3.1. Households

Households supply labor to different types of firms which are characterized by different levels of carbon intensity ( $L_t^i$ , where $i = \{HCI,LCI\}$ indicates the classification of firms by carbon emissions, high or low carbon intensity) for which they get paid an hourly wage ( $w_t^i$ ), consume a mixed basket of goods from all firms ( $C_t^H$ ), and save their income in the form of deposits $D_t$ which are remunerated at the risk-free rate $R_t$ . Households are also the owners of banks and of retail firms from which they receive dividends ( $\Pi _t^H$ ). In addition, they receive benefits $G_t$ from the government. They maximize their utility so as to choose consumption, hours worked, and deposits:

(1) \begin{eqnarray} \max _{\{C_t^{H,i},L_t^i,D_t^H\}} \mathbb{E}_{t}\left [\sum _{t=0}^{\infty } \beta ^{H^t} \left (\frac {C_{t}^{{H}^{1-\gamma }}}{1-\gamma } - \sum _i \overline {L}^i\frac {L_{t}^{i^{1+\sigma ^i}}}{1+\sigma ^i}\right )\right ] \end{eqnarray}

subject to the budget constraint expressed in nominal terms:

(2) \begin{eqnarray} \sum _i P_t^i C_t^{H,i}+P_t D_t^H \leq P_t \frac {1+R_{t-1}}{1+\pi _t}D_{t-1}^H + \sum _i w_t^i L_t^i + \Pi _t^H +G_t. \end{eqnarray}

where $\pi _t$ is the aggregate inflation rate and $P_t$ is the aggregate price index. The parameters $\overline {L}^i$ in the utility function are calibrated such that at the steady state total labor is normalized to one. Household consume a basket $C_t^H$ of goods produced by all firms and $C_t^{H,i}$ indicates the consumption of goods with a specific emission intensity. Overall, the households’ preferences across different types of goods follow a CES form:

(3) \begin{eqnarray} C_t^H &=& \left [ \sum _i \kappa ^{i^{\frac {1}{\varepsilon }}} C_t^{{H,i}^{\frac {\varepsilon -1}{\varepsilon }}} \right ]^{\frac {\varepsilon }{\varepsilon -1}}, \end{eqnarray}

where $\sum _i \kappa ^i = 1$ .

3.2. Entrepreneurs

Firms produce differentiated goods of the same product category (e.g. electric and gas cars), and they are classified according to their level of carbon emission ( $i = \{HCI,$ $LCI\}$ , high or low carbon intensity). This classification could include both the production and the product, similarly to the Scope 3 ESG score. Low-carbon-intensive (LCI) firms use more technologically advanced (and costly) capital than high-carbon-intensive (HCI) firms allowing them to produce either with less emissions or more environmentally friendly products. Firms have to pay taxes for their carbon emissions, which are the source of transition risk in the model. Without loss of generality, we suppose that firms have otherwise the same solvency profile (i.e., the same ‘traditional’ credit risk) and differ only in their production technology and emission costs. Entrepreneurs own the firms and use their earnings for consumption, maximizing the utility from the consumption of a basket of differentiated goods:

(4) \begin{eqnarray} \max _{\{C_t^{E,i,j},L_t^i,K_t^i,B_t^i,u_t^i,\overline {\omega }_t^i\}} \mathbb{E}_{t}\left [\sum _{t=0}^{\infty } \beta ^{E^t} \frac {C_t^{{E,i}^{1-\gamma }} }{1-\gamma } \right ], \end{eqnarray}

where $C_t^{E,i}$ is the basket of differentiated goods consumed by entrepreneurs of type $i$ . As for the households, the consumption of goods with different degree of carbon intensity follows CES preferences:

(5) \begin{eqnarray} C_t^{E,i} &=& \left [ \sum _j \theta ^{j^{\frac {1}{\varepsilon }}} C_t^{{E,i,j}^{\frac {\varepsilon -1}{\varepsilon }}} \right ]^{\frac {\varepsilon }{\varepsilon -1}}, \end{eqnarray}

with $j = \{HCI,$ $LCI\}$ the type of good consumed by entrepreneur $i$ . The production function of each firm ( $Z_t^i$ ) is Cobb-Douglas:

(6) \begin{eqnarray} Z_t^i &=& \epsilon _t^i \left (u_t^i K_{t-1}^i\right )^a \left (L_t^i\right )^{1-a} \end{eqnarray}

where $u_t^i$ is the capacity utilization, $K_t^i$ is the capital, and $\epsilon _t^i$ is a technology shock following an AR(1) process. Each period, firms take loans $B_t^{E,i}$ from banks to finance their activities. The interest rate associate with the loan is $R_{t}^{E,i}$ . However, firms are subject to idiosyncratic shocks affecting their revenues, $\omega _t^i$ , causing the default of some firms on the loan contract. If a firm does not repay its loan, the bank can seize the collateral $(1-\delta )Q_t^i K_{t-1}^i$ , where $Q_t^i$ is the nominal price of capital and $\delta$ a depreciation factor (see Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rodriguez-Palenzuela2011, Reference Darracq-Pariès, Kok and Rancoita2019); Gerali et al. (Reference Gerali, Neri, Sessa and Signoretti2010), among others). Calling $\overline {\omega }_t^i$ the idiosyncratic shock at which the entrepreneur is indifferent between defaulting or not, firms are willing to pay the interest rate implied by this threshold:

(7) \begin{eqnarray} \frac {1+R_{t-1}^{E,i}}{1+\pi _t}P_t B_{t-1}^{E,i} &=& \overline {\omega }_t^i(1-\delta )Q_t^i K_{t-1}^i. \end{eqnarray}

This also implies that the expected loan repayment can be written as (see Bernanke et al. Reference Bernanke, Gertler and Gilchrist1999):

(8) \begin{eqnarray} H(\overline {\omega }_t^i)(1-\delta )Q_t^i K_{t-1}^i &\equiv & (1-\delta )Q_t^i K_{t-1}^i \left [ \int _0^{\overline {\omega }_t^i} \omega dF(\omega ) + \left (1-F\left (\overline {\omega }_t^i\right )\right )\overline {\omega }_t^i\right ]. \end{eqnarray}

Firms use different capital in their production functions which they acquire from the capital goods producers. In line with previous literature, we assume that both types of firms face adjustment costs related to capacity utilization, which we model as $\Phi _i(u_t^i) = \phi ^i r^{i,SS} (\exp [\frac {1}{\phi ^i}(u_t^i - 1) ] - 1)$ . Smets and Wouters (Reference Smets and Wouters2007) found that adjustment costs are key to fit New Keynesian models with empirical data. Our adjustment cost function is based on Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rodriguez-Palenzuela2011) and implies that the cost of capacity utilization is zero at the steady-state level of the utilization rate ( $\Phi ^i(1) = 0$ ), and increases non-linearly as utilization deviates from this level. Furthermore, we assume that the adjustment cost parameter is higher for LCI firms than for HCI firms (i.e., $\phi ^{LCI} \gt \phi ^{HCI}$ ),Footnote ¹⁴ reflecting the greater technological and operational constraints faced by cleaner production technologies. While HCI firms often rely on conventional technologies (e.g., fossil fuel-based production), which allow relatively easy and low-cost adjustments to capacity utilization, LCI firms tend to use cleaner but more rigid technologies. For example, in the electricity sector, traditional gas or coal power plants can ramp up or down production relatively quickly, incurring relatively small costs when adjusting utilization. In contrast, renewable energy sources like wind or solar power are subject to intermittency and external conditions (e.g., weather), limiting their ability to flexibly adjust production. Increasing the effective use of capital in such contexts often requires costly complementary investments (e.g., battery storage, grid integration, or hybrid systems).

Firms also differ because they are subject to emission taxes $T(e_t^i)$ on the basis of their carbon intensity. In addition, each firm sells its goods to retailers, who will then distribute them to households at a price $P_t^i$ charging a markup on the price at which they buy the intermediate goods from entrepreneurs. The inverse of the markup charged by retailers on the intermediate good price is indicated with $\mu _t^i$ . The budget constraint in nominal terms writes:

(9) \begin{eqnarray} &\sum _j P_t^j C_t^{E,i,j} + Q_t^i\left [K_t^i - (1-\delta )K_{t-1}^i \right ] + w_t^i L_t^i + \Phi _i(u_t^i)K_{t-1}^i \nonumber \\&\quad +\, H(\overline {\omega }_t^i)(1-\delta )Q_t^i K_{t-1}^i + T(e_t^i) \leq \mu _t^i P_t^i Z_t^i + P_t B_t^{E,i} \end{eqnarray}

where the tax on emissions is a linear function of production:

(10) \begin{align} T(e_t^i) &= \epsilon ^T_t\eta ^i e_t^i \end{align}

(11) \begin{align} e_t^i &= \zeta Z_t ^i. \end{align}

where the parameter $\eta ^i$ represents the tax level and where $\zeta$ is the fraction of emissions to output (Benmir and Roman Reference Benmir and Roman2020). In our framework, we model a transition risk shock as a shock to the emission tax, represented in Eq. (10) by the variable $\epsilon ^T_t$ . This shock is assumed to be correlated with a shock to the riskiness of high-carbon-intensive entrepreneurs,Footnote ¹⁵ to capture the broader effects of transition policy shocks that go beyond a simple linear rise in production costs. While the increase in costs alone would already raise default probabilities, this representation does not fully reflect the nature of transition risk. Some policies have far-reaching implications for certain sectors, including fundamental changes to the competitive environment, the need to adopt new production technologies, or exposure to future regulation.Footnote ¹⁶ In this sense, the correlation captures the increased uncertainty surrounding the production environment in which HCI firms operate following the announcement or implementation of transition measures.”

Firms in each sector are in perfect competition in producing their goods; this implies the following zero-profit condition on production:

(12) \begin{eqnarray} \mu _t^i P_t^i Z_t^i - T(e_t^i) &=& \Phi _i'(u_t^i)u_t^i K_{t-1}^i + w_t^i L_t^i \end{eqnarray}

When maximizing their utility, firms also take into account the participation constraint of commercial banks to the lending contract. Commercial banks have financing costs $R_t^{F,i}$ for their loan contract and face some monitoring costs, $\rho$ to collect the collateral in case of default. Their participation constraint can be written as:

(13) \begin{eqnarray} \frac {1+R_{t-1}^{F,i}}{1+\pi _t}P_t B_{t-1}^{E,i} &\leq & (1-\delta )Q_t^i K_{t-1}^i G(\overline {\omega }_t^i) \end{eqnarray}

where:

(14) \begin{eqnarray} G(\overline {\omega }_t^i) & \equiv & \bigg [ (1-\rho ) \int _0^{\overline {\omega }_t^i} \omega dF(\omega ) + (1-F(\overline {\omega }_t^i))\overline {\omega }_t^i\bigg ]. \end{eqnarray}

3.3. Capital goods producers

There is a capital goods producer for each type of firm, HCI and LCI. Capital goods producers operate under perfect competition and are owned by households. At the beginning of each period, they purchase the undepreciated capital $(1-\delta )K_{t-1}^i$ from entrepreneurs at real prices. Then they augment the capital stock using distributed goods and facing adjustment costs proportional to the investment, $I_t^i$ . The augmented capital stocks are sold back to entrepreneurs at the same prices at the end of the period. The maximization problem of capital producers can be written as:

(15) \begin{eqnarray} \max _{\{K_t^i,I_t^i\}} \mathbb{E}_{t}\left \{\sum _{t=0}^{\infty } \beta ^{H^t} \Big [ Q_t^i\left [ K_t^i - (1-\delta )K_{t-1}^i \right ] - I_t^i \Big ] \right \}\!, \end{eqnarray}

subject to the law of motion of capital:

(16) \begin{eqnarray} K_t^i = (1-\delta )K_{t-1}^i + \left [1-S\left (\frac {I_t^i}{I_{t-1}^i}\right )\right ]I_t^i, \end{eqnarray}

where $S(.)$ is the adjustment cost function defined as $S(x) = s0.5(x-1)^2$ and $s$ is a parameter and where $x= \tfrac {I_t}{I_{t-1}}$ is the gross rate of change in investment. Following standard practice in the DSGE literature (e.g. Christiano et al. Reference Christiano, Eichenbaum and Evans2005; Smets and Wouters Reference Smets and Wouters2007), we assume that capital goods producers face convex investment adjustment costs.Footnote ¹⁷ This functional form ensures that adjustment costs are zero at steady state ( $S(1) = 0$ , no costs when investment is stable) and increase with the magnitude of investment changes, whether positive or negative. The economic rationale is that rapid increases in investment may require urgent reallocation of resources, while sharp reductions can lead to inefficiencies such as underutilized capacity or cancelation costs.

3.4. Retailers

Retailers are in monopolistic competition. They buy homogeneous intermediate goods $Z_t^i(j)$ at price $\mu _t^i P_t^i$ from the entrepreneurs; they differentiate the products and sell them to households and entrepreneurs. As aforementioned, $\mu _t^i$ represents the inverse of the gross markup of retail goods over intermediate goods, or otherwise stated the selling price of intermediate products. Retailers set their prices on a staggered basis à la Calvo (Reference Calvo1983): in each period only a fraction $1- \chi$ of retailers is able to re-optimize its nominal prices ( $P_t^i(j)=\tilde {P}_t^i(j))$ , where $\tilde {P}_t^i(j)$ is the optimal price for retailer $j$ , while the remaining fraction $\chi$ cannot re-optimize and will set the prices as in the previous period ( $P_t^i(j)=P_{t-1}^i(j)$ ). The aggregate price dynamics is given by a weighted average of prices set by firms that re-optimize and prices from the previous period kept constant by non-reoptimizing firms:

(17) \begin{eqnarray} P^i_t=\left [\chi {P_{t-1}^i}^{1-\epsilon } + (1-\chi ) \tilde {P}_t^i(j)^{1-\epsilon }\right ]^{\frac {1}{1-\epsilon }} \end{eqnarray}

In aggregate, the production and price index functions of retailers follow a CES functional form:

(18) \begin{align} Y_t^i &= \left [ \int _0^1 Y_t^i(j)^{\frac {\epsilon -1}{\epsilon }}dj \right ]^{\frac {\epsilon }{\epsilon -1}} \end{align}

(19) \begin{align} P_t^i &= \left [ \int _0^1 P_t^i(j)^{1-\epsilon }dj \right ]^{\frac {1}{1-\epsilon }} \end{align}

which imply the following demand of intermediate goods of the individual retailer: $Y_t^i(j) = ( \frac {\tilde {P}_t^i(j)}{P_t^i} )^{-\epsilon }Y_t^i$ . Then, each retailer who can re-optimize at $t$ maximizes the expected discounted stream of profits under the assumption that once the price $\tilde {P}_t^i(j)$ is set, he will not re-optimize with probability $\chi$ for a number of periods $k\in [0,\infty ]$ . The maximization of the retailer writes:

(20) \begin{eqnarray} \max _{\{\tilde {P}_t^i(j)\}} \sum _{k=0}^{\infty } \chi ^k \mathbb{E}_t \left [\lambda _{t+k}^{r,i}\left (P_{t+k}^i(j)- \mu _{t+k}^i P_{t+k}^i \right )Y_{t+k}^i(j)\right ] \end{eqnarray}

where $P_{t+k}^i(j)=\tilde {P}_t^i(j)$ for the assumptions above that the retailer will not re-optimize until $t+k$ .

3.5. Market clearing conditions for goods

For all goods, the aggregate demand and production are given by:

(21) \begin{align} Y_t^i &= C_t^{H,i} + \sum _j C_t^{E,j,i} + I_t^i + \Phi _B(u_t^i)K_{t-1}^i + \eta ^i\zeta Z_t^i \end{align}

(22) \begin{align} Z_t^i &= \varepsilon ^i\left ( u^i K_{t-1}^i\right )^a\left ( L^i_t\right )^{(1-a)} \end{align}

The market clearing condition in each good markets leads to the following relations:

(23) \begin{eqnarray} Z_t^i &=& \Delta ^i_t Y_t^i, \end{eqnarray}

where $\Delta _t^i = \int \left ( \frac {P_t^i(j)}{P_t^i}\right )dj$ measures the price dispersion among retailers.

3.6. The banking sector

The banking sector is modeled following Gerali et al. (Reference Gerali, Neri, Sessa and Signoretti2010) and Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rodriguez-Palenzuela2011). As in this literature, we represent the banking system as composed of multiple specialized branches within a banking group, each with distinct role, as detailed below. This approach facilitates both the exposition and the mathematical tractability of the model.Footnote ¹⁸ In our framework, each banking group is composed of two branches that operate in a perfectly competitive environment. The wholesale branch receives deposits from households and allocates these funds to the commercial lending branch. The wholesale branch of the group also manages the capital position of the bank taking into account risk-sensitive capital requirements, and incurs a cost whenever the capital to risk-weighted assets ratio deviates from a target value, $CR$ . The commercial lending branch obtains funds from the wholesale branch and uses them to give credits to firms.

As shown in Section 3.2, taxes on carbon emissions affect credit risk increasingly with the level of carbon emission as they represent an additional cost. As the idiosyncratic shock $\omega ^i$ has the same distribution across types of firms, transition risk (i.e., the risk due to taxes on emissions) is the main source of differentiation of credit risk in the model. It is reasonable to assume that proportionally, credit risk due to transition risk is not more impactful than the more traditional source of credit risk as emission taxes cannot be raised abruptly to very high levels owing to the high costs this would impose on firms.

Internalizing the difference in credit risk of firms due to transition risk is costly for banks as this risk is quite challenging to identify and it would imply a number of additional costs for banks, such as investment in databases, the re-estimation or development of new credit risk models or the recruitment of specialized staff. Furthermore, part of the information would potentially not even be available or sufficient considering the short history of emission taxes or emission measurements.Footnote ¹⁹ As mentioned earlier, we compare two different specifications of the model which differ mainly in the modeling of the banking sector. The first specification of the model abstracts from any climate-prudential policy, while the second specification assumes that these policies are implemented. In our first model specification (without climate-prudential policies), banks have no incentive to internalize credit risk due to carbon taxes, i.e., transition risk, and therefore they do not distinguish between the degree of carbon intensity when lending. Thus, the estimation of the model is performed as if there was a single type of firm (indicated by $E$ ) in the economy. Banks estimate their models based on aggregate data (for example, on capital investments), which is the weighted average of data from all firms. At the same time, entrepreneurs assume that banks can easily identify the carbon intensity of firms and therefore believe that banks provide individualized contracts. In terms of modeling, this implies that the participation constraint of commercial banks in the lending contract (eq. 13) remains as presented in Subsection 3.2, i.e., the participation constraint is specific to the type of firm.

In our second model specification, we assume that climate-prudential policies are implemented and banks have full incentives to identify the degree of firms’ carbon intensity and provide individualized contracts. In the next sections, we will describe each branch of the banking group.

3.6.1. The wholesale branch

We first present the wholesale branch for the model without climate-prudential policies before outlining the changes that are made to the model when we assume that banks have to identify firms on the basis of their carbon intensity. The wholesale branches receive deposits from households and choose the allocations of loans. The wholesale branches maximize their profits, taking interest rates as given and taking into account a penalty if the risk-weighted capital ratio deviates from a target capital ratio. Their profit maximization writes:

(24) \begin{eqnarray} \max _{\{B_{t}^{E}, D^{H}_t\}} R_{t}^{F,E}B_{t}^{E} - R_t D^{H}_{t} - PD_t^E LGD^E B^{E}_{t} - \frac {\Xi }{2} \left (\frac {Bankcap_t}{rw_t^E B_{t}^{E}} - CR\right )^2 Bankcap_t \end{eqnarray}

which is subject to the balance sheet identity:

(25) \begin{eqnarray} B_{t}^{E}=D^{H}_t+Bankcap_t \end{eqnarray}

where $D^H_t$ represents households’ deposits which are remunerated at the risk-free rate $R_t$ . $R_t^{F,E}$ represents the interest rate at which the wholesale branch gives funds to its commercial financing branch, $CR$ is the target capital ratio, and $rw_t^E$ is the risk weight associated to the total amount of credit $B_t^{E}$ distributed to firms. In equilibrium, total credit to firms equals the sum of loans actually granted to entrepreneurs with different degrees of carbon intensity, $B_t^{E} = \sum _{i} B_t^i$ . The term $PD_t^E LGD^E B^{E}_{t}$ corresponds to provisions for expected credit risk losses, with $PD_t^E$ being the 1-year ahead probability of default of the undistinguished representative firm, $LGD^E$ being a parameter capturing the loss given default. Without prudential policies, banks’ provide a unique credit contract (the same financing conditions apply to all types of firms, irrespective of their transition risk), implying also a unique financing rate in equilibrium, $R^{F,i}_t$ identical for all firms. The contract is designed based on the probability of default, $PD_t^E$ , which is a function of the cumulative distribution of the idiosyncratic shocks $\omega ^E$ , $F\left ({\omega }^E_t\right )$ at the threshold $\overline {\omega }^E_t$ (see eq. 30). As in the first model specification banks do not distinguish among different types of entrepreneurs, $F\left ({\omega }^E_t\right )$ represents a pooled distribution across all entrepreneurs . The threshold $\overline {\omega }^E_t$ is estimated by banks as the level of the idiosyncratic shock at which they expect the representative firm of the pooled distribution of all firms to be indifferent between defaulting and repaying:

(26) \begin{eqnarray} \frac {1+R_{t-1}^{E}}{1+\pi _t}P_t B_{t-1}^{E} &=& \overline {\omega }_t^E(1-\delta )Q_t^E K_{t-1}^E \end{eqnarray}

where $Q_t^E$ is the weighted average price of capital, $Q^E_t = \sum _i Q_t^i\frac {K^i_t}{K_t^E}$ , and $K^E_t$ the total amount of capital needed by entrepreneurs for their production $K^E_t= \sum _i K^i_t$ . Therefore, according to banks, firms with different carbon intensity do not have different probabilities of default. Furthermore, the credit contract will reflect the average level of risk, which will be underestimated for high-carbon-intensive firms (as transition risk is not directly taken into account in this case) and overestimated for low-carbon-intensive firms (who are offered a higher interest rate that covers the transition risk emerging from high-carbon-intensive firms). As capital requirements are a non-linear function of credit risk ( $PD$ s), then calculating the capital requirements based on the average credit risk will not lead to the same aggregate capital requirements as taking into account firm-specific credit risk.

Bank capital accumulates out of retained earnings from the bank group profits:

(27) \begin{eqnarray} Bankcap_t = (1-\delta ^{bk})Bankcap_{t-1} +\nu \Pi _t^{bk} \end{eqnarray}

where $\delta ^{bk}$ represents the resources used in managing bank capital, $\Pi _t^{bk}$ is the overall profit of the banking group which is partially distributed to households as dividends, and $\nu$ is the share of retained earning.

The risk weights, $rw_t^E$ are computed according to the Basel III IRB approach, as most of the euro area banking system non-financial corporations credit risk is calculated using this approach. According to the Basel III IRB approach, risk weights are defined as follows:

(28) \begin{align} rw_{t}^{E} & = 12.5 LGD^E \left \{ \Phi \left ( \frac {\Phi ^{-1}(PD_t^E)+(\tau ^{rw^E})^{0.5}\Phi ^{-1}(0.999)}{(1-\tau ^{rw^E})^{0.5} } \right ) - PD_t^E \right \} \end{align}

(29) \begin{align} \tau ^{rw^E} &= n_1^E \left [ \frac {1-\exp (-n_3^E PD_t^E)}{1-\exp (-n_3^E)}\right ] + n_2^E \left [ 1- \frac {1-\exp (-n_3^E PD^E_t)}{1-\exp (-n_3^E)} \right ] \end{align}

(30) \begin{align} PD_t^E &= \alpha ^{PD}PD^E_{t-1}+4(1-\alpha ^{PD})F\left (\overline {\omega }_t^E\right ) \end{align}

As aforementioned, $PD_t^E$ is the 1-year ahead probability of default of the representative firm, with $\alpha ^{PD}$ being the autoregressive coefficient of the PD process and $\tau ^{rw^E}$ the asset-value correlation. The parameters $n_x,$ with $ x=\{1,2,3\}$ are derived from the Basel III regulation for the non-financial corporate sector.

From the maximization problem of the wholesale banks, we obtain the following relation on the interest rate spread between the refinancing rate and the risk-free rate:

(31) \begin{eqnarray} R_t^{F,E} - R_t = PD^E_{t} LGD^E - \Xi \left (\frac {Bankcap_t}{rw_t^E B_t^{E}} - CR\right ) \left (\frac {Bankcap_t}{rw_t^E B_t^{E}}\right )^2 rw_t^E \end{eqnarray}

We now turn to the second model specification, where banks are required to reflect climate risk in their regulatory constraint. As for the case without climate-prudential policies, the wholesale branch receives deposits from households and chooses the allocation of credit between firms. However, giving credit to firms with different levels of carbon intensity entails different risk weights reflecting individual transition risk. The wholesale branch maximizes the following profit function:

(32) \begin{align} \max _{\{B_t^{E,i}, D^{H}_t\}} & \sum _i R_t^{F,i} B_t^{E,i} - R_t D^{H}_t - \sum _i PD_t^i LGD^i B_t^{E,i} - \frac {\Xi }{2} \left (\frac {Bankcap_t}{\sum _i rw_t^i B_t^{E,i} } - CR\right )^2 Bankcap_t - \mathbb{T} \end{align}

subject to the following balance sheet identity:

(33) \begin{eqnarray} \sum _i B_t^{E,i} = D^{H}_t+Bankcap_t \end{eqnarray}

where $CR$ is the target capital ratio and $rw_t^i$ are the risk weights that apply to each type of firm and are defined following the Basel III IRB approach, similarly to eq. 28–30. $\mathbb{T}$ is a sunk cost that banks pay when they have to identify the transition risk of each of their exposures (for example due to the hiring of new experts or the acquisition of data). The probabilities of default of entrepreneurs are different for firms with different degrees of carbon intensity and depend on different idiosyncratic shock thresholds $\overline {\omega }_t^i$ . As described in Section 3.2, the threshold value $\overline {\omega }^i_t$ depends on the level of carbon emissions, implying a higher probability of default if the firm is more carbon-intensive and, thus, higher credit (transition) risk. As in the case without regulation, bank capital accumulates out of retained earnings from the bank group profits (see eq. 27). Solving the maximization problem, we obtain the following spread between the financing rate for commercial lending branches and the risk-free rate:

(34) \begin{align} R_t^{F,i}-R_t = PD_t^i LGD^i - \Xi \left (\dfrac {Bankcap_t}{\sum _i rw^i_t B_t^{E,i}} - CR\right ) \left ( \dfrac {Bankcap_t}{\sum _i rw^i_t B_t^{E,i}} \right )^2 rw_t^i \end{align}

where $R_t^{F,i}$ is a differentiated financing rate reflecting the specific firms’ transition risk.

3.6.2. The commercial lending branch

As for wholesale branch, we first present the commercial lending branch for the model specification without climate-prudential policies before outlining the changes that are made to the model when we assume that banks have to identify firms on the basis of their carbon intensity. Commercial lending branches issue credit to entrepreneurs without distinguishing between different types of firms. These branches, which obtain funds from the wholesale part of the group, are also in perfect competition and have zero profits in equilibrium. Their profit maximization is given by:

(35) \begin{eqnarray} \!\!\max _{R_t^E} \!\int _0^{\infty } \frac {\left(1 + R_{t-1}^E\right) B_{t-1}^{E} - \left(1 + R_{t-1}^{F,E}\right)B_{t-1}^{E}}{1+\pi _t} P_t dF\left (\omega _t^E\right ) - \rho \!\!\int _0^{\overline {\omega }_t^E} \!\! (1-\delta )Q_t^EK_{t-1}^E \omega _t^E dF\left (\omega _t^E\right )\,\,\, \end{eqnarray}

where $\rho \int _0^{\overline {\omega }_t^E} (1-\delta )Q_t^E K_{t-1}^E \omega _t^E dF\left (\omega _t^E\right )$ are the (real) expected monitoring costs paid by the bank to seize collateral in case of the entrepreneur’s default on its loan commitment. From the zero profit condition, the lending rate applied to the entrepreneur by the commercial lending bank is given by:

(36) \begin{eqnarray} R^E_{t-1} = R^{F,E}_{t-1} + \frac {1+\pi _t}{B_{t-1}^E P_t}\left [H\left(\overline {\omega }_t^E\right)-G\left(\overline {\omega }_t^E\right)\right ](1-\delta )Q_t^E K_{t-1}^E \end{eqnarray}

As banks do not distinguish between firms, in equilibrium the same financing conditions will be proposed to all types of firms, i.e., $R^{E,i}_t=R^E_t,\ \forall i$ .

We now turn to the model specification with climate-prudential regulation. Without loss of generality, but keeping calculations simpler, each commercial lending branch specializes in giving credit to only one type of firm. As in the case without prudential policies, the commercial lending branches are in perfect competition and have zero profits in equilibrium. They get funds from the wholesale branch and distribute credit to entrepreneurs. Similarly to the model without climate policy, for each type of credit contract, the maximization problem of each commercial lending branch can written as:

(37) \begin{eqnarray} \!\!\!\!\max _{R_t^{E,i}} \!\int _0^{\infty }\! \frac {\left(1 + R_{t-1}^{E,i}\right) B_{t-1}^{E,i} - \left(1 + R_{t-1}^{F,i}\right)B_{t-1}^{E,i}}{1+\pi _t} P_t dF\left (\omega _t^i\right ) - \rho \!\int _0^{\overline {\omega }_t^i}\!\! (1-\delta )Q_t^i K_{t-1}^i \omega _t^i dF\left (\omega _t^i\right ) \end{eqnarray}

From which we obtain:

(38) \begin{eqnarray} R^{E,i}_{t-1} = R^{F,i}_{t-1} + \frac {1+\pi _t}{B_{t-1}^{E,i} P_t}\left [H\left(\overline {\omega }_t^i\right)-G\left(\overline {\omega }_t^i\right)\right ](1-\delta )Q_t^i K_{t-1}^i \end{eqnarray}

This implies that in equilibrium different financing conditions will be proposed to each firm type.

4.1. Calibration

The calibrated values of most parameters are drawn from Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rancoita2019) and Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rodriguez-Palenzuela2011), as detailed in Appendix B, Table B1. Given that our economy differs slightly from the settings of these papers, some adjustments are introduced. In particular, while the cited works distinguish between firms across different sectors, our framework focuses on firms operating within the same sector but exhibiting different degrees of carbon intensity. To capture this distinction, we calibrate the two types of entrepreneurs differently in terms of their risk profiles ( $\sigma _{\omega ^i}$ ) and the costs of acquiring and adjusting capital for production ( $\phi ^i$ ). We also differentiate between the share of green and more polluting goods in households’ consumption baskets ( $\kappa ^{LCI}$ and $\kappa ^{HCI}$ ) and the applicable carbon tax ( $\eta$ ).

Specifically, the parameter $\sigma _{\omega ^{i}}$ is calibrated in previous literature (see Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rancoita2019)) to match the steady-state probability of default for each entrepreneur type. While there is a growing body of work examining sustainability as a long-term risk factor for corporate viability (Gao et al. (Reference Gao, Li, Wang and Zhong2021), Li et al. (Reference Li, Zhang and Zhao2022), Kanno (Reference Kanno2023)), only Ferriani and Pericoli (Reference Ferriani and Pericoli2024) provide some quantitative evidence on the impact of higher ESG scores on credit risk, which largely corresponds to less carbon-intensive production. Based on this evidence, we adopt the value of $\sigma _{\omega ^{LCI}}$ (0.154) from Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rancoita2019) and set $\sigma _{\omega ^{HCI}}$ to a higher value (0.18) to account for the higher riskiness of HCI entrepreneurs. This calibration ensures that the difference in steady-state default probabilities between HCI and LCI entrepreneurs aligns with the estimates of Ferriani and Pericoli (Reference Ferriani and Pericoli2024), who find that a one-standard-deviation increase in the ESG score is associated with up to a $15\%$ reduction in the average probability of default.

Similarly, the adjustment cost parameter for HCI entrepreneurs, $\phi ^{HCI}= 0.2755$ , mirrors the value in Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rancoita2019), whereas $\phi ^{LCI} = 1.2755$ is calibrated to be marginally higher. As discussed in Section 3.2, the higher value for $\phi ^{LCI}$ reflects the greater technological and operational constraints faced by cleaner production technologies. The parameter $\phi ^i$ does not affect the steady state of the model, since the adjustment cost function equals one in steady state. However, $\phi ^i$ influences the sensitivity of the model’s impulse response functions, particularly the lending response, as it impacts the cost of capital and, consequently, firms’ borrowing needs.

Finally, the share of green (polluting) goods in households’ consumption baskets, $\kappa ^{LCI}$ ( $\kappa ^{HCI}$ ), is set to 0.6 (0.4) to align with data presented in Figure 1.

In terms of environmental dimension, we use the emission-to-output ratio for the Euro Area, $\zeta = 0.3$ , as estimated by Benmir and Roman (Reference Benmir and Roman2020). The tax level, $\eta$ , is set to $10\%$ such that overall taxes collected on emissions are $3\%$ of total production of HCI firms.

Admittedly, the calibration of these key parameters for high- and low-carbon-intensity firms is constrained by the very limited empirical evidence available in the literature. Quantitative studies on this topic remain scarce, and our primary objective is not to provide precise quantitative policy estimates but rather to demonstrate—qualitatively—the necessity of climate-related prudential regulation. To strengthen this point, we conduct extensive robustness checks, reported in Section 5, which show that our main findings are not driven by a specific parametrization. Instead, they hold consistently across a wide and plausible range of parameter values. This provides strong evidence that the core mechanisms identified in the paper are robust and economically relevant.

It is important to stress that the main results of the paper hinge on the non-linearity of the risk-weighted assets formula. In the absence of prudential policies, banks do not distinguish between the two types of firms or their idiosyncratic shocks; instead, they calculate risk weights based on the average firm. By contrast, under climate-prudential policies, risk-weighted assets are computed as a weighted sum of exposures, where risk weights are tailored to the specific carbon intensity of each firm.

4.2. Results

To make the case for introducing climate-prudential policies, we compare the results of the two versions of the model described above—with and without climate-prudential policy intervention.

Figure 2 provides a comparison of steady-state values for various financial variables and for the output of LCI and HCI firms. The bar charts highlight how the introduction of climate-prudential regulation leads to better results for the financial and real sectors. However, there are some caveats to our analysis. First, the model does not have an endogenous level of target capital ratio, and we assume in both cases that this ratio has the same level. In addition, the relative preference of consumers for the two types of products is assumed not to change between the two cases.

Keeping this in mind, we observe that the level of bank capital is higher without climate-prudential policies, as overall there is more risk (lending to the more carbon-intensive firms is higher) implying that banks allocate capital more efficiently when they explicitly consider transition risk. Provisions to cover credit risk losses are about $9\%$ lower relative to the case where banks are not submitted to climate-prudential policies as more losses than expected materialize and banks do not correctly internalize the credit risk of their exposures. This result can be explained by the higher steady-state default rates without climate-prudential policies.Footnote ²⁰

When climate-prudential policies apply, the steady-state lending to HCI firms is lower as they are explicitly identified as being riskier, whereas LCI firms receive more credit. This is an important result as it implies that if banks were to fully internalize transition risk, they would have less exposures to HCI firms. Overall credit to the real economy increases when climate-prudential policies are implemented.

Finally, the different allocation of lending between the two institutional settings is also reflected in the output of the two types of firms. The share of productions of HCI firms decreases with respect to the case where no climate-prudential policy is enforced. The opposite is true for LCI firms who benefit from better credit conditions and produce more when climate policy is enforced.

Figure 2.

Steady state comparison policy [p] and no-policy [np] case.

Note: The bars represent the ratio (or difference) between the steady-state value from the model where green prudential regulation in enforced with respect to the value from the model where prudential regulation does not take climate transition risk into account. $\Delta \%$ is defined as (p-np)/np, pp is defined as (p-np)

We next turn to the analysis of impulse response functions. As outlined in Section 3.2, we model the transition risk shock as a shock to the emission tax, which affects in turn the riskiness of HCI firms, $\sigma _{\omega ^{HCI}}$ . This correlation captures additional effects that a sudden increase in the tax rate could have on firms. For the analysis, we calibrate the emission tax shock such that the tax increases by 10%, while the riskiness of entrepreneurs rises by one standard deviation. This calibration allows for a meaningful comparison of our results with those from more conventional macroprudential models.

Figure 3 shows how financial variables respond to an unexpected transition risk shock. We start by looking at the overall dynamics of the model. The shock leads first to an increase in the probability of default of HCI firms. This increase is identical across the policy and no-policy models, as both the initial shocks and all structural parameters are the same in the two scenarios. The higher default risk of these firms increases their financing cost which in turn reduces the amount of credit they can obtain from the bank. When no distinction is made by banks between HCI and LCI firms in terms of transition risk (no policy), lending to LCI firms decreases as well, implying that this type of firms are penalized even if their default risk does not change. The drop in lending can also be explained by the financial constraints that banks have once losses materialize. Indeed, risk-sensitive regulation calls for higher capital requirements when PDs increase, binding the bank to reduce its credit activity. Moreover, provisions considerably increase (up to 10% of their steady-state value) in reaction to the rise in the PD of polluting firms, as more firms default on their credit engagements. When no climate-prudential policy is implemented, the common equity tier 1 ratio (CET1) decreases. This can be explained by the fact that the higher default rate of HCI firms implies not only losses to bank capital but also higher total risk-weighted assets, with risk weights on both high- and low-carbon-intensive firms increasing in the no-policy scenario. Note that the impact on bank capital is limited as banks need to obey capital requirements, but the increase in the PD of polluting firms has a rather persistent impact on risk-weighted assets.

Figure 3.

Impulse response functions for the financial sector [lending: in % deviation from the steady state; all other variables: pp difference from the steady state].

Note: The figure presents the IRFs of financial variables to a transition risk shock implying 10% higher emission taxes and 1 standard deviation shock to $\sigma _{\omega ^{HCI}}$ , the riskiness of HCI firms.

When comparing the two models—with and without climate-prudential policies—we can see that the introduction of climate-prudential policies weakens the negative effect of the transition shock.Footnote ²¹ In response to an increase in the riskiness of the more polluting firms, banks deleverage more with respect to this type of firms when the policy is implemented. This clearly shows that regulation increases the sensitivity of banks to transition risk. At the same time, lending to LCI firms is rather stable with respect to its steady-state value when climate-prudential policies are implemented. The penalty seen before for this type of firm is thus alleviated with climate-prudential policies in place. Notice that when banks are not obliged to distinguish between HCI and LCI firms, the lending rate is the same for both of them. With policy intervention, LCI firms obtain more favorable financing conditions than HCI firms for which the increase in the lending rate is more important than in the model without climate-prudential policies. Enforcing climate-related prudential policies leads thus to more equitable financing conditions, riskier firms having to pay higher interest rates on their credit. Total lending decreases less under the policy case (mainly driven by credit to more polluting companies). The difference is of approximately 15 basis points at its maximum, implying less consequences on the real economy when climate-prudential policy is in place. Furthermore, in the case where these type of policies are enforced, we assume that regulation is relaxed with respect to polluting firms if a transition shock would materialize. This translates into a release of capital requirements allowing banks to diverge from the steady state ratio with lower bank capital for several periods. At the same time, risk-weighted assets decrease for the first period as lending to HCI firms decreases, to increase immediately afterwards when the decrease in lending is more than compensated by the increase in the risk weights applied to polluting firms. In the simulations, it is assumed that the relaxation of prudential policies is in magnitude of about 30 bps (which is close but below the release of other capital requirements in previous crises). Due to the relaxation of the capital requirements, in the policy case the CET1 ratio slightly increases in the beginning of the simulation period, to decrease immediately afterwards. Overall, implementing climate-prudential policies to account for transition risk seems beneficial for the financial system as banks better internalize the actual credit risk of their exposures. Different values of the capital requirements release would lead to similar results. However, in this simulation we do not provide a precise estimate of the size of the excess in credit risk generated by transition risk. As mentioned earlier, the model is calibrated with values already used in the literature but due to lack of data we cannot estimate the distribution of transition risk shocks. In the current example, we assume that the size of the transition risk shock is of half the standard deviation of the calibrated riskiness of firms in Darracq-Pariès et al. (Reference Darracq-Pariès, Kok and Rancoita2019). This reflects the idea that transition risk is currently a less relevant source of credit risk, but at the same time it allows us to work with realistic magnitudes despite the lack of data for the calibration.

Figure 4 shows the response of the real economy for the above mentioned exercise.Footnote ²² As expected, the increase in transition risk of HCI borrowers translates in lower total output and investment, reflecting the deleveraging of banks and the higher cost of credit in both sectors. In the case where climate-prudential policies are implemented, the impact on the real economy is better contained, as investment decreases less. The decline in output is mainly driven by the investment level, as consumption of both low- and high-carbon-intensive goods tends to support output (recall that it is assumed here that consumers do not change their preferences). Looking at the production breakdown, it is relevant to notice that the output of polluting firms decreases a lot more when climate-prudential policy is implemented, whereas the production of less polluting goods is only slightly impacted. However, without policies in place the production in both sectors would considerably diminish, as banks would deleverage in a similar way on all exposures. Finally, as inflation and output diminish in the economy, the monetary authority reduces its interest rate, but the impact is less pronounced when explicit transition risk policies are implemented.

Figure 4.

Impulse response functions for the real sector [% deviation from the steady state, CPI and risk-free rate in pp. difference from the steady state].

Note: The figure presents the IRFs of real economic variables to a transition risk shock implying 10% higher emission taxes and 1 standard deviation shock to $\sigma _{\omega ^{HCI}}$ , the riskiness of HCI firms.

In order to highlight the stabilization trade-offs and show more general results, we compare the efficiency policy frontiers implied by the models with and without climate-prudential policies. The efficiency policy frontier (EPF) portrays the surface where it is not possible to attain lower variance in one objective variable without increasing the one of the others. In the case under consideration, the efficiency policy frontiers reflect the three target variables of the monetary and macroprudential policy authorities: inflation, output gap, and credit volatilities. The efficiency policy frontiers abstracts from the specific loss function and the strategic interaction between the monetary and macroprudential authorities, and the ‘best’ allocation is given by the intersection with the efficiency policy frontiers and the authorities loss function/s. We conducted two simulations assuming either that climate-prudential policies are implemented or that they are not. In each case, we optimized the monetary policy rule in terms of the coefficient of the inflation gap and of the output gap. The model does not specify any particular rule for the climate-prudential policies, but we assume either that they are not implemented at all or that they allow a perfect identification of transition risk. In all cases, we activate the transition shocks. The resulting standard deviations for inflation, output gap, and credit for each coefficient combination are illustrated in Figure 5. Depending on the assumptions about the loss function/s of the monetary authority and the activation of climate-prudential policies, we can select a different point on each efficiency policy frontier to be the best.

Figure 5.

Efficiency frontier between output-lending policy outcomes (left) and inflation-output outcomes (right).

Note: The chart represents the efficiency policy frontier for given shocks to borrower riskiness. The efficiency frontier portrays, for all sets of policymaker’s preferences, the lending, output and inflation volatilities implied by the corresponding optimized rules.

In Figure 5, we can observe that the activation of climate-prudential policies leads overall to lower output, inflation, and lending volatility in equilibrium for any optimal monetary policy rule. We can derive some relevant policy conclusions from Figure 5 even without being specific about the loss functions of the policy authorities or about the strategic interactions among the authorities. Introducing climate-prudential policies Pareto dominates the institutional configuration without them and this induces an inward shift in the efficiency frontier. Relevantly, this also enables monetary policy to achieve a superior performance in terms of macroeconomic stabilization.