# Why is a high government debt/GDP bad?

Why is a high government debt/GDP bad? It is frequently mentioned as something bad. Today here, for example.

I get that when the government spends, real resources like workers or raw materials are used, which is a real cost to society.

I also get that the government needs to tax, because otherwise the increase in money supply in the private sector would be too great. Perhaps the government also need to tax in order to ensure a demand for currency, I don’t know.

But why focus on the debt/GDP ratio? In Sweden, most of the government debt is to the central bank. Why does that matter?

Isn’t it more important to focus on how much the government should increase (or decrease) the money supply? Are these two things equivalent?

Firstly, the use of debt/GDP as the ratio is somewhat arbitrary. One could easily look at debt/government revenue, and it may be a more useful metric. However, the convention to use GDP for scaling these series. (One can argue that GDP represents the full income capacity of the economy for debt service.)

For countries that borrow in a foreign currency (or in a currency where they do not directly control the central bank), a high debt ratio indicates a greater risk of default. There is no gurantee that they can their hands on the foreign currency to repay debt. You need to look at other things as well, but it's one common metric.

If the country controls the currency it borrows in, it should be able to arrange its affairs to avoid default. (There is no guarantee, however.)

However, even if we ignore default risk, the greater the debt level, the greater the interest expense for the government. The exact mechanisms are debated by various schools of thought, but it is reasonably safe to argue that greater interest payments will squeeze out other spending if we want to keep inflation around a target level. There are two ways in which a greater debt load increases interest payments.

1. Even if the rate of interest is unchanged, a greater amount of debt implies more interest to pay. This effect holds by definition.
2. A greater debt-to-GDP ratio might increase interest rates. The magnitude of this effect is controversial. The example of Japan in recent decades (high debt ratios, low nominal yields) demonstrates that the effect is not very large, even if it exists.

There is a school of thought that argues that we need to "pay back" debt in some sense; this is often referred to as the governmental budget constraint. This view can be summarised as: greater debt now means greater future taxes, and people do not like taxes. (This is sometimes called Ricardian Equivalence.) The exact mechanism is controversial. (I have severe doubts about the mathematics behind it, for what that's worth.)

In the case where the central bank has bought a lot of government debt (quantitative easing), the expectation is that the central bank will eventually reverse that policy. In any event, the central bank needs to pay interest on resserves if it wishes to raise market interest rates to control inflation, and the consolidated government will face a similar interest cost as the case of bill issuance.

Finally, the money supply is related to debt levels; both are forms of government liabilities. In most modelling traditions, people only target a certain anount of money holdings (that earn no interest), and the rest is invested in bonds/bills. Therefore, we only expect money to grow in line with transaction needs, and this level may have little resemblance to total debt levels.

• There is the point that high debt reduces the value of the nation's goods overseas and increases the cost of imports. – Hot Licks Sep 3 '17 at 19:55
• Hot Licks - how does the high debt level do this? Japan has had a relatively high debt-GDP ratio for almost two decades, yet its curency is not weak. – Brian Romanchuk Sep 4 '17 at 1:14
• It drives up the cost of money. – Hot Licks Sep 4 '17 at 1:40

Ben,

Let me dispute the premise of the question. A high debt to GDP ratio cannot be bad by itself. The debt to GDP ratio becomes a bad thing when it is too high. Too much alcohol. Too much ice cream. Too much time spent online. These are all bad things because they are too much. But how do you know that these are too much?

Let's take alcohol as an example. Too much alcohol can make you do stupid things which you'll later regret. But how much alcohol is too much? When you're with a group of friends and you all drink five or six glasses of beer, and do stupid things together then you're probably having a good time. Drink five or six glasses of beer in the afternoon at the office and you can get fired. This is generally considered a bad thing. The same quantity of alcohol is just right in one situation and too much in another situation because of the consequences.

Now you've mentioned some consequences of public debt. The government usually borrows funds to spend it and re-allocate scarce resources. This can be a bad thing, but this can also be a good thing. The United States for example borrowed funds (and compelled its citizens to lend it funds) to fight the Nazi's. This is generally agreed to have been a good thing. The United States also borrowed funds to invade Iraq under George W. Bush. This is something that many individuals considered (ex ante or ex post) to be a bad thing. We can say that when the United States borrowed funds the debt to GDP ratio was high, but it was not too high because the costs were exceeded by the benefits (fewer Nazi's). The resources used could've been used elsewhere but the highest value of those resources was when they were used to decrease the number of Nazi's. Whereas some will argue that when the debt to GDP ratio was increased to invade Iraq, this debt to GDP ratio became too high. The costs were not exceeded by the benefits. The resources could've been used better elsewhere.

In addition to the costs of re-allocating resources, there are some other costs of public debt. It has to be repaid through taxation and individuals don't like taxation and it distorts incentives. Some others have argued that a public debt can lead to higher inflation because the central bank might monetize it. Others have argued that it means less private investment as people save in terms of government bonds instead of corporate bonds. And this might eventually lead to lower output due to a decrease in the quantity of capital per inhabitant. There are many other potential costs. And these costs depend on the situation. There is not one economic theory of debt to gdp ratio. There are many economic models that are appropriate to make sense of different situations where the debt to gdp ratio might play a role.

Returning to the question why a high debt to GDP ratio is bad, I hope you can see that it isn't. A high debt to GDP ratio is only bad if it is too high. And you can only know whether it is too high when you compare the costs and the benefits of the debt to GDP ratio and these depend on the circumstances. In addition whether it is good or bad is purely subjective. If you think that the consequences are worth it, then it's not bad.

Next time that you might encounter a situation where someone declares that something is good or bad try making the distinction between what is and what ought to be. A statement that something is bad implies that the situation should be different and this is premised on a value judgement. You can't arrive at the conclusion that something is bad without a normative premise, a value judgement. The real world consequences of a high public debt to gdp ratio are is up for dispute. We can learn from what we see. But what value you attach to these consequences whether these are good or bad is not up for dispute. It's a preference. Just like chocolate ice cream is better than vanilla is a preference.

Here's a little contribution from what I learnt in school:

A large government deficit comes about from $G - T$ where $G$ refers to government spending and $T$ is the taxes that the government collects from its citizens. There are two possible ways to fund the deficit - issue government bonds to the public to get the cash to fund new government purchases, or increase the monetary base. We can then say that

$G - T = ΔMB + ΔB$

Issuing debt to fund the deficit isn't a problem, but increasing the monetary base can cause inflation and too much of that is bad for the economy. eg. Hyperinflation by excessive money printing. How ΔMB finances the debt is by first, government issues debt to the public and gets new financing, then the central bank buys back these debt from the public using freshly printed money. The net result of ΔB = 0, but ΔMB rises due to more currency in circulation. Money supply thus increases.

So what happens when $G-T$ gets really big? People get worried that the government would not be able to pay back the government debts previously issued and then not buy the newly issued ones. So the government resorts to monetizing the debt by printing money and that leads to bad inflation for the economy. So the question is, why does the U.S. have trillions of debt and can still finance its deficit with government bonds? The answer is because people believe the economy is productive and long-lasting enough to eventually pay back the government bonds. So the cycle goes on.

About money supply, governments shouldn't target raising or decreasing money supply to influence output of the economy. In the past, it does work using the Quantity Theory of Money where $MV=PY$ M = money supply, V = velocity of money P = price level and Y = output level. If and only if V is constant would M have a direct impact on nominal GDP, PY. But over time, V changes rapidly due to credit cards, changes in financial systems, etc, and V becomes unpredictable. Thus, M doesn't have a strong impact on PY anymore so central banks target interests rates instead to influence consumption and investment patterns.

• What I don’t understand is that Sweden, for example, has a government surplus. At the same time, the central bank struggles to raise inflation. Shouldn’t the government just lower taxes and finance that by increasing the monetary base? – Ben Apr 30 '17 at 20:43

It should come to no surprise that some government debt is sometimes optimal, even if the country can pay off all its debt. The present value of paying off the interest rate on a loan in perpetuity and paying off the entirety of the loan in one go are equal to each other, but you can imagine a government might not be indifferent between those two options. For example, a short-sighted government will want to put off paying back any loans to the next government, for all else equal. (There are of course other reasons to hold some debt, outside the scope of this question.)

Speaking of which, now consider a country that chronically keeps increasing its debt relative to its output. As suggested under Ricardian Equivalence, consumers won't respond to fiscal policy, because they know taxes will have to increase in the future. There are plenty of different exceptions that can break Ricardian Equivalence (e.g. consumers can be shortsighted too) but a high GDP to debt ratio suggests that a government will not only face increasing payments/spending on interest instead of government goods and services, but also that fiscal policy will become less effective.

There is a lot going on in this question:

1. Debt
2. GDP
3. Government spending
4. Taxes
5. Money supply

All of these are good topics for conversation. I'm going to just focus on Debt and GDP.

GDP is the market value of all the goods and services in a country. The government has the authority to tax and, in a sense, owns this value and could tax at 100% of GDP if it wished. For example, total country has a GDP of $\$100$, a government could tax it's citizens at 100%, meaning the government now has$\$100$ in it's coffers.

(Note that the above assumption is purely theoretical and is simply trying to put things into perspective.)

Debt is the amount that a government owes. Debt and spending are not the same thing. Governments go into debt when they spend more that they have on hand (so to speak). If a government spends $\$500$over a year and has a budget of$\$1,000$ then the government is said to have a budget surplus (took in through taxes more than it spent). If a government spends $\$5,000$over a year and has a budget of$\$1,000$ then the government is said to have a budget deficit (took in less than it spent). Money is borrowed to cover these deficits. The sum of all deficits make up the national debt.

A high Debt/GDP is worrisome because the government owes almost as much as it could conceivably tax.

Government debt doesn't translate well to individuals, but here is an example that may put it in context: If you as an individual are valued at $\$1,000$and you owe$\$50$, this isn't so bad. If you are valued at $\$1,000$and you owe$\$950$, this is problematic. Just as you become hampered if you have too much debt, so too does the government.

As you dive into this topic you will find that it's pretty nuanced, but this should provide a good, quick overview.

Just quickly on money supply: this affects GDP because a change in the money supply affects interest rates which then affect consumer consumption.