Academic journal article Economic Inquiry

Buying a Dream: Alternative Models of Demand for Lotto

Academic journal article Economic Inquiry

Buying a Dream: Alternative Models of Demand for Lotto

Article excerpt


Lotteries are pervasive phenomena worldwide. Lotto, the most popular and widespread state lottery game, is a very simple numbers game where individuals select a set of numbers in a given range and win prizes according to how many numbers are guessed correctly. Wessberg (1999) finds that, in the 1990s, world lottery sales grew by 9% on average and some values of the highest prize (the jackpot) exceeded US $20 million in Italy, Spain, and the United Kingdom with comparable levels for state lotteries in the United States. Participation rates in lotteries are high, in excess of 50% of the adult population in the United Kingdom, according to King (1997), and span the whole distribution of incomes. Over time, an increasing number of state and national governments have opted to use lotto as an important source of revenue.

Several economists have attempted to model lotto demand. Clearly, different demand specifications have the potential to offer different policy implications, for example for the level of taxation and take-out to be imposed on consumers. The most popular empirical approach to lotto demand takes the nominal price of a ticket as a unit value and then examines variations in the "effective price" of a lottery ticket, defined as one minus the expected value of prize payments per ticket. Cook and Clotfelter (1993), Gulley and Scott (1993), Scott and Gulley (1995), Walker (1998), Farrell et al. (1999), Purfield and Waldron (1999) and Forrest et al. (2000b) all follow this approach. (1) If the first (jackpot) prize is not claimed in a particular draw, then the jackpot pool rolls over into the next draw. Such rollovers provide the greatest source of variation in effective price. Variables representing information on occurrence and size of rollovers can be used as instruments to determine effective price in a two-stage approach to modeling lotto sales.

This procedure for modeling time-series lotto demand is remarkably successful. Lotto appears to exhibit a standard downward-sloping demand curve in effective price-sales space and the derived effective price elasticities of lotto sales vary plausibly around minus one. The fit of the estimated equation is typically high. Sales, price, and rollover are typically found to be stationary from unit root tests and particular features such as time trend, structural breaks, and special events surrounding particular lotto draws can be accounted for. Forrest et al. (2000a) offer evidence that lotto players act rationally, making use of the best information available given that they choose to wager in the first place. (2) Farrell et al. (2000) show that their lotto demand model, which follows the orthodox approach, appears to be robust to the problem of "conscious selection," where players do not necessarily select their numbers randomly but overselect particular groups of numbers (memorable dates, birthdays, superstiti on, etc.).

In this article, we reestimate demand for U.K. National Lottery (UKNL) tickets, bringing up to date the earlier work of Forrest et al. (2000b), which only considered the first three years of play in the United Kingdom. Although the traditional model still appears to perform well, it is pertinent to question the underlying theory. The "effective price" approach is grounded in expected utility theory and runs foul of the classic problem facing analysis of any wagering market: why do gamblers accept a manifestly unfair bet and yet in many or most cases simultaneously reveal aversion to risk by purchasing insurance? Why would risk-averse individuals buy lottery tickets? We suggest that existing models of lotto demand are seriously flawed in their treatment of this problem.

Rather than simply claim that our empirical evidence using the traditional model is consistent with the theory of downward-sloping demand for lotto, which it is at a simple level, we test this model against a rival, using the UKNL as our particular case. …

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