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Econ-535 · economics · Economics

Mechanisms of discrimination

LLM status Open unverified

Statement

Original atlas ID: L6 (entry 26). Classification: Editorial mechanism identification and career-policy problem.

Original atlas question: How much disparity comes from tastes, statistical inference, networks, evaluation rules or accumulated disadvantage?

Definitions and assumptions

Fix a hiring stage, employer population, and distribution $G$ of standardized application characteristics $X$. Let $A\in\{0,1\}$ be a randomized identity cue, such as a name convention that changes perceived group membership, and let $B$ specify an independently randomized information or evaluation regime. Denote the potential callback by $C_j(a,b,x)\in\{0,1\}$. Assume randomized assignment, consistency, positive assignment probabilities, and the announced interference restriction. A cue may convey multiple perceived attributes; interpreting it solely as group identity requires additional evidence. For careers, define discounted earnings $Y_i(\pi)$ under a specified employer policy $\pi$, including nonhire and nonemployment outcomes.

Formal research question

Identify the standardized callback contrast \[ \Delta(b)=\int \mathbb E_j[C_j(1,b,x)-C_j(0,b,x)]\,dG(x) \] and its change across evaluation regimes. Then, for an explicit class $\mathcal M$ of employer-belief, preference, network, and household-history models, define \begin{align*} \vartheta(M)&=(\theta_{\mathrm{taste}},\theta_{\mathrm{belief}},\theta_{\mathrm{network}}),\\ \chi(M)&=\mathbb E_M[Y_i(\pi_1)-Y_i(\pi_0)],\\ \mathcal T(P)&=\{(\vartheta(M),\chi(M)):M\in\mathcal M(P)\}. \end{align*} Here $P$ is the observed joint law of experimental and career measurements, $\mathcal M(P)$ consists of models in $\mathcal M$ matching that law, and each $\theta$ is an announced structural parameter, not a share inferred merely from an outcome gap. Characterize $\mathcal T(P)$. Determine which factorial experiments, belief elicitations, quality signals, or follow-up designs distinguish models with the same callback contrasts but different policy responses.

Interpretation and scope

Randomized cues can establish differential treatment in the tested setting. They do not by themselves partition it into taste-based and statistical mechanisms: unobserved employer beliefs and cue interpretations can generate observational equivalence. Revealing validated quality can help only under assumptions about employers' comprehension and use of the signal. Blind evaluation can change both information and attention. Conditioning subsequent wage analysis on successful hiring creates treatment-dependent selection; unconditional baseline-cohort outcomes or an explicitly justified selection model are required. The total earnings disparity between actual groups also includes unequal opportunity histories and application composition, which the standardized résumé experiment intentionally holds fixed. Interventions on networks or evaluation rules must be defined separately to measure those pathways.

Source audit and status

[S1] studies orchestral screening, while [S2] and [S3] provide correspondence-experiment evidence. Their findings are existing evidence, not unresolved questions. The mechanism-identification and career-policy program is an editorial synthesis with an explicitly restricted model class. The sources do not prove a single cause of discrimination or certify universal unresolved status as of 2026.

References

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  1. Claudia Goldin and Cecilia Rouse (2000). Orchestrating Impartiality: The Impact of Blind Auditions on Female Musicians. American Economic Review 90(4), 715--741. https://doi.org/10.1257/aer.90.4.715. Locator: Primary publisher, working-paper, or author record: bibliographic information and abstract; full-text theorem verification is not claimed. Role: Evidence on screened identity in auditions; a specific evaluation setting.
  2. Marianne Bertrand and Sendhil Mullainathan (2004). Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination. American Economic Review 94(4), 991--1013. https://doi.org/10.1257/0002828042002561. Locator: Primary publisher, working-paper, or author record: bibliographic information and abstract; full-text theorem verification is not claimed. Role: Randomized résumé-name callback evidence; supports unequal treatment, not a unique mechanism.
  3. Patrick Kline, Evan K. Rose, and Christopher R. Walters (2022). Systemic Discrimination Among Large U.S. Employers. The Quarterly Journal of Economics 137(4), 1963--2036. https://academic.oup.com/qje/article-abstract/137/4/1963/6605934. Locator: Primary publisher, working-paper, or author record: bibliographic information and abstract; full-text theorem verification is not claimed. Role: Employer-level correspondence experiment and heterogeneity in contact gaps.

Common conventions: Source mathematical conventions

Unless an entry states otherwise, agent and firm sets are finite. State and action spaces are measurable, strategies and outcome maps are measurable, probability laws are specified, and expectations exist for the targets under discussion. Infinite-horizon discount factors lie in $(0,1)$ and discounted objectives are finite. Norms, tolerances and complexity input sizes must be specified for computational comparisons. Constants or primitives that appear locally are inputs, not empirical facts asserted by this catalogue.

Identification. A statistical model $m\in\mathcal M$ implies an observable law $P_m$ and target $\theta(m)$. At law $P$, its identified set is \[ \Theta(P;\mathcal M)=\{\theta(m):m\in\mathcal M,\ P_m=P\}. \] Point identification holds when this set is a singleton, or equivalently when $P_{m_1}=P_{m_2}$ implies $\theta(m_1)=\theta(m_2)$ for all compatible models. Sharp bounds mean bounds attained, or approached when the boundary is not attained, by compatible models. Writing this set is a definition, not a solution: the substantive task is to establish informative restrictions and derive or estimate the set. An unrestricted-confounding model may give only trivial bounds.

Inference. Identification, estimability and valid uncertainty quantification are separate questions. Fix $\alpha\in(0,1)$. A confidence procedure $C_n$ over a declared law class $\mathcal P$ has asymptotic uniform coverage at level $1-\alpha$ when \[ \liminf_{n\to\infty}\inf_{P\in\mathcal P}\Pr_P\{\theta(P)\in C_n\}\geq1-\alpha. \] For set-identified targets the coverage event must be defined separately, for example coverage of the full identified set. If an entry uses identification-indexed models instead of uniquely indexed laws, the same coverage convention is applied over those models. Pointwise limits do not establish uniform validity, and asymptotic validity does not guarantee finite-sample precision. Sample sizes, dependence structures and weak-identification sequences are part of each application.

Counterfactuals. $Y_i(a)$ is a potential outcome under a specified intervention, including its timing, implementation and versions. It is not $Y_i$ conditional on voluntarily choosing $a$. A full intervention vector permits interference; shorthand scalar treatment notation does not silently impose no interference. Assignment, selection, attrition, anticipation and measurement must be specified. A claim about an instrument's local effect is not automatically a population policy effect.

Economic equilibrium. A counterfactual model includes best responses, constraints, feasibility, market clearing, state transitions and expectations consistent with the stated information. When several equilibria exist, either a declared selector is an input or the target is set-valued. Comparisons across policy regimes must use the stated selection convention. Reduced-form relationships are not presumed invariant after an equilibrium-changing intervention.

Optimization and welfare. Optimization is over the stated feasible set. If attainment is not established, $\sup$ or $\inf$ and $\varepsilon$-optimal choices replace an asserted maximizer or minimizer. For example, with value $V=\sup_{a\in\mathcal A}W(a)<\infty$, an $\varepsilon$-optimal set is $\{a\in\mathcal A:W(a)\geq V-\varepsilon\}$ for $\varepsilon>0$. Benefits, costs, risk and health or environmental outcomes can be aggregated only using declared units and conversion weights. Interpersonal utility weights, the treatment of fiscal transfers and foreign profits, discounting, and the behavioral welfare criterion are explicit inputs. A comparative-static derivative additionally requires existence and appropriate differentiability of the selected counterfactual.

Sources. Local labels [S1], [S2], and so forth restart in every question. Locators identify the relevant abstract, model, section or result at the level actually checked; a bibliographic or abstract-level verification is not represented as inspection of an entire proof. Working papers are distinguished from later publications and changing versions. Source summaries are paraphrased. All URL checks and editorial formulations refer to the audit date stated above.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-535-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-535

Callback mechanisms and the selection of career outcomes

Problem ID: J71-531. Status: Unresolved. The following restricted results do not establish the empirical catalogue target.

The target has two levels

The canonical question fixes standardized applications, employer population and assignment rules, then asks for a mechanism-and-career identified set. Randomized identity cues identify differential treatment at the tested stage. They do not alone reveal whether employers hold different beliefs, attach different preferences to group membership, recruit through different networks, or respond differently to later outcomes. The correspondence design in Bertrand and Mullainathan [bm] provides the source context. This attempt gives exact observational equivalence, a restrictive experiment that breaks it, and a career-selection counterexample. It supplies no estimate of the actual mechanism shares.

Let $A\in\{0,1\}$ be an independently randomized cue and $B$ an evaluation regime. Randomize within measured application characteristics $X$, with known positive assignment probabilities and no cross-application interference. Consistency and randomization give \[ p_{ab}(x)={\mathbb{P}}(C=1\mid A=a,B=b,X=x) ={\mathbb{E}}[C(a,b,x)\mid X=x]. \tag{1} \] Thus the standardized callback contrast is $\Delta(b)=\int(p_{1b}-p_{0b})\,dG$. When the experiment's characteristic distribution differs from $G$, overlap and the relevant sampling or transport restriction are additionally needed. Multiple applications to one employer may interact through a fixed vacancy quota, invalidating the individual-level no-interference condition; employer-level assignments or an explicit joint application regime then define a different experiment.

A structural decomposition and its ambiguity

Fix $x$ and consider the following explicit employer model. The expected productive value of an applicant is $\mu_{ab}$, the taste cost attached to cue $a$ is $\tau a$, and the employer calls back when \[ \mu_{ab}-\tau a-k\ge\epsilon, \qquad {\mathbb{P}}(\epsilon\le z)=F(z), \tag{2} \] where $F$ is known and strictly increasing and $k$ is a common threshold. Assume the same taste cost and noise law in all regimes. For interior probabilities define the transformed difference \[ d_b=F^{-1}(p_{1b})-F^{-1}(p_{0b}). \] Equation (2) then yields \[ d_b=\delta_b-\tau,\qquad \delta_b=\mu_{1b}-\mu_{0b}. \tag{3} \] This is an index-scale statement: raw callback differences generally cannot be additively partitioned in the same way.
Proposition (Beliefs and tastes are observationally equivalent): In an ordinary regime $b=0$, if belief levels are unrestricted, every scalar $t$ is compatible with the observed callback probabilities through $\tau=t$, $\mu_{00}=k+F^{-1}(p_{00})$ and $\mu_{10}=k+F^{-1}(p_{10})+t$. Therefore only $\delta_0-\tau$ is identified by (2).
Proof: Substitute these values in (2). The cue-zero index is $F^{-1}(p_{00})$ and the cue-one index is $F^{-1}(p_{10})$ regardless of $t$. Both callback probabilities and the entire binary conditional response law are unchanged. If tastes or beliefs have known bounds, intersect this line with those bounds; point identification still requires that the intersection have one point. ∎

For a numerical index check, suppose $d_0=-0.4$. A pure-taste model $(\tau,\delta_0)=(0.4,0)$ and a pure-belief model $(0,-0.4)$ have identical transformed callback gaps. Levels can be chosen by the proposition so the whole observed callback law agrees. The models react differently to a policy that makes productive quality perfectly observable. This is a policy-relevant nonidentification result, not a statement that either mechanism is absent.

When an information factorial identifies the decomposition

Suppose regime $b=1$ reveals validated productive quality, employers understand and trust the revelation, and the distribution of revealed quality conditional on standardized $x$ is the same under either randomized cue. Impose the structural implication $\mu_{11}=\mu_{01}$, while keeping the taste cost, threshold and index-noise law unchanged across regimes. Then (3) gives the explicit solution \[ \tau=-d_1,\qquad \delta_0=d_0-d_1. \tag{4} \] The proof is substitution of $\delta_1=0$ followed by the ordinary-regime equation. For example $d_0=-0.4,d_1=-0.1$ implies taste cost $0.1$ and ordinary belief difference $-0.3$ in this model. If $d_1>0$ but maintained tastes require $\tau\ge0$, the restrictions are rejected rather than repaired by silently changing the interpretation.

The identifying content comes from the equal-beliefs and stability assumptions, not merely from adding another treatment arm. A certificate that is distrusted differently by cue need not make $\delta_1=0$. Quality revelation may change attention, scrutiny or social preferences, so a regime-specific taste $\tau_1$ cannot identify $\tau_0$ through (4). An unknown regime-specific noise scale also destroys the common index comparison. Belief elicitation offers additional observables only with a stated link from incentivized reports to the beliefs used in hiring. Blind evaluation can remove both a taste trigger and predictive information; its effect is not mechanically a taste estimate.

Networks are absent from (2). To identify network effects one would need a separate intervention on referral access or exposure and a model of how it alters the opportunity set. Reinterpreting $\delta_b$ as a network share would change the model after observing the data. The full catalogue set $\mathcal T(P)$ must retain such observationally compatible alternatives unless excluded by declared measurements or restrictions.

A selection reversal in career data

Consider a fixed baseline cohort with equal numbers of high- and low-productivity individuals. Their earnings if hired are respectively $2$ and $1$; nonhire earnings are zero. Policy $\pi_0$ hires everyone. Policy $\pi_1$ hires only the high-productivity half, with no change in any person's wage conditional on hiring. Then \[ {\mathbb{E}}[Y\mid\text{hired},\pi_0]=1.5,\qquad {\mathbb{E}}[Y\mid\text{hired},\pi_1]=2, \] but the unconditional cohort means are \[ {\mathbb{E}} Y(\pi_0)=1.5,\qquad {\mathbb{E}} Y(\pi_1)=1, \qquad \chi=-0.5. \tag{5} \] Thus an increase of $0.5$ in selected workers' average earnings coexists with an equally sized decrease in the correct cohort outcome. This example uses no wage discrimination at all: the reversal arises solely from selection into employment. Discounting a constant repetition of these outcomes multiplies both effects by the same positive annuity factor and preserves the reversal.

Moreover, callback-only data contain no restriction on future promotion, hours, separation or earnings beyond whatever structure is explicitly imposed. Two models can agree on every $p_{ab}(x)$ while assigning different future earnings under the career policy, producing different $\chi$. Following only successful applicants does not resolve this missing information. A randomized employer policy with baseline-cohort follow-up identifies its total career effect under assignment, interference and attrition restrictions; component effects still need feasible factorial interventions.

The remaining work is empirical and structural: specify credible quality signals, obtain comparable belief and career measurements, test the stability assumptions, and characterize the larger identified set allowing networks and accumulated disadvantage. The exact submodel inversion (4) and reversal (5) delimit what such data must add. They do not settle the multi-mechanism catalogue question.

Completion Estimate

50%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt identifies standardized callback contrasts, proves taste-belief observational equivalence, and derives a quality-revelation inversion under strict stability assumptions. Full mechanism and career policy sets still require validated cue interpretation, belief and network interventions, accumulated-history models, and unconditional baseline-cohort earnings follow-up.

References

  • [bm] M. Bertrand and S. Mullainathan (2004), Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination, American Economic Review 94(4), 991--1013. Primary publisher record. The cited experiment motivates the standardized callback target; the structural equivalence and numerical examples above are self-contained illustrations.

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