## CPI vs GDP Deflator

In this article the Consumer Price Index and GDP deflator will both be covered, leading on from introducing them in the article on Macroeconomics – Theory & Data. The increase in the overall price level is called inflation, therefore, economists use the GDP deflator and CPI to measure Inflation. “The first difference is that GDP deflator measures the prices of all goods and services produced, whereas the CPI measures the prices of only goods and services bought by consumers.” (Mankiw, 2010)

Source: (Mankiw, 2010).

**Gross Domestic Product deflator**

GDP measures aggregate spending in dollars, which only attempts to measure accounting performance, and ignores all non-market forms of production, illegal production, economic profits and losses, value of leisure, clean environment, and volunteer work. “Economists call the value of goods and services measured at current prices **nominal GDP**.” (Mankiw, 2010) Nominal GDP multiplies current prices by current quantities. Changes in nominal GDP stem from changes in both prices and quantities. This would distort GDP if only a rise in prices increased GDP, where no extra goods or services have been produced. “For this purpose, economists use **real GDP**, which is the value of goods and services measured using a constant set of prices.” (Mankiw, 2010) Real GDP multiplies current quantities by base prices. Changes in real GDP stem from changes in quantities only.

After you have learned how to calculate the nominal and real GDP you can calculate the GDP deflator. “The **GDP deflator**, also called the implicit price deflator for GDP, is the ratio of nominal GDP to real GDP: GDP deflator = Nominal GDP [divided by] Real GDP [times 100.]” (Mankiw, 2010) The change in GDP deflators over the term (chain-weighted real GDP updates base year annually) is the inflation rate. Two tricks of arithmetic “[1] the percentage change of a product of two variables is approximately the sum of the percentage changes in each of the variables, [ and 2 the] percentage change of a ratio is approximately the percentage change in the numerator minus the percentage change in the denominator.” (Mankiw, 2015)

**Consumer Price Index**

“The most commonly used measure of the level of prices is the **consumer price index** **(CPI)**.” (Mankiw, 2010) The CPI is calculated by the Bureau of Labor Statistics for the United States. “And this is, then, taken to be a fair and reasonable estimate – to the decimal point! – about the cost of living and the rate of price inflation for all the people of the United States.” (Embeling, 2016) CPI being a statistical measure of average changes in consumer prices brought about by inflation. CPI uses are that it tracks changes in household cost of living, adjusts many contracts/government benefits for inflation, allows comparisons of dollar amount over time. CPI measuring prices of purchased goods and services is different from the GDP deflator measuring prices of produced goods and services. GDP Deflator is the ratio of nominal to real GDP.

Drawbacks include it is merely a statistical calculation based on averages of other price data – not an economic variable of its own, being a derivative, surveys consumers and decides on the composition of a typical consumer’s basket of goods. Having every month collected data and prices of all items in the basket, and computed cost of the basket. “[However, due] to the costs of doing detailed consumer surveys and the desire to have an unchanging benchmark for comparison, this consumer basket of goods is only significantly revised about every ten years or so.” (Embeling, 2016) Meaning that consumers are assumed to be continuing to be buying the same amount of goods, even though new goods in reality come on the market and old goods are no longer sold, while quality of goods are improved, and changes in prices accurately reflect consumers preferences and market price signals. “[Also, this] means that your household basket of goods is different in various ways from mine, and our respective baskets are different from everyone else’s.” (Embeling, 2016)

Summary of issues of CPI (i) using fixed weights it does not reflect consumers’ ability to substitute toward goods whose relative prices have fallen, (ii) introduction of new goods makes consumers better off and then increases the real value of the dollar, however does not reduce CPI as for fixed weights, (iii) changes in quality are not fully measured even though quality improvements increase the value of the dollar.

If the government were to impose a significant increase in the price of gasoline in the name of “saving the planet” from carbon emissions, it will impact people very differently depending up whether an individual is a traveling salesman or a truck driver who has to log hundreds or thousands of miles a year, compared to a New Yorker who takes the subway to work each day, or walks to his place of business. (Embling, 2016)

“The Consumer Price Index is an artificial statistical creation from an arithmetic adding, summing and averaging of thousands of individual prices, a statistical composite that only exists in the statistician’s calculations.” (Embling, 2016) That is why when CPI is low as of its statistical flaws “[most] monetary central planners at the Federal Reserve seem to have concluded, therefore, that they have plenty of breathing space to continue their aggressive monetary expansion when looking at the CPI and related price indices as part of the guide in deciding upon their money and interest rate manipulation policies.” (Embeling, 2016)

**CPI vs GDP deflator**

Firstly, the prices of capital goods are included in the GDP deflator if they are produced domestically, whilst they are excluded from CPI. Secondly, the prices of imported consumer goods are included in CPI, whilst excluded from the GDP deflator. As CPI is a fixed basket of goods and changing prices, whilst GDP deflator has a fixed price, with changing quantities. “Economists call a price index with a fixed basket of goods a Laspeyres index [CPI overstates increases in cost of living as no account for substitute goods,] and a price index with a changing basket a Paasche index [GDP deflator understates the increase in the cost of living, even though it accounts for substitute goods, it does not count any resulting reduction in consumer welfare from such goods].” (Mankiw, 2010) To measure the average there is an index called the Fisher index.

Now you try:

A. Consider the following economy that produces two products, oranges and apples:

Oranges Apples

2014 p $10 $5

2014 qty 50 100

2015 p $20 $6

2015 qty 45 110

With 2014 as the base year,

(i) Calculate the implicit price deflator

(ii) Calculate the CPI

(iii) Explain the difference between the two

Answers:

(i) From the workings out below there is a 56% inflation rate over the years 2014-15.

The implicit price deflator (Paasche index) as nominal spending divided by real spending multiplied by 100, you must compute for both base and current years.

First, compute nominal GDP (P x Q both same year) and real GDP (Q x base year P):

Nominal GDP

2014: $1000 = ($10 x 50 + $5 x 100)

2015: $1560 = ($20 x 45 + $6 x 110)

Real GDP

2014: $1000 = ($10 x 50 + $5 x 100)

2015: $1000 = ($10 x 45 + $5 x 110)

GDP deflator

2014: 100 = 100 x ($1000 / $1000)

2015: 156 = 100 x ($1560 / $1000)

= 156 – 100 = 56 or 56%

(ii) From the workings out below there is a 60% increase in prices over years 2014-15.

The CPI (Laspeyres index) as the cost of the basket current divided by basket base multiply by 100, to compute for base and current years.

First, compute the cost of baskets (current P x base Q):

Cost of Basket

2014: $1000 = ($20 x 50)

2015: $1600 = ($6 x 100)

CPI

2014: 100 = ($1000 / $1000 x 100)

2015: 160 = ($1600 / $1000 x 100)

= 160 – 100 = 60 or 60%

(iii) Explain the difference between the two, GDP deflator and CPI. Where a Laspeyres index (CPI) tends to overstate the price change, and a Paasche index (GDP deflator) tends to understate the price change.The GDP deflator has increased 56% and the CPI has increased 60%.

B. Sarah only consumes apples. In year 1, red apples cost $1 each, green apples cost $2 each, and Sarah buys 10 red apples. In year 2, red apples cost $2, green apples cost $1, and Sarah buys 10 green apples.

(i) Compute a CPI for apples for each year. Assume that year 1 is the base year in which the consumer basket is fixed. How does your index change from year 1 to year 2?

(ii) Compute Sarah’s nominal spending on apples in each year. How does it change from year 1 and year 2?

(iii) Using year 1 as the base year, compute Sarah’s real spending on apples in each year. How does it change from year 1 and year 2?

(iv) The implicit price deflator as nominal spending divided by real spending, compute the deflator for each year. How does the deflator change form year 1 to year 2?

(v) Suppose Sarah is equally happy eating red or green apples. How much has the true cost of living increased for Sarah? Compare this answer to your answers to part (i) and (ii). What does this example tell you about Laspeyres and Paasche price indexes?

Answer:

An increase by 100 index points from year 1 and year 2:

CPI year 1 = 100

CPI year 2 = 200

Years 1 2

Apples Q P Q P

Red 10 $1 0 $2

Green 0 $2 10 $1

(i) Sarah’s CPI for apples in each year, if year is the base year, the index in year one is 100 and in year two is 200, with a 100 index point increase.

Cost of Basket (current P x base Q)

year 1 = 10 (10 x $1 + 0 x $2)

year 2 = 20 (10 x $2 + 0 x $1)

CPI (current year / base year x 100)

year 1 = 100 (10 / 10 x 100)

year 2 = 200 (20 / 10 x 100)

(ii) Sarah’s nominal spending on apples in each year are both 10 and do not change from year 1 or year 2:

Nominal GDP (P x Q + P x Q in current year)

year 1 = 10 (10 x $1 + 0 x $2)

year 2 = 10 (0 x $2 + 10 x $1)

(iii) If year 1 is the base year Sarah’s real spending on apples in each year is 10 in year 1 and 20 in year 2, with a 10 index point change.

Real GDP (base P x current Q)

year 1 = 10 (10 x $1 + 0 x $2)

year 2 = 20 (0 x $1 + 10 x $2)

(iv) The GDP deflator for year 1 is 100 and for year 2 is 50, with a decrease of 50 index points.

GDP deflator (Nom / Real)

year 1 = 100 = 100 x 10 / 10

year 2 = 50 = 100 x 10 / 20

(v) Sarah being equally happy with red or green apples, the true cost of living has increased for Sarah by prices doubling by 50%, with CPI in year 1 being 100 and in year 2 being 200.

By comparing it with the answers from (i) and (ii) CPI (Laspyres index) rises from 100-200 in years 1-2, GDP deflator (Paasche index) decreases from 100-50 in years 1-2. As the GDP deflator counters for rises in prices and CPI overstates price increases.

*Reference List*

Mankiw, G. (2010). *Macroeconomics*. (International 3^{rd} ed.). New York, United States of America: Worth Publishers.

Embeling, R. (2016). *Price inflation and the consumer price index*. Capitalism Magazine. Retrieved [06/06/2016] from <http://capitalismmagazine.com/2016/05/price-inflation-and-the-consumer-price-index/>.

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*Copyright ©* 2016 Zoë-Marie Beesley

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