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A daily inflation index.

"Inflation," according to authority, "is characterized by a general and widely diffused rise in prices and costs."(1) The objective of this study was to capture this attribute in a daily inflation index that could be constructed from data available in the commodity and financial markets. Therefore, such a index would capture the market's assessment of inflation.

Need for a Daily Inflation Index

The 1981 Economic Report of the President suggested that accurate inflation monitoring indexes are needed:

... in July 1980 the consumer price index showed inflation at zero while the producer price index (PPI) for finished goods showed inflation at an annual rate of almost 20 percent. It is therefore useful to construct measures which better reveal the true cost of inflation.(2)

A study done by William Cullison of the Federal Reserve Bank of Richmond demonstrated that rising inflation was difficult to forecast in the 1970's and diminishing inflation was overpredicted in the early 1980's. Cullison suggested that the sources of inflation forecast error were the result of the inability to foresee supply shocks, the difficulty of modeling the inflation process, and the tendency for actual money growth to exceed the target range in the seventies.(3)

Given the increasing attention that has been focused on the Consumer Price Index for personal and business decision-making, the need for daily inflation information is easily argued. The CPI has been used as the cost-of-living adjustment escalator in major collective bargaining agreements and as a means to index payments from mortgage to rental contracts to alimony and child support payments. It has also figured prominently in the indexation of Federal Government entitlement programs, such as Social Security. A daily index of inflation, therefore, would be suitable for hedgers interested in inflation risks associated with the CPI.

A daily inflation index could also be used as a deflator of various daily indexes such as the S & P 500 and the various Dow averages. Weekly money supply statistics could also be deflated by means of a weekly average of a daily inflation index, thereby enhancing the value of this measure of monetary policy. In addition, various interest rate series could be deflated to determine real interest rates on a daily basis.

Since the Federal Reserve is always interested in timely price information, a daily inflation index would be useful to the Fed in monitoring monetary policy.

The need for a daily inflation index can be questioned in view of the existence of currently available daily inflation-monitoring tools such as the Commodity Research Bureau's Futures and Spot Price Indexes, the Journal of Commerce Industrial Materials Price Index, and the Coffee, Sugar and Cocoa Exchange's now extinct inflation-based futures contract. However, these competing daily inflation monitoring tools are unsuitable in targeting consumer inflation. The CRB Futures Price Index has been found to be heavily weighted towards agriculture; the CRB Spot Price Index displays an unreliable relationship with CPI inflation. In addition, these indexes are calculated using an equal weighting system and geometric mean averaging which precludes empirical weighting for economic significance. The Journal of Commerce Industrial Materials Price Index, although a superior leading index of inflation, includes only industrial commodities and a major portion of the CPI is not captured by its 18 industrial materials. The above three indexes are also all leading indexes of inflation and the proposed daily inflation index will be designed to produce a coincident index. Finally, the CPI-W Futures Contract was unsuccessful because of its design in terms of index numbers rather than in the more popularly understood inflation rate change from a previous period.


More than a dozen monthly series that are available daily, representing commodity prices, interest rates, exchange rates, and other variables that are likely to influence or reflect inflation were compiled and initially analyzed over the period January 1967 to June 1986.

Series requiring smoothing were calculated using the six-month smoothed change calculation developed by Geoffrey H. Moore.(4) In this smoothing method, the rate is obtained by dividing the current month's CPI, for example, by the average CPI for the preceding twelve months and expressing the result as an annual rate. To obtain the annualized compound rate, the ratio is raised to the 12/6.5 power since the 12-month average is centered 6.5 months before the current month. A smoother index results because a single month's index in the denominator is replaced with the average of twelve observations. Thus, the random element in the base from which the change is measured is reduced. This same procedure can be used for a daily series by dividing the current day's index by the average of the index for the preceding 250 working days and expressing it as a compound annual rate (250/125 power or squared) since the 250-day average is centered 125 working days before the current date. These smoothed changes answer the question, "How much higher are prices now than they were on average during the past year?" The twelve-month change calculation answers the question, "How much higher are prices now than they were a year ago?" Hence, in this research, six-month and 250-day smoothed growth rates are used for the CPI and for commodity prices.

Experimental CPI-U (CPI-UX) was selected as the target inflation rate. Experimental CPI is the historical series of the revised Consumer Price Index for Urban Consumers that has been in effect since January 1983 when the Bureau of Labor Statistics changed the homeownership component of the Consumer Price Index to the recommended "flow of services" approach which excluded mortgage interest rates and measured homeownership on a rental-equivalent basis. As shown in Figure 2 comparing CPI-U with CPI-UX, this change substantially reduced swings in the inflation rate thus correcting the wide discrepancy between inflation as measured by the CPI and as captured by the Gross National Product deflator. It was fortunate for this research endeavor that the BLS constructed this "experimental consumer price index" (CPI-UX) starting in 1967 and continues to use this method for CPI-U. This allowed for historical testing of the revised CPI and hence the results of this study are applicable in the future.

Cyclical timing charts of each data series studied were prepared and analyzed to further identify the relationship of components to CPI-UX. Turning points were initially determined by the computer program developed by Bry and Boschan.(5) These computer turns were then accepted or rejected by visual inspection to avoid inconsistencies that may occur because the computer program does not take explicit account of the amplitude of the cycles identified.

Various weighting schemes were investigated for computing a daily inflation index including weighting by relative importance, the National Bureau of Economic Research (NBER) method, and weighting by coefficients of determination.

The theoretically ideal but practically impossible weighting method would have been weighting by relative importance. This method would have entailed locating daily series that would serve as daily proxies of the seven CPI groups and/or expenditure categories and weighting them according to CPI relative importance in a base year. The seven major groups include food and beverages, housing, apparel and upkeep, transportation, medical care, entertainment, and other. Although it would have been possible to find series for some of the items in some groups, there are no daily published indexes for most items measured by the CPI, such as doctors' services, rents, movie tickets, or airline fares, nor could such indexes be easily or cost-efficiently reproduced. Therefore, this method was rejected.

The formal, detailed National Bureau of Economic Research procedure for selecting economic indicators for inclusion in the economy's leading, coincident and lagging indicators was developed by Moore and Shiskin and first applied in 1966.(6) Each indicator is evaluated using six criteria: economic significance, statistical adequacy, cyclical timing record, historical conformity, smoothness, and promptness of publication which includes accounting for the number of revisions. After these categories are scored, they are averaged and used to weight the index, with the components having the highest scores receiving the highest weights. Although this procedure disciplined and systematized the judgment of both the reviewer and reviewee of economic indicators, Zarnowitz and Boschan comment:

... Clearly, any scoring plan, no matter how carefully conceived, will include some subjective or arbitrary elements about which judgments could differ considerably, but these are largely matters of detail which seem unlikely to impair seriously the value of the system as a whole.(7)

It is apparent that the National Bureau method for evaluating indicators requires the keen insight and evaluation of experienced economists. Given the complexity and judgmental nature of the National Bureau of Economic Research method, it was felt that a more empirical and generally applicable weighting procedure should be sought for this research.

It seems reasonable to assume that weighting index components by coefficients of determination (RSQ) will maximize forecast accuracy. R. A. Holmes tested this methodology in his forecast of industrial employment in British Columbia and substantially improved explanatory power from 15 to 92 percent at a six month lead and from 38 to 79 percent at a 12-month lead over the best available alternative.(8)

In this study, correlograms were computed to initially identify components to be considered for inclusion in a daily inflation index. Holmes' empirical method of weighting components based upon coefficients of determination (RSQ) was adopted. Thus weights were assigned to components based upon the coefficient of determination calculated between each daily inflation index component and the six-month smoothed rate of change of the experimental consumer price index.

The daily inflation index was constructed at the Center for International Business Cycle Research. The CIBCR method of composite index construction corresponds closely to that used by the Department of Commerce and described in its Handbook of Cyclical Indicators, 1984.(9)

The goal was to develop an index targeted to experimental CPI-U -- both its rate of change and its price level. The computations of a composite index, however, results in index numbers having their own unique values that are not comparable with actual CPI index numbers or annualized rates of change. The Daily Inflation Index level was transformed by linear regression to exhibit the same scale as the rate of change of the target inflation rate. By using the six-month smoothed rate of change of the experimental CPI-U as the dependent variable and the daily inflation index as the independent variable, the regression equation yielded a measure expressed in terms of rates of change that was directly comparable with the target inflation series' rate of change.

The Daily Inflation Index was also transformed into an index of CPI price levels. One might wish to know the price index that yielded the particular rate of change as one knows when actual data are released. One might also wish to compute the rate over a different time span or one might want to use the underlying index as a deflator.

Although the testing of the new Daily Inflation Index was done with monthly data (averages of daily figures), daily figures for each component and the index were also compiled since 1985. The method of compiling the daily index so that it has the same properties as the monthly index uses averages of daily figures for the 21 preceding working days, which cover approximately one calendar month. For each working day a new 21-day average for each component is obtained, and a new index computed.

The Daily Inflation Index

An extensive examination of the past behavior (1967-86) of commodity prices and various financial rates and indexes has identified those daily series which target the Consumer Price Index. The rationale for the selection of time series for inclusion in the daily inflation index was supported by empirical evaluation considering correlation analysis, cyclical analysis at inflation turning points, and graphical evaluation. The eight component series which were selected for inclusion in Daily Inflation Index are listed below.

The six-month smoothed rate of change was computed for the following series:

Crude Oil Price, West Texas Intermediate

Foodstuffs Price Index, Commodity Research Bureau

Metals Price Index, Journal of Commerce

Textiles Price Index, Journal of Commerce

Gold Price, New York, Englehard

The following series were inverted so peaks and troughs would correspond with peaks and troughs in the target inflation series:

Exchange Rate Index, 15 Countries, Morgan Guaranty

Utility Stock Price Index, Standard & Poor's

The following series was utilized as reported:

Average Yield of Three-Month Treasury Bills

The above listed components were selected because of their significant bearing on inflationary trends either direct or indirect. Commodity prices react quickly to demand and supply factors and directly influence prices of finished goods. Gold prices, exchange rates, utility stock prices and interest rates reflect the market's assessment of inflationary forces and expectations. Five of these eight components rely on broad averages of prices rather than on particular prices. The weights given to the eight components are based on the squared simultaneous correlation between the monthly data for each component taken separately and the CPI-UX rate of inflation during the 1968-86 period. That is, components that were more closely correlated with the target rate received more weight than those that were less closely correlated.

Many sample Daily Inflation Indexes from various combinations of data were constructed and tested historically by compiling them monthly from January 1968 through June 1986. An index, theoretically sound and the most empirically successful of the potential daily inflation indexes tested, was selected as the new Daily Inflation Index (DII). The DII was updated with the results in Figure 1 and accounts for 84 percent of the variation in the consumer price inflation rate from January 1968 through June 1990. Except for the period overlapping the onset of wage and price controls (1972-74), when the DII warned of the failure of the government program, the new Daily Inflation Index performs well as a coincident monitor of consumer price inflation.

With a statistical transformation, the new Daily Inflation Index also closely approximates the Producer Price Index for Finished Goods (PPI-FG) published by the Bureau of Labor Statistics. The Producer Price Index for Finished Goods includes only the prices of finished goods such as automobiles, groceries, and capital equipment, and reflects the selling prices received by business firms. The new index accounts for 86 percent of the variation in the rate of inflation as measured by the Producer Price Index from January 1968 through June 1990.

Applications for the Daily Inflation Index

The applications for the Daily Inflation Index are as a deflator of time series, a short-term inflation forecasting guide, or as a hedging vehicle in the form of a futures contract based on the Daily Inflation Index. The Daily Inflation Index may also be used to monitor worldwide inflation as measured by the OECD inflation index.

The Daily Inflation Index as a Deflator

The Daily Inflation Index may be used as a deflator of various financial and commodity market statistics. The accompanying Figures 4 and 5 detail the results of the S & P 500 deflated by the monthly and daily versions of the Daily Inflation Index targeted to CPI-U index levels. Other stock market indexes (Dow Industrials, Dow Transportations, Wilshire 500, etc.) as well as individual securities could also be deflated as such. The market assessment of real interest rates could be determined by deflating various risk categories of corporate bond yields. Policy makers would especially be interested in deflating the money supply statistics with the weekly average version of the Daily Inflation Index.

The Daily Inflation Index as a Forecasting Tool

The Daily Inflation Index could be used by economists to fine tune short term inflation forecasts. When the CPI is released in the third week of each month reporting the inflation record of the previous month, the Daily Inflation Index has already completed its assessment on an up-to-date basis. For example, in July 1989 CPI-U registered inflation at a six-month smoothed annual rate of 5.0%. Meanwhile the Daily Inflation Index estimate for that month was 4.7% and with over two weeks more of daily data, the DII had already suggested that inflation pressures would subside in August. August's actual CPI-U inflation rate was 4.3% down from 5.0% and the DII estimate was 4.1%. In September. Both indexes, CPI-U and DII, recorded inflation at 4.1%.

A Daily Inflation Index as a Hedging Vehicle

"Central to all the departures from the standard theory is the fact that the market has failed to develop an asset that serves as a satisfactory hedge against inflation."(10) While investments in hard assets such as real estate, oil, or gold may indirectly provide protection from inflation over the long run, a futures contract based on the Daily Inflation Index might be successful as a means of directly hedging inflation risk. Given the growing interest in the addition of commodities and other inflation hedges in investment portfolios, a suggestion for further research would be to restructure the DII with components for which futures contracts are available. Both lenders and borrowers would be able to lock in a real interest rate by using a futures contract based on the Daily Inflation Index. Further, if a firm contracted with its labor union for wages indexed to inflation as measured by the DII, the firm could hedge inflation risk by purchasing futures contracts based on the DII. This hedge would be particularly important if the firm were not able to raise its product prices along with the price level.

The Daily Inflation Index as a Global Monitor of Inflation

United States' consumer prices represent 42 percent of the worldwide inflation of industrialized countries as measured by the 24-country Organization of Economic Cooperation and Development (OECD) Inflation Index. It is expected, therefore, that there would be a positive correlation between the rate of change of the United States CPI-U and the OECD Inflation Index. The actual correlation coefficient (R) was ."787, RSQ = .62 over the period January 1969 through June 1990. Given the makeup of the Daily Inflation Index of financial market variables, most of which are traded in world financial markets, it was hypothesized that the Daily Inflation Index would also correlate well with the OECD Inflation Index. Over the same period, the correlation coefficient for the Daily Inflation Index with respect to the OECD Inflation Index was higher than that recorded by CPI-U. The actual coefficient was .822, RSQ = .68. The accompanying Figure 8 comparing inflation as measured by the OECD, CPI-U and the DII also visually supports our conclusion that the Daily Inflation Index may be considered as good or better a global monitor of inflation as is CPI-U.


1. Geoffrey H. Moore, Business Cycles, Inflation, and Forecasting (Cambridge: Ballinger Publishing Co., 1980), p.214.

2. U.S. Council of Economic Advisers, Economic Report of the President, Washington, D.C.: U.S. Government Printing Office, 1981, p.34.

3. William E. Cullison, "On Recognizing Inflation," Federal Reserve Bank of Richmond Economic Review (July/August 1988) 12.

4. Geoffrey H. Moore, "How Much Inflation Depends on How You Measure It," Inflation Watch (May-June 1982) 7-8.

5. Gerhard Bry and Charlotte Boschan. Cyclical Analysis of Time Series: Selected Procedures and Computer Programs. New York: National Bureau of Economic Research Technical Paper 20, 1971.

6. Geoffrey H. Moore, and Julius Shiskin, Indicators of Business Expansions and Contractions (New York: National Bureau of Economic Research, 1967).

7. U.S. Department of Commerce, Bureau of Economic Analysis, "Cyclical Indicators: An Evaluation and New Leading Indexes," by Victor Zarnowitz and Charlotte Boschan, Handbook of Cyclical Indicators, p. 171.

8. R. A. Holmes, "Leading Indicators of Industrial Employment in British Columbia," International Journal of Forecasting 2 (1986), 87.

9. U.S. Department of Commerce, Bureau of Economic Analysis, "Composite Indexes of Leading, Coincident, and Lagging Indicators: A Brief Explanation of their Construction," pp. 65-70.

10. Philip Cagan and Robert E. Lipsey, The Financial Effects of Inflation (Cambridge: Ballinger Publishing Co.), 1978, p. 11.
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Author:Hiris, Lorene S.
Publication:American Economist
Date:Sep 22, 1992
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