Loving the Long Shot

The latest recipient of the 2012 Carolyn Shaw Bell Award is Professor Catherine Eckel of Texas A&M. This award is given annually by the American Economic Association Committee on the Status of Women in the Economics Profession (CSWEP) to recognize an individual who has furthered the status of women in economics. Eckel is an experimental economist who has studied the role of a wide range of social and psychological factors in economic exchange-- attitudes toward risk, gender differences, beauty, trust, corruption, and charitable giving, to name a few.

One of her recent papers is particularly interesting from a macroeconomics and finance perspective: "Loving the Long Shot: Risk Taking with Skewed Lotteries" (2012, with coauthor Philip Grossman). The study addresses a widely noted conundrum, that risk-averse individuals voluntarily play the lottery. The expected payoff of a lottery ticket is less than the price of the ticket. Lotteries are positively skewed, since the vast majority of tickets have low payoff but there is a very small probability of a very large prize. Eckel and Grossman use a laboratory protocol to elicit the skewness preferences of 93 test subjects. They can isolate the effect of positive skewness on subjects' willingness to take risky gambles. If you haven't read an experimental economics paper before, I highly recommend reading Section 3 (pages 7-9) of their paper for an idea of how experimental design works in this field. From the conclusions:

We find that, controlling for risk preferences, individuals are overwhelmingly skewness-seeking in their lottery choices; lotteries with skewed payoffs are more attractive than lotteries with the same expected earnings and risk (variance) but lacking skewness.  Given equal expected earnings and risk, 84.9 percent of our subjects select a lottery with skewness = 1 over a lottery with skewness = 0 and 88.2 percent also prefer a lottery with skewness = 1 or 2 to a lottery with skewness = 0... More importantly, we find that increased skewness in the payoff structure entices a sizeable share of our sample (37.6 percent) to take on greater risk in their choice of lotteries. The change in lottery choices resulting from the skewing of payoffs increases the risk subjects face more than three times as much as it increases their expected payoffs.

The first thing that came to mind when I read this paper was the remarkable lottery loan governemnt fundraising scheme in England in the late 17th and early 18th century, shortly before the South Sea Bubble. An unprecedentedly large lottery was called the "Two Million Adventure." Tickets cost £100 and guaranteed a 6% yield annuity. In addition, tickets won prizes. The maximum prize was £20,000 and every ticket won a prize of at least £10. Prizes were paid in the form of a fixed sum annuity over a period of years, meaning the government held the prize money as a loan until it was paid out to the winners. Investors went crazy for tickets, and all tickets were sold within 9 days. Lottery payoffs were positively skewed. Including the prizes, the great mass of investors earned around a 6.5% yield, but a few lucky winners won much larger amounts, including one grand prize winner. Overall, the average yield was 8%, but the vast majority earned less and a few earned much more. Standard risk preferences suggest that investors would have preferred to buy annuities that simply guaranteed 8% yield, but Eckel's findings explain why investors so loved the lottery tickets. Richard Dale's book "The First Crash: Lessons from the South Sea Bubble" explains how the lottery loans were related to the notorious South Sea Bubble.

Lottery loans were hugely popular in other countries too. The New York Times in 1889 noted that "The new lottery loan has caused a perfect mania among the public of St. Petersburg... At least one hundred times the amount of the 172,000,000 rubles required have already been offered."

Today in the U.S., 42 states and the District of Colombia have lotteries, but positively-skewed payoffs in finance are much more pervasive than explicit lotteries. Most data on stock prices or asset returns has positive or negative skew (unlike normally-distributed data which has zero skew.) For large banks, an implicit or explicit bailout guarantee can put a lower bound on the payoff of risky investments without imposing an upper bound, a widely recognized source of moral hazard which has frequently been blamed for the financial crisis. Prevalent and strong skewness-seeking preferences could make the moral hazard problem stronger than standard models would predict. 

I am glad that CSWEP recognized Eckel's contributions to women in economics and hope the wider economic community will spend some time reviewing and discussing her very interesting research.