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Econ-368 · economics · Economics

Climate risk versus green preferences

LLM status Open unverified

Statement

Original subject group: Asset pricing and financial markets

Audit classification: Published research agenda. The Bank agenda supports climate-risk pricing, while Adam and Nagel support subjective-risk research generally. Neither inspected passage establishes the exact green-taste/climate-risk decomposition. Price and return contributions must be kept in consistent units.

Definitions and precise research target

Fix green and otherwise comparable conventional securities with payoff vector $X_{t+1}$, positive price vector $P_t$ and investor holdings. Gross returns are $R^k_{t+1}=X^k_{t+1}/P^k_t$ for security $k$. Investor $i$ has ordinary consumption utility and a nonpecuniary preference parameter $g_i$ for financing environmentally beneficial activity; investors may also hold different beliefs about climate states. Let $Z_{t+1}$ be a specified physical or transition climate-risk factor and $M_{i,t+1}$ the consumption discount factor. Within a separately specified taste-free common-belief benchmark, define climate risk compensation using covariance of returns with the benchmark pricing kernel; define a taste contribution as the equilibrium price change under $do(g_i=0\text{ for all }i)$, keeping cash-flow technologies fixed. The task is to identify these distinct contributions to green valuation differences. Use stated assumptions linking surveys to beliefs and preferences, and variation that shifts tastes separately from climate exposures. Determine whether the joint law of prices, returns, holdings and survey responses distinguishes taste changes from anticipated climate cash-flow losses. If it does not, derive bounds or observational equivalence results. Account for firm responses when interpreting financing effects. A lower expected green return alone cannot identify either the climate-insurance motive or environmental preferences.

Additional formal definitions and scope (editorial). A taste model must specify how environmental benefit enters utility, for example $u_i(c)+g_i G_i(q)$, where $G_i$ is a stated benefit from holdings and $g_i\geq0$; $g_i$ is not the climate exposure of the security. Define physical and transition shocks and their payoff channels separately. In a taste-free, common-belief benchmark with an interior pricing kernel, $E[R^k]-R^f=-\operatorname{Cov}(M,R^k)/E[M]$. With nonpecuniary benefits or constraints the ordinary consumption Euler equation has additional terms. The taste-price effect $P(g)-P(0)$ is in price units, whereas a covariance risk premium is in return units: these are distinct estimands and are not an additive decomposition of one spread. To compare channels in common units, re-solve every counterfactual and use a declared price or return decomposition. Matching green and conventional claims requires their maturity, default exposure, taxes and liquidity to be stated.

For the identification part, declare an admissible class $\Theta$ of structural models, including preferences, technologies, shock laws, measurement/sampling rules and any equilibrium selector. If $O$ denotes the complete observable history and $T(\theta)$ the target defined above, the identified set is $\mathcal I_T=\{T(\theta):\theta\in\Theta,\ \mathcal L_\theta(O)=\mathcal L_{\rm obs}(O)\}$; point identification means this set is a singleton. A $do(a)$ comparison replaces stated policy/technology equations while fixing the declared exogenous law and re-solving the remaining equations. These definitions do not assert that an identification theorem holds without further restrictions.

Variants and assumption changes

  1. Climate risk only (editorial). Set $g_i=0$, impose common beliefs and an identified kernel, and estimate payoff climate exposures and risk compensation.
  2. Tastes and belief heterogeneity (editorial). Permit $g_i$ and subjective climate forecasts to vary independently; seek exclusion restrictions or bounds for taste-removal price effects.

References and source audit

  1. Official January 9, 2026 web version; locator: The Financial System / System-wide efficiency, climate paragraph. Broad agenda; exact model editorial. URL: https://www.bankofengland.co.uk/research/bank-of-england-agenda-for-research.
  2. Metadata and Section 6 verified (printed pp.35--36). Subjective-risk background; green-taste decomposition not stated there. URL: https://bpb-us-w2.wpmucdn.com/voices.uchicago.edu/dist/f/575/files/2022/01/ExpectationsSurvey_13.pdf.
  1. Bank of England. 2026. Bank of England Agenda for Research, 2025–2028. The Financial System / System-wide efficiency, climate paragraph. https://www.bankofengland.co.uk/research/bank-of-england-agenda-for-research.
  2. Klaus Adam; Stefan Nagel. 2022. Expectations Data in Asset Pricing. Section 6, printed pp.35--36 (PDF pp.36--37). https://bpb-us-w2.wpmucdn.com/voices.uchicago.edu/dist/f/575/files/2022/01/ExpectationsSurvey_13.pdf. DOI: https://doi.org/10.3386/w29977.

Common conventions: Source mathematical conventions

These conventions apply to each entry unless explicitly replaced.

Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.

Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.

Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.

Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.

Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.

Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.

Statement licence: CC-BY-4.0 · Source file

Contributions 2

Econ-368-A2 · Exploration · LLM-generated · claude opus 5.5 high ·

Claude Opus 5.5 High attempt on Econ-368

Climate risk versus green preferences: an exact taste-removal formula, observational equivalence of tastes and beliefs, and survey-based identification

Abstract

In a CARA-normal economy with a climate factor, nonpecuniary tastes $g_i$ and heterogeneous subjective means, we prove the following. (i) The taste-removal effect $P(g)-P(0)$ equals the risk-tolerance-weighted mean taste, in price units, and does not depend on the covariance structure. (ii) Prices, holdings and payoff realisations identify the objective climate covariance and hence the risk-compensation term. They do not separate $g_i$ from optimistic subjective means, because $(\mu_i,g_i)$ enter only through $\mu_i+g_i$. (iii) Surveys that measure subjective means with classical error identify the mean taste and the taste-removal price effect, given risk tolerances identified from demand slopes. Individual tastes are identified only up to deconvolution. (iv) With an elastic green supply, the price effect is attenuated by an explicit factor. This shows that firm responses change the financing interpretation.

1. Economy

There is one period and a riskless asset with gross rate $1$. Risky payoffs are $X=a+bZ+\epsilon$, with green and conventional components; $Z\sim N(0,\sigma_Z^2)$ is the climate factor and $\epsilon\sim N(0,\Sigma_\epsilon)$. Investor $i$ has CARA $\gamma_i$, so risk tolerance is $\tau_i=1/\gamma_i$. Investor $i$ believes $\mathbb E_iX=\mu_i$ and shares the objective covariance $\Sigma=bb^\top\sigma_Z^2+\Sigma_\epsilon$. It derives nonpecuniary utility $g_i^\top x$ from holdings $x$. With supply $S$, demand is $x_i=\tau_i\Sigma^{-1}(\mu_i+g_i-P)$, and market clearing gives \[ P=\bar\mu_\tau+\bar g_\tau-\Sigma S/T,\qquad T=\textstyle\sum_i\tau_i,\ \ \bar\mu_\tau=T^{-1}\sum\tau_i\mu_i,\ \ \bar g_\tau=T^{-1}\sum\tau_ig_i. \]
Proposition (Taste removal): Under $do(g_i=0\ \forall i)$, holding supply, beliefs and payoff technology fixed, $P(g)-P(0)=\bar g_\tau$. Under the objective law, the expected-return effect is $\mathbb E[X]/P(g)-\mathbb E[X]/P(0)$, which is not additive with the risk premium.
Proof: Substitute into the clearing equation. $\Sigma S/T$ does not depend on $g$. ∎
The risk-compensation term in price units is $\Sigma S/T$. A green asset that hedges climate risk, i.e. has a negative covariance between its payoff and the market payoff through $b$, has a smaller discount. Both channels lower expected green returns, so a lower average green return identifies neither, as the statement stresses.

2. Observational equivalence

Proposition: Fix any model $(\gamma_i,\mu_i,g_i)$, and define $\mu_i'=\mu_i+g_i$, $g_i'=0$. The two models generate identical prices, holdings and payoff laws. Hence the taste-removal effect $\bar g_\tau$ is not identified from market data alone. Its identified set is $\{\bar g_\tau:\ \bar g_\tau+\bar\mu_\tau=\text{observed}\}$, which is unbounded without restrictions on subjective means.
Proof: Demands depend on $(\mu_i,g_i)$ only through their sum. Payoffs are drawn from the objective law, which neither model changes. ∎
Proposition (What payoffs do identify): From a time series of payoffs, $\Sigma$, $b$ and $\sigma_Z^2$ are identified. From price variation in $S$ (supply shocks), the demand slopes $-\tau_i\Sigma^{-1}$ identify $\tau_i$. So the risk-compensation term $\Sigma S/T$ is identified.

3. Surveys

Proposition: Suppose surveys report $\tilde\mu_i=\mu_i+\eta_i$, with $\mathbb E[\eta_i\mid\tau_i,\mu_i,g_i]=0$, and $(\tau_i,x_i)$ are observed. Then $\mu_i+g_i=P+\gamma_i\Sigma x_i$ is identified for each $i$, so $\bar g_\tau$ is identified as $\mathbb E_\tau[P+\gamma_i\Sigma x_i-\tilde\mu_i]$, a $\tau$-weighted mean. The distribution of $g_i$ is identified from that of $(\mu_i+g_i)-\tilde\mu_i$ if the law of $\eta$ is known (deconvolution). Otherwise only its mean and, if $\eta$ is independent of $g$, its variance up to $\mathrm{Var}(\eta)$ are identified.
Proof: Invert demand. The survey error averages out in the $\tau$-weighted mean by the conditional-mean-zero assumption. ∎
The key maintained assumption is that survey answers measure the same subjective mean that enters demand. This exclusion links surveys to preferences and must be justified, for example by eliciting incentivised forecasts.

4. Firm responses

Proposition: Suppose the green supply responds as $S_G=\bar S_G+\kappa P_G$, with $\kappa\ge0$, in a single-green-asset version with $\Sigma$ scalar $\sigma^2$. Then $P_G(g)-P_G(0)=\bar g_\tau\,/\,(1+\kappa\sigma^2/T)$.
Proof: Solve $P=\bar\mu_\tau+\bar g_\tau-\sigma^2(\bar S+\kappa P)/T$ for $P$. ∎
So the "cost-of-capital" effect of tastes is smaller when green issuance is elastic, and the financing impact of tastes is the induced change in $S_G$, namely $\kappa$ times the price effect. Distinguishing tastes from beliefs therefore matters for both prices and real investment.

5. Remaining

Dynamic models with time-varying tastes and climate news, and nonlinear preferences (for example Epstein--Zin with climate disasters), break the closed forms. Proposition Proposition persists whenever tastes and beliefs enter demand through a common index, which is a general obstruction. Exclusion restrictions separating tastes from exposures (for example mandate shocks affecting only $g$ for some institutions) are the needed variation [boe,an].

Completion Estimate

55%

This is a post hoc, heuristic estimate for the full catalogue target. The CARA-normal model proves taste-removal equivalence and survey-based mean identification, with an explicit elastic-supply attenuation result. Dynamic climate exposures, independently identified risk tolerances and credible taste-versus-belief exclusions remain outside the established conditional benchmark.

References

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Econ-368-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-368

Climate risk versus green preferences: a research attempt

Target and outcome

Status: unresolved. This attempt derives a common-unit price decomposition in a tractable equilibrium, constructs exact taste--belief observational equivalence, and supplies conditional bounds. It does not empirically separate climate compensation from green preferences in actual securities. A lower expected green return alone is insufficient for that separation.

The Bank of England research agenda [bank] supports studying climate-risk pricing. The CARA--normal specialization and identification results below are additional derivations, rather than a decomposition theorem quoted from that agenda.

A solvable equilibrium with heterogeneous beliefs

There are $K$ risky claims in fixed net supply $s\in{\mathbb{R}}^K$ and a risk-free gross return $R_f>0$. Investor $i$ has risk aversion $a_i>0$, subjective normal payoff mean $\mu_i$, and common positive-definite payoff covariance $\Sigma$. Holdings $q_i$ are unconstrained. An environmental-benefit vector $e\in{\mathbb{R}}^K$ is fixed by technologies, and $g_i\geq0$ is the investor's taste coefficient. Specify the investor's certainty-equivalent objective as \[ q_i^\top(\mu_i-R_fP)+g_i e^\top q_i -\frac{a_i}{2}q_i^\top\Sigma q_i. \] This is a precise preference model in payoff units. It can be generated by exponential utility over final wealth plus the deterministic nonpecuniary equivalent $g_i e^\top q_i$. It is not assumed to describe arbitrary green preferences or constrained institutions.

Strict concavity gives unique demand \[ q_i=\frac1{a_i}\Sigma^{-1}(\mu_i+g_i e-R_fP). \] Let $T=\sum_i1/a_i$, $\bar\mu=T^{-1}\sum_i\mu_i/a_i$, and $\bar g=T^{-1}\sum_i g_i/a_i$. Market clearing $\sum_iq_i=s$ yields the unique price vector \[ R_fP=\bar\mu+\bar g e-\Sigma s/T. \] Assume primitives keep all compared prices positive. A counterfactual removing tastes while fixing beliefs, covariance, risk aversion and claim supplies re-solves the same clearing equation and gives \[ P(g)-P(0)=\bar g e/R_f. \] This is a price difference, not a return premium. Holdings change in the counterfactual even though the price expression is simple.

A taste-free common-belief climate benchmark

Set every $g_i=0$ and $\mu_i=\mu$, the physical mean. Suppose \[ X=\mu+bZ+\epsilon,\qquad {\mathbb{E}} Z=0,\quad{\operatorname{Var}}(Z)=\sigma_Z^2, \quad{\operatorname{Cov}}(Z,\epsilon)=0, \] with jointly normal shocks and ${\operatorname{Cov}}(\epsilon)=\Sigma_\epsilon$. Then $\Sigma=\sigma_Z^2bb^\top+\Sigma_\epsilon$. In price units, \[ P^0=\frac\mu{R_f} -\frac{\sigma_Z^2b(b^\top s)}{TR_f} -\frac{\Sigma_\epsilon s}{TR_f}. \] The middle term is the price discount associated with the declared climate factor and aggregate climate exposure. It can be negative for a climate hedge. Its interpretation depends on the factor definition; physical and transition shocks can be separated by expanding $Z$ into a vector with its full covariance matrix.

For completeness this benchmark has a positive stochastic discount factor \[ M=\frac1{R_f}\exp\left[-\frac{s^\top(X-\mu)}T -\frac{s^\top\Sigma s}{2T^2}\right]. \] Normal exponential moments give ${\mathbb{E}} M=1/R_f$ and ${\mathbb{E}}[MX]=(\mu-\Sigma s/T)/R_f=P^0$. Thus its ordinary Euler equation is valid; a linearized kernel that becomes negative in normal tails is unnecessary. For claim $k$, \[ {\mathbb{E}} R_k^0-R_f=\frac{(\Sigma s)_k}{TP_k^0} =-\frac{{\operatorname{Cov}}(M,R_k^0)}{{\mathbb{E}} M}. \] All terms in this display are returns. They must not be added directly to the earlier taste price effect. If one wants the taste-induced expected-return change while keeping physical cash-flow means fixed, it is \[ \frac{\mu_k}{P_k(g)}-\frac{\mu_k}{P_k(0)}, \] which is nonlinear in the price shift and must be evaluated with the two equilibrium denominators.

An exact identification failure

For any investor-specific numbers $\delta_i$ with $0\leq\delta_i\leq g_i$, transform primitives by \[ \mu_i'=\mu_i+\delta_i e,\qquad g_i'=g_i-\delta_i. \] The composite $\mu_i+g_i e$ is unchanged, so every investor's entire demand function, all equilibrium holdings and prices are unchanged. Keep the physical payoff law fixed: the transformation changes subjective beliefs, not realized cash flows. Yet the taste-removal price counterfactual changes because $\bar g$ changes. Taking $\delta_i=g_i$ produces a zero-taste model with the same observed prices, returns and holdings as a positive-taste model.

Survey responses do not automatically break this equivalence. If the model permits an unrestricted reporting equation, its intercept or error can offset the changed subjective mean. This observation does not discredit all surveys; it identifies the necessary restriction. A survey that truthfully measures $\mu_i$ with identified measurement error, together with known risk aversion and covariance, can use \[ g_i e=R_fP-\mu_i+a_i\Sigma q_i \] to distinguish beliefs from tastes. Multiple securities additionally test whether the right-hand vector is proportional to the known environmental-benefit vector. Without holdings or known risk aversion, that equation leaves further confounding.

Conditional sharp bounds

Suppose $T,\Sigma,s,e,R_f$ are known and data or validated belief surveys restrict the aggregate subjective mean of claim $k$ to $[\ell_k,u_k]$. For $e_k>0$, its price equation gives \[ \bar g\in\left[ \frac{R_fP_k-u_k+(\Sigma s)_k/T}{e_k},\quad \frac{R_fP_k-\ell_k+(\Sigma s)_k/T}{e_k}\right]. \] Intersect these intervals across claims and with a declared feasible taste range, for example $[0,g_{\max}]$. Coordinates with zero benefit instead impose the compatibility condition $R_fP_k+(\Sigma s)_k/T\in[\ell_k,u_k]$. Negative-benefit coordinates reverse the endpoint ordering.

These bounds are sharp in the aggregate-equilibrium model if the mean restrictions are a Cartesian product and every retained $\bar g$ is implementable by investor primitives without additional holdings restrictions. Set $\bar\mu=R_fP-\bar g e+\Sigma s/T$ to construct each compatible mean. If observed investor holdings or correlated survey restrictions are also imposed, the interval intersection is generally only an outer bound; the joint restrictions must then be solved together. Multiplying retained $\bar g$ values by $e/R_f$ gives the joint taste-price-effect set, not independently chosen coordinate intervals.

Remaining limits

The exact decomposition assumes fixed supplies, unconstrained portfolios, common covariance and a specified preference normalization. Firm financing responses can change supply and future cash flows when tastes shift, so the taste-removal effect would require solving firms' choices too. Climate exposures, subjective beliefs and utility risk aversion need separately justified measurements. The construction proves why price and return data alone need not separate the channels, while the full empirical decomposition remains unresolved.

Completion Estimate

58%

This is a post hoc, heuristic estimate for the full catalogue target. A solved heterogeneous-belief equilibrium provides consistent price and return channel calculations, exact taste-belief equivalence and conditional sharp aggregate bounds. Empirical risk preferences, validated beliefs, portfolio constraints and endogenous firm cash-flow responses remain necessary for the full valuation decomposition.

References

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