The Quantity Theory of Inequality

For the last several years, I have been among a small group of economic professionals arguing that income and wealth inequality is America’s most pressing problem, and beyond that, the way the economy works, that the distribution of income and wealth throughout the population is the primary determinant of prosperity and stagnation. Since 2013, more and more economists are moving in the direction of that conclusion, but I have seen no one else, as yet, put it that bluntly.

All of the evidence has pointed to this conclusion, but the theoretical underpinning has been lacking. The evidence has shown that rising income inequality suppresses overall income growth. When income inequality becomes excessive, slowing growth turns into ever-longer recessions and, eventually, a depression. This perception conflicts with the mainstream theories of growth and depression. It is not, however, a matter of conjecture. Now I have the missing theoretical underpinning, and it is found in “The Quantity Theory of Money.” 

The Evidence

uneven ditribtion of gains

Persuasive evidence was provided several years ago in a report from the Center on Budget and Policy Priorities (CBPP) [“Top 1 Percent of Americans Reaped Two-thirds of Income Gains in Last Economic Expansion,” Avi Feller and Chad Stone, September 9, 2009, here.]

This chart shows the cumulative growth of U.S. aggregate income over two consecutive 30-year periods, 1946-1976 and 1976-2007, as well as the cumulative growth over these periods of the top 1% and the bottom 90% income shares. This comparison reveals a pronounced, inverse relationship between income concentration and the aggregate income level.

The difference in the patterns of U.S. income growth between the two periods is extraordinary: The ability to realize income – to make money – shifted substantially to those higher on the income ladder. In the second of those two periods, in other words, household income had become more “concentrated.” Moreover, the phenomenal cumulative growth of top 1% income in the second period was accompanied by a severely stunted income growth for the bottom 90%. Thus, in the second period the top 1% was claiming so much of the new income growth for itself that very little growth was left for the bottom 99%.

The net effect of this trend was about a 25% lower cumulative growth of aggregate (per capita) income in the second period, and that is the key point: The extraordinary inequality growth since the late 1970s has reduced the overall growth rate, depressing the U.S. economy. All of this, it must be emphasized, took place before the Crash of 2008. The economic changes of the early 1980s abruptly terminated a long period of stable growth, which had been distributed more evenly among the income quintiles, and the economy commenced a gradual but relentless decline toward the Crash of 2008 and an incipient depression.

This reality is only gradually dawning on the mainstream economic community, which is accustomed to thinking of income inequality only from a subjective, qualitative perspective. Neoclassical economics has for more than a century denied that income and wealth distribution has any macroeconomic significance. The relationship of income inequality to growth has gained increasing attention, however, in the years since the Crash of 2008 and the advent of “The Great Recession.” IMF economists published studies in 2011 and 2014 which tested the statistical correlation of income (GDP) growth with income inequality, along with a variety of exogenous variables. [“Redistribution, Inequality, and Growth,” by Jonathan D. Ostry, Andrew Berg, and Charalambos G. Tsangarides, IMF Staff Discussion Note, February, 2014 , here; and “Inequality and Unsustainable Growth: Two Sides of the Same Coin?,” by Andrew G. Berg and Jonathan D. Ostry, International Monetary Fund, IMF Staff Discussion Note, April 8, 2011, here.] Their studies found income inequality to be the most highly correlated factor, and to be a consistently “robust and powerful” determinant of growth. 

A few months later in 2014, Standard & Poor’s (S&P) issued a report unequivocally concluding that “too much inequality can undermine growth.” This report seemed to have been prompted mainly by the IMF studies, but it surveyed other information as well. [“How Increasing Income Inequality is Dampening U.S. Economic Growth, and Possible Ways to Change the Tide,” S&P Capital IQ, August 5, 2014, here.] Primarily, firms like S&P rate the earnings prospects and riskiness of securities. It is therefore noteworthy for Wall Street securities analysts to sound such an alarm, especially since it repudiates the neoclassical presumption that distribution lacks macroeconomic significance. That S&P reached this conclusion should not be surprising, however, for there is no other reasonable explanation for the facts. The explosive growth of top 1% real incomes and the steady decline of bottom 90% real income fr more than 30 years necessarily implies a steady transfer of money to the top.

The Dynamics of Redistribution

To date, income inequality has rarely been explained in terms of money transfers. The macroeconomic impacts of inequality cannot be properly understood, however, without taking into account the redistribution of money. It is true that the income gap will vary considerably with changes in qualitative supply-side factors, such as labor union strength, technological change, globalization of markets, trade agreements like NAFTA and the Trans Pacific Partnership (TPP), education, skill development, and so forth. Inequality increases when factors such as these enhance corporate profits, export jobs, or restrain the growth of wages.

Income and wealth inequality by definition, however, are characteristics of the overall distribution of an economy’s money supply throughout the population. These various direct “causes” of inequality determine and direct the flow of an economy’s money, but it is the total redistribution of the money supply in all of these flows which determines whether an economy is growing or declining. The IMF economists phrased it nicely when they suggested that income growth and the redistribution of income are “two sides of the same coin.”

The Quantity Theory of Money (QTM)

Economic historians have traced the QTM back to the 16th Century, and more recently to the Scottish philosopher/economist David Hume (1711-1776) and the British economist Henry Thornton (1760-1815), but more recently the development of the concept has been attributed to the British economist Alfred Marshall (1842-1924) and especially the renowned American economist Irving Fisher (1867-1947). The basic principles are rather straightforward — indeed the fundamental proposition states a tautology. However, major difficulties in its application have led to untenable conclusions, leaving this valuable tool in limbo for many years. An underlying reason for that, I would argue, is the fundamental problem the QTM shares with the neoclassical and Keynesian income models — it has failed to take into account the distribution of wealth and incomes. 

The starting point is the “Equation of Exchange,” today generally attributed to Irving Fisher, which says:

(1)    MV = PY

Where: M is money, V is velocity, P is the average price level, and Y is real income (GDP). [This formulation can be found in the summary of lecture 15, “The Demand for Money,” by Yamin Ahmad, here, Econ 354 – Money and Banking, posted at the University of Wisconsin – Whitewater, 2011 ff., here.] The “equation of exchange” is an expression of the exact correspondence between the value assigned to all transactions in a year (PY) and the nominal value of the money used to compensate for these transactions (MV). This relationship is a tautology, because the value assigned to the transactions is defined as the amount of money expended.

Velocity (V), as Ahmed puts it, is “the number of times per year that a dollar is used in buying the total amount of goods and services produced in the economy”:

(2)   V = P x Y /M

This equation expresses the number of times the money supply “turns over” in a year, as money circulates in exchange for goods and services. Similarly, annual income is expressed as:

(3)   Y = M x V /P

Of course, statistics exist for all four of these variables, and as Fisher opined a century ago, they are fairly precise statistics.  [“The Purchasing Power of Money, its Determination and Relation to Credit, Interest, and Crises,” by Irving Fisher (1911), Preface to the First Edition, the Online Library of Liberty, here.] Despite the tautological, definitional nature of the basic formulation, however, the framing and use of the QTM creates some problems: 

Problem #1

To understand the consequences of the QTM, much depends on what is understood to be the nature of “Y”: I have pointed out in this blog that neoclassical theory is based on the presumption of a long-run “equilibrium” in which all money saved is fully invested and put to use.  To heterodox economists, however, the “long run” never arrives. GDP overstates “goods and services produced in the economy,” because it also includes great quantities of excess profits and economic rent, which are compensation paid above and beyond the real production and capital costs of purchased goods or services. There is never a state of full employment equilibrium, but instead a continuous state of disequilibrium. The implications for the QTM of this perspective are clear: Equation #3 will always produce an inflated impression of how well an economy is actually doing. 

This perspective can be visualized hypothetically: In the extreme hypothetical case that (Y) consists of 90% rent, the result would clearly be the depression from hell. Consumers would only be getting 10% of the goods and services they ostensibly paid for, money would be rushing to the top, and Irving Fisher’s nightmare scenario of a “debt-deflation depression,” if his theory is sound, would be in full swing. [Irving Fisher, Booms and Depressions: Some First Principles, 1st published, Adelphi Company, 1932, Kindle edition, 2011.] Regardless of how the depression played out, in any event, income inequality would have exploded to inconceivable levels. The QTM assumes zero rent, so it would be oblivious to this outcome.   

Problem #2

Sometimes “Y” is denoted as “T,” representing the total “volume of transactions” or, variously, the “number of transactions” [“What is the Quantity Theory of Money?,” by Reem Heakal, Investopedia, here]. This gives rise to a conceptual issue that must be guarded against: It is erroneous to think in terms of anything other than GDP, or other suitable measure of national income, for “Y” in the QTM.  Heakal’s formula is specified as follows:

(1)    MV = PT

Any definition of “T” that represents “the number of transactions,” however, would improperly introduce an index of the number of transactions as a proxy for the dollar amount of all transactions (GDP). Of course, for M, P, and T must all be comparable (measured in dollars) or the formula becomes meaningless. More importantly, specifying the income variable as some sort of index nullifies the velocity factor, reducing the equation to the observation that the purchasing power of the money supply is the reciprocal of the average price level. But that fact is a tautology — true by definition — so the QTM has no explanatory value if the actual velocity of money is factored out. (The velocity of transactions is a meaningless concept.)

Problem # 3

The typical assumption has been that the velocity of the money supply is fairly constant over time. To assume a constant velocity has the same effect as introducing an index of income (T) instead of its actual value (Y): it reduces the formula to the underlying proposition that the price level is directly determined by the volume of money. As Heakal puts it:

The quantity theory of money states that there is a direct relationship between the quantity of money in an economy and the level of prices of goods and services sold. According to QTM, if the amount of money in an economy doubles, price levels also double, causing inflation (the percentage rate at which the level of prices is rising in an economy). The consumer therefore pays twice as much for the same amount of the good or service.  

Basically, I would submit, that part of the QTM is a tautology, a mathematical certainty. This formulation makes no reference to the key variable — velocity; and ignoring the implications of velocity leads immediately to mischief, as Heakal reports:

In its most basic form, the theory assumes that V (velocity of circulation) and T (volume of transactions) are constant in the short term. These assumptions, however, have been criticized, particularly the assumption that V is constant. The arguments point out that the velocity of circulation depends on consumer and business spending impulses, which cannot be constant.

If we presume that velocity is constant, the formula is modified as follows:  

(1)    MV = PY

(2)   Y = M x V /P

                      and, if V = k, then             (3)  Y = k (M/P)

Removing the velocity as a variable makes income a function entirely of the money supply and the price level. Whether it is mainly income or prices that rise in response to increasing the money supply was the “great debate” between the Keynesians and the Austrians (Friedrich Hayek) in the early 20th Century: The Austrians argued that increasing the money supply would increase prices, not income. I always thought the Austrians had a decent argument, but that’s beside the point: Plainly, understanding how the velocity of money changes with changes in the money supply would greatly influence the outcome of that debate. To merely presume a constant velocity of money erroneously over-simplifies the QTM.  

Problem #4

This leads directly to an even bigger problem: The reality is that the velocity of circulation depends upon, and in fact is an inherent characteristic of, income distribution. We get into immediate trouble if we imagine, as Haekal’s discussion implies, that the velocity of money is somehow equivalent to the velocity of an index of transactions. All transactions are not equal in terms of their effect on velocity, and hence, on income. Transactions involving larger amounts of money, by definition, represent higher levels of income: But they also, by definition, create greater increases in the velocity of money. 

The reason it is erroneous to think of the number of events (T) as a proxy for total income (Y) in the QTM,  although perhaps not obvious, is straightforward:

Velocity is determined not just by the number of events, but also by the size of events. And the size of events is integrally related to the distribution of income.

For example, if $3 million is used to purchase 100 new automobiles, its velocity is much greater than if it is only used to purchase 100 cans of soup. Therefore, to compute the aggregate velocity of the money supply it is not enough just to count the number of “events.” 

You might object: “So what? People are always buying soup and cars, and many other things as well: Why isn’t the number of events a reasonable proxy for the total of aggregate economy-wide expenditures?” It probably would be a reasonable approximation if income distribution was more or less constant, but with income transferring to the top, more and more money has been rapidly concentrating in the hands of fewer and fewer people. The assumption made by Irving Fisher and Milton Friedman and others has always been that the velocity of money is relatively constant; but by making that assumption, economists have effectively presumed a reasonably constant distribution of income, thus assuming away the implications for income growth of inequality growth.  

This brings us to a very significant, and (so far as I know) previously overlooked, observation:

The degree of inequality in the distribution of money throughout the population controls the velocity of its circulation, thereby constraining the growth of income and the ultimate allocation of resources and products.

This point can be pinned down to a logical certainty:

  • Varying the amount of money, that is, the size of the money supply, affects the value of the money because the amount of money, all else equal, directly determines the average price level;
  • However, that is the only consequence of varying the amount of money. Doing so does not affect velocity: Hypothetically doubling the money supply while holding all else unchanged simply doubles all prices; and halving of the money supply merely cuts all prices in half. Only the value of money changes, not its velocity;
  • Apart from the volume of money, the money supply’s only other characteristics are its distribution and its velocity;
  • Therefore, if we change the money supply without holding everything else constant, which is what happens in the real world, we are introducing redistribution of the money supply, and changing its velocity;
  • Even if there is no change in the money supply, the velocity of money must be entirely determined by its distribution. Thus, the distribution and velocity of money that are “two sides of the same coin.”

Put another way, a changing money supply not only changes the amount in circulation, but also redistributes money among the population; and it is that redistribution of money that determines the velocity of money, as well as the nature and the amount of human activity. 

Distribution, it should now be clear, is the controlling factor in an economy’s performance. Statistically, growing income inequality has been consistently shown to depress growth. Now we know why: The properly specified QTM shows that result to be a mathematical certainty. The more any given amount of money is distributed among lower-income groups, the faster its velocity necessarily becomes: For example, $1 million dollars in the possession of one thousand people, each with $1,000, will tend to circulate more quickly than $1 million dollars in the hands of a single individual, for it can be spent one thousand times more quickly on goods and services within comparable price ranges, necessarily increasing the growth of aggregate income. Conversely, government policies that enhance corporate profits and redistribute money to the top necessarily reduce the velocity of money and reduce income growth.

Correctly specified, the QTM shows that these conclusions can no longer be considered a matter of conjecture: Of course, an example can be constructed of a few individuals that are circulating money more quickly than a different, larger group of people; but for the entire population and the entire money supply, such a result would be mathematically impossible.

The fact that redistribution of the money supply changes its velocity can reasonably be understood to be the core macroeconomic trait of income distribution.

More Evidence

As discussed above, the QTM requires that any increase in the concentration of income at the top will reduce the velocity of money and the growth of income. Following the Crash of 2008, the data shows, the velocity of the active money supply declined significantly. This graph from the St. Louis Fed shows the trends in the velocity of M2 money since 1950. [“The Velocity of Money In The U.S. Falls To An All-Time Record Low,” By Michael Snyder, The Economic Collapse, June 1, 2014, here.]


The M2 category includes most liquid forms of money, including cash and checking deposits (M1) plus “near money,” which includes savings deposits, money market mutual funds, and other time deposits, which can be quickly converted into cash or checking deposits. [“Definition of ‘M2,” Investopedia, here.]  As shown in the next graph from the Fed Board of Governors, the upward trend in the supply of M2 was scarcely affected, implying from the QTM equation that rate of income growth was substantially curtailed in the years following the 2008 Crash:


Another graph from the same period showing the “monetary base” reveals the relative futility of the monetary policy that has followed in the years after the crash. [“Monetary Base Definition,” by Tejvan Pettinger, Economics Help, August 16, 2011, here.]


As Pettinger explains: “The Federal Reserve created money to buy bonds from commercial banks. Banks saw a rise in their reserves. However, commercial banks didn’t really lend this money out. Therefore the growth of the broader money supply didn’t change much.” So long as inequality continues to rise, the velocity of money will continue to decline as will the growth of income.


A proper understanding of the QTM substantially changes everything:

(1) Milton Friedman’s theory that the Great Depression was the result of the Fed failing to pump enough money into the economy soon enough must be thoroughly reconsidered in light of its failure to reflect the declining velocity of money and the depression’s increased income inequality;

(2) The failure of the QTM to perform as expected since the 1980s, which caused its abandonment by monetarists, now has a rational explanation;

(3) No longer will opponents of the trickle-down mythology be limited to arguing, a la Hillary Clinton, “We tried that and it didn’t work.” Cutting taxes at the top necessarily increases inequality and reduces growth;

(4) The 2015 Republican budget plans would destroy what is left of our economic growth, ensuring the collapse of the federal government and the economy, and possibly not too far into the future;

(5) Taxes must be quickly raised on the highest incomes, on the largest estates, and on all forms of economic rent, and the revenues productively recirculated down into the economy, if we want to recover and grow properly. 

And so forth. We already knew, or at least suspected, many or most of these things. The QTM tells us that they are a mathematical certainty.

JMH – 3/28/2015 (revised 3/29/2015)

This entry was posted in - FEATURED POSTS -, - MOST RECENT POSTS -, Action Plans, Econ 101, Economics, Perspectives, Wealth and Income Inequality. Bookmark the permalink.

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