{"id":"2cd80326-f40c-4afb-88de-ee9540b45515","arxiv_id":"2608.09219","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The paper introduces, identifies, and estimates a model of asymmetric peer effects and shows that standard symmetric models can misguide treatment targeting, producing large welfare losses.","lead":"This paper builds an economic model where students respond differently to friends who perform better or worse than they do, and estimates it on U.S. school data. It finds that ignoring these asymmetries can make targeted anti-smoking or anti-violence policies waste most of their social spillovers.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Asymmetry estimates hinge on untested rank condition Assumption 3(ii); the reported KP tests check a different matrix, so identification of β_l≠β_h is not empirically verified.","rationale":"The central claim is that β_l ≠ β_h in Add Health and that ignoring asymmetry causes large welfare losses. Both claims are downstream of point identification of the structural parameters. The proof of Proposition 3 is a standard coefficient-matching argument; its validity requires Assumption 3(ii). The paper's own discussion (Section 3.2) concedes that no low-level conditions are given and that the condition is 'likely' to hold because of the indicator function. This is the weakest link in the chain because, unlike the equilibrium existence proof (Proposition 1) which is fully worked out and internally consistent, the identification condition is not derived or directly tested. The empirical KP LM tests reported in Table 2 are often cited as supporting identification, but they test the rank of the instrument-regressor matrix Ẑ'V (Assumption 4(ii)), not the structural rank condition A'A (Assumption 3(ii)). Thus, the empirical evidence in the paper does not actually rule out failure of Assumption 3(ii). The Monte Carlo simulations show the estimator works in the four simulated DGPs, but these are designed to have variation and do not cover configurations where E(ˇy) might be nearly collinear with the controls. A direct rank check on the actual data (using the cross-fitted predictions or a simulation-based approximation of E(ˇy)) would settle whether the concern is real. If the rank holds, the paper's claims stand; if not, the asymmetry estimates and policy conclusions are unverified. Given the high stakes of the empirical claims, a conditional acceptance requiring this verification is appropriate. This does not impugn the theoretical contribution, which is novel and largely sound; it simply ensures the central empirical findings are not artifacts of an unverified identification condition.","tokens_in":37386,"tokens_out":16802,"duration_ms":113692,"concrete_test":"Construct the matrix Â_m = [Ê(ˇy_m), G_m Ê(ˇy_m), 1_nm, X_m, G_m X_m, G^2_m X_m] on the Add Health sample using the paper's cross-fitted random-forest predictions Ê(ˇy_m) (Supplemental Appendix B), and compute the smallest singular value (or condition number) of (1/M) Σ Â'_m Â_m. If the minimum singular value is close to zero (e.g., condition number > 10^5), the rank condition is empirically fragile. To avoid noise in the predictions, also run a simulation-based check: fix the estimated parameters and the actual (X_m, G_m) from Add Health, draw ε_m, solve the equilibrium fixed point (5) for each network, average over draws to approximate the true E_m(ˇy_m), and re-check the rank of A'A. If either check indicates deficiency, re-estimate without relying on the rank condition or report sensitivity of β_h−β_l to alternative instrument sets.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central identification claim (Proposition 3) depends entirely on Assumption 3(ii): full rank of A'A with A_m = [E_m(ˇy_m), G_m E_m(ˇy_m), 1_nm, X_m, G_m X_m, G^2_m X_m]. This is a high-level condition; the paper offers only the heuristic that the indicator function in ˇy makes failure 'unlikely' (Section 3.2). The empirical underidentification tests reported in Table 2 (Kleibergen–Paap LM test, p-values) assess the rank of 1/M Σ Ẑ'_m V_m (Assumption 4(ii)), not the rank of 1/M Σ A'_m A_m. These are different matrices: the former checks instrument relevance for the two endogenous regressors, while the latter is the actual identification condition used in the proof of Proposition 3. In particular, the proof sets to zero coefficients on E(ˇy), G E(ˇy), 1, X, GX, G^2X in equation (A.8); if G E(ˇy) or E(ˇy) lies in the span of the controls (or if the columns are otherwise collinear), the conclusion that θ=ϑ does not follow. Consequently, the statistically significant β_h−β_l estimates in Table 2 for smoking, fighting, and optimism—and the policy-loss calculations in Section 5.3 that rely on them—are not identified unless Assumption 3(ii) holds. No primitive conditions or direct verification of this rank condition is provided.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a structural model of asymmetric peer effects in which the social cost of deviating from a friend's outcome depends on whether the friend performs better or worse than the individual. The model yields an implicit best-response function and a reduced-form equation with two endogenous regressors: the standard average peer outcome and a new 'above-peer deviation' term. The authors prove existence and uniqueness of equilibrium, establish point identification under high-level rank conditions, propose an ML-based IV estimator with cross-fitting, and derive an analytical result showing that the standard symmetric model estimates a weighted average of the two asymmetric effects with potentially negative weights. Monte Carlo simulations illustrate finite-sample performance and the bias of the symmetric model. In Add Health data, the authors find statistically significant asymmetries for smoking, fighting, and optimism (but not drinking), and show in a targeted-intervention exercise that ignoring asymmetries can lead to large losses in spillovers.","tokens_in":37653,"tokens_out":11171,"duration_ms":94378,"significance":"If the identification conditions hold, the paper makes a valuable contribution: it provides a microfoundation for asymmetric social comparisons, a computationally feasible estimation strategy, and evidence that the widely used linear-in-means model can mislead both inference and policy design. The paper's analytical results (Propositions 1, 3, and 5) are carefully proved, and the Monte Carlo design includes a segregated-network DGP that demonstrates the finite-sample relevance of the theoretical bias. The replication code is publicly available, which strengthens the paper's reproducibility. The empirical findings on the direction of asymmetry across outcomes and the targeting application are novel and policy-relevant.","major_comments":[{"comment":"Point identification of β_l and β_h in Proposition 3 hinges on the full-rank condition on A_m = [E_m(ˇy_m), G_mE_m(ˇy_m), 1, X_m, G_mX_m, G_m^2X_m]. This is a high-level condition: the paper offers only the heuristic that the indicator function in ˇy makes failure 'unlikely', and it does not supply primitive sufficient conditions. The tests reported in Table 2 (first-stage F statistics and Kleibergen–Paap LM p-values) assess Assumption 4(ii), i.e., the rank of the instrument–regressor covariance matrix, not Assumption 3(ii); strong instruments can coexist with a rank-deficient A. Consequently, the statistically significant β_h − β_l estimates for smoking, fighting, and optimism, and the policy-loss calculations in Section 5.3 that rely on them, are not backed by a verification of the identification condition. I ask the authors to provide either low-level conditions on (G, X, and the distribution of ε) that imply Assumption 3(ii), or an empirical check based on a sample analog of A'A, for instance using nonparametric or ML estimates of E_m(ˇy_m).","section":"Section 3.2, Assumption 3(ii)"},{"comment":"The welfare analysis treats the estimated asymmetric model as the true data-generating process and reports spillover losses as point estimates, without confidence intervals or sensitivity analysis. Given the estimated standard errors on β_l and β_h (Table 2), the reader cannot judge whether the large losses for fighting and optimism, or the near-zero losses for drinking, are statistically distinguishable from zero. The abstract's claim of 'substantial welfare losses' would be more credible if accompanied by inference on the loss curves, such as delta-method bands or a bootstrap over networks.","section":"Section 5.3.2, Figure 2"}],"minor_comments":[{"comment":"The phrase '2 ni possible configurations' should be written as '2^{n_i} possible configurations' to avoid ambiguity.","section":"Section 2.2"},{"comment":"The abstract states 'we uncover strong evidence of asymmetries'; given that the drinking outcome does not show statistically significant asymmetry, the wording could be softened to 'we find evidence' or 'we document asymmetries for most outcomes'.","section":"Abstract"},{"comment":"After defining Ẑ_m, the paper says the predictions 'need not coincide with E_m(¯y_{m,i}) or E_m(ˇy_{m,i})'. This is correct but could be clarified by noting that consistency of the instruments is in the sense of Assumption 4(i), not mean-square consistency of the conditional expectation estimates.","section":"Section 3.3"},{"comment":"The row 'Total Peer Effect' lists ranges such as [0.549, 0.775] for smoking alongside the symmetric point estimate 0.740. It would be clearer to add a footnote explaining that the range is defined by β_l/(1+β_l) and β_h/(1+β_h) and that the symmetric estimate is β/(1+β).","section":"Table 2"},{"comment":"In the notes to Table 1, the standard deviations for the symmetric model in DGP 1 are lower than for the asymmetric model, as expected; this could be mentioned in the text to highlight the efficiency cost of the flexible specification.","section":"Section 4, DGP 1"}],"recommendation":"major_revision","confidential_remarks":"This is a solid and well-executed paper that makes a meaningful contribution to the peer-effects literature. My main reservation is the unverified high-level identification condition in Assumption 3(ii); I would like the editor to ensure the authors address this before publication, either with primitive conditions or an empirical verification. The policy-loss computations without inference are a secondary concern. The paper is within scope for the journal and, once the identification issue is dealt with, would be a strong publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid, inventive paper that deserves a serious referee. The model is genuinely new — asymmetric social distance with status-dependent weights, an implicit best response, and a contraction proof that handles the kinks. Proposition 5, on what the symmetric estimator recovers and why the implied weights can be negative, is a useful standalone result. The Monte Carlo is honest and the replication code is public. The theory is internally consistent and the empirical asymmetries for smoking, fighting, and optimism are plausible.\n\nThe main soft spot is exactly the one the stress-test flags, and it holds up on reading. Assumption 3(ii) is the central rank condition: no nonzero linear combination of E_m(\\check y) and G_m E_m(\\check y) lies in the span of 1, X, GX, G^2X. The proof of Proposition 3 needs it. But the paper's only defense is that the indicator function in \\check y makes failure \"unlikely,\" and the Kleibergen–Paap tests reported in Table 2 check the instrument-relevance matrix used in Assumption 4(ii), not the A'A matrix of Assumption 3(ii). Those are different matrices. So the empirical β_l≠β_h estimates and the welfare-loss numbers are not backed by a direct check of the condition that identifies them. This is a real gap, but it is patchable: give primitive conditions (variation in network structure or dyadic covariates, for example) or add a rank test or sensitivity analysis for A'A. The Monte Carlo helps, but it only shows the condition holds in the simulated DGP.\n\nOther soft spots are minor. The policy algorithms are heuristics with no regret bounds; the paper says so outright, and the forward/backward agreement is some reassurance but not a formal guarantee. The unmatched-links issue in Add Health is acknowledged and robustness-checked. The citation pattern looks appropriate.\n\nBottom line: the core — new model, equilibrium, identification, estimator, decomposition — is strong and worth engaging. This is for econometricians and applied micro people working on networks and peer effects. The rank-condition gap is real but fixable, not a refutation. I would send this to referees and ask them to focus on Assumption 3(ii) and on whether the empirical rank condition can be verified.","headline":"A credible new structural model of asymmetric peer effects with a real identification gap: the rank condition that carries the empirical results is not verified, and the reported KP tests check a different matrix.","tokens_in":38245,"tokens_out":3612,"would_cite":true,"duration_ms":32512,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["91D30","62P20","91A10"],"pacs":[],"model":"deepseek-v4-flash","headline":"Peer effects are asymmetric: students respond differently to friends who outperform them than to friends who underperform them, and ignoring this can waste or reverse the benefits of targeted interventions.","keywords":["asymmetric peer effects","peer effects","social interactions","conformity","network identification","targeted interventions","spillover effects","Add Health"],"falsifier":"Recompute the Table 2 estimates using linear first-stage instruments constructed from $X_m$, $G_mX_m$, $G_m^2X_m$, and the dyadic margins instead of random-forest predictions, with the same cross-fitting. If the estimated gaps $\\hat{\\beta}_h - \\hat{\\beta}_l$ for smoking, fighting, or optimism become small or change sign, the empirical asymmetry is an artifact of the instrument construction rather than a feature of peer influence.","tokens_in":37138,"feed_emoji":"🎓","tokens_out":8570,"duration_ms":72933,"temperature":0.7,"pith_summary":"The paper sets out to establish that peer effects are asymmetric: an individual's behavior responds differently to friends who outperform her than to friends who underperform her, and the standard symmetric peer-effects model misses this distinction. The authors build a game-theoretic model with two conformity parameters, one for lower-performing peers and one for higher-performing peers, prove that the game has a unique equilibrium, and derive a linear reduced form that can be identified and estimated with instrumental variables. Applying the method to Add Health data, they report significant asymmetry for smoking, fighting, and optimism, with the direction of asymmetry varying by outcome: students conform to heavier smokers, to more aggressive peers, and to more pessimistic peers, while the reverse comparisons have little effect. They then show that, in a budget-constrained targeting problem, selecting students with the symmetric model can leave spillover effects near zero and produce welfare losses of 40 to 100 percent relative to allocations that respect asymmetry. If the paper is right, empirical peer-effect estimates and network-based policies should treat the influence of higher-performing and lower-performing peers as two distinct objects rather than one.","feed_headline":"Peer effects are asymmetric in student behavior","feed_subtitle":"Add Health shows smoking, fighting, and optimism respond differently to higher- and lower-performing friends; symmetric models miss the…","key_machinery":"The load-bearing object is the asymmetric social distance function $S_i(y_i, y_{-i}) = \\frac{\\beta_l}{2}\\sum_{j:y_j \\leq y_i} g_{ij}(y_i-y_j)^2 + \\frac{\\beta_h}{2}\\sum_{j:y_j > y_i} g_{ij}(y_i-y_j)^2$, which assigns different conformity penalties depending on whether each peer is below or above the individual. This produces an implicit best response that can be rewritten as the linear reduced form in $\\bar{y}_i$ and $\\check{y}_i$, where $\\check{y}_i$ measures the status-weighted gap: the sum, over peers who beat the individual, of each peer's advantage, weighted by link strength. Identification is carried by the cross-network moment conditions combined with a rank condition requiring that $E_m(\\check{y}_m)$ and $G_m E_m(\\check{y}_m)$ cannot be reproduced by the span of own characteristics, friend characteristics, and friends-of-friends characteristics. Estimation uses machine-learned cross-fitted predictions of these conditional expectations as instruments, with the moment function shown to be orthogonal to the generated instruments.","core_discovery":"The central claim is that the asymmetric peer-effects model $y_i = (\\alpha_i + \\beta_l \\bar{y}_i + (\\beta_h - \\beta_l) \\check{y}_i)/(1+\\beta_l)$, where $\\check{y}_i = \\sum_j g_{ij} \\mathbf{1}\\{y_j > y_i\\}(y_j - y_i)$, is identified and estimable, and that in data its two parameters are not equal. The paper argues that the standard linear-in-means model estimates a weighted average of $\\beta_l$ and $\\beta_h$ with weights that can be negative, so the single symmetric parameter can lie outside the interval spanned by the two asymmetric effects. Empirically, using Add Health data, the paper finds that smoking, fighting, and optimism exhibit statistically significant asymmetry, while drinking is approximately symmetric. The policy consequence is that optimal targeting depends on students' positions in the outcome distribution, not only on network centrality, and that ignoring asymmetry can reduce welfare to levels comparable to a world with no social interactions.","pith_inferences":["The paper leaves implicit that its results call into question key-player policies based on symmetric models: if fighting is driven by conformity to more aggressive peers and optimism by conformity to more pessimistic peers, then the most effective targets may be the most extreme students, not the most central ones, in each outcome's distribution.","Because the identification argument rests on a high-level rank condition that is only asserted to be likely, a constructive low-level condition would make the method portable to other datasets; without it, every application must re-verify the rank condition empirically.","The two sequential allocation algorithms, forward and backward, are approximations and can disagree; a sharper test of the policy-loss claim would compare both against the oracle optimum in small networks where exhaustive search is feasible.","Since the reduced form is linear in parameters, the asymmetry estimates could in principle be reproduced with any standard IV routine once instruments are constructed; re-estimating on other school or workplace network datasets would show whether the qualitative pattern generalizes."],"forward_implications":["In the Add Health population, the null hypothesis $\\beta_l = \\beta_h$ is rejected for smoking, fighting, and optimism but not for drinking, so the symmetric model misstates peer influence for most outcomes.","A single symmetric peer-effect estimate can lie outside the range spanned by $\\beta_l$ and $\\beta_h$, so reporting an average influence can be misleading when the true effects are asymmetric.","Budget-constrained targeting rules built on the symmetric model can select students who exert little influence under the true asymmetric model; for fighting and optimism, spillovers can become zero or negative, with welfare losses reaching 70 to 100 percent.","Uniform productivity shocks still raise every individual's outcome by the same amount, so the asymmetry matters specifically for targeted, budget-constrained interventions rather than for uniform policies.","Simulations indicate that the symmetric specification also biases the coefficients on exogenous variables, suggesting that treatment-effect estimates in network settings can be distorted when peer effects are asymmetric."],"supporting_citations":[{"why":"Defines the reflection problem that motivates the need for network-based exclusion restrictions to identify endogenous peer effects.","marker":"Manski, 1993"},{"why":"Supplies the network restrictions that the paper's identification proof extends to the asymmetric model.","marker":"Bramoullé et al., 2009"},{"why":"Provides the standard symmetric linear social interactions model that serves as the baseline and supplies the stability condition that Assumption 1 mirrors.","marker":"Blume et al., 2015"},{"why":"Provides the double/debiased machine learning cross-fitting framework used so that the generated instruments do not distort inference.","marker":"Chernozhukov et al., 2018"},{"why":"Defines the budget-constrained targeting problem and the benchmark policy that the paper compares against asymmetric allocations.","marker":"Galeotti et al., 2020"},{"why":"Represents the recent approach to heterogeneous peer effects through the distribution of peer outcomes, which the paper shows is insufficient without accounting for the individual's own position.","marker":"Boucher et al., 2024"},{"why":"Provides the negative-weights analogy that explains why the symmetric estimate can lie outside the range of the asymmetric effects.","marker":"De Chaisemartin and d'Haultfoeuille, 2020"},{"why":"Supplies the rank LM test used to assess whether the instrument matrix satisfies the relevance condition in Assumption 4(ii).","marker":"Kleibergen and Paap, 2006"},{"why":"Documents status-structured friendship networks that can produce negative weights for the symmetric estimate, motivating the segregated-network simulation design.","marker":"Ball and Newman, 2013"}],"fun_headline_variants":["Peer effects are asymmetric: higher and lower peers differ","Asymmetric peer effects change how to target interventions","Better and worse peers affect students differently, study finds","Peer effects asymmetry: smoking, fighting, optimism respond differently","Ignoring asymmetric peer effects wastes resources, new model shows"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole argument hinges on a rank condition stating that the status-weighted gap variable $\\check{y}$ cannot be reproduced by own characteristics, friend characteristics, and friends-of-friends characteristics; the paper says this is likely because of the indicator function inside $\\check{y}$, but gives no primitive conditions, and if it fails the point estimates and policy-loss numbers collapse.","fun_headline_variants_meta":{"raw":{"variants":["Peer effects are asymmetric: higher and lower peers differ","Asymmetric peer effects change how to target interventions","Better and worse peers affect students differently, study finds","Peer effects asymmetry: smoking, fighting, optimism respond differently","Ignoring asymmetric peer effects wastes resources, new model shows"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000675,"raw_usage":{"total_tokens":3037,"prompt_tokens":877,"completion_tokens":2160,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":493,"completion_tokens_details":{"reasoning_tokens":2097}},"tokens_in":493,"tokens_out":2160,"duration_ms":14433,"temperature":1.0,"reasoning_tokens":2097,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:26:04.897859+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the Table 2 estimates using linear first-stage instruments constructed from $X_m$, $G_mX_m$, $G_m^2X_m$, and the dyadic margins instead of random-forest predictions, with the same cross-fitting. If the estimated gaps $\\hat{\\beta}_h - \\hat{\\beta}_l$ for smoking, fighting, or optimism become small or change sign, the empirical asymmetry is an artifact of the instrument construction rather than a feature of peer influence.","supporting_citations":[],"review_version":2}