Back in January, I wrote a post that contained some mistakes.  I argued that part of the reason that the M1 money multiplier in America fell below unity was because foreign banks with branches in America and American banks with branches in other countries were taking deposits from other countries and placing them in (excess) reserve at the Federal Reserve.

My first mistake was in believing that that was the only reason why the multiplier fell below one.  Of course, even if the United States were in a state of autarky it could still fall below one as all it requires is that banks withdraw from investments outside the standard definitions of money and place the proceeds in their reserve account at the Fed.

And that was certainly happening, because by paying interest on excess reserves, the Fed placed a floor under the risk-adjusted return that banks would insist on receiving for any investment.  Any position with a risk-free-equivalent yield that was less than what the Fed was paying was very rapidly unwound.

Nevertheless, I believe that my idea still applies in part.  By paying interest on excess reserves, the Fed (surely?) also placed a floor under the risk-adjusted returns for anybody with access to a US depository institution, including foreign branches of US banks and foreign banks with branches in America.  The only difference is that those groups would also have had exchange-rate risk to incorporate.  But since the US dollar enjoys reserve currency status, it may have seemed a safe bet to assume that the USD would not fall while the money was in America at the Fed because of the global flight to quality.

The obvious question is to then ask how much money held in (excess) reserve at the Fed originated from outside of America.  Over 2008:Q4, the relevant movements were: [1]

• the m1 money stock rose roughly US$190 billion
• the monetary base rose a little over US$756 billion
• currency rose slightly more than US$42
• excess reserves rose just over $707 billion

Remember that, roughly speaking, the definitions are:

• monetary base = currency + required reserves + excess reserves
• m1 = currency + demand deposits

So we can infer that next to the $707 billion increase in excess reserves, demand deposits only increased by $148 billion and required reserves by $7 billion.

In a second mistake in my January post, I thought that it was the difference in growth between m1 and the monetary base that needed explaining.  That was silly.  Strictly speaking it is the entirety of the excess reserve growth that we want to explain.  How much was from US banks unwinding domestic positions and how much was from foreigners?

Which is where we get to Brad’s post.  In looking at the latest Flow of Funds data from the Federal Reserve, he noted with some puzzlement that over 2008:Q4 for the entire US banking system (see page 69 of the full pdf):

• liabilities to domestic banks (floats and discrepancies in interbank transactions) went from $-50.9 billion to $-293.4 billion.
• liabilities to foreign banks went from $-48.1 billion to $289.5 billion

I’m not sure about the first of those, but on the second that represents a net loan of $337.6 billion from foreign banks to US banks over that last quarter.

Could that be foreign banks indirectly making use of the Fed’s interest payments on excess reserves?

No matter what the extent of foreign banks putting money in reserve with the Fed, that process – together with the US government-backed settlements of AIGs foolish CDS contracts – amounts to America (partially) recapitalising not just its own, but the banking systems of the rest of the world too.

[1] M1 averaged 1435.1 in September and 1624.7 in December.  Monetary base averaged 936.138 in September and 1692.511 in December.  Currency averaged 776.7 in September and 819.0 in December. Excess reserves averaged 60.051 in September and 767.412 in December.  Remember that the monthly figures released by the Federal Reserve are dated at the 1st of the month but are actually an average for the whole of the month.

Update: You can (finally) see the improved post here.  You’ll probably still want to refer back to this one for the graphs.

Via Greg Mankiw, I see that in the USA the M1 money multiplier has just fallen below one:

M1 Money Multiplier (USA, Accessed: 7 Jan 2009)

At the time of writing, the latest figure (for 17 December 2008) was 0.954.  That’s fascinating, because it should be impossible.  As far as I can tell, it has been made possible by the wonders of financial globalisation and was triggered by a decision the US Federal Reserve made at the start of October 2008.  More importantly, it means that America is paying to recapitalise some banks in other countries and while that will help them in the long run, it might be exacerbating the recessions in those countries in the short run.

Money is a strange thing.  One might think it would be easy to define (and hence, to count), but there is substantial disagreement of what qualifies as money and every central bank has their own set of definitions.  In America the definitions are (loosely):

• M0 (the monetary base) = Physical currency in circulation + reserves held at the Federal Reserve
• M1 = Physical currency in circulation + deposit (e.g. checking) accounts at regular banks
• M2 = M1 + savings accounts

They aren’t entirely correct (e.g. M1 also includes travelers cheques, M2 also includes time/term deposits, etc.), but they’ll do for the moment [you can see a variety of countries' definitions on Wikipedia].

The M1 Money Multiplier is the ratio of M1 to M0.  That is, M1 / M0.

In the normal course of events, regular banks’ reserves at the central bank are only a small fraction of the deposits they hold.  The reason is simple:  The central bank doesn’t pay interest on reserves, so they’d much rather invest (i.e. lend) the money elsewhere.  As a result, they only keep in reserve the minimum that they’re required to by law.

We therefore often think of M1 as being defined as:  M1 = M0 + deposits not held in reserve.

You can hopefully see why it should seem impossible for the M1 money multiplier to fall below 1.  M1 / M0 = (M0 + non-reserve deposits) / M0 = 1 + (non-reserve deposits / M0).  Since the non-reserve deposits are always positive, the ratio should always be greater than one.  So why isn’t it?

Step 1 in understanding why is this press release from the Federal Reserve dated 6 October 2008.  Effective from 1 October 2008, the Fed started paying interest on both required and excess reserves that regular banks (what the Fed calls “depository institutions”) held with it.  The interest payments for required reserves do not matter here, since banks had to keep that money with the Fed anyway.  But by also paying interest on excess reserves, the Fed put a floor under the rate of return that banks demanded from their regular investments (i.e. loans).

The interest rate paid on excess returns has been altered a number of times (see the press releases on 22 Oct, 5 Nov and 16 Dec), but the key point is this:  Suppose that the Fed will pay x% on excess reserves.  That is a risk-free x% available to banks if they want it, while normal investments all involve some degree of risk.  US depository institutions suddenly had a direct incentive to back out of any investment that had a risk-adjusted rate of return less than x% and to put the money into reserve instead, and boy did they jump at the chance.  Excess reserves have leapt tremendously:

Excess Reserves of Depository Institutions (USA, Accessed: 7 Jan 2009)

Corresponding, the monetary base (M0) has soared:

Adjusted Monetary Base (USA, Accessed: 7 Jan 2009)

If we think of M1 as being M1 = M0 + non-reserve deposits, then we would have expected M1 to increase by similar amounts (a little under US$800 billion).  In reality, it’s only risen by US$200 billion or so:

M1 Money Stock (USA, Accessed: 7 Jan 2009)

So where have the other US$600 billion come from?  Other countries.

Remember that the real definition of M1 is M1 = Physical currency in circulation + deposit accounts.  The Federal Reserve, when calculating M1, only looks at deposits in America.

By contrast, the definition of the monetary base is M0 = Physical currency in circulation + reserves held at Federal Reserve.  The Fed knows that those reserves came from American depository institutions, but it has no idea where they got it from.

Consider Citibank.  It collects deposits from all over the world, but for simplicity, imagine that it only collects them in America and Britain.  Citibank-UK will naturally keep a fraction of British deposits in reserve with the Bank of England (the British central bank), but it is free to invest the remainder wherever it likes, including overseas.  Since it also has an arm in America that is registered as a depository institution, putting that money in reserve at the Federal Reserve is an option.

That means that, once again, if Citibank-UK can’t get a risk-adjusted rate of return in Britain that is greater than the interest rate the Fed is paying on excess reserves, it will exchange the British pounds for US dollars and put the money in reserve at the Fed.  The only difference is that the risk will now involve the possibility of exchange-rate fluctuations.

It’s not just US-based banks with a presence in other countries, though.  Any non-American bank that has a branch registered as a depository institution in America (e.g. the British banking giant, HSBC) has the option of changing their money into US dollars and putting them in reserve at the Fed.

So what does all of that mean?  I see two implications:

1. Large non-American banks that have American subsidiaries are enjoying the free money that the Federal Reserve is handing out.  By contrast, smaller non-American banks that do not have American subsidiaries are not able to access the Federal Reserve system and so are forced to find other investments.
2. The US$600+ billion of foreign money currently parked in reserve at the Fed had to come out of the countries of origin, meaning that it is no longer there to stimulate their economies.  By starting to pay interest on excess reserves, the US Federal Reserve effectively imposed an interest rate increase on other countries.