### Tutorial 4: A Beginner's Guide to Choosing the Best Deflator

Joanna Short, Augustana College

For various reasons, users often want to adjust historical values for inflation, using a price index, such as the CPI (as we did in Tutorial 1 for the Model T Ford) or the GDP deflator (as we did for 1990-1992 U.S. GDP, in Tutorial 3). Depending on the object of interest and the specific question we have about its value, it may be more appropriate to deflate by the growth in the value of a consumption bundle, or the growth in wages, or the growth in GDP per capita. Notice that the Relative Values calculators provide results using several different deflators. The results vary considerably. Which one is right for you?

First, narrow down the options by identifying the object of interest. Is it:

1. A commodity (a good or service that might be purchased by a consumer. For example: a Model T Ford)
2. Income or wealth (wages, profits, the value of an asset. For example: Ford wages, or the value of an inheritance)
3. A project (an investment by a business or government. For example: the cost of producing a movie or building the Titanic).

1. For example, let¡¯s say we¡¯re interested in the value of a commodity. The most relevant deflators are :

Deflator Result
A. U.S. CPI/U.K. RPI Real price
B. Value of the Consumer Bundle Real value in consumption
C. Wages/Earnings Labor value
D. GDP per capita Income value

Which one we choose depends on the context of our question. For example, recall that we found that an \$850 Model T cost about \$23,600 in 2017 money when we used the CPI. This is the real price, considering the average increase in the cost of a fixed basket of goods and services between 1909 and 2017. However, this may not be appropriate when we want to know how much something ¡°cost¡± to people in the past, in the sense of how much of the household¡¯s budget went to that item.

The problem is that while prices rise over time, our standard of living is rising, too. Thus, overall, the value of what we collectively produce (nominal GDP, or roughly income) tends to grow faster than inflation. This is economic growth. Using the Annualized Growth Rates calculator from 1909 to 2017, U.S. nominal GDP grew at an average of 6.10% per year, while the GDP deflator grew at an average of 2.81% per year. The difference represents economic growth, an increase in real income. Thus, despite inflation, we are able to consume more over time. One can see the gain in the standard of living by thinking about how much more the average person consumes, relative to his or her parents or grandparents generation. It wasn¡¯t that long ago that a standard newly-constructed home featured one bathroom and perhaps a one-car garage. Today, new homes are much larger and in many suburban areas three-car garages are common. As a result, \$23,600 for a Model T is too low as an estimate of the effect the purchase had on household budgets in 1909. Using the CPI, we have adjusted for the inflation for a fixed basket of goods, but not for the fact that, on average, people consumed less in 1909 because the standard of living was much lower. So, spending \$850 on a Model T at the time had a larger effect on the household budget than the \$23,600 indicates. An alternative is to deflate by the Value of the Consumer Bundle, which rises with both changes in inflation and consumption. Using the Relative Values-US \$ calculator, let¡¯s use 1909 as the initial year, \$850 as the initial value, and 2017 as the desired year. Now, scan the results for the real value in consumption of the Model T, which uses the Value of the Consumer Bundle as the deflator. By this measure, the Model T ¡°cost¡± \$49,300 in 2017 dollars. This is probably a better measure of the ¡°cost¡± of the Model T, assuming the effect on a person¡¯s budget¡ªwhat one had to give up¡ªis what we think of as the ¡°cost.¡± Since most people use the CPI for these calculations, most people probably understate the cost of things in the past. However, the Value of the Consumer Bundle is only available after 1900.

Alternatively, we can use options (C) or (D), to adjust by the growth in wages or income over time. This is more appropriate if, rather than wondering how much a Model T cost in terms of the goods or services it would buy today, we are more concerned with how much income one must use to buy a Model T. The distinction may seem slight, but this is a very different question. Wages and income tend to grow faster than the CPI and the VCB, thanks to economic growth and the fact that some gains in income over time are saved rather than consumed. So, we will tend to get an even larger estimate. In fact, using the Relative Values-US \$ comparator, an \$850 Model T is worth \$101,100 in 2017 dollars if adjusted by the growth in the unskilled wage; \$165,000 when adjusted by the growth in production worker compensation; and \$141,000 when adjusted by the growth in GDP per capita.

These results are much larger than our earlier estimates of \$23,600 and \$49,300. However, recall that in Tutorial 1 we used the wage series to estimate that at a nominal compensation rate of \$0.17 per hour for a production worker in 1909, an \$850 Model T ¡°cost¡± 5000 hours of work, or nearly two years¡¯ wages. The \$23,600 and \$49,300 estimates are much too low to represent two years¡¯ income today, as they would imply two years¡¯ wages only for those earning \$11,800 and \$24,650 per year, respectively. These seem much too low by today¡¯s standards of annual income. It¡¯s only when we adjust by wage or GDP per capita that we get an amount that genuinely reflects two years¡¯ wages or income by today¡¯s standards.

2. Now let¡¯s suppose our object of interest is income or wealth. The most relevant deflators are:

Deflator Result
E. CPI /RPI Real wage/wealth
F. Value of the Consumer Bundle Household purchasing power
G. Wage Relative labor earnings
H. GDP per capita Relative income
I. Share of GDP Economic power

Consider Ford¡¯s production worker wages of \$5 per day (\$0.625 per hour, or \$1250 annually) in 1914. We showed in Tutorial 2 that, adjusting by the CPI, this amount is equivalent to \$1770 in 1935 dollars. This showed, in our hypothetical example that a Ford worker who started in 1914 earned more in real terms than his son who began working at Ford in 1935 at \$6 per day, or \$1500 per year. We¡¯ll call this estimate ¡°the real wage that amount would have bought in 1935.¡± Since we have adjusted only by the growth in the CPI, we have accounted only for the inflation of a fixed basket of goods. There has been no adjustment for the change in consumption habits over time. The \$1770 estimate also does not represent an equivalent amount of income, by 1935 standards.

Adjusting for the change in consumption habits over time, we get household purchasing power--\$1540. Note that on this basis, the father and son earned nearly equivalent amounts¡ªwhile not quite keeping up with the inflation of a fixed basket of goods, the son¡¯s wages kept up with contemporary spending (which declined during the Depression era). If instead we¡¯d like to represent an equivalent amount of income, we can adjust using the growth in GDP per capita. Recall that GDP per capita reflects average income. Recall that Ford paid wages that were far above average for production workers. Even in 1935, the \$5 per day (or \$1250 per year) that Ford paid his workers in 1914 would be considerably more than most people earned. To be more precise, according to the data series GDP-US, GDP per capita was \$583.38 in 1935. So, in 1935 \$1250 would ¡°pay¡± the average earnings of:

\$1250 / \$583.38 = 2.14 people.

In 1914, \$1250 represented even more income, because average earnings were much lower. A quick look at the data series shows that nominal GDP per capita in 1914 was \$371.61. Thus, \$1250 could have paid the average earnings of:

\$1250 / \$371.61 = 3.36 people in 1914.

This puts the number into perspective: \$1250 in 1914 was a very good wage. To find the equivalent amount of income in 1935, we could multiply 3.36 by average earnings in 1935 (\$583.38). The result is about \$1960. Notice that the same result is reported by the Relative Values-US \$ calculator as the relative income of \$1250. As before, the \$1960 estimate is a bit larger than the estimate using the CPI (\$1770). This occurs because earnings have risen faster than inflation, thanks to productivity growth which ultimately generates real economic growth. Since this result represents the equivalent amount of income, we¡¯ll call it the ¡°relative income of \$1250.¡±

Finally, we can deflate by the share of GDP that one Ford worker¡¯s earnings represented. Recall that GDP represents the total value of all goods and services produced. Some small fraction of 1914 GDP can be traced to the production of one Ford worker. Then we can apply that fraction to 1935 GDP. This is reported by the Relative Values-US \$ calculator as the economic power of the worker¡¯s earnings, \$2520. A worker as well off as a Ford worker, in terms of the share of GDP devoted to his earnings, would have to earn \$2510 in 1935. We¡¯ll call this result the ¡°economic power of the \$1250,¡± since it represents the equivalent share of GDP. Notice that we get a larger estimate here than we did when deflating by GDP per capita. This occurs because GDP grows faster than GDP per capita when the population is increasing.

3. Finally let¡¯s suppose our object of interest is a project. Now the most relevant deflators are:

Deflator Result
J. GDP deflator Real cost
K. Value of the Consumer Bundle Household cost
L. Wages/Earnings Labor cost
M. Share of GDP Economy cost

Take, for example, the cost to build the Titanic--1.5 million pounds over three years from 1909 to 1912. Suppose we want to adjust that amount for inflation, to see what ¡ê1.5 million could buy today. Frequently we use the CPI or RPI as our measure of inflation, but this only accounts for the inflation of a specific basket of consumer goods. The GDP deflator is a more comprehensive measure of inflation, including capital goods and government spending for goods and services. Since projects like the building of the Titanic are typically financed by firms or government, and would not generally be thought of part of a typical family¡¯s consumption basket, we should use the GDP deflator. This is reported by the Relative Values-UK ¡ê calculator as the real cost of the project. Using this measure, we see that ¡ê1.5 million in 1912 would buy the equivalent of ¡ê147.1 million in 2017 (the latest available desired year at this writing).

Alternatively, we could adjust the ¡ê1.5 million construction cost by the growth in earnings over time. Certainly, a portion of the cost of construction went toward all the labor required to build a massive luxury steamship. Suppose that all of it went toward labor. What would the equivalent amount of labor cost today? Deflating by the growth in average earnings, we find that spending ¡ê1.5 million on labor in 1912 would be the equivalent of ¡ê546 million in 2017.

Finally, we can think of the cost of building the Titanic a little more broadly. What would the economy have to give up, in terms of other production, if today we took on a project taking up the same share of GDP as the building of the Titanic? We can call this result the ¡°economy cost of the project.¡± Deflating by the share of GDP, we find that the economy cost of ¡ê1.5 million in 1912 is about ¡ê1.316 billion in 2017.

More practice examples:

1. What is the real value, in 2017, of purchasing a Model T Ford for \$290 in 1925?
2. What is the equivalent amount of income, in 2017, needed to buy a 1925 Model T?
3. What is the relative income, in 2017, of the prime minister¡¯s salary in 1982 (¡ê38,200)?
4. What is the real cost, in 2017, of the construction of Fenway Park (in 1912 for \$650,000)?
5. What is the economic cost, in 2009, of the construction of Fenway Park? How does this compare to the new Yankee Stadium (\$1.5 billion in 2009)?
6. How does the relative income of the minimum wage in 1938 (\$0.25 per hour) compare to the minimum wage in 2009 (\$7.25 per hour)?

Solutions:

1. \$8,920 is the real value (representing the amount it would take from an average consumer¡¯s budget).
2. The equivalent amount of income would be \$14,100 (using the unskilled wage), \$18,700 (using production worker compensation) or \$21,800 (using GDP per capita).
3. ¡ê207,800 (using GDP per capita)
4. \$12,200,000
5. Fenway¡¯s economy cost is \$248 million, which is only about 16% of the cost of the new Yankee Stadium.
6. The relative income of the 1938 minimum wage is \$19.20, which is more than twice as large as in 2009.
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