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The Fed maintains its target interest rates by "lending" money to commercial banks:

When the actual federal funds rate is higher than the target, the Federal Reserve Bank of New York will usually increase the money supply via a repurchase agreement (or repo), in which the Fed "lends" money to commercial banks.

How much money is owed to the Fed? If the interest rates are lower than the inflation, does this not constitute (effectively) a subsidy of the banks? Is there an estimate of how much this is costing the Fed?

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How much money is, on average, "on loan" from the Fed?

For repos you mention previously average was 0.165 billion for year 2021 (FRED), the value is different every year. Some years almost none are used. In other years a lot more. For example, in 2020 average was over 100 billion.

If the interest rates are lower than the inflation, does this not constitute (effectively) a subsidy of the banks?

Not necessarily, Banks make profit on intermediation margin. To oversimplify a bit banks are ‘buying’ funds from Fed or sometimes also from regular people in forms of deposits for the federal funds rate or whatever people get on deposit accounts. They then sell these loans to customers for higher interest rate.

However, because of competition they cannot choose the interest rate arbitrarily.

If the competition would be perfect they would simply set the interest rate to consumers equal to federal funds interest rate + their marginal costs (see Freixas and Rochet Microeconomics of Banking).

The bank won’t necessarily make profit thanks to inflation because even though inflation makes its debt to Fed smaller in real terms by the same token the loan that bank issued to customers to make money will have smaller real value.

However, depending on exact market structure the banking sector has and all the details it could turn out to be effective subsidy for the banks.

Is there an estimate of how much this is costing the Fed?

It’s not costing Fed anything. Money for loans Fed makes are made at a keystrokes of keyboard by the Fed employees. There are no real costs Fed incurs for those loans marginal cost of issuing them is effectively 0.

If you want to be pedantic if they issue a lot of loans to private banks they might perhaps need to hire some extra employees which would make marginal costs of those loans non-zero but it’s not a value worth worrying about and there are no estimate for it to my best knowledge.

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  • $\begingroup$ "It’s not costing Fed anything" -- the creation of money, the lending, and the destruction of money complete the cycle, and so this whole cycle costs the Fed nothing. However, I was only asking about the middle bit. The lending. There is an opportunity cost, as the Fed could presumably have parked this money in a more inflation-proof way. What is this opportunity cost? $\endgroup$
    – MWB
    Commented Feb 18, 2022 at 5:45
  • $\begingroup$ "0.165 billion" -- is this the average total amount of debt that the Fed owns? (or per-contract, or per-day issued?) $\endgroup$
    – MWB
    Commented Feb 18, 2022 at 5:48
  • $\begingroup$ @MWB there isn’t an opportunity cost here. Opportunity cost requires alternatives to exist. Fed is government institution constrained by law. Fed can’t really invest money how it wants let’s say to housing because housing is an inflation hedge. Fed is supposed to conduct monetary policy, investing money in let’s say housing would violate Fed mandate. Even when it comes to things like gold which Fed can hold as an reserve, Fed again cannot just increase its holding of gold because it expects inflation as that would violate the mandate. So there isn’t any opportunity cost for Fed because it does $\endgroup$
    – 1muflon1 ♦
    Commented Feb 18, 2022 at 7:10
  • $\begingroup$ Not have any choice. If someone mugs you in the street then there is no opportunity cost for the money you ‘spend on mugging’ because you did not had any alternative or even a choice and opportunity cost can only exist among different alternatives that can be chosen. The 0.165 is just for repos, you were talking about repos in your q so I assumed that’s what you are interested in. For every type of loans Fed makes there is data on that link I provided you can use the search bar at the top of FRED site. You can see totals also from a balance sheet but you wanted averages for averages $\endgroup$
    – 1muflon1 ♦
    Commented Feb 18, 2022 at 7:16
  • $\begingroup$ There isn’t an aggregate time series provided (you could construct it but I won’t do that because it would be time consuming) if you are ok with totals then just look at its balance sheet here federalreserve.gov/monetarypolicy/files/… $\endgroup$
    – 1muflon1 ♦
    Commented Feb 18, 2022 at 7:21

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