2. A macroclimate model with risky government debt

We introduce a streamlined yet comprehensive closed-economy macroclimate model designed to evaluate the interplay between green transition policies, public debt, and macroeconomic variables. We integrate a macroclimate neo-classical real model inspired by Annicchiarico and Di Dio (Reference Annicchiarico and Di Dio2015), with a framework for risky government debt based on insights from Corsetti et al. (Reference Corsetti, Kuester, Meier and Müller2013) and Darracq-Pariès et al. (Reference Darracq-Pariès, Jacquinot and Papadopoulou2016). The core aim is to scrutinize the impact of green policies on public finances and the consequent sustainability of public debt under alternative mitigation strategies. The model incorporates a carbon budget constraint, which aligns with the global commitments undertaken with the Paris Agreement. The economy is made of a competitive private sector, households, and the government. Emissions are a by-product of the production of final goods. Firms engage in profit maximization, factoring in labor, capital, carbon taxation, abatement costs, and green subsidies. They adapt over time to environmental policies, established by the government. Households make decisions regarding consumption, labor supply, and investment in private capital and in government bonds. Their investment in public debt is risky, since in case of default they would be only partially compensated by their loss through public transfers. Their behavior aims to maximize their own utility and it is shaped by taxation, and the overall economic conditions. The government’s role is multifaceted, involving bond issuance, the management of taxes and public spending according to policy rules, and ensuring the respect of the political constraints on carbon emissions. It determines carbon taxes, green subsidies to firms and direct public mitigation efforts in line with the available carbon budget. The model also potentially includes climate damages on productivity as a consequence of cumulative carbon emissions, according to different functional forms proposed in the macroclimate literature.

The model captures the main channels through which reducing carbon emissions impacts the real economy and public finances. For different shares of the public direct effort over total mitigation and the level of green subsidies to the private sector, we determine, thus, the sustainability of public debt in alternative mitigation scenarios. Figure 1 shows the structured interaction of the model components, which is described in detail below.

Figure 1.

The model’s structure (variables in parentheses are nonzero only in the event of government debt default).

The carbon budget. The economy operates within a binding total carbon budget imposed by the government, in line to its commitment to international agreements, which aim to limit global temperature under a certain threshold (1.5 $^{\circ }$ C on average over preindustrial levels):

(1) \begin{equation} \sum _{t=0}^{+\infty } E_t \leq \bar {E}^n_0 \end{equation}

where $E_t$ represents national emissions in one period, and $\bar {E}^n_{0}$ the carbon budget available to the economy from period 0 onwards. The imposition of this constraint captures the political willingness to avoid adverse effects of climate change, generated by the use of carbon emissions. The national carbon budget would represent a fraction of a global carbon budget $\bar {E}^G_{0}$ in line with these environmental commitments.

Final Good Production. In our economy a unique final good $Y_t$ , which is used for consumption and investment, is produced by a continuum of competitive firms $i\in (0,1)$ .Footnote ⁴ We assume a standard Cobb-Douglas production function with capital $K_t(i)$ and labor $L_t(i)$ as inputs, with the potential addition of climate damages on productivity. Each firm produces:

(2) \begin{align} Y_{t}(i) =D_f(H^G_t) K_{t}(i)^\kappa [Z_t L_{t}(i)]^{1 - \kappa } , \quad \kappa \in (0,1), \end{align}

where $\kappa$ is the elasticity of output with respect to capital and $Z_t = Z_0 e^{z t}$ is labor-intensive technological progress. We will normalize $Z_0=1$ , for the sake of simplicity. $D_f$ represents the damaged total factor productivity (TFP), which is potentially decreasing (according to a given function $f$ ) in global cumulative GHG emissions, since 1850, $H^G_t$ .

Temperature, cumulative and flow emissions. The global average temperature increase, with respect to preindustrial levels, corresponds to a linear function of cumulative emissions: $T_t=\gamma H^G_t$ . We assume that the examined country, when selecting its own transition path, will automatically set the path for the global economy.Footnote ⁵ Therefore, in order to define global emissions and temperature, we multiply national emissions by a factor equal to the ratio between the global and the national carbon budget. Then, global cumulative emissions write as:

\begin{equation*}H^G_t= H^G_{-1} + \frac {\bar {E}^G_0}{\bar {E}^n_{0}}H_{t}= H^G_{t- 1} + \frac {\bar {E}^G_0}{\bar {E}^n_{0}}E_t,\end{equation*}

where $\bar {E}^G_0$ and $\bar {E}^n_{0}$ are, respectively, the global and the national carbon budget from 2024 onward, whose first quarter represents our period 0.Footnote ⁶ National cumulative emissions at time t $H_t$ are defined as: $H_{t}=\sum _{j=0}^{t} E_{j}= H_{t-1} + E_{t}$ .

Emissions of firm $i$ in one period are defined as a by-product of output, and this relationship is affected by the private abatement effort $m_{t}(i)$ and the public abatement intervention $m^g_t$ ,Footnote ⁷ which we assume to be constant across firms :

(3) \begin{equation} E_{t}(i) = \xi _t [1- m_{t}(i) - m^g_t] Y_{t}(i) \end{equation}

where $\xi _t = \xi _0 e^{-\omega t} = \xi _{t-1} e^{-\omega }$ , $\xi _0\gt 0$ , is output’s carbon intensity (emissions per unit of output in the absence of abatement effort), which is decreasing over time at rate $\omega \gt 0$ .

Private abatement technology cost. Similarly to Nordhaus (Reference Nordhaus2008), Annicchiarico and Di Dio (Reference Annicchiarico and Di Dio2015), and Jondeau et al. (Reference Jondeau, Levieuge, Sahuc and Vermandel2023), the private abatement technological cost is defined as:

(4) \begin{equation} A_{t}(i) = \theta _1 [m_{t}(i)]^{\theta _2} Y_{t}(i) \end{equation}

where $\theta _1\gt 0, \theta _2\gt 1$ are parameters of the abatement cost function.

Profit maximization. Each firm $i$ maximizes profits:

(5) \begin{equation} \Pi _{t}(i) = Y_{t}(i) - {W_t} L_{t}(i) - {R^k_t}K_{t}(i) - (1-s^A_t) A_{t}(i) -{\tau ^E_t} E_{t}(i) , \end{equation}

subject to the production function (2). $W_t$ , $R^k_t$ , $\tau ^E_t$ , and $s^A_t$ are, respectively, the real wage, the rental rate on capital, the carbon tax, and the public subsidy to abatement costs. The latter two depend on the environmental policy regime, decided by the government. Cost minimization at the margin implies:Footnote ⁸

(6) \begin{align} & \left (\delta L_{t}(i)\right ) \quad {W_t} =\Theta _{t}(i)D_f(H^G_t)K_{t}(i)^\kappa (1-\kappa ) Z_t^{1-\kappa } L_{t}(i)^{-\kappa } \end{align}

(7) \begin{align} & \left (\delta K_{t}(i)\right ) \quad {R^k_t}=\Theta _{t}(i)D_f(H^G_t) \kappa K_{t}(i)^{\kappa -1} (Z_tL_{t}(i))^{1-\kappa } \end{align}

(8) \begin{align} & \left (\delta m_{t}(i)\right ) \quad {\tau ^E_t} =\frac {(1 -s^A_t) \theta _1 \theta _2}{ \xi _t} [m_{t}(i)]^{\theta _2-1} \end{align}

where $\Theta _{t}(i)$ is the Lagrange multiplier associated to (2), corresponding to the marginal cost’s component attached to labor and capital.Footnote ⁹ In the following, we drop the $i$ index for simplicity—the index was necessary for representing climate damages as an externality, where the contribution of emissions from firm $i$ is marginal— since in equilibrium all firms are identical and perfectly competitive, thus, will make the same choice. The marginal cost of output is:

(9) \begin{align} MC_t= \quad &\Theta _{t} + (1-s^A_t)\theta _1 m_{t}^{\theta _2} +{\tau ^E_t} \xi _t (1- m_{t}-m^g_t) \end{align}

(10) \begin{align} \text{where } \quad &\Theta _{t} =\frac {\left ({W_t}\right )^{1-\kappa } \left ({R^k_t}\right )^\kappa }{D_f(H^G_t)Z_t^{(1-\kappa )} \kappa ^{\kappa }(1-\kappa )^{(1-\kappa )} } \end{align}

Notice that in this real model with perfect competition, $MC_t=1$ .

Carbon tax and total abatement. The carbon tax $\tau ^E_t$ (8) is defined by the government to motivate firms to carry out the collective private mitigation effort $m_t=\int _0^1m_t(i)\mathrm{d} i$ . The government also conducts direct public mitigation efforts $m^g_t$ . The sum of $m_t$ and $m^g_t$ represents total abatement and needs to satisfy over time a mitigation rule consistent with the carbon budget (1), the country has committed to:

(11) \begin{align} &m_t +m^g_t= \left (\frac {H_{t-1}}{\bar {E}^n_0}\right )^p \end{align}

(12) \begin{align} &\frac {m^g_t}{m_t +m^g_t} = \theta \end{align}

where $p\gt 0$ represents the curvature of the mitigation policy rule. According to (11), the total abatement the country needs to carry out in a given period is equivalent to a function of the ratio between its past cumulative emissions $H_{t-1}$ and the national carbon budget $\bar {E}^n_0$ . When the latter is exhausted ( $H_{t-1} = \bar {E}^n_{0}$ ), we obtain that total mitigation needs to be equal to 1 and zero emissions are associated with production processes. We also assume that the fraction $\theta$ , which represents the share of government direct efforts in total abatement, is constant, for the sake of simplicity. In Section 5, we will optimally determine this share over time through a welfare maximization exercise.

Households. The economy is inhabited by a representative, infinitely lived household, who maximizes her intertemporal utility:

\begin{equation*} \mathbb{E}_t \sum _{i=0}^{\infty } \beta ^i\left (\ln C_{t+i}-\mu _L \frac {L_{t+i}^{1+\sigma _l}}{1+\sigma _l}\right ), \quad \sigma _l\gt 0, \mu _L\gt 0. \end{equation*}

Here, $\beta \in (0,1)$ is the discount factor, which is constant over time. $C_t$ and $L_t$ denote, respectively, the consumption of the final goods and the work hours supplied by the household. The disutility of labor is weighted by $\mu _L$ , while $\sigma _l$ serves as the inverse of the Frisch elasticity of labor supply. Similarly to Corsetti et al. (Reference Corsetti, Kuester, Meier and Müller2013), the household’s budget constraint for each period is given by:

(13) \begin{equation} C_t+ I_t+B_t=(1-\vartheta _t)R^d_{t-1}B_{t-1} +W_t L_t+ \Pi _t+R^k_t K_t-T_t +V_t. \end{equation}

$B_t \equiv \frac {d_{t}Y_t}{R^d_t}$ , as defined below, corresponds to the investment in government bonds made by the household. This corresponds to the amount of bonds $D_{t+1}\equiv d_tY_t$ she bought, divided by the gross interest rate $R^d_t$ , the government must pay on each bond to compensate the investor. Typically, in dynamic general equilibrium models, government debt is considered risk-free, and $R^d_t$ is treated as equivalent to the risk-free interest rate. However, in this model, to capture the implications of the transition for sovereign financing and sustainability, government debt is modeled as risky: $\vartheta _t$ represents the haircut, which is zero when the government fully honors its debt commitments, and $\vartheta _t= \vartheta \in (0,1)$ , when the government partially defaults on debt, event which happens with probability $\mathsf{PD}_t$ . The latter represents the probability of default on currently outstanding debt $D_t \equiv R^d_{t-1}B_{t-1}$ , to be repaid at $t$ .Footnote ¹⁰ Investors evaluate the probability of default according to the following condition:

(14) \begin{equation} b_M e^{\varepsilon _t}\lt b_t \quad \text{where} \quad \varepsilon _t\sim N(0, \sigma _B) \end{equation}

where $b_M$ is the fiscal limit of our economy, in terms of maximum sustainable government borrowing-to-GDP ( $b_t\equiv \frac {B_t}{Y_t}$ ). This fiscal limit is subjected to uncertainty, represented by the random log-normal shock $e^{\varepsilon _t}$ with zero-mean and volatility $\sigma _B$ . The probability of default writes then as a standard normal c.d.f.:

(15) \begin{equation} \mathsf{PD}_{t+1}=\Phi \bigg ( \frac {\ln (b_{t})-\ln (b_M)}{\sigma _B}\bigg ), \end{equation}

similarly to Darracq-Pariès et al. (Reference Darracq-Pariès, Jacquinot and Papadopoulou2016), Collard et al. (Reference Collard, Habib and Rochet2015) and Seghini (Reference Seghini2024a), with parameter $\sigma _B$ and $b_M$ . $V_t\equiv (1-f) \vartheta _tR^d_{t-1}B_{t-1}$ is a lump-sum transfer that, should a government default on its debt, partially reimburses bondholders for a fraction $1-f$ of the financial losses they sustain due to the default. The standard lump-sum taxes or transfers from the government are given by $T_t$ , and dividends from owning firms that produce the final goods are $\Pi _t$ . Labor income and rental income from capital services are represented by $ W_t L_t$ and $R^k_t K_t$ , respectively. In each period $t$ , each member inherits $K_{t-1}$ units of physical capital from the prior period, devalued by a depreciation rate $\delta$ , and makes investment decisions $I_t$ . The capital accumulation equation is expressed as:

(16) \begin{align} &K_{t+1} = (1-\delta )K_{t}+I_t \left [1- S\left (\frac {I_t}{I_{t-1}}\right )\right ], \quad \delta \in (0,1). \nonumber \\ &\text{where} \quad S\left (\frac {I_t}{I_{t-1}}\right ) = \frac {\iota }{2}\left (\frac {I_t}{I_{t-1}}- e^z\right )^2 \end{align}

where $S(\cdot )$ represents the investment adaptation cost function and $e^z$ the steady-state growth rate of investment. The first-order conditions obtained from the household’s maximization problem, are:Footnote ¹¹

(17) \begin{align} &\left (\delta C_t\right ) \,\, \frac {1}{C_t}= \lambda _t \end{align}

(18) \begin{align} &\left (\delta L_t\right ) \,\, \mu _lL_t^{\sigma _l}=\lambda _t { W_t} \end{align}

(19) \begin{align} &\left (\delta B_{t}\right ) \,\, {\lambda _t}= \beta \mathbb{E}_t \left [\lambda _{t+1}(1-f\vartheta _{t+1})R^d_t \right ]\end{align}

(20) \begin{align} &\left (\delta I_t\right ) \,\, \lambda _t=\lambda _t^k \left [1-S\left (\frac {I_t}{I_{t-1}}\right )-S^{\prime }\left (\frac {I_t}{I_{t-1}}\right ) \frac {I_t}{I_{t-1}}\right ]+\beta \mathbb{E}_t\left [\lambda _{t+1}^k S^{\prime }\left (\frac {I_{t+1}}{I_t}\right )\left (\frac {I_{t+1}}{I_t}\right )^2\right ] \nonumber \\ & \quad \quad \quad \, = \lambda _t^k \left [1 - \frac {\iota }{2} \left (\frac {I_t}{I_{t-1}} - e^z\right )^2 - \iota \left (\frac {I_t}{I_{t-1}} - e^z\right )\frac {I_t}{I_{t-1}}\right ] +\beta \mathbb{E}_t\left [\lambda _{t+1}^k \iota \left (\frac {I_{t+1}}{I_{t}} - e^z\right )\left (\frac {I_{t+1}}{I_t}\right )^2\right ]\nonumber\\[5pt] \end{align}

(21) \begin{align} & \left (\delta K_{t+1}\right ) \,\, \lambda ^k_t =\beta \mathbb{E}_t\left [\lambda _{t+1} {R^k_{t+1}}\right ] + \beta (1-\delta )\mathbb{E}_t\left [\lambda ^k_{t+1} \right ] \end{align}

where $\lambda _t$ and $\lambda _t^k$ are the Lagrange multipliers assigned to the budget constraint and the capital accumulation constraint. Tobin’s $\mathrm{Q}$ corresponds to $q_t^k=\lambda _t^k / \lambda _t$ , and is equal to 1 when there are no investment adjustment costs ( $\frac {I_t}{I_{t-1}}= e^z$ ).Footnote ¹² Therefore, from the first-order conditions (FOCs), we can derive the following equality between the stochastic discount factor—representing the risk-free interest rate—and the rental rate on capital:

(22) \begin{align} R_{t}\equiv \frac {\lambda _t}{\beta \mathbb{E}_t \left [\lambda _{t+1}\right ]} =\frac {1}{q_t^k \mathbb{E}_t \left [\lambda _{t+1}\right ]}\bigg\{\mathbb{E}_t\left [\lambda _{t+1} {R^k_{t+1}}\right ] + (1-\delta )\mathbb{E}_t\left [\lambda _{t+1}q^k_{t+1} \right ]\bigg\}. \end{align}

Therefore, we can rewrite the FOC with respect to investment in government debt (19) as:

(23) \begin{align} R_{t}&= \frac { \mathbb{E}_t \left [\lambda _{t+1}(1-f\vartheta _{t+1})R^d_t \right ]}{ \mathbb{E}_t \left [\lambda _{t+1}\right ]} \approx (1-f\vartheta \mathsf{PD}_{t+1})R^d_t . \end{align}

The approximation at the right-hand side of (23) is shown to highlight the role of the term between parentheses as a wedge between the risk-free rate of the economy and the return $R^d_t$ required by households to invest in risky government bonds. It holds in the first-order log-linearized version of the model and in steady state.Footnote ¹³

Government budget constraint and abatement costs. The government levies the lump-sum tax $T_t$ (which can also take the form of transfers) and the carbon tax $\tau ^E_t$ on emissions, to finance the purchases of goods and services in quantity $G_t$ , provide subsidies $s^A$ to private abatement costs, and finance direct public mitigation efforts $m^g_t$ . It issues bonds $D_{t+1}$ , which pay a rate of return $R^d_t$ to households (bondholders), in order to borrow $B_t$ , and has to repay old debt $D_{t}$ . In case of default, it also pays lump-sum transfers $V_t$ to households for compensation and is forced to unexpectedly face additional public expenditure $G^d_t\equiv f\vartheta _{t} B_{t-1}R^d_{t-1}$ , which corresponds to a proportion $f$ of financial losses. $G^d_t$ represents unexpected debt restructuring or reputational costs, which arise in case of default (Borensztein and Panizza, Reference Borensztein and Panizza2009).Footnote ¹⁴ For the sake of tractability, and in similar spirit to Corsetti et al. (Reference Corsetti, Kuester, Meier and Müller2013), we assume that the combination of transfers and post-default government spending is set such that a sovereign default does not change the actual debt level. Consequently, ex post, regardless of whether a sovereign default has occurred, the sovereign risk premium remains unaffected.Footnote ¹⁵ This setup prevents the counterintuitive scenario of lower risk premia before a default due to anticipations of a reduced debt stock post-default.Footnote ¹⁶

Thus, the government budget constraint can be written as:

(24) \begin{equation} B_t = (1-\vartheta _{t}) B_{t-1}R^d_{t-1} - S_t + V_t + G_t^d, \end{equation}

where we use $D_t\equiv d_{t-1}Y_{t-1} \equiv B_{t-1}R^d_{t-1}$ for the face value of debt to be repaid at $t$ , which is decided in the previous period $t-1$ .

The consolidated government budget constraint is given by:

(25) \begin{equation} B_t = B_{t-1}R^d_{t-1} - S_t, \end{equation}

$S_t$ denotes the “consolidated” total primary surplus (excluding default transfers and expenditure):

(26) \begin{align} &S_t = T_t + \tau ^E_t E_t - G_t - s^A_t A_t -A^g_t = \left\{\tau _t + \tau ^E_t \xi _t (1- m_t-m^g_t) -g - \theta _1 s^A_t m_t^{\theta _2} - \theta _3 (m^g_{t})^{\theta _4}\right\} Y_t \end{align}

where $g$ represents the exogenous public expenditure as a fraction to GDP, assumed constant. Public abatement costs are assumed to be less convex than private costs ( $\theta _4\lt \theta _2$ ):

(27) \begin{equation} A^g_{t}= \theta _3 (m^g_{t})^{\theta _4} Y_{t}. \end{equation}

First, the public administration usually implements bigger scale economies than private firms. Secondly, the typical type of public green investment require greater initial investments and lower future operative costs, than in private mitigation efforts. This assumption on convexity aims to schematically capture these observations. Further justifications, in particular for the French case, are provided in the next section on calibration.

Total borrowing proceeds can be written as:

(28) \begin{align} B_t \equiv b_t Y_t = \frac {D_{t+1}}{R^d_t}\equiv \frac {d_{t}Y_t}{R^d_t} \end{align}

where the return promised on government bonds $R^d_t$ has to satisfy the FOC (23).

We also recover $b_t$ from the government budget constraint as:

(29) \begin{equation} b_t = \frac {b_{t-1}Y_{t-1}R^d_{t-1} - S_t}{Y_t}, \end{equation}

and the face value of debt-to-GDP $d_t$ implicitly from:

(30) \begin{equation} b_t = \frac {d_t}{R^d_t} \end{equation}

We add a debt stabilization rule on the lump-sum tax rate $\tau _t$ , as in Corsetti et al. (Reference Corsetti, Kuester, Meier and Müller2013) and Darracq-Pariès et al. (Reference Darracq-Pariès, Jacquinot and Papadopoulou2016), adapted in order to take into account our transition scenario from an initial brown to a final green steady state:

(31) \begin{equation} \tau _t = \tau (b_t, b_{t-1}, b_*, \tau _{t-1},\tau _*,f, y_{0,\,f}). \end{equation}

where $y_{0,f}$ represents the initial steady-state for the detrended GDP, and $f$ reflects our assumption in terms of the damage function for the particular scenario. $\tau (\cdot )$ will be a function which reacts to the deviation of $b_t$ from its final steady-state value $b_*$ , and to its deviation from the previous period. This debt stabilization rule will be further discussed in Section 3.

Resource constraint The market clearing condition for the final goods market is obtained integrating the household budget constraint, combined with the government constraint:

(32) \begin{align} & Y_t= C_t + I_t + G_t + G^d_t +{A_t} +A^g_t \end{align}

3. Calibration

Our model contains thirty-two calibrated parameters, shown in Table 2, of which eight (at the bottom of the table) take country-specific values. Our reference time period is one quarter. The calibration for the traditional aspects of our real neo-classical model ( $\kappa , \beta , \sigma _l, \mu _l, \delta , \iota$ ) follows standard assumptions in the existing literature, as in Annicchiarico and Di Dio (Reference Annicchiarico and Di Dio2015). For the transition setup, global greenhouse gas cumulative emissions until 2023, $H^G_{-1}$ , are estimated to have been around 3497 Gt in $\textrm{CO}_{2}$ -equivalent.Footnote ¹⁷ The abatement cost function coefficients are calibrated to match a (detrended) long-term carbon tax for France of US$ 1000 per ton of $\textrm{CO}_{2}$ , in the case of a transition to 1.5 $^{\circ }$ C with 67% probability, achieved only through carbon pricing. This is in line with the evidence provided by D’Arcangelo et al. (Reference D’Arcangelo, Pisu, Raj and van Dender2022), Quinet et al. (Reference Quinet, Bueb, Hir, Mesqui, Pommeret and Combaud2019) and Bilal and Känzig (Reference Bilal and Känzig2024).

Table 2.

Parametrization

We assume that abatement costs are relatively higher for the public sector than for the private sector. Marginal costs are lower for the private at the beginning of the transition, and increasing above public marginal costs as we approach a full decarbonization. Conversely, marginal public costs are much higher immediately, in line with huge investment in green infrastructure (See Appendix B—Figures 11 and 12). This translates into a lower degree of convexity, that is, $\theta _4\lt \theta _2$ . This assumption is based on sectoral estimates of abatement costs, which show that sectors that typically require public intervention (such as electricity and building renovation) are those with the highest costs (Criqui, Reference Criqui2023). For example, in the cement production sector in France, where large private companies operate, it is estimated that one-third of emissions could be reduced at low economic cost - between $\unicode {x20AC}$ 0/t $\textrm{CO}_{2}$ and $\unicode {x20AC}$ 40/t $\textrm{CO}_{2}$ . On the other hand, the assessment of the cost of decarbonizing the electricity system, which must take into account not only the production costs of each type of power plant but also all the associated “system costs,” puts the abatement cost at around $\unicode {x20AC}$ 400/t $\textrm{CO}_{2}$ . In France, as in most countries, this sector is dominated by the public sector, and the costs of maintaining and adapting the electricity system (about 15% of the decarbonization of electricity), which include the costs of modifying generation profiles, short-term balancing of supply and demand, and network reconfiguration, can only be borne by a public operator (RTE-Réseau de Transport d’Electricité, in the case of France). Similarly, in the residential sector, extending the renovation from 6 million to 12 million buildings would increase the abatement cost from about 150 to 400 $\unicode {x20AC}$ /t $\textrm{CO}_{2}$ (Criqui, Reference Criqui2023). The role of the public sector in supporting private efforts, but also in renovating public buildings and social housing, is therefore key. Its contribution is estimated at more than half in the case of France to reach net-zero emission targets (Pisani-Ferry and Mahfouz, Reference Pisani-Ferry and Mahfouz2023).

We will assume three functional forms and calibrations for the damaged TFP $D_f$ :

\begin{align*} &D_{\text{NC}}(H^G_t)= \bar {D}, \quad D_{\text{AD}}(H^G_t)= \bar {D}(1- \gamma _0 - \gamma _1 H^G_t - \gamma _2 {H^G_t}^2), \quad D_{\text{DV}}(H^G_t)= \bar {D}\exp \left \{-\frac {\gamma _3}{2}(\gamma _4 H^G_t)^2\right \} \end{align*}

NC stands for “No Climate” impact, AD for the specification proposed by Annicchiarico and Di Dio (Reference Annicchiarico and Di Dio2015), and DV for the more convex one proposed by Dietz and Venmans (Reference Dietz and Venmans2019). The temperature objective of 1.5 $^{\circ }$ C with 67% probability corresponds to a global carbon budget of $240$ Gt $\textrm{CO}_{2}$ (IPCC (2023)). According to a fair per capita criterion, this entails a national budget of 1.9, 1.7, and 2.4 Gt $\textrm{CO}_{2}$ for, respectively, France, Italy, and Germany. In Section 4.2, we will show that, despite imposing the respect of this carbon commitment and an immediate and successful transition scenario, climate damages still have an adverse impact on the macroeconomy. The other country-specific parameters are calibrated to match national characteristics.Footnote ¹⁸ We define the debt stabilization function (31) as:

\begin{align*} \tau _t = \phi _{\tau ,t}&[\tau _{t-1} +\phi _{b} (b_{t}-b_{t-1})] +(1-\phi _{\tau ,t})[\tau _*+ \phi _{b} (b_{t}-b_*)]\\ \text{where }\quad &\phi _{\tau ,t} = \frac {1}{1 + \phi _{\tau ,*} \tau _{*}} +\unicode {x1D7D9}_{D_f(H^G_t)\neq \bar {D}} \phi _{\tau ,y}(y_{0, \text{NC} } - y_{0,n}) (b_{t-1} - b_*), \end{align*}

In the long-run this rule guarantees $\tau _t= \tau _*$ , which is the lump-sum tax consistent with the final steady-state value of borrowing-to-GDP $b_*$ . The function’s parametrization aims to capture the generally limited tax buoyancy in the short-term, highlighted by the empirical literature on tax responsiveness (e.g., recently Cornevin et al. (Reference Cornevin, Flores and Angel2023)). The parameter $\phi _{b}$ represents the response of $\tau _t$ to debt-to-GDP values; $ \phi _{\tau ,t}$ represents a smoothness weight on past values of taxes and indebtedness. The baseline value of this smoothness parameter is defined to be decreasing in the long-term lump-sum tax value $\tau _*$ : if higher public financing needs through taxes are planned in the long-run, taxation changes are less difficult. In the presence of climate damages, we allow $ \phi _{\tau ,t}$ to be time-varying, and reacting to the distance of the current debt level to its steady state, $(b_{t-1} - b_*)$ . This creates additional difficulty in dealing with high debt in the presence of climate challenges.Footnote ¹⁹

The parameters of the log-normal probability of default are determined in order to match government risk premia with current evidence. The national values for the fiscal limits are (conservatively) in line with the evidence provided by Collard et al. (Reference Collard, Habib and Rochet2015) and Seghini (Reference Seghini2024a). Despite the selection of a quite high haircut $\vartheta = 0.7$ , this is balanced by the parameter $f$ , representing the post-default government expenditure as a fraction of investors’ lost value $\vartheta _tR^d_{t-1}B_{t-1}$ . Therefore, we can interpret the product $f \vartheta =0.21$ as a consolidated haircut, whose value is, in the end, reasonably conservative for advanced economies.

5. Welfare maximization and the optimal public abatement

To complete our analysis, we employ a dynamic Ramsey model to determine the optimal share of public abatement. The results thus far highlight a key trade-off for policymakers: placing the burden of the green transition on the private sector risks undermining the country’s economic performance, while relying heavily on public spending threatens the sustainability of public debt. In this context, we aim to identify the optimal degree of government intervention that maximizes citizens’ welfare, balancing economic, fiscal, and environmental considerations.

Figure 6.

The financial impact of higher government debt on private sector financing conditions. Variables between parentheses are not null only in case of default on government debt.

Figure 7.

Spillover of high public risk to the the private sector. Fiscal and macroeconomic developments in Italy for 3 carbon budget-consistent scenarios: (1) carbon tax (green line); (2) direct public mitigation (red line); (3) carbon tax with subsidies at 90% (blue line).

We define the social planner’s problem as the committed choice of the share of government direct investment in total abatement efforts, $\theta _t$ , in order to maximize welfare, defined as the present discounted value of utility:

(34) \begin{align} \max _{\theta _t} \mathcal{V}_t = \max _{\theta _t} \left (\ln C_{t}-\mu _L \frac {L_{t}^{1+\sigma _l}}{1+\sigma _l}\right ) + \beta \mathbb{E}_t \mathcal{V}_{t+1}, \end{align}

subject to all the equations describing the competitive equilibrium.

We start by defining the optimal share of public abatement by ignoring the possibility for the government to subsidize the private effort. We also neglect spillover effects through financing costs in a first exercise.

The results in Figure 8 show that to keep public debt on a sustainable path, the effort should be borne by the private sector at the beginning of the transition, implying a sharp increase in the carbon tax. As in our benchmark results, the carbon tax increase might appear excessively steep and high, raising questions about its feasibility. However, as previously noted, the level reflects the social cost of carbon required to stay within the carbon budget, while the trajectory is designed to provide the incentives needed for the private sector to accelerate decarbonization. This triggers some economic costs with a decline of about 0.4% of GDP. This immediate involvement of the private sector is related to the fact that, at the beginning of the transition, when the effort to decarbonize is still minimal, abatement costs are lower for the private sector.Footnote ²⁰ As the transition path progresses, the abatement effort increases and becomes more costly, even more so for the private sector. To limit these costs and their impact on welfare, the government should increase gradually its contribution. This intervention through public mitigation limits the cost in terms of GDP, which even benefits from public intervention from 2030–35, and stabilizes the decline in consumption at around 2%. The optimal share of public mitigation is around 40% at its highest, from 2040 onwards. By relying initially more on the private sector, public debt can be stabilized and the pressure on interest rates on government bonds remains limited.

Figure 8.

Optimal public over total abatement. Fiscal and macroeconomic developments in France, Germany, and Italy, under zero subsidies and no spillover.

Figure 9.

Optimal public over total abatement and economic output in France, under various degrees of subsidies.

The long-term equilibrium share of public mitigation, in line with the evaluation proposed by Pisani-Ferry and Mahfouz (Reference Pisani-Ferry and Mahfouz2023) in the case of France, depends on public finance conditions and relative mitigation costs. In Appendix G, we provide some sensitivity of this optimal share to different relative abatement costs between the public and private sectors and to the share of public spending in GDP (Figures 17--20). The results show that changing the convexity parameter of mitigation costs ( $\theta _4$ ) changes both the steady state of the optimal public share of abatement and its transition path.

When the parameter is assumed to be the same for both sectors (while it is lower by 40% in our benchmark results), the optimal public share of abatement rises immediately to 45%, while it rises more gradually to 40% in our benchmark results. Regarding the share of public expenditure in GDP, the higher the level of government consumption, the lower the optimal public share of abatement in the steady state (from 45% with public expenditure at 10% of annual GDP to 35% when it is at 45%). These results show that for countries with high levels of public consumption, the remaining fiscal space is more limited to take on a larger share of mitigation efforts.

In terms of cross-country differences, we find very little variation in the optimal share of public abatement between France, Germany, and Italy. The fact that France already has a favorable energy mix implies a later involvement of the public sector, but a higher level of carbon tax to incentivize the private sector to decarbonize even more. Italy’s high initial public debt does not prevent the government from investing public funds in the transition, but it does lead to higher interest rates on government bonds to keep the debt under control. In all countries, the cost in terms of lost consumption is relatively similar (around −2%) and relatively contained compared to previous scenarios involving only the private sector, while remaining broadly in line with the loss that occurs when only the public sector bears the cost of the transition.

The second-to-last exercise considers the possibility for the government to subsidize private abatement efforts. Figure 9 presents the welfare-maximizing results for France under various levels of subsidies. Including subsidies in the policy mix increases the optimal share of public abatement and leads to more positive effects on GDP. It is important to recall that the marginal cost of private mitigation remains the same for a given level of mitigation effort, whether it is incentivized through a carbon tax or through green subsidies. However, these two instruments have opposite effects on GDP and public debt. By contrast, subsidies have economic implications that are similar to those of direct public investment in mitigation. Nonetheless, at higher levels of abatement, public intervention is more efficient when implemented through direct public mitigation rather than through subsidies to the private sector. This explains why the optimal $\theta$ reaches a greater value when a higher level of subsidies is assumed, given their similar effects on public debt and borrowing costs, but their different marginal abatement costs. These results raise an important question regarding the role of carbon taxes in our model. A Pigouvian carbon tax is typically regarded as the first-best policy instrument to internalize environmental externalities. However, our simulations suggest that a combination of direct public investment and private mitigation maximizes welfare while stabilizing the debt-to-GDP ratio. A related question concerns how this result compares to what the optimal debt level would be. Our analysis does not aim to compute an optimal debt level, but rather to identify the optimal policy mix to support the transition, given the current level of debt-to-GDP. The concept of the fiscal limit adopted here, which determines the probability of default, is drawn from the literature on involuntary government debt default and is not related to welfare maximization. The underlying assumption is that, in advanced economies, governments do not strategically choose their debt levels; instead, the maximum amount they can borrow is determined by market forces. The last exercise analyses the implication of approaching the fiscal limit by including spillovers from higher public debt costs to economy-wide financing conditions. Figure 10 shows the results for Italy. The higher involvement of the public sector puts pressure on debt sustainability and, therefore, the economic costs become larger when financial spillovers are taken into account.

Figure 10.

Optimal public over total abatement and economic output in Italy, without and with spillover.

Figure 11.

Normalized abatement cost function for different convexity of the curve. The red (green) curve represents the benchmark assumption for the public (private) sector.

Overall, this welfare-maximizing exercise shows that to be optimal, the abatement effort can be shared equally by the public and private sectors, thereby limiting the welfare costs while keeping public debt in check. Moreover, the optimal policy path derived endogenously from the Ramsey framework already captures important elements of differentiated timing and intensity of interventions. In particular, it implies a sequencing of policies in which private sector action is frontloaded through strong price signals (i.e., a rising carbon tax), while public investment gradually scales up as abatement becomes more costly. This policy profile reflects not only a balance of macroeconomic and fiscal trade-offs but also improves political feasibility by smoothing adjustment costs over time. While this analysis does not explicitly test alternative policy mixes defined ex ante, it offers a robust benchmark for assessing the desirability of such differentiated and time-varying strategies.