Under current institutional arrangements (where deficits are matched $-for-$ by debt-issuance), the change in the ratio of public debt to GDP will exactly equal the primary deficit plus the interest service payments on the outstanding stock of debt both expressed as ratios to GDP minus the changes in the monetary base arising from official foreign exchange transactions.
Answer: False
The answer is False.
If we left out the last part of the question "minus the changes in the monetary base arising from official foreign exchange transactions" then the answer is true. The offical foreign exchange transactions do change the monetary base but have no accounting impact on the ratio of public debt to GDP
So without that addition, the answer would be true as long as you note the caveat "under current institutional arrangements". What are the institutional arrangements that are applicable here? I am referring, of-course, to the voluntary choice by governments around the world to issue debt into the private bond markets to match $-for-$ their net spending flows in each period. A sovereign government within a fiat currency system does not have to issue any debt and could run continuous fiscal deficits (that is, forever) with a zero public debt.
The reason they is covered in the following blogs - On voluntary constraints that undermine public purpose.
So given they are intent on holding onto these gold standard/convertible currency relics the answer is true.
The framework for considering this question is provided by the accounting relationship linking the fiscal flows (spending, taxation and interest servicing) with relevant stocks (base money and government bonds).
This framework has been interpreted by the mainstream macroeconommists as constituting an a priori financial constraint on government spending (more on this soon) and by proponents of Modern Monetary Theory (MMT) as an ex post accounting relationship that has to be true in a stock-flow consistent macro model but which carries no particular import other than to measure the changes in stocks between periods. These changes are also not particularly significant within MMT given that a sovereign government is never revenue constrained because it is the monopoly issuer of the currency.
To understand the difference in viewpoint we might usefully start with the mainstream view. The way the mainstream macroeconomics textbooks build this narrative is to draw an analogy between the household and the sovereign government and to assert that the microeconomic constraints that are imposed on individual or household choices apply equally without qualification to the government. The framework for analysing these choices has been called the government budget constraint (GBC) in the literature.
The GBC is in fact an accounting statement relating government spending and taxation to stocks of debt and high powered money. However, the accounting character is downplayed and instead it is presented by mainstream economists as an a priori financial constraint that has to be obeyed. So immediately they shift, without explanation, from an ex post sum that has to be true because it is an accounting identity, to an alleged behavioural constraint on government action.
The GBC is always true ex post but never represents an a priori financial constraint for a sovereign government running a flexible-exchange rate non-convertible currency. That is, the parity between its currency and other currencies floats and the the government does not guarantee to convert the unit of account (the currency) into anything else of value (like gold or silver).
This literature emerged in the 1960s during a period when the neo-classical microeconomists were trying to gain control of the macroeconomic policy agenda by undermining the theoretical validity of the, then, dominant Keynesian macroeconomics. There was nothing particularly progressive about the macroeconomics of the day which is known as Keynesian although as I explain in this blog - Those bad Keynesians are to blame - that is a bit of a misnomer.
This is because the essential insights of Keynes were lost in the early 1940s after being kidnapped by what became known as the neo-classical synthesis characterised by the Hicksian IS-LM model. I cannot explain all that here so for non-economists I would say this issue is not particularly important in order to develop a comprehension of the rest of this answer and the issues at stake.
The neo-classical attack was centred on the so-called lack of microfoundations (read: contrived optimisation and rationality assertions that are the hallmark of mainstream microeconomics but which fail to stand scrutiny by, for example, behavioural economists). I also won't go into this issue because it is very complicated and would occupy about 3 (at least) separate blogs by the time I had explained what it was all about.
For the non-economists, once again I ask for some slack. Take it from me - it was total nonsense and reflected the desire of the mainstream microeconomists to represent the government as a household and to "prove" analytically that its presence within the economy was largely damaging to income and wealth generation. The attack was pioneered, for example, by Milton Friedman in the 1950s - so that should give you an idea of what the ideological agenda was.
Anyway, just as an individual or a household is conceived in orthodox microeconomic theory to maximise utility (real income) subject to their fiscal constraints, this emerging approach also constructed the government as being constrained by a fiscal or "financing" constraint. Accordingly, they developed an analytical framework whereby the fiscal deficits had stock implications - this is the so-called GBC.
So within this model, taxes are conceived as providing the funds to the government to allow it to spend. Further, this approach asserts that any excess in government spending over taxation receipts then has to be "financed" in two ways: (a) by borrowing from the public; and (b) by printing money.
You can see that the approach is a gold standard approach where the quantity of "money" in circulation is proportional (via a fixed exchange price) to the stock of gold that a nation holds at any point in time. So if the government wants to spend more it has to take money off the non-government sector either via taxation of bond-issuance.
However, in a fiat currency system, the mainstream analogy between the household and the government is flawed at the most elemental level. The household must work out the financing before it can spend. The household cannot spend first. The government can spend first and ultimately does not have to worry about financing such expenditure.
From a policy perspective, they believed (via the flawed Quantity Theory of Money) that "printing money" would be inflationary (even though governments do not spend by printing money anyway. So they recommended that deficits be covered by debt-issuance, which they then claimed would increase interest rates by increasing demand for scarce savings and crowd out private investment. All sorts of variations on this nonsense has appeared ranging from the moderate Keynesians (and some Post Keynesians) who claim the "financial crowding out" (via interest rate increases) is moderate to the extreme conservatives who say it is 100 per cent (that is, no output increase accompanies government spending).
So the GBC is the mainstream macroeconomics framework for analysing these "financing" choices and it says that the fiscal deficit in year t is equal to the change in government debt (&DeltaB) over year t plus the change in high powered money (&DeltaH) over year t. If we think of this in real terms (rather than monetary terms), the mathematical expression of this is written as:
which you can read in English as saying that Budget deficit (BD) = Government spending (G) - Tax receipts (T) + Government interest payments (rBt-1), all in real terms.
However, this is merely an accounting statement. It has 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 is erroneously depicted as the government asking the central bank to buy treasury bonds which the central bank in return then prints money. 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. Anyway, the mainstream claims that if the government is willing to increase the money growth rate it can finance a growing deficit but also inflation because there will be too much money chasing too few goods! But an economy constrained by deficient demand (defined as demand below the full employment level) responds to a nominal impulse by expanding real output not prices.
But because they believe that inflation is inevitable if "printing money" occurs, mainstream economists recommend that governments use debt issuance to "finance" their deficits. But then they scream that this will merely require higher future taxes. Why should taxes have to be increased?
Well the textbooks are full of elaborate models of debt pay-back, debt stabilisation etc which all "prove" (not!) that the legacy of past deficits is higher debt and to stabilise the debt, the government must eliminate the deficit which means it must then run a primary surplus equal to interest payments on the existing debt.
Nothing is included about the swings and roundabouts provided by the automatic stabilisers as the results of the deficits stimulate private activity and welfare spending drops and tax revenue rises automatically in line with the increased economic growth. Most orthodox models are based on the assumption of full employment anyway, which makes them nonsensical depictions of the real world.
More sophisticated mainstream analyses focus on the ratio of debt to GDP rather than the level of debt per se. They come up with the following equation - nothing that they now disregard the obvious opportunity presented to the government via &DeltaH. So in the following model all net public spending is covered by new debt-issuance (even though in a fiat currency system no such financing is required). 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.
Thus, if we ignore the possibilities presented by the &DeltaH option (which is what I meant by current institutional arrangements), the proposition is true but largely irrelevant.
You may be interested in reading these blogs which have further information on this topic: