The Fed increases the interest rate on bank reserves - effects?

Banks are required by law to hold reserves equal to a fraction of the deposits held by customers at their banks. Banks generally try to keep reserves to the legal minimum, because reserves (kept either as vault cash or as a ledger entry with the Federal Reserve) are idle funds, as opposed to loaned or otherwise invested funds, which make money for the bank. Obviously, money sitting in a vault doesn't do this.

So, banks are more or less treading a fine line on a daily basis. It may be that at the end of the day they need more reserves than they have. Other banks have more reserves than they need (excess reserves). Banks with excess reserves can make overnight loans to banks which are short of reserves. The interest rate on such loans is called the federal funds rate. (Strictly speaking, this is the average of the interest rates charged for such loans, which may vary from institution to institution and transaction to transaction.)

Obviously, the more excess reserves there are available to loan, the easier it is to negotiate such a loan under better terms (lower interest rate), since banks compete with each other to make such loans. Conversely, if excess reserves are in short supply, then banks can charge more for this rare commodity.

The Federal Reserve influences the federal funds rate by influencing the amount of reserves, hence the amount of excess reserves. It does this by selling or buying Treasury securities on the open market (hence the name Open Market operations).

When the Fed buys Treasury securities from a private seller (generally an institution), it does two things: (1) transfers the purchase payment into their bank account; (2) credits their bank with an equivalent amount of reserves.

Lets say that the Fed buys a hundred million dollars worth of Treasury securities. The seller gets that paid into their account. The Fed credits their bank with the same amount in reserves. But under a fractional reserve system, the bank may only need to keep reserves equal to 10 percent of the new deposits. Since the new deposit equals a hundred million dollars, the bank is only required to hold ten million in reserves to cover it. So the bank now has 90 million dollars in excess reserves, which it can loan. This drives down the federal funds rate.

If the Fed instead buys Treasury securities, it debits the bank's reserves. Now the bank has lost reseves and total systemwide reserves have decreased by a hundred million dollars. That makes reserves more scarce and drives up the federal funds rate.

The federal funds rate is the rate at which banks obtain overnight loans from other banks. That affects the banks's bottom line. The bank passes on its costs, plus a profit margin, to individuals and businesses which in turn borrow money from it. Thus, the federal funds rate influences the prime lending rate. The prime rate in turn influences such things as mortgage rates. So the Fed can more or less set the federal funds rate, and from there its influence spreads, but less predictably, since factors other than reserves influence the other lending rates.

It is important to understand that in controlling the federal funds rate, the Fed is controlling excess reserves in the banking system as a whole. It is not controlling the money supply directly. The amount of Fed Open Market operations needed to set the federal funds rate will depend on many factors, including existing reserve levels, inflation, the velocity of the money supply (which is how fast money circulates), foreign trade, and other factors. So the Fed these days doesn't target money supply measures, but merely the federal funds rate.

The Fed can also loan reserves to banks, directly, through its Discount Window. The interest rate of these loans is called the discount rate. This is generally higher than the federal funds rate. The distinction is important: the federal funds rate involves private commercial banks loaning money to each other overnight; the discount rate involves direct loans by the Fed to banks. The Fed can set the discount rate by fiat. It sets the federal funds rate by Open Market operations which determine systemic excess reserves in the private commercial banking system.

Note that the Fed only recently was granted the legal authority to pay private commercial banks interest on their reserves.

Before the banking crisis, excess reserves were relatively small. After the banking crisis began, the Fed injected massive amounts of money into the banking system via its quantitative easing operations. As a result, the banking system as a whole has massive amounts of excess reserves.

Since the Fed wants to be able to control the federal funds rate through Open Market operations, it introduced interest payments on excess reserves. The interest rate paid to the banks on their excess reserves is set higher than the Fed's federal funds target rate. This is supposed to encourage banks to hold reserves rather than loan them to other banks. This in turn limits the amount of excess reserves available as interbank overnight loans, which helps maintain the federal funds rate; otherwise, the massive excess reserves would drive down the federal funds rate uncontrollably.

http://www.frbsf.org/education/publications/doctor-econ/2013/march/federal-reserve-interest-balances-reserves

There is something fishy about this, in my opinion. First, note from the link above that the interest paid to banks on excess reserves is just 0.25 percent. This keeps the federal funds rate between zero and 0.25 percent; but zero is a natural minimum in any case. The excess reserves are held by a handful of top tier banks which are involved in Open Market operations.

Why don't these banks invest these excess reserves in something other than overnight interbank loans -- something with a substantially higher return than the 0.25 percent interest rate paid by the Fed on their excess reserves? I don't know.

Note: The link above is out of date. The current federal funds rate is 0.50 percent:

http://www.bankrate.com/rates/interest-rates/federal-funds-rate.aspx

However, this is also the current interest rate paid by the Fed to banks on their excess reserves:

http://www.federalreserve.gov/monetarypolicy/reqresbalances.htm

Let me take another stab at answering your question.

The monetary base is increased whenever reserves are increased. But the money multiplier is determined by the percentage of deposits which banks are required to hold as reserves, i.e., the fractional reserve requirements. Increasing the reserves does not change the fractional reserve requirement, hence it doesn't change the money multiplier. Furthermore, an increase in reserves will not be multiplied unless they are used to support new loans. Finally, interest paid to banks on their reserves will not increase the monetary base unless these interest payments are themselves credited as reserves rather than transferred from the Fed's operating budget (which is paid by the Treasury).

First of all, note that as of 2015, excess reserves totalled about three trillion dollars:

https://www.clevelandfed.org/newsroom-and-events/publications/economic-trends/2015-economic-trends/et-20150811-who-is-holding-all-the-excess-reserves.aspx

The Fed pays banks half a percentage point interest on their reserves. That's only 15 billion dollars. At present, M1 (the most liquid measure of the money supply) is about $3.1 trillion dollars.

http://www.tradingeconomics.com/united-states/money-supply-m1

So the $15 billion in interest paid on reserves by the Fed is a drop in the bucket.

Second, most of the excess reserves are held by a tiny number of banks. From the first (Cleveland Fed) link above:

"The largest banks by our classification hold the greatest share of excess reserves, and this share has grown substantially over time. The primary dealers that act as counterparties for the Federal Reserve’s liquidity injections are some of the nation’s largest financial institutions, and larger banks have more assets to sell to create excess reserves. So while we might expect larger banks to hold more cash, we observe that small and mid-sized banks have only modestly increased their holdings of excess reserves, and now the level of reserves of small banks is roughly consistent with levels predicted by a pre-crisis growth rate. This indicates that liquidity is not diffusing through the banking system, but is instead staying concentrated on the balance sheets of the largest banks."

So, these excess reserves are not being loaned and thus are not multiplied.

Second, according to the same source, about a third of excess reserves are held by foreign banks. That means a third of the interest payments go to foreign banks. M1 is, I believe, a measure of domestic liquidity.

The formula M = m * b that you cite is merely an expression of basic relationships. It is only literally true if all reserves are multiplied to the maximum extent. And an increase in b (reserves) doesn't change m (the money multiplier). That can only be changed by changing the fractional reserve requirements.

Incidentally, it seems to me that the Fed's quantitative easing has fundamentally changed the way that the federal funds rate is determined.

Because it created such large excess reserves, the federal funds rate strongly tends to zero, because excess reserves are not a premium commodity, at least systemically. In fact, they're about as abundant as water. So the Fed can't increase the money supply by Open Market operations anymore. It sets the federal funds rate by fiat, that is, by setting the interest rate it pays banks on their reserves. The big banks that hold most of the excess reserves simply charge small banks needing overnight loans, a borrowing rate equivalent to this.

Note that when the Fed conducted quantitative easing, it purchased large amounts of Treasury securities from private (non-U.S. Government) sellers. Those purchases resulted in the transfer of roughly three billion dollars to private bank accounts. That money in turn was used for whatever purpose its recipients saw fit, including stock market purchases which bid up the paper value of stocks and the stock market. But the equivalent amount of reserves credited to the banks holding those deposits, are not being used. Instead of supporting new loans, the banks are largely just sitting on them. So there is no multiplier effect proportional to the increase in reserves.