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Deflating Nominal Values to Real Values

How to remove the price effect from a data series or change nominal data to real values

The Economic Problem

Importance of Tracking Economic Data
Business and economic researchers like to tally things. They count everything from jobs and houses to cars and toasters. In the aggregate, such information is important because it helps show at what rate the economy is expanding or contracting. And the rate at which the economy grows (independent of population growth) plays an integral part in overall economic well-being.

But Some Economic Concepts Are Difficult to Measure
Even though measuring any part of the economy creates certain logistical challenges, some concepts are simply harder to quantify than others. For example, keeping track of a meaningful measure of retail sales over a 10-year period presents more difficulty than simply recording housing starts in a given neighborhood.

So Count Dollar Value, Not Quantity
Enumerating housing starts is straightforward. Measuring retail sales, on the other hand, is not so easy. Retail goods comprise any number of different products, ranging from computers, kitchen appliances and clothing to auto parts and garden tools. This characteristic of the variable complicates the counting. Statistics keepers avoid the problem by tracking retail sales by dollar amounts, not quantity.

But Price Fluctuations Distort the Data
However, tracking data in this way presents another problem. Since retail sales are measured in dollars, changes in price levels over time tend to distort reported figures. In the case of retail transactions, economists are interested in tracking actual sales, independent of any price movements. This enables them to make sensible comparisons across time periods even as prices move. Unadjusted for, price fluctuations distort the measurement of economic variables measured in dollar values.

$1 Doesn't Buy What It Used to
While there’s still debate over which measure of overall price fluctuation is best, the phenomenon of general price movements over time—either deflation or inflation—is undisputed (Chart 1). A few anecdotes help make the point. Some folks can still remember five-cent candy bars and 29-cent gasoline. It hasn't been too long since hamburger sold at three pounds for a dollar and chicken went for 29 cents a pound. The same four-bedroom house that changed hands for $23,500 in 1970 could easily sell for over $120,000 today.

Solution: Remove Price Effects from the Data
In effect, $20 will buy less retail output today than it did 20 years ago. But for data collectors, a $20 purchase gets added to total sales in the same manner today as it did 20 years ago, even though it represents a different quantity of goods. Separating out the price effect leaves researchers with a clearer picture of what’s really happening to sales levels relative to any time period. The object then becomes to remove any part of the variable’s change that is attributable to price movements, arriving at a real, or inflation adjusted, indicator.

The Technical Solution

Lesser Known Data Unadjusted for Inflation
Though many prominent economic series such as gross domestic product (GDP) and exports are adjusted for inflation, some less prominent indicators are not. A simple methodology can be used to deflate any nominal data series to real values.

Changing Nominal to Real
To transform a series into real terms, two things are needed: the nominal data and an appropriate price index. The nominal data series is simply the data measured in current dollars and gathered by a government or private survey. The appropriate price index can come from any number of sources. Among the more prominent price indexes are the Consumer Price Index (CPI), the Producer Price Index (PPI), the Personal Consumption Expenditure index (PCE) and the GDP deflator.

Common price indexes measure the value of a basket of goods in a certain time period, relative to the value of the same basket in a base period. They are calculated by dividing the value of the basket of goods in the year of interest by the value in the base year. By convention, this ratio is then multiplied by 100.

Generally speaking, statisticians set price indexes equal to 100 in a given base year for convenience and reference. To use a price index to deflate a nominal series, the index must be divided by 100 (decimal form). The formula for obtaining a real series is given by dividing nominal values by the price index (decimal form) for that same time period:

Nominal Value divided by Price Index (decimal form) equals Real Value

Mechanics of Price-Level Effects on Economic Data
But how does this simple formula remove price fluctuations from actual changes in a variable’s overall value? Economic variables measured in dollar values like GDP, exports, construction contract values, venture capital and retail sales are calculated from the product of the quantity sold and the selling price. Analysts want to get their hands around the changes in quantity sold and disregard changes in prices because it’s the quantity of goods and services consumed by households that affects well-being, not the prices. In effect, the percentage change in real values over a given time period should mirror the percentage change in quantity.

Three Sample Scenarios
Table 1 provides three scenarios that show how to correct the data for price fluctuations.

In each scenario price and quantity are multiplied together to arrive at a nominal value in 2005 and 2010. Then the 2010 nominal value is divided by the ratio of the 2010 price index and the 2005 price index to arrive at a real value (or the 2010 value in 2005 dollars).

Table 1            
Deflating 2010 Values to 2005 Dollars
Scenario
Period
Price
Quantity
Nominal value
Deflating nominal to real
Real value
1. Price rises 50%, quantity stays same
2005
100
12
1,200
 
1,200
2010
150
12
1,800
1,800/
(150/100) =
1,200
2. Price stays the same, quantity rises 50%
2005
100
12
1,200
 
1,200
2010
100
18
1,800
1,800/
(100/100) =
1,800
3. Price rises 20%, quantity rises 25%
2005
100
12
1,200
 
1,200
2010
120
15
1,800
1,800/
(120/100) =
1,500

 

The Mechanics of Each Scenario

  • Scenario 1
    Prices rise 50 percent from 2005 to 2010 but the quantity stays the same.
    Result: The nominal value increases 50 percent, but the real value remains the same.
  • Scenario 2
    The price remains constant but quantity increases by 50 percent.
    Result: The real value rises by 50 percent.
  • Scenario 3
    The price rises 20 percent and quantity rises 25 percent.
    Result: After deflating the 2010 value to 2005 dollars, the real value rises 25 percent.

Real-World Example

Finally, a real-world example is in order. Table 2 shows how to deflate four-and-a-half years of nominal quarterly GDP data to real GDP. Column 2 shows nominal GDP. Column 3 is the price series. Column 4 reindexes the price series to the first quarter of 2005 by dividing all price values by 98.8 and multiplying by 100. Column 5 puts the price index in decimal form. Column 6 divides nominal GDP by the price index in decimal form to arrive at real GDP—or GDP not affected by price volatility.

Table 2          
Deflating Nominal GDP
Period
Nominal GDP
(billions of dollars)
Price
index
Reindex to 2005
Decimal
form
Real GDP (2005 dollars)
2005 - Q1
12,362
98.8
100.0
1.000
12,362
2005 - Q2
12,500
99.4
100.6
1.006
12,424
2005 - Q3
12,729
100.5
101.7
1.017
12,510
2005 - Q4
12,901
101.4
102.6
1.026
12,570
2006 - Q1
13,161
101.8
103.1
1.031
12,770
2006 - Q2
13,330
102.5
103.8
1.038
12,839
2006 - Q3
13,433
103.3
104.6
1.046
12,845
2006 - Q4
13,584
103.3
104.6
1.046
12,992
2007 - Q1
13,759
104.3
105.6
1.056
13,033
2007 - Q2
13,977
105.2
106.5
1.065
13,127
2007 - Q3
14,126
105.7
107.1
1.071
13,195
2007 - Q4
14,253
106.8
108.2
1.082
13,177
2008 - Q1
14,274
107.9
109.2
1.092
13,071
2008 - Q2
14,416
109.1
110.4
1.104
13,056
2008 - Q3
14,395
110.2
111.6
1.116
12,899
2008 - Q4
14,082
108.7
110.0
1.100
12,800
2009 - Q1
13,923
108.1
109.4
1.094
12,725
2009 - Q2
13,885
108.5
109.9
1.099
12,640
2009 - Q3
13,952
109.3
110.7
1.107
12,606
2009 - Q4
14,134
110.1
111.5
1.115
12,674
2010 - Q1
14,270
110.6
112.0
1.120
12,738
2010 - Q2
14,414
110.8
112.2
1.122
12,848
2010 - Q3
14,576
111.2
112.5
1.125
12,951
2010 - Q4
14,736
111.8
113.1
1.131
13,024
2011 - Q1
14,815
112.6
114.0
1.140
12,990
2011 - Q2
15,004
113.6
115.1
1.151
13,040
2011 - Q3
15,163
114.3
115.7
1.157
13,103
2011 - Q4
15,321
114.6
116.0
1.160
13,205
2012 - Q1
15,478
115.3
116.7
1.167
13,259
2012 - Q2
15,586
115.5
116.9
1.169
13,328
2012 - Q3
15,811
116.0
117.4
1.174
13,467
2012 - Q4
15864
116.4
117.9
1.179
13,459

Chart 2 illustrates the point graphically. As expected, nominal GDP grows faster than real GDP because it includes inflation. Real GDP growth appears more moderate because the calculation has separated out any pricing effects. The real measure is a better overall indication of the change in output over the sample time period.

Summary

Increases in nominal values, such as the total dollars of retail sales, may arise from increases in prices or increases in quantities sold. Only an increase in quantity points to an improvement in economic well-being, so analysts need an effective way to determine the importance of these competing explanations. Converting nominal values to real values provides a consistent measure across time.

Glossary at a Glance

Deflator: A numeric pricing measure used to change nominal values into real values.

Homogeneous: Of the same or a similar kind or nature.

Nominal: The value of an economic variable in terms of the price level at the time of its measurement; or, unadjusted for price movements.

Real: The value of an economic variable adjusted for price movements.

 

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