If only lottery winnings were randomly assigned

Editor—The causal effect of income on health has important policy implications, and yet its identification is dogged by the problem of income not being randomly assigned. Researchers continue to ignore this, including Rodgers in his editorial,¹ but the idea that the problem can be overcome by exploiting lottery winnings as a “natural experiment”² is superficial because winners are not randomly selected from the population since playing is not a random event.

Although playing is popular, it is far from universal. The probability of winning is directly proportional to the number of tickets bought, so winners, on average, will be disproportionately heavy players.

Survey evidence suggests that players and non-players differ systematically in terms of their observable characteristics such as age, education, and sex.³ Indeed, expenditure survey data show that, compared with non-players, players insure less, smoke more, work less, have more modest pension provision, are more likely to live in social housing, have larger credit card debts, and save less. Controlling for all of these observable differences through matching or multivariate methods may well be possible, but considerable unobservable heterogeneity that would be difficult to control for would probably remain.

Data suggest that lottery players have higher rates of “time preference” than non-players do. In games in the United States most states offer jackpot winners the choice between $x a year for the next 20 years or $10x in cash today; most winners choose the latter even though the present value of the former far exceeds it at typical interest rates. This suggests that the time preference among players is high—higher than would be suggested by typical interest rates. This raises the problem that winners are more likely to be impatient people with a high time preference who have invested less than others in their health (by diet, exercise, not smoking, etc) throughout their lives.

It is important to know not only whether money matters but also when (if ever) it matters. Does having more money when we are young—perhaps money given by our parents—make for better health in the long run than having more money when we are old (and perhaps already sick)? Having lottery winnings randomly distributed would have been a useful way of answering important policy questions—if only winning were random.