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### Course: Macroeconomics>Unit 1

Lesson 4: Real and nominal GDP

# Adjusting nominal values to real values

Learn how and why we adjust GDP numbers for inflation.

## Key points

• 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.

## Introduction

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 $\mathrm{}14,958$ billion in 2010 divided by GDP of $\mathrm{}543$ 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
YearNominal GDP in billions of dollarsGDP deflator, 2005 = 100
1960543.319.0
1965743.720.3
19701,075.924.8
19751,688.934.1
19802,862.548.3
19854,346.762.3
19905,979.672.7
19957,664.081.7
200010,289.789.0
200513,095.4100.0
201014,958.3110.0
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.
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.

$\text{Value}=\text{Price}×\text{Quantity}$
or
$\text{Nominal GDP}=\text{GDP Deflator}×\text{Real GDP}$

### Step 2: Calculate real GDP using the formula below.

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

### 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:
$\frac{\text{2010 real GDP}–\text{1960 real GDP}}{\text{1960 real GDP}}×100=\text{percent change}$
$\left(13,598.5-2,859.5\right)/2,859.5×100=376$
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.

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. $\text{Real GDP}=\frac{\text{Nominal GDP}}{\text{Price Index}/100}$ ### Step 3. Use the same formula to calculate the real GDP in 1965. $\text{Real GDP}=\frac{\text{Nominal GDP}}{\text{Price Index}/100}$ ### 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 YearNominal GDP in billions of dollarsGDP deflator, 2005 = 100CalculationsReal GDP in billions of 2005 dollars 1960543.319.0543.3 / (19.0/100)2859.5 1965743.720.3743.7 / (20.3/100)3663.5 19701075.924.81,075.9 / (24.8/100)4338.3 19751688.934.11,688.9 / (34.1/100)4952.8 19802862.548.32,862.5 / (48.3/100)5926.5 19854346.762.34,346.7 / (62.3/100)6977.0 19905979.672.75,979.6 / (72.7/100)8225.0 19957664.082.07,664 / (82.0/100)9346.3 200010289.789.010,289.7 / (89.0/100)11561.5 200513095.4100.013,095.4 / (100.0/100)13095.4 201014958.3110.014,958.3 / (110.0/100)13598.5 Source: Bureau of Economic Analysis, www.bea.gov ## Summary • 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. ## Self-check question 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? ## Review questions • 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? ## Problems 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? YearPrime interest rateInflation rate 19707.9%5.7% 197410.8%11.0% 19789.1%7.6% 198118.9%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? YearMortgage interest rateInflation rate 198412.4%4.3% 199010%5.4% 20017.0%2.8% ## Want to join the conversation? • In last problems about primer interest rate and mortgage interest rate: What will be the answers? (8 votes) • I would say that the best year to be a lender is the year in which the difference between the lender's interest rate and the inflation is the highest and the best year for being a borrower is when it is the lowest. If you are a lender you will want to receive at year-end an amount of money that will compensate for the inflation in that year, for the risk taken and will also want a profit. If, for example, the lender's interest rate is below the inflation of that year, it means the lender has a loss, because the money he receives would be less than what would be the compensation for loss in purchasing power. (20 votes) • In the self-question resolution why the deflator is being measured in dollars? - ($72.7−$48.3)/($48.3/100)=51% - This should be a number without unit right?
• I don't think it really matters here because the $cancels out and so it is still without a unit. It was only used as an indicator of the avg price of all goods and services in order to show that prices have increased (positive inflation). (1 vote) • For the self test question, how do we get to 57% of GDP as inflation? I understand how we get the 51% and 39% numbers, but why do we divide 51% by (51+39)? How does this give us our inflation value? (6 votes) • According to the article, an increase in GDP occurs for two reasons: (1) an increase in prices or (2) an increase in output. In the problem, therefore, we had a price increase of 51% and an output increase (i.e., a positive change in real GDP) of 39%. Since an increase in GDP can only occur for two reasons, we can use the ratio 51/(51+39) to determine the percentage of the increase in GDP due to price increases (i.e., inflation). Hope this helps. (3 votes) • But how can we calculate inflation rate ? (2 votes) • There are various ways to do so. For example, you can calculate the inflation rate on chocolate. Let's say that in 2000, you could buy 1 chocolate tablet for 1$. Now, in 2017, the same tablet, same brand, quantity, etc, costs you 1.50$. You'd say that between 2000 and 2017, there was a 50% inflation rate. (5 votes) • In step 3: 2010 real GDP–1960 real GDP / 1960 real GDP why are we dividing by the 1960 real GDP? (3 votes) • Because we are comparing with the GDP of 1960 (based on GDP of 1960, how much has it grown?) (1 vote) • So what if a House gains value? Say it sells for$30,000 in 1970. But in 2010 it's worth is now $300,000 and has been sold again. Is that$270,000 not counted into GDP?
• It's not counted because it's just money changing hands. That $270,000 will be counted later when it is spent on new goods and services/taxed and spent by the government. (3 votes) • why is it important for inflation when comparing nominal quantities ( for example, workers average wages) at different points in time? (2 votes) • Problem 1 "[...] 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?" I have calculated the Real interest rate. So 1974 is the best year for borrowers (they would even get real 1.4% of profit that year). 1981 is the best year for lenders (they would earn real 6.6% that year). Year | Prime interest rate | Inflation rate | Real rate-----+---------------------+----------------+-----------1970 | 7.9% | 5.7% | 1.7%1974 | 10.8% | 11.0% | -1.4%1978 | 9.1% | 7.5% | 0.8%1981 | 18.9% | 10.3% | 6.6% It's interesting how the gut instinct tells us to just subtract the inflation rate from nominal interest rate, but this simplification can give wrong results. It works good when both numbers are small, but the error grows quite sharply: An 1% increase followed by 1% decrease gives 0.01% decrease, that is very close to the same number as before. But a 10% increase followed by 10% decrease gives 1% decrease, which is quite substantial. And, of course 100% decrease gives zero combined with any increases. So just to keep value of money with higher inflation rates the interest rate has to be even higher (in percents). Don't be fooled by +% and -%, they are not the same. (2 votes) • This is driving me nuts! In one of the questions: ''How much of the nominal GDP growth from 1980 to 1990 was real GDP and how much was inflation?'' It tells me that the solution is: ''From 1980 to 1990, real GDP grew by 39%. (\$8,225.0 - \$5,926.5) / \$5,926.5 = 39\%($8,225.0−$5,926.5)/$5,926.5=39%'' Where did they get the$8,225.0 figure from? I can't find it anywhere on any of the tables. The year 1980 never had $8,225.0 as nominal GDP. (2 votes) •$8,225 is Real GDP in billions of 2005 dollars for 1990. It's on the table.
• Nominal rates are the stated rate of something (e.g. nominal interest rate of a $10,000 loan where you have to pay 5% back every year is 5% which is$500 interest per month)