Experimental

Testing for Prudence

Many economists over time have tried to measure how risk averse (or risk loving) people are. For instance, some risk averse individuals would prefer having \$40 for sure compared to playing a game where if the coin lands heads you get \$100 and if the coin lands tails you get \$0. Risk averse individuals are willing to accept a lower expected value (\$40 vs. \$50 for the coin flip).

However, another feature of individuals preferences can also influence how individuals evaluate risky situation. This concept is prudence. Let us go back to the coin flip game (\$100 heads; \$0 tails). Imagine you make \$50,000 this year and you are going to get a raise next year so you will earn \$60,000. Would you rather play the coin flip game this year or next year? A prudent person would want to take the risk when they are in the better financial situation.

Measuring prudence, however, is not a simple task. A working paper by Deck and Schlesinger tries to estimate prudence preferences in an experimental setting. The experimental question is posed as follows:

• You will receive \$10.50 + (1|-1) if the con lands on Heads or Tails and \$9.00 if the coin lands on the Same or Different outcome.

I think the phrasing of the question is unnecessarily complicated, but the question is fairly straight-forward. Everyone gets \$10.50. Individuals must choose between Heads or Tails; and Same or Different. To simplify, let us assume that everyone chooses Heads, which means you earn \$1 if the coin lands on heads and lose \$1 if the coin lands.

Now we must decide between Same or Different. If you choose Same, that means that you get \$9 if the first coin toss lands on heads and you also flip the coin a second time to see if you win or lose \$1; if the first coin toss lands on tails then you get \$0, but do not have to play the win/lose \$1 game. If you choose Different, then if the coin lands on heads you get \$9, and do not play the second coin toss; if the coin lands on tails you get \$0 and do not play the second coin toss.

Individuals who choose Same are prudent because they take the financial risk (win/lose \$1) when they are richer (\$9 extra). Those who choose Different, are imprudent because they take the financial risk (win/lose \$1) when they are poorer (\$0 extra)

The authors asked 6 of these prudence of questions. They found that 61% of subjects responded to the questions in a prudent manner, but only 14% of individuals responded to all six questions prudently. A Kolmogorov-Smirnov statistic of 0.2225 indicates that people are making prudent choice more than would be the case if they were choosing randomly.

APPENDIX

The other 6 prudence questions were:

1. You will receive \$30 + (25|-25) if the con lands on Heads or Tails and \$25.00 if the coin lands on the Same or Different outcome.
2. You will receive \$12.50 + \$9.00 if the coin lands on Heads or Tails and (5|-5) if the coin lands on the Same or Different outcome.
3. You will receive \$12.50 + (5|-5) if the con lands on Heads or Tails and \$1.00 if the coin lands on the Same or Different outcome.
4. You will receive \$10.50 + \$9.00 if the coin lands on Heads or Tails and (1|-1) if the coin lands on the Same or Different outcome.
5. You will receive \$12.50 + \$5.00 if the coin lands on Heads or Tails and (5|-5) if the coin lands on the Same or Different outcome.
6. You will receive \$14.50 + (9|-9) if the con lands on Heads or Tails and \$1.00 if the coin lands on the Same or Different outcome.