Back Matter

Back Matter

Jan Martijn, Gabriel Di Bella, Shamsuddin Tareq, Benedict Clements, and Abebe Aemro Selassie
Published Date:
July 2006
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    Appendix I The Accuracy of Consecutive Updates of Monetary Projections

    As more information becomes available over time, the monetary projections in consecutive program revisions should show increasing accuracy. This expectation is supported by Table 3.3 in the main text, which shows a decreasing mean deviation of the outcomes from the consecutive projections. However, the mean does not provide a full picture. The correlation of successive projections with the outcomes provides additional insight.

    For each of the key monetary variables in the panel of 13 countries with observations from 1999 to 2003, Table A1.1 shows the correlation coefficients between the projected percentage changes in the consecutive program updates and the realizations.1 This statistical procedure follows that used by Atoian and others (2004). To allow for comparison across a balanced panel (given that often projections for broad money and, especially, reserve money are not available), the table includes three lines for each variable. The first (second) line reflects only those cases in which a projection was included in the final IMF staff report for the country circulated two years (one year) before the year in question, referred to as the t – 2 (t – 1) staff report; the third line is based on all cases and relates only to the projections presented in the first—t(SR1)—and the last—t(SR2)—staff report during the target year.

    Table A1.1.Accuracy of Program Updates(Correlation coefficients between projections and outcomes)
    Projection at Time1
    No. of observationst – 2t – 1t(SR1)t(SR2)
    Inflation (end-year CPI)
    Inflation (GDP deflator)290.290.350.570.57
    Real GDP growth290.480.690.880.89
    Broad money growth170.610.690.680.82
    Reserve money growth10–0.06–0.190.820.76
    Velocity (% change)150.440.380.520.70
    Money multiplier (% change)
    Sources: IMF staff reports and World Economic Outlook database.

    The year the projections are for is t. The projections as of year t – 1 and t – 2 are those from the last staff reports in the previous year and the year before that, respectively. The projection as of t(SR1) is from the first staff report in year t, and the one at t(SR2) is from the final staff report in that year. If one staff report was issued in year t, the last two observations coincide.

    The results indicate that the accuracy of the projections indeed improves as the time horizon shortens: in almost all cases, the correlation coefficient is higher for projections closer to the realization. The correlation coefficients for reserve money (and the money multiplier), however, are lower for SR2 than for SR1 for the small subset of cases in which observations were already presented two years in advance.

    A second test of projection accuracy, suggested by Musso and Phillips (2001), considers the predictive value of the projections relative to a forecast based on a random walk model (that is, assuming the same percentage change as observed in the previous year). The comparison of the two forecasts is made using Theil’s U-statistic (which equals the ratio of the RMSE of the projection to the RMSE of the alternative forecast based on the “no change” scenario). A lower U-statistic implies greater relative accuracy of the program projection; a value of 1 would indicate that the program forecast is no more accurate than the random walk alternative.

    The results presented in Table A1.2 show that, in all cases, the program projections had smaller errors than the random walk alternative. In line with the results in the previous table, the later projections with a shorter horizon had smaller deviations.2

    Table A1.2.Test of the Accuracy of Program Projections (Theil’s U-Statistic)1
    Projection at Time2
    Inflation (end-year CPI)0.780.76
    Inflation (GDP deflator)0.740.75
    Real GDP growth0.390.39
    Broad money growth0.830.75
    Reserve money growth0.670.64
    Velocity (% change)0.840.77
    Money multiplier (% change)0.640.62
    Source: IMF staff reports and World Economic Outlook database.

    The ratio of the RMSE of the actual projections to the RMSE based on a “no change” forecast.

    The projection as of t(SR1) is from the first staff report in year t, and the one at t(SR2) is from the final staff report in that year. If only one staff report was issued in year t, the last two observations coincide.

    Consistent with the section on financial programming, this analysis excludes Benin and Senegal in view of their membership in the CFA franc zone.

    The previous year’s rate of change could not be observed at time t – 2 or at t – 1; thus a comparison of the random walk projection with the program projections made at these earlier stages would not be meaningful.

    Appendix II The Efficiency of Monetary Projections

    A standard test of projection efficiency is based on a regression of the actual change on a constant term and the program projection (Musso and Phillips, 2001). A projection is deemed weakly efficient if given an information set that consists of only the historical projection, no systematic projection error can be identified (that is, if the constant does not deviate significantly from zero, and the slope does not deviate from one). The results are shown in Table A2.1 for the projections made in the previous year—t – 1—and in the current year—t(SR1) and t(SR2). The asterisks (*) in the body of the table indicate the cases in which the hypothesis of efficiency can be rejected.

    Table A2.1.Test of the Weak Efficiency of Program Projections
    Regression results: XA = b0 + b1*XPb1b11R2No. of Observations
    Projections at time (t – 1)2
    Inflation (end-year CPI)0.671.000.1241
    Inflation (GDP deflator)2.550.700.1143
    Real GDP growth–1.981.230.2443
    Broad money growth2.411.280.2833
    Reserve money growth13.60*0.140.0029
    Velocity (% change)–5.14***–0.01***0.0035
    Money multiplier (% change)2.650.230.0029
    Projections at time t(SR1)2
    Inflation (end-year CPI)1.230.840.1752
    Inflation (GDP deflator)0.780.950.3554
    Real GDP growth–
    Broad money growth6.82**0.880.2154
    Reserve money growth6.83***0.920.2154
    Velocity (% change)–4.05***0.65*0.1554
    Money multiplier (% change)1.160.48**0.0754
    Projections at time t(SR2)2
    Inflation (end-year CPI)0.411.060.2152
    Inflation (GDP deflator)1.020.950.3554
    Real GDP growth–
    Broad money growth6.86***0.810.2954
    Reserve money growth6.90***0.850.2654
    Velocity (% change)–3.38***0.590.1954
    Money multiplier (% change)0.630.58*0.1154
    Sources: IMF staff reports and World Economic Outlook database.

    Indicating that the null hypotheses of b0 = 0 and b1 = 1 can be rejected at the 90 percent (*), 95 percent (**), or 99 percent (***) confidence level.

    The projections as of year t – 1 are those from the last staff report in the previous year. The projections as of t(SR1) and t(SR2) are from the first and the last staff reports in the year the projections are for.

    The results corroborate the findings presented in the main text based on a comparison of the mean deviations between projections and outcomes: the hypothesis of weak efficiency is rejected for the projections of money growth and velocity, but not for inflation. The higher R2 for projections made at a later stage support the finding reported in Appendix I of increasing projection accuracy.

    Appendix III Measuring the Fiscal Stance and Accounting Issues

    The coverage of fiscal statistics varies across countries, as do measures of the fiscal stance. This issue has taken on heightened importance in recent years—it has been argued that alternative measures of the deficit (for example, the current balance) suggest greater scope for expanding public spending than has hitherto been recognized.1 This appendix reviews best practices in the measurement of the fiscal stance.

    The appropriate fiscal stance should be assessed by use of multiple indicators. A single fiscal measure is unlikely to determine whether the fiscal stance is sustainable and appropriate in the context of a country’s macroeconomic circumstances. At a minimum, it is appropriate to measure the overall fiscal balance before and after grants and a breakdown of financing into domestic and foreign sources. In some cases, presentations may vary in light of differing institutional arrangements (for example, West African Economic and Monetary Union countries). Regardless of presentation, programs should continue to monitor a range of indicators of the fiscal stance. Key indicators should be tailored to each country’s circumstances.2

    If public debt is at high levels, measures of both external and total public indebtedness should be closely monitored. In this regard, ratios of the NPV of external public debt to exports and the NPV of total public debt to GDP and revenue are useful summary variables of total indebtedness.3 Ratios of debt service to revenue and gross financing needs to GDP can also indicate whether the path of debt payments is sufficiently smooth to avoid liquidity problems.4 Similarly, program design should focus on targeting flow variables that have the most direct impact on debt sustainability. These could include the minimum level of concessionality and the overall deficit.5 Both of these indicators, however, have limitations: minimum levels of conditionality do not necessarily restrict the total accumulation of new debt, and overall deficit targets do not incorporate the differing effects that concessional and nonconcessional borrowing have on NPV ratios. For these reasons, the new DSA framework for low-income countries also suggests the use of indicative ceilings on NPV ratios (IMF, 2004a). Primary balances, non-oil balances, and arrears may also be useful indicators, depending on country circumstances.

    If crowding out or monetary financing of the deficit is a concern, it may be useful to focus on the level of domestic financing or net credit to the government. In cases where external debt is high and growing, however, an exclusive focus on domestic credit would be inadequate.

    To ensure comprehensive measurement of the fiscal stance and debt sustainability, fiscal data covered in programs should ideally extend to the general government and noncommercial, nonfinancial public corporations. This approach seeks to strike the appropriate balance between adequately covering fiscal activities and avoiding inappropriate constraints on the investments of commercially run public enterprises (IMF, 2004g). In practice, however, data limitations necessitate a much more narrow coverage. In Africa, for example, less than 20 percent of fiscal statistics monitored by the IMF cover the nonfinancial public sector.6 In countries where significant fiscal activities are being undertaken outside the area of coverage, PRGF-supported programs should seek to broaden the institutional coverage of the fiscal sector accounts.

    For a review of these arguments, see IMF (2004g).

    This discussion focuses on program design, rather than on fiscal conditionality per se, which is beyond the scope of this paper. Such an assessment would need to take into account, among other things, the timeliness and quality of data and the authorities’ ability to control the variables in question.

    Separate monitoring of NPV-based indicators is also important because changes in the overall deficit do not accurately reflect changes in government net worth as a result of the grant element of concessional borrowing.

    The path of these variables under multiple scenarios can usefully be examined in the context of the DSA.

    For further discussion of these measures, see IMF (2004e).

    Figures are based on the assessment of country documents in IMF (2004c).

    Appendix IV NPV of Debt-Stabilizing Primary Balances

    A commonly used statistic in the debt sustainability literature is the debt-stabilizing primary balance. Following Buiter (1985), the debt-stabilizing primary balance (as a share of GDP), p* can be expressed as

    where r is the real interest rate on debt, g is the real GDP growth rate, and d is nominal debt as a share of GDP.1 Incorporating exchange rate effects on debt denominated in foreign currency, equation (1) can be reformulated as

    where s is the share of debt held in foreign currency and e is the rate of real exchange rate depreciation. The real interest rate in this expression should be defined as the weighted average of the domestic and foreign real interest rates, where the domestic real interest rate is the nominal interest rate minus inflation and the foreign real interest rate is the nominal interest rate on foreign currency debt minus foreign inflation.

    Following Baldacci and Fletcher (2004), an analogous expression for the primary balance that stabilizes the NPV of debt would be

    where z is the real discount rate, n is the NPV of debt, and f is the grant element of new concessional financing (the difference between the nominal value of new financing and the NPV of new financing) as a share of GDP. Intuitively, equation (3) is the same as equation (2), except that the real discount rate, rather than the actual real interest rate, affects the evolution of the NPV of debt and the grant element of new financing is an important factor in determining the debt-stabilizing primary balance. In effect, the grant element of loans is treated as revenue in equation (3) to derive the augmented primary balance, (p* + f).

    The DSA template for low-income countries defines the NPV of total debt in these countries as the NPV of external debt plus the nominal value of domestic debt. In this case, the debt-stabilizing primary balance would be

    where rd is the real domestic interest rate. If rd is the same as the foreign real discount rate, then equation (4) collapses back to equation (3).

    What does equation (4) imply about the sustainability of the sample of mature stabilizers? Assuming a nominal dollar discount rate of 5 percent and an average U.S. inflation rate over the next 10 years of 2 percent, the real discount rate (z) would be 3 percent. If real domestic interest rates and medium-run growth in the sample countries are assumed to be 3 percent and the real exchange rate appreciation is assumed to be zero, then the augmented primary balance that stabilizes the NPV of debt is zero, irrespective of the level of debt:

    Equation (5) can then be used to examine whether fiscal policy in these countries has been consistent with the objective of debt sustainability.

    Unfortunately, data on the actual grant element of new borrowing are not readily available. Using data on net external financing, the grant element of new borrowing can be estimated by assuming that gross external borrowing is 1.25 times net external borrowing and the average grant element is 40 percent of gross borrowing.

    These assumptions yield the average debt-stabilizing augmented primary balances for the countries in the sample over the years 2000 to 2003 (Table A4.1). Of the 15 countries, only 6 ran augmented primary surpluses, implying that their fiscal positions were sustainable under the growth and financing assumptions above. In contrast, the majority of countries ran augmented primary deficits and therefore unsustainable policies. However, all but two countries were within 2 percent of GDP of the debt-stabilizing augmented primary balance.

    Table A4.1.Average Augmented Primary Balance, 2000–2003
    CountryPercent of GDP
    Kyrgyz Republic–1.5
    Sources: IMF, World Economic Outlook database and staff estimates.

    These estimates are, however, sensitive to the assumptions made:

    • For example, if these countries grew at 5 percent rather than 3 percent, then a country with an NPV of debt of 50 percent of GDP could run an augmented primary deficit of 1 percent of GDP and still stabilize its debt at the 50 percent level. In this case, 10 of the 15 countries would have been running sustainable policies. Conversely, a growth rate of only 1 percent would require an augmented primary surplus of 1 percent of GDP.

    • Similarly, if the real exchange depreciated by 2 percent a year, then a country with 75 percent of the debt in foreign currency would need to run an augmented primary surplus of 0.75 percent of GDP to stabilize the NPV of debt at the 50 percent level. Conversely, a constant real appreciation of 2 percent a year would allow an augmented primary deficit of 0.75 percent of GDP.

    • Also, the assumption of a common grant element of 40 percent may be quite high for some countries. For example, Guyana’s high augmented primary surplus in Table A4.1 is due to high external borrowing, which implies a high effective grant element. In reality, however, the grant element in Guyana may have been much lower, which would mean that the high augmented primary surplus may be misleading.

    • The effect of changes in the discount rate is, however, less straightforward. A higher discount rate would affect three variables in equation (4)—the discount rate itself, the NPV of debt, and the grant element of new borrowing. An increase in the discount rate itself would tend to increase the debt-stabilizing primary balance, but would also tend to lower the NPV of existing debt and increase the grant element of new borrowing, both of which would tend to decrease the debt-stabilizing primary balance. The net effect would depend on the structure of the debt.

      Some additional caveats should also be borne in mind:

    • The fiscal outturns for 2000–03 may not reflect more recent developments. For example, whereas these estimates indicate that Guyana ran a comfortable fiscal policy, they do not reflect the recent large deterioration in Guyana’s fiscal position.

    • Second, the calculations above assume that countries continue to receive the current level of grants. If the grant to GDP ratio declines, then a corresponding reduction in spending, increase in revenues, or both is needed.

    • Third, these calculations do not take account of extrabudgetary activities that increase debt but not deficits.

    Therefore, a more detailed, country-specific analysis would be required before any firm conclusions could be reached on the sustainability of any particular country’s fiscal policy.

    Nevertheless, these calculations may still provide a useful general picture of the average fiscal positions across these countries. The picture that emerges is that many of these countries still do not have sustainable fiscal positions, but they are not far away. An improvement in the augmented primary fiscal balance by 1–2 percent of GDP through additional effective grants (either through outright grants or higher grant elements of concessional loans) could result in sustainable fiscal positions for almost all countries in the sample.

    Note that equation (1) could also be written using the nominal interest and growth rates (because the inflation elements of both variables would cancel each other out) or in terms of nominal debt and primary balances (by multiplying both sides of the equation by nominal GDP).


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