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EDITORIALS: Anthony Rodgers Income, health, and the National Lottery BMJ 2001; 323: 1438-1439 [Full text]

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Are lottery winnings randomly assigned?

ian walker   (17 January 2002)

Are lottery winnings randomly assigned? 17 January 2002
ian walker, professor of economics university of warwick cv4 7al Send response to journal: Re: Are lottery winnings randomly assigned?	A recent editorial (A Rodgers, "Income, Health and the National Lottery", BMJ 2001; 323;1438-1439) suggested that the UK National Lottery could be used as a "natural" experiment to reveal the relationship between income and health (and other outcomes of interest). It is suggested that winners be offered (or perhaps forced to have) annuities as an alternative to lump sum prizes and that winners be compared over time with non-winners for their health, diet, smoking, drinking etc. The editorial further suggests that such a prize fund could itself constitute a "good cause" and that this may itself generate additional sales as well as contributing to policy objectives for a healthier population. The operator may want to feature long-lived winners in its advertising - and, perhaps even "match" such individuals with "similar" individuals who didn't "invest" in their health in this way and had recently died. "If only Mr X had played the game (scene of dismal cemetery fades out) he too could be on the beach (tropical island scene fades in) with (tanned, healthy) Mr Y who has been regular player in the lottery". Quotes from Mr Y might include "who said money can't buy health"; advertising copy might incorporate ghoulish images and the byline "your ticket out of here". The possibility of using lottery winnings has not escaped non-medical researchers. Apart from the work of colleagues at Warwick which is cited, researchers have also used lottery winnings to identify the importance of income in determining working patterns and other aspects of economic behaviour (G Imbens et al "Estimating the effect of unearned income on labor earnings, savings and consumption: evidence from a survey of lottery players" American Economic Review, 91,4, 778-794, Sept 2001). While I am a firm believer in the importance of experimental evidence and the usefulness of "natural experiments", in this case I feel that there are several reasons why the appeal of this idea is superficial. In particular winners are not randomly selected. The probability of winning is directly proportional to the number of tickets bought so winners will be disproportionately heavy players. While we know very little about the characteristics of winners, the survey evidence that we do have suggests that there are very systematic differences between players and non-players in terms of their observable characteristics (see L Farrell and I Walker "The welfare effects of lotto: evidence from the UK" Journal of Public Economics 72, 1, 99-120, April 1999) - players (of the on-line draw) are more likely to be middle aged (the young have more interesting ways of having fun, and the old don't have time to spend the money if they do win); more likely to be men than women (it is unclear to me why this should be so - especially since women live longer than men); less likely to have occupational or private pension arrangements, more likely to be poor than rich; more likely to be married than single; and more likely to be badly educated than well educated. While it may well be possible to control for observable differences (like age and education) through matching or multivariate methods, it seems likely that if there are observable differences between players and non-players (some of which will be correlated with long term health outcomes) the there will also be unobservable heterogeneity that would be very difficult to control for. Inspection of the Family Expenditure Surveys (a continuous large household survey) since November 1994 (when the UK game started) shows that lottery players are - educated less, insure less (including health insurance), smoke more, work less, have fewer children, are more likely to live in social housing, have larger credit card debts, and save less than non-players (although there seems to be no significant difference in the amount they give to charities). There is strong suggestion here that lottery players have systematically different preferences - in particular, it would seem that lottery players are less likely want to postpone current gratification of their desires in return for higher future consumption. Economists use the term "time preference" to indicate the degree of impatience that individual exhibit in their behaviour. The data suggests that lottery players have higher rates of time preference than non- players. This raises the immediate problem that winners are more likely to have invested less in their own health throughout their lives - through diet, exercise, not smoking, etc. While it may be possible to survey winners and then control for some of these effects there will inevitably be some differences that remain - perhaps personality differences that are correlated with both play and with health. These differences in attitudes may also affect the decision to accept a prize that is an annuity rather than a lump sum. In US games, most states offer jackpot winners the choice between $x p.a. for the next 20 years or £10.x today and most choose the latter even though the present value of the former exceeds the latter even at very high interest rates! The suggestion is that rate of time preference amongst players are indeed quite high - higher than suggested by the interest rates that we commonly observe and which succeed in getting many people to postpone their spending. You might then think that this offers the tempting prospect that half of the existing jackpots could be donated to good causes instead of to a few lucky players without affecting sales - of course, there is no free lunch and it seems likely that almost halving the (present) value of jackpots would deter many, especially the high discount rate people, from playing. Thus, either option (making prizes into annuities for all, or allowing people to choose one or the other) will make the treatment/control problem worse. This is doubly unfortunate because what we would dearly like to know is, not only “does money matter?” (i.e. does income affect health outcomes) but also “when does money matter?”. Does money when we are young, perhaps money given our parents, make for better health in the long run than more money when we are old and sick? Lump sum lottery wins, which would be randomly distributed across ages (of players) would have been a useful way of answering this issue – if only playing was random.