THE (AGGREGATE) DEMAND FOR STATE‐LOTTERY TICKETS: WHAT HAVE WE REALLY LEARNED?

I. INTRODUCTION Empirical estimation of aggregate-demand functions (aggregated over individuals) is quite common in the literature that examines the demand for state-lottery tickets (e.g., Cook and Clotfelter 1993; Garrett 2012; Garrett and Coughlin 2009; Ghent and Grant 2010; Hansen 1995; Miksell 1989; Price and Novak 1999, 2000; Tosun and Skidmore 2004). (1) Estimation of aggregate-lottery demand is due to a general lack of individual-level data on a consumer's income and lottery-ticket purchases, and therefore these data have only been used in a small percentage of all lottery-demand studies (Farrell and Walker 1999; Perez and Humphreys 2011; Scott and Garen 1994). Aggregate data on lottery sales and income, which are commonly at the zip-code or county level, are often used in regression analysis of an aggregate lottery-demand function to estimate an income elasticity of demand for lottery tickets. The income elasticity of demand for lottery tickets is the most common statistic in the policy debate on the efficacy of state lotteries as an appropriate means of state government finance, as it provides evidence on the distributional burden (by income) of lottery-ticket expenditures (i.e., lottery "regressivity"). In addition, aggregate lottery-demand models have been used to estimate the own-price elasticity of demand and the cross-price elasticity of demand for lottery tickets, with the latter providing evidence on the substitutability or complementarity of different lottery games (Forrest, Gulley, and Simmons 2000; Grote and Matheson 2006; Perez and Forrest 2011). Most studies using aggregate lottery-demand models have estimated an income elasticity of demand that is less than one (and conclude that lotteries are regressive), whereas evidence on the cross-price elasticity of demand is mixed. This area of research has implicitly assumed and has tacitly accepted that an income elasticity of demand and cross-price elasticity of demand estimated from an aggregate lotterydemand model reflect the behavior of individual consumers. However, the income elasticity of demand and the cross-price elasticity of demand have strict microeconomic definitions that result from an individual's utility maximizing calculus. The literature has provided no discussion of the essential microeconomic assumptions needed for equating the estimated behavior from aggregate lottery-demand models with the behavior of an individual consumer and, therefore, the questionable interpretation of empirical estimates for the "income elasticity" and the "cross-price elasticity" obtained from aggregate lottery-demand models. This is true even for the few aforementioned studies that have estimated an income elasticity of demand using cross-sectional microlevel data. The fact that individuals have different utility functions lies at the heart of the problem of making inferences about an individual consumer's behavior based on the estimation of aggregatedemand functions. After all. because individuals have different utility functions they thus have different demand curves, so it is unclear how behavior inferred from an estimated aggregate-demand function will reflect the consumption behavior of individuals. The consumer theory literature on aggregation, such as Deaton and Muellbauer (1980) and Chiappori and Ekeland (2011), provides much discussion and theoretical evidence on the assumed form of consumer preferences (utility function) that can be aggregated so that the estimates from an aggregate-demand function reflect the behavior of a representative consumer, while imposing the fewest restrictions on consumer behavior. As will be shown in this article, the form of consumer preferences inherently assumed in the estimation of aggregate lotterydemand functions is amenable to aggregation, but the assumed form of preferences imposes unrealistic restrictions on consumer behavior as well as assumes the preferences of all consumer are equal. …