2.1. The evolutionary firms’ technological choices

For the sake of simplicity, we focus on an industry composed of $n$ homogeneous firms where two different technologies are available: a green/renewable energy generator ( $G$ ) and a brown/fossil-fuel-based energy generator ( $B$ ). To make a fair comparison, the total lifetime of the two investment project options is considered to be the same. We assume each period of time to be a quarter; thus, if we consider a realistic expected financial life of the plants of e.g. 25 years, $T = 100$ .

To make analytically treatable the LCOE formula in (1), we assume only two periods of time: present and future. Each firm evaluates the initial investment expenditure $I$ at present time $t = 0$ , whereas the electricity generated and the operations, maintenance, and fuel expected expenditures will be sustained at a unique point in the future that should well approximate the range of the expected lifetime of the power plant, e.g. from $t = 1$ to $T = 100$ . To perform this, we employ the concept of the Average Time to Maturity (ATM), which is applicable when the sum of OPEX payments $M_t$ and electricity produced $E_t$ is expected to be fairly uniform over all quarters $t$ of the project duration.Footnote ¹⁴ ATM is defined by the parameter $m \gt 0$ , which, in our case, given $T = 100$ , is equal to $m = 50$ . Consequently, it is possible to aggregate all expected OPEX of the green or brown energy plant, $j = G, B$ , in a unique parameter $M_j$ and discount this value for $i_t$ with a simple interest rate regime in eqs. (2) and (3). The same applies to the expected sum of electricity $E_j$ generated over the system’s operational life.

LCOE is a “cost” indicator; the lower its value, the better the average cost per energy unit of the plant. The simplified version in eqs. (2) and (3) measure the expected average net present cost of the initial capital and OPEX expenditures over the expected electricity produced during the plant’s lifetime. The levelized cost of electricity indicator for the green/renewable technology is:

(2) \begin{equation} LCOE_{G,t} = \frac {I_G + \frac {M_G}{1+i_t m}} {\frac {E_G}{1+i_t m}} \end{equation}

The levelized cost of electricity indicator for the alternative brown/fossil-fuel-based technology is:

(3) \begin{equation} LCOE_{B,t} = \frac {I_B + \frac {M_B}{1+i_t m}} {\frac {E_B}{1+i_t m}} \end{equation}

As pointed out in Section 1, the adoption of renewable energy-based processes requires significant up-front investments. Consequently, we expect the green technology to have a higher CAPEX cost than the brown one, i.e., $I_G \gt I_B$ . However, once established, renewable plants (e.g. solar photovoltaic, biomass, and wind energy) offer an advantage over fossil-fuel-based generators due to the lower cost of maintenance and no fuel expenditure required for energy production (for further details, see the Calibration Section 4). Thus, OPEX are relatively lower for sustainable energy generators: $M_G \lt M_B$ . Given the cost structure of the two alternative technologies, the interest rate $i_t$ plays a key role in discriminating which investment project, characterized by the same financial duration, is less expensive for the firm in every quarter $t$ .

For the monetary policy framework, we introduce a simple Taylor rule that links the quarterly nominal interest rate controlled by the CB $i_t$ with the actual inflation rate $\pi _t$ :

(4) \begin{equation} i_t = \bar {i} + \beta \: (\pi _t - \bar {\pi }) \end{equation}

where $\bar {\pi }$ is the quarterly inflation target of the CB, $\bar {i}$ is the quarterly nominal interest rate target of the CB, and $\beta \gt 0$ is the parameter that regulates the sensitivity of the interest rate changes to the actual inflation gap.Footnote ¹⁵

It follows that the inflation rate has an indirect effect on the investment projects’ convenience through the monetary policy instrument, i.e., substituting eq. (4) in eqs. (2), (3).

Given the industry of fixed dimension $n$ , we introduce a dynamic adjustment to study the evolution of firms’ green and brown investments over time. The dynamic variable $0 \leq x_t = \frac {G}{n} \leq 1$ represents the share of green investment (i.e., renewable electric generator) employed in the industry in quarter $t$ . The complementary dynamic variable $0 \leq 1-x_t = \frac {B}{n} \leq 1$ represents the share of brown investment (fossil-based electric generator) employed in the industry in quarter $t$ .

The decision of the firms in the industry to invest in the green technology $x_t \in [0, 1]$ is assumed to evolve in discrete time, according to an exponential Replicator Dynamics (RD) as in Cabrales and Sobel (Reference Cabrales and Sobel1992):

(5) \begin{equation} x_{t+1} = (1 -\alpha ) \: x_t + \alpha \frac {x_t}{x_t + (1 - x_t) \: e^{\: \tau (LCOE_{G,t} - LCOE_{B,t})}} \end{equation}

with $0 \leq \alpha \leq 1$ and $\tau \gt 0$ .

The RD in eq. (5) provides an evolutionary mechanism such that the share of green technology adoption in the industry $x_t$ , in the next quarter $t+1$ , increases (decreases) when its expected levelized cost $LCOE_G$ is lower (higher) than the expected levelized cost of the brown investment $LCOE_B$ . The parameter $\alpha$ is a proxy of the speed of adjustment in time of the share $x(t)$ . A smaller value of $\alpha$ signifies greater inertia, reflecting the influence of firms’ switching costs when transitioning from one technology to another. Furthermore, the parameter $\tau \gt 0$ measures the firms’ sensitivity to the expected LCOE differential in the technologies available in the industry.

Based on the shares of firms that adopt either the green or brown technology at time $t$ , the industry’s level of carbon emissions $P_t$ can be identified. $P_t$ , expressed in tons of CO $_{2}$ per quarter, is a weighted average of the pollution intensity of green generators $P_G$ and brown generators $P_B$ , with $P_B \gt P_G \geq 0$ (see Section 4 for calibration details):

\begin{equation*} P_t = x_t P_G + (1 - x_t) P_B \end{equation*}

Defining $\lambda \equiv P_B - P_G \gt 0$ as the marginal contribution of brown generators to pollution, the expression can be rewritten as:

(6) \begin{equation} P_t = P_G + \lambda \: (1 - x_t) \end{equation}

2.2. The inflation dynamics

The inflation dynamics is inspired by Galı and Gertler (Reference Galı and Gertler1999) and represented by the following difference equation:

(7) \begin{equation} \pi _{t+1} = (1-\gamma ) \: \pi _{t} + \gamma \: E(\pi _{t+1}) \end{equation}

Inflation in the next quarter is a weighted average between actual inflation $\pi _t$ (i.e., based on the well-known literature on the viscosity of price changes) and inflation expectation $E(\pi _{t+1})$ . Agents’ expectations of inflation can have a greater influence on the next quarter’s realization based on the weight $0 \leq \gamma \leq 1$ , while $1-\gamma$ measures the inertia derived from the actual inflation value. For the equilibrium condition $\pi _{t+1} = \pi _t = \pi ^*$ , eq. (7) is a rational expectation equilibriumFootnote ¹⁶ (REE) as agents’ inflation expectation coincides with the inflation equilibrium rate: $\pi ^{\ast } = E^{\ast }(\pi )$ .

The inflation expectation of agentsFootnote ¹⁷ in eq. (8) includes the CB quarterly inflation target $\bar {\pi }$ , i.e., the publicly announced CB’s inflation objective around which operators’ expectations are centered, and two expected inflationary effects related to climate change:

(8) \begin{equation} E(\pi _{t+1}) = \bar {\pi } + \kappa \: P_t + \rho \: (x_t - \bar {x}) \end{equation}

The first expected effect $\kappa \: P_t$ is defined in the literature as Climateflation.

Climate change can have significant economic consequences, including damage to infrastructure, disruptions and interruptions of product supply, increased healthcare costs due to climate-related illnesses, and higher insurance premiums for properties exposed to climate risks. These impacts can lead to increased production costs, reduced productivity, and supply chain disruptions, all of which can contribute to inflationary pressures. This effect is positively associated with the number of polluting companies in the economy, contributing to worsening climate-related disasters. In our framework, pollution is positively dependent on the share of firms adopting fossil-fuel-based generators, as highlighted in eq. (6). The emissions related to adopting the brown technology accelerate the pace and the frequency of natural disasters. This creates supply shocks and bottlenecks that, mediated by the parameter $\kappa \gt 0$ , ultimately lead to Climateflation.

The second expected effect $\rho \: (x_t - \bar {x})$ is denominated Greenflation.

It refers to the rising prices of goods and services due to the costs associated with transitioning to a more environmentally sustainable economy. In fact, in the short to medium term, the supply of intermediate goods (given the scarcity of resources) is given, as is technology, making it complicated to adjust the supply to a growing demand for green technologies. In addition to the expenses related to the implementation and transition to green technologies, complying with regulations to meet environmental standards and adapting to climate change impacts can be expensive. These forces generate upward pressure on prices captured by the term $\rho \: (x_t - \bar {x})$ . When the share of green investment in the industry $x_t$ (i.e., the demand) exceeds the supply $\bar {x}$ , given by the actual level of technology and the number of raw materials and commodities employed in the transition, inflationary pressure mounts mediated by the parameter $\rho \gt 0$ .Footnote ¹⁸ Changing the fixed supply $\bar {x}$ Footnote ¹⁹ allows us to consider technological advancements that reduce the shortages or make it possible to assume different supply constraints depending on the specific industrial sector considered.

The result is that Climateflation and Greenflation relate to green firms in an opposite way. The first positively depends on $1-x_t$ through the emission generated by this typology of investment, while the second positively depends on $x_t$ due to the transition cost associated with the sustainable transition. Generally, the literature distinguishes based on the time horizon of these two effects, identifying the first as a long-run effect on inflation and the second as a short-medium consequence as the economy adjusts to new production and consumption patterns.

In this framework, the CB internalizes the inflation expectation in its monetary policy rule in eq. (4) so that the change of the interest rate instrument could also address the inflation components related to climate change (i.e., dealing with a typical externality) and green transition. In turn, interest rate changes affect the decisions of the firms in the industry because they act as a discount rate in eqs. (2) and (3), changing the cost, measured by the LCOE indicator, of one technology over the other.Footnote ²⁰ All in all, it is possible to close the system by inserting the Taylor rule (4) into the eqs. (2) and (3) and plugging the pollution function (6) in eq. (8).

The resulting two-dimensional non-linear system in discrete time can be concisely represented as the dynamics of the share of firms adopting green technology in the industry and inflation:

(9) \begin{equation} \begin{cases} x_{t+1} = f (x_{t}, \pi _{t})=(1 -\alpha ) \: x_t + \alpha \dfrac {x_t}{x_t + (1 - x_t) \: e^{\: \tau (LCOE_{G,t} - LCOE_{B,t})}} \\ \pi _{t+1} = g (\pi _{t}, x_{t})= (1-\gamma ) \: \pi _{t} + \gamma \: \left [ \bar {\pi } + \kappa P_{G} + \kappa \lambda \: (1-x_t) + \rho \: (x_t - \bar {x}) \right ] \end{cases} \end{equation}

where $LCOE_{G,t}$ and $LCOE_{B,t}$ are defined in (2) and (3), respectively, after the insertion of (4).

Since the dynamic adjustment process reported by (9) is expressed in terms of differential equations, the usual methods for analyzing stability, bifurcations and different types of attractors can be applied. This will be the subject of Section 3.

3.1. Boundary equilibria

Map (9) is a two-dimensional discrete-time non-linear dynamical system. The map admits two equilibria that we can label “boundary equilibria” because they are characterized by a share of green investment equal to 0 and 1, respectively:

(10) \begin{equation} \begin{array} [c]{ccc} E_{0}=\left ( 0, \bar {\pi }+\kappa \left (P_{G}+\lambda \right )-\rho \overline {x} \right ) \,E_{1}=\left ( 1,\bar {\pi }+\kappa P_{G}+\rho \left (1- \overline {x}\right )\right ) \end{array} \end{equation}

We can note that the inflation rate at the equilibrium $E_0$ is lower than the inflation rate at the equilibrium $E_1$ as long as $\rho \gt \kappa \lambda$ .

3.2. Interior equilibrium

Besides boundary equilibria, the map (9) may admit an internal equilibrium ( $E^*$ ), where the share of green investments is neither 0 nor 1. By using the equilibrium condition $x_{t+1}=x_{t}=x^{\ast }$ into eq. (5), we find that the interior equilibrium must satisfy the condition:

\begin{equation*} LCOE_{G}=LCOE_{B} \end{equation*}

which is solved by the following equilibrium value of the nominal interest rate:

(11) \begin{equation} i^{\ast }=\frac {1}{m}\left [ 1+\frac {E_{G}M_{B}-E_{B}M_{G}}{E_{B}I_{G}-E_{G}I_{B}}\right ] \end{equation}

It follows that the equilibrium value of the nominal interest rate is positively correlated with $E_G$ , $M_B$ and $I_B$ , while it is negatively correlated with $E_B$ , $I_G$ , $M_G$ and $m$ .

Given the equilibrium value of the nominal interest rate (11), we can use it into the Taylor rule (4) to get the equilibrium value of the inflation rate:

(12) \begin{equation} \pi ^{\ast }=\frac {1}{\beta }\left ( i^{\ast }-\overline {i}+\beta \overline {\pi } \right ) \end{equation}

So, the higher is the equilibrium value of the nominal interest rate, the higher is the equilibrium value of the inflation rate. Moreover, while the quarterly inflation target of the CB ( $\overline {\pi }$ ) is positively correlated with the equilibrium value of the inflation rate, the quarterly nominal interest rate target of the CB ( $\overline {i}$ ) is negatively correlated with it. Finally, more complicated is the role of the parameter $\beta$ that is positively correlated with $\pi ^{\ast }$ if $i^{\ast }\lt \overline {i}$ and negatively correlated in the opposite case.

By using the equilibrium condition $\pi _{t+1}=\pi _{t}=\pi ^{\ast }$ into eq. (7) combined with eq. (6), we can derive the equilibrium share of green investments:

(13) \begin{equation} x^{\ast }=\frac {\pi ^{\ast }-\overline {\pi }-\kappa \left ( P_{G}+\lambda \right ) +\rho \overline {x}}{\rho -\kappa \lambda } \end{equation}

to which it corresponds an equilibrium value of pollution:

(14) \begin{equation} P^{\ast }=P_{G}+\lambda (1-x^{\ast }) \end{equation}

The higher are $P_{G}$ and $\lambda$ , the lower is the equilibrium share of green investments. It is interesting to look at the relation between inflation rate and share of green investments at the equilibrium. If $\rho \gt \kappa \lambda$ they are positively correlated. With feasible values of the parameters (See Table 1 in Section 4), this condition always holds, at least when the equilibrium of the map is the internal one, and not one of the boundary equilibria.

From eq. (7) we also know that at the equilibrium the inflation expectation is equal to the actual value of inflation: $E^{\ast }(\pi )=\pi ^{\ast }$ .

3.3 Local stability

In order to study the local stability of the three equilibria, we need to calculate the Jacobian matrix of the dynamical system (9):

(15) \begin{equation} J:\begin{bmatrix} J_{11} &\quad J_{12}\\ J_{21} &\quad J_{22}\end{bmatrix} \end{equation}

where:

\begin{equation*} \begin{array} [c]{l} J_{11}=1-\alpha +\alpha \left \{\dfrac {x+(1-x)e^{\tau (LCOE_{G}-LCOE_{B})}-x\left ( 1-e^{\tau (LCOE_{G}-LCOE_{B})}\right ) }{\left [ x+(1-x)e^{\tau (LCOE_{G}-LCOE_{B})}\right ] ^{2}}\right \} \\ \\ J_{12}=\alpha \left \{ \dfrac {-x(1-x)e^{\tau (LCOE_{G}-LCOE_{B})}m\beta \tau \left ( \frac {I_{G}}{E_{G}}-\frac {I_{B}}{E_{B}}\right ) }{\left [ x+(1-x)e^{\tau (LCOE_{G}-LCOE_{B})}\right ] ^{2}}\right \} \\ \\ J_{21}=\gamma ({-}\kappa \lambda +\rho )\\ \\ J_{22}=1-\gamma \end{array} \end{equation*}

The Jacobian matrix (15) must be evaluated at each equilibrium point.

3.3.1. Local stability of $E_0$

When we consider the boundary equilibrium $E_0$ , we get the following Jacobian:

\begin{equation*} J_{0}: \begin{bmatrix} 1-\alpha +\dfrac {\alpha }{e^{\tau (LCOE_{G0}-LCOE_{B0})}} &\quad 0\\ \gamma ({-}\kappa \lambda +\rho ) &\quad 1-\gamma \end{bmatrix} \end{equation*}

that is triangular, so it displays the (always real) eigenvalues on the main diagonal:

\begin{equation*} \begin{array} [c]{lll} \xi _{1}=1-\alpha +\dfrac {\alpha }{e^{\tau (LCOE_{G0}-LCOE_{B0})}}; \,\, \xi _{2}=1-\gamma \end{array} \end{equation*}

Note that $LCOE_{G0}$ and $LCOE_{B0}$ denote the values of $LCOE_{G}$ and $LCOE_{B}$ calculated at the equilibrium $E_0$ .

While $\xi _{2}$ is always positive and lower than one, so it cannot lead to instability, the first eigenvalue $\xi _{1}$ may become larger than one for some parameters’ values. In particular the boundary equilibrium $E_0$ is locally stable provided that: $LCOE_{B0}\lt LCOE_{G0}$ .

3.3.2. Local stability of $E_1$

Let us consider now the boundary equilibrium $E_1$ and the Jacobian matrix (15) calculated at this point:

\begin{equation*} J_{0}: \begin{bmatrix} 1-\alpha +\alpha e^{\tau (LCOE_{G1}-LCOE_{B1})} &\quad 0\\ \gamma ({-}\kappa \lambda +\rho ) &\quad 1-\gamma \end{bmatrix} \end{equation*}

that is also triangular and the (always real) eigenvalues are:

\begin{equation*} \begin{array} [c]{lll} \xi _{1}=1-\alpha +\alpha e^{\tau (LCOE_{G1}-LCOE_{B1})}; & & \xi _{2}=1-\gamma \end{array} \end{equation*}

Here $LCOE_{G1}$ and $LCOE_{B1}$ denote the values of $LCOE_{G}$ and $LCOE_{B}$ calculated at the equilibrium $E_1$ .

Also for $E_1$ the eigenvalue $\xi _{2}$ does not create stability issues, while the first eigenvalue $\xi _{1}$ may become larger than one for some parameters’ values. In particular, the boundary equilibrium $E_1$ is locally stable provided that: $LCOE_{G1}\lt LCOE_{B1}$ .

5.1. Deterministic model

The four panels of Figure 1 present the time series of the green technology adopted by the industry $x$ (panel a), industry pollution $P$ Footnote ²⁷ (panel c) over 120 quarters, and the evolution of inflation rate $\pi$ (panel b) and nominal interest rate $i$ (panel d) over 40 quarters.Footnote ²⁸

Figure 1.

Time series with $i.c.$ $x_0 = 0.15$ for different inflation values.

Note: The time series represent the evolution of the share of green technology adopted by the industry (panel a) and pollution (panel c) over 120 quarters, the dynamics of the inflation (panel b) and nominal interest rate (panel d) over 40 quarters. On the red curve $\pi _0 = 0$ , on the blue curve $\pi _0 = 0.005$ ( $2\%$ yearly), on the green curve $\pi _0 = 0.01$ ( $4\%$ yearly). Parameters: Table 1, $i.c.$ $x_0 = 0.15$ .

We show different evolution of the key variables depending on three different initial conditions ( $i.c.$ ) or shocks for the inflation rate (i.e., $\pi _0$ ). Figure 1, obtained from the parameters in Table 1, represents an industry characterized by a realisticFootnote ²⁹ initial share of renewable energy generators amounting to $x_0 = 0.15$ (15%). The initial quarterly inflation rate in the red curve is very low at $\pi _0 = 0$ . On the blue curve, $\pi _0 = 0.005$ , corresponding to the annual CB objective of 2%. On the green curve, it is at a considerably higher value of $\pi _0 = 0.01$ , meaning a 4% yearly rate.

In the former case, the green transition is more rapid than in the other scenarios, particularly with a sharp increase in renewable technology adoption in the first period. This is benefited by low initial inflation rates and, consequently, interest rates closer to the zero lower bound for the first quarters (i.e., the CB undertakes an expansionary monetary policy). The industry pollution falls down more quickly as more and more firms switch to the less pollutant technology.

Conversely, in the last case, the transition is much slower with even a brief initial phase of increased adoption of the fossil-fuel-based technology. This recall what occurred in the Eurozone following the COVID-19 pandemic, a rapid and sudden spike in energy prices and inflation that slowed down the decarbonization strategy set by the Paris climate goals.Footnote ³⁰ The transition slows as the CB is forced to tackle the positive inflation shock with a restrictive monetary measure: the interest rate remains above the equilibrium for almost ten quarters. This initially hampers the transition with the industry pollution that remains at higher levels for a longer period of time than in the other scenarios, highlighting the monetary policy trade-off at the core of the model. In the event of positive inflationary shocks exceeding the $\bar {\pi } = 2\%$ annual target, the CB faces a challenging dilemma: should it prioritize a low and stable inflation environment by raising interest rates, or should it support the green transition by maintaining low interest rates despite elevated inflation?

It is only after 120 quarters (30 years) that all three scenarios converge to the long-run interior equilibrium $E^*$ characterized by $x^* = 0.4273$ (42.73%), $\pi ^* = 0.0078$ (3.12% yearly), $i^* = 0.0085$ (3.4% yearly), $P^* = 85.3$ . These numerical values of $E^*$ can be easily found substituting the set of parameters in Table 1 in equilibrium eqs. (11) - (14). Even though, independently from the initial conditions, the system converges to the same values of $E^*$ , the transition to this equilibrium can clearly differs as a result of diverse initial shocks in inflation rates. In all the three scenarios, starting from an initial 15% share of green firms in the industry at $t = 0$ results in a yearly Climateflation rate of 0.96%. Following the transition, the green share increases to approximately 43%, leading to a decrease in Climateflation to 0.682%, representing a reduction of −0.278%. Since the actual share or demand of green technology at the beginning of the period equals the fixed supply (i.e., $x_0 = \bar {x} = 0.15$ ), Greenflation is zero. However, as the sustainable transition occurs Greenflation steadily increases (as $x$ rises in time), until reaching the maximum yearly Greenflation rate 0.4437% after the transition at $t = 120$ . The two inflation components move in opposite ways with Climateflation prevailing in the first phase of the transition and Greenflation prevailing in the final period. This is in line with the view of the European Central Bank and Schnabel (Reference Schnabel2022) important speech, where one passage reads: ‘So far, Greenflation has had a much smaller impact on final consumer prices than Climateflation. It is therefore misleading to claim that the greening of our economies is responsible for the painful increase in energy prices. However, as more and more industries switch to low-emission technologies, Greenflation can be expected to put upward pressure on the prices of a wide range of products during the transition period.’

To sum up, for all the above dynamics, the share of firms adopting the renewable technology in the industry increases after the transition, as a result pollution decreases, while the movements of inflation and nominal interest rates depend on the size and sign of the shocks. Shocks in monetary variables are transitory and disappear after a few quarters (e.g. 10 quarters) due to the adjustment of inflation expectations and monetary policy interventions by the CB. However, their effects on real variables persist over time even after several years beyond the period at which interest and inflation rates have reached equilibrium (e.g. 10 vs 120 quarters). The slow pace at which the industry responds to changes in inflation and interest rates is primarily due to the high initial and fixed costs of investing in a particular technology and, more broadly, the legal, technological, and logistical complexities involved in establishing power plants (captured by the parameters $\alpha$ and $\tau$ ). This means that even a relatively small inflationary shock can have a prolonged impact on the transition process. Projection estimates that global renewable capacity is expected to grow by 2.7 times by 2030, driven by climate and energy security policies implemented in nearly 140 countries (International Energy Agency (IEA) (2024). These policies have been instrumental in making renewable energy cost-competitive with fossil-fuel power plants. The European Union and the United States are both forecast to double the pace of renewable capacity growth between 2024 and 2030,Footnote ³¹ reaching a level of 25% of overall electricity generation.Footnote ³² This is very similar to the share of firms adopting green technology after 24 quarters in the average scenario ( $\pi _0 = 0.005$ , 2% yearly) represented by the blue curve of Figure 1.

5.2. Stochastic models

In this section, we analyze the model dynamics under different scenarios (see Table 2 for a summary). For all the simulations, we show the main parameters’ change over the time span and the time series of the green share of firms ( $x$ ), inflation ( $\pi$ ), pollution ( $P$ ) and nominal interest rates ( $i$ ). The time series are shown for 120 quarters as in the deterministic model. In our first stochastic model we endogenize the CAPEX costs as follows:

Table 2.

Summary of the six stochastic models

\begin{equation*} \begin{array} [c]{l} I_{G,t+1}=I_{G,t}\cdot tr_{G}+\xi _{I_{G}}\\ I_{B,t+1}=I_{B,t}\cdot tr_{B}+\xi _{I_{B}} \end{array} \end{equation*}

where $tr_{G}$ and $tr_{B}$ can be considered trend component and $\xi _{I_{G}}$ and $\xi _{I_{B}}$ are additive random noise terms. By interpreting the two CAPEX costs as updating parameters instead of new dynamic variables, we need to update, at each time period, also the equilibrium values of the endogenous variables accordingly.Footnote ³³ In particular, we entail a relative reduction in green fixed costs over brown fixed costs by assuming a downward trend $tr_{G}=0.9998$ lower than the downward trend $tr_{B}=0.9999$ . We also assume the both random noise terms are normally distributed with zero mean, while that standard deviation of the noise term $\xi _{I_{G}}$ lower than the standard deviation of the noise term $\xi _{I_{B}}$ (1 and 2.5, respectively). The scenario is motivated by expected cost savings for green technologies, and the historical presence of higher variability for brown fixed costs.

Figure 2.

Negative trend and noise on CAPEX. Parameters: Table 1.

Figure 2 and 3 illustrate actual values (in black) and equilibrium $E^*$ values (in blue) for each variable. Actual variables adjust slowly to the equilibrium variables due to the inertia parameters ( $\gamma$ , $\alpha$ ). Considering the long-run, the share of green firms is increasing due to the greater trend reduction of the green fixed costs compared to the brown ones ( $x^* = 0.58$ compared to $x^* = 0.43$ of Figure 1). However, CAPEX volatility due to the addition of the random noise leads to short-term variability of the variables. On average, we assist to a larger reduction of the green LCOE vs the brown LCOE that favor the sustainable transition. Pollution, on average, decreases accordingly. Inflation is rather stable after an initial surge due to adjustment toward the equilibrium value. Interest rates show little variations due to the efficacy of their movements in fighting inflation (i.e., $\beta \gt 1$ ). There are blue flat areas in the graphs such that the equilibria do not move after reaching one of the two extremes. Those are the equilibrium values where the transcritical bifurcations occur: after reaching the extreme, the interior equilibrium $E^*$ is no longer stable while one of the boundary one $E_0$ or $E_1$ becomes stable. This condition may last until a big enough shock makes the interior equilibrium stable again as it moves away from the extreme. Although the equilibrium value changes in a relevant way, the actual and observable variables (in black) such as the actual firms’ share, inflation rate, etc. moves much more gradually. In general, the simulation shows a negative trend and an additive noise to real variables (the two CAPEX) to reflect the technological advancement in time of the two investment options. Compared to the deterministic model, the trade-off between inflation control and green transition improves when structural costs of green technology decreases more than structural costs of the brown.

Figure 3.

Model with negative trend and noise on CAPEX $I_G$ and $I_B$ .

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .

In the second stochastic model we introduce an additive noise term ( $\xi _{\bar {x}}$ ) to the amount of green share of firms that the industry can handle (i.e., in $\bar {x}$ ) to ensure the avoidance of significant supply-side shortages:

\begin{equation*} \bar {x}_{t+1}=\bar {x}_{t}+\xi _{\bar {x}} \end{equation*}

In the simulations we consider a normally distributed noise term with positive mean (0.1) to make positive noise more frequent than negative ones. It is not a trend, but in the long run an increasing force on $\bar {x}$ should prevail. The standard deviation of the noise term is 0.0002. This implies that the impact on inflation expectations of the Greenflation component is decreasing and may even turn negative (i.e., if $x_t - \bar {x} \lt 0$ ). The consequence is that as $\bar {x}$ increases, the monetary policy trade-off between low inflation and low pollution reduces because the shortage share will become smaller compared to the deterministic model where $\bar {x}$ is fixed.

The model is motivated by a growing efficiency in production of green energy technologies that may decrease the bottlenecks due to shortages of rare materials, especially minerals. Economies would eventually learn to decarbonize in a quicker way, hence relaxing the Greenflation constraint and potentially transform it in a positive force for decarbonization (through economies of scale).

Figure 4 and 5 show both actual values (in black) and equilibrium values (in blue) for each variable. Considering the long run, the share of green firms is higher due to the lower shortage share compared to the deterministic model. This causes Greenflation to decrease, or at least not increase, during the transition phase. The reduction in the Greenflation effect increases the long-run share from $x^* = 43\%$ of Figure 1 to $x^* = 66\%$ , ceteris paribus. This implies lower inflation expectations, hence lower inflation and lower nominal interest rate, that stimulate the adoption of green energy technology. Pollution decreases accordingly and a virtuous cycle starts as Climateflation decreases too. After an initial surge to converge toward the equilibrium value, both actual inflation and equilibrium inflation decrease, improving the monetary trade-off.

There are flat areas in the graphs such that the equilibria do not move after reaching one of the two extremes. Those are the equilibrium values where the transcritical bifurcations occur: after reaching the extreme, the interior equilibrium is no longer stable while the boundary one becomes stable. This happens at the end of the simulation period for $x$ and $P$ .

Figure 4.

Noise on $\bar {x}$ . Parameters: Table 1.

Figure 5.

Model with noise on supply of technology and materials $\bar {x}$ .

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .

Our third stochastic model entails an additive random noise on inflation ( $\xi _{\pi }$ ) to capture possible supply-side shocks or other inflationary effects not explicitly considered in our model:

\begin{equation*} \pi _{t+1}=g(\pi _t,x_t)+\xi _{\pi } \end{equation*}

where $g(\pi _t,x_t)$ is the inflation dynamics defined in map (9).

In the simulations, we use a normally distributed random term with zero mean and standard deviation equal to 0.001. Equilibrium values are not affected (they remain the same as the deterministic model of Figure 1) but there is transitory divergence. Indeed, a temporary increase (shock) in inflation spurs an increase in nominal interest rate and thus a decrease in adoption of green energy technologies (i.e., a decrease in $x$ ). This reduction implies higher pollution levels of the industry, hence higher Climateflation and then inflation, generating a vicious cycle until a big enough countershock hits. The monetary policy trade-off between low inflation and low pollution is stable. The variability of nominal interest rate is higher than the one on inflation due to the efficacy of monetary policy reaction (i.e., $\beta \gt 1$ ): deviations of inflation from the target are met by higher deviations of interest rates. Figure 6 shows both actual values (in black) and equilibrium values (in blue) for each variable. The change in the green share and pollution levels of the industry reflects the interest rate movements.

Figure 6.

Model with noise on inflation rate $\pi _{t+1}$ .

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .

Our fourth stochastic model entails an additive random noise on inflation expectations ( $\xi _{E}$ ) to consider the inherent uncertainty of expectations (i.e., it can also be interpreted as the expectation error term):

\begin{equation*} E(\pi _{t+1}) = \bar {\pi } + \kappa \: P_t + \rho \: (x_t - \bar {x})+\xi _{E} \end{equation*}

In the simulations we use a noise term normally distributed with zero mean and standard deviation equal to 0.001. The overall effect is very similar to the third one. Equilibrium values are not affected but transitory divergences can occur. For example an increase in inflation expectations (shock) positively affects inflation and spurs a tightening in nominal interest rate. The latter leads to a rise in adoption of brown energy technologies. This means higher industry pollution, hence higher Climateflation and inflation, generating a vicious cycle until a big enough countershock hits. Also in the case, the monetary policy trade-off between low inflation and low pollution is stable as equilibrium values are constant. The variability of nominal interest rate is higher than the one on inflation due to the efficacy of monetary policy reaction (i.e., $\beta \gt 1$ ): deviations of inflation from the target are met by higher deviations of interest rates.

Figure 7 shows both actual values (in black) and equilibrium values (in blue) for each variable.

Figure 7.

Model with noise on inflation expectation $E(\pi _{t+1})$ .

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .

Our fifth stochastic model entails a one-time positive shock in the inflation target at the 15-year mark (i.e., a one-time increase in $\bar {\pi }$ from 0.005 to 0.0055). We interpret this shock on the target level of inflation $\bar {\pi }$ as the effect of a permanent increase in past pollution flows that contributes to raising the average level of temperatures and, ultimately, food inflation and headline inflation (Kotz et al., Reference Kotz, Levermann and Wenz2024b). The CB could move toward a more flexible monetary policy framework and reassess its inflation target to better respond to the supply-side shocks that are likely to become more frequent due to climate change (Barmes et al., Reference Barmes, Claeys, Dikau and da Silva2024). In this case, from the 60th semester, the CB inflation target permanently moves from the yearly 2% to a 2.2% (Figure 8). This implies a decrease in the nominal interest rate by the Taylor rule through the inflation gap component $\pi _t - \bar {\pi }$ of eq. (4) and an increase in inflation expectations through eq. (8). The overall short-run effect on nominal interest rate is always negative (since $\gamma \Delta \bar {\pi }\lt \beta \Delta \bar {\pi }$ ), but then the actual nominal interest rate (in black) slowly increases back to reach its equilibrium value (in blue) at the end of the period. The equilibrium value of the interest rate does not change because it only depends on technological characteristics of the two plants (costs, energy produced and expected lifetime), see eq. (11). Instead, inflation equilibrium is affected. After an initial increase of actual inflation to reach its equilibrium, a second spike at $t = 60$ occurs to meet the new higher inflation equilibrium. The effect of a lower actual interest rate (even if only transitory, from $t = 60$ to $t = 120$ ) implies that, in this period, the cost efficiency of the green energy technology increases more than the cost efficiency of the brown technology (i.e., $LCOE_G$ decreases more than $LCOE_B$ ). This is evident from the vertical increase of equilibrium share $x^*$ (in blue) that implies an acceleration in green technology adoption $x$ (in black). The share of green firms keeps increasing toward this higher equilibrium, while the pollution decreases more quickly toward the lower equilibrium. Overall, the $\bar {\pi }$ one-time increase has a large positive effect on the actual green technology adoption (i.e., at the end of the period $x^* = 0.59$ compared with $x^* = 0.43$ of Figure 1) and, consequently, a beneficial effect on pollution. This at the expense of a moderate increase in long-run inflation. This happens because, given the parameter set, the monetary policy trade-off between low inflation and low industry pollution slightly improves.

Figure 8.

One-time positive shock on $\bar {\pi }$ (from 0.005 to 0.0055). Parameters: Table 1.

This scenario can be traced back to the impact of climate change on the natural real interest rate, which can be defined as $\bar {r} = \bar {i}-\bar {\pi }$ (Drudi et al., Reference Drudi, Moench, Holthausen, Weber, Ferrucci, Setzer, Adao, Dees, Alogoskoufis and Delgado-Téllez2021). Research shows that the sign of change is uncertain. Lower natural interest rate (shown above) would mean that supply-side effects of climate change are larger than demand side effects: the increase in prices is structural and not counterbalanced by lower demand due to precautionary motives. The opposite would be true in the scenario below.

Figure 9.

Model with one-time positive shock in $\bar {\pi }$ (from 0.005 to 0.0055).

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .

Figure 10.

One-time negative shock on $\bar {\pi }$ (from 0.005 to 0.0045). Parameters: Table 1.

Our sixth stochastic model entails one-time negative shock in the inflation target at the 15-year mark (i.e., a one-time reduction in $\bar {\pi }$ from 0.005 to 0.0045). In this case, from the 60th semester, the CB inflation target permanently moves from the yearly 2% to a 1.8% (Figure 10). It is the symmetric opposite scenario of the fifth model (see Figure 11).

5.3. The effect of climate tipping points

Climate tipping points refer to large-scale discontinuities in the climate system that can trigger abrupt and potentially catastrophic releases of polluting materials, especially CO $_{2}$ . Examples include the melting of Arctic or Antarctic ice sheets or the collapse of the North American boreal forest (Lenton et al., Reference Lenton, Rockström, Gaffney, Rahmstorf, Richardson, Steffen and Schellnhuber2019). While some of these events may materialize only in the distant future, others have already been set in motion. Moreover, a growing body of empirical and theoretical research suggests that such tipping points may be reached more rapidly than previously anticipated.Footnote ³⁴ These large-scale shocks may be modeled as temporary increases in the flow of pollution, under the assumption that they do not result in a permanent increase in pollution stock (see Figure 12). If, instead, the tipping event leads to irreversible changes in the climate system, the corresponding shock to pollution flows would also be permanent, thereby generating persistent effects on both climate and economic dynamics (see Figure 13). For the events expected to occur further in the future than the temporary or permanent pollution shocks described above, the most appropriate modeling strategy is to represent them as positive shocks to inflation expectations. This approach is observationally equivalent to a shock to the long-run inflation target $\bar {\pi }$ (see Figure 8 and Figure 9).

Figure 11.

Model with one-time negative shock in $\bar {\pi }$ (from 0.005 to 0.0045).

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .

Figure 12.

One-time positive shock to $P_t$ ( +10).

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .

Figure 13.

Permanent positive shock to $P_t$ ( +10).

Note: The time series show the dynamics of green technology share (panel a), inflation (panel b), pollution (panel c), and nominal interest rate (panel d) over 120 quarters. Parameters: Table 1, $i.c.$ $x_0 = 0.15$ , $\pi _0 = 0.005$ .