Page 67 - ES 2020-21_Volume-1-2 [28-01-21]

50 Economic Survey 2020-21 Volume 1

On dividing both sides of the equation by GDP , and denoting all ratios as proportion
t
of GDP by their lower-case letters, i.e. d ≡ D ⁄ GDP for instance, we get:
t
t
t
1 + i t
d = d t – 1 – pb t
t
1+γ t
GDP t
where we substitute = (1+γ ).
t
GDP t–1
Subtracting d from both sides of the above equation, we get the first equation above
t-1
using real interest and growth rates.

We know from the Fisher’s equation that (1 + i ) = (1 + r )(1 + π ) and (1 + γ ) = (1 +
t
t
t
t
g ) (1 + π ), where π denotes the inflation in year t. Using the same, we get:
t
t
t
1 + r t
d = d t – 1 – pb t
t
1 + g t
Note that both the equations – the one using nominal interest and growth rates and that
one using real interest and growth rates – are identical and equivalent to each other.
Sometimes, doubt arises if the two equations are indeed identical? This is because of
r – g t i – γ t
t
t
the comparison between the fractions and . It appears as though the
1 + g t 1 + γ t
only difference is in the denominator of the fraction with the real growth rate replaced
by the nominal growth rate because the differences (r-g) and (i-γ) must be identical. The
confusion arises from using the approximation i ≈ r + π and γ ≈ g + π, which leads to
the incorrect inference that (r-g) and (i-γ) must be identical. However, the confusion gets
settled when one recognizes that these are only approximations where the product terms
in the Fisher equation (r∙π and g∙π) have been ignored.

2.5 As a norm in India, over the last two and a half decades, GDP growth rates have been
greater than interest rates (Figure 2a). This evidence is consistent with the phenomenon
described by Blanchard (2019) in his 2019 Presidential Address to the American Economic
Association: “If the interest rate paid by the government is less than the growth rate, then the
intertemporal budget constraint facing the government no longer binds.” Intuitively, when
i > γ or nominal growth rate exceeds the nominal interest rate for the foreseeable future,
t
t
debt sustainability is obtained as explained in the figure below. Here, i and γ are taken to
t
t
be their historical averages for last 25 years, 8.8 per cent and 12.8 per cent respectively. As
the government’s investment of a ` 100 produces ` 112.8 while the principal and interest
repayment equals ` 108.8, ` 4 can be added to the economy after the loan of ` 100 is rolled
over to the next period. Of course, this roll-over of the debt that yields debt sustainability
can only manifest if i > γ . If the inequality reverses, then rollover of debt does not become
t
t
automatic, thereby jeopardizing debt sustainability.