Academic journal article Contemporary Economic Policy

Own- and Cross-Price Elasticities for Games within a State Lottery Portfolio

Academic journal article Contemporary Economic Policy

Own- and Cross-Price Elasticities for Games within a State Lottery Portfolio

Article excerpt


The prevalence and growth of lotteries around the world is typically explained in terms of the desire of governments to identify new sources of revenue without recourse to new or higher taxes. Thus, in most developed countries, specialist public agencies have been created and now offer a wide variety of lottery games to suit the tastes of players, seeking to maximize revenue for the state or its nominated organizations (such as those promoting sport). But the potential and performance of this source of revenue still needs to be better understood. In particular, as agencies have expanded the number of games on offer, there has been little analysis undertaken concerning the structure of the portfolio of games available. Looking at one game in isolation, the dominant approach in previous lottery studies, runs the risk of yielding recommendations (on, e.g., take-out) that are suboptimal because they fail to take into account impacts on sales of other lottery products (if these prove to be either substitutes or complements).

The Spanish lottery agency, Loterias y Apuestas del Estado (LAE), one of the biggest in the world, has followed international practice in expanding the number of games in its portfolio over time. Its first lotto product, La Primitiva, was launched in 1985; Bonoloto was added in 1988; and El Gordo de la Phmitiva followed in 1993. Extra drawings of individual games were also introduced to present players with greater choice over when, as well as how, to play. It is the relationship between these various game offerings that is explored in this article. (1)

All three games have long odds against winning the biggest prize (2) and in each case this generates frequent rollovers, permitting spectacular jackpots to accumulate on occasions. Thus, even though take-out rates are uniform across the games, there may be very substantial variation from week to week in the relative value for money available at each draw of each game. It depends on which games have accumulated large rollovers. Because the games are drawn on adjacent days over the course of a week, and are widely available through the same retail networks, they may then be expected to be revealed as either substitutes or complements by modeling of the response of sales of each product to the set of expected values of tickets available that week. Whether the relationship between games is that of substitutes or complements (and the strength of the relationship), it has implications for the pricing and marketing of the games offered by the lottery agency.

According to standard economic usage, the definition of substitutes (or complements) depends on the sign of the cross-price elasticity. This study uses draw-by-draw data to examine the sign of the cross-price elasticities among Spanish lotto games and therefore to determine whether these games are substitutes or complements. Following practice since Clotfelter and Cook (1987) and Gulley and Scott (1993), price in the lottery literature is usually identified with the expected loss from the purchase of a single ticket. This is termed "effective price" and it will vary with the pattern of rollovers even if the nominal entry fee for a game is held constant. Here in the Spanish case, there is the complication that two changes in the nominal entry fee were in fact introduced during the data period. We will therefore model demand for each game as a function of its own effective price per euro paid for a ticket and of the (similarly defined) effective prices of rival games available at the same outlets. Estimates of own - and cross-price elasticities will then enable inference concerning whether net-of-prizes revenue is being maximized at current take-out rates and whether there are significant relationships between the demands for each game, which need to be taken into account.

There have been a number of previous studies attempting to evaluate own-price elasticity for a lotto game (see, e. …

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