### Is there a link between public debt and growth? Yes, in all periods since the 1950s

The results obtained by Reinhart and Rogoff (RR) (loss of growth when the public debt-to-GDP ratio exceeds 90%) have recently been criticised by Herndon-Ash and Pollin (HAP) (see Bibliography at the end), especially because of calculation errors. However, RR have for the most part maintained their conclusions that public debt has a negative impact on growth.

Our own examination of the analysis carried out by RR, over a long period (around 50 years), shows a substantial dispersion of the data, which leads to a very low explained variance (in terms of linear regression) and therefore does not provide a convincing link.

We wanted to pursue a more in-depth analysis of the data initially used by RR by limiting the calculations to shorter periods in order to determine whether a more explanatory character in terms of the correlation can be observed. We also want to look at the link between public debt and growth by introducing a possible non-linearity and by looking not only at the effect of public debt on growth, but also the effect of the primary fiscal surplus that stabilises the public debt ratio.

We use the same sample of OECD countries as Reinhart and Rogoff: United States, Canada, United Kingdom, Japan, Australia, New Zealand, Germany, France, Spain, Italy, Netherlands, Norway, Belgium, Denmark, Sweden, Finland, Ireland, Austria, Portugal, Greece. We will limit the analysis to a method similar to that initially proposed by RR, knowing that models incorporating more data and more structured statistical approaches could have been considered.

## 1 – Public debt ratio/growth link

Charts 1A to F show, for the 20 OECD countries, the average public debt ratio and average growth over the following periods:

The regression between the 20 countries of average growth on the average public debt ratio gives a convincing result only for the periods 1990-2012 and 2000-2012.

The figures in brackets under the coefficients are Student’s t, which indicate the significance of the coefficient when they exceed 2. The important criterion in this analysis is R2 (part of variance explained), which is markedly (6 to 10 times) higher when we analyse more homogenous time periods (excluding post-war periods, away from oil shocks) than the approach initially used by RR.

**1990-2012**

Growth = 3.05 – 0.0128 Public debt % nominal GDP

(7.3) (2.4)

R² = 0.25

**2000-2012**

Growth = 2.64 – 0.0131 Public debt % nominal GDP

(8.4) (3.4)

R² = 0.39

The explanatory nature (R² close to 0.4) is therefore totally acceptable.

**A quadratic regression:**

Growth = a + b (debt ratio) + c (debt ratio)², which would have introduced a nonlinear effect of the debt ratio, did not give any result.

We can see that from 1990 to 2012 and even more from 2000 to 2012, the link between public debt ratio and growth rate is significantly negative. This can be seen clearly in Chart 1F.

This correlation does not appear over a very long period (1950-2012, 1960-2012, Charts 1A and B). The R² are very small over the periods: 0.003; 0.010; 0.016.

But the problem is the sequence of two heterogeneous periods, around oil shocks. If we look at the period 1950-1969, we can also see a negative relationship between public debt ratio and growth from 1950 to 1969.

Growth = 6.50 – 0.032 Public debt % nominal GDP

(11.7) (3.6)

R² = 0.42

## 2 – Required primary fiscal surplus/growth link

But the effect of the public debt ratio on growth normally depends on the level of interest rates, not only on the level of debt. A natural way to examine this idea is to look at the link between growth and the primary fiscal surplus that is required to stabilise the public debt ratio, and which is equal to:

Public debt ratio x (Long-term interest rate – Nominal growth)

A particularly low level of interest rates makes a high debt ratio sustainable by requiring only a small primary surplus.

**Econometric analysis gives:**

**1980-2012**

Growth = 2.68 – 0.32 Required primary surplus

(13.3) (2.6)

R²= 0.27

**1990-2012**

Growth = 2.47 – 0.26 Required primary surplus

(10.6) (2.1)

R² = 0.20

Growth = 3.04 – 1.26 required + 0.15 (required

(10.6) (3.4) primary primary

R² = 0.45 surplus surplus)²

**2000-2012**

Growth = 1.87 – 0.19 Required primary surplus

(10.7) (2.3)

R² = 0.22

Since the 1980s, there has therefore been a positive link between the required primary fiscal surplus and growth: (Charts 2D, E and F). The empirical correlation would even be far stronger if we removed Greece from the sample, where, given the abnormally high level of interest rates, the required primary fiscal surplus is itself abnormally high.

**We obtain, for example:**

**1990-2012 excluding Greece**

Growth = 2.84 – 0.62 Required primary surplus

(12.4) (3.9)

R² = 0.47

**Public debt reduces growth in the period 1950-1969 as well as in the period 1980-2012.** For the entire period (1950-2012), this relationship disappears, probably because of the heterogeneity of the two periods around the 1970s, due to oil shocks.

In the 1980s, 1990s and 2000s, until 2012, the public debt and the primary fiscal surplus required to stabilise the public debt ratio are clearly significantly negatively correlated to growth.

Accordingly, it seems that Rogoff and Reinhart’s conclusion is confirmed if we look only at the past 20 or 30 years or if we look only at the 1950s and 1960s.

**Correlation does not equal causality:** we could even imagine the opposite causality, i.e. that it is growth that makes it possible to reduce the public debt.