From Brown to Green: Climate Transition and Macroprudential Policy Coordination ^†

Abstract

We develop a dynamic, stochastic general equilibrium (DSGE) model for the euro area that accounts for climate change-related risk considerations. The model features polluting (“brown”) firms and non-polluting (“green”) firms and a climate module with endogenous emissions modeled as a byproduct externality. In the model, exogenous shocks propagate throughout the economy and affect macroeconomic variables through the impact of interest rate spreads. We assess the business cycle and policy implications of transition risk stemming from changes in the carbon tax, and the implications of the micro- and macroprudential tools that account for climate considerations. Our results suggest that a higher carbon tax on brown firms dampens economic activity and volatility, shifting lending from the brown to the green sector and reducing emissions. However, it entails welfare costs. From a policy-making perspective, we find that when the financial regulator integrates climate objectives into its policy toolkit, it can minimize the trade-off between macroeconomic volatility and welfare by fully coordinating its micro- and macroprudential policy tools.

1. Introduction

“Climate change has consequences for us as a central bank pursuing our primary mandate of price stability, and our other areas of competence, including financial stability and banking supervision.”

Christine Lagarde, President of the European Central Bank.

International Climate Change Conference, Venice, 11 July 2021.

A fundamental aspect in the climate crisis mitigation strategy of the European Union’s Green Deal involves the reduction in greenhouse gas emissions (GHG) by at least 55 percent by 2030 compared to 1990 levels and ensure reaching “net zero” by 2050 (Allen et al. 2018). Achieving the above targets is paramount to the ability of limiting global warming to well below 2 °C relative to pre-industrial levels by the end of the century and preventing severe and potentially irreversible impacts on the planet’s ecosystems, human health, and economies.1 To unlock a massive shift of investment from fossil fuel to renewable energy sources, the Green Deal commitment requires a sizable capital mobilization. The European Commission estimates that by combining public and private funding sources, a capital mobilization of at least EUR 1 trillion in sustainable investments is needed over the next decade (European Commission 2019). The substantial changes in policies, technologies, and market dynamics as economies shift towards carbon neutrality create financial uncertainty and potential losses. These factors represent a significant source of transition risk that impact households, firms, and the financial sector. In this respect, the banking sector in the euro area is exposed to high emitters for over 70 percent of the corporate lending portfolio.

Economists generally consider the carbon tax on emitters to be the most economically efficient approach to reducing emissions (Akerlof et al. 2019). However, there is a growing consensus that carbon pricing alone cannot fully address the chronic effects of climate change. In addition, the implementation of carbon pricing mechanisms give rise to several challenges, which include asymmetric distributional impacts that disproportionately affect lower-income groups and regions (Grainger and Kolstad 2010), potential carbon leakages and lack of harmonization (Aichele and Felbermayr 2015), and political resistance (Blanchard et al. 2023). These considerations make carbon pricing a necessary but insufficient measure. Thus, achieving carbon neutrality hinges on an integrated approach encompassing a set of complementary policies, including monetary and prudential policies within the limits of their mandate. Against this background, policymakers have initiated work to quantify, monitor, manage and mitigate climate-related risks. A prominent example of such an effort is the Network for Greening the Financial System (NGFS), which has been pioneering work for the assessment of climate-related risks and it has been developing reference scenarios to explore plausible pathways for climate policy, technological developments and their economic impacts on socioeconomic variables (Bertram et al. 2020). In the same vein, the Financial Stability Board (FSB) has put forward views on the need for tools and policies to sufficiently address systemic risks arising from climate change. It acknowledged how climate systemic risks can give rise to abrupt increases in risk premia across a wide range of assets, altering asset price (co-)movements and amplifying credit and liquidity risks in ways that are hard to predict. In addition, from a financial stability perspective, the FSB’s assessment calls for wide policy coordination, as microprudential tools alone may not sufficiently address the cross-sectoral, global and systemic dimensions of climate-related risks, as well as tail risks and the potential for the financial system to amplify its effects (FSB 2023).

Despite a broad consensus regarding the relevance of climate-related risk for financial stability, the positions of policymakers on the policy options available to account for climate-related risks in the prudential framework are a source of debate and are constantly evolving. In 2023, the European Banking Authority (EBA) ruled out the introduction of a green supporting factor or a brown penalizing factor in the short-term, first advocated for by the European Commission, on the ground that the use of such adjustment factors presents challenges in terms of design, calibration, and complex interactions with the existing Pillar 1 framework. At the same time, the EBA has put forward recommendations for targeted enhancements to accelerate the integration of environmental and social risks across Pillar 1, in order to support the green transition, while ensuring that the banking sector remains resilient.2 In this context, in 2023 the European Central Bank (ECB), jointly with the European Systemic Risk Board (ESRB), released a comprehensive common EU strategy for macroprudential policies to address climate risk, recognizing climate change as a systemic risk and paving the way toward a regulatory framework where microprudential and macroprudential policies can complement each other to ensure that the financial system is robust and resilient in the face of climate-related financial risk (ESRB 2021). Finally, in its March 2024 statement on the review of the monetary policy operational framework, the Governing Council of the ECB acknowledged that the design of the new operational framework for steering very short-term interest rates will incorporate climate change-related considerations into the structural monetary policy operations.3

In light of the above policy debates and the challenges of climate change, there is a pressing need to develop models that help in understanding the complex interactions between climate policies, regulatory policies, and other business cycle shocks. Such models are crucial for assessing their impact on macroeconomic variables under different sources of uncertainty and for quantifying the trade-offs associated with different policy measures. Despite the broad recognition that climate change-related financial risks pose micro- and macroprudential concerns, analysis and research is at an early stage and the literature is scant. This paper aims at filling this gap. We build on the ongoing policy discussions, and design an environmental, dynamic, stochastic general equilibrium (E-DSGE) that focuses on the interplay between microprudential and macroprudential policies in a context of transition risk and assess policy implications.4 The key contribution of our paper is to show that a financial regulator aiming at accounting for climate considerations can successfully adopt a combination of borrower-based and capital-based measures to contribute reducing emissions in the short-term, but with longer-term welfare costs. We show that if the financial authority commits to the climate objective by fully coordinating its micro- and macroprudential measures, the financial stability–efficiency trade-off improves.

The reminder of this paper is structured as follows. Section 2 provides a review of the related literature. Section 3 introduces the framework of the model and the economic agents. Section 4 provides the quantitative analysis of the model. Section 5 presents our micro- and macroprudential policy experiments and assesses the welfare implications. Section 6 concludes.

2. Related Literature

Recent literature has shown that there are several mechanisms through which financial institutions can affect environmental outcomes, such as by promoting environmental sustainability through bank lending practices and by using green bonds for financing sustainable projects as a way for the financial sector to support the transition to a green economy. For instance, empirical evidence for the bond market has shown that climate-related factors matter for borrowing costs, as firms with high pollution levels generally incur higher capital costs, which appear to be a significant factor in providing incentives to firms for adopting greener practices (Bolton and Kacperczyk 2021, 2023; Krueger et al. 2020). In taking climate-related considerations into account in our DSGE framework, our paper shares many features with canonical medium-scale DSGE models (Christiano et al. 2005; Smets and Wouters 2007) and with a growing body of literature that introduces financial intermediation into well-established quantitative macroeconomic frameworks (Gertler and Kiyotaki 2010; Gertler and Karadi 2011; De Walque et al. 2010; Brunnermeier and Sannikov 2014; Sims and Wu 2020; Lubello and Rouabah 2024). Most importantly, our paper relates to a burgeoning macroeconomic body of literature that attempts to introduce climate-related considerations into standard general equilibrium models. These models belong to different classes, which fundamentally differ in their underlying assumptions and modeling approach. A non-exhaustive classification includes: computational general equilibrium models (CGE), agent-based models (ABM), Integrated Assessment Models (IAM) and more recently DSGE models. Early attempts to integrate climate risk into general equilibrium models largely focused on the impact of environmental policies and carbon taxes. Nordhaus’s DICE (Dynamic Integrated model of Climate and the Economy) and the RICE (Regional Integrated model of Climate and the Economy) models, while not DSGE models in the strict sense, laid foundational work by incorporating economic activity and environmental feedback loops. These models paved the way for DSGE models by illustrating the economic costs of climate change and the benefits of mitigation policies (Nordhaus 1992, 2011; Nordhaus and Yang 1996) and (Dietz and Stern 2015). Acemoglu et al. (2012) introduced a model where innovation in clean technologies reduces the long-term impact of climate change. They emphasized the role of government policy in directing research and development (R&D) towards green technologies. Their model demonstrated that optimal policy could balance economic growth with environmental sustainability. Another strand of the literature examines the interaction between climate policies and macroeconomic stability. For instance, Annicchiarico and Di Dio (2015) developed a DSGE model incorporating environmental policies such as carbon taxes and subsidies for green investment. Their findings suggest that well-designed environmental policies can enhance macroeconomic stability by reducing the economic volatility caused by climate shocks, while (Van der Ploeg and Rezai 2021) developed a DSGE model for the optimal carbon pricing with stranded assets. However, none of the existing literature has assessed the role of micro- and macroprudential policy and their interaction in the context of climate transition risk.

3. The Model

In this section, we introduce the key ingredients of the model. The economy consists of households, labor unions, retailers, polluting (“brown”) and non-polluting (“green”) intermediate good firms, and banks. A central government conducts fiscal policy, a monetary authority conducts monetary policy and a regulatory authority conducts micro- and macroprudential policies. In the model, households derive utility from consumption and from health status, which is positive influenced by their health expenditure and negatively affected by emissions. Finally, households derive disutility from labor, which is supplied to labor unions at a nominal wage rate. Labor unions bundle together household labor supply according to a CES aggregator and provide labor inputs to each intermediate good producer. Households allocate their labor income between consumption of a composite of brown and green goods and bank deposit earning interest. Production is horizontally integrated. Intermediate good firms produce output to be sold to sectoral retailers and are subject to a microprudential regulatory constraint that governs their ability to issue debt and obtain bank funding for new investment. Retailers transform the intermediate good at no cost into a final consumption good for each sector, in monopolistic competition and staggered price setting. The economy features a pollution externality arising as a byproduct of brown production. The central government sets a carbon tax on firms and levies an environmental tax on households proportional to brown consumption to internalize the negative externality of emissions on aggregate health. We assume that the resulting tax revenues are rebated to the green firm in the form of a subsidy to R&D expenditure of green firms, which boosts endogenous growth and productivity in the emission-free green sector. Hereafter, we denote the variables and parameters related to the brown sector with superscript or subscript $“B”$ and those related to the green sector with superscript or subscript $“G”$.

3.1. Households

There is a continuum of identical households of measure unity. Preferences are defined over a consumption bundle $\left(\widehat{C_t}\right)$, labor supply $\left(N_t\right)$ and a health-related indicator $\left(H_t\right)$, according to the following per-period utility:

$$U_t\left(C_t,C_{t-1},N_t,H_t\right)=\left[{\displaystyle \frac{\nu }{1-\nu }}\ln {\widehat{C}}_t+\omega {{\displaystyle \frac{H_t}{1+\upsilon }}}^{1+\upsilon }-\psi {\displaystyle \frac{N_t^{1+\eta }}{1+\eta }}\right],$$

(1)

where $\widehat{C_t}$ follows a preference specification as in Bouakez and Rebei (2007) and Wolff and Sims (2017), with $\widehat{C_t}$ being a composite of brown and green consumption, $C_t^B$ and $C_t^G$, respectively:

$$\widehat{C_t}=\varphi {\left(C_t^B-h{C}_{t-1}^B\right)}^{{\displaystyle \frac{\nu }{\nu -1}}}+\left(1-\varphi \right)C_t^{G{\displaystyle \frac{\nu }{\nu -1}}}.$$

(2)

The parameter $\varphi$ measures the relative weights on brown and green consumption, and $\nu >0$ is a measure of their elasticity of substitution. When $\nu >1$, brown and green consumption are utility substitutes; when $\nu <1,$ they are utility complements. If $\nu \to 1,$ utility becomes additive separable. The parameter $h\in [0,1)$ is the coefficient governing the intensity of internal habit in consumption, $\psi >0$ is a scaling parameter for hours worked, $\omega$ is the relative importance of health for the household, $N_t={\sum }_{j\in \left\{B,G\right\}}{\int }_0^1{w}_{j,i,t}{L}_{j,i,t}di$ is the labor supply across sector j to unions indexed by i. The parameter $\eta >0$ is the inverse of the Frisch elasticity of labor supply. To capture the impact of emissions on households, we postulate a negative nexus between health and emissions (see Coyle et al. 2003, Conceiçao et al. 2001 and Daellenbach et al. 2020, inter alia, for supporting evidence) and similarly to Grossman (2017) and Halliday et al. (2019) we assume that household health evolves according to the following law of motion:

$$H_{t+1}=\left[1-\delta \left(E_t\right)\right]H_t+I_t^H,$$

(3)

where $\delta \left(E_t\right)={\delta }_1^E{E}_t$ captures the impact of of emissions ($E_t$) on household health, the magnitude of which is governed by the parameters ${\delta }_1^E>0.$ The stock of emissions evolves as

$$E_t=\left(1-{\delta }_x\right)E_{t-1}+X_t,$$

(4)

where ${\delta }_x$ is a constant rate of emissions abatement and $X_t$ is the flow of new emissions.5 Equation (3) captures the fact that health is negatively affected by both the cumulative stock of emissions and the continuous flow of new emissions. As a consequence, the household needs to increase health-related expenditure, $I_t^H$, in order to restore health status in $t+1$.6

Each household can smooth consumption through nominal bank deposits $\left(D_t\right)$ that pay a gross interest rate, $R_t^D$. The household is subject to the following nominal budget constraint:

$$P_t{C}_t^B\left(1+{\tau }_{c,t}\right)+P_t{C}_t^G\left(1-{\tau }_{c,t}\right)+D_t+I_t^H=R_{t-1}^D{D}_{t-1}+\widetilde{W_t}{N}_t++DI{V}_t-P_t{T}_t-P_t{Z}_t,$$

(5)

where $P_t$ is the price of the consumption good, ${\tau }_{c,t}$ a tax on the consumption good produced by the brown sector, $\widetilde{W_t}$ is the nominal rate for supplying labor inputs to labor unions, $DI{V}_t$ denotes net real lump-sum transfers including profits from the ownership of all non-financial firms and net worth from exiting intermediaries, as well as tax transfers to the government; $Z_t$ is a real transfer to new financial intermediaries paid by households upon the entry of new intermediaries. The household maximizes (1) subject to the law of motion of their health status (3) and the budget constraint (5).

The first-order conditions with respect to brown consumption $\left(C_t^B\right)$, green consumption, $\left(C_t^G\right),$ labor supply $\left(N_t\right),$ deposits $\left(D_t\right),$ health expenditure $\left(I_t^H\right)$ , and health status $\left(H_{t+1}\right)$ are as follows:

$$\begin{array}{ccc}& & {\lambda }_t^h\left(1+{\tau }_c\right)={\displaystyle \frac{1}{{\widehat{C}}_t}}\varphi {\left(C_t^B-h{C}_{t-1}^B\right)}^{-{\displaystyle \frac{1}{\nu }}}-\beta h{\mathbb{E}}_t{\displaystyle \frac{1}{{\widehat{C}}_{t+1}}}\varphi {\left(C_{t+1}^B-h{C}_t^B\right)}^{-{\displaystyle \frac{1}{\nu }}},\hfill \end{array}$$

(6)

$$\begin{array}{ccc}& & {\lambda }_t^h={\displaystyle \frac{1}{{\widehat{C}}_t}}\left(1-\varphi \right){\left(C_t^G\right)}^{-{\displaystyle \frac{1}{\nu }}}\hfill \end{array}$$

(7)

$$\begin{array}{ccc}& & N_{j,i,t}={\left({\displaystyle \frac{{\lambda }_t^h\overline{w_{j,i,t}}}{\psi }}\right)}^{{\displaystyle \frac{1}{\eta }}},\hfill \end{array}$$

(8)

$$\begin{array}{ccc}& & 1={\mathbb{E}}_t{\Lambda }_{t,t+1}{\Pi }_{t+1}^{-1}{R}_t^D,\hfill \end{array}$$

(9)

$$\begin{array}{ccc}& & {\lambda }_t^h={\lambda }_{2,t},\hfill \end{array}$$

(10)

$$\begin{array}{ccc}& & {\lambda }_{2,t}={\displaystyle \frac{\omega }{H_{t+1}}}\beta \left[1-\delta \left(E_{t+1}\right)\right]\hfill \end{array}$$

(11)

where ${\lambda }_t^h$ is the (real) marginal utility of consumption, ${\lambda }_{2,t}$ is the real marginal utility of health, ${\overline{w}}_t=\tilde{W}/P_t$ is the real wage relevant for the household, ${\Lambda }_{t,t+1}=\beta {\lambda }_{t+1}^h/{\lambda }_t^h$ is the stochastic discount factor, ${\Pi }_{t+1}=P_t/P_{t-1}$ is the gross inflation rate. Equations (6)–(9) represent, respectively, the marginal utility of brown and green consumption, the labor supply and the Euler equation governing the intertemporal decision between consumption and saving. Equation (11) describes how the household must balance the marginal utility of consumption with the marginal utility of health, taking into account the emissions’ externality on health. The trade-off between health and emissions implies that higher economic activity leads to a higher deterioration rate of the health status, which requires higher health investments to maintain a given level of health.

3.2. Production

There is an investment firm that creates new physical capital and sells it to intermediate good producers, which can be “brown” or “green”. The brown firm generates anthrophogenic emissions, which we model as byproduct externality of production in the brown sector. Both firms rely on bank funding to finance the acquisition of productive inputs and face a “loan-in-advance constraint”. A continuum of retail firms repackage the intermediate output at no cost and resell it to a final good producer.7

3.2.1. Emission Externality

In the spirit of Heutel (2012), Golosov et al. (2014) and Barrage (2020), we model emissions as a negative consequence of economic activity. Therefore, we assume that flow emissions $\left(X_t\right)$ and brown economic activity $\left(Y_t^B\right)$ are linked by a pro-cyclical emission function:

$$X_t=\zeta Y_t^B,$$

(12)

where $\zeta >0$ is the emission-to-output ratio (or the emission intensity) at time t.8 The central government levies carbon tax, ${\tau }_t$, proportional to emissions, thus levying ${\tau }_t{X}_t$ on emitters.

3.2.2. Brown Firm

The representative brown firm adopts a production function that takes brown capital $\left(K_t^B\right)$ and labor $\left(N_{d,t}^B\right)$ as inputs:

$$Y_t^B=A_t{\left(u_t{K}_t^B\right)}^{\alpha }{\left(N_{d,t}^B\right)}^{1-\alpha }$$

(13)

where $A_t$ is the aggregate technological shifter, and $\alpha$ is the elasticity of capital. Brown capital accumulates according to the law of motion

$$K_{t+1}^B=\left(1-\delta \right)K_t^B+{\tilde{I}}_t^B,$$

(14)

where ${\tilde{I}}_t^B$ is new investment and $\delta$ is the depreciation rate of capital. The brown firm issues debt $\left(B_t\right)$ to finance new investment and is subject to a loan-in-advance constraint as in Sims and Wu (2020), which postulates that only a fraction ${\psi }^B>0$ of investment can be financed by issuing new debt

$${\psi }^B{\tilde{I}}_t^B\le Q_t^B\left(B_t^B-{\kappa }^B{B}_{t-1}^B\right),$$

(15)

where ${\kappa }^B\in \left[0,1\right]$ is a parameter that proxies for the time duration of nominal debt priced at market price $Q_t^B$, so that $Q_t^B\left(B_t^B-{\kappa }^B{B}_{t-1}^B\right)$ is the value of new issuance. The brown firm’s maximization plan is to maximize profits, subject to the capital accumulation Equation (14), the loan-in-advance constraint (15), the emission function (12), and the carbon tax ${\tau }_t{X}_t$.

The first-order conditions with respect to labor demand $N_{d,t}^B$, brown capital, $K_t^B,$ capital utilization, $u_t^B$, and investment, $\widetilde{I_t^B}$, are the following:

$$\begin{array}{ccc}& & \left(p_{w,t}-{\tau }_t\zeta \right)\left(1-\alpha \right)A_t{\left(u_t^B{K}_t^B\right)}^{\alpha }{\left(N_{d,t}^B\right)}^{-\alpha }=w_t^B\hfill \end{array}$$

(16)

$$\begin{array}{ccc}& & p_t^{B,k}{M}_{2,t}^B{\delta }^{\prime }\left(u_t^B\right)=\alpha \left(p_{w,t}-{\tau }_t\zeta \right)A_t{\left(u_t^B{K}_t^B\right)}^{\alpha -1}{\left(N_{d,t}^B\right)}^{1-\alpha },\hfill \\ & & p_t^{B,k}{M}_{2,t}^B={\mathbb{E}}_t{\Lambda }_{t,t+1}\left[\alpha \left(p_{w,t}-{\tau }_t\zeta \right)A_t{\left(u_t^B{K}_{t-1}^B\right)}^{\alpha -1}{\left(N_{d,t}^B\right)}^{1-\alpha }\right]\hfill \end{array}$$

(17)

$$\begin{array}{ccc}& & +{\mathbb{E}}_t{\Lambda }_{t,t+1}\left[1-\delta \left(u_{t+1}^B\right)\right]p_{t+1}^{B,k}{M}_{2,t+1}^B\hfill \end{array}$$

(18)

$$\begin{array}{ccc}& & {\displaystyle \frac{M_{1,t}^B-1}{M_{2,t}^B-1}}={\left({\psi }^B\right)}^{-1},\hfill \end{array}$$

(19)

$$\begin{array}{ccc}& & Q_t^B{M}_{1,t}^B={\mathbb{E}}_t{\Lambda }_{t,t+1}{\Pi }_{t+1}^{-1}\left[1+{\kappa }^B{Q}_{t+1}^B{M}_{1,t+1}^B\right],\hfill \end{array}$$

(20)

$$\begin{array}{ccc}& & {\psi }^B{p}_t^{B,k}{\tilde{I}}_t^B=Q_t^B\left(B_t^B-{\kappa }^B{B}_{t-1}^B{\Pi }_t^{-1}\right),\hfill \end{array}$$

(21)

where $w_t^B$ is real wage, $p_t^{B,k}$ is the price of new capital. The terms $M_{1,t}^B$ and $M_{2,t}^B$ are auxiliary variables, which equal one when the loan-in-advance constraint is slack.

3.2.3. Green Firm

The representative green firm adopts a production function that takes green capital $\left(K_t^G\right)$ and labor $\left(N_{d,t}^G\right)$ as inputs, and receives the proceeds from the carbon tax as a production subsidy $\left(G_t^G\right)$

$$Y_t^G=A_t{\left(u_t{K}_t^G\right)}^{\alpha }{J}_t^{\xi }{\left(N_{d,t}^G\right)}^{1-\alpha -\xi },$$

(22)

where $A_t$ is the aggregate technological, $\alpha$ is its elasticity of green capital. At the end of each period, the green firm purchases capital to be used for production in the subsequent period at nominal price, $P_t^{G,k}$. Physical capital accumulates according to a standard law of motion

$$K_{t+1}^G=\left(1-\delta \right)\left(K_t^G\right)+{\tilde{I}}_t^G.$$

(23)

The green firm issues perpetual nominal debt $\left(B_t^G\right)$ to finance new investment. Denoting with ${\psi }^G>0$ the constant fraction of investment that can be financed by the issuance of new debt, the following “loan in advance constraint” holds:

$${\psi }^G{\tilde{I}}_t^G\le Q_t^G\left(B_t^G-{\kappa }^G{B}_{t-1}^G\right),$$

(24)

where ${\kappa }^G\in \left[0,1\right]$ is the decay parameter of coupon payments, which proxies for the time duration of nominal green bonds ($B_t^G$) with market price $Q_t^G$, so that $Q_t^G\left(B_t^G-B_{t-1}^G\right)$ is the value of new issuance.

The green firm chooses $K_t^G$ and ${\widetilde{I_t}}^G$. The first-order conditions in real terms are the following:

$$\begin{array}{ccc}& & w_t^G=p_{w,t}\left(1-\alpha \right)A_t{\left(u_t^G{K}_t^G\right)}^{\alpha }{J}_t^{\xi }{\left(N_{d,t}^G\right)}^{-\alpha }\hfill \end{array}$$

(25)

$$\begin{array}{ccc}& & p_t^{G,k}{M}_{2,t}^G{\delta }^{\prime }\left(u_t^G\right)=\alpha p_{w,t}{A}_t{\left(u_t^G{K}_t^G\right)}^{\alpha -1}{J}_t^{\xi }{\left(N_{d,t}^G\right)}^{1-\alpha },\hfill \\ & & p_t^{G,k}{M}_{2,t}^G={\mathbb{E}}_t{\Lambda }_{t,t+1}\left[\alpha p_{w,t}{A}_t{\left(u_t^G{K}_{t-1}^G\right)}^{\alpha -1}{J}_t^{\xi }{\left(N_{d,t}^G\right)}^{1-\alpha }\right]\hfill \end{array}$$

(26)

$$\begin{array}{ccc}& & +{\mathbb{E}}_t{\Lambda }_{t,t+1}\left[1-\delta \left(u_{t+1}^G\right)\right]p_{t+1}^{G,k}{M}_{2,t+1}^G\hfill \end{array}$$

(27)

$$\begin{array}{ccc}& & {\displaystyle \frac{M_{1,t}^G-1}{M_{2,t}^G-1}}={\left({\psi }^G\right)}^{-1},\hfill \end{array}$$

(28)

$$\begin{array}{ccc}& & Q_t^G{M}_{1,t}^G={\mathbb{E}}_t{\Lambda }_{t,t+1}{\Pi }_{t+1}^{-1}\left[1+{\kappa }^G{Q}_{t+1}^G{M}_{1,t+1}^G\right],\hfill \end{array}$$

(29)

$$\begin{array}{ccc}& & {\psi }^G{p}_t^{G,k}{\tilde{I}}_t^G=Q_t^G\left(B_t^G-{\kappa }^G{B}_{t-1}^G{\Pi }_t^{-1}\right)+G_t^G,\hfill \end{array}$$

(30)

where $w_t^G$ is real wage, $p_t^{G,k}$ is the price of new capital. The terms $M_{1,t}^G$ and $M_{2,t}^G$ are auxiliary variables, which equal one when the loan-in-advance constraint does not bind. $J_t={\tau }_t{Y}_t^B$ represent the carbon revenues obtained by the central government, which are rebated to the green firm as a R&D subsidy. The firm takes this input as given and employs it in the Cobb–Douglas production function with elasticity $\xi >0$.

3.3. Banks

There is a continuum of banks indexed by i. Their liabilities consist of household deposits $\left(D_t^B\right)$ and bank capital $\left(S_t^B\right)$. Their assets consist of holdings of brown and green corporate bonds, $L_t^B$ and $L_t^G,$ respectively, with market price $Q_t^B$ and $Q_t^G$. The balance sheet of bank i at time t reads as

$$Q_t^B{L}_{i,t}^B+Q_t^G{L}_{i.t}^G=D_{i,t}^B+S_{i,t}^B.$$

(31)

The bank is subject to a capital constraint that endogenously limits leverage derived as a weak contract enforcement problem (Gertler and Karadi 2011). It is possible to show that enforcement constraint is given by (see Appendix A.1 for the derivation):

$$v_{i,t}\ge {\theta }_t\left({\rho }^B{Q}_t^B{l}_{i,t}^B+{\rho }^G{Q}_t^G{l}_{i,t}^G\right),$$

(32)

where $v_{i,t}$ is the continuation value of bank i at time $t,$ and ${\rho }^B,{\rho }^G>0$ are the degree of asset pledgeability, which can also be interpreted as risk-weights. The term ${\theta }_t$ follows a macroprudential policy rule defined later in Section 3.6. The enforcement constraint (32) embodies the notion that brown and green bonds carry different degrees of liquidity (see also Bernanke and Gertler 1995, Benigno and Nistico’ 2017; Sims and Wu 2020).

Each period, an exogenous fraction $(1-\sigma )$ of commercial banks stochastically exits and transfers their net worth to the household. The household replaces the exiting banks with the same number of new banks. The stochastic exit assumption makes banks extra impatient and prevents bank capital from accumulating indefinitely.

The objective of a surviving bank in period t is to choose its balance sheet variables to maximize expected terminal net worth given the probability $1-\sigma$ of exiting after $t+1$. Given the probability of exiting after j periods $\left(1-\sigma \right){\sigma }^{j-1}$, the commercial bank seeks to maximize the value function:

$$v_{i,t}=\max (1-\sigma ){\mathbb{E}}_t\sum _{j=1}^{\infty }{\sigma }^{j-1}{\Lambda }_{t,t+j}{s}_{i,t+j}^B,$$

(33)

subject to the enforcement constraint (32), where ${\Lambda }_{t,t+j}\equiv \beta {\lambda }_{t+j}/{\lambda }_{t+j-1}$ is the household’s stochastic discount factor.

It can be shown that the aggregate real bank net worth, $s_t^B=S_t^B/P_t$ (with $P_t$ being the price index) accumulates from retained earnings as

$$\begin{array}{c}\hfill s_{t+1}^B=\sigma {\Pi }_{t+1}^{-1}{Q}_t^B{l}_t^B\left(R_{t+1}^B-R_t^D\right)+Q_t^G{l}_t^G\left(R_{t+1}^G-R_t^D\right)+s_t^B{R}_t^D\end{array}$$

(34)

where $R_t^B$ and $R_t^G$ are the gross return on the brown and the green asset, respectively. As in (Carlstrom et al. 2017), we assume that these returns are given by

$$\begin{array}{c}{R}_t^B={\displaystyle \frac{(1+\kappa Q_t^B)}{Q_{t-1}^B}},\\ R_t^G={\displaystyle \frac{(1+\kappa Q_t^G)}{Q_{t-1}^G}}.\end{array}$$

(35)

The bank solves an optimization problem where it chooses the optimal real holdings of brown and green bonds, $l_t^B,l_t^G,$ respectively:

At the symmetric equilibrium, the first-order conditions are as follows:

$$\begin{array}{ccc}& & {\displaystyle \frac{\partial {\mathbb{L}}_t}{\partial l_t^B}}:{\mathbb{E}}_t{\Lambda }_{t,t+1}{\Pi }_{t+1}^{-1}{\Omega }_{t+1}\left[\left(R_{t+1}^B-R_t^D\right)\right]={\rho }^B{\theta }_t{\displaystyle \frac{{\lambda }_t}{1+{\lambda }_t}},\hfill \end{array}$$

(36)

$$\begin{array}{ccc}& & {\displaystyle \frac{\partial {\mathbb{L}}_t}{\partial l_t^G}}:{\mathbb{E}}_t{\Lambda }_{t,t+1}{\Pi }_{t+1}^{-1}{\Omega }_{t+1}\left[\left(R_{t+1}^G-R_t^D\right)\right]={\rho }^G{\theta }_t{\displaystyle \frac{{\lambda }_t}{1+{\lambda }_t}},\hfill \end{array}$$

(37)

where ${\Omega }_{t+1}$ is defined as

$${\Omega }_{t+1}=1+\sigma \left({\displaystyle \frac{\partial v_{t+1}}{\partial s_t^B}}-1\right).$$

(38)

Moreover, as we assume that the bank can always access the central bank’s deposit facility, in equilibrium the deposit rate equals the policy rate, thus $R_t^D=R_t^{.}.$ To provide some insight into the mechanisms at play, it is worth examining the following relationship relating interest in the risk premium to the degree of asset pledgeability, which emerges by combining the bank’s first-order conditions:

$${\displaystyle \frac{{\rho }^B}{{\rho }^G}}={\displaystyle \frac{\left(R_{t+1}^B-R_t\right)}{\left(R_{t+1}^G-R_t\right)}}.$$

(39)

The above condition provides a key insight into the relationship between interest rate spreads and the enforcement constraint. First, differences in the degree of liquidity determine the presence of a “yield premium” or “excess return” (i.e., risk premium) between the interest rate on corporate bonds and the risk-free interest rate. In fact, as long as ${\rho }^B,{\rho }^G>0$ there exists a risk premium between the corporate asset and the risk-free rate, as it typically emerges in general equilibrium models where borrowing constraints and interest rate spreads lie at the root of business cycle amplification and capital misallocation (Kiyotaki and Moore 1997). Second, differences in the degree of pledgeability, or “liquidity risk”, determine the existence and the magnitude of the “greenium”, the negative differential to maturity between a green asset and a brown asset with otherwise similar characteristics. As (39) must hold in equilibrium, for the green and the brown assets to carry the same risk premium and no “greenium” to exist, it would require ${\rho }^G={\rho }^B$. In line with recent empirical studies showing that climate corporate bonds in Europe are priced at a discount to the same-risk conventional corporate bonds (Sergei and Alesya 2022), we assume the following:

Assumption 1.

${\rho }^G<{\rho }^B$.

Therefore, the following proposition holds throughout:

Proposition 1.

A negative spread between $R_t^G$ and $R_t^B$ (greenium) arises in equilibrium as ${\rho }^G<{\rho }^B$ holds by Assumption 1.

It can be shown that in equilibrium, the aggregate bank leverage ratio satisfies

$${\varphi }_t={\displaystyle \frac{{\rho }^B{Q}_t^B{l}_t^B+{\rho }^G{Q}_t^G{l}_t^G}{s_t^B}}={\displaystyle \frac{{\mathbb{E}}_t{\Lambda }_{t,t+1}{\Omega }_{t+1}{\Pi }_{t+1}^{-1}{R}_t^D}{\left[{\theta }_t-{\mathbb{E}}_t{\Lambda }_{t,t+1}{\Omega }_{t+1}{\Pi }_{t+1}^{-1}\left(R_{t+1}^B-R_t^D\right)\right]}}.$$

(40)

The above condition links the endogenous leverage ratio to the role of macroprudential policy, where ${\theta }_t$ broadly captures the dynamics of counter-cyclical capital requirements, with $\partial \varphi /\partial \theta <0$ and $\partial \varphi /\partial \theta >0$ corresponding to a tightening macroprudential policy (higher capital requirements lower leverage) and a loosening macroprudential policy (lower capital requirements relax leverage), respectively.

3.4. Government and Climate Policy

The central government acts as the fiscal authority. It collects taxes from households and firms, and issues debt $B_t^{gov}$ at market price $Q_t^{gov}.$ In real terms, carbon tax revenues stemming from the household sector are $T_{H,t}={\tau }_{c,t}{C}_t^B$ and those stemming from the corporate sector are $T_{F,t}=$${\tau }_t{Y}_t^B$. We assume that the government consumes an exogenous and stochastic amount of final output $\left(G_t\right)$. In addition, it transfers corporate carbon tax revenues one-to-one to green firms as subsidy $\left(G_t^G\right)$ and transfers the revenues from the carbon tax levied on households back to households as subsidy for green consumption $\left(G_t^C\right)$. The government’s budget constraint is

$$P_t{G}_t+B_{t-1}^{gov}+P_t{G}_t^G+P_t{G}_t^C=P_t{T}_{H,t}+P_t{T}_{F,t}+Q_t^{gov}\left(B_t^{gov}-\kappa B_{t-1}^{gov}\right).$$

(41)

The left-hand consists of government spending, nominal debt issuance, green subsidies expenditure and household subsidies to green consumption. The right-hand consists of the carbon tax revenues and nominal coupon payments on issued debt. For the government spending, $G_t$, and government debt, $B_t$, we assume they follow an exogenous AR(1) process.

3.5. Central Bank and Monetary Policy

The central bank controls the risk-free interest rate according to the Taylor principle (Taylor 1993) with interest rate smoothing:

$$R_t={\left(R_{t-1}\right)}^{{\varphi }_r}{\left(R{\left({\displaystyle \frac{{\Pi }_t}{\Pi }}\right)}^{{\varphi }_{\pi }}\right)}^{\left(1-{\varphi }_r\right)}{ϵ}_{m,t}^{{\sigma }_m},$$

(42)

where $R_t$ is the policy rate and R its steady-state level, ${\varphi }_r$ is the coefficient on the interest rate smoothing, ${\varphi }_{\pi }$ is the inflation coefficient, and ${ϵ}_{m,t}$ is a monetary policy shock with standard deviation ${\sigma }_m$.

3.6. A Climate-Related Macroprudential Policy Rule

In following up with the ongoing policy discussions oriented toward a macroprudential approach to climate-related risks already presented in the introduction, we propose a macroprudential rule by which the financial authority aims at maintaining financial stability by addressing systemic risks also arising from climate-related risks.9 In this respect, we postulate a formulation that targets credit and emissions dynamics, such as the following:

$$\ln \left({\theta }_t\right)=\left(1-{\rho }_{\theta }\right)\ln \left(\theta \right)+{\rho }_{\theta }\ln {\theta }_{t-1}+{\theta }_e\left(\ln \left(X_t\right)-\ln \left(\overline{X}\right)\right)+{\sigma }_{\theta }{ϵ}_{\theta ,t},$$

(43)

where ${\theta }_e$ represents the share of the capital requirements that depends on environmental factors expressed as the deviation of emissions from a target (“emission gap”), and ${ϵ}_{\theta ,t}$ is a shock with standard deviation ${\sigma }_{\theta }$.

3.7. Exogenous Shocks

The economy is subject to a technology shock and a shock to the corporate carbon tax. For these shocks we assume an AR(1) process, respectively:

$$\begin{array}{cc}\hfill & \ln \left(A_t\right)=+{\varrho }_A\ln A_{t-1}+{\sigma }_A{ϵ}_{A,t},\hfill \\ \hfill & \ln \left({\tau }_t\right)=\left(1-{\varrho }_{\tau }\right)\ln \left(\tau \right)+{\varrho }_{\tau }\ln {\tau }_{t-1}+{\sigma }_{\tau }{ϵ}_{\tau ,t},\hfill \end{array}$$

where ${\varrho }_A,{\varrho }_{\tau }\in (0,1)$ are persistence parameters, and ${ϵ}_{A,t},{ϵ}_{A,t}$ are the technology shock and the carbon tax rate, with standard deviations ${\sigma }_A,{\sigma }_{\tau },$ respectively.

4. Quantitative Analysis

4.1. Calibration

The model parameters are set to match key quarterly features of the euro area (EA) over the period 2013Q1–2023Q4. Data are based on the ECB Statistical Database Warehouse and the estimated version of the New Area-Wide Model (NAWM) (Christoffel et al. 2008). For the climate-related block of the model, we use IPCC Assessment Reports, NGFS scenarios, the IEA and the academic literature. By focusing on the zero inflation steady state, we have $\Pi =1,{\Pi }^{\ast }=1,/v^p=1,v^w=1,w^{\ast }=w$. This also means that investment adjustment costs in steady state are irrelevant. From the household block we obtain $\Lambda =\beta$, and $R^D=1/\beta .$ In line with the average bank deposit interest rate over our benchmark period, we target $R^D=1.0050$, which implies a subjective discount factor $\beta =0.9950.$ The habit formation parameter is set to $h=0.8$ as in Gerali et al. (2010).

Next we target the spreads. We target the brown risk premium to 2.0% to match average yields of 10-year maturity BBB-rated corporate bonds, as they account for about 60% of the total investment-grade corporate bond market in Europe. This implies a return on brown bonds of 2.5%. We set the “greenium” at −0.02%, in the range of values found in Pietsch and Salakhova (2022). This returns a green risk premium of 1.8%, which implies a steady-state return on green bonds of 2.3%. Spread targeting and yields calibration gives a ratio of “risk-weights” ${\rho }^B/{\rho }^G=1.28$. Thus, we set ${\rho }^B=0.99$ and ${\rho }^G=0.77$, which captures the idea that households demand higher pledgeability for brown bonds relative to green bonds. We set the physical capital depreciation rate $\delta =0.025$ on a quarterly basis to match an annual rate of capital depreciation of 10%. We set $\alpha =1/3$ as standard in the literature (Smets and Wouters 2002). We set the elasticity of the R&D input to $\xi =1\%$ to remain conservative on the actual availability of green technology. This approach is consistent with the assumptions underlying NGFS scenario narratives. The parameter on the disutility of labor is set to $\psi =0.953$ and the Frisch elasticity is set to $\eta =1$ to be consistent with the normalization to one of the steady-state aggregate labor supplies. The elasticity of substitution parameters are set to ${ϵ}_P={ϵ}_w=11$ to match the steady-state price and wage markups of 10% as in Quint and Rabanal (2014). The firm LTV microprudential tool parameters governing firms’ loan-in-advance constraints are set in the baseline calibration to ${\psi }^B={\psi }^G=0.8$, in the range of values used by Sims and Wu (2020). The monetary policy rule calibration follows conventional values adopted in the literature. Therefore, we set these parameters, respectively, to ${\rho }_r=0.8,{\varphi }_{\pi }=2.5,$ and ${\varphi }_y=0.12$, which are in the range of values found in Gerali et al. (2010) and Quint and Rabanal (2014) suggesting a high interest rate inertia, a strong response of inflation, and a weaker response of output. As for the banking sector, the survival rate of bankers, $\sigma =0.095$ adopts the value set by Gertler and Karadi (2011). The steady-state ratio between system-wide bank exposures and commercial banks net worth is set to 5, which implies banks’ capital requirements to be well above the regulatory levels of Basel III. On the climate module, we set the emission intensity $\zeta$ to match the observed emissions to output ratio of $0.025\%$ quarterly. To calibrate emissions and the emission target, we consider the NGFS orderly scenario. Therefore, the average quarterly reduction needed to achieve a 50% reduction in emissions by 2030 is approximately 2.85%, which we use to set emission target $X^{\ast }$. The parameter capturing the rate at which the stock of existing emissions decay, ${\delta }_x$, is pinned down by combining the emission function and the law of motion for the stock of emissions. In particular, it gives $E/Y^B=\zeta /{\delta }_x.$ After manipulation and using the known steady-state value, we find a very small abatement rate for the stock of existing emissions, ${\delta }_x=0.00031\%$, in line with our conservative assumptions on limited availability of carbon-capture technology. Following a sequential approach, we can turn to setting the parameter governing the impact of emissions on household health. In this respect, data from the World Health Organization (WHO) show that about 20% to 30% of respiratory diseases globally are attributed to outdoor air pollution. Therefore, we set the coefficient ${\delta }_1^E=0.30$ and obtain a steady-state ratio of health investment to health status of 0.25. Finally, in the macroprudential policy rule, the coefficient ${\theta }_e$ turns out to be a free parameter in steady-state flow emissions are zero. Therefore, we set it to ${\theta }_e=0.05$ to capture a mild increase in capital requirements, adjusting for climate risk.

Table 1. Parameters.

Parameter	Description	Value
$\alpha$	Elasticity of output to capital	0.330
$\beta$	Household subjective discount factor	0.995
$\kappa$	Duration parameter on bonds	0.975
h	Coefficient on consumption habit	0.800
$\omega$	Health-related parameter	1
${\psi }_B$	Brown firm LTV	0.800
${\psi }_G$	Green firm LTV	0.800
$\psi$	Scaling parameter on disutility of labor	0.953
${\kappa }_c$	Capital adjustment cost	2.000
${\delta }_1$	Intercept parameter on capital utilization costs	0.030
${\delta }_2$	Slope parameter on capital utilization costs	0.01
$\eta$	Frish elasticity	1.000
${\varphi }_{\pi }$	Taylor rule parameter on inflation	2.500
Z	Lump sum transfer to new entering commercial banks	0.05
${\rho }_m$	Persistence parameter of monetary policy shock	0.800
${\delta }_1^E$	Emission impact on health parameter	0.30
${\sigma }_m$	Standard deviation monetary policy shock	0.005
${\rho }_A$	Persistence parameter of technology shock	0.900
${\sigma }_A$	Standard deviation technology shock	0.010
${\rho }_{\theta }$	Persistence parameter of credit shock	0.900
${\sigma }_{\theta }$	Standard deviation credit shock	0.010
${\rho }^G$	Pledgeability parameter on green bond	0.77
${\rho }^B$	Pledgeability parameter on brown bond	0.99
${ϵ}_p$	Elasticity of substitution for consumption goods	11
${ϵ}_w$	Elasticity of substitution for labor services	11
${\varphi }_p$	Price stickiness parameter	0.75
${\varphi }_w$	Wage stickiness parameter	0.750
$\sigma$	Survival rate of bankers	0.95
${\delta }_x$	Emission abatement rate	0.0000031
$\zeta$	Carbon intensity	0.00025
$X^{\ast }$	Emission reduction target rate	0.0285
$\kappa$	Coupon bond parameter	0.975
${\theta }_e$	Macroprudential policy rule parameter	0.05

summarizes the calibration.

Table 2. Business cycle properties.

Variable	Description	Model		Data
	Key ratios	Mean	St. Dev.	Mean	St. Dev.
Y	GDP	1.000	1.000	1.000	1.000
$C/Y$	Consumption	0.3350	0.0113	0.4581	0.0215
$I/Y$	Investment	0.3013	0.0198	0.2588	0.0434
$L/Y$	Total bank credit	0.5010	0.0119	0.6702	0.0635
$X/Y$	Flow emission-to-output ratio	0.0056	0.0001	0.0003	0.0001
$\varphi$	Leverage ratio banking system	4.8491	0.1514	5.5506	0.2334
Key rates (gross, %)
$R^D$	Bank deposit rate	1.0050	0.0065	1.0065	0.3200
$R^B$	Brown bond rate	1.0205	0.0082	1.0250	0.6900
$R^G$	Green bond rate	1.0171	0.0085	1.0230	0.6901

reports the business cylce properties of the model.

4.2. Impulse Response Functions

In this subsection, we provide the model results conditional on the realization of a variety of shocks. All impulse response functions are expressed in terms of the percentage deviation from the steady state. Interest rates and inflation are annualized.

To provide a general insight into the mechanisms at work, we first report the impulse response functions of key macroeconomic variables conditional on the realization of a one-percent positive shock to total factor productivity (TFP) under different regimes of transition risk. To capture the transition risk over the business cycle, we shut off the dynamic rule for the corporate carbon tax, setting the tax to constant values, capturing a regime of low corporate carbon tax and high corporate carbon tax such as ${\tau }_t={\tau }_{\mathrm{Low}},{\tau }_{\mathrm{High}}.$ Solid lines denotes a regime of low transition risk where the corporate carbon tax is set to the baseline level with a low transition risk, ${\tau }_{\mathrm{low}}=5\%$. In contrast, dotted lines denote a regime of a higher transition risk, where the corporate carbon tax rate is increased to ${\tau }_{\mathrm{high}}=25\%$. Figure 1 shows that, as standard, a positive technology shock generates expansionary effects in aggregate variables such as output, consumption, investment and credit. In fact, the positive technology shock triggers higher factors demand due to increasing aggregate productivity. Firms would like to increase investment, thus the demand for external funding increases in order to finance new capital acquisition. Banks accommodate the higher demand by increasing holdings of both brown and green corporate bonds, although at different intensities due to general equilibrium effects. Therefore, credit supply increases. The shock pass-through exerts upward pressures on corporate bond prices, compressing yields on firm debt and risk premiums. Brown and green firms demand more credit and increase bond issuance. Banks accommodate higher demand for credit by purchasing more brown and green bonds. However, bank demand for brown bonds is higher than that for green bonds, due to the higher rate of return carried by holding the brown asset. Therefore brown bond prices increase more than green bond prices, causing brown bond yields to compress more than green bond yields. Therefore, “greenium” increases. This mechanism is also amplified by our Assumption 1 via the enforcement constraint, as different degrees of asset pledgeability affect the magnitude of the greenium. Compressing yields on corporate debt relaxes firm’s financing constraints and reduces borrowing costs which, in turn, decreases bank financial intermediation margins. The expansionary credit cycle triggers higher counter-cyclical capital buffers, which lower leverage. On the monetary policy side, inflation falls due to higher firm productivity, lower marginal costs and price stickiness. The central bank reacts to disinflation by lowering the policy rate. Under the assumptions of our model, the carbon tax is generally able to dampen business cycle volatility. As a result, flow emissions decrease while health status increases, reflecting the positive effects of lower emissions. These results rest on key assumptions. In particular, the presence of a carbon tax on brown consumption that is rebated to household as a “tax credit” for the purchase of green consumption goods, and carbon revenues stemming from the corporate carbon tax which are reinvested in the green sector as subsidy to R&D expenditure, employed by the green firm as input of production. These assumptions are key in explaining the underlying amplification mechanisms of this model, and the particularly desirable ability of shifting lending from the brown sector to the green sector following the realization of a positive technology shock.

4.3. Micro- and Macroprudential Policy Coordination

To enhance understanding of the implications of micro-, and macroprudential policy over the climate transition, we define four scenarios of micro- and macroprudential policy coordination over the climate transition triggered by a shock to the corporate carbon tax rate. In this model, we refer to “coordination” as the process by which the financial regulatory authority aligns its micro- and macroprudential policies when accounting for climate change-related considerations. Therefore, conditional on the realization of a transition risk triggered by a positive shock to the corporate carbon tax, the financial authority faces the following four scenarios. The first, the baseline scenario, corresponds to a situation where the financial authority does not no commit to account for climate-related considerations. Therefore, this baseline scenario is by definition a scenario of “no coordination” between micro- and macroprudential measures. In this scenario, the microprudential tools are set such that ${\psi }^B={\psi }^G$. In this scenario macroprudential policy also ignores climate factors by setting ${\theta }_e=0$. In the second scenario, the financial authority aligns (coordinates) only microprudential policies to account for climate factors, thus it sets ${\psi }^B<{\psi }^G$ to reduce leverage of the carbon intensive non-financial corporation sector. In contrast, macroprudential policy does not coordinate, thus ${\theta }_e=0$. We call this scenario of partial coordination “microprudential coordination”. The third scenario is a partial coordination scenario where only macroprudential policy coordinates by setting ${\theta }_e>0$, while microprudential does not, thus ${\psi }^B={\psi }^G.$ We label this scenario as “macroprudential coordination”. In the fourth scenario, which we label as “full coordination”, both micro- and macroprudential policies are aligned in accounting for climate-change factors. Therefore, ${\psi }^B<{\psi }^G$ and ${\theta }_e>0.$ In the next section, we discuss the results of these scenario exercises and assess the normative implications of micro- and macroprudential policy coordination in terms of welfare and output volatility.

5. Micro- and Macroprudential Policy Coordination and Welfare

To assess the welfare implications of micro- and macroprudential policies and their coordination over the risky climate transition, we follow the standard approach in the literature (Schmitt-Grohe and Uribe 2007; Wolff and Sims 2017), and express welfare costs in steady-state consumption equivalents (or compensating variations), which is the proportion of each period’s consumption that the representative household would need to give up in a deterministic world so that its welfare is equal to the expected conditional utility in the stochastic world. Let ${\mathbb{W}}_0^i$ denote the welfare associated with a state of the world where micro- and macroprudential policies do not take into account climate-related factors; that is a scenario of “no coordination” $(i=l)$, or any of the alternative scenarios $(i=h)$:

$${\mathbb{W}}_0^i={\mathbb{E}}_0\sum _{t=0}^{\infty }{\beta }^t\left({\displaystyle \frac{\nu }{1-\nu }}\ln {\widehat{C^i}}_t+\omega {{\displaystyle \frac{H_t^i}{1+\upsilon }}}^{1+\upsilon }-\psi {{\displaystyle \frac{N_t^i}{1+\eta }}}^{1+\eta }\right),$$

(44)

where $C_t^i$, $N_t^i$, $H_t^i$ denote consumption, labor, and health status optimal paths under regime i.

Let $c_e$ denote the welfare costs of adopting an alternative policy regime; that is, any of the other three micro- and macroprudential policy scenarios defined above, instead of the baseline scenario regime. Formally, $c_e$ is implicitly defined by

$${\mathbb{W}}_0^h={\mathbb{E}}_0\sum _{t=0}^{\infty }{\beta }^t\left(\ln \left(1-c_e\right)\left({\widehat{C}}_t^l-h{\widehat{C}}_{t-1}^l\right)+\omega {{\displaystyle \frac{H_t^l}{1+\upsilon }}}^{1+\upsilon }-\psi {{\displaystyle \frac{N_t^l}{1+\eta }}}^{1+\eta }\right).$$

(45)

We can write

$${\mathbb{W}}_0^h={\displaystyle \frac{\ln \left(1-c_e\right)}{1-\beta }}{\mathbb{W}}_0^l.$$

(46)

This approach allows us to obtain welfare costs (if $c_e<0$) or welfare gains (if $c_e>0$) of policy regime i in steady-state percentage consumption equivalents, as follows:

$$c_e=1-\exp \left[{\displaystyle \frac{{\mathbb{W}}_0^h}{{\mathbb{W}}_0^l}}(1-\beta )\right]\times 100$$

(47)

Table 3. Welfare, volatility, and micro- and macroprudential coordination.

	Scenario
	No Coordination	Micro	Macro	Full
Welfare (conditional) $\left(c_e\right)$	−4.057	−3.815	−2.851	−3.923
Welfare (unconditional) $\left(c_e\right)$	−5.501	−2.401	−2.012	−2.787
Output volatility	0.0696	0.0812	0.0265	0.0217

reports the results of this exercise. In particular, the table reports the welfare costs in percentage consumption equivalents of adopting each micro- and macroprudential policy regime together with values of output volatility in each regime to show the presence of a welfare–volatility trade-off.

The results show that conditional on the realization of a positive shock to the corporate carbon tax, transition shocks entail higher welfare costs under those scenarios of partial or absent micro- and macroprudential policy coordination in incorporating climate factors. These regimes, however, are also the ones with lower output volatility. From a climate policy-making perspective, our results point to the existence of a trade-off between short-run output stabilization, which appears more effective under the regime of “full coordination”, and long-run welfare improvements carry lower relative costs under partial cooperation. Therefore, the policymaker faces a trade-off between two desirable objectives. It is useful to discuss the key mechanisms underlying these results. First, the quantitative effects of the policy regimes ultimately depend on the non-linearity involved in the welfare objective. At the first-order, these effects relate to the (net) welfare impact that the adoption of a policy regime has on the welfare objective, and particularly on aggregate consumption and aggregate employment in a decentralized equilibrium that is inefficient due to the presence of real, nominal, and financial distortions. Therefore, they depend on the ultimate effect on welfare of the consumption/employment and the consumption/health trade-off faced by the representative household. Second, at the second-order approximation, welfare losses also relate to impacts stemming from the volatility of consumption, employment, health status, price inflation, and wage inflation. Finally, our results crucially depend on the assumptions made in the main text, which involve the specific modeling of carbon taxes, the way carbon revenue is rebated, the elasticity parameters regarding the reinvestment of carbon revenues in the green sector, and the parameters related to the emission abatement and emission target. In addition, the model’s sensitivity is also affected by the parameters governing the impact of emission on household utility, as well as the parameter governing the importance of health to the household.

6. Conclusions

Despite the broad recognition by academics and policymakers of the importance of accounting for climate-related factors in public policies, the debate on the appropriate tools to adopt when addressing systemic risk arising from climate transition risk shocks from a micro- and macroprudential policy perspective is still an open issue. The divide particularly concerns the complexity of the design and the calibration of climate-related tools for prudential regulation and their degree of interaction.

In this paper, we have adopted a climate-DSGE model to shed light on the plausible policy options available for the regulatory authority that intends to include climate factors into its prudential framework while pursuing the institutional mandate. We have shown that a carbon tax generates business cycle amplification, dampening the economic activity and emissions as a consequence of their pro-cyclical nature. This result lends support to the dominant consensus that a Pigouvian approach is an effective tool in lowering emissions. In addition, we have also shown that, conditional on the realization of a carbon tax shock, the financial regulator that intends to manage the resulting systemic risk can successfully adopt both micro- and macroprudential policy tools. In this respect, both micro and macroprudential policies independently pursued are able to dampen amplification stemming from transition risks, reducing business cycle volatility and emissions, while facing moderate welfare costs. However, if micro- and macroprudential policies are jointly pursued toward the objective of reducing emissions in “full coordination”, business cycle stabilization following the transition risk shock can be achieved with lower welfare costs. Therefore, this paper generally calls for higher micro- and macroprudential policy coordination in order to minimize the trade-off between efficiency and financial stability. Our framework does not explicitly model technological change or capacity transformation across sectors. In addition, it could also be expanded to account for higher sectoral and geographical granularity, or adapted to study specific policy cases. We leave this potential exploration as future research avenues.