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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.
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.
Competing interests: No competing interests