Public policies for household recycling when reputation matters

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 pro-environmental 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 Agent-based 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 crowding-out 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.

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 crowding-out effect is always positive at a decreasing rate.

Appendix B: Parameter values used in the model simulations

Table 2 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 crowding-out 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.

Fig. 9

The impact of $\bar {v}^a$’s variations on $a_{i}^{*}$

Fig. 10

The impact of $\bar {v}^t$’s variations on $a_{i}^{*}$

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.

Fig. 11

The impact of $\bar {v}^a$’s variations on $a_{i}^{*}-\hat {a}_i$

Fig. 12

The impact of $\bar {v}^t$’s variations on $a_{i}^{*}-\hat {a}_i$

Figures 13 and 14 refer to the crowding-out effect. The different values for the crowding-out effect show that the variation in $\bar {v^{a}}$ (see Fig. 13) has no effect on the crowding-out effect. Similarly, the policy mix level has no effect on the crowding-out effect. Figure 14 indicates, as expected a decreasing relation between the extrinsic value of the population mean, and the crowding-out effect, regardless of the policy level. The confidence intervals observed for the different values of the crowding-out effect show that the variations in $\bar {v}^{t}$ do not significantly affect the crowding-out effect.

Fig. 13

The impact of $\bar {v}^a$’s variations on $\partial r(a_{i}^{*}(t))/\partial t$

Fig. 14

The impact of $\bar {v}^t$’s variations on $\partial r(a_{i}^{*}(t))/\partial t$

The impacts of $\bar {\gamma }$ on the optimal recycling decision and the social influence and crowding-out 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 crowding-out 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 crowding-out effect.

Fig. 15

The impact of $\bar {\gamma }$’s variations on $a_{i}^{*}$

Fig. 16

The impact of $\bar {C}$’ variations on a_i ∗

Fig. 17

The impact of $\bar {\gamma }$’s variations on $a_{i}^{*}-\hat {a}_i$

Fig. 18

The impact of $\bar {C}$’ variations on $a_{i}^{*}-\hat {a}_i$

Fig. 19

The impact of $\bar {\gamma }$’s variations on $\partial r(a_{i}^{*}(t))/\partial t$

In relation to the cost parameter c, we observe that it has no significant impact on the optimal recycling decision, social influence and the crowding-out effect (Figs. 16, 18, 20). We observe a relation only between policy level and crowding-out effect.

Fig. 20

The impact of $\bar {C}$’ variations on $\partial r(a_{i}^{*}(t))/\partial t$

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 crowding-out 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 crowding-out.

Fig. 21

The impact of x_i variations on $a_{i}^{*}$ without nudge

Fig. 22

The impact of x_i variations on $a_{i}^{*}$ with the BV nudge

Fig. 23

The impact of x_i variations on $a_{i}^{*}-\hat {a}_i$ without nudge

Fig. 24

The impact of x_i variations on $a_{i}^{*}-\hat {a}_i$ with the BV nudge

Fig. 25

The impact of x_i variations on $\partial r(a_{i}^{*}(t))/\partial t$ without nudge

Fig. 26

The impact of x_i variations on $\partial r(a_{i}^{*}(t))/\partial t$ with the BV nudge

Appendix D: The evolution of the recycling rate over time of the simulation

Fig. 27

Optimal recycling decision without and with nudge over time

Appendix E: Mean of beliefs on the recycling norm vs. the mean of optimal recycling decisions under the BV nudge

Fig. 28

Evolutions of the mean of beliefs on the norm and of the mean of optimal recycling decisions under the BV nudge

Appendix F: Micro level results vs. aggregate level results

Table 3