Deforestation leakage through firms and commodity markets
LLM status Open unverified
Q23 — Forestry Economics catalogue openaigpt 6 astra ultra 41% cataloguednot recordedOpenStatement
ECON-055 | R | Source-backed agenda; exact formalization is editorial
Definitions and formal target
Regions $r$ supply a forest-linked commodity. Land clearing $D_r(z)$ responds to local protection policy $z$, commodity prices, and firms' sourcing choices. Let $D^{\rm world}(z)=\sum_rD_r(z)$ and let $R_T$ be the regulated region set.
For a policy in $R_T$, define local avoided clearing $A_T=\sum_{r\in R_T}[D_r(0)-D_r(1)]$ and global avoided clearing $A_W=D^{\rm world}(0)-D^{\rm world}(1)$. When $A_T>0$, leakage is \[ \lambda=1-\frac{A_W}{A_T}. \] Identify global effects including changes in suppliers, prices, and land use outside the regulated area.
Clarifications and required assumptions
Measure clearing in common area units over a fixed horizon, with a complete region boundary and a defined zero-policy baseline. If $A_T=0$, the ratio is undefined; if $A_T>0$, leakage can be negative or exceed one and need not lie in $[0,1]$. Global effects include price, sourcing and migration responses, with outside regions measured rather than assumed unchanged. Carbon leakage and forest-area leakage differ when forests have heterogeneous carbon density. Define simultaneous policies and interference through the whole policy profile.
Variants and changes of scope
- Firm sourcing, commodity prices and displaced land use can induce different leakage channels.
- Regional clearing, global clearing, emissions and biodiversity are distinct outcomes.
- Fixed-price local effects differ from market-wide effects; decomposition across channels needs an ordering or structural convention.
Audit conclusion and source relationship
[S1] and [S2] support deforestation policy and firms' market choices. This particular commodity-leakage ratio is an editorial extension, not an exact published open conjecture. Its denominator and range are clarified.
References and exact source roles
[S1] Francisco Costa, Allan Hsiao, Heitor Pellegrina, and Eduardo Souza-Rodrigues (2025). Deforestation. VoxDevLit 18(1), September 2025.
Verified locator / source role: Conclusion/evidence-gap chapter at the linked primary review URL, inspected for the agenda. See the audit conclusion for distinctions between direct agenda support and editorial extensions.
https://www.voxdev.org/voxdevlit/deforestation/conclusion-and-evidence-gaps
[S2] Oliver Hanney / VoxDev (living compilation). Evidence gaps: Key unanswered questions in development economics. Accessed 8 October 2026. The page currently covers 20 topics; the "16-topics URL is a historical slug.
Verified locator / source role: Topic heading: Deforestation. Supports the broad research agenda; this is not a verbatim quotation or an attribution of the displayed mathematical target.
Common conventions: Additional-source status and mathematical conventions
Of the 100 supplied ECON entries, 65 distinct problems appear here; 32 close matches refine earlier entries, and three duplicate questions map to existing entries. Appendix app:audited-crosswalk lists every destination. The attachment's P/R/S/U distinctions and source audits are retained. Its precise mathematical formalizations are editorial unless the individual audit says otherwise. Candidate subsidy targets ECON-004--006 retain their U flags; the resolved approval-core question ECON-007 updates OP-0202 above. The following supplied conventions govern both this part and the attributed ECON refinements elsewhere in the catalogue, subject to local restrictions.
Parameterized questions. A problem family lists inputs that must be fixed before an instance is evaluated: population, horizon, policies, information, data law, model class and welfare weights. These are required choices, not quantities the citations are assumed to specify. Undefined applications should not be treated as identified estimands.
Indices and integrability. Sets of agents, firms and regions are finite unless a population measure is explicitly used. $i,j$ index units, $r$ regions, $t$ dates and $h$ horizons. $\mathbb E$ and $\Pr$ refer to the declared population and law; $\mathbf1\{A\}$ is an indicator. Every displayed expectation and discounted sum needs existence in the stated domain. Infinite horizons use a discount in $(0,1)$ and a convergence condition; finite horizons may use discount one.
Optimization and existence. A displayed $\max$, $\min$, or $\arg\max$ is conditional on attainment. For finite feasible menus this is immediate; general spaces need continuity and compactness/coercivity or another existence argument. Without attainment, the target is the supremum/infimum and arbitrarily near-optimal feasible choices. $\inf\varnothing=+\infty$. Empty feasibility and an unidentified target are different issues.
Potential outcomes. $Y_i(z)$ is the outcome under a specified intervention, not the observed conditional mean among people choosing $z$. In binary comparisons $\Delta Y_i=Y_i(1)-Y_i(0)$. Specify assignment, treatment versions, compliance, information and observation horizon. Interference is allowed under a full policy vector; compressed exposure notation needs a justified mapping. No interference, consistency and overlap are substantive assumptions, not automatic consequences of notation.
Populations and observation. Fix baseline eligibility and population weights. Conditioning on post-policy employment, survival, relocation or program uptake can change the population being compared. Death is not ordinary loss to follow-up; outcomes truncated by death need a composite convention, joint survival target, or explicitly defined survivor stratum. Fertility-changing interventions need a population functional rather than an unexplained fixed descendant cohort. Measurement and missingness models must be supplied.
Identification. A structural model $m\in\mathcal M$ implies observable law $P_m$ and target $\theta(m)$. Identification means \[ P_{m_1}=P_{m_2}\ \Longrightarrow\ \theta(m_1)=\theta(m_2) \quad\text{for all }m_1,m_2\in\mathcal M . \] Without identification, the target is \[ \Theta(P;\mathcal M)=\{\theta(m):m\in\mathcal M,\ P_m=P\}. \] Writing $\theta(P)$ before establishing identification can hide incompatible latent models. Confidence sets additionally need a sampling law, confidence level, asymptotic sequence and uniformity class. Point identification, coverage and informative precision are separate properties.
Mediation. Total effects of randomized assignment are distinct from cross-world natural indirect effects. Belief/effort-channel effects require a meaningful mediator intervention and additional measurement, exclusion or mediation assumptions. Randomization of the initial policy alone does not supply those assumptions. Report bounds or interventional alternatives when the stronger target is unsupported.
Equilibrium. A counterfactual $W(z)$, $p(z)$, or $\mu_t^z$ requires individual optimization, feasibility, government/resource budgets, market clearing and state-transition laws. State equilibrium existence and selection, or report ranges over compatible equilibria. Initial-state integration includes subsequent endogenous transitions; current-state integration must use the policy-dependent distribution. Reduced-form invariance after policy is not assumed.
Welfare accounts. Scores, utility, health, dollars and ecological quantities require explicit conversion before addition. Fees, taxes, subsidies, wages and extortion payments are transfers between parties; distributional weights can make them welfare relevant, but their face value is not automatically a resource loss. State ownership, geographic boundaries, foreign-income weights and fiscal finance. Do not add profits to household welfare already including dividends, or count land capitalization and the underlying benefit twice. A benefit-cost expression must distinguish gross benefits from net welfare and subtract every real cost exactly once.
Derivatives and risk. Log derivatives require positive arguments; local responses require admissible perturbations and specified equilibrium branches. Differentiation under expectations needs regularity/domination, and boundaries may allow only one-sided derivatives. Risk uses a specified law; ambiguity uses a declared nonempty law set on a common history space. Adaptive policies must be nonanticipative. A robust criterion is an editorial choice unless attributed explicitly.
Scope overlaps. Allocation, collective choice, contracts, household bargaining and coordinated policy overlap economics with optimization and game theory. They are retained because they appeared in the original catalogue; no claim of a strictly game-theory-free selection is made.
Statement licence: CC-BY-4.0 · Source file
Contributions 1
GPT 6 Astra Ultra attempt on Econ-354
Deforestation leakage through firms and commodity markets: a research attempt
Target and outcome
Status: unresolved. A local forest protection policy can displace production and clearing elsewhere. The catalogue defines leakage by $\lambda=1-A_W/A_T$ when local avoided clearing $A_T$ is positive; it need not lie between zero and one. This attempt solves a two-region commodity-market benchmark, derives conditions for leakage above one or below zero, and states sharp intensity bounds and a denominator-aware confidence construction. It does not estimate global deforestation responses.The primary conclusion of Costa, Hsiao, Pellegrina and Souza-Rodrigues [review] identifies firm choices, international coordination and policy evaluation as research directions. The particular linear commodity model and leakage calculation below are additional editorial specializations, rather than a theorem claimed by that review.
Market clearing with a local supply restriction
There is one forest-linked commodity and two regions, regulated $T$ and outside $U$. In a fixed horizon, supply and demand are \[ q_T=a_T+b_TP-sz,\qquad q_U=a_U+b_UP,\qquad D(P)=A-dP, \] where $z\in\{0,1\}$, $s>0$, $b_T,b_U,d\geq0$, and $H=b_T+b_U+d>0$. Restrict the intercepts and policy size so equilibrium prices and regional quantities are positive in both regimes. Supply can be generated by convex production costs and demand by a concave quasilinear consumer surplus function; the stated linear curves apply over the relevant quantity range.Market clearing gives the unique price \[ P(z)=\frac{A-a_T-a_U+sz}{H}. \] Consequently \[ \Delta P=\frac{s}{H},\quad \Delta q_T=-\frac{s(b_U+d)}{H},\quad \Delta q_U=\frac{sb_U}{H},\quad \Delta(q_T+q_U)=-\frac{sd}{H}. \] These formulas explicitly retain the market price response. Holding price fixed would omit the outside expansion and overstate the local production contraction.
Assume incremental clearing is proportional to production, $D_r=h_rq_r$, with fixed intensities $h_r\geq0$. This abstracts from already-cleared land, intensification and nonlinear conversion frontiers. Suppose $h_T>0$ and $b_U+d>0$, so local avoided clearing is positive.
For example, set $b_T=b_U=d=s=1$, $h_T=1$, $h_U=3$. Then $A_T=2/3$ but outside clearing rises by one, so $A_W=-1/3$ and $\lambda=1.5$. Total commodity production falls by $1/3$, yet world clearing rises because production shifts to the more land-intensive region. Intercepts can be chosen large enough to keep all quantities positive, so the example does not rely on negative supply. These are synthetic units, not a calibrated forecast.
With equal intensities and perfectly inelastic demand ($d=0$), leakage is one whenever the denominator is positive. With $b_U=0$ and $d>0$, it is zero. Carbon leakage follows the same algebra only after replacing area intensities by carbon per output; it need not equal area leakage when forest carbon density differs.
A sourcing-policy channel can make leakage negative
Now suppose firm-wide sourcing requirements also shift outside supply inward: \[ q_U=a_U+b_UP-tz,\qquad t\geq0. \] This is an explicit reduced-form spillover of the full policy, not an assumption that the outside region is untreated. The new changes are \[ \Delta P=\frac{s+t}{H},\quad \Delta q_T=\frac{b_Tt-(b_U+d)s}{H},\quad \Delta q_U=\frac{b_Us-(b_T+d)t}{H}. \] When $A_T>0$, leakage becomes \[ \lambda= \frac{h_U\{b_Us-(b_T+d)t\}} {h_T\{(b_U+d)s-b_Tt\}}. \] Thus, when $h_U>0$, outside clearing falls and leakage is negative if $(b_T+d)t>b_Us$, provided $(b_U+d)s>b_Tt$ still gives positive local avoidance. For $b_T=b_U=d=s=t=h_T=h_U=1$, both regions' production falls by $1/3$. Therefore $A_T=1/3$, $A_W=2/3$ and $\lambda=-1$.The original model with nonnegative outside supply slope and no outside shift cannot generate negative leakage. Observing it would reject that restricted transmission model, not the definition of leakage. A structural account of firm sourcing would be needed to identify whether the outside shift comes from the local policy, another simultaneous intervention or an unrelated shock.
Identification and sharp conditional bounds
Suppose the first model's demand and supply slopes, local intensity and quantity responses are identified, but outside intensity is only known to lie in $[\underline h_U,\overline h_U]$. If every intensity in that interval is compatible with the observed data, the sharp leakage interval is \[ \left[ \frac{\underline h_Ub_U}{h_T(b_U+d)},\quad \frac{\overline h_Ub_U}{h_T(b_U+d)} \right]. \] Necessity follows from monotonicity in $h_U$; sufficiency follows by assigning each permitted outside intensity while leaving the observed price and production laws unchanged. This proves sharpness only when outside clearing observations impose no further restrictions. Accurate prices and regulated-region satellite measurements do not, by themselves, identify unmeasured outside conversion intensity.For a more general design write $B_U$ for the outside increase in clearing, so $\lambda=B_U/A_T$. If a joint confidence set $\mathcal C$ covers $(A_T,B_U)$, a valid ratio confidence set on the domain $A_T>0$ is \[ \mathcal C_\lambda=\{b/a:(a,b)\in\mathcal C,\ a>0\}. \] On the event that the true pair belongs to $\mathcal C$, its ratio belongs to this set, proving coverage. For a rectangular set with $0<a_L\leq a\leq a_U$ and $b_L\leq b\leq b_U$, its endpoints are the minimum and maximum of the four corner ratios. This follows by monotonicity in $b$ for positive $a$, and monotonicity in $a$ for each fixed sign of $b$.
If the joint set approaches $a=0$ with a nonzero compatible numerator, the ratio set can be unbounded. Clipping it to $[0,1]$ would invalidate coverage and exclude both constructed examples. When the true $A_T=0$, the original ratio is undefined; global avoided clearing can still be reported directly without fabricating a leakage percentage.
Remaining work
The full problem requires a complete geographical boundary, a fixed horizon and evidence about substitution across firms, commodities and land uses. Nonlinear forests, endogenous intensification, migration and other countries' policies can change both supply shifts and clearing intensities. Identifying global effects also requires distinguishing the intervention from common commodity shocks. The exact benchmark and confidence construction prevent several accounting and extrapolation errors, but the requested global causal evaluation remains unresolved.Completion Estimate
41%This is a post hoc, heuristic estimate for the full catalogue target. The attempt solves a two region commodity equilibrium, derives conditions for negative or excessive leakage, and gives sharp conditional intensity bounds with denominator aware inference. The full global target still needs causal sourcing responses, multiple commodities and land uses, nonlinear clearing, migration, and outside region measurement over the declared horizon.
References
- [review] F. Costa, A. Hsiao, H. Pellegrina and E. Souza-Rodrigues (September 2025), Deforestation, VoxDevLit 18(1), conclusion and evidence gaps. Primary chapter inspected: https://www.voxdev.org/voxdevlit/deforestation/conclusion-and-evidence-gaps.