## wpiea2023175-print-pdf

## Source details

**Canonical URL:** [wpiea2023175-print-pdf](https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023175-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2023/english/wpiea2023175-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2023/english/wpiea2023175-print-pdf.pdf.json)

---

### Climate change impacts and risks
- Climate change is generating unprecedented impacts on the global economy; the IPCC highlights increasingly observed adverse economic effects attributable to human-induced climate change (IPCC 2022).
- Physical hazards (increasing frequency and intensity of extreme climate events such as hurricanes, floods, drought, and wildfires) are projected to increase further with global warming.
- Limiting global warming requires significant efforts to reduce global greenhouse gas (GHG) emissions; such actions can have material economic and financial impacts on emissions-intensive firms/sectors, households, and governments.
- Transition risks arise as the economy moves toward a low-carbon economy and can affect various segments of the economy and the financial sector.

### Global policy context and recent developments
- COP26: more than 120 countries, representing about 70 percent of global emissions, pledged to bring emissions to net zero by around 2050.
- Climate Action Tracker (2022) reports weakened global engagement since COP26; COP27 showed limited stronger global climate ambitions relative to COP26.
- Global non-renewable-energy- and fossil-fuel-related CO2 emissions in 2021 bounced back almost to pre-COVID-19 pandemic emission levels (IEA 2021; EDGAR 2022).
- Longer delays in transitioning imply more stringent future policy measures will likely be required; delays increase the risk of more abrupt and sizeable future policy action.

### Energy and emissions structure (global and Mexico)
- Global energy supply remains dominated by non-renewable sources; renewables remain a minor portion.
- Power generation and transportation contributed about two-thirds of total global emissions in 2019 (IEA 2021).
- Mexico:
  - Oil and natural gas amounted to about 85 percent of Mexico’s total energy supply in 2020.
  - In 2018, about 38 percent of Mexico’s total CO2 emissions were attributable to utilities/power generation, about 25 percent to manufacturing, about 16 percent to transportation; mining accounted for about 11 percent; all other sectors combined about 10 percent.
  - Mexico is the second largest emitter of GHGs in Latin America (after Brazil) with one of the highest per capita emissions levels.

### Financial sector exposure and regulatory focus
- Global regulators and central banks increasingly recognize climate-related risks to financial stability and are developing scenario-based analysis and stress testing.
- The IMF’s Financial Sector Assessment Program (FSAP) has made climate-related financial stability analysis a mounting priority.
- Mexican banking exposures:
  - About 37 percent of the commercial banking system’s corporate credit is concentrated in emission-intensive sectors.
  - Manufacturing accounts for about 15 percent of total credit; exposures to mining are about 4 percent of total credit.

### Contribution: integrated micro-macro framework and novel scenario class
- Methodology:
  - Integrated micro-macro framework linking macro-sectoral pathways (from a CGE model) to firm-level balance-sheet simulations.
  - New class of scenarios: delayed-uncertain pathways implemented via a binomial tree evolution structure.
  - Stochastic financial model layer for corporate spreads using a jump-diffusion process (mean-reverting square-root process with jumps).
- Distinctions:
  - Macro: projections from IMF-ENV CGE (recursive-dynamic, multi-regional, multi-sectoral) covering 25 regions and 37 sectors.
  - Micro: firm-level balance sheet data (DataStream and S&P Capital IQ) 2002–2020; on average about 100 firms per year; the sample represents about 42 percent of total outstanding debt of the nonfinancial corporate sector.
  - Delayed-uncertain pathways generate time-varying distributions of risk metrics (PDs, bank capital impact) rather than single deterministic paths.

### Scenario design
- Two main scenario classes:
  - Global action (orderly): countries act early and gradually; broadly in line with limiting global temperature increase to within 2°C by the end of the century (with 1.5°C as the Paris goal).
  - Delayed-uncertain (disorderly and uncertain): binomial-tree evolution with an embedded jump-diffusion model for corporate spreads to capture changing risks and sudden large movements.
- Delayed-uncertain setup enables quantification of distributions and tail risks over time.

### Mapping scenarios into firm impacts and bridge to PDs
- Firm projection mechanics:
  - Recursive evolution of EBIT incorporates sensitivity of sales to sectoral gross output/GVA paths (Ft), elasticity of COGS to sales (G), and direct additional operating cost = carbon price × emissions in tCO2eq.
  - Assumed elasticity of sales to sectoral output/GVA = 1.5.
  - Elasticity G estimated at 0.97 via panel fixed effects regression.
  - Only scope 1 emissions used to treat carbon prices as direct operating cost component of EBIT.
- Firm vulnerability indicators projected over a five-year horizon (till 2026):
  - Interest coverage ratio (ICR) = EBIT / interest expenses.
  - Leverage ratio (LR) = total debt / total assets.
  - Current ratio (CR) = current assets / current liabilities.
- Bridge equation (panel fixed effects with logit-transformed PDs):
  - S C C l o g i t ( P D )_{i,t} = α_i + β_1 ICR_{i,t} + β_2 CR_{i,t} + β_3 LR_{i,t} + ε_{i,t}
  - Logit transformation ensures projected PDs lie in the unit interval.

### Key findings from the Mexico application (with global implications)
- Sectoral heterogeneity: exposure to transition risks varies substantially across sectors.
- Under global action:
  - Aggregate impact on the financial sector is modest, but certain sectors and banks are more exposed.
  - Examples of CGE sectoral impacts by 2030:
    - Chemicals: decline in output about 10 percent (global action).
    - Fossil fuel sector: decline about 12 percent.
    - Some sectors (e.g., transportation equipment) are positively impacted by 2030.
- Under delayed-uncertain pathways:
  - Chemicals sector impact more than doubles from 10 percent to 23 percent by 2030 if action delayed to 2025/26.
  - Right tails of sectoral PD distributions become significantly heavier with longer delays.
  - Chemicals and non-metallic manufacturing segments are among the most vulnerable despite sound initial distress metrics.
  - Sectors not highly emission intensive (e.g., construction) can be negatively affected depending on initial financial conditions.
  - Financial markets channel amplifies risks: delays increase need for stronger future policy, investor reassessments raise market risk and volatility, and sharply raise corporate spreads and risk premia.

### Stochastic financial model and simulation details
- Corporate spread dynamics modeled by affine jump-diffusion (Cox-Ingersoll-Ross with jumps):
  - dr_t = κ(μ − r_t + s_t) dt + σ sqrt(r_t) dW_t + dJ_t.
  - Feller condition assumed: 2κμ ≥ σ^2.
  - Square-root volatility term σ sqrt(r_t) yields higher effective volatility when spreads are higher.
  - Jump process J_t captures large/sudden shocks.
- Calibration and simulation:
  - Target index: Corporate Emerging Markets Bond Index (CEMBI) used as representative aggregate corporate bond spreads index.
  - Monte Carlo simulation: 20,000 paths, daily frequency, horizon till end-2026.
  - Mapping: scaling factor s_t constructed from sectoral outputs maps climate risk into corporate spreads; corporate spreads mapped into firm-level micro-simulations as time-varying interest rates.
- Key calibration choices for delayed-uncertain construction:
  - Single jump at end-2022 calibrated to the 99th percentile of rolling two-year changes in the corporate spread.
  - For constructed delayed paths:
    - Delayed-2023 path: average across all possible paths.
    - Delayed-2024 path: 75th percentile.
    - Delayed-2025 path: 90th percentile.
    - Delayed-2026 path: 95th percentile.
  - Elasticity of corporate spreads to changes in aggregate output in Mexico: about 0.30 percent.

### Sensitivity and calibration notes
- Mean reversion sensitivity:
  - Slower mean reversion (small κ consistent with Feller lower bound) yields more persistent elevated spreads; PD distributions shift further right with longer delays.
- Jump and square-root amplification:
  - Jumps increase frequency of tail shocks; square-root diffusion increases effective volatility after jumps, raising tail mass.
  - Example outcome alterations due to jumps: a 500 basis points shock observed 1 percent of the time without jumps could be observed 5 percent of the time with jumps.
- Monte Carlo output provides full time-varying distributions of spreads at each future time slice.

### Appendix I: PD sensitivities, mapping, and banking impact methodology
- PD sensitivities (panel regression coefficients, t-values in parentheses):
  - Interest Coverage Ratio: -0.002 (-4.366)
  - Current Ratio: -0.255 (-4.166)
  - Leverage Ratio: 2.10 (3.871)
  - R-squared: 0.54; Observations: 762; Firm-level fixed effects: Yes.
- Conclusion: PDs are most sensitive to leverage ratio, followed by current ratio and interest coverage ratio.
- From firm PDs to sectoral and bank-level PDs:
  - Sector delta PD = projected PD in each year 2022–2026 minus starting PD in 2021.
  - For each bank, sector delta PDs weighted by the bank’s credit exposures to that sector; sectoral credit exposures assumed constant at the starting point.
  - Five possible paths through 2026 constructed under the binomial-tree delayed-uncertain setup.
- Banking capital impact methodology and assumptions:
  - Simplified calculation considers only expected credit losses under a static balance sheet assumption.
  - RWAs held constant at the starting value.
  - A common LGD used across all banks; system average implied LGD from coverage ratios found to be 53 percent.
  - Tax and dividend payout impacts ignored.
  - Result: estimates driven solely by loan impairment charges.

### Quantitative distributional results and tail-risk magnification
- Corporate PDs under delayed-uncertain:
  - Acting in year 2023: maximum possible credit risk around 3 percent.
  - Delayed to 2026: risk could increase to as high as 14 percent.
  - Support of PD distribution increases by more than four times under climate action in 2026 relative to acting in 2023.
- Bank delta PDs (exposure-weighted) tails:
  - Early action in 2023: maximum delta PD across banks around 0.2 percent.
  - Delayed till 2026: delta PDs could rise as high as 1.5 percent (more than seven-fold rise in maximum tail risk).
- Bank capital ratios (expected credit losses, static balance sheet):
  - Cumulative impact on bank capital under global action: about 0.35 percent.
  - Cumulative bank capital impact under delayed-uncertain path could reach as high as 0.8 percent with non-trivial probability.
  - Maximum impact under global action: around 0.3 percent.
  - Relative increases: maximum range of the bank capital distribution increases by almost five times if actions delayed till 2026 versus 2023.

### Caveats and limitations
- Analysis abstracts away from physical risks; delays could further affect asset valuations via physical hazards.
- General equilibrium feedbacks from the financial sector to the real economy are not captured.
- Mexico-specific exercise focused on commercial banking corporate loan portfolios; other channels (market risks, consumer portfolios) not covered.
- Data limitations: sample comprised large/listed Mexican firms; limited granular data on SMEs.

### Policy implications and recommendations
- Early and orderly global action to transition to a low-carbon economy mitigates future tail risks to corporates and financial sectors.
- Delays in policy action compound future tail risks through financial markets channels (market reassessment, higher spreads, volatility).
- Policymakers and financial supervisors should integrate forward-looking stochastic approaches (such as delayed-uncertain pathways with jump-diffusion financial layers) into climate-related risk assessment and stress-testing frameworks to capture distributional and tail-risk effects.
- Continued vigilance is required at the global level because tail risks increase the longer the delay toward a low-carbon economy.
- Framework scalability: adaptable and can be scaled with more granular firm-level data to explore additional channels and spillovers.

*Source: IMF staff — Introduction and Appendix material from wpiea2023175-print-pdf*

### Introduction

### Introduction

### Climate change impacts and risks
- Climate change is generating unprecedented impacts on the global economy and human society; the IPCC highlights increasingly observed adverse economic effects attributable to human-induced climate change (IPCC 2022).
- Physical hazards (increasing frequency and intensity of extreme climate events such as hurricanes, floods, drought, and wildfires) are projected to increase further with global warming.
- Limiting global warming requires significant efforts and commitments to reduce global greenhouse gas (GHG) emissions; such actions can have material economic and financial impacts on emissions-intensive firms/sectors, households, and governments.
- Transition risks arise as the economy moves toward a low-carbon economy and can affect various segments of the economy and the financial sector.

### Global policy context and recent developments
- At COP26, more than 120 countries, representing about 70 percent of global emissions, pledged to bring emissions to net zero by around 2050.
- Climate Action Tracker (2022) reports weakened global engagement since COP26, with progress stalled on more ambitious 2030 climate targets; COP27 showed limited stronger global climate ambitions relative to COP26.
- Global non-renewable-energy- and fossil-fuel-related CO2 emissions in 2021 bounced back almost to pre-COVID-19 pandemic emission levels (IEA 2021; EDGAR 2022).
- The longer delays in transitioning to a low-carbon economy, the more stringent future policy measures will likely need to be to attain climate goals; delays increase the risk that future policy action must be more abrupt and sizeable.

### Energy and emissions structure (global and Mexico)
- Global energy supply remains dominated by non-renewable sources (coal, oil, natural gas), while renewables (hydro, solar, wind) remain a minor portion.
- Power generation and transportation contributed about two-thirds of total global emissions in 2019 (IEA 2021).
- Mexico specifics:
  - Oil and natural gas amounted to about 85 percent of Mexico’s total energy supply in 2020.
  - In 2018, about 38 percent of Mexico’s total CO2 emissions were attributable to utilities/power generation, about 25 percent to manufacturing, and about 16 percent to transportation; mining (including oil, gas, coal extraction) accounted for about 11 percent; all other sectors combined about 10 percent.
  - Mexico is the second largest emitter of GHGs in Latin America (after Brazil) with one of the highest per capita emissions levels.

### Financial sector exposure and regulatory focus
- Global regulators and central banks increasingly recognize climate-related risks to financial stability and are developing scenario-based analysis and stress testing (examples cited: De Nederlandsche Bank 2018; Bank of England 2019; Bank of Canada 2020; European Central Bank 2021; others).
- The IMF’s Financial Sector Assessment Program (FSAP) has made climate-related financial stability analysis a mounting priority.
- Mexican banking exposures:
  - About 37 percent of the commercial banking system’s corporate credit is concentrated in emission-intensive sectors.
  - The manufacturing sector accounts for about 15 percent of total credit; exposures to mining (including oil, gas, coal extraction) are about 4 percent of total credit.

### Contribution: integrated micro-macro framework and new scenario class
- The paper develops a forward-looking analytical approach to transition risk analysis using:
  - An integrated micro-macro framework linking macro-sectoral pathways to firm-level balance-sheet simulations.
  - A new class of scenarios called delayed-uncertain pathways implemented via a binomial tree evolution structure.
  - A stochastic financial model layer for corporate spreads using a jump-diffusion process to capture large/sudden market movements.
- Key methodological distinctions:
  - Macro: projections of macro-sectoral pathways (from a CGE model).
  - Micro: firm-level balance sheet information and simulations to project vulnerability indicators and probabilities of default (PDs).
  - The delayed-uncertain pathways generate time-varying distributions of risk metrics (PDs, bank capital impact) rather than single deterministic paths.

### Scenario design and comparison
- Two sets of scenarios:
  - Global action (baseline/adverse in standard stress-testing spirit): countries act early and gradually to implement climate policies; broadly in line with limiting global temperature increase to within 2°C by the end of the century (with 1.5°C as the Paris goal).
  - Delayed-uncertain (disorderly and uncertain): characterized by binomial tree evolution and an embedded stochastic jump-diffusion model for corporate spreads to capture continuously changing risks and large/sudden movements.
- The delayed-uncertain setup allows quantification of distributions and tail risks over time, addressing limitations of deterministic scenario-based stress tests.

### Key findings from the Mexico application (with global implications)
- Sectoral heterogeneity: exposure to transition risks varies substantially across sectors.
- Under a global action scenario, aggregate impact on the financial sector is modest, but certain sectors and banks are more exposed.
- Under delayed-uncertain pathways:
  - Right tails of sectoral PD distributions can become significantly heavier with longer delays.
  - Chemicals and non-metallic manufacturing segments in Mexico are among the most vulnerable despite sound initial distress metrics.
  - Sectors not highly emission intensive (e.g., construction) can still be negatively affected depending on initial financial conditions.
  - Bank capital impacts appear modest under global action but delayed-uncertain scenarios reveal non-trivial increases in tail risk of bank capital impact, suggesting potential for material future effects.
- Financial markets channel amplifies risks: delays create the need for stronger future policy action, uncertainty about timing/mechanism of action can trigger reassessments by global investors, increase market risk and volatility, disrupt capital markets, and sharply raise corporate spreads and risk premia.

### Modeling framework and data
- Macro inputs:
  - Transition risk scenarios produced by the IMF-ENV CGE model (recursive-dynamic, multi-regional, multi-sectoral) covering 25 regions and 37 sectors; scenarios aligned with NGFS scenario narratives and IPCC temperature/emission targets.
- Micro modeling:
  - Firm-level corporate data from DataStream and S&P Capital IQ, balance sheet data 2002 to 2020; on average about 100 firms per year in the sample.
  - Large firms are 2 percent of the universe of firms with outstanding loan facilities across 44 commercial banks but account for more than 65 percent of outstanding bank credit; the sample represents about 42 percent of total outstanding debt of the nonfinancial corporate sector.
  - Key firm variables: EBIT, sales revenue, cost of goods sold, interest expenses, average/effective interest rates, total debt, total assets, current assets, current liabilities.
- Mapping scenarios into firm impacts:
  - Recursive evolution of EBIT incorporates sensitivity of sales to sectoral gross output/GVA paths (Ft), elasticity of COGS to sales (G), and direct additional operating cost due to firm-level emissions times carbon prices (carbon price × emissions in tCO2eq).
  - An assumed elasticity of sales to sectoral output/GVA of 1.5 (informed by Gross et al. (2022)); elasticity G estimated at 0.97 via panel fixed effects regression.
  - Only scope 1 emissions used to be consistent with treating carbon prices as direct operating cost component of EBIT.
- Corporate vulnerability indicators projected over a five-year horizon (till 2026):
  - Interest coverage ratio (ICR) = EBIT / interest expenses.
  - Leverage ratio (LR) = total debt / total assets.
  - Current ratio (CR) = current assets / current liabilities.
- Bridge to PDs:
  - A bridge equation estimated via panel fixed effects regression with logit-transformed firm-level PDs from Moody’s EDF database:
    - S C C l o g i t ( P D )_{i,t} = α_i + β_1 ICR_{i,t} + β_2 CR_{i,t} + β_3 LR_{i,t} + ε_{i,t}
  - Logit transformation ensures projected PDs lie in the unit interval.

### Caveats and limitations
- Analysis abstracts away from physical risks; delays in transition could further affect asset valuations through increasing frequency and severity of physical hazards.
- General equilibrium feedbacks from the financial sector to the real economy are not captured; results could underestimate impacts from transition delays and interactions with physical risk.
- Mexico-specific exercise focused on the commercial banking sector’s corporate loan portfolio due to data limitations; other channels (market risks, consumer portfolios) were not covered.
- Data limitations: sample comprised large/listed Mexican firms; limited granular data on SMEs constrained scope and generalizability.
- The framework itself is general and adaptable when more granular/better data are available.

### Policy implications and recommendations
- Early and orderly global action to transition to a low-carbon economy mitigates future tail risks to corporates and financial sectors.
- Delays in policy action compound future tail risks through financial markets channels (market reassessment, higher spreads, volatility).
- Policymakers and financial supervisors should integrate forward-looking stochastic approaches (such as delayed-uncertain pathways with jump-diffusion financial layers) into climate-related risk assessment and stress-testing frameworks to capture distributional and tail-risk effects.
- Continued vigilance is required at the global level because tail risks increase the longer the delay toward a low-carbon economy.

*Source: IMF staff — Introduction from wpiea2023175-print-pdf*

### Appendix I) shows that PDs are most sensitive to leverage ratio, followed by current ratio and interest coverage

### wpiea2023175-print-pdf - Appendix I) shows that PDs are most sensitive to leverage ratio, followed by current ratio and interest coverage

### Sensitivity of PDs to firm vulnerability indicators
- PDs are most sensitive to leverage ratio, followed by current ratio and interest coverage ratio.
- Sensitivities are driven by:
  - Different coefficients in the bridge equation across indicators.
  - The paths of indicators being affected by the CGE model’s sectoral pathways and carbon prices during simulations.
- Projections of PDs depend on multiple factors (a full-fledged micro-macro framework), so outputs require careful interpretation.

### Bridge equation, right-hand-side variables, and projection mechanics
- The right-hand-side variables of the bridge equation do not contain any macro-financial variables because those indicators are already affected by the state variables of the economy in historical data used for the panel regression.
- Projection drivers:
  - CGE sectoral outputs.
  - Carbon prices.
  - Other shocks (for example, shocks to interest rates).
- Example mechanism:
  - Changes to sales revenue for each scenario affect EBIT, which affects projections of the ICR ratio, thereby linking sectoral transition scenarios to firm default risks structurally.

### From firm-level PDs to sectoral and bank-level PDs
- The bridge equation generates scenario-dependent PD paths for each firm; these are aggregated into exposure-weighted sectoral PD paths.
- Data limitations:
  - Only aggregated credit exposures by broad economic sectors were available, preventing mapping of bank exposures to individual firms.
  - This required constructing exposure-weighted projections of sectoral PDs for each scenario.
- Bank-level delta PD computation:
  - Delta PD for each sector = projected PD in each year from 2022 to 2026 minus starting PD in 2021.
  - For each bank, sector delta PDs over the projection horizon were weighted by the bank’s credit exposures to that sector.
  - Sectoral credit exposures were assumed constant at the starting point.
  - Five possible paths through 2026 are effectively constructed under the binomial-tree delayed-uncertain setup (as depicted in the analysis).

### Banking capital impact methodology and key assumptions
- Calculation of changes to bank capital:
  - Simplified approach considering only the impact from expected credit losses under a static balance sheet assumption.
  - Risk-weighted assets (RWAs) were held constant at the starting value.
  - A common loss given default (LGD) value was used across all banks due to absence of sector- and bank-specific LGD rates.
  - Tax and dividend payout impact was ignored.
  - Result: estimates of impact on bank capital ratios driven solely by loan impairment charges.
- Empirical LGD note:
  - The system average corporate portfolio implied the LGD from the coverage ratios of non-performing corporate exposures was found to be 53 percent.

### Transition scenarios explored
- Two main classes of climate policy scenarios:
  - (i) global action — an orderly transition analogous to the NGFS “below 2 degrees” scenario.
  - (ii) delayed-uncertain — a disorderly transition analogous to the NGFS “delayed transition” scenario, augmented with a jump-diffusion stochastic financial modeling layer of corporate spreads.
- Global action scenario features:
  - Global mitigation effort to limit warming to below 2°C with early and gradual policy implementation.
  - Carbon price floors by 2030:
    - $25 tCO2e for low-income countries,
    - $50 tCO2e for middle-income countries,
    - $75 for high-income countries.
  - International burden sharing implies Mexico faces significantly lower carbon prices relative to some high-income countries because Mexico is a middle-income country.
- Delayed-uncertain scenario features:
  - No global action in 2022 and uncertainty about timing of future action.
  - Binomial-tree construction where, at each year (2023, 2024, 2025, 2026), the world may branch into action or continued delay, producing multiple possible states and enabling distributional and tail-risk analysis.

### CGE model outputs and sectoral impacts (Mexico)
- Sectoral impacts under global action (examples):
  - Chemicals sector (a sub-segment of manufacturing): decline in level of output of about 10 percent.
  - Fossil fuel sector (dominated by extractive/mining segments such as oil, gas, and coal): decline of 12 percent.
  - Non-metallic, transportation services, and utilities sectors see notable impact.
  - Some sectors, such as transportation equipment, are positively impacted by 2030.
- Differential impact under delayed action:
  - Example: chemicals sector impact more than doubles from 10 percent (global action) to 23 percent by 2030 if global action is delayed to 2025/26.
  - Longer delays imply increasingly severe negative impacts for vulnerable sectors (e.g., fossil fuel, transportation services), implying stronger future mitigation measures and greater potential risks to the financial sector compared with orderly early action.

### Jump-diffusion model of corporate spreads (overview)
- Corporate spread dynamics are modeled by a mean-reverting jump-diffusion stochastic differential equation with the following components and properties as used in the analysis:
  - Dynamics: dr_t = κ(μ − r_t + s_t) dt + σ sqrt(r_t) dW_t + dJ_t.
  - Parameters and terms:
    - κ > 0 is the rate of mean-reversion.
    - μ > 0 is the long-run mean.
    - σ > 0 is the volatility parameter.
    - W_t is a standard Brownian motion.
    - J_t is a pure jump process with intensity and jump-size distribution.
    - The Feller condition 2κμ ≥ σ^2 is assumed to ensure non-negativity of spreads.
    - The square-root volatility term σ sqrt(r_t) yields higher effective volatility when spreads are higher.
  - A scaling factor s_t is constructed from sectoral outputs to map climate risk impacts into corporate spread evolution.

*Source: IMF staff (wpiea2023175-print-pdf).*

### Appendix I for more details).

### wpiea2023175-print-pdf - Appendix I for more details)

### Stochastic financial model (jump-diffusion / Cox-Ingersoll-Ross)
- Model described: Cox-Ingersoll-Ross (square root process with jumps), an affine jump-diffusion.
- Role of model components:
  - Diffusion term: captures continuously changing smooth risks.
  - Jump term: captures large/sudden and discontinuous shocks (examples: global financial crisis, the COVID-19 crisis, the Russia-Ukraine conflict).
  - Square-root amplification: the square root term 흈흈 � 풓풓 풕풕 increases spread volatility after large jumps.
- Literature pointers (for technical details in source): Duffie et al. (2000), Lando (2004), Cont and Tankov (2004), Jarrow (2018).
- Feller condition used in sensitivity: ퟐퟐ휿휿흁흁 ≥ 흈흈ퟐퟐ (used to obtain the lower bound of mean reversion parameter 휅휅).

### Simulation and calibration approach
- Target variable: corporate spreads (aggregate corporate bond spreads index) for Mexican financial markets.
- Calibration choice: Corporate Emerging Markets Bond Index (CEMBI) used as representative aggregate corporate bond spreads index.
- Monte Carlo simulation setup:
  - Number of simulated paths: 20,000 paths.
  - Frequency: daily.
  - Horizon: till end-2026.
  - Output: full time-varying distribution of spreads at each future time slice.
- Rationale for focus on spreads: practical constraints—most firms lack liquid corporate bond or CDS market data and coherent Mexico-specific segment indexes; individual firm calibration possible if data permits.

### Mapping to micro-macro framework and firm balance sheets
- Corporate spreads are mapped into micro-simulation of firms’ balance sheet and P&L items as time-varying interest rates to capture effects from debt capital markets.
- After the jump at end-2022 (driven by lingering policy uncertainty), corporate cost of debt capital changes and is reflected in simulations (Appendix I contains implementation details).

### Heterogeneous sectoral and firm impacts
- Key heterogeneities affecting outcomes:
  - Diverse initial risk characteristics and financial health of firms across sectors.
  - Heterogeneous sectoral impacts from the CGE model mapping into firms’ sales revenues and vulnerability indicators.
  - Different sensitivity coefficients (betas) in the bridge equation projecting climate scenario-dependent PD paths.
  - Diverse credit exposures of banking system across sectors.
- Notable sectoral PD impacts under the global action scenario:
  - Chemicals sector and non-metallic sector: difference between maximum PDs in the global action scenario and the average in the baseline reaches almost 10 percent.
  - Construction sector: deviation in PDs around 0.65 percent.
  - Mining and transportation: deviations also described as notable.
- Explanation: Some low-emission sectors with weak initial solvency/liquidity (for example low interest coverage ratio, low current ratio) can be highly sensitive to small shocks, producing asymmetric vulnerability results.

### Banking-sector effects under global action
- Delta PDs (exposure-weighted) across banks:
  - For some banks delta PDs reach almost 1 percent.
  - System-wide delta PD rises to above 0.7 percent by 2026.
- Bank capital impacts under static balance sheet assumption:
  - Cumulative impact on bank capital due to expected credit losses: about 0.35 percent.
  - Diversification: about 37 percent of the banking sector portfolio belongs to the vulnerable sectors, but diversified exposures contain the system-wide capital impact.

### Delayed-uncertain pathways: distributions and tail risks
- Core feature: risk metrics (sectoral PDs and bank capital impacts) are characterized by time-varying distributions rather than single deterministic deviations.
- Comparative distributional outcomes:
  - Corporate PDs:
    - Acting in year 2023: maximum possible credit risk around 3 percent.
    - Delayed to 2026: risk could increase to as high as 14 percent.
    - Support of PD distribution increases by more than four times under climate action in 2026 relative to acting in 2023.
  - Bank delta PDs (exposure-weighted):
    - Early action in 2023: maximum delta PD across banks around 0.2 percent.
    - Delayed till 2026: delta PDs could rise as high as 1.5 percent (more than seven-fold rise in maximum tail risk).
  - Bank capital ratios:
    - Absolute impacts appear modest (determined by expected credit losses under static balance sheet), but relative increases are large:
      - Maximum range of the distribution increases by almost five times if actions delayed till 2026 versus 2023.
      - Cumulative bank capital impact under delayed-uncertain path could reach as high as 0.8 percent with non-trivial probability.
      - Maximum impact under global action: around 0.3 percent.
- Mechanisms increasing tail mass:
  - Jumps increase frequency of tail shocks (example in source: same 500 basis points shock observed 1 percent of the time without jumps could be observed 5 percent of the time with jumps).
  - Square root diffusion term increases effective volatility after jumps, further increasing tail mass.

### Sensitivity analysis: slow mean reversion scenario
- Mean reversion parameter 휅휅 governs speed at which spreads revert to long-run level; smaller 휅휅 = slower reversion.
- Sensitivity test: set mean reversion parameter as small as possible using Feller condition ퟐퟐ휿휿흁흁 ≥ 흈흈ퟐퟐ to explore highly persistent elevated spreads.
- Findings:
  - Time-varying distributions of corporate PDs shift further to the right with longer delays.
  - Tail mass increase is more pronounced than in the baseline jump-diffusion calibration.

### Conclusions and policy implications
- Framework contribution:
  - Integrated micro-macro framework with delayed-uncertain pathways augmented by a jump-diffusion stochastic financial layer.
  - Allows quantification of time-varying distributions of future risk metrics and tail risks.
- Main insight:
  - Delays in transition combined with future policy uncertainty increase future tail risks to financial stability.
  - The longer climate actions are delayed, the larger the future actions may have to be to achieve the same climate goals.
- Application to Mexico:
  - Global action scenario found relatively modest effects overall.
  - Delayed-uncertain pathways revealed potential for significant risks, with chemicals and non-metallic segments appearing most vulnerable.
  - Despite data limitations and coverage of limited channels, pockets of corporate-sector vulnerability were identified.
- Policy recommendation:
  - Early transition to a low-carbon economy mitigates the tail risk of larger future actions and reduces financial stability tail risks.
  - Continued vigilance at the global level is required because tail risks become larger the longer the delay in transition.
- Scalability:
  - Framework is flexible and can be scaled up and adapted with more granular firm-level data to explore additional channels and spillovers.

*Source: IMF staff calculations and associated material in the provided content unit.*

### Appendix I . Mapping CGE Model Sectors to Corporate Sectors

### Appendix I . Mapping CGE Model Sectors to Corporate Sectors and NAICS Sector Classification

### Sector mapping between the CGE model, corporate SIC grouping, and two-digit NAICS
- Corporate data were grouped by SIC codes and aggregated where necessary to match CGE model sectors given small firm sample size and four-digit SIC code affiliations.
- Aggregated sector mappings used to translate sectoral PD paths into impacts on bank credit exposures via NAICS codes:
  - Fossil fuel / Mining incl. oil & gas → Mining, 21
  - Utilities → Utilities, 22
  - Construction → Construction, 23
  - Food & Textiles and Pulp & Paper Manuf. Other → Manufacturing, 31
  - Chemicals and Non-Metallic → Chemicals & Non-Metallic Minerals Manufacturing, 32
  - Iron-steel and Transp. eqpmt. → Metals & Related Manufacturing, 33
  - Transportation svcs. → Transportation, 48

### Projection of corporate variables and vulnerability indicators (formulae and accounting relations)
- Interest Coverage Ratio (ICR):
  - 퐸퐸퐶퐶푅푅
    푡푡
    = 퐸퐸퐸퐸퐸퐸 푇푇
    푡푡
    퐸퐸퐶퐶푙푙푆푆퐶퐶푆푆푠푠푙푙 퐸퐸푥푥 퐸퐸푆푆퐶퐶푠푠  푆푆
    푡푡
    ⁄
- Evolution of components (as presented in source):
  - 퐸퐸퐶퐶푙푙푆푆퐶퐶푆푆푠푠푙푙 푆푆푥푥퐸퐸푆푆퐶퐶푠푠푆푆
    푡푡
    = 푅푅
    푡푡−1
    ∗ 푇푇퐶퐶푙푙푆푆푆푆 푑푑푆푆퐶퐶푙푙
    푡푡−1
  - 퐶퐶푆푆퐶퐶퐶퐶퐶퐶퐶퐶 푇푇푆푆 푥푥
    푡푡
    = 퐸퐸퐸퐸푙푙푠푠푠푠푙푙퐶퐶퐶퐶푠푠
    푡푡
    ∗ 퐶퐶푆푆퐶퐶퐶퐶퐶퐶퐶퐶 푃푃퐶퐶푙푙푃푃 푆푆
    푡푡
- Leverage Ratio (LR) and Cash and Equivalents (CE):
  - 퐿퐿푅푅
    푡푡
    = 푇푇퐶퐶푙푙푆푆푆푆 퐷퐷푆푆퐶퐶푙푙
    푡푡
    / 푇푇퐶퐶푙푙푆푆푆푆 퐴퐴푠푠푠푠푆푆푙푙푠푠
    푡푡
  - 퐶퐶퐸퐸
    푡푡
    =  max (0, 퐶퐶퐸퐸
    푡푡−1
    + 퐸퐸퐸퐸퐸퐸푇푇
    푡푡
    − 퐶퐶푆푆퐶퐶퐶퐶퐶퐶퐶퐶 푇푇푆푆푥푥
    푡푡
    − 퐸퐸퐶퐶푙푙푆푆퐶퐶푆푆푠푠푙푙 퐸퐸푥푥 퐸퐸푆푆퐶퐶푠푠푆푆
    푡푡
    )
  - 푇푇퐶퐶푙푙푆푆푆푆 퐷퐷푆푆퐶퐶푙푙
    푡푡
    = 푇푇퐶퐶푙푙푆푆푆푆 퐷퐷푆푆퐶퐶푙푙
    푡푡−1
    − min (0, 퐶퐶퐸퐸
    푡푡−1
    + 퐸퐸퐸퐸퐸퐸푇푇
    푡푡
    − 퐶퐶푆푆퐶퐶퐶퐶퐶퐶퐶퐶 푇푇푆푆푥푥
    푡푡
    − 퐸퐸퐶퐶푙푙푆푆퐶퐶푆푆푠푠푙푙 퐸퐸푥푥 퐸퐸푆푆퐶퐶푠푠푆푆
    푡푡
    )
  - 푇푇퐶퐶푙푙푆푆푆푆 퐴퐴푠푠푠푠푆푆푙푙푠푠
    푡푡
    =  푇푇퐶퐶푙푙푆푆푆푆 퐴퐴푠푠푠푠푆푆푙푙푠푠
    푡푡−1
    + 퐶퐶퐸퐸
    푡푡
    − 퐶퐶퐸퐸
    푡푡−1
- Current Ratio (CR):
  - 퐶퐶푅푅
    푡푡
    = 퐶퐶퐶퐶퐶퐶퐶퐶  푆푆퐶퐶푙푙 퐴퐴푠푠푠푠푆푆푙푙 푠푠
    푡푡
    퐶퐶퐶퐶퐶퐶퐶퐶  푆푆퐶퐶푙푙 퐿퐿푙푙푆푆퐶퐶𝑙𝑙𝑆푆𝑙𝑙𝑙𝑙𝑙𝑙𝑆푆   푠푠
    푡푡
    ⁄
  - 퐶퐶퐶퐶퐶퐶퐶퐶  푆푆퐶퐶푙푙 퐴퐴푠푠푠푠푆푆푙푙푠푠
    푡푡
    = 퐶퐶퐶퐶퐶퐶퐶퐶  푆푆퐶퐶푙푙 퐴퐴푠푠푠푠푆푆푙푙푠푠
    푡푡−1
    − 퐶퐶퐸퐸
    푡푡
    − 퐶퐶퐸퐸
    푡푡−1
  - 퐶퐶퐶퐶퐶퐶퐶퐶  푆푆퐶퐶푙푙 퐿퐿푙푙푆푆퐶퐶𝑙𝑙𝑆푆𝑙𝑙𝑙𝑙𝑙𝑙𝑆푆𝑠푠
    푡푡
    = 퐶퐶퐶퐶퐶퐶퐶퐶  푆푆퐶퐶푙푙 퐿퐿푙푙푆푆퐶퐶𝑙𝑙𝑆푆𝑙𝑙𝑙𝑙𝑙𝑙𝑆푆𝑠푠
    푡푡−1
    − min
    (
    0, 퐶퐶퐸퐸
    푡푡−1
    + 퐸퐸퐸퐸퐸퐸푇푇
    푡푡
    − 퐶퐶푆푆퐶퐶퐶퐶퐶퐶퐶퐶 푙푙푆푆𝑥𝑥
    푡푡
    − 퐸퐸퐶퐶𝑙𝑙푆푆퐶퐶𝑆푆𝑠𝑠𝑙𝑙 푆푆𝑥𝑥퐸퐸푆푆퐶퐶𝑠𝑠𝑆푆
    푡푡
    )
    ∗ (1/2)
- Note: Accounting identities based on a similar set of relations between corporate variables, as in Chile FSAP (2021).

### Panel regression estimation of firm-level default risk (Table A3)
- Data sources: Moody’s EDF, DataStream, Capital IQ, and IMF staff calculations.
- Regression specification: dependent variable logit(PD)
- Coefficients and reported t-values (in parentheses):
  - Interest Coverage Ratio: -0.002 (-4.366)
  - Current Ratio: -0.255 (-4.166)
  - Leverage Ratio: 2.10 (3.871)
- Additional regression statistics:
  - Firm-Level Fixed Effects: Yes
  - R-squared: 0.54
  - Observations: 762
- Note: t-values are reported in parentheses. Intercept is set to equal to the average of fixed effects across firms, because firms that are used in the projections are a subset of the firms used in the panel regression.

### Mapping stochastic model outputs to the micro-macro framework and construction of delayed-uncertain pathways
- Key assumption for delayed-uncertain analysis:
  - No action by end-2022 leads corporate bond markets to sharply react, with a single jump at end-2022 calibrated to shocks seen during past crises.
  - Jump size magnitude is set equal to the 99th percentile of rolling two-year changes in the corporate spread.
  - Historical example cited: spreads increased from around 2 percent to almost 12 percent during the 2007-2009 global financial crisis.
- Rationale and conservatism:
  - The analysis emphasizes heightened and persistent uncertainty following large shocks rather than only the initial jump magnitude.
  - Large jump increases effective volatility due to the square root process (reference to Box 1 and historical rolling six-month volatility in Figure 8).
  - Random jumps before or after 2022 could be allowed but are not necessary for this simplified analysis.
- Constructing increasingly higher funding cost pathways:
  - For the delayed-2023 path: use the average across all possible paths between each time slice (vertical lines between years in Figure 8, bottom panel).
  - For the delayed-2024 path: use the 75th percentile.
  - For the delayed-2025 path: use the 90th percentile.
  - For the delayed-2026 path: use the 95th percentile.
  - From each sequence, subtract the initial value of the corporate spread to obtain constructed time-varying spreads mapped into uncertain pathways (Figure 6) as shocks to interest rates in the firm-level micro-simulations.
- Scaling factor linking sectoral outputs to corporate spreads:
  - The scaling factor in Box 1 is a random variable: a uniform random variable between zero and the weighted average of sectoral outputs as deviations from the baseline by 2030 (as in Figure 5).
  - The range of the uniform distribution is multiplied by the elasticity of corporate spreads to changes in aggregate output in Mexico, which was about 0.30 percent.
  - Interpretation: the random scaling factor maps macro randomness induced by uncertain policy pathways into effects on corporate spreads; the jump term captures a one-time large shock from sudden rise in macro policy uncertainty.
- Practical tradeoffs and flexibility:
  - The CGE model is not run stochastically; the uniform distribution is the simplest assumption consistent with multiple delayed-uncertain pathways (Figure 6).
  - The financial model delivers full distributions at each day into the five-year horizon (Figure 8), enabling experimentation with different parts of the distribution; the present analysis uses the average, 75th, 90th, and 95th percentiles to highlight increasing draws from the tail.

*Source: Appendix I . Mapping CGE Model Sectors to Corporate Sectors and NAICS Sector Classification (from wpiea2023175-print-pdf).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023175-print-pdf.pdf_