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Econ-523 · economics · Economics

Workplace harassment prevention and economic outcomes

LLM status Open unverified

Statement

ECON-052 | R | Source-backed agenda; exact formalization is editorial

Definitions and formal target

Let $z$ be a workplace policy specifying reporting, investigation, protection, and sanctions. Worker $i$ has latent experienced harassment $H_i(z)$, reporting indicator $R_i(z)$, retention $E_i(z)$, and earnings $Y_i(z)$. Employer profit is $\Pi_f(z)$.

Determine effects on the joint target \[ \theta(z)=\left(\mathbb E[H_i(z)-H_i(0)],\, \mathbb E[E_i(z)-E_i(0)],\, \mathbb E[Y_i(z)-Y_i(0)],\, \mathbb E[\Pi_f(z)-\Pi_f(0)]\right). \] Separate changes in experienced harm from changes in willingness or ability to report it.

Clarifications and required assumptions

Define harm, reporting window, workforce cohort and the no-policy regime. A simple model is observed report $O=H R$ for binary true harm and truthful reports; false allegations, incomplete disclosure and measurement error require a richer model. More reports can reflect more harm or better reporting. Track all baseline eligible workers, recording earnings as zero during nonemployment as appropriate; restriction to retained workers selects an outcome of policy. Specify firm-profit accounting and safe measurement capable of validating or bounding latent harm.

Variants and changes of scope

  • Reporting access, prevention, investigation and protection are distinct policy components.
  • Reported incidents and latent experienced harm are different estimands.
  • Survivor-only effects require principal-stratum assumptions or bounds, not ordinary conditioning on retention.

Audit conclusion and source relationship

[S1] and [S2] directly support workplace safety/harassment as a research gap. The latent-harm versus reporting distinction and joint causal vector are editorial specifications.

References and exact source roles

[S1] Rachel Heath, Arielle Bernhardt, Girija Borker, Anne Fitzpatrick, Anthony Keats, Madeline McKelway, Andreas Menzel, Teresa Molina, and Garima Sharma (2025). Female Labour Force Participation. VoxDevLit 11(2), October 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/female-labour-force-participation

[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: Female Labour Force Participation. 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-523-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-523

Harassment prevention: sharp reporting bounds and validation designs

Problem ID: J71-519. Status: Unresolved. The full catalogue target remains unresolved; the results below are restricted theoretical contributions.

Joint policy target

For a fixed baseline workforce, the catalogue seeks policy effects on latent experienced harassment $H$, retention $E$, earnings $Y$, and firm profit $\Pi$. A complete policy includes reporting access, investigation, protection and sanctions. These components can affect both experienced harm and disclosure. In the truthful-report benchmark the observed report is $O=HR$, where $H,R\in\{0,1\}$. Define the harm prevalence $p_z={\mathbb{P}}(H=1\mid Z=z)$ and reporting sensitivity $r_z={\mathbb{P}}(R=1\mid H=1,Z=z)$; then $o_z=E[O\mid Z=z]=p_zr_z$.

Assume workplace-level randomized assignment, complete baseline-worker follow-up and either no cross-workplace interference or an explicitly randomized exposure regime. These assumptions identify report, retention and earnings means under each policy. They do not identify $p_z$ merely because assignment is randomized. The workplace-safety research agenda in the VoxDev review motivates the question; no outcome magnitudes are borrowed from it.

Sharp bounds with reporting restrictions

Suppose independent validation justifies $0<l_z\le r_z\le u_z\le1$. If the restrictions fit the observed report rate, the sharp prevalence interval is \[ p_z\in\left[\frac{o_z}{u_z},\ \min\left\{1,\frac{o_z}{l_z}\right\}\right]. \tag{1} \] An empty interval rejects the validation restrictions. If $o_z=0$ and $l_z>0$, the interval is the singleton zero.
Proof: The identity $o_z=p_zr_z$ and the sensitivity bounds imply (1). Conversely for any positive $p_z$ in the interval, set $r_z=o_z/p_z$, generate $H$ with probability $p_z$, and among harmed workers report with probability $r_z$. This reproduces the entire binary-report law. The zero-prevalence case is realized by $H=0$ almost surely. With unrestricted coupling of potential outcomes across policy arms, the lower and upper harm-effect bounds are obtained by opposite endpoint subtraction, and are attainable. ∎
For example suppose reports rise from $0.10$ to $0.15$. One compatible explanation has harm fall from $0.50$ to $0.30$ while sensitivity rises from $0.20$ to $0.50$. Another has sensitivity fixed at $0.50$ and harm rise from $0.20$ to $0.30$. The observed policy effect on reports is identical, while the harm effects have opposite signs. A reporting policy may therefore look worse on the incident register while preventing harm.

Validation restrictions need to apply separately to each policy: a reporting intervention is designed to change $r_z$. Transporting a control sensitivity mechanically to treated workplaces would build the desired conclusion into the measurement model. Likewise a lower bound on the unconditional probability of making any report is not a lower bound on reporting conditional on actually experiencing harm.

What a reporting encouragement does not identify

Within a fixed policy regime, randomize an encouragement $A\in\{0,1\}$ that changes reporting access but, by assumption, cannot affect experienced harm in the reporting window. Let harm prevalence be the common $p$ and report rates $o_a=pr_a$. Even if encouragement weakly increases reporting, every $p\in[\max(o_0,o_1),1]$ can fit by choosing $r_a=o_a/p$ when $p>0$. Thus encouragement identifies a change in reporting but not its absolute sensitivity or the prevalence level. This impossibility follows with perfect randomization and an exact exclusion restriction, so additional observations rather than improved randomization precision are needed.

A substantive exclusion must also address anticipation: if workers or perpetrators know that encouragement will occur, the later harm process may change. An intervention applied after a fixed reporting window is conceptually closer to the exclusion, although recall and disclosure still require validation. This is a causal-design distinction, not a proposed operational protocol for vulnerable workers.

Two ascertainment channels and a testable sensitivity model

Suppose the same harm window is measured by two truthful ascertainment channels, $O_1=HR_1$ and $O_2=HR_2$. Denote $o_j=E[O_j]$ and $b=E[O_1O_2]$. Under conditional independence of $R_1,R_2$ given $H=1$, positive marginals and $b>0$, \[ p=\frac{o_1o_2}{b},\qquad r_1=\frac b{o_2},\qquad r_2=\frac b{o_1}. \tag{2} \] Indeed $o_j=pr_j$ and $b=pr_1r_2$, so direct division proves the identities. This is the standard two-list ascertainment calculation. It is not automatically credible: workers who trust one channel may also trust the other, and heterogeneous severity can correlate the reporting events even if the instruments differ.

There is a useful sharp relaxation. Let conditional reporting covariance satisfy $|{\operatorname{Cov}}(R_1,R_2\mid H=1)|\le\eta$. Assume $o_1+o_2-b>0$. Then the sharp prevalence set is \[ \left\{p\in[o_1+o_2-b,1]:\ |bp-o_1o_2|\le\eta p^2\right\}. \tag{3} \]

Proof: No truthful channel reports when $H=0$, so every person with at least one report is harmed, giving the lower bound. For any candidate $p$, the conditional covariance is $b/p-o_1o_2/p^2$, giving the polynomial inequality. Conversely allocate unconditional probabilities $b$, $o_1-b$, $o_2-b$ to harmed people in report cells $(1,1),(1,0),(0,1)$; allocate $p-o_1-o_2+b$ to harmed people in cell $(0,0)$; and allocate $1-p$ to unharmed people in cell $(0,0)$. All are nonnegative because the observed binary table is valid and $p$ is in the stated interval. The resulting model reproduces the full report table and has exactly the required covariance. Thus every retained prevalence is attained. ∎
Equation (3) can be solved by elementary quadratic inequalities and plotted against $\eta$. At $\eta=0$ it reduces to (2), when the independent solution is feasible. This makes the otherwise hidden dependence restriction measurable as a sensitivity input. If false reports occur, the zero-harm cells are no longer fixed: with sensitivity $r$ and false-positive rate $f$, one instead has $o=f+(r-f)p$. Known $r\ne f$ gives $p=(o-f)/(r-f)$; uncertain values require an explicitly enlarged feasible set. One cannot combine false-positive data with the truthful formulas unchanged.

Retention, earnings and profit accounting

For baseline workers, define earnings over a fixed window including zeros during nonemployment and record earnings after workplace exit when they are part of the target. Under random assignment, their arm mean difference is identified with complete follow-up. The conditional mean among retained workers is a different statistic. For example a policy retaining low-wage workers can lower average wages among retained workers while raising both cohort employment and total earnings. Specifically, let half the baseline workers earn $2$ and half earn $1$. If only the first group is retained under control, retained mean earnings equal $2$ and cohort mean equals $1$; retaining both under treatment lowers the retained mean to $1.5$ but raises the cohort mean to $1.5$.

Firm profits require revenues less wages, verification and investigation expenditure, production costs and any specified liabilities. Workers' earnings and employer profits are distinct coordinates of the catalogue target; an earnings increase can partly be a transfer from profit. Adding them as social benefits without a common resource account would misinterpret that transfer, and omits disutility of harm and other normative costs in any case.

Remaining gap

This attempt gives sharp latent-harm sets under declared reporting restrictions and a concrete reason why reporting encouragement alone is insufficient. The broad policy target still requires trustworthy and safe validation, workplace causal variation, baseline-cohort tracking and reliable profit data. Conditional reporting independence and numerical sensitivity limits are not established here. No harassment prevalence or causal effectiveness claim is made, so the catalogue question remains unresolved.

Completion Estimate

55%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt derives sharp latent-harassment bounds, reporting-encouragement limitations, and two-channel ascertainment sensitivity while preserving baseline-worker outcomes. Full prevention effects still require safe reporting validation, workplace causal variation, complete cohort earnings follow-up, and employer-profit evidence under the actual bundled policies.

References

  • [flfp] R. Heath, A. Bernhardt, G. Borker, A. Fitzpatrick, A. Keats, M. McKelway, A. Menzel, T. Molina and G. Sharma (2025), Female Labour Force Participation, VoxDevLit 11(2), October. Primary review page: https://voxdev.org/voxdevlit/female-labour-force-participation. The reference provides the labor-market research setting; the identification bounds above are self-contained.

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