Analyzing Background Risk with Morgan Dollars

Their have been much economic research to determine how individuals evaluate risk. Most of this work takes place in a laboratory setting using hypothetical monetary payoffs. Further, the issue of “background risk” is often ignored. For instance, “…mortality risks from alternative occupations tend to be highly correlated with morbidity risks. It is implausible to ask subjects their attitude toward one risk without some coherent explanation as to why a higher or lower level of that risk would not be associated with a higher or lower risk of the other.”

A recent paper by Harrison, List and Towe (Econometrica 2007) attempts to analyze the issue of background risk. The authors attend a 2004 Florida coin show. Individuals attended the show were given a series of binary choices. For each binary choice, those participating in the survey stated their preferred choice. For example, in the money specification, choices include:

Question Option A Option B
1 5/100 of $200; 95/100 $125 5/100 of $350; 95/100 $40
2 10/100 of $200; 90/100 $125 10/100 of $350; 90/100 $40
3 15/100 of $200; 85/100 $125 15/100 of $350; 85/100 $40

Then the authors decided to give individuals an option of making real world risk judgements. Four coins (denoted coins A, B, C and D) were displayed and the participants again were to choose whether they preferred option A or B in each pair.

Question Option A Option B
1 5/100 of Coin A; 95/100 Coin B 5/100 of Coin C; 95/100 Coin D
2 10/100 of Coin A; 90/100 Coin B 10/100 of Coin C; 90/100 Coin D
3 15/100 of Coin A; 85/100 Coin B 15/100 of Coin C; 85/100 Coin D

Their are two different treatments using the coins. The first is the graded treatment. Here the Morgan Dollar coins are presented with a 1-to-70 ‘ Sheldon scale‘ rating. This way, respondents can be sure as to the coins’ quality or worth. The second coin treatment is to use ungraded coins. In this case, the coins are presented without any certification as to their quality or grade. This way, the authors can introduce background risk into the game.


Harrison and co-authors find risk aversion distributions (using CRRA utility functions) are very similar between the money payoffs and the graded coin treatments. However individuals are significantly more risk averse when in the ungraded coin treatment. In the authors own words: “the use of artificial monetary prizes provides a reliable measure of risk attitudes when the natural counterpart outcome has minimal uncertainty, but that it can provide an unreliable measure when the natural counterpart outcome has background risk.”

Healthcare Economist comments
One concern I have with the results is that of the lemon’s problem. Respondents may believe that ungraded coins are less valuable. If they were of high quality, why wouldn’t the vendor have paid to have the coins certified. Thus, the respondents may believe that high value ‘Coin C’ is actually of a much lower value. It could be the case that the respondents may select option A more frequently, which would inflate their risk aversion estimates. In the presence of a the lemons problem, the conclusion would be that individuals are game-theoretically rational, and not that they have concerns over background risk.

Nevertheless, I do appreciate that this paper examines risk in a more complex and rich setting than has previously been studied. Also, collecting data from outside the university environment is very useful.