Abstract
An important strand in the economic literature focuses on how to provide the right incentives for households to recycle their waste. A growing number of studies, inspired by psychology, seek to explain waste sorting and proenvironmental behavior, and highlight the importance of social approval and the peer effect. The present theoretical work explores these issues. We propose a model that considers heterogeneous households that choose to recycle, based on three main household characteristics: their environmental preferences, the opportunity costs of their tax expenditures, and their reputations. The model is original in depicting the interactions among households, which enable them to form beliefs about social recycling norms, allowing them to assess their reputation. These interactions are explored through Agentbased simulations. We highlight how individual recycling decisions depend on these interactions and how the effectiveness of public policies related to recycling are affected by a crowdingout effect. The model simulations consider three complementary policies: provision of incentives to recycle through taxation; provision of information on the importance of selective sorting; and an ‘individualized’ approach that takes the form of a ‘nudge’ using social comparison. Interestingly, the results regarding these policies emerging from households interactions at the aggregate level cannot be fully predicted from “isolated” individual recycling decisions.
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Notes
Households’ behaviors impact on the environment and the importance of household choices are also stressed in OECD (2014).
For instance, in the study by Brekke et al. (2003), individuals are able to state their ideal prosocial behavior.
ABM is particularly appropriate to study complexity, heterogeneity, evolving norms (or institutional environment), etc. In the evolutionary literature, ABM allows new perspectives on financial (Leal et al. 2016; Veryzhenko et al. 2017) and macroeconomic issues (Dosi et al. 2015; Haldane and Turrell 2018).
See the discussion in the introduction.
In the model simulation presented in Section 4, we suppose that \({v_{i}^{a}}\), \({v_{i}^{t}}\), and c_{i} are normally distributed.
As in Fullerton and Kinnaman (1995), for example.
This functional form implies that the environmental value is increasing at a decreasing rate in the information η and reaches its maximum level “1” when η = 1.
This allows us to explore the idea of Thaler and Sunstein (2008) according to which “If choice architects want to shift behavior and to do so with a nudge, they might simply inform people about what other people are doing”.
Schultz (1999) shows that this type of nudge resulted in an increase in the volume of recycled waste that persisted over time, even after the experiment stopped.
This nudge might deliver biased information since only the best household recycling rates observed are communicated (the top 50% of the observed recycling rates). This nudge might cause the household to overestimate the mean of others’ recycling rates. Therefore, the risk of failing to comply with “consumer sovereignty”, the nudges’ major drawback, is a serious issue for this kind of nudge.
As in Bénabou and Tirole (2006).
This duration ensures that the socialization process and the recycling decisions are stable.
In the model simulation, a tolerance threshold of ± 3% is introduced.
The values used for the means and standard deviations of each parameter are presented in Table (2) in Appendix B.
Simulation results for the configuration corresponding to \(\bar {v}^{t}(=0.3)<\bar {v}^{a}(=0.7)\) are presented in online supplementary materials.
This result is confirmed in the other situation where \(\bar {v}^{t}<\bar {v}^{a}\) depicted in figures provided in online supplementary materials.
These results are confirmed in the other configuration (where \(\bar {v}^{a} >\bar {v}^{t}\)) in online supplementary materials
We have \(\partial r(a_{i}^{*}(t))/\partial t = (\gamma _{i} x_{i} (1 + {v_{i}^{t}}))/(c_{i} + \gamma _{i} x_{i})\).
75% may appear a quite high threshold; however, this value ensures that the nudge reinforces tax and information delivery policies, reactivating an almost stable socialization process.
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Appendices
Appendix A: Proofs of the Propositions and Corollary
1.1 Proof of Proposition 1
We consider the case where the condition \(c_{i}>\frac {1}{2}\left ({{v_{i}^{a}}}^{\left (1\eta \right )^{2}} + t\left ({v_{i}^{t}}+1\right ) + 2 x_{i} \gamma _{i} \left (\bar {a}_{i}1\right )\right )\), ensuring that both \(a_{i}^{*}\) and \(\hat {a}_{i}\) are less than 1, is satisfied. Social influence is defined by \(a_{i}^{*}\hat {a}_{i}\) with \(\hat {a}_{i}\) and \(a_{i}^{*}\) defined respectively in Eqs. 6 and 10. Developing \(a_{i}^{*}\hat {a}_{i}>0\) gives \(\frac {{{v_{i}^{a}}}^{(1\eta )^{2}} + t\left (1+{v_{i}^{t}}\right )}{2c_{i}}<\bar {a}_{i}\) (or \(\hat {a}_{i}<\bar {a}_{i}\)).
1.2 Proof of Proposition 2
With \(\hat {a}_{i}\) and \(a_{i}^{*}\) defined in Eqs. 6 and 10, \(\partial \left (a_{i}^{*}\hat {a}_{i}\right )/\partial t = \frac {x_{i}\gamma _{i}(1+{v_{i}^{t}})}{2c_{i}(c_{i}+x_{i}\gamma _{i})}\). This derivative is always negative. The same holds true for \(\partial \left (a_{i}^{*}\hat {a}_{i}\right )/\partial \eta \).
1.3 Proof of Proposition 3

1.
The impact of x_{i} on \(a_{i}^{*}\) (and on social influence) is given by \(\partial a_{i}^{*}/\partial x_{i} = \gamma _{i}\frac {2c_{i}\bar {a}_{i}{{v_{i}^{a}}}^{(1\eta )^{2}}t(1+{v_{i}^{t}})}{2(c_{i}+x_{i}\gamma _{i})^{2}}\). It is positive when \(2c_{i}\bar {a}_{i}{v_{i}^{a}}t(1+{v_{i}^{t}})>0\), or when \(\bar {a}_{i}>\hat {a}_{i}\). It is negative otherwise.

2.
The impact of the tax on social influence is given by \(\partial (a_{i}^{*}\hat {a}_{i})/\partial t = \frac {x_{i}\gamma _{i}(1+{v_{i}^{t}})}{2c_{i}(c_{i}+x_{i}\gamma _{i}}\). The effect of x_{i} on it is given by \(\partial ^{2} (a_{i}^{*}\hat {a}_{i})/\partial t \partial x = \frac {2\gamma _{i}(1+{v_{i}^{t}})}{(2c_{i}+2x_{i} \gamma _{i})^{2}}\). This effect is always negative. As \(\partial ^{3} (a_{i}^{*}\hat {a}_{i})/\partial t \partial x^{2} = \frac {{\gamma _{i}}^{2}(1+{v_{i}^{t}})}{(c_{i}+x_{i} \gamma _{i})^{3}}\), this effect is decreasing in absolute value.

3.
Calculated in \(a_{i}^{*}\), \(\partial r(a_{i}^{*}(t))/\partial t\) is equal to \(\frac {x_{i}\gamma _{i}\left (1+{v_{i}^{t}}\right )}{c_{i}+x_{i}\gamma _{i}}\). The impacts of x_{i} on \(\partial r(a_{i}^{*}(t))/\partial t\) is measured by \(\partial ^{2} r(a_{i}^{*}(t))/\partial t \partial x= \frac {c_{i}\gamma _{i}\left (1+{v_{i}^{t}}\right )}{\left (c_{i}+x_{i}\gamma _{i}\right )^{2}}\), and is negative. It is easy to check that \(\partial ^{3} r(a_{i}^{*}(t))/\partial t \partial x^{2}= \frac {2c_{i}{\gamma _{i}^{2}}\left (1+{v_{i}^{t}}\right )}{\left (c_{i}+x_{i}\gamma _{i}\right )^{3}}\) is positive. So that the effect of x_{i} on the absolute value of the crowdingout effect is always positive at a decreasing rate.
Appendix B: Parameter values used in the model simulations
Appendix C: Robustness check
In the two configurations presented in this article, the mean values \(\bar {v}^{a}\), \(\bar {v}^{t}\), and \(\bar {\gamma }\) used in the normal distributions of these individual parameters are fixed at, respectively, 0.7, 0.3, 0.5, and 0.3, 0.7, 0.5. However, we also tested the separate impact of a variation in the individual parameters (keeping the other parameters fixed) on the results (optimal decision to recycle, social influence and crowdingout effect). We performed extensive Monte Carlo simulations to exclude simulation variability. The results presented below refer to averages over several replications. All the simulation results refer to 1000 independent Monte Carlo simulations, each involving 300 time steps (households’ moves in the model). The simulations are run for four different cases. The first case considers a ‘low’ policy mix (t = 2 and η = 0.2), the second a ‘medium’ policy mix (t = 4 and η = 0.4), and the last two cases, a ‘high’ policy mix (t = 6 and η = 0.6) and a ‘very high’ policy mix (t = 8 and η = 0.8).
Regarding the impact of \(\bar {v}^{a}\) and \(\bar {v}^{t}\) on the optimal recycling decision, Figs. 9 and 10 indicate, as expected, an increasing relation between the intrinsic value of the population mean and the optimal recycling decision, regardless of the policy level. The confidence intervals observed for the different values of the optimal recycling decisions show that the variations in \(\bar {v}^{a}\) do not significantly affect the optimal recycling (since the confidence intervals overlap). By contrast, the variation in \(\bar {v}^{t}\) significantly affects the optimal recycling decision. Similarly, the policy mix level has a significant effect on the optimal recycling decisions, in the expected direction.
The confidence intervals observed in Figs. 11 and 12 depict the same results for social influence. In fact, the different values of social influence show that the variations in \(\bar {v^{a}}\) and \(\bar {v^{t}}\) have no significant effect on social influence. However, it appears that the different policy mix levels have a significant effect on social influence.
Figures 13 and 14 refer to the crowdingout effect. The different values for the crowdingout effect show that the variation in \(\bar {v^{a}}\) (see Fig. 13) has no effect on the crowdingout effect. Similarly, the policy mix level has no effect on the crowdingout effect. Figure 14 indicates, as expected a decreasing relation between the extrinsic value of the population mean, and the crowdingout effect, regardless of the policy level. The confidence intervals observed for the different values of the crowdingout effect show that the variations in \(\bar {v}^{t}\) do not significantly affect the crowdingout effect.
The impacts of \(\bar {\gamma }\) on the optimal recycling decision and the social influence and crowdingout effect are presented in Figs. (15, 16, 17, 18, 19). Note that the policy level has a significant effect on the optimal recycling decision. However, the variations in \(\bar {\gamma }\) do not affect the optimal recycling decision significantly (Fig. 15). We observe that both the policy level and the variations in \(\bar {\gamma }\) have a significant effect on social influence (Figure 17). In relation to the crowdingout effect (Fig. 19), the variations in \(\bar {\gamma }\) have a significant effect. By contrast, variations in the policy level have no significant effect on the crowdingout effect.
In relation to the cost parameter c, we observe that it has no significant impact on the optimal recycling decision, social influence and the crowdingout effect (Figs. 16, 18, 20). We observe a relation only between policy level and crowdingout effect.
Finally, we observe that the variations in visibility do not significantly affect optimal recycling (Figs. 21 and 22). These results are observed without a nudge (Fig. 21) and with the BV nudge (Fig. 22), which latter increases the number of contacts to four. In the case of social influence (Figs. 23 and 24), the low variations in visibility (between 0 and 2) have a significant effect on social influence. For both optimal recycling and social influence, the policy level differences significantly affect the impact of visibility. In relation to the crowdingout effect (Figs. 25 and 26), the policy level variations do not have a significant effect on the impact of visibility (the curves cannot be distinguished). With the exception of ow values (between 0 and 2), the variations in visibility do not significantly affect the crowdingout.
Appendix D: The evolution of the recycling rate over time of the simulation
Appendix E: Mean of beliefs on the recycling norm vs. the mean of optimal recycling decisions under the BV nudge
Appendix F: Micro level results vs. aggregate level results
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Charlier, C., Kirakozian, A. Public policies for household recycling when reputation matters. J Evol Econ 30, 523–557 (2020). https://doi.org/10.1007/s00191019006485
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DOI: https://doi.org/10.1007/s00191019006485
Keywords
 Household recycling
 Waste
 Environmental regulation
 Behavioral economics
 ABM
 Social interaction
JEL Classification
 D100
 D030
 Q530
 Q580