Disaggregating the Equation of Exchange

The equation of exchange states that MV=PQ. As formulated by Friedman, the equation is stated as MV=PY. Money times velocity equals the price level times total output Q, or total income Y, or transactions T, which are the same in what might be called a “closed” economy.

Let me further explain this simple tautology. All of the money in a given closed; i.e. hermetically-sealed economy, multiplied by the number of times each individual unit of money (the “dollar,” “euro,” etc) is spent, necessarily equals the (hypothetical) perfectly-average price of any given good or service, multiplied by either the amount of goods and services produced, or the amount of money received for the goods and services sold (whether you want to measure it in real or nominal terms). However, I intend to go beyond the simple mechanics of axiomatic, classical monetarism.

I mentioned in an earlier article entitled The Genius of Roger Garrison, Part Two that Garrison has successfully synthesized a satisfactory disaggregation of the variable Q. Specifically, that the structure of production is entirely composed of the capital that constitutes its own production processes. This is why he always explains that the Hayekian triangle is only the sum of its parts compiled throughout time: it is composed of capital goods that form pieces of the puzzle, these pieces themselves composed of yet-smaller pieces: capital. This is essentially a disaggregated form of Mark Skousen’s GO, or Gross Output, a statistic that the Fed now includes in its statistical calculations. Skousen’s GO includes not only the output of final consumer goods, but also the capital created and used in the structure of production (hence the name of his book).

More precisely, all production is comprised of individual production mechanisms in various stages; mechanisms that instantiate themselves as singly coordinated streams of processes that cannot be distinguished when combined, other than throughout time. That is not to say that the market cannot slowly attempt to estimate the value of a given part of the production process with increasing precision, but rather that it is literally impossible to fully aggregate any group of stages of a given production process without mental construction. Garrison makes it clear that he only intends to use these numbers is his description of output, Q, as a pedagogical tool:

I intend to disaggregate the entire equation. Let’s start with perhaps the hardest to tackle, velocity. We can understand that various forms of money (a disaggregated M) would correspond with varying velocities. The closer to physical cash a type of money might be would indicate a velocity higher than something like reserve deposits at the Fed. One can imagine that printing money and throwing it out of helicopters, a la Friedman’s mind-experiment, would be used faster and this more times than, say, excess reserves at the central bank, or thirty-year savings bonds. These latter forms of money are plainly less liquid, and represent “slower” money, unlike handing a homeless person a thousand dollars in cash. For an example that might be more amenable to a mainstream economist, M0 (paper money and coins, in circulation) and M2 (paper money in circulation, checkable deposits, savings deposits, and smaller time deposits) plainly have different velocities, just the same as M1 (paper money in circulation, traveler’s checks and demand deposits) would have a different velocity than M3, and so on. Just the same, the yield curve demonstrates the price of nearer- and further- termed money. Output is comprised of sooner and later production, as exemplified by the fantastic (though perhaps slightly misleading) Hayekian triangle.

From here, we see clearly that velocity and the price structure can be disaggregated, just as M is currently disaggregated (to a small degree) in the modern literature, and just as Garrison has disaggregated output (really, the capital structure). Austrians have a penchant for finding and displaying the cracks in aggregate numbers because, after all, they understand methodological individualism and thus ultimately believe that econometrics and statistics are insufficient for building a wholly logical theory of economics itself. Let’s take Garrison’s scheme and apply it to the other three variables in tandem with output.

What this is intended to show is that there are varying levels of velocity that correlate with various forms of money; just as there are varying sets of prices that correlate with various levels of production. For example, the money generated via QE has been stuck at a very low velocity (somewhere around zero) while sitting in bank reserves, leaving it at perhaps the minimum level of velocity present in the monetary system for any given type of money.

This is more of a nuanced latticework of the various factors involved in the pseudostatic monetarist theory of prices, rather than the aggregated oversimplification advanced by your average Chicagoan, New-Keynesian, or even “market” monetarist. What this explanation is conveying goes something like: well of course the exchange of physical cash (M0) for various goods (Q1-Q10) affects the prices of consumer goods more quickly than, say, corporate bonds or Treasury bills: cash is, as a rule, used for the purchase of goods that are closer to the final stages of production; yes, individuals may purchase houses in “cash” (really, via bank transfer), but that is not the rule, and is still much closer to the final stages of production, as opposed to the cranes purchased by a company intending to build skyscrapers in Manhattan. Yes, at some point all economic, physical goods are purchased in what must eventually become liquidated into cash, but these smaller pieces of production Similarly, one would be hard-pressed to argue that the prices of higher factors of production, such as factory space or machine tools, are somehow directly influenced by the speed at which consumer products like blunt wraps and candy canes are exchanged for money (i.e. purchased).

This analysis extends further into our everyday understandings of how various forms of money move at various speeds to affect various prices of various goods and services. One can easily see how, for example, a “helicopter drop” of money (which was not advocated by Friedman despite what people who’ve never read his work purport, but was rather an explanatory device for these precise purposes) would quickly raise prices across the board, first in consumer goods and subsequently working its way up to the highest factors of production. Similarly, one can easily see how quantitative easing (purchasing government bonds, mortgage-backed securities a la the Fed, corporate bonds a la the ECB, et cetera) affects prices higher up in the chain of production, which slowly work their way down to the most trifling and fleeting of consumer goods. Anyone with even the simplest understanding of supply and demand can plainly see that the government buying up mortgage-based debt instruments boosts the prices of those exact instruments. Those instruments, however, are plainly far-removed from the price of a pack of disposable razors, even if the owner(s) or employee(s) of the company making those razors see their housees rise in price. This simple illustration makes it easy to understand why the QE aimed at banks has taken so long to “leak” into the price structure associated with the capital structure: nobody buys packs of gum with corporate bonds; nobody buys a factory with dump trucks full of pocket change.

I’ll expand on this concept in related future articles. Have a good one.