## 1 Introduction

^{1}In August 2022, the ECB corporate bond holdings from the CSPP and other collateral monetary policy operations were €344,558 mil, while the overall APP holdings were €3,262,730 mil.

^{2}Thus, around 10.5% of ECB balance sheet is private corporate bonds and, as long as reinvestments in these assets will continue, this amount is expected to remain stable in the next few years (ECB 2022a).

## 2 Literature review and institutional background

^{3}: the monetary authority buys a proportion of the market portfolio of available corporate and bank bonds (usually investment-grade bonds) to reduce price distortions from their eligible asset purchases.

^{4}However, this strategy might imply a carbon bias because capital-intensive companies and sectors tend to be more carbon-intensive (Papoutsi et al. 2021).

^{5}For these reasons, some CBs have started to greener monetary policy operations to reduce the financial risk related to climate change and to promote a green transition of industries and firms.

## 3 The model

^{6}:

^{7}

### 3.1 Neutral monetary policy

^{8}Therefore, we focus only on the relative composition (i.e green or non-green) of purchase program \(B_T\) and study the impact of a CB strategy that includes environmental considerations (i.e., green monetary policy), to analyze the occurrence of portfolio re-balance and its effect on the cost of bonds for firms.

^{9}The covariance \(\sigma _{G,N}\) is related to the correlation coefficient \(r_{G,N}=\frac{\sigma _{G,N}}{\sigma _G \, \sigma _N}\), which, to be economically meaningful, must range between \(-1\) (i.e., perfect negative correlation) and \(+1\) (i.e., perfect positive correlation). Thus, we impose that:

^{10}Consequently, corporate bonds come in a variety of risk-reward levels depending on the issuing company’s creditworthiness. While the CB prefers assets that have the highest expected return, it also seeks to minimize uncertainty about corporate bonds’ future return. We assume that the CB chooses the combination of green and non-green bonds with the optimal risk-reward level and thus, the portfolio allocation that offers the maximum return-to-risk ratio, i.e., the optimal portfolio \(x^*\) in the CAPM. The CB risk-averse preference function in a neutral monetary policy setup can be formalized as a capital allocation line defined by the following (7):

^{11}:

### 3.2 Green monetary policy

^{12}In this way, the CB internalizes the externalities and public failures through the inclusion of climate-related risks in the portfolio assessment. Therefore, following the market efficiency principle, the optimal portfolio choice in a green monetary policy setting encompasses three objectives: maximizing returns, containing risk/volatility, and reducing firms’ environmental footprint, are defined equivalently to Eqs. (6) and (8) and given by:

Type of mon. pol. (p) | \(x^*\) (%) | \(1-x^*\) (%) | \(B_G^*\) | \(B_N^*\) | \(\mu _G^*\) (%) | \(\mu _N^*\) (%) |
---|---|---|---|---|---|---|

Neutral (\(p =1\)) | 36.8 | 63.2 | 51, 579 | 88, 421 | 4.46 | 4.52 |

Green (\(p = 1.1\)) | 40.9 | 59.1 | 54, 473 | 85, 527 | 4.22 | 4.68 |

## 4 Green monetary policy and firm investment choice

^{13}

^{14}

^{15}The total earnings \(E_i(t)\) from a given technology investment in/adoption of i(t) are the integral of (23a),(23b) with respect to the correspondent share of investment, i.e.,:

^{16}The cost of the two alternative types of bonds is determined by the portfolio optimization problem of the monetary authority in relation to its policy and defined by (21). For the sake of simplicity and to ensure equivalence of the two firms’ investment opportunities, both types of bonds are assumed to have the same maturity (e.g., one year). This does not alter by any means the conclusion. As a result, the borrowing cost of a firm is given by the principal amount to be reimbursed at maturity (i.e., after a year), which coincides with the value of the investment, and the (fixed) interest rate \(\mu _G^*\) or \(\mu _N^*\) on this debt,

^{17}

^{18}

^{19}; indeed, switching technology might be very expensive. Thus, the larger the adjustment costs, the lower the value of \(\gamma\) and firms’ ability to switch technology of production, ceteris paribus.

^{20}

### 4.1 Analysis

^{21}:

^{22}The derivatives \(R'(y^*)\) at each of the four fixed points are:

^{23}We take the parameter values in Table 1 as a benchmark case for a neutral monetary policy setting and investigate how a change in p influences the share of green and non-green investment in the industry.

### 4.2 Unstable internal equilibrium and path dependency

^{24}Starting from the initial condition (i.c) \(y_o=0.56\) at which \(56\%\) of the investment in the industry is in green technology and the remaining \(44\%\) is in the conventional non-green technology, the time series shown in red and given by (27), converges to \(y^* = 0\). All the firms of the sector eventually invest in non-green technology in the long-run. This holds for all \(y_o<y_1^*\) as highlighted by the arrows in the phase plot of Fig. 3b. For all \(y_o>y_1^*\) (such as \(y_o = 0.57\) of the blue time series in Fig. 3a), R converges to \(y^* = 1\), i.e., all the companies invest in green technology after a certain period of time t.

^{25}In the previous scenario, the CB ran a neutral monetary policy (i.e., \(p = 1\)). By increasing p, the monetary authority moves toward a green monetary policy and reduces the cost of corporate green bonds. Consequently, increasing p shifts the internal equilibrium and increases the basin of attraction of the all green investment. At \(y_o = 0.56\), a value of \(p = 1.04\) now leads to a convergence toward the all green investment equilibrium. For higher p values, lower initial conditions converge to the same equilibrium.

### 4.3 Stable internal equilibrium and transition to deterministic chaos

^{26}An increase in the average financial risk of green bonds \(\sigma _G\) translates into a lower share of these assets in the CB portfolio, and it leads to a rise in the cost of borrowing for these firms. Consequently, the share of green investment gradually falls at the equilibrium (Fig. 7a). The opposite holds for an increase in average financial risk of non-green bonds \(\sigma _N\) as shown in Fig. 7b. The share of green investment rises and the share of non-green investment falls. Lastly, increasing the covariance \(\sigma _{G,N}\) from a negative correlation to a positive correlation slightly decreases the share of green investment at the equilibrium (Fig. 7c).

^{27}In economic terms, lower adjustment costs cause a larger share of firms to switch to the alternative technology in each period.

^{28}

^{29}We should specify that high values of \(\gamma\) (e.g., \(\gamma > 300\)), as in this instance, are associated with cases of adjustment costs that tend to zero and full reversibility of investments. For these reasons, the scenario depicted in Fig. 9 is more hypothetical than a realistic dynamics noticeable in industries. Nonetheless, from a policy makers perspective, it is relevant to point out that such dynamics could potentially arise in a few extreme cases. In this particular example, the time evolution of the green investment share is erratic (see Fig. 9a). The economic consequence of such erratic motion is a low level of predictability regarding the proportion of each manufacturing technology adopted in the sector. Furthermore, an (almost) zero switching cost generates an even greater share of firms that change investment decisions in each period (Fig. 9a) when compared to the time series in Fig. 8a.