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: http://schmidt-bremen.de/Material/econs/UNCW_board_Money-Demand_Monetarists.jpg, and Peter Schmidt of University of Bremen http://schmidt-bremen.de

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.

White Graph 1, cropped

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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.

  • John M

    wow. Never though about the opportunity cost angle of the government sponsored housing bubble. The unintended consequences of the Ownership society initiative keep coming.

  • Rich

    Should commodity price targeting by the Fed, in a more formal, non-discretionary fashion than that practiced by the Manley Johnson-Wayne Angell Fed during the "great moderation", be considered a viable alternative to NGDP targeting? The Fed would expand/contract the monetary base in response to an increade/decrease in the dollar's commodity value (ie. a decline/increase in a broad, equally weighted commodity index.)

    As you mention, market price setters are better than central planners in assessing shocks real time. There is a history of tying money to commodity value. The NGDPers want to introduce a futures like contract to compensate for the lag in GDP reporting, but doesnt a deeper, more liquid market already exist in the form of a global commodities market? The signals sent by the dollar's declining commodity value in the early 2000's would have meant a reduction in base money then, possibly averting the boom (malinvestment) in real assets (real estate, oil) and the subsequent busts. Rather than conducting QE based on labor market variables, the Fed would have expanded/contracted base money in sufficient magnitude to stabilize the dollar's commodity value real time.

    If market participants knew the Fed would always act in a manner consistent with stabizing the dollar's commodity value, wouldn't that improve transparency, accountability and independence? Would more resources flow into productive investment, repairing the capital stock, because less would have to be hedged?

    Would a dollar that's stable in terms of commodities lead to a more stable gold price, and one more aligned with other commodities and the price level? Would this be a credible step toward restoring dollar-gold parity, which could lead to the issuance of competitive gold backed banknotes?

  • Andrew_FL

    The short version is: you can throw the plucking model out the window, folks!

    • George Selgin

      Nicely put!

  • Andrew_FL

    "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 don't know if this document from the CBO is still accurate, they estimate Okun's Law like relationships, statistically, between Unemployment-NAIRU and hours worked and total factor productivity, and calculates their potential levels at NAIRU. But they do not estimate an Okun's Law for capital because "Unlike the labor input and TFP, the capital input does not need to be cyclically adjusted to create a “potential” level—the unadjusted capital input already represents its potential contribution to output. Although use of the capital stock varies greatly during the business cycle, the potential flow of capital services will always be related to the total size of the capital stock, not to the amount currently being used."

    It's not clear to me what data they use to estimate the size of the "capital stock" or what methods they may use-putting aside for the moment strong arguments that aggregating capital is not really something that can be done-but the properties whatever time series they're using almost certainly has to have to yield the potential GDP trend they get, seem counter-intuitive.

  • "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."
    The problem is that the cities associated with the bubble were not building houses. The problem is that not enough capital was diverted to housing construction in cities where housing is valuable. Everyone has the problem upside down. There is no place that was building a lot of housing in the past 20 years that ever had an oversupply.

    • Andrew_FL

      "Bubbles" don't mean excessive supply, they mean artificially elevated demand. You think people have got the story upside down because you're holding the book upside down.

      • Maybe I misspoke. I meant oversupply in terms of quantity. No city built too many homes.

        • Andrew_FL

          Probably true. What happens when government inflated demand meets government restricted supply? Rapidly increasing prices. When the artificially stimulated demand collapses, the snap back is hard. Boom and bust, if anything exacerbated by the issue you're talking about.

          • I am currently working on a book where I have concluded that it was entirely supply and we have been fooled into thinking demand was the problem. Demand is part of it in the same way that you could say oxygen causes forest fires. But it's a tautology. But it's too complicated to explain here. Just as a brief hint of the issue, ask yourself, were many homes being built where they were the most expensive? The problem is that the price mechanism cannot work where location is valuable today. Migration away from valuable locations is happening on a grand scale. That is the misallocation of resources. The price signal from housing has nothing to do with it.

          • Andrew_FL

            This doesn't make sense. Was there some sudden increase in the level of zoning regulations in the 2000's? What changed? You really think demand was where it would have been without the government encouraging mortgage lending, especially to certain classes and groups, and the Federal Reserve increasing the effective money stream?

          • Domestic out-migration from urban California and New England was at Detroit-like levels during the boom. The Fed was growing currency very slowly, because like everyone else they mistook a supply problem for a demand problem. George Selgin has explained on this site how even in 2007 they were being very contractionary, though he doesn't accept my thesis (yet) either. There was no new government support of mortgage lending. I certainly would support getting rid of the tax breaks, etc., but the marginal actions of the government in the 2000s were to undermine federal support. Here is my latest post on securitizations:
            http://idiosyncraticwhisk.blogspot.com/2016/05/housing-part-150-securitizations-and.html

          • Andrew_FL

            "The Fed was growing currency very slowly, because like everyone else they mistook a supply problem for a demand problem."

            This is just completely wrong.

            Take Final Sales to Domestic Purchasers. Divide it by the Civilian Labor Force. Take Quarterly growth rates. Apply an HP Filter (Lambda 1600) Take the filtered growth rate, and change it to be constant after Q3 of 2005 (Unemployment was at NAIRU, according to FRED series NROU and UNRATE), equal to the filtered growth rate of that quarter. Compound the growth rates. Set the trend like to be equal to the series Final Sales/Civilian Labor Force at Q2 of 1997 (Again, at NAIRU). The series will be above this trend line from Q1 of 2004 all the way til Q3 of 2008, peaking at a little over 3 percent above trend in Q1 of 2006.

            The path of spending suggests the opposite of your "Money Is Always Tight" view.

            "George Selgin has explained on this site how even in 2007 they were being very contractionary"

            I have never seen him say this. I have seen him say they were contractionary in 2008, for good reason. Not in 2007. Point me in the direction of what you're talking about?

          • I said they were contractionary in 2007, which I hope isn't that controversial at this point. Before that I said they were growing currency slowly. All you say is true. Nominal growth was about right. Certainly not too loose, though. Part of my thesis is that much of core inflation is coming from the housing supply problem. It's not so much monetary inflation as it is a transfer of rents. Core CPI minus shelter has been pretty reliably under 2% since 2000. I think we sort of had an accidental NGDP targeting recession in 2006-2007 until the crisis hit. Nominal growth was ok partly because the housing shortage was causing rent inflation to be high. Real incomes were starting to fall, but nominal incomes were doing ok, so unemployment was avoided until 2008. I realize it seems wrong. It's why I'm writing a book. It takes a few hundred pages to address all the things that everyone knows that are wrong.

            Oh, here is a post where George talks about them sterilizing their emergency lending in 2007.
            http://www.alt-m.org/2015/12/04/sterilization-fed-style/

          • Andrew_FL

            You and I interpreted that article very differently, since I explicitly saw him say that policy was too tight in 2008 but make no such statement about 2007. George can comment if he wishes as to which of us is reading him correctly.

            "All you say is true. Nominal growth was about right. Certainly not too loose, though."

            This is self contradictory. I said it was above trend from 2004 to 2006. If that's true, it was too loose. Either what I said is not true, or it is true. Which is it?

            I actually think there is much stronger evidence for a classic mis-allocation of resources-"malinvestment" in other industries than housing construction. Indeed the swing in Construction employment was much larger than in other recessions I've looked at. Which is strange, if there was no building being allowed, I wonder what all those people were employed doing.

          • There was misallocation, but the misallocation is due to the supply constraints. This is all too complicated to go into more details here. You can click on the link to my blog if you are interested. The misallocation is that we are forcing a significant migration out of our most productive cities. This is insanity, from a macro level perspective, whatever the local issues are. The misallocation has absolutely nothing to do with price signals in housing. You can't build where prices are signaling to build. So, what happens is that someone who is making $80,000 in San Francisco sends their income to the landlord who is earning rents from housing rules that amount to capital repression. They are living in a unit that is worth $800,000, but would cost $200,000 to build anywhere else. So, they take a $30,000 cut in pay, move to Dallas, use $200,000 in materials to build a $220,000 house in Dallas, and the country ends up with (1) less total income (2) a bunch of transfers to rent seekers in the closed cities that claim some of that income, and (3) getting a really poor return on investment on the construction in Dallas compared to where it should have been built. The reason construction was up so high was that we were building McMansions in the interior instead of much more valuable multi-unit condos in the coastal cities. But, the problem isn't that people were so revved up about the McMansions. They were only building them as a second-best option because it isn't legal for them to build where they want to live, in Manhattan, LA, San Francisco, or Boston. The misallocation comes from supply constraints, not excess demand. They were actually REDUCING their housing consumption by moving out of the closed cities, even though it took more materials to create the houses. In the current age, these cities have tremendous value, and we can't utilize it. It's like we are Britain in the 18th century and we passed a law against mining for coal, then when coal prices went up, everyone decided we had too much money.

          • Andrew_FL

            We're talking past each other. My problem is that I have no problem with the story you're trying to tell, except that you want it to be mutually exclusive from anything else.

          • Bonnie

            I think that perhaps you both are making different arguments that can both explain some part of reality at the same time. To what extent, though, is unknown as the method Andrew used for estimating the level of housing demand is incomplete, lacking a modifier for population growth or household formation in order to eliminate possible anomalies in the trend.

            But if even if Andrew's argument that government incentives stoked demand to the maximum extent of 3% above trend is valid, it does not counter your argument that zoning laws were not accommodative, or not accommodative enough.

            The demand-stoking argument, however, does little to persuasively offer any validation of the misallocation claim above, its supposed linkage to prolonged recession and current helplessness of the monetary authority, a claim that, even considering the data presented in the OP, is anecdotal and borders on non sequitur when compared to the economic effects predicted by the equation of exchange of a persistent increase in fluidity (emphasis on "persistent"). Notice that there is no velocity graph when the presence of one would be most helpful.

          • Andrew_FL

            Bonnie-"it does not counter your argument that zoning laws were not accommodative, or not accommodative enough." I completely agree. It isn't intended to. I've said multiple times I do think he is right about the impacts of zoning laws.

            "To what extent, though, is unknown as the method Andrew used for estimating the level of housing demand is incomplete, lacking a modifier for population growth or household formation in order to eliminate possible anomalies in the trend."

            I am attempting to estimate the deviation from trend of the Effective Money Stream or as Economists like to call it nowadays, "aggregate demand" not housing demand specifically. But I did account for population growth, by dividing by the civilian labor force.

            "The demand-stoking argument, however, does little to persuasively offer any validation of the misallocation claim above, its supposed linkage to prolonged recession"
            Personally I think the OP overemphasizes the role of housing in misallocation to the exclusion of everything else. To get at that, I go by somewhat different measures. More specifically I use the Establishment Survey's employment level statistics by broadly defined industries. I focus on: Construction employment, Durable Goods Manufacturing, Non Durable Goods Manufacturing, Mining and Logging, Retail Trade, Wholesale Trade, Transportation and Warehousing, and the non-Trade non-Transportation/Warehousing Service sector. I use an HP filter with a Lambda of 1.44×10^6 to estimate the long term trend, and I take percent deviations from trend. Total non-farm payroll employment peaked at about 3% above trend and bottomed out at about 3.7% below, a decrease of almost seven points. And no question Construction is the stand out sector of this recession, peaking at ~12.5% above trend and bottoming out at about 14.4% below, for a full decrease of about 27%. But it is followed closely behind by the drop in Mining and Logging employment, from about 9.4% above to about 10.8% below, decreasing about 20.1% overall. The next largest change was in Durable Goods manufacturing, from 4.7% above to 11.2% below, dropping 15.9 points, then Transportation and warehousing from about 4.2 above to 6.5 below (10.7 point swing), Wholesale Trade from 4.9 above to 4.9 below (9.8 point swing), Nondurable goods 1.9 above to 4.9 below (6.9 point swing) and a measily swing of all other services from just 2.1 above to 2.1 below, for a swing of 4.2 points.
            What those numbers indicate is that, for the most part, the industries which saw the biggest booms and busts were those further stages of production away from the consumer of final goods. This is exactly what you'd expect to see from malinvestment and misallocation of resources during the boom.

          • Put another way, if you think high home prices are leading to resource misallocation, go find the place with the highest home prices right now and try to allocate some capital there. See how far you can get.

  • Central bankers cannot get the timing right because they don't want to. Here is an example. The bill HR 1424 was introduced by Patrick Kennedy in early 2007 as a means to legalize the purchasing of commercial paper by the Fed, resulting in the CPFF. But that paper buying should have commenced in August of 2007 when the subprime crisis occurred. But the Fed did nothing, the bill languished. It was originally set up for purchases beginning in 2011 but was moved up to 2008, but that was still too late. If Patrick Kennedy knew that the Fed would have to buy paper, then surely the Fed knew it would have to, but it fiddled while the middle class burned. Buying commercial paper would have allowed some bubble areas to crash but not every house in America to lose value or the Great Recession that followed. The Fred chart clearly shows that the Fed waited way too long to introduce the CPFF.

  • When, for the purpose of deciding the capital requirements for banks, you assign a risk weight of only 35 percent to residential housing finance (35 to 1 leverage) but one of 100 percent for lending to any unrated SME or entrepreneur (12 to 1 leverage)… how can you think this kind of misallocation will not occur… it still happens because the distortion Basel’s regulations produce seems to be of little interest to academicians.

    http://subprimeregulations.blogspot.com/2016/03/please-let-us-not-favor-financing-our.html

    Never ever before has a generation consumed as much of any existing borrowing capacity to sustain its own consumption