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Do people plan ahead?
John D. Bonea; John D. Hey; John R. Sucklinga
a
Department of Economics, University of York, Heslington, York YO10 5DD, UK.
To cite this Article Bone, John D. , Hey, John D. and Suckling, John R.(2003) 'Do people plan ahead?', Applied Economics
Letters, 10: 5, 277 — 280
To link to this Article: DOI: 10.1080/1350485032000056882
URL: http://dx.doi.org/10.1080/1350485032000056882
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Applied Economics Letters, 2003, 10, 277–280
Do people plan ahead?
J O H N D . B O N E { , J O H N D . HE Y *{ { and J O H N R . S U C K L I N G {
{ Department of Economics, University of York, Heslington, York YO10 5DD, UK
and { University of Bari
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A crucial basic assumption of economic theories of dynamic behaviour is that people
plan ahead. This paper reports on an extremely simple experimental test of this
fundamental principle. Indeed the experiment is so simple and so straightforward
that it is difficult to believe that anyone would not plan ahead. However subjects are
found who do not. What are they doing?
I. INTRODUCTION
The three co-authors of this paper were divided as to
whether this experiment was worth running. It was thought
that the set-up was so simple that no subjects would be
found whose behaviour violated a key economic principle
– that people plan ahead. However, it was agreed that if
such subjects were found then it would be interesting.
Moreover it is wanted to run a particularly simple experiment – as a ‘special promotion’ to attract subjects to our
Register. The basic idea of the experiment was one on
which we have been working for some time – to set up
an experiment in which a first move by a subject reveals
– where pertinent – what they are planning to do in the
future. One of us (Hey, 2001) has shown that such an
experiment is impossible in general unless some assumptions are made. In this experiment, the only assumption
made is that subjects’ preferences respect dominance. As
will be seen, the weakness of this assumption means that
the predictions are similarly weak.
I I . T H E E X P E R IM E N T A L D E S I G N
The experiment is extremely simple – an outline of the
instructions can be found in the Appendix to this paper.
These instructions were publicly available (in this format,
via the web, and hence in colour) to subjects in advance of
the experiment, except that the exact payoffs were not disclosed in advance. Each subject undertook the experiment
individually, in our laboratory office, in the presence of two
experimenters. The subject made decisions by ticking boxes
on an individual form, and realizing the chance events by
drawing a ball from a bag. On average it took a little over
two minutes for each subject to complete the experiment.
There are two Stages – Stage 1 and Stage 2. In Stage 1
subjects are presented with a bag which contains four red
balls and one green ball. They have two options from
which to choose, (1) and (2), after which a ball is drawn
at random from the bag. The choice must be made before
the ball is drawn, but the outcome depends on the colour of
the ball that is drawn. If the ball drawn is green then the
implications are: (1) to enter Stage 2; (2) to take £4.50
without entering Stage 2; if the ball drawn is red then the
subject is dismissed from the experiment without any payment. After the subject has chosen (1) or (2) a ball is drawn
and the subject either enters Stage 2 (if the ball drawn is
green and if he or she has chosen (1)), or gets paid £4.50
and does not enter Stage 2 (if the ball drawn is green and if
he or she has chosen (2)), or gets dismissed from the experiment (if the ball drawn is red). If Stage 2 is reached then the
subject is immediately presented with another bag which
contains one red ball and one green ball. The subject again
has two options from which to choose: (1) to draw a ball at
random from the bag, being paid £10 if the ball drawn is
green (and nothing otherwise); (2) to be paid £4 without
drawing from the bag.
It may be noted that the payoffs and probabilities used in
this experiment are motivated by considerations similar to
those employed when experimenters wish to design an
* Corresponding author. E-mail: [email protected]
Applied Economics Letters ISSN 1350–4851 print/ISSN 1466–4291 online # 2003 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/1350485032000056882
277
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278
experiment in which common ratio effects may be
observed. As viewed from Stage 2, the two options available in Stage 2 are (A) £4 for sure and (B) a 50–50 gamble
between £0 and £10, whereas as viewed from Stage 1 the
two options available in Stage 2 are (C) a gamble which
yields £4 with probability 0.2 and £0 with probability 0.8
and (D) a gamble which yields £10 with probability 0.1 and
£0 with probability 0.9. Note that if a subject obeys the
axioms of Expected Utility theory then he or she would
prefer (A) to (B) if and only if he or she prefers (C) to
(D) – so if he or she planned to go for Stage 2 and then
go for the risky choice (the 50–50 gamble on £0 and £10)
then he or she would not change his or her mind if he or she
managed to pass to Stage 2. However, if the individual
does not obey the axioms of Expected Utility theory,
then it could be the case that he or she preferred A to B
and yet preferred D to C, or that he or she preferred B to A
and yet preferred C to D. The former is the interesting case
from the point of view of this experiment – the individual
might choose to enter Stage 2 planning to go for the risky
choice (the 50–50 gamble on £0 and £10) – because he or
she prefers D to C – yet change his or her mind upon
entering Stage 2 – because he or she prefers A to B. But
all this is beside the point if the individual plans ahead –
because he or she would be able to anticipate this behaviour – and, in anticipating it, realize that he or she would
end up, if lucky, with £4 at the end of the day rather than
the £4.50 gained from not entering Stage 2. So the design of
the experiment is such that we will capture non-EU people
only if they do not plan ahead.
For non-EU people who do plan ahead we can argue in
the following way. Being non-EU it is possible that they are
dynamically inconsistent in that they plan to do one thing
but change their minds – as illustrated above. If such nonEU people want to be dynamically consistent, then they
have two choices – they can either act in a sophisticated
manner (to use the terminology of Machina, 1989) or can
act in a resolute manner (to use the terminology of
McClennen, 1990). Let us start with the non-EU person
discussed above – one who prefers A to B yet prefers D
to C. If this person is sophisticated in Machina’s sense then
he or she anticipates that he or she will choose A if she
succeeds in entering Stage 2. This would give the individual
£4 on entering Stage 2. However the individual can work
out that not opting to enter Stage 2 gives him or her £4.50
under the same circumstances – which is obviously preferable. This individual chooses not to enter Stage 2. No
inconsistency will be observed. If the individual has the
opposite non-EU preferences – prefers B to A yet prefers
C to D – this individual would anticipate that if he or she
opted for Stage 2 and were successful he or she would go
for the 50–50 gamble in Stage 2 – therefore at Stage 1 the
individual has the choice between C and D. He or she
prefers C to D and would therefore not opt for Stage 2
in Stage 1. No inconsistency will be observed.
J. D. Bone et al.
If, instead, the individual acts in a resolute manner in
McClennen’s sense then he or she chooses the best strategy
as viewed from the beginning of the experiment – and then
resolutely implements it. The possible strategies are: (a) in
Stage 1 opt for Stage 2 and, if successful, go for the gamble;
(b) in Stage 1 opt for Stage 2 and, if successful, go for the
£4 for sure; (c) in Stage 1 opt for the £4.50 for sure. It can
be seen that (a) is a gamble between £0 and £10 with respective probabilities 0.9 and 0.1; that (b) is a gamble
between £0 and £4 with respective probabilities 0.2 and
0.8 and that (c) is a gamble between £0 and £4.50 with
respective probabilities 0.2 and 0.8. What is crucial is
that strategy (c) (first-degree) dominates strategy (b) –
which implies that strategy (b) will never be chosen by
our non-EU individual. He or she might opt to enter
Stage 2 but will then resolutely go for the gamble, or he
or she might opt to go for the certainty in Stage 1. Never
would this resolute non-EU individual opt to enter Stage 2
and then go for the £4 certainty.
Therefore the predictions of the experiment are simple: if
the subject chooses option (1) at Stage 1 then he or she
must choose option (1) at Stage 2. Note that we only get a
prediction if the subject chooses (1) at Stage 1 – for if he or
she chooses (2) at Stage 1 then there are no further decisions to take. Note further that a test of this prediction is
only obtained if the subject chooses (1) at Stage 1 and then
if a green ball is drawn – for if a red ball is drawn in Stage 1
then there are no further decisions to take. Moreover it is
noted that this prediction requires only the assumption that
the subject’s preferences respect dominance – for the choice
of (1) in Stage 1 followed by (2) in Stage (2) is dominated
by the choice of (1) in Stage 1 followed by (1) in Stage (2).
To put it in simpler terms – opting for £4 in Stage 2 (rather
than go for the 50–50 gamble over £0 and £10) is dominated by opting for £4.50 if the ball drawn in Stage 2 is
green. £4.50 dominates £4. Why settle for £4 in the event
that the ball drawn in Stage 1 is green when you can have
£4.50?
I I I . D I F F E R E N T T R EA T M E N T S
The above describes the basic story. In practice two treatments were run – but with the same basic structure.
Treatment 1 is as described above; Treatment 2 has the
£4.50 at Stage 1 replaced by £5 and the £4 at Stage 2
replaced by £4.50. The prediction in both treatments is
the same: if the subject chooses option (1) at Stage 1 then
he or she must choose option (1) at Stage 2. And the argument is the same: in Treatment 1, why settle for £4.00 in the
event that the ball drawn in Stage 1 is green when you can
have £4.50?; in Treatment 2, why settle for £4.50 in the
event that the ball drawn in Stage 1 is green when you
can have £5.00?
279
Do people plan ahead?
Treatment 1
9
10
40
16
30
3
13
1
6
£10
3
£0
£4
£0
£4.50
£0
Treatment 2
9
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11
65
52
54
12
40
2
3
£10
6
£0
£4.50
£0
£5
V. DISCUSSION AND CONCLUSION
£0
Fig. 1.
Was different behaviour expected in the two treatments?
Some of us said ‘no’ – the predictions are the same. Some
of us said ‘perhaps’ – in Treatment 2 one is more likely to
see subjects having ‘cold feet’ having reached Stage 2 than
in Treatment 1 (because £4.50 is more attractive relative to
the 50–50 gamble between £0 and £10 than is £4.00).
IV. THE RESULTS
A total of 173 subjects took part in the experiment – 56 on
Treatment 1 and 117 on Treatment 2. The results are
shown in Fig. 1 – Treatment 1 at the top and Treatment
2 at the bottom – in which a square box denotes a choice
node and a round box a chance node. The numbers on the
various branches show the number of subjects following
that branch – either through choice or by chance. The
interesting numbers are those following the second choice
node: it will be seen that in Treatment 1 of the 10 subjects
opting to enter Stage 2 and succeeding in so doing, nine of
them chose option (1) in Stage 2 while one chose option (2);
in Treatment 2 of the 11 subjects opting to enter Stage 2
and succeeding in so doing, nine of them chose option (1)
in Stage 2 while two chose option (2). So in Treatment 1
there is one subject (out of 10) violating the prediction and
in Treatment 2 there are two subjects (out of 11) violating
1
the prediction – a total of three subjects out of 21 violating
the prediction. Obviously these numbers significantly reject
the null hypothesis of the prediction at any level of significance – but this is hardly interesting. It is also the case that
the hypothesis that subjects choose between (1) and (2) in
Stage 2 by picking at random is rejected at most conventional significance levels, but again this is not particularly
interesting.
What is interesting is that these three subjects are there at
all. What are they doing? It could be argued that they have
developed ‘cold feet’: having reached Stage 2 they might
think that they have been lucky once and are unlikely to be
lucky again; they might feel that they have pushed their
luck too far.
But why did they not anticipate this? They have no new
information than they could have realized they would have
if they had thought ahead. But perhaps the answer is
simple – that they did not plan ahead?
There is an alternative story – that these three subjects did
not plan ahead but they did think ahead. Choosing to enter
Stage 2 opens up the possibility of choosing either to go for
the 50–50 gamble or to go for the £41 for sure. If the subject
opts to enter Stage 2 then he or she may face the choice set
{[£0, £10]; £4}, containing two elements, £4 for sure and
[£0, £10] where this denotes a 50–50 gamble between £0
and £10. Choosing not to enter Stage 2 opens up the possibility of the choice set {£4.50}, containing a single element.
Maybe the choice set {[£0, £10]; £4} containing two elements looks more attractive to the subjects who chose to
enter Stage 2 than the choice set {£4.50} containing one
element?
Well that may be true but what would the economist
now say? That the subject should anticipate his or her decision if he or she opted for Stage 2 and were successful. There
are two possibilities: (1) that the subject would choose
the gamble [£0, £10] from the choice set {[£0, £10]; £4}; (2)
that the subject would choose £4 from the choice set
{[£0, £10]; £4}. Consider these in order. Under (1) the
subject eliminates the non-chosen option from the choice
set at Stage 2 and therefore considers the choice between
{[£0, £10]} and {£4.50} in deciding whether to enter Stage 2
or not. He or she may or may not decide to enter Stage 2
under these circumstances, but if he or she does then (as
already argued) he or she will choose the gamble [£0,£10] in
Stage 2. Under (2) the subject eliminates the non-chosen
option from the choice set at Stage 2 and therefore considers the choice between {£4} and {£4.50} in deciding
whether to enter Stage 2 or not. It is obvious which is best.
£4 in Treatment 1; £4.50 in Treatment 2. Stated here is the argument for Treatment 1; a similar argument applies to Treatment 2.
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But these arguments assume that the subjects are able to
anticipate their own future behaviour. There is evidence
from elsewhere (see, for example, Carbone and Hey, 2001)
that this is something that some subjects are not particularly
good at – either because they are unable to anticipate what
they will do in the future, or because they do not know now
what their preferences in the future will be. Indeed, in
Carbone and Hey (2001) there seemed to be many subjects
who looked ahead but did not plan ahead in the sense of
anticipating their own future decisions. To such subjects,
possibly choosing from the choice set {[£0, £10]; £4} might
appear to be more attractive than possibly choosing from
the choice set {£4.50}, not least because the former of these
has two elements while the latter has just one. If this argument is correct, perhaps it should be concluded that subjects
think ahead but do not plan ahead?
A C K NO WL E D G E M E N T S
We wish to thank the European Community under its
TMR Programme Savings and Pensions (TMR Network
J. D. Bone et al.
Contract number ERB FMR XCT 96 0016 (‘Structural
Analysis of Household Savings and Wealth Positions
over the Life Cycle’)) for part financing the research
reported in this paper. We would also like to thank
Miguel Costas-Gomes, Tibor Neugabauer and Giorgio
Coricelli for comments and help in running this experiment.
REFERENCES
Carbone, E. and Hey, J. D. (2001) A test of the principle of
optimality, Theory and Decision, 50, 263–81.
Hey, J. D. (2001) ‘Are Revealed Intentions Possible?’, under submission.
Machina, M. J. (1989) Dynamic consistency and non-expected
utility models of choice under uncertainty, Journal of
Economic Literature, 27, 1622–68.
McClennen, E. F. (1990) Rationality and Dynamic Choice:
Foundational Explorations, Cambridge University Press:,
Cambridge.
APPENDIX
Instructions2
STAGE 1
Bag 1 contains four red balls and one green ball. If you draw the green ball then you may either:
. enter Stage 2, or
. take £4.50 without entering Stage 2
You will be asked to make your choice before drawing from Bag 1. If you choose ‘enter Stage 2’ and
then draw the green ball from Bag 1, you will proceed to . . .
STAGE 2
Bag 2 contains one red ball and one green ball. If you draw the green ball then you win £10.
However, you may choose not to draw from Bag 2, but to take £4 instead. So in Stage 2 you
may either:
. draw from Bag 2, winning £10 if green, or
. take £4 without drawing from Bag 2
You will be asked to make your choice if, and only if, you have won entry to Stage 2.
2
For Treatment 1. For Treatment 2,the £4.50 in Stage 1 is replaced by £5 and the £4 in Stage 2 is replaced by £4.50.