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Econ-412 · economics · Economics

Intergenerational economic effects of organized crime

LLM status Partially solved unverified

Statement

ECON-061 | R | Source-backed agenda; exact formalization is editorial

Definitions and formal target

Let $Z_p$ denote parental exposure to organized-crime control during a specified period. Child $i$ has later schooling $S_i(z)$, mental-health measure $H_i(z)$, lawful earnings $Y_i(z)$, and migration $M_i(z)$. Exposure can affect families through violence, institutions, income, or displacement.

For birth cohort $c$, identify \[ \theta_c=\mathbb E[(S_i(1)-S_i(0),H_i(1)-H_i(0),Y_i(1)-Y_i(0))\mid c]. \] Account for selective survival, fertility, and migration when defining the population and interpreting persistence across generations.

Clarifications and required assumptions

Define parental exposure, its period, the child's baseline cohort and a common follow-up age. If the policy changes fertility, a fixed cohort born after treatment cannot automatically be the same population in both worlds: use an aggregate cohort functional or an explicit principal-stratum target. Death, migration and missingness are different events. For a pre-existing child cohort, specify outcomes after death or analyze survival and survivor outcomes separately with bounds/assumptions. Repeated crime exposure must be distinguished from persistence after exposure ends.

Variants and changes of scope

  • Children already born before exposure and descendants born under each regime require different population definitions.
  • Total parental-exposure effects differ from effects mediated by income, schooling, violence or institutions.
  • Local follow-up and destination-inclusive follow-up estimate different effects when families migrate.

Audit conclusion and source relationship

[S1] and [S2] support long-run effects on children and intergenerational organized-crime exposure. This fixed-cohort causal formulation is editorial; survivor or fertility selection is not assumed away.

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.

https://voxdev.org/topic/evidence-gaps-key-unanswered-questions-across-16-topics-development-economics

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

Econ-412-A1 · Partial result · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-412

Intergenerational economic effects of organized crime

Target population before exposure

The catalogue concerns parental organized-crime exposure and children's later schooling, health and lawful earnings. This attempt fixes a cohort of children already born before exposure, distinguishes death from migration and missing follow-up, and derives sharp selection bounds. It does not posit an ethically or practically available experiment that assigns crime exposure; randomization below is a mathematical identifying benchmark that could instead describe an exogenous protection policy with its own treatment definition.

Let $Z\in\{0,1\}$ label the complete parental-exposure regime. Assume for the benchmark $Z$ is independent of all potential survival and outcomes, consistency, and no interference across sampled families. Survival at the common follow-up age is $S(z)$. A scalar outcome $Y(z)\in[0,1]$ is defined when $S(z)=1$; an earnings outcome requires a defended cap/rescaling to use this bound. The survivor-average causal effect is \[ \tau_{AS}={\mathbb{E}}[Y(1)-Y(0)\mid S(1)=S(0)=1]. \tag{1} \] It is different from a population outcome after assigning a numerical value to death, and different again from the difference of means among actual survivors.

Sharp bounds when exposure weakly reduces survival

Assume $S(1)\le S(0)$, a substantive monotonicity restriction. Write $p_z=\Pr(S=1\mid Z=z)$, with $0<p_1\le p_0$, and $q=p_1/p_0$. Let $F_0$ be the observed outcome distribution among regime-zero survivors and $Q_0$ its generalized quantile function, including atoms. Set \[ L_0(q)=q^{-1}\int_0^q Q_0(u)du,\quad U_0(q)=q^{-1}\int_{1-q}^1 Q_0(u)du,\quad \mu_1={\mathbb{E}}[Y\mid Z=1,S=1]. \]
Theorem (Trimmed survivor interval): Under the stated assumptions the sharp identified set for (1) is \[ [\mu_1-U_0(q),\ \mu_1-L_0(q)]. \tag{2} \]
Proof: By monotonicity, every regime-one survivor is an always survivor. Among regime-zero survivors, always survivors constitute fraction $q$, while the remaining fraction survives only under zero. Therefore $\mu_1$ identifies the always-survivor treated mean. The unobserved always-survivor membership within $F_0$ may select any subpopulation of mass $q$. The smallest possible mean of such a selection takes the bottom $q$ quantiles, splitting mass at a boundary atom if necessary; an exchange of a selected larger value with an unselected smaller value weakly lowers the mean until this arrangement is reached. The largest takes the top quantiles. This proves necessity. For attainment, assign always-survivor membership to either trimmed segment in the zero-survivor population and assign its treated outcomes with exactly the observed regime-one survivor distribution, using any coupling. Give the remaining zero survivors $S(1)=0$, and baseline nonsurvivors survival zero under both regimes. Randomize $Z$ independently. All observed distributions and survival probabilities are reproduced. Mixtures of these latent models preserve the same observed law and attain the intermediate effects. ∎
If $p_1=p_0$ then $q=1$ and the interval collapses: monotone equal survival implies identical survivor populations. If $p_1=0$, the conditioning event in (1) has zero mass and the target is undefined, not estimated as zero. If $p_1>p_0$, the maintained monotonicity is refuted at the population law. These boundary cases should be reported before calculating ratios.

For a numerical check let $p_0=0.8,p_1=0.6$, let $F_0$ be uniform on $[0,1]$, and let $\mu_1=0.4$. Then $q=0.75$, $L_0=0.375$, $U_0=0.625$, so $\tau_{AS}\in[-0.225,0.025]$. The raw survivor difference $0.4-0.5=-0.1$ falls inside the interval but its sign is not the sign of every compatible causal effect. The construction explains exactly how survivor selection changes that interpretation.

What if survival monotonicity is not credible?

Let $\pi_{AS}=\Pr(S(1)=S(0)=1)$. Its feasible mass obeys the sharp Frechet bounds \[ \max(0,p_0+p_1-1)\le\pi_{AS}\le\min(p_0,p_1). \] For a fixed positive $\pi_{AS}$, always survivors form fractions $\pi_{AS}/p_z$ of the survivor distributions in both regimes. Let $L_z,U_z$ be the corresponding trimmed means. Then a valid sharp interval at that mass is \[ [L_1(\pi_{AS}/p_1)-U_0(\pi_{AS}/p_0), U_1(\pi_{AS}/p_1)-L_0(\pi_{AS}/p_0)]. \tag{3} \] The construction selects each potential survivor subset independently and couples the selected outcomes into the always-survivor stratum; the other survival strata fill the remaining masses. Taking the union over positive feasible masses describes the identified set, or its closure if masses tend to zero. A zero lower bound allows models with no always survivors, so a population-wide well-defined target needs a separate positive-mass assumption. Monotonicity is therefore useful but cannot be justified by an average survival comparison alone.

Migration is not death, and three outcomes are joint

A migrant survivor remains part of the fixed cohort. If outcome observation indicator $R$ is missing for some survivors, with response rate $r_z$ and observed mean $m_z$, then \[ {\mathbb{E}}[Y(z)\mid S(z)=1]\in[r_z m_z,r_z m_z+1-r_z]. \tag{4} \] Proof: decompose the survivor mean by $R$, and bound the missing conditional mean in $[0,1]$. This is sharp absent restrictions on missingness. For trimmed bounds one needs the full survivor distribution, not only (4); optimize over all completions of its missing mass before trimming. Assuming destination follow-up is missing at random can narrow this class but must be stated and supported. Treating migration as a zero outcome changes the estimand.

Schooling, mental health and earnings can each have bounds like (2), yet their coordinate intervals need not be jointly sharp. The same always-survivor membership must explain all three observed outcomes. An exact finite-support implementation assigns weights to observed outcome vectors, constrains selected mass to $q$, and minimizes any declared linear welfare index. Selecting the bottom schooling quantiles and the bottom earnings quantiles independently may require different children and hence an impossible joint construction.

Remaining causal and intergenerational issues

Randomization was used to expose the selection problem cleanly. With naturally occurring exposure, conditional exchangeability or a defensible instrument is still needed; controlling for post-exposure displacement may remove part of the total effect. Persistence after parental exposure ends must be distinguished from repeated childhood exposure. Mediation through parental income, violence or schooling requires stronger cross-regime assumptions than the total-effect bounds.

For descendants conceived after the policy, the two regimes can produce different children. A fixed-cohort individual contrast is then not defined without a principal-stratum conception rule or a population aggregate target. These bounds solve a restricted selection problem for existing children and do not bypass fertility, confounding or long-run measurement. No real-world effect estimate is asserted.

Completion Estimate

45%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt establishes sharp survivor-selection bounds with and without survival monotonicity and distinguishes migration missingness from death in a fixed child cohort. Causal parental exposure, joint outcome restrictions, post-policy fertility, and persistence beyond repeated exposure still need identification and long-run evidence.

References

  • [source] S. Tobon, M. M. Sviatschi and N. Cabra-Ruiz (2025), Organised Crime, VoxDevLit 17(1). https://voxdev.org/voxdevlit/organised-crime. The publisher page supplies development and intergenerational context. The trimming argument is an explicit application of standard selection-bound reasoning, proved here; it is not a claim of a novel general bounding method.

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