## 2.1 Empirical analysis of policy diffusion ## Source details **Canonical URL:** [2.1 Empirical analysis of policy diffusion](https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022115-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2022/english/wpiea2022115-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2022/english/wpiea2022115-print-pdf.pdf.json) --- ### Theoretical mechanisms and empirical strategy - Mechanisms considered: learning, competition, emulation, coercion (as framed in Braun and Gilardi, 2006; Simmons et al., 2006; Shipan and Volden, 2008; Volden et al., 2008; Shipan and Volden, 2012; Jordan and Huitema, 2014). - Prior literature emphasis: emulation and learning for climate policies and similar diffusion for cash transfer programs. - Empirical goal: identify how adoption in country i at time t influences adoption of the same policy in other countries j prior to t, accounting for mutual influences via spatial lags (weighted averages of prior policy adoption). ### Econometric model and covariates - Model: semi-parametric Cox proportional hazard models (survival / event history analysis) for binary, right-censored adoption data observed through 2021. - General 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) - Stratified model: h(t, X_{i,t−1}, W_{i,t−1}) = h_{0,k}(t) exp(X_{i,t−1} β_X) exp(W_{i,t−1} β_W) with stratification by six continents (North-America, Latin-America, Europe, Africa, Asia, and Oceania). - Covariates (all lagged one year) in X_{i,t−1}: - GDP per capita - Growth rate of GDP per capita - Emissions of CO2 per GDP - Service share of GDP - Export share of GDP - Implementation details: - Adoption variable set to 1 for all years t, t+1, ..., T if policy adopted prior to or in year t. - Cluster standard errors at the country level. - Proportional hazard assumption checked with Schoenfeld residuals test (Grambsch and Therneau, 1994). - Robustness: similar results with longer lag times (Appendix Table 4). ### Construction of spatial lag and weighting schemes - Spatial lag formula: - W_{i,t} = (Σ_{j=1, j≠i}^{N_c} w_{i,j,t} Y_{j,t}) / (Σ_{j=1, j≠i}^{N_c} w_{i,j,t}) - Weighting schemes: - Trade-based: w_{i,j,t} = x_{i,j,t} (export share) or m_{i,j,t} (import share); asymmetric. - Geographic proximity: binary land-border indicator; inverse distance w_{i,j} = 1 / d_{i,j}. - Gravity-like: w_{i,j,t} = GDP_{j,t} / d_{i,j}. - Placebo: random w_{i,j} drawn from a Weibull distribution fitted to empirical distances. ### Data sources and sample - Carbon pricing: World Bank Carbon Pricing Dashboard (national and subnational carbon taxes and ETS). - Subnational schemes assigned to corresponding countries; only the first national or subnational pricing policy retained per country. - For EU member countries, year of adoption set to 2003 regardless of accession year. - Robustness checks: ignore subnational pricing; keep only carbon tax or only ETS. - Additional variables: World Development Indicators (World Bank) and replication data from Best et al., 2020. - Sample: 179 countries, years 1988 to 2021. ### Descriptive patterns (leader–follower examples) - Europe: initial diffusion from Finland to other Scandinavian countries and the Baltics; Poland influential for Slovenia; EU-ETS influenced adoption in UK, Switzerland, Ukraine via neighboring adopters. - Americas: diffusion from North to South beginning with subnational policies in Canada and USA; Mexico central for subsequent adoption in South America (Colombia, Chile, Argentina). - Asia and Oceania: initial emulation of Europe and North-America; Japan influential for Korea, China, Singapore. - Note: descriptive links illustrative; Cox models account for baseline hazards, country characteristics, and prior adoption in all other countries. ### Descriptive sample statistics (Table 1; 179 countries; 1988–2021) - log GDP per capita PPP (2010 USD): Mean 8.42; Std. 1.50; Min. 5.23; Max. 11.63; No. obs. 6086 - GDP per capita PPP growth rate: Mean -0.02; Std. 0.05; Min. -1.05; Max. 0.88; No. obs. 6086 - Exports share of GDP (percent): Mean 39.82; Std. 27.92; Min. 0.01; Max. 228.99; No. obs. 6086 - Imports share of GDP (percent): Mean 46.85; Std. 28.96; Min. 0.00; Max. 224.82; No. obs. 6086 - Services share of GDP (percent): Mean 21.31; Std. 13.63; Min. 0.15; Max. 55.47; No. obs. 6086 - Emissions CO2eq per GDP (t per k 2010 USD): Mean 0.62; Std. 0.95; Min. 0.00; Max. 8.39; No. obs. 6086 --- ### 3.2 Model estimates ### Evidence for diffusion and preferred proximity metric - Spatial lag constructed from six proximity metrics: inverse geographic distance, shared land border, import shares, export shares, average proximity, gravity metric (inverse distance × GDP). - For all six metrics the spatial lag has a statistically significant and positive coefficient — evidence for international diffusion of carbon pricing. - Model fit (AIC) indicates the gravity metric provides the best fit; gravity metric used as preferred metric (baseline estimates: Column 6 in Table 2). ### Key estimated coefficients (baseline, Column 6) - Spatial lag of carbon pricing: 6.7053 (standard error 1.3469), significance ∗∗∗ (p <0.01). - GDP per capita PPP: 11.5662 (standard error 3.6787), significance ∗∗∗. - GDP per capita PPP sq.: -0.5529 (standard error 0.1895), significance ∗∗∗. - GDP per capita PPP growth: 2.0597 (standard error 3.1010), not statistically significant. - Export share: -0.0054 (standard error 0.0045), not statistically significant. - Services share of GDP: 0.0271 (standard error 0.0136), significance ∗∗. - Emissions CO2 per GDP: -0.0121 (standard error 0.1140), not statistically significant. - Time at risk: 527752775277 (reported as dataset time-at-risk). - log-likelihood (Column 6): -177.5. - AIC (Column 6): 369.1. - N (Column 6): 525252. - Notes: Standard errors clustered by country. Significance codes: ∗ p <0.1, ∗∗ p <0.05, ∗∗∗ p <0.01. ### Magnitude interpretations (using gravity metric, Column 6 spatial-lag coefficient) - Pairwise implied hazard increases: - USA: prior adoption by Canada increases the hazard by about 16%, or by a factor of 1.16 (95% CI of 1.10 to 1.22). - Germany: prior adoption by France increases the hazard by 17% (10% to 24%). - China: prior adoption by Japan increases the hazard by 10% (6% to 14%). - USA: prior adoption by China increases the hazard by 3%. - Germany: prior adoption by Japan increases the hazard by slightly more than 1%. - Income association: - Increase of average income from 20,000 USD to 30,000 USD associated with an increase of the hazard by about 17%. - Increase from 30,000 USD to 40,000 USD associated with an increase of the hazard by about 0.2%. - Service share of GDP: statistically significant positive association with hazard. ### Baseline hazard and proportional hazard tests - Baseline hazard relatively flat except for a peak in 2003 (coinciding with EU ETS adoption). - Schoenfeld-residual tests: - Model with only spatial lag: proportional hazards rejected (p = 0.01). - Models with six covariates (Table 2): cannot reject proportional hazards for any metric. ### Robustness checks (selected) - Excluding subnational schemes: coefficients very similar to baseline including subnational policies. - Separate estimations for carbon taxes and ETS alone: positive but insignificant spatial-lag coefficients. - Stratified by continent: results barely change. - Including Kyoto Annex I dummy: Kyoto Annex I coefficient 40.5713 (standard error 20.6120), significance ∗ (p <0.1) in Table 3 Column 5. - Lag times 1–5 years: similar results; possibly best AIC for lag time of 3 years. - Placebo test with random proximities: placebo spatial lag not significant (Column 6 Table 3). --- ### 3.3 Emission reductions ### Back-of-the-envelope approach and assumptions - Use estimated diffusion coefficient β_W = 6.7053 (Column 6 Table 2). - Baseline hazard assumed h_0? = 0.01; robustness check h_0? = 0.05. - Policy assumed to reduce total annual GHG emissions by r = 1 percent per year, uniformly across countries. - Policy implementation assumed at end of year t = 2018; calculations based on actual domestic emissions E in year t+1 = 2019. - Methodology: compute hazard differences for other countries j between scenarios with and without country i adopting; map hazard differences to CO2 emissions (Equations 10 and 11). ### Back-of-the-envelope results (one-year after adoption) - Indirect emission reductions can be substantial and similar in size to direct reductions. - For baseline hazard h_0? = 0.01: indirect emission reductions exceed direct emission reductions for about 38 percent of countries (Figure 3 left). - For baseline hazard h_0? = 0.05: indirect emission reductions exceed direct emission reductions for about 73 percent of countries (Figure 3 right). - Note: indirect reductions per country are not additive across countries. ### Monte Carlo simulations (1988–2021; assumed r = 1 percent per year in simulations) - Purpose: capture iterative diffusion and country-specific baseline hazards. - Simulation setup: - Simulate policy adoption and diffusion over 1988–2021 using estimated Cox coefficients (Column 6). - Assumption: adoption reduces greenhouse gas emissions by one percent per year. - Simulation outputs: - Indirect emission reductions are as large as or larger than direct reductions in the majority of countries. - Overall, 89 % of countries have larger indirect than direct emission reductions (Figure 4 left). - For most of these countries, indirect reductions exceed direct reductions by a factor of 1-100; a few small economies exhibit even larger factors. - Countries with large indirect reductions tend to be centrally located and close to countries with relatively large emissions (examples: Belgium and Czech Republic). - Most of the world’s largest emitters (G20 members) generally have larger direct than indirect reductions, though magnitudes can be similar. ### Additional simulation scenario (starting from observed 2020 adoption; 1988–2019 and 2020–2050 analyses summarized) - Simulations starting from observed adoption by end-2019 and projecting 2020-2050 show diffusion increases coverage and emission-share of adopters (details in subsequent section). --- ### 4 Discussion and Conclusions ### Principal empirical findings - Empirical diffusion parameter: βW = 6.7053; counterfactual set to zero βW = 0. - Prior adoption by a neighbouring country increases the probability of adoption in a given year by on average about 10 percent. - Monte Carlo simulations: - For 1988-2019, indirect emission reductions larger than direct domestic reductions in 89 % of countries. - For 2020-2050, indirect emission reductions larger than direct domestic reductions in 76 % of countries. - Indirect emission reductions are more evenly distributed across countries than direct reductions. ### Simulations of geographical coverage (2020-2050; starting from end-2020 adoption) - With baseline hazard estimated for 1988-2020 and covariates as of 2019: - By 2030, with diffusion versus without diffusion: about 3.5 percentage points more countries and a 3 percentage points larger share of global greenhouse gas emissions covered. - By 2050, with diffusion effect increases to 11 percentage points more countries and 9 percentage points larger share of global emissions. - With diffusion, similar share of countries adopt by 2030 as without diffusion by 2050. - Sensitivity: doubling baseline hazard (applied in both scenarios) increases diffusion benefits substantially: - Example: share of countries with carbon pricing in 2030 about 23 percentage points larger with diffusion than without. - By 2050 effect increases to 29 percentage points in this sensitivity case. ### Interpretation of mechanisms and international context - Timing suggests emulation may be important given short intervals between neighbouring adoptions; learning and international coordination (Kyoto, Paris, International Carbon Action Partnership) also likely contributed. - Early adopters’ promotion of carbon pricing internationally likely partially explains diffusion. ### Policy relevance - Spillovers (indirect emission reductions) can be substantial and matter relatively more in small economies, increasing global impacts of domestic adoption. - Accounting for diffusion makes policy effectiveness more equal across countries. - Under baseline assumptions diffusion increases geographical coverage modestly by 2050 (about 11 percentage points; 29 percentage points in doubled-hazard sensitivity). ### Limitations and caveats - Simulated indirect reductions are not precise estimates of actual reductions: - 1988-2019 results rely on hypothetical first-adopter scenarios. - 2020-2050 extrapolate 1988-2020 empirical estimates into the future. - Uniform annual reduction rate r assumed across countries; stringency heterogeneity ignored. - Indirect reductions attributed to a pioneering country are not additive across pioneers. - Analysis focuses on adoption decisions and not on differences in policy stringency; limited data on initial carbon prices. - Empirical period may reflect cooperative international environment; extrapolation to a more fragmented future requires caution. ### Directions for future research - Examine how policy stringency affects diffusion and subsequent stringency of followers. - Extend analysis to other climate policies (feed-in-tariffs, renewable energy quotas, local funding schemes) and sectoral-level diffusion. - Integrate international and domestic influences in a unified empirical framework and explore additional diffusion channels beyond geographic proximity and trade (for example international climate diplomacy). *wpiea2022115-print-pdf* ### 2.1 Empirical analysis of policy diffusion ### 2.1 Empirical analysis of policy diffusion ### Theoretical mechanisms and empirical strategy - Mechanisms of diffusion considered: learning, competition, emulation, coercion (as framed in Braun and Gilardi, 2006; Simmons et al., 2006; Shipan and Volden, 2008; Volden et al., 2008; Shipan and Volden, 2012; Jordan and Huitema, 2014). - Prior literature emphasis: emulation and learning for climate policies (Biedenkopf et al., 2017; Thisted and Thisted, 2020) and similar diffusion for cash transfer programs (Sugiyama, 2011). - Empirical goal: identify how adoption in country i at time t influences adoption of the same policy in other countries j prior to t, accounting for mutual influences via spatial lags (weighted averages of prior policy adoption). ### Econometric model specification - Model type: semi-parametric Cox proportional hazard models (survival / event history analysis) to handle binary, right-censored adoption data observed through 2021. - General model form estimated (as presented): - 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) - Hazard h(.) for unit i in year t: probability policy is adopted in year t conditional on it not yet being implemented at t−1; composed of baseline hazard h_0(t) and partial hazard from time-dependent matrices X_{i,t−1} and W_{i,t−1}. - Stratified model form (allows different baseline hazards h_{0,k}(t) across strata): - h(t, X_{i,t−1}, W_{i,t−1}) = h_{0,k}(t) exp(X_{i,t−1} β_X) exp(W_{i,t−1} β_W) - Stratification used: six continents (North-America, Latin-America, Europe, Africa, Asia, and Oceania). ### Covariates and controls (matrix X_{i,t−1}) - Included variables (all lagged by one year): - GDP per capita - Growth rate of GDP per capita - Emissions of CO2 per GDP - Service share of GDP - Export share of GDP - Rationale: capture domestic influences on adoption and address proportional hazard assumption concerns via controls and stratification. - Robustness: similar results with longer lag times (Appendix Table 4). ### Construction of spatial lag (matrix W_{i,t−1}) and weighting schemes - General weighted average: - W_{i,t} = (Σ_{j=1, j≠i}^{N_c} w_{i,j,t} Y_{j,t}) / (Σ_{j=1, j≠i}^{N_c} w_{i,j,t}) - For trade-based weights: w_{i,j,t} = x_{i,j,t} (export share) or m_{i,j,t} (import share); trade weights are generally asymmetric (w_{i,j,t} ≠ w_{j,i,t}). - Geographic proximity weights: - Binary land-border indicator for (i,j). - Inverse distance: w_{i,j} = 1 / d_{i,j}. - Gravity-like metric incorporating size: - w_{i,j,t} = GDP_{j,t} / d_{i,j} (closer and larger economies exert more influence). - Placebo test for spurious diffusion: - Construct W_{i,t} with random w_{i,j} drawn from a Weibull distribution fitted to empirical distribution of distances between countries. ### Model implementation details - Adoption variable modeled as binary equal to 1 for all years t, t+1, ..., T if policy adopted prior to or in year t. - Panel setting: time-varying covariates; cluster standard errors at the country (unit) level to account for within-unit dependence. - Proportional hazard assumption checked with Schoenfeld residuals test (Grambsch and Therneau, 1994). ### Data sources and sample construction - Carbon pricing data: World Bank Carbon Pricing Dashboard, includes national and subnational carbon taxes and ETS. - Subnational schemes assigned to corresponding countries; for each country, only the first national or subnational pricing policy retained. - For EU member countries, year of adoption set to 2003 regardless of accession year (to avoid staggered EU accession being interpreted as diffusion). - Robustness checks: ignore subnational pricing; keep only carbon tax or only ETS policies for alternative tests. - Additional explanatory variables: World Development Indicators (World Bank) and replication data from Best et al., 2020. - Sample: 179 countries covering years 1988 to 2021. ### Back-of-the-envelope calculation of diffusion-driven emissions reductions (overview) - Approach: compare scenario where country i adopts carbon pricing in year t versus scenario where it does not. - For each scenario, compute hazard rate of adoption at t+1 for all other countries j based on Equation 1; difference interpreted as additional hazard attributable to diffusion from i. - Mapping hazard differences to CO2 emissions: - Assume carbon pricing reduces emissions in all countries by the same percentage r (assumption used in prior literature: Eskander and Fankhauser, 2020; Best et al., 2020). - Acknowledged limitation: ignores heterogeneity in policy stringency (price and sectoral coverage). - Empirical check: examined trends in economy-wide average price in year of first implementation (Appendix Figure 8); found no clear trend that would invalidate the equal-percentage assumption. ### Monte-Carlo simulations (overview) - Purpose: address limitations of back-of-the-envelope approach (neglect of country-specific baseline hazards and iterative diffusion). - Method: feed estimated coefficients of control variables and spatial lag into Monte Carlo simulations of policy adoption and diffusion using the Cox model (Equation 1). - Simulation details: - Simulate policy adoption and diffusion over 1988–2021 (period of empirical estimates). - Assumption used in simulations: adoption reduces greenhouse gas emissions by one percent per year. - Outcome computed: cumulative emission reductions up to year 2021 attributable to diffusion. ### Descriptive evidence and patterns - Conceptualization: leader-follower relationships where earlier adopters influence later adopters. - Visualization approach: for each follower, plot diffusion from the closest leader according to the gravity metric (Figure 2); EU-ETS member diffusion excluded from figure readability. - Observed patterns: - Europe: initial diffusion from Finland to other Scandinavian countries and the Baltics; Poland influential for Slovenia; EU-ETS influenced adoption in UK, Switzerland, Ukraine (via neighboring countries Ireland, Luxemburg, Romania). - Americas: diffusion from North to South beginning with subnational policies in Canada and USA; Mexico central in subsequent adoption in South America (Colombia, Chile, Argentina). - Asia and Oceania: initial emulation of Europe and North-America; Japan influential for Korea, China, Singapore. - Note: these descriptive links are illustrative; econometric Cox models used subsequently to account for baseline hazards, country characteristics, and prior adoption in all other countries. ### Key statistics (descriptive sample statistics from Table 1; sample contains 179 countries and covers years 1988 to 2021) - log GDP per capita PPP (2010 USD): Mean 8.42; Std. 1.50; Min. 5.23; Max. 11.63; No. obs. 6086 - GDP per capita PPP growth rate: Mean -0.02; Std. 0.05; Min. -1.05; Max. 0.88; No. obs. 6086 - Exports share of GDP (percent): Mean 39.82; Std. 27.92; Min. 0.01; Max. 228.99; No. obs. 6086 - Imports share of GDP (percent): Mean 46.85; Std. 28.96; Min. 0.00; Max. 224.82; No. obs. 6086 - Services share of GDP (percent): Mean 21.31; Std. 13.63; Min. 0.15; Max. 55.47; No. obs. 6086 - Emissions CO2eq per GDP (t per k 2010 USD): Mean 0.62; Std. 0.95; Min. 0.00; Max. 8.39; No. obs. 6086 _Source: wpiea2022115-print-pdf - 2.1 Empirical analysis of policy diffusion_ ### 3.2 Model estimates ### 3.2 Model estimates ### Evidence for international diffusion and best-connectedness metric - Estimated Cox proportional hazard models include six explanatory variables and a spatial lag of carbon pricing constructed from six proximity metrics: the inverse geographic distance, the presence of a shared land border, import shares, export shares, the average proximity based on these four metrics, and a gravity metric equal to the product of inverse distance and the GDP of a country. - For all six proximity metrics the spatial lag of policy adoption has a statistically significant and positive coefficient, interpreted as evidence for international diffusion of carbon pricing policies. - Model fit (AIC) indicates the gravity metric provides the best model fit, followed by inverse geographical distance and the average metric. The paper uses the gravity metric as the preferred metric and treats Column 6 in Table 2 as the baseline estimates. ### Key estimated coefficients (selected, from Table 2 and baseline Column 6) - Spatial lag of carbon pricing: 6.7053 (standard error 1.3469), significance ∗∗∗ (p <0.01). - GDP per capita PPP: 11.5662 (standard error 3.6787), significance ∗∗∗. - GDP per capita PPP sq.: -0.5529 (standard error 0.1895), significance ∗∗∗. - GDP per capita PPP growth: 2.0597 (standard error 3.1010), not statistically significant. - Export share: -0.0054 (standard error 0.0045), not statistically significant. - Services share of GDP: 0.0271 (standard error 0.0136), significance ∗∗. - Emissions CO2 per GDP: -0.0121 (standard error 0.1140), not statistically significant. - Time at risk: 527752775277 (reported as dataset time-at-risk). - log-likelihood (Column 6): -177.5. - AIC (Column 6): 369.1. - N (Column 6): 525252. Notes: Standard errors clustered by country in parentheses. Significance codes: ∗ p <0.1, ∗∗ p <0.05, ∗∗∗ p <0.01. ### Magnitude interpretation using baseline (gravity metric, Column 6) - Pairwise implied hazard increases using Column 6 spatial-lag coefficient: - USA: prior adoption by Canada increases the hazard by about 16%, or by a factor of 1.16 (95% CI of 1.10 to 1.22). - Germany: prior adoption by France increases the hazard by 17% (10% to 24%). - China: prior adoption by Japan increases the hazard by 10% (6% to 14%). - USA: prior adoption by China increases the hazard by 3%. - Germany: prior adoption by Japan increases the hazard by slightly more than 1%. - GDP per capita shows a negative quadratic association with hazard (Column 6). Illustrative magnitudes: - Increase of average income from 20,000 USD to 30,000 USD associated with an increase of the hazard by about 17%. - Increase from 30,000 USD to 40,000 USD associated with an increase of the hazard by about 0.2%. - Service share of GDP has a statistically significant positive association with the hazard of adoption. ### Baseline hazard and proportional hazard tests - Baseline hazard is relatively flat except for a peak in the year 2003 (coinciding with EU ETS adoption). - Schoenfeld-residual based tests: - Model with only spatial lag: proportional hazards rejected with high confidence (p = 0.01). - Models with six covariates (Table 2): cannot reject the null of proportional hazards for any metric. ### Robustness checks (summarized results) - Excluding subnational carbon pricing schemes produces estimated coefficients very similar to the model including subnational policies. - Separate estimations for carbon taxes alone and ETS alone yield positive but insignificant spatial-lag coefficients, suggesting importance of allowing alternative implementations when examining diffusion. - Stratified model by continent (North-America, Latin-America, Europe, Africa, Asia, Oceania) barely changes results. - Including a Kyoto Annex I dummy (countries with specific obligations) produces robust results; Kyoto Annex I coefficient reported as 40.5713 (standard error 20.6120), significance ∗ (p <0.1) in Table 3 Column 5. - Varying spatial-lag lag times between 1 and 5 years yields similar results; possibly best AIC for lag time of 3 years. - Placebo test assigning random numbers to proximities yields no significance for the placebo spatial lag (Column 6 Table 3), supporting non-spurious diffusion. ### 3.3 Emission reductions ### Approach and assumptions for back-of-the-envelope calculations - Use estimated coefficient of diffusion from model with average proximity metric β_W = 6.7053 (Column 6 Table 2). - Baseline hazard assumed h_0? = 0.01; additional robustness check sets baseline hazard to 0.05. - Policy assumed to reduce total annual GHG emissions by r = 1 percent per year, irrespective of total emissions of a country. - Policy implementation assumed at end of year t = 2018; calculations base on actual domestic emissions E in year t+1 = 2019. - Direct and indirect emission reductions calculated via Equations 11 and 10 in Appendix A.1 (methodology described in text). ### Back-of-the-envelope results (one-year after adoption) - Indirect emission reductions can be substantial and similar in size to direct emission reductions. - For baseline hazard h_0? = 0.01: indirect emission reductions exceed direct emission reductions for about 38 percent of countries (Figure 3 left). - For baseline hazard h_0? = 0.05: indirect emission reductions exceed direct emission reductions for about 73 percent of countries (Figure 3 right). - Note: Indirect emission reductions calculated per country are not additive across countries. ### Monte Carlo simulations (diffusion dynamics and expected reductions) - Simulations assume first introduction of carbon pricing in a given country in 1988 and diffusion thereafter; baseline hazard assumed constant (exponential survival function) and coefficients taken from Column 6 Table 2. - Monte Carlo output translated into expected direct and indirect emission reductions using Equations 12 and 13 in Appendix A.2. - Key findings from simulations: - Indirect emission reductions are as large as or larger than direct emission reductions in the majority of countries. - Overall, 89 % of countries have larger indirect than direct emission reductions (Figure 4 left). - For most of these countries, indirect emission reductions exceed direct emission reductions by a factor of 1-100; a few small economies exhibit even larger factors. - Countries with large indirect emission reductions tend to be centrally located and close to countries with relatively large emissions (examples: Belgium and Czech Republic have the largest indirect emission reductions). - Most of the world’s largest emitters (G20 members) generally have larger direct than indirect emission reductions due to large economies, though for many the two are of a similar order of magnitude. ### Additional scenario: simulations starting from observed 2020 adoption - A subsequent exercise (described in the text and shown in Figure 4) simulates diffusion from 2020 starting from actually observed adoption by end-2019; results presented for periods 1988-2019 and 2020-2050 in figures (summarized above). _Italic: Content derived from "3.2 Model estimates" and "3.3 Emission reductions" sections of the supplied IMF working paper content unit._ ### 1988. Right: Emission reductions calculated over period 2020-2050 starting from imple- ### 4 Discussion and Conclusions ### Main empirical findings on diffusion and emission reductions - Empirical estimate of the diffusion parameter: βW = 6.7053; counterfactual set to zero: βW = 0. - Prior adoption of carbon pricing by a neighbouring country increases the probability of adoption in a given year by on average about 10 percent. - Using Monte Carlo simulations: - For the period 1988-2019, indirect emission reductions are larger than direct domestic reductions in 89 % of countries in the sample. - For the period 2020-2050, indirect emission reductions are larger than direct domestic reductions in 76 % of countries in the sample. - Indirect emission reductions are far more equally distributed across countries than direct emission reductions. ### Simulations of geographical coverage (2020-2050) - Simulations start from carbon pricing policies implemented by the end of 2020 and compare scenarios with diffusion (βW = 6.7053) and without diffusion (βW = 0). - With the baseline hazard estimated for 1988-2020 and covariates as of 2019: - By 2030, carbon pricing policies cover about 3.5 percentage points more countries and a 3 percentage points larger share of global greenhouse gas emissions in the scenario with diffusion than in the scenario without diffusion. - By 2050, the effect of diffusion increases to 11 percentage points more countries and 9 percentage points larger share of global emissions. - With diffusion a similar share of countries has adopted carbon pricing by 2030 as without diffusion by 2050. - Sensitivity analysis doubling the baseline hazard (applied in both with-diffusion and without-diffusion scenarios): - The benefits of diffusion become several times larger, especially in 2030. - Example: the share of countries with carbon pricing in 2030 is about 23 percentage points larger in the scenario with diffusion than in the scenario without diffusion. - By 2050 the effect of diffusion increases to 29 percentage points in this sensitivity analysis. ### Interpretation of mechanisms and international context - Possible diffusion mechanisms include learning and emulation; evidence and timing in the sample suggest emulation may be more important given short intervals between neighbouring adoptions. - International coordination and multilateral initiatives (for example, incentives created by the Kyoto protocol and the Paris climate agreement, and knowledge exchange via initiatives such as the International Carbon Action Partnership) likely contributed to observed diffusion. - Early adopters’ efforts to promote carbon pricing internationally likely partially explain diffusion. ### Policy relevance and implications - Indirect emission reductions (spillovers) can be substantial and tend to matter relatively more in relatively small economies, making domestic adoption more consequential globally than domestic-only estimates imply. - Accounting for policy diffusion makes the overall effectiveness of domestic policy adoption more equal across countries. - While international diffusion substantially increases geographical coverage of carbon pricing, its contribution to achieving high geographical coverage over the next decades appears limited in magnitude under baseline assumptions (about 11 percentage points more countries by 2050; 29 percentage points in the doubled-hazard sensitivity case). ### Limitations and caveats - The simulated indirect emission reductions should not be interpreted as precise estimates of actual emission reductions: - 1988-2019 results rely on hypothetical scenarios in which a country adopted carbon pricing as the first and only country in 1988. - 2020-2050 simulations use empirical estimates from 1988-2020 extrapolated into the future. - Assumption that carbon pricing in all countries reduces GHG emissions proportionally with a uniform annual rate; direct and indirect reductions both scale with this parameter. - Indirect emission reductions attributed to policy diffusion for a specific pioneering country are not additive with those attributed to other pioneering countries due to scenario construction. - Analysis focuses on adoption decisions and does not account for differences in policy stringency; stringency assumed similar across leaders and followers given limited data on initial carbon prices for many countries. - Empirical period 1988-2020 may reflect a generally cooperative international political environment; extrapolation to a potentially more fragmented future political environment should be made with caution. ### Directions for future research - Examine how the stringency of carbon pricing policies affects diffusion and the stringency of subsequent policies. - Extend analysis to other climate policies (for example, feed-in-tariffs, renewable energy quotas, local funding schemes) and to sectoral-level diffusion. - Integrate international and domestic influences on adoption in a unified empirical framework and explore additional channels of diffusion beyond geographic proximity and trade relationships (for example international climate diplomacy). *wpiea2022115-print-pdf* ### References ### References ### Bibliographic corpus - List of cited works on policy diffusion, carbon pricing, emissions trading systems, political economy of climate policy, and statistical methods. (Authors include Abel D., Baier S., Baldwin E., Bang G., Barrett P., Best R., Biedenkopf K., Braun D., Bullock D., Crowley K., Dechezleprêtre A., Dolphin G., Eskander S. M. S. U., Fankhauser S., Grambsch P. M., Gulbrandsen L. H., Harrison K., Heggelund G., H ̈ohne N., Jordan A., Kammerer M., Klenert D., Lee E. T., Levi S., Linsenmeier M., Ryan D., Sauquet A., Schwerhoff G., Shipan C. R., Simmons B. A., Skovgaard J., Steinebach Y., Sugiyama N. B., Thisted E. V., Torney D., Volden C.) - Methodological and empirical foundations cited include Cox proportional hazards, gravity models, survival analysis, studies of carbon taxes and ETS diffusion, and Monte Carlo simulation approaches. ### Appendix A — Quantification of the global benefits of diffusion: methods and calculations - Two-step quantification approach: - Back-of-the-envelope calculation comparing two counterfactual scenarios: - Scenario A: country i adopts carbon pricing in year t. - Scenario B: country i does not adopt the policy in year t. - Monte Carlo simulations to capture subsequent diffusion and dynamic effects. - Hazard formulations (preserve exact functional form references): - Hazard in scenario A: h_A(t+1, X_{j,t}, W^A_{j,t}) = h_0(t+1) exp(X_{j,t} β_X) exp(W^A_{j,t} β_W) (Equation 6). - Hazard in scenario B: h_B(t+1, X_{j,t}, W^B_{j,t}) = h_0(t+1) exp(X_{j,t} β_X) exp(W^B_{j,t} β_W) (Equation 7). - Additional hazard due to diffusion: ∆h_{j,t+1} = h^*_0(t+1) [exp(W^B_{j,t} β_W) − 1] (Equation 8). - Spatial lag in scenario B (only country i adopts): W^B_{j,t} = w_{i,j,t} / ∑_{i=1, i≠j}^{N_c} w_{i,j,t} ∀j (Equation 9). - Direct and indirect emission reduction formulas: - Indirect reductions attributable to diffusion in year t+1: R^{indirect}_{i,t+1} = r ∑_{j≠i} ∆h_{j,t+1} E_{j,t+1} (Equation 10). - Direct reductions: R^{direct}_{i,t+1} = r E_{i,t+1} (Equation 11). - Data choices and assumptions: - Use actual CO2 emissions in the year 2019 (last pre-pandemic year). - Back-of-the-envelope quantifies reductions only in year t+1; Monte Carlo captures later periods and onward diffusion. ### Appendix A.2 — Monte Carlo simulations: implementation details - Simulation start and assumptions: - Simulations start in year t = 1988; assume no country has adopted the policy prior to 1988. - Two scenarios per country i: - Scenario A: no country adopts the policy in t = 1988. - Scenario B: only country i adopts the policy in t = 1988. - Temporal simulation window and update rule: - For each timestep 1989 ≤ t ≤ 2021, update spatial lag W_{j,t} for every country, compute hazard of adoption, and draw adoption outcomes from the hazard-based probability. - Simulation runs: - Conduct 5,000 simulations for every country for scenario B. - Conduct 10,000 simulations for scenario A. - Outputs and probability matrices: - Scenario B yields matrix of adoption probabilities P^B_{i,j,t} with ∑_{t=1988}^{2021} P^B_{i,j,t} = 1 ∀i,j. - Scenario A yields matrix P^A_{j,t} with ∑_{t=1988}^{2021} P^A_{j,t} = 1 ∀j (same for all i). - Calculation of expected emission reductions (preserve exact formulas): - Direct reductions 1988–2019 for country i implementing policy in 1988: - R̂^{direct}_{i,2019} = ∑_{t=1988}^{2019} [E_{i,t} − E_{i,1988} ∏_{l=1988}^{t} (1 + g_{i,l} − r)] (Equation 12). - Indirect reductions attributable to diffusion from country i: - R̂^{indirect}_{i,2019} = ∑_{j≠i} [ ∑_{ξ=1988}^{2019} [ (P^B_{i,j,ξ} − P^A_{j,ξ}) [ ∑_{t=1988}^{ξ} E_{j,t} + E_{j,ξ} ∏_{l=ξ}^{2019} (1 + g_{j,l} − r) ] ] ] (Equation 13). - Variables and notation preserved as in source: - E_{j,t}: total CO2 emissions of country j in year t. - g_{j,t}: observed growth rate of CO2 emissions of country j in year t. - r: rate at which emissions are reduced per year (policy effectiveness). ### Appendix B — Additional results and selected numeric findings - Figures and maps: - Figure 7: Cumulative baseline hazard of the Cox proportional hazard model (with six covariates). Estimated coefficients correspond to Column 2 in Table 2. - Figure 8: Scatter plot of economy-wide emission-weighted average carbon prices over time. - Figure 9: Time of adoption of the first carbon tax policy by country; hashes indicate subnational first adoptions. - Figure 10: Time of adoption of the first ETS policy by country; hashes indicate subnational first adoptions. - Figure 11: Map of the sample of 179 countries used in this study. - Table 4 — Results of estimation with different lag times (Policy: Carbon price; Proximity metric: Gravity; Lag time columns 1–5). Selected coefficient estimates and model statistics (preserve numbers and significance): - Spatial lag of carbon pricing: - Column 1: 6.7053 ∗∗∗ (1.3469) - Column 2: 6.3749 ∗∗∗ (1.3561) - Column 3: 6.5309 ∗∗∗ (1.4128) - Column 4: 6.5649 ∗∗∗ (1.4821) - Column 5: 6.9365 ∗∗∗ (1.5248) - GDP per capita PPP: - Column 1: 11.5662 ∗∗∗ (3.6787) - Column 2: 11.0535 ∗∗∗ (3.5089) - Column 3: 11.2919 ∗∗∗ (3.3388) - Column 4: 10.1004 ∗∗∗ (3.0844) - Column 5: 9.7194 ∗∗∗ (2.9444) - GDP per capita PPP squared: - Column 1: -0.5529 ∗∗∗ (0.1895) - Column 2: -0.5279 ∗∗∗ (0.1806) - Column 3: -0.5368 ∗∗∗ (0.1730) - Column 4: -0.4788 ∗∗∗ (0.1610) - Column 5: -0.4623 ∗∗∗ (0.1535) - GDP per capita PPP growth: - Column 1: 2.0597 (3.1010) - Column 2: 2.0058 (4.2026) - Column 3: 8.1873 ∗∗∗ (1.6269) - Column 4: 5.6635 ∗∗∗ (2.1262) - Column 5: 3.9481 (3.8003) - Export share: - Column 1: -0.0054 (0.0045) - Column 2: -0.0054 (0.0043) - Column 3: -0.0069 (0.0044) - Column 4: -0.0057 (0.0045) - Column 5: -0.0042 (0.0041) - Services share of GDP: - Column 1: 0.0271 ∗∗ (0.0136) - Column 2: 0.0251 ∗ (0.0135) - Column 3: 0.0230 ∗ (0.0124) - Column 4: 0.0219 ∗ (0.0123) - Column 5: 0.0206 ∗ (0.0115) - Emissions CO2 per GDP: - Column 1: -0.0121 (0.1140) - Column 2: -0.0083 (0.1107) - Column 3: -0.0049 (0.1203) - Column 4: -0.0197 (0.1013) - Column 5: -0.0008 (0.0976) - Time at risk: 52775 2775 2775 2775 2777 (as listed). - log-likelihood: - Column 1: -177.5 - Column 2: -179.5 - Column 3: -177.3 - Column 4: -180.3 - Column 5: -182.1 - AIC: - Column 1: 369.1 - Column 2: 373.0 - Column 3: 368.6 - Column 4: 374.6 - Column 5: 378.1 - N (observations per column): 5252 5230 5203 5174 5142 - Notes: Standard errors clustered by country in parentheses. Significance notation: ∗ p <0.1, ∗∗ p <0.05, ∗∗∗ p <0.01. - Baseline hazard and adoption probabilities (Figure 12 and text): - Histogram of estimated baseline hazard adjusted for covariates in 2020 for sample of 179 countries. - Median baseline hazard: 0.14 percent. - Mean baseline hazard: 0.32 percent. - Statement on interpretation: Probabilities of 0.32, 1, and 5 percent imply a cumulative probability of policy adoption by the end of a period of 30 years of 9, 26, and 79 percent, respectively. *The International Diffusion of Policies for Climate Change Mitigation — Working Paper No. WP/2022/115* --- _Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022115-print-pdf.pdf_