Monday, March 22, 2010

The Equation of Exchange Still Makes Sense

Over at Alphaville, Isabella Kaminska is fretting over what seems to be a breakdown in the equation of exchange:
So what’s wrong with Irving Fisher’s famous MV = PT equation? Why has throwing money at the problem not affected the relationship between money and income in the equation the way it supposedly should?
Drawing on a research note by Standard Chartered, Isabella concludes the answer must be with velocity. Let me reassure Isabella that the equation of exchange still holds and that there is more to story than just velocity. As I showed in an earlier post, the way to see this is to first note that M, the money supply, is the product of the monetary base, B, times the money multiplier, m:

M = Bm.

Now substitute this into the equation of exchange to get the following (I use PY instead of PT ):

BmV = PY

Now we have an identity that says the sources of nominal spending, PY, are the monetary base, the money multiplier, and velocity. Here, V = velocity or the average number of times a unit of money is spent, P = price level, Y = real GDP, and thus, PY = nominal GDP. This accounting identity allows us to think about what causes may have been behind the the dramatic decline in nominal spending, PY. Using MZM as the measure of M and monthly nominal GDP from Macroeconomic Advisers to construct velocity (i.e. V=PY/M), the three series on the left hand side of the expanded equation of exchange are graphed below in levels (click on figure to enlarge):

The last time we saw this figure was in September 2009. I noted then that the surge in the monetary base was largely offset by decline in the money multiplier leaving velocity as the main factor pulling down nominal GDP. This doesn't seem to have changed much, though velocity looks like it has bottomed out. I also noted then that the decline in the money multiplier probably reflects (i) the problems in the banking system that have led to a decline in financial intermediation as well as (ii) the interest the Fed is paying on excess bank reserves. The decline in the velocity is presumably the result of an increase in real money demand created by the uncertainty surrounding the recession. For the sake of completeness, the below figure graphs the the right-hand side of equation (2):


  1. 25bps interest on excess reserves is a tiny amount that should have no significant impact on money multiplier.

  2. If you look at the M1 money multiplier


    In order for this equation to go below 1, reserves held by banks must be greater than the deposits they hold. What's going on here?

  3. But no one has actually thrown any money at the problem!

    Why do you think that the money supply is the product of the monetary base and the money multiplier? None of this makes sense theoretically and it doesn't seem to have any empirical support.

    If a bank wants to make a loan, it can do so and then go to the market for funds to acquire more. If the market is short on aggregate the Fed just gives em some more.

    The NY Fed say here:

    "[T]he Federal Reserve operates in a way that permits banks to acquire the reserves they need to meet their requirements from the money market, so long as they are willing to pay the prevailing price (the federal funds rate) for borrowed reserves. Consequently, reserve requirements currently play a relatively limited role in money creation in the United States."

  4. Hmm, I didn't phrase that too well.

    The way I see it, the CB does not control the monetary base, monetary velocity, the money supply, the money multiplier or anything else except the price of funds.

    The "money multiplier" is based on a flawed view of banking as the quote from the Fed shows.

  5. Vimothy:

    Several comments. First, the monetary base is controlled by the Fed, though in the short-run the base is endogenously determined given the Fed's interest rate target. Note, though, the Fed adjusts is ffr target based on something like a Taylor Rule, albeit imperfectly. As a consequence,the Fed--not the public or the banking system--is determing the monetary base over the long-run. And of course, the Fed could choose to explicitly target monetary base instead of the ffr (think Volker's monetarist's experiment
    in the earl 1980s).

    Second, I never argued the money multiplier is a slave to the Fed. Rather, it is largely determined by the public and banking system. The Fed, however, can exert influence on it as we saw in the 1938 debacle . I also believe that its payment of interest on excess reserves has influenced the multiplier (though clearly not the only one factor). In fact, Bernane and the Fed assume as much as they tell us they are using the payment on ER to keep them in check and may continue to do so durring its exit strategy.

    Finally, the Fed can do much to stabilize velocity by setting and ensuring a target. My preference would be a NGDP target, but even an inflation target would have gone far in stabilizing the velocity decline seen above.