Macroeconomics is the analysis of the economy as a whole, an examination of overall supply and demand. At the broadest level, macroeconomists want to understand why some countries grow faster than others and which government policies can help growth.
Alex Berenson
Measuring National Output and National Income
(Part E)
by
Charles Lamson
Nominal versus Real GDP
So far, we have looked at GDP measured in current dollars, or the current prices we pay for things. When a variable is measured in current dollars, it is described in nominal terms. Nominal GDP is GDP measured in current dollars---all components of GDP valued at their current prices. In many applications of macroeconomics, nominal GDP is not a very desirable measure of production. Why? Assume there is only one good---say, pizza. In each year 1 and 2, 100 units (slices) of pizza were produced. Production thus remained the same for year 1 and year 2. Suppose the price of pizza increased from $1 per slice in year 1 to $1.10 per slice in year 2. Nominal GDP in year 1 is $100 (100 units * $1 per unit), and nominal GDP in year 2 is $1.10 (100 units * $1.10 per unit). Nominal GDP has increased by $10, even though no more slices of pizza were produced. If we use nominal GDP to measure growth, we can be misled into thinking production has grown when all that has really happened is a rise in the price level (inflation). If there were only one good in the economy---like pizza---it would be easy to measure production and compare one year's value to another's. We would add up all the pizza slices produced each year. In the example, production is 100 in both years. If the number of slices had increased to 105 in year two, we would say production increased by 5 slices between year one and year two, which is a 5 percent increase. Alas, however, there is more than one good in the economy. The following is a discussion of how the Bureau of Economic Analysis (BEA) adjusts nominal GDP for price changes. As you read the discussion, keep in mind that this adjustment is not easy. Even in an economy of just apples and oranges, it would not be obvious how to add up apples and oranges to get an overall measure of output. The BEA's task is to add up thousands of goods, each of whose price is changing over time.  In the following we will use the concept of a weight, either price weights or quantity weights. What is a weight? It is easiest to define the term by an example. Suppose in an economics course there is a final exam and two other tests. If the final exam counts for one-half of the grade and the other two tests for one-fourth each, the "weights" are one-half, one-fourth, and one-fourth. If instead the final exam counts for 80 percent of the grade and the other two tests for 10 percent each, the weights are .8, .1, and .1. The more important an item is in a group, the larger its weight. Calculating Real GDP Nominal GDP adjusted for price changes is called real GDP. All the main issues involved in computing real GDP can be discussed using a simple three-good economy and 2 years. Table 6 presents all the data that we will need. The table presents price and quantity data for two years and three goods. The goods are labeled A, B, and C, and the years are labeled 1 and 2. P denotes price, and Q denotes quantity. TABLE 6  The first thing to note from Table 6 is that nominal output in current dollars in year one for good A is the price of good A in year 1 ($0.50) times the number of units of good A produced in year 1 (6), which is $3.00. Similarly, nominal output in year 1 is 7 * $0.30 = $2.10 for good B and 10 * $0.70 = $7 for good C. The sum of these three amounts, $12.10 in column 5, is nominal GDP in year 1 in this simple economy. Nominal GDP in year 2---calculated by using the year 2 quantities and the year 2 prices---is $19.20 (column 8). Nominal GDP has risen from $12.10 in year 1 to $19.20 in year 2, an increase of 58.7 percent. You can see that the price of each good changed between year 1 and year 2---the price of good A fell ($0.50 cents to $0.40) and the price of goods B and C rose (B from $0.30 to $1.00; C from $0.70 to $0.90). Some of the change in nominal GDP between years 1 and 2 is due to price changes and not production changes. How much can we attribute to price changes and how much to production changes? Here, things get tricky. The procedure that the BEA used prior to 1996 was to pick a base year and use the prices in that base year as weights to calculate real GDP. This is a fixed-weight procedure because the weights used, which are the prices, are the same for all years---namely, the prices that prevailed in the base year.  This example shows that growth rates can be sensitive to the choice of the base year---24.8 percent using year 1 prices as weights and 4.3 percent using year 2 prices as weights. The old BEA procedure simply picked one year as the base year and did all the calculations using the prices in that year as weights. The new procedure makes two important changes. The first (using the current example) is to "split the difference" between 24.8 percent and 4.3 percent. What does "splitting the difference" mean? One way would be to take the average of the two numbers, which is 14.55 percent. What the BEA does is to take the geometric average (The geometric mean is most appropriate for series that exhibit serial correlation. This is especially true for investment portfolios (investopedia.com)], which for the current example is 14.09 percent. These two averages (14.55 percent and 14.09 percent) are quite close, and the use of either would give similar results. The point here is not that the geometric average is used, but that the first change is to split the difference using some average. Note that this new procedure requires two "base" years, because 24.8 percent was computed using year 1 prices as weights and 4.3 percent was computed using year 2 prices as weights. The second BEA change is to use years 1 and 2 as the base years when computing the percentage change between years 1 and 2, then use years 2 and 3 as the base years when computing the percentage change between years 2 and 3, and so on. The two base years change as the calculations move through time. The series of percentage changes computed in this way is taken to be the series of growth rates of real GDP, and so in this way nominal GDP is adjusted for price changes. To make sure you understand this, review the calculations in Table 6; all the data you need to see what is going on are in this table.  Calculating the GDP Deflator We now switch gears from real GDP, a quantity measure, to the GDP deflator, a price measure. One of economic policymakers' goals is to keep changes in the overall price level small. For this reason policymakers need not only good measures of how real output is changing but also good measures of how the overall price level is changing. The GDP deflator is one measure of the overall price level. We can use the data in Table 6 to show how the GDP deflator is computed by the BEA. In Table 6 the price of good A fell from $0.50 in year 1 to $0.40 in year 2; the price of good B rose from $0.30 to $1; and the price of good C rose from $0.70 to $0.90 cents. If we were interested only in how individual prices change, this is all the information we would need. However, if we are interested in how the overall price level changes, we need to weight the individual prices in some way. The obvious weights to use are the quantities produced, but which quantities---those of year 1 or of year 2? The same issues arise here for the quantity weights as for the price weights in computing real GDP. Let us first use the fixed-weight procedure and year 1 as the base year, which means using year 1 quantities as the weights. Then in Table 6, the "bundle" price in year 1 is $12.10 (column 5), and the bundle price in year 2 is $18.40 (column 7). Both columns use year 1 quantities. The bundle price has increased from $12.10 to $18.40, an increase of 52.1 percent. Next use the fixed-weight procedure in year 2 as the base year, which means using year 2 quantities as the weights. Then the bundle price in year 1 is $15.10 (column 6), and the bundle price in year 2 is $19.20 (column 8). Both columns use year 2 quantities. The bundle price has increased from $15.10 to $19.20, an increase of 27.2 percent.  This example shows that overall price increases can be sensitive to the choice of the base year: 52.1 percent using year 1 quantities as weights and 27.2 percent using year 2 quantities as weights. Again, the old BEA procedure simply picked one year as the base year and did all the calculations using the quantities in the base year as weights. The new procedure first split the difference between 52.1 percent and 27.2 percent by taking the geometric average, which is 39.1 percent. Second, it uses year 1 and 2 as the base years when computing the percentage change between years 1 and 2, years 2 and 3 as the base years when computing the percentage change between years 2 and 3, and so on. The series of percentage changes in the GDP deflator, that is, a series of inflation rates of the overall price level. The Problems of Fixed Weights To see why the BEA switched to the new procedure, let us consider a number of problems with using fixed-price weights to compute real GDP. First, 1987 price weights, the last price weights the BEA used before it changed procedures, are not likely to be very accurate for, say, the 1950s. Many structural changes have taken place in the U.S. economy in the last 30 to 40 years, and it seems unlikely that 1987 prices are good weights to use for the 1950s. Another problem is that the use of fixed-price weights does not account for the responses in the economy to supply shifts. Say bad weather leads to a lower production of oranges in year 2. In a simple supply and demand diagram for oranges, this corresponds to a shift of the curve to the left, which leads to an increase in the price of oranges and a decrease in the quantity demanded. As consumers move up the demand curve, they are substituting away from oranges. If technical advances in year 2 result in cheaper ways of producing computers, the result is a shift of the computer supply curve to the right which leads to a decrease in the price of computers and an increase in the quantity demanded. Consumers are substituting toward computers. (You should be able to draw supply and demand diagrams for both these cases.) Table 6 shows this tendency. The quantity of good A rose between years 1 and 2 and the price decreased (the computer case), whereas the quantity of good B fell and the price increased (the orange case). The computer supply curve has been shifting to the right over time, due primarily to technical advances. The result has been large decreases in the price of computers and large increases in the quantity demanded.  To see why these responses pose a problem for the use of fixed-price weights, consider the data in Table 6. Because the price of good A was higher in year one, the increase in production of good A is weighted more if we use year 1 as the base year than if we used year 2 as the base year. Also, because the price of good A was lower in year 1, the decrease in production of good B is weighted less if we use year 1 as the base year. These effects make the overall change in real GDP larger if we use year 1 price weights than if we use year 2 price weights. Using year 1 price weights ignores the kinds of substitution responses discussed in the previous paragraph and leads to what many feel are too-large estimates of real GDP changes in the past, the BEA tended to move the base year forward about every five years, resulting in the past estimates of real GDP growth being revised downward. It is undesirable to have past growth estimates change simply because of the change to a new base year. The new BEA procedure avoids many of these fixed weight problems. Similar problems arise when using fixed quantity weights to compute price indexes. For example, the fixed-weight procedure ignores the substitution away from goods whose prices are increasing and toward goods whose prices are decreasing or increasing less rapidly. The procedure tends to overestimate the increase in the overall price level. As discussed in upcoming posts, there are still a number of price indexes that are computed using fixed weights. The GDP deflator differs because it does not use fixed weights. It is also a price index for all the goods and services produced in the economy. Other price indexes cover fewer domestically produced goods and services but also include some imported (foreign-produced) goods and services. It should finally be stressed that there is no "right" way of computing real GDP. The economy consists of many goods, each with its own price, and there is no exact way of adding together the production of the different goods. We can say that the BEA's new procedure for computing real GDP avoids the problems associated with the use of fixed weights, and it seems to be an improvement over the old procedure. We will see in upcoming posts, however, that the Consumer Price Index (CPI)---a widely used price index---is still computed using fixed weights.  *CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 401-404* end |
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