*Note: In this series, I am outlining the fundamental relationship between prices and yields. Additional research over the last month has both delayed further installments and compelled me to address the Barsky-Summers thesis somewhat earlier in the series than I had originally intended. In this article, I hope to begin to clear a way to a general construction of the price complex, especially with respect to industrial commodities, its relationship with equity yields, and show how traders and investors can use this to their advantage.*

Since the 1980s, you have not been able to walk out the front door without the postman, the cop walking the beat, or the next-door neighbor saying something about how real gold prices are an inverse function of real interest rates.

I kid. But, it is received wisdom that real interest rates are the driving force behind gold prices. This theory was developed by Robert Barsky, an economics professor at the University of Michigan, and Lawrence Summers, former Treasury Secretary in the Clinton administration and economic adviser to President Obama, in a paper [PDF]. I have often mentioned here, and it is their solution to Gibson's Paradox (the observation that price *levels* rather than the rate of inflation were historically correlated with bond yields). Brad DeLong, who was involved in some capacity with the original paper, recently reiterated this position.

Unfortunately, apart from certain historical episodes, that theory has never held true.

By my reading, Barsky and Summers make at least four fundamental arguments that I would like to briefly examine, after which I will suggest a tentative new approach to Gibson's Paradox in subsequent installments.

Those four claims are as follows:

1. From the early eighteenth century, when Britain (and soon the world) first "accidentally" went on the gold standard (thanks to Sir Isaac Newton), up until the point the world began moving off the gold standard with the establishment of the Fed, price levels were strongly correlated with bond yields.

2. Real gold prices, as just noted, are an inverse function of real interest rates.

3. Real nonferrous metal prices (for example, copper, tin, aluminum, zinc, nickel, etc.) are even more negatively correlated to real interest rates than is gold.

4. Real interest rates are negatively correlated with equity yields.

I have to confess that on this fourth point, I fear I have either read too much into Barsky-Summers or simply misread them. I have never read anyone who mentioned this aspect of their paper, but then again, nobody ever mentions the third point either. The focus is always on the relationship between gold and real interest rates, even though both Barsky and Summers point out that this is weaker than the link between nonferrous metals and real rates.

In any case, if I have either misread or over-interpreted their argument, I nevertheless will hold that equity yields are the key, and that there is some question as to why Barsky and Summers did not take this approach in their subsequent analysis, since they base much of their theory on equity yields and returns from 1872-1913.

But, let's begin with their first argument.

**Gibson's Paradox in Britain**

That is, world price levels and yields were correlated during the age of the gold standard. More precisely, they argue that this was:

a) more true of wholesale prices (WPI) or what we now call producer prices (PPI) than it was consumer prices (CPI),

b) more true of long-term yields than short-term, and

c) more true of the heyday of the gold standard (1820-1913) than for the 1730-1820 period when the gold standard was still consolidating itself.

As you can see below, it does indeed appear that although consumer prices are broadly correlated with consol (bond) yields, wholesale prices fit the bill rather better. In fact, it appears that wholesale prices were more correlated with bond yields than they were with consumer prices.

(Source: WPI data from Roy Jastram's *The Golden Constant*; CPI and bond data from Bank of England)

Gibson's Paradox in Great Britain 1730-1913: Correlation btwn Prices and Consol Yield

Period (per Barsky-Summers) | CPI | WPI | WPI/CPI |

1730-1913 | 0.34 | 0.71 | 0.18 |

1730-1796 | 0.63 | 0.30 | -0.63 |

1797-1820 | -0.45 | -0.29 | 0.60 |

1821-1871 | 0.48 | 0.43 | -0.01 |

1872-1913 | 0.82 | 0.80 | 0.75 |

1821-1913 | 0.61 | 0.82 | 0.73 |

Interestingly, the "real" wholesale price (WPI/CPI) has been falling for nearly three centuries in the UK. There is little commentary that I can find on this phenomenon, except as it may relate to the Prebisch-Singer Thesis (which attempts to account for why raw commodity prices have fallen relative to those for manufactured goods), but I believe this ratio will prove to be a significant element in our understanding of Gibson's Paradox.

In the US, for which I only have the data generously provided by Robert Shiller going back to 1870, the results appear to be the same for that period.

So far, so good.

Let's move on to Barsky and Summer's more famous and original second point, that real gold prices are inverse functions of real interest rates.

**Gold and real interest rates**

Although people sometimes say that their paper compared real gold prices and real interest rates over the last three centuries, actually they only compared them over the course of a dozen years, from 1973 to 1984.

A comparison of the last 140 years shows that there is no direct relationship between the two. The correlation of the real one-year interest rate and real gold prices for this period is actually fractionally positive.

I am unsure why Barsky and Summers did not deflate gold prices using WPI, but over the long-term, using WPI or long-term bond yields rather than CPI or short-term yields, respectively, makes little difference in this comparison.

(Source: Real gold data from Roy Jastram's *The Golden Constant*; real yield data from Robert Shiller)

The British data from 1703-2007 tell a similar story. Real long bond rates are slightly positively correlated with both gold deflated by WPI and CPI, not negatively correlated.

(Source: Real consol yield data from Bank of England; Gold and WPI data from Roy Jastram's *The Golden Constant*)

In that brief historical interval examined by Barsky and Summers from 1973 to 1984, you can just see how real interest rates correlated with gold, and even I have to confess that my eyes "see" a long-term correlation, but it's not there.

**Nonferrous metals and real interest rates**

The third point they made is that real nonferrous metal prices, as measured by the Bureau of Labor Statistics [BLS], are even more powerfully inversely correlated with real interest rates than is gold. Unfortunately, although this may have been true for the 1973-1984 period they analyzed, it does not hold over the long-term.

The BLS WPU102 series only goes back to 1926. It is, as Barsky and Summers hold, more negatively correlated with real interest rates than is gold, but there is only a fractional inverse correlation (about -0.08).

(Source: Real yield data from Robert Shiller; nonferrous metals data from BLS series WPU102; nonferrous metals data deflated by CPI according to Jastram)

In order to take a longer-term look at nonferrous metals, I came up with a rough reconstruction of copper prices going back to the American Civil War. As a member of the nonferrous family, it is highly correlated with the BLS nonferrous series from 1960 to the present, although not as highly as aluminum, lead, or tin.

At any rate, since 1860, real copper prices have been slightly positively correlated with real interest rates.

(Source: Real interest rate from Shiller; copper proxy reconstructed from Federal Reserve price series M0415BUS000NYM267NNBR and M0415AUS35620M267NNBR and World Bank Pink Data; CPI from Jastram)

Looking at the bits and pieces of other metals data over the last two centuries that I have accumulated, I can find little to suggest any relationship at all with real interest rates.

Even if we were to assume that Barsky and Summers were only referring to the period after the gold window was closed in the early 1970s, the correlation coefficients since then are virtually identical to the numbers going back to 1926. I have not come across any evidence that commodity prices have any direct relationship with real interest rates.

Keeping that in mind, let's move on to the last and perhaps most difficult and critical point.

**Equity yields and real interest rates**

Barsky and Summers turn to real interest rates as a substitute for equity yields. As I have written previously, under the gold standard in the United States, both equity and bond yields were correlated with the general price level. In other words, during the gold standard period, insofar as things were effectively priced in terms of gold, the real price of gold was inversely correlated with all (nominal) yields.

For reasons I cannot grasp, they turned to real bond rates, however. As I have shown in the second article of this series, since the 1960s, the rate of inflation and bond and equity yields have functioned along the lines of the equation,

EY - DY + 1y - 10y = CPI%*

which suggests that it is nearly impossible for any yield to simply be a substitute for any other yield. This is especially true when crossing over from bonds to equities or vice versa, and throwing real bond rates in is even more problematic. I can think of no theoretical reason to regard equity yields or (inverted) real bond yields as interchangeable.

Barsky and Summers seem to make the connection through the equity "internal rate of return yield" [IRR], finding that the IRR yield, the earnings yield, and the dividend yield were highly correlated with the price level from 1872-1913. They then dismiss the equity yields as merely "cruder…proxies for real returns," arguing that this correlation of correlations supported their "view that Gibson's Paradox involved the real rate." They seem to have simply substituted inverted real Treasury yields.

Again, the fine relationship that has existed between equity and bond yields and price movements strongly suggests that equity yields are not as "crude" as Barsky and Summers made them out to be. One has to wonder why they did not extend their analysis of gold and metals prices to include equity yields during the 1973-1984 period, if only for the sake of curiosity.

In any case, whether or not Barsky and Summers were indeed arguing that equity yields were inversely correlated with real bond yields or connecting the dots that I interpret them having done, it appears that up until the 1960s, they were negatively correlated -- at least the earnings yield was. Even up until the mid-1970s, it seems as if there was still some kind of relationship, although it was becoming increasingly frayed. Ironically, almost precisely when Barsky and Summers wrote their paper, the connection between real rates and the earnings yield completely broke down.

(Source: Shiller data)

In fact, this breakdown in the relationship has been a cornerstone of the argument by organizations such as the Gold Anti-Trust Action Committee [GATA], who kindly provide the link to the Barsky-Summers paper, that the gold price has been manipulated by Larry Summers himself among others in a nefarious cabal of some kind. But, if that argument were to hold any water, then those who made it would also have to hold that the government is manipulating the copper, zinc, aluminum, tin, and nickel markets, as well, and equity yields to boot.

The original (inverse) connection between real interest rates and the earnings yield, however, is entirely incidental. If one briefly reflects on the history of yields and inflation, it is easy to see why this is so. Prior to the Federal Reserve, inflation was far more volatile than it is now and interest rates far less so.

(Source: Shiller)

Moreover, equity yields, particularly the earnings yield, have always been more positively correlated with the rate of inflation than have bond yields. (The following chart is another view of the surprising way in which bond yields have changed their relationship with inflation and equity yields).

(Source: All data from Shiller, except BAA yields from Federal Reserve)

With an effectively stable nominal interest rate and a highly volatile rate of inflation under the gold standard, that virtually made real interest rates an inverse function of the rate of inflation.

So, the historical negative correlation between real interest rates and equity yields is just another way of saying that equity yields have been positively correlated with inflation. Throwing the Treasury yield into the mix adds nothing from what I can tell.

Suffice it to say, I am perplexed by a number of elements in the Barsky-Summers paper. The most curious thing perhaps is that further analysis of the relationship between commodity prices and equity yields or equity returns would have been a much more profitable line of inquiry, and this seemed to be staring them right in the face, but they dismissed it in favor of real interest rates. On a more positive note, their paper did a great service in keeping the question of Gibson's Paradox alive and identifying the connection to commodity prices.

At any rate, in the subsequent installment, we will try to put the pieces back together on the basis of a relationship between commodities and equity yields.

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*Since having written that, I have come to the conclusion that the rate of change in PPI is a marginally better fit than CPI, but only marginally so.

**Disclaimer: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

**Disclosure:** I am short gold and S&P500 futures.

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