Heterogeneity, aggregation and long memory in lottery sales: some empirical evidence for Brazil

ABSTRACT

The paper investigates the prevalence of long memory for lottery sales, as previous literature suggests that aggregation of heterogeneous agents can potentially lead to a fractional differencing parameter consistent with highly persistent processes. Applications are considered for sales of 7 different lottery modalities in Brazil and also disaggregated at the level of federative units. The selected estimated models considered controls in terms of dummy variables for prize rollovers, special draws and weekends´ draws. The effects of rollovers and special draws on lottery sales are typically positive and non-negligible with an exception for the latter variable. The effect of draws that take place at weekends are mixed and not always positive. One observes long memory, for Brazil as a whole, only in the case of one modality. The evidence by federative units is mixed and indicates contrasts that suggest heterogeneities across regions and lottery modalities. At a more exploratory level, the evidence obtained with a stacked sample suggests relevant effects accruing from income inequality. on the probability of prevalence of highly persistent lottery sales, taking into account controls for regional heterogeneities. The initial evidence suggests that positional concerns may be relevant in the case of Brazil.

KEYWORDS:

• Lottery sales
• long memory
• Brazil
• aggregation

JEL CLASSIFICATION:

• C22
• D12
• L83

Acknowledgement

The author acknowledges the comments from an anonymous referee, but the usual caveats apply. Moreover is grateful to Stela Teles for the research assistance and to Conselho Nacional de Desenvolvimento Científico e Tecnológico–CNPq for the research funding

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ Conlisk (1993), for example, considers an expected utility function that embodies a component that captures the pleasure of merely participating in a gambling activity that adds to the components that reflect probabilistic concerns.

² The paper followed the approach by Forrest, Gulley, and Simmons (2000a) that only considered one major lottery modality in the UK.

³ In particular, it is worth mentiniong news reports from an influential sports´s magazine [see e.g. Placar no. 1.032-A, Editora Abril, March 1990, page 55].

⁴ The decline of the Brazilian dominance in the world scenario and the fact that the main players no longer play in Brazilian clubs may also have some role in the aforementioned trend.

⁵ In particular, the special draw related to new year´s eve was created only in 2006.

⁶ Ocasionally the first case is referred as having intermediate memory but Brockwell and Davis (1987) and Box, Jenkins, and Reinsel (2008) classify those cases as long memory processes.

⁷ The dataset used in the estimations can be provided upon request.

⁸ Gini index for the average real income of people aged 14 years and over, usually received in all jobs, at average prices at the given year for the different federative units.

⁹ Lotofácil (for Pará), Loteca (for Espírito Santo and Mato Grosso) and Lotogol (for Mato Grosso, Rio de Janeiro, Rio Grande do Sul, São Paulo and Brazil).

¹⁰ Box and Pierce (1970) and Ljung and Box (1978).

¹¹ The obtained residual autocorrelations can be provided upon request.

¹² See Specht et al. (2014) for an overview.

¹³ Different expenditures within various goods´ categories could fit that concept and refer to categories within motor vehicles; apparel; jewellery and watches; skin and body care; hosiery goods/headpieces; dental treatments and prostheses; furniture; valuable electronic household appliances; phones, TVs, radio sets, cameras; optical instruments; collections, art objects, music instruments; sporting and other leisure goods; food and drinks in restaurants and holidays.

¹⁴ A two-step procedure takes into account sample selection does not appear to have been applied.

¹⁵ See Guo and Zhao (2000) for an overview of those models in the context of binary.

response data and also the survey by Rabe-Hesketh and Skrondal (2012)

¹⁶ A more extreme lottery modality involving scratch cards [Loteria Instantânea, popularly known as ‘raspadinha’] was also operated by Caixa Econômica Federal starting in 1991 but was discontinued in 2016. Investigations could be pursued should the necessary data be available.

Additional information

Funding

The work was supported by the CNPq [401042/2016-2].