Abstract
Dynamically inconsistent decision makers have to decide, implicitly or explicitly, what to do about their dynamic inconsistency. Economic theorists have identified three possible responses—to act naively (thus ignoring the dynamic inconsistency), to act resolutely (not letting their inconsistency affect their behaviour) or to act sophisticatedly (hence taking into account their inconsistency). We use data from a unique experiment (which observes both decisions and evaluations) in order to distinguish these three possibilities. We find that the majority of subjects are either naive or resolute (with slightly more being naive) but very few are sophisticated. These results have important implications for predicting the behaviour of people in dynamic situations.
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Notes
We presume that he is male to avoid expositional clumsiness.
Or in some other way—these three ways of reacting to the potential dynamic inconsistency are not the only ones.
We should note that the issue could also be regarded as one of framing. As we shall see later when we discuss the actual decision problems used in the experiment, different ways of framing the problem might lead to different solutions, for a potentially dynamically-inconsistent person. Indeed, it could be argued that dynamic-consistency and immunity-to-framing-effects are one and the same thing.
A tree with a similar structure is found in McClennen (1990).
Whom we assume here is female to avoid expositional clumsiness.
The Independence Axiom of Expected Utility theory implies that £30 for sure is preferred to a 80:20 lottery over £50 and £0 if and only if a 25:75 lottery over £30 and £0 is preferred to a 20:80 lottery over £50 and £0.
Note that lottery N stochastically dominates lottery M.
Machina though does not use directly the term sophisticated choice for this kind of approach. Also Karni and Safra’s (1989) model of “behavioural consistency” represents a way of implementing the sophisticated choice approach, and represents a solution to the problem of dynamic inconsistency with non-linear preferences.
Machina’s model of choice is equivalent even if differently formalised to McClennen’s model of resolute choice. According to Machina, resolute choice represents one of the “antecedents of the formal approach” presented in his paper.
An interesting point is how this person can force him- or herself to behave resolutely.
Busemeyer and his associates in psychology have carried out some related experiments (see, for example, Busemeyer et al. 2000) but without such incentives.
We note that valuation data is potentially more informative than choice data, as the latter only tells us which choice is preferred and nothing about the strength of preference.
We take this as a sign that the subjects understood the second-price sealed-bid auction method. Besides, the raw data on the subjects’ bids (see Web Technical Appendix 1) show that no case of under or over-bidding occurred.
Recall that there were five subjects in each group, implying an average probability of 1/5 that any subject would be paid from playing out a particular tree, and that there were 12 trees, each chosen with probability 1/12.
Recall that subjects were presented with three sets of trees with the structure as in Fig. 2.
We should also note that one of the referees asked us to record that he or she “judged that this feature of the design was both unethical and unnecessary”. We agree with the ‘unethical’ but would argue that it was necessary to increase the number of useful observations and save expense on paying the subjects: if we had not used this deception, we would have had to have many more subjects in the experiment.
We note that the presence of this error means that inevitably our inferences can not be certain.
Before arriving at this particular specification, we tried several others, of varying degrees of sophistication. One simple alternative was that subjects made all evaluations with error but then ‘trembled’ (see Moffatt and Peters 2001) when taking decisions and when making bids; the trouble with this story (in addition to the fact that it does not seem empirically valid) is that, while the tremble story is simple to apply to decisions, it is not obvious how to interpret it with respect to bids. There are also other variations that we have tried on the basic story that we report in this paper; in particular, we explored the hypothesis that subjects made no mistakes when evaluating certainties—this performed worse than the variant reported in the paper; and also a variant that takes into account that the extreme value distribution incorporates a bias (the expected value of a variable with an extreme value distribution with parameters m and 1/s is not m but rather m + γs where γ is the Euler-Mascheroni constant 0.5772156649), by exploring the notion that the subjects corrected for this bias when making their bids; this also performed worse than the variant we have used in the paper.
It should be noted that we do not consider reduction by substitution of certainty-equivalents for the naive and resolute types. In this we follow McClennen (1990) which implies simplification by reduction to hold for these models.
To be strictly correct we should attribute this to Tversky and Kahneman (1992), who proposed this variation on the original specification proposed by Quiggin, namely: w(p) = p g/[p g + (1 - p)g]
We should note that for 25 subjects there was one combination which fitted best on all four specifications; there were 20 subjects for whom one combination fitted best on three of the four specifications; and there were five subjects for whom one combination fitted best on two of the four specifications. The conclusion seems to be clear—for virtually all subjects, the data seems to be telling us that one combination (of utility function and weighting function) fits best independently of the specification.
To avoid problems with the maximum likelihood algorithm we transformed our parameters to restrain their range (for example to stop the s parameter becoming negative). The returned estimates and variance-covariance matrix are thus those of the transformed parameters—and they need to be transformed back before they can be interpreted.
In this case the maximised log-likelihoods for the Type 1 and Type 2 sophisticated specifications were −13.32295 and −12.49711 and we accordingly prefer Type 2 to represent sophistication.
But see Busemeyer et al. (2000) for the psychologists’ way round the problem.
See, for example, Harris and Laibson (2001).
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Further Reading
Beggs, S., Cardell, S., & Hausman, J. (1981). Assessing the potential demand for electric cars. Journal of Econometrics, 16, 1–19.
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Hey, J.D., Lotito, G. Naive, resolute or sophisticated? A study of dynamic decision making. J Risk Uncertain 38, 1–25 (2009). https://doi.org/10.1007/s11166-008-9058-5
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DOI: https://doi.org/10.1007/s11166-008-9058-5