How does inflation erode away debt in a practical sense?

Question

Intuitively it makes sense that if inflation is above nominal interest rates, businesses/central banks can erode away their debt. I wanted to understand how it would work practically such as in some examples below:

(a) say I borrow at 3% for my business activity and inflation is 5%. Now unless my business activity revenue is able to grow my initial cash (which I obtained through debt) by 5% this argument doesn't hold, right? Plus, is there an implicit assumption that the revenue now will comprise of two components i.e.
(i) revenue assuming no inflation
(ii) additional revenue due to bump in prices caused by inflation
It's possible that the business outruns the debt just using (i), and it would be optimal if (ii) happens too. The question is, (ii) is not always guaranteed, right?

(b) similarly what mechanism would central bank use to utilize inflation to grow its assets that it obtained by borrowing, at the inflation rate, so it has surplus on top after paying off its debt in the future, since inflation is above nominal rate? (Surplus might not be important but at least grow at a rate that's not behind the nominal rate)

(c) for an individual wage worker, this will work only if his nominal wages keep up with inflation, which might not always happen? So maybe for individuals, the argument is for the aggregate economy in which you can assume that statistically, wages are able to keep up with the inflation rate and hence able to outpace debt?

Edit: I understand that inflation rates below nominal rates can also erode debt, but the essence of the question is that unless inflation actually works on my income cashflow side as well, only then the effect of debt erosion would work in a practical sense. Because if I have to pay back debt, it doesn't matter if the world thinks its value has eroded due to inflation unless I personally too have positively benefited with more nominal dollars on the income side due to inflation: the gist of the question is that nominal dollars on the income side might not always see the effect of inflation.

Answer 1

I will only answer part a) of the question.

Inflation means a permament increase in the general price level, i.e. the prices of most goods and services (this is not precise, actually index calculation is involved).

(ii) is not always guaranteed, right?

It is possible, even likely, that the prices of some particular goods and services do not increase by this level, or perhaps even decrease. The businesses providing these do not benefit from inflation.

E.g., the price of a certain new consumer electronics device will likely decrease as the years go on even if there is inflation otherwise.

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it would be optimal if (ii) happens too

An economist's peeve: the phrase you are looking for is "better", not "optimal".

Answer 2

How does inflation erode away debt in a practical sense?

Typically debts are set in nominal terms. That is a debt will be typically set as some monetary value like for example \$1000. The interest payments are also usually fixed and nominal (although adjustable interest rate loans are more common then let's say loans with indexed principal).

Inflation reduces value of that debt because it reduces value of that money. What ultimately matters is not how much money person has but how much goods and services one can purchase with that money. If you would have million dollars but you are only able to purchase one chocolate bar that would not make you very rich.

This is how inflation practically erodes the debt. Even though nominally you return the creditor the same amount of money borrowed, if originally you could buy let's say second hand car for \$1000 but you return \$1000 dollars that are not having enough purchasing power to buy a tire the debt got in a very practical sense (in economics we would say in real terms eroded).

Intuitively it makes sense that if inflation is above nominal interest rates, businesses/central banks can erode away their debt. I wanted to understand how it would work practically such as in some examples below:

It actually does not requires that inflation is above interest rate ($i> \pi$) inflation erodes the debt even if its below interest rate. The real value of debt and interest payments is still smaller because of inflation.

For example, if debt value was \$1000, interest is 10% pa (implying interest payment is \$100) and the debt is issued for one year, inflation rate is 5% (i.e. CPI went from 100 to 105 over that period) then we have situation where interest rate is higher than inflation. The debt is still being eroded.

With 5% inflation when you return the \$1000 you are returning only approximately \$952 in real value (real value can be calculated as $\frac{\text{nominal value}}{\text{deflator}}$ deflator is based of CPI for example here it would be 1.05). Also the pre-agreed interest payment of \$100 now has a real value of only about \$95.2. So in real terms creditor only gets approximately \$1047.2 once the debt and interest on debt is repaid. Sure the interest rate in this case compensates for inflation, but receiving \$1047.2 is still more than 50 bucks less than receiving \$1100 (if there is no inflation). Thus inflation always erodes debts that are set in fixed nominal terms.

(a) say I borrow at 3% for my business activity and inflation is 5%. Now unless my business activity revenue is able to grow my initial cash (which I obtained through debt) by 5% this argument doesn't hold, right? Plus, is there an implicit assumption that the revenue now will comprise of two components i.e.

(i) revenue assuming no inflation

(ii) additional revenue due to bump in prices caused by inflation

It's possible that the business outruns the debt just using (i), and it would be optimal if (ii) happens too. The question is, (ii) is not always guaranteed, right?

This is not good example to understand effect of inflation on debts because you are mixing various things not related to debts at at all like business revenue.

Earning more cash then from some business activity than interest you pay for your business does not mean the debt is eroded if the debt remain to be at the same level. Vice versa having loss in your business does not mean debt is somehow getting bigger. If you are interested in debt erosion you have to look at real value of the debt.

In your example above with 5% inflation, the debt is being eroded by 5% drop in value of dollar each time period all those other numbers are not relevant for debt erosion.

It's possible that the business outruns the debt just using (i), and it would be optimal if (ii) happens too. The question is, (ii) is not always guaranteed, right?

Depends what do you mean by 'outrun the debt'. If you are asking if the debt is being eroded, it is still eroded even under (i). Business still got let's say \$100 of real value and it will be returning lower real value for the principal. If you are asking if for business itself the debt gets easier to pay then the answer is no. If there is inflation but the business prices stay same then its not any easier for the business to repay the debt.

Also optimal for whom? Business, creditors, society as a whole? For that single business it would be certainly welfare improving (better) if the prices increased. However, your example does not contain enough info to determine what would be optimal even just for the business.

Also yes the price increase is not guaranteed. 5% inflation means that prices on average increase. Maybe you are stuck in an industry where that is not possible for some reason (e.g. maybe its regulated sector or there is too strong price competition). Also businesses are not guaranteed to get customers.

(b) similarly what mechanism would central bank use to utilize inflation to grow its assets that it obtained by borrowing, at the inflation rate, so it has surplus on top after paying off its debt in the future, since inflation is above nominal rate? (Surplus might not be important but at least grow at a rate that's not behind the nominal rate)

Central bank does not have regular assets like regular business, and they do not typically really borrow them in regular sense of the world (although technically you can say that because they do have liabilities). Let me give you an example. For central bank, a government debt will be an asset and banknotes in circulation are liabilities (e.g. see ECB balance sheet). I suppose strictly from accounting perspective you could say that ECB is 'borrowing' government debt (asset) if it pays for the government debt with newly created bank notes (liabilities). However, I somehow doubt that this is what you have in mind when you are asking about central bank debt.

Also central banks can create money at a keystroke of a keyboard. If anything central banks could just in principle buy any asset they want by just creating new money out of thin air and then the increase of money in circulation could (depending on other parameters in economy) increase inflation. Although central banks are not allowed to spend money willy-nilly they are government organization so its not like they could just buy Mona Lisa for the office, but at least in principle they could buy anything. Least of central bank's worries is any 'regular' debt they have since they can create unlimited amount of money at almost no cost to them to pay for any debt they have.

This being said, if there is an inflation, central bank's assets will naturally expand because, for example, governments will have to borrow higher nominal amounts for example to sustain the same level of real deficit spending.

Nonetheless, it is important to note central banks are government institutions tightly constrained by law. They also forward all their profits to the government. Moreover, regular central banks have strict mandate to focus on price stability or price stability and unemployment. Given this I don't see how they could care about size of their balance sheet from any other than monetary policy perspective.

c) for an individual wage worker, this will work only if his nominal wages keep up with inflation, which might not always happen? So maybe for individuals, the argument is for the aggregate economy in which you can assume that statistically, wages are able to keep up with the inflation rate and hence able to outpace debt?

If wages keep up with inflation individuals will find it easier to repay their debts.

Answer 3

Attempting to answer (b). I am not sure of this answer but hoping others will chip in and correct if there are mistakes/gaps.

Central banks are not in the business of borrowing and investing to make money. In fact it is not correct that Central banks borrow money. Their liabilities are mainly comprised of Banknotes and Commercial Banks' Reserves.

The closest to borrowings are commercial banks' reserves which serve a number of functions such as settlement of payments, statutory requirements and banknote disbursement in the economy. But it is also true that some central banks pay interest on these reserves which are aligned with the policy rates (so they are always lower than policy rate - eliminating direct arbitrage opportunity).

The key point here is that CBs are not in the business of leveraging high inflation and low rates to increase reserves and use them to acquire other assets (although I do not know if there is always a legal framework to prevent this). But there is still a possibility that high inflation may help CB unintentionally.

To see this the link between income of CB and inflation needs to be explored:

1. As inflation grows printing money is likely to be dearer too. This will erode the Seigniorage income. So negative impact on income.

2. High inflation, ceteris paribus, will mean more demand for banknotes in circulation. Since printing money is a source of income for CB this is a positive impact.

(the above are basically increase in business volume with low margin)

3. Higher operational costs (wages, building maintenance, etc.) due to high inflation (most likely a small factor). So negative impact.

4. Returns from investing foreign assets. Most CBs, especially that of import dependent economies, hold foreign currency reserves. They are also free to invest these reserves. However, the investments are done in most liquid assets, return to which may or may not be linked to high inflation directly. So this may be a positive or negative impact.

Overall CBs may have the avenues to capitalize on high inflation and low rates to grow its assets but they certainly do not.

Answer 4

Over the span of a century, inflation as (GDP/p)/yr+ occurs at nearly 2%, homes 5%, and bonds 7%/yr+. The average principal is 1/11 down for 5%APR. Mathematically, collateral equity appreciation only tapers the loss of leisure from the purchase. 65% mortgage and 35% rent, however, and inequality tends to market concentration and supply inelasticity more than demand.