Conceptual framework

By considering the previously described scenario, we adapt the approach developed by Börner et al. (2015, 2014) to simulate the effect of a forest conservation policy mix on landholders’ deforestation decisions. To do so, we develop a spatially explicit model that simulates the landholders’ decision to deforest—within spatial units of 4 × 4 km—based on an assumed rational choice of weighing the resulting agricultural rents against the likelihood of being fined when deforesting and/or compensated, if deforestation is reduced.

The policy mix is conceived as a mixture of C&C and incentive-based forest conservation instruments, namely, fines and PES, respectively. Our approach relies on (1) economically motivated decisions, (2) spatially explicit information on costs and benefits, and (3) imperfect compliance (Sandmo, 2002). We simplify the complexities previously explained by, first, assuming that only one enforcement authority conducts field-based operations against illegal deforestation. Second, this authority is also responsible for implementing PES. Third, any effect of implementing this policy approach is additional to any previous effect of law enforcement and PES initiatives.

The landholder’s decision to deforest is conditioned on the difference between agricultural rents and expected sanctions, subject to an enforcement probability. We introduce PES, which could further reduce the incentive to deforest but, as opposed to a fine, would increase the landholders’ income as defined in:

𝑑_1,0=∶ {0, 𝑓𝑜𝑟 𝑟 − 𝑝_𝑒𝑛𝑓(𝐹 + 𝑃𝐸𝑆) ≤ 0

1, 𝑓𝑜𝑟 𝑟 − 𝑝_𝑒𝑛𝑓(𝐹 + 𝑃𝐸𝑆) > 0 (Eq. 4. 1) where illegal deforestation⁹ 𝑑 is modeled as a binary choice and equals zero if 𝑟, the NPV of the 10-yr expected agricultural rents after deforesting (10% discount rate), is smaller than the expected fine (𝐹) or an equivalent sanction cost, and a payment (𝑃𝐸𝑆) conceived as a per-ha disincentive and incentive, respectively. Alternatively, if 𝑟 is greater, deforestation equals one, and an annual mean deforestation is assigned to a gridcell of 4 × 4 km. This deforestation represents a baseline scenario prior to the policy mix implementation.

Enforcement is imperfect because of a logistical budget constraint, a common situation in LMIC (Robinson et al., 2010). Thus, the enforcement probability (𝑝_𝑒𝑛𝑓) in our model varies between zero and one. Depending on this probability, an illegal deforester expects to be detected, fined, and lose the payment. Hence, the enforcement authority cannot go everywhere to deter deforestation, which, we assume, is achieved by enforcing the law after the deforestation has occurred. Offenders and potential offenders are deterred from continuing the deforestation by demonstrating that deforestation is sanctioned. In that sense, we assume that the enforcement authority’s strategy seeks to maximize deterrence by maximizing the deforested area inspected at the lowest cost possible. Hence, the authority prioritizes the locations with historically larger total deforested areas and fewer deforested patches to visit

9 PES will not only be conditional on complying with the law but could also include other conditions, such as, for example, taking children to the health post to comply with immunization schedules. We assume that the opportunity costs of these other conditions for an entire year are constant across space and are negligible.

50

that could be reached at the lowest logistical costs. Thus, cells with such characteristics present greater enforcement probability.

The CE of the policy mix is measured in terms of reduced deforestation (𝐷_𝑖− 𝐷_𝑖^𝑅), where 𝐷_𝑖 and 𝐷_𝑖^𝑅 represent, respectively, the baseline deforestation and the deforestation after the policy mix implementation, as determined in Eq.4.1, and total implementation costs:

𝐶𝐸 = ∑^𝐼_𝑖=1(𝐷𝑖− 𝐷_𝑖^𝑅)

𝐵 + ∑^𝐼_𝑖=1𝑃𝐸𝑆(𝐷_𝑖− 𝐷_𝑖^𝑅𝑝_{𝑒𝑛𝑓,𝑖}) + ∑^𝐽_𝑗=1𝑃_𝑗∗ 𝑐 ∗ 𝑝_{𝑒𝑛𝑓,𝑖} (Eq. 4. 2)

The denominator in Eq.4.2 is the sum of the enforcement authority’s logistical budget to cover field enforcement operations (B), the sum of PES to compliers and to undetected non-compliers, and the sum of the administrative costs (𝑐) incurred to determine the illegality and liability of deforestation cases. 𝑃_𝑗represents the number of deforested patches (i.e., cases) within each grid cell for which deforestation equals one (Eq.4.1) after the policy mix is implemented and 𝑝_{𝑒𝑛𝑓,𝑖}> 0. Thus, if deforestation is avoided (𝐷_𝑖^𝑅= 0), the landholder receives the full amount of PES (i.e., 𝑃𝐸𝑆 ∗ 𝐷_𝑖). Our model allows some deforestation to be compensated for as a function of the enforcement probability. Thus, if deforestation is not avoided (𝐷_𝑖^𝑅= 𝐷_𝑖), compensation could be greater than zero such that the compensation is larger when 𝑝_{𝑒𝑛𝑓,𝑖}tends to zero, and the compensation is smaller when it tends to one. The denominator in Eq.4.2 could additionally include the value of all of the fines that the enforcement authority could collect from detected offenders (−𝐷_𝑖^𝑅𝑝_{𝑒𝑛𝑓,𝑖}𝐹), which reduces the total implementation costs.

The welfare effect (𝑊) is defined by the aggregated income changes in all cells as determined by:

𝑊 = ∑ 𝑃𝐸𝑆(𝐷_𝑖− 𝐷_𝑖^𝑅𝑝_{𝑒𝑛𝑓,𝑖})

𝐼

𝑖=1

− (𝐷_𝑖− 𝐷_𝑖^𝑅)𝑟_𝑖− 𝐷_𝑖^𝑅𝑝_{𝑒𝑛𝑓,𝑖}𝐹 (Eq. 4. 3)

The first term in Eq.4.3 represents the compliers’ and undetected non-compliers’ income from PES, the second term represents the opportunity costs for those who reduced deforestation, and the third represents the value of the fines paid by detected non-compliers.

Using our model, we can assess how changes in the logistical budget, the fine, and PES simultaneously affect the policy’s CE and the landholders’ aggregated income. Thus, based on the model structure previously described and on the spatial dynamics of deforestation in the Peruvian Amazon (Figure 4.1), the following predictions can be made. First, increasing the logistical budget leads to (1) increasing the reduction in deforestation but at a diminishing rate, given that most deforestation and the largest deforested patches are concentrated around major cities and main roads (Figure 4.1); (2) for the same reason, increasing total administrative costs and total imposed fines at a diminishing rate; (3) decreasing total PES payments, given that the number of non-compliers receiving PES will decrease as the logistical budget increases; (4) consequently, the CE will increase up to the point at which the marginal costs of enforcement become too large relative to the marginal effectiveness gains.

51

The CE will then decrease as compliance increases and marginal deforestation reductions become smaller; and (5) aggregated income losses will increase because of the fewer PES payments to non-compliers, higher total opportunity costs, and more fines being imposed.

Second, increasing the fine level, at constant enforcement probabilities and PES levels, will lead to (1) more deforestation being avoided, given that more landholders face higher fines and decide not to deforest; (2) decreasing administrative costs and fines because less deforestation exists to be sanctioned (i.e., fewer field operations are necessary); (3) thus, increasing the CE; and (4) increasing aggregated income loses because of increasing opportunity costs.¹⁰

Third, increasing the PES level at constant enforcement probabilities and fine levels leads to (1) more reduced deforestation because the incentive to avoid deforestation will increasingly compensate for the opportunity costs; (2) decreasing administrative costs (for the same reason as above), (3) increasing total PES payments; (3) hence, increasing CE up to the point at which too large payments (i.e., large overcompensation of opportunity costs) outweigh the gains in effectiveness—and then the CE decreases; and (4) increasing aggregated income.

Finally, at constant levels of avoided deforestation and based on the previous predictions, we expect a trade-off between CE and welfare, with gains in CE and losses in welfare as the fine level is increased and vice-versa when the PES level is increased. In other words, the CE of a policy mix that relies more on fines will be more cost effective than one based more on PES.

However, in contrast, the former policy mix will generate larger aggregated income losses than the latter.

10 We expect that the effect of higher total opportunity costs is stronger than that of higher imposed fines on the aggregated income change attributable to the prevailing low opportunity costs in the study area (Börner et al., 2016b). In other words, higher fine levels lead to lower total imposed fines but higher total opportunity costs.

52

Figure 4.1 Locations from which enforcement field trips depart and historical deforestation in Peruvian Amazon.

53