The Money Multiplier

David Beckworth, on Macro and other Market Musings, discussed the Fed's "exit" strategy for reducing the large quantity of excess reserves. He was reporting on Bernanke's statement that the Fed would use increases in the interest rate on excess reserve balances to prevent any excess supply of base money. He then criticized the Fed's policy of holding large quantities of mortgage-backed securities as "fiscal policy."

Beckworth received a flurry of comments claiming that these excess reserves irrelevant, because bank lending depends on loan risk and bank capital. There were claims that worry about excess reserves reflects wrongheaded "money multiplier" reasoning.

Nick Rowe commented in that thread (as did I) and prepared a post on Worthwhile Canadian Initiative about fallacies of composition and decomposition, relating bank reserves and the quantity of money. Rowe's focus was on the difference between the individual bank and the banking system. His focus was on how a single bank faces an effective 100 percent reserve requirement on lending.

My basic model of the individual bank is financial intermediation under monopolistic competition. Banks borrow money from depositors and lend it to borrowers. Bank set interest rates on both deposits and loans so that they grow together.

If deposits grow more slowly than than loans, a bank raises both the interest rates it pays and charges. This attracts more depositors, so that deposits grow more rapidly. It makes loan less attractive, so loans grow more slowly.

If, on the other hand, deposits grow more rapidly than loans, then the bank lowers the interest rates it both pays and charges. Deposits are less attractive, so deposit growth slows. Bargain interest rates attract borrowers, so loan demand grows more rapidly.

A bank that wishes to expand more rapidly raises the interest rates paid on deposits and lowers the interest rates charged on loans. Both deposits and loans expand more rapidly. If the marginal revenue from the increased size of the balance sheet is greater than the marginal cost of expanding the operations of the bank, then profits grow more rapidly.

Of course, lower growth might expand profits, (or, sadly, reduce losses.) A bank raises the interest rates charged on loans and lowers the interest rate paid on deposits. The margin between the two expands, but the balance sheet grows more slowly, or in the extreme, shrinks. If the savings in operational cost are greater than the decrease in marginal revenue, then profit expands or losses shrink.

Even if the interest rates a bank sets balance the growth of deposits and loans on average, they will not balance continuously. Banks trade money market instruments, like T-bills and interbank lending, to balance temporary imbalances between loans and deposits. For example, a bank receiving many loan repayments and seeing few new loan customers might buy T-bills. If a bank's depositors make payments and few receive payments, the bank might borrow overnight from another bank.

This basic analysis of the banking business ignores bank capital as well as reserves. I think both are very important, but I think this sort of model is the right starting point.

Bank capital, or net worth, plays a key role in reassuring depositors and other bank creditors. Of course, capital requirements play a key role in current banking regulation. I think it is essential to understand that the fundamental nature of banking, as financial intermediation, makes asimplistic application of the concept of "leverage" inappropriate. Of course banks are highly leveraged.

Bank reserves-vault cash and reserve balances- reduce the need to trade money market instruments and so reduce transactions costs. Again, reserve requirements play a role in current banking regulations.

Why would anyone instead start with a model of an individual bank that passively receives deposits and then makes commercial loans equal to a fixed proportion of the deposit, say, 90%?

Suppose that bank "deposits" are banknotes. Paying interest on banknotes is difficult, and is ignored. The banks borrow at zero interest.

Now, suppose, that there are usury laws--binding interest rate ceilings on loans, so that borrowers face a shortage of bank loans.

If a bank receives a zero-interest deposit, then it has more funds to ration out. Presumably, a prudent banker rations by credit risk, and so, expands lending to slightly worse credit risks.

The notion that banks would simultaneously adjust the interest rates paid and charged to maximize profit would be foreign in such a scenario.

As a monetary theorist, the key element of banking is the issue of deposits used as money--as medium of exchange. At one time, banks issued banknotes--private currency. More recently, they issue transactions accounts--deposits that can be transferred electronically or by means of check. From the individual bank's point of view, these are simply one source of funds. Various classes of savings accounts, certificates of deposits, are alternative funding sources. And, of course, banks can issue bonds, commercial paper, or fund their activities by equity--capital.

Bank lending is of little intrinsic interest to a monetary theorist. Of course, banks must match their liabilities, including monetary liabilities, as well as their net worth, with some kind of assets. Banks can make loans, but they can hold various sorts of government bonds, as well as private securities--bonds, commercial paper, or mortgage backed securities.

However, there is one kind of asset that banks hold that is of special interest to the monetary theorist--what we call "reserves." These can be either vault cash, hand-to-hand currency issued by the government, or else balances at the central bank. Currency, of course, serves as medium of exchange. And balances at the central bank also serve as a type of medium of exchange, but only for banks making payments from one to another.

Return the the scenario of the bank funded entirely by the issue of zero-issue banknotes rationing commercial loans. All the bank's liabilities serve as the medium of exchange. The only bank assets are commercial loans or else reserves--vault cash or balances with the central bank. Instead of all of the complications of a variety of deposits, loans, other assets, liabilities, and bank capital, the two items of interest to the monetary theorist--monetary liabilities of the banks and the central bank, are at center stage, with only commercial lending as a complication. And bank lending is not of special interest--it is just an afterthought.

Further, what is interesting to the monetary theorist is the relationship between the monetary liabilities created by the banks--transactions accounts these days--and the monetary liabilities created by the central bank--hand-to-hand currency and reserve balances kept at the central bank. It is not the individual bank that is of interest, but rather how the interactions of the banks impact the total quantity of the medium of exchange.

In particular, the point of the money multiplier process is not that an individual bank with excess reserves will create more commercial loans. Rather the point is understanding how an excess supply of reserves in the banking system results in an expansion in the amount of transactions accounts that businesses and households hold in banks until the excess supply of reserves ends--either through withdrawals of currency from banks or an increase in the demand by banks to hold reserves.

From the point of view of the individual bank, the most obvious thing to do with excess reserves is to purchase liquid assets--such as purchasing T-bills or making overnight loans to other banks. Alternatively, the funds could be used to pay off debts coming due--for example, repaying overnight loans received from other banks. However, these actions simply shift reserves to other banks.

Because reserves serve as medium of exchange from the point of view of banks, there is no reason to believe that banks only accept reserves in payment if they want to hold more of them. For example, suppose a bank has "excess reserves," an excess supply of reserves, and purchases a T-bill on the secondary market. The bank wires funds to the seller's bank. The bank that had the excess reserves now has T-bills. The seller of the T-bills now has a balance in his or her transactions account at his or her bank. And the seller's bank now has an additional balance in its reserve account at the central bank. The seller's bank didn't choose to accumulate more reserves. Other things being equal, it has excess reserves.

Whether this will lead to banks to make more loans is not central to the process. The seller has a larger balance in his transaction account. If banks' demand for reserves are positively related to the balances their customers have in transactions accounts, then this raises the demand for reserves. If the demand for currency by firms or households is positively related to their balances in their transactions deposits, then currency will be withdrawn from the banks, and so help clear up the excess supply of reserves.

Of course, if banks are purchasing T-bills or other money market instruments, the yields on those instruments would tend to fall. This would motivate banks to lower the interest rates changed on loans and expand lending. It also would motivate them to lower the interest rates paid on deposits.

Loans are created by crediting funds to transactions deposits, and as those funds are spent by the borrowers, the transactions deposits is extinguished. But when those selling to the borrowers deposit the funds, they have a transactions deposit. As far as the impact on transactions deposits and the excess supply of reserves in the banking system, the process is similar to a bank purchasing a T-bill.

To the degree lower interest rates on deposits results in an increase in the demand for currency by households and firms, this would be an avenue by which an excess supply of reserves clears up as vault cash leaves the banking system.

Returning to the simple scenario of a bank rationing commercial loans funded by zero-interest banknotes, the excess reserves can have no other immediate effect than an increase in commercial lending. However, the increase in commercial lending is not the point of the analysis. It is that those selling to the borrowers end up with additional money balances, which they deposit. The surplus of reserves is not extinguished through the loan. It simply moves to another bank. However, if the demand for bank reserves is positively related to the outstanding issues of the banks' monetary liabilities, then the process will lead to an increase in the banks' monetary liabilities and close off the excess supply of reserves.

If central banks manipulate the quantity of base money in order to target short term interest rates, and an excess supply of reserves results in downward pressure on the yields on money market instruments, the result will be a prompt response by the central bank to reduce the quantity of reserves. Among monetary economists, one of the the rationales of interest rate targeting is that it prevents the process described by "the money multiplier" from occurring. That doesn't make the money multiplier analysis pointless. It rather explains what would happen if the central bank targeting interest rates didn't take action that forestalls the market process that corrects for an excess supply (or demand for) of reserves in the banking system.

I oppose interest rate targeting. I believe it is better for all interest rates, including short term, low risk interest rates, to freely float depending upon market conditions. On the other hand, I think that the nominal quantity of bank reserves should change to accommodate the demand to hold them--consistent with nominal expenditure growing on a 3 percent growth path. If such a system were implemented, the market process by which an excess supply or demand for a fixed nominal quantity of reserves would be cleared, would not happen. That doesn't mean that it isn't an important for monetary theorists to understand the process.