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Can Labor Markets Function in the Age of AI? The Evaluation Bottleneck in Hiring
Itai Ashlagi, Ramesh Johari, Jon Kleinberg, Anushka Murthy
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
Last extracted: 9/26/2026, 2:49:10 AM
Summary
This paper analyzes how AI-assisted job search tools create an 'evaluation bottleneck' in hiring markets. By lowering application costs but reducing the informativeness of application materials, AI forces firms to rely more heavily on coarse observables like prior experience. This disproportionately harms inexperienced but compatible applicants, leading to inefficient screening failures. The authors propose that multistage hiring processes, involving inexpensive intermediate assessments, can emerge as an endogenous solution to restore screening opportunities and preserve market functioning.
Entities (6)
Relation Signals (5)
AI-assisted job-search tools → reducesinformativenessof → application materials
confidence 95% · by making it easier for applicants to generate and tailor application materials, they can also reduce how informative those materials are about applicant fit.
AI-assisted job-search tools → increasesrelianceon → prior experience
confidence 94% · As application materials become less informative, a Bayesian firm rationally relies more heavily on coarse observables such as prior experience.
Inexperienced-compatible applicants → ismostharmedby → AI saturation
confidence 93% · inexperienced-compatible applicants are the most exposed: they lack observable experience and lose the individualized information that could distinguish them
Multistage hiring → mitigates → screening failures
confidence 92% · This can restore screening opportunities that disappear under one-stage hiring and give inexperienced-compatible applicants a path to screening.
Intermediate assessment → enables → acquisition of fit evidence
confidence 91% · a relatively inexpensive intermediate assessment allows firms to acquire new evidence of fit before costly full screening.
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Abstract
Abstract:AI-assisted job-search tools have become increasingly popular by making it easier to find and apply to jobs. But by making it easier for applicants to generate and tailor application materials, they can also reduce how informative those materials are about applicant fit. We study this tradeoff in a hiring market where applicants differ in experience and latent match quality and firms use noisy application materials to decide whom to screen. We ask how AI affects downstream screening and hiring, and which applicants are most adversely affected. As application materials become less informative, a Bayesian firm rationally relies more heavily on coarse observables such as prior experience. Among the four applicant types defined by experience and compatibility for the job, inexperienced-compatible applicants are the most exposed: they lack observable experience and lose the individualized information that could distinguish them from other inexperienced candidates. When screening is costly, these changes can also generate inefficient screening failures in which firms screen no applicants or screen only experienced applicants. We then show that multistage hiring can arise as an endogenous firm response: a relatively inexpensive intermediate assessment allows firms to acquire new evidence of fit before costly full screening. This can restore screening opportunities that disappear under one-stage hiring and give inexperienced-compatible applicants a path to screening. Our results show how AI can shift the central friction in hiring from submitting applications to obtaining credible evaluation, creating entry barriers for high-fit workers without prior experience. Multistage hiring can endogenously arise in response, restoring evaluation opportunities that would otherwise disappear and helping preserve market functioning.
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- Source: https://arxiv.org/abs/2609.30058v1
- Canonical: https://arxiv.org/abs/2609.30058v1
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Can Labor Markets Function in the Age of AI? The Evaluation Bottleneck in Hiring Preliminary Draft – Comments Welcome! Itai Ashlagi Ramesh Johari Jon Kleinberg Anushka Murthy September 24, 2026 Abstract AI-assisted job-search tools have become increasingly popular by making it easier to find and apply to jobs. But by making it easier for applicants to generate and tailor application materials, they can also reduce how informative those materials are about applicant fit. We study this tradeoff in a hiring market where applicants differ in experience and latent match quality and firms use noisy application materials to decide whom to screen. We ask how AI affects downstream screening and hiring, and which applicants are most adversely affected. As application materials become less informative, a Bayesian firm rationally relies more heavily on coarse observables such as prior experience. Among the four applicant types defined by experience and compatibility for the job, inexperienced-compatible applicants are the most exposed: they lack observable experience and lose the individualized information that could distinguish them from other inexperienced candidates. When screening is costly, these changes can also generate inefficient screening failures in which firms screen no applicants or screen only experienced applicants. We then show that multistage hiring can arise as an endogenous firm response: a relatively inexpensive intermediate assessment allows firms to acquire new evidence of fit before costly full screening. This can restore screening opportunities that disappear under one-stage hiring and give inexperienced-compatible applicants a path to screening. Our results show how AI can shift the central friction in hiring from submitting applications to obtaining credible evaluation, creating entry barriers for high-fit workers without prior experience. Multistage hiring can endogenously arise in response, restoring evaluation opportunities that would otherwise disappear and helping preserve market functioning. 1 Introduction There has been a proliferation of AI-assisted job-search tools. Applicants increasingly use AI systems to draft resumes and cover letters, tailor materials to specific vacancies, search across platforms, and submit applications at scale [46, 19]. Yet the experience of many job seekers and employers has not improved accordingly. Recent accounts describe applicants submitting large numbers of applications with little response, while firms report receiving growing volumes of increasingly similar and difficult-to-verify materials [36, 1, 45]. Critics have consequently warned that AI-mediated hiring may push firms toward relying on existing brand-name signals and referral networks rather than a more open and meritocratic labor market [17]. This concern is especially salient for new labor-market entrants: recent college graduates continue to face elevated unemployment and underemployment [25]. These developments point to a tension in AI-mediated job search. AI can make it easier for workers to enter an applicant pool without necessarily making it easier for firms to determine which applicants are good matches. Indeed, if widespread AI assistance makes written applications less individually informative, the central friction in hiring may shift from submitting an application to the provision and generation of credible, individualized evidence of fit. Recent evidence suggests that AI weakens applicant-generated signals. Galdin and Silbert [28] find that customized applications predicted hiring before the introduction of large language models but became less valuable afterward; eliminating the signaling value of written applications can make hiring substantially less meritocratic. Studying the rollout of an AI-assisted cover-letter tool, Cui et al. [22] find that AI increased tailoring and callbacks but reduced tailoring’s predictive content, shifting employers to rely more heavily on past work history and potentially disadvantaging new workers. More generally, Cowgill et al. [20] show that sender-side access to generative AI reduces screening accuracy on average, although its effects depend on how AI changes the relative informativeness of experts’ and non-experts’ messages. Together, these studies suggest that AI can weaken applicant-generated signals and shift the evidence firms use for screening. This paper develops a model of how such a change in the information structure affects access to screening and hiring. While a large literature studies the effects of automation and AI on tasks, productivity, wages, employment, and vacancy creation [11, 12, 2, 3, 51, 26, 15], we focus on job search and screening. We consider a firm with a vacancy and heterogeneous potential applicants. Greater AI saturation lowers applicants’ costs of applying, reduces the informativeness of application materials, and raises the firm’s effective cost of identifying compatible candidates. Applicants differ in observable experience and latent match quality. The firm observes experience and noisy application materials, forms Bayesian posterior beliefs about compatibility, and chooses whom to screen. Our first set of results shows how degrading individualized information can create an entry barrier for compatible workers without prior experience. As application materials become noisier, the firm places less weight on applicant-specific evidence and more on experience-based priors. Inexperienced applicants therefore need stronger favorable evidence to overcome experienced applicants’ prior advantage. This mechanism is analogous to classic models of statistical discrimination [44, 4], but with respect to applicant experience. This reweighting is privately rational but disproportionately harms inexperienced-compatible candidates. As individualized signals deteriorate they lose the evidence that could offset the lower prior associated with inexperience. As a result, increasing AI saturation can harm labor-market entry even for workers who are good matches. We then show that private screening can be inefficient. The firm screens applicants only when the expected private value of doing so exceeds the screening cost, but it does not internalize the worker’s surplus from a successful match. This creates a gap between the firm’s privately optimal screening cutoff and the socially efficient screening cutoff, resulting in some applicants who are worth screening being rejected. We characterize two resulting market failures: one in which the firm screens no applicant even though a social planner would screen at least one, and another in which the firm excludes all submitted inexperienced-compatible applicants even though screening at least one of them would increase expected total surplus. As application materials become uninformative, applicants’ posterior compatibility converges toward their experience-group priors. These failures can therefore arise systematically: screening either shuts down or continues only for experienced applicants while excluding inexperienced-compatible candidates. Finally, we study whether a multistage hiring process can mitigate these failures. Rather than making hiring decisions entirely from increasingly noisy application materials, firms may create lower-stakes opportunities for applicants to generate additional credible evidence of fit. In our model, this takes the form of a relatively inexpensive intermediate assessment, such as a work-sample task, live skill test, or structured preliminary interview, which allows the firm to acquire additional applicant-specific information before undertaking costly full evaluation. More broadly, internships, predoctoral positions, and other temporary or probationary roles may serve a related function by allowing workers—particularly those with limited prior experience—to demonstrate their match quality through performance. We characterize an intermediate-assessment region consisting of applicants whose posterior compatibility is too low to justify immediate full screening but high enough that acquiring an additional signal is valuable. These applicants are rejected under one-stage hiring but can advance under multistage hiring after a favorable intermediate assessment. When this region is nonempty, the firm strictly prefers a multistage hiring process, which can avoid the screening failures that occur under one-stage hiring. It also gives inexperienced-compatible applicants who would otherwise be rejected a positive-probability path to screening and hiring. At high levels of AI saturation, this benefit extends to nearly all submitted inexperienced-compatible applicants. Taken together, our results explain why easier application need not improve job access or welfare. As applicant-generated materials become less informative, firms rely more on experience-based priors and allocate costly evaluation more selectively, disproportionately harming inexperienced-compatible applicants. Nevertheless, we find a hopeful feasible path forward: we show that multistage hiring emerges as a privately beneficial firm response that creates a new channel for credible, individualized evidence, and gives inexperienced workers an opportunity to demonstrate fit before firms rely on coarse experience-based priors. 2 Related Literature Our paper connects three streams of research: AI, signaling, and screening in labor markets; directed and sequential search; and statistical discrimination and talent discovery. AI and labor-market signaling. We build on classic models of signaling, screening, and cheap talk [47, 49, 21, 24]. Recent evidence shows that generative AI can weaken applicant-generated signals and change the information employers use [28, 22, 20]. We study how this deterioration affects access to costly individualized screening and whether multistage evaluation can mitigate the resulting screening failures. Closest to our work, Jungbauer [35] studies how AI-induced deterioration in initial-stage screening signals disrupts assortative matching. Jungbauer also shows that the optimal redesign of a common screening signal need not restore pre-AI levels of informativeness. In contrast, we study how degraded initial information affects access to costly individualized evaluation across experience groups, and how multistage hiring processes can adapt when initial applicant signals become less informative. Directed and sequential search Our model also relates to work on directed search, decentralized matching, and sequential information acquisition. Classic job-search models study costly search under uncertainty [39], while directed and competitive search models study decentralized markets in which workers direct applications based on observable opportunities and expected competition [43, 40, 16, 53, 5, 29]. Related work on online labor markets shows how application costs, congestion, and screening frictions shape applicant and employer behavior [8, 31, 30, 27, 23]. Most closely, Arnosti et al. [8] study a decentralized market in which applicants pay to apply and employers pay to screen. We focus on an additional information friction: the signals firms use to decide whom to screen can themselves become less informative. The firm’s problem also has a sequential-search interpretation. Our one-stage baseline specializes Weitzman [52] to hiring: the firm orders applicants by posterior compatibility and inspects them until it finds an acceptable candidate or further inspection is not worthwhile. The multistage model allows partial information acquisition before full screening, connecting to sequential inspection problems such as Aouad et al. [7] and to hiring models with intermediate assessments or interviews [34, 37, 10, 33]. We study how the value of this sequential evaluation changes as applicant-generated information deteriorates and experience generates heterogeneous prior beliefs about fit. Statistical discrimination and entry barriers Our entry-barrier results are closely related to statistical discrimination. When firms observe noisy individual signals, they may rationally condition decisions on observable characteristics correlated with expected productivity [44, 9, 4]. In our setting, experience plays this role: as applicant-generated materials become less informative, the firm places greater weight on experience-group priors. High-fit inexperienced applicants are especially harmed because they lose the applicant-specific information that could distinguish them from lower-fit workers in the same group. Related employer-learning models study how firms initially rely on observable characteristics and update as better information arrives [6]. We instead study whether applicants receive the costly information acquisition needed to overcome an unfavorable prior. This connects to work on inefficient talent discovery and certification in entry-level labor markets [42, 48, 50, 38]. Although our baseline is static, reduced access to interviews and jobs may also limit inexperienced workers’ ability to accumulate the experience firms increasingly rely on, potentially reinforcing initial disparities [18, 41, 13]. Related to us, Hu and Chen [32] show that temporary two-stage hiring can shift a market toward a more equitable long-run equilibrium; our multistage process instead generates additional applicant-specific information before full screening. 3 Model We study a firm with one vacancy and n>1n>1 potential applicants. AI saturation is modeled by an exogenous parameter q∈[0,1)q∈[0,1), which affects three screening and application primitives described below: the application-cost scale ca(q)c_a(q), the variance σm2(q) _m^2(q) of the noise in the application-materials signal mim_i, and the effective firm screening cost cs(q)c_s(q). Environment and payoffs. If the firm hires a compatible applicant, the firm receives payoff vF>0v_F>0. The hired applicant receives payoff vA>0v_A>0. We interpret vFv_F and vAv_A as the respective gains to the firm and applicant from a compatible match, relative to their outside options, so total surplus from a compatible match is vF+vAv_F+v_A. If no hire occurs, no match surplus is generated; applicants still bear any application costs they have incurred, and the firm still bears any screening costs it has incurred. Applicants. Applicant i has observable experience ei∈0,1,e_i∈\0,1\, where ei=1e_i=1 denotes experienced and ei=0e_i=0 denotes inexperienced. Let λe=Pr(ei=e),λ0+λ1=1. _e= (e_i=e), _0+ _1=1. Applicant i also has latent match quality zi∈ℝz_i . Match quality is not observed by the firm before screening. Applicant compatibility is given by ki=zi≥0.k_i=1\z_i≥ 0\. The firm seeks to hire an applicant with ki=1k_i=1. We refer to the pair (ei,ki)∈0,12(e_i,k_i)∈\0,1\^2 as applicant i’s realized type. Thus (1,1)(1,1) denotes an experienced-compatible applicant, (1,0)(1,0) an experienced-incompatible applicant, (0,1)(0,1) an inexperienced-compatible applicant, and (0,0)(0,0) an inexperienced-incompatible applicant. Priors and application materials. Conditional on experience, zi∣ei=e∼(μe,σz2),e∈0,1,z_i e_i=e ( _e, _z^2), e∈\0,1\, (1) with μ1>μ0>0 _1> _0>0. Thus experienced applicants have higher expected match quality. Conditional on applying, applicant i generates a materials signal mi=zi+εi,εi∼(0,σm2(q)).m_i=z_i+ _i, _i (0, _m^2(q)). (2) Application decisions. Applicant i observes her experience eie_i and application cost ca(q)ηic_a(q) _i before applying, but does not observe ziz_i. Let di∈0,1d_i∈\0,1\ denote applicant i’s application decision. If she applies, she pays ca(q)ηi.c_a(q) _i. The cost scalings ηi _i are nonnegative, with ηi|ei=e _i e_i=e having CDF FeF_e on ℝ+R_+, and capture idiosyncratic differences in the time, effort, or opportunity costs applicants face when preparing and submitting an application. We assume these scalings are independent of match quality and application signal noise conditional on experience. Let αe(q):=Pr(di=1∣ei=e) _e(q):= (d_i=1 e_i=e) denote the equilibrium group-specific application rate. Given application rates (a0,a1)(a_0,a_1), let Ve(q,a0,a1):=vAPr(hired∣ei=e,di=1;q,a0,a1)V_e(q;a_0,a_1):=v_A (hired e_i=e,d_i=1;q,a_0,a_1) denote the expected value of applying for an applicant from experience group e. An applicant with experience e applies if and only if Ve(q,a0,a1)≥ca(q)ηi.V_e(q;a_0,a_1)≥ c_a(q) _i. Thus, when ca(q)>0c_a(q)>0, equilibrium application rates satisfy αe(q)=Fe(Ve(q,α0(q),α1(q))ca(q)). _e(q)=F_e\! ( V_e(q; _0(q), _1(q))c_a(q) ). When ca(q)=0c_a(q)=0, we choose a tie-breaking convention that selects αe(q)=1. _e(q)=1. Firm screening technology. The firm observes (ei,mi)(e_i,m_i) for each submitted application. Screening applicant i costs cs(q)c_s(q) and reveals ziz_i perfectly. The firm must screen an applicant before hiring them. Let pi=Pr(ki=1∣mi,ei)p_i= (k_i=1 m_i,e_i) denote applicant i’s posterior compatibility. Assumptions. We complete the model specification by describing how AI saturation affects the key primitives, and by imposing a regularity condition that ensures positive participation by both experience groups. The following assumption captures the idea that as AI tools become more prevalent, submitted materials become less individually informative about latent match quality. Assumption 3.1 (AI saturation lowers signal informativeness). The signal-noise variance σm2(q) _m^2(q) is strictly increasing in q. The next assumption captures the contrasting effects of AI on costs faced by the two sides of the market. AI tools can reduce the time and effort required to generate applications, lowering applicants’ effective cost of applying. At the same time, AI may increase the firm’s effective cost of identifying compatible applicants, for example because AI-generated application materials can become more homogeneous or less informative. Assumption 3.2 (AI saturation lowers application costs and raises effective screening costs). The application-cost scale ca(q)c_a(q) is strictly decreasing in q, and the effective screening cost cs(q)c_s(q) is strictly increasing in q. The final assumption on the distribution of experience groups and application costs ensures that both experience groups apply with positive probability; we expand more on this at the end of Section 4. Assumption 3.3 (Positive participation assumptions). Both experience groups occur with positive probability, λe>0,e∈0,1, _e>0, e∈\0,1\, and zero lies in the support of each experience-specific application-cost distribution: Fe(x)>0for every x>0,e∈0,1.F_e(x)>0 every x>0,\ e∈\0,1\. Timing. The timing is as follows. First, for each applicant i, their experience eie_i, latent match quality ziz_i, and application cost scaling ηi _i are sampled, independently across applicants. Applicants observe (ei,ηi)(e_i, _i) but do not observe ziz_i. Second, applicants decide whether to apply. Applicants who apply pay ca(q)ηic_a(q) _i. Third, submitted applications generate materials signals mim_i, and the firm observes (ei,mi)(e_i,m_i) for each applicant in the realized pool of applications. Fourth, the firm forms posterior compatibility beliefs pi=Pr(ki=1∣mi,ei)p_i= (k_i=1 m_i,e_i) and chooses whom to screen. Screening costs cs(q)c_s(q) per applicant and reveals ziz_i. The firm hires the first compatible applicant it screens, if any, and applicant and firm values are realized. 4 Bayesian Reweighting and Firm Screening In this section, we characterize how AI saturation changes the firm’s posterior beliefs and optimal one-stage screening decisions. Posterior beliefs and Bayesian reweighting. Among submitted applicants, the firm updates from the experience-group prior in Equation (1) using the materials signal in Equation (2). Let Δμ:=μ1−μ0>0 _μ:= _1- _0>0 denote the experience-group prior difference. Define κ(q):=σz2σz2+σm2(q)κ(q):= _z^2 _z^2+ _m^2(q) and σpost2(q):=σz2σm2(q)σz2+σm2(q). _post^2(q):= _z^2 _m^2(q) _z^2+ _m^2(q). For each applicant, define the posterior-mean score Si(q):=[zi∣mi,ei;q].S_i(q):=E[z_i m_i,e_i;q]. Finally, let θ(q):=(1−κ(q))Δμ.θ(q):=(1-κ(q)) _μ. The following result describes how the firm updates their posterior after receiving an application. Proposition 4.1 (Bayesian reweighting toward experience). Fix q with σm2(q)>0 _m^2(q)>0. Conditional on a given level of AI saturation and applicant i’s materials mim_i and experience eie_i, the firm assigns them a posterior compatibility probability given by: pi(q)=Φ(Si(q)σpost(q)),p_i(q)= ( S_i(q) _post(q) ), where Si(q)=κ(q)mi+(1−κ(q))μei=(1−κ(q))μ0+θ(q)ei+κ(q)mi.S_i(q)=κ(q)m_i+(1-κ(q)) _e_i=(1-κ(q)) _0+θ(q)e_i+κ(q)m_i. For any submitted applicants i and j, pi(q)≥pj(q)⟺Si(q)≥Sj(q).p_i(q)≥ p_j(q) S_i(q)≥ S_j(q). Under Assumption 3.1, for any q~>q q>q, κ(q~)<κ(q),θ(q~)>θ(q),κ( q)<κ(q), θ( q)>θ(q), and θ(q)κ(q)=Δμσm2(q)σz2 θ(q)κ(q)= _μ\, _m^2(q) _z^2 is strictly increasing in q. The proposition formalizes the statistical-discrimination mechanism. As application materials become noisier, the firm’s Bayes-optimal response is to place less weight on the applicant-specific materials signal and more weight on the applicant’s prior experience. Equivalently, the amount of materials evidence required to offset the prior difference between experienced and inexperienced applicants increases with AI saturation. Optimal one-stage screening. Suppose the firm receives M submitted applications and observes posterior compatibilities for each applicant in the realized pool. Relabel the submitted applicants so that p1(q)≥p2(q)≥⋯≥pM(q).p_1(q)≥ p_2(q)≥·s≥ p_M(q). Define the firm’s private screening cutoff by pF(q):=cs(q)vF.p^F(q):= c_s(q)v_F. The following proposition characterizes the firm’s optimal one-stage screening rule.11 1 This problem is a binary-payoff special case of Weitzman’s Pandora problem; see [52]. Each applicant is a “box,” screening is inspection, and the hidden payoff is vFkiv_Fk_i. To remain self-contained, we give a direct proof of the optimal screening rule. Proposition 4.2 (Optimal one-stage screening rule). Fix q and a realized applicant pool. Suppose vF>0v_F>0 and consider pF(q):=cs(q)vF∈(0,1)p^F(q):= c_s(q)v_F∈(0,1). The firm’s optimal screening policy is to order applicants by decreasing posterior compatibility and screen them sequentially until either a compatible applicant is found or no remaining applicant satisfies pi(q)≥pF(q).p_i(q)≥ p^F(q). Equivalently, the firm’s screening list consists of applicants whose posterior compatibility satisfies pi(q)≥pF(q)=cs(q)vF.p_i(q)≥ p^F(q)= c_s(q)v_F. Under Assumption 3.2, for every q~>q q>q, pF(q~)>pF(q).p^F( q)>p^F(q). The result follows from comparing the marginal value of screening the next applicant to the marginal screening cost. Conditional on reaching applicant n, screening is profitable exactly when vFpn≥cs(q).v_Fp_n≥ c_s(q). Thus the posterior compatibility cutoff is given by pF(q)=cs(q)vF.p^F(q)= c_s(q)v_F. Proposition 4.2 implies that the firm can equivalently use a score cutoff. Since pi=Φ(Si(q)σpost(q))p_i= ( S_i(q) _post(q) ) and Φ is strictly increasing, the posterior cutoff pi≥pF(q)p_i≥ p^F(q) is equivalent to Si(q)≥sF(q),S_i(q)≥ s^F(q), where sF(q):=σpost(q)Φ−1(pF(q)).s^F(q):= _post(q) ^-1 (p^F(q) ). Thus the firm may equivalently rank applicants by their posterior-mean scores and include applicant i in its screening list if and only if Si(q)≥sF(q)S_i(q)≥ s^F(q). Positive application rates. We end this section by noting that the results in the following sections require only that applicants from both experience groups submit applications with positive probability. Assumption 3.3 ensures that this occurs for any q such that pF(q)∈(0,1)p^F(q)∈(0,1). Because the Gaussian materials signal has full support, an applicant from either experience group has positive probability of being compatible and drawing materials that place their posterior above pF(q)p^F(q). There is also positive probability that every other potential applicant is incompatible. Hence Ve(q,α0,α1)>0,e∈0,1,V_e(q; _0, _1)>0, e∈\0,1\, and therefore αe(q)>0,e∈0,1. _e(q)>0, e∈\0,1\. 5 Impact on Workforce Entry and Market Failure Section 4 shows that noisier application materials shift the firm toward experience-based priors and change its screening decisions. We now show that the effects of this reweighting are uneven across the applicant pool: inexperienced-compatible applicants are especially exposed, and sufficiently high AI saturation can generate screening failures in which the firm forgoes screening anyone or screens only experienced candidates. 5.1 Shortlisting Exposure Recall that applicants have realized types (e,k)∈0,12,(e,k)∈\0,1\^2, where e denotes experience and k denotes compatibility. Although compatibility is observed only after screening, conditioning on realized compatibility allows us to identify which types are helped or harmed by the firm’s Bayes-optimal scoring rule. By Proposition 4.1, the firm’s posterior-mean score is Si(q)=[zi∣mi,ei;q]=κ(q)mi+(1−κ(q))μei.S_i(q)=E[z_i m_i,e_i;q]=κ(q)m_i+(1-κ(q)) _e_i. Higher AI saturation lowers κ(q)κ(q), so the firm places less weight on application materials and more weight on experience. We first study how this reweighting changes the average score of each realized type. We then study how higher AI saturation affects the probability that an applicant clears the firm’s posterior screening threshold. Conditional mean score. For applicants who apply, define the conditional mean score of type (e,k)(e,k) by S¯ek(q):=[Si(q)∣ei=e,ki=k,di=1]. S_ek(q):=E[S_i(q) e_i=e,\ k_i=k,\ d_i=1]. Because applicants do not observe ziz_i before applying and the application costs are independent of match quality conditional on experience, conditioning on application does not change the distribution of ziz_i within an experience group. Hence, S¯ek(q)=κ(q)μek+(1−κ(q))μe, S_ek(q)=κ(q) _ek+(1-κ(q)) _e, where μek:=[zi∣ei=e,ki=k]. _ek:=E[z_i e_i=e,k_i=k]. For AI saturation levels q,q~q, q, let ΔS¯ek(q,q~):=S¯ek(q~)−S¯ek(q) S_ek(q, q):= S_ek( q)- S_ek(q) denote the change in conditional mean score. Proposition 5.1 (Conditional mean score effects). Consider AI saturation levels q<q~q< q. Under Assumption 3.1, ΔS¯ek(q,q~)=[κ(q~)−κ(q)](μek−μe). S_ek(q, q)= [κ( q)-κ(q) ] ( _ek- _e ). Moreover, ΔS¯01(q,q~)<ΔS¯11(q,q~)<0<ΔS¯00(q,q~)<ΔS¯10(q,q~). S_01(q, q)< S_11(q, q)<0< S_00(q, q)< S_10(q, q). Proposition 5.1 shows that among the four realized types, inexperienced-compatible applicants face the largest negative change in their conditional mean score. In particular, Bayesian reweighting toward experience creates an entry barrier for new but high-fit candidates. The intuition behind the result is that conditional on experience, compatible applicants have above-average match quality: μe1>μe _e1> _e. As κ(q)κ(q) falls, their favorable individualized information receives less weight, so their conditional mean scores fall. Incompatible applicants have below-average match quality so reducing the weight on individualized information raises their mean posterior scores. Within the pool of compatible applicants, inexperienced-compatible applicants experience a greater decrease than experienced-compatible applicants because their experience-group prior has a lower mean. In other words, they don’t have pre-existing experience to compensate for the decreased weight given to their application materials. Probability of clearing the screening threshold. The mean-score result captures how AI saturation shifts the average position of each realized type in the firm’s screening score. However, inclusion in the firm’s screening list is instead a threshold event: applicant i is included only if pi(q)≥pF(q).p_i(q)≥ p^F(q). We therefore next study the probability that a type-(e,k)(e,k) applicant clears the shortlisting score threshold. To separate the effect of declining signal informativeness from movement in the firm’s screening threshold, we study the standardized match quality and application materials across experience groups. Fix an experience group e and define Xi:=zi−μeσz,Yi(q):=mi−μeσz2+σm2(q).X_i:= z_i- _e _z, Y_i(q):= m_i- _e _z^2+ _m^2(q). Conditional on ei=e_i=e, both variables are standard normal, with correlation r(q):=σzσz2+σm2(q).r(q):= _z _z^2+ _m^2(q). Thus r(q)r(q) summarizes how informative application materials are about match quality. Under Assumption 3.1, r(q)r(q) is strictly decreasing in q. Compatibility is equivalent to Xi≥ae,ae:=−μeσz.X_i≥ a_e, a_e:=- _e _z. Since μ1>μ0 _1> _0, we have a1<a0a_1<a_0. The firm’s screening cutoff can also be expressed in units of the standardized materials signal. Since Si(q)=μe+σzr(q)Yi(q),S_i(q)= _e+ _zr(q)Y_i(q), and pi(q)=Φ(Si(q)σpost(q)),p_i(q)= ( S_i(q) _post(q) ), the condition pi(q)≥pF(q)p_i(q)≥ p^F(q) is equivalent to Yi(q)≥be(q),Y_i(q)≥ b_e(q), where be(q):=σpost(q)Φ−1(pF(q))−μeσzr(q).b_e(q):= _post(q) ^-1 (p^F(q) )- _e _zr(q). Thus be(q)b_e(q) is the number of within-group standard deviations by which an applicant’s materials must exceed their experience-group mean to enter the firm’s screening list. For b∈ℝb and r∈(0,1)r∈(0,1), let (X,Y)(X,Y) be a standard bivariate normal pair with correlation r, and define ψe1(b,r):=Pr(Y≥b∣X≥ae), _e1(b,r):= (Y≥ b X≥ a_e), and ψe0(b,r):=Pr(Y≥b∣X<ae). _e0(b,r):= (Y≥ b X<a_e). The screening-list inclusion probability of a submitted type-(e,k)(e,k) applicant is therefore Pr(pi(q)≥pF(q)∣ei=e,ki=k,di=1)=ψek(be(q),r(q)). (p_i(q)≥ p^F(q) e_i=e,\ k_i=k,\ d_i=1 )= _ek (b_e(q),r(q) ). Proposition 5.2 (Signal informativeness and relative experience thresholds). Suppose pF(q)∈(0,1)p^F(q)∈(0,1), σm2(q)>0 _m^2(q)>0, and σm2(q) _m^2(q) is differentiable with dσm2(q)dq>0. d _m^2(q)dq>0. For each e∈0,1e∈\0,1\, b∈ℝb , and r∈(0,1)r∈(0,1), ∂ψe1(b,r)∂r>0,∂ψe0(b,r)∂r<0. ∂ _e1(b,r)∂ r>0, ∂ _e0(b,r)∂ r<0. Moreover, b0(q)−b1(q)=Δμσzr(q),b_0(q)-b_1(q)= _μ _zr(q), and hence dq[b0(q)−b1(q)]=−Δμr′(q)σzr(q)2>0. ddq [b_0(q)-b_1(q) ]=- _μr (q) _zr(q)^2>0. The first part of Proposition 5.2 isolates the effect of increased AI saturation on threshold clearing probability through changing signal informativeness while holding the standardized screening threshold fixed. Because increasing AI saturation reduces signal informativeness, i.e., r′(q)<0r (q)<0, noisier application materials reduce the probability that a compatible applicant clears a fixed threshold and increase this probability for an incompatible applicant. The second part identifies how AI saturation affects the threshold clearing probability by changing the relative experience-group thresholds. The standardized threshold for inexperienced applicants is higher compared to experienced applicants, and this difference grows as application materials become less informative. Inexperienced-compatible applicants are therefore the only group on the adverse side of both of these mechanisms: compatibility makes them vulnerable to the decline in signal informativeness, while inexperience requires them to clear a higher relative screening threshold compared to experienced applicants. 5.2 Market Failure The preceding results show that inexperienced-compatible applicants are especially exposed to the loss of individualized information at the shortlisting stage. We now show that the firm’s privately optimal screening decision can also be socially inefficient. The source of inefficiency is that the firm does not internalize the worker’s surplus from a successful match. The firm receives value vFv_F from hiring a compatible applicant, while total surplus from a compatible match is vF+vAv_F+v_A. Recall from Proposition 4.2 that the firm’s private screening cutoff is pF(q)=cs(q)vF.p^F(q)= c_s(q)v_F. Define the following screening cutoff; in the next proposition, we show it is the cutoff a social planner would use: pP(q):=cs(q)vF+vA.p^P(q):= c_s(q)v_F+v_A. We suppose throughout this subsection that vF>0v_F>0, vA>0v_A>0, and pF(q)∈(0,1)p^F(q)∈(0,1). Then it follows that 0<pP(q)<pF(q)<1.0<p^P(q)<p^F(q)<1. Proposition 5.3 (Firm and social planner screening cutoffs). Fix q and a realized applicant pool. The social planner’s optimal screening rule is to order applicants by decreasing posterior compatibility and include applicant i in the screening list if and only if pi(q)≥pP(q).p_i(q)≥ p^P(q). Consequently, applicant i is included in the planner’s screening list but not the firm’s screening list if and only if pP(q)≤pi(q)<pF(q).p^P(q)≤ p_i(q)<p^F(q). The difference between the private and social screening cutoffs is pF(q)−pP(q)=vAcs(q)vF(vF+vA)>0.p^F(q)-p^P(q)= v_Ac_s(q)v_F(v_F+v_A)>0. Thus the preceding shows that there is a nonempty range of applicants whom the planner would screen but the firm would reject. Under Assumption 3.2, the gap between the private and social screening cutoffs increases with AI saturation: dq[pF(q)−pP(q)]=vAcs′(q)vF(vF+vA)>0. ddq [p^F(q)-p^P(q) ]= v_Ac_s (q)v_F(v_F+v_A)>0. Higher effective screening costs therefore expand the range of posterior compatibilities for which screening is socially valuable but privately unprofitable. Two screening-failure events. We first characterize two screening-failure events conditional on the firm’s realized pool of submitted applications. We eventually show that these screening-failure events occur with probability approaching one in the high-AI limit. Let (q)A(q) denote the submitted applicant pool. When (q)A(q) is nonempty, define pmax(q):=maxi∈(q)pi(q).p (q):= _i (q)p_i(q). This is the highest posterior compatibility among submitted applications. Proposition 5.4 (No-hire screening failure). Suppose (q)A(q) is nonempty and pP(q)<pmax(q)<pF(q).p^P(q)<p (q)<p^F(q). Then the firm’s screening list is empty, while the social planner’s screening list is nonempty. Under the conditions of this result, the firm screens no applicants since pmax(q)<pF(q)p (q)<p^F(q) and hence makes no hire. However, a social planner would screen at least the applicant with posterior compatibility pmax(q)p (q) and would hire that applicant if they are compatible. Thus the firm does not screen anyone even though screening and potential hiring would increase expected total surplus. A more targeted failure occurs when the firm excludes all inexperienced-compatible applicants from screening even though at least one such applicant is socially worth screening. Let 01(q):=i∈(q):ei=0,ki=1A_01(q):= \i (q):e_i=0,\ k_i=1 \ denote the set of submitted inexperienced-compatible applicants. When 01(q)A_01(q) is nonempty, let p01max(q):=maxi∈01(q)pi(q)p_01 (q):= _i _01(q)p_i(q) be the highest posterior compatibility across the inexperienced-compatible applicants. Proposition 5.5 (Inexperienced-compatible screening failure). Suppose 01(q)A_01(q) is nonempty and pP(q)<p01max(q)<pF(q).p^P(q)<p_01 (q)<p^F(q). Then no inexperienced-compatible applicant is included in the firm’s screening list, while at least one inexperienced-compatible applicant is included in the social planner’s screening list. Under the conditions of Proposition 5.5, inexperienced-compatible candidates can therefore be fully excluded from screening even though screening and potentially hiring an inexperienced-compatible candidate would increase expected total surplus. The preceding two propositions characterize the conditions under which the two screening failures occur. On their own, however, these fixed-pool conditions do not imply that the failures are systematically likely to arise. We therefore turn next to the high-AI limit, where we show that the same failure events can occur with probability approaching one as individualized information disappears. Screening failures in the high-AI limit. We now turn to the central result of this subsection. Although the preceding propositions characterize when the two failures occur for a realized pool, the high-AI limit shows that these failures can occur with probability approaching one. As application materials lose their informativeness, applicants’ posterior compatibility probabilities collapse toward their experience-group priors. Screening therefore increasingly depends on coarse group-level information rather than applicants’ realized compatibility, allowing the private and social screening thresholds to generate persistent screening failures. For each experience group, define the prior compatibility probability πe:=Pr(ki=1∣ei=e)=Φ(μeσz). _e:= (k_i=1 e_i=e)= ( _e _z ). Because μ1>μ0 _1> _0, π1>π0 _1> _0. Consider a sequence qn\q_n\ such that σm2(qn)→∞ _m^2(q_n)→∞ and pF(qn)→p∞F∈(0,1).p^F(q_n)→ p_∞^F∈(0,1). Since pP(q)=vFvF+vApF(q),p^P(q)= v_Fv_F+v_Ap^F(q), the social cutoff converges to p∞P:=vFvF+vAp∞F,p_∞^P:= v_Fv_F+v_Ap_∞^F, where 0<p∞P<p∞F<10<p_∞^P<p_∞^F<1. The following lemma shows that when application materials become uninformative, individual posterior compatibility converges to the prior associated with the applicant’s experience group. Lemma 5.6 (High-noise posterior pooling). For any fixed submitted applicant with realized type (e,k)(e,k), pi(qn)→πep_i(q_n)→ _e in probability, conditional on ei=e,ki=k,di=1.e_i=e, k_i=k, d_i=1. Consequently, for any fixed finite submitted pool ℬB, maxi∈ℬ|pi(qn)−πei|→0 _i |p_i(q_n)- _e_i |→ 0 in probability, conditional on the realized types in ℬB. Note that the convergence in the above lemma holds even after conditioning on an applicant’s realized compatibility: the firm cannot recover that compatibility from increasingly noisy materials. Now fix a finite submitted pool ℬB, viewed as given at the screening stage, and condition on its realized applicant types. Define πℬmax:=maxi∈ℬπei. _B := _i _e_i. Also define ℬ01:=i∈ℬ:ei=0,ki=1,ℬ1:=i∈ℬ:ei=1.B_01:= \i :e_i=0,\ k_i=1 \, _1:= \i :e_i=1 \. Corollary 5.7 (High-noise screening failures). The following statements hold along the sequence qn\q_n\. 1. If p∞P<πℬmax<p∞Fp_∞^P< _B <p_∞^F, then Pr(pP(qn)<maxi∈ℬpi(qn)<pF(qn))→1. (p^P(q_n)< _i p_i(q_n)<p^F(q_n) )→ 1. 2. Suppose ℬ01B_01 is nonempty. If p∞P<π0<p∞Fp_∞^P< _0<p_∞^F, then Pr(pP(qn)<mini∈ℬ01pi(qn)≤maxi∈ℬ01pi(qn)<pF(qn))→1. (p^P(q_n)< _i _01p_i(q_n)≤ _i _01p_i(q_n)<p^F(q_n) )→ 1. If, in addition, ℬ1B_1 is nonempty and p∞F<π1p_∞^F< _1, then Pr(mini∈ℬ1pi(qn)>pF(qn)>maxi∈ℬ01pi(qn))→1. ( _i _1p_i(q_n)>p^F(q_n)> _i _01p_i(q_n) )→ 1. Part (i) implies that, conditional on the submitted pool ℬB, the no-hire screening failure in Proposition 5.4 occurs with probability approaching one. Part (i) implies that every submitted inexperienced-compatible applicant lies below the firm’s cutoff but above the social cutoff with probability approaching one. Thus the inexperienced-compatible screening failure in Proposition 5.5 occurs with probability approaching one. Under the additional condition π0<p∞F<π1, _0<p_∞^F< _1, the firm continues to include experienced applicants in its screening list while excluding all submitted inexperienced-compatible applicants. The limiting outcome is therefore a screening failure concentrated on inexperienced candidates rather than a complete shutdown of screening. Taken together, these results show that the screening failures identified above can arise with probability approaching one as AI saturation grows. As application materials become uninformative, the firm can no longer distinguish compatible from incompatible applicants within an experience group, and posterior beliefs collapse toward group-level priors. The hiring process is therefore governed increasingly by observable experience rather than realized compatibility. Depending on the location of the experience-group priors relative to the private and social screening cutoffs, this produces either a complete shutdown of privately provided screening or continued screening of experienced applicants alongside the systematic exclusion of inexperienced-compatible applicants. 6 Multistage Hiring as a Response to AI-Induced Entry Barriers The preceding section shows that AI saturation can raise entry barriers by making written application materials less informative and full screening more expensive. This section studies a firm response: adding a cheaper intermediate assessment before costly full screening. Examples include live skill tests, work-sample exercises, or other verifiable tasks that are harder for AI-generated application materials to mimic. We show that the firm strictly benefits from adding an intermediate screening stage and that doing so can restore hiring opportunities for inexperienced-compatible applicants who are disadvantaged by degraded initial signals. These benefits become especially strong as AI saturation grows. 6.1 Multistage Screening After observing (mi,ei)(m_i,e_i) and forming the baseline posterior pi(q):=Pr(ki=1∣mi,ei;q),p_i(q):= (k_i=1 m_i,e_i;q), the firm may pay an intermediate-assessment cost cℓ(q)∈[0,cs(q))c_ (q)∈[0,c_s(q)) to observe an additional signal aia_i. After observing this signal, the firm’s posterior compatibility belief is p~i(q):=Pr(ki=1∣mi,ei,ai;q). p_i(q):= (k_i=1 m_i,e_i,a_i;q). The firm may then reject the applicant or pay the full screening cost cs(q)c_s(q), which reveals compatibility perfectly. Submitted applications remain available until the vacancy is filled or the firm terminates search, and retaining an unassessed application in the pool is costless. Let Π1S(q)andΠMS(q) ^1S(q) ^MS(q) denote the sets of feasible one-stage and multistage policies, respectively, conditional on the realized submitted pool (q)A(q) and the pre-assessment information (mi,ei):i∈(q) \(m_i,e_i):i (q) \ observed by the firm. For any feasible policy π, let U(π,q)U(π;q) denote the firm’s expected payoff under π, conditional on this information and net of all intermediate-assessment and full-screening costs. Define U1S,∗(q):=supπ∈Π1S(q)U(π,q)U^1S,*(q):= _π∈ ^1S(q)U(π;q) and UMS,∗(q):=supπ∈ΠMS(q)U(π,q).U^MS,*(q):= _π∈ ^MS(q)U(π;q). Because the firm can implement any one-stage policy by never using the intermediate assessment, Π1S(q)⊆ΠMS(q). ^1S(q) ^MS(q). Consequently, UMS,∗(q)≥U1S,∗(q).U^MS,*(q)≥ U^1S,*(q). (3) This inequality follows directly from nesting. The results in the next subsection therefore focus on conditions under which the inequality is strict and the intermediate assessment is used with positive probability. The value of the intermediate assessment comes from its ability to refine the firm’s posterior before the full screening cost is incurred. By iterated expectations, [p~i(q)∣mi,ei;q]=pi(q).E [ p_i(q) m_i,e_i;q ]=p_i(q). Thus the refined posterior is a mean-preserving refinement of the baseline posterior. To isolate the value of this refinement, suppose the vacancy remains open and applicant i is the firm’s only remaining option. If the firm’s current posterior compatibility belief is x, its optimal continuation payoff without an intermediate assessment is fq(x):=(vFx−cs(q))+=vF(x−pF(q))+,f_q(x):= (v_Fx-c_s(q) )_+=v_F (x-p^F(q) )_+, where (y)+:=maxy,0(y)_+:= \y,0\ and pF(q)=cs(q)vFp^F(q)= c_s(q)v_F is the one-stage screening cutoff from Proposition 4.2. Because fqf_q is convex, Jensen’s inequality implies [fq(p~i(q))∣mi,ei;q]≥fq(pi(q)).E [f_q ( p_i(q) ) m_i,e_i;q ]≥ f_q (p_i(q) ). This is the standard “value-of-information” [14]: before accounting for the cost of acquiring it, an additional posterior refinement cannot lower the firm’s optimal expected continuation payoff. The firm administers the intermediate assessment to applicant i whenever the expected value of the additional information is at least as large as the assessment cost: [fq(p~i(q))∣mi,ei;q]−fq(pi(q))≥cℓ(q).E [f_q ( p_i(q) ) m_i,e_i;q ]-f_q (p_i(q) )≥ c_ (q). The next subsection specializes the assessment to a binary signal and characterizes the applicants whose posterior compatibility lies below the one-stage hiring cutoff but for whom the firm would strictly prefer to administer the assessment if the applicant were the firm’s only remaining option. 6.2 A Binary Assessment and Multistage Screening To identify which below-cutoff applicants can benefit from the additional stage, for simplicity we consider a binary intermediate assessment with outcome Ai∈H,L,A_i∈\H,L\, where H is favorable and L is unfavorable. For each experience group e∈0,1e∈\0,1\, assume Pr(Ai=H∣ki=1,ei=e,mi;q)=τe, (A_i=H k_i=1,e_i=e,m_i;q)= _e, and Pr(Ai=H∣ki=0,ei=e,mi;q)=ℓe, (A_i=H k_i=0,e_i=e,m_i;q)= _e, where 0≤ℓe<τe≤1.0≤ _e< _e≤ 1. Thus, conditional on experience and compatibility, application materials do not provide additional information about the assessment outcome. The parameters τe _e and ℓe _e may differ across experience groups but τe>ℓe _e> _e requires that within each experience group, compatible applicants are more likely to pass. For an experience-e applicant with pre-assessment posterior compatibility p∈(0,1)p∈(0,1), Bayes’ rule gives the posterior compatibility probability following a favorable outcome: pHe(p):=τepτep+ℓe(1−p),p_H^e(p):= _ep _ep+ _e(1-p), and the posterior following an unfavorable outcome: pLe(p):=(1−τe)p(1−τe)p+(1−ℓe)(1−p).p_L^e(p):= (1- _e)p(1- _e)p+(1- _e)(1-p). Because τe>ℓe _e> _e, pHe(p)>p>pLe(p).p_H^e(p)>p>p_L^e(p). We next consider the continuation problem in which the vacancy remains open and an applicant is the firm’s only remaining option. Recall that the firm’s one-stage screening cutoff is pF(q)=cs(q)vF.p^F(q)= c_s(q)v_F. For each experience group e, define the intermediate-assessment cutoff p¯eA(q):=cℓ(q)/vF+ℓepF(q)τe(1−pF(q))+ℓepF(q). p_e^A(q):= c_ (q)/v_F+ _ep^F(q) _e (1-p^F(q) )+ _ep^F(q). (4) Lemma 6.1 (Binary intermediate-assessment cutoff). Fix q such that pF(q)∈(0,1)p^F(q)∈(0,1) and fix an experience group e∈0,1e∈\0,1\. Consider an applicant with pre-assessment posterior p<pF(q)p<p^F(q) who is the firm’s only remaining option. The firm weakly prefers to administer the intermediate assessment and proceed to full screening only following H if and only if p≥p¯eA(q).p≥ p_e^A(q). The preference is strict if the inequality above is strict. This lemma suggests a simple continuation rule for screening: if the vacancy remains open and a remaining applicant has posterior compatibility p∈(p¯eA(q),pF(q)),p∈( p_e^A(q),p^F(q)), then the firm administers the intermediate assessment. After a favorable outcome H, the applicant’s posterior rises above the full-screening cutoff, so the firm proceeds to full screening. After an unfavorable outcome L, the applicant remains below the cutoff and is rejected. This rule does not characterize the globally optimal order of assessment and screening when multiple applicants remain. In that problem, the firm’s decision may depend on the continuation values generated by its other options. Nevertheless, this rule is useful because it identifies a set of below-cutoff applicants who are valuable whenever they become the only remaining option. It also provides a feasible multistage policy that can be used to prove strict adoption of the multistage technology. Corollary 6.2 (Strict ex ante value of multistage hiring). Suppose σm2(q)>0 _m^2(q)>0 and that, for some e∈0,1e∈\0,1\, λeαe(q)>0 _e _e(q)>0 and cℓ(q)<vFpF(q)(1−pF(q))(τe−ℓe).c_ (q)<v_Fp^F(q) (1-p^F(q) )( _e- _e). Then [UMS,∗(q)−U1S,∗(q)]>0.E [U^MS,*(q)-U^1S,*(q) ]>0. Consequently, the firm strictly prefers access to the multistage technology ex ante, and every ex ante optimal multistage policy administers the intermediate assessment with positive probability. To establish Corollary 6.2, observe that the condition on cℓ(q)c_ (q) in the statement of the corollary implies p¯eA(q)<pF(q). p_e^A(q)<p^F(q). Because the Gaussian application signal has full support, conditional on experience e and submission, posterior compatibility places positive probability on (p¯eA(q),pF(q)). ( p_e^A(q),p^F(q) ). Thus there is positive probability that the submitted pool contains an experience-e applicant who is rejected under one-stage hiring but is strictly worth assessing if reached. A feasible multistage policy can first replicate the optimal one-stage policy. If no hire occurs and such an applicant remains available, the firm can then administer the intermediate assessment. This policy strictly improves the firm’s payoff on a positive-probability event. Since the globally optimal multistage policy performs at least as well as this feasible policy, access to the intermediate assessment has strictly positive ex ante value. 6.3 Implications for Screening Failure Section 5.2 showed that applicants satisfying pP(q)<pi(q)<pF(q)p^P(q)<p_i(q)<p^F(q) are socially worth screening but are rejected under one-stage hiring. Lemma 6.1 shows that under multistage hiring, an experience-e applicant is strictly worth assessing when they are the firm’s only remaining option whenever p¯eA(q)<pi(q)<pF(q). p_e^A(q)<p_i(q)<p^F(q). Thus, for applicants in experience group e, multistage hiring creates a path to screening for those satisfying maxpP(q),p¯eA(q)<pi(q)<pF(q). \p^P(q), p_e^A(q) \<p_i(q)<p^F(q). In particular, if p¯eA(q)≤pP(q), p_e^A(q)≤ p^P(q), then every experience-e applicant who is strictly socially worth screening but rejected under one-stage hiring is strictly worth assessing if they become the firm’s only remaining option. Corollary 6.3 (Multistage hiring mitigates one-stage screening failures). Fix q and a realized submitted pool. 1. Suppose the one-stage process exhibits the no-hire screening failure in Proposition 5.4. If there exists a submitted applicant i such that maxpP(q),p¯eiA(q)<pi(q)<pF(q), \p^P(q), p_e_i^A(q) \<p_i(q)<p^F(q), then UMS,∗(q)>U1S,∗(q)=0.U^MS,*(q)>U^1S,*(q)=0. Consequently, an optimal multistage policy administers the intermediate assessment with positive probability and proceeds to full screening with positive probability. 2. Suppose the one-stage process exhibits the inexperienced-compatible screening failure in Proposition 5.5. If p01max(q)>p¯0A(q),p_01 (q)> p_0^A(q), then there exists an applicant i∈01(q)i _01(q) satisfying pP(q)<pi(q)<pF(q)p^P(q)<p_i(q)<p^F(q) and pi(q)>p¯0A(q).p_i(q)> p_0^A(q). At any history at which the vacancy remains open and applicant i is the firm’s only remaining option, an optimal multistage policy administers the intermediate assessment and proceeds to full screening following H. The corollary above shows that multistage hiring can mitigate the market failures where no applicants are screened or where no inexperienced-compatible applicants are screened. For part (i), the firm can improve strictly on one-stage hiring by assessing the applicant identified in the statement and otherwise terminating search. By Lemma 6.1, this feasible policy has strictly positive expected payoff, whereas the optimal one-stage policy screens no one and receives zero. Thus introducing the intermediate assessment restores screening that would otherwise not occur. Part (i) establishes a different form of mitigation. When an inexperienced-compatible applicant lies above the assessment cutoff but below the firm’s one-stage screening cutoff, the applicant is excluded under one-stage hiring but becomes worth assessing if reached while the vacancy remains open. The intermediate assessment therefore creates a route to full screening that is absent under the one-stage process. The next subsection shows that such a history occurs with positive ex ante probability, implying a strictly positive gain in the applicant’s hiring probability. 6.4 Implications for Inexperienced-Compatible Applicants We now quantify the benefit of multistage hiring for inexperienced-compatible applicants. These applicants are high-fit matches, but they are precisely the group most exposed to the adverse effects of AI on screening in one-stage hiring. Let hi1Sh_i^1S denote the indicator that applicant i is hired under the one-stage technology, and let hiMS,∗h_i^MS,* denote the indicator that applicant i is hired under a globally optimal multistage policy. Probabilities are evaluated ex ante over the other potential applicants, their application decisions, the realized application pool, the firm’s screening and assessment decisions, and any intermediate-assessment signals. For a submitted inexperienced-compatible applicant with baseline posterior p, define the hiring-probability gain from optimal multistage hiring by G01∗(p,q):= G_01^*(p;q):= Pr(hiMS,∗=1∣ei=0,ki=1,di=1,pi=p) \! (h_i^MS,*=1 e_i=0,\ k_i=1,\ d_i=1,\ p_i=p ) −Pr(hi1S=1∣ei=0,ki=1,di=1,pi=p). - \! (h_i^1S=1 e_i=0,\ k_i=1,\ d_i=1,\ p_i=p ). The key observation is that an inexperienced-compatible applicant satisfying p¯0A(q)<pi(q)<pF(q) p_0^A(q)<p_i(q)<p^F(q) has zero probability of being hired under one-stage hiring but has a strictly positive path to hiring under an optimal multistage policy. In particular, if the vacancy remains open until the applicant becomes the firm’s only remaining option, Lemma 6.1 implies that the firm strictly prefers to administer the intermediate assessment. A favorable assessment then leads to full screening and, because the applicant is compatible, to hiring. Proposition C.1 in Appendix C formalizes this argument and gives an explicit positive lower bound on the applicant’s hiring-probability gain. To measure how many inexperienced-compatible applicants fall into this region, define ν01(q):=Pr(p¯0A(q)<pi(q)<pF(q)∣ei=0,ki=1,di=1). _01(q):= ( p_0^A(q)<p_i(q)<p^F(q) e_i=0,\ k_i=1,\ d_i=1 ). Thus ν01(q) _01(q) is the share of submitted inexperienced-compatible applicants who are rejected under one-stage hiring but have a strictly positive path to hiring under multistage hiring. Whenever p¯0A(q)<pF(q), p_0^A(q)<p^F(q), the full support of the Gaussian materials signal implies ν01(q)>0. _01(q)>0. Moreover, every applicant in this region obtains a strictly positive hiring-probability gain under optimal multistage hiring. Corollary C.2 in Appendix C states this finite-q result formally. We now turn to the main result of this subsection. In the high-AI limit, the share of inexperienced-compatible applicants who benefit from multistage hiring can converge to one. Recall that π0=Pr(ki=1∣ei=0)=Φ(μ0σz) _0= (k_i=1 e_i=0)= ( _0 _z ) is the inexperienced-group prior compatibility probability. Corollary 6.4 (Almost all inexperienced-compatible applicants benefit in the high-AI limit). Let qn\q_n\ satisfy σm2(qn)→∞ _m^2(q_n)→∞ and pF(qn)→p∞F∈(0,1).p^F(q_n)→ p_∞^F∈(0,1). Suppose lim supn→∞p¯0A(qn)<π0<p∞F. _n→∞ p_0^A(q_n)< _0<p_∞^F. Then ν01(qn)→1. _01(q_n)→ 1. Consequently, Pr(G01∗(pi(qn),qn)>0∣ei=0,ki=1,di=1)→1. (G_01^* (p_i(q_n);q_n )>0 e_i=0,\ k_i=1,\ d_i=1 )→ 1. As application materials become uninformative, the pre-assessment posterior of a submitted inexperienced-compatible applicant converges to π0 _0. If π0 _0 remains strictly above the assessment cutoff and strictly below the one-stage screening cutoff, almost every submitted inexperienced-compatible applicant is rejected under one-stage hiring but obtains a strictly positive hiring-probability gain under optimal multistage hiring. Thus the benefit of the additional screening stage is not confined to an exceptional set of applicants: in the high-AI limit, it extends to almost the entire inexperienced-compatible group. When the high-noise screening-failure condition from Section 5.2 also holds, i.e., p∞P<π0<p∞F,p_∞^P< _0<p_∞^F, the intermediate stage benefits the same inexperienced-compatible applicants who are socially worth screening but rejected under one-stage hiring. 7 Conclusion AI-assisted job search changes the hiring market not only by affecting how many applications workers submit, but also by changing what firms can infer from those applications. In our model, less informative application materials lead firms to rely more heavily on applicants’ experience. Inexperienced-compatible applicants are especially harmed as they lose the individualized evidence that could distinguish them from others with little experience. Because firms do not internalize workers’ surplus from a successful match, they may also reject applicants who are socially worth screening. In very noisy, high-AI environments, these failures can become systematic: the firm may screen no one or screen only experienced applicants. Multistage hiring can mitigate this problem. A sufficiently informative and inexpensive intermediate assessment allows firms to acquire new evidence of fit before committing to costly full screening. We identify conditions under which this option strictly increases firm payoffs and gives some inexperienced-compatible applicants rejected under one-stage hiring a positive-probability path to employment. As AI saturation becomes sufficiently high, this benefit extends to almost all such applicants. Expanding evaluation opportunities can therefore serve firms’ interests as well as those of applicants otherwise excluded. Our results highlight that easier access to applying is not the same as access to credible evaluation. 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Under (1) and (2), standard Gaussian updating gives zi|mi,ei=e;q∼(Si(q),σpost2(q)),z_i m_i,e_i=e;q (S_i(q), _post^2(q) ), where σpost2(q)=(1σz2+1σm2(q))−1=σz2σm2(q)σz2+σm2(q) _post^2(q)= ( 1 _z^2+ 1 _m^2(q) )^-1= _z^2 _m^2(q) _z^2+ _m^2(q) and Si(q) S_i(q) =σpost2(q)(μeσz2+miσm2(q)) = _post^2(q) ( _e _z^2+ m_i _m^2(q) ) =κ(q)mi+(1−κ(q))μe, =κ(q)m_i+(1-κ(q)) _e, with κ(q)=σz2σz2+σm2(q).κ(q)= _z^2 _z^2+ _m^2(q). Let Δμ:=μ1−μ0>0. _μ:= _1- _0>0. Since μe=μ0+Δμe, _e= _0+ _μe, the posterior mean can equivalently be written as Si(q)=(1−κ(q))μ0+θ(q)ei+κ(q)mi,S_i(q)=(1-κ(q)) _0+θ(q)e_i+κ(q)m_i, where θ(q)=(1−κ(q))Δμ.θ(q)=(1-κ(q)) _μ. Compatibility is the event ki=1k_i=1 if and only if zi≥0z_i≥ 0. Therefore, pi(q) p_i(q) =Pr(ki=1∣mi,ei;q) = (k_i=1 m_i,e_i;q) =Pr(zi≥0∣mi,ei;q) = (z_i≥ 0 m_i,e_i;q) =Φ(Si(q)σpost(q)). = ( S_i(q) _post(q) ). Because σpost(q)>0 _post(q)>0 and Φ is strictly increasing, for any submitted applicants i and j, pi(q)≥pj(q)⟺Si(q)≥Sj(q).p_i(q)≥ p_j(q) S_i(q)≥ S_j(q). Now consider q~>q q>q. By Assumption 3.1, σm2(q~)>σm2(q). _m^2( q)> _m^2(q). It follows immediately that κ(q~)=σz2σz2+σm2(q~)<σz2σz2+σm2(q)=κ(q).κ( q)= _z^2 _z^2+ _m^2( q)< _z^2 _z^2+ _m^2(q)=κ(q). Since Δμ>0 _μ>0, θ(q~)=(1−κ(q~))Δμ>(1−κ(q))Δμ=θ(q).θ( q)=(1-κ( q)) _μ>(1-κ(q)) _μ=θ(q). Finally, θ(q)κ(q) θ(q)κ(q) =Δμ1−κ(q)κ(q) = _μ 1-κ(q)κ(q) =Δμσm2(q)σz2. = _μ\, _m^2(q) _z^2. Assumption 3.1 therefore implies that θ(q)/κ(q)θ(q)/κ(q) is strictly increasing in q. ∎ Proof of Proposition 4.2. Fix q and a realized pool of M submitted applications. Write V:=vFandc:=cs(q).V:=v_F c:=c_s(q). By assumption, V>0V>0. Conditional on the observed application information, applicant i is compatible with probability pi(q)p_i(q). Because applicant primitives are independent across applicants, compatibility realizations are independent conditional on the firm’s observed information. We first establish the optimal ordering. Consider two applicants i and j who are screened consecutively, conditional on the vacancy remaining open when the firm reaches them. The probability that at least one of the two applicants is compatible, and the probability that both applicants are incompatible, do not depend on their order. Thus the expected hiring payoff and the continuation value after both applicants fail are the same under either order. If the firm screens i before j, its expected screening cost over these two applicants is c+(1−pi(q))c.c+(1-p_i(q))c. If it screens j before i, the corresponding expected cost is c+(1−pj(q))c.c+(1-p_j(q))c. Hence the expected-payoff difference between placing i before j and placing j before i is c(pi(q)−pj(q)).c (p_i(q)-p_j(q) ). Therefore, pi(q)≥pj(q)p_i(q)≥ p_j(q) implies that placing i weakly before j is optimal. Repeated pairwise interchanges imply that applicants can be ordered so that p1(q)≥p2(q)≥⋯≥pM(q).p_1(q)≥ p_2(q)≥·s≥ p_M(q). Now suppose the firm screens the first L applicants in this order, unless it discovers a compatible applicant earlier. Its expected payoff is UL(q)=V[1−∏j=1L(1−pj(q))]−c∑ℓ=1L∏j=1ℓ−1(1−pj(q)),U_L(q)=V [1- _j=1^L(1-p_j(q)) ]-c _ =1^L _j=1 -1(1-p_j(q)), where the empty product is equal to one. The first term is the firm’s expected hiring payoff, and the second is its expected total screening cost. The marginal payoff from adding applicant L to the end of the screening list is UL(q)−UL−1(q) U_L(q)-U_L-1(q) =∏j=1L−1(1−pj(q))[VpL(q)−c]. = _j=1^L-1(1-p_j(q)) [Vp_L(q)-c ]. The product preceding the bracket is the probability that applicant L is reached. It is nonnegative. Thus applicant L is weakly worth including if and only if VpL(q)≥c.Vp_L(q)≥ c. Substituting V=vFV=v_F and c=cs(q)c=c_s(q) gives pL(q)≥cs(q)vF=pF(q).p_L(q)≥ c_s(q)v_F=p^F(q). Because applicants are ordered by decreasing posterior compatibility, once an applicant fails this inequality, every remaining applicant also fails it. Hence the firm optimally screens applicants sequentially in decreasing order of posterior compatibility until either it finds a compatible applicant or no remaining applicant satisfies pi(q)≥pF(q).p_i(q)≥ p^F(q). At equality the firm is indifferent; the proposition adopts the tie-breaking convention that an indifferent applicant is included in the screening list. Finally, under Assumption 3.2, for every q~>q q>q, cs(q~)>cs(q).c_s( q)>c_s(q). Since vF>0v_F>0, pF(q~)=cs(q~)vF>cs(q)vF=pF(q).p^F( q)= c_s( q)v_F> c_s(q)v_F=p^F(q). ∎ Appendix B Proofs for Section 5 Proof of Proposition 5.1. Because applicants do not observe ziz_i before applying and application costs are independent of (zi,εi)(z_i, _i) conditional on experience, conditioning on submission does not change the distribution of (zi,mi)(z_i,m_i) within an experience group. Hence [mi∣ei=e,ki=k,di=1]=[zi∣ei=e,ki=k]=μek,E[m_i e_i=e,k_i=k,d_i=1]=E[z_i e_i=e,k_i=k]= _ek, where we use [εi]=0E[ _i]=0. Therefore, S¯ek(q)=κ(q)μek+(1−κ(q))μe. S_ek(q)=κ(q) _ek+(1-κ(q)) _e. For q<q~q< q, ΔS¯ek(q,q~) S_ek(q, q) =S¯ek(q~)−S¯ek(q) = S_ek( q)- S_ek(q) =[κ(q~)−κ(q)](μek−μe). = [κ( q)-κ(q) ] ( _ek- _e ). It remains to establish the ordering of these changes. Define te:=μeσz.t_e:= _e _z. Since zi|ei=e∼(μe,σz2)z_i e_i=e ( _e, _z^2) and compatibility is the event zi≥0z_i≥ 0, the conditional means are μe1=μe+σzϕ(te)Φ(te) _e1= _e+ _z φ(t_e) (t_e) and μe0=μe−σzϕ(te)Φ(−te). _e0= _e- _z φ(t_e) (-t_e). Thus μe1−μe=σzϕ(te)Φ(te)>0 _e1- _e= _z φ(t_e) (t_e)>0 and μe0−μe=−σzϕ(te)Φ(−te)<0. _e0- _e=- _z φ(t_e) (-t_e)<0. The inverse Mills ratio ϕ(t)Φ(t) φ(t) (t) is strictly decreasing in t, while ϕ(t)Φ(−t) φ(t) (-t) is strictly increasing in t. Since μ1>μ0 _1> _0, we have t1>t0t_1>t_0 and therefore μ01−μ0>μ11−μ1>0, _01- _0> _11- _1>0, while μ10−μ1<μ00−μ0<0. _10- _1< _00- _0<0. By Assumption 3.1, κ(q~)−κ(q)<0.κ( q)-κ(q)<0. Multiplying the preceding inequalities by this negative quantity gives ΔS¯01(q,q~)<ΔS¯11(q,q~)<0<ΔS¯00(q,q~)<ΔS¯10(q,q~), S_01(q, q)< S_11(q, q)<0< S_00(q, q)< S_10(q, q), as required. ∎ Proof of Proposition 5.2. Fix an experience group e. Recall that Xi=zi−μeσz,Yi(q)=mi−μeσz2+σm2(q).X_i= z_i- _e _z, Y_i(q)= m_i- _e _z^2+ _m^2(q). Conditional on ei=e_i=e, (Xi,Yi(q))(X_i,Y_i(q)) is standard bivariate normal with correlation r(q)=σzσz2+σm2(q).r(q)= _z _z^2+ _m^2(q). For a,b∈ℝa,b and r∈(−1,1)r∈(-1,1), let Φ2(a,b,r)=Pr(X≤a,Y≤b) _2(a,b;r)= (X≤ a,Y≤ b) denote the standard bivariate normal CDF, and let ϕ2(a,b,r) _2(a,b;r) denote its density. The standard derivative identity ∂rΦ2(a,b,r)=ϕ2(a,b,r)>0 ∂ r _2(a,b;r)= _2(a,b;r)>0 implies ∂rPr(X≥ae,Y≥b)=ϕ2(ae,b,r)>0. ∂ r (X≥ a_e,Y≥ b)= _2(a_e,b;r)>0. Since Pr(X≥ae) (X≥ a_e) does not depend on r, ∂ψe1(b,r)∂r=ϕ2(ae,b,r)Pr(X≥ae)>0. ∂ _e1(b,r)∂ r= _2(a_e,b;r) (X≥ a_e)>0. Similarly, Pr(X<ae,Y≥b)=Pr(Y≥b)−Pr(X≥ae,Y≥b). (X<a_e,Y≥ b)= (Y≥ b)- (X≥ a_e,Y≥ b). The first term is independent of r, so ∂ψe0(b,r)∂r=−ϕ2(ae,b,r)Pr(X<ae)<0. ∂ _e0(b,r)∂ r=- _2(a_e,b;r) (X<a_e)<0. We next derive the relative standardized thresholds. By the definition of Yi(q)Y_i(q), mi=μe+σz2+σm2(q)Yi(q).m_i= _e+ _z^2+ _m^2(q)\,Y_i(q). Because κ(q)=σz2σz2+σm2(q)κ(q)= _z^2 _z^2+ _m^2(q) and r(q)=σzσz2+σm2(q),r(q)= _z _z^2+ _m^2(q), the posterior-mean score can be written as Si(q)=μe+σzr(q)Yi(q).S_i(q)= _e+ _zr(q)Y_i(q). The screening condition pi(q)≥pF(q)p_i(q)≥ p^F(q) is equivalent to Si(q)≥σpost(q)Φ−1(pF(q)).S_i(q)≥ _post(q) ^-1 (p^F(q) ). Therefore it is equivalent to Yi(q)≥be(q),Y_i(q)≥ b_e(q), where be(q)=σpost(q)Φ−1(pF(q))−μeσzr(q).b_e(q)= _post(q) ^-1 (p^F(q) )- _e _zr(q). The term involving the posterior cutoff is common across experience groups, so b0(q)−b1(q)=μ1−μ0σzr(q)=Δμσzr(q).b_0(q)-b_1(q)= _1- _0 _zr(q)= _μ _zr(q). Differentiating gives dq[b0(q)−b1(q)]=−Δμr′(q)σzr(q)2. ddq [b_0(q)-b_1(q) ]=- _μr (q) _zr(q)^2. Assumption 3.1 implies r′(q)<0r (q)<0, and Δμ>0 _μ>0, so dq[b0(q)−b1(q)]>0. ddq [b_0(q)-b_1(q) ]>0. ∎ Proof of Proposition 5.3. At the screening stage, application costs are sunk. A compatible hire generates total surplus vF+vA.v_F+v_A. Thus the planner’s screening problem has exactly the same structure as the firm’s problem in Proposition 4.2, except that the value of discovering a compatible applicant is vF+vAv_F+v_A rather than vFv_F. The same pairwise-interchange argument therefore implies that the planner screens applicants in decreasing order of posterior compatibility. Conditional on reaching applicant i, the expected marginal social value of screening is (vF+vA)pi(q)−cs(q).(v_F+v_A)p_i(q)-c_s(q). Hence the planner screens applicant i if and only if pi(q)≥cs(q)vF+vA=pP(q).p_i(q)≥ c_s(q)v_F+v_A=p^P(q). Because vA>0v_A>0, pP(q)=cs(q)vF+vA<cs(q)vF=pF(q).p^P(q)= c_s(q)v_F+v_A< c_s(q)v_F=p^F(q). Thus an applicant is included in the planner’s screening list but not the firm’s if and only if pP(q)≤pi(q)<pF(q).p^P(q)≤ p_i(q)<p^F(q). ∎ Proof of Proposition 5.4. Suppose pP(q)<pmax(q)<pF(q).p^P(q)<p (q)<p^F(q). Since every submitted applicant satisfies pi(q)≤pmax(q)<pF(q),p_i(q)≤ p (q)<p^F(q), Proposition 4.2 implies that the firm’s screening list is empty. On the other hand, an applicant attaining pmax(q)p (q) satisfies pmax(q)>pP(q).p (q)>p^P(q). By Proposition 5.3, the social planner includes this applicant in its screening list. Hence the planner’s screening list is nonempty while the firm’s is empty. ∎ Proof of Proposition 5.5. Suppose pP(q)<p01max(q)<pF(q).p^P(q)<p_01 (q)<p^F(q). Every submitted inexperienced-compatible applicant satisfies pi(q)≤p01max(q)<pF(q),p_i(q)≤ p_01 (q)<p^F(q), so none is included in the firm’s screening list. An applicant attaining p01max(q)p_01 (q) satisfies p01max(q)>pP(q),p_01 (q)>p^P(q), so Proposition 5.3 implies that this applicant is included in the planner’s screening list. Hence at least one submitted inexperienced-compatible applicant is socially worth screening but excluded by the firm. ∎ Proof of Lemma 5.6. Fix an applicant with experience ei=e_i=e and realized compatibility ki=k_i=k. Recall that Si(q)=κ(q)mi+(1−κ(q))μe=μe+κ(q)(zi−μe)+κ(q)εi.S_i(q)=κ(q)m_i+(1-κ(q)) _e= _e+κ(q)(z_i- _e)+κ(q) _i. Along a sequence qnq_n such that σm2(qn)→∞, _m^2(q_n)→∞, we have κ(qn)=σz2σz2+σm2(qn)→0.κ(q_n)= _z^2 _z^2+ _m^2(q_n)→ 0. Conditional on (ei=e,ki=k)(e_i=e,k_i=k), ziz_i has a truncated normal distribution and therefore has finite second moment. Hence κ(qn)(zi−μe)→0κ(q_n)(z_i- _e)→ 0 in probability. Also, Var(κ(qn)εi)=κ(qn)2σm2(qn)=σz4σm2(qn)(σz2+σm2(qn))2→0.Var (κ(q_n) _i )=κ(q_n)^2 _m^2(q_n)= _z^4 _m^2(q_n) ( _z^2+ _m^2(q_n) )^2→ 0. Therefore, κ(qn)εi→0κ(q_n) _i→ 0 in probability, and consequently Si(qn)→μeS_i(q_n)→ _e in probability conditional on (ei=e,ki=k)(e_i=e,k_i=k). Moreover, σpost2(qn)=σz2σm2(qn)σz2+σm2(qn)→σz2. _post^2(q_n)= _z^2 _m^2(q_n) _z^2+ _m^2(q_n)→ _z^2. Since pi(qn)=Φ(Si(qn)σpost(qn)),p_i(q_n)= ( S_i(q_n) _post(q_n) ), the continuous mapping theorem gives pi(qn)→Φ(μeσz)=πep_i(q_n)→ ( _e _z )= _e in probability. Application is independent of (zi,mi)(z_i,m_i) conditional on experience, so the same convergence holds conditional on di=1d_i=1. For any fixed finite submitted pool ℬB, maxi∈ℬ|pi(qn)−πei|→0 _i |p_i(q_n)- _e_i |→ 0 in probability by a union bound over the finitely many applicants. ∎ Proof of Corollary 5.7. By Lemma 5.6, conditional on the realized types in the fixed finite submitted pool ℬB, maxi∈ℬ|pi(qn)−πei|→0 _i |p_i(q_n)- _e_i |→ 0 in probability. For part (i), it follows that maxi∈ℬpi(qn)→πℬmax _i p_i(q_n)→ _B in probability. By assumption, p∞P<πℬmax<p∞F,p_∞^P< _B <p_∞^F, while pP(qn)→p∞P,pF(qn)→p∞F.p^P(q_n)→ p_∞^P, p^F(q_n)→ p_∞^F. The strict inequalities therefore imply Pr(pP(qn)<maxi∈ℬpi(qn)<pF(qn))→1. (p^P(q_n)< _i p_i(q_n)<p^F(q_n) )→ 1. Proposition 5.4 then gives the no-hire screening failure with probability approaching one. For part (i), every applicant in ℬ01B_01 has experience e=0e=0. Hence maxi∈ℬ01|pi(qn)−π0|→0 _i _01 |p_i(q_n)- _0 |→ 0 in probability. If p∞P<π0<p∞F,p_∞^P< _0<p_∞^F, then Pr(pP(qn)<mini∈ℬ01pi(qn)≤maxi∈ℬ01pi(qn)<pF(qn))→1. (p^P(q_n)< _i _01p_i(q_n)≤ _i _01p_i(q_n)<p^F(q_n) )→ 1. Thus every submitted inexperienced-compatible applicant lies below the firm’s cutoff and above the planner’s cutoff with probability approaching one. Finally, if ℬ1B_1 is nonempty and p∞F<π1,p_∞^F< _1, then mini∈ℬ1pi(qn)→π1 _i _1p_i(q_n)→ _1 in probability. Combining this convergence with maxi∈ℬ01pi(qn)→π0 _i _01p_i(q_n)→ _0 and π0<p∞F<π1 _0<p_∞^F< _1 gives Pr(mini∈ℬ1pi(qn)>pF(qn)>maxi∈ℬ01pi(qn))→1. ( _i _1p_i(q_n)>p^F(q_n)> _i _01p_i(q_n) )→ 1. ∎ Appendix C Proofs and Supporting Results for Section 6 Proof of Lemma 6.1. Fix q, experience group e, and a pre-assessment posterior p<pF(q).p<p^F(q). Write V:=vF,pF(q)=cs(q)V.V:=v_F, p^F(q)= c_s(q)V. The probability of a favorable assessment outcome is Pr(Ai=H∣p,e)=τep+ℓe(1−p). (A_i=H p,e)= _ep+ _e(1-p). Bayes’ rule gives pHe(p)=τepτep+ℓe(1−p)p_H^e(p)= _ep _ep+ _e(1-p) and pLe(p)=(1−τe)p(1−τe)p+(1−ℓe)(1−p).p_L^e(p)= (1- _e)p(1- _e)p+(1- _e)(1-p). Because τe>ℓe _e> _e, pHe(p)>p>pLe(p).p_H^e(p)>p>p_L^e(p). Since p<pF(q)p<p^F(q), it follows immediately that pLe(p)<pF(q),p_L^e(p)<p^F(q), so the firm never proceeds to full screening following L in the one-applicant continuation problem. Consider the policy that administers the intermediate assessment and proceeds to full screening only following H. Its expected payoff is −cℓ(q)+Pr(Ai=H∣p,e)[VpHe(p)−cs(q)] -c_ (q)+ (A_i=H p,e) [Vp_H^e(p)-c_s(q) ] = = −cℓ(q)+[τep+ℓe(1−p)][Vτepτep+ℓe(1−p)−cs(q)] -c_ (q)+ [ _ep+ _e(1-p) ] [V _ep _ep+ _e(1-p)-c_s(q) ] = = −cℓ(q)+Vτep−cs(q)[τep+ℓe(1−p)]. -c_ (q)+V _ep-c_s(q) [ _ep+ _e(1-p) ]. Substituting cs(q)=VpF(q)c_s(q)=Vp^F(q) gives −cℓ(q)+V[p(τe(1−pF(q))+ℓepF(q))−ℓepF(q)].-c_ (q)+V [p ( _e(1-p^F(q))+ _ep^F(q) )- _ep^F(q) ]. This payoff is nonnegative if and only if p≥cℓ(q)/V+ℓepF(q)τe(1−pF(q))+ℓepF(q)=p¯eA(q).p≥ c_ (q)/V+ _ep^F(q) _e(1-p^F(q))+ _ep^F(q)= p_e^A(q). It is strictly positive if and only if p>p¯eA(q).p> p_e^A(q). For any p≥p¯eA(q)p≥ p_e^A(q), the preceding inequality also implies that a favorable assessment raises the posterior above the full-screening cutoff, so screening following H is optimal. Thus, among applicants satisfying p<pF(q)p<p^F(q), the firm weakly prefers assessment if and only if p≥p¯eA(q),p≥ p_e^A(q), with strict preference when p¯eA(q)<p<pF(q). p_e^A(q)<p<p^F(q). Finally, there exist below-cutoff applicants for whom assessment is strictly preferred if and only if p¯eA(q)<pF(q). p_e^A(q)<p^F(q). Substituting the definition of p¯eA(q) p_e^A(q) and rearranging, p¯eA(q)<pF(q)⟺cℓ(q)V p_e^A(q)<p^F(q) c_ (q)V <pF(q)(1−pF(q))(τe−ℓe). <p^F(q)(1-p^F(q))( _e- _e). Multiplying by V=vFV=v_F gives cℓ(q)<vFpF(q)(1−pF(q))(τe−ℓe),c_ (q)<v_Fp^F(q)(1-p^F(q))( _e- _e), as required. ∎ Proof of Corollary 6.2. Suppose that for some experience group e, λeαe(q)>0 _e _e(q)>0 and cℓ(q)<vFpF(q)(1−pF(q))(τe−ℓe).c_ (q)<v_Fp^F(q)(1-p^F(q))( _e- _e). By Lemma 6.1, p¯eA(q)<pF(q). p_e^A(q)<p^F(q). Conditional on ei=e_i=e and di=1d_i=1, the application-materials signal has full support on ℝR. Moreover, posterior compatibility pi(q)=Pr(ki=1∣mi,ei=e;q)p_i(q)= (k_i=1 m_i,e_i=e;q) is continuous and strictly increasing in mim_i, with limits zero and one as mi→−∞m_i→-∞ and mi→∞m_i→∞, respectively. Hence Pr(p¯eA(q)<pi(q)<pF(q)∣ei=e,di=1)>0. ( p_e^A(q)<p_i(q)<p^F(q) e_i=e,d_i=1 )>0. Because λeαe(q)>0 _e _e(q)>0, there is positive probability that the submitted pool contains such an applicant. Consider a feasible multistage policy that first replicates the optimal one-stage policy. If the vacancy remains open after the one-stage screening list is exhausted, the policy administers the intermediate assessment to one such below-cutoff applicant. Conditional on reaching this applicant, Lemma 6.1 implies that the assessment has strictly positive expected value. There is positive probability that the vacancy remains open until this point; for example, the event that all other potential applicants are incompatible has strictly positive probability. Therefore this feasible policy weakly improves on the optimal one-stage policy at every history and strictly improves on it with positive probability. It follows that [UMS,∗(q)−U1S,∗(q)]>0.E [U^MS,*(q)-U^1S,*(q) ]>0. If an ex ante optimal multistage policy never administered the intermediate assessment, it would be a feasible one-stage policy and could achieve at most the one-stage value. Hence every ex ante optimal multistage policy must administer the intermediate assessment with positive probability. ∎ Proof of Corollary 6.3. For part (i), suppose the one-stage process exhibits the no-hire screening failure. Then every submitted applicant satisfies pi(q)<pF(q),p_i(q)<p^F(q), and the optimal one-stage payoff is U1S,∗(q)=0.U^1S,*(q)=0. Suppose there exists a submitted applicant i satisfying maxpP(q),p¯eiA(q)<pi(q)<pF(q). \p^P(q), p_e_i^A(q) \<p_i(q)<p^F(q). The firm can ignore all other applicants and treat i as its only remaining option. By Lemma 6.1, administering the intermediate assessment then has strictly positive expected payoff. Hence there exists a feasible multistage policy with strictly positive payoff, so UMS,∗(q)>0=U1S,∗(q).U^MS,*(q)>0=U^1S,*(q). Any optimal multistage policy must therefore administer an intermediate assessment with positive probability. Because a favorable assessment outcome has positive probability and raises the posterior above pF(q)p^F(q), the firm also proceeds to full screening with positive probability. For part (i), suppose the one-stage process exhibits the inexperienced-compatible screening failure and p01max(q)>p¯0A(q).p_01 (q)> p_0^A(q). Choose an applicant i∈01(q)i _01(q) attaining p01max(q)p_01 (q). By the definition of the one-stage failure, pP(q)<pi(q)<pF(q).p^P(q)<p_i(q)<p^F(q). Together with the assumed inequality, p¯0A(q)<pi(q)<pF(q). p_0^A(q)<p_i(q)<p^F(q). At any history at which the vacancy remains open and i is the firm’s only remaining option, Lemma 6.1 implies that the firm strictly prefers to administer the intermediate assessment. Following H, the posterior exceeds pF(q)p^F(q) and the firm proceeds to full screening. ∎ Proposition C.1 (Hiring gain for below-cutoff inexperienced-compatible applicants). Fix q and suppose p¯0A(q)<p<pF(q). p_0^A(q)<p<p^F(q). Then Pr(hiMS,∗=1∣ei=0,ki=1,di=1,pi(q)=p)≥τ0χn−1, (h_i^MS,*=1 e_i=0,\ k_i=1,\ d_i=1,\ p_i(q)=p )≥ _0χ^n-1, where χ:=Pr(ki=0)=∑e∈0,1λeΦ(−μeσz)>0.χ:= (k_i=0)= _e∈\0,1\ _e (- _e _z )>0. By contrast, Pr(hi1S=1∣ei=0,ki=1,di=1,pi(q)=p)=0. (h_i^1S=1 e_i=0,\ k_i=1,\ d_i=1,\ p_i(q)=p )=0. Consequently, G01∗(p,q)≥τ0χn−1>0.G_01^*(p;q)≥ _0χ^n-1>0. Proof. Fix a submitted inexperienced-compatible applicant i satisfying p¯0A(q)<pi(q)<pF(q). p_0^A(q)<p_i(q)<p^F(q). Under one-stage hiring, Proposition 4.2 implies that i is not included in the firm’s screening list. Hence Pr(hi1S=1∣ei=0,ki=1,di=1,pi(q))=0. (h_i^1S=1 e_i=0,k_i=1,d_i=1,p_i(q) )=0. Now consider the multistage process. Let E−i:=kj=0 for every j≠iE_-i:= \k_j=0 for every j≠ i \ be the event that all other n−1n-1 potential applicants are incompatible. Applicant primitives are independent across applicants, so conditional on the tagged applicant’s type, submission decision, and posterior, Pr(E−i)=χn−1. (E_-i)=χ^n-1. On E−iE_-i, no other applicant can fill the vacancy. Because retaining an unassessed application is costless, applicant i can remain available while the firm evaluates its other options. If the vacancy remains open until i is the firm’s only remaining option, Lemma 6.1 implies that administering the intermediate assessment has strictly positive value. Thus an optimal multistage policy cannot terminate search while i remains available. Conditional on ki=1k_i=1, applicant i receives a favorable intermediate assessment with probability τ0. _0. Following H, the applicant’s posterior exceeds pF(q)p^F(q), so full screening is strictly profitable. Screening reveals that ki=1k_i=1, and the firm hires the applicant. Therefore, Pr(hiMS,∗=1∣ei=0,ki=1,di=1,pi(q))≥τ0χn−1. (h_i^MS,*=1 e_i=0,k_i=1,d_i=1,p_i(q) )≥ _0χ^n-1. Subtracting the zero one-stage hiring probability gives G01∗(pi(q),q)≥τ0χn−1>0.G_01^*(p_i(q);q)≥ _0χ^n-1>0. ∎ Corollary C.2 (Positive share of inexperienced-compatible applicants helped). Suppose σm2(q)>0 _m^2(q)>0 and p¯0A(q)<pF(q). p_0^A(q)<p^F(q). Then ν01(q)>0. _01(q)>0. Moreover, Pr(G01∗(pi(q),q)>0∣ei=0,ki=1,di=1)≥ν01(q)>0. (G_01^*(p_i(q);q)>0 e_i=0,\ k_i=1,\ d_i=1 )≥ _01(q)>0. Proof. Suppose σm2(q)>0 _m^2(q)>0 and p¯0A(q)<pF(q). p_0^A(q)<p^F(q). Conditional on ei=0,ki=1,di=1,e_i=0, k_i=1, d_i=1, the materials signal mim_i has a continuous density that is strictly positive on ℝR. Moreover, pi(q)=Pr(ki=1∣mi,ei=0;q)p_i(q)= (k_i=1 m_i,e_i=0;q) is a continuous and strictly increasing function of mim_i whose range is (0,1)(0,1). Therefore the conditional distribution of pi(q)p_i(q) places positive probability on every open subinterval of (0,1)(0,1). In particular, ν01(q)=Pr(p¯0A(q)<pi(q)<pF(q)∣ei=0,ki=1,di=1)>0. _01(q)= ( p_0^A(q)<p_i(q)<p^F(q) e_i=0,k_i=1,d_i=1 )>0. For every posterior in this interval, Proposition C.1 implies G01∗(pi(q),q)>0.G_01^*(p_i(q);q)>0. Hence Pr(G01∗(pi(q),q)>0∣ei=0,ki=1,di=1)≥ν01(q)>0. (G_01^*(p_i(q);q)>0 e_i=0,k_i=1,d_i=1 )≥ _01(q)>0. ∎ Proof of Corollary 6.4. By Lemma 5.6, conditional on ei=0,ki=1,di=1,e_i=0, k_i=1, d_i=1, we have pi(qn)→π0p_i(q_n)→ _0 in probability. By assumption, lim supn→∞p¯0A(qn)<π0<p∞F, _n→∞ p_0^A(q_n)< _0<p_∞^F, and pF(qn)→p∞F.p^F(q_n)→ p_∞^F. Therefore there exists ε>0 >0 such that for all sufficiently large n, p¯0A(qn)<π0−ε<π0+ε<pF(qn). p_0^A(q_n)< _0- < _0+ <p^F(q_n). Consequently, ν01(qn) _01(q_n) =Pr(p¯0A(qn)<pi(qn)<pF(qn)∣ei=0,ki=1,di=1) = ( p_0^A(q_n)<p_i(q_n)<p^F(q_n) e_i=0,k_i=1,d_i=1 ) ≥Pr(|pi(qn)−π0|<ε∣ei=0,ki=1,di=1)→1. ≥ (|p_i(q_n)- _0|< e_i=0,k_i=1,d_i=1 )→ 1. Thus ν01(qn)→1. _01(q_n)→ 1. Finally, Proposition C.1 implies G01∗(pi(qn),qn)>0G_01^*(p_i(q_n);q_n)>0 whenever p¯0A(qn)<pi(qn)<pF(qn). p_0^A(q_n)<p_i(q_n)<p^F(q_n). Therefore, Pr(G01∗(pi(qn),qn)>0∣ei=0,ki=1,di=1)≥ν01(qn)→1. (G_01^*(p_i(q_n);q_n)>0 e_i=0,k_i=1,d_i=1 )≥ _01(q_n)→ 1. ∎