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The Tathagata has no theories.

--Siddhartha Gautama, the Tathagata

In a recent article, I wrote that Larry Summers and Paul Krugman were wrong about the relationship between "bubbles," specifically stock (SPY,DIA,QQQ) bubbles, and disinflation, because of the simple fact that P/E ratios have always, under all monetary regimes, been positively correlated with disinflation. Therefore, to argue that bubbles saved us from deflation and may be a necessary evil in a fight against chronic stagnation is a highly improbable proposition. If bubbles cause disinflation or are created by the same conditions that cause disinflation, any policy or institutional regime that neglected that relationship or supposed that bubbles were inflationary would be, technically speaking, a hot mess. So would a trading strategy that was waiting for 'reflation' to confirm a bull market, incidentally.

I was somewhat surprised at the reaction to the article, and because there was some hint of impropriety on my part, I thought it was necessary to compose an extended reply. If one can generalize, those reactions seem to have been:

1. The correlation between bubbles and disinflation are statistically iffy. (Thus, the impropriety).

2. Even if there is a correlation, everybody knows correlation is not causation.

3. Everybody knows the causation would have to flow from the inflation side of the relationship to the yield side.

Points two and three were sometimes fused within a single comment, without elaboration or any sense of the lurking potential of a contradiction.

I would like to respond to these claims by sharing the thinking behind that article and the data that suggests to me that the correlations are real and significant, whether causation can be determined or not. For readers who are less interested in my demonstration of the relationship between yields and inflation as such, they may want to skip to the sections at the end.

From Great Stagflation to Great Stagnation

When I composed the original article, I felt that the argument that Summers had kicked off already ran against the grain of conventional narrative (that we are recovering from an abnormally severe cyclical downturn), that my critique of his formulation was even more out of left field, and that it was best to avoid petty differences about definitions and so forth and focus on the things-in-themselves insofar as that was possible. Fortunately, it was an argument about secular trends rather than annual gyrations, so that permitted a degree of simplification.

His point was that apart from cyclical fluctuations, there was no inflation to speak of over the course of these bubbles. 'Despite' the bubbles, as he argued. To quote: "Inflation was entirely quiescent. So, somehow, a great bubble wasn't enough to produce any excess in aggregate demand."

(click to enlarge)Great Stagflation to Great Stagnation

The 'despite,' the 'even though,' the "somehow" is the point I challenged him on, rather than his generalization about inflation, and I focused on stocks.

About a year ago, I began to write a series of articles exploring the relationship between yields and inflation. It was called, cleverly, "Inflation and Yields," and it comprised twelve articles covering the relationship between long- and short-term bond yields, the earnings and dividend yields, and commodity, producer, consumer, services, and high- and low-technology goods prices over the last three hundred years. Suffice it to say, it is, all told, a complicated web of relationships.

For all of that complexity, which I was not brave enough to condense into a single position before, I nevertheless feel quite confident in making the following two points in defiance of the (unsubstantiated? unproven? unexplained? unaccounted for?) assumptions Summers and Krugman have about the relationship between stocks and inflation:

1. The earnings yield (E/P) is highly correlated with inflation.

2. Therefore, "bubbles" in equities (if we define them as high valuations determined primarily by a rise in stock prices) should coincide with disinflation.

Most people, of course, assume that inflation is highly correlated with bond yields, and I thought that a couple of charts, the two below, comparing the stock yields to bond yields, commodity prices, and a cyclically adjusted rate of inflation would draw out that relationship adequately without losing the forest for the trees, "trees" being the nuances I will get into below.

(click to enlarge)

(click to enlarge)

I did point out that the relationship between the earnings yield and [real] commodity prices was stronger than between that yield and inflation, and that that had something to do with the transition from the classical depiction of "Gibson's Paradox" (which emphasizes absolute price levels) to Fisher's emphasis on the rate of change of prices.

For example, where I wrote,

"The relationship between commodity prices and the earnings yield goes back as far as we have reliable data for the earnings yield, and it appears to go back centuries before that....What is somewhat newer is the connection between inflation and the earnings yield. That only goes back a little over a century and is part of what Friedman called the shift 'from Gibson to Fisher.' It is also, incidentally, much stronger than the relationship between inflation and interest rates,"

I felt that was enough to acknowledge that there was more to the story without undermining what I felt and still feel is a perfectly worthy summary of things in point (1) above. Perhaps it is necessary to explain why I said that the connection between the earnings yield and inflation is "much stronger" than that between interest rates and inflation.

We will get to the correlation coefficients in a moment, but I want to point out first that this statement has to be taken in the context of the nature of the yield complex, which is that yields appear to have a natural tendency to cluster around one another but they also appear to have a quite specific way of doing so. If it is true that they have this tendency to "cluster" (correlate, if you insist), one might expect that if one of these yields has a tendency to correlate with inflation, all of them might be expected to. And, that is true. We will also see that when we look at the structure of the yield complex, it suggests that equity and bond yields play an equal role in assimilating to (and/or determining) inflation. Even so, I believe the data suggests that the earnings yield "sets the tone" (leaving aside for now the content of that formulation) for the other yields.

Here is how I draw the connection between the earnings yield and inflation. It is at once simple, complex, and improbable.

Gibson's Paradox 2.0

First, the earnings yield has always (1871-present) been highly correlated with real commodity and producer prices. Keynes noted that nominal producer prices had been highly correlated with nominal interest rates from 1730-1914, and I have shown that that was true for the majority of commodity prices, too. My account (note: not explanation) is that producer prices had always been highly correlated with the broad spectrum of yields, but that after the Fed was established to "stabilize" interest rates and provide an "elastic" currency, interest rates veered from this relationship, while the long-term inflationary bias of the Fed shifted the relationship from nominal producer/commodity prices to "real" prices. Another way of saying that is that nominal prices prior to the Fed were real prices because the gold standard had been neutral with respect to inflation.

(click to enlarge)

I also wrote that it appears the institution of a central bank has not only changed the underlying behavior of consumer prices, it has done so in no small part by changing the composition of consumption and the economy more generally. If you compare, for example, cotton prices with commodity and consumer prices going back to 1800, you will see that the rate of change of consumer prices (I feel slightly uncomfortable calling this the "rate of inflation," which strikes me as anachronistic for the gold standard) tended to shadow the rate of change of cotton up until Bretton Woods I. Greater volatility in cotton prices coincided with greater volatility in consumer prices. During Bretton Woods I and II, consumer inflation becomes much less volatile while cotton and commodity prices appear "unreconstructed."

(click to enlarge)

One can assume that the Fed has not done a better job of managing inflation; rather, the composition of consumer prices and the economy has changed in favor of services, which have been more consistently "inflationary" than the prices of capital-intensive goods such as commodities and technological goods. Modern economists refer to this divergence in the inflationary profiles of labor-intensive and capital-intensive goods as "Baumol's cost disease." Unfortunately, they tend to regard it as an inevitable characteristic of the respective markets rather than being a function of modern conditions. Doubly unfortunate, we do not have (or, I have not been able to find) data for services prior to 1937. The period from 1937-1950 confirms (to the extent that it can) my suspicion that inflation at the consumer level has been transmitted chiefly through services. After 1950 or thereabouts, real medical service inflation became routinely positive (except during the two oil shocks in 1973-1974 and 1980), exactly opposite the trend for real inflation in automobiles, for example.

(click to enlarge)

Even if one rejects my account of things, it does not change the fact that producer/commodity prices deflated by consumer prices have been highly correlated with the earnings yield for as long as we have records of the earnings yield. For more information and correlations between bond and stock yields and dozens of commodities and producer price indices going back to 1730, please read "Inflation and Yields: The Evolution of Gibson's Paradox and the Revolution in Prices."

Gibson's Paradox 2.1

All well and good, you may say, but what about the more specific assertion that there is a correlation between the earnings yield and inflation? After all the talk about the changing composition and behavior of consumer prices, can you still say that?

I think so. There is a complex way to demonstrate that and a difficult way. Let's do both.

Below is a chart of fifty-year rolling correlations between the log of the earnings, dividend, and long- and short-term bond yields and a cyclically adjusted rate of inflation, the comparison in the second chart in this article that was intended to be an illustration of my claim that inflation and the earnings yield have the connection I have been asserting.

(click to enlarge)Using the log of the yields and a cyclically-adjusted rate of inflation may sound fishy, but I thought it was superior in its illustration of the relationship, because the behavior of consumer inflation has changed so radically as described above (particularly with respect to its volatility) and it would spare us arguments over whether the economy overheated in this or that year, although John Taylor has raised that issue.

In any case, below is the same type of comparison as the previous chart, but this time using arithmetical yields and the standard, annualized rate of inflation.

(click to enlarge)

In the table below, I make the same comparisons as in the previous two charts, except I divide them more idiosyncratically by what I have labeled as 'monetary regimes' (i.e., gold standard, gold/dollar transition, dollar standard) in previous articles.

Correlations btwn cyclically adjusted inflation and yields (log)EYDY10yr1yr
1872-19130.07-0.23-0.380.19
1914-19590.400.350.150.19
1960-20110.660.690.780.58
1914-20110.320.040.390.21
1872-20110.360.190.410.37
Correlations btwn annualized inflation and yieldsEYDY10yr1yr
1872-19130.09-0.25-0.120.28
1914-19590.420.210.070.12
1960-20110.710.690.650.74
1914-20110.400.140.310.35
1872-20110.32-0.010.260.26

In my opinion, the secular connection with the earnings yield is consistently stronger than any other. Our eyes are not lying to us when we look at the second chart in this article. I think it has to be remembered that the correlations themselves are not the things that we are looking for. Like charts, they are tools that we use to discover and illustrate relationships. And, these suggest that through an incredible amount of historical change, the earnings yield and prices remain strongly linked, especially with respect to commodities, but also in terms of inflation.

An interesting question is why the 1914-2011 earnings yield correlation is lower than the correlations for the 1914-1959 and 1960-2011 periods. I suspect that is because, since the institution of the Fed, the trend of inflation has risen but the trend of the stock yields has fallen, even though the peaks of inflation and stock yields both tend to be lower.

The easy answer, I think, is that the earnings yield and inflation have converged over the last century, with the former falling and the latter rising (see trend lines in chart below). So are interest rates, also from a low level. Even so, they struggle to compete with the consistency of the earnings yield correlation.

(click to enlarge)convergence of yields

If you do the math, you will see that at the level of secular swings, the earnings yield (E/P) is highly correlated with inflation, but that equity valuations like the P/E ratio have also become increasingly correlated with the absolute level of CPI! Indeed, the price/dividend ratio has been strongly correlated with the consumer price level while strongly negatively correlated with the rate of change of that level.

The Dividend Yield Paradox

Ah! So, which is it? Are these yields positively correlated with consumer prices or negatively? Both, but that is the wrong question, I think, which is partly why the "correlation is not causation" reminders tend to miss the point. There has certainly been a structural shift in the trend of prices and inflation (up) and equity valuations (up), and those trends coincide in that they began at roughly the same periods. But, the historical strength of the relationship between equity yields and commodity prices throughout and the consistency of the secular correlations with the rate of inflation strongly suggest that the link between the earnings yield and inflation is primary.

(click to enlarge)price paradox

This sort of paradox, which appears to be almost perfectly inverted to the gold standard relationship (where the dividend yield was positively correlated with CPI and uncorrelated to the rate of change) is certainly confusing, but we can fit this into a more comprehensive model that speaks to this shift.

That model suggests that a sustained period of inflation (such as we have had since 1950), will, all things being equal, reduce the dividend yield and/or the long bond yield and/or raise the earnings and/or short bond yield. It is clear from the tables above that although the dividend yield still rises and falls with the earnings yield, virtually the entire brunt of inflation has been felt as a suppression of dividends relative to stocks and to earnings. It also suggests that, where stocks are rising relative to both dividends and earnings over the long term, a sustained period of inflation will tend to result in a long-term upward trend in interest rates, just as presented in the charts above, but without altering a certain underlying continuity.

In simpler terms, yields have had to adjust to the inflationary bias of the modern American economic system. Although a very good case could be made that interest rates are more highly correlated with inflation over the very long term (what I call a structural relationship), at secular intervals, which is the issue raised by Summers, the earnings yield is critical.

Gibson's Paradox 2.11

In order to illustrate this relationship, I have to go back to how the "Inflation and Yields" series came about. It was originally supposed to be a relatively simple recounting of the change in the way yields behave since the establishment of the Fed. The last yield I had examined was the short-term bond yield, and I noticed that it seemed to respond to changes in other yields in a formulaic way, such that it could be written as,

[a] 10y + DY - EY = 1y.

This equation was just a shorthand way of saying that, under the gold standard, changes in the short-term rate (e.g., the one-year yield) tended to be a function of changes in long-term bond yields and the dividend and earnings yields. For example, a sharp rise in stocks would tend to coincide with rising short-term yields, all else being equal. When I started fooling around with it, I realized that the accidental equation did a decent job of representing movements in each of the variables. Or, decent enough for me. The correlations for each yield were around 0.35-0.40.

After that, I began to wonder what lay on the right side of the equation,

[b] EY - DY - (10y - 1y) = 0,

since it did not actually equal zero.

Intriguingly, the right side of the equation looked a lot like the annual rate of change of consumer prices, with a correlation of about 0.5. By including inflation, however, it lowered the correlations for the yields.

What really blew my socks off was when I applied this equation to the full expanse of history, particularly the Bretton Woods I & II economy.

I quickly realized that,

[c] EY - DY - (10y - 1y) - CPI% = 0,

did a superb job of modeling levels of each of the variables (with most correlation coefficients being in the 0.7-0.8 range) and their spreads (such as the yield curve, the real short-term interest rate, and the equity premium) from 1960.

For a detailed list of correlations by period, please see "Inflation and Yields: The Dollar Equilibrium."

Our interest in the article under fire was the relationship between the earnings yield and inflation, so we can focus on the following formulation:

[d] EY - DY - (10y -1y) = CPI%.

It appears that the earnings yield plays a role equal to the other yields in this equation in 'determining' the rate of inflation. But, the strength and consistency of the relationship between the earnings yield and the rate of inflation relative to the other yields suggests that that is not the case.

If you look at equation [d], because the yield curve spread stays within a relatively narrow range over time, the primary determinant for secular moves becomes the spread between the earnings yield and the dividend yield. As I believe Robert Shiller pointed out, the dividend yield more or less behaves as a moving average of the earnings yield.

So, although it may be far more precise to stick with equation [d] in modeling the rate of inflation, generally it introduces a lot of confusion when it comes to speaking of broad, secular changes, as I tried to do in that Summers/Krugman article.

In any case, all of that hoopla brings us to this final demonstration, which is where we began.

(click to enlarge)

(click to enlarge)

The two charts are the same. The only difference is that inflation has been shifted from one scale to another. Considering the precision of the model for the 1960-2011 period, and it's ability to model yields throughout the last 140 years, this suggests that, as we have already seen, there has been a structural shift, a phase shift, as one reader termed it, with respect to inflation and yields, but that they have settled around a familiar equilibrium. More importantly for us, I think it shows that the connection between the model and the earnings yield, which suggests that inflation is not simply a function of the earnings yield, but operates at the same frequency as the earnings yield. The earnings yield is the decisive element in the model.

Correlations between model and inflation

EY-DY-(10y-1y)

1872-19130.48
1914-19590.46
1960-20110.71
1872-20110.43

I conclude, therefore, that in spite of all the vital and intriguing relationships and historical transitions, the simple claim that the earnings yield is highly correlated with prices, commodity and consumer, suggests that the net impact of a stock bubble would be deflationary.

A final response

In response to the three points that I regarded as representative of the general thrust of the criticism directed towards my original article, I would, therefore, say,

1. Yes, the correlations are a little iffy.

2. Correlation is not causation. Agreed.

3. Inflation causes yields to rise? Okay, but see #1 and #2.

In other words, except for point three, I am broadly sympathetic.

And, I think they almost wholly miss the point.

First, consider Summer's speech and Krugman's lavish support. They clearly imply that stock bubbles should have a net inflationary impact at secular intervals. Certainly, the correlations are more in my favor than they are theirs. Call my presentation iffy, weird, whatever, if you wish. But, there's no way that I can see how one could argue that stock bubbles should have an inflationary impact from the historical data. Surely, skeptics could grant me that much?

Second, with respect to "correlation is not causation." I do not know how to mold a causal narrative around these correlations one way or another. Although many readers said or implied that inflation clearly impacts yields, I cannot share their certainty. Over the last 140 years, we have instances of rising yields coming from a surge in profits as well as from a plateauing of stocks while earnings grow at a constant rate.

If,

x/y = z,

as in this instance (where E/P = CPI%), and both 'x' and 'y' can vary, which side of the equation is more likely to be the causal element? Left, right, or neither? I would think that the lowest probability would be right, 'z,' unless one has a very good idea that 'z' is also determined by multiple factors.

Interestingly, that's exactly what we are debating, isn't it? People appear to be very certain that yields do not cause or even contribute to inflation, even though we evidently have a very poor understanding of how inflation functions. Otherwise, we'd be debating something else, and you wouldn't be reading this. You'd have written the classical economic tome, What Causes Inflation.

And, it's not like I've conjured up some bizarre, obscure, variable in this debate. When Summers was trying to tie together Gibson's Paradox, he had to find a way to connect the nominal interest rate under the gold standard to the real interest rate after Nixon closed the gold window. What was the rickety bridge Summers used to cross from one to the other? Stock yields. It is a mystery to me why he did not notice that that bridge from nominal to real interest rates was itself the bridge between yields and prices, but that is another story.

I am still not 100% sure why the correlation-is-not-causation meme irritates me so. Maybe because it vastly overestimates both the quality of our causal accounts of inflation and our capacity to come up with reliable causal accounts. More generally, I suspect that it is just a sign of intellectual laziness or lack of imagination. How could it be so inconceivable that stock bubbles drove down inflation?

There must be an extensive amount of work on how stocks impact inflation, right?! Well, try Googling, "how do stocks impact inflation?" Apparently, the skeptics are right: the question is so obviously pointless that no one has deemed it worthy of investigation. Even granting that Google has yet to assimilate all information, the failure of the search engine to turn up even one awkward blog post or wonky academic article on the topic, and its insistence that I must mean "how inflation affects stocks," says more than enough.

People who pretend to know one way or another about the influence of stocks on inflation are almost certainly talking out of their hats. That apparently includes Summers and Krugman. Never mind the correlations. What theory is there that says rising stock prices should have a net inflationary impact? I think that is why I am unsettled about how Summers and Krugman have not been challenged to show their homework. What model are they using? What theory are they appealing to? What research suggests that stocks (especially stock bubbles) have a net inflationary impact? Where are their correlations?

So, what are our options in the meantime?

At the end of the day, there are only three solutions to this particular question: either stock markets, notably bubbles, are net inflationary, net deflationary, or neutral. In the absence of any competent account of this relationship, I cannot see why suggesting that they are likely to be disinflationary can be dismissed so easily. If a rise in the P/E ratio or market capitalization/GDP can be regarded as representing a real expansion--not captured by measures such as national investment rates--beyond levels justified by profits and economic activity, might not that result in both rising employment and lowered inflation, thus accounting for the collapse of the Phillip's Curve, which just coincidentally coincided with the phase shift described earlier? Might not a tendency for stock valuations to rise over the last fifty years or so result in bouts of rising capacity utilization in the midst of a long-term decline in utilization?

I don't think I am the right person to be hypothesizing about the different possibilities, but I cannot believe that no one can even conceive of a dynamic (presumably more sophisticated than the ones I am spitballing) that would see at least one channel of causation flowing from equity valuations to the rate of inflation.

Think again about the phenomenal rise in stocks and bonds in the 1980s and 1990s. How is it that that coincided so well with the conclusion of the Great Stagflation and the beginning of the Great Moderation Stagnation? What a strange coincidence! Isn't it possible we have something backwards? And, here we are again in 2013: a stock market boom and worries about deflation.

Some may say, 'correlation is not causation.' Fat Tony says, 'there are no coincidences.' I say, what are the alternatives precisely?

We are not in a state to provide absolute conclusions with respect to how all these factors interact. Prudence suggests that we should eschew fetishizing causality and theory in favor of something like the Buddhist logic of "dependent origination," which deemphasizes unidirectional, linear causality:

Why does one desire? The Buddha says, because of contact with the world. Why does one have contact with the world? Because of desire.

The purpose of this kind of logic is to break the tyranny of both excess skepticism and excess theory in order for the path to become accessible, to see what is actually happening outside of one's preconceptions and prejudices. So, I say, look again at the second and third charts: bubbles are deflationary.

Source: How Do Stocks Impact Inflation?