Although over-purchasing in times of crisis might be considered as irrational, scholars in economics, operations research and marketing have proposed theoretical models explaining when and how individuals rationally decide to stockpile. Besides rational motives, many behavioral aspects can also motivate over-purchase decisions.
Stockpiling as a rational decision involving risk and time
Decisions to purchase and store quantities in prevision of future hazards are not infrequent, and may concern not only individuals, but also states and companies. At the State level, decisions to stockpile goods such as oil, weapons, medical masks and drugs are highly strategic. It can also be in the interest of the companies and consumers to stockpile primary or consumption goods, as an insurance against variations of future prices (as in the case of shortage risks).
It can be in the interest of the companies and consumers to stockpile primary or consumption goods, as an insurance against variations of future prices.
In all these contexts, the decision can be analyzed using the same framework. Stockpiling is a safe but costly option: the costs relate to purchasing additional quantity at the present time rather than smoothing the expense across time, as well as to storage costs (e.g. warehouse space and guarding). Not stockpiling is a risky option that exposes the decision maker to future price variations.
The best option, or optimal amount of stockpiling is therefore a decision involving risk and time and as such involves many factors: the perceived risk of price variations, the attitude towards time (how the decision maker values future consequences) and the risk attitudes (how the decision maker values risky consequences). In rational decision making these factors are combined using a model called “discounted expected utility”. For example, under this model, a consequence received at a future time period t with a perceived probability p is valued p exp(-rt)u(x), where r is the discount rate that captures attitudes towards the future, and u is a utility function that characterizes risk attitudes. Assuming that the decision maker has well-defined risk perception, discount rate and risk attitudes, the model makes recommendations about how much to stock pile.
Decision to stockpile depends on the perceived probability of shortage, risk aversion, discount rate and storage costs.
As one could expect, recommended stockpiling will increase with the perceived probability of shortage and risk aversion; it will decrease with the discount rate and storage costs.
The discounted expected utility model can be used to study many other decisions involving risk and time in various domains such as strategy, finance, marketing and industrial organization.
Deviations from the rational decision-making model
Beyond its normative appeal, the model underlying such recommendations cannot satisfactorily describe observed behavior. See Machina (1987) for violations of this model in the context of risk, and Loewenstein and Prelec (1992) for the context of time. We have investigated several of these anomalies in a recent laboratory experiment where subjects had to make decisions involving both risk and time with real possible gains. We observed systemic deviations from the predictions of the rational model. As previously observed, subjects did not exhibit stable risk attitudes. They took more risks in decisions involving small probabilities than in decisions involving medium or large probabilities. Another result regards the impact of time. Here again, time preferences were not constant.
More impatience was observed towards the near future than concerning periods further away in time. This pattern is responsible for several anomalies in decisions involving time, such as reversal of preferences over time or procrastination. Though well documented in the literature, several scholars have hypothesized that this pattern would disappear in decisions involving both risk and time. Our results, recently published in Games and Economic Behavior(1), show that this pattern holds even in these more general contexts.
Another source of irrational decisions regards the way people perceive risks when probabilities are not available (e.g. Tversky and Kahneman 1974). For example, in their evaluation of the likelihoods of uncertain future events, people generally tend to overestimate rare events and underestimate frequent ones. In another recently published paper, we propose a method for measuring people's beliefs about uncertain events(2) from simple choices. The method allows to put beliefs into numbers and to test if peoples’ perception is accurate.
Another important research question in the decision sciences relates to how people formulate and update their beliefs in the light of available evidence. In the context of stockpiling, decision makers can also be influenced by the behavior of their peers.
The social dimension of stockpiling: an analogy with bank runs
Stockpiling is an individual decision that can have dire social consequences. Indeed, in the context of shortage risk, individuals deciding to overpurchase effectively contribute to the risk. This kind of situation is called “self-fulfilling prophecy”.
Like bank runs, stockpiling decisions show two equilibria: one where decision makers stay calm, one where they panic, leading to a catastrophic situation.
When considered as a game involving many players, the decision to stockpile can be studied in game theory and is analogous to bank run games. These games have two equilibria: one where decision makers stay calm and do not overpurchase; another where decision makers panic and decide to overpurchase, leading to a catastrophic situation of real shortage. The first equilibrium is obviously better than the second one. Nevertheless, regarding individual rationality, both are “Nash equilibria”, meaning that when one sees that other people start to stockpile, individual rationality recommends you to stockpile too! In a social context, stockpiling can therefore be considered as a rational but selfish decision.
The role of herding behavior
Considering stockpiling as a social game introduces the fact that the beliefs and actions of each decision maker can be influenced by the actions of the other decision makers. Updating beliefs after observing the behavior of the others can be rational. Such situations are called information cascades. But behavioral studies reveal that people are sensitive to the behavior of others, even when it is uninformative or even misleading! In particular, people tend to conform to the dominant behavior, even in the absence of rational reasons to do so. In the present case of COVID 19, we can speculate that the sudden but notable stockpiling of toilet paper was due to herding.
People can probably easily convince themselves that, even if there were a major economic collapse, toilet paper is not the good that need be given the highest priority. However, observing that other people stockpile creates a social pressure: “it is not possible that so many people behave so irrationally: there must be a good reason for them to do so”.
Decision science suggests that stockpiling can be rational from an individual perspective. But in practice, people do not stockpile optimally because of individual irrationality and group pressure.
Overall, decision science focusing on both individual decision making and game theory suggests that stockpiling can be rational from an individual perspective. However, in practice, there are many reasons to think that people do not stockpile optimally because they violate the rules of individual decision rationality or are irrationally influenced by the behavior of others.
(1)Abdellaoui, M., Kemel, E., Panin, A., & Vieider, F. M. (2019). Measuring time and risk preferences in an integrated framework. Games and Economic Behavior, 115, 459-469.
(2)Abdellaoui, M., Bleichrodt, H., Kemel, E., & L’Haridon, O. (2017). Measuring beliefs under ambiguity. Operations Research, in press.
Loewenstein, G., & Prelec, D. (1992). Anomalies in intertemporal choice: Evidence and an interpretation. The Quarterly Journal of Economics, 107(2), 573-597.
Machina, M. J. (1987). Decision-making in the presence of risk. Science, 236(4801), 537-543.
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. science, 185(4157), 1124-1131.
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