public debt accumulates when this difference is negative, since in this case part of the expenditure has to be financed through government bond issues. As it can be expected, the government debt is characterised by the payment of interests to the investor that compensate him for the risks borne. From the government point of view, these flows of interests represent an expense known, in technical jargon, as the cost of debt servicing. It follows that the debt grows over time if the government produces primary deficits or if the primary surplus is not sufficient to cover the interests expense on the accumulated debt.
In the following we will assume for the sake of simplicity that the primary balance of the government will be always zero, i.e. that at every moment the tax revenues match exactly the public expenditure. However, a debt exists since it has been inherited from the past. It's not so difficult to argue that under this hypothesis the debt dynamics are influenced only by the interest burden; for example, if at a given year the debt is equal to €2,000 billion and its servicing cost is €100 billion, the year after the debt will grow to €2,100 billion.
Hence, if the interest rates are positive, the public debt tends to grow indefinitely over time. At first glance one could think that this phenomenon should increase the debt amount up to a level to be considered unsustainable, and it should trigger soon or later the state's default. However, the sustainability of the public debt depends also on another important factor: the size of the economy of the issuing state. By following again an intuitive reasoning, the same stock of debt can be more easily sustained the bigger (in terms of GDP) is the reference economy. In fact, a high GDP implies the capacity for generating sufficient streams of fiscal revenues to service the debt adequately (i.e. paying interest and principal at maturity). For these reasons, what really matters is not the size of the debt in absolute terms but in relative terms with respect to the GDP: this new quantity is the Debt/GDP ratio. We will discover shortly that the Debt/GDP ratio is a key quantity in the definition of the so called “Maastricht parameters” that lie at the foundations of the Eurozone.
Let's see what the variables are that influence the Debt/GDP ratio. Given the hypothesis of a primary balance in equilibrium, the debt growth is mainly governed by the nominal interest rate. Economic theory tells us that this rate is set in order to compensate the investor for the market and credit risks borne. But there's much more: in fact, we also have to consider the inflation rate. A rational investor, in fact, will not want the money earned in the form of yields on securities purchased to be reduced or zeroed by the growth of prices and therefore he will require that the nominal interest rate also includes the inflation rate. In other words, the nominal interest rate is the sum of a component that rewards such risks, known as “real interest rate”, and the inflation rate. These two components therefore govern the dynamics of public debt.
Figure 1.11 sums up the concepts contained in the definition of real interest rate.
Figure 1.11 The real interest rate
Let's study now how GDP behaves. The variation of GDP from one period to another depends on a quantity known as “nominal growth rate”. Also this rate (as the nominal interest rate) is formed by two components: the “real growth rate” that measures how the quantity of goods and services produced by an economy changes over time and the inflation rate that is used to express the overall value of goods and services by using the current level of prices.
From this perspective one can comprehend why economists claim that the Debt/GDP ratio should remain constant if the real interest rate on debt matches the real GDP growth rate. If the real interest rate on debt is higher (lower) than the real growth rate, this ratio will increase (decrease) over time. Apart from our simplification in setting the primary balance to 0, this explanation is exactly how the standard theory for the evolution of Debt/GDP ratio is explained in economic textbooks.
In order to better understand the meaning and implications of this theory let's observe that inflation rate influences in the same manner both the evolution of the public debt and that of the GDP. Accordingly the dynamics of the Debt/GDP ratio (and hence the sustainability of public debt) turn out to be invariant with respect to inflation.
Is this theory really true? Not exactly. The theory that we have seen so far assumes that the interest rate paid by the government is the same for the entire stock of public debt. However, in any single period only a given percentage of the overall debt has to be repaid; if we maintain, for the sake of simplicity, the hypothesis of a null primary deficit, it follows that the expiring part of the debt will be refinanced at an interest rate aligned with the current market conditions. Conversely, the remaining stock of debt that has not to be refinanced has an interest cost connected with the previous market conditions.
In this more realistic framework, debt and GDP are always connected with the dynamics of the inflation, but in a different way. In fact the GDP is measured at current prices and grows automatically when inflation increases, while the debt follows the dynamics of the inflation rate only partially. Numerous reasons can be considered: the fact that only a part of the debt expires at a given period, the different interest rate (fixed or variable) paid on the various classes of government bonds, the term structure of the debt and the discrepancy between the current inflation rate and the one embedded in the servicing cost of the debt.
Anyway, what matters is that the inflation rate affects in different ways the two components of the Debt/GDP ratio and so it has a net effect on its dynamics. In other words, if the inflation rate is positive, the denominator grows more than the numerator and so the ratio improves. Vice versa, if the inflation rate is negative (deflation), the GDP decreases faster than the debt and hence the ratio deteriorates.
In normal market conditions the inflation makes the public debt more sustainable for reasons connected with the technical features of the debt. It is clear, hence, that when the debt becomes difficult to manage, the control of the inflation rate is an important policy tool.
Let's make a further passage ahead in our line of reasoning. As it has been said above, the possibility of using the inflation to contain the growth of the Debt/GDP ratio comes from the fact that the debt servicing cost reflects only partially altered the current inflation rate. But then, if the government policy is able to manage the sensitivity of the interest rates to the growth rate of the prices, the abating effect that the inflation rate has on the debt can be amplified. In other words, the inflation increases but the nominal interest rates remain constant; in economic theory this policy measure is known as “financial repression”, since in the long term it induces negative real interest rates and hence an erosion of private savings invested in government bonds.
Empirically, it can be proved that negative real interest rates have characterised the economy of numerous countries in different historical periods. For example, in Italy (see Figure 1.12) several sub-periods of negative real rates can be found for short-term government bonds (BOT); in some cases the values are relevant, (up to −6 % in the second half of the 70s). But there's more. Also in more recent times–in 2003 or in 2010–2011–Italy has experienced negative real interest rates, even if limited to a minimum of −1 %.
Figure 1.12 Inflation, nominal and real interest rates in Italy (1975–2014)
Source: Bank of Italy
Italy is not an isolated case. Among the countries that have witnessed negative real interests rate can be included Japan, USA and Germany. Figures 1.13, 1.14 and 1.15 illustrate the pattern of inflation, nominal and real interest rate in the period 2000–2014 for United States, Germany and Japan.
