On GDP, Nominal and Real—Lecture Notes for ECO 11

Ó Udayan Roy, Fall 1998.

1. Gross Domestic Product (GDP) is the market value of all final goods and services produced in a country during a year. To calculate the GDP of the United States for 1993 one could follow the steps described below.

Step 1. Write down the amounts produced, in the United States in 1993, of each final good or service and write down the prices at which those final goods and services were sold.

Step 2. Multiply the amount produced of each good by its price to get the market value.

Step 3. Simply add together the market values of the amounts produced of all final goods and services to get the GDP.

2. Consider an economy with only two final goods and services, and let us call them A and B. A and B could be apples and bananas, or airplanes and balloons, or houses and haircuts, ¼ whatever. Table 1 gives some made-up data on this imaginary economy for the years 1980 to 1983. The quantities are in the units of the two goods and the prices are in dollars. (For the time being, ignore the last four columns.)

 Table 1 Outputs Prices Current Prices GDP Constant Prices GDP, measured with the prices of the year... A B A B 1980 1981 1982 1983 1980 1 1 1 1 2 2 8 4.01 5 1981 1 1 4 4 8 2 8 4.01 5 1982 4 2 0.01 4 8.04 6 24 8.04 12 1983 8 2 1 4 16 10 40 8.08 16

The sixth column gives Current Prices GDP. This is simply a more elaborate name for the GDP that I defined above. The qualifier "Current Prices" is added to emphasize the fact that the market value of the quantities produced in each year is calculated with the prices of the same year, rather than the prices of some other year. Apart from being called Current Prices GDP, GDP is sometimes also called Nominal GDP. All three terms mean the same. (Note that Current Prices GDP is calculated using the steps outlined in section 1 above.)

(ALERT: At this point you should take a look at the actual Current Prices GDP data for the United States from 1929 onwards, both annual and quarterly, as published by the U.S. Commerce Department. Here you will also find data on the components of GDP, such as Consumption, Gross Investment, Government Spending, and Net Exports and on the components of those components! The growth rate of Current Prices GDP is also given. Be warned that, owing to the large amount of data at this site, you may need to wait a little for all the data to appear on your screen.)

It should be clear that if the GDP of the United States changes from one year to the next, that change may be caused by changes in the amounts produced of the various final goods and services or by changes in the prices of those final goods and services, or both. This creates a problem because the GDP data tells us nothing about the year to year changes in production alone or the year to year changes in prices alone.

We are particularly interested in measuring the year-to-year changes in overall production because the whole reason for measuring GDP is to get a handle on the economic vigor of a country. We ought to be able to tell, by comparing the economy over several years, whether the economy is getting better or worse. A look at the Table 1 data for 1980 and 1981, however, shows how misleading Current Prices GDP can be in this respect. Although the outputs of A and B are the same in the two years, the Current Prices GDP in 1981 is four times as large as the Current Prices GDP in 1980 simply because the prices of A and B are four times as high in 1981 as in 1980! If you knew only that GDP was \$2 in 1980 and \$8 in 1981—i.e., if you could only see columns 1 and 6 of Table 1—you would be able to say absolutely nothing about how the two years compared purely in terms of production. So, it is clear that we need to find a way to measure GDP in a way that adjusts for changes in prices.

Such inflation-adjusted GDP is also called Real GDP.

3. Note that if we calculated the dollar value of the 1980 outputs and the dollar value of the 1981 outputs using, in both cases, the prices that prevailed in, say, 1981, then it would indeed be possible to make sensible year to year comparisons. This type of GDP is called Constant Prices GDP to highlight the fact that a single set of prices is used, in GDP calculations, for all years.

The seventh column of Table 1 shows that the GDP at 1980 prices was \$2 in 1980, \$2 in 1981, \$6 in 1982 and \$10 in 1983. (Similarly, the table also shows the GDP at 1981 prices, the GDP at 1982 prices and the GDP at 1983 prices for all four years.) Year to year changes in Constant Prices GDP represent only the year to year changes in the amounts of A and B produced. Price variations are not allowed to play any role because the same set of prices—namely, the prices that prevailed in 1980—are used to calculate not only the dollar value of the 1980 outputs, but also the dollar values of the outputs produced in all the other years.

4. When we compare two magnitudes we often calculate the percentage difference between them. If Ms. A earns \$55, 000 a year and Mr. B earns \$50,000 a year, we can say that Ms. A earns 10% more than Mr. B. (We get the 10% answer as follows: [(55,000-50,000)¸ 50, 000]´ 100=10.) Similarly, if the 1981 GDP at 1980 prices is \$55,000 and the 1980 GDP at 1980 prices is \$50,000, we can say that, when measured at 1980 prices, Real GDP was 10% higher in 1981 than in 1980.

The year to year growth rates of Constant Prices GDP can be calculated for the hypothetical data of Table 1. For example, GDP measured at 1981 prices grew from \$8 to \$24 from 1981 to 1982. This is an increase of 200%—the calculation is as follows: [(24-8)¸ 8]´ 100=200. Columns 2–5 of Table 2 give the other percentage growth rates for Constant Prices GDP. (Ignore the last column for the time being.)

 TABLE 2 Growth Rate of Constant Prices GDP (for each year over the previous year) measured at the prices of¼ Chained Growth Rate 1980 1981 1982 1983 1981 0 0 0 0 0 1982 200 200 100 140 145 1983 67 67 0 33 15.33

5. Now, while Constant Prices GDP may seem better than Current Prices GDP for the purpose of comparing the vigor of an economy over different years, it is not without its own problems. Note that Constant Prices GDP measured in 1981 prices grew 200% over 1981-82, whereas Constant Prices GDP measured in 1982 prices grew only 100% over the same period! It is troubling that the 1981-82 growth of Constant Prices GDP depends so heavily on whether the constant prices used are those of 1981 or those of 1982. A way around this problem is to take the average of 200% and 100% as the compromise number for the 1981-82 growth rate. This number is called the Chained Growth Rate for 1981-82.

6. Specifically, the chained growth rate for 1981-82 is calculated from the data in Tables 1 and 2 as follows:

Step 1. Note that the first year of the 1981–1982 period is 1981 and that the second year is 1982. (In steps 2 and 3 below we will concentrate on 1981 prices. Later, in steps 4 and 5 we will use 1982 prices.)

Step 2. Note that GDP at 1981 prices is \$24 in 1982 and \$8 in 1981.

Step 3. Note that \$24 is 300% of \$8. (This is another way of saying that the GDP at 1981 prices grew 200% over 1981-82 as shown in Table 2.)

Step 4. Note that GDP at 1982 prices is \$8 in 1982 and \$4 in 1981.

Step 5. Note that \$8 is 200% of \$4.

Step 6. The chained growth rate for 1981-82 is then given by percent.

For another demonstration of this method, let us calculate the chained growth rate for 1982-83. The first year of the 1982-83 period is 1982. From Table 2, GDP at 1982 prices grew zero percent over 1982-83. The second year of the 1982-83 period is 1983. From Table 2, GDP at 1983 prices grew 33% over 1982-83. Then the chained growth rate for 1982-83 is percent. Finally, it can be checked that the chained growth rate of GDP over 1980-81 is zero, which is not a big surprise since the outputs of A and B do not change over those two years.

To recap, the Chained Growth Rate of Constant Prices GDP for the year y over the previous year, which is year y - 1, can be calculated by working out the following steps.

Step 1. Calculate the Constant Prices GDP for the years y and y - 1using the prices of the year y - 1.

Step 2. Calculate the growth rate for year y (over year y - 1) of Constant Prices GDP measured with the prices of year y - 1. The relevant formula is:

Step 3. Calculate the Constant Prices GDP for the years y and y - 1 using the prices of the year y.

Step 4. Calculate the growth rate for year y over year y - 1 of Constant Prices GDP measured with the prices of year y. This can be done by changing the above formula in the obvious way.

Step 5. Add 100 to the growth rate obtained in step 2. Add 100 to the growth rate obtained in step 4.

Step 6. Multiply the two numbers obtained in step 5 and take the square root of the resulting number.

Step 7. Subtract 100 from the number obtained in step 6. Done!

7. Now that we have got the chained growth rate formula out of the way, let us return to the issue that created the need for the chained growth rate in the first place: Why is it that the 1981-82 growth rate of constant prices GDP is 200% when GDP is measured with 1981 prices, but just 100% when GDP is measured with 1982 prices? To see why, let us look at Table 1. Over 1981-82 the output of commodity B doubled but the output of commodity A quadrupled. Since the price of A was \$4 in 1981 and only one cent in 1982, it is obvious that the quadrupling of the production of A receives substantial weight when 1981 prices are used and virtually no weight when 1982 prices are used. This is why the 1981-82 growth rate is so much smaller when 1982 prices are used than when 1981 prices are used. (This is not to be thought of as a mathematical issue of abstract importance. The boom in the production of computers in the United States over the past decade has been accompanied by a steep fall in computer prices. So, if we calculate the growth, over a typical year, of GDP measured at 1987 prices, the surge in computer output would push up the overall growth rate significantly because computer prices were relatively high in 1987. But if we instead used 1992 prices to calculate constant prices GDP the computer boom would have a smaller effect on the overall growth rate because computer prices were much cheaper in 1992.)

On the other hand, if we consider the 1982-83 period, while we again see sector A's growth outstripping sector B's growth, now the price of A rises over the 1982-83 period. So the growth of sector A pushes up the overall growth rate to a greater extent when 1983 prices are used to calculate constant prices GDP than when 1982 prices are used. This makes the 1982-83 growth of constant prices GDP zero percent when 1982 prices are used and 33 percent when 1983 prices are used.

So, the use of the prices of a later year, rather than an earlier year, in calculating constant prices GDP may reduce or increase the growth rate of constant prices GDP depending on whether prices are falling or rising in the sector that is undergoing relatively rapid growth.

(From even an introductory discussion of supply and demand we would know that when output increases because of an increase in supply, prices tend to fall, and when output increases because of an increase in demand prices tend to rise. In the numerical example that I have been discussing, the growth of the production of A outstrips the growth of the production of B for both the 1981-82 and the 1982-83 periods. But the price of A falls over 1981-82 and rises over 1982-83, reflecting respectively, a supply driven output increase and a demand driven output increase.)

Anyway, to summarize, we don't want growth rates of constant prices GDP to change every time we change the year whose prices are used to measure constant prices GDP. This is the reason why the US Department of Commerce nowadays publishes chained growth rates.

8. Finally, the US Commerce Department nowadays also publishes what it calls GDP at Chained Constant Dollars. So, one could talk, for example, about the 1983 GDP at Chained 1981 dollars or the 1982 GDP at Chained 1983 dollars, etc. The calculations for GDP at Chained Constant Dollars are given in Table 3.

 TABLE 3 Chained GDP at the constant dollars of the year... 1980 1981 1982 1983 1980 2 8 3.28 5.66 1981 2 8 3.28 5.66 1982 4.9 19.6 8.04 13.87 1983 5.6 22.6 9.27 16

In calculating GDP at chained dollars, two rules need to be followed.

First, the GDP for some year X at chained year X dollars is defined to be the Current Prices GDP for year X. Thus, for example, the 1981 GDP at chained 1981 dollars is simply \$8, which is the Current Prices GDP for 1981. Similarly, the 1983 GDP at chained 1983 dollars is \$16, which is the Current Prices GDP for 1983, and so on. So, this first rule allows us to fill in the numbers for the cells on the diagonal of Table 3; these numbers are in boldface.

Second, the GDP for year X+1 at chained year Y dollars—you can put in some actual years for X and Y, as you please—and the GDP for the previous year, year X, at chained year Y dollars should be such that the former exceeds the latter, in percentage terms, by the chained growth rate from year X to year X+1. For example, since the chained growth rate for 1981-82 is 145%, any number in the third row of Table 3 must be 145% higher than the second row number in the same column. That is, any number in the third row must be obtained by multiplying the second row number in the same column by (100+145)/100=2.45. Or, putting it another way, any number in the second row must be obtained by dividing the third row number in the same column by 2.45. So, since the 1983 GDP at chained 1983 dollars was earlier shown to be \$16, and since the 1982-83 chained growth rate was earlier shown to be 15.33%, the 1982 GDP at chained 1983 dollars can be obtained by dividing \$16 by 1.1533. This gives \$13.87. In this way, the reader can use the second rule to fill in the numbers in the off-diagonal cells of Table 3.

9. The GDP for year y in chained year x dollars can also be calculated by working out the following steps.

Step 1. Calculate the Current Prices GDP for year x. (See section 1 if you have forgotten how this is done.)

Step 2. Calculate the Chained Growth Rate of GDP for every pair of adjacent years between the years x and y. (See section 6 if you have forgotten how this is done.)

Step 3. Take each growth rate obtained in step 2 and add 100.

Step 4. Divide each number obtained in step 3 by 100.

Step 5. Multiply together all the numbers obtained in step 4.

Step 6. If the year x precedes the year y, multiply the number obtained in step 1 by the number obtained in step 5. If the year y precedes the year x, divide the number obtained in step 1 by the number obtained in step 5. Done!!

Note: I have assumed that the years x and y are distinct. I have already mentioned that the GDP for year x in chained year x dollars is simply the Current Prices GDP for year x.

(ALERT: Please take a look at the Commerce Department's data on the Real GDP of the United States from 1929 onwards in chained 1992 dollars. This link also gives you the chained growth rates for Real GDP¼ and much much more! And once again, you are warned that you may need to wait a while for all the data to appear on your screen.)

10. To conclude, today's lecture not only highlights some important issues in measuring GDP in a way that allows us to sensibly compare the GDP of various years, it also provides the knowledge of statistical procedure that you would need to understand the GDP statistics published at regular intervals by the US Commerce Department. (See the Commerce Department's "GDP and Other Major NIPA Series, 1929–1997". NIPA is short for National Income and Product Accounts.)