Youth recruitment into organized crime and expectations
LLM status Partially solved unverified
K42 — Illegal Behavior and the Enforcement of Law Economics catalogue openaigpt 6 astra ultra 45% cataloguednot recordedPartially solvedStatement
ECON-059 | R | Source-backed agenda; exact formalization is editorial
Definitions and formal target
Youth $i$ chooses between lawful activity and gang involvement using perceived income distributions, survival risks, social rewards, and future opportunities. Policy $z$ may change opportunities or beliefs. Let $G_i(z)$ indicate entry by a fixed age and $Y_i(z)$ future lawful earnings.
Identify the effects \[ \tau_G=\mathbb E[G_i(1)-G_i(0)],\qquad \tau_Y=\mathbb E[Y_i(1)-Y_i(0)], \] and the extent to which altered expectations rather than realized opportunity changes account for reduced entry. Network recruitment can produce spillovers between treated and untreated youth.
Clarifications and required assumptions
Fix the cohort before policy and a common age/time horizon. With recruitment spillovers, use potential outcomes under the whole policy vector or a justified exposure mapping. Define gang entry, lawful earnings, mortality and observation: death is a competing outcome, not ordinary missing data. Belief and opportunity channels require separate interventions or explicit mediation restrictions; surveys of expectations plus total policy effects do not identify their separate causal contributions. Earnings during nonemployment need a stated zero convention.
Variants and changes of scope
- Opportunity, information and peer-network interventions differ.
- Gang entry, duration, exit, survival and lawful earnings are distinct outcomes.
- Individual effects can coexist with recruitment displacement; aggregate network outcomes must be measured.
Audit conclusion and source relationship
[S1] and [S2] directly support youth recruitment, expectations and network mechanisms. The potential-outcome and channel formulation is editorial.
References and exact source roles
[S1] Santiago Tobón, Maria Micaela Sviatschi, and Nicolás Cabra-Ruiz (2025). Organised Crime. VoxDevLit 17(1), September 2025.
Verified locator / source role: Primary publisher page checked for review identity, authors, version and background. The specific published agenda is corroborated in [S2]; the exact formal target is editorial.
https://voxdev.org/voxdevlit/organised-crime
[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: Organised Crime. 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-510
Youth recruitment prevention: interventions, beliefs, and network effects
What a randomized policy can and cannot identify
The target cohort is fixed before a prevention intervention and followed to a common age. This attempt establishes identification of separately randomized information and opportunity packages, supplies an exact decomposition of their interaction, and derives a bounded linear network benchmark. It also constructs an observational equivalence showing why total effects and post-policy beliefs alone do not identify a belief-mediated effect. The actual effects on gang entry and lawful earnings remain unresolved without data.Let $I,O\in\{0,1\}$ denote an information package and an opportunity package. Randomize whole noninterfering recruitment clusters to the four policy cells, with positive known assignment probabilities. Outcomes may depend arbitrarily on assignments within their own cluster, but here the cluster package is the complete intervention. For a baseline youth define gang entry $G(I,O)$ by a fixed age, and cumulative lawful earnings $Y(I,O)$ with a declared zero-after-death and zero-during-nonemployment convention. The latter is a composite earnings outcome, not earnings conditional on survival.
Under consistency, random assignment independent of the four potential outcomes, and complete follow-up, cell means identify $m_{io}=E[G(i,o)]$ and the analogous earnings means. If cluster sizes differ, the analysis must use baseline youth weights to target a youth-average effect; unweighted cluster means target a different population. Independent clusters, not individual youth observations, are the independent sampling units for variance and concentration calculations.
A complete intervention decomposition
The joint package effect is $m_{11}-m_{00}$. Its factorial interaction is \[ \iota=m_{11}-m_{10}-m_{01}+m_{00}. \] Two order-specific decompositions are valid: \[ m_{11}-m_{00}=(m_{10}-m_{00})+(m_{11}-m_{10}) =(m_{01}-m_{00})+(m_{11}-m_{01}). \] A symmetric allocation assigns \[ \phi_I=\tfrac12[(m_{10}-m_{00})+(m_{11}-m_{01})],\qquad \phi_O=\tfrac12[(m_{01}-m_{00})+(m_{11}-m_{10})]. \tag{1} \] Expanding terms proves $\phi_I+\phi_O=m_{11}-m_{00}$. Each component averages the intervention's incremental effect across the two possible orders. This is an explicit allocation convention for package effects, not identification of a psychological mediator.For example, let $(m_{00},m_{10},m_{01},m_{11})=(0.4,0.3,0.2,0.05)$. The total entry reduction is $0.35$, interaction is $-0.05$, and $(\phi_I,\phi_O)=(-0.125,-0.225)$. The information intervention's effect depends on whether opportunities are also changed. Calling the first component "the expectations mechanism" would require proving that the information package has no direct effect on social support, monitoring, or actual opportunities.
A nonidentification witness for natural mediation
Even a perfectly randomized binary policy $Z$ and a perfectly measured binary belief $M$ need not identify a natural indirect effect. Consider two models with $M(z)=z$ for every youth. Define potential entry outcomes conditional on imposed policy and mediator as follows: \[ \text{Model A: }G(z,m)=1-m,\qquad \text{Model B: }G(z,m)=1-z. \] Both models produce exactly $M=Z$ and $G=1-Z$ under random assignment, so the joint observed law of $(Z,M,G)$ agrees. The total effect is $-1$ in each. But the natural indirect contrast at baseline policy is \[ E[G(0,M(1))-G(0,M(0))]=-1\text{ in A},\quad0\text{ in B}. \tag{2} \] The calculation evaluates the displayed functions. Model A makes the effect run through beliefs; Model B makes it direct. Their unobserved cross-policy mediator interventions differ. Recording expectations more accurately does not distinguish the models. The deterministic mediator also lacks within-policy overlap, highlighting an additional obstacle; no positivity condition should be silently presumed from policy randomization.A mediator experiment that directly randomizes a well-defined information state while holding the opportunity intervention fixed would identify a controlled effect under its own exclusion and consistency assumptions. It generally targets a different quantity from (2). Sequential ignorability, mediator overlap and absence of exposure-induced mediator-outcome confounding are possible alternative identifying restrictions, but they require justification rather than follow from the total-policy trial.
A solvable network propagation benchmark
For a finite network, take a nonnegative adjacency-weight matrix $A$, baseline entry propensity vector $a$, direct prevention shift $bz$ with $b\ge0$, and peer coefficient $\gamma\ge0$. The benchmark expected propensities satisfy \[ q(z)=a-bz+\gamma A q(z). \tag{3} \] Assume $\gamma\|A\|_\infty<1$ and that the resulting vector lies in $[0,1]^n$ for every intervention considered. The probability restriction is separate; a linear system need not automatically define valid probabilities.Mortality and observation
By the fixed horizon, report mutually exclusive states such as entry before death or horizon, death without prior recorded entry, and survival without entry. Death after entry belongs to the first state; survival is also worth reporting separately. Treating death as ordinary missing entry data can make a harmful mortality increase look like successful prevention. The earnings convention should remain the same across regimes. Conditioning on survivors changes the target and introduces principal-stratum selection.For bounded $G\in[0,1]$ with observation rate $r_z$ and observed mean $g_z$, the full-cohort entry mean lies in $[r_zg_z,r_zg_z+1-r_z]$. These bounds follow by assigning all missing outcomes zero or one. They do not justify substituting zero for missing records. Administrative validation of entry and mortality can narrow observation uncertainty, while misclassification requires a separate sensitivity analysis.
Remaining gap
The factorial design identifies packages and their interaction; the counterexample blocks an unsupported mediation interpretation; the network equations give a conditional propagation theorem. A full solution needs real cluster assignments, implementation fidelity, independent measurement of entry and survival, and evidence about changes in expectations and opportunities. Different policies can produce the same short-run reported beliefs while changing long-run lawful earnings differently. No factual youth recruitment rate or policy effect is asserted here.Completion Estimate
45%This is a post hoc, heuristic estimate for the full catalogue target. The attempt identifies information-opportunity factorial packages, proves natural-mediation nonidentification, and solves stable linear recruitment-network propagation with bounded observation uncertainty. Full youth policy effects still need implementation and longitudinal evidence, separate expectations exclusions, mortality validation, and endogenous recruitment displacement and network changes.
References
- [crime] S. Tobón, M. M. Sviatschi and N. Cabra-Ruiz (2025), Organised Crime, VoxDevLit 17(1), September. https://voxdev.org/voxdevlit/organised-crime. Source motivation for expectations, recruitment and networks; the experimental and mathematical benchmarks above are self-contained.