Determining External Debt Sustainability
Fishlow(1988), Barbosa and Cal(1989), Gunning and Mash(1998) and Rapu(2003). Drawing from equation 4.7 from the theoretical framework/methodological issues, and representing the level of debt each period by Dt and the level of real output or income by Yt with real interest rate given as r and the growth of real output by g and for the level of resource gap (e.g. trade gap) by H. The level of stock of debt and output evolve according to:
Dt = Dt-1 (1+r) - Ht 4.18
Yt = Yt-1 (1+g) 4.19
From which the dynamics of the debt to GDP ratio are:
(D/Y)t = (D/Y)t-1 ((1+r)/(1+g)) – Ht/Yt 4.20
In a steady state defined by a stable debt to GDP ratio, shown by D/Y without a time subscript, this implies that ratio of the trade gap – output ratio (H/Y) must be:
H/Y = ((r-g)/(1+g))D/Y 4.21
Some implications could be derived from the mathematical relationship above and they are: An increase in the growth rate of debt is sustainable only when the real growth rate of output is greater than the interest rate (g > r) since the debt-GDP ratio would continue to fall without limit unless the government were to run a deficit sufficient to offset the effects of the excess of the rate of growth over the interest rate. Moreover, a smaller trade surplus would be needed to stabilize
the debt ratio. However, when the real interest rate exceeds the rate of growth of output (r > y), an increasing debt is unsustainable as the ratio of debt and GDP will rise sharply while the trade deficit gap will at the same time increase. The government must run a trade surplus sufficient to offset the effect on the debt ratio of the excess of the interest rate over the growth rate, otherwise, the debt ratio would grow without limit;
If there is a trade balance(exports equals imports), and interest rates are equal to growth rate of GDP, then the debt/GDP ratio will be stable;
To sustain an increase in the level of debt/GDP ratio, enough non-interest current surplus must be generated to cover a portion of the interest cost while a deficit may be sustainable as long as it is not large; alternatively, interest rates must be lower than GDP growth;
If the trade deficit position deteriorates into large deficits, then an upward pressure may be mounted on the real interest rate. This may precipitate further borrowing which could put pressure on interest rate. It highlights the fact that the debt cannot be serviced indefinitely by issuing new debt;
For a government to stabilize its debt/output ratio, and ignoring the 1+g term in the denominator of equation 4.21 that has only a small effect, it needs to make resource balance equal to the real rate of interest minus the real rate of economic growth per unit of debt. Similarly, the trade balance must also exceed by this amount what it would be as a result of capital flows alone; In a transition to steady state during which extra debt is being incurred, the debt to GDP ratio will tend to grow. Clearly, the return to the investments financed by that debt is crucial in determining the path of output over time and hence the debt to GDP ratio that actually occurs; and
If steady state trade balance of (r-g) per unit of debt is made the total stock of debt will be
continually expanding but that stock relative to GDP will be stable. It is the value of debt relative to GDP that matters for sustainability since the government’s ability to raise revenue(or exports) is likely to rise in line with increases in GDP.
Further Evidence from Sustainability Ratios
In this section we compare Nigeria’s external debt ratios with some qualifying international criteria. Table 2.8 below illustrates that
Table 2.8: A Comparative Analysis of Nigeria’s External Debt Sustainability viz-a-viz International Benchmarks
Debt Indicators International Benchmark Nigeria’s Threshold Remark
External Debt/GDP [DSC4] 50 64.4 Unsustainable External
Debt/Revenue[DSC6]
250 173.9 Sustainable External Debt Service to
Export[DSC1]
15 9.8 Sustainable Debt to Export [DSC3] 150 176.9 Unsustainable
Revenue[DSC]
Note: International Benchmarks are based on HIPCs standards and sustainability of threshold
implies that the threshold values are equal or close to the meeting benchmark values. Table 2.8 indicates sustainability of external debt for DSC4, DSC1 and DSC9 which are
below the critical values. On the other hand, DSC4 and DSC3 ratios are outside the limits of the baseline scenarios. Thus, the conclusion that can be drawn from the ratios is that the government has problem servicing its external debt particularly, if we take note that there are huge arrears on the debt.
Measuring the Resource Gap consistent with Debt Sustainability
The approach specified above permits an assessment of the sustainability of a given debt plan or strategy and the extent to which it departs from the sustainable path. Given an initial debt-to-GDP ratio and projections of r and g, and for export revenue and imports, the
sustainability of a debt plan can be gauged by comparing the projected resource balance with the steady state position, which, if it were maintained throughout the planning period would prevent the external debt from growing more rapidly than national income. The difference between the projected trade deficit and the sustainable trade deficit is the resource or trade gap which
provides an indication of the need to tighten debt strategy in order to stabilize the debt ratio. The formula for the trade gap defined over a single time period can be derived directly from equation 4.4. Let d* be the level of trade balance that would leave the debt/GDP ratio unchanged over one period, given the values of r and g. It follows from equation 4.21 that
d* = - ((r-g)/(1+g))D/Y 4.22
The trade gap for one period may then be defined as the difference between the trade deficit projected for that period on the basis of the existing plan (d*) and the trade balance consistent with sustainability(d*):
d – d* = d + ((r – g)/(1+g))D/Y 4.23
A negative value for this indicator suggests that the non-interest current account is in surplus and can serve to stabilize the debt-output ratio and that the debt strategy is thus sustainable, and vice versa.
Attempt is then made to provide estimates of the trade gaps that are compatible with debt sustainability for Nigeria. The debt sustainability determination requires the forecast of the real interest rate ( r ) and output growth rates (g). The uncertainty about future direction of the two variables makes the determination a probalistic concept. The simulation exercises assumed the growth rate of 5 per cent which has featured in the budgets as the government underlying assumption for the growth of the economy. On the other hand, a real interest rate of 6 per cent based on the past trend.
IMF Debt Sustainability Template
In this sub-section, we use the IMF debt sustainability template to simulate alternative policy stances and discuss consequences and implications of such alternative stances. The
template attempts to provide a decomposition of both the historical and projected debt dynamics. It argues that such decomposition is useful for identifying whether the purported stability of the debt ratio arises essentially from the behaviour of interest rates, growth rates, exchange rate movement and/or through adjustment of the trade balance. The decomposition is based on the following debt dynamic equation:
Dt+1 = (1 + r)Dt – tbt+1 (4.24)
Where: D is external debt stock and tb is the non-interest current account or trade balance. Let g denote real GDP growth, p the growth rate of US $ value of the GDP deflator, d the external debt-GDP ratio, then:
dt+1 = (1 + r) dt – tbt+1 (4.25) (1+g)(1+p)
Or dt+1 (1 + g + p + gp) = (1 - r)dt – (1+ g + p + gp)tbt+1 (4.26) Rearranging yields an expression for the change in the net debt ratio: dt+1 – dt = (r - g - p - gp) dt - tbt+1 (4.27) (1+ g + p + gp)
If p = 0 dt+1 – dt = (r - g) dt - tbt+1 (4.28a) (1 + g)
Then equation 4.28 collapses to equation 4.20 and the likes.
(1 + g)
Chalk and Hemming (2000) attempted to examine external debt sustainability in a consistent manner as the IMF template. Let Ft be external debt and TBt represent the trade balance in real domestic currency, then the evolution of net foreign debt is given as
et Ft+1 = Rt* et Ft – TBt (4.29)
Where et is the inverse of the average real exchange rate and Rt* = (1 + rt*) is the world interest rate. Equation 4.29 implies that a positive trade balance leads to an improvement in a country’s net indebtedness to the rest of the world, while a higher foreign interest rate increases a country’s indebtedness.
Rewriting equation (4.29) in terms of ratios to output yields:
(1 + qt)(1 + nt)ft+1 = Rt* ft – tbt (4.30)
Where q is the real appreciation/depreciation of the domestic currency. Net foreign debt as a ratio to output is reduced by a positive trade balance, an appreciating currency, or by faster economic growth or lower interest rate.
ft = tbt / (rt – qt – nt) = f (4.31)
ft (rt* – qt - nt) = tbt = f (4.32)
net debt will be a constant share of output (f), when ft > f, net debt will increase relative to output over time, which can be regarded as unsustainable.