Carbon Pricing versus Green Finance: Pedersen (2026)

What this is. The paper’s core results, the model it builds on (a dynamic general-equilibrium model with firms, households, and carbon externalities), and the theory it contributes (sustainable discount rates as a second-best substitute for carbon taxes) with the defining equations: enough to know what it found and how, without reading all 42 pages. To replicate or extend it, read the full source at the original (CC BY 4.0; open access).

TL;DR

In a dynamic general-equilibrium model with green and brown firms, carbon taxes, and ESG investors, Pedersen shows: (i) when the carbon price is at the social cost, green finance should not be used; (ii) when carbon prices are too low, green finance can restore the social optimum if each firm’s cost of capital is set to its sustainable discount rate, which equals the normal rate plus the ratio of untaxed carbon externality to firm value. Calibration with Trucost emissions and CRSP/Compustat values shows the market-value-weighted average sustainable discount rate adjustment for U.S. firms is only 0.19 pp at a 43 $/tCO2 social cost, while the brown electricity sector requires a 3.2 pp (average) to 8 pp (alternative calibration) increase. Empirical evidence from Eskildsen et al. (2024) suggests current green finance has an effect equivalent to only ~4 $/tCO2, far below what a green transition requires.

Core results

Magnitudes and significance are as reported. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Carbon tax at the social cost is sufficient; green finance should not be used when carbon is efficiently priced	Proposition 1, p. 576	Social optimum implemented by scope-1 taxes at $\tau = S$; discount rates stay at $r$ for all firms; green finance distorts the equilibrium if applied on top
R2	Sustainable discount rate implements the social optimum when carbon tax is too low, if firms can commit to future emissions	Proposition 4, pp. 578-579, eq. (17)	$r^*_{it} = r + (S_{t+1} - \tau_{it+1}) X_{it+1} / v_{it}$; equals normal rate plus firm’s carbon burden rate (untaxed externality scaled by firm value)
R3	Scope 1+2 sustainable discount rates can handle stranded assets where scope-1-only rates fail	Proposition 5, pp. 579-580, eq. (18)	Discount rate adds both direct (scope 1) and indirect (scope 2) carbon burden; brown electricity firms collapse as in the social optimum; stranded-asset problem resolved
R4	Green electricity firms can receive subsidized discount rates as compensation for implicit over-taxation via scope-2 rules	Proposition 6, pp. 580, eqs. (19)-(20)	Green electricity discount rate $r_{gt} = r - (S_{t+1} - \tau_{t+1})(F_b - F_g) G_{t+1} / v_{gt}$; lower than normal rate $r$; mirrors Proposition 3 green-subsidy result
R5	Market-value-weighted average sustainable discount rate adjustment is 0.19 pp for U.S. firms at S = 43 $/tCO2 (scope 1)	Figure 1 / Figure 3, pp. 564, 584; §VI.A	Median scope-1 burden rate 0.01%; market-weighted average 0.19%; scope 1+2 weighted average 0.23% (median 0.04%); most firms near baseline, a minority account for bulk of economy-wide emissions
R6	Brown electricity sector requires a 3.2 pp average increase in cost of capital (scope 1); alternative calibration gives 8 pp	Figure 1, p. 564; §VI.C, p. 587, eq. (27)	Brown electricity average 8.2% (3.2 pp above 5% baseline) at S = 43 $/tCO2; alternative calibration (zero-profit, $F_b = 820 \times 10^{-6}$ tCO2/kWh, 40% profit margin): $r_{bt} = 5\% + 8.0\% = 13\%$
R7	Empirical green finance implies an effective carbon tax of only ~4 $/tCO2, far below the social cost	Figure 1, p. 564-565; Eskildsen et al. (2024)	Slope of 4 on emission-to-value ratio from regressing firms’ implied cost of capital; corresponds to implicit $S - \tau = 4$ $/tCO2; at least an order of magnitude below what a green transition requires
R8	Carbon offset markets exhibit low and variable prices, predicted by the model as a sign of greenwashing	Appendix D, pp. 599-600	In equilibrium, offset prices must be proportional to quality ($\phi_q = \bar{\phi} \cdot q$); any price dispersion implies poor-quality offsets; firms buying low-quality offsets face an effective carbon tax reduced to ~10% of intended level

Overall (paper’s conclusion). Green finance is a second-best response when carbon pricing is inadequate, but implementation challenges (commitment problems, stranded assets, heterogeneous investors, greenwashing) make it difficult to deliver the required cost-of-capital adjustments. Regions able to impose a carbon tax have a clearer path to a green transition.

Theory / model

The model is a dynamic general-equilibrium model (Section III, pp. 572-575). There are $N$ goods-producing firms, green and brown electricity producers, and a representative household. The paper extends the equilibrium ESG investing framework of Pastor, Stambaugh, and Taylor (2021) to show exactly when green finance can and cannot replicate a carbon tax.

Goods-producing firms. Firm $i$ at time $t$ chooses labor $L_{it}$, green electricity $G_{it}$, brown electricity $B_{it}$, scope-1 emissions $X_{it}$, and investment $I_{it}$ to maximize endogenous firm value $V_{it}$. Output is $Y_{it}(z_{it})$ where $z_{it} = (K_{it}, L_{it}, G_{it}, B_{it}, X_{it})$. Capital accumulates as $K_{it} = (1 - \delta) K_{it-1} + I_{it-1}$. Firm profit (eq. 8, p. 573):

$$\Pi_{it}(z_{it}) = Y_{it} - w_t L_{it} - p_{gt} G_{it} - p_{bt} B_{it} - \tau_{it} X_{it} - \tau_{it}^{(2)} f_b B_{it} - \tau_{it}^{(2)} f_g G_{it}$$

where $\tau_{it}$ is a scope-1 carbon tax on direct emissions $X_{it}$; $\tau_{it}^{(2)}$ is a scope-2 carbon tax on indirect emissions via electricity use; $f_b$ ($f_g$) is the fossil intensity of brown (green) electricity in tCO2/kWh.

The firm maximizes its endogenous value (eq. 9, p. 573):

$$V_{it}(K_{it}) = \max_{z_{it+1}} \frac{\Pi_{it+1}(z_{it+1}) + V_{it+1}(K_{it+1})}{1 + r_{it}} - I_{it}$$

taking the discount rate $r_{it}$ as given.

Stylized two-period model (Section II, pp. 570-572). A single firm uses capital $K$ and fuel $X$, with output (eq. 4, p. 570):

$$Y = AK - \frac{1}{fK}(fK - X)^2$$

where $A > 0$ is productivity and $f > 0$ captures how polluting the firm is. Given a carbon tax $\tau$, profit is (eq. 5, p. 570):

$$\Pi = AK - \frac{1}{fK}(fK - X)^2 - \tau X$$

The profit-maximizing emission is $X = (1 - \tau/2) fK$.

Electricity firms. Green electricity producer profit (eq. 10, p. 574):

$$\Pi_{gt}(z_{gt}) = (p_{gt} + v_{gt} - \tau_{gt} F_g) G_t(z_{gt}) - \chi_{gt}(z_{gt})$$

where $v_{gt}$ is a proportional government subsidy and $\chi_{gt}$ is production cost. Brown electricity producer profit (eq. 11, p. 574):

$$\Pi_{bt}(z_{bt}) = (p_{bt} - \tau_{bt} F_b) B_t(z_{bt}) - \chi_{bt}(z_{bt})$$

where $\tau_{bt}$ is the direct carbon tax and $F_b > F_g$ is the fossil intensity of brown electricity.

Households. The household owns shares $\theta_{it}$ in each firm. Consumption (eq. 12, p. 574):

$$C_t = w_t L_t + \sum_{i \in I} \theta_{i,t-1} (\Pi_{it} + V_{it}) - \sum_{i \in I} \theta_{it} (V_{it} + I_{it}) + G_t$$

where $G_t$ is the government budget (carbon taxes net subsidies). Household utility (eq. 13, p. 574):

$$U = \sum_{t=1}^{\infty} \beta^t [ u_t(C_t) - d_t(X_t) ]$$

where $\beta$ is the time-preference rate, $u_t$ is consumption utility, $d_t$ is the damage of aggregate emissions $X_t = \sum_i X_{it} + X_{gt} + X_{bt}$.

Social planner’s problem. The planner maximizes $U$ subject to resource constraints (eq. 14, p. 575):

$$\sum_i G_{it} = G_t, \quad \sum_i B_{it} = B_t, \quad \sum_i L_{it} = L_t, \quad \theta_{it} = 1$$

The social cost of carbon $S_t = d'_t(X_t) / u'_t(C_t)$ is the marginal utility cost of pollution relative to the marginal utility of consumption.

Key propositions.

• Proposition 1 (p. 576): The social optimum is a competitive equilibrium with scope-1 carbon taxes $\tau_{it} = S_t$ for all firms, no green subsidies, and discount rate $r_{it} = r$ for all $i$.
• Proposition 2 (p. 576): The social optimum can also be implemented via scope-2 carbon taxes $\tau_{it}^{(2)} = S_t$ with no direct scope-1 taxes on goods producers.
• Proposition 3 (p. 577): With scope-2 taxes treating all electricity as brown, the social optimum requires a proportional subsidy to green electricity producers $v_{gt} = S_t(F_b - F_g)$.

Chittaro, Piazzesi, Sena, and Schneider (2025) generalize this framework with a rich input-output structure and short-sale constraints (p. 565).

Method

The paper is theoretical; it derives closed-form sustainable discount rates analytically and then calibrates them with external data. The method builds on dynamic-general-equilibrium and pigouvian-taxation.

Deriving the sustainable discount rate (Section V.A, pp. 577-579). Green finance must set each firm’s discount rate $r_{it}$ such that the firm’s optimization problem under the too-low carbon tax $\tau_{it}$ yields the same choices $z_{it+1}$ as the star-equilibrium under the social cost $S_t$. The condition (eq. 15, p. 577) is:

$$\max_{z_{it+1}} \frac{\Pi_{it+1}(z_{it+1}) + V_{it+1}}{1 + r_{it}} - I_{it} = V_{it} = \max_{z_{it+1}} \frac{\Pi_{it+1}(z_{it+1}) + V_{it+1} - (S_{t+1} - \tau_{it+1}) X_{it+1}}{1 + r} - I_{it}$$

where the right side is the star-equilibrium firm problem under the optimal carbon tax. Solving for $r_{it}$ (eq. 16, p. 578; full derivation pp. 578):

$$r_{it} = \frac{(1+r)(\Pi_{it+1} + V_{it+1})}{\Pi_{it+1} + V_{it+1} - (S_{t+1} - \tau_{it+1}) X_{it+1}} - 1 = r + \frac{(S_{t+1} - \tau_{it+1}) X_{it+1}}{v_{it}}$$

where $v_{it} = (\Pi_{it+1} + V_{it+1} - (S_{t+1} - \tau_{it+1}) X_{it+1}) / (1 + r)$ is the firm’s social value, equal to its market value in equilibrium. This is the carbon-burden-rate term: the missing carbon tax $(S - \tau)$ times emissions $X$, scaled by firm value $v$. Equations (17)-(20) state the four Propositions (4, 5, 6) in this notation (pp. 578-580).

Investor preferences that generate the sustainable discount rate (Section V.B, p. 581). When investors experience a disutility proportional to their carbon-footprint ownership (eq. 21, p. 581):

$$\sum_i \theta_{it} (\Pi_{it+1} + V_{it+1}) + \left(W_t - \sum_{i \neq 1} \theta_{it} v_{it}\right)(1+r) - \sum_i (S_{t+1} - \tau_{it+1}) \theta_{it} X_{it+1}$$

the FOC w.r.t. $\theta_{it}$ yields the required return (eq. 22, p. 581):

$$r_{it} = r + \frac{(S_{t+1} - \tau_{it+1}) X_{it+1}}{v_{it}}$$

which is exactly the sustainable discount rate (17). This shows green finance works precisely when the marginal investor fully internalizes externalities.

Long-term sustainable discount rate (Section VII.A, pp. 587-588). Using a Gordon growth model with dividend growth $g_{\Pi}$ and externality growth $g_X$ (eq. 30, p. 588):

$$\bar{r}^x_i = r + \frac{(S - \tau_i) X_i}{v_i} \cdot \frac{r - g_{\Pi}}{r - g_{X_i}} = r + \frac{\text{PV}[(S - \tau_i) X_i]}{v_i} \cdot \frac{1}{\text{Dur}_i}$$

where $\text{Dur}_i = 1 / (r - g_{\Pi})$ is the modified duration of dividends. The long-term sustainable discount rate is smaller than the short-term rate $r^*_{it}$ when emission growth is below dividend growth ($g_X < g_{\Pi}$).

Alternative calibration for brown electricity (Section VI.C, pp. 586-587). With a constant-returns-to-scale brown electricity technology $B_t = a K_{bt}$, cost $\chi_{bt} = \bar{\chi} \cdot a K_{bt}$, and the zero-profit condition (eq. 24-27):

$$p_{bt+1} = \tau_{bt+1} F_b + \bar{\chi} + \frac{r_{bt} + \delta}{a} \tag{24}$$ $$r_{bt} = r + (S_{t+1} - \tau_{bt+1}) F_b \cdot a \tag{25}$$ $$r_{bt} = r + \frac{(S_{t+1} - \tau_{bt+1}) F_b}{(r+\delta)/a} \cdot (r + \delta) \tag{26}$$

Calibrated at S = 43 $/tCO2, $F_b = 820 \times 10^{-6}$ tCO2/kWh, $(r+\delta)/a = 0.40 \times 0.11$ $/kWh (eq. 27, p. 587):

$$r_{bt} = 5\% + \frac{43 \times 820 \times 10^{-6}}{0.40 \times 0.11} \times (5\% + 5\%) = 5\% + \frac{0.035}{0.044} \times 10\% = 5\% + 8.0\% = 13\% \tag{27}$$

Empirical specifications

The paper is primarily theoretical; there is no econometric estimation. The empirical content is a calibration exercise (Section VI, pp. 582-587) using external data, plus a single regression from Eskildsen et al. (2024).

Calibration of sustainable discount rates (Section VI.A, pp. 582-584). For each U.S. publicly listed firm with Trucost scope-1 emissions data (fiscal year 2021), the scope-1 sustainable discount rate from Proposition 4 is computed as (eq. 17):

$$r^x_{it} = r + \frac{(S_{t+1} - \tau_{it+1}) X_{it+1}}{v_{it}}$$

• $X_{it+1}$: Trucost scope-1 CO2 emissions in tCO2 for fiscal year 2021
• $v_{it}$: firm market value = CRSP market equity + Compustat book value of debt, beginning of calendar year 2021
• $S_{t+1} - \tau_{it+1}$: set to $S = 43$ $/tCO2 (Nordhaus (2019) baseline; $\tau = 0$ for illustration)
• $r$: set to 5% for illustration

The social cost of carbon $S_t$ is taken as given from the Nordhaus (2019) calibrations and translated into a cost-of-capital adjustment. The resulting firm-level rates are aggregated to value-weighted industry averages using two-digit GICS sectors (Utilities split into Renewable Electricity, Brown Electricity, and Other Utilities).

Scope 1+2 calibration (Section VI.B, p. 585). Same procedure as above but using Proposition 5, adding scope-2 emissions $X^{\text{scope2}}_{it+1} = F_b B_{it+1} + F_g G_{it+1}$ (also from Trucost). Each firm’s scope-2 electricity estimate is multiplied by 1/0.6 = 1.67 to proxy total brown-equivalent consumption (60% of U.S. electricity from fossil fuels, 40% from renewables/nuclear).

Empirical regression (Figure 1, pp. 564-565; Eskildsen et al. 2024). Eskildsen et al. (2024) regress firms’ implied cost of capital on their emission-to-asset ratio, controlling for risk characteristics:

$$\text{implied\_COC}_i = \alpha + \beta \cdot \frac{X_i}{v_i} + \gamma \cdot \text{controls}_i + \epsilon_i$$

The estimated slope $\beta = 4$ ($/value per tCO2/value = $/tCO2). The paper reads this as empirical evidence that the market is pricing carbon externalities as if the implicit social cost minus explicit carbon tax is $S - \tau = 4$ $/tCO2, far below Nordhaus’s 43 $/tCO2 estimate (R7 above).

No panel regressions, fixed effects, or standard-error treatments are applied by the paper itself; the calibration is a direct plug-in of equation (17) into data.

Datasets used

Dataset	Role in paper	Wiki page
Trucost (scope 1 and scope 2 emissions, fiscal year 2021)	Firm-level carbon emission data for calibrating sustainable discount rates; scope 1 emissions in tCO2 per fiscal year; scope 2 electricity-based emissions	Trucost (licensed)
CRSP and Compustat (2021)	Market value of equity and book value of debt for constructing firm value $v_{it}$ used in calibration; also used to identify GICS industry sectors	WRDS / CRSP / Compustat (licensed)
Eskildsen et al. (2024) working paper data	Cross-sectional regression of firms’ implied cost of capital on emission-to-asset ratio; slope estimate of 4 used as empirical calibration of effective implicit carbon tax	No page yet
U.S. Energy Information Administration (electricity price data, 2021)	Average electricity price 0.11 $/kWh used in alternative calibration (§VI.C)	No page yet

Sample: U.S. publicly listed firms with Trucost emission data, fiscal year 2021; roughly 3,000+ firms ranked by scope-1 externality rate (Figure 3, p. 584). The paper’s model is calibrated at a single cross-section; no time-series econometrics are performed.

When to read the full paper

Use the original article if you are: extending the model to heterogeneous investors or multiple externalities (see also Pedersen 2026, J. Finance: Insights and Perspectives, forthcoming); calibrating sustainable discount rates for a specific sector or carbon-tax scenario using the exact proposition formulas; auditing a specific proposition or appendix proof (all proofs are in Appendix A); or doing a literature review on the carbon-pricing versus ESG debate. The Appendix B Cobb-Douglas model provides an alternative tractable derivation of the sustainable discount rate for readers preferring that functional form.

Attribution and rights

Source: peer-reviewed, The Journal of Finance 81(2). This distillation was extracted by an LLM on 2026-05-31 and augmented on 2026-06-01; it is not human-verified or independently reproduced. The article is open access under CC BY 4.0; this page is an adaptation (core results extracted and re-expressed; changes were made).

Attribution (CC BY 4.0). Pedersen, Lasse Heje. “Carbon Pricing versus Green Finance.” The Journal of Finance 81, no. 2 (April 2026): 561–602. DOI: 10.1111/jofi.70022. © 2026 The Author(s). Licensed under CC BY 4.0. This page is an adaptation by the Institute for Automated Research: core results extracted and re-expressed; changes were made.