Public Debt: How It Is Measured and When It Matters

Public debt is the accumulated total of past borrowing that has not been repaid. Public debt is a stock, and a deficit is a flow that adds to it each year. A rupee total alone says nothing about whether a debt can be carried, so the debt is stated as a share of output. The share has two moving parts, and reading only one of them misleads.

Two ideas do the work here, and both are settled elsewhere. The first is that a government's borrowing in a single year has a name and a size, being the gap between what it spends and what it receives. The second is that the country's output for that same year also has a name and a size. Public debt is what many years of the first leave behind, and the debt ratio is that leftover set against the second. Placing those two numbers side by side and then watching both of them move at once is the whole of the arithmetic.

All the figures below belong to the Republic of Sankhya, an invented country used here so a full account can be shown without any live number attached to it. Sankhya is not a stand-in for anywhere. The arithmetic is what carries over.

What is public debt, and how is it different from a deficit?

Public debt is a level. The level is the amount a government has borrowed over its whole history and has not yet paid back, sitting there on a particular date, and every rupee of it is owed to some creditorWhoever is owed the money. For a government this is usually a mix of banks, insurers, pension funds, households and, sometimes, lenders outside the country.. A deficit is a rate. The rate is the amount borrowed during one period, and a period is a length of time rather than a moment. The deficit is a flow and the debt is the stock that flow runs into, so a deficit of any size at all still makes the debt larger.

Think of a household with a credit card. The balance on the card is a level, and it can be read off the statement this evening. The amount the household overspent this month is a rate, and the overspending moved the balance. If the household overspent by less this month than last month, that is a real change and it is worth noticing, but the balance still went up. The balance only comes down in a month when the household spends less than it earns and puts the difference against the card. A government's debt is that idea with more zeroes.

The Republic of Sankhya carries debt of Rs 10,00,000 crore. During the year covered here its fiscal deficitThe full gap between everything a government receives and everything it spends in one year, which is the amount it has to borrow to close. How the three deficit measures differ is covered separately. was Rs 1,00,000 crore. The government borrowed that much, and the stock ended the year at Rs 11,00,000 crore. Had the deficit been Rs 60,000 crore instead, the stock would have ended at Rs 10,60,000 crore. Both of those are larger than Rs 10,00,000 crore. A narrowing deficit changes how fast the level climbs; it does not turn the climb into a fall.

Why is public debt stated as a share of output rather than in rupees?

A rupee total on its own cannot be read. Rs 10,00,000 crore is a large number, but large compared with what? A debt is carried out of income, so the only sensible thing to set it against is the income available to carry it, and for a country that measure is its annual output. Dividing the one by the other produces a share, and a share can be compared across time and across places. The rupee figure states the size of the debt. The share states the size of the debt relative to the output that has to carry it, and only the share can be read.

The household version is familiar to anyone who has applied for a loan. A card balance of Rs 4,00,000/- means one thing for a household earning Rs 15,00,000/- a year and something quite different for a household earning Rs 3,00,000/- a year. The lender never looks at the balance alone. The lender looks at the balance next to the income. A debt ratio does exactly that for a government.

For the Republic of Sankhya, debt of Rs 10,00,000 crore is set against output for the year of Rs 17,47,200 crore. The division gives 57.23 per cent. Note what has been placed in the denominatorThe lower half of a fraction, the number that divides the upper one. When it changes, the fraction changes, even when the upper half has not moved at all.: not tax receipts, not spending, but the whole output of the country for the year. The choice of denominator matters. Output can move on its own, so the ratio can move without the debt moving at all.

How can the debt ratio rise in a year when output grew?

A ratio behaves in a way that a single number does not, and careful readers are caught by the difference. A debt ratio has two moving parts, the debt above and the output below, and its direction is set by the race between them rather than by either one on its own. Output growing is not by itself good news for the ratio. Output is one runner in a two runner race, and output can be beaten.

Watch it happen with the Sankhya numbers. All of them move in a single year. The debt starts at Rs 10,00,000 crore and the deficit of Rs 1,00,000 crore is added, ending the year at Rs 11,00,000 crore. The stock has risen 10.00 per cent. Output starts at Rs 17,47,200 crore and grows 4.00 per cent, ending at Rs 18,17,088 crore. Now take the ratio again: Rs 11,00,000 crore against Rs 18,17,088 crore is 60.54 per cent. The share has risen from 57.23 per cent to 60.54 per cent, a rise of 3.30 percentage pointsThe plain difference between two percentages. Moving from 57.23 per cent to 60.54 per cent is a rise of 3.30 points. A rise of 3.30 per cent is a different statement., in a year when output grew.

Nothing went wrong in that arithmetic and nothing was hidden. The debt grew at 10.00 per cent and output grew at 4.00 per cent, so the upper half of the fraction outran the lower half and the fraction got bigger. Had the two grown at the same rate, the share would have finished exactly where it started. Had output grown faster, the share would have fallen even with the debt rising in rupees. Note that the growth rate being used here is nominal growthGrowth in output measured at the prices actually charged, so it carries both the change in the quantity produced and the change in prices. Real growth strips price changes back out and is a different figure, covered separately., measured at the prices actually charged, because the debt is a rupee amount and both halves of a ratio have to be counted the same way.

How does a stock of past borrowing reach this year's spending account?

A debt built up over decades is not a museum piece sitting in a separate ledger. The stock arrives in the current year through one line, and that line is interest. Interest is the point of contact between the debt stock and the annual account. Through interest, a decision taken years ago consumes money that could otherwise be spent today.

Sankhya paid Rs 90,000 crore of interest on a stock of Rs 10,00,000 crore. Divide the one by the other and the average cost of the whole stock comes to 9.00 per cent. A stock built up over many years carries many different terms agreed at many different moments. Read that 9.00 per cent as an average across everything outstanding rather than as the rate on any single borrowing. The blended figure is the one the arithmetic needs.

The Rs 90,000 crore does not sit apart. The interest is already inside the Sankhya spending account as part of revenue spendingSpending that is consumed within the year and leaves no asset behind, such as salaries, subsidies and interest. Its contrast with capital spending is covered separately., which totals Rs 3,30,000 crore against capital spending of Rs 70,000 crore and a total of Rs 4,00,000 crore. So interest is a little over a quarter of everything spent on the revenue side, and it is committed before any choice is made about anything else. The level of debt is worth measuring for a practical reason. The level sets the size of the claim that arrives every year without being decided.

What does the arithmetic of a steady debt ratio actually say?

Put the last three sections together and a question falls out on its own. If the debt grows at the pace set by borrowing and output grows at its own pace, what combination leaves the share exactly where it started? A debt ratio is most often misread at exactly this point, so the clean arithmetic answer to that question is worth working through carefully.

Start from what makes the share hold still: the debt has to grow at the same rate as output. Sankhya debt of Rs 10,00,000 crore growing at a nominal 4.00 per cent means the debt may rise by Rs 40,000 crore and no more. But interest alone is Rs 90,000 crore. So the rest of the account has to run a surplus of Rs 50,000 crore before interest to bring the total borrowing down to Rs 40,000 crore. The balance before interest has a name, the primary balanceThe gap between receipts and spending once interest has been taken out of the spending side. How it differs from the fiscal and revenue measures is covered separately., and the general statement is that the ratio holds still when the primary balance offsets the average cost of the debt less nominal growth, applied to the debt.

Run it at three growth rates against the same 9.00 per cent average cost, and the pattern is easy to see. At 4.00 per cent growth the share holds still with a primary surplus of Rs 50,000 crore. At 9.00 per cent growth, exactly equal to the cost of the debt, the share holds still with a primary balance of nil. At 12.00 per cent growth, above the cost of the debt, the share holds still even while the government runs a primary deficit of Rs 30,000 crore. Every one of those three figures is a statement about what the arithmetic requires at that pair of rates, and not one of them is a target, a recommendation or a view about what any government should do.

What does the debt ratio leave out?

The ratio is a starting question, not a verdict, and treating it as a verdict is the commonest way to misuse it. The ratio compresses out everything about the shape of the debt and keeps only its size. Two countries can report the same debt ratio to the decimal and be in completely different positions. Four things in particular disappear into that single number.

The first is who is owed. Interest paid to savers, banks and pension funds inside the country stays inside the same economy. Debt held at home therefore behaves differently from debt held by lenders outside it. The second is the currency. A government that borrowed in a currency it issues itself is in a different position from one that borrowed in a currency it does not, and the ratio shows neither. The third is when it falls due. A stock that matures gradually over many years is not the same as one where a large slice comes due within twelve months. The fourth is what it will cost to roll overReplacing borrowing that has come due with fresh borrowing, so the amount stays outstanding while the terms are new. The cost of that fresh borrowing is covered separately., since a stock has to be replaced as it matures and the terms of the replacement are set at the moment of replacement, not at the moment of the original borrowing.

So the ratio gives the size of the claim relative to the income available. The ratio does not give the composition of the claim, and the composition is where most of the difference between two situations at 57.23 per cent actually lives. The ratio is worth reading first because it is quick, but the four things it leaves out still have to be found.

How does an analyst separate the direction of the ratio from its reason?

A working reader does not stop at the direction. A share that fell because output grew quickly and a share that fell because borrowing was repaid are not the same event, and they do not carry the same implication for next year. The direction and the reason for the direction are two separate readings. The first depends on growth continuing; the second does not.

The way to keep the two apart is to split the movement into the part contributed by each half of the fraction. Take the Sankhya step. Move the debt first and hold output still: Rs 11,00,000 crore against the original Rs 17,47,200 crore would be 62.96 per cent, so the borrowing on its own pushed the share up 5.72 points. Now let output grow to Rs 18,17,088 crore: that pulls the share back down from 62.96 per cent to 60.54 per cent, a fall of 2.42 points. The two contributions net to a rise of 3.30 points, exactly the movement observed. Nothing has been added or assumed; the observed change has simply been read as the sum of the two forces inside it.

How does the whole worked step read in one table?

Every number below comes from the Sankhya government account. The table sets the arithmetic out in order, so the movement can be checked line by line. A stray minus is the easiest error to make and the hardest to see, so direction is written as a word rather than as a sign.