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The majority of the monetary supply results from credit, with every loan creating pairs of assets and liabilities representing the same underlying value. Considering that every time someone pays back a loan, the asset and liability collapse back into a single copy of the money, intuitively it feels like people paying back loans causes a reduction in the monetary supply, which should cause deflation. Forgiveness or "writing off" of loans would seem to have the same effect, removing the value of an asset being used as the basis of additional monetary supply, so in theory reducing the monetary supply and causing deflation.

Is this the case? If not, why?

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It is true that paying back loans causes contraction of money supply (if not offset by faster creation of new loans). However, it is not correct to say that this generally happen when debt is forgiven and it does not need to lead to deflation.

First, debt forgiveness can actually be thought of as a permanent expansion of money supply not contraction. An example: central bank buys $\\\$100$ of government bonds that government then gets to spend. Afterwards, central bank decides that the bond will be destroyed without asking for government to pay back the $\\\$100$. The $\\\$100$ still exists and still can be used to purchase goods and services and circulate in the economy. Moreover, since the debt which originally created it was scrapped that $\\\$100$ can continue to exist forever leading to permanent expansion in money supply.

Second, for money supply to contract it is not enough that one loan gets repaid if new loans are issued at the same time - money supply is aggregate quantity. Furthermore, money supply can be expanded even by different ways than just by loans (see this past question on Economics.SE), so also in principle if central bank intervened money supply could expand or stay constant even when borrowing drops. However, lets assume that that there will be on net less loans in economy and central banks will just do nothing and so money supply actually indeed contracts. That is still in itself not necessary enough to cause deflation.

For deflation to happen the price level has to drop, and the price level $P$ is by standard textbook monetary equation given as $P = MV/Y$. Where $M$ is the money supply, $V$ velocity of money, $Y$ real output. Thus for decrease in $M$ to cause deflation we also have to additionally assume that such decrease won't be offset by changes in velocity or real output. That is not always realistic. Usually, credit drops during recessions for various reasons (for example as argued by Bernanke in his research during recessions it might be hard to distinguish good and bad borrowers which would lead to credit rationing and consequently drop in borrowing). More generally, the amount of credit in economy is very pro-cyclical (see for example Gaiotti (2013) and sources cited therein). Hence, often when $M$ contracts due to lower amount of loans $Y$ contracts at the same time and the two can in principle cancel each other. $V$ also does not stay constant across business cycle generally decreasing during the recessions (see for example Anderson, Bordo & Duca (2017)). Thus while ceteris paribus decrease in credit and contraction of money supply would lead to deflation in real world you might not observe deflation whenever credit drops due to effects of other factors that are changing at the same time.

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so in theory reducing the monetary supply and causing deflation.

This statement is too simplistic, as it assumes there is a direct link between the money supply and the price level. Whatever relationship exists is far more complex than suggested by quantity of money theories.

Considering that every time someone pays back a loan, the asset and liability collapse back into a single copy of the money,

This statement is misleading. Under the assumption that a loan is paid back by a transfer from a deposit account, both the loan and deposit disappear. A bank making a loan effectively creates a new deposit/loan pair “out of nothing” (a bank needs capital/liquidity to undertake this, but the loan act creates new assets/liabilities), and paying the loan back reverses the operation.

Loans are expected to be repaid, and they are repaid all the time. The aggregate amount of loans normally rises, as new loans are larger than paid off loans. Therefore, the typical situation in modern economies is that the price level is rising, and loans are being paid back. As such, we cannot observe the effect that paying back loans causing deflation.

In a recession/crisis, loans outstanding (and thus bank deposits) falls. It seems more plausible that the fall in loans is the result if new lending being curtailed than a large number of entities paying back loans. That is a deflationary environment, but one cannot really trace it directly to loans being paid back.

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