Inflation And Yields: The Evolution Of Gibson's Paradox And The Revolution In Prices, Part II

by: John Overstreet

(Note: In this "Inflation and Yields" series, I am outlining the fundamental relationships between and within yield and price complexes. In Part I of this article, we noted that deflated commodity and producer prices have been highly correlated with equity yields since 1871, in much the same way that producer prices were correlated with bond yields under the gold standard, a phenomenon Keynes called Gibson's Paradox. Is there a connection? Part II looks at Britain. Parts III-V look at America.)

Gibson's Paradox in Britain, 1730-1913

The proportion which the usual market rate of interest ought to bear to the ordinary rate of clear profit, necessarily varies as profit rises or falls. Double interest is in Great Britain reckoned what the merchants call a good, moderate, reasonable profit…

--Adam Smith

There are a few general statements I can make about the period from 1730-1913 in Britain, the period of the conventional formulation of Gibson's Paradox.

First, of the roughly 80 goods I checked from Britain, only one produced a rather clear negative correlation with bond yields, namely potatoes. (Pork does look a little iffy, too, though). Strangely, potatoes were also the most negatively correlated with equity yields in the United States. All of the other goods produced positive correlations over the long run.

Second, very few goods were as highly correlated with bond yields as was WPI itself. I assume that is because individual goods would tend to be more volatile than a basket of goods.

Third, contrary to my expectation, I could not find much evidence that one sector of the commodity complex was more prone to Gibson's Paradox than another. That is, based on raw correlations, I could not see that agricultural goods were more or less prone to a "Gibson effect" than were industrial commodities, for example. Nor could I detect any shift from one group of commodities to another. Even allowing for the relative lack of metals data, this seems to be true.

I also have a hunch that segmented markets are less prone to Gibson's Paradox than are globally integrated markets, but I am not sure. This Gibson effect that I am describing appears to be most pronounced during periods of global integration such as during the 1871-1913 period and the post-war dollar period. In addition, in markets such as Japan and Sweden, where equity and bond yields, respectively, and inflation have deviated from world rates (such as in the 1980s and '90s), Gibson's Paradox does not seem to be as strong.

Whatever the role of globalization, what seems most important in understanding Gibson's Paradox is monetary regimes.

So, I am going to follow Barsky and Summers' division of these regimes from 1730-1913 and then tack on two more periods (1914-1959 and 1960-today) that I have found to be significant in the yield complex as modeled in the equation(s),

EY - DY - 10y + 1y (- CPI%) = 0,

where 'EY' and 'DY' refer to the earnings and dividend yields, '10y' and '1y' refer to long- and short-term bond yields, and 'CPI%' to the rate of inflation.

Monetary Regimes, 1730-present
Period Monetary standard Note
1730-1796 Gold Newton's 'accidental' gold standard
1797-1821 Gold suspended Napoleonic Wars, Cont'l System
1822-1870 Gold Return to gold, growing global convergence
1871-1913 Gold Global gold standard, global integration
1914-1959 Dollar/gold condominium Fed, World Wars, Bretton Woods
1960-today Dollar Bretton Woods II, global reintegration

In effect, I am going to show how Barsky and Summers' structuring of the evidence to show that Gibson's Paradox is necessarily a gold standard phenomenon can actually be turned around to show that it is a 'real prices' phenomenon, so long as 'real prices' are properly understood.

So, first, I am going to show all of the correlations between nominal goods prices and long-term bond yields from 1730-1913 in the UK.

UK correlations by Barsky-Summers periods, nominal prices 1730-1913(Source: Please see Part I for information on sources of data).

British individual price series
Almonds, 1877-1914 Barley, 1730-1914 Beans, 1730-1914 Beer, 1730-1869
Bricks, 1730-1867 Books, 1730-1770, 1796-1869 Bread, 1818-1869 Butter, 1730-1914
Candles, 1730-1869 Charcoal, 1730-1868 Cheese, 1730-1869 Citrus, 1867-1914
Clothing, 1730-1869 Coal (5), 1730-1869 Coal gas, 1816-1869 Coffee (2), 1764-1869, 1846-1914
Copper, 1846-1914 Cork, 1886-1914 Cotton, 1770-1914 Cotton cloth, 1762-1869
Eggs, 1730-1869 Firewood, 1730-1869 Fish (5), 1730-1914* Flax, 1846-1914
Flour, 1730-1869 Fruit & nuts, 1867-1914 Ginger, 1730-1866 Hay, 1730-1914
Hemp, 1846-1914 Housing, 1730-1869 Iron (2), 1782-1914, 1730-1869

Jute, 1846-1914

Lead, 1846-1914 Linseed, 1846-1914 Linen cloth, 1730-1868 Maize, 1846-1914
Lamb, 1730-1869 Beef, 1730-1914 Pork, 1730-1902 Milk, 1730-1914
Nails, 1730-1868 Nitrates, 1730-1804 Oatmeal, 1730-1868 Oats, 1730-1914
Lamp oil, 1730-1869 Olive oil, 1846-1914 Opium, 1861-1913 Palm oil, 1846-1914
Paper, 1730-1869 Peas, 1730-1902 Pepper, 1730-1861 Petroleum, 1863-1914
Pewter, 1730-1864 Potato, 1730-1914 Raisins & currants, 1730-1914 Rice (2), 1730-1868, 1848-1914
Rubber, 1871-1913 Rye, 1730-1860 Salt, 1730-1869 Shoes, 1730-1869
Silk, 1730-1914 Soap, 1730-1869 Shovels, 1733-1866 Stockings, 1730-1868
Straw, 1730-1866 Suet, 1730-1869 Sugar (2), 1846-1914, 1848-1914 Tea (2), 1730-1869, 1848-1914
Timber, 1730-1914 Tin, 1846-1914 Tobacco, 1744-1914 Vinegar, 1744-1864
Wheat, 1730-1914 Wheat flour, 1730-1869 Wine & spirits (2), 1730-1869, 1871-1914 Wool, 1730-1914
Wool cloth, 1730-1869      

As you can see, during the first, third, and fourth periods, the Gibson effect is quite powerful, especially in the 1871-1913 period when virtually the entire world was on the gold standard, even allowing for changes in the composition of the data.

But, because commodity prices deflated by CPI are strongly correlated with equity yields since 1871, it is also necessary to compare deflated prices.

UK correlation btwn deflated goods & consol yield, barsky-summers

There are two interesting things to note about this chart.

First, the Gibson effect is still fairly distinct in 1871-1913, even though we have deflated these prices by CPI, reflecting the sharper bounce in producer prices relative to consumer prices.

Second, the 1797-1821 period during which Britain went off the gold standard has significantly stronger correlations for prices deflated by CPI than for nominal prices in every single instance. By itself, that does not prove anything, but it does jive conveniently with the notion that it is real prices that are critical.

There is nothing too earth-shattering about this so far. It simply tends to show what was already well-established: that price levels were correlated with the consol yield. There is some limited indication that deflated prices are more correlated with yields when a metallic standard is suspended.

What about commodities?

Unfortunately, I had also hoped to find that this would be more apparent among primary commodities, but I found no clear evidence of that. Indeed, comparing CPI and WPI by period tends to show that CPI was more highly correlated with bond yields.

Correlation nominal UK WPI CPI Sauerbeck vs consol yield Barsky-Summers

It is only in the long-term comparisons where the strength of WPI shows itself.

WPI CPI consol yields UK 1730-1913

Also it appears to manifest itself (although not overwhelmingly) in longer-term estimations of the individual price series.

Most of the price data either concludes in the 1860s or begins in the 1840s, so the Barsky-Summers periodization does not fit perfectly with the shape of the data. Using periods that better conform to the topography of the data produces marginally better evidence that primary commodities are more prone to Gibson's Paradox, although not strong enough to be especially convincing. At any rate, the correlations generally remain positive for nearly all of the price series from this perspective.

UK correlations nominal by data period

For the few items for which there is data stretching across the entire span, primary commodities appear to fare better.

correlations nominal long-range individual goods UK

Iron, cotton, raisins, timber, and wheat have the strongest correlations, while butter, beef, pork, milk, potatoes, and wool have the weakest correlations. On it's own, this is not exceptional, but it does appear to conform to the notion that the closer a good is to being in a state ready for consumption, the weaker the Gibson effect.

I have to note, in passing, the unexpected inverse correlation between real wages and the long bond and wholesale prices.

UK yield, nominal WPI, real wages 1730-1914

Because inflation is often attributed either to commodities or wages, we will have cause to discuss the question of wages again in the context of the American experience.

I would like to have looked at British equity yield and price data, but neither seems to be as reliable or comprehensive as the US data prior to 1926, although a number of attempts have been made.

estimates UK dividend yield 1825-2010

So, let's conclude our treatment of British data with the simple acknowledgement that virtually all goods, with very few exceptions, were correlated with bond yields from 1730-1913. And, if both Adam Smith was right in the quote at the beginning and my interpretation of the yield equation is valid, we might expect the rate of profit to have generally traced bond yields, as well.

The question is, what happened to Gibson's Paradox after 1913?

At this point, we can turn to the much more reliable and increasingly abundant American data for an answer.

Disclosure: 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.