The public debt ratio will always fall when economic growth is positive because the primary fiscal deficit falls due to the automatic stabilisers (more tax revenue, less welfare spending), and, the denominator, GDP rises.
Answer: False
The answer is False.
First, some background.
We start with ex post accounting statement that connects the fiscal flows to the debt ratio (the mainstream call this the 'government budget constraint' but, for a currency-issuing government there is no such constraint):
FDt = Gt + rBt-1 - Tt = ΔB + ΔH
which you can read in English as saying that fiscal deficit (FD) = Government spending (G) - Tax receipts (T) + Government interest payments (rBt-1), all in real terms.
The subscripts t and t-1 just refer to time, t being now, and t-1 being last period (whatever the period is - annual, quarterly, etc).
r is the yield on outstanding bonds, B, measured at t-1, so rBt-1 are the total interest payments on outstanding government debt in time t.
The fiscal position (assume a deficit), which is a flow (the difference between outflows from the government to the non-government sector and inflows the other way, have a stock manifestation = ΔB + ΔH.
So the government can match the deficit with a mix of ΔB and ΔH
These expressions are merely accounting statements and have to be true if things have been added and subtracted properly in accounting for the dealings between the government and non-government sectors.
In mainstream economics, money creation (ΔH) is erroneously depicted as the government asking the central bank to buy treasury bonds which the central bank in return then 'prints' money.
According to the narrative, the government then spends this money. This is called debt monetisation and we have shown in the - Deficits 101 series - how this conception is incorrect.
We usually express the ratio of public debt to GDP rather than discuss the level of debt per se.
The following expression is typically used, with the reality that government may deploy ΔH ignored because it has generally been considered to be taboo.
Accordingly, the change in the public debt ratio is:
So the change in the debt ratio is the sum of two terms on the right-hand side: (a) the difference between the real interest rate (r) and the GDP growth rate (g) times the initial debt ratio; and (b) the ratio of the primary deficit (G-T) to GDP.
A growing economy can absorb more debt and keep the debt ratio constant. For example, if the primary deficit is zero, debt increases at a rate r but the debt ratio increases at r - g.
Now to the question at hand.
First, the use of the word always makes the proposition false per se.
Second, the primary deficit may not fall when economic growth is positive if discretionary policy changes offset the declining net spending as tax revenue increases and welfare payments fall (the automatic stabilisation).
Using the framework developed and explained above we saw that a change in the change in the debt ratio is the sum of two terms on the right-hand side: (a) the difference between the real interest rate (r) and the GDP growth rate (g) times the initial debt ratio; and (b) the ratio of the primary deficit (G-T) to GDP.
Consider the following table which simulates two different scenarios. Case A shows a real interest rate of zero and a steadily increasing annual GDP growth rate across 10 years. The initial public debt ratio is 100 per cent.
The primary fiscal deficit also starts at 5 per cent of GDP then reduces as the GDP growth induce the automatic stabilisers. It then reaches a steady 2 per cent per annum which might be sufficient to support the saving intentions of the non-government sector while still promoting steady economic growth.
You can see that the even with a continuous deficit, the public debt ratio declines steadily and would continue to do so as the growth continued. The central bank could of-course cut the nominal interest rate to speed the contraction in the debt ratio although I would not undertake that policy change for that reason.
In Case B we assume that the government stops issuing debt with everything else the same. The public debt ratio drops very quickly under this scenario.
However, should the real interest rate exceed the economic growth rate, then unless the primary fiscal balance offsets the rising interest payments as percent of GDP, then the public debt ratio will rise.
The only concern I would have in this situation does not relate to the rising ratio.
Focusing on the cause should be the policy concern. If the real economy is faltering because interest rates are too high or more likely because the primary fiscal deficit is too low then the rising public debt ratio is just telling us that the central bank should drop interest rates or the treasury should increase the discretionary component of the fiscal statement.
In general though, the public debt ratio is a relatively uninteresting macroeconomic figure and should be disregarded. If the government is intent on promoting growth, then the primary deficit ratio and the public debt ratio will take care of themselves.