Econometric Proofs.pdf

Equations (14) and (15) yield pUW = wχRW, indicating households choose optimal recycling when marginal recycling cost equals marginal unsorted waste generation cost. The utility-maximizing recycling solution is RW∗ = pUW / wχ. Differentiating this equation with respect to pUW gives δRW∗ / δpUW = 1 / wχ > 0. The utility-maximizing unsorted waste solution is obtained by substituting RW∗ into equation (16), resulting in equation (19). Differentiating (19) with respect to pUW yields δUW∗ / δpUW = −1 / wχ − UW∗ / αUc / λ < 0.

The econometric model considers the partially linear waste outcome model (8), and taking the conditional expectation with respect to Xi on both sides yields equation (21). Substituting Yi on the right-hand side gives equation (22), which simplifies to equation (9): Yi − E[Yi|Xi] = (Pi − E[Pi|Xi])δ(Xi) + ϵi(Pi).

Descriptive statistics are presented in Table 6, including variables such as PAYT price, recycling waste, unsorted waste, total waste, and various demographic and socioeconomic characteristics.

The overlap assumption is visualized in Figure 9, showing the common support condition for treated and never-treated groups. Additional results include testing for effect heterogeneity using Levene's tests and residual-on-residual regression, which reveal statistically significant differences in APE between subgroups for all outcomes and policy years (Table 7). CAPE heterogeneity across price levels is also examined, with fitted lower- and upper-bound CAPE estimates at each price level shown in Figure 10.