2.1 Households

The economy is populated with infinitely many utility maximizing households. We adopt the large family assumption where each household contains a large and constant number of workers, dirty and clean entrepreneurs such that also the income from entrepreneurial activities belongs to the household ultimately (cf. Christiano et al. (Reference Christiano, Motto and Rostagno2014); Gertler and Karadi (Reference Gertler and Karadi2011)). The representative household maximizes its intertemporal utility by choosing consumption $C_{t}$ , labor supply $L_{t}$ , and one-period deposits $D_{t+1}$ Footnote ⁷ at the CMF. Bank deposits are risk-free assets paying an ex post real return $R_{t+1}$ . The households’ lifetime utility is

\begin{equation*} U_{t}=\sum _{t=0}^{\infty }\beta ^{t} u\left ( C_{t},L_{t}\right ) \ \mbox {with}\ u(C_t,L_t)=\log \left ( C_{t}\right ) +\log \left ( 1-L_{t}\right ) \end{equation*}

where $\beta$ is the discount factor. Consumption and savings are financed by labor income $w_{t}L_{t}$ , interest-bearing deposits from the previous period $R_{t}D_{t}$ , lump-sum tax transfers $T_{t}$ , and net transfers from entrepreneurs $M_{t}$ . This yields the following budget constraint:

\begin{equation*} C_{t}+D_{t+1}=w_{t}L_{t}+R_{t}D_{t}+T_{t}+M_{t} \end{equation*}

with

\begin{equation*} M_{t}=C_{dt}+C_{ct}-M_{d}-M_{c} \end{equation*}

Net transfers from entrepreneurs $M_{t}$ consist of entrepreneurial wealth from the clean sector $C_{ct}$ and dirty sector $C_{dt}$ and seed finance to entrepreneurs in both sectors, $M_{c}$ and $M_{d}$ . The exact characteristics of transfer payments are provided in Section 2.3.

2.2 Final goods production

A representative, perfectly competitive final goods producer combines intermediate dirty goods $Y_{dt}$ and intermediate clean goods $Y_{ct}$ into a final good $Y_{t}$ used for consumption and investment. The final goods producer purchases the intermediate output from the dirty and clean sector at prices $p_{dt}$ and $p_{ct}$ , respectively. The price of the final good is normalized to one. Production uses standard constant elasticity of substitution technology:

\begin{equation*} Y_{t}=z_{At}A\left [ \phi Y_{dt}^{1-\varepsilon }+\left ( 1-\phi \right ) Y_{ct}^{1-\varepsilon }\right ] ^{\frac {1}{1-\varepsilon }} \end{equation*}

where $A$ is constant total factor productivity, $z_{At}$ is a shock process, $\phi$ is a share parameter, and $\varepsilon$ is the inverse of the elasticity of substitution between dirty and clean intermediate goods.

2.3 Entrepreneurs and intermediate goods production

Intermediate goods are produced by identical, perfectly competitive firms belonging to either the dirty sector $d$ or the clean sector $c$ . Dirty and clean firms are owned and managed by entrepreneurs $j$ that are heterogeneous with respect to the levels of their net worth. Bank loans (external finance) and entrepreneurial net worth (internal finance) are the two sources of funds that firms use to finance operations. Entrepreneurial net worth positions thus change with retained earnings. At the end of period $t-1$ , entrepreneur $j$ is characterized by his level of net worth $N_{it}^{j}$ where $i\in \{d,c \}$ denotes sector affiliation.Footnote ⁸ Entrepreneurs maximize period $t$ profits in two steps: they first decide the amount of capital to purchase, before learning the true productivity of their technology. Second, they decide the level of labor, which is chosen as the optimal complement to the capital once the entrepreneurs have learned their productivity.

To determine optimal capital acquisition in the first step, entrepreneurs decide on the loan volume $B_{it}^{j}$ obtained from the CMF to combine it with their net worth $N_{it}^{j}$ and the amount of capital $K_{it}^{j}$ to buy at market price $Q_{it-1}$ at the end of period $t-1$ .Footnote ⁹

(1) \begin{equation} Q_{it-1}K_{it}^{j}=B_{it}^{j}+N_{it}^{j} \end{equation}

The first-order conditions that determine the choice of $B_{it}^j$ are detailed in a financial contract between entrepreneurs and CMF as described in Section 2.4 below. At the beginning of period $t$ , entrepreneurs learn their idiosyncratic productivity $\omega _{it}^{j}$ and hence their effective capital stock $\bar{K}_{it}^{j}=\omega _{it}^{j}K_{it}^{j}$ . The productivity shocks $\omega _{it}^{j}$ are unit mean and log-normally i.i.d. variables with standard deviation $z_{\sigma t}\sigma _{i}$ . The stochasticity of effective capital captures the volatility of entrepreneurial success, e.g. due to market trends or the adoption of technological standards. The standard deviation $z_{\sigma t}\sigma _{i}$ is subject to a risk shock $z_{\sigma t}$ , capturing that the riskiness of entrepreneurs’ production changes over time (Christiano et al. (Reference Christiano, Motto and Rostagno2014)). The dynamics of the risk shock are characterized below. The probability density function of $\omega _{it}^{j}$ is denoted by $f( \omega _{it}^{j})$ and the cumulative distribution function by $F( \omega _{it}^{j})$ .

In the second step, once they have learned the level of their effective capital stock $\bar{K}_{it}^{j}$ , entrepreneurs decide how much labor $L_{it}^{j}$ to hire as the second input to their intermediate goods technology $Y_{it}^{j}$ .

(2) \begin{equation} Y_{it}^{j}=A_{i}\left ( \bar{K}_{it}^{j}\right ) ^{\alpha _{i}}\left ( L_{it}^{j}\right ) ^{1-\alpha _{i}} \end{equation}

The constant $A_{i}$ expresses sectoral productivity, output elasticities of capital, and labor are denoted by $\alpha _i$ and $( 1-\alpha _{i})$ , respectively. Entrepreneurs can only access the production technology of their sector and pay $w_{t}$ for each unit of labor employed. The production of $Y_{it}^{j}$ is associated with $\xi _{i}Y_{it}^{j}$ emissions of greenhouse gases. Parameter $\xi _{i}$ denotes the emission intensity of the production technology within sector $i$ . Intermediate goods are sold to final goods producers at price $p_{it}$ . Emissions are taxed $\tau _{it}^{E}$ . Entrepreneurs sell their depreciated capital stock $ ( 1-\delta ) \bar{K}_{it}^{j}$ back to capital goods producers at price $\bar{Q}_{it}$ . The depreciation rate is denoted by $\delta$ . Ultimately, the gross return on capital to entrepreneur $j$ is composed of revenues from selling intermediate goods to final goods producers, the depreciated capital stock to capital goods producers, less taxes and wages:

(3) \begin{equation} \Pi _{it}^{j}=\left ( p_{it}-\xi _{i}\tau _{it}^{E}\right ) Y_{it}^{j}-w_{t}L_{it}^{j}+\bar{Q}_{it}\left ( 1-\delta \right ) \bar{K}_{it}^{j} \end{equation}

At this point, entrepreneurs’ effective capital stocks $\bar{K}_{it}^{j}$ are fixed (first step profit maximization) and the maximization of the gross return on capital with respect to labor (second step profit maximization) yields

(4) \begin{equation} w_{t}=\left ( p_{it}-\xi _{i}\tau _{it}^{E}\right ) \frac{\partial Y_{it}^{j}}{\partial L_{it}^{j}} \end{equation}

such that entrepreneurial gross returns on capital can be expressed asFootnote ¹⁰

\begin{equation*} \Pi _{it}^{j}=R_{it}^{k}Q_{it-1}\omega _{it}^{j}K_{it}^{j} \end{equation*}

where $R_{it}^{k}$ is the average gross rate of return on capital across sector $i$ entrepreneurs in $t$ and defined as

\begin{equation*} R_{it}^{k} = \frac {\left ( p_{it}-\xi _{i}\tau _{it}^{E}\right ) \alpha _{i} \left ( A_{i}^{\frac {1}{1-\alpha _{i}}}\left ( 1-\alpha _{i}\right ) \frac {p_{it}-\xi _{i}\tau _{it}^{E}}{w_{it}} \right )^{\frac {1-\alpha _{i}}{\alpha _{i}}} +\left ( 1-\delta \right ) \bar {Q}_{it}}{Q_{it-1}} \end{equation*}

The first term of the sum is the marginal product of capital in the production function of sector $i$ entrepreneurs, relative to the gross price for which they purchased capital. The second term represents the value appreciation or depreciation of capital. Entrepreneurs obtain external finance in the form of one-period loans from the CMF where a standard debt contract stipulates a loan amount $B_{it}^{j}$ and interest rate $Z_{it}^{j}$ to be repaid by borrowers after the disposal of intermediate goods and depreciated capital stocks. The financial contract is derived in Appendix B. Entrepreneurs only repay the loan when they can, i.e. they have non-negative equity after debt repayment. This implies a minimum productivity level $\bar{\omega }_{it}^{j}$ that entrepreneurs need in order to repay their debt. This cutoff productivity or bankruptcy threshold is defined as follows:

(5) \begin{equation} R_{it}^{k}Q_{it-1}\bar{\omega }_{it}^{j}K_{it}^{j}=Z_{it}^{j}B_{it}^{j} \end{equation}

If $\omega _{it}^{j}\gt \bar{\omega }_{it}^{j}$ , the entrepreneur repays the lender $Z_{it}^{j}B_{it}^{j}$ and keeps the equity $(\omega _{it}^{j}-\bar{\omega }_{it}^{j})R_{it}^{k}Q_{it-1}K_{it}^{j}$ . The entrepreneur defaults for values $\omega _{it}^{j}\lt \bar{\omega }_{it}^{j}$ in which case the CMF claims the entrepreneur’s assets and the entrepreneur end up with $V_{it}^j=0$ .Footnote ¹¹ Bankruptcy is costly (Hotchkiss et al. (Reference Hotchkiss, John, Thorburn and Mooradian2008), cf.) and CMFs have to incur bankruptcy cost $\mu _i$ when claiming a defaulting entrepreneur’s assets. We assume bankruptcy costs are proportional to gross return on capital and the CMF can claim $ ( 1-\mu _{i} ) \omega _{it}^{j}R_{it}^{k}Q_{it-1}K_{it}^{j}$ . Therefore, before knowing the precise size of the productivity shock $\omega _{it}^{j}$ , the expected individual entrepreneurial equity is given by

\begin{equation*} E_{t-1}\left [V_{it}^{j}\right ] = E_{t-1}\left [z_{Vt}\left ( R_{it}^{k}Q_{it-1}\int _{\bar {\omega }_{it}^{j}}^{\infty }\omega _{it}dF\left ( \bar {\omega }_{it}^{j}\right ) K_{it}^{j}-Z_{it}^{j}B_{it}^{j}\left [ 1-F\left (\bar {\omega }_{it}^{j}\right ) \right ] \right ) \right ] \end{equation*}

Similar to Christiano et al. (Reference Christiano, Motto and Rostagno2014), we introduce a financial wealth shock $z_{Vt}$ to entrepreneurial equity positions which effects entrepreneurs indiscriminately of sector affiliation. Shock dynamics are characterized in Section 2.7. Substituting equation (5) allows to eliminate $Z_{it}^{j}B_{it}^{j}$ .

(6) \begin{eqnarray} E_{t-1}\left [V_{it}^{j}\right ]&=&E_{t-1}\left [ z_{Vt}R_{it}^{k}l_{it}^{j}N_{it}^{j}\left [ 1-\Gamma \left ( \bar{\omega }_{it}^{j}\right ) \right ] \right ] \end{eqnarray}

Here, $l_{it}^{j}$ denotes leverage and is defined as the purchase value of entrepreneurial capital stock divided by current net worth

(7) \begin{equation} l_{it}^{j}=\frac{Q_{it-1}K_{it}^{j}}{N_{it}^{j}} \end{equation}

and $\Gamma ( \bar{\omega }_{it}^{j} ) =\int _{0}^{\bar{\omega }_{it}^{j}}\omega _{it}dF ({\omega }_{it}^{j} ) +\bar{\omega }_{it}^{j} [ 1-F ( \bar{\omega }_{it}^{j} ) ]$ represents the gross share of profits going to the lender such that the share of average entrepreneurial earnings that remains with the entrepreneur corresponds to $1-\Gamma ( \bar{\omega }_{it}^{j} )$ .Footnote ¹² For the discussion of simulation results, we consider a more intuitive measure of leverage, the debt-to-assets ratio which we refer to as leverage ratio and define it as

\begin{equation*} lr_{it}^{j}=\frac {B_{it}^{j}}{Q_{it-1}K_{it}^{j}}=1-\frac {1}{l_{it}^{j}} \end{equation*}

After loan repayment, end-of-period $t$ entrepreneurial net worth $N_{it+1}^{j}$ is determined. At any $t$ , a share $1-\nu _{i}$ of entrepreneurs liquidate their firms and become working members of their household. Each period, a sufficient amount of workers become entrepreneurs such that the number of entrepreneurs is constant. Upon firm liquidation, entrepreneurs transfer their wealth in the form of consumption $C_{it}$ to households as part of their “large family.” Households in turn provide seed finance $M_{i}$ to entrepreneurs in every period. These assumptions reflect that entrepreneurs enter and exit the economy, frequently invest their individual wealth and always rely on external finance to some extent. A share $\nu _{i}$ of entrepreneurs continue operating their businesses such that individual entrepreneurial net worth $N_{it+1}^{j}$ of the remaining and new entrepreneurs is given by $N_{it+1}^{j}=V_{it}^{j}+M_{i}^{j}$ . Aggregate net worth is given by $N_{it+1}=\nu _{i}V_{it}+M_{i}$ and Appendix C shows that this corresponds to:

(8) \begin{align} N_{it+1}=\nu _{i}z_{Vt}\left [ \left ( R_{it}^{k}Q_{it-1}K_{it}-\left \{ R_{t}+\frac{\mu _{i}G\left ( \bar{\omega }_{it}\right ) R_{it}^{k}Q_{it-1}K_{it}}{Q_{it-1}K_{it}-N_{it}}\right \} \left ( Q_{it-1}K_{it}-N_{it}\right ) \right ) \right ] +M_{i} \end{align}

The net worth is then used together with fresh loans $B_{it+1}^{j}$ to purchase next periods capital stock $K_{it+1}^{j}$ and then move on to the next period.

2.4 Financial intermediation

The loans required by entrepreneurs in order to purchase capital are provided by households through perfectly competitive CMFs. We model this by a representative CMF who, at the end of period $t$ , takes deposits $D_{t+1}$ at interest rate $R_{t+1}$ from households and extends one-period loans $B_{it+1}^{j}$ to entrepreneur $j$ belonging to sector $i$ according to an optimal financial contract. The contract is characterized by loan volume $B_{it+1}^{j}$ and a gross nondefault loan rate $Z_{it+1}^{j}$ . The loans are retired at the end of the subsequent period. Perfect competition and the assumption of free entry gives rise to the following zero-profit condition for the representative CMF.

\begin{equation*} \left [ 1-F\left ( \bar {\omega }_{it+1}^{j}\right ) \right ] Z_{it+1}^{j}B_{it+1}^{j}+\left ( 1-\mu _{i}\right ) R_{it+1}^{k}Q_{it}\int _{0}^{\bar {\omega }_{it+1}^{j}}\omega _{it+1}dF\left ( \omega _{it+1}^{j}\right ) K_{it+1}^{j}=R_{t+1} B_{it+1}^{j} \end{equation*}

The left-hand side represents the expected return on the loan provided to entrepreneur $j$ . The first term on the left-hand side corresponds to the payment received from nondefaulting entrepreneur $j$ and the second term corresponds to the payment received in case of default net of bankruptcy costs. The right-hand side is equivalent to the opportunity cost of funds. There are two opposing effects of changing entrepreneurial interest rates with respect to the zero-profit condition: Increasing $Z_{it+1}^j$ yields higher nondefault payments from the entrepreneurs who can repay their debt but also rises the default probability which reduces the amount of entrepreneurs that are able to repay loans and vice versa. Substituting equation (5) allows to express the zero- profit condition in terms of $B_{i,t}^{j}$ and $\bar{\omega }_{i,t}^{j}$ :

\begin{equation*} \left ( \left [ 1-F\left ( \bar {\omega }_{it+1}^{j}\right ) \right ] \bar {\omega }_{it+1}^{j}+\left ( 1-\mu _{i}\right ) \int _{0}^{\bar {\omega }_{it+1}^{j}}\omega _{it+1}dF\left ( \omega _{it+1}^{j}\right ) \right ) R_{it+1}^{k}Q_{it}K_{it+1}^{j}=R_{t+1}B_{it+1}^{j} \end{equation*}

Substituting (1) and (7) and rearranging allows

(9) \begin{equation} \left [ \Gamma \left ( \bar{\omega }_{it+1}^{j}\right ) -\mu _{i}G\left ( \bar{\omega }_{it+1}^{j}\right ) \right ] R_{it+1}^{k}l_{it+1}^{j}= R_{t+1}\left ( l_{it+1}^{j}-1\right ) \end{equation}

where, if $\Gamma ( \bar{\omega }_{it+1}^{j} )$ represents the gross share of entrepreneurial profits going to the lender as above, the net share of profits going to the lender equals $\Gamma ( \bar{\omega }_{it+1}^{j} ) -\mu _{i}G ( \bar{\omega }_{it+1}^{j} )$ and $G ( \bar{\omega }_{it+1}^{j} ) =\int _{0}^{\bar{\omega }_{it+1}^{j}}\omega dF ( \omega _{it+1} )$ . The combinations of $ ( \bar{\omega }_{it+1}^{j},l_{it+1}^{j} )$ that are implied by the zero- profit condition define a range of contingent standard debt contracts of which the entrepreneur will choose the one that maximizes expected return from equation (6). This optimization is the first step in the profit maximization of entrepreneurs. The solution is derived in Appendix B and consists of the optimality condition

(10) \begin{equation} 0=\frac{R_{it+1}^{k}}{ R_{t+1}}\left [ 1-\Gamma \left ( \bar{\omega }_{it+1}\right ) \right ] +\frac{\Gamma ^{\prime }\left ( \bar{\omega }_{it+1}\right ) }{\Gamma ^{\prime }\left ( \bar{\omega }_{it+1}\right ) -\mu _{i}G^{\prime }\left ( \bar{\omega }_{it+1}\right ) }\left ( \left [ \Gamma \left ( \bar{\omega }_{it+1}\right ) -\mu _{i}G\left ( \bar{\omega }_{it+1}\right ) \right ] \frac{R_{it+1}^{k}}{ R_{t+1}}-1\right ) \end{equation}

and the aggregated zero-profit condition for CMFs:

(11) \begin{equation} \left [ \Gamma \left ( \bar{\omega }_{it+1}\right ) -\mu _{i}G\left ( \bar{\omega }_{it+1}\right ) \right ] R_{it+1}^{k}l_{it+1}= R_{t+1}\left ( l_{it+1}-1\right ) \end{equation}

The term $\frac{R_{it+1}^{k}}{ R_{t+1}}$ in equation (10) describes the return a unit of capital has to generate, discounted by the interest rate demanded by households. If above one, it can be thought of as an external finance premium the entrepreneur has to pay on top of the risk-free rate.Footnote ¹³ Note that $j$ -specific variables vanished from equations (10) and (11), i.e. all entrepreneurs within a sector will choose a financial contract which allows them to sustain the same optimal leverage ratio (yielding identical cutoff productivities $\bar{\omega }_{it+1}$ ), irrespective of their heterogeneous net worth positions. Entrepreneurs with minor net worth positions will thus borrow less than entrepreneurs with larger net worth positions such that leverage ratios are identical. It is the external financing premium that harmonizes optimal leverage ratios across individual entrepreneurs.Footnote ¹⁴ Entrepreneurs within a sector operate perfectly competitive firms and exhibit identical expected efficiencies (the financial contract is concluded prior to the realization of the next productivity shock).Footnote ¹⁵ Appendix B shows that equation (11) can be condensed to:

(12) \begin{equation} \frac{R_{it+1}^k}{R_{t+1}}=s_i(l_{it+1}) \end{equation}

with $s_i'(l_{it+1})\geq 0$ . It is now obvious that increasing leverage rises external finance premiums charged by CMFs. The severity of the increment is mainly driven by the financial characteristics of entrepreneurs (uncertainty $\sigma _i$ and bankruptcy cost $\mu _i$ ) which are parameters to the function $s(\!\cdot\!)$ .

2.5 Capital goods producers

Within each sector, there are perfectly competitive capital goods producers that buy the old, depreciated capital stock of intermediate goods producers $ ( 1-\delta ) K_{it}$ at real price $\bar{Q}_{it}$ . They then combine it with investment goods $I_{it}$ and produce capital stock for production processes in the next period $K_{it+1}$ sold to entrepreneurs at price $Q_{it}$ . Capital goods producers’ profits are

\begin{equation*} \Pi _{it}^{I}=Q_{it}K_{it+1}-I_{it}-\frac {\chi }{2}\left ( \frac {I_{it}}{K_{it}}-\delta \right ) ^{2}K_{it}-\bar {Q}_{it}\left ( 1-\delta \right ) K_{it} \end{equation*}

where $p_{t}$ is the price of the numeraire and normalized to one, $\chi$ determines investment adjustment costs. Capital evolves according to:

\begin{equation*} K_{it+1}=\left ( 1-\delta \right ) K_{it}+I_{it} \end{equation*}

The capital goods producers’ profit maximization yields the following levels for capital pricesFootnote ¹⁶ :

\begin{eqnarray*} Q_{it} &=&\left (1+\chi \left ( \frac{I_{it}}{K_{it}}-\delta \right ) \right ) \\[5pt] \bar{Q}_{it} &=&Q_{it}-\frac{1}{1-\delta }\left [ \frac{\chi }{2}\left ( \frac{I_{it}}{K_{it}}-\delta \right ) ^{2}-\chi \left ( \frac{I_{it}}{K_{it}}-\delta \right ) \frac{I_{it}}{K_{it}}\right ] \end{eqnarray*}

2.6 Government

In this model, the government sets the level of taxes in order to reach an exogenous climate target. This exogenous target reflects for the short-term time horizon that we model, the feedback of greenhouse gas emissions and climate change impacts will not be decisive for climate policy due to the delays and inertia of the climate system and the limited influence of emissions from the Euro Area on global greenhouse gas concentration. Acknowledging that emissions are proportional to dirty intermediate output, the tax $\tau _{t}^{E}$ can be interpreted as a price on emissions. The government ensures a balanced budget each period, i.e. all tax revenues are rebated in a lump-sum transfer $T_t$ to households:

\begin{equation*} T_{t}=\tau _{t}^{E}(\xi _{c}Y_{ct}+\xi _{d}Y_{dt}) \end{equation*}

2.7 Shocks

We consider three structural shocks: a shock to total factor productivity $z_{At}$ , the risk shock $z_{\sigma t}$ , and a shock to entrepreneurial net worth positions $z_{Vt}$ . Shocks are modeled as log deviations from steady-state values in the form of univariate first-order autoregressive processes:

\begin{equation*} \log x_{t}=\rho _{x}\log x_{t-1}+\varepsilon _{xt} \end{equation*}

where $x_{t}$ is the innovation, $\rho _{x }\in (0,1)$ measures persistence of the shock and $\varepsilon _{xt}$ is normally distributed, zero-mean white noise with standard deviation $\sigma _{x}$ . We follow the standard assumption that statistical innovations of shocks are learned by agents at the time the innovation materializes.

2.8 Market clearing

The aggregate resource constraint is given by the goods market clearing.

(13) \begin{align} Y_{t} &= C_{t}+I_{ct}+I_{dt}\nonumber \\ &\quad +\mu _{c}G\left ( \bar{\omega }_{ct}\right ) R_{ct}^{k}Q_{ct-1}K_{ct} +\mu _{d}G\left ( \bar{\omega }_{dt}\right ) R_{dt}^{k}Q_{dt-1}K_{dt} \end{align}

(14) \begin{align} &+\frac{\chi }{2}\left ( \frac{I_{ct}}{K_{ct}}-\delta \right ) ^{2}K_{ct}+\frac{\chi }{2}\left ( \frac{I_{dt}}{K_{dt}}-\delta \right ) ^{2}K_{dt} \end{align}

Line (13) corresponds to the bankruptcy costs of the two sectors and line (14) to the investment adjustment costs. Labor and debt market clearing imply

\begin{eqnarray*} L_{t} &=&L_{ct}+L_{dt} \\[5pt] D_{t+1} &=& B_{ct+1}+ B_{dt+1} \end{eqnarray*}

2.9 Frictionless economy

When simulating the behavior of the benchmark economy in response to shocks, we compare the results to the behavior of the frictionless economy. Frictions are eliminated by setting $\mu _i=0$ , ensuring that banks can learn entrepreneurs’ idiosyncratic productivity without any cost. Without the existence of bankruptcy costs, CMFs charge no risk premiums on top of the risk-free rate and $R^k_i= R_{t+1}$ . Rearrange equation (8) in steady state to see that mainly transfers from households determine entrepreneurial net worth.

\begin{equation*} N_i=\frac {M_i}{1-vz_{vt}R} \end{equation*}

Given minuscule transfers, entrepreneurs have close to zero net worth. But in the absence of risk premiums, entrepreneurs can disregard net worth and take highly leveraged positions with high bankruptcy probabilities. CMFs can recover the full value of assets from defaulted entrepreneurs and are thus able to perfectly diversify entrepreneurial idiosyncratic risk by charging high-interest rates. The frictionless economy exhibits high-interest rates, high bankruptcy probabilities, minuscule net worth positions, and leverage ratios close to one. Without the small fraction of entrepreneurs for which $\omega ^j_i\gt \bar{\omega }^j_i$ and who accumulate net worth, seed finance $M_i$ would be the only source of funding for entrepreneurs. Despite the substantial difference in financial variables, the frictionless economy generates a steady state with nonfinancial variables close to the benchmark economy.

3.1 Non-financial parameters

The quarterly household discount factor $\beta$ is set to 0.993 and is within conventional ranges (cf. Smets and Wouters (Reference Smets and Wouters2003); Christiano et al. (Reference Christiano, Motto and Rostagno2010)). Data from the AMECO database suggest a quarterly depreciation rate $\delta$ of 1.46%. We set the elasticity of substitution between clean and dirty goods $1/\epsilon$ to 7 which is at the high end of the range of Acemoglu et al. (Reference Acemoglu, Aghion, Bursztyn and Hemous2012). The high value reflects our sector definition where both sectors produce similar intermediate goods. We set the share parameter $\phi$ to 0.5725 such that the fraction of clean intermediate goods in total intermediate goods production fits the data discussed in Section 3.3. The output elasticity of capital $\alpha _{i}$ is adopted from Christiano et al. (Reference Christiano, Motto and Rostagno2010). We follow Donadelli et al. (Reference Donadelli, Grüning and Hitzemann2019) and set the emission intensity for the clean sector to zero and to 0.1 for the dirty sector. Steady-state emission taxes are calibrated to generate tax revenues equal to 2.4% of GDP (i.e. $\bar{\tau }_E$ = 0.147) which corresponds to the data discussed in Section 3.3. Parameter $\chi _{c/d}$ governs the severeness of investment adjustment costs. We use the value from Christensen and Dib (Reference Christensen and Dib2008). Persistence parameters $\rho _A$ , $\rho _V$ , and $\rho _\sigma$ that guide the impact of shocks on the economy are taken from Christiano et al. (Reference Christiano, Motto and Rostagno2010).

3.2 Financial parameters

The relevance of frictions increases along with three financial characteristics: liquidation probability ( $1-\nu _i$ ), bankruptcy cost ( $\mu _i$ ), and uncertainty about entrepreneurial success ( $\sigma _i$ ). For the liquidation probability $1-\nu$ , we use the death rates of entrepreneurs in the Euro Area as a proxy, for which the European Commission (2021b) reports a value of 1.7% for 2017. We assume the same liquidation probability for both sectors, i.e. $\nu _i=\nu$ . Bankruptcy cost $\mu$ and uncertainty about entrepreneurial success $\sigma$ are however distinct in both sectors. We first derive economy-wide aggregate values of $\mu$ and $\sigma$ for the Euro Area from data. We then use the calibration approach from Su (Reference Su2019) to approximate the degree of financial asymmetry in bankruptcy costs and uncertainty. We calculate the degree of financial asymmetry in bankruptcy costs as $\mu _c/\mu _d$ and likewise $\sigma _c/\sigma _d$ for success uncertainty. In the following paragraphs, we discuss the estimation and calibration for $\mu$ and $\mu _i$ . The same procedure was followed to calibrate $\sigma$ and $\sigma _i$ .

The aggregate share of profits lost in bankruptcy $\mu$ is approximated by one minus the recovery rate. Recovery rates measure the percentage of a loan recovered by secured creditors through judicial reorganization, liquidation, or debt enforcement. The World Bank (2021a) reports estimates for the countries in the Euro Area. We use a weighted average over countries where weighing factors are gross issues of debt securities per country extracted from the European Central Bank (Securities Issues Statistics (SEC) (2020)) and then average over the years 2013−2017. Uncertainty $\sigma$ is set to 0.33 such that the model mirrors the macroeconomic characteristics discussed in Section 3.3, especially debt-to-equity ratios and external finance premiums.

We assume that economy-wide aggregate values for financial parameters $\mu$ and $\sigma$ relate to sector-specific values in the following way: aggregate values are the averages of sector level values weighted by the market share of the sectors. Formally, when $\eta =Y_c/(Y_c+Y_d)$ represents the clean market share then aggregates are defined as follows.

(15) \begin{equation} \mu = \eta \mu _c+(1-\eta )\mu _d \end{equation}

To our knowledge, there exists no data set which applies our sector definition and reports data on financial parameters bankruptcy cost $\mu _i$ and success uncertainty $\sigma _i$ aggregated over sectors. We follow the calibration approach from Su (Reference Su2019) where we invert the equations governing the financial part of the model, fix endogenous observable variables to their empirical values obtained from Refinitiv (2020), and then quantify $\mu _i$ and $\sigma _i$ . We assume that the data represents a steady state and hence omit time indices for the remainder of the section.

Following Su (Reference Su2019), we construct a system of four equations. For the first equation, we rearrange (5):Footnote ¹⁷

(16) \begin{equation} \frac{Z_{i}}{R}=\bar{\omega }_{i}\frac{R_{i}^{k}}{R}\frac{l_{i}}{l_{i}-1} \end{equation}

The second and third equations are equations (10) and (11) from Section 2.4. Equation (23) from Appendix D is the fourth equation:

(17) \begin{equation} F\left ( \bar{\omega _i}\right ) =\Phi \left [ \frac{\log \bar{\omega _i}+\frac{\sigma _{xi}^{2}}{2}}{\sigma _{xi}}\right ] \end{equation}

This equation expresses default probability where $\Phi$ is the cumulative distribution function of the standard normal distribution. In the system (10), (11), (16), and (17), we fix leverage $l_{i}$ , default probability $F (\bar{\omega }_{i} )$ , and credit spread $Z_{i}/R$ to empirical values. This allows us to quantify four (now) endogenously determined variables: cutoff productivity $\bar{\omega }_{i}$ , risk premium $R_{i}^{k}/R$ , bankruptcy cost $\mu _i$ , and success uncertainty $\sigma _i$ . We use these estimates to calculate the degree of financial asymmetry ${\mu _c}/\mu _d$ as described above. We then use the degrees of financial asymmetry ${\mu _c}/\mu _d$ and equation (15) to compute $\mu _c$ and $\mu _d$ relative to the aggregate value for bankruptcy cost $\mu$ (and likewise for $\sigma _i$ ):

\begin{eqnarray*} \mu _d &=& \frac{\mu }{\eta \frac{\mu _c}{\mu _d}+(1-\eta )} \\[5pt] \mu _c &=& \frac{\mu \frac{\mu _c}{\mu _d}}{\eta \frac{\mu _c}{\mu _d}+(1-\eta )} \end{eqnarray*}

To gather the estimates for leverage $l_i$ , spreads $Z_i/R$ , and default probabilities $F(\bar{\omega }_i)$ , we consult the data base EIKON ((Refinitiv (2020)), data sets: equities, fixed income) and construct a data set for firms in the Euro Area over the period 2013−2017. We restrict the data set to nonfinancial firms and collect emissions data to allocate firms to the clean and dirty sectors. Emission intensities are calculated as estimated $\text{CO}_2$ equivalent emissions divided by total revenue. Since the availability of historical emissions data is limited in EIKON, we use emissions data from 2019. A company whose emission intensity is below the median emission intensity of all companies within the same industry (following The Refinitiv Business Classification) is considered part of the clean sector and otherwise the dirty sector. We cluster companies into industries in order to avoid a comparison of industries with each other but to compare firms within the same industry instead. This is in line with the sector definition in Section 2, and guarantees that firms are allocated to the clean and dirty sector within each industry. Without clustering, all firms from a relatively emission intense industry (e.g. transportation) are allocated to the dirty sector and firms from a less emission intense industry (e.g. IT services) to the clean sector. Resulting differences in financial parameters are then more likely due to industry-specific characteristics instead of environmental performance. In line with Su (Reference Su2019), financial leverage is calculated as total long-term debt divided by total equity. Sectoral leverage $l_i$ is calculated by taking the median leverage per sector per year and then averaging over time. Bond spreads serve as a proxy for interest rate spreads of bank loans. Spreads are calculated as the difference in coupon rates of corporate bonds with a 2-, 5- or 10-year maturity and German government bonds of equal maturity. We calculate the median spread per sector of all bond issuances within a month per sector, average over time, and calculate quarterly spreads. Corporate default probabilities are obtained from the StarMine Combined Credit Risk Model (through EIKON) which indicates the probability that the company will go bankrupt, or default on its debt obligations over the next 1-year period. We take median probabilities of all firms within a sector per year, average over time, and calculate quarterly probabilities.

The resulting degree of financial asymmetries is reported in Table 1. Bankruptcy costs and success uncertainty in the clean sector are 107% and 113% of their counterparts in the dirty sector. Final values for $\mu _i$ and $\sigma _i$ are reported in Table 2 (rows 6 and 7). We choose an infinitesimal small value for the transfer of funds from households to entrepreneurs $M_{i}$ as to not generate an additional significant source of net worth.

Table 2. Steady state moments

Ranges represent minimum and maximum values in the years from 2013−2017 or ranges found in the literature. Data sources by rows: 1−3: European Commission (2021a); 4−5, 11: European Commission (2021b); 6: World Bank (2021a, Doing Business); 7: Bernanke et al. (Reference Bernanke, Gertler and Gilchrist1999), Christiano et al. (Reference Christiano, Motto and Rostagno2010), Christiano et al. (Reference Christiano, Motto and Rostagno2014); 8: Jordà et al. (Reference Jordà, Knoll, Kuvshinov, Schularick and Taylor2019);Footnote ¹⁸ 9: Creditreform Wirtschaftsforschung (2019); 10: European Commission (2021a), World Bank (2021a, Doing Business), European Central Bank (2020, Securities Issues Statistics (SEC)).

3.3 Model fit

Table 2 reports key macroeconomic indicators in the steady state of the model and corresponding empirical values. The reported variables are mostly in line with the data.

Data for the GDP shares of capital, investment, and consumption are obtained from AMECO (European Commission (2021a)) for the years 2013−2017 (rows 1−3). Estimates for leverage (row 4) are obtained through Eurostat’s reports on financial balance sheets of nonfinancial corporations (European Commission (2021b)). We calculate leverage as the sum of loans and debt securities divided by equity and investment fund shares for the years 2013−2017. The relative size of the clean sector (row 5) is compared to the share of renewable energy in total energy supply. With data from the SHARES tool (European Commission (2021b)), we calculate the share of renewable energy in total energy supply for the years 2013−2017 to range from 15.3% to 17.3%. Acknowledging that the energy sector is one sector where decarbonization is relatively advanced, we use this estimate as an upper bound and calibrate our model such that it produces a share of clean intermediate goods in total intermediate goods equal to 12%. Rows 6 and 7 report estimates for financial parameters bankruptcy cost and uncertainty. Given moderate financial asymmetries, sectoral values are relatively close to macroeconomic aggregates reported in Table 1 and are well within the range of conventional literature estimates (e.g. Bernanke et al. (Reference Bernanke, Gertler and Gilchrist1999) and Christiano et al. (Reference Christiano, Motto and Rostagno2010)). The steady-state external finance premiums (row 8) for the clean an dirty sector are similar to the rates reported in Jordà et al. (Reference Jordà, Knoll, Kuvshinov, Schularick and Taylor2019). In comparison to the 2018 estimate from Creditreform Wirtschaftsforschung (2019), the model overestimates default rates (row 9). We consider this a reasonable fit as the model estimate is in the same order of magnitude, we only have data on 2018 and our model area is not perfectly aligned with the countries in Creditreform Wirtschaftsforschung (2019). With data from European Commission (2021a), World Bank (2021a, Doing Business) and European Central Bank (2020, Securities Issues Statistics (SEC)), we calculate the percentage of final goods lost due to bankruptcy as one minus recovery rate, multiplied by debt issues and default rates, divided by GDP (row 10). The model is calibrated such that it generates tax revenues (row 11) in line with the revenue from environmental taxes in the Euro Area as reported in European Commission (2021b).

3.4 Sensitivity

Figure 1 shows the sensitivity of key model variables in the steady state to changes in aggregate uncertainty $\sigma$ and aggregate bankruptcy cost $\mu$ as well as the degrees of asymmetry for both parameters, ${\mu _c}/{\mu _d}$ and ${\sigma _c}/{\sigma _d}$ . The equilibrium is moderately robust to changes in financial parameters. Figure 1 shows that macroeconomic variables (row 1) only slightly react. For instance, an increase of uncertainty $\sigma$ within both sectors by 25% reduces steady-state consumption by less than 2%. Sector-specific variables (rows 2 and 3) are however more sensitive. Financial variables (e.g. leverage, net worth) exhibit a higher sensitivity than nonfinancial variables (e.g. capital, labor (not shown)). All model variables exhibit a larger sensitivity to changes in uncertainty compared to changes in bankruptcy costs ( $\sigma$ , ${\sigma _c}/{\sigma _d}$ vs. $\mu$ , ${\mu _c}/{\mu _d}$ ). The steady state reacts more sensitively to reductions of parameter values than to increments. This suggests that the impact of frictions and asymmetries on the economy follows some concave functional relation, an observation that is reiterated in the dynamic sensitivity analysis in Section 4.2. In general, the clean sector is more sensitive to changes in financial asymmetries compared to the dirty sector ( ${\sigma _c}/{\sigma _d}$ , ${\mu _c}/{\mu _d}$ , row 2 vs. row 3). This is intuitive. Following the definition of financial asymmetries from Section 3.2, a changing degree of asymmetry alters the financing conditions for the clean sector relative to the dirty sector. It directly impacts the clean sector’s competitiveness. However, due to the small size of the clean sector in the total economy, this has negligible ramifications for the dirty sector. Even if the market share of the clean sector doubles, dirty output would decline by less than 14%. For the dirty sector, the implications of changes to aggregate uncertainty and bankruptcy costs are much larger than the effects of changes to financial asymmetries ( $\sigma$ and $\mu$ vs. ${\sigma _c}/{\sigma _d}$ and ${\mu _c}/{\mu _d}$ , row 3).

Figure 1. Steady-state sensitivity of sectoral variables with respect to key financial parameters bankruptcy cost $\mu$ , uncertainty $\sigma$ , and their asymmetric distribution among sectors $\mu _c/\mu _d$ and $\sigma _c/\sigma _d$ . Plots show the effect of increments (orange) and reductions (blue) of parameter values by 25%. Abscissas show the percentage change of variables in steady state.

In general, parameters that drive the degree of financial frictions and financial asymmetries have a small to modest influence on the equilibrium values especially for nonfinancial variables. This is intuitive because financial frictions matter for accumulation, adjustment, and transition dynamics such that given some disturbance, net worth positions adjust slower over time.

4.1 Transition dynamics

We now turn to the implication of financial frictions and financial asymmetries on the transition dynamics from a “dirty” to a “cleaner” economy. This transition is initiated by raising the carbon tax. We take as an exemplary scenario the ambition of the European Union 2030 Climate Target Plan: a reduction of domestic greenhouse gas emissions by at least 55% by 2030 compared to 1990. Relative to 2017 levels, that translates to a reduction by 45%.Footnote ¹⁹

Our research interest is whether and by how much frictions and asymmetries slow down and delay the transition and increase its cost in terms of lost consumption. We simulate the economy from 2017 to 2030, with a sudden, permanent emissions tax increment in 2017 calibrated to reduce emissions by 45% in 2030 in a counterfactual frictionless economy. We then study the behavior of our benchmark economy with financial frictions exposed to the same tax in order to identify the implications of inattention to frictions of policy makers when designing carbon taxes.

We find that financial frictions and financial asymmetries significantly delay the transition. More precisely, the EU will miss its 2030 climate target by approximately 11 percentage points if the implications of financial frictions are not considered when determining a carbon tax (Figure 3b). Instead of 55%, EU would only achieve emission reductions of 44% in 2030. If frictions were considered when determining the necessary tax rate to reach the climate target, the emissions tax implemented in 2017 would have to increase by 24% (Figure 5) to achieve the EU policy target. Delaying the implementation of climate policy to 2020 or even 2025 exacerbates both findings: the EU climate target is missed by 12 and 15 percentage points, respectively, and the necessary tax rates increase to 29% and 37%, respectively. We furthermore find that financial frictions generate financial transition risk in the clean sector which increases with the policy delay. In addition to its decelerating effects, frictions increase the social cost of the transition. We find that frictions can lead to a maximum reduction of per period consumption of approximately 4 percentage points.Footnote ²⁰ Inertia and resulting costs are caused by the less pronounced redirection of investment flows between sectors and higher frictional losses.

Figure 3. Transition of the Euro Area economy from 2017 to 2030 under the impact of increased emission taxes. Graphs report percentage deviation relative to the 2017 economy. The triangle in panel (b) represents the 2030 climate target.

Figure 4. The effect of delayed climate policy. Graphs show percentage deviations from the economy in 2017. Column one is a reproduction from Figure 3. Columns two and three display the impact of an emissions tax implemented in 2020 and 2025, respectively. Triangles indicate the Euro Area 2030 climate target. In all three scenarios, the policy is not anticipated by agents.

Figure 5. The ratio of required tax rates (benchmark economy to frictionless economy) subject to the year of policy implementation.

Figure 3 shows the effect of the increment in emissions taxes for benchmark and counterfactual scenarios. In 2017, a new emissions tax (approximately nine times the current tax level) is implemented. The counterfactual frictionless and the benchmark economy share the basic transmission mechanism of the permanent policy change: a higher emissions tax rate raises the marginal costs of production for the dirty sector, lowers the return on investment (f) and devalues dirty capital goods (j), which leads to corresponding adjustments in investment and capital stock (e, d), including divestment by capital goods producers (e), and consequently production of dirty goods is reduced. A loss of relative competitiveness of the dirty sector versus the clean sector exacerbates this effect. The clean sector expands production and gains market share. The clean sector’s relative competitive advantage caused by the higher emissions tax manifests in increasing prices of clean capital goods (j) and return on investment (f). Clean sector entrepreneurs adjust investment accordingly, financed primarily by increasing borrowing (h). As clean intermediate goods production grows, it crowds out dirty intermediate goods and changes the composition of the economy leading to lower emission intensities and lower per period emissions. Furthermore, carbon pricing triggers an immediate revaluation of entrepreneurial net worth $N_i$ (g). When the unexpected policy change hits the economy at the beginning of the period, returns on dirty investment decrease. However, entrepreneurs are stuck with the loans and capital stocks acquired during the previous period. With everything else fixed, the unexpected decline in profitability thus precipitates in a reduction of dirty net worth vice versa for the clean sector.

Even though the responses to the policy change is qualitatively similar for the frictionless and the benchmark economy, their quantitative implications are different. We first consider the frictionless economy (dashed and dotted lines in Figure 3) and then discuss major deviations in the benchmark economy. In the counterfactual frictionless economy, net worth positions adjust immediately and substantially after the policy change.Footnote ²¹ The absence of external finance premiums allows the clean sector to substantially expand borrowing, rapidly accumulate capital and scale up production. In the frictionless economy, investment adjustment costs are the only mechanism inhibiting an instant reallocation of capital from the dirty to the clean sector. The tax increment provides a sufficient steering effect to incentivize clean capital accumulation at scale such that the 2030 climate target is met.

When we account for financial frictions in the benchmark economy, the steering effect of the tax increment is dampened by frictional losses in addition to investment adjustment costs. With financial frictions, clean entrepreneurs increase investment (e) by less because borrowing is constrained by their net worth. In contrast to the frictionless economy, entrepreneurs have to build up sizable net worth positions (g) to limit the chance of bankruptcy and thus keep external finance premiums low. Entrepreneurs therefore maintain leverage ratios below 40% and utilize a combination of retained earnings and debt to finance their capital goods acquisitions. In the benchmark economy, the policy change causes a qualitatively similar immediate revaluation of net worth positions as in the frictionless economy, but on a smaller magnitude (approximately 5% more/less for clean/dirty entrepreneurs, barely visible in (g)). Net worth is accumulated through retained earnings from entrepreneurs with $\omega ^j_{it}\gt \bar{\omega }_{it}$ . This process requires time such that entrepreneurs rely on debt (h) when financing the scaling up of investment expenditures. Higher leverage (i) induces CMFs to charge higher premiums (l) to cover for the increased probability of bankruptcy. The higher premium reduces clean entrepreneurs’ ability to scale up investment (e), decelerates the accumulation of clean capital (d), and slows the transition (b).

Financial frictions slow the transition to such an extent that emissions in 2030 relative to 2017 are 9 percentage points above emissions in the frictionless scenario (b). Relative to 1990, emissions are 11 percentage points above the policy target in the friction economy. This implies that the European Union would miss its 2030 climate target, achieving emission reductions of approximately 44% instead of the envisaged 55%. Even though post-transition emissions of frictionless and benchmark economy eventually converge (not shown), cumulative emissions are higher in the delayed transition of the friction economy. Policy makers are well advised to consider the effect of financial frictions when designing climate policy, otherwise we see a risk that climate targets will not be met. Scenario analysis and climate policy assessments that include financial market frictions will therefore be particularly valuable to policy makers.

The precise impact of financial frictions on carbon budgets depends on their severity, the degree of financial asymmetry between the sectors, and the time available for the transition. In the following, we demonstrate how each of these criteria impacts transitional dynamics.

4.2 Policy delay, financial risk, and sensitivity

Time takes on a decisive role when debt is constrained by the borrowers’ net worth, which can only slowly be extended. With sufficient time, entrepreneurs could accumulate enough net worth to keep leverage ratios and external finance premiums low. Shortening the time horizon for the transition hence raises the relevance of financial frictions. If the implementation of climate policy is delayed and thus less time is available to realize the 2030 climate target, clean entrepreneurs have less time to increase their net worth positions through retained earnings. Therefore, they have to resort to debt financing to a greater extent. This further raises external finance premiums and limits the economic incentive for clean investment originating from the policy change. The transition is thus slowed down and emissions remain at higher levels for a longer transition period. Figure 4 visualizes the impact of delayed climate policy implementation on emissions and premiums. The first column of plots replicates the policy base case from the previous paragraph. Columns two and three show the response of the economy to a carbon tax increment implemented in 2020 and 2025, respectively. Tax rates are set such that the 2030 climate target is always met in the frictionless case. The gap in 2030 between the benchmark and the frictionless economy increases with the delay of the policy change. If implemented in 2017, frictions decelerate the response to the policy change such that emissions in 2030 are 9 percentage points higher compared to the frictionless economy. Delaying the policy change to 2020 and 2025 increases this difference to 10 and 12 percentage points, respectively. Translating the gap in emission reduction to the base year 1990 yields 11 percentage points for a policy change in 2017, and 12 and 15 percentage points for 2020 and 2025, respectively.

When the implementation of policy change is delayed, the carbon tax rates that provide the necessary steering effect have to be larger. Even in the frictionless scenario, the investment incentive from the tax must compensate for higher investment adjustment costs. In the benchmark economy, the tax has to compensate for larger frictional losses associated with a rapid transition in addition to higher investment adjustment costs. Due to the importance of retained earnings and net worth positions, the required compensation increases with the velocity of the transition.Footnote ²²

Figure 5 helps to disentangle the contribution of adjustment costs and frictional losses. We show the ratio of the required tax rates of the friction economy over the frictionless economy. If the policy change is implemented in 2017, the tax rate to reach the 2030 climate target in the friction economy is approximately 24% higher than the required rate in the frictionless economy. This divergence increases until 2025 where the required rate in the friction economy is approximately 37% higher. Any additional delay beyond 2025 causes required rates to converge. This is due to the fact that delaying the transition to the last years before 2030 alters the response of the economy fundamentally. Once the transition period is too short to restructure the economy and reallocate investment at scale and reasonable cost, it is less costly to achieve the reductions in emissions primarily by down-sizing the economy. In that case, no additional capital stock needs to be accumulated and frictions lose relevance. Hence, required tax rates for both scenarios converge.

Note that, in the benchmark economy, higher taxes increase financial transition risk in the clean sector. The more pressure policy makers apply to the economy, the larger the implications for leverage, default rates and risk premiums in the clean sector. At higher levels of the carbon tax, clean entrepreneurs find it profitable to finance investments through higher leverage ratios, pay larger premiums, and accept a higher likelihood of default. Figure 6 shows the response of the three financial indicators for clean entrepreneurs to the required tax rates (we show the maximum value across all time periods). When climate policy is implemented immediately (in 2017), the maximum values for leverage ratios, default rates, and risk premiums increase by 26%, 225%, and 194% relative to the pre-transition state. If climate policy is delayed until 2020 (but raised to the required rate), these values increase to 28%, 241%, and 208%, respectively. Implementing the required rate in 2025 implies maximum values of 34%, 289%, and 249%, respectively. The necessarily increased ambition in climate policy after a delay thus generates a “clean transition risk” for investments in the clean sector, which increases the social costs of the low-carbon transition due to higher default probabilities and hence a larger number of costly bankruptcies. Within the framework of our model, the default costs are fully recovered by financial intermediaries by charging a higher risk premium. However, policy makers may also be concerned about consequences of bankruptcy such as involuntary loss of employment and livelihood.

Figure 6. Required rates, leverage ratios, external finance premiums, and default rates for the benchmark economy. For the latter three financial indicators, only the maximum deviation from the pre-transition state is plotted (approx. 2 years after policy implementation).

Larger entrepreneurial leverage ratios undermine their capacity to cope well with business cycle dynamics or adverse shocks and might potentially endanger transition dynamics. With a clean sector that is vulnerable to financial transition risks, climate policy may benefit from sector specific policies to shield the clean sector, e.g. by derisking lending to the sector using instruments like loan guarantees (Steckel and Jakob (Reference Steckel and Jakob2018)). “Clean transition risk” also provides an additional reason to implement climate policy sooner rather than later, adding to the urgencies created, for example, by irreversibilities in climate change impacts, or by the limited feasible speed in rolling out new technologies.

The speed of the transition triggered by a carbon price increase has turned out to be sensitive to financing conditions. Our base calibrations include two culprits that complicate financing the transition: first, the existence of financial frictions make any reallocation of capital involving external financing more costly. Second, financial asymmetries between the clean and dirty sector (in uncertainty and bankruptcy costs) generate relatively larger external finance premiums for the green sector. In this section, we disentangle the influence of these two (frictions and asymmetries) on the transition path of variables in a dynamic setting. For this, we vary both the degree of financial frictions and asymmetries. We find that the degree of financial frictions is a stronger determinant of transition dynamics. The counterfactual frictionless economy turns out to be an outlier. Even compared to the scenario with very small frictions, transition paths are substantially different. In line with the results from the static sensitivity analysis in Section 3.4, we find that the post-transition steady state equilibrium is robust to changes in frictions and asymmetries.

Figures 7 and 8 show parameter variations of financial frictions and financial asymmetries, respectively, where we reduce the degree of the frictions ( $\mu$ ) and the asymmetries ( ${\mu _c}/{\mu _d}$ , ${\sigma _c}/{\sigma _d}$ ) in steps of 10%. Paler shades of curves indicate lower frictions or less financial asymmetry. The frictionless economy (palest shade) is an extreme case in terms of invoked dynamics (Figure 7). Even a small increment in bankruptcy costs from 0 to $\mu =0.033$ (10% of the benchmark estimate from Table 1) dampens the intermediate effect of the emissions tax considerably reducing mitigation in 2030 by approximately 7 percentage points (b).Footnote ²³ The strong reaction is caused by the fact that the slightest introduction of bankruptcy cost allocates an additional role to net worth such that it is not only used to finance capital internally but also limits the cost of external finance. Furthermore, time becomes an essential resource for entrepreneurs (net worth accumulation feeds from retained earnings) further stretching the transition period.

Figure 7. Sensitivity of the transition with respect to the degree of frictions in the economy. Graphs report percentage deviation relative to the 2017 economy where colors fade with decreasing $\mu \in [0,0.33]$ in steps of 10%. Darkest lines correspond to the benchmark calibration, whereas palest lines to the frictionless economy where $\mu =0$ .

Figure 8. Sensitivity of the transition with respect to the degree of financial asymmetry between sectors. Graphs report percentage deviation relative to the 2017 economy where colors fade with decreasing ${\mu _c}/{\mu _d}$ in steps of 10%. Darkest lines correspond to the benchmark calibration, whereas palest lines to the economy where ${\mu _c}/{\mu _d}=1$ .

Without financial asymmetries and in equilibrium (Figure 8), clean entrepreneurs maintain larger debt positions as compared to the benchmark economy. Their external finance premium is less sensitive towards leverage which makes the latter less costly. Therefore, given higher steady-state levels of leverage, the relative increment of debt (h) and leverage (i) in response to the policy change is less pronounced than in the benchmark economy. If financial asymmetries are eliminated, absolute increments however are more pronounced (not shown) such that dirty sector production is crowded out faster. The difference in emission reductions (b) between the benchmark economy and the economy without financial asymmetries amounts to 0.37 percentage points. Although the elimination of financial asymmetries increases the speed of the transition, their effect is of a different order of magnitude compared to the impact of frictions in general (Figure 7).

4.3 Temporary fluctuations

Sections 4.1 and 4.2 showed how the ability to borrow for entrepreneurs affects capital accumulation in climate policy scenarios. Macroeconomic fluctuations which affect financing conditions will thus affect capital accumulation in clean and dirty sector. In this section, we study the effect of short-run temporary disturbances on the performance of the clean and dirty sector. Specifically, we look at the dynamics generated by shocks to entrepreneurial net worth and uncertainty in the presence of financial frictions and asymmetries. We then show how the same shocks applied to both sectors affect clean and dirty sectors with different intensity thus altering their market shares (we use emission intensity as an indicator).

We attribute the different sectoral responses to their exposure to a risk effect and a volume effect. Both effects are rooted in the financial contract, which is sensitive to the financial frictions and financial characteristics of the lender. With respect to emission intensity, the consequences of the shocks depend on the susceptibility of the sectors to the effects as well as their relative strength.

The risk effect captures the change of the external finance premium with leverage. The strength of the risk effect is determined by the function $s_i(\!\cdot\!)$ in equation (12) which depends on uncertainty $\sigma _i$ and bankruptcy cost $\mu _i$ as parameters. Given a certain leverage, larger uncertainty $\sigma _i$ translates to a larger probability of default. Likewise, higher bankruptcy costs $\mu _i$ translate to a larger economic loss in case of default. Therefore, entrepreneurs that are subject to stronger financial frictions (via higher $\sigma _i$ and/or $\mu _i$ ) face external finance premiums that are more sensitive to changes in leverage.

The volume effect is determined by the volume of the loan portfolio of an entrepreneur to which the external finance premium applies. As the external finance premium homogeneously applies to each unit of debt, changes in the premium have a stronger impact on entrepreneurs with larger volumes of debt outstanding.

In our setting, both effects partly counteract each other with respect to the distribution of sectoral market shares and hence emission intensity of the total economy. Due to the financial asymmetry in the benchmark calibration, $s'_c(\!\cdot\!)\gt s'_d(\!\cdot\!)$ and clean entrepreneurs are more susceptible to the risk effect. In equilibrium, the total debt volume of entrepreneurs in the dirty sector is more than eight times the volume of debt for clean sector entrepreneurs, making dirty entrepreneurs more susceptible to the volume effect.

We find that of the two shocks considered, the risk effect exhibits the larger persistence, and hence economically adverse shocks tilt the economy towards a higher emission intensity (Figures 9c and 11c). However, we do not find that these effects have a strong influence on the total emission intensity of the economy.

Figure 9. Financial wealth shock (1 SD). Impulse response functions show quarterly percentage deviation from steady state.

4.3.1 Financial wealth shock

As seen above, the role of entrepreneurial net worth positions and accumulation is crucial for the duration and cost of the transition. For publicly traded companies, their net worth is priced at exchanges through transactions between market participants. The valuation of net worth positions is thus subject to volatility induced by e.g. irrational behavior or imperfect information among traders. We study the impact of such volatility in the form of shocks to net worth positions to investigate if and how they impact clean sector performance and therefore the transition. Specifically, we consider a temporary negative and symmetric shock on clean and dirty entrepreneurial net worth positions. We show that such a financial wealth shock has strong implications for the economy. With financial asymmetries and thus risk and volume effects at work, sectoral responses are differentiated but the overall change in emission intensity is small.

We utilize impulse response function analysis to study the impact of a temporary symmetric negative shock $z_{Vt}$ of one standard deviation to entrepreneurial net worth positions in both sectors. Results in Figure 9 show how net worth positions decrease by 1% (g) upon impact and continue to decline as the shock fades. Since net worth positions are small and the shock is multiplicative, ramifications in the frictionless economy are negligible. The loss of up to 3% of net worth positions is compensated by slightly increasing debt (h) with infinitesimal effects on leverage.

In the friction economy, entrepreneurs substitute part of the foregone internal finance with debt (h) increasing their leverage ratios (i) at the cost of higher finance premiums (l) as CMFs will charge higher interest rates to cover for the increased bankruptcy probability. This in turn cripples prices of capital as well as entrepreneurial returns (j,f) and investment (e), producing lower capital stocks (d) and a contraction of output (a) and emissions (b). The financial wealth shock eliminates the same share of net worth from entrepreneurs in both sectors but the volume and risk effect produce differentiated sectoral responses. In our setting, the risk effect dominates the volume effect and the clean sector is at a disadvantage. Clean entrepreneurial returns and sector investment are reduced relatively more (e,f) creating a bias towards the dirty sector such that emission intensity (c) rises temporarily.

Figure 10 shows the response of the economy when both sectors exhibit identical financial characteristics and hence the risk effect impacts both sectors identically. Here, only the volume effect determines differentiated sectoral responses. Returns for dirty entrepreneurs decline more (f), slowing investment (e) and leading to a larger reduction in capital stock and the composition of the economy changes in favor of the clean sector. Comparing panels (c) in Figures 9 and 10, it becomes evident that the risk effect creates relatively more amplification and persistence in response to the financial wealth shock and compared to the volume effect. The magnitudes of changes to the composition of the economy and emission intensities are however small in both cases. The financial wealth shock that reduces net worth positions by 1% initially, increases the emission intensity of the economy by 0.02% at maximum (see panel (c) in Figure 9). Thus, a financial downturn simulated by a 10% negative financial wealth shock during the transition scenario from Section 4.1 does not alter transition dynamics substantially (not shown).

Figure 10. Financial wealth shock (1 SD) to an economy where financial asymmetries are eliminated. Impulse response functions show quarterly percentage deviation from steady state.

4.3.2 Uncertainty shock

We demonstrated in Sections 4.1 and 4.2 that the presence and strength of financial frictions can have a substantial influence on the performance of the clean sector during a transition. We further showed in Section 3.4 that, if frictions are present, changes to uncertainty $\sigma$ are a much stronger driver of results than changes to bankruptcy cost $\mu$ . This seems intuitive as uncertainty about idiosyncratic productivity shocks directly influence the risk associated with the profitability of entrepreneurs. Similar to Christiano et al. (Reference Christiano, Motto and Rostagno2014), who identify these uncertainty shocks (therein called “risk shocks”) as the most important shock driving business cycles, we introduced a disturbance $z_\sigma$ to the standard deviation $z_{\sigma t}\sigma _{it}$ of the productivity shock $\omega ^j_{it}$ . We confirm the finding from Section 4.3.1 that the risk effect exhibits a larger persistence, but this time the volume effects create larger amplification.

A shock to $z_{\sigma t}$ of one standard deviation temporarily increases the standard deviation $\sigma _{it}$ of the productivity shock $\omega _{it}$ and leads to higher uncertainty with respect to entrepreneurial profits and bankruptcies. The response of the economy is shown in Figure 11. Again, the shock has no impact on macroeconomic variables in the frictionless economy. A temporary increase in uncertainty is not a problem since bankruptcies are costless. In the benchmark economy however, increased uncertainty induces CMFs to ramp up external finance premiums (l) thereby diminishing returns to entrepreneurs (f) to which they react with deleveraging (i) and a contraction of investment (e). They accumulate net worth (g) to reduce individual premiums. As the shock fades and net worth positions have improved, after 10 quarters entrepreneurs start borrowing more from CMFs and leverage ratios converge back to the steady-state level. Together with relatively strong net worth positions, entrepreneurs temporarily invest above their steady state levels. Differentiated sector responses are again generated by the risk and volume effect.

Figure 11. Uncertainty shock (1 SD). Impulse response functions show quarterly percentage deviation from steady state.

In the beginning, the volume effect dominates: dirty entrepreneurs maintain larger debt positions and the contraction of dirty sector entrepreneurs’ return is more pronounced (f) as increasing risk premiums (l) apply to a larger loan volume. Dirty sector entrepreneurs sharply reduce expenditure for capital goods and divestment is more pronounced (e). During this time, clean entrepreneurs gain market share and emission intensity declines (c). As the volume effect fades, the dirty sector manages to retain a greater share of its earnings (g). This allows for a reduced contraction of borrowing compared to the clean sector’s response. After 10 quarters, the risk effect dominates. In comparison to the dirty sector, entrepreneurs in the clean sector have to cope with initially larger uncertainty $\sigma _c$ . An identical positive innovation to uncertainty exerts higher pressure on deleveraging (i) as leverage is more costly in terms of the external finance premium. The dirty sector gains market share and emission intensity temporarily exceeds the steady-state level as the risk effect outlasts the volume effect. Figure 12 shows impulse response functions for the risk shock in an economy that abstracts from financial asymmetries. The risk effect thus impacts sectors equally while the dirty sector remains more susceptible to the volume effect. Therefore, the clean sector occupies a market share above steady state throughout the shock horizon and the emission intensity is below its equilibrium value (c). The drop in emission intensity is twice that of Figure 11 and only a negligible overshoot materializes after period 20.

Figure 12. Uncertainty shock (1 SD) to an economy where financial asymmetries are eliminated. Impulse response functions show quarterly percentage deviation from steady state.