new publication: Threshold Preferences and the Environment

wordleI am happy to announce that my article entitled “Threshold Preferences and the Environment”, co-authored with Benteng Zou from the University of Luxembourg, has been accepted for publication in the Journal of Mathematical Economics. While the journal will publish a slightly shortened version of the article (without section 2), you can find the full version HERE. What is the paper about?

In this article we study the implication of thresholds in preferences. To model this we extend the basic model of John and Pecchenino (1994) by allowing the current level of environmental quality to have a discrete impact on how an agent trades off future consumption and environmental quality. Thus, we endogenize the semi-elasticity of utility based on a step function. We find that for low (high) thresholds, environmental quality converges to a low (high) steady state. For intermediate levels it converges to a stable p-cycle, with environmental quality being asymptotically bounded below and above by the low and high steady state. As policy implications we study shifts in the threshold. Costless shifts of the threshold are always worthwhile. If it is costly to change the threshold, then it is worthwhile to change the threshold if the threshold originally was sufficiently low. Lump-sum taxes lead to a development trap and a proportional income tax should be preferred.

The main question that drove us to write this paper was as follows: When looking at public opinion, one sees that it tends to be sticky and requires enough pressing issues for it to change. However, if sufficiently pressing problems are identied, then preferences undertake radical changes. This has been observed to be especially true for concerns directed to the environment. Studies in political science describe this as the so-called issue-attention cycle:

Downs (1972) describes the “issue-attention cycle”, which proceeds in five stages. In stage 1, which he calls “the pre-problem stage”, some undesirable social condition exists without being fully incorporated into the public opinion. In stage 2, dubbed the stage of “alarmed discovery and euphoric enthusiasm”, a drastic worsening of the social condition leads to an euphoric public that wants to take care of the problem. His third stage, the
“realizing the cost of signicant progress” stage, is then followed by the stage of “gradual decline of intense public interest” followed by a so-called “post-problem” stage. In this fifth stage, potentially new institutions or laws that were originally designed to treat the social condition continue to exist and may still have some impact. In this paper we mostly focus on stage 1 and 2 of the issue-attention cycle. In the article interested readers will also find more motivations, coming from cultural economics, from ecological economics, and also from the implementation of regulations and standards.

However, our current macroeconomic economic models have difficulties in re-creating this radical changes in preferences. Nevertheless, it seems to be clear that these radical changes should not be ignored and may have significant influences in how we undertake policies and in how public opinion may support policy. We view our contribution here along two ways – one, we find an interesting mathematical equilibrium that we study which comes out of this radical preference change; two, we obtain some relevant policy results.

The problem obviously was in how one could model this mathematically. I believe we found a simple way that allows to extend this model in many ways. The solution of the model, however, gave rise to an interesting equilibrium that we did not come across yet: We find that for low (high) thresholds, environmental quality converges to a low (high) steady state. For intermediate levels it converges to a stable p-cycle, with environmental quality being asymptotically bounded below and above by the low and high steady state. This was a somewhat fun result that made us consider a more mathematically-oriented economics journal as a publication outlet.

In terms of policy results, we suggest to take the following away. We discuss under which circumstances policy interventions are useful despite a policy maker being faced with this endogeneity in preferences. The policy intervention that we look at is a shift in the threshold. Our criteria for a potential policy intervention is that, if each individual in every potential steady state of the world would be better off by the policy intervention, then the policy should be undertaken. Our results are that, if it is costless to shift the threshold, then it is obviously always worthwhile to do so. This has implications e.g. for the setting of environmental standards. In case a standard needs to be imposed, our results indicate that it is always better to set the standard at a higher level than a lower one. This, obviously, rests on the assumption that it is costless to set the standard. In contrast, if it is costly to change the threshold,  e.g. in case educational measures need to be undertaken, then it is worthwhile to change the threshold if the threshold originally was very low. In that case, it is certainly important to know more precisely about the costs and benefits involved in changing the threshold, and the policy would be case-specific. For example, we have shown that in the case of a lump-sum tax, a policy maker could essentially create a development trap. The results in this article suggest that only richer societies should consider applying a lump-sum tax, since otherwise they may be caught in a development trap. Our results thus indicate that a proportional income tax may generally be a safer means of policy intervention than a lump-sum tax.


Benteng Zou is an Associate Professor in the Faculty of Law, Economics and Finance at  the University of Luxembourg since Feb. 2007. He holds two Ph.Ds: one in Mathematics from Peking University, China, 1999, and one in Economics from the Catholic University of Louvain, Belgium, 2005. Benteng’s current research interests lie in the broad area of theory and application of Optimal Control Theory and Dynamics Games with focus on foreign direct investment and technology spillover, transboundary pollution and strategic choices for different players, dynamic fiscal competition and international migration study. His researches have been presented in international conferences in economics and published in scientific reviews  such as,  European Journal of Operational Research, Journal of Environmental Economics and Management, Journal of Economic Dynamics and Control, Ecological Economics, Economics Letters, Macroeconomics Dynamics.

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