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Kurs: Makroekonomia > Rozdział 1

Lekcja 4: Realny i nominalny PKB

Dostosowywanie wartości nominalnych do wartości realnych

Dowiedz się w jaki sposób dostosowujemy PKB do danych o inflacji.

Kluczowe pojęcia

The nominal value of any economic statistic is measured in terms of actual prices that exist at the time.
The real value refers to the same statistic after it has been adjusted for inflation.
To convert nominal economic data from several different years into real, inflation-adjusted data, the starting point is to choose a base year arbitrarily and then use a price index to convert the measurements so that they are measured in the money prevailing in the base year.

Wprowadzenie

When we examine economic statistics, it's crucial to distinguish between nominal and real measurements so we know whether or not inflation has distorted a given statistic.

Looking at economic statistics without considering inflation is like looking through a pair of binoculars and trying to guess how close something is—unless you know how strong the lenses are, you cannot guess the distance very accurately. Similarly, if you do not know the rate of inflation, it is difficult to figure out if a rise in gross domestic product, or GDP, is due mainly to a rise in the overall level of prices or to a rise in quantities of goods produced.

The nominal value of any economic statistic means the statistic is measured in terms of actual prices that exist at the time. The real value refers to the same statistic after it has been adjusted for inflation. Generally, it is the real value that is more important.

Converting nominal GDP to real GDP

The table and graph below shows US GDP at five-year intervals since 1960 in nominal dollars, in other words, GDP measured using the actual market prices prevailing in each stated year.

If an unwary analyst compared nominal GDP in 1960 to nominal GDP in 2010, it might appear that national output had risen by a factor of 27 over this time—GDP of

$ 14, 958

billion in 2010 divided by GDP of

$ 543

billion in 1960. This conclusion would be highly misleading, though.

We need to figure out the change in real GDP from 1960 to 2010 to truly understand how much the national output has risen.

US nominal GDP and the GDP deflator
Year	Nominal GDP in billions of dollars	GDP deflator, 2005 = 100
1960	543.3	19.0
1965	743.7	20.3
1970	1,075.9	24.8
1975	1,688.9	34.1
1980	2,862.5	48.3
1985	4,346.7	62.3
1990	5,979.6	72.7
1995	7,664.0	81.7
2000	10,289.7	89.0
2005	13,095.4	100.0
2010	14,958.3	110.0

Source: www.bea.gov

Remember, nominal GDP is defined as the quantity of every good or service produced multiplied by the price at which it was sold, summed up for all goods and services. In order to see how much production has actually increased, we need to extract the effects of higher prices on nominal GDP. We can do this using the GDP deflator.

The GDP deflator is a price index measuring the average prices of all goods and services included in the economy. The data for the GDP deflator are given in the table above and shown visually in the graph below.

When you read "2005=100" in the table, you know that 2005 is our base year.

Whenever you compute a real statistic, one year—or period—plays a special role. This year or period is called the base year or base period.

The base year is the year whose prices are used to compute the real statistic. When we calculate real GDP, for example, we take the quantities of goods and services produced in each year—for example, 1960 or 1973—and multiply them by their prices in the base year—in this case, 2005—to get a measure of GDP that uses prices that do not change from year to year. That is why you'll see real GDP labeled “2005 dollars,” indicating that in this instance real GDP is constructed using prices that existed in 2005.

The formula used to calculate the GDP deflator is below.

GDP deflator = \frac{Nominal GDP}{Real GDP} \times 100

Rearranging the formula and using the data from 2005, we get the following:

Real GDP = \frac{Nominal GDP}{Price Index / 100}

Real GDP = \frac{$ 13, 095.4 billion}{100 / 100}

Real GDP = $ 13, 095.4 billion

If you compare the real GDP you just calculated for 2005 and the nominal GDP listed for 2005 in the table above, you'll see they are the same. This is no accident. It is because 2005 has been chosen as the base year in this example. Since the price index in the base year always has a value of 100—by definition—nominal and real GDP are always the same in the base year.

Now let's take a look at the data for 2010.

Real GDP = \frac{Nominal GDP}{Price Index / 100}

Real GDP = \frac{$ 14, 958.3 billion}{110 / 100}

Real GDP = $ 13, 598.5 billion

We can use this new data to come to another conclusion—as long as inflation is positive, meaning prices increase on average from year to year, real GDP should be less than nominal GDP in any year after the base year.

This is because the value of nominal GDP is increased by inflation. Similarly, as long as inflation is positive, real GDP should be greater than nominal GDP in any year before the base year.

The graph above shows that the price level has risen dramatically since 1960. The price level in 2010 was almost six times higher than in 1960—the deflator for 2010 was 110 versus a level of 19 in 1960. Based on this information, we know that much of the apparent growth in nominal GDP was due to inflation, not an actual change in the quantity of goods and services produced—in other words, not in real GDP.

The graph below shows the US nominal and real GDP since 1960. Because 2005 is the base year, the nominal and real values are exactly the same in that year. However, over time, the rise in nominal GDP looks much larger than the rise in real GDP—the nominal GDP line rises more steeply than the real GDP line—because the rise in nominal GDP is exaggerated by the presence of inflation, especially in the 1970s.

Okay! Now to solve our problem! How much did the national output rise between 1960 and 2010? In other words, what was the change in real GDP?

Nominal GDP can rise for two reasons: an increase in output and/or an increase in prices. Knowing that, we can extract the increase in prices from nominal GDP in order to measure only changes in output.

Step 1: Understand that nominal measurements are in value terms.

Value = Price \times Quantity

lub

Nominal GDP = GDP Deflator \times Real GDP

Let’s step aside for a minute and look at an example at the micro level to better understand the concept. Suppose a t-shirt company, Coolshirts, sells 10 t-shirts at a price of $9 each. We can calculate Coolshirts' nominal revenue from sales using the formula below:

Nominal revenue from sales = Price \times Quantity

Nominal revenue from sales = $ 9 \times 10

Nominal revenue from sales = $ 90

Next, let's calculate Coolshirts' real income.

Real income = \frac{Nominal revenue}{Price}

Real income = \frac{$ 90}{$ 9}

Real income = 10

In other words, when we compute real measurements we are trying to get at actual quantities—in this case, 10 t-shirts.

Step 2: Calculate real GDP using the formula below.

Real GDP = \frac{Nominal GDP}{Price Index}

Mathematically, a price index is a two-digit decimal number like 1.00 or 0.85 or 1.25. But—because some people have trouble working with decimals—the price index has traditionally been multiplied by 100 to get integer numbers like 100, 85, or 125 when it's published. This means that when we deflate nominal figures to get real figures—by dividing the nominal by the price index—we also need to remember to divide the published price index by 100 to make the math work. So, we change our real GDP formula slightly:

Real GDP = \frac{Nominal GDP}{Price Index / 100}

Step 3: Calculate rate of growth of real GDP from 1960 to 2010.

To find the real growth rate, we apply the formula for percentage change:

\frac{2010 real GDP - 1960 real GDP}{1960 real GDP} \times 100 = percent change

13, 598.5 - 2, 859.52, 859.5 \times 100 = 376

In other words, the US economy has increased real production of goods and services by 376%—nearly a factor of four—since 1960. Of course, that understates the material improvement since it fails to capture improvements in the quality of products and the invention of new products.

Try it on your own!

The table below contains all the data you need to compute real GDP.

Step 1. Pull necessary information from the table.

To compute real GPD for 1960, we need to know that in 1960 nominal GDP was $543.3 billion and the price index, or GDP deflator, was 19.0.

Step 2. Calculate the real GDP in 1960.

Real GDP = \frac{Nominal GDP}{Price Index / 100}

Real GDP = \frac{$ 543.3 billion}{19 / 100}

Real GDP = $ 2, 859.5 billion

Step 3. Use the same formula to calculate the real GDP in 1965.

Real GDP = \frac{Nominal GDP}{Price Index / 100}

Real GDP = \frac{$ 743.7 billion}{20.3 / 100}

Real GDP = $ 3, 663.5 billion

Step 4. Continue using this formula to calculate all of the real GDP values from 1970 through 2010.

You can double check your answers by looking at the far-right column in the table below.

Converting nominal to real GDP
Year	Nominal GDP in billions of dollars	GDP deflator, 2005 = 100	Calculations	Real GDP in billions of 2005 dollars
1960	543.3	19.0	543.3 / (19.0/100)	2859.5
1965	743.7	20.3	743.7 / (20.3/100)	3663.5
1970	1075.9	24.8	1,075.9 / (24.8/100)	4338.3
1975	1688.9	34.1	1,688.9 / (34.1/100)	4952.8
1980	2862.5	48.3	2,862.5 / (48.3/100)	5926.5
1985	4346.7	62.3	4,346.7 / (62.3/100)	6977.0
1990	5979.6	72.7	5,979.6 / (72.7/100)	8225.0
1995	7664.0	82.0	7,664 / (82.0/100)	9346.3
2000	10289.7	89.0	10,289.7 / (89.0/100)	11561.5
2005	13095.4	100.0	13,095.4 / (100.0/100)	13095.4
2010	14958.3	110.0	14,958.3 / (110.0/100)	13598.5

Source: Bureau of Economic Analysis, www.bea.gov

Podsumowanie

The nominal value of any economic statistic is measured in terms of actual prices that exist at the time.
The real value refers to the same statistic after it has been adjusted for inflation.
To convert nominal economic data from several different years into real, inflation-adjusted data, the starting point is to choose a base year arbitrarily and then use a price index to convert the measurements so that they are measured in the money prevailing in the base year.

Pytania do samodzielnego sprawdzenia swojej wiedzy

Based on data from the table in the Try it on your own! section, how much of the nominal GDP growth from 1980 to 1990 was real GDP and how much was inflation?

Pytania do powtórzenia

What is the difference between a series of economic data over time measured in nominal terms versus the same data series over time measured in real terms?
How do you convert a series of nominal economic data over time to real terms?

Critical thinking question

Should people typically pay more attention to their real income or their nominal income? If you choose the latter, why would that make sense in today’s world? Would your answer be the same for the 1970s?

Zadania

The prime interest rate is the rate that banks charge their best customers. Based on the nominal interest rates and inflation rates given in the table below, in which of the years given would it have been best to be a lender? In which of the years given would it have been best to be a borrower?

Year	Prime interest rate	Inflation rate
1970	7.9%	5.7%
1974	10.8%	11.0%
1978	9.1%	7.6%
1981	18.9%	10.3%

A mortgage loan is a loan that a person makes to purchase a house. The table below provides a list of the mortgage interest rate being charged for several different years and the rate of inflation for each of those years. In which years would it have been better to be a person borrowing money from a bank to buy a home? In which years would it have been better to be a bank lending money?

Year	Mortgage interest rate	Inflation rate
1984	12.4%	4.3%
1990	10%	5.4%
2001	7.0%	2.8%

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