In the week after a large-prize winning ticket has been purchased at a given store, that store experiences a 12 to 28% relative sales increase in lottery ticket sales. This increase fades over time, but the store’s lottery ticket sales remain elevated for up to 40 weeks. This effect increases with the size of the jackpot and with the economically disadvantaged proportion of the population.
These are among the results that Jonathan Guryan (Graduate School of Business, University of Chicago) and Melissa S. Kearney (Department of Economics, University of Maryland, and NBER) report in the March 2008 issue of the American Economic Review.
To try to explain this phenomenon, Guryan and Kearney consider two possibilities. The “response to advertising” explanation holds that the sale of a winning ticket merely advertises the lottery in the local market. This explanation falls by the wayside because stores located close to the winning store don’t experience the same bump. The “lucky store” explanation, by contrast, holds that consumers erroneously increase their estimate of winning with a ticket from the store that has already produced a big winner.
By contrast, earlier studies have indicated tha tthe amount of money people bet on a particular lottery number falls sharply after the number is drawn and only gradually returns to its former level — the opposite of the effect that Guryan and Kearney observe for store sales. Thus, these two results play off two “well-documented but seemingly contradictory misperceptions of randomness,” the hot hand fallacy and the gambler’s fallacy, against one another. Guryan and Kearney begin to reconcile these differences by referring to a belief in “representativeness”:
bq. Individuals expect random series to demonstrate self-correction, or negative serial correlation, per the gambler’s fallacy. The explanation posits that individuals reject randomness in a particular way: they rationalize the streaks they observe by inferring heterogeneity in the underlying rate of success (e.g., the probability that a basketball player successfully makes a shot).
They conclude, though, that:
bq. …The perception of heterogeneity … necessary for a belief in the hot hand comes not from the signals produced by the data-generating process — as the representativeness explanation would require — but rather from the characteristics of the data-generating process itself, namely, whether the data-generating process is perceived as having an imate or an intentional element.
Yet another example of the increasing tendency of economists to formulate and test models of types of behavior that largely escaped the notice of previous generations of economists. Perhaps soon freakonomics will constitute the core of economics?