The question economic historians are asked most frequently is "How much is that in today's money?" George Washington was paid $25,000 per year, Babe Ruth was paid $80,000, the Panama Canal cost $487 million, but how much is that in today's money? Typically, economic historians use one of three "measuring rods" for comparing values over long periods of time: prices, wages, and per capita GDP, although at times other measures, such as total GDP, are used. Below I will discuss how to use each of these measuring rods and some of the problems you will need to think about. As with most questions in economics there is usually more than one "right" answer. The answer you choose depends on your motives for asking the question. As an example consider the following. The price of a healthy low-skilled male slave who was 18 years old in 1860 was approximately $1,600. How much is that in today's money? If we use the consumer price index from Table 2, we get a figure of $31,422. [$1600 x (163/8.3)]. But if we use the wage index, we get a much larger figure of $194,743. [$1600 x (8.52/. 07)] And if we use per capita GDP we get the astonishing figure of $456,056. [$1600 x (32,494/114)] The reason we get different answers is that we are implicitly asking different questions. Let us take each calculation in turn and see what it means.
 
 

Using Prices as the Measuring Rod

Problems encountered when comparing prices over long periods of time

SAMPLING ERRORS arise because we cannot observe every price in every transaction. The prices that go into our indexes are a small sample of the total universe of prices, and as anyone knows who has studied statistics, samples do not always replicate the universe we are trying to measure. Sometimes the sample of prices may be misleading because people are deliberately trying to hide the prices they charge. If the government has set official maximums on prices (as happens on a very wide scale in wartime) then many transactions may take place at "black market" prices. Prices reported to government officials will not reflect these transactions, and the resulting price indexes may understate the true inflation. For this reason, price indexes tend to be particularly misleading in wartime.Today, the government hires price-checkers who go into the market place in order to get accurate readings on prices. But as we go backward in time we may reach a point where all that an economic historian can find are the prices reported in the financial press or in government documents, or in the records of a few individuals, businesses, or public institutions that kept track of the prices they paid. These records often do not provide us with an unbiased sample of prices. Typically, what we find are the prices of basic commodities traded on organized national or international markets. The price of wheat is likely to be available; the price of haircuts is not. There is a general tendency for prices to move together, but they do not always do so, so sampling errors mean that there is a margin of uncertainty surrounding our estimates of prices, a margin that probably grows wider as we move backwards in time.

CHANGES IN RELATIVE PRICES – the price of haircuts relative to the price of wheat, for example – affect price indexes because they affect the way people allocate their income. People tend to consume more of those items that rise least in price and less of those items that rise most in price. This makes sense; the smart consumer takes advantage of bargains and sales, and avoids items that seem to them to be "overpriced." But as we noted above, price indexes are normally computed by comparing the cost today of buying exactly the same market basket that was purchased in the past. Thus, price indexes overstate the amount of money that it would take to make someone as well off today as in the past in terms of their basic standard of living or utility. For example, suppose that in the base period it cost $10,000 to buy a certain market basket of goods and that today that same market basket costs $15,000. We know that if someone has $15,000 they would be at least as well off as someone with $10,000 in the base period. But we know that most people with $15,000 in their pockets would be better off than before because they could shop for bargains and take advantage of changes in relative prices. They would need less money, say $14,000, to reach exactly the same standard of living or utility they had enjoyed in the base period. So the "true" increase in prices is smaller than the measured increase. In this example, the true price level is 140 ($14,000/$10,000). Updating the market basket helps with short-run comparisons. But over the long run there is some upward bias in the price indexes we use because they are weighted by base period consumption. This way of computing price indexes, by the way, produces what is known as a Laspeyres index. There is an alternative way of computing a price index: by asking what it would have cost in the past to buy the basket of goods consumed today. This sort of index, known as a Paasche index, understates the extent of price increases over time. The reasoning is analogous. Suppose that a Paasche index stands at 150 today and at 100 in the base period. That means that if someone were transported backward in time and given $10,000 they could buy exactly the same goods that $15,000 would buy today. But in terms of their standard of living they could probably do just as well in the base period with a little less money, say $9,000, if they were given the freedom to shop for things that happened to be relatively inexpensive in the base period. Thus, the "true" increase in price is a little more than 50 percent. In terms of a constant standard of living, the true index if we could measure it would have risen from 100 to 158, ([150/90] x 100).The Paasche index is seldom used for long-term comparisons, partly because we would not want our wages adjusted by price indexes that understate inflation. The Paasche index, however, is used at times in regional or international comparisons. We want to know how costly it would be to buy the drugs that Americans usually buy if they were bought in Canada; we might also want to know how costly it would be to buy the drugs that Canadians usually buy if they were bought in the United States. As one economics student remarked, "I will not Laspeyres, because with hard work I know I can Paasche."

QUALITY CHANGE is the most important problem affecting price indexes. The car we bought 10 years ago is not the car we will buy today. The surgery we had 10 years ago is not the surgery we have today. Usually we think of quality increasing over time. But this is not always the case. The taste of the tomato we consume today may not match that of the tomato consumed 100 years ago. Economists have developed some clever ways of dealing with quality change. For one thing it is sometimes possible to price quality change. If air bags become standard in cars we may be able to price them if they were available as an extra a few years before. Only if the price of the car rises by more than the price of a air bag, when air bags become standard, can we say that there has been a true increase in price.

THE INVENTION OF TOTALLY NEW PRODUCTS is simply an extreme case of quality change. Many of the things we buy today -- cars, radios, computers, antibiotics, and so -- simply did not exist 100 years ago. How much of a problem quality change and new products pose for our measures of prices is a matter of debate. But there appears to be a consensus among economists that the indexes that we currently use probably overstate the amount of inflation because the indexes fail to take fully into account the introduction of new products and the improvements in quality of existing ones, despite the best efforts of economics and government officials to adjust their indexes for these problems.

Using Wages As the Measuring Rod

Wages are one of the oldest, and still a very useful measuring rod. In The Wealth of Nations Adam Smith argued that 

Using wages as a measuring rod has an immediate intuitive appeal because we have a sense, or believe that we have a sense, of the disutility of an hour of common labor. But it is worth remembering that the disutility of labor has changed over time. For one thing technological change alters the conditions of work. Heavy lifting has been greatly reduced; medical advances treat the aches and pains associated with work: and so on. Hours of work have also changed. The disutility of the marginal hour, and therefore of the average hour of work will increase when people are typically working long hours.

If we divide the price of some commodity, say wheat, at some time in the past by the wages of low-skilled labor at that time, we find the commodity's price in terms of hours of low-skilled labor. We have, in other words, computed how long a low-skilled worker would have to work to buy that particular item. If we then multiply our result by the wages of low-skilled labor today, we have an estimate of what that item would cost today, if it still took as many hours of work to purchase it. If we compare our updated price with the actual price today, we can get some idea of how much of the change is real (due to changes in the supply of raw materials, technology, and so on) and how much is monetary. The wages of low-skilled labor are also useful for updating salaries, business profits, and similar values. When we divide the salary of, say, a lawyer at some past time by the wages of low-skilled labor at that time, and then multiply by the wages of low-skilled labor today, we get a number which helps us understand how much power or influence that lawyer had.
 
 

Using Per Capita GDP as a measuring rod

2. Are There Other Useful Measuring Rods? Although consumer prices, wages, and per capita income are the most common measuring rods, they are by no means the only ones that can be used. Often time, to give to take one example, we are interested in how much effort society was making to accomplish a certain goal. In that case using total income rather than per capita income might be more appropriate. For example, the Erie Canal was completed in 1807 at a cost of $7,000,000. How much is that in today's money? We might use consumer prices to get a figure of $98.7 million. [7,000,000 x (163/11.6)]. Or we might use wages to get a figure of $1.2 billion [7,000,000 x (8.52/.05)]. Or we might use per capita income to get a figure of $2.99 billion [7,0000 x (32,494/76)]. But it could also be illuminating for some purposes to use total national income. The result would be $121.0 billion [7,000,000 x (8,781,500/508)]. This last figure conveys an idea of how large a project we would have to engage in to claim that we were making the same effort they were making. 

<span style='font-size:16.0pt;mso-bidi-font-size:9.0pt;font-family:"Arial Unicode MS"; mso-bidi-font-family:"Times New Roman"'>Once one begins to think about specific cases, additional calculations come to mind. In the case of the Erie Canal, we could ask how much it would cost to actually build a canal like the Erie today. Moving the earth with modern earth moving machines would be relatively easy. But how much would it cost to settle all of the law suits likely to be generated by digging a trench through the state of New York?<o:p></o:p></span>

3. There are a lot of different price indexes around, wholesale prices, consumer price indexes, GNP deflators, and so on. Which one should I use?

<span style='font-size:16.0pt;mso-bidi-font-size:10.0pt;font-family: "Arial Unicode MS";mso-bidi-font-family:"Times New Roman"'>Again, the answer depends on the reason for posing the question. If you want to know how well someone could live in past times on a certain income, you would want to use the consumer price index, if its available. If you wanted to compare income of a city or state at different times, you might want to use the GDP deflator. If you wanted to find out how much a foreign currency was worth you might want to use the wholesale price index because it tends to be weighted more heavily toward internationally traded goods.<o:p></o:p></span>

4. What about values expressed in foreign currencies?

If you want to find out the value of a an amount valued in a foreign currency you must use the exchange rate to convert the foreign currency into dollars. For example, the Titanic was built in 1912 for, it is said, about1.5 million pounds. To get that into today's money we can convert it into dollars using the exchange rate prevailing in 1912, about $5 per pound or $7,500,000. Then we can use our various series to bring that amount forward to the present. Using prices we get $147million, using wages $336 million, and using per capita GDP, we get $614 million. You could also use British prices or wages to move forward in time and then use the current exchange rate to convert from pounds into dollars. In general the two answers will be similar. If a country experiences a lot of inflation its exchange rate will generally depreciate. But so many forces impinge on exchange rates that the two answers are unlikely to be the same. The website eh.net listed in the references will help with converting from dollars to pounds.

References