Theory and Experiments

 

This post was prompted by the most recent episode of Hidden Brain Putting Our Assumptions to the Test in which Shankar Vedantam talked to Abhijit Banerjee about the use of experiments in economics, specifically randomized controlled trials RCTs to study development economics.  I like the Hidden Brain, and I always enjoy listening to Banerjee. There was, however, one thing about the episode that bothered me. I thought Vedantam made it sound like Banerjee's work reflected a contest between theory and experiment, rather than emphasizing the importance of both.

The problem with this approach was most glaring when they talked about an experiment that Banerjee conducted in India to study policies to encourage vaccination. They first discussed a number of relatively unsuccessful interventions that had been made to encourage vaccination. Then they turned to Banerjee’s successful experiment. Families were randomly selected to receive an offer of a bag of lentils (1 kilo) if they got their children vaccinated. Families that received the offer were significantly more likely to have their children vaccinated. Vedantam stated that they had gained this knowledge from an experiment, not a grand theory about why poor people do not get vaccinated. But there was a grand theory, and it was clear when Banerjee talked about why it worked. He pointed out that going to get vaccinated had significant costs in terms of time and effort, and the usual unpleasantness of having small children vaccinated. The lentils, while seemingly a small thing relative to not having your children get sick, provided an immediate observable benefit to help compensate for those costs. The grand theory is that people make choices by weighing the costs and benefits. If you increase the benefits of something people will be more likely to do it. If you increase the costs, they will be less likely to do it.

In randomized controlled trials the selection of who will receive the treatment is random; the selection of the treatment is not random. Banerjee did not randomly assign people to a group that would have people pray for them to get vaccinated or to a group that would not receive prayer. He randomly assigned them to a group that would receive an incentive to get vaccinations or to a group that would not receive the incentive. The experiment was based on the theory that increasing the benefits of vaccination would make people more likely to get their children vaccinated.

Vendantam several times made comparisons to the use of RCTs in medicine and the advances in medical knowledge arising from them. But the situation is no different in medicine. People do not go to the expense of running an RCT on randomly selected drugs, nutrients, activities, etc. They have selected a treatment based upon some theory that suggests that it might work. A science with experiments absent any theory would not be possible. There are too many possible treatments.

Although the discussion on the podcast was about experiments, the argument that some theory is necessary to guide the empirical research applies to other kinds of empirical research as well. There is too much data in the world to not have some means of identifying what is useful.

Relative Values (with special reference to the antebellum period)

 

This is the second post related to Sharon Ann Murphy’s recent paper "The Financialization of Slavery by the First and Second Banks of the United States," in the Journal of Southern History (Murphy 2021). I started it several months ago, but just got around to finishing it. As with another paper published earlier this year in Enterprise & Society, Murphy converts monetary figures from the first half of the nineteenth century to comparable current values:

“On October 5, 1818, Baltimore residents Philemon C. Wederstrandt, Henry Didier Jr. (in trust for Rebecca Smith), and Henry Thompson entered into a seven-year partnership to purchase the Magnolia Grove plantation from Samuel B. Davis. Sugar prices were on the rise, and this fully operational plantation in St. Bernard Parish, Louisiana, would enable the Baltimoreans to get in on the lucrative emerging market. Included in the purchase price of $140,000 (about $3 million in 2020) were the land, buildings, improvements, stock, crop, utensils, and forty-three enslaved workers (Murphy 2021, 385).”

These relative values are reported to provide a sense of the magnitude. I suspect that most people would think that $140,000 was a large amount of money in 1830. But how large? Comparable values are an attempt to answer that question. Murphy reports that the relative value of $140,000 in 1818 was $3 million in 2020, but what does that mean?

Around the same time that Murphy’s paper came out, someone showed me a Twitter discussion about relative values in which one of the participants in the discussion suggested that calculating relative values was complicated, but that one could use a simple rule of thumb to approximate such calculations. They went on, however, to question the utility of calculating relative values for the antebellum period because of the chaotic money and banking system that existed before the Civil War.

The purpose of this post is to show that

(1)    the calculation of relative values is not that complicated,

(2)    that a rule of thumb cannot produce a reasonable approximation, and

(3)    that the antebellum banking system, though quite different from our own, was not so chaotic as to eliminate the utility of calculating relative values.

Perhaps the person on Twitter was an aberration, though no one was disagreeing with them. If they were an aberration, this post probably isn’t necessary, but I’m going to go ahead and post it on the off chance that there may be other people who do not understand relative values.

 

Calculating relative values by adjusting for inflation

 

I’ll come back to the Murphy paper, but I’m going to start with a more recent example. Reportedly both Muhammad Ali and George Foreman were paid $5 million for their 1974 fight in what was then Zaire. Five million dollars is still a lot of money today, yet most people know that prices were generally lower in 1974 so that $5 million would have purchased more than it does now.  It would have been more valuable than $5 million is now. One way to understand how much more valuable $5 million would have been in 1974 is to ask how much we would need today to purchase the same amount of goods and services at today’s higher prices. In other words, what amount today would purchase as much as $5 million did in 1974? Answering this sort of question is the most common approach to calculating relative worth. It is done by adjusting for changes in the overall level of prices as measured by a price index.

If, for instance, the overall level of prices doubled between 2002 and 2020, you would need $200 in 2020 to buy what $100 bought in 2002. In that sense, the $100 in 2002 is comparable to $200 in 2020. Because prices are twice as high in 2002, we need to multiply 2002 value by 2 to get the 2020 relative value. If prices had been 3 times as high, we would have to multiply by three. If we know the price level in two different years, we can figure out how much we need to multiply by to find the relative value.  

The most commonly used measure of the price level is the Consumer Price Index (CPI). Using the Consumer Price Index if we want to know what value in one year (year x) is comparable to a value from another year (year y) we use this simple formula

Dividing the CPI in year x by the CPI in year y tells you how many times higher the price level was in year x than in year y. For example, the CPI in 1974 was 49.33 and the CPI in 2020 was 258.81. If you divide 258.81 by 49.33 you get 5.2465; overall prices were a little more than 5 times as high in 2020 as in 1974. If we multiply $5 million by 5.2465 we get $26,232,516. You would need $26 million in 2020 to have the same purchasing power as $5 million in 1974.

Murphy used the website measuringworth.com to do these conversions. You can go to measuringworth.com and plug in a value, the year that value is from, and the year that you want to use for comparison, and it will give you’re your answer. But measuringworth.com is just doing what I described above. The CPI is 12.33 for 1818 and 258.81 for 2020. Dividing 258.81 by 12.33 gives 20.99. Multiplying 140,000 by 20.99 gives 2,938,637. Measuringworth.com rounds to 2,940,000, and Murphy describes it as about $3,000,000.

If you use measuringworth.com, you will find that it actually gives you a number of different options for the relative value. These are the ones for the $5 million dollars in 1974 relative value in 2020.

 

Rather than adjusting for changes in prices one can try to understand how large a value from the past was by comparing it to other things. Ali’s $5 million was 919,117 times the average hourly wage of a production worker ($5.44). For a fighter to make 919,117 times the average hourly wage of a production worker in 2020 ($32.54) they would need to earn $29,908,088 (labor value using production worker wages).

Alternatively, you might try to understand how large some value was by considering how large it was relative to total output. GDP in 1974 was equal to $1,545,200,000,000 or about $1.5 trillion. If you divide $5,000,000 by $1,545,200,000,000 you find that what Ali got paid was equal to a very small fraction (.00000032358) of the total U.S. GDP in 1974.  But how much would a boxer have to get in 2020 for it to equal the same fraction of GDP as Ali’s pay? GDP in 2020 was $20,893,700,000,000 (almost $21 trillion). If we multiply that GDP by .00000032358 we get $67,608,400 (economic share relative value).

 

Notice that it gives you different options for commodities and income, but those aren’t the important distinctions in terms of the actual calculation.

Like adjusting for changes in the price level the math is not complicated, but why might you take these alternative approaches rather than just adjusting for changes in prices? In his most recent book, The Ledger and the Chain Joshua Rothman includes some of these conversions as well as the conversions based upon changes in prices.

 

Although most people simply adjust for changes in prices, describing the relative size of some past value in terms of average wage or GDP may provide a more accurate sense of how large a value was because it takes into consideration the increase in real incomes and output not just the change in prices.

 

Why you cannot use a rule of thumb to adjust for changes in the price level

The conversation on Twitter suggested that one could use a basic rule of thumb: multiply values for 1830 by 60 and values from 1860 by 30, for instance.  Why won’t a simple rule like this work? Note that when you are adjusting for changes in the price level between year y and year x you are using the following formula

If you want to know what value now is comparable to some value from a year in the past (year y) you put the current CPI in the numerator (CPI year x) the current CPI and the CPI for the earlier year in the denominator (CPI year y). This number will only decline steadily over time if prices rose steadily over time. Prices in the nineteenth century did not rise steadily over time. The figure below shows the Consumer Price Index for the 19^th century. The overall trend was downward, and it was anything but steady.

Consumer Price Index, 1800-1900

 

 

The figure below shows the CPI for 2020 divided by the CPI for each year, which is the number you would multiply a value by to estimate the comparable value in 2020. For instance, the highest peak is 35.7 in 1844; $100 in 1844 would be comparable to $3,570 in 2020. You can also see that you should multiply values from 1860 by more (32.11) than values from 1830 (28.94).

 

CPI for 2020 Divided by the CPI for Each Year, 1800-2020

 

 Even if prices had followed a steady trend a simple rule of thumb wouldn’t work because prices are still changing. The correct multiple is the current CPI divided by the CPI in the year for the value you are converting (shown for 2020 in the above graph). The numerator in that fraction, the current CPI changes every year, so the correct multiple changes every year. You would have to update your rule of thumb on a regular basis, which would kind of diminish its utility as a rule of thumb. As prices continue to rise the line in the above graph will continue to shift upward. You would have to continually recalibrate your rule of thumb.

 

The system of money and banking before the Civil War does not render calculation of relative worth meaningless.

Both Rothman and Murphy write about the antebellum period. Consequently, we need to consider the argument that the antebellum money and banking system interferes with out ability to determine relative values.

The system of money and banking before the Civil War was quite different than ours.

The value of the U.S. dollar was legally defined in terms of precious metals, both gold and silver were legal tender. One dollar was equivalent to a certain amount of each metal, which meant that there was also a defined exchange rate between the two metals. As of 1834, the U.S. dollar was defined as 23.22 grains of pure gold.

So legally, the value of a dollar was the same wherever you were in the country, a dollar was worth a certain amount of gold or silver. But people also used bank notes as money. States chartered banks, and these banks issued notes that were redeemable at the bank they were issued from. A bank note acted as money to the extent that people believed that they could redeem it for the stated amount without incurring significant cost. To the extent that people were uncertain about whether a note would be redeemed or that redeeming a note would be costly, the note was discounted: you might get only $97 of gold or goods in exchange for a $100 note. Because there were hundreds of different banks, there were hundreds of different notes and discount rates. This system is sometimes portrayed as one of extreme chaos and uncertainty, in which there was no way to really know the value of money. Consequently, every transaction required bargaining not just over the value of the good but over the value of the money that was being used to pay for it.

Research doesn’t really support this view of a completely chaotic monetary system.  Because it was important to know the value of different banknotes, some people collected information on the going rates of discount and published it in newspapers or specialized bank note reporters. Economic historians have studied these published discounts.  The notes of new banks were more heavily discounted than those of established banks (Gorton 1996). Notes from banks that enacted regulation requiring adequate backing for notes were discounted less than bank in states that did not (Rolnick and Weber 1988). Bank notes tended to trade at par near the bank they were issued from (Ales et al 2008). That means that if you were in Philadelphia your $20 note from an established Philadelphia bank was basically as good as gold. As you moved away from the point of issue the discount tended to increase because of increased uncertainty and increased cost of presenting the note to the issuing bank. Bank note discounts reflected factors that influenced the riskiness of the bank (Gorton 1999). In general notes were discounted more heavily the higher the expected cost of redemption and the greater the expected risk of default. All this adds up to a market in which people appear to have been well enough informed to reasonably evaluate the value of notes. People using local notes from established banks would have valued them at par because of low cost of redemption and low risk of default. People did not have to bargain over the value of money for every transaction.

In addition, people that regularly needed to move large amounts of money from one part of the country to another knew of the potential problems associated with taking money from one part of the country to another and developed means of minimizing these problems. The larger the potential costs the more people had an incentive to find solutions. See Bodenhorn (2003) and Schermerhorn (2015) for some of ways in which people used things like business connections and bills of exchange to deal with problems associated with moving funds from one place to another.

It is true that the value of a dollar varied from one place to another in the antebellum period. The value of a dollar varied from one part of the country to another for the same reason that the value of a dollar varies from one part of the country to another today: the price level varies from one part of the county to another. Below is a map from the Tax Foundation showing the relative value of $100 in each state in 2017. 

 

Finally, while it is true that the world of antebellum money and banking is very different than our own, the world in which people do not have to worry about how to pay for things when they travel is fairly new. Much of our money supply is checkable deposits, but people do not have to accept you check any more than people during the antebellum period had to accept your banknotes. Now we count on using our credit cards, but in 1970, still only 16 percent of households had a bank credit card. When they traveled, they couldn’t expect people to accept their out of town checks. They had to carry cash or travelers checks.

 

The Bottom Line

The calculations for these comparable values are simple and (I think) reasonably intuitive. The hard part is creating the numbers that go into the calculation. Collecting the data on prices and wages and production from the past and determining how to use it to come up with the best estimates of the price level, or average wages, or GDP that you can. It is important to note that we still produce estimates of these values today. Even with all the resources we use to collect and analyze data we don’t get the True value. That’s just not the way the word works. In general, the further you go back in time the less data you will have and it may not be the data you would ideally like to have. But they do not need to be perfect. Historians generally report estimates of relative values to try to convey the magnitude of some value from the past not to make an argument about the exact or true relative value.

 

 

References

Ales, Laurence, Francesca Carapella, Pricila Maziero, and Warren E. Weber. "A model of banknote discounts." Journal of Economic Theory 142, no. 1 (2008): 5-27.

Bodenhorn, Howard. State banking in early America: A new economic history. Oxford University Press, 2003.

Gorton, Gary. "Reputation formation in early bank note markets." Journal of political Economy 104, no. 2 (1996): 346-397.

Gorton, Gary. "Pricing free bank notes." Journal of Monetary Economics 44, no. 1 (1999): 33-64.

Jaremski, Matthew. "Bank-specific default risk in the pricing of bank note discounts." The Journal of Economic History 71, no. 4 (2011): 950-975.

Murphy, Sharon Ann. "Securing human property: Slavery, life insurance, and industrialization in the upper south." Journal of the Early Republic 25, no. 4 (2005): 615-652.

Murphy, Sharon Ann. "Collateral Damage: The Impact of Foreclosure on Enslaved Lives during the Panic." Journal of the Early Republic 40, no. 4 (2020): 691-696.

Murphy, Sharon Ann. "Enslaved Financing of Southern Industry: The Nesbitt Manufacturing Company of South Carolina, 1836–1850." Enterprise & Society (2021): 1-44.

Murphy, Sharon Ann. 2021. "The Financialization of Slavery by the First and Second Banks of the United States." Journal of Southern History, 87 (3) 385-426.

Rolnick, Arthur J., and Warren E. Weber. "Explaining the demand for free bank notes." Journal of Monetary Economics 21, no. 1 (1988): 47-71.

Rothman, Joshua D. The Ledger and the Chain: How Domestic Slave Traders Shaped America. Basic Books, 2021.

Schermerhorn, Calvin. "Slave Trading in a Republic of Credit: Financial Architecture of the US Slave Market, 1815–1840." Slavery & Abolition 36, no. 4 (2015): 586-602.