SIMSIP DEBT: ANALYZING DEBT SUSTAINABILITY

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1 SIMSIP DEBT: ANALYZING DEBT SUSTAINABILITY Bernhard G. Gunter, Humberto Lopez, Krishnan Ramadas, and Quentin Wodon World Bank DRAFT COMMENTS WELCOME Trial version: June 25, 2002 Objective and Acknowledgment SimSIP (Simulations for Social Indicators and Poverty) is a set of user-friendly Excelbased simulators that facilitate the analysis of issues related to social indicators and poverty. The simulators can be downloaded from the web at and used without charge, provided acknowledgment is given for their use. A CD Rom will soon be made available. Originally, the simulators were prepared to help Governments preparing Poverty Reduction Strategies, but they can be used for other purposes as well. Some simulators are "generic", hence they can be used for any country. Other simulators are regional, so that their applicability is restricted to the countries of a given region. In some cases, different simulators are available for different regions. Some simulators are countryspecific, but here again different simulators can be made available for different countries. Most simulators are still in the development stage. Even when trial versions are provided, the user is advised to check the web site for updates. The World Bank accepts no responsibility for the conclusions which maybe reached from the use of the simulators, or for any mistakes in the simulators themselves. Please address all inquires regarding SimSIP to Quentin Wodon at qwodon@worldbank.org. SimSIP was developed in the Poverty Group of the Poverty Reduction and Economic Management Division (PREM) in the Latin America and the Caribbean Region at The World Bank. The work received financial support from the Central America and Andean country departments, the Regional Studies Program in the Office of the Chief Economist, the Dutch trust fund, and the Norwegian trust fund. Although the World Bank sponsored this work, the opinions expressed by the various authors of the manuals are theirs only, and should not be attributed to the World Bank, its Executive Directors, or the countries they represent. 1

2 This chapter presents an Excel -based worksheet related to the practical analysis of debt sustainability issues. The worksheet has two components. The Debt Projection Module can be used to simulate a country s debt sustainability based on initial conditions and projections for government expenditures, government revenues, and other parameters. Looking at levels and trends of various debt sustainability indicators, it provides policymakers and other interested parties with indications whether a country s debt is likely to be sustainable over a 15-year horizon. The Deficit-Debt Consistency Module presents a variety of matrices to determine the consistency of overall budget deficits with a country s desired level of indebtedness for a given growth rate. This is especially useful for fiscal aspects of public debt sustainability. The Debt Projection Module is described in more details in sections 1 to 3. Section 1 provides the key issues related to the definition of debt sustainability. Section 2 provides an overview of the Debt Projection Module, with a discussion about the data requirements, the main results, and the graphics capabilities. Section 3 outlines the model and assumptions used in the Debt Projection Module. Appendix 1 gives additional information available in the module, which may be of use to the user for setting some of the parameters of this module. The Deficit-Debt Consistency Module is described in more details in sections 4 to 6. Section 4 provides the key issues related to the consistency between public deficits and public debts. Section 5 provides an overview of data requirements, the short-term versus medium-term analysis, and the main results. Section 6 describes the main model assumptions behind the Deficit-Debt Consistency Module. Appendix 2 derives the various deficit-debt consistency equations used in this module. 1. INTRODUCTION TO THE DEBT PROJECTION MODULE A common definition of debt sustainability is whether a country can meet its current and future debt service obligations in full, without recourse to debt relief, rescheduling, or accumulation of arrears. To determine if a country s debt is sustainable or not is a complex issue. If debt sustainability is approached from a human and social development perspective, most of the poorest countries have an unsustainable debt simply because they have more urgent needs to reduce poverty than to make debt service payments. 1 However, if approached from a more technical perspective, debt sustainability can be defined by a variety of macroeconomic debt sustainability indicators (please see Box 1) that depends on variables like GDP growth, export growth, interest rates, 1 For more details, see Sachs, Jeffrey, Botchwey, Kwesi, Cuchra, Maciej and Sievers, Sara, Implementing Debt Relief for the HIPCs, Cambridge, MA: Center for International Development, Harvard University, 1999 (available at and European Network on Debt and Development (EURODAD), Putting Poverty Reduction First: Why a Poverty Approach to Debt Sustainability Must be Adopted, Brussels: EURODAD, 2001 (available at 2

3 inflation, changes in the exchange rate, changes in grants or debt relief provided to the government, and others. Box 1: Practitioners suggestions of debt sustainability indicators The following are some examples of debt sustainability indicators as they are used in the World Bank s Global Development Finance (GDF), the HIPC Initiative, the Millennium Development Goals (MDGs), and the European Union s (EU) Maastricht Treaty. The World Bank s Global Development Finance (GDF, formerly World Debt Tables) classifies external indebtedness based on two ratios, the ratio of the net present value (NPV) of total external debt (calculated based on all future debt service) to the three-year backward looking average of gross national product (GNP), and the ratio of the NPV of total external debt (calculated based on all future debt service) to the three-year backward looking average of exports of goods and services (including workers remittances). If either ratio exceeds a critical value 80 percent for the NPV debt to GNP ratio and 220 percent for the NPV debt to exports ratio the country is classified as severely indebted. If the critical value is not exceeded but either ratio is three-fifths or more of the critical value (that is, 48 percent for the present value of debt service to GNP and 132 percent for the present value of debt service to exports), the country is classified as moderately indebted. If both ratios are less than threefifths of the critical value, the country is classified as less indebted. 2 In the framework of the Initiative for Heavily Indebted Poor Countries (HIPC-Initiative), a country is considered to have a sustainable external debt if the ratio of the present value external debt (calculated based on all future debt service) to the three-year backward looking average of exports of goods and non-factor services (excluding workers remittances) is smaller or equal to 150 percent. However, given to the limitations of the export criterion, especially for countries with a high export to GDP ratio, the HIPC Initiative added a fiscal criterion of debt sustainability for countries that have an export to GDP ratio of at least 30 percent and a government revenue to GDP ratio of at least 15 percent. For HIPCs satisfying both of these thresholds, the HIPC Initiative considers an additional fiscal criterion: a HIPC s external debt is sustainable if the ratio of the present value of public and publicly guaranteed external debt to government revenues is smaller or equal to 250 percent. 3 Within the recently enlarged set of Millennium Development Goals (MDGs), target 15 is defined as to deal comprehensively with the debt problems of developing countries through national and international measures in order to make debt sustainable in the long-term. The four indicators for this target are (a) the proportion of official bilateral HIPC debt cancelled, (b) the debt service as a percentage of exports of goods and services, (c) the proportion of ODA provided as debt relief, and (d) the number of countries reaching HIPC decision and completion points. 4 The European Union s (EU) Maastricht Treaty (signed in early 1992) limited the ratio of government debt to GDP to 60 percent, though it was also agreed that higher ratios are acceptable as long as the debt to GDP ratio is sufficiently falling over time. Indeed, most countries of the EU had debt to GDP ratios above 60 percent for most of the times during the 1990s, and at least three countries (Belgium, Greece, and Italy) had debt to GDP ratios of more than 100 percent. Anyway, it should be stressed that the Maastricht Treaty s debt to GDP ratio should not be interpreted as debt sustainability indicator, but as convergence criteria set by a group of European countries that intended to adopt a single currency by the end of Please see for more detailed information. 3 Please see the World Bank s HIPC website: for more information. 4 Please see for further information. 3

4 Reflecting the fact that for a broad group of countries debt sustainability cannot be determined by one specific indicator, the Debt Projection Module adopts a flexible approach to debt sustainability. Depending on user preferences, the composition of the government s debt, and the possible existence of private foreign debt, the user of the Debt Projection Module has various options on how to define debt sustainability using four indicators: the NPV public debt to GDP ratio, the NPV external debt to export ratio, the NPV public debt to revenue ratio, and the debt service (on public debt) to government revenue ratio. The Debt Projection Module presents results for these four ratios over a projection period of 15 years based on initial values and assumptions provided by the user. The Debt Projection Module does not limit the value of any of the four indicators. Instead, it allows the user to see the impact of programmed government expenditures and revenues, together with other assumptions, on the four debt sustainability indicators. By looking at the level and the evolution of the four debt sustainability indicators over the next 15 years (as displayed in the graphs in the lower part of the simulator), the user can assess if the programmed expenditures are likely to cause a problem of unsustainable debt or not. Though decreasing trends usually indicate that the debt is sustainable, the user might want to keep in mind that high levels of debt can nevertheless imply a debt overhang with negative implications on investment and growth, especially if investors are not convinced that the long-term trends of the various debt sustainability indicators are indeed decreasing. Although the Debt Projection Module focuses on the sustainability of public foreign debt, it also allows the inclusion of public domestic debt and private foreign debt. The inclusion of these two types of debt is important for non-heavily Indebted Poor Countries (non-hipcs). For HIPCs, the user may want to concentrate on the NPV debt to export criterion and if applicable, the NPV debt to government revenue criterion. For non-hipcs, the user has more flexibility, though the levels and time paths of the four debt sustainability indicators usually provide useful insights. In any case, if the user comes to the conclusion that the debt is not sustainable, policy makers might make adjustments on the expenditure side, the revenue side, or both. For example, there may be options to reduce expenditures, especially in non-priority sectors, without undermining the poverty reduction objective. There may also be options for higher tax efficiency and/or temporary increased money financing without jeopardizing macroeconomic stability. In cases where non-priority expenditures have already been minimized, there may also be an option for more grants in order to finance the increased expenditures targeted at reducing poverty. 4

5 2. DESCRIPTION AND USE OF THE DEBT PROJECTION MODULE 2.1. Structure of the Debt Projection Module When opening the Debt Projection Module an Excel based Worksheet appears as shown below in Figure 1. The Worksheet displays the initial conditions, parameters, and results of the latest simulation saved by the user (when the worksheet is first launched, the simulation shown was saved by the authors). Figure 1 shows the Worksheet saved by the authors. Figure 1: Worksheet saved by the authors Vertically, the Worksheet is divided into three panels. The top panel is allocated to initial values and parameters, which are used for the simulations. In addition to the assumptions that can be typed directly in the displayed cells of the top section, there is one button to determine the base year and two optional buttons to include additional assumptions on debt relief, public domestic debt, and private foreign debt. If the user wants to exclude debt relief, public domestic debt, and private foreign debt from the analysis, the values for the variables in these buttons need to be set to zero. The middle and lower sections present the outcomes of the simulations. The middle section displays results in nominal terms (US$) or in relative terms (as a percentage of GDP, exports, or government revenues). The bottom section presents graphs for key results. 5

6 Horizontally, the Worksheet is divided into two identical parts. The left- and right-hand sides can be used to compare results with different assumptions for the same country, or to compare results for two different countries Required information The top panel of the Debt Projection Module contains initial conditions and parameters, which must be entered by the user. The first step in using the s Debt Projection Module is to enter the base year in the button called Year t0. This information is needed simply for the display of results. Next, the user must enter the information in the white cells shown in Figure 2. The user might find it convenient to enter the US dollar amounts in units of e.g. million US dollar (or any other unit); the inputs just need to be consistent throughout the module. All the initial values will need to be put in as nominal US dollar (though for example in units of million US dollar) and all the growth rates will need to be put in as percentage. The values for t0 and t15 of the first six variables of the lower sub-section are defined in percent, the last variable (called Average Maturity ) is defined in years. The following paragraphs provide some more detailed information for the various data to be entered. Figure 2: The data to be entered in the top panel Public foreign debt (stock and interest payments) and nominal GDP. The three initial values to enter in the top left sub-section of the panel are the stock of public and publicly guaranteed foreign debt, interest payments on public and publicly guaranteed foreign debt, and nominal GDP. Clicking on the gray button called Info-debt provides some country-specific historical values for total external debt, which includes private external debt. This popping-up data sheet can be closed by clicking on the DONE button located in cell G3 of the popping-up data sheet. Grants: Initial value and growth rates. Grants are funds available to the government for which there is no repayment requirement 5. The growth rates of grants are 5 Grants that do not enter into the government s budget should not be included. For example, a donor country may provide a technical cooperation grant to finance a consultant to execute a specific investment 6

7 determined by decisions of donor countries and international organizations, depending on many factors such as the country s per capita income or the degree donors agree with the grant-receiving-country s policies. Due the increasing attention given to aid effectiveness, growth rates for grants are likely to be determined by how effective previous aid was in a country. Exports: Initial value and growth rates. Exports are defined as exports of goods and non-factor services, that is, we follow the HIPC definition, which excludes workers remittances. The initial value refers to the value of the base year; the simulator calculates the three-year backward-looking average for every year based on the entered initial value, the growth rate for t0, and the growth rate for t15. The growth rates for exports are nominal and in US dollar. Exceptional circumstances in the base year may be taken into account when setting the growth rate (if the base year s exports were exceptionally low/high, the growth rate for t0 could be adjusted upward/downward). Exchange rate: Initial value and growth rates. The exchange rate is defined as local currency per U.S. dollar. The growth rate of the exchange rate is the percentage rate depreciation per year. Although future depreciation is difficult to predict, some indication can be obtained by estimating future differences between local and US inflation rates (even though relative purchasing power parity does not hold perfectly, it is still one of the best reference points.) Assumptions for future depreciation and inflation should thus be consistent. Discount rate: values for t0 and t15. In the HIPC framework, the discount rate for public foreign debt is based on the official lending rate of export credit agencies (the Commercial Interest Reference Rates or CIRRs) for each currency a loan is denominated in. 6 In the simulator, an average discount rate must be provided. If most loans are contracted in US$, the discount rate may be close to the CIRR for the US$. While small changes in discount rates may have large impacts on the NPV of outstanding debt, the implications on a country s long-term debt sustainability are marginal. Yet differences in discount rates are crucial for comparisons across countries and for the calculation of the amount of HIPC debt relief to be provided. Since CIRRs fluctuate in the short-run, it is best to use long-term averages of CIRRs. HIPC uses 6-month backward looking averages of CIRRS, though it has been suggested to use longer-term averages. Monthly CIRRs from 1993 to 2001 are provided when clicking the gray button called Info-CIRR. This popping-up data sheet can be closed by clicking on the DONE button located in cell G3 of the popping-up data sheet. project. If the consultant is paid directly by the donor country, this grant should not be included. If the donor country gives the grant money to the government to hire a consultant, the grant should be included. 6 CIRRs are calculated monthly and are based on government bonds issued in the country's domestic market for the country's currency. In the case of the US dollar, the CIRR is based on the U.S. Treasury bond rate. For more information about CIRRs, see 7

8 Interest rate: values for t0 and t15. The interest rate is the average interest rate on outstanding public foreign debt. As for the discount rate, small changes in interest rates have implications for the NPV of the debt. They also have budgetary implications. It is suggested to test for the sensitivity of results to changes in the average interest rate by running scenarios with different interest rate averages. The gray button called Infointerest provides some country-specific historical values for all new public and publicly guaranteed loans contracted during a year. This popping-up data sheet can be closed by clicking on the DONE button located in cell G3 of the popping-up data sheet. Inflation rate: values for t0 and t15. The inflation rate for t15 should be chosen taking into consideration the depreciation rate of the exchange rate for t15. Although high inflation rates tend to have negative implications on the growth rate, there is no feedback loop to this effect in the simulator. Real GDP growth: values for t0 and t15. Real GDP growth rates are probably the most crucial determinant of a country s debt sustainability. Higher growth implies higher revenues, and possibly lower deficits and debt (even when higher revenues lead to higher expenditures). Given the sensitivity of a country s debt sustainability to the assumptions for growth, users should be cautious about highly optimistic growth rates. Revenue and primary expenditure to GDP ratios: values for t0 and t15. The revenue-to-gdp and the expenditure-to-gdp ratios are key determinants of a country s debt sustainability. Revenues include all tax and non-tax revenues, but exclude grants. Primary expenditures include all government expenditure except debt service (interest and principal payments) on public debt (foreign and domestic). By comparing these two ratios, the user can calculate the primary deficit (before grants and debt relief) as a ratio of GDP. When comparing scenarios with different growth rates, the user may want to also adjust the government-to-gdp and the expenditure-to-gdp ratios. The impact on debt sustainability of increases in tax revenues or expenditures as shares of GDP can also be simulated. Average maturity: values for t0 and t15. The data on average maturity will need to be provided for public and publicly guaranteed external debt, defined in years. The gray button called Info-matur provides some country-specific historical values on the average maturity for all new public and publicly guaranteed loans contracted during a year. This popping-up data sheet can be closed by clicking on the DONE button located in cell G3 of the popping-up data sheet Optional information There are two optional buttons in the middle of the top section of the panel. The first button (called Debt Relief ) provides optional information related to debt relief. The second button (called Priv. & Dom. Debt ) provides optional information related to private foreign debt and public domestic debt. The user must set all these optional values 8

9 to zero if he/she prefers to exclude these options. When using the options, the user must adapt the data to the country under review. Debt relief. When clicking on the Debt Relief button, a box appears as illustrated in Figure 3. The user is requested to provide the estimated reduction in debt service for each year, for up to 20 years. In most cases, even if debt relief is provided over more than 20 years, the difference in NPV results will be small due to the discounting of future debt service reductions when calculating the NPV. Figure 3: Optional Button for Debt Relief Private and domestic debt. When clicking on the button Priv. & Dom. Debt, a box appears as illustrated in Figure 4. The left-hand section of the box requires information for private foreign debt. The right-hand requires information for public domestic debt. The user is not required to include both additional debt categories, but for each category to be included, all the required information must be provided. Private foreign debt: The user must specify the initial stock of foreign private debt and its projected growth rates in the base year and for the last period. The growth rate is in nominal terms, corresponding to US dollar. One option for suggesting a growth rate is to assume that the private sector s demand for foreign financing grows at the same rate as the growth rate of foreign debt from the public sector (this keeps the ratio of foreign private debt to foreign public debt constant). Another option is to assume that the growth rate follows the GDP growth rate. Public domestic debt: The required information includes: the initial stock of public domestic debt, the initial interest payments, the percentage share of government budget deficits (after grants and debt relief) to be financed by domestic sources in t0 and t15, the average interest rate in t0 and t15, and the average maturity of the outstanding debt stock. The dialog box also asks for the discount rate on public domestic debt, which may be used in a later version of the Simulator (it is not used in this version, because we assume that the NPV of the public debt equals the nominal value of the public domestic debt). There should be consistency between inputs for the public domestic debt outstanding at t0, the (paid) interest in t0, and the average interest rate in t0, whereby the multiplication 9

10 of initial interest rate times initial public domestic debt should equal the initial interest on the debt. Figure 4. Optional Button for Foreign Private and Public Domestic Debt 2.4. Numerical outputs of the simulator As shown in Figure 5, results for ten variables are presented in (nominal) US Dollar and in percent of GDP, whereby the NPV of total public debt to GDP ratio represents the first of our four debt sustainability indicators. The numerical results for the other three debt sustainability indicators are presented to the right of table, whereby the NPV debt to exports and the NPV debt to government ratios follow the HIPC definition (that is, they exclude public domestic and private foreign debt and are based on threeyear backward looking averages of exports and revenues, respectively). However, within the table, exports are defined as single-year exports of goods and non-factor services and revenues are also provided as single-year values. Figure 5: Key Results 10

11 2.5. Graphs with and without debt relief In the lower part of the panel, the user can display graphs that differentiate between (a) results with and without debt relief and (b) results with and without private/domestic debt. All graphs combine a bar diagram showing public or foreign debt in US dollar and a line diagram showing one of four debt sustainability indicators. The graphs with and without debt relief should be useful for countries that (a) receive debt relief (traditional debt relief and/or HIPC debt relief) and (b) have small levels of public domestic debt and private foreign debt. Nominal public debt (bar diagram) and NPV public debt to GDP (line diagram): In Figure 6, the NPV debt to GDP ratio expresses overall debt in terms of GDP (the broadest measure of income generation in an economy). It would make sense to include public foreign debt, public domestic debt, as well as any private foreign debt when using this indicator. Yet for consistency considerations in displaying various results, we exclude private foreign debt from this debt sustainability indicator. Figure 6: Nominal public debt and NPV public debt to GDP Nominal foreign debt (bar diagram) and NPV foreign debt to exports (line diagram): The export criterion assesses the external sustainability of a country s debt. The standard HIPC definition excludes private non-guaranteed external debt from the export criteria, mainly due to the facts that (a) private non-guaranteed external debt is marginal in HIPCs (during the 1990s, less than 3 percent of the HIPCs total long-term debt was private non-guaranteed) and (b) the collection of the necessary data on a loanby-loan basis is difficult to obtain. Since the simulator may be used for non-hipc countries that have substantial private external debt, we allow the user to include private foreign debt for the export criterion. If the user want to analyze the export criteria using the classical HIPC definition, the user should set private foreign debt to zero. 11

12 Figure 7: Nominal foreign debt and NPV foreign debt to exports Nominal public debt (bar diagram) and NPV public debt to revenues (line diagram): The fiscal criterion assesses the government s ability to service its debt. The standard HIPC definition excludes public domestic debt mainly because it is marginal for most of the HIPCs, and the main goal of the HIPC Initiative is to provide external debt sustainability. To enable the use of the simulator for non-hipc countries, we allow the user to include domestic public debt in the fiscal criterion. If the user wants to analyze debt sustainability based on the classical HIPC definition, he/she needs to set public domestic debt to zero. Note that HIPC considers the fiscal criterion only if a) the exportto-gdp ratio is at least 30 percent, and b) the revenue-to-gdp ratio is at least 15 percent. Figure 8: Nominal public debt and NPV public debt to revenues 12

13 Nominal public debt (bar diagram) and public debt service to revenues (line diagram): The debt service to revenue ratio is an additional useful indicator provided in order to analyze yearly flows. While the ratio is not a formal HIPC indicator, it has been looked at in early stages of the HIPC initiative (for looking at a country s capacity to pay, the debt service to revenue ratio may well be the most accurate indicator). Figure 9: Nominal public debt and public debt service to revenues 2.6. Graphs differentiating categories of debt Av second set of graphs differentiates between various debt categories, in order to see the impact of debt sustainability of public domestic debt and private foreign debt apart from public foreign debt. Again, four graphs are presented, and the interpretation is similar to that discussed above. Figure 10: Nominal public debt and NPV public debt to GDP with and without public domestic debt 13

14 Figure 11: Nominal foreign debt and NPV foreign debt to exports with and without private foreign debt Figure 12: Nominal public debt and NPV public debt to revenues with and without public domestic debt 14

15 Figure 13: Nominal public debt and public debt service to revenues with and without public domestic debt service 3. WHAT S THE BLACK BOX BEHIND THE SIMULATOR There are three basic elements: the modeling of government expenditures, the modeling of government revenues, and the specification of the government deficit, which is financed by new borrowing after deducting grants and debt relief. Though the model is mostly determined in domestic nominal currency (in order to take into account the effects of inflation), all data inputs by the user are in US dollar. Inputs in US dollar are converted into nominal domestic currency through the exchange rate for each period, which is determined exogenously. Gross domestic product (Y) is determined by the initial value in t0, the projected growth rate for the year (g), and the inflation rate (π): Y(t)=(1+π(t))(1+g(t))Y(t-1) (1) On the expenditure side, we differentiate between interest payments on public foreign debt, interest payments on public domestic debt, principal repayments on foreign and domestic debt, and other government expenditures. The average interest rates (not the interest payments) on outstanding foreign and domestic debts are fixed for any given year due to loan contracts, but we differentiate between interest rates on public domestic and foreign debt. The user may change the interest rates by specifying different initial and final rates. Given that new loans (due to principal repayments and deficit financing) are generally a small fraction of the debt stock, interest rates on domestic and foreign debts change only slowly over time. Depending on the degree of concessionality of the foreign 15

16 debt, the interest rate on foreign debt may be considerably lower than on domestic debt. (Data is available on these rates in the spreadsheet). For simplicity, principal repayments are financed by new loans, though not necessarily from the same source (domestic or foreign) and at the same interest rate and maturity 7. Other expenditures (all expenditures excluding interest and principal payments) are a predetermined percentage of GDP, which may change over time. If we denote the interest rates on domestic and foreign debt by i f and i d (averages for the various loan contracts), the stocks of debt by D f (t-1) and D d (t-1), and the exchange rate by E(t), we have three kind of expenditures: interest payments on foreign government debt [i f (t-1)*d f (t-1)*e(t)]; interest payments on domestic government debt [i d (t-1)*d d (t-1)]; and government expenditures on social and non-social sectors [G sec (t)] = α(t)*y(t). Total government spending is: G(t) = i f (t-1)*d f (t-1)*e(t) + i d (t-1)*d d (t-1) + α(t)*y(t) (2) On the revenue side, we simplify the analysis by combining tax-, seignorage- and all other non-tax revenues to one percentage value [β(t)] of GDP, whose change over time reflects changes in tax rates, the efficiency of revenue collection, and moneyfinancing, 8. The simulator calculates the intermediate values based on a linear trend. Grants N(t) and debt service relief DSR(t) are exogenously determined by foreign donors. Like foreign borrowing, grants and debt service relief are converted into domestic currency at the end of each period. If revenues before grants and before debt relief are denoted by REV bef (t) = β(t)*y(t), revenues with grants and debt relief are: REV aft (t) = β(t)*y(t) + E(t)*N(t) + E(t)*DSR(t). (3) Budget deficits BD(t) are simply the difference between total revenues (including grants and debt relief) and total government expenditures: BD(t) = G(t) - REV aft (t) (4) We assume that the government faces no constraints in financing expenditures through new borrowing, and the user is free to choose what share of the new debt comes from domestic sources. If new domestic and foreign borrowing by the government are denoted respectively by BD d (t) and BD f (t), the change in debt is: BD(t) = E(t)*BD f (t) + BD d (t) (5) 7 Changes in the source of new borrowing are reflected in the ratio of public foreign debt to public domestic debt in the box for including public domestic debt, while changes in the average interest rate and maturity are reflected in the parameters in the top section of the panel. 8 To avoid negative implications of increased money-financing on growth, money-financing is usually restricted. In general, the non-inflationary level of seignorage is limited to about one percent of GDP. 16

17 The simulator makes no assumptions for the impact of new borrowing on GDP growth, inflation, the exchange rate, and the level of loan concessionality 9. The assumptions for GDP growth, inflation, exchange rate depreciation, and average interest rates on domestic and foreign loans are provided by the user. It is however suggested to adjust the growth rate of real GDP downward, the inflation rate and the exchange rate depreciation upward, and the interest rates on domestic and foreign loans upward the higher the average ratio of government deficit to GDP is over the projection period. For countries with sustainable poverty reduction strategies in place, these considerations are less crucial since consultations with donors would reduce the existence of excessive financing gaps. Combining (4) and (5) yields: G(t) - REV aft (t) = BD(t) = E(t)*BD f (t) + BD d (t) (6) The model is dynamic since the current year s budget deficit is linked to the previous year s budget deficit through the current year s total government expenditures that include interest payments on previous year s debt stock. Once the level of debt is known over time, it is easy to compute the net present value (NPV) of a country s public foreign debt by using debt service projections based on the average interest rate and the average maturity 10 of outstanding public foreign debt. Useful country-specific information on these averages (together with information on previous nominal and NPV debt) is accessible by clicking on the four gray Info-buttons in the top panel of the worksheet. For a country s public domestic debt and a country s private foreign debt, the NPV values are set equal to the nominal values. 4. INTRODUCTION TO THE DEFICIT-DEBT CONSISTENCY MODULE The Deficit-Debt Consistency Module of the SimSIP Debt presents a variety of matrices that can be useful to determine the consistency of overall budget deficits with a range of values for one of six debt indicators and a range of real GDP growth. The six debt indicators of the deficit-debt consistency module are: the nominal debt-to-gdp ratio, the NPV debt-to-gdp ratio, the nominal debt-to-exports ratio, the NPV debt-to-exports ratio, 9 In reality, increased borrowing tends to increase the growth rate of real GDP up to some critical level (which is difficult to determine), and consistently high government deficits tend to have negative impacts on real GDP growth and price stability. Depending on the country s access to foreign concessional financing, the costs of new borrowing may also increase with a rising fiscal deficit. At low levels of fiscal deficits, the portion of concessional financing will be relative high. With rising financing gaps, more and more new loans will have increased interest rates. 10 The maximum average maturity on outstanding public foreign debt the module can handle for the NPV calculation is currently 45 years. 17

18 the nominal debt-to-revenue ratio, and the NPV debt-to-revenues ratio. All matrices show 25 budget deficit-to-gdp ratios that are consistent with a range of real GDP growth rates (on the horizontal) and a range of one specific debt indicator (on the vertical). For example, Figure 14 shows a matrix for a range of nominal debt-to- GDP ratios (from 40 percent to 80 percent). Excluding the matrices for the nominal and NPV debt-to-export ratios, the user can also specify if she/he wants to include or exclude public domestic debt. 11 External private debt is always excluded in the Deficit-Debt Consistency Module as this module intends to highlight the relationship between public debt and public deficits. Figure 14: Illustrative example of a matrix The deficit-to-gdp ratios provided in the matrices are the deficit-to-gdp ratios consistent with a specific fixed growth rate and a given nominal or NPV debt ratio (debtto-gdp, debt-to-exports, or debt-to-revenues). There are a couple of other variables that are kept constant for a specific matrix, especially the inflation rate, the devaluation rate, the average maturity of debt, the composition of the public debt (external public debt versus domestic public debt), and the discount rate. The user will need to provide the values for these variables and parameters in the white cells of the top part of the deficitdebt interface. We also keep the average interest rates on each category of debt stock (public external debt and public domestic debt) constant, though the Deficit-Debt Consistency 11 The option to include domestic public debt has been excluded for the matrices with the debt-to-export ratios on the vertical axis as the inclusion of domestic public debt is inappropriate for the external debt sustainability criteria. 18

19 Module allows the user to specify different interest rates on newly contracted debt to finance current budget deficits. As will be shown below in more detail, differences in the average interest rates for the stock of debt and the newly contracted debts are the driving force for the determination of the NPV debt indicators. The Deficit-Debt Consistency Module also allows for differences between real growth rates for GDP, exports, and revenues. This will also be shown in more detail below and constitutes the driving force for differences in the resulting deficit-to-gdp ratios. However, for the matrices with debt-to-exports and debt-to-revenues ratios on the vertical axis, the module will automatically adjust the real growth rates of exports and revenues to the range of real growth rates of GDP shown in the matrix. For example, if the user specifies a real GDP growth rate of 5 percent (which implies that the matrix s GDP growth ranges from 3 percent to 7 percent) and a real exports growth rate of 8 percent, the matrices with debt-to-export ratios on the vertical axis will adjust the real growth rate for exports from 6 percent to 10 percent. These adjustments are necessary to keep the macroeconomic framework of the module consistent. The Deficit-Debt Worksheet displays the initial conditions, parameters, and results of the latest simulation saved by the user (when the worksheet is first launched, the simulation shown was saved by the authors). Figure 15 shows the Worksheet saved by the authors. Figure 15: Deficit-debt worksheet saved by the authors 19

20 Vertically, the Worksheet is divided into three panels. The top panel is allocated to initial values and parameters, which are used for the consistency module. The middle and lower sections present the outcomes of the Deficit-Debt Consistency Module. The middle section displays the numerical results for consistent deficit-to-gdp ratios in a 5- by-5 matrix. The bottom section presents graphs of five iso-debt ratio curves reflecting the numerical results of the matrix displayed in the middle section of the panel. Horizontally, the Worksheet is divided into two identical parts. The left- and right-hand sides can be used to compare results with different assumptions for the same country, or to compare results for two different countries. 5. DESCRIPTION AND USE OF THE DEFICIT-DEBT CONSISTENCY MODULE 5.2. Required information The top panel of the deficit-debt consistency module contains initial conditions and parameters that must be entered by the user. The user must enter the information in the white cells shown in Figure 16. The two gray cells with the implicit real growth rates for exports and revenues on the bottom right corner of the top panel are calculated automatically by the module, based on the inputs provided by the user. They serve as quick-checks for the change in the exports-to-gdp and the change in the revenues-to- GDP ratio provided by the user. The following paragraphs provide more information on some of the variables and parameters the user will need to specify. Figure 16: The data to be entered in the top panel GDP: Initial value and real growth rate (%). The two values to enter in the top left sub-section of the panel are the initial nominal value of GDP in units and the annual real growth rate of GDP in percent. The value for nominal GDP can be entered in domestic currency units or in US dollars. The user just needs to make sure that the values for the public foreign and public domestic debt stocks are provided in the same currency. 20

21 The user might find it convenient to enter the domestic currency or US dollar amounts in units of e.g. millions or billions; the inputs just need to be consistent throughout the module. Public foreign debt. The four values to provide here are the initial stock of public foreign debt, the weighted-average maturity of public foreign debt, the weighted-average interest rate on the outstanding stock of public foreign debt, and the weighted-average interest rate on newly contracted public foreign debt. Some useful information for this can be found in the information sheets of SimSIP Debt that can be viewed by clicking on the gray info-buttons in the worksheet of the Debt Projection Module. Public domestic debt. The three values to provide here are the initial stock of public domestic debt, the weighted-average interest rate on the outstanding stock of public domestic debt, and the weighted-average interest rate on newly contracted public domestic debt. In most cases, the difference between these two interest rates may be small, especially if these two interest rates are the medium term values. Discount rate, inflation rate, and devaluation. Please provide the current annual or medium-term annual values in percent, whereby the devaluation rate will need to be provided as the percentage rate devaluation of the exchange rate defined in currency per US dollar (independent on if the values for GDP and debt stocks are provided in domestic currency or US dollar. Please see section 2.2 of this SimSIP Debt manual for more detailed information for each variable. Exports: initial ratio to GDP (%) and real growth rate of exports (%). The two values to enter are the initial exports-to-gdp ratio and the real growth rate of exports. These values are needed for the debt-to-export matrices. The user is free to provide these export-related data in- or excluding workers remittances; however, the user should keep in mind the resulting matrices are based on the data provided. Revenues: initial ratio to GDP (%) and real growth rate of revenues (%). The two values to enter are the initial revenue-to-gdp ratio and the real growth rate of revenues. These values are needed for the debt-to-revenue matrices. The user is free to provide these revenue-related data before or after grants. The standard definition of debt-torevenue ratios usually exclude grants. If the user provides the ratio to GDP and the real growth rates of revenues including grants, the resulting matrices will also include grants Short-term versus medium-term consistency checks The Module is flexible enough to analyze the current or medium-term consistency of deficit-to-gdp ratios with debt ratios, depending on if the user has provided the current or medium-term values for the GDP growth rate, the various interest rates, the discount rate, the inflation rate, the devaluation rate, and the growth rates for exports and revenues. Though the module can also be used to check the long-term consistency of 21

22 deficit-to-gdp ratios with long-term debt ratios, the user should be careful to draw such long-term conclusions based on current or projected values of parameters as it is unlikely that the user will be able to provide realistic predictions for differences in interest rates as they are needed to draw reasonable long-term conclusions. It is important that the information on average interest rates on debt outstanding and on average interest rates on newly contracted debt is provided as accurate as possible since relative small differences between the two interest rates can lead to relative large differences in the results for the consistency of deficit-to-gdp ratios with one of the three NPV debt ratios (NPV debt-to-gdp, NPV debt-to-exports, and NPV debt-to-revenues). If the user is mainly interested to use the matrix as a short-term consistency check, the values for the average interest rates should reflect current values. If the user is interested to use the matrix as a medium-term consistency check, the values for the average interest rates should reflect medium-term averages, which the user will need to estimate based on current trends of interest rates and maturities. The example in Box 2 and calculation tool provided when clicking on the button called Calculate future average interest rate provide some useful information in this regard. Box 2: Example of evolution of average interest rates due to increasingly less concessional borrowing Assumptions: (a) the maturity on public external debt is 10 years, (b) the current interest rate on the outstanding stock of public external debt is 3 percent, (c) the interest rate on newly contract public external debt has increased gradually over the last 5 years and is currently 8 percent (and is expected to remain at 8 percent). Result in 5 years: The medium-term average interest rate on the outstanding stock of public external debt (in about 5 years) will be around 5 percent; in the long-run, it will of course be close to 8 percent. Note that the increase in the average interest rate on the outstanding stock of debt is not linear. Implications: If the user is interested in a current consistency check, the user should use an average interest rate on the outstanding stock of public external debt of 3 percent; if the user is interested in a medium-term consistency check, the user should use an average interest rate on the outstanding stock of public external debt of 5 percent. Once the user clicks on the Calculate future average interest rate button, a dialogue box appears which asks the user to specify values for the maturity (in years), the average interest rate on debt stock at t=0 (in percent), the average interest rate on newly contracted loans (in percent) and for which year the user wants the tool to calculate the new average interest rate on debt stock. The tool calculates the average interest rate as it will be on the assumptions provided by the user and assuming that the average interest rate on newly contracted debt before t=0 was equal to the average interest rate on the debt stock at t=0. Taking into account that we usually see some gradual movement of the changes in interest rate and maturity on newly contracted loans, the calculated values on average interest rates on outstanding debt in the future can be interpreted as lower limits 22

23 for gradually increasing interest rates and gradually decreasing maturities, and as upper limits for interest rate decreases and increasing maturities on newly contracted debt Outputs of the deficit-debt consistency module As shown in Figure 17, numerical results for one of the 12 matrices (4 for the debt-to-gdp indicator, 2 for the debt-to-export indicator, and 4 for the debt-to-revenue indicator) are provided in a 5-by-5 matrix displayed in the middle section of the panel. For real GDP growth rates of 7.5 percent and below, the module determines the range of real GDP growth rates two percent below and two percent above the given value. For real GDP of more than 7.5 percent, the module determines the range of real GDP growth rates 4 percent below and 4 percent above the given value. For debt ratios below 100 percent, the module determines the range of the debt ratio 20 percent below and 20 percent above the existing debt ratio. For debt ratios of 100 percent or more, the module determined the range of the debt ratios 40 percent below and 40 percent above the existing debt ratio. Figure 17: Example of a Matrix with Numerical Results Though the results for each matrix obviously depend on country-specific initial conditions and parameters, which the user provides, there are a couple of general results that can be pointed out: The higher the real GDP growth rate and the higher the value of a debt indicator, the higher is the value of the consistent budget deficit-to-gdp ratio (and vice versa), though it should be stressed that high debt indicators can lead to a debt overhang and then lead to low growth. The higher the inflation rate and the lower the devaluation rate, the higher is the value of the consistent budget deficit-to-gdp ratio (and vice versa), though it should be stressed that the two variables are usually moving the same direction as higher inflation rates usually imply higher devaluations. If a country is in the process of obtaining increasingly concessional loan terms from external creditors, the deficit-to-gdp ratios consistent with a specific NPV 23

24 debt indicator and a given growth rate are higher than with a specific nominal debt indicator (and vice versa). If GDP and exports grow at the same rate, there will be no difference between the consistent ranges of deficit-to-gdp ratios for the debt-to-gdp ratios or the debtto-export ratios. Similarly, if GDP and revenues grow at the same rate, there will be no difference between the consistent ranges of deficit-to-gdp ratios for the debt-to-gdp ratios or the debt-to-revenues ratios. The higher the growth rates of exports relative to growth rates of GDP, the higher are the ranges of consistent deficit-to-gdp ratios for the debt-to-export ratios compared to the consistent deficit-to-gdp ratios for the debt-to-gdp ratios (and vice versa). Similarly, the higher the growth rates of revenues relative to growth rates of GDP, the higher are the ranges of consistent deficit-to-gdp ratios for the debt-to-revenues ratios compared to the consistent deficit-to-gdp ratios for the debt-to-gdp ratios (and vice versa). Finally, the higher the growth rates of exports relative to growth rates of revenues, the higher are the ranges of consistent deficit-to-gdp ratios for the debt-to-export ratios compared to the consistent deficit-to-gdp ratios for the debt-to-revenues ratios (and vice versa). As displayed in Figure 18, the corresponding graphical illustrations to each matrix are provided in the bottom section of the panel. Each line of Figure 18 presents an isodebt ratio curve (the debt ratio is fixed for each curve). The top curve displays the highest debt ratio, the lowest curve displays the lowest debt ratio of the corresponding matrix in the middle section of the panel. Figure 18: Graphical Display of a Matrix 24

25 6. WHAT S THE BLACK BOX BEHIND THE DEFICIT-DEBT CONSISTENCY MODULE The basic equation behind all 10 matrices can be derived from the difference between the current year s stock of debt [D(t)] and previous year s stock of debt [D(t-1)], which is by definition the current year s budget deficit [BD(t)] after grants and after debt relief: D(t) D(t-1) = BD(t) (7) As is shown in Appendix 2, equation (7) can be expressed in percentages of GDP [denoted by Y] and depending on if we look at the dynamics of the domestic or external debt stock, we can derive a simple equation, which says that the difference between this year s and last year s debt-to-gdp ratios is equal to this year s deficit-to-gdp ratio minus a factor k times the last year s debt-to-gdp ratio: [D(t)/Y(t)] [D(t-1)/Y(t-1)] = [BD(t)/Y(t)] k * [D(t-1)/Y(t-1)] (8) For a given set of parameters, some of which determine the factor k (whereby k is defined slightly different for the foreign and domestic debt dynamics), we can then solve the equation for the deficit-to-gdp ratio that keeps the debt-to-gdp ratios constant; i.e.: Inserting equation (9) into (8) yields: [D(t)/Y(t)] = [D(t-1)/Y(t-1)] (9) or 0 = [BD(t)/Y(t)] k * [D(t-1)/Y(t-1)] (10) [BD(t)/Y(t)] = k * [D(t-1)/Y(t-1)] (11) For domestic debt dynamics: k d = (g+π)/(1+g+π+gπ) (12) For foreign debt dynamics: k f = (g+π-e)/(1+g+π+gπ) (13) whereby g = GDP growth rate π = inflation rate, and e = rate of devaluation. Please note that if the rate of devaluation (e) is larger than the sum of the GDP growth rate (g) and the inflation rate (π), k f will be a negative number, which implies that a surplus is needed to keep the debt-to-gdp ratio constant. In case rate of devaluation (e) is the same as the sum of the GDP growth rate (g) and the inflation rate (π), k f will be equal to zero, which implies that a balanced budget would be needed to keep the debt-to- GDP ratio constant over time. Simple extensions of equation (8) also allow for the derivation of deficit-to-gdp ratios that keep the debt-to-exports and the debt-to-revenues ratios constant. Furthermore, 25

26 equation (8) can also be expressed in NPV terms, which after some simplifying assumptions (please see Appendix 2) and after keeping the NPV debt-to-gdp ratios constant results in equation (12). Similar NPV equations can also be derived for the extensions of equation (8) that keep the NPV debt-to-exports and the NPV debt-torevenues ratios constant. [BD(t)/Y)(t)] = (i old /i new ) k * [D(t-1)/Y(t-1)] (14) whereby i old = average interest rate on the previous year s debt stock, and i ew = average interest rate on the newly contracted loans. Based on equations (11) and (14), and their extensions for the (NPV) debt-toexport and the (NPV) debt-to-revenue ratios, a matrix is calculated for a range of GDP growth rates and a range of one specific debt ratio. The results for the range of each debt ratio is approximated using a linear approximation based on the parameters provided. For example, if the calculated debt-to-gdp ratio is 100 percent and the consistent deficit-to- GDP ratio is 2 percent, then the consistent deficit-to-gdp ratio for a debt-to-gdp ratio of 120 percent is approximated by multiplying the original deficit-to-gdp ratio of 2 percent by a factor of 1.2 [which is the ratio of the upper range of the debt-to-gdp ratio (120 percent) to the calculated debt-to-gdp ratio (100 percent)]. While this is a reasonable approximation of the consistent deficit-to-gdp ratio for most realistic parameter specifications, the approximation is inappropriate for a negative k factor and/or a negative debt ratio. The user should therefore neglect any negative results the matrix may provide. 26

27 APPENDIX 1: HISTORICAL INFORMATION ACCESSIBLE IN THE DEBT PROJECTION MODULE The debt sustainability worksheet includes information on (a) historical values on the stock of public and publicly guaranteed debt, (b) average maturity rates, (c) average interest rates, and (d) currency-specific discount rates. These are intended to help the user in determining some of the parameters needed for running the simulator. The information on interest rates contains country-specific information on previous average interest rates on new public and publicly guaranteed debt. A value for the average interest rate may be obtained by dividing the initial debt stock by the initial interest payments. When determining future values for the average interest rates, the user may want to take into account the historical trend as well as other information that may be helpful to determine if a country s future debt stock is likely to be more or less concessional. The data for the NPV and nominal debt, average maturity rates, and average interest rates are from the World Bank s Global Development Finance database. The NPV and nominal debt refer to a country s total (public and private) external debt. The data on average maturity and average interest rates refer to newly contracted public or publicly guaranteed debt. The data for the discount rates from January 1993 to December 2001 are from the OECD website. The World Bank and the OECD provide regular updates that the user might consult to see the latest developments. Appendix Figure 1: Historical values of stocks of public & publicly guaranteed debt 27

28 Appendix Figure 2: Historical values of average maturity and average interest rates Appendix Figure 3: Historical values of average maturity and average interest rates 28

29 Appendix Figure 4: Historical values of currency-specific discount rates 29