Debt, Growth, and the Carbon Lock-In

Abstract

Despite decades of climate policy and rapid improvements in energy efficiency, global CO2 emissions continue to rise, suggesting the presence of structural drivers that offset efficiency gains. Here we identify financial leverage as a key mechanism underpinning this persistent overshoot. We develop a stochastic macro-financial model linking credit dynamics, economic growth, bankruptcy risk, and cumulative carbon emissions. The model shows that debt-financed growth systematically amplifies cumulative emissions, locking economies into high-carbon trajectories even as emissions intensity declines. This arises from a double constraint: debt repayment requires sustained growth, while growth remains energy-dependent and thus generates emissions. When growth becomes increasingly dependent on leverage, financial instability and cumulative emissions rise, while gains in real wealth diminish, revealing a leverage frontier beyond which additional credit primarily generates risk. Calibrating the model to multi-decade data for the US, China, France and Denmark, we find a robust coupling between debt accumulation, cumulative GDP and cumulative emissions across distinct economic structures. These results indicate that achieving net-zero targets requires aligning credit allocation with decarbonisation objectives

Figures (12)

• Figure 1: The debt-carbon spiral: leverage enhances economic growth, but it also increases emissions and default risk, thereby establishing a feedback loop that locks in carbon-intensive development and jeopardizes climate targets and financial stability. In this scheme, the letters (R) and (B) represent reinforcing and balancing loops, respectively. The primary reinforcing loop (R1) illustrates how the expansion of credit and leverage stimulates GDP growth, leading to increased energy consumption and CO$_2$ emissions. A secondary reinforcing loop (R2) describe the necessity of additional borrowing to maintain the same level of resource extraction as the energy return on investment (EROI) declines and the costs relative to climate change damages rise hall_peak_2018kotz_economic_2024. This, in turn, leads to more aggressive fiscal and credit policies that further intensify debt-financed growth. Two balancing loops counteract these self-propelling cycles: (B1) captures the negative economic effects of environmental externalities, such as pollution, climate-related losses, and reduced productivity, that constrain growth kotz_economic_2024, while (B2) captures technological and structural decarbonization mechanisms that reduce the carbon intensity of energy use and improve efficiency. Feedback that are qualitatively supported in the literature but are not explicitly quantified in our model are indicated by dashed lines.
• Figure 2: A Path-dependent intensities $\mathfrak{I}_{\tau}\left(\{C_{\tau}\}\right)$ starting from year 2000 and yearly carbon intensities $I(\tau)$ (consumption-based) for different countries. Data for path-dependent intensities and yearly carbon intensities are shown as dotted lines. The theoretical prediction obtained by computing $C_{\tau}$ from our model, and combining it with $I_{\tau}$ from data, is shown as the solid line representing the average trend, with the colored area around that line representing the standard deviation. In practice, we used country-specific measured values of the intrinsic growth rate, interest rate, and leverage, to estimate $C_{\tau}$. B Comparison of cumulative $CO_2$ emissions (data in dotted lines) for different countries (US, China, Denmark, and France) to the predictions of our stochastic model as solid lines, with standard deviation represented by the colored area. We report the mean average errors (MAE) and coefficients of determination between the theory and data for plot A and B in Supplementary Information. C Relationship between cumulative emissions per capita and cumulative GDP per capita from the data: we observe a clear increasing trend between both, with a slope that varies according to the country. As in Fig A, one observes that that China has the most carbon-intensive economy, while the US has the highest cumulative emissions, owing to its high cumulative GDP per capita. D Correlation between cumulative GDP and cumulative debt (left axis), and correlation between cumulative emissions and cumulative debt (right) axis. Cumulative GDP (circles) is mostly a linear function of cumulative debt, except for Denmark, where it is slightly faster than linear. Concerning cumulative emissions (pentagons), the trend is initially linearly correlated with cumulative debt, then becomes slower than linear (in particular for China). Again, this is an effect of the decrease in carbon intensity with time.
• Figure 3: AEffect of leverage: predictions for cumulative emissions (starting from 1998) depending on leverage in different countries. For each country, the color gradient indicates increasing leverage from $1.00$ to $1.05$, resulting in higher cumulative emissions per capita. A linearly decreasing carbon intensity has been assumed, with different parameters for each country friedlingstein_persistent_2014, based on consumption-based emissions from 1998 to 2022. We also assume that the distributions of $\gamma$ remain constant for each country. We use $W=\left< \ln(\gamma_{\tau}) \right>$ and $\sigma_{X}$ (see values in Methods), as well as a fixed value of leverage, as inputs for the model. As expected, the larger the leverage, the greater the potential for GDP growth, leading to higher cumulative emissions despite decreasing carbon intensities. Changes by a few percent in leverage are enough to trigger changes of almost $1$ order of magnitude in cumulative emissions per capita after $25$ years. BEffect of policies: Predictions for cumulative emissions (starting from 1998) depending on how strong the effort is to reduce carbon intensity. For each country, the color gradient corresponds to increasing $\left|dI_{\tau}/d\tau\right|$ (where $dI_{\tau}/d\tau$ is negative), indicating an increasing effort to reduce the carbon intensity of the economy. $\left|dI_{\tau}/d\tau\right|$ varies between $0$ and $1.5$ times the current trend for each country. We observe that for high enough values of $\left|dI_{\tau}/d\tau\right|$, $I_{\tau}$ becomes negative (carbon capture), leading to decreasing cumulative emissions. The leverage is taken equal to the average leverage measured over the period $1998-2022$ for each country.
• Figure 4: Illustration of trade-off between solvency and payback time. Solvency probability $P_S$ is shown for model B with the color scale as function of payback time $t_p$ and interest rate $\rho-1$. Solvency becomes less likely with time in this model whenever $\left< \gamma \right><\rho$ for all leverages $L$, i.e. when debt increases faster than the capital. This means that this strategy is not viable on long timescales, and is just a way to increase short-term GDP (resulting in increased carbon emissions).
• Figure 5: Comparing primary deficit to GDP for different countries. In dotted lines we show the data, in full lines the average values and the colored areas represent standard deviations. We see that the typical variations are of a few percent. The trend for the US, China and France seems to be a slight increase in the ratio. We also notice that the ratio is negative on average for Denmark, meaning that the government typically has surpluses.