u m b e r 0 8 34304 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). Supporting the delivery of basic services in developing countries pproaches 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. Supporting the delivery of basic services in developing countries pproaches 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. Supporting the delivery of basic services in developing countries pproaches 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