The consumption–investment decision of a prospect theory household: A two-period model with an endogenous second period reference level

Hlouskova, J., Fortin, I., & Tsigaris, P. (2019). The consumption–investment decision of a prospect theory household: A two-period model with an endogenous second period reference level. Journal of Mathematical Economics 85 93-108. 10.1016/j.jmateco.2019.10.003.

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Abstract

In this paper we analyze the two-period consumption–investment decision of a household with prospect theory preferences and an endogenous second period reference level which captures habit persistence in consumption and in the current consumption reference level. In particular, we examine three types of household depending on how the household’s current consumption reference level relates to a given threshold which is equal to the average discounted endowment income. The first type of household has a relatively low reference level (less ambitious household) and can avoid relative consumption losses in both periods. The second type of household (balanced household) always consumes exactly its reference levels. The third type of household has a relatively high reference level (more ambitious household) and cannot avoid to incur relative consumption losses, either now or in the future. Note that these households may act very differently from one another and thus there will often be a diversity of behavior. For all three types we examine how the household reacts to changes in: income (e.g., income fall caused by recession or taxation of endowment income), persistence to consumption, the first period reference level and the degree of loss aversion. Among others we find that the household increases its exposure to risky assets in good economic times if it is less ambitious and in bad economic times if it is more ambitious. We also find that in some cases more income can lead to less happiness. In addition, the less ambitious household and the more ambitious household with a higher time preference will be less happy with a rising persistence in consumption while the more ambitious household with a lower time preference will be happier if it sticks more to its consumption habits. Finally, the household’s happiness decreases with an increasing consumption reference level and thus not comparing at all will lead to the highest level of happiness. In addition, the sensitivity of happiness with respect to the reference level gets larger the closer the household moves to the threshold level, and it is smaller for less ambitious households than for more ambitious households due to loss aversion.

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