# PRICE INDEXES

Price indexes are used to measure the rate of inflation in the economy. There are three key price indexes that are routinely calculated and reported to the public by government agencies in the United States. These three measures differ with respect to the number of items they take into account. Before discussing these measures, it is worthwhile to explain why an index is needed to calculate the rate of inflation.

## THE NEED FOR AN INDEX

Most economic variables are measured in absolute terms. For example, it was reported that 12 million cars were produced in 1994 in the United States and that the gross output of goods and services in the United States was estimated at \$8.7 trillion during 1998. It is not possible, however, to measure the price associated with a group of commodities in absolute terms; only the price for one commodity can be measured in absolute terms. For example, we can thus say that the average price of a loaf of bread in the United States, was \$1.75 in 1998. The difficulty arises when we have to deal with a number of commodities together. So, once we start asking what happened to Joe Smith's cost of living in 1998 compared to 1997, it is no longer logical to compute the average price of all the goods and services bought by him in 1997 and compare it with the average price of all the goods and services bought by him in 1998. After all, what meaning can we attach to the average of prices paid for, for instance, a fancy stereo system and a pound of hamburger? An index helps us out of this quandary. In the most basic terms, an index attaches weights to the prices of items whose collective price movement we are interested in. Below is a detailed discussion of the three main price indexes used widely in the United States and how they are constructed.

## THREE MAIN PRICE INDEXES AND THE INFLATION RATE

The inflation rate is derived by calculating the rate of change in a price index. A price index, in turn, measures the level of prices of goods and services at a particular time. The number of items included in a price index varies depending on the objective of the index. Government agencies periodically report three types of price indexes, each having particular advantages and uses. The first, the consumer price index (CPI), measures the average retail prices paid by consumers for goods and services. A couple thousand products, grouped into 207 sets of items, are included in this index. These items are selected on the basis of their inclusion in the household budget of a consumer. Each of the product prices is assigned a weight based on the importance of the item in the household budget. As a result, the CPI reflects changes in the cost of living of a typical urban household. The CPI is considered the most relevant inflation measure from the point of view of consumers, as it measures the prices of goods and services that are part of their budgets. Nevertheless, the CPI will not precisely measure changes in the cost of living of every consumer due to differences in consumption patterns.

A second price index used to measure the inflation rate is called the producer price index (PPI). It is a much broader measure than the consumer price index. The PPI measures the wholesale prices of approximately 3,000 items. The items included in this index are those that are typically used by producers (manufacturers and businesses) and thus include many raw materials and semi-finished goods. A change in the PPI reflects a change in the cost of production, as encountered by producers. Since producers may pass a part or all of the increase in the cost of production to consumers, movements in the PPI indicate future movements in the CPI. The producer price index can thus forewarn consumers of coming increases in the cost of living.

The implicit price deflator is the third measure of inflation. This index measures the prices of all goods and services included in the calculation of the current output of goods and services in the economy, known as gross domestic product (GDP). It is the broadest measure of price level. This index includes prices of fighter planes purchased by the Defense Department as well as paper clips used in any office. Thus, the implicit price deflator is a measure of the overall or aggregate price level for the economy. Movements in the implicit GDP price deflator capture the inflationary tendency of the overall economy.

The three measures of the inflation rate are most likely to move in the same direction, even though not to the same extent. Differences can arise due to the differing number of goods and services included in compiling the three indexes. The preceding three price indexes are discussed in further detail below.

## CALCULATIONS OF THE CONSUMER PRICE INDEX AND THE INFLATION RATE

The construction of the consumer price index employs an index number technique in which a fixed basket of commodities (a collection of goods and services considered relevant to the index) is valued using prices at different points of time. This type of index is technically known as a Laspeyres index, named after the statistician who invented the method.

First, a point of reference is selected, commonly known as the base year. Normally, a particular year is selected as the base year—prices prevailing in the selected base year are used in comparing changes in the price level. Currently, however, the 1982-84 period (rather than a single year) is used as the base in the construction of the consumer price index in the United States. In this case, the average price of a commodity over the three-year period is used as the base price for the commodity. This implies that the average of 1982, 1983, and 1984 prices for any given item included in the CPI is used in comparing the prices of that commodity in successive months and years. The price of each item in the basket of commodities selected is attached a weight in accordance with its importance in the budget of a typical urban family. In other words, the government first identifies the goods and services that are used by a typical urban consumer. Then, it assigns a weight to each of the items in the fixed basket—the basket thus contains a collection of goods and services in quantities that, presumably, a representative consumer consumes. Next, the government evaluates the fixed basket of commodities using prices at successive points and compares its costs (or values) with the cost to buy the same basket in the base period. This results in a series of price ratios that are usually multiplied by 100 for convenience. Thus, the price index is 100 in the base period and its value at other points reflect movements in the price level, which can be used to calculate the inflation rate between any two points of time.

For example, the CPI in the United States for 1982 was 96.5, for 1983 it was 99.6, and for 1984 it was 103.9. The average of the CPI numbers for these three years is equal to 100, since the 1982-84 period is used as the base period or point of reference. The consumer price index stood at 141.9 at the end of 1992, and at 145.8 at the end of 1993. The latter two values of the CPI imply that the cost of the fixed basket of commodities, compared to the 1982-84 period, had gone up by 41.9 percent by the end of 1992, and by 45.8 percent by the end of 1993. They also imply that the inflation rate during 1993 was roughly 2.7 percent on an annual basis (inflation rate = {(145.8 - 141.9)/141.91}*100).

### ITEMS INCLUDED IN THE CONSUMER PRICE INDEX.

The consumer price index is calculated by the U.S. Bureau of Labor Statistics (BLS) and is published on a monthly basis. The broad categories of items that are included in construction of the CPI, in a highly simplified form, are: food and beverages, housing, apparel and upkeep, transportation, medical care, entertainment, and other goods and services. In reality, however, the CPI is based on a couple thousand products that are grouped into 207 sets of items. BLS employees visit thousands of stores in 85 geographical areas every month and collect more than 100,000 prices. Then the average prices of related items, such as poultry and honey are combined to yield group indexes—in this particular case, food and beverages. Next, the group indexes are combined to yield the overall price index called the "all-items CPI."

### THE MEASUREMENT ERROR IN THE CONSUMER PRICE INDEX.

Until 1983, the consumer price index data inflated the extent of true inflation, due to a measurement error. This error arose from the treatment of mortgage interest rates. The BLS attached excessive weights to this item, which rose quite rapidly during the 1970s. The government agency, in calculating price statistics, assumed that increased mortgage rates led to higher housing costs for homeowners—this is incorrect, since homeowners do not take out new mortgages every month. The mention of this measurement error is important, since the CPI series, unlike many other economic statistics, is not revised to correct for errors. Thus, the measurement error is still present in the CPI series and it can lead to misleading impressions. For example, consumer price index data suggest that real earnings (earnings adjusted for inflation) fell between 1972 and 1982, but according to another price index—also published by the federal government—real earnings grew slightly from 1972 to 1982.

### THE USEFULNESS OF THE CONSUMER PRICE INDEX.

The consumer price index is widely used, both in the private and public sectors. The CPI is most commonly used in calculating the inflation rate for general purposes. The movement in the CPI reflects changes in the cost of living for urban consumers. Labor unions often use the CPI in bargaining for wage increases. Also, most government pensions, including the level of Social Security benefits, are indexed to the consumer price index.

## CALCULATIONS OF THE PRODUCER PRICE INDEX AND THE INFLATION RATE

The producer price index (PPI) is also published by the U.S. Bureau of Labor Statistics (BLS) on a monthly basis. For the PPI, the BLS collects prices on more than 3,000 commodities that are not bought by consumers directly but instead are purchased by businesses. In a simplified form, the producer price index can be thought of as having the following broad categories: finished goods; intermediate materials, supplies, and components; and crude materials for further processing. Each of these broad categories is further subdivided in smaller groups. For example, the finished goods category consists of foods, energy, and finished goods excluding food and energy (the last subcategory includes capital equipment).

The PPI uses an index number construction methodology similar to at used for the CPI. While price data are directly collected by the BLS workers, the actual prices for the PPI index are obtained from questionnaires that are mailed to thousands of firms that sell products included in the PPI.

Currently, 1982 is used as the base year for the producer price index series. The interpretation of the PPI series is similar to the CPI series—the PPI can also be used to calculate the inflation rate.

### USEFULNESS OF THE PRODUCER PRICE INDEX.

One should recognize that the producer price index serves as an index relevant to the producers' cost. In other words, the PPI tells what is happening to the cost of production. If the cost of production is rising, however, producers may also increase the prices at which they sell. This, in turn, is likely to increase the retail prices that consumers pay in stores across the nation. The importance of the producer price index, then, is that it forewarns of changes in the consumer price index and, therefore, the cost of living of ordinary households.

## CALCULATIONS OF THE IMPLICIT PRICE DEFLATOR AND THE INFLATION RATE

The implicit price deflator is arrived at in an indirect manner, thus the adjective "implicit." Calculation of the consumer price index (CPI) and the producer price index (PPI) are explicit—or direct—indexes calculated from price data on the items included. The implicit price deflator, on the other hand, is inferred indirectly from the estimates of gross domestic product (GDP) in nominal terms (in current dollars) and in real terms (the nominal value of GDP adjusted for inflation by reevaluating the GDP in prices that prevailed during a chosen base year).

Currently, 1992 is used as the base year for calculating the real value of GDP in the United States. For example, the 1998 U.S. output of goods and services is first evaluated at prices prevailing in 1998. Then, the 1998 output of goods and services is also evaluated at prices that prevailed in 1992 (thus the term "GDP in 1992 dollars" or "GDP in constant dollars." One can easily see how the ratio of GDP in 1998 prices and GDP in 1992 prices would yield a measure of the extent of the rise in price level between 1992 and 1998. According to federal government statistics, this ratio is estimated at 1.1307 or 113.07 when multiplied by 100 (as is customarily done to be able to see the extent of price increase more conveniently). The value of the implicit price deflator of 113.07 in 1998 implies that the price level increased by 13.07 percent from 1992 to 1998 (note that the value of the implicit price deflator in the 1992 base year, is equal to 100).

The above method of expressing nominal or current gross domestic product into its value in 1992 prices is routinely done every year (of course, sometimes the base year itself, may be changed to a later year to keep the data series closer to the current period). Thus, we have 1997, 1996, 1995 (and so on) gross domestic products expressed in 1992 prices. This helps to calculate the inflation rate between subsequent years. For example, the implicit price deflator stood at 112.08 at the end of 1997. Given that the deflator was at 113.07 at the end of 1998, we arrive at the annual inflation rate of roughly 0.88 percent during 1998 (1998 inflation rate = [(113.07 - 112.08) / 112.08] * 100).

One should also notice that the term "deflator" is not used in the CPI or PPI. This is because, if you know the implicit price deflator, say, for 1998 and the 1998 GDP in current prices, you can arrive at the GDP in 1992 prices by deflating the 1998 GDP in current prices by the deflator for 1998 (expressed in plain ratio form, rather than the one multiplied by 100). Despite the use of term "deflator," one should not lose sight of the fact the implicit price deflator is essentially a price index.

### USEFULNESS OF THE IMPLICIT PRICE DEFLATOR.

As was pointed out earlier, the implicit price index is the broadest measure of price level. Although this index is all-inclusive and changes in it reflect inflation pressure underlying the whole economy, it may not be directly useful to ordinary households and even businesses—the CPI and PPI are more relevant to these units.

## USEFULNESS OF THE THREE PRICE INDEXES

As mentioned earlier, all three price indexes can be used to calculate the inflation rate. There are, however, two important differences among these indexes. First, the consumer and producer price indexes are published every month, whereas the implicit price deflator figures are reported on a quarterly basis. Thus, more frequent users of inflation data would be inclined to use the CPI or the PPI. Second, the coverage of the three indexes differs dramatically. Thus, one of these price index series can be more suitable than another in a particular case. To measure the cost of living for an urban consumer, for example, the CPI will be overwhelmingly preferred to the PPI and the implicit price deflator. Nevertheless, one must be aware that even the CPI is an average price measure that is based on certain weights. While the CPI may reflect the cost of living changes for the average consumers, it cannot precisely reflect changes in the actual cost of living for a particular consumer—his or her consumption pattern may be quite different from that assumed in assigning weights to the fixed basket of commodities. One thus needs to interpret the price index numbers carefully.

Despite the slight caution one must exercise in interpreting the price indexes, a good understanding of the inflation rate is important for every individual and household. Most economies face positive rates of inflation year after year. If the inflation rate is positive and an individual's income remains constant, his or her real standard of living will fall since the individual's income will be worth less and less in successive periods. For example, a household earns \$50,000 per year and its income remains fixed at this level in the future. If the inflation rate persists at 10 percent per year, the purchasing power of the household income will also keep declining at the rate of 10 percent per year. At the end of a five-year period, prices will be one and a half times greater. This will lead to the household being able to buy only two-thirds of the goods and services it was able to buy at the beginning of the period.

An understanding of inflation is also crucial in making plans to save for retirement, college education, or a boat. One must use an appropriate price index in calculating the funds required for a given purpose. The CPI is a good guide for retirement purposes. But if one is saving to buy a boat, even the CPI may not produce a good result—the individual may want to specifically know the way boat prices are increasing. Nevertheless, an understanding of price indexes prepares an individual adequately to explore such questions further.

[ Anandi P. Sahu , Ph.D. ]

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Gordon, Robert J. Macroeconomics. 7th ed. Reading, PA: Addison-Wesley, 1998.

Sommers, Albert T. The U.S. Economy Demystified. Lexington, MA: Lexington Books, 1985.