Some Simple Monetarist Arithmetic of the Great Recession and Recovery

Nominal GDP, Output Gap, productiviy, resource misallocation, velocity of money
Equation of exchange on blackboard, courtesy of University of North Carolina Wilmington:, and Peter Schmidt of University of Bremen

Nominal GDP, Output Gap, productiviy, resource misallocation, velocity of moneyThe familiar chart below illustrates the depth of the decline in real output during the 2007-09 Great Recession (the shaded period), and the failure of the recovery to return real output to its “potential” path (in other words, to eliminate the estimated “output gap”) during the subsequent years up to the present day.  The second chart puts the same 2007-16 period in the context of the previous decades, showing how exceptionally prolonged the current below-potential period is by contrast to previous postwar recessions and recoveries.

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It is instructive to decompose the path of real GDP into its components, nominal GDP and the price deflator. Here are the natural logs of nominal GDP (call it Y) and real GDP (call it y).  From the definition y = Y/P, it follows that ln y = ln Y – ln P, so the growing vertical difference between the two series reflects the rising price level.

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Here is the path of the natural log of the GDP deflator, which is the difference between the real and nominal GDP series. (Note: FRED uses 2009=100 as the index base; I have re-normalized to 2004=1 by dividing by 90).

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Monetarist theory sharply distinguishes real from nominal variables.  Nominal shocks (changes in the path of the money stock or its velocity) have only transitory effects on real variables like real GDP. Accordingly an account of the path of real GDP in the long run (and 6+ years of recovery should be enough time to reach the long run) must be explained by real and not merely by nominal factors.  An account of the path of nominal GDP, by contrast, cannot avoid reference to nominal factors.  So we need distinct (but compatible) accounts of the two paths.

To account for the path of nominal GDP we can use the simple accounting decompositions M = φY and ln M = ln φ + ln Y, where φ (“phi”), following the notation of Michael Darby’s canonical monetarist textbook, is a mnemonic for fluidity, defined as M/Y, and thus the inverse of velocity. Before the Great Recession, the velocity of M2 was on a gradual downward path, falling around 1% per year.  During the Recession it fell much more steeply.  Since the Recession it has been falling around 2% per year.  Correspondingly, φ was on the rise, but its path shifted upward and become slightly steeper.  Meanwhile, the path of M2 has hardly budged, with M2 rising at an annualized 5.9% rate between the midpoint of the previous recession and the midpoint of the Great Recession, and at a 6.7% rate since.  Here are the observed paths of log M2 and log nominal GDP on the same scale, and in the next chart the path of log M2 fluidity:

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As a stylized approximation, let us treat the path of log M2 as a smooth line without variation.  Then all the variation in nominal GDP is explained by the variation in fluidity.  The downward displacement of the path of nominal GDP during the Great Recession, and its slower growth afterward, corresponds to the upward displacement of fluidity (drop in velocity) during the Recession and its more rapid growth since the recession.  Further simplifying, let us treat the shift in fluidity as due to an upward shift in desired fluidity at a single date t*.  We can explain the downward shift in the steady-state path of the log of nominal Y as the result of an exogenous upward shift in the steady-state path of the log of fluidity resulting from the public’s demand to hold larger M2 balances relative to income Y, in the face of an unvarying path of M2.  The next diagram shows the shifts in steady-state paths, constrained by the accounting identity that ln M = ln φ + ln Y.

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Assuming gradual adjustment of actual to desired fluidity, we can add hand-drawn transitory adjustment paths.  This yields a stylized representation of the actual time series seen above.

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A downward displacement of the steady-state path of nominal GDP, due to a contractionary money supply or velocity shock, can bring a transitory decline in real GDP.  As is familiar, people try to remedy a felt deficiency in money balances by reducing their spending.  In the face of sticky prices, reduced spending generates unsold inventories and hence cutbacks in production and layoffs until prices fully adjust.  As Market Monetarists have long argued, the Federal Reserve could have avoided the downward displacement of the path of nominal GDP if policy-makers had immediately recognized and met the rise in fluidity (the drop in velocity) with appropriately sized expansionary monetary policy.  (I leave aside the Traditional Monetarist critique of the track record of stabilization policy, which argues that central bankers cannot be expected to get the timing and magnitude right in a world where to do so they would have to forecast velocity shocks better than market price-setters.)

Although a one-time un-countered rise in desired fluidity can temporarily knock real GDP below course, such a nominal shock should not persistently displace its growth path, as the first chart above indicates has happened.  We can expect monetary equilibrium to be roughly restored by appropriate adjustment in the price level relative to the nominal money stock, bringing real balances up to the newly desired level, within three or four years at most.  (In the data plot above, we see the GDP deflator shift to a lower path already in 2009.)  Real GDP should around the same time return to its steady-state path as determined by non-monetary factors (labor force size and skills, capital stock, total factor productivity as governed by technologic improvements, policy distortions, and so on).  To explain the continued low level of real GDP relative to estimated potential since 2011 or so, we need a persistent shock to the path of real GDP.

I suggest that real GDP has shifted to a lower path because of a shrinkage in the economy’s productive capital stock — a problem that better monetary policy (not feeding the boom) could have helped to avoid, but cannot now fix.  During the housing boom, investible resources that could have gone into augmenting human capital, building useful machines and sustainable enterprises, and conducting commercial research and development, were instead diverted to housing construction. In the crisis it became evident that the housing built was not worth the opportunity cost of the resources allocated to it.  That major misallocation of resources has lowered the path of the capital stock below its previous trend.  I do not know precisely how the contribution of capital input is measured when the CBO estimates potential output, but I hypothesize that potential output is currently overestimated because capital wastage has not been fully recognized.  I welcome comments and evidence on this hypothesis.