AI paper checks

I've run most of my pre-AI-era, theory-heavy published papers through an AI check. I created a skill in Claude that checks for objective errors — mathematical and computational errors, as well as expositional errors (such as when the interpretation in the text doesn't match the formal model), typos, and other instances of imprecision. The reviewer also flags ambiguities and violations of implicit assumptions. The reviewer does not judge the papers, assess robustness, or offer other arguably subjective assessments. The review is designed to be adversarial; it looks for errors and often classifies unimportant ones as consequential. It runs on Claude Fable 5.1 (max effort). Most reviews take about two hours to run; some take much longer.

It's a somewhat scary and humbling exercise. The reviewer uncovered probably more errors than I expected or hoped for. That said, I am glad to report that all papers hold up as essentially correct, although in a few cases that conclusion requires restating a few assumptions.

The AI checks were all excellent; I couldn't find anything wrong with them. The reports don't work without the context; by design, they sound harsher than their findings warrant. To understand the reports, you also need to read the original papers. All papers have several errors. Most errors are inconsequential — what the check calls "minor slips." Some proofs contain errors that don't change the results. Some statements require minor adjustments or qualifications. Some implicit assumptions are missing. There is also a lot of nitpicking. Below, I summarise the conclusions for each paper and, when needed, my "reply" to some of the issues I found. Click for the paper and the full review.

1 - Options Can Increase Risk Taking for Arbitrary Preferences (Braido and Ferreira, Economic Theory, 2006) (Paper)(Review)

"The paper is correct," the review concludes.

2 - A Theory of Friendly Boards (Adams and Ferreira, Journal of Finance, 2007). (Paper)(Review)

All formal propositions and results hold as stated, with one exception: In items (b-c) of Proposition 7, a threshold is missing a term; no implications or qualitative conclusions are affected. As the review states, "no error compromises the paper’s conclusions."

3 - Corporate Strategy and Information Disclosure (Ferreira and Rezende, RAND Journal of Economics, 2007). (Paper)(Review)

All propositions hold as stated. A few secondary statements in lemmas and corollaries need qualifications to be correct; these imprecise statements are contained and have no further implications. The numerical example has wrong numbers due to a typo. We introduced the numerical example in the last revision round at a referee's request; funny how this goes. Don't read the example; the formal model is perfectly fine.

4 - Who Gets to The Top? Generalists versus Specialists in Managerial Organizations (Ferreira and Sah, RAND Journal of Economics, 2012). (Paper)(Review)

All formal results are correct as stated, except Property 5, which needs a condition (nonnegative mean) to be true always. Even without that condition, the economic intuition holds. A few informal statements throughout the paper need qualification.

5 - Incentives to Innovate and the Decision to Go Public or Private (Ferreira, Manso, and Silva, Review of Financial Studies, 2014). (Paper)(Review)

"Every lemma, proposition and corollary is correct as stated," the review says. Two proofs contain typos, but their results remain correct (the corrections are straightforward). The AI reviewer seems to interpret "without loss of generality" very literally and goes on and on about one such claim in footnote 8. Under a less stringent interpretation (i.e., economically speaking), our claim in that footnote is also correct.

6 - Unbundling Ownership and Control (Ferreira, Ornelas, and Turner, Journal of Economics and Management Strategy, 2015). (Paper)(Review)

Proposition 1 and every formal result that follows are mathematically correct as stated and proven. The first result in the paper — Lemma 1 — is correct only under an implicit assumption (we should have stated that "ex post shares are predetermined"). We use that assumption in the proof, and our notation implicitly suggests it; it was always in our minds but, fair enough, we did not make it explicit. So the results must be interpreted as correct "in the class of mechanisms with predetermined shares" (as opposed to all conceivable mechanisms). The reviewer essentially re-did all the analysis without predetermined shares (i.e., all conceivable mechanisms). All qualitative conclusions hold in that case too. Proposition 1 does not depend on this assumption anyway, and remains exactly true. Propositions 4-6 — the most economically relevant — hold exactly under general mechanisms once we adjust the threshold. The other propositions need minor adjustments. Overall, if anything, the review strengthens the paper's main conclusion: unbundling ownership and control facilitates control transfers.

7 - When Does Competition Foster Commitment? (Ferreira and Kittsteiner, Management Science, 2016). (Paper)(Review)

The reviewer says, "The paper is correct. (...) I found no error that affects a result or an insight."

8 - Talent Discovery and Poaching under Asymmetric Information (Ferreira and Nikolowa, Economic Journal, 2023). (Paper)(Review)

The reviewer says: "No error compromises the paper’s main conclusions. The equilibrium the paper analyses exists and is characterised correctly." Double thumbs up, in my view. This is probably the most technically challenging paper, so I was happy to learn that everything seems fundamentally correct here. Most of the reviewer's findings are technically correct, but nitpicky and inconsequential. The reviewer's main finding concerns an alleged non-uniqueness result that a subsequent equilibrium-selection assumption immediately remedies. Several of the points that follow relate to cases with multiple fixed points, unstated conditions, and imprecise statements. In addition, a continuity result at the very end of our very long Internet Appendix seems incorrect, with no consequences for any result that follows. 

9 - Corporate Capture of Blockchain Governance (Ferreira, Li, and Nikolowa, Review of Financial Studies, 2023). (Paper)(Review)

Another monster of a model. Everything in the main model checks out (including the IA; the numerical example is replicated exactly). Proposition 2 holds as stated but can be streamlined (error in the proof; no consequences). The reviewer even found some sufficient conditions for the existence of pure-strategy equilibria. The only consequential error is in the last extension to the model ("miner governance"); the qualitative implications still hold there, though.

10 - Prestige, Promotion, and Pay (Ferreira and Nikolowa, Journal of Finance, 2024). (Paper)(Review)

The reviewer says: "Every lemma, proposition and corollary of the main text is correct as stated." All errors are minor and inconsequential, or nitpicking.

11 - Polarization, Purpose and Profit (Ferreira and Nikolowa, Journal of Financial Economics, 2025). (Paper)(Review)

All headline results hold. Essentially, everything in the main text is correct, except in the investor extension, where the non-monotonicity doesn’t hold (Figure 3 is incorrect). Annoying, but no real harm done. All propositions are correct as stated (Proposition 10 is “imprecise” according to the reviewer; I'll take that).

12 - Subtle Discrimination (Pikulina and Ferreira, Journal of Finance, 2026). (Paper)(Review)

The reviewer says, "The equilibrium analysis and the principal’s problem of the main model are correct: Proposition 2 with its corner, Corollaries 1–3, Proposition 3, Propositions 4, 6 and 7, equations (10) and (16), Figures 1–4, and every formula of the IA except (IA.44) hold as stated and are reproduced." One minor error is that the symmetry used in the proof of Proposition 1 is not general; it holds for the quadratic cost function used in the paper, though. Inconsequential nitpicking. All else is minor slips (impossible to avoid, I now realise). Despite its recency, I note that we did not use AI to review the paper before publication. So, very happy with this one, especially with such a long Internet Appendix.