Tuesday, June 16, 2009

The Economic Crisis in One Equation

I just finished reading Tyler Cowen and Alex Tabarrok's new chapter on the dynamic aggregate demand-aggregate supply model. It was a great read and started me thinking about how the current economic crisis could be viewed in light of the equation of exchange. Interestingly, just as I started thinking along these lines I saw that Nick Rowe had a post praising the equation of exchange. With this inspiration, it seemed only natural for me to go ahead and attempt to frame the current economic crisis in terms of the equation of exchange.

Let me begin by defining the equation of exchange:

MV = PY,

where M is the money supply, V is the velocity or average number of times a unit of money is spent, P is the price level, and Y is real GDP. This identity states that the money supply multiplied by the number of times it is spent must be equal to the current dollar value of the economy. This identity can be further decomposed by noting that the money supply is the product of the monetary base, B, times the money multiplier, m:

M = Bm


BmV = PY

With this equation of exchange we can now consider the economic crisis. First, assume that causality typically flows from the left-hand side of the equation to the right-hand side. It is well known what is happening on the right-hand side: both nominal and real GDP are plunging. Here is a figure showing monthly values for both series as well as the trend for 2003-2007. The data comes from Macroeconomic Advisers. (Click on figure to enlarge.)

So what is driving these declines? From the left-hand side of the equation we know it could be (1) change in the monetary base, (2) a change in the money multiplier, a (3) a change in velocity, or (4) some combination of the above. Using the MZM measure of the money supply (see here for why MZM is preferred over M1 and M2), the figure below shows what has happened to the monetary base, the money multiplier, and velocity (Click on figure to enlarge):

Source: Macroeconomic Advisers, St. Louis Federal Reserve

This figure shows that that declines in the money multiplier and velocity have both been pulling down nominal GDP. The decline in the money multiplier reflects (1) the problems in the banking system that have led to a decline in financial intermediation as well as (2) 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. This figure also shows that the Federal Reserve has been trying to offset these moves by significantly increasing the monetary base. Therefore, the large increase in the monetary base has been far from inflationary; rather it is fighting off the deflationary forces created by by the declines in the money multiplier and velocity.

This figure also has several policy implications. First, remove any obstacles that hinder the money multiplier. That means cleaning up the bank's balance sheets and dropping the Fed's payment of interest on excess reserves. Unfortunately, neither of these seem imminent. Second, adopt policies that will increase velocity. As noted by Alex Tabarrok this is where fiscal policy could potentially play a role. So far, though, it appears from the figure that the current stimulus package is failing to arrest the decline in velocity. (One could ague, though, it is higher than it would otherwise be.) Alternatively, the Fed could do more to increase inflationary expectations which, in turn, would reduce real interest rates, decrease real money demand, and increase velocity. Third, there is no reason yet to pull the plug on the existing expansionary policies. Rather, as Paul Krugman notes (HT Mark Thoma) policymakers need to stay the course until it is clear that the money multiplier and velocity have recovered.


  1. "Assume causality runs from the left hand side....."
    Can we get causality out of an identity ? Seems like I can always ex post parse events through this equation, because, well, its an identity!! But I dont think it illuminates the "Causes" of any of it....does it ?

  2. The West and America very much in particular have operated for the last 65 years under a forward growth, debt dependent economy. Along the way with promised Ponzi federal, state, and local future incentive entitlements, there was a steady decoupling from investments that might produce real sustainable wealth for the middle class as the central bank , CEO's of corporations, and politicians devoid of any real nationalism or alignment to America knowingly or unknowingly interacted to leverage and skim electronic money from electronic money and outsource America's substantive economy placing the American middle class under a twin yoke of debt and working conditions unable to maintain inflated debt servicing. And now the suggestion is more of the same. This is a hollow game and pathway that the elite are pursuing.

  3. Dr. SupereconomicusJune 16, 2009 at 10:54 PM

    So the "money multiplier" is not the Velocity, but instead an unexplainable force derived from the power of FIIK ("F if I know"). Boyle's Law then applies and energetic bloviation expands the volume of frenetic arm-waving.

    It is so neat to be able to explain why the unprecedented explosion in the monetary base is so "far from inflationary." It's because the blue squiqqly line is so forceful, imminence-repulsive, oratorical and stylish.