## 2.1  The Neoclassical Investment Model: Capital Adjustment Costs

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### Model setup and assumptions
- Firm objective:
  - Representative oil and gas firm maximizes V0 = ∑∞_{t=0} β^{t} [p_{t} y_{t} − I_{t} (1+τ_{p,t})] choosing {I_{t}, k_{t}}.
- Technology and accumulation:
  - Production function: y_{t} = A_{t} k_{t−1}^{α}.
  - Capital accumulation: k_{t} = (1−δ) k_{t−1} + I_{t} − Φ(I_{t}/k_{t−1}) k_{t−1}.
  - Adjustment costs: Φ(x_{t}) = 0.5 φ (x_{t} − δ)^{2}, where δ is the depreciation rate.
  - Relative price of investment normalized to 1.
- Climate policy instruments:
  - τ_{c,t}: carbon tax announced along a path and implemented at t_{0}, enters demand via the cum-tax price (1+τ_{c,t}) p_{t}.
  - τ_{p,t}: investment tax that increases the relative price of investment in oil and gas.
- Demand closure:
  - Iso-elastic demand: y_{t} = [(1+τ_{c,t}) p_{t}]^{−η}.
- Key modelling choices:
  - Capital k is the sole factor of production; reserves are not depleted, so production features diminishing returns to capital (captures large/unconventional reserves and the extensive margin of production).

### First-order conditions and equilibrium conditions
- First-order condition for I_{t} (from ∂L/∂I_{t}=0):
  - α p_{t+1} A_{t+1} k_{t}^{α−1} + λ_{t+1} [1−δ−Φ_{t+1} + Φ'_{t+1} I_{t+1}/k_{t}] = λ_{t}/β.
- First-order condition for k_{t} (from ∂L/∂k_{t}=0):
  - 1+τ_{p,t} = λ_{t} (1−Φ'_{t}).
- Market clearing / demand-supply equilibrium (assuming no change in inventories):
  - y_{t} = [(1+τ_{c,t}) p_{t}]^{−η}.

### Illustrative scenario: delayed permanent carbon tax (qualitative dynamics)
- Scenario specification:
  - Permanent 25 percent carbon tax announced at time 0 and implemented with certainty after 5 years.
- Reported qualitative dynamic responses:
  - On impact, Tobin’s Q (value of installed capital) drops as expected future demand is lower.
  - Investment declines immediately as firms anticipate transition costs to a lower capital stock.
  - Due to adjustment costs, investment does not immediately fall to the new steady state after tax implementation but slowly converges toward it.
  - Prior to year 5 (pre-implementation delay), existing capital retains value; reducing capital too quickly is inefficient.
  - Production declines slowly as capital erodes (depreciation outweighs investment).
  - In the initial transition phase, as production declines, prices increase, but prices fall once the carbon tax is implemented.
  - Firms’ profits py − (1+τ_{p}) I increase initially, while market valuations V_{0} decline.
- Comparative policy note:
  - An increase in taxes on fossil fuel investment (capturing a higher cost of capital for oil and gas companies) yields a similar cut in investment and increase in energy prices, even though firms’ profits would decline.

### Numerical solution and parameterization used for charts
- Parameter values used:
  - A = 1; α = 0.85; δ = 0.07; φ = 8; β = 0.96; c_{0} = 1; and η = 0.7.
- Adjustment cost functional form reiterated:
  - Φ(x_{t}) = 0.5 φ (x_{t} − δ)^{2}.
- Solution method:
  - Transition path computed by numerically solving the system of difference equations given by equations (1) to (5) for y, k, p, I, and λ starting from a zero tax steady state, with tax policies fed as exogenous processes.

*Source: IMF Working Paper chapter "2.1 The Neoclassical Investment Model: Capital Adjustment Costs" (wpiea2023140-print-pdf).*

### 2.1  The Neoclassical Investment Model: Capital Adjustment Costs

### 2.1  The Neoclassical Investment Model: Capital Adjustment Costs

### Model setup and assumptions
- Representative oil and gas firm maximizes V0 = ∑∞_{t=0} β^{t} [p_{t} y_{t} − I_{t} (1+τ_{p,t})] choosing {I_{t}, k_{t}}.
- Production function: y_{t} = A_{t} k_{t−1}^{α}.
- Capital accumulation: k_{t} = (1−δ) k_{t−1} + I_{t} − Φ(I_{t}/k_{t−1}) k_{t−1}.
- Adjustment costs specified as Φ(x_{t}) = 0.5 φ (x_{t} − δ)^{2}, where δ is the depreciation rate.
- Relative price of investment normalized to 1.
- Climate policy instruments:
  - τ_{c,t}: carbon tax announced along a path and implemented at t_{0}, enters demand via the cum-tax price (1+τ_{c,t}) p_{t}.
  - τ_{p,t}: investment tax that increases the relative price of investment in oil and gas.
- Demand (iso-elastic) closed by y_{t} = [(1+τ_{c,t}) p_{t}]^{−η}.
- Key modelling choices: capital k is sole factor of production; reserves not depleted (production features diminishing returns to capital), capturing large/unconventional reserves and the extensive margin of production.

### First-order conditions and equilibrium conditions
- First-order condition with respect to I_{t} (from ∂L/∂I_{t}=0):
  α p_{t+1} A_{t+1} k_{t}^{α−1} + λ_{t+1} [1−δ−Φ_{t+1} + Φ'_{t+1} I_{t+1}/k_{t}] = λ_{t}/β.
- First-order condition with respect to k_{t} (from ∂L/∂k_{t}=0):
  1+τ_{p,t} = λ_{t} (1−Φ'_{t}).
- Market clearing / demand-supply equilibrium (assuming no change in inventories): y_{t} = [(1+τ_{c,t}) p_{t}]^{−η}.

### Illustrative scenario: delayed permanent carbon tax
- Scenario: permanent 25 percent carbon tax announced at time 0 and implemented with certainty after 5 years.
- Qualitative dynamic responses reported:
  - On impact, Tobin’s Q (value of installed capital) drops as expected future demand is lower.
  - Investment declines immediately as firms anticipate transition costs to a lower capital stock.
  - Due to adjustment costs, investment does not immediately fall to the new steady state after tax implementation but slowly converges toward it.
  - Prior to year 5 (pre-implementation delay), existing capital retains value; reducing capital too quickly is inefficient.
  - Production declines slowly as capital erodes (depreciation outweighs investment).
  - In the initial transition phase, as production declines, prices increase, but prices fall once the carbon tax is implemented.
  - Firms’ profits py − (1+τ_{p}) I increase initially, while market valuations V_{0} decline.
- Comparative policy note:
  - An increase in taxes on fossil fuel investment (capturing a higher cost of capital for oil and gas companies) yields a similar cut in investment and increase in energy prices, even though firms’ profits would decline. Results available upon request to the authors.

### Numerical solution and parameterization used for charts
- Parameter values used: A = 1; α = 0.85; δ = 0.07; φ = 8; β = 0.96; c_{0} = 1; and η = 0.7.
- Adjustment cost functional form reiterated: Φ(x_{t}) = 0.5 φ (x_{t} − δ)^{2}.
- Transition path computed by numerically solving the system of difference equations given by equations (1) to (5) for y, k, p, I, and λ starting from a zero tax steady state, with tax policies fed as exogenous processes.

*Source: IMF Working Paper chapter "2.1 The Neoclassical Investment Model: Capital Adjustment Costs" (wpiea2023140-print-pdf).*

### 3.3  Estimation Sample

### 3.3  Estimation Sample

### Estimation sample and period
- Estimation sample: around 9200 firm-year observations.
- Estimation period: 2012-2019.
- Unbalanced panel composition (by year): between 73 and 117 energy firms and between 940 and 1500 non-energy firms.
- Oil and gas firms in the sample represent 40% of total capex and production in global oil and gas upstream industry and are distributed as:
  - North America (79), Europe (18), Australia and New Zealand (6), Asia (5), Latin-America (5), Middle East and North Africa (2), SSA (2).
- Compustat does not break down firm investment into brown vs green activities; authors note available evidence suggests fossil fuel firms remain predominantly focused on oil and gas activities.

### Descriptive dynamics (figures and patterns)
- Two notable features in the outcome and regressors:
  - Fall in fossil fuel investment between 2014 and 2016.
  - Slower recovery of fossil fuel investment relative to the rest of the economy in subsequent years.
- Possible drivers:
  - Ample oil supply following the shale gas revolution (and perhaps anticipation associated with the signing of the Paris Agreement) for the 2014–2016 fall.
  - Strengthening climate policies that affected the two groups differently for the slower recovery after 2015.
- Climate policy measures:
  - The market-based component of the Environmental Protection Score that captures carbon taxes and cap-and-trade schemes in OECD countries increased by 29% by 2019 relative to its pre-Agreement average.
- Cross-group exposure dynamics:
  - Comparison group’s exposure to the first and second moment of climate policy shows relatively stable dynamics.
  - Exposure in the oil and gas sector is mostly above that of the rest of the economy and rises substantially after 2015.
  - Dispersion of climate policy exposure increases dramatically over time within the oil and gas sector, mostly driven by European oil and gas companies.
- Variation decomposition:
  - Between 70 and 97 percent of variation in the exposure measures plays out at the firm level.
  - Only half of this firm-level variation is persistent.

### Sample summary statistics (Table 1; pre-2015 = 2012-15, post-2015 = 2016-2019)
- Note: Standard deviations in parenthesis. Capex and total assets are in millions of USD. For industries and regions the table shows the share of firms in each category.
- Capex:
  - Non-energy pre-2015: Mean 376 (SD 948)
  - Oil and gas pre-2015: Mean 3498 (SD 6762)
  - Non-energy post-2015: Mean 342 (SD 1003)
  - Oil and gas post-2015: Mean 1791 (SD 3901)
- Altman:
  - Non-energy pre-2015: Mean 3.100 (SD 3.561)
  - Oil and gas pre-2015: Mean 1.737 (SD 1.513)
  - Non-energy post-2015: Mean 3.312 (SD 5.236)
  - Oil and gas post-2015: Mean 1.370 (SD 1.911)
- Total assets (million US $):
  - Non-energy pre-2015: Mean 8029 (SD 16044)
  - Oil and gas pre-2015: Mean 28954 (SD 65311)
  - Non-energy post-2015: Mean 7740 (SD 16518)
  - Oil and gas post-2015: Mean 22396 (SD 54392)
- Asset turnover:
  - Non-energy pre-2015: Mean 0.994 (SD 0.658)
  - Oil and gas pre-2015: Mean 0.408 (SD 0.565)
  - Non-energy post-2015: Mean 0.918 (SD 0.591)
  - Oil and gas post-2015: Mean 0.391 (SD 0.546)
- Debt-equity:
  - Non-energy pre-2015: Mean 1.685 (SD 10.72)
  - Oil and gas pre-2015: Mean 0.851 (SD 1.269)
  - Non-energy post-2015: Mean 1.464 (SD 8.142)
  - Oil and gas post-2015: Mean 1.333 (SD 3.451)
- Regional shares (sample; pre/post columns mirror each other in table formatting):
  - Europe 0.176, Asia 0.070, Latin America 0.032, North America 0.676, Sub-Saharan Africa 0.008, MENA 0.012, Oceania 0.026.
- Industry shares (comparison-group industries shown; oil & gas excluded in those rows in table formatting):
  - Manufacturing 0.547, Transport and Comm 0.182, Wholesale trade 0.049, Retail trade 0.005, Services 0.186.

### Authors’ interpretation of summary statistics
- Oil and gas companies have higher total assets reflecting larger average firm size and higher capital intensity.
- Financial capital structure differences:
  - Before 2015, oil and gas firms were considerably less indebted.
  - Post-2015, the two groups appear to have a similar financing mix as oil and gas firms increased their debt capital over time.
- Non-energy firms show better financial health on average (higher Altman score).
- Asset turnover is higher among non-energy firms, indicating greater efficiency in generating revenues from assets.

---

### 4  Empirical Strategy

### Difference-in-difference (DiD) baseline (equation 9)
- Identification: use signing of the Paris Agreement as regime change; compare before-after change in investments for oil and gas firms (treatment) vs non-energy firms (control).
- Baseline specification (notation from text):
  - y_it = β0 D_i + β1 T_t + (β2 P_oil,t + β3 T_t) D_i + β4 X_it + λ_s + λ_r + λ_rt + ε_it
  - y_it: log capital expenditure for firm i in year t.
  - D_i: treatment dummy (1 for oil and gas firms, 0 otherwise).
  - T_t: post-2015 period dummy.
  - X_it: controls include constant, log total assets, debt to equity ratio, asset turnover, Altman score.
  - P_oil,t: log oil prices (interacted with group dummy).
  - λ_s, λ_r, λ_rt: industry fixed effects, region fixed effects, region-specific time fixed effects.
- Identification concerns:
  - Anticipatory effects: possible but authors argue bias would be upward toward zero.
  - Parallel trends: concern because time-varying macro factors (e.g., shale-induced oil price slump 2014–2016) may differentially affect groups.
  - Spot oil prices may not capture changes in long-dated oil price expectations; omission could bias ˆβ3.
- Authors’ view: OLS estimate of β3 identifies economically meaningful treatment effect under parallel trends and no anticipatory effects assumptions, but caution that β3 may be upward biased if other unobserved factors widened the cross-group investment gap after 2015.

### Richer preferred specification exploiting firm-level heterogeneity (equation 10)
- Move from sector-time comparison to firm-specific exposure to climate policy:
  - y_it = β0 D_i + β1 C_t + β2 C_t D_i + β3 X_it + β4 R_it + β5 D_i R_it + λ_s + λ_r + λ_rt + ε_it
  - R_it: text-based measures (exposure to climate policy or to climate policy uncertainty).
  - C_t: full set of year dummies; C_t D_i captures group×year fixed effects.
  - β4 + β5 captures the differential impact on fossil fuel investment.
- Advantages:
  - Group×year effects capture business cycle factors that may affect groups differently (including oil prices).
  - Comprehensive fixed effects help reduce omitted-variable bias and initial endogeneity concerns about R_it.
- Potential remaining concern:
  - Greenwashing—firms talking about climate policy to justify unrelated cuts—authors cite literature indicating analysts often initiate climate topics and that evidence for systemic greenwashing is limited.

---

### 5  Results

### Baseline DiD findings (equation 9; Table 2)
- After the Paris Agreement, capital expenditure of a typical oil and gas company was 22.6 percent lower than the control group (authors’ calculation: e^{ˆβ3}−1 = −0.226).
- Effect of oil prices:
  - Halving oil prices (as happened between 2014 and 2015) implies a 20 percent fall in investment by oil and gas firms vis-à-vis non-energy firms.
- Selected coefficient estimates from Table 2:
  - D_i×T_t: -0.256*** (standard error 0.091)
  - D_i×P_oil,t: 0.326** (standard error 0.141)
  - Log Total Assets: 0.998*** (standard error 0.006)
  - Log Asset Turnover: 0.221*** (standard error 0.027)
  - R^2 = 0.83, N = 9174.
- Authors’ caveat: DiD estimates may be upward biased because they cannot fully disentangle effects of climate policies and the shale revolution on long-term industry prospects; move to richer specification for more credible inference.

### Effects of firm-level climate policy exposure and uncertainty (equation 10; Table 4)
- Text-based measures: R_1it = climate policy exposure (first moment), R_2it = climate policy uncertainty (second moment).
- Core coefficient estimates (Table 4 columns 1–3):
  - D_i: positive and significant (e.g., 1.083*** in column 1).
  - D_i × R_1it: -0.078*** (standard error 0.020) in column 1.
  - R_1it: 0.049*** (standard error 0.014) in column 1.
  - D_i × R_2it: -0.064*** (standard error 0.019) in column 2.
  - R_2it: 0.023*** (standard error 0.007) in column 2.
  - Column 3 includes interactions D_i × R_1it × R_2it: -0.002*** (standard error 0.001).
  - R^2 ≈ 0.82–0.83, N = 9174.
- Magnitude interpretation:
  - A 1 standard deviation increase in climate policy exposure leads to a 3 percent fall in investment in the oil and gas sector (calculated as 0.078 − 0.049 = 0.029 ≈ 3 percent).
  - Climate policy uncertainty shock reduces investment by around 4 percent (calculated as 0.023 − 0.064 = -0.041 ≈ -4 percent).
  - In the control group, investment increases by 4.9 percent associated with climate policy exposure (main effect of R_1it = 0.049).
- Distributional example:
  - Moving from the median to the 95th percentile of climate policy exposure implies an approximate 6 percent fall in investment: (0.078 − 0.049) × (2.42 − 0.24).
- Aggregate industry effect:
  - Authors estimate upstream oil and gas investment fell by 6.5 percent in the post-2015 period as a result of strengthening climate policies (calculation: aggregate of firm-level implied changes divided by total industry investment in 2015).
  - Repeating the exercise for change in climate policy exposure over 2015-2021 yields an even larger reduction in investment of 12.7 percent.
- Interaction findings:
  - Climate policy uncertainty has a stronger negative effect conditional on higher climate policy exposure; reverse interaction is not as strong.

### Mechanisms (authors’ hypotheses supported by results)
- Two main channels consistent with the Neoclassical investment model:
  1. Expectation channel: future demand-side climate policies aimed at curbing demand for carbon reduce expected returns on oil and gas investment.
  2. Supply channel: Paris Agreement may increase costliness of current oil and gas investment (higher cost of capital for oil and gas firms or stricter climate regulatory stance, e.g., tougher methane emissions regulation), and push investors to factor environmental concerns into decisions.

*Italic source: wpiea2023140-print-pdf - 3.3  Estimation Sample*

### 10.  In column 3, we add

### 10.  In column 3, we add

### Model specification and interaction terms
- The regression augments equation 10 by adding an interaction of the two text-based measures (R1it, R2it) among each other and of these two with the group dummy (Di = 1 for oil and gas firms and 0 otherwise).
- Di = 1 for oil and gas firms and 0 otherwise.
- Rit represents climate policy in column 1 and climate policy uncertainty in column 2.
- The augmented specification for testing post-2015 (Paris Agreement) momentum:
  - yit = β0 Di + β1 Ct + β2 Ct Di + β3 Xit + β4 Rit + β5 Di Rit + β6 Tt Rit + β7 Tt Di Rit + λs + λr + λrt + ǫit (equation 11)
  - Tt = 1[t>2015].

### Sensitivity analysis and instrumental-variables evidence
- Two-stage least squares (2SLS) is estimated for equation 10 using internal instruments constructed as lagged values: {Ri,t−1, Ri,t−2} and {Di Ri,t−1, Di Ri,t−2}.
- Identification assumption: past climate policy exposure affects current investment only via current exposure.
- Hansen’s J statistic p value = 0.97 for the first moment of climate policy exposure (over-identification test could not reject exogeneity of instruments).
- Instruments are sufficiently strong predictors of current exposure for the first moment; 2SLS estimates of β4 + β5 remain negative, statistically significant and similar in magnitude to OLS.
- For climate policy uncertainty (second moment) the instrument passes over-identifying restrictions (p value = 0.82) but is only weakly correlated with current levels of climate policy uncertainty; this weak relevance inflates β4 and β5 while their sum is similar to OLS.
- Selected coefficients and diagnostics from Table 5 (2SLS estimates of equation 10):
  - Di: 1.908*** (0.095) in column (1); 1.878*** (0.098) in column (2).
  - Di × Rit: -0.108*** (0.041) in column (1); -0.452 (0.300) in column (2).
  - Rit: 0.080** (0.038) in column (1); 0.476 (0.295) in column (2).
  - Altman: -0.003* (0.002) in column (1); -0.002 (0.002) in column (2).
  - Log Total Assets: 1.007*** (0.007) in both columns.
  - Log Asset Turnover: 0.229*** (0.030) in column (1); 0.224*** (0.030) in column (2).
  - Debt-Equity: 0.001 (0.001) in column (1); 0.000 (0.001) in column (2).
  - R2: 0.84 in column (1); 0.83 in column (2).
  - Over-identification test: 0.03 (0.97) in column (1); 0.39 (0.82) in column (2).
  - Di (weak identification) F-statistic: 28.06 (0.000) in column (1); 1.24 (0.291) in column (2).
  - Di × Rit (weak identification) F-statistic: 5.81 (0.000) in column (1); 0.72 (0.58) in column (2).
  - N: 6956 in column (1); 6956 in column (2).
- Note: ***, **, * denote p<0.01, p<0.05, p<0.1 respectively (as in table note).

### Effects over time and the Paris Agreement (post-2015)
- Table 6 reports estimates from equation 10 augmented with interactions Tt × Rit and Di × Tt × Rit.
- Key coefficients and estimates from Table 6:
  - Di: 1.122*** (0.145) in column (1); 1.034*** (0.145) in column (2).
  - Di × Rit: -0.124*** (0.047) in column (1); 0.027 (0.029) in column (2).
  - Rit: 0.021 (0.022) in column (1); 0.020*** (0.006) in column (2).
  - Tt × Rit: 0.047* (0.027) in column (1); 0.010 (0.018) in column (2).
  - Di × Tt × Rit: 0.035 (0.051) in column (1); -0.111*** (0.040) in column (2).
  - Altman: -0.001 (0.002) in both columns.
  - Log Total Assets: 0.999*** (0.006) in both columns.
  - Log Asset Turnover: 0.221*** (0.027) in both columns.
  - Debt-Equity: 0.000 (0.001) in both columns.
  - R2: 0.84 in both columns.
  - N: 91,749 in column (1); 91,74? (source shows 91749174 unclear spacing) — table reports N 91749174.
- Interpretation:
  - The triple-interaction term Rit Di Tt is not statistically significant for the first moment of climate policy exposure, indicating no intensification of the investment effect after the Paris Agreement for the first moment.
  - The triple-interaction term is negative and statistically significant for the second moment (climate policy uncertainty), indicating that the effects of exposure to climate policy uncertainty intensified after the Paris Agreement.
  - Calculated effects reported:
    - The effect of uncertainty on oil and gas investment turns negative only after 2015: β4 + β5 = -0.054 se=0.021.
    - The effect is positive before the Agreement: β4 + β5 + β6 + β7 = 0.047 se=0.028.
  - Interpretation offered: firms began to more prominently factor in climate policy after the Paris Agreement, with ambiguity around impacts on future profits being a stronger driver than actual legislative changes.

### Main empirical findings and magnitudes
- A perceived increase in exposure of oil and gas firms to climate policies led to a 6.5 percent global decline of their capital expenditures between 2016 to 2019 (i.e., a -1.45 percent annual rate), after controlling for oil market tightness (i.e., spot oil prices), global factors, and standard firm-level controls.
- The investment gap is larger relative to the non-energy control group.
- Substantial within-industry heterogeneity: European oil and gas companies are affected the most.
- Extrapolation reported:
  - Climate policy exposure accounted for a cumulative 12 percent reduction in oil and gas investment between 2015 and 2021.
  - This contributed to the reduced price elasticity of supply observed during the 2021-2022 energy crisis.

### Comparison to IEA projections and interpretation
- IEA (2016) estimated that implementation of pledges up to that point (including the Paris Agreement) would result in an average annual decrease in oil and gas investments of 0.7 percent through 2040, relative to a business-as-usual scenario.
- Empirical evidence in this study suggests a larger actual contribution of climate policy exposure to divestment: compare -1.45 to -0.7.
- Interpretation: potential underinvestment as global oil and gas demand is curbed only in the more distant future.
- Economic mechanism consistent with theory:
  - Neoclassical investment theory predicts announcing a stricter path of climate policy reduces investment and increases oil and gas prices (raising free cash flow) in the initial stage.
  - Uncertainty around climate policies imposes an additional negative impact on investment, consistent with real options theory (Dixit and Pindyck (1994)).
  - Investment cuts can be rationalized as optimal responses to downward revisions of future demand to minimize stranded-asset risk.
  - Financial risks from stranded assets appear minor due to an initial period of relatively high free cash flow allowing adjustment.

### Policy implications and recommendations
- A credible commitment to a climate policy path by policymakers is vital for guiding market actors through the energy transition.
- Policy coordination between fossil fuel consumer and producer countries is required because of the international dimension of the problem.
- From the private sector perspective, clear and consistent signals by trusted authorities about the direction of climate policy and the pace of the energy transition can:
  - Help firms adjust investment plans and align expectations with low-carbon transition goals.
  - Reduce uncertainty, encourage investment in renewable energy, and incentivize appropriate levels of fossil fuel divestment.
- Key policy challenge: ensure the pace of fossil fuel phase-out is commensurate with investment in renewable energy to minimize the risk of a disorderly transition and macroeconomic shocks.
- Overly optimistic expectations about the pace of the energy transition by fossil-fuel firms coupled with negative effects of climate policy uncertainty may result in energy supply shortfalls, sustained upward pressure on fossil fuel prices, and a more volatile energy price environment.

*Source: wpiea2023140-print-pdf - 10.  In column 3, we add (canonical PDF).*

### References

### wpiea2023140-print-pdf - References

### References list (selected themes and topics)
- Empirical investment and firm dynamics: Abel and Blanchard (1986); Jorgenson (1963); Hayashi (1982); Lucas Jr (1967); Dixit and Pindyck (1994).
- Climate policy, stranded assets, and the Green Paradox: Sinn (2009); Pittel, van der Ploeg, and Withagen (2014); van der Ploeg and Rezai (Oct. 2020a; Mar. 2020b); Pless (2023).
- Climate risk pricing, financial markets, and bank lending: Bolton and Kacperczyk (2021); Delis, De Greiff, and Ongena (2019); Ehlers, Packer, and de Greiff (Mar. 2022); Fard, Javadi, and Kim (Dec. 2020); Seltzer, Starks, and Zhu (Apr. 2022).
- Oil market modeling and macro implications: Baumeister and Kilian (2016); Bornstein, Krusell, and Rebelo (2023); Golosov et al. (2014); Hotelling (1931).
- Divestment and corporate behavior toward decarbonization: Bauer et al. (2018); Egli, Schärer, and Steffen (Jan. 2022); Green et al. (2022); Sen and von Schickfus (2020).
- Text-based measures and uncertainty in climate policy: Krueger, Sautner, and Starks (Nov. 2019); Bingler et al. (2022); Ginglinger and Moreau (Jan. 2019).

### Appendix: Tables and figures — key estimates (preserve reported values exactly)
- Table 7: Baseline DiD estimates without regional FE (estimates from equation 9 omitting regional fixed effects and their interactions; D_i = 1 for oil and gas firms and 0 otherwise, T_it = 1[t > 2015]; N 9174)
  - D_i: -0.587 (0.635)
  - T_t: 0.032 (0.154)
  - D_i × T_t: -0.252*** (0.090)
  - D_i × P_oil,t: 0.324** (0.139)
  - Altman: -0.001 (0.002)
  - Log Total Assets: 0.997*** (0.005)
  - Log Asset Turnover: 0.220*** (0.026)
  - Debt-Equity: 0.000 (0.001)
  - Region FE: NO
  - Industry FE: YES
  - Region x Year FE: NO
  - R^2: 0.83
  - N: 9174
  - Note: *** p<0.01, ** p<0.05, * p<0.1

- Table 8: Effects of climate policy exposure and risk without regional FE (Columns 1–3, N 9174; note on equation 10 and interactions)
  - Column 1
    - D_i: 1.001*** (0.105)
    - D_i × R_1it: -0.078*** (0.019)
    - R_1it: 0.048*** (0.014)
    - D_i × R_2it: -0.065*** (0.019)
    - R_2it: 0.022*** (0.007)
    - Altman: -0.001 (0.002)
    - Log Total Assets: 0.998*** (0.005)
    - Log Asset Turnover: 0.220*** (0.026)
    - Debt-Equity: 0.000 (0.001)
    - Region FE: NO
    - Industry FE: YES
    - Year FE: YES
    - Group x Year FE: YES
    - Region x Year FE: NO
  - Column 2
    - D_i: 0.950*** (0.103)
    - D_i × R_1it: -0.071*** (0.021)
    - R_1it: 0.045*** (0.015)
    - D_i × R_2it: -0.082 (0.064)
    - R_2it: 0.039*** (0.015)
    - Altman: -0.001 (0.002)
    - Log Total Assets: 0.998*** (0.005)
    - Log Asset Turnover: 0.221*** (0.026)
    - Debt-Equity: 0.000 (0.001)
    - Region FE: NO
    - Industry FE: YES
    - Year FE: YES
    - Group x Year FE: YES
    - Region x Year FE: NO
  - Column 3 (adds interaction of text-based measures R_1it, R_2it among each other and with group dummy D_i)
    - D_i: 1.045*** (0.109)
    - D_i × R_1it × R_2it: -0.002*** (0.001)
    - R_1it × R_2it: 0.004 (0.009)
    - Altman: -0.001 (0.002)
    - Log Total Assets: 0.998*** (0.005)
    - Log Asset Turnover: 0.220*** (0.026)
    - Debt-Equity: 0.000 (0.001)
    - Region FE: NO
    - Industry FE: YES
    - Year FE: YES
    - Group x Year FE: YES
    - Region x Year FE: NO
  - Note: *** p<0.01, ** p<0.05, * p<0.1

### Supplementary Appendix: Models — structure, key equations, and qualitative outcomes
- Neoclassical Oil and Gas Investment Model
  - Model variables and equilibrium: system of 5 equations in 5 unknowns {y, k, λ, I, p}.
  - Key structural equations (as presented):
    - y_t = A_t k_{t−1}^α  (eq. 12)
    - (1−δ) k_{t−1} + I_t − Φ(I_t/k_{t−1}) k_{t−1} = k_t  (eq. 13)
    - α p_{t+1} A_{t+1} k_{t}^{α−1} + λ_{t+1} [1−δ−Φ_{t+1} + Φ'_{t+1} I_{t+1}/k_t] = λ_t / β  (eq. 14)
    - 1+τ_{p,t} = λ_t [1−(I_t − δ k_{t−1})]  (eq. 15)
    - y_t = c_0 [(1+τ_{c,t}) p_t]^{−η}  (eq. 16)
  - Exogenous processes: {A_t} and {τ_t} with τ = (τ_c, τ_p). Initial steady state solved under zero taxes and constant A. In numerical exercise τ_p = 0 at all times.
  - Solution method: transition path found by numerically solving the system of difference equations.

- Green paradox model — Hamiltonian, Hotelling’s rule, and demand closure
  - Current value Hamiltonian: H_c = P_t R_t − λ_t R_t  (eq. 17)
  - First-order/necessary conditions:
    - ∂H_c/∂R_t: P_t − λ_t = 0 when R_t > 0  (eq. 18)
    - ̇λ_t − i λ_t = −∂H_c/∂S = 0  (eq. 19)
  - Hotelling’s rule derived: ̇P/P = i  (eq. 20), yielding P(t) = P_0 e^{it}  (eq. 21).
  - Inverse demand function with carbon tax: (1+τ_{c,t}) P_t = K e^{−a R_t}  (eq. 22), where a>0 and K is choke-price.
  - Scenario: regulator announces constant carbon tax at time 0 implemented at time t_0 > 0. Two solution regimes:
    - Interior solution (0 < t_0 < T): oil firms supply before and after tax; terminal condition P_T = P_0 e^{iT} = K / (1+τ_c) for t_0 ≤ t_0 (eq. 23). Extraction path:
      - R_t = [i(T−t) + log(1+τ_c)] / a for 0 < t < t_0
      - R_t = [i(T−t)] / a for t_0 ≤ t ≤ T  (eq. 26)
      - T = sqrt{2 i (a S_0 − t_0 log(1+τ_c))}  (eq. 27) and T = sqrt{2 a S_0 / i} when t_0 = 0 (expression noted in text)
      - Comparative statics: ∂T/∂t_0 < 0; ∂T/∂τ_c < 0.
    - Corner solution (t_0 ≥ t_0 < T): firms deplete stock just before tax implementation, T = t_0 until tax no longer binds. Terminal price bounds:
      - P_{t_0} = P_0 e^{i t_0} = K e^{−a R_{t_0}} ∈ [K/(1+τ_c), K]  (eq. 29)
      - Extraction as function of terminal price: R_t = i(t_0 − t) + log(K / P_{t_0}) / a  (eq. 30)
      - Terminal price solved: P^*_{t_0} = K e^{−[a S_0 − i(t_0)^2 / 2]}  (eq. 31)
      - Minimum delay t_0 satisfies i^2 t_0^2 + log(1+τ_c) t_0 − a S_0 = 0  (eq. 32), identical to eq. (28) where interior and corner regimes join.
  - Green Paradox: non-monotonic relationship between delay t_0 and depletion time T:
    - For 0 < t_0 < t_0: dT/dt_0 < 0 (larger delay brings extraction forward).
    - For t_0 ≥ t_0: dT/dt_0 > 0 (further delay pushes extraction backward).
    - Piecewise expression for T:
      - T = sqrt{2 / i (a S − log(1+τ_c) t_0)} ≡ T^*(t_0) for 0 < t_0 < t_0
      - T = t_0 for t_0 ≤ t_0 < T
      - T = T for T < t_0  (eq. 33)

*The Impact of Climate Policy on Oil and Gas Investment: Evidence from Firm-Level Data — Working Paper No. WP/2023/140*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023140-print-pdf.pdf_