WB, three gap and debt
Halvor Mehlum April 2009
The World Bank is concerned with long-term challenges. This has implications for the choice of models
used. IMF has historically been most concerned with short term balance of payments challenges and not
too concerned with growth. The models are simple and consists mainly of accounting identities. The parts
describing the behavior of the different economic actors are few. This feature makes the models easy to handle
(feasible data collection and limited need for estimation), and the same models can be used without adjustment
for a wide range of countries. For the World Bank investment and growth are the main concern. The question
is: How to achieve growth, i.e. how to achieve investment.
The three-gap model (a cousin of RMSM) is essentially built on four equations:
R=C +I +G+H
H = X − hR R − hI I,
hR , hI ∈< 0, 1 >
C = C0 + c(R − T )
(1)
(2)
(3)
R =GDP, C =Private consumption, G=Government expenditure, H =current account surplus, X =Exports,
hR =Import contents in GDP, hI =Import contents in investment, c = (1 − s) =propensity to consume. From
(1)-(3) we get the savings gap
I =S =R−C −G−H =
1
1
(s + hR )R −
(C0 + G + X − cT )
1 − hI
1 − hI
(4)
The world Bank policy recommendation is clear: Reduce government deficit via cut in G and/or increased T .
What if the government also has a target for a not to high current account deficit, i.e. a target for H not to
big negative. This introduces the foreign exchange gap. By altering (2) we get
I=−
0.1
hR
1
1
R+
(X − H)
R + (X − H) → I = −
hI
hI
0.3
0.3
(5)
where H indicates that H has a target value. (5) represents a downward sloping constraint in the R − I plane,
the numbers are taken from Yemen. H is smaller to the right and higher to the left. This foreign exchange
constraint represents an constraint to investment if it is to far to the left. According to the World Bank this
constraint can be relaxed by devaluation.
Devaluation: hI & hR & X % all shifting the foreign exchange gap to the right.
This is the essence of RMSM (revised minimum standard model) devalue and stimulate savings.
Another alternative approach to the two gap model is again to allow the capacity to be under utilized because
of import compression through rationing. The equilibrium of the economy is then found in the intersection
between the foreign exchange gap and the savings gap.
Lastly introduce an investment demand function
I = d0 + d ∗ R
This is in the literature named the demand gap or the fiscal gap. The three gap model consists of these three
gap’s. How is equilibrium established: Either through 1: Adjusting H Standard Keynesian. 2: Adjusted
exchange rate. 3:Import compression and credit schemes compulsory savings as in Zimbabwe. 4: Income
redistribution and adjusted savings.
Financial crisis
will affect several dimensions: From the bottomn: d0 down as FDI stops. H̄ up as there is less generous
financing arround. X down as export markets deteriorates. G and T down as the government tries to
stimulate production.
Sustainable debt
There are many countries in the world that have debt levels that are far above what they possibly can handle.
For these countries some kind of debt reduction is unavoidable. Given that some countries should get debt
relief it is essential to decide what debt level a country can possibly handle. One important principle in debt
relief is that it should be once and for all so that the country do not end up in similar problems after a year
or ten. The relief should bring the debt down to a level that is sustainable.
Sustainable debt can be defined in a number of ways. One definition is that it is a level of debt such that the
debt does not grow faster than GNI. Hence it should be possible to hold the DEBT/GNI ratio constant over
1
time. That implies that if the growth rate of GNI is 3% a year the growth rate of DEBT should be no more
than 3% a year.
The growth of the debt is determined by many factors. Two important factors that I will focus on is the 1)
export surplus and 2) interest on the existing debt (r∗DEBT where r is the rate of interest). Abstracting from
other factors it follows that
∆D=rD − H
Assume that the expected growth rate of GNI is g. From the definition above, the D is sustainable if the
growth in D is equal to g ∗ D. Assume that the export surplus realistically can be a fraction a times the GNI
(Y ). Hence, a requirement for sustainable debt (D̄) is that
g ∗ D̄ = rD̄ − aY ⇐⇒
a
D̄
=S =
Y
r−g
Sufficient debt relief then implies bringing the debt level down to the level D̄, or to put it differently bringing
the debt to GNI ratio down to S. What determines S? Assume that a = 0.01 (that the export surplus is
expected to be positive and equal to 1% of GNI) and assume that r = 0.07 (7%) then
S=
0.01
0.07 − g
If the growth rate is zero (g = 0) then S = 14%(and D̄ = 0.14 ∗ Y ), if g = 2% then S = 20%, if g = 5% then
S = 50%, if g = 6% then S = 100%. (If the growth rate is large, g > 7%, then a can be negative. That implies
that if the growth rate of GNI is higher than the interest rate it is possible to have a small export deficit at
the same time as the debt is sustainable. The important condition is that debt does not run faster than the
GNI).
Anyway, the main message is that the answer to the question ”What level of debt is sustainable?” depends
critically on the assumptions regarding r, a and g. If one for example is too optimistic with regards to the
growth rate g and expect g = 6%, a debt ratio of 100% may appear sustainable. Debt relief based on that
premise will prove not to be sufficient if g turn out to be 2% instead (in which case only a debt ratio of 20%
is sustainable).
As a result of the financial crisis realisticvalues of r may go up while realistic values of a and g drops. Before
the crisis the realistic scenario was perhaps: g = 5%, a = 2% and r = 6%. Then S = 200%. After the crisis it
might be the case that a = 1%, r = 8%, and g = 2%, then S = 17%. If a goes to zero then obviously S = 0.
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