Entries from May 1, 2020 - May 31, 2020
The quantity theory of wealth, continued
The “quantity theory of wealth” described in the previous post rests on the following propositions:
1) The demand to hold (broad) money is a stable function of income (nominal GDP) and wealth (financial and tangible).
2) A persistent divergence between money demand and the actual stock of money causes changes in income and / or wealth to restore equilibrium.
3) To the extent the income response is small – as predicted by conventional economic models – asset prices / wealth will bear the burden of adjustment.
One implication of the “theory” is that the conventional measure of velocity (i.e. the ratio of income to the money stock) is misleading because it fails to account for the dependence of money demand on wealth as well as income. A fall in conventional velocity – often regarded as a “bearish” development by commentators – is associated with rising not falling wealth.
The previous post showed that G7 broad money demand can be adequately modelled by the simple equation
M = (PY)0.5W0.5/V* (1)
where PY = nominal GDP (P = prices, Y = real GDP), W = a wealth proxy encompassing equities, bonds and housing, and V* = “true” velocity, which is stationary / mean-reverting.
The first chart, reproduced from the previous post, compares the actual stock of money with modelled money demand since the 1960s. The second chart focuses on the last 15 years.
A large positive gap opened up between the actual money stock and money demand during the GFC. “Excess” money balances, on the view here, “caused” the subsequent recovery in economic activity and asset prices.
The gap narrowed significantly over 2009-15, after which it remained broadly stable at a modest level by historical standards until late 2019. The actual money stock was 4% above the modelled level in September 2019.
Growth of income and wealth in recent years has aligned with money growth: M3 rose by 4.7% per annum in the three years to September 2019 while the combined income / wealth measure on the right-hand side of equation (1) increased by 4.5% pa. Wealth outpaced nominal GDP, rising by 5.4% pa versus 3.6%.
Annual M3 growth firmed during 2019 and has surged this year, reaching an estimated 13% in April, the fastest since 1976. With lockdowns reducing GDP and equity prices weakening, the gap between the actual money stock and modelled money demand has ballooned to 15%, not far below a GFC peak of 19% reached in February 2009 just before equity markets bottomed.
A reasonable expectation is that the rise in the money gap from 4% to 15% will be reversed over the next 2-3 years. A fall requires some combination of monetary weakness, a rise in real GDP, higher prices of goods and services and an increase in wealth.
Monetary weakness contributed to the reduction of the gap after the GFC. G7 M3 rose by only 1.4% pa in the three years from February 2009. Similar sluggishness now is unlikely. Post-GFC weakness was driven by banks restricting lending to boost their capital ratios, as demanded by regulators. They are now being encouraged to extend credit to support the economy. QE is on a larger scale than then and is likely to be sustained while fiscal deficits remain wide. M3 growth may remain well above the 4.7% pa average over September 2016-September 2019.
A recovery in real GDP as health restrictions on economic activity are relaxed will make a small contribution to reducing the money gap. The current GDP undershoot (Q1 data) accounts for 2 percentage points of the rise in the gap from 4% to 15%.
This leaves 9 percentage points of the required adjustment from 15% to 4% to be borne by rises in goods and services prices and / or wealth. If the adjustment were shared equally between the two, equation (1) implies that both would need to increase by 9-10%.
G7 goods and services prices, as measured by the GDP deflator, rose by 1.6% pa in the three years to Q4 2019. A 9% boost over 3 years would imply a rise in inflation to 4-5% pa. The immediate impact of the crisis and an oil supply shock are suppressing inflation currently, suggesting an offsetting overshoot in 2021-22. A reasonable base case scenario, therefore, is that G7 inflation will rise above 5% in 2021-22.
Against this backdrop, a 9% boost to wealth would probably reflect increases in equity and / or house prices, with bond prices weakening.
Other scenarios can be considered sharing the burden of adjustment differently between the various factors. If "excess" money fails to lift asset prices / wealth, for example, the implication is an even stronger pick-up in goods and services inflation, to 7-8% pa. Conversely, continued low inflation would suggest an even more bullish outlook for asset markets.
The quantity theory of wealth
G7 annual broad money growth is the highest since the 1970s. The consensus argues that this will not be reflected in strong nominal GDP growth and / or rising asset prices because of a faster fall in the velocity of circulation, which has been in trend decline for 50+ years. The purpose of this note is to point out that the trend fall in velocity has been a reflection of a trend rise in the wealth to income ratio. A faster fall in velocity would imply, over the medium term, a stronger path for asset prices and wealth.
The quantity theory of money, in its income version, is based on the accounting identity
MV = PY (1)
where M = the stock of (broad) money, PY = nominal national (or global) income and velocity V is derived as a residual. Nominal income is usually proxied for convenience by GDP. P is a price index of value added in goods and services production and Y represents real income or GDP.
The identity is transformed into a “theory” by assumptions that 1) causation in the equation flows from left to right, 2) velocity is determined exogenously and 3) velocity is significantly less variable than the money stock. Large changes in money are then likely to cause large changes in nominal GDP.
The theory does not require that a given percentage change in the money stock leads to an equal change in nominal GDP. This applies only in the limiting case when velocity is stationary.
Assumption 3) is supported by empirical evidence. The standard deviation of the three-year percentage change in G7 M3 over 1967-2019 was 12.2 percentage points. The standard deviation of the corresponding change in M3 velocity, derived from equation (1), was 4.5 pp.
Velocity, as noted, has been in secular decline or, equivalently, money has grown consistently faster than nominal GDP. Velocity fell at an average rate of 1.2% pa over the 56 years to January 2020. G7 annual M3 growth is estimated to have risen to nearly 13% in April. If such growth were to be sustained, a reasonable expectation would be that nominal GDP expansion would rise to 11-12% pa.
The Cambridge cash-balance approach to the quantity theory interprets equation (1) as a demand function for money. Money is held as a temporary store of purchasing power to bridge purchase / sale transactions and as a component of a wealth portfolio. The Cambridge economists assumed, for simplicity, that both the transactions and portfolio demands for money were related to income. They recognised that the portfolio demand would also depend on wealth but chose to model this effect as an influence on velocity V rather than allowing for it explicitly.
The first chart compares growth since the 1960s in G7 M3, nominal GDP and a wealth proxy encompassing equities, bonds and housing. M3 has outpaced nominal GDP but lagged wealth. Indeed, the ratio of M3 to nominal GDP approximately doubled in the 55 years between 1964 and 2019, while the ratio of M3 to wealth approximately halved. This suggests that income and wealth have been equally important in explaining rising demand for M3.
The “quantity theory of wealth” is a reformulation of equation (1) to incorporate explicitly the wealth effect on money demand:
MV* = (PY)0.5W0.5 = PYw0.5 (2)
where W = wealth and w = W/(PY) = the ratio of wealth to income.
If wealth rises at the same rate as income w is constant and the equation simplifies to (1).
The second chart compares growth of actual M3 and modelled demand based on equation (2), assuming a constant value of V* equal to its full-period average.
Note that V* in equation (2), which could be termed “true” velocity, measures the sensitivity to money stock changes of income and wealth combined, rather than income alone. Dividing (1) by (2) and rearranging
V = V*w-0.5
showing that “conventional” velocity V is inversely related to the wealth to income ratio w.
The third chart compares the two velocity measures. The secular downward trend in conventional velocity V, as explained, reflects the secular rise in the wealth-to-income ratio. By contrast, there has been no trend in “true” velocity V* over the period as a whole. V* did, however, fall significantly during the tech bust (2000-03) and GFC (2006-09). These declines probably reflected cash “hoarding” due to heightened risk aversion, i.e. an additional demand for money unrelated to economic transactions or wealth. V* subsequently recovered in both cases, though not to prior peaks.
Following its post-GFC recovery, “true” velocity V* stabilised at close to its full-period average over 2013-19. The coronavirus crisis, however, has resulted in another drop, which is likely again to prove temporary.
Equation (2) can be rearranged to solve for the level of wealth W consistent with the current money stock M and nominal income PY:
W = (MV*)2/(PY) (3)
The fourth chart compares growth of actual wealth and the modelled level based on equation (3). Wealth overshot the modelled level significantly during the tech bubble of the late 1990s. The subsequent bust resulted in convergence but no undershoot. By contrast, equity and house price falls over 2007-09 pushed wealth significantly below the modelled level. Wealth has been close to but slightly below the modelled level in recent years but is now undershooting significantly again, reflecting monetary strength and weakness in nominal GDP and equity prices.
The consensus view that high money growth will not lead to an increase in nominal GDP growth and / or asset prices assumes an offsetting increase in cash hoarding. The evidence presented above suggests that episodes of significant cash hoarding are infrequent and temporary. The long-term decline in conventional velocity mainly reflects a rising wealth to income ratio. If the consensus forecast of no rise in nominal GDP growth proves correct, the implication is a stronger, not weaker, medium-term path for asset prices and wealth.
Global monetary update: back to the 1970s
US money measures continued to explode into late April: annual growth rates of M1 and a proxy for the old M3 measure (“M2+”) rose to new post-WW2 highs of 29.1% and 23.3% in the week ending 27 April – see first chart.
Chinese April data released today, meanwhile, showed further rises in annual and six-month growth rates of narrow and broad money as well as the “total social financing” credit measure – second chart. The Chinese pick-up, however, is of garden variety and pales next to US trends.
The US surge partly reflects the scale of Fed intervention: the boost to bank reserves from QE and various lending / liquidity support programmes has amounted to 7.2% of annual GDP over the last 13 weeks. The Bank of England has moved ahead of the ECB in the stimulus stakes, with an injection of 5.3% – third chart.
Based on April monetary data for the US, China and India and an expected plunge in consumer price momentum, six-month growth rates of global real narrow and broad money are estimated to have breached the highs reached ahead of the post-GFC economic recovery, implying the fastest expansion since the early 1970s – fourth chart. The estimates will be refined as additional April money numbers are released, starting with Japan and Brazil this week, but the above characterisation is unlikely to change.
Pessimists argue that the monetary surge is being offset by an even larger fall in velocity. This is trivially true currently but the velocity collapse is likely to prove temporary – it mainly reflects, after all, physical limitations on demand and production due to the shutdowns – while the monetary addition will almost certainly prove permanent: does anyone seriously believe that the current crop of “independent” central bankers will be prepared to argue for a reversal of QE, or even its cessation, as the crisis starts to abate?
An epic battle is continuing between monetary and economic / earnings theories of risk asset pricing. The monetary theory, so far, is winning: who would have imagined that global equity indices would be little changed from a year ago despite collapsed GDP and profits?