Strategic Wishful Thinking: Implications for Forecasts

That the direction of the bias in individual forecasts varies across forecasters and across settings, which existing explanations tend to address only in part. Regressing forecast errors on forecast revisions, Coibion and Gorodnichenko (2012, 2015) show consensus forecasts under-react for macroeconomic variables, while Bordalo, Gennaioli, Ma and Shleifer (2020) show individual forecasts tend to over-react. Against that, Bouchaud, Krueger, Landier and Thesmar (2019) document under-reaction in individual forecasts of financial variables like earnings per share, suggesting the biases vary across settings; the same paper documents that the degree of under-reaction varies across forecasters. Ahn and Farmer (2024) find forecasters assign heterogeneous weights to public information and that this is an important source of forecast dispersion, especially during downturns. The paper’s stated complaint about existing models is not only that they target a subset of these patterns, but that they typically assume individuals are symmetric, so they cannot account for differences in the interpretation of public information — and where heterogeneity is introduced by assuming forecasters hold different beliefs, such assumptions do not explain when or why the disagreement should arise.

It is a deliberate choice of subjective belief: the forecaster picks the precision she attributes to the public signal so as to maximise her anticipatory utility, subject to a penalty from taking suboptimal actions. Anticipatory utility — the idea that anticipation of a future experience directly affects current utility — dates at least to Jevons (1905), and the paper builds on Brunnermeier and Parker (2005), Caplin and Leahy (2019) and Banerjee, Davis and Gondhi (2024). Importantly, individuals do not exhibit “multiple selves”: they consciously hold a single set of beliefs, so subjective beliefs affect actions too, which generates a tension between holding accurate beliefs that lead to ex-post optimal actions and desirable beliefs that raise contemporaneous utility. The paper draws an explicit contrast with ambiguity aversion and robust control, where the agent minimises over a set of reasonable beliefs while maximising over actions; here the agent maximises over both, choosing actions that perform well given favourable rather than adverse outcomes. It notes both are likely relevant and leaves a model incorporating both to future work.

The quadratic-Gaussian coordination framework of Angeletos and Pavan (2007), with a continuum of players whose payoffs depend on the state, the average action and the dispersion of others’ actions, plus subjective beliefs about public-signal precision. Each of a unit measure of players chooses an action to maximise expected payoff, which is quadratic in its arguments and symmetric across other players’ actions. The state θ is normally distributed, and each player observes a private signal and a public signal, each equal to θ plus independent normal noise. Players face uncertainty about the quality of the public signal and may entertain subjective beliefs about its precision: player i perceives the public-signal error variance scaled by 1/δ_{η,i}, so δ = 1 means her beliefs coincide with the objective distribution (rational expectations), while δ greater or less than one means she over- or underestimates the precision. Assumption 1 (own-action concavity, and the strategic-response coefficient below one) ensures equilibrium actions are unique and bounded.

A forecaster’s payoff has three terms: her own accuracy, a coordination term, and a pure externality from the consensus forecast’s accuracy. Writing θ for the target variable, k_i for forecaster i’s forecast and K for the consensus, the payoff is −(k_i − θ)² − ρ(k_i − K)² − γ(K − θ)². The first term captures the incentive to produce an accurate forecast. In the second, ρ ∈ (−1, 1) reflects strategic considerations: ρ < 0 means forecasters want to stand out (forecasts are strategic substitutes), ρ > 0 means they want to herd (strategic complements). The third captures the externality: when γ < 0, forecaster i is better off when the consensus is further from the truth — the paper describes this as a natural feature of many forecasting settings, that “being right” is more valuable when others are wrong. A key observation is that under rational expectations the optimal forecast depends on ρ but is independent of γ; it is only when forecasters choose subjective beliefs that γ affects behaviour.

A fundamental-uncertainty channel that always pushes towards overestimating public precision, and an aggregate-error channel whose sign is set by the combination χ = −ρ − γ(1 + ρ). With no strategic considerations or externalities (ρ = γ = 0), a wishful thinker tends to over-estimate the public signal’s precision, because doing so raises her perceived accuracy and hence her anticipatory utility — the fundamental-uncertainty channel — and this leads to over-reaction in individual forecasts. Separately, when γ > 0, errors in the consensus reduce payoffs, so there is an incentive to overestimate public precision; when γ < 0 an individual is better off when others make mistakes, creating an incentive to underestimate it. Strategic considerations work analogously: ρ > 0 (herding) creates an incentive to overestimate, ρ < 0 (standing out) to underestimate. The net impact is summarised by χ: when χ is sufficiently positive (negative), an individual has an incentive to under-estimate (over-estimate) the precision of the public information. This is what distinguishes the analysis from rational-expectations models, where absent strategic considerations actions are informationally efficient.

For intermediate values of γ, where neither channel dominates for all individuals — and the equilibrium is unique. For a fixed ρ: when γ is sufficiently high the two channels reinforce each other and all individual forecasts over-react; when γ is sufficiently low the aggregate-errors channel dominates for everyone and forecasts under-react. In either case the unique equilibrium is symmetric. For intermediate γ, symmetric equilibria do not exist, and the unique equilibrium features mixed strategies in which players endogenously choose to “agree to disagree” about the public information — some underestimating its precision, others overestimating it. The logic is a best-response reversal: if an individual believes many others are overestimating the public signal’s precision, she tends to underestimate it, since she is better off believing others are wrong; if she believes enough others are dismissive of the public information, she is better off conditioning on it. The equilibrium is pinned down by the fraction of individuals on each side that makes every individual indifferent between the two sets of subjective beliefs.

Because aggregate mistakes there indicate mispricing, which is a profitable trading opportunity. The paper offers a microfoundation and an empirical link. Banerjee, Davis and Gondhi (2024) provide the microfoundation for γ < 0 by showing that in a trading setting with heterogeneously informed investors, each investor’s private information is more valuable when others are not informed and the price is noisy. Empirically, Bouchaud et al. (2019) show that when consensus analyst forecasts of EPS deviate significantly from fundamentals, the market prices of such firms are also substantially misaligned relative to fundamentals, as evidenced by the pronounced profitability anomaly — so to the extent such anomalies represent profitable trading opportunities, an analyst forecasting financial variables is better off when others’ forecasts are more incorrect on average. The paper’s phrasing is that this suggests the externality among such analysts is characterised by a negative γ.

The paper argues professional incentives amplify rather than suppress the bias. It acknowledges the natural objection — that professional forecasters, given their training, experience and access to data, might be largely immune to biases such as wishful thinking — and answers that a substantial earlier literature emphasises the strategic considerations affecting such forecasters’ incentives to distort their reports, some having incentives to stand out from the rest and others to shade towards consensus to avoid being too wrong. These pressures, it argues, can induce wishful thinking and subtly shift beliefs toward more favourable outcomes, especially when there is enough ambiguity in the data to allow motivated interpretation without overtly violating statistical norms — so that wishful thinking becomes not just a quirk but a behavioural bias amplified by professional incentives.

It generates individual over-reaction and consensus under-reaction even with no strategic considerations and no externalities, which is the feature distinguishing it from strategic explanations. Under rational expectations, individual forecasts exhibit over-reaction (CG_i < 0) if and only if ρ < 0, and consensus forecasts exhibit under-reaction (CG_a > 0) whenever private signals carry information — the latter because individuals have dispersed private signals with uncorrelated errors, so the aggregate information available is more precise than any individual’s, and the consensus under-reacts to it. With wishful thinking, individual over-reaction and consensus under-reaction both arise even when ρ = γ = 0, provided private-signal precision is sufficiently large: absent strategic considerations, a forecaster’s objective is to get as close to the target as possible, so her anticipatory utility is higher when she perceives the public signal as more informative, which produces individual over-reaction. More generally, over-reaction at the individual level holds when γ is sufficiently large, and for γ sufficiently small the individual CG coefficient turns positive.

By mapping the sign of the externality onto the type of variable being forecast, within one mechanism. The paper states the stylised fact it wants to explain: consensus forecasts under-react across most variables, while individual forecasts tend to over-react for macroeconomic targets but under-react for financial ones — Bordalo et al. (2020) and Gemmi and Valchev (2023) show individual forecasts of short-term treasuries under-react, and Bouchaud et al. (2019) show analyst-level EPS forecasts under-react. Existing models, it observes, often target either individual-level over-reaction or under-reaction and therefore cannot usually reconcile both in the same framework. In this model, for relatively larger (or less negative) γ, individual forecasts over-react while the consensus under-reacts — the region corresponding to macroeconomic forecasts; for sufficiently negative γ, individual forecasts under-react while the consensus continues to under-react — the region corresponding to financial forecasts such as earnings or interest-rate forecasts.

Zero dispersion in a symmetric equilibrium; positive and hump-shaped in γ in a mixed equilibrium — and dispersion that cannot arise at all under rational expectations. This is presented as a distinctive prediction. The paper’s argument for why it discriminates between theories is careful: dispersion in forecasts can arise either because players have private signals or because they disagree about the interpretation of the public signal, so forecast dispersion alone cannot distinguish the settings. But dispersion in CG coefficients can: even when private signal precisions differ across players — through different information acquisition decisions, or staggered attention — there cannot be dispersion in individual CG coefficients when players exhibit rational expectations, since they use all their information efficiently and CG_i = 0. The prediction is described as consistent with the heterogeneity in individual CG coefficients Bouchaud et al. (2019) document for EPS forecasts and the disagreement about public information Ahn and Farmer (2024) document for macroeconomic forecasts, with the further implication that dispersion for financial-market forecasts should be greater than or equal to that for macroeconomic forecasts.

Yes, and the paper claims to produce both of their results in one setting. Kohlhas and Walther (2021), using SPF forecasts of output growth and inflation, document that individual forecasts exhibit under-reaction to new information alongside over-reaction to recent realisations — in their specifications, a negative coefficient on the public signal and a positive coefficient on the consensus forecast revision, both of which would be zero under full-information rational expectations. In a symmetric equilibrium of this model there is over-reaction to public information if and only if the chosen precision multiplier exceeds one, which holds if and only if γ > −1; and there is under-reaction to consensus forecast revisions under a stated precision condition. The paper notes that Kohlhas and Walther claim the evidence of over-reaction in individual forecasts is driven by outliers and provide a generalised model with a bias to accommodate this, whereas its own model gives rise to both results in the same setting through what it describes as a transparent and intuitive mechanism.

Dispersion falls with public-signal precision under rational expectations and in symmetric equilibrium, but can rise with it in the mixed equilibrium — which is the regime the paper associates with downturns. Under rational expectations, more precise public information leads forecasters to put less weight on private signals, so dispersion falls, and dispersion is independent of γ. In a symmetric equilibrium with subjective beliefs, dispersion is higher than under rational expectations if and only if γ < −1, and still decreases in public-signal precision — which the paper matches to Ahn and Farmer’s evidence on dispersion in “normal times”. In a mixed equilibrium, dispersion is driven both by private information and by heterogeneous interpretation of the public signal, can increase with public information quality, and is non-monotonic in γ, because the fraction of players on each side shifts endogenously — disagreement is low when that fraction is near zero or one and higher in the middle. The paper relates the increasing case to evidence that increased central bank communication can increase forecast dispersion (Lustenberger and Rossi 2018), which it argues is difficult to reconcile with symmetric rational-expectations models where a more precise public signal crowds out private information acquisition and reduces belief dispersion.

When public information quality is low — which the paper links, with a stated qualification, to downturns. Part (iv) of its dispersion result states that for sufficiently low ψ (the penalty parameter on suboptimal actions), all else equal, the mixed equilibrium in which forecasters disagree about the interpretation of public information is more likely when the precision of the public signal is low. The paper’s connection to the data is explicitly conditional: to the extent that public information quality is worse and public uncertainty higher during economic downturns, this prediction is broadly consistent with Ahn and Farmer’s evidence about when disagreement about public information drives forecast dispersion.

It lists five stylised facts and argues its single mechanism covers all of them, while explicitly describing rival mechanisms as complementary rather than wrong. The five are: (1) over-reaction to forecast revisions for macroeconomic variables but under-reaction for financial variables; (2) cross-sectional heterogeneity in individual CG coefficients; (3) over-reaction to public information; (4) under-reaction to consensus forecast revision; and (5) disagreement in the interpretation of public information, increasing during downturns. The paper reports that its model generates consensus under-reaction plus (1)(i), (3) and (4) even with ρ = γ = 0, and gives rise to (1)(ii), (2) and (5) when γ is negative but not too small. Against rational-inattention and noisy-rational-expectations models (Woodford; Maćkowiak and Wiederholt; Myatt and Wallace; Kohlhas and Walther), it argues these can generate consensus under-reaction and (4), but focus on symmetric equilibria and assume players hold correct beliefs about the information they observe and update by Bayes’ rule — the first making (2) and (5) unlikely to be generated. It states its goal is to provide distinctive predictions while viewing its mechanism as complementary to the alternatives, a number of which it expects are relevant in practice.

Yes, and the results there are asymmetric between own and others’ signals. Extending the framework to subjective beliefs about private-signal precision, the paper shows wishful thinking leads to overestimating the precision of one’s own signal — that is, to overconfidence — while subjective beliefs about others’ signals depend on the relative impact on payoffs of aggregate volatility versus dispersion in others’ actions. An appendix also allows forecasters’ payoffs to depend on forecast dispersion, which the paper reports provides an incentive to distort beliefs about the precision and correlation of others’ signals; it abstracts from dispersion-based externalities in the main text for expositional clarity.

Three directions, each of which it names as a limitation of the current setting. First, studying how information acquisition or attention interacts with players’ endogenous perception in the presence of externalities — the current analysis takes the information structure as given. Second, extending to dynamic settings to characterise the implications of wishful thinking for the term structure of forecasts and disagreement, and how this interacts with the persistence of fundamentals. Third, recognising that individuals are likely to exhibit wishful thinking in some settings but a preference for robust control in others, exploring the implications of a setting in which individuals can choose to exhibit both.