Real Inflation

By: Stephen J. Church | Wed, Aug 30, 2006
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Steve Church is an investment consultant with 20 years of experience with large investors. The following is a synopsis of more complete paper. The full paper is available at no charge to registered users of

Note: This document is a synopsis of the full paper. The key analytical items have been preserved in this synopsis, but there is more detail and commentary in the full paper. The full paper is available at no charge to registered users of

In our paper, "A Recipe for a Depression," we advanced the concept of real inflation. In this paper, we develop a formula for extracting monetarily-induced price change from total price change. We call monetarily-induced price change "real inflation."

The popular description of monetary policy may be based on a faulty understanding of inflation. In order to evaluate monetary policy, it is important to understand that inflation is only one of the components of price change. Monetary policy targets price change as expressed by the CPI. It does not target inflation.

The Research

This paper develops a process for calculating monetarily-induced price change. We also identify the goods, services, and assets that are likely to be the best available indicators of monetarily-induced price change.

We test one of these items: real estate. Our test shows that real estate prices track monetarily-induced price change very close to the level that we expect and no less reliably than those prices track the CPI. In effect, our calculation of inflation may be a better predictor of long-term real estate price change than is the CPI.


Our research indicates that inflation is approximately 3% to 4% per year higher than the CPI. The mathematical expression of this relationship will be investigated in this paper.

The Price Change Equation

The price change equation is presented below. This equation contains an expanded calculation of price change and identifies key components of the equation.












Price Level at Time 0



Price Level at Time 1



Price change caused by money expansion



Price change caused by quality changes



Price change caused by productivity improvements



Price change caused by population growth



Price change caused by substitution effects(where sub is negative)

Over time, the change in price level became synonymous with "inflation". However, inflation is recognized as a monetary effect. The change in price level includes many effects which are not monetary effects.

The original consumer price index calculation included all of the effects except for the substitution effect. Since the calculation was based on a fixed basket of goods, the substitution effect did not exist. Here is the equation:








In 1998, the BLS adopted the recommendations of the Boskin Commission and made two primary changes to the calculation of the CPI: 1) it began estimating the price impact of quality changes; and 2) it adopted a substitution adjustment that allowed the substitution of comparable goods when price changes improved the value of one good versus the value of the other good.

These adjustments converted the consumer price index from a price change measure into a cost of living measure. Clearly, the cost of living should not be adjusted upward for improvements in the quality of goods. Also clearly, living involves making choices and substitution of comparable goods to lower the impact of price changes is part of living.

In a June, 1997 letter from Katharine Abraham, Commissioner of the BLS, to Jim Saxton, Chairman of the Joint Economic Committee, we find an estimate of the total price change effect of these two components:

"The commission, using empirical evidence and the members' own judgments about the magnitude of these biases, concludes that the CPI overstates the true cost-of-living change by 1.1 percentage points per year."

So, removing (1+q) from the original CPI calculation and adding (1+sub) causes a 1.1% per year reduction in "cost-of-living". Though some skeptics may disagree, we believe that the BLS has the correct mathematical formula for a cost of living calculation. The important information for us is that the price change calculation includes components for quality-induced price increases and for substitution-induced price decreases.

The CPI is now a different mathematical expression of the underlying price change components. The new CPI produces a price change estimate that is correct for evaluating the "cost of living." It also produces a number that is on average approximately 1.1% lower than the previous CPI. Here is the mathematical transformation:





Old CPI *




The new CPI brings adjustments that the economics community appears to have ignored. The most obvious is that the standard real interest rate calculation produces a real interest rate that is approximately 1.1% per year higher than it was prior to 1999.

To identify the other components of the total price calculation, we relied on a presentation from David Stockman to the Federal Open Market Committee on December 18, 1989. The presentation identifies the other two components included in our calculation of price change: productivity and population growth.

Here is a quick way to understand the price equation. The money-induced price effects(m) are the result of price changes caused by a change in the money available. After identifying all of the other effects(q, prod, pop, and sub), the remaining price change is primarily monetarily-induced price change.

Essentially, these calculations are derived from the work of Irving Fisher and applying the Quantity Theory of Money. The Quantity Theory of Money holds that the sum of the nominal product (Price(P)*Quantity(Q)) equals the sum of the available money (Money Supply(M)*Monetary Velocity(V)). If you hold the available money constant, then you can evaluate the effect of other changes on the price level.

In general, the absolute size of the individual effects, other than m, is small. Based on known information, Piscataqua Research estimates that the sizes of the non-monetary effects on price change average approximately:


-2.0% to -2.5% per year

Population Growth:

-1.0% per year


-0.5% per year

Quality Improvements:

+0.6% per year

The monetarily-induced price change could exceed the Consumer Price Index, or the cost of living, by about 3% prior to 1999 and 4% after 1998. This evaluation of the price equation shows that "inflation" is significantly higher than the Consumer Price Index.

After reading many Federal Reserve speeches and documents, including the presentation by David Stockman and his team, it is clear that the Federal Reserve views its policies in the context of total price change.

The rest of this paper tests the price change proposition. We will show that our description of inflation appears to be a better estimator of inflation and provides a more robust interpretation of monetary policy.

Real Inflation

Our concept of inflation is monetarily-induced price change. It is closest to the generally understood meaning of inflation. However, it differs from observed price change because it is only one of the components of price change.

We call the monetarily-induced price change: "real inflation." The chart of our estimates of monetarily-induced price change is shown below.

In general, monetarily-induced price change is substantially higher than the consumer price change. The productivity data explains the majority of the difference between the two measures.

The next chart shows real interest rates when calculated using real inflation and the CPI.

The two measures produce two very different economic analyses. The standard inflation adjusted real interest rate would indicate a generally benign Federal Reserve exercising reasonable monetary caution. Other than during the 1970s and from 2001, the Federal Reserve has appeared to run a reasonably cautious monetary policy in the context of the standard definition of real interest rates.

During the 1960s and 1970s, Federal Reserve policy, as evaluated using real interest rates based on real inflation, appears to be more consistent with the observed CPI history. The real inflation adjusted real interest rate shows constantly aggressive monetary policy. CPI inflation rose dramatically during the 1960s and exploded higher during the 1970s. The rise in inflation is consistent with what one would expect under these circumstances.

The high levels of real interest rates in the 1980s calculated using the CPI price change is inconsistent with the high debt expansion during the mid-1980s. Consumers would not willingly grow debt in excess of 10% annually from 1983 to 1988 if real consumer interest rates were as high as 8%. The real inflation-based calculation shows that real interest rates were lower than the standard calculation shows.

Since 1992, the real-inflation adjusted series would again provide a more reasonable explanation of rising asset prices and debt levels when considered in the context of high productivity change. It appears that the Federal Reserve has run an aggressive monetary policy for the last 15 years and a very aggressive monetary policy for the last 7 years.

Overall, real interest rates calculated with our crude calculation of real inflation provides a more robust analysis of economic and financial outcomes than real interest rates computed using the Consumer Price Index. The next section provides evidence that "real inflation" is an accurate measure of monetarily-induced price change.

Proving Real Inflation

This section identifies the best goods, services and assets for measuring inflation. It also shows that our "best" asset for measuring inflation appears to follow a long-term price pattern more consistent with real inflation than with CPI inflation.

The first step in our test involves identifying a good, service, or asset whose price change over relatively short periods of time should be primarily influenced by monetarily-induced price change. The second step involves testing the price changes of the best good, service or asset for this purpose against real inflation and the CPI.

We began with a long list of goods, services and assets. We included the general categories tracked in the Consumer Price Index; well-known "inflation hedges" such as gold and commodities; and stocks, bonds, real estate, timberland, art, etc.

We then applied the following criteria for determining whether a good, service, or asset could be useful for testing the hypothesis:

Using these questions, we quickly developed a short list of possibilities. The following items appear to offer the best opportunities to measure monetarily-induced price change:

Overall, these five goods, services and assets provide an excellent set for determining inflation. Food and oil are the least reliable for relatively short-term measures of monetarily-induced price inflation. Education is a great potential to test, but the data set is not readily available. Gold is also a great potential, but it responds to general money inflation on a world-wide basis rather than specifically to dollar money inflation.

Real estate is clearly the best of the five available choices. It is as good as education and gold. It also has the benefit of reliable and readily available data. It should respond directly to monetarily-induced price inflation from changes in the supply of US dollars. Finally, price response lags should be relatively short in relation to changes in the supply of money.

Expectations for Real Estate Price Change

In general, the price of existing housing should respond directly to monetarily-induced price change. The only negative to real estate is that it is a depreciating asset and subject to obsolescence. This implies that deferred capital investment would on average be required after the purchase of properties. However, we would also expect that existing properties increase in value with additional investment.

As a result, we would expect that actual price appreciation for existing homes would be less than monetarily-induced price inflation. From this perspective, we can estimate how monetarily-induced price change should correspond to actual price change. The estimates on page 5 can be used to develop an estimate.

Expected Price Change of Existing Housing

Real Inflation:

CPI + Adjustments


Population Growth

+1.0% per year


Growth in Housing Stock:

-1.0% per year



-1.0% per year


Total Price Change:

Real Inflation - 1.0%

The price of the existing housing stock should respond directly to real inflation. The annual growth in the housing stock should be comparable to the annual growth in population. The monetarily-induced price increase should then be diminished by the depreciation on housing.

Our expectation is that housing price change should be about 1.0% per year less than real inflation. Since real inflation is approximately 3% to 4% higher than CPI price change on an annual basis, we expect that housing prices will appreciate at a rate of 2% to 3% greater than the CPI price change. It is also important to remember that this calculation should be 1% to 2% prior to 1999 because of the different CPI.

The Evidence

The evidence shows that existing home prices have escalated at a rate approximately equal to our rough expectations of price change.

The price change of existing housing is the result of inflation and is a hedge against inflation. However, real estate prices actually increase at a rate below inflation instead of at a rate above inflation. Real estate does not preserve inflation-adjusted value because it depreciates in value from use and obsolescence.

Our conclusion: house prices change as we predicted they would if our theory of inflation was correct. Our best test of our hypothesis shows that our equation is probably the proper equation for calculating monetarily-induce price change. Though we expect that others can fine-tune our estimates, we expect that they will reach similar conclusions.


The next charts show the relationships between price change when compared to CPI inflation and our calculation of real inflation. We use median price changes as reported by the National Association of Realtors, our calculation of real inflation, and CPI price changes as calculated by the Bureau of Labor Statistics.

The chart below shows that existing home prices have changed on a basis almost exactly as predicted. Home prices outperformed during the 1970s because of high formation of

new households as the baby-boomers entered the market. By the late 1980s, the housing stock had caught up to the household formation of the baby boomers. Price changes had fallen close to the 1.0 to 2.0% of CPI and -1.0% of real inflation levels.

Price change in housing remained near the 1.0% to 2.0% level versus CPI and the -1.0% level versus real inflation predicted until the Federal Reserve began extraordinarily aggressive monetary policy in 2001. Since 2001, the cumulative effect of aggressive monetary policy has caused unusual levels of investment in pre-existing homes.

We also compare these same relationships on a 5-year rolling basis. The following chart very clearly shows that our measure of inflation, real inflation, offers a much more reliable calculation of monetarily-induced price change than the traditional CPI.

Other than the obvious five year periods where demand/supply and monetary effects predominate, the real inflation calculation fluctuates nicely with a +/-1.0% range around our expectation of -1.0%. The evidence is reasonable that "real inflation", as we define it, is a good definition of inflation.

The traditional calculation based upon the CPI produces much less reliable evidence and indicates that there are other effects at work if the CPI is the correct measure of inflation.

"Real inflation" has met our test and appears to have passed it. We identified an asset that should respond well to real inflation. We determined the expectation of how it should respond. We tested the information. Our test provides strong evidence that "real inflation" adequately describes monetarily-induced price change.

A Reinterpretation of History

Under the assumption that this mathematical description of inflation has validity, how would we re-interpret the monetary history? We will use two primary charts in this reinterpretation: real inflation; and real interest rates based on real inflation. The first measures overall monetarily-induced price change. The second measures the aggressiveness of monetary policy.

We are also able to interpret these charts in comparisons to the reputations of the four Federal Reserve Chairman that have been the primary participants during the last 50 years: Chairman Martin(ending 1971), Chairman Burns(ending 1978), Chairman Volcker(ending 1987), and Chairman Greenspan(ending 2006).

The chart below shows 5-year levels of real and CPI inflation. It is important to realize that the CPI is two mathematically different formulas before and after 1998. After 1998, one must add at least 1% to the CPI level in order to have a mathematical expression of price change that is mathematically equivalent to the CPI prior to 1998.

Using this chart, real inflation averaged 6% during the first two-thirds of Chairman Martin's stewardship; during Chairman Volcker's term, and during the first decade of Chairman Greenspan's term. Real inflation averaged 7% or more during the last few years of Chairman Martin's term, during Chairman Burns' term and during the last 8 years of Chairman Greenspan's term. Only Chairman Burns and Chairman Greenspan have had a 5 year period where real inflation compounded near 8% or higher.

The next chart shows real interest rates and provides information on the aggressiveness of Federal Reserve monetary expansion.

From the perspective of interest rates in relation to real inflation, Chairman Volcker is again the most conservative Federal Reserve Chairman. Chairman Martin and Chairman Burns were equally aggressive as Federal Reserve Chairmen. Though the first decade of Chairman Greenspan's term shows a conservative approach, the last 8 years show the most aggressive monetary policies of the last 50 years.

During the last 6 years, short interest rates have averaged 5% per year less than real inflation! This measure is far lower than the -3% average during Chairman Burns' years. During the last 6 years, interest rates compared to CPI inflation have averaged as low as during Chairman Burns' years. There is nothing in the modern U.S. economic record that compares with the aggressive use of monetary policy during the last decade.


We have developed and analyzed a new mathematical expression of "inflation": real inflation. Our expression aids in a robust analysis of the economic and financial effects of monetary policy.

Our expression of inflation also allows the user to differentiate price change by the type of good, service or asset and to develop methodical relationships to monetarily-induced price change. A price change model using real inflation and productivity levels could provide a much better planning tool for anyone making financial and economic decisions that are subject to price change. It allows price change differentiation.

Our expression of inflation identifies that the economics community does not appear to have adjusted its evaluation of monetary policy to be consistent with the mathematical transformation of the CPI. Economists are comparing real interest rates prior to 1998 with real interest rates after 1998 as if they are the same mathematical expression. This comparison is mathematically incorrect!

Finally, our mathematical expression of inflation allows a re-interpretation of the monetary history. It shows that the Federal Reserve has historically been much more aggressive than previously interpreted. It shows that Chairman Volcker was the most conservative Chairman. It also shows that Chairman Greenspan was at least as aggressive during the last 7 years as Chairman Burns ever was during the 1970s.

It appears that real inflation has been close to 8% per year during the last few years. Based on our calculations, real inflation only exceeded this level during the 1970s.

Real interest rates based on real inflation have been lower during the last 7 years than at any other time during the last 50 years. This observation helps to explain why debt levels have risen as high and as fast as they have during the last few years. Since real interest rates based on this measure have not been lower, we would expect faster debt expansion than at any other time.

Real inflation could provide an alternative analytical avenue for economists. It is easily converted into reliable statistics useful in developing robust economic analyses. In every way that we could determine, our statistic appears equal to or better than the CPI as an expression of inflation.



Stephen J. Church

Author: Stephen J. Church

Stephen J. Church, President
Piscataqua Research, Inc.
Portsmouth , NH 03801

Piscataqua Research, Inc. was founded in 1992 by Stephen J. Church. Steve has provided investment consulting service to wealthy investors and large pension funds since 1986. We provide investment supervisory, investment management or investment consulting services to clients with sizable assets.

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