Intertemporal choice under timing risk

How do managers make decisions about long-term investment projects when the completion times are uncertain at the outset? What amount of timing risk will consumers take in the delivery of products, compared to certain delivery times? Is the expected discounted utility model a reliable predictor of an individual's timing risk? This paper fills in a gap in research into intertemporal decisions concerning timing risk.

by Ayse Onculer and Selçuk Onay

When it comes to time, just how prepared are people to take risks? How much are they swayed by factors such as the chances of receiving a payoff sooner rather than later, the size of the payoff, and the length of time they have to wait? How do people choose which course to take?

The answers to these questions will help us understand how managers make decisions about long-term investments in R&D projects when completion times are unknown at the outset, and how much delivery time consumers are prepared to risk when buying online.

Most research in this area has concentrated on outcome risk rather than timing risk. This working paper fills a gap in research into intertemporal decisions concerning timing risk where there is more than one possible delay.

Studies have concluded that animals prefer payoffs with risky rather than fixed delays with the same average time to reinforcement. A rare study with human participants intriguingly produced results that were the opposite of those predicted by the expected discounted utility model (EDU), finding 31% of the participants (146 business managers) to be risk averse when faced with a choice between a timing lottery and a sure timing payoff with the same expected delay (Chesson and Viscusi, 2003).

The authors of this working paper, Selçuk Onay, PhD student, and Ayse Öncüler, assistant professor of decision sciences at INSEAD, tested several similar hypotheses in a more systematic way, using the EDU model as a benchmark in three experimental studies. Under the EDU model, participants' decisions depended only on their intertemporal preferences -- the magnitude of discount rates and the shape of discount function.

The authors predicted that individuals would be timing-risk prone (preferring the timing lottery to the sure timing option with the same average delay to the outcome) in the gain domain (when the payoffs are positive). However, they predicted individuals would be timing-risk averse in the loss domain (when the payoffs are negative).

For each study, volunteer undergraduates from Bogazici University, Istanbul, were given scenarios with gain and loss framings. They then answered a series of hypothetical intertemporal choice questions. The first two studies focused on evaluating timing lotteries by comparing them to a sure alternative or by eliciting the certain timing equivalents (CTE) in pricing and matching tasks.

In the third study, subjects chose between pairs of timing lotteries where there was no sure realization time, with one task stochastically more variable than the other.

The first study manipulated the probabilities attached to possible realization times. It showed that aversion to timing risk is actually probabilistic risk aversion and that individuals distort probabilities attached to risky delays by overweighting small probabilities and underweighting large probabilities.

The second study elicited present values of timing lotteries and manipulated the magnitude of payoffs to see how these changes affected the CTEs. It revealed that individuals evaluate timing lotteries in a rank-dependent fashion. From the third study the authors concluded that observed aversion to timing risk can be explained only by non-linear treatment of probabilities, given that individual discount functions are convex shaped.

All the observations indicated that individuals are risk averse to timing lotteries and use decision weights rather than objective probabilities, evaluating risk delays in a rank-dependent fashion. A substantial number of subjects behaved as if they were risk averse in the gain domain and risk prone in the loss domain, with these tendencies increasing as the probability of the early realization time reduced.

As an EDU model cannot capture individual behaviour, there is a need for a behaviourally more appealing model allowing for probability transformation, such as a rank-dependent model.

Eliciting discount functions using timing lotteries, and eliciting the probability weighting function and the discount function simultaneously, are promising research directions. Understanding how people think about risky time horizons is important, but the current state of our understanding of the issue is far from complete.

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