## 2.1 Methods

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---

### 2.1.1 Data
- Dataset:
  - Adoption of 26 climate policies collected by Bergquist and Warshaw (2023); 3 policies with continuous adoption scales dropped (level of gasoline taxes, energy efficienty resource standards, and RPS targets), leaving 23 binary-coded policies.
- Policy classification:
  - Policies classified into six instrument types based on an adjusted IEA classification (Linsenmeier et al., 2022).
  - Instrument type with the highest number is regulatory instruments, followed by grants, subsidies, and other financial incentives.
  - All policies listed in SI Table A1; adoption over time shown in SI Figure A1.
- Control variables:
  - 15 state-level controls (see Table 1); sources in SI Table A3.
  - GHG emissions by state and sector from the US Energy Information Administration.
- Descriptive statistics (Table 1) — Variable | Unit | Mean | Sd | Min | Max:
  - log GDP pc | USD per capita | -3.47 | 0.51 | -4.64 | -2.39
  - GHG intensity | t CO2eq per USD | 58.64 | 11.71 | 25.65 | 85.70
  - Democratic control | Binary | 0.45 | 0.50 | 0.00 | 1.00
  - Employment in mining | Percent | 2.19 | 2.22 | 0.22 | 14.29
  - Employment in transport and utilities | Percent | 24.27 | 2.22 | 18.01 | 31.86
  - GDP of mining | Percent | 3.18 | 6.72 | 0.00 | 46.36
  - GDP of transport and utilities | Percent | 6.91 | 2.74 | 2.62 | 18.67
  - Population density | People per km2 | 69.76 | 95.23 | 0.27 | 472.81
  - log Population | People | 15.04 | 1.02 | 12.90 | 17.49
  - log Land area | km2 | 11.61 | 1.16 | 7.89 | 14.21
  - Wind power potential | m/s | 6.61 | 0.63 | 5.26 | 7.80
  - Solar power potential | kWh per m2 per day | 4.40 | 0.58 | 2.27 | 5.68
  - Coal production | Binary | 0.50 | 0.50 | 0.00 | 1.00
  - Share evangelical | Percent | 19.32 | 14.21 | 1.10 | 74.00
  - Concern about climate change | Score | 0.13 | 0.77 | -2.67 | 2.86

### 2.1.2 Econometric analysis
- Motivation for pooled approach:
  - Individual policy instruments often too weak to show short-term effects.
  - A single policy yields too few observations for statistical significance.
  - Prior single-policy studies concentrate on carbon pricing due to price variation.
- Main empirical strategy:
  - Canonical distributed lag model per policy with state_i and year_t fixed effects:
    - Growth rate in emissions_{i,t} = sum_{n=0}^5 Policy adoption_{i,t−n} β + μ_i + ξ_t + ε_{i,t}. (Equation (1))
  - Pooled regression stacks policy-by-state and policy-by-year fixed effects; with policy index p:
    - Growth rate in emissions_{i,t,p} = sum_{n=0}^5 Policy adoption_{i,t−n,p} ̃β + μ_{i,p} + ξ_{t,p} + ε_{i,t,p}. (Equation (2))
  - Coefficient ̃β quantifies the average effectiveness of all policies.
  - Standard errors clustered by state.
- Main explanatory variable:
  - Cumulative number of climate policies in a state by year (from Bergquist and Warshaw (2023)), using three policy groups:
    - All policies (23).
    - R/E: policies that target renewable energy or the energy sector broadly (marked “R/E” in Table A1; 11 policies in tables).
    - Sect.: policies that target sectors other than energy (transportation or buildings) or target GHG emissions without sectoral limitation (marked “Sect.” or “Other”; 8 policies in tables).
- Dependent variable groups:
  - Group 1: share of renewable energy in total energy capacity; disaggregated into total renewables, solar, wind, hydropower.
  - Group 2: share of renewable energy in net generation of electric power; disaggregated similarly.
  - Group 3: state energy-related CO2 emissions — total and per capita (energy-related emissions only).
- Lag structure:
  - Main reported results use the third lag (outcome observed three years after policy variables); effects estimated for other lags and robustness checks with similar results.

### Key estimation results (summary of Tables 2–4)
- Design notes:
  - Unit of observation: state-year-policy (stacked specification).
  - For “All policies”: 23 distinct policy variables per state-year; for R/E and Other regressions: 11 and 8 observations per state-year respectively.
  - All regressions include full set of state X climate policy and year X climate policy fixed effects.
  - Standard errors clustered at the state level. Significance denotations: *** p < 0.01, ** p < 0.05, * p < 0.1.
- Table 2 — Share of renewables in total energy capacity (selected coefficients):
  - Climate policies (All policies): -0.00379 (se 0.0388)
  - Climate policies (R/E): 0.00290 (se 0.0482)
  - Climate policies (Other): -0.0352 (se 0.0500)
  - Solar — Climate policies (All): 0.0288** (se 0.0140)
  - Solar — Climate policies (R/E): 0.0257** (se 0.0126)
  - Solar — Climate policies (Other): 0.0262 (se 0.0231)
  - Wind — Climate policies (Other): -0.0925* (se 0.0534)
  - Observations: 34,350 (All policies); 16,437 (R/E); 11,947 (Other)
  - Number of states: 50
  - R-squared (within) examples: 0.139 (All renewables), 0.205 (Solar), 0.0402 (Hydro), 0.159 (Wind)
- Table 3 — Share of renewables in net generation of electric power (selected coefficients mirror capacity results):
  - Climate policies (All renewables): -0.004 (se 0.0388)
  - Solar — Climate policies (All): 0.028** (se 0.0140)
  - Solar — Climate policies (R/E): 0.026** (se 0.0126)
  - Wind — Climate policies (Other): -0.093* (se 0.0534)
  - Observations and state counts same as Table 2.
- Table 4 — Energy-related CO2 emissions (million metric tons and per capita metric tons):
  - Total state energy-related CO2 emission — Climate policies (All): -0.72 (se 0.46)
  - Total state energy-related CO2 emission — Climate policies (R/E): -0.30 (se 0.51)
  - Total state energy-related CO2 emission — Climate policies (Other): -1.28** (se 0.53)
  - Per capita state energy-related CO2 emissions — Climate policies (All): 0.220 (se 0.223)
  - Per capita state energy-related CO2 emissions — Climate policies (R/E): 0.249 (se 0.220)
  - Per capita state energy-related CO2 emissions — Climate policies (Other): 0.204 (se 0.239)
  - Observations: 34,500 (All policies); 16,500 (R/E); 12,000 (Other)
  - Number of states: 50
  - R-squared (within): 0.342 (total emissions), 0.507 (per capita emissions)
- Interpretation of main findings:
  - Pooling all policies yields no significant effect on the share of all renewable energy sources in total energy capacity.
  - Positive and significant effects of climate policies identified for solar energy capacity and solar net generation:
    - Solar capacity coefficient (All policies): 0.0288**; driven by R/E policies (R/E: 0.0257**).
  - Hydropower capacity shows no significant response to climate policies.
  - Wind energy coefficients are negative; the wind result for sectoral and GHG reduction policies is significant at 10% (Other: -0.0925* / -0.093*), interpreted as arising from state heterogeneity rather than a causal discouragement effect.
  - Results for net generation of electric power largely mirror capacity results.
  - Despite positive and significant effects on solar capacity and generation, climate policies do not produce a significant decrease in aggregate state energy-related GHG emissions in these estimates:
    - Solar electricity share grew from 0.1% in 2012 to 4.8% in 2022, still small relative to aggregate emissions — implying detectable emission effects may appear in future years.
  - Estimations of policy effects on energy-sector-only emissions were also insignificant (results in appendix).

---

### 3.1 Methods (Empirical model and simulations)

### 3.1.1 Empirical model
- Model specification:
  - Cox proportional hazard model:
    - h(t,X_i,t,W_i,t) = h_0(t) exp (X_{i,t−1} β_X) exp (W_{i,t−1} β_W) (3)
  - Hazard h(.) is the probability that the policy is adopted by state i in year t conditional on non-adoption to date.
  - Baseline hazard h_0(t) is non-parametric.
  - Standard errors clustered at the level of states.
- Data and exclusions:
  - Model estimated using panel data and the same climate policy dataset as Section 2.
  - Three policies dropped because the model does not converge:
    - state preemption of local gas bans: adopted by only four states;
    - low income energy efficiency policies: adopted in only three different years;
    - environmental policy acts: with one exception, already adopted in the 1970s.
- Controls and testing:
  - Matrix X_{i,t−1} contains 15 control variables (Table 1) and is lagged by one year.
  - Proportional hazard assumption tested using Schoenfeld residuals; assumption generally satisfied for most models.
  - Binary outcome P_{i,t} is policy adoption in state i in year t and used to construct spatial lags.

### 3.1.2 Proximity metrics
- Spatial lag construction:
  - W_{i,t} = (sum_{j=1,j≠i}^N w_{i,j,t} P_{j,t}) / (sum_{j=1,j≠i}^N w_{i,j,t}) (4)
  - Six alternative specifications for weights tested.
- Specific weight metrics:
  - Geographical contiguity: binary indicator whether states (i,j) border each other.
  - Inverse centroid distance: w_{i,j} = 1/d_{i,j}, where d_{i,j} is centroid distance.
  - Gravity-style metric: w_{i,j} = log GDP_j / d_{i,j}.
  - Political control metric:
    - Political control C measured from majority of state house, state senate, and governor.
    - C values: Democrats = 0, Republican = 1, Split = 0.5.
    - Weight: w_{i,j} = 1 − |C_i − C_j|.
- Placebo test:
  - Construct an additional W_{i,t} with random proximity values w_{i,j,t} drawn from a Weibull distribution fit to the distribution of physical distance between states.

### 3.1.3 Monte Carlo simulations
- General simulation approach:
  - Use estimated model (Equation 3) to predict hazards given covariates X and spatial lag W.
  - Keep covariates constant and iteratively simulate adoption and diffusion.
  - Simulations start in 2024 and stop in 2050.
  - Each scenario simulated 10,000 times.
- Exercise 1 — Quantify benefits of diffusion:
  - Two counterfactual scenarios starting in 2024 with no policy adopted:
    - Baseline scenario: β_W = 0 (no diffusion).
    - Other scenarios: β_W > 0 with different baseline hazards.
  - Effect of diffusion computed as difference in number of states adopting the policy in a given year relative to baseline.
- Exercise 2 — Leadership and indirect emission reductions:
  - For each state simulate two counterfactuals:
    - One where the state adopts the policy in 2024.
    - One where the state does not adopt in 2024.
  - All other states assumed not to adopt in 2024.
  - Diffusion parameter set to the empirical estimate.
  - Difference yields benefits of that state's adoption and subsequent diffusion; translate additional adopting states into cumulative emission reductions (indirect emission reductions).
- Exercises 3 and 4 — Translating policy adoption into solar capacity and emissions:
  - Use estimated coefficient from Table 2 Column 4: about 0.029 percentage points per year in every year following adoption.
  - Translate adoption into additional direct and indirect solar generation capacity; convert capacities into cumulative greenhouse gas emissions by assuming solar replaces the dirtiest existing electricity generation technology in each state.

---

### 3.2 Results

### 3.2.1 Empirical analysis of policy diffusion
- Scope and improvements vs prior work:
  - Includes 20 climate policies (versus 14 in Bromley-Trujillo et al. (2016)).
  - Focuses on mitigation policies; excludes “Adaptation Plan” and “Advanced Coal Technology”.
  - Covers years 1980-2020.
  - Employs multiple proximity metrics: neighbor states, physical distance, size of a state’s economy, and political alignment.
- Modeling considerations:
  - Trade-off between omitted variable bias and collinearity when including controls.
  - Spatial lag constructed from history of adoption is mechanically correlated with variables that affect adoption, causing omitted-variable effects to bias the spatial-lag coefficient downward.
  - Some control variables (notably log GDP per capita) are strongly correlated with the spatial lag (Pearson correlation coefficient > 0.8).
  - Addressed collinearity using principal component analysis and recursive feature selection; preferred specification uses 6 principal components from 15 controls.
- Comparison of proximity metrics (log likelihood ratio; smaller = better fit) — Table 5 (llr):
  - All: PoliciesDistance169.2 | Gravity169.0 | Neighbour168.9 | Party167.6
  - R/E: PoliciesDistance168.6 | Gravity168.7 | Neighbour168.2 | Party168.6
  - Others: PoliciesDistance169.9 | Gravity169.4 | Neighbour169.7 | Party166.5
  - Result: Political alignment ("Party") metric models diffusion best overall; party metric performs particularly well for "other" policies; for energy policies, metric performance is very similar across metrics.
- Estimated diffusion parameters:
  - Considerable variation across 20 climate policies.
  - Interquartile range of the parameter is [-0.5, 4.6] with a median estimate of 1.95.
  - Central estimate 1.95 lies within prior literature ranges.
- Control-variable influences (Lasso and predictive approach — standardized effects):
  - Largest positive effect: GDP per capita (log GDP pc).
  - Other positive effects: population density; expressed concern about climate change.
  - Largest negative associations: share of transportation, utilities, and mining in state GDP; employment in transport and utilities; share evangelical; presence of coal mines.
  - "Other" policies show stronger sensitivity to political-context variables (population density; concern about climate change; negative: share of evangelicals, employment in transport and utilities, GDP of mining and utilities).

### 3.2.2 The indirect benefits from policy diffusion
- Simulation setup and key parameters:
  - Baseline hazard (mean across states) varied between 1 and 10 percent in sensitivity analysis; example covariate-adjusted baseline hazards shown for mean baseline hazard of 5 percent.
  - Strength of policy diffusion: empirical estimate β_W = 1.95; sensitivity varied β_W between 0 and 10. Scenario β_W = 0 is no diffusion counterfactual.
- Effects of diffusion on adoption by 2030 (selected results):
  - For empirical β_W = 1.95 and mean baseline hazard of 5 percent:
    - Share of states adopting by 2030 increases by 10 percentage points relative to no diffusion: 40% versus 31%.
  - For β_W = 4:
    - Effect of diffusion increases to 38 percentage points: 69% versus 31%.
  - For β_W = 1.95 and baseline hazard doubled to 10 percent:
    - Effect of diffusion increases to 30 percentage points: 80% versus 50%.
- Temporal acceleration due to diffusion:
  - For empirical β_W = 1.95, the coverage achieved in the no-diffusion scenario by the year 2050 is reached about 15 years earlier, by around the year 2035.
- Quantifying benefits of state leadership via diffusion (state-by-state simulations):
  - For each state S, simulate S adopting in 2024 and diffusion until 2050; compare with counterfactual where no state adopts in 2024.
  - Baseline hazard used: 5%; diffusion parameter: β_W = 1.95.
- Translating adoption into climate benefits (solar capacity → emissions):
  - Use estimated solar effectiveness: about 0.029 percentage points per year in every year following adoption.
  - Emission-displacement assumptions:
    - Additional solar replaces coal where state uses more than 0.5% coal in electricity mix.
    - If state has less than 0.5% coal, additional solar replaces natural gas.
    - Vermont uses neither coal nor natural gas; additional solar assumed not to reduce emissions in Vermont.
    - Use respective emissions per MWh for coal and natural gas to determine emission reductions (state overview in Table A2).
- Main outcomes on direct vs indirect benefits:
  - Installed solar capacity:
    - 38% of states have larger indirect than direct benefits in terms of additionally installed solar capacity.
  - Cumulative emission reductions:
    - Indirect emission reductions are larger than direct emission reductions for 46% of states.
  - Geographic distribution of indirect emission reductions shown in SI Figure C5.
- Robustness checks:
  - Alternative simplification (Linsenmeier et al. (2023)): assume policy reduces GHG emissions by 1% per year after adoption, same effectiveness in all states.
    - Result: indirect > direct for 46% of states (essentially same relative magnitudes).
  - Repeat using physical distance proximity metric:
    - Result: indirect emissions larger than direct for 56% of states.
- Interpretation:
  - Benefits of diffusion are of similar magnitude to domestic (direct) benefits of adoption for many states.
  - Leadership by some states yields particularly large indirect emission-reduction benefits for the US overall.

---

*Source: wpiea2024198-print-pdf - 2.1 Methods / 3.1 Methods / 3.2 Results (IMF working paper content unit).*

### 2.1    Methods

### 2.1 Methods

### 2.1.1 Data
- Dataset: adoption of 26 climate policies collected by Bergquist and Warshaw (2023); 3 policies with continuous adoption scales dropped (level of gasoline taxes, energy efficienty resource standards, and RPS targets), leaving 23 binary-coded policies.
- Policy classification: policies classified into six instrument types based on an adjusted IEA classification (Linsenmeier et al., 2022). The instrument type with the highest number is regulatory instruments, followed by grants, subsidies, and other financial incentives (see Figure 1). All policies are listed in SI Table A1. Adoption over time shown in SI Figure A1.
- Control variables: 15 state-level controls (see Table 1); sources in SI Table A3. GHG emissions by state and sector from the US Energy Information Administration.
- Descriptive statistics (Table 1) — Variable | Unit | Mean | Sd | Min | Max:
  - log GDP pc | USD per capita | -3.47 | 0.51 | -4.64 | -2.39
  - GHG intensity | t CO2eq per USD | 58.64 | 11.71 | 25.65 | 85.70
  - Democratic control | Binary | 0.45 | 0.50 | 0.00 | 1.00
  - Employment in mining | Percent | 2.19 | 2.22 | 0.22 | 14.29
  - Employment in transport and utilities | Percent | 24.27 | 2.22 | 18.01 | 31.86
  - GDP of mining | Percent | 3.18 | 6.72 | 0.00 | 46.36
  - GDP of transport and utilities | Percent | 6.91 | 2.74 | 2.62 | 18.67
  - Population density | People per km2 | 69.76 | 95.23 | 0.27 | 472.81
  - log Population | People | 15.04 | 1.02 | 12.90 | 17.49
  - log Land area | km2 | 11.61 | 1.16 | 7.89 | 14.21
  - Wind power potential | m/s | 6.61 | 0.63 | 5.26 | 7.80
  - Solar power potential | kWh per m2 per day | 4.40 | 0.58 | 2.27 | 5.68
  - Coal production | Binary | 0.50 | 0.50 | 0.00 | 1.00
  - Share evangelical | Percent | 19.32 | 14.21 | 1.10 | 74.00
  - Concern about climate change | Score | 0.13 | 0.77 | -2.67 | 2.86

### 2.1.2 Econometric analysis
- Challenges motivating pooled approach:
  - Individual policy instruments often too weak to show short-term effects.
  - Introduction of a single policy yields too few observations for statistical significance.
  - Studies of single policies have focused on carbon pricing because of price variation; literature examples summarized (Pretis 2022; Bayer and Aklin 2020; Yan 2021; Green 2021).
- Main empirical strategy:
  - Canonical distributed lag model per policy with statei and yeart fixed effects:
    - Growth rate in emissions_{i,t} = sum_{n=0}^5 Policy adoption_{i,t−n} β + μ_i + ξ_t + ε_{i,t}. (Equation (1))
  - Pooled regression stacks policy-by-state and policy-by-year fixed effects; with policy index p:
    - Growth rate in emissions_{i,t,p} = sum_{n=0}^5 Policy adoption_{i,t−n,p} ̃β + μ_{i,p} + ξ_{t,p} + ε_{i,t,p}. (Equation (2))
  - Coefficient ̃β quantifies the average effectiveness of all policies.
  - Standard errors clustered by state.
- Main explanatory variable: cumulative number of climate policies in a state by year (from Bergquist and Warshaw (2023)), using three policy groups:
  - All policies (23).
  - R/E: policies that target renewable energy or the energy sector broadly (marked “R/E” in Table A1; 11 policies in tables).
  - Sect.: policies that target sectors other than energy (transportation or buildings) or target GHG emissions without sectoral limitation (marked “Sect.” or “Other”; 8 policies in tables).
- Dependent variable groups:
  - Group 1: share of renewable energy in total energy capacity; disaggregated into total renewables, solar, wind, hydropower.
  - Group 2: share of renewable energy in net generation of electric power; disaggregated similarly.
  - Group 3: state energy-related CO2 emissions — total and per capita (energy-related emissions only; total emissions not available at state level).
- Lag structure: main reported results use the third lag (outcome observed three years after policy variables); effects estimated for other lags and robustness checks with similar results (available in appendix).

### Key estimation results (summary of Tables 2–4)
- Sample and design details shown in table notes:
  - Unit of observation: state-year-policy (stacked specification).
  - For “All policies”: 23 distinct policy variables per state-year; for R/E and Other regressions: 11 and 8 observations per state-year respectively.
  - All regressions include full set of state X climate policy and year X climate policy fixed effects.
  - Standard errors clustered at the state level. Significance denotations: *** p < 0.01, ** p < 0.05, * p < 0.1.
- Table 2 / Share of renewables in total energy capacity — climate policy coefficients and selected covariates:
  - Climate policies (All policies): -0.00379 (se 0.0388)
  - Climate policies (R/E): 0.00290 (se 0.0482)
  - Climate policies (Other): -0.0352 (se 0.0500)
  - Solar — Climate policies (All): 0.0288** (se 0.0140)
  - Solar — Climate policies (R/E): 0.0257** (se 0.0126)
  - Solar — Climate policies (Other): 0.0262 (se 0.0231)
  - Wind — Climate policies (Other): -0.0925* (se 0.0534)
  - Observations: 34,350 (All policies); 16,437 (R/E); 11,947 (Other)
  - Number of states: 50
  - R-squared (within) examples: 0.139 (All renewables), 0.205 (Solar), 0.0402 (Hydro), 0.159 (Wind)
- Table 3 / Share of renewables in net generation of electric power — climate policy coefficients mirror capacity results:
  - Climate policies (All renewables): -0.004 (se 0.0388)
  - Solar — Climate policies (All): 0.028** (se 0.0140)
  - Solar — Climate policies (R/E): 0.026** (se 0.0126)
  - Wind — Climate policies (Other): -0.093* (se 0.0534)
  - Observations and state counts same as Table 2.
- Table 4 / Energy-related CO2 emissions (million metric tons and per capita metric tons) — climate policy coefficients:
  - Total state energy-related CO2 emission — Climate policies (All): -0.72 (se 0.46)
  - Total state energy-related CO2 emission — Climate policies (R/E): -0.30 (se 0.51)
  - Total state energy-related CO2 emission — Climate policies (Other): -1.28** (se 0.53)
  - Per capita state energy-related CO2 emissions — Climate policies (All): 0.220 (se 0.223)
  - Per capita state energy-related CO2 emissions — Climate policies (R/E): 0.249 (se 0.220)
  - Per capita state energy-related CO2 emissions — Climate policies (Other): 0.204 (se 0.239)
  - Observations: 34,500 (All policies); 16,500 (R/E); 12,000 (Other)
  - Number of states: 50
  - R-squared (within): 0.342 (total emissions), 0.507 (per capita emissions)
- Interpretation of main findings:
  - Pooling all policies yields no significant effect on the share of all renewable energy sources in total energy capacity.
  - Positive and significant effects of climate policies identified for solar energy capacity and solar net generation:
    - Solar capacity coefficient (All policies): 0.0288**; driven by R/E policies (R/E: 0.0257**).
  - Hydropower capacity shows no significant response to climate policies (hydropower largely driven by large individual projects and technical potential).
  - Wind energy coefficients are negative; the wind result for sectoral and GHG reduction policies is significant at 10% (Other: -0.0925* / -0.093*), interpreted as arising from state heterogeneity (rural, windy states less likely to pass GHG policies yet more likely to have wind capacity), not a causal discouragement effect.
  - Results for net generation of electric power largely mirror capacity results.
  - Despite positive and significant effects on solar capacity and generation, climate policies do not produce a significant decrease in aggregate state energy-related GHG emissions in these estimates:
    - Solar electricity share grew from 0.1% in 2012 to 4.8% in 2022, still small relative to aggregate emissions — implying detectable emission effects may appear in future years.
  - Estimations of policy effects on energy-sector-only emissions were also insignificant (results in appendix).

Italic source attribution line:
*Source: wpiea2024198-print-pdf - 2.1 Methods (IMF working paper content unit).*

### 3.1    Methods

### 3.1    Methods

### 3.1.1    Empirical model
- Model specification:
  - We model diffusion with a Cox proportional hazard model. In mathematical notation:
    - h(t,X_i,t,W_i,t) = h_0(t) exp (X_{i,t−1} β_X) exp (W_{i,t−1} β_W) (3)
  - The hazard function h(.) of state i in year t represents the probability that the policy is adopted by that state in that year conditional on it not yet being adopted.
  - The hazard is composed of a baseline hazard h_0(t) and a partial hazard term including time-dependent matrices of control variables X_{i,t−1} and spatial lags W_{i,t−1}.
  - The Cox baseline hazard is non-parametric, improving robustness to miss-specification relative to parametric survival models.
  - Standard errors are clustered at the level of states to account for serial correlation.
- Data and exclusions:
  - Model estimated using panel data and the same climate policy dataset as Section 2.
  - Three policies dropped because the model does not converge:
    - state preemption of local gas bans: adopted by only four states;
    - low income energy efficiency policies: adopted in only three different years;
    - environmental policy acts: with one exception, already adopted in the 1970s.
- Controls and testing:
  - The matrix X_{i,t−1} contains 15 control variables (Table 1) and is lagged by one year to reduce reverse causality.
  - Proportional hazard assumption tested using Schoenfeld residuals (Grambsch and Therneau, 1994); assumption generally satisfied for most models estimated.
  - Binary outcome variable P_{i,t} is policy adoption in state i in year t and is used to construct spatial lags.

### 3.1.2    Proximity metrics
- Spatial lag construction:
  - W_{i,t} = (sum_{j=1,j≠i}^N w_{i,j,t} P_{j,t}) / (sum_{j=1,j≠i}^N w_{i,j,t}) (4)
  - w_{i,j,t} is the weight of state j for state i in year t.
  - Six alternative specifications for weights are used.
- Specific weight metrics:
  - Geographical contiguity: binary indicator whether states (i,j) border each other.
  - Inverse centroid distance: w_{i,j} = 1/d_{i,j}, where d_{i,j} is distance between geometric centroids.
  - Gravity-style metric: w_{i,j} = log GDP_j / d_{i,j}.
  - Political control metric:
    - Political control C measured based on majority of state house, state senate, and governor.
    - C takes three possible values: Democrats = 0, Republican = 1, Split = 0.5.
    - Weight computed as w_{i,j} = 1 − |C_i − C_j| (assigns weight 1 to same-party control, 0 to opposite-party control).
- Placebo test:
  - Construct an additional W_{i,t} with random proximity values w_{i,j,t} drawn from a Weibull distribution fit to the distribution of physical distance between states.

### 3.1.3    Monte Carlo simulations
- General simulation approach:
  - Use empirically estimated model (Equation 3) to predict hazards given covariates X and spatial lag W.
  - Keep all covariates constant and iteratively simulate adoption and diffusion.
  - Simulations start in 2024 and stop in 2050.
  - At each timestep:
    - Calculate adoption probability for every state based on covariates and spatial lag.
    - Simulate adoption using a random variable.
    - Update spatial lags and proceed to next timestep.
  - Each scenario simulated 10,000 times to capture probabilistic variation.
- Exercise 1 — Quantify benefits of diffusion:
  - Two counterfactual scenarios simulated, both starting in 2024 with no policy adopted:
    - Baseline scenario: β_W = 0 (no diffusion).
    - Other scenarios: β_W > 0 with different baseline hazards.
  - Effect of diffusion computed as difference in number of states adopting the policy in a given year relative to baseline.
- Exercise 2 — Leadership and indirect emission reductions:
  - For each state simulate two counterfactuals:
    - One where the state adopts the policy in 2024.
    - One where the state does not adopt in 2024.
  - All other states assumed not to adopt in 2024.
  - Diffusion parameter set to the empirical estimate.
  - Difference between scenarios yields benefits of that state's adoption and subsequent diffusion.
  - Translate additional states with the policy (from diffusion) into cumulative emission reductions in those other states — termed indirect emission reductions.
  - Compare indirect emission reductions with direct emission reductions in the adopting state under assumption that the policy is equally effective in all states.
- Exercises 3 and 4 — Translating policy adoption into solar capacity and emissions:
  - Use estimated coefficient from Table 2 Column 4: about 0.029 percentage points per year in every year following adoption (quantifies how much adoption increases the share of total installed generation capacity of solar power relative to a counterfactual).
  - Translate policy adoption into:
    - Additional direct solar generation capacity in the first-adopting state.
    - Additional indirect solar generation capacity in all other states.
  - Convert additional installed capacities into cumulative greenhouse gas emissions:
    - Assume solar replaces the dirtiest existing electricity generation technology in each state.

*Source: wpiea2024198-print-pdf - 3.1    Methods*

### 3.2    Results

### 3.2    Results

### 3.2.1    Empirical analysis of policy diffusion

- Scope and extensions relative to prior work:
  - Includes 20 climate policies (versus 14 in Bromley-Trujillo et al. (2016)).
  - Focuses consistently on mitigation policies (excludes “Adaptation Plan” and “Advanced Coal Technology”).
  - Covers years 1980-2020 (versus 1994-2009 in Bromley-Trujillo et al. (2016)).
  - Employs multiple proximity metrics: neighbor states, physical distance, size of a state’s economy, and political alignment.

- Modeling considerations:
  - Trade-off between omitted variable bias and collinearity when including control variables.
  - Spatial lag constructed from history of policy adoption is mechanically correlated with variables that affect adoption, causing omitted-variable effects to bias the spatial-lag coefficient downward (negative/downward bias).
  - Some control variables (notably log GDP per capita) are strongly correlated with the spatial lag (Pearson correlation coefficient>0.8).
  - Addressed collinearity using principal component analysis and a machine learning algorithm for variable selection.
  - Preferred specification uses 6 principal components constructed from 15 control variables as the best trade-off between omitted-variable bias and collinearity (SI Section B).

- Comparison of proximity metrics (log likelihood ratio, smaller value indicates better model fit):
  - Table 5 (llr):
    - All: PoliciesDistance169.2 | Gravity169.0 | Neighbour168.9 | Party167.6
    - R/E: PoliciesDistance168.6 | Gravity168.7 | Neighbour168.2 | Party168.6
    - Others: PoliciesDistance169.9 | Gravity169.4 | Neighbour169.7 | Party166.5
  - Result: Political alignment ("Party") metric models diffusion best overall; party metric performs particularly well for "other" policies; for energy policies, metric performance is very similar across metrics.

- Estimated diffusion parameters:
  - Considerable variation in estimated spatial-lag parameter across the 20 climate policies (SI Figure C1).
  - Across policies, the interquartile range of the parameter is [-0.5, 4.6] with a median estimate of 1.95.
  - Central estimate 1.95 is within the range of prior literature estimates (comparison shown in Figure 2 left).

- Control-variable influences (approach and key predictors):
  - Used policy-specific models to predict adoption probabilities, averaged predicted values across policies, and regressed average predicted values on original variables using Lasso to identify important predictors.
  - Main predictors (average effect on policy adoption, coefficients standardised):
    - Largest positive effect: GDP per capita (log GDP pc).
    - Other positive effects: population density; expressed concern about climate change.
    - Largest negative associations: share of transportation, utilities, and mining in state GDP; employment in transport and utilities; share evangelical; presence of coal mines.
  - Distinction by policy group:
    - "Other" policies (more about climate than energy) show stronger positive influence of population density and concern about climate change and stronger negative influence of share of evangelicals, employment in transport and utilities, and GDP of mining and utilities — consistent with stronger political-context influence for these policies.

### 3.2.2    The indirect benefits from policy diffusion

- Simulation setup and key parameters:
  - Simulates future policy adoption to quantify additional adoptions due to diffusion.
  - Two key parameters:
    - Baseline hazard (mean value across states); sensitivity analysis varies baseline hazard between 1 and 10 percent. Example covariate-adjusted baseline hazards shown for mean baseline hazard of 5 percent (SI Figure C3).
    - Strength of policy diffusion: coefficient of spatial lag β_W. Empirical estimate β_W = 1.95; sensitivity analysis varies β_W between 0 and 10. Scenario β_W = 0 is the counterfactual with no diffusion.

- Effects of diffusion on adoption by 2030 (selected results):
  - For empirical β_W = 1.95 and mean baseline hazard of 5 percent:
    - Share of states adopting by 2030 increases by 10 percentage points relative to no diffusion: 40% versus 31%.
  - For β_W = 4 (baseline hazard unspecified in this specific comparison):
    - Effect of diffusion increases to 38 percentage points: 69% versus 31%.
  - For β_W = 1.95 and baseline hazard doubled to 10 percent:
    - Effect of diffusion increases to 30 percentage points: 80% versus 50%.

- Temporal acceleration due to diffusion:
  - For empirical β_W = 1.95, the coverage achieved in the no-diffusion scenario by the year 2050 is reached about 15 years earlier, by around the year 2035.

- Quantifying benefits of state leadership via diffusion (state-by-state pioneering simulations):
  - For each state S, simulate scenario where S is the first adopter in 2024 and diffusion/adoption runs until 2050; compare with counterfactual where no state adopts in 2024.
  - Baseline hazard used in these simulations: 5%; diffusion parameter used: β_W = 1.95.

- Translating adoption into climate benefits:
  - Use empirical estimates of policy effectiveness in increasing solar electricity generation (from Section 2).
  - Simulate expansion of solar capacity, translate into GHG emission reductions.
  - Assumptions for emission displacement:
    - Additional solar electricity replaces coal where the state uses more than 0.5% coal in its electricity mix.
    - If state has less than 0.5% coal, additional solar replaces natural gas.
    - Vermont uses neither coal nor natural gas; additional solar assumed not to reduce emissions in Vermont.
    - Use respective emissions per MWh for coal and natural gas to determine emission reductions (see table A2 for state overview).

- Main outcomes on direct vs indirect benefits:
  - Installed solar capacity:
    - 38% of states have larger indirect than direct benefits in terms of additionally installed solar capacity (Figure 4 left).
  - Cumulative emission reductions:
    - Indirect emission reductions are larger than direct emission reductions for 46% of states (Figure 4 right).
  - Geographic distribution of indirect emission reductions shown in SI Figure C5.

- Robustness checks:
  - Alternative simplification following Linsenmeier et al. (2023): assume a policy reduces GHG emissions by 1% per year in every year after adoption, same effectiveness in all states.
    - Result: essentially same relative magnitudes — indirect > direct for 46% of states (SI Figure C4 left).
  - Repeat simplified simulations using metric based on physical distance between states:
    - Result: indirect emissions larger than direct emission reductions for 56% of states (SI Figure C4 right).

- Interpretation:
  - Benefits of diffusion are of similar magnitude to domestic (direct) benefits of adoption for many states.
  - Leadership by some states yields particularly large indirect emission-reduction benefits for the US overall.

*Source: 3.2 Results, wpiea2024198-print-pdf*

### 8812.  Publisher:  Proceedings of the National Academy of Sciences.

### wpiea2024198-print-pdf - 8812.  Publisher:  Proceedings of the National Academy of Sciences.

### References and cited literature
- The unit contains an extensive bibliography of works on policy diffusion, climate policy, carbon pricing, and related empirical methods. Selected cited works include:
  - Bergquist, P. and Warshaw, C. (2019). Does Global Warming Increase Public Concern about Climate Change? TheJournalofPolitics, 81(2):686–691.
  - Bergquist, P. and Warshaw, C. (2023). How climate policy commitments influence energy systems and the economies of US states. NatureCommunications, 14(1):4850.
  - Bistline, J., Blanford, G., Brown, M., Burtraw, D., Domeshek, M., Farbes, J., Fawcett, A., Hamilton, A., Jenkins, J., Jones, R., et al. (2023). Emissions and energy impacts of the inflation reduction act. Science, 380(6652):1324–1327.
  - Linsenmeier, M., Mohommad, A., and Schwerhoff, G. (2022). Policy sequencing towards carbon pricing among the world’s largest emitters. NatureClimateChange, 12(12):1107–1110.
  - Nordhaus, W. (2015). Climate clubs: Overcoming free-riding in international climate policy. AmericanEconomicReview, 105(4):1339–1370.
  - Additional methodological and domain-specific references include Grambsch and Therneau (1994), Lee and Wang (2003), Shipan and Volden (2008), Way et al. (2022), Pretis (2022), Yan (2021), among others.

### Supplementary Information: Descriptive statistics (SI A)
- Table A1: Climate policies collected by Bergquist and Warshaw (2023).
  - Policy instrument types adopt Linsenmeier et al. (2022) taxonomy. Examples (policy — Count — Instrument type — Group — Diffusion — Effects):
    - On-site renewable generation — 44 — Incentives — R/E — Yes — Yes
    - Environmental utility deregulation — 17 — Regulatory instruments — R/E — Yes — Yes
    - Fuel generation mix disclosure — 24 — Information and education — R/E — Yes — Yes
    - Public Benefit Fund — 24 — Incentives — R/E — Yes — Yes
    - Environmental Building Standards — 42 — Regulatory instruments — Other — Yes — Yes
    - Low-income energy efficiency programs — [Simultaneous adoption] — 43 — R/E — No — Yes (excluded from diffusion analysis because adopted simultaneously in 39 states)
    - Environmental Policy Act — [Adopted before 1990] — 16 — Other — No — Yes (excluded because passed between 1970 and 1990)
    - State preemption of local gas bans — [Less than 5 adoptions] — 4 — Other — No — Yes (too few observations)
    - Three policies excluded due to non-binary coding: Gas tax, Energy efficiency resource standard, RPS target.
  - Note: “Incentives” is short for “Grants, subsidies, and other financial incentives”.

- Table A2: Solar effectiveness by state (solar capacity factor–based metric and 2022 fuel shares)
  - Shares for coal and natural gas are 2022 data from the U.S. Energy Information Administration.
  - Solar effectiveness based on capacity (last column) is calculated from capacity factor using solar capacity and solar electricity generation in the state.
  - Special imputations:
    - (1) Alaska didn’t have utility-scale solar in 2022. Inserted the average capacity factor of Canada. Canada’s capacity factor is 6% according to the cited source.
    - (2) North Dakota didn’t have utility-scale solar in 2022. Inserted the capacity factor of Montana.
    - (3) West Virginia didn’t have utility-scale solar in 2022. Inserted the capacity factor of Virginia.

- Figure A1: Temporal pattern of adoption of climate policies in US states (visual timeline of state adoptions across policies between 1980 and 2020).

- Table A3: Sources of control variables used in the study
  - Examples of variables and sources:
    - State GDP — U.S. Department of Commerce, Bureau of Economic Analysis
    - Population — U.S. Census Bureau
    - GHG intensity — U.S. Energy Information Administration
    - Democratic control — Hillman (2023)
    - Employment in mining; Employment in transport and utilities — U.S. Bureau of Labor Statistics
    - Wind and Solar power potential — U.S. Department of Energy (NREL)
    - Share evangelical — Sellers (2017)
    - Concern about climate change — Bergquist and Warshaw (2019)

### Model specification and identification challenges (SI B)
- Control variables and omitted variable bias:
  - The study considers 15 different control variables to address omitted variable bias in estimating diffusion effects.
  - Specific concern: inclusion of the spatial lag of policy adoption in a Cox model can introduce bias because state-year observations are conditional on not having adopted the policy yet, creating systematic correlations between latent selection factors and the spatial lag.
  - Illustrative logic: a binary time-invariant variable A that prevents adoption (A = 1) will be over-represented in later-state-year observations, and because the spatial lag increases with cumulative adoptions, A correlates with the spatial lag and will bias the spatial-lag coefficient if A is omitted.

- Tradeoff between omitted variable bias and multicollinearity:
  - Including many controls mitigates omitted variable bias but raises multicollinearity because variables that affect selection into treatment correlate with the spatial lag.
  - Variance Inflation Factor (VIF) analysis: the VIF of a model that includes all 15 variables (without the spatial lag) is below the critical threshold of 5 for all variables, indicating estimability in that setting.

- Variable selection and dimensionality reduction:
  - Recursive feature selection (logistic models with RFE) used to identify most influential control variables for policy adoption (see scikit-learn RFE reference).
  - Correlation analysis showed high correlation between some control variables and the spatial lag; notably log GDP per capita has mean Pearson correlation with the spatial lag larger than 0.8.
  - Principal Component Analysis (PCA) applied to the 15 control variables yields 15 orthogonal principal components; mean correlation between components and spatial lag across policies is now smaller than 0.6.

- Model comparison and chosen specification:
  - Logistic models with 10-fold cross-validation and recursive feature selection evaluated both original controls and principal components.
  - Finding: A model with six variables has the largest predictive power; models with fewer or more variables have lower explanatory power.
  - The explanatory power of the 6 most important original control variables is almost identical to that of the 6 most important principal components.
  - Given reduced collinearity with the spatial lag, the model with six principal components is chosen as the preferred specification.

- Quantifying bias from omitted variables (placebo experiment):
  - Cox model estimated with only the spatial lag using a placebo metric (random weights for states) should yield an expected coefficient of zero.
  - Empirical result: Coefficients tend to be negative across climate policies when controls omitted, indicating bias from latent variables.
  - For the preferred model with six principal components, the mean coefficient becomes much closer to zero, suggesting substantial remediation of selection bias.

- Numerical diagnostics from figures (preserved exactly):
  - Figure B1: Shows explanatory power of models across number of variables 1..15; reported that six variables maximize predictive power.
  - Figure B2 (placebo spatial-lag coefficients across 20 climate policies):
    - Model without control variables: Median: -2.91; IQR: [-6.89, 0.70].
    - Model with six principal components: Median: -1.08; IQR: [-5.07, 2.39].

### Additional results and robustness (SI C)
- Spatial-lag coefficients with political proximity metric (model with six principal components; distribution across 20 policies):
  - Figure C1: Median: 1.96; IQR: [-0.56, 5.64].

- Subgroup analyses for the political-proximity metric (Figure C2 — distributions across renewable/energy policies and other/sectoral policies):
  - Renewable/energy policies (left): Median: 1.68; IQR: [-0.81, 6.35].
  - All other/sectoral policies (right): Median: 2.56; IQR: [-0.26, 5.49].

- Baseline hazard and emission-reduction simulations (Figures C3–C5):
  - Figure C3: Map showing predicted covariate-adjusted baseline hazard for a baseline hazard of 5 percent.
  - Simulation assumptions for emission-reduction figures:
    - Baseline hazard assumed at 5 percent.
    - A reduction of GHG emissions of 1 percent per year after adoption of a policy is assumed in the simulations.
  - Figure C4: Direct and indirect emission reductions for each US state under two proximity metrics:
    - Left panel: Proximity metric based on party.
    - Right panel: Proximity metric based on physical distance.
    - Panel denotes states and shows direct emission reductions (Mt CO2eq) up to 300 and indirect emission reductions (Mt CO2eq); simulations note NE = 94 in one panel and AK = 56 in another panel annotations.
  - Figure C5: Indirect emission reductions for each US state with proximity metric based on party; simulations use baseline hazard of 5 percent and empirical estimates of policy effectiveness.

### Key methodological takeaways and implications
- Omitted-variable bias in Cox models with spatial lags is a real risk because selection into treatment affects which state-year observations enter risk sets, systematically correlating latent determinants with the spatial lag.
- Dimensionality reduction via PCA can substantially reduce multicollinearity between control variables and spatial lag (mean component–spatial-lag correlation reduced to <0.6).
- A parsimonious model with six principal components balances predictive power and collinearity mitigation and is preferred for estimating diffusion (and indirect effects) of climate policies.
- Placebo and subgroup analyses indicate diffusion effects are sensitive to proximity metric choice (party alignment vs physical distance) and policy subgrouping (renewable/energy vs sectoral).

*Source: wpiea2024198-print-pdf - 8812.  Publisher:  Proceedings of the National Academy of Sciences.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024198-print-pdf.pdf_