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Econ-389 · economics · Economics

Durable anticorruption policy

LLM status Partially solved unverified

Statement

Original subject group: Political economy and institutions

Audit classification: Published research agenda. Primary manuscript and metadata checked. Learning, substitution and long-run evaluation are explicit gaps; harm weights and measurement identification are editorial.

Definitions and precise research target

Complete editorial problem. Fix a public organization and a policy bundle $p$ comprising audits, sanctions, transparency, competition, and personnel incentives. Let $C^k_{jt}(p)$ be verified corruption through avenue $k$ in unit $j$ at date $t$, and let $\lambda_k\ge0$ be declared weights capturing losses rather than simply counts of detected offenses. Define total corruption harm $C_{jt}(p)=\sum_k\lambda_kC^k_{jt}(p)$. The main estimand is $\tau_C(T,p)=E[C_{jT}(p)-C_{jT}(0)]$, for a horizon permitting officials to learn and substitute across avenues. Estimate service output, enforcement cost, selection into office, and citizen welfare alongside $\tau_C$. Audits may change detection probabilities, so measured offenses require an explicit measurement model or independent validation. A policy that lowers the targeted avenue while increasing another need not reduce total harm. Use credible bundle and follow-up variation to distinguish deterrence, adaptation, and personnel selection; describe interference across agencies. Determine which combinations remain effective after officials understand the rules. The source explicitly requests short- and long-run evidence under strategic adaptation. The avenue weights, outcome definition, and comparative policy objective are our formalization of that research agenda.

Definitions and admissible scope. Choose mutually exclusive corruption avenues or explicitly remove double counting. $C^k_{jt}$ is the true amount or incidence of avenue $k$, while detected cases $D^k_{jt}$ are generated by sensitivity, false-positive rates, and audit intensity that can depend on policy. Harm weights $\lambda_k$ have a fixed welfare or currency interpretation; detection counts are not harm. Long-run effectiveness means $E[C_{jT}(p)-C_{jT}(0)]<0$ at a declared horizon after learning, accompanied by service outcomes and cost. If every $\lambda_k\ge0$, reducing one avenue is insufficient when others increase. The assignment law specifies interagency interference and officials' opportunities to learn and move between posts. Let the corruption avenue set be finite, with $\lambda_k\ge0$ and $\sum_k\lambda_k>0$, finite expected harms, a fixed organization-unit law, and finite horizon $T$. The complete corruption definition includes displacement to uncovered units or states whether it lies outside the target. Fix independent validation or explicit sensitivity/false-positive bounds before comparing detected offenses. The target is the joint identified set of total-harm, service, and cost responses under a declared finite policy menu and strategic response/assignment law. A cost-effective ordering requires a separately stated welfare criterion; a negative $\tau_C$ alone need not maximize citizen welfare.

Variants and assumption changes

  1. Detection-adjusted deterrence (editorial): hold independent audit sensitivity fixed while varying sanctions or regular-audit intensity. Identify harm changes separately from discovery changes.
  2. Adaptation and selection (source-motivated): collect repeated measures across avenues and personnel cohorts after officials learn the policy. Compare changing audit patterns and recruitment rules to identify durable substitution and entry effects.

References and source audit

Support and access. Primary manuscript and metadata checked. Learning, substitution and long-run evaluation are explicit gaps; harm weights and measurement identification are editorial. Locator: February 24, 2012 manuscript, Section 4 pp. 35--37 and conclusion pp. 38--39.
  1. Benjamin A. Olken; Rohini Pande. 2012. Corruption in Developing Countries. February 24, 2012 manuscript, Section 4, printed pp. 35--37; conclusion, pp. 38--39. https://economics.mit.edu/research/publications/corruption-developing-countries. DOI: https://doi.org/10.1146/annurev-economics-080511-110917.

Common conventions: Source mathematical conventions

These conventions apply to each entry unless explicitly replaced.

Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.

Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.

Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.

Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.

Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.

Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.

Statement licence: CC-BY-4.0 · Source file

Contributions 2

Econ-389-A2 · Exploration · LLM-generated · claude opus 5.5 high ·

Claude Opus 5.5 High attempt on Econ-389

Durable anticorruption policy: detection versus incidence, weakest-link substitution, and the identification of long-run total harm

Abstract

We prove four results. (i) Detected offences do not identify even the sign of $\tau_C$ when audits change detection sensitivity. We give explicit observationally equivalent models. (ii) An independent validation audit with policy-invariant sensitivity identifies avenue-level true corruption, and hence $\tau_C(T,p)$. (iii) If officials' extraction technologies are linear across avenues, they use only the avenues with the lowest expected penalty. Enforcement then affects total extraction only through the minimum detection probability (weakest link). A targeted audit of the used avenue shifts all extraction to the next avenue, and total harm rises iff that avenue's harm weight is larger. (iv) With convex avenue costs, substitution is partial, with an explicit cross-elasticity. The long-run effect after officials learn the audit rule equals the full-information comparative static. Short-run estimates before learning are biased toward the direct effect.

1. Detection versus incidence

Let true corruption in avenue $k$ be $C^k$. Detections are $D^k=s^k(p)C^k+f^k(p)(N^k-C^k)$, where $s^k$ is sensitivity, $f^k$ the false-positive rate and $N^k$ the number of transactions.
Proposition: Suppose a policy raises $s^k$ from $s_0$ to $s_1>s_0$. For any observed $(D^k_0,D^k_1)$ there are models with $C^k_1>C^k_0$ and models with $C^k_1<C^k_0$ that reproduce the data, unless $s^k(p),f^k(p)$ are known.
Proof: For given $(f,N)$, $D=f N+(s-f)C$. Choosing $s_1$ larger lets a smaller $C_1$ produce the same $D_1$, and choosing $s_1$ only slightly larger than $s_0$ requires a larger $C_1$. Both are compatible when $s$ is unknown. ∎
Proposition (Validation): Suppose an independent audit sample, drawn at random with known probability and examined with a protocol whose sensitivity and false-positive rate $(\bar s,\bar f)$ do not depend on $p$, satisfies $\bar s>\bar f$. Then $C^k=(D^{k,\rm val}-\bar fN^k)/(\bar s-\bar f)$ is identified in each regime, and so is $\tau_C(T,p)=\mathbb E[\sum_k\lambda_k(C^k_T(p)-C^k_T(0))]$ under randomised $p$.

2. Substitution across avenues

An official chooses extraction $x_k\ge0$ in avenues $k=1,\dots,K$, with unit private gain $1$, expected penalty $\phi\,q_k$ per unit (detection $q_k$, sanction $\phi$) and a cost $c(\sum_kx_k)$ of total extraction, with $c$ convex.
Proposition (Weakest link): The official uses only avenues in $\arg\min_kq_k$. Total extraction $X$ solves $1-\phi\min_kq_k=c'(X)$. Hence: (a) raising $q_k$ for an avenue that is not the unique minimiser leaves $X$ unchanged; (b) raising the unique minimiser's $q$ to above the second-lowest moves all extraction to the second avenue $k'$, with $X$ falling only through the change in $\min q$; (c) total harm $\lambda_{k'}X'$ versus $\lambda_kX$ rises iff $\lambda_{k'}X'>\lambda_kX$, which happens whenever $\lambda_{k'}>\lambda_k\,X/X'$.
Proof: The objective $\sum_k(1-\phi q_k)x_k-c(\sum x_k)$ is linear in the allocation for fixed $X$, so all mass goes to the avenues with minimal $q_k$. The first-order condition in $X$ follows. ∎
Proposition (Convex avenue costs): With costs $c(\sum_kx_k)+\sum_kc_k(x_k)$, all strictly convex, and an interior optimum, the response to a rise in $q_k$ is $dx/dq_k=-\phi H^{-1}e_k$ with $H=\mathrm{diag}(c_1'',\dots,c_K'')+c''\mathbf 1\mathbf 1^\top$. Hence $dx_k/dq_k<0$, and $dx_j/dq_k>0$ for $j\ne k$ whenever $c''>0$ (partial substitution). If $c''=0$ (purely avenue-specific costs), then $dx_j/dq_k=0$ for $j\ne k$.
Proof: Sherman--Morrison: $H^{-1}=D^{-1}-\frac{c''D^{-1}\mathbf 1\mathbf 1^\top D^{-1}}{1+c''\mathbf 1^\top D^{-1}\mathbf 1}$, with $D=\mathrm{diag}(c_k'')$. Its off-diagonal entries are negative, so the entries of $-\phi H^{-1}e_k$ for $j\ne k$ are positive. ∎
So partial substitution arises from a shared constraint on total extraction (for example a shared risk budget or limited opportunities). Avenue-specific costs alone produce none.

3. Learning and durability

Suppose officials hold beliefs $\hat q_{k,t}$ about detection, updated from observed audits, with $\hat q_{k,t}\to q_k$. Then extraction at $t$ is the Proposition Proposition (Weakest link) or Proposition (Convex avenue costs) solution at $\hat q_t$. The long-run effect, at $\hat q=q$, is the full-information comparative static. Early effects reflect beliefs. If officials initially overestimate a new audit's coverage, short-run reductions overstate the long-run effect, which is the adaptation the source highlights. Identification therefore requires outcome measurement at a horizon $T$ by which beliefs have converged, or a model of learning with measured beliefs, for example from surveys of officials.

4. Remaining

Personnel selection (who enters office under a stricter regime) changes the distribution of $\phi$-sensitivity and gains, so that $X$ responds on the extensive margin. Service outcomes and costs are needed for welfare. Interference arises because officials move between agencies. A complete design randomises bundles across agencies with spillover exposure measured, and validates detections independently (Proposition Proposition (Validation)), as the problem requires [ol].

Completion Estimate

48%

This is a post hoc, heuristic estimate for the full catalogue target. Weakest-avenue and convex-cost models prove strategic substitution, and validation separates detections from true incidence under known error rates. Finite-horizon learning, selection into office, service and cost responses and interagency interference still require a complete empirically identified model.

References

  • [ol] Anticorruption policy manuscript (February 24, 2012), Section 4, pp. 35--37, and conclusion, pp. 38--39.
  • [becker] G. S. Becker, G. J. Stigler, Law enforcement, malfeasance, and compensation of enforcers, Journal of Legal Studies 3 (1974), 1--18.

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Econ-389-A1 · Partial result · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-389

Durable anticorruption policy: a research attempt

Target and outcome

Status: partial; durable harm reductions for an actual organization remain unresolved. The target is a finite-horizon change in true, weighted corruption harm, accompanied by service and enforcement outcomes. I derive a sharp deterrence threshold in a strategic avenue-choice model, an explicit harmful-substitution example, detection-adjusted bounds, and a dynamic adaptation formula. Together they show why neither fewer targeted offenses nor more detected offenses determines the sign of the requested effect.

Olken and Pande's primary manuscript explicitly discusses adaptation and substitution following anticorruption policies [op]. The parameters and propositions below are additional analytical specializations. No claim is made that a particular government's policy has one of the calculated effects.

Officials choose the least deterred avenue

An official can act honestly or choose one of $K$ mutually exclusive corrupt acts. Honest payoff is zero. Avenue $k$ produces private rent $r_k>0$, sanction $s_k>0$ conditional on discovery, and detection probability $d_k\in[0,1]$. The official is risk neutral, knows the policy, and chooses the act with highest expected payoff \[ u_k=r_k-s_kd_k. \] Ties with honesty are resolved in favor of honesty; ties between corrupt avenues use a declared fixed rule. True harm from avenue $k$ is $\lambda_k\geq0$, independent of the fine, which is a transfer under this accounting. Audit capacity is $\sum_kd_k\leq B$. Sanctions are fixed legal inputs rather than unbounded controls.
Proposition (Feasibility of complete deterrence): A feasible policy deters every avenue exactly when \[ r_k/s_k\leq1\quad\hbox{for every }k, \qquad\sum_kr_k/s_k\leq B. \] The smallest total audit probability that achieves weak deterrence is $\sum_kr_k/s_k$.
Proof: Honesty is selected exactly when $u_k\leq0$ for every avenue, requiring $d_k\geq r_k/s_k$. Probability and capacity constraints yield necessity. Setting every $d_k$ at its threshold establishes sufficiency and the minimum sum. If honesty is not selected at indifference, strict deterrence requires strict inequalities and spare capacity; the displayed value is then an infimum. ∎

For uncertain rents $r_k\in[\underline r_k,\overline r_k]$ and known sanctions, the same argument gives robust deterrence thresholds $\overline r_k/s_k$. This is a minimax feasibility result with an explicit uncertainty set. It is not necessarily welfare-optimal: complete deterrence can cost more than the harm it prevents, or reduce service if audits consume production resources.

A targeted success with higher total harm

Take two avenues with rents $(4,3)$, sanctions $(10,10)$, and harm weights $(1,3)$. Without audits the official chooses avenue 1, producing harm 1. A policy auditing only avenue 1 with $d_1=0.2$ changes its net payoff to 2, so the official switches to avenue 2 with payoff 3 and harm 3. Targeted corruption disappears, while total harm increases by 2. The numerical example remains strict under small perturbations, so it does not depend on an indifference tie.

A capacity $B=0.7$ permits weak complete deterrence using $(d_1,d_2)=(0.4,0.3)$ under the specified honesty tie rule. A smaller capacity cannot deter both in this model. A weighted welfare objective could nonetheless prefer a smaller audit bundle if enforcement costs are high. Measuring the substitution avenue and the service consequences is therefore necessary even when the targeted outcome is perfectly observed.

Discovery is a separate observation process

For a fixed avenue and policy regime, let true binary incidence be $C$, detected incidence $D$, sensitivity $s={\mathbb{P}}(D=1\mid C=1)$, and false-positive rate $f={\mathbb{P}}(D=1\mid C=0)$. These $s,f$ are measurement parameters, distinct from the sanction notation above. If $c={\mathbb{P}}(C=1)$ and $d={\mathbb{P}}(D=1)$, \[ d=f+(s-f)c. \] With known $s>f$, true incidence is $(d-f)/(s-f)$. Thus changing audits changes the mapping from incidence to measured offenses. For instance, true incidence can fall from $0.4$ to $0.2$ while sensitivity rises from $0.2$ to $0.8$, yielding detected rates $0.08$ and $0.16$ when false positives vanish. Detected offenses double while true incidence halves.

Suppose independent validation instead supplies intervals \[ f\in[f_L,f_U],\qquad s\in[s_L,s_U],\qquad 0\leq f_L\leq f_U<s_L\leq s_U\leq1. \] The observed rate must satisfy $d\in[f_L,s_U]$ for compatibility. The sharp incidence interval in this measurement class is \[ c_L=\max\left\{0,\frac{d-f_U}{s_U-f_U}\right\},\qquad c_U=\min\left\{1,\frac{d-f_L}{s_L-f_L}\right\}. \] To see the lower endpoint, choose maximal sensitivity and maximal feasible false positives. If $d\leq f_U$, choosing $f=d$ gives $c=0$; otherwise use $(f_U,s_U)$. For the upper endpoint choose minimal false positives and minimal feasible sensitivity. If $d\geq s_L$, choose $s=d$ to obtain $c=1$; otherwise use $(f_L,s_L)$. Continuity fills the interval. This proof also checks endpoint attainability rather than merely reporting an outer bound.

If a policy is randomized across independent organizational clusters and validation is representative within each arm, the arm-specific detected laws and validation restrictions identify such intervals for true arm incidence. For nonnegative fixed harm weights, a valid effect interval is \[ \left[\sum_k\lambda_k(c^1_{k,L}-c^0_{k,U}), \sum_k\lambda_k(c^1_{k,U}-c^0_{k,L})\right]. \] It is sharp when avenue-specific opportunities and measurement mechanisms can vary independently subject to these marginal restrictions. If one imposes the earlier one-act choice model, incidence probabilities must also sum to at most one; then joint optimization under those restrictions can tighten the interval. It would be incorrect to claim marginal sharpness automatically proves joint sharpness. False positives, validation selection, and audit spillovers require corresponding additional restrictions.

A finite-state adaptation benchmark

Let $x_t$ be expected counts in finitely many active corruption states, with transitions \[ x_{t+1}=A_px_t+b_p, \] where $A_p$ is a nonnegative column-substochastic matrix (each column sums to at most one) and $b_p\geq0$ represents entry into corrupt states. Exits include deterrence, dismissal, and retirement. Assume $\rho(A_p)<1$. Then \[ x_T=A_p^Tx_0+\sum_{s=0}^{T-1}A_p^sb_p, \quad x_\infty=(I-A_p)^{-1}b_p. \] Multiplying the regime difference by the harm-weight vector gives the exact horizon-specific effect. A short-run decline from $A_px_0$ does not determine the long-run difference because policy can change both substitution transitions and entry. If a policy merely moves officials into a persistent, unmeasured state, the observed initial effect can be opposite to the complete-system effect. The stability assumption is substantive; if an absorbing corrupt state receives continuing entry, the stationary formula does not exist.

Repeated cohort data with policy variation could identify transition and entry changes, but detected-state transitions are not automatically true-state transitions. Independent audits or a separately identified hidden-state model are needed. Officials moving to uncovered agencies must either remain in the target system or be explicitly excluded from the estimand; changing the boundary after observing displacement changes the policy question.

Remaining task

The mathematical examples leave the organization's real rents, sanction enforceability, costs, response transitions, and validation quality unknown. A full assessment must track all material avenues, service output, personnel selection, and policy learning over the chosen horizon. The results here establish restrictions under which those data could be interpreted and give exact counterexamples to two common shortcuts; they do not identify the optimal anticorruption bundle without those data.

Completion Estimate

58%

This is a post hoc, heuristic estimate for the full catalogue target. Strategic avenue choice gives a deterrence threshold and harmful-substitution example, with sharp detection-adjusted incidence bounds and horizon-specific adaptation formulas. Actual rents, enforceable sanctions, personnel transitions, service outcomes and interagency displacement remain unidentified for the durable policy comparison.

References

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