### Six Ways to Compute the Relative Value of a U.S. Dollar Amount, 1774 to Present

 using: CPI GDP Deflator Consumer Bundle Unskilled Wage GDP Per Capita (relative share of)      GDP Initial Year *: Initial Amount: Desired Year *: * Select initial and desired from 1774 to present. Enter data as a number without a \$ sign or commas. Why Not 2008?

Determining the relative value of an amount of money in one year compared to another is more complicated than it seems at first. There is no single "correct" measure, and economic historians use one or more different indicators depending on the context of the question.

Most indices are measured as the price of a "bundle" of goods and services that a representative group buys or earns. Over time the bundle changes; for example, carriages are replaced with automobiles, and new goods and services are created such as cellular phones and heart transplants.

These considerations do not stop the fascination with these comparisons or even the necessity for them. For example, such comparisons may be critical to determine appropriate levels of compensation in a legal case that has been deferred. The context of the question, however, may lead to a preferable measure and that measure may not be the Consumer Price Index (CPI), which is used far too often without thought to its consequences.

The example below of what Babe Ruth's salary was "worth" can demonstrate this point. His earnings had a "purchasing power" in today's price of a million dollars, but he could not purchase any effective cure for cancer. His income compared to what the average household spends is three million dollars today and yet there were no television sets to buy and if he could there would be nothing to watch.

However, if the question was how to compare his salary with that of a current super star such as Tiger Woods or Barry Bonds, using Ruth's wage compared to an unskilled worker, the average income or the percent of Gross Domestic Product (GDP) he earned gives comparable numbers.

Presented here are six indicators for making such comparisons in US dollars between any two years from 1774 to 2007. They are the CPI, the GDP Deflator, the consumer bundle, the unskilled wage rate, the GDP per capita, and the GDP. Note that only two indicators, the CPI and unskilled wage are available from 1774 to 1790, and the consumer bundle is only available from 1900 to the present.

One or more of the indicators may be most appropriate for you depending on the nature of your query. See below for the definitions of the indicators and some examples.

### Descriptions of the indicators

• The CPI is most often used to make comparisons partly because it is the series with which people are most familiar. This series tries to compare the cost of things the average household buys such as food, housing, transportation, medical services, etc. For earlier years, it is the most useful series for comparing the cost of consumer goods and services. It can be interpreted as how much money you would need today to buy an item in the year in question if its price had changed the same percentage as the average price change.

• The GDP Deflator is similar to the CPI in that it is a measure of average prices. The "bundle" of goods and services here includes all things produced in the economy, not just consumer goods and services that are reflected in the CPI.

• The Consumer Bundle is the average dollar value of the annual expenditures of a "consumer unit". The consumer unit could be a family or another type of household. The main point is that spending is a joint decision of the members of the unit. The bundle increases over time as household income increases. Unlike the CPI, not only the cost but also the amount of goods and services increases over time. Note, the 2006 value of the consumer bundle will not be published until November 2007.

• The Unskilled Wage Rate is good way to determine the relative cost of something in terms of the amount of work it would take to produce, or the relative time it would take to earn its cost. It can also be useful in comparing different wages over time. The unskilled wage is a more consistent measure than the average wage for making comparisons over time.

• The GDP per capita is an index of the economy's average output per person and is closely correlated with the average income. It can be useful in comparing different incomes over time.

• The GDP is the market value of all goods and services produced in a year. Comparing an expenditure using this measure, tells you how much money in the comparable year would be the same percent of all output.

(Note that these are comparisons of the relative value of an amount of money, and thus the last two are using nominal GDP.)

### Here Are Some Examples

• George Washington was paid a salary of \$25,000 a year from 1789 to 1797 as the first president of the United States. The current salary of the president has recently been doubled to \$400,000, to go with a \$50,000 expense account, a generous pension and several other benefits. Has the remuneration improved?

Making a comparison using the CPI for 1790 shows that \$25,000 corresponds to over \$585,000 today, so the recent raise means current presidents have an equal command over consumer goods as the Father of the Country.

When comparing Washington's salary to an unskilled worker, or the measure of average income, GDP per capita, then the comparable numbers are \$11 and \$24 million. Granted that would not put him in the ranks of the top 25 executives today that make over \$200 million. It would, however, be many times more than any elected official in this country is paid today. Finally, to show the "economic power" of his wage, we see that his salary as a share of GDP would rank him equivalent to \$1.8 billion.

• The Erie Canal was built between 1817 and 1825, for a price of \$7 million. This waterway is regarded as one of the most important investments in the nineteenth century as it opened the Midwest to trade and migration. How does its cost compare to what its cost would be today?

Using the GDP deflator for 1825 shows that it would be \$165 million, not more than the cost today of a few miles of Interstate highway. Using the unskilled wage measure the cost is \$1.6 billion, a bit more, by GDP per capita the cost is close to \$4.4 billion and as a fraction of GDP it comes in close to \$120 billion. As a comparison the current budget of the U.S. Department of transportation is \$60 billion.

Because of the volatility of prices in that period, if we had chosen 1817 instead of 1825, the GDP deflator computations would have been about 25% less and the other three variables are different by similar magnitudes as well. This is a good example of how "approximate" these comparisons are.

• The Civil War was one of the most devastating events in the history of the United States. It lasted from 1861 to 1865 and has been estimated to have direct cost about \$6.7 billion valued in 1860 dollars. If this number were evaluated in dollars of today using the GDP deflator it would be \$139 billion, less that one year of the cost of the current war in Iraq. This would be inappropriate, as would be using the wage or income indexes. The only measure that makes sense for an expenditure of this size is to use the share of GDP, as the four year cost of the war was more that the entire output of the country. Thus the relative value of \$6.7 billion of 1860 would be \$21 trillion today, or about 145% of our current GDP.

The \$6.7 billion does not take into account that the war disrupted the economy and had an impact of lower production into the future. Some economic historians have estimated this additional, or indirect cost, to be another \$7.3 billion measured on 1860 dollars. This means the cost of the war (as a share of the output of the economy) was nearly \$45 trillion as measured in current dollars.

• The Model T Ford cost \$850 in 1908; however by 1925 the price had fallen to \$290. How do we compare these values? If you wanted to compare the two years you would see that by using the CPI, the GDP deflator or the consumer bundle, \$850 in 1908 is equivalent to between \$1,485 and \$1,670 in 1925. Using the wage indicator we see that the labor cost (of the 1908 car in 1925 wages) was \$2,094 and by using the GDP per capita indicator it was \$1,957. Thus in 1925 the \$290 was less than 20% of its cost in 1908 using the price indexes and only 14% using the wage indicators and 15% using the GDP per capita.

If we wanted to consider the costs of the Model T using today's prices we would find that the \$850 cost in 1908 is \$19,760 in today's prices using the CPI, \$14,700 using the GDP deflator, about \$45,000 using the consumer bundle, \$84,700 using the wage indicators, and \$115,000 when comparing using the GDP per capita.

The \$290 in 1925, on the other hand, would be only \$3,400 in today's prices using the CPI, \$2,900 using the GDP deflator, \$7,600 using the consumer bundle, \$11,700 using the wage indicators, and \$17,000 when comparing its cost as a share of GDP per capita.

• Babe Ruth's salary in 1932 was \$80,000. In 2006 the CPI was 15.2 times larger than it was in 1932 and the GDP deflator 13.1 times larger. This means that if we are interested in Ruth's purchasing power of housing or meals, then he was "earning" the equivalence of about \$1,000,000 today.

In 2007, the average consumer unit spends about 40 times in dollars as it spent than 75 years earlier. Thus, if we want to compare Ruth's earnings using the index of what the average household buys, it would be over \$3,200,000 today. The relative cost of (unskilled) labor is 46 times higher in 2007 than in 1932. So if we wanted to compare his wage to what someone selling hot dogs would earn, we could say his "relative wage" is \$3,700,000.

GDP per capita and GDP are 97 and 235 times larger in 2007 than they were in 1932. Thus Ruth's earnings relative to the average output would be \$7,800,000 today. Finally, as a share of GDP, Ruth "output" that year would be \$18,800,000 in today's money.

• Putting a man on the moon: During March (1966): NASA told Congress the "run-out cost" of the Apollo program (to put men on the moon) would be an estimated \$22.718 billion for the 13 year program that accomplished six successful missions of putting astronauts on the moon between July 1969 and December 1972. (http://www.hq.nasa.gov/office/pao/History/SP-4009/keyev4.htm) According the Steve Garber, NASA History Web Curator, the final cost was between \$20 and \$25 billion.

How much would that be today? If we used the CPI, it would be \$136 billion, but this would not be a very good measure since the CPI does not reflect the cost of rockets and launch pads. Using the consumer bundle would not be relevant either. Using the broader based GDP deflator gives a present cost of \$117 billion. The alternative of using the wage indicators would be a rough measure of the labor cost in current terms and it would be \$155 billion. By using the GDP per capita, we are measuring the cost in terms of average product and would get a number of \$259 billion. Finally, a way to consider the "opportunity cost" to society, the best measure might be the cost as a percent of GDP, and that number would be \$390 billion. This amount over thirteen years would be \$30 billion per year. As a comparison, the NASA budget for the current fiscal year is approximately \$15 billion.

• The "real" price of gasoline: Gasoline cost 27 cents a gallon in 1949 compared to around \$4.00 today.* How has the relative cost of buying gas changed over the last 59 years? Presented here are two tables computing the annual "real" cost using our five indicators, one in 2007 dollars, the current number used for real GDP, and the other in 1949 dollars. While the two tables show the same trends, they do give a different perspective.

Using the 2007 table and the CPI and the GDP deflator, we see that gasoline was quite expensive in 1980 and 1981 and the cheapest in 1998 and 1999. Today, the real price using these two measures is higher than the period at the beginning of the 1980s.

By looking at the share of the Consumer Bundle and GDP per capita, the story is a bit different. In 1981, a gallon of gas took as much out of what the average consumer spent as \$4.00 does in 2007. And as a share of GDP per capita, gas was even more expensive in those earlier days with it at over \$4.50 in 1980 and more expensive in the earlier years.

The other table tells the story in a different way. Let us look at relative cost to an unskilled worker to fill up using 1949 dollars. That year the 27 cents it cost for a gallon of gas, took a certain share of the worker's wage. The interesting question is, has the cost as a share or percent of the worker's wage increased or decreased over time? The table shows that for the wage rate and price of gasoline in other years, this cost has fallen. Since wages have increased faster than the price of gasoline, by 2007 an unskilled worker spends only two-thirds as much, as a percent of wage, for a gallon of gasoline than the 1949 worker. The table shows that the \$2.85 a worker paid in 2007 would be comparable to only 20 cents (in 1949 prices "share" of the wage.

When we use the GDP per capita, the cost has fallen faster. Looking at the table shows that a gallon of gasoline costs around 11 cents a gallon (in 1949 prices) if measured as a "share" of the GDP per capita. This is because in 1949, 27 cents was .015% of per capita GDP, while in 2007, \$2.85 was .006%.

Finally, comparing its cost as a share of GDP, we see that in 1949 prices, it is about 6 cents. This means that a gallon gasoline was a four and a half times larger share of output in 1949 than it is today.

* The nominal price of gasoline can be found at found at http://www.eia.doe.gov/emeu/aer/petro.html and http://tonto.eia.doe.gov/dnav/pet/pet_pri_gnd_dcus_nus_a.htm For the tables used here, I used the price of a gallon of leaded regular from 1949 to 1976, the average of the price of leaded regular and unleaded regular from 1977 to 1990 and the price of unleaded regular from 1991 to 2007.

##### Citation

Samuel H. Williamson, "Six Ways to Compute the Relative Value of a U.S. Dollar Amount, 1774 to present," MeasuringWorth, 2008.