The trend is the general long-term direction of movement in the series and is thought to arise when growth in long-run demand differs from growth in long-run supply. A positive trend, such as that shown in Demonstration 1, would result when increases in long-run demand outpace those in long-run supply. Similarly, a negative trend would occur when increases in long-run supply outpace increases in long-run demand.
One way to analyze a trend is through regression analysis. The analyst would estimate a model such as
\(P_{t} = \alpha + \beta t + \epsilon_{t},\)
where \(P_{t}\) is the price at time \(t\), \(\alpha\) is the average price over the period analyzed, \(\beta\) is the trend coefficient, and \(\epsilon\) is an error term. The regression model could be augmented to include shift variables to remove seasonal components as well as quadratic terms to model cyclical patterns. Provided that the regression model captures the trend, seasonality, and cyclical components, ϵtϵt would reflect the random component of the time series. Another way to visualize a trend is to filter out seasonality and randomness through a moving average as described later in the chapter.
Because trends characterize the longer-term direction in prices, it is often necessary to account for inflation. Inflation refers to general increases in price levels over time. Deflation, by contrast, refers to general decreases in price levels over time. Because of inflation and deflation, the purchasing power of the dollar differs from year to year. In the post World-War II era, the US economy and most other economies have been characterized by inflation. Thus, you may incorrectly conclude that there is a positive trend in prices and that demand has outpaced supply, when in fact the price series simply reflects changes in the purchasing power of the dollar.
Real (Constant) vs. Nominal (Current) Prices
If you had a time machine that took you back to 1970, you would find that the supermarket price of a no-frills loaf of bread was about 24 cents. In 2016, a similar loaf of bread would have costed you about $1.40. These prices are
nominal prices
. Nominal prices are what consumers actually paid for a product at the time of purchase. In 1970, the nominal price was 24 cents, and in 2016 the nominal price was $1.40. However, between 1970 and 2016, the purchasing power of the dollar changed considerably. The 24 cent price reflects the purchasing power of the dollar in 1970 and the $1.40 price reflects the purchasing power of the dollar in 2016. Of course, wages and consumer incomes have increased in nominal terms since 1970 as well.
The adjective “nominal” applies to any monetary value that has not been adjusted for inflation, e.g., nominal incomes, nominal tuition costs, nominal health care costs. Sometimes you will see monetary units expressed as “current dollars”. The adjective “current” is a synonym for “nominal.” Monetary units designated as current have similarly not been adjusted for inflation. If you see a table that has a note indicating that prices are in
current dollars
then you know that you are looking at nominal prices. With this in mind, the following two statements mean the same thing:
-
In nominal terms, the price of a loaf of bread was $0.24 in 1970 and $1.40 in 2016.
-
In current dollars, the price of a loaf of bread was $0.24 in 1970 and $1.40 in 2016.
Real prices
(or
constant prices
), by contrast, always refer to prices in terms of the purchasing power of the dollar in some reference year. Real prices (or constant prices) are adjusted for inflation. With real prices, the purchasing power of the dollar is held constant at some reference or base period. In a table or figure presenting real prices, the title, caption or a footnote will typically indicate the base period. For example, if prices are in constant 1990 dollars, this tells you that
-
The prices are adjusted for inflation, and
-
Prices reflect the purchasing power of the dollar in 1990.
As you will see below, it turns out that in constant 2016 dollars the price of bread was $1.48 in 1970 and $1.40 in 2016. Because these constant prices use 2016 as the reference period. The real price and nominal price will be the same for 2016.
In any kind of analysis with time series data, you would generally want to use real, not nominal, prices, especially if you are examining prices over an extended period of time. However, many sources where you might obtain data for your analysis will present nominal monetary values. For example, total sales figures from a company’s income statement will reflect nominal prices for the year the income statement was generated. If you are looking at a company’s sales over a period of several years, we might erroneously conclude that sales had grown when in actuality inflation, not true sales growth, resulted in higher values of total sales.
Converting Nominal (Current) Values into Real (Constant) Values
To convert any nominal price to a real price you need a broad price index that measures inflation. The most common index used in the United States is the Consumer Price Index for all Urban Consumers (CPI-U). The Consumer Price Index is provided by the US Department of Labor and is released each month. Annual values of the Consumer Price Index for some selected years are reported in Table \(\PageIndex{1}\). You can obtain values of the CPI-U directly from the US Department of Labor’s Bureau of Labor Statistics website (US-BLS 2017).
Table \(\PageIndex{1}\). Consumer Price Index for All Urban Consumers (1982-84 = 100), Selected Years
|
Year
|
CPI-U
|
Year
|
CPI-U
|
|
1960
|
29.6
|
1995
|
152.4
|
|
1965
|
31.5
|
2000
|
172.2
|
|
1970
|
38.8
|
2005
|
195.3
|
|
1975
|
53.8
|
2010
|
218.1
|
|
1980
|
82.4
|
2011
|
224.9
|
|
1982
|
96.5
|
2012
|
229.6
|
|
1983
|
99.6
|
2013
|
233.0
|
|
1984
|
103.9
|
2014
|
236.7
|
|
1985
|
107.6
|
2015
|
237.0
|
|
1990
|
130.7
|
2016
|
240.0
|
A price index, such as the CPI-U presented in Table 1, reflects price levels as a percentage of prices in some base period. 1982-84 is the base period currently being used by the US Bureau of Labor Statistics, the entity responsible for computing the CPI (US-BLS 2017). Take an average of the index values reported in Table 1 for 1982, 1983, and 1984 and you will see that this average is 100.
\(\dfrac{96.5 + 99.6 + 103.9}{3} = 100\)
The BLS has been using the 1982-84 base period since January 1988.
The numbers in Table 1 present price levels as a percentage of the 1982-84 base period. To illustrate, consider the value of the index in 2000. In 2000, the CPI is 172.2. This means that general price levels in 2000 were (172.2 ) = 72.2 percent higher than they were during the 1982-84 base period. Similarly, the value of the index in 2016 is 240.0. Price levels in 2016 were (240-100) = 140 percent higher than in the base period. In 1980, the value of the index is 82.4. This means that price levels were (82.4-100) = -17.6 percent higher (or 17.6 percent lower) than they were during the 1982-84 base period.
The CPI-U reflects prices that consumers pay over a broad category of expense items including, food, housing, transportation, apparel, health care, education, and so forth (US-BLS 2017). As such, it is a measure of the purchasing power of the dollar relative to the base year and can be used to convert nominal prices into real prices.
Notice from Table 1 that the CPI-U increases as time passes. This indicates that the economy has been characterized by inflation. If the CPI fell from one year to the next, it would indicate deflation. Deflation occurred in the US during the great depression of the 1930s. The CPI-U with a base year of 1982-84 fell from 17.2 in 1929 to 12.9 in 1933. During the post-war period, year-to-year changes in the CPI have been positive with few exceptions. In the recent great recession, the annual-average CPI did fall slightly from 215.3 in 2008 to 214.5 in 2009.
Given a broad price index like the CPI-U, nominal prices can be converted into real prices via the following formula:
\(Real \: Price = \dfrac{Nominal \: Price}{Index} \times 100\)
When you do this conversion, your real prices will reflect the purchasing power of the dollar in the base period of your index. Consequently, if we used the CPI in Table \(\PageIndex{1}\) to adjust nominal prices for inflation, we would get a real price series that reflects the purchasing power of the dollar during the 1982-84 period. Using Table \(\PageIndex{1}\), we could get real prices for bread in constant 1982-84 dollars as shown in Table \(\PageIndex{2}\).
Table \(\PageIndex{2}\). Converting Bread Prices from Nominal to Real Terms
|
Year
|
Nominal Price
|
Real Price (1982-84 dollars)
|
|
1970
|
\($0.24\)
|
\(\dfrac{$0.24}{38.8} \times 100 = $0.62\)
|
|
2016
|
\($1.40\)
|
\(\dfrac{$1.40}{240.0} \times 100 = $0.58\)
|
Thus you can conclude that in real terms, the price of a no-frills loaf of bread decreased by 4 cents. The problem is that these 4 cents reflect the purchasing power of 1982-84 dollars. 1982-84 was a long time ago, before most of you were even born. Even old timers might have problems remembering what prices were way back in 1982-84.
Changing the Base Period
Fortunately, the base period of any price index can be changed. All you need to do is
-
choose a new base period,
-
divide the index numbers in all periods by the value of the original index for the new base period, and
-
multiply the resulting new index by 100.
For example, suppose you wanted 2016 to be the base period. Divide every index number in the series by the 2016 value of 240.0 and multiply the resulting new numbers by 100:
\(I^{t}_{2016=100} = \dfrac{I^{t}_{1982-84=100}}{I^{2016}_{1982-84=100}} \times 100,\)
where \(I\) refers to the index, and \(t\) reflects the year in question. This conversion is presented in Table \(\PageIndex{3}\). Note that the index value in column 3 of the table for 2016 is now 100. Because there has been positive inflation during recent years, index values in years prior to 2016 in column 3 all have values less than 100. Take a moment to replicate a few of the transformed index values in the third column of the table.
Table \(\PageIndex{3}\). Consumer Price Index for All Urban Consumers
|
Year
|
1982-84=100
|
2016=100
|
|
1970
|
38.8
|
16.2
|
|
1980
|
82.4
|
34.3
|
|
1990
|
130.7
|
54.5
|
|
2000
|
172.2
|
71.7
|
|
2010
|
218.1
|
90.9
|
|
2016
|
240.0
|
100.0
|
If you use this transformed index (2016=100) to adjust for inflation, you will obtain a real price series that reflects the purchasing power of the dollar in 2016. With this in mind, the real price of bread can be expressed in constant 2016 dollars as shown in Table \(\PageIndex{4}\).
Table \(\PageIndex{4}\). Real and Nominal Prices for Bread
|
Year
|
Nominal Price
|
Real Price (2016 = 100)
|
|
1970
|
\(0.24\)
|
\(\dfrac{0.24}{16.2} \times 100 = 1.48\)
|
|
2016
|
\(1.40\)
|
\(\dfrac{1.40}{100.0} \times 100 = 1.40\)
|
Be sure to notice that the real price equals the nominal price in the base year. This is because real prices reflect the purchasing power in terms of nominal base-year dollars.