Correlations between Money Supply, Inflation and GDP

With high inflation impacting almost everyone both in the developed and developing countries, there’s a discussion about its future course. There is the “Team Transitory” suggesting inflation is about to subside and those that think the price increases will continue for much longer, perhaps for many years. The discussion has been going on for about a year now and has luminaries on both sides of the isle. In the US perhaps the most well-known are Nobel laureate Paul Krugman for “Team Transitory” and former Harvard president Lawrence Summers for the ”Higher for Longer” team.

Bloomberg consensus is for inflation to fall more rapidly than in historical precedents.

Milton Friedman has famously said that that “Inflation is always and everywhere a monetary phenomenon”, but we know that short outbursts of inflation can be attributed to other factors, such as temporary imbalances in food and energy markets. Hence the distinguishment between core and headline inflation. It is not that black and white by any means.

In this post and analysis I wanted to establish some baseline position – to what extent inflation (as measured by the CPI index) is correlated with money supply expansion? I was also interested in the fact, whether increased money supply can help economic growth – as measured by Real GDP. Then, I have looked at another effect – can inflation positively impact money creation? In the end, to be thorough, I looked at all the possible combinations of these variables. The data for the analysis comes from St. Louis FED website (FRED). I took December 1959 as the earliest common starting point for M2 Money Supply, CPI index (headline and core) and Real GDP. I have run correlations between annualized changes of the variables – for different combinations of the length of time the change is measured for the correlated variables and delays of the starting points of the measurements. I think it will be best to explain the logic behind my approach looking at an example. The following table contains correlation coefficients for two variables: M2 Money Supply and Core CPI. In the columns (labeled 1 through 36) we have the length of time (in calendar quarters) for the measurements of changes of both the M2 and Core CPI. In the rows (labeled 1 through 20) we have the delay (in calendar quarters) of the start of measurement of the dependent variable (here: the Core CPI) vs. the independent variable (here: the M2).

To make the example even clearer: if we take the intersection of column ‘8’ and row ‘8’ it will include, among many others, the following data:
– M2 annualized increase between Dec 1970 and Dec 1972 (8 quarters of measurement) correlated with,
– Core CPI annualized increase between Dec 1972 and Dec 1974 (8 quarters delay).

An intersection of column ‘8’ and row ‘7’ included, among other data points, the following data:
– M2 annualized increase between Dec 1970 and Dec 1972 (8 quarters of measurement) correlated with,
– Core CPI annualized increase between Sep 1972 and Sep 1974 (7 quarters of delay).

Table 1. Correlations between M2 Money Supply and Core CPI (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

The table is the result of the longest possible dataset combination for the starting periods of Dec 1969- Jun 2022 (the first 40 quarters are needed for the formation of the longest measurement period). So, for the ‘1’/’0′ and ’36’/’0′ correlation results we correlate 210 datapoints in both data series, but for the ‘1’/’20’ or ’36’/’20’, just 190 datapoints, due to the 20 quarters of delay.

The thick black line separates data that is wholly independent timewise (lower-left part of the table) from data that is at least a bit time-overlapping (upper-right part of the table). We can see it in the examples above: ‘8’/’8′ intersection is non-overlapping, while ‘8’/’7′ intersection is overlapping (the Oct-Dec 72 quarter belongs to both time series in the second example, but not the first).

The table is a heatmap going from the lowest correlations (red) to the highest (green). The rightmost column is an average of the correlations in a given row (heatmapped separately from the table). The lowest row is an average of the correlations presented in a given column (also heatmapped separately from the table and the rightmost column).

We can notice that there’s virtually no correlation (-2%) in quarter-to-quarter changes of M2 Money Mupply and Core CPI. In other words, in a typical quarter, say between Dec 1996 and Mar 1997, the annualized change of M2 had no impact on the pace of change of the Core CPI. However the longer the measurement, the higher the correlations. If we take a 5 year (20 quarter) measurement period and a 5 year delay, the correlations increase to as much as 70%. An example would be a period of M2 increase during the period of Dec 1982-Dec 1987 correlated with the Core CPI increase 5 year later – between Dec 1987 and Dec 1992 (and all other combinations like that between 1959 and 2022).

The results highlighted in bold represent highest correlations for any given measurement period. We can notice that increase in money supply over any given 3 year period has the highest correlations with 3-year Core CPI increases 14 to 19 quarters later, at 68%. This is a rather long term impact: 3.5 to 4.75 years. Overall for all the measurement periods between 1 and 36 quarters the correlations seem to peak with a delay of about 3.5 years (13-14 quarters). We can clearly see that for longer measurement and delay periods there are high correlation between increase of M2 and Core CPI. How about Real GDP? Does the increase in money supply affect the Real GDP? It’s complicated:

Table 2. Correlations between M2 Money Supply and Real GDP (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

The short term correlation is negative (e.g. -29% for the 1 quarter measurement period). Then, with increased delay, correlations switch to positive, then back to negative again. My hypothesis is that it works as follows:
1) initial relatively strong negative correlation is due to a reactive nature of the FED and the financial system. When RGDP growth is slow or slowing down, monetary policy becomes looser, which results in higher growth of monetary aggregates (“money printing”)
2) money creation impact the economy positively over the next several (4-6) quarters – a positive impact on RGDP growth from increased money supply.
3) the effect partially reverses over the following 6-8 quarters, as the economy establishes a new equilibrium.

Please note, that this process can also work in an opposite way – FED slowing down the economy that is growing too fast – but my perception is that this was less common (I haven’t checked the data, though). It is also possible that this line of reasoning is totally flawed – the strength of correlations is quite weak anyway.

We can also notice, that any potential impact on Real GDP seems to be substantially weaker than impact on the CPI. Average correlation in Table 2 is 7% (bottom right corner), while average correlation in Table 1 is 58%. It seems that money supply has more than 8 times stronger impact on inflation than on the GDP – at least in the analyzed period and given the methods used.

Let’s look at another set of correlations. Does inflation impact the money supply?

Table 3. Correlations between CPI and M2 Money Supply (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

It seems that it does. The average correlation in this table is 35% – weaker than M2 -> Core CPI correlation, but much stronger than the impact of M2 on Real GDP. It is mostly coming from the overlapping periods – upper right corner, lower left correlations peak at relatively modest 36% for ’12’/’12’ and ’16’/’16’ combination of measurement period and delay period. So, how can we understand these results? It seems that money supply and, by extension, monetary policy is not independent from the level of inflation. If inflation is high, M2 will be somewhat high as well. The impact seems to linger for at least 2-3 years, perhaps longer.

The hypothesis here is that if inflation gets too high, the FED and the banking system cannot decelerate the money supply as fast as they would like to. If inflation is ~10% and RGDP grows by ~2% annually, perhaps it is difficult or detrimental to manage the financial system so that it delivers only a 4% M2 increase. The data suggests that the level of inflation, at least in the past, informed (correlated with) the level of future money supply increases. That may mean that instead of the preferred 4% M2 increase that would be consistent with 2% RGDP growth and 2% inflation, the FED has to, temporarily, opt for a 6% or 8% growth of the money supply for several quarters, even when they are in a tightening mode.

Overall this analysis of the past supports, to some extent, the team “Higher for Longer”. There seems to be a moderate correlation between past money supply increases and future inflation – for many subsequent quarters. The annualized M2 increases have been 13.7%, 9.3%, 5.9%, 1.7% and -1.3% for the past 12, 8, 4, 2 and 1 quarters to June 2022. It is only in the past 2 quarters that the Money Supply started to stabilize, decelerate and decrease. However, the overhang of the money creation of the past 3 years seems to be substantial.

Higher than average inflation is far from certain outcome. If money supply decreases for several more quarters, as it did recently, it would be a braking force. We would have a tug-of-war between the effects of money created in 2020-2021 and money supply extinguished or stable in 2022 and beyond.

Addendum:

The following table presents the average correlations (lower right corner) of all 12 combinations between variables (M2, Core CPI, headline CPI and RGDP).

Table 4. Summary of correlations between 4 macro aggregates (1959-2022)

Source: St. Louis FED (FRED). See text for detailed explanation of the methodology.

With the exception of the two CPI index cross-correlations, the highest correlation is between M2 as an independent variable and Core CPI (dependent): 58%. The lowest correlation is between Real GDP as independent variable and M2 as a dependent variable: just 3%. This is ironic and perhaps a little bit sad. The full quote from Friedman was: “Inflation is always and everywhere a monetary phenomenon in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output.” On the one hand GDP growth does not seem to inform/impact future Money Supply increases (and it should), while Money Supply seems to inform/impact future inflation growth (while it better shouldn’t, or should to a lesser extent).

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Bonds & Money Supply

Over the past week I have noticed several voices from respectable investors or investment managers that the expected returns on bonds are finally attractive. See the thoughts of Jeffrey Gundlach’s and Ben Carlson’s.

The biggest risk to (nominal) bonds is, obviously, inflation. The latest figure for the US is for the month of August and is as high as 8.3%. It has come down from the four decade high of 9.1% in June. That’s quite a bit higher than recent yields for Treasury bonds, which are generally in the 3.70%-4.20% range for maturities between 1 year and 30 years. Quite simply, the inflation is generally expected to come down substantially, towards the 2% mark, as the FED is very serious about fighting the dragon.

Not everyone agrees. Larry Summers, who was the Secretary of Treasury under Clinton and President of Harvard afterwards warned recently: “If we’re going to bring down inflation, you likely need a policy more restrictive than the policy that’s contemplated by the markets or the Fed. The Fed continues to be excessively optimistic.” There you have it. FED is tightening at a fastest pace in several decades, some think it has gone too far, others think it will not be enough. The thing is, Larry Summers was generally right being concerned about too much money being created/given away, so one should definitely listen to him as a valid side in this discussion.

I had a look at the data for the money supply (M2), Real GDP growth (RGDP) and inflation (CPI) in order to look for some hints concerning the future trajectory of inflation. I took long time series of data (since 1960) and have analysed the growth of these aggregates over 10 years. I was mildly surprised to notice that the average 10y growth rate of M2 was 6.9%, RGDP averaged 2.9%, while CPI averaged 4.0% over this period. In a sense, this should be expected: the M2 should increase with the growth of the economy, and the “excessive” M2 growth should be reflected in the average price growth – the CPI index’s. But my surprise was that this relationship was so close: 6.9% = 2.9% + 4.0%. This is likely a coincidence, as the compounded average growth rates over the past 62 years (as opposed to average 10 years growth rates) are slightly off: 7.1% for the M2, 3.0% for the RGDP and 3.8% for the CPI. In any case, the relationship seems to hold. This is how the growth rates look over the past 5+ decades:

What one can notice is that there are two distinct periods. The first one is of monetary tightness (1978-2004), when the 10y growth of the monetary supply was below the combined growth rates of RGDP and CPI. In the second period (2004-present) the opposite is true: the M2 growth rates were in excess of the growth of GDP and price index. Note that these are 10y growth rates, the dates mentioned are the end-dates of a 10y period. What we can notice is that ever since 2004, and more so from 2008, the growth in the monetary aggregate was stronger than the growth of RGDP and CPI. While GDP and prices grew at about 2% pace, M2 grew at 6% or slightly higher for ~15 years. The pandemic exacerbated the disconnect – over the past 2 years the difference between the money supply growth and the GDP+price growth increased to more than 4pp. I have quantified the cumulative monetary ‘overhang’ of the past 14-18 years (since 2004-08) and it amounts to 60-65%. This is the red area between the blue and orange lines. What might it all mean?

It might mean that there has been a lot of money printed over the past decade+ which is more than enough to ‘service’ future GDP and price growth. If the whole overhang is to be ‘used’ over the next decade, we’d get about 5% annual RGDP+CPI growth. With a GDP growth of 2% we’d get a 3% CPI growth, which is not bad. But that assumes no increase in money supply for a decade! Which has never happened and is unlikely to happen. If the money supply expanded at a slow pace of 4% p.a. and the whole overhang were to be reflected in prices, we’d get a 7% inflation for a decade. Not a good environment for bonds – especially nominal bonds.

However, the uncertainty concerning future inflation does not concern the TIPS – inflation protected Treasury bonds. They have offered 2.2% real return at the end of September ’22 (for short term TIPS of 1-5 years – STIP ETF) or 1.86% for the TIP ETF, which holds all of the TIPS bonds (with average maturity of 7.3 years). The STIP ETF had a volatility of 2.6% over the past 3 years, while the TIP ETF – 5.7%. This seems like a safer bet to me given all the uncertainty surrounding future inflation rates.

Caveats:
– the model might be wrong, inaccurate or too simplified. Even though the relationship between M2, RGDP and CPI held closely over the past 5+decades, doesn’t mean it will hold in the future.
– the starting point for the period of excessive money printing (2004-08) might be too early and one should only look at the past several years. If one took the monetary overhang only since the start of the pandemic, it is just ~17% and the potential for future inflation is much smaller.

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