Page 66 - ES 2020-21_Volume-1-2 [28-01-21]

Does Growth Lead to Debt Sustainability? Yes, But Not Vice-Versa! 49

.
(g-r) d /(1+g), where g and r denote the real growth rate and real cost of general government
t-1
debt respectively while d denotes the debt-to-GDP ratio in the previous year. When g > r, this
t-1
threshold level of primary deficit is positive. Therefore, as long as the primary deficit remains
below this threshold, debt remains sustainable. Along these lines, De Luca (2012) show that as
long as primary deficit is a constant fraction of GDP, (r-g) still remains a sufficient statistic for
debt sustainability. Thus, the ease with which a government can reduce its debt-to-GDP ratio
(d ) depends primarily on the interest rate-growth differential (IRGD hereafter) or (r-g). More
t
negative the IRGD, the easier (and quicker) it is for the Government to ensure debt sustainability.
Conversely, if the IRGD is positive, the harder (and slower) it is for the Government to ensure
debt sustainability. A negative IRGD thus creates an enabling environment for debt sustainability.

Box 3: Theory of Debt dynamics

The simple identity for debt dynamics provides an accounting framework to decompose change
in the ratio of government debt-to-GDP into its key drivers, namely (i) the difference between
the (real or nominal) interest rate charged on the government debt and (real or nominal) growth
rates; (ii) the debt-to-GDP ratio in the previous period, and (iii) the ratio of primary deficit to
GDP.

The identity for debt dynamics is written as:
∆d = (r – g ).d t–1 / (1+g ) – pb ,
t
t
t
t
t
where Δd : change in general government debt-to-GDP in year t;
t
r t : real interest rate paid in year t;
g t : real GDP growth in year t;
d t-1 : general government debt-to-GDP in in year (t-1);
pb : primary balance-to-GDP in year t.
t
The same identity can also be written using nominal interest rate and nominal growth rate:

∆d = (i – γ ).d ⁄ (1+γ ) – pb ,
t
t-1
t
t
t
t
where i : nominal interest rate paid in year t;
t
γ : nominal GDP growth in year t
t
and other variables are as above.
This equation can be derived from the basic identity that inflows and outflows have to be
equal for the Government i.e.

or
D = D + i D – PB t
t
t–1
t–1
t
where PB is the primary balance defined as NIE - R and
t
t
t
i is the interest paid on the debt in year t.
t