A Time Series Analysis of U.K. Lottery Sales: Long and Short Run Price Elasticities

Abstract

This paper estimates the long‐ and short‐run elasticities for Lotto. It is particularly concerned with the dynamic response to price variations since, for some goods, this has sometimes been used to infer the presence of addiction. The price elasticity is identified through variation in the expected value of a Lotto ticket induced by rollovers whose high frequency results in surprisingly high variation in the expected value of holding a ticket. Unit root tests are applied to the series in order to identify their time series properties and to avoid a spurious regression problem. The series are found to be stationary. We apply instrumental variables to account for the endogeneity which arises due to correlation between the expected value and the dependent sales variable. The estimated long‐run elasticity exceeds the short‐run elasticity and this supports the hypothesis that there is an element of addictive behaviour in sales. The Lottery is regulated and the regulator’s objective is to maximize sales. Our estimated long‐run price elasticity of demand is inconsistent with revenue maximization and we find that greater revenue for the ‘good causes’ could be raised from the game if a smaller proportion of sales revenue were allocated to them.

Behavioral Household Finance

“…37 of a winning lottery ticket, lottery purchases in the zip code of the winning sale increase by 14%, and approximately half of this increase remains six months later. Farrell et al (1999) similarly find evidence for habit formation in time-series analysis of aggregate U.K. lottery data.Another possible explanation for lottery participation is that households perceive the probability of winning the lottery to be higher than the objective probability. Relatedly, households that correctly perceive the win probability may nonetheless make decisions as if it were higher, as modeled by the prospect theory probability weighting function.…”

The Illusion of Control, The Structures of Prizes and The Demand For Football Pools in Spain

“…The estimated effect of addiction, obtained as the sum of the coefficients of the lag endogenous variables varies from 0.171 to 0.360 depending on the subsample considered (from 0.226 to 0.485 in the case of the effective price model). These values are similar to those obtained by Farrell et al (1999) for the British lotto but slightly smaller than 0.45, which is the addiction effect found by Becker et al (1994) for the demand for tobacco.…”

“…Additionally, it would be interesting to analyse the separability of the expenditure on these games by families with respect to other types of expenditures, in order to be more precise about the implications of changing the structure of the game and that of the prizes. 3 See Cook and Clotfelter (1993), Gulley and Scott (1993), Scott and Gulley (1995), Walker (1998), Farrell et al (1999) and Forrest et al (2000) as examples of empirical applications of the effective price model to for the analysis of the determinants of lotto sales.…”

“…Farrell et al (1999) reinterpret this expected prize as the jackpot multiplied by the probability of having at least one winner (1-P) divided by the total sales, i.e.…”

A Global Lottery and a Global Premium Bond

“…This 'long-shot' bias is evident in other types of gambling (Forrest 2003). Empirical studies show that rollovers (when nobody wins the top prize and the jackpot is added to the jackpot of the next draw) raise sales not only for the draw in question but also for successive draws (Farrell, Morgenroth and Walker 2000). This is referred to as the 'halo' effect in the industry.…”