JOHN HEY THE CHALLENGES OF EXPERIMENTALLY INVESTIGATING DYNAMIC ECONOMIC BEHAVIOUR DEMADYN’15, Heidelberg, 2 nd – 4 th March 2015

DYNAMIC CHOICE Passage of real time. Sequentiality of decision-making. Acquisition of new Information.

WHAT DO I/WE WANT TO DO? Different disciplines have different objectives. Test axioms. Test propositions. Test comparative static propositions. Construct theories to ex post rationalise things. Describe what people do. See how people learn. Fit preference functionals. Predict.

DYNAMIC INCONSISTENCY Are people dynamically inconsistent? Two ways of reacting to its existence. Specify new axioms/new preference functionals. Describe what do they do about it. Are they: sophisticated resolute naïve myopic ?

HOW DO WE WANT TO DO IT? ‘Obviously’ with experiments. Length of decision tree? short? long? Type of decision problem? pairwise choices? allocations? other? Repetitions? Incentives?

AXIOMS Expected Utility theory is central. I regard this a theory of static decision-making. But note Cubitt et al 1998: “It is well-known that expected utility theory can be derived [my emphasis] from standard axiom-sets…. It has been established more recently that several of these axioms, including the controversial independence axiom, follow from appealing principles of dynamic choice.” These are called by Cubitt et al Separability timing independence frame independence reduction of compound lotteries.

AN EXAMPLE OF TESTING AXIOMS CUBITT ET AL 1998 Could ask them to pre-commit in the right-hand tree as to what they would do if they did get to the decision box. Key: rectangle - decisions; ovals – moves by nature

AN OBSERVATION Most axiomatic theories of decision-making are static. Theories of dynamic decision-making usually combine one of these with some story as to how dynamic problems are tackled… …sometimes adding additional axioms ( Cubitt et al cite separability, timing independence and reduction )… … usually reducing the dynamic problem to a (series of) static problems.

WHAT I HAVE DONE Try to discover the method people use for tackling dynamic problems. Fit preference functionals. Look at particular dynamic problems (savings, search,…). Can one tackle these without knowing the preferences of the individuals?

TESTING AXIOMS WITHOUT ASSUMPTIONS ON PREFERENCES (Except consistency and dominance.) Here progress can be made. See, for example, Cubitt et al (2004). An example is where effectively the ‘same’ problem is framed in different ways – people do different things (but this could be noise). But there is a limit.

NoTypeDescription 1Scaled-Up Problem The decision-maker faces a choice between two options, each of which is a simple prospect: Option A: (q, 0) Option B: (0, 1). 2Prior Lottery Problem The decision-maker faces a lottery in which, with probability (1 — r), she receives x3 and, with probability r, she faces a subsequent choice between two options, each of which is a simple prospect: Option A: (q, 0) Option B: (0, 1). 3Pre- commitment Problem The decision-maker faces a lottery in which, with probability (1 — r), she receives x3 and, with probability r, she receives one of the options listed below, each of which is a simple prospect. She is required to choose which option to receive in this eventuality before the initial lottery is resolved. Option A: (q, 0) Option B: (0, 1). 4Two-Stage Problem The decision-maker faces a choice between two options, each of which is a two- stage lottery: Option A: First stage gives x3 with probability (1 — r) and the simple prospect (q, 0) with probability r; Option B: First stage gives x3 with probability (1 — r) and the simple prospect (0, 1) with probability r. 5Scaled-Down Problem The decision-maker faces a choice between two options, each of which is a simple prospect: Option A: (rq, 0) Option B: (0, r)

AXIOMATIC CONNECTIONS According to the the separability principle Problems 1 and 2 are equivalent. According to the timing independence principle, Problems 2 and 3 are equivalent. According to the frame independence principle, Problems 3 and 4 are equivalent. According to the compound lotteries principle, Problems 4 and 5 are equivalent.

WHAT DID THEY FIND? “The results lead us to reject the theoretical strategies for dealing with dynamic choice adopted both by standard theory and by some well- known explanations of the common ratio effect, including those of Machina, Segal and Kahneman and Tversky. In contrast, the explanation implied by Karni and Safra's theory of behaviourally consistent choice is not rejected by our data. Our main finding is a violation of a principle which we call timing independence. Assuming that this violation is robust, it is potentially important for any branch of economics which is concerned with risk and uses sequential models, because it suggests that the precise sequence of decisions and chance events has a systematic effect on the risk attitudes that govern the decisions taken. We offered two explanations for the finding. One implies that agents consciously make use of pre- commitment facilities that are available to them to make choices which are more risky than they would make in the absence of those facilities. The other is that agents experience endogenous preference shifts, as a result of their experiences of risk, which they fail to anticipate. The latter interpretation is particularly troubling, since it appears to undermine the standard assumption that preferences are exogenous.”

CHECKING WHETHER SUBJECTS PLAN Perhaps a better phrase is ‘look ahead’. (Assuming dominance.) Seeing what people do. Bone et al (2009) and Hey and Knoll (2011). There is only so far that you can go. Here are 2- and a 3- period examples.

CAN WE HAVE MORE THAN 3 PERIODS? Savings and pensions problems. Individual receives a stochastic flow of income y t through time. Can save it at an interest rate of r. Income not saved is consumed c t. Objective to maximise expected value of u(c t ) + ρu(c t+1 ) + ρ 2 u(c t+2 ) + … where u(.) is specified by the experimenter.

ROLLING STRATEGY

A GAME CONTEXT Two players playing the same consumption problem but with different discount rates… … thus being forced to be dynamically inconsistent.

How (should) people process a dynamic decision problem? Convert it into a strategy choice problem? (resolute) Solve it by backward induction – with either reduction or with certainty equivalents? (sophisticated) With EU these all lead to the same decisions. With non- EU not necessarily.

SEEING WHAT BEST EXPLAINS BEHAVIOUR Here you need to start estimating preference functionals. We can see whether people are sophisticated, naïve, myopic or resolute. Do these categories reveal which of Cubitt et al’s dynamic principles are respected?

OUR METHODOLOGY Give subjects a two-period dynamic allocation problem. Assume that their preferences are represented by a Rank-Dependent Preference Functional. Fit (by maximum likelihood, and estimate the parameters of) the preference functional assuming the four methods of tackling the problem (sophisticated, naïve, myopic or resolute). See which fits best.

WHAT WE LEARN FROM THIS “We find that the majority are resolute, a significant few are sophisticated, rather few are naïve and similarly few are myopic.” How does this help us? We can fit mixture models and work out the proportions. But does it matter?

WHERE NOW? But this is just a two-period problem. In multi-period problems (savings, pensions) people depart from the EU solution. Why? Is it myopia? The Rolling Strategy? But is it theoretically motivated?

NOISE? Does it exist? Where does it come from? What do we do about it?

WHAT OTHERS ARE DOING Extension to ambiguous settings. Updating rules.

CONCLUSIONS I think that you can only get so far with testing axioms. I think that one needs to understand how people process dynamic problems. The trouble with this is one needs to estimate preference functionals, and this relies on specific functional forms and specific stochastic specifications. But then the results can be used for prediction.

THE END Many thanks for listening.