HOW TO USE PRICE INDEXES

Larry DeBoer

Indiana Legislative Services Agency

and

Department of Agricultural Economics

Purdue University

REVISED

October 1993

PRICES AND QUANTITIES

Most dollar amounts can be thought of as the product of a price and a quantity. Dollar sales of automobiles is the product of the price of cars and the number of cars sold. Income earned is the product of the wage paid (the price of labor) and the number of hours (or weeks or months) worked. The market value of improvements is the product of the market prices of buildings and the number of buildings.

Frequently we have dollar figures, such as consumer expenditures on gasoline, but would like to know the quantity figures, how much gasoline have consumers purchased? If prices never changed, expenditures on gasoline would be a good indication of how much gasoline was purchased. But prices usually increase, which means that a change in any dollar figure over time is a combination of price increases and quantity changes.

If we know how prices have changed, we can find out what has happened to quantity. We can simply divide the expenditure figures by the prices, and get the quantities.

Here are the expenditures by Americans on gasoline in 1973 and 1990:

1973 $28.1 billion 1990 $93.8 billion.

Have consumers actually increased the amount of gasoline they've bought, or does this increase represent increases in the price of gasoline only?

The price of a gallon of leaded regular gasoline in these two years was:

1973 $0.40 1990 $1.12

Dividing the dollar expenditures (price times quantity) by the price gives us the number of gallons purchased:

1973 $28.1 bil/$0.40 = 70.3 gallons

1990 $93.8 bil/$1.12 = 83.8 gallons

The quantity of gasoline has increased, but not nearly as much as expenditures. Most of the expenditure increase has been due to price rises.

Most of the time the dollar figures we have are not for particular commodities with single prices. Instead, they are sums of dollar amounts of many different products: sales of motor vehicles (cars, trucks, tractors); total consumer expenditures (on food, clothing, rent, medical care); taxable sales (of all taxable commodities). No single price will do to adjust these dollar figures. Instead, we can use price indexes, which show averages of changes in many prices.

HOW THEY CONSTRUCT PRICE INDEXES

Price indexes are averages of the prices of many goods and services. Calculation of a price index begins with the selection of a "market basket" of goods and services. The Consumer Price Index, for example, uses the results of a consumer expenditure survey taken in the early 1980s, to determine a set of goods and services typically purchased by consumers. The market basket serves to identify which prices will be included in the index, and how much weight each will be given.

As an example, suppose we derive a price index based on a very small market basket, including gasoline, pizza and plumber's services:

DeBoer's Price Index (DPI) market basket

10 gallons gasoline

2 14 inch 2 item pizzas

1 hour of work by a plumber

Suppose we want to compare prices in this market basket in 1982 and 1992. We would find the prices of these items in those two years

and multiply the prices by the quantities of each in our market basket to get expenditures on each

We now have the total cost of our market basket in each of two years. To change these dollar figures into indexes, we select a "base year." The year selected is arbitrary, and the real price indexes occasionally change their base years. Let's select 1982 as the base year. We then divide the cost of the market basket in each year by its cost in the base year, and multiply by 100.

Price indexes are always presented in index form. These calculations are done by the people who publish the price indexes -- you don't have to do them.

Our DPI price index says that "prices" rose by 19% between 1982 and 1992. Note that this includes a 46% increase in pizza prices (from $6.50 to $9.50), a 20% rise in plumbing prices ($25 to $30) and a 12.5% drop in gasoline prices ($1.20 to $1.05). A different market basket (including, say, automobile prices) would give a different index. So would a market basket with these three items in different quantities (for example, 5 gallons of gas and 3 pizzas).

The index numbers themselves are only useful in relation to one another. Knowing that the index is 119 in 1992 means nothing unless we know that it was 100 in 1982 (or 117.5 in 1989).

We could have chosen 1992 as the base year. In that case we could divide expenditures in each year by expenditures in 1992, $59.50, and the indexes would be 84.03 in 1982 and 100.00 in 1992. The index is always 100 in its base year. When there is inflation, the index will be less than 100 in years before the base year, more than 100 after. With 1992 as the base year, the percent change in prices between 1982 and 1992 is still 19% -- the base year is arbitrary and should not make a difference in calculation of index percent changes.

SEVERAL USEFUL PRICE INDEXES

The Consumer Price Index (CPI) This is the most widely publicized price index. It is published monthly by the U.S. Department of Labor's Bureau of Labor Statistics. The "market basket" of the CPI is determined by a survey of the expenditures of consumers, and includes the prices of products which consumers typically purchase. There are two versions of the CPI, the CPI-U, which is most frequently used, uses expenditure survey results for all urban consumers. The CPI-W is based on the expenditures of wage earners and clerical workers, excluding professional, managerial, self-employed, unemployed, retirees and others. It is less frequently used, though it has a longer history. There is seldom a very big difference between these two versions of the index. The base years of the CPI are 1982-84, the years during which the expenditure surveys upon which the market basket is based were taken. The average for the index over these three years is 100. Until the early 1980s, the base year of the CPI was 1967.

CPI Component Indexes A very large number of CPI component indexes are available. These include indexes for parts of the CPI market basket, such as food and beverages, housing, fuel and utilities, apparel and upkeep, transportation, medical care, entertainment, and many others. The base years for each are 1982-84. Also available are special indexes, such as "All items less food," "All items less medical care," and so forth.

The Gross Domestic Product Price Deflator The GDP deflator is the broadest measure of price change available, since it averages prices of all goods and services included in the Gross Domestic Product. It is published quarterly by the U.S. Department of Commerce's Bureau of Economic Analysis, as part of the National Income and Product Accounts (NIPA). The "market basket" of the GDP deflator is essentially the whole production of the nation, including consumer goods and services (like the CPI), investment goods, government purchases, imports and exports. The base year of the GDP deflator is 1992. The market basket for the implicit price deflator is not constant -- it changes each year with the changing composition of national production. Some people recommend against using the GDP implicit price deflator for this reason. The NIPA data includes "fixed weight" price indexes that overcome this problem, however. Note that the Bureau of Economic Analysis recently revised NIPA statistics. They changed the base year of the GDP deflator from 1987 to 1992.

GDP Deflator Component Indexes Like the CPI, the GDP deflator is divided into many components, including durable and non-durable consumer goods, structures and producers' durable equipment, imports and exports, and government purchases. Of special interest is the State and Local Purchases Deflator, which shows price changes of goods and services purchased by state and local governments. The state and local index is further divided into durable goods, non-durable goods, compensation of employees, other services, and structures.

The Producer Price Index (PPI) The PPI is published monthly by the Bureau of Labor Statistics. It used to be known as the Wholesale Price Index, but the name was changed several years ago to better reflect what is included in the index. The PPI measures price received by domestic producers of commodities in all stages of production. The "market basket" of the PPI represents their importance in the total value of production in 1982, which is the PPI's base year. The PPI also has many component indexes, by stage of processing (finished goods, intermediate goods and raw materials) and by industry (agriculture, manufacturing, mining and public utilities).

MEASURING INFLATION WITH PRICE INDEXES

One of the main uses of price indexes is measuring inflation. Inflation is a general increase in the level of all prices. Contrast this with an increase in the price of a particular product, which may be the result of inflation, but may also be the result of cost increases in a particular industry, that is, a relative price increase. Since the broad based price indexes, such as the CPI or GDP deflator, are averages of price of many products, increases in these indexes must represent inflation rather than relative price increases.

The percentage change in a price index from year to year (or month to month, or quarter to quarter) is a measure of the inflation rate. The percent change in the CPI is the most frequently reported inflation rate. The CPIs for 1991 and 1992 were

1991 136.2 1992 140.3

You can get the two most recent annual average indexes from the Survey of Current Business, blue page S-5.

The inflation rate for 1992 is the percent change from 1991,

STEP ONE: divide the second year's index by the first year's

140.3/136.2 = 1.0301

STEP TWO: subtract one, then multiply by 100

(1.0301 - 1) x 100 = 3.01%

The CPI inflation rate for 1992 was 3%. The rate has fallen since 1990, when it was 5.4%. Recessions tend to do that.

Percent changes also can be calculated by subtracting the first year's index from the second year's index, dividing by the first year's index, and multiplying by 100. Perhaps this is more conventional. I find the above method faster on a calculator, though, and you get the same result. Note that the inflation rates measured using the CPI are different from the rates measured using the GDP deflator. This is because the "market baskets" of these two indexes are different. The CPI uses a basket of goods and services that surveys say consumers typically purchase. The GDP deflator is an average of price increases of all goods and services produced in the U.S. in one year -- including consumer goods, but also investment goods (like steel or machine tools) and government goods (like teacher salaries or guided missiles). The GDP deflator is the broader measure of price changes, but the CPI is more likely to reflect the experience of consumers.

HOW AND WHY TO DEFLATE A DOLLAR FIGURE

Price inflation often distorts the dollar figures we use. Revenue totals grow faster when inflation is high, but the revenue's power to purchase goods and services may not be growing. Expenditure totals grow faster with inflation, too, but may not represent increases in services delivered to citizens. Inflation causes wages to rise, but since prices also are rising, higher wages may not purchase any more bread or gasoline or refrigerators.

To eliminate the influence of inflation on dollar figures, we can "deflate" them with a price index. The resulting figures are sometimes called "real", because they represent quantities of goods and services, rather than "nominal" dollar amounts. Sometimes the deflated dollar amounts are said to be "in 1987 dollars" or "constant dollars," meaning they represent what the figure would have been had prices been constant at 1987 levels. Sometimes the deflated figures are described simply as "adjusted for inflation." Any of these descriptions will do, but "real figures in constant 1987 dollars adjusted for inflation" is overkill.

Here is a series of per capita personal income figures for Indiana residents:

1990 $16,814 1991 $17,193 1992 $18,043

These numbers are from the Survey of Current Business, April 1993, p. 60. Growth of per capita income in Indiana averaged 3.6% per year between 1990 and 1992. Without considering inflation, this seems to imply that Indiana residents are better off in 1992 than in 1990. However, this does not take account of the fact that the prices they pay have increased as well. The quantity of goods and services that Indiana residents can buy with their income has not increased 3.6% per year, because prices have increased.

To eliminate the influence of inflation on these income figures, in order to measure how the quantity of goods and services purchased has increased, we can deflate the income figures with the Consumer Price Index (CPI). For these three years the CPI is

1990 130.7 1991 136.2 1992 140.3

Taking the percentage change in these index numbers shows that prices also have risen 3.6% per year, on average.

To deflate:

STEP ONE: divide the CPI for 1990 by 100. 1.307

STEP TWO: divide the 1990 income figure by the CPI.

$16,814/1.307 = $12,865

STEP THREE: do the same for 1991 and 1992.

$17,193/1.362 = $12,623 $18,043/1.403 = $12,860

The resulting figures are in 1982-84 dollars, that is, they show what income would have been had prices remained at their 1982-84 average. The figures could also be called "real per capita income" or "income adjusted for inflation."

The real income figures show that the "purchasing power" of Indiana residents has not risen at all. Real income is slightly lower in 1992 than in 1990. All of the increase in income has been due to inflation.

Note that another way to present this information is to compare the percent increase in income with the percent increase in prices--the inflation rate. The increase in income averaged 3.6% per year, and inflation averaged 3.6% per year. The difference between the two is approximately the increase in real income, meaning the increase in real income was approximately zero.

SELECTING A PRICE INDEX

There are hundreds of different price indexes. Which one you select depends on the dollar series you want to deflate, and the question you want to answer.

When we wanted to know the quantity of gallons of gasoline purchased, we divided expenditures by the price per gallon of gasoline. It would not have been appropriate to divide by the price of movie tickets or pianos. The first guide to selecting a price index is to consider the products included in the dollar figure you want to deflate.

For example:

Deflate wages earned by consumers, to determine how their purchases of goods and services have changed. The goods and services they buy include food, clothing, housing, personal services, etc. The prices of these items are included in the "market basket" that makes up the Consumer Price Index. Deflate wages with the CPI. You could also use the personal consumption deflator from the NIPA.

Deflate investment expenditures of firms, to determine how their purchases of plant, equipment and materials have changed. This is an entirely different set of goods -- consumers don't buy steel, machine tools or factory buildings. None of these things is included in the CPI market basket. But all are included in the PPI, the producer price index. Deflate using the PPI. Or, use the investment spending deflator from the NIPA.

Deflate total state government expenditures, to determine how much in goods and services are being delivered to citizens. Government purchases a different market basket than consumers do, so deflating with the CPI is not appropriate. Government buys some of the things in the PPI market basket, but the match isn't that close. The NIPA provides a price index for the purchases of state and local governments.

Deflate medicaid payments, to determine the volume of medical services delivered. You need a price index that includes only medical services. There is an index of medical services prices which is a component of the CPI, and there is a price deflator for medical purchases in the NIPA.

Sometimes your audience is not so sophisticated. If they've heard of any price index, it will probably be the CPI, since it gets all the press coverage. Most of the time prices rise together, so the CPI is often an acceptable deflator for any series, if ease in explaining what you are doing is a consideration.

Sometimes there is no price index available which matches your dollar figure. It might be appropriate to use the broadest possible price index in these cases -- the GDP deflator. No matter what your dollar figure is, its components are probably a part of the GDP deflator, if only a small part.

Sometimes the question you want to answer determines what price index you use. Suppose you want to know how much in private goods and services taxpayers lost by paying their taxes. Ordinarily you might deflate tax receipts by the state and local government deflator, since those are the goods and services that tax receipts buy. But if you are asking what consumers would have purchased had the taxes not been collected, that is, what taxpayers gave up in real terms, then you could deflate with the CPI. Since government prices usually rise faster than consumer prices, you'll get a different answer.

Or, you might want to know how much inflation contributed to growth in sales tax receipts. Ideally you would use a price index that had as its market basket the composition of taxable sales -- retail commodities less food consumed at home, less rent, less most services. Such an index would tell you how much of the increase in sales tax receipts is due to increases in the prices of commodities subject to the sales tax. You could construct such a price index if you knew the composition of taxable sales and had the CPI or NIPA component price indexes for each taxable good or service. This would be a major undertaking, however. Instead, you could use one of the CPI special indexes, such as "commodities less food and beverages", which does not include services. Percent changes in this index show inflation in something like taxable sales; deflating with this index yields real tax receipts, which would show the growth in taxable sales at constant prices.

USING A PRICE INDEX TO MEASURE RELATIVE PRICE CHANGES

Inflation represents a general increase in all prices. Increases in broad price indexes like the CPI or the GDP deflator represent inflation. Increases in individual prices may be due to inflation, but they may also represent "relative price increases." Sometimes prices will increase because producers' costs have increased, or because there is a shortage of the product, or for some other reason. A price index can measure the change in the price of a specific product relative to all other prices.

Consider the average price of a gallon of regular leaded gasoline in 1973 and 1992:

1973 $0.40 1992 $1.05

Is this increase due entirely to inflation? Or, has the price of gasoline increased relative to all other prices? The CPI is a measure of what has happened to all other consumer prices. For 1973 and 1992 it is

1973 44.4 1992 140.3

To measure relative price change

STEP ONE: divide the CPI for 1973 by 100 0.444

STEP TWO: divide the 1973 gasoline price by the 1973 CPI

$0.40/0.444 = $0.90

STEP THREE: do the same for 1992

$1.05/1.403 = $0.75

Relative to all other prices, gasoline actually costs less in 1992 than it did in 1973. The increase in gasoline prices has been less than the average increase in all other prices. Had there been no inflation, the price of gasoline would have dropped, a little bit. The actual level of these relative prices, 90 and 75 cents, is what gasoline would have cost had prices been at their 1982-84 levels in both 1973 and 1992.

Another way to make this comparison is to look at the percentage changes in the price of gas and the CPI:

Gasoline, 1973-92: 163% CPI, 1973-92: 216%.

Gasoline prices have risen more slowly than prices in general over this period. Relative to all other goods and services that consumers buy, gasoline now costs less.

Relative price changes can also be measured by comparing price indexes. Suppose we want to know how the prices of goods and services purchased by state and local governments compares to prices generally. We could compare the NIPA state and local government purchases deflator to the GDP deflator. For 1989 and 1992, the state and local government purchases deflator was

1989 108.6 1992 119.6

The GDP deflator was

1989 108.5 1992 121.1

A simple way to compare these figures is to take the percent changes in each index:

Government: ((119.6/108.6) -1) x 100 = 10.1%

General Prices: ((121.1/108.5) -1) x100 = 11.6%

Government prices have risen about 1.5 percentage points faster than prices in general during 1989-92. This is an exception to the long term trend which has prices paid by state and local governments rising faster than prices in general. Since one component of the state and local government deflator is wages, perhaps this relatively small increase in government prices reflects low wage increases in times of budget stringency.

YOU CAN CHANGE THE BASE YEAR OF ANY PRICE INDEX

The base year of any price index is essentially arbitrary. The CPI's base years are 1982-84, the index averages 100 over 1982-84; the earlier version was 100 for 1967. The GDP deflator is 100 in its base year 1987; before that, a base year of 1982 was used.

The base year is important when figures are deflated. If sales tax receipts are deflated with an index that has a base year of 1987, the "constant dollar" results show receipts in "1987 prices", that is, what sales tax receipts would be had prices not changed since 1987.

It might be convenient for explanatory purposes to use a different base year, for example, the first year of your data series, or the most recent year. To change any price index to the base year you choose, simply divide all the index values by the index in the year you want, and multiply by 100. This will assure that the index is 100 in the base year you select.

For example, suppose you want the NIPA GDP deflator with a base year of 1992, rather than 1987. The published values of the index for selected years are

1980 71.7 1987 100.0 1989 108.5 1992 120.9

Divide each of the published indexes by the value for 1992, 120.9, and multiply by 100. This gives

1980 59.3 1987 82.7 1989 89.7 1992 100.0

Using one or the other of these versions of the state and local purchases index should not change the results of your analysis at all. But doing calculations in "1992 dollars" may be easier on your readers -- the numbers may seem more familiar. For example, compare the results of deflating Indiana sales tax receipts for 1982 and 1992 using each version of the index:

Sales tax receipts (millions): 1982 $1,097 1992 $2,264

The state and local purchases deflator is an appropriate index if the question is how the purchasing power of sales taxes has changed since 1982. The published index uses 1987 as its base year:

1982 82.3 1992 118.7

Real sales tax receipts would be

1982 $1,333 1992 $1,907

Neither of these figures will look familiar to your readers, since they are in 1987 dollars. Real sales taxes could be shown in 1992 dollars, however. The index can be converted to 1992 dollars by dividing each year's index by 118.7, the index for 1992, and multiplying by 100:

1982 69.3 1992 100.0

The result using an index with a base year of 1992 gives the purchasing power of receipts in 1992 dollars:

1982 $1,583 1992 $2,264

The 1992 number will look familiar to your readers. Note that the percent increase in constant dollar receipts is identical using either version of the index, 43%.

A disadvantage of this approach is that most people think of "deflating" as making numbers smaller -- had it not been for inflation, sales tax receipts this year would have been less. Using the current year as the base year inflates past numbers.