{"id":"7168d861-1f44-43fa-8bf8-ab50830732d6","arxiv_id":"2511.21446","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A continuous-time discrete choice model with endogenous peer attention is shown to be nonparametrically identifiable from long choice panels using variation in the number of potential peers.","lead":"This paper builds a model in which people or firms, when making choices, pay attention to only some of their peers, with which peers they notice depending on recent choices. It shows how a long record of choices could reveal who influences whom, how the attention mechanism works, and the underlying preferences.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unproven full-support claim in Proposition 3.1 is load-bearing: without it, CCPs used for identification may be unobservable in a long panel.","rationale":"The reader's weakest_assumption was Assumption 3, the rank condition needed to recover the network. While that is a legitimate concern, it is an explicit assumption that could be generically satisfied and is not internally inconsistent. The more load-bearing concern is the unproven Proposition 3.1, which the reader also flagged as a secondary issue. My stress-test elevates it: full support is a prerequisite for the CCPs at the configurations used in Proposition 4.1's network test to be estimable from a long panel. Without full support, the empirical claim 'identified from a single long panel of choices' is not justified. The gap is concrete—an isolated agent with a degenerate choice rule violates the theorem under the stated assumptions. This reinforces the reader's CONDITIONAL verdict: the identification argument is coherent if a strict-positivity or no-isolated-agent assumption is added, but as written the manuscript lacks a key proof and a necessary condition. Hence no change to the verdict is needed.","tokens_in":11268,"tokens_out":11994,"duration_ms":111993,"concrete_test":"Attempt to prove Proposition 3.1 or find a counterexample. Specifically, construct a two-agent model satisfying Assumptions 1 and 2 with N_1={2}, N_2=∅, Y={0,1}, Q_1 in (0,1), R_1 with full support, and R_2(·|y,∅)=δ_0. Compute the invariant distribution of the CTMC with transition rates (1). If the distribution assigns zero probability to states with y_2=1, Proposition 3.1 is false and the paper must add a strict-positivity condition on R_a(·|y,∅) for all a (or exclude empty reference groups) before the identification result can be interpreted as applying to a long panel.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central identification claim (Propositions 4.1–4.4) presumes the researcher can estimate CCPs at configurations such as y=0 and y=0^v_{a'} from a single long panel. That presumption rests on Proposition 3.1, which asserts a unique, full-support invariant distribution under Assumptions 1 and 2. Yet Appendix A contains no proof of Proposition 3.1, and the stated assumptions do not imply it. The model explicitly allows agents with empty reference groups (e.g., Agent 4 in Example 1, Section 2.1). For such an agent, Assumption 2(iii) is vacuous because there is no nonempty N⊆N_a. If that agent's choice rule R_a(·|y,∅) is degenerate—say, always chooses 0—then the continuous-time Markov chain defined by (1) has an invariant distribution with zero mass on configurations where this agent chooses 1. Full support fails. Moreover, even for non-isolated agents, nothing in Assumptions 1 and 2 rules out R_a(·|y,∅) being degenerate at 0 for some alternative v, although Assumption 2(iii) forces R_a(v|y,N)>0 for all nonempty N when R_a(v|y,∅)=0, so P_a(v|y)>0 in that case. The primary failure is isolated agents. If full support fails, the CCPs at the off-support configurations are not identified from data, so the network test in Proposition 4.1 (which relies on P_a(v|0^v_{a'})−P_a(v|0)) cannot be implemented for links involving such agents. The paper's identification results are mathematical statements conditional on knowing P_a for all y, but the claim that they are recoverable from a long panel of choices requires the unproven and false-as-stated full-support theorem. This is a more fundamental gap than the opacity of Assumption 3, which is at least an explicit rank condition.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a continuous-time discrete choice model with endogenous peer selection. Each agent, upon a Poisson alarm, first selects a subset of potential peers based on recent choices and then chooses an alternative conditional on the selected peers. Under type-homogeneity and independent peer selection, the paper claims that the social network, the peer-selection probabilities, and the choice rules are nonparametrically identified from a single long panel of choices, without exogenous covariate variation. The identification argument proceeds from conditional choice probabilities (CCPs): Proposition 4.1 recovers the network from CCP differences; Proposition 4.2 recovers selection probabilities and choice rules for empty and singleton peer sets using variation in reference-group size; Propositions 4.3 and 4.4 extend to parametric and fully nonparametric settings; Proposition 4.5 connects CCPs to panel data. The abstract also announces an empirical application to fast-food restaurant expansion and contraction, but no such application appears in the manuscript.","tokens_in":11725,"tokens_out":8872,"duration_ms":89897,"significance":"If the identification results hold, this is a meaningful contribution to the peer-effects and limited-attention literatures. The idea of using variation in the number of potential peers as a source of identification is elegant, and the monotonicity argument in the proof of Proposition 4.2 is a nice construction. The paper is generally clearly written and the examples are helpful. However, the full-support equilibrium result that underpins the empirical content is neither proved nor implied by the stated assumptions, and the abstract-promised empirical application is entirely missing. These issues must be addressed before the claims can be taken at face value.","major_comments":[{"comment":"The proposition asserts existence, uniqueness, and full support of the invariant distribution under Assumptions 1 and 2, but the stated assumptions are insufficient. Assumption 2(iii) is vacuous when N_a is empty, and empty reference groups are explicitly allowed (Example 1, Agent 4). If such an agent's choice rule R_a(·|y,∅) is degenerate at 0, then any configuration with y_a=1 has zero transition rate into it and zero invariant mass, so full support fails. No proof of Proposition 3.1 appears in Appendix A. This is load-bearing because Propositions 4.1–4.4 require CCPs at configurations y=0 and y=0^v_{a'}; if full support fails, those CCPs are not consistently estimable from a single long panel, and the network recovery test in Proposition 4.1 cannot be implemented for links involving isolated agents. The authors should add explicit strict positivity conditions on R_a(·|y,∅) (or rule ou","section":"Section 3, Proposition 3.1"},{"comment":"The abstract announces an empirical application to fast-food restaurant expansion and contraction and claims 'evidence of limited attention to actions of competitors.' No such application, data description, estimation, or results appear anywhere in the manuscript; the body ends with Section 5, Concluding Remarks. As submitted, this is an unsupported empirical claim and cannot be evaluated. The authors should either include the application in a revised version or remove the claim from the abstract.","section":"Abstract / main text"},{"comment":"Assumption 3 is the rank condition that makes the CCP difference in the proof of Proposition 4.1 nonzero, and therefore is load-bearing for network identification. It is stated in terms of Q, R, and the unknown network N_a, no primitive sufficient conditions are given, and it is not shown to be testable from the CCPs. Because the entire recursive identification collapses if Assumption 3 fails, the paper should provide at least one class of primitive models (e.g., logit or linear-in-means specifications) in which Assumption 3 holds, or an explicit discussion of when it is violated.","section":"Section 4.1, Assumption 3"}],"minor_comments":[{"comment":"The manuscript states 'All proofs can be find in Appendix A'; the appendix contains proofs of Propositions 4.1–4.3 only. Propositions 3.1, 4.4, and 4.5 are either unproved or deferred to related work. Please add proofs or explicit references.","section":"General"},{"comment":"In Example 1, 'NC3 = {2}' appears to be a typo for N_3 = {2}.","section":"Section 2.1"},{"comment":"The paragraph following Assumption 5 says 'Assumption 4.4 means that...' and should read 'Assumption 5 means that...'. Also, Assumption 2(i) writes Q_a(a'|y,N_a), but Q_a is defined as a function of y only; please be consistent.","section":"Section 4"},{"comment":"The notation 0^v_{a'} is used before it is defined; please define it in the main text.","section":"Section 4.1"},{"comment":"The identification of P and λ from Dataset 2 is delegated to Kashaev et al. (2025). Please state the identification condition more explicitly, since the current manuscript only mentions a generic eigenvalue restriction.","section":"Section 4.2"}],"recommendation":"major_revision","confidential_remarks":"This is a promising theoretical paper, but the submitted version is incomplete: the abstract promises an empirical application that is absent from the body, and the central equilibrium full-support result (Proposition 3.1) lacks a proof and is not implied by the stated assumptions. These issues need to be fixed before the paper can be considered for publication. I would also check that the identification arguments do not rely on circular normalizations beyond the stated assumptions, and that the dependence on prior working papers by the same authors is properly scoped."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The real contribution here is the identification strategy: recovering the reference network, peer-attention probabilities, and choice rules from a single long panel of choices, using only variation in the number of potential peers within types. That is new relative to the cited literature, and the recursive argument in Proposition 4.2 is clever and algebraically sound. The two-agent example showing how attention based on similarity can flip comparative statics is also nice. This is a solid theoretical core. The problem is at the base. Proposition 3.1 asserts a unique, full-support invariant distribution under Assumptions 1 and 2. It is not proven, and it is false as stated. The model explicitly allows agents with empty reference groups (Agent 4 in Example 1). If such an agent has a degenerate choice rule, say always chooses 0, then configurations where she chooses 1 have zero probability in the long run. Even for non-isolated agents, nothing in Assumptions 1 and 2 rules out a degenerate choice rule conditional on an empty active set. So the CCPs used in Proposition 4.1's network test, P_a(v|0^v_{a'}) - P_a(v|0), are not recoverable from a long panel when they involve off-support configurations. This is not a minor technicality: it breaks the chain from data to the identified structural objects. The identification theorems themselves are fine as statements conditional on knowing P_a for all configurations, but the paper's claim that they are recoverable from data needs a strict-positivity amendment. That is a fixable gap, add an assumption that all choice rules have full support on Y conditional on any active set, but it is load-bearing. Two smaller issues. Assumption 3, the rank condition that makes Proposition 4.1 work, is opaque. It is an explicit algebraic inequality, so not circular, but it deserves more discussion or a primitive sufficient condition; as written, you have to trust that it is the right sort of condition. Second, the abstract promises an application to fast-food restaurant expansion and contraction, but there is no empirical section in the body. Either include the exercise or drop the claim from the abstract. Who is this for? People working on empirical social interactions, especially dynamic discrete choice with networks. The central idea is worth a serious referee, and the equilibrium gap is specific enough that a good referee could help the authors fix it. I would not cite it in its current form, but I would recommend sending it to review with a request to amend and prove Proposition 3.1, and to sort out the empirical content.","headline":"Genuinely new identification idea undone by an unproven and false-as-stated full-support equilibrium claim; fixable, but currently the central results are conditional on unobservable CCPs.","tokens_in":690,"tokens_out":967,"would_cite":false,"duration_ms":38825,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"From a long panel of choices alone, an econometrician can recover the social network, the probability each agent attends to each peer, and the preferences that drive decisions — no covariates or network surveys required.","keywords":["peer effects","limited attention","identification","continuous-time Markov process","conditional choice probabilities","network","nonparametric identification","panel data"],"falsifier":"Construct two structurally distinct models satisfying Assumptions 1, 2, 4, and 5 that generate identical conditional choice probabilities for every possible history; such a pair would refute Proposition 4.4. Empirically, run a controlled experiment where the true network and attention probabilities are known, then apply the method and check whether it recovers those links and probabilities exactly.","tokens_in":11187,"feed_emoji":"🕸️","tokens_out":4844,"duration_ms":54924,"temperature":0.7,"pith_summary":"This paper asks whether a social network and the way agents pay attention to their peers can be recovered from the record of their choices alone. The authors build a continuous-time model in which each agent, when her alarm rings, first selects a random subset of peers (with probabilities depending on recent choices) and then makes a choice influenced by that subset. They show that if the econometrician observes choices over a long period, the reference groups, the peer-selection mechanism, and the choice rules are all nonparametrically identified — no exogenous covariates or network surveys needed. The key is that variation in the number of peers within an agent type creates a monotone relation between observed choice probabilities and the unobserved attention probabilities. This matters because ignoring limited attention in peer-effect models can bias estimates and mislead counterfactuals.","feed_headline":"Choice data alone reveals peer networks and attention","feed_subtitle":"Variation in friend counts lets economists separate who you notice from how you react to them.","key_machinery":"The engine of the argument is the mixture representation of conditional choice probabilities, P_a(v|y) = Σ_{N⊆N_a} R_a(v|y,N) S_a(N|y,N_a), combined with independent peer selection (Assumption 1), which makes S_a a product over individual peers. The identification lever is the strictly monotone function f(x) = (1 - x^{n3})/(1 - x^{n2}) linking observed CCP differences across agents with different numbers of peers to the selection probability q; because f is monotone, q is uniquely recoverable. The recursive step then identifies R for all peer subsets.","core_discovery":"The central claim, formalized as Proposition 4.4, is that the network (the set of potential peers for each agent), the peer-selection mechanism Q, and the choice rules R are all identified from the conditional choice probabilities (CCPs) alone, under Assumptions 1–5. The proof first shows that the CCP difference P_a(v|0^v_{a'}) - P_a(v|0) is zero exactly when a' is not a peer of a (Proposition 4.1), so the network is recoverable. Then, comparing same-type agents with different numbers of peers, the ratio of CCP differences equals a strictly monotone function f(x) = (1 - x^{n3})/(1 - x^{n2}) of the selection probability q, allowing q to be solved from data. With q in hand, choice rules for em","pith_inferences":["The monotone-ratio identification strategy may transfer to other settings where consideration sets vary in size, such as consumer choice over products with endogenous consideration, suggesting a general template for nonparametric identification of consideration-set models.","The paper's reliance on variation in reference-group sizes within types means that empirically, identification is strongest in populations with heterogeneous degree distributions; in nearly regular networks, the model may be only partially identified unless parametric restrictions are imposed.","The full-support equilibrium claim (Proposition 3.1) appears to require an unstated strict positivity of the choice and selection probabilities; if some configurations are unreachable, the CCP-based argument would need adjustment.","A potentially testable extension: use the recursive identification to check the independent-selection assumption by comparing Q estimates derived from different active-set sizes; systematic disagreement would signal correlated peer selection."],"forward_implications":["If the identification result is correct, researchers can map who influences whom from standard panel data, without administering network surveys.","The model provides a direct test of the full-attention assumption: if the rank condition behind Proposition 4.1 fails in a systematic way, agents likely do not consider all peers.","For linear-in-means logit peer effects, the paper implies that only the choice rules under no peer and one peer are needed for estimation, simplifying practical implementation.","The recovered attention probabilities Q allow separate measurement of two channels of peer influence: who you notice and how you react once you notice them.","Counterfactual policy analysis (e.g., informing a firm of competitor moves) becomes feasible from observational data."],"fun_headline_variants":["Choice data reveals who you notice","Peer networks from choices alone","Choices unmask hidden peer attention","Who you watch, from what you choose","Attend to peers: identified from choices"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is Assumption 3, a rank/relevance condition asserting that changing a peer's choice always alters an agent's choice probability in a way that is not cancelled by simultaneous changes in attention; if this condition fails, the network cannot be distinguished from the CCPs and the whole identification chain collapses.","fun_headline_variants_meta":{"raw":{"variants":["Choice data reveals who you notice","Peer networks from choices alone","Choices unmask hidden peer attention","Who you watch, from what you choose","Attend to peers: identified from choices"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000404,"raw_usage":{"total_tokens":1911,"prompt_tokens":683,"completion_tokens":1228,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":427,"completion_tokens_details":{"reasoning_tokens":1178}},"tokens_in":427,"tokens_out":1228,"duration_ms":10676,"temperature":1.0,"reasoning_tokens":1178,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T19:58:23.716262+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct two structurally distinct models satisfying Assumptions 1, 2, 4, and 5 that generate identical conditional choice probabilities for every possible history; such a pair would refute Proposition 4.4. Empirically, run a controlled experiment where the true network and attention probabilities are known, then apply the method and check whether it recovers those links and probabilities exactly.","supporting_citations":[],"review_version":1}