MACROECONOMIC PRICE INDEXES
Roy H. Webb and Rob Wil’l’emse*
Price indexes allow one to compare the average During World War I the BLS collected data on the levels of prices at different times. By summarizing pattern of consumer expenditures and retail prices. information on price trends, the indexes help The data were used in adjusting wages of workers people adjust for inflation when they choose how for wartime inflation. After the war, the “cost-of- much to save, spend, work, and invest. Government living” index2 was regularly published; by one ac- officials, as well as voters, use price indexes to count, more than half the settlements in wage evaluate economic policies. In addition, both private disputes in 1923 were based on that index.~The cost- contracts and government programs often use a par- of-living index was the predecessor of the Consumer ticular price index to adjust payments for inflation. Price Index (CPI). In short, the subject of price indexes was of great interest even before the sustained inflation of the last EXAMPLES OF EARLY USES half century. That prolonged period of inflation has One of the first uses of a price index in the United in turn stimulated more interest in the subject of price States arose from the substantial inflation of the indexes. And that additional interest has in turn led Revolutionary War period. In order to maintain the to the use of economic and statistical theory to make real, or inflation-adjusted, pay of soldiers, officials in the indexes more accurate and more relevant. Massachusetts tracked the price of acquiring a market basket of thefollowing goods: 5 bushels of corn, 68% pounds of beef, 10 pounds of wool, and.16 pounds THE MAJOR INDEXES of leather. The basic idea was simple: the percent- Consumer Price Index age increase in the price of the market basket would have to be matched by the same percentage increase The CPI is the most widely used barometer of the in soldiers’ wages to compensate for inflation.’ average price level. The index is watched closely by The federal government began collecting national workers, retirees, participants in financial markets, price statistics in the late nineteenth century to and government officials. The CPI’s prominence as evaluate the effects of tariffs. A particularly notable an inflation measure is reflected in its widespread use achievement was the production of a SO-year as an escalator for wages and benefit payments. Many historical series of wholesale prices by the federal collective bargaining agreements, other private con- Bureau of Labor. In 1902 the Bureau began to tracts, social security benefits, and federal and state regularly publish a Wholesale Price Index that could assistance programs allow for increases in wages and be used to track recent data. That price index was transfer payments tied to increases in the CPI. the forerunner of the current Producer Price Index Elements of the federal income tax structure, in- (PPI); the agency is now known as the Bureau of cluding tax brackets and personal exemptions, are Labor Statistics (BLS) and remains the primary also adjusted to reflect movements in the CPI. In source for aggregate price data in the United States. addition, the CPI is used to adjust other economic statistics, including hourly and weekly earnings and median family income, for price changes. l Webb is a vice president and economist at the Federal Reserve The CPI is expressed as the ratio of average prices Bank of Richmond;Willemse is a financial analyst at Corestates Financial Corp., and was an assistant economist at the Federal currently paid by consumers to the average prices Reserve Bank of Richmond when he contributed to this article. paid in a reference, or base, period. Since items vary The authors received helpful comments from Paul Armknecht, in importance in personal budgets, both the Dan M. Bechter, Timothy Q. Cook, Dennis Fixler, Thomas M. Humphrey, John Marcoot,Ray Owens, Thomas Tibbetts, numerator and denominator of the ratio are weighted and Kim Zieschane. The views and ooinions exnressed in this article are solely d&e of the authors and should not be attributed to any other institution or person. a The index was not a true measure of the cost of living, however. While it did measure the prices of goods and services, it did not 1 This and many other early uses are described in W. Erwin include other outlays such as taxes and interest. In addition, there Diewert, “The Early History of Price Index Research,” National was no consideration of goods and services provided by govern- Bureau of Economic Research Working Paper No. 2713, 1988. ment, nor of fringe benefits provided by employers.
22 ECONOMIC REVIEW, JULY/AUGUST 1989 awxagfl. For example, since most people spend more speaking, however, the entire record is a set of several on housing than on socks, the price of housing has time series of fixed-weight indexes that are spliced a larger weight in the index than the price of socks. together. Since one set of expenditure weights is not More precisely, the CPI is an estimate of the ratio used to calculate the CPI for every date, it is pos- of the current price of a fixed market basket of con- sible that a user viewing different dates will use in- sumer goods and services of constant quality to the dex numbers based on different market baskets. price of that market basket in a specific base period. Calculating inflation from 1980 to 1988, for ex- (See the Appendix for algebraic formulae for the CPI ample, the 1980 index would be based on the and other price indexes discussed in this 1972-73 Consumer Expenditure Survey and the article; in addition, numerical examples are also 1988 index would be based on the 1982-84 survey. presented.) This market basket is designed to repre- Once the expenditure weights are determined, the sent the average expenditures of a certain segment computation of the CPI for each month requires data of the population at a certain time. The CPI is ex- on the current prices of items in the market basket. pressed as an index number. In 1988 the value of To obtain the price data, the,BLS sends agents to the CPI was 118.3, which means that the market many retail establishments in different parts of the basket cost 18.3 percent more in 1988 than it did country to obtain prices for about 100,000 items each in 1982-84, the base period. month. The BLS then uses the individual prices to -Two versions of the CPI are published monthly calculate CPI statistics at the local, regional, and by the BLS. They are published with a lag of roughly national levels. In addition to the
FEDERAL RESERVE BANK OF RICHMOND 23 Chart 1
CONSUMER PRICE INDEX 1913 -1945
b 1915 1920 1925 1930 1935 1940 1945 has grown rapidly in the United States during the used by businesses as material inputs. Finished goods twentieth century.4 will not undergo further processing; that category in- Producer Price Indexes are presented in a number cludes consumer goods as well as capital equipment. of ways based on different classifications of goods. Indexes are also calculated for special commodity The classification by Stage of Procesing divides goods groupings, organized by similarity of end-use or into three main categories: cmde, intermediate, and JiniYzedgoods. Crude goods are items that are enter- ing the market for the first time, that have not been Table I manufactured or fabricated, and that are not sold COMPOSITION OF directly to consumers. They include items like grains, PRODUCER PRICE INDEX livestock, cotton, and crude oil. Items like lumber, DECEMBER 1986 fertilizer, machine belts, and yarn are intermediate goods. They have been processed but may require Manufacturing 83.6 percent further processing, or may be complete but will be Mining 7.2 percent Agriculture 5.1 percent 4 The BLS is studying price indexes for services. It is possible that experimental indexes could be introduced for those services Electric Power 3.4 percent for which the quantity produced can be most accurately measured, such as transportation and communication. It would Other 0.7 percent be much more difficult to produce meaningful indexes for ser- vices such as medical care, banking, and insurance where the quantity and quality produced is difficult to measure accurately. Source: Monthly Labor Review, August 1987, page 14.
24 ECONOMIC REVIEW, JULY/AUGUST 1989 Chart 2
CONSUMER PRICE INDEX CHANGES Percent 1945-1988 16
8
6
1945 1950 1955 1960 1965 1970 1975 1980 1985
material composmon. J3xamples mclude the H’ls tOr received m primary markets for a group of items had industrial commodities and for farm products. Also, increased 0.17 percent since 1982, with the prices there are producer price indexes for the net output of those items weighted by the relative’values of 1982 of different industries and their products. shipments. The PPI is calculated from approximately 70,000 individual prices. Like the CPI, it is constructed Price Measures from the National Income using fixed weights for relatively long times. The and Product Accounts weight for each individual component is the relative In the process of estimating GNP and its com- value of shipments of that item. Periodically, the ponents, the Bureau of Economic Analysis (BEA) also Bureau of the Census conducts industry surveys that estimates corresponding price measures, including the BLS uses to update the value weights. Among fixed-weight price indexes, implicitpricedeflators and the most important surveys are the Census of chain price indexes. Manufactures, the Census of Agriculture, and the To calculate GNP and its components, the BEA Census of Minerals, which includes oil and gas pro- estimates the dollar value of spending for current pro- duction. The latest surveys, conducted in 198’2, have duction. It then calculates what that spending would been incorporated in the PPI as of 1987. Previous have been if current quantities had not been valued value weights, which were used from 1976 through at current prices, but rather at prices paid during a 1986, were based on Census results of 1972. reference (base) period. The ratio of the two spend- The PPI for all commodities in 1986 was 100.17. ing totals, current dollar spending divided by con- That is a concise way of saying that prices producers stant dollar spending, is an implicitprke deflator.
FEDERAL RESERVE BANK OF RICHMOND 25 Implicit price deflators are computed for GNP, for deflator, which can result from changes in relative broad expenditure categories such as consumer quantities produced between two particular quarters.s spending, and for more narrow categories such as Chart 3 shows the GNP fixed-weight price index consumer spending for stationery and writing and the implicit price deflator for the last ten years. supplies. Note that they both reveal the decline in inflation In the Appendix it is shown that an implicit deflator in the early 1980s and the gradual rise since 1986. is unlike the indexes discussed above in two impor- The implicit deflator is more volatile, however, as tant respects. First, instead of using historic weights exemplified in 1986. a deflator uses current quantities as weights. Second, an implicit deflator is not a pure price index, since CAUTIONS changes in the index may reflect other factors than Price indexes are invaluable tools; however, no changes in prices. In fact, when two periods are com- single index gives unambiguous answers to all ques- pared (neither being the base period), the calculated tions. Some important cautions should be kept in change in the deflator depends both on the price mind. change and also on any change in the relative quan- tities exchanged. Quality Change An implicit deflator can therefore behave differently Ideally, one can use price indexes for different dates from a fixed-weight index. For example, if people to measure the average price change of goods and spend their money for different products, that by itself services of constantqua&y. Therefore if a price in- does not immediately affect the CPI or PPI, which crease of an item is due solely to quality improve- are not affected unless individual prices change. The ment, then that price increase should not affect the implicit deflators, however, can be -very much index. affected when relative quantities change. To provide To adjust for significant quality changes, statisti- users with better data on price movements, the BEA cians sometimes use a practice known as linking. That procedure estimates a price change for a new also publishes fixed-weight price indexes for GNP product by the price change of a similar product for and many of its components. The weights are the which quality did not change. In other instances amounts produced in a particular base period, which statisticians estimate the amount of quality change at present is 1982. by the cost of producing it. For example, car Since the National Income and Product Accounts manufacturers routinely provide the BLS with cost are used to study the economy over long periods of data for new features or additional items that were time, there is also a disadvantage to the fixed-weight once optional before becoming standard equipment. price indexes: the farther from the base period, the Thus if a new audio system added one percent to less representative will be the base-period weights. a car’s cost of production and the new car price rose The BEA therefore provides another alternative, a three percent, the quality-adjusted price increase chinprice in&x. It uses past prices for weights, but would be two percent. with the previous quarter as the base period. The While those adjustments are clearly better than no change between two adjacent quarters is therefore adjustment for quality change, many observers determined solely by price changes. In that respect believe they do not go far enough. As Robert J. it is like the fixed-weight indexes. Unlike a fixed- Gordon has put it: weight index, however, shifting expenditure patterns The typical product, whether automobiles in the 1920% will be incorporated in the chain index with only a TV sets in the 19.50s or electronic calculators in the one-quarter lag. 197Os, experiences after its invention an initial period of declining price, as its manufacturers spread the fixed cost Although the differing measures of price levels may of development over more and more units sold. Then, as seem confusing, they usually tell similar stories over the product becomes mature, there is less opportunity for time. For example, between 1959 and 1988 the im- plicit price deflator for GNP and the GNP chain price 5 Although not regularly published, another type of index ap- index each grew at a 4.9 percent annual rate; the peals to many economists. It is simply the geometric average- that is, the square root of the product-of an index based on GNP fixed-weight price index grew at a 4.2 percent historical fixed weights and an index based on current weights. rate. Quarterly changes in the statistics, however, can For the case of GNP, one could use the average of the GNP fixed-weight price index and the implicit price deflator. This type diverge substantially; when they do, it is best to dis- of index was labeled an Ideal index by Irving Fisher, who was count extreme movements in the implicit price one of the first to note many of its advantages.
26 ECONOMIC REVIEW, JULY/AUGUST 1999 Chart 3
PRICE MEASURES OF GROSS NATIONAL PRODUCT QUARTERLY CHANGES: 1Q 1979 - 4Q 1988 (Compound Annual Rate) Percent 14
6
1979 1980 1981 1982 1983 1984 i 985 1986 1987 1988
efficiency gains to cancel out increased wages and other assumed to be zero. Over the last few decades, costs, so prices begin to rise. Three aspects of the CPI however, the price of computing has fallen substan- cause it to understate quality improvements and to over- tially; the price indexes therefore overstated the state price movements. First, the use of obsolete weights from decade-old expenditure surveys tends to place too average inflation rate. Recently, the BEA has re- little weight on modern products where price increases are vised the national income and product accounts back relatively slow. Second, new models and products are to 1970 to account for computer prices, which they typically introduced in the index much later than the date now estimate have been falling by 1.5 percent per when their sales volume becomes important. And finally, year. In contrast, the CPI is not revised once it is the linking procedure, by far the most common quality- adjustment technique used by the BLS, tends both to published;’ it will therefore never be revised to treat new products as if they were mature products and to account for the price declines found by the BEA for ignore performance improvements.6 personal computers. Other durable goods may also have higher quality For example, consider the difficulty in measuring levels that are not accurately reflected in price in- the price of computers. For many years computer dexes. For example, Gordon has calculated that pro- price changes were not included in the PPI, nor in ducers durable equipment prices grew by 66 percent the CPI’s market basket, nor in the-national income from 1947 to 1983; in contrast, the BEA’s official and product accounts; the price change was simply
6 Robert J. Gordon, “The Consumer Price Index: Measuring 7 Since the CPI is so frequently used to adjust contractual Inflation and Causing It.” T’e Pub/it Znteresr (Spring 1981), payments and government benefits, revising historical values pp. 129-30. could lead to complex revisions of liabilities and payments.
FEDERAL RESERVE BANK OF RICHMOND 27 deflator for that category grew by 383 percent.8 The that flaws in the measurement of the cost of huge difference is accounted for by Gordon’s de- homeownership in the CPI contributed to its sharp tailed quality adjustments for many items using increase.” At that time the CPI’s cost of home- sources other than the BLS or BEA. In some cases ownership contained two main components, the his estimates were based on conventional methods house purchase price and the mortgage interest cost, such as linking; in other cases, however, he went as well as other expenses such as taxes, maintenance, beyond usual methods when new models performed and insurance. That method overweighted the cost much better than old ones.9 of homeownership for two reasons. First, it treated Problems in measuring quality change are espe- the investment in a house much like the purchase cially severe for services, which are of growing of a nondurable good. Second, it confused the pur- importance in the economy. Traditional methods to chase price with the method of financing. That correct for quality improvement are difficult to method therefore tended to overstate the CPI in the apply since by their very nature services leave little late 1970s as house prices and mortgage rates in- tangible product to examine once they have been creased sharply. rendered. For example, suppose that as a result of Economists usually consider the purchase of a advances in medical knowledge a physician’s effec- house to be an investment, and the use of a house tiveness doubled, while the hourly fee increased by to be consumption. The CPI, as a measure of the 50 percent. While only the fee could be accurately cost of consuming a bundle of goods and services, measured, it would dramatically overstate the price should therefore incorporate only the change in the change for constant-quality physician’s services. current cost of housing services. One estimate of the Due to technical progress and increasing current cost of using owner-occupied housing is the knowledge, many observers believe that the average amount it would cost to rent a similar property. quality of goods and services has risen over time, and Starting in 1983 with the CPI-U and in 198.5 with that unmeasured quality change has caused inflation the CPI-W, the BLS adopted a rental eqz&a/ence in the United States to be overstated by most price approach to measure the cost of housing services. indexes.‘0 That belief, however, is extremely diffi- cult to quantify. The examples above certainly indi- Rental equivalence approximates the change in the cate that the problem of measuring quality change cost of services of homeownership with an index of is important and should be studied. Unfortunately, rental prices.‘* they do not provide the final word on the magnitude The rental equivalence approach was already of unmeasured quality changes. used in another index of consumer prices, the per- sonal consumption expenditure fixed-weight price Homeownership index. Chart 4 shows the period in which the dif- ferent measures diverged substantially: from 1978 The CPI increased sharply in the late 1970s and to 1982, the CPI rose 10.7 percent whereas the fured- early 1980s with its annual rate of increase peaking weight price index for consumer spending rose 8.9 at 15 percent in 1980. Some analysts have argued percent. The most important difference in the two statistics is their different methods of estimating 8 Robert J. Gordon, The h4easwement of LlurabL’e Goods Prices, prices for housing, Since the BLS does not revise Chicago: University of Chicago Press for the National Bureau CPI data once they are published, users of old CPI of Economic Research, forthcoming. Part of the work is sum- marized in Martin N. Bailey and Robert J. Gordon, “The Pro- data should realize that the CPI-U data before 1983 ductivity Slowdown, Measurement Issues, and the Explosion (and the CPI-W before 1985) still use the old of Comouter Power.” Bfuo&?s PaDe7s on Economic ActiviiY 2 measurement of housing cost and thus overstate the (1988): 347-431. The figures-in the text are from the BPEA article, page 382. actual price increases. 9 Gordon’s estimates are probably not universally accepted, however. As Jack Triplett put it (not referring to these particular estimates), “Just because an economist produces an index that 1’ For example, see Alan S. Blinder, “The Consumer Price differs from an official index, this does not necessarily imply that Index and the Measurement of Recent Inflation,” Btvokin~ Papers it is the official index that must be the incorrect one.” l“Quality on Economic Actitity 2 (1980). Bias in Price Indexes and New Methods of Quality Measure- 12The same type of problem applies to other durable goods as ment,” in Zvi Griliches, ed., Prke hdxes ad @blity change well. The theoretically appropriate price to include is usually (Cambridge: Harvard University Press, 1971), p. 21’2.1 the price of obtaining the services of that good, not the purchase ‘0 On the other hand, it is of course possible to find products price of the durable itself. The normal approach in constructing where quality has deteriorated. One example could be the the indexes, however, considers only the purchase price. Autos, growing use of graduate students for undergraduate instruction therefore, are priced by the cost of buying a car, not the cost in many universities. of driving a mile.
28 ECONOMIC REVIEW, JULY/AUGUST 1989 Chart 4 CHANGES IN CONSUMER PRICE MEASURES lQ1976-441983 Percent (Compound Annual Rates) 20
18
16
8
6
1976 1977 1978 1979 1980 1981 1982 1983
Changing Quantities Table II People shift their buying habits over time due to COMPOSITION OF CONSUMER SPENDING changes in relative prices, real incomes, demographic Consumer Expenditure Survey characteristics, and tastes. The CPI, however, is Expenditure Group 1972-73 1982-84 based on a market basket that is fixed for long inter- vals. Table II provides a contrast between the Food and Beverages 18.7 18.1 major expenditure shares based on the 1972-73 and Food away from home 3.8 4.9 the 1982-84 consumer expenditure surveys. Housing 28.0 30.7 The CPI’s fixed expenditure weights become less Apparel and Services 7.8 5.4 representative over time as consumption patterns Transportation 18.7 19.7 change. For example, consumers normally reduce Gasoline and motor oil 4.3 5.6 consumption of items for which price increases are relatively large. This problem is often referred to as Medical Care 4.6 4.4 substitution bias. It is inherent in any price index Other 22.2 21.7 whose weights are fixed and it becomes more serious Note: Relative. importance of items,-stated as percentages of annual when price movements are widely dispersed. In prac- expenditure. tice, substitution bias may not be very large. One Source: Monthly Labor Review, June 1986, page 17.
FEDERAL RESERVE BANK OF RICHMOND 29 recent study found substitution bias for the CPI from affect the weights in the CPI’s market basket, the 1959 to 1985 was only about 0.18 percent per year.‘3 index could overweight items such as snow blowers and underweight other items such as swimwear. Lack of Good Data on Individual Prices There has long been concern that the indexes may include list prices for some items rather than actual The BEA uses prices of individual items that were transaction prices. Since departures from list prices first collected for the CPI and PPI to estimate over usually reflect sale items or negotiated discounts, any 90 percent of the private sector prices in the National failure to use actual transaction prices would tend to Income and Product Accounts. Since the accounts overstate the price level. I4 Moreover, if the number attempt to cover all current production, whereas the of sales or discounts increases when the economy CPI and PPI cover limited areas, prices of some items is relatively weak, indexes calculated from list prices remain to be estimated by the BEA. They may not would overstate cyclical price rigidity. have usable data for some of those remaining items, such as financial services like banking where both Conclusion price and quantity may be difficult to define. In those cases the BEA may use the cost of production to These caveats indicate that price indexes do not estimate a product’s price; the quantity produced is answer all questions as well as we might wish. then estimated as total spending divided by that Despite their imperfections, however, the existing estimated price. If there are substantial productivity price indexes are invaluable. As Irving Fisher put it: gains in those industries, however, then that pro- But, although in the science of optics we learn that a cedure will overstate price change and correspond- perfect lens is theoretically impossible, nevertheless, for all ingly underestimate real output growth. practical purposes lenses may be constructed so nearly perfect that it is well worth while to study and construct International Comparisons them. So, also, while it seems theoretically impossible to devise an index number, P, which shall satisify all of the As should now be apparent, compiling a price tests we should like to impose, it is, nevertheless, possible index involves many choices among imperfect alter- to construct index numbers which satisfy these tests so natives. Not surprisingly, statistical agencies of dif- well for practical purposes that we may profitably devote serious attention to the study and construction of index ferent nations have made different choices. Thus one numbers.‘5 cannot assume that the price indexes of different nations are exactly comparable even if they have the same title. The CPI for Belgium, for example, does SUGGESTIONS FOR FURTHER READING not include housing. The Bureau of Labor Statistics is the primary Miscellaneous Statistical Problems source for the CPI and the PPI and publications The value weights now used to calculate the PPI explaining their construction. The monthly publica- are based on data from 1982, when the economy was tions CPI Detailed Repoti and The Pmducer Prike In- in a severe recession. By contrast, during the previous dexes present the actual data and contain brief survey year, 1972, the economy was rapidly ex- introductions to the construction of the CPI and the panding. The different phases of the business cycle PPI; they also announce and explain periodic re- in 1972 and 198’2 would have led to substantial visions in the series. The BLS Handbookof Methods, changes in the value weights in the PPI, whether or Part I and ZZ, describe in more detail the construc- not there was any structural change in the economy. tion of the CPI and the PPI. The MOM@ Labor Thus the latest weights have fallen for industrial Review contains recent data as well as articles on materials used in cyclically sensitive industries, such topics related to the CPI and PPI. The following were as construction and automobiles. particularly valuable for this article: Jack E. Triplett, There is an inevitable lag between population “Reconciling the CPI and the PCE Deflator,” Mon- movements, changes in regional weights of the tMy Labor&v&~, September 1981; and Andrew G. indexes, and changes in expenditure patterns. For Clem and William D. Thomas, “New Weight Struc- example, consider net population migration from cold to warm areas. If that migration did not promptly 14In countries with price controls, however, the actual trans- action price is often higher than the list price. In that case the price index would understate the price level. r3 Marilyn E. Manser, and Richard J. McDonald, “An Analysis of Substitution Bias in Measuring Inflation, 1959-85,” 15 The Pudusitzg Power of Money (19 11; reprint, New York: Economettica 56 CJuly 1988): 909-30. Augustus M. Kelley, 1963), p. 212.
30 ECONOMIC REVIEW, JULY/AUGUST 1989 ture Being Used in the PPI,” Mont//y Labor Review, official indexes include: Phillip Cagan and Geoffrey August 1987. H. Moore, TXeConsumer Price Index: IsstcesandAbeT- The implicit PCE and GNP deflators are ex- natives, American Enterprise Institute, Washington, plained in most macroeconomic textbook discussions 198 1; and Council on Wage and Price Stability, The of the National Income and Product Accounts, such WhoZesale Price Index: Review and Evaluation, as in Macr~ecotzomicsby R. Dornbusch and S. Fischer Washington, 1977. (1984). The Survey of Curt Bplsines, published On the relation of economic theory and index monthly by the Commerce Department, presents the numbers, an accessible account is Peter Hill’s “Re- data and regularly provides brief explanations of the cent Developments in Index Number Theory and deflators and price indexes. Practice,” OECD Economic&z&es #lo, Spring 1988. Problems of quality adjustment in the price indexes A classic comparison of many different price indexes are discussed in Robert J. Gordon’s articles cited in is Irving Fisher, Th Making of Index Numbers, River- footnotes 6 and 8 above. Other useful critiques of side Press, Cambridge, 1922.
APPENDIX
PRICE INDEXES AND IMPLICIT DEFLATORS
The CPI, PPI, and GNP fixed-weight price where Pr is the price index in period t, the summa- indexes all reflect weighted averages of prices relative tion signs represent summation over all commodities to average prices in a base period. Since the weights coverd by the index, pt is the price of a specific item on specific prices remain fixed for long periods of in period t, qt is the current quantity consumed of time, the indexes are often referred to as fixed-weight that specific item, and pb is the price of a specific indexes. In symbols, a fixed-weight index can be item in the base period. In words, equation (2) states represented as in equation (la) or its possibly more that the price index is the ratio of current expenditure intuitive form, (1 b): to current quantites times base period prices. When compared to the base period, an implicit deflator is p _ %‘b (14 a current-weight price index. That is, it is a weighted * - CPbqb average of prices with the weights being current quan- tities. When two periods other than the base period == (:)(g$) (lb) are compared, however, the change in the deflator is a muddle of price and quantity changes that can where Pt is the price index in period t, the summa- be difficult to interpret. tion signs represent summation over all commodities The chain price indexes reported in the accounts covered by the index, pt is the price of a specific item are base-weighted, with the base period for any in period t, qb represents either the quantity of a quarter being the previous quarter; a chain index can specific item included in the market basket (CPI) or be constructed using equation (la) or (lb) above. the quantity produced in the base period (PPI or Since the base shifts over time the weights can more GNP indexes), and pb is the price of a specific item accurately represent current production than would in the base period. In words, equation (lb) states that a fixed-weight index based in a distant period. the price index is a weighted average of the relative Moreover, it avoids much of the difficulty of inter- price changes for specific items (the first term in pretation of an implicit deflator for quarterly changes. parentheses), with the weights being the relative im- On the down side, however, changes in the chain portance of the items in the base period (the second index over long periods of time may themselves be term in parentheses). difficult to interpret, since the items produced can The deflators used in the National Income and vary substantially. Product Accounts are somewhat different since the A simple example may help clarify the types of weights of individual prices can vary over time. A indexes. Suppose that one wishes to construct a price deflator can be represented as in equation (2): index for fruit. There are two types of fruit, apples and oranges. Table III shows the prices of apples and oranges in April, May, June, and July and the amounts Pt = -CPtqt (2) zPb% consumed. A fixed-weight Fruit Price Index (FPI)
FEDERAL RESERVE BANK OF RICHMOND 31 Table III NUMERICAL EXAMPLES OF PRICE STATISTICS
APRIL MAY JUNE JULY
Price per apple 12 20 20 20 Number of apples bought 6 3 2 2
Price per orange 4 4 4 2 Number of oranges bought 7 10 15 30
FPI: Level 100 148 148 134 Percentage change 48 0 -9
IFD: Level 100 132 119 69 Percentage change 32 -10 -42
CFI: Level 100 148 100 70 Percentage change 48 -32 -30
Avg. : Level 100 140 133 96 Percentage change 40 -5 -28
is calculated, using quantities consumed in April as strutted. The differences in this example are extreme the base; as is conventional, the index value in the since the relative price changes are also extreme. base period is 100. An Implicit Fruit Deflator (IFD) Second, the implicit deflator is less than the fixed- is also calculated, as is a Chain Fruit Index (CFI). weight index. That is often the case in the real world Finally, as suggested in footnote 4, the geometric as well, since it results from the tendency to switch average of the FPI and IFD is presented (Avg.). consumption toward relatively less expensive goods For example, using equation (la) to construct the when relative prices change. FPI for May, Third, although neither price changed in June, both
FPI = (20 ~6) + (4 x7) = 120+28 = 148 the implicit deflator and the chain index changed substantially. (12x6) + (4x7) 72+28 ’ Fourth, in July there was a substantial decline in Similarly, using equation (2) to construct the IFD the price of oranges. The fixed-weight index put for June, little weight on that decline due to the small relative importance of oranges in the base period, April. 40 +60 IFD = (z” xz) + t4 x 15) = - = 119. Finally, note that the geometric average occupies (12x2) + (4x15) 24+60 the middle ground between the extremes. In this case it shows relatively little average price change over A few points are worth emphasizing. First, the the summer; in contrast, the fixed-weight index monthly estimates of price change can differ substan- shows substantial inflation and the implicit deflator tially, depending only on how the index is con- and chain index both show substantial deflation.
32 ECONOMIC REVIEW, JULY/AUGUST 1989