## wp1856

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---

### Overview and motivation
- Reassesses decoupling between greenhouse gas (GHG) emissions and economic activity by decomposing growth in emissions and real GDP into trend and cyclical components.
- Simple regression for the 20 largest emitters (1990–2014) yields positive elasticities for all countries with an average of 0.6.
- Decomposition shows clearer evidence of decoupling in richer nations (particularly European countries) when focusing on trend components; not yet evident in emerging markets.
- Distinguishes production-based and consumption-based emissions to assess the role of international trade in shifting emissions across countries.

### Main sample, data choices, and summary statistics
- Time period and coverage:
  - Main sample: 1990 through 2014; twenty largest GHG emitters accounting for 74 percent of the world total level of emissions, 63 percent of the world population, 77 percent of global GDP.
- Emissions measures:
  - Broad GHG: CO2, methane (CH4), nitrous oxide (N2O), fluorinated gases; aggregated by WRI using GWP-100 weights per IPCC 2nd Assessment Report.
  - About 25 percent of emissions do not derive from CO2.
  - Longer CO2 series from CDIAC.
  - Consumption-based emissions from Eora MRIO database.
- Output measures:
  - Real GDP growth from IMF WEO; longer-run output from the Maddison Project for extended analyses.
- Policy and country characteristics:
  - Germanwatch's Climate Change Performance Index (CCPI) and EY's Renewable Energy Attractiveness Index (RECAI) used as policy indices.
  - CCPI compares 58 countries starting in 2006 and weights policies to foster efficiency and renewables at 40 percent.
  - RECAI covers 40 advanced and emerging economies for renewable energy investment attractiveness.
- Sectoral data: value added shares (agriculture, industry, services) from World Bank WDI.

- Selected exact statistics (from Table 1):
  - Total GHG emission excl. land use (Production based): Mean 1348; Standard Deviation 1912; Minimum 187; Maximum 11911
  - Total GHG emission excl. land use (Consumption based): Mean 1389; Standard Deviation 1849; Minimum 113; Maximum 9337
  - Co2 emission excl. land use (Production based): Mean 1058; Standard Deviation 1596; Minimum 145; Maximum 10328
  - Agriculture, value added (percent of GDP): Mean 7; Standard Deviation 6; Minimum 0.6; Maximum 29
  - Industry, value added (percent of GDP): Mean 34; Standard Deviation 9; Minimum 19; Maximum 67
  - Services, etc., value added (percent of GDP): Mean 60; Standard Deviation 12; Minimum 26; Maximum 79
  - RECAI score: Mean 57; Standard Deviation 9; Minimum 42; Maximum 75
  - Climate Change Performance Index score: Mean 44; Standard Deviation 28; Minimum -78; Maximum 116
  - GDP per capita, PPP (constant 2011 international $): Mean 22356; Standard Deviation 13686; Minimum 1554; Maximum 52067

### Econometric framework and identification
- Baseline (not preferred) specification:
  - Δe_t = α + ω Δy_t + u_t — yields ω estimates all positive.
- Preferred decomposition into trend and cycle:
  - Cyclical equation: e_t^c = β^c y_t^c + ε_t^c — β^c is cyclical elasticity.
  - Trend equation: e_t^τ = β^τ y_t^τ + γ + ε_t^τ — β^τ is trend elasticity; γ captures different initial levels.
- Trend/cycle extraction:
  - Hodrick-Prescott (HP) filter used with smoothing parameter λ = 100 for annual data.
- Endogeneity and robustness:
  - Cointegration tests: Augmented Dickey Fuller, Philipps-Perron, Kwiatkowski–Phillips–Schmidt–Shin; residuals stationary in vast majority for 1990-2014.
  - Instrumental variables: real output instrumented by trade-weighted real output of trading partners (UN COMTRADE, top 20 partners weighted by export share); first-stage F-statistics (or robust rk Wald) exceeded Stock and Yogo (2005) thresholds.
  - IV vs OLS: IV estimates differ from OLS in two cases (Italy and Ukraine); overall correlation between IV and OLS estimates is 0.9.
  - Bivariate VAR evidence: stronger causality from output to emissions than vice versa.

### Core empirical findings — cyclical vs trend elasticities
- Cyclical elasticities (β^c), production-based emissions (20 countries):
  - All positive: emissions are procyclical.
  - Average cyclical elasticity = 0.5.
  - Statistically significant in all but four cases: Australia, Saudi Arabia, Germany, Brazil.
  - Group averages: Advanced economies = 0.6; Emerging markets = 0.4.
  - Note: cyclical elasticities using consumption-based emissions are generally higher (left for future work).

- Trend elasticities (β^τ), production-based emissions:
  - Average trend elasticity = 0.4.
  - Trend elasticity significantly positive for 14 countries; most of those are well below 1 ("relative decoupling").
  - Group differences:
    - Advanced economies: average trend elasticity close to 0.
    - Emerging markets: average trend elasticity nearly 0.7.
  - Six countries with non-significant or significantly negative trend elasticities:
    - Not significantly different from zero: Italy, Russia, Ukraine.
    - Significantly negative: France, Germany, UK.
  - Interpretation: these countries have reduced or stabilized trend emissions and have implemented national decarbonization policies.

- Production-based vs consumption-based trend elasticities:
  - Average consumption-based trend elasticity = 0.6 (higher than production-based average of 0.4).
  - Group averages:
    - Advanced economies: consumption-based average increases to 0.5 from production-based zero.
    - Emerging markets: consumption-based average remains ≈ 0.7.
  - Notable country examples:
    - Germany: consumption-based elasticity = -0.4; production-based elasticity = -0.8.
    - France and Italy: consumption-based elasticity positive while production-based elasticity negative.
    - Ukraine: notable exception among emerging markets with larger differences.

### Determinants of cross-country differences
- Income and patterns:
  - Trend elasticities tend to decline with per capita income; some support for an inverted-U relationship when plotting trend elasticities against Real GDP per Capita (PPP, 2011).
- Sectoral composition:
  - Trend elasticities positively correlated with agriculture-to-services and industry-to-services ratios (higher shares of agriculture or industry → higher trend elasticities).
  - Correlation coefficients:
    - Agriculture VA / Services VA vs Trend Elasticity (Production): Correlation coef. = 0.315
    - Agriculture VA / Services VA vs Trend Elasticity (Consumption): Correlation coef. = 0.165
    - Industry VA / Services VA vs Trend Elasticity (Production): Correlation coef. = 0.535
    - Industry VA / Services VA vs Trend Elasticity (Consumption): Correlation coef. = 0.289
  - Relationship stronger for production-based than consumption-based emissions.
- Policy indices:
  - Trend elasticities negatively correlated with climate policy indices (higher policy index → lower trend elasticity).
  - Correlation coefficients (policy indices averaged over 2006-14):
    - Trend Elasticity and G's CCPI (Production): Correlation coef. = -0.579
    - Trend Elasticity and G's CCPI (Consumption): Correlation coef. = -0.480
    - Trend Elasticity and EY's RECAI (Production): Correlation coef. = -0.273
    - Trend Elasticity and EY's RECAI (Consumption): Correlation coef. = -0.237
  - Simple regressions controlling for real GDP per capita and sectoral ratios confirm negative and statistically significant influence of policy indices on long-run emissions; authors note small sample size and interpret results as suggestive.

### Changes in trend elasticities over time
- Exercise 1: 1946-1982 (Post-WWII) vs post-1983 (Great Moderation) — averages for 20 countries (Table 2):
  - Trend Elasticity (average):
    - Post-WWII period (1946-1982): 1.11
    - Great Moderation (post-1983): 0.66
  - Cyclical Elasticity (average):
    - Post-WWII period (1946-1982): 0.64
    - Great Moderation (post-1983): 0.65
  - Interpretation: trend elasticities declined substantially over time (average ~0.7 in later period); post-WWII era had high elasticities driven by rapid energy demand growth (mostly oil). China’s trend elasticity more than halved between periods.

- Exercise 2: Full-period vs since-1990 trend elasticities for 16 countries with long CO2 series (Table 3). Selected country values:
  - Australia: Initial Date 1860 — Full Period 1.4 — Since 1990 0.7
  - Canada: Initial Date 1870 — Full Period 1.0 — Since 1990 0.5
  - France: Initial Date 1850 — Full Period 0.7 — Since 1990 0.1
  - Germany: Initial Date 1850 — Full Period 0.9 — Since 1990 -0.6
  - Italy: Initial Date 1860 — Full Period 1.5 — Since 1990 0.6
  - Japan: Initial Date 1950 — Full Period 0.9 — Since 1990 0.7
  - Korea: Initial Date 1911 — Full Period 1.4 — Since 1990 0.7
  - U.K.: Initial Date 1850 — Full Period 0.4 — Since 1990 -0.2
  - U.S.A: Initial Date 1850 — Full Period 1.0 — Since 1990 0.3
  - Brazil: Initial Date 1901 — Full Period 1.2 — Since 1990 1.2
  - China: Initial Date 1950 — Full Period 1.0 — Since 1990 0.6
  - India: Initial Date 1884 — Full Period 1.8 — Since 1990 0.8
  - Indonesia: Initial Date 1889 — Full Period 1.7 — Since 1990 1.2
  - Mexico: Initial Date 1900 — Full Period 1.1 — Since 1990 0.8
  - South Africa: Initial Date 1950 — Full Period 0.9 — Since 1990 0.7
  - Turkey: Initial Date 1923 — Full Period 1.3 — Since 1990 1.0
  - Averages:
    - Average (all countries): Full Period 1.1 — Since 1990 0.6
    - Advanced (average): Full Period 1.0 — Since 1990 0.3
    - Emerging (average): Full Period 1.3 — Since 1990 0.9
  - Interpretation: except for Brazil, trend elasticities since 1990 are much lower than full-sample values; decline is more pronounced for advanced economies.

### Conclusions and policy implications
- Framework:
  - Trend/cycle decomposition is a practical framework to separate long-run (trend) relationships from short-run (cyclical) co-movements when assessing decoupling.
- Summary of empirical conclusions:
  - For the twenty largest emitters, average trend elasticity = 0.4 (response of trend emissions to a 1 percent change in trend GDP).
  - For advanced economies in this group, average trend elasticity ≈ 0; some countries have negative elasticities indicating progress in decoupling trend emissions from trend GDP.
  - Accounting for consumption-based emissions weakens measured progress but does not overturn evidence of decoupling for many advanced economies.
  - Suggestive evidence that policy efforts (as captured by CCPI and RECAI) can lower trend elasticities.
  - Historical evidence: elasticities in recent decades are considerably lower than in previous decades.
- Policy implication:
  - Targeted policy efforts appear capable of reducing trend elasticities, implying that policy can contribute to long-run decoupling even when consumption-based accounting moderates measured progress.

*Source: IMF Working Paper wp1856 (excerpts: 1. Introduction; 3.2 Econometric framework; 4. Results; 5. Conclusions).*

### 1. Introduction ........................................................................................................

### 1. Introduction

### Overview and motivation
- The paper revisits the extent of decoupling between greenhouse gas (GHG) emissions and economic activity by decomposing growth in emissions and real GDP into trend and cyclical components.
- A straightforward regression of emissions growth on real GDP growth for the 20 largest emitters (1990–2014) yields positive elasticities for all countries with an average of 0.6.
- The decomposition shows clearer evidence of decoupling in richer nations (particularly European countries) when focusing on trend components, but not yet in emerging markets.
- The analysis distinguishes production-based and consumption-based emissions to assess the role of international trade in shifting emissions across countries.

### Main sample and data choices
- Time period and country coverage: main sample covers 1990 through 2014 and includes the twenty largest GHG emitters, which account for:
  - 74 percent of the world total level of emissions,
  - 63 percent of the world population,
  - 77 percent of global GDP.
- Emissions measures:
  - Broad GHG measure includes CO2, methane (CH4), nitrous oxide (N2O), and fluorinated gases, aggregated by the World Resources Institute (WRI) using GWP-100 weights per the IPCC's 2nd Assessment Report.
  - About 25 percent of emissions do not derive from CO2; methane is important in major agricultural producers.
  - Longer time series: CO2 emissions from CDIAC.
  - Consumption-based emissions: Eora multi-region input-output (MRIO) database.
- Output measures:
  - Real GDP growth from the IMF World Economic Outlook (WEO) database.
  - Longer-run output for extended analyses from the Maddison Project.
- Policy and country characteristics:
  - Environmental policy indices used: Germanwatch's Climate Change Performance Index (CCPI) and EY's Renewable Energy Attractiveness Index (RECAI).
  - CCPI compares 58 countries starting in 2006 and weights policies to foster efficiency and renewables at 40 percent.
  - RECAI measures attractiveness for renewable energy investment across 40 advanced and emerging economies.
- Sectoral data: value added shares (agriculture, industry, services) from World Bank World Development Indicators.

### Data summary (selected exact statistics from Table 1)
- Total GHG emission excl. land use (Production based):
  - Mean 1348; Standard Deviation 1912; Minimum 187; Maximum 11911
- Total GHG emission excl. land use (Consumption based):
  - Mean 1389; Standard Deviation 1849; Minimum 113; Maximum 9337
- Co2 emission excl. land use (Production based):
  - Mean 1058; Standard Deviation 1596; Minimum 145; Maximum 10328
- Agriculture, value added (percent of GDP): Mean 7; Standard Deviation 6; Minimum 0.6; Maximum 29
- Industry, value added (percent of GDP): Mean 34; Standard Deviation 9; Minimum 19; Maximum 67
- Services, etc., value added (percent of GDP): Mean 60; Standard Deviation 12; Minimum 26; Maximum 79
- RECAI score: Mean 57; Standard Deviation 9; Minimum 42; Maximum 75
- Climate Change Performance Index score: Mean 44; Standard Deviation 28; Minimum -78; Maximum 116
- GDP per capita, PPP (constant 2011 international $): Mean 22356; Standard Deviation 13686; Minimum 1554; Maximum 52067

### Key empirical approach (framework highlights)
- Trend/cycle decomposition of emissions and output is used to separate long-run (trend) elasticities from short-run (cyclical) elasticities.
- Comparison of production-based vs consumption-based emissions quantifies the effect of international trade on measured decoupling.
- Longer historical CO2 series (for 16 of the 20 countries from 1946 onwards, and for 13 countries extending further in some cases) are used to document changes in trend elasticities over time.

### Principal findings
- Trend elasticities:
  - Trend elasticities range from -0.6 to 1.2 across countries.
  - For six countries, including Italy, trend elasticities are essentially zero or negative, indicating decoupling of trend emissions from trend output.
  - Accounting for consumption-based emissions weakens evidence of decoupling for many richer nations: example given for Germany—trend elasticity based on consumption-based emissions is -0.4 compared to -0.8 for production-based emissions.
  - Using longer time series, trend elasticities declined over time: average elasticity declined to 0.7 in the post-1983 sub-period from 1.1 in the earlier sub-period (1946–1982).
  - For post-1990 periods compared to full-sample estimates, trend elasticities are much smaller; example for Germany: the two estimates are -0.6 and 0.9, respectively (post-1990 vs full sample).
- Cyclical elasticities:
  - The cyclical elasticity is positive for all countries and averages 0.5.
  - Example: Germany’s cyclical elasticity is nearly 0.2, which can help explain emissions increases observed during economic booms (e.g., 2016).
  - Cyclical elasticities have not declined much between recent decades and earlier ones and can obscure trend relationships.
- Determinants of cross-country differences:
  - Trend elasticities tend to be lower (greater decoupling) for richer countries measured by per capita GDP.
  - Sectoral structure matters: higher shares of services in value added (relative to industry or agriculture) are associated with lower trend elasticities.
  - Policy measures: actions to encourage use of renewables are associated with stronger decoupling.
- Trade effects:
  - Distinguishing consumption-based emissions (which add emissions embodied in net exports) affects estimates in the expected direction but does not greatly change trend-elasticity estimates in most cases.

### Contribution and scope
- The paper’s contributions:
  - Provides an account of how the link between emissions and output has evolved for the largest world GHG emitters by separating trend and cyclical movements.
  - Shows that accounting for international trade linkages does not greatly affect estimates of trend elasticities in most cases.
  - Relates cross-country differences in trend elasticities to country characteristics and policy indicators.
- The main sample period is 1990–2014; longer CO2 series are used to assess changes over extended historical periods.

*Source: IMF Working Paper — 1. Introduction (content from the provided PDF chapter).*

### 3.2 Econometric framework

### 3.2 Econometric framework

### Specification and objectives
- Baseline introductory specification used to produce elasticity estimates shown in Figure 1(a):
  - Equation (1): Δe_t = α + ω Δy_t + u_t
  - Here Δe_t and Δy_t are the growth rates of emissions and real GDP, respectively.
  - The ω estimates from this specification are all positive.
  - The authors state explicitly that equation (1) is not the preferred specification for measuring decoupling because it does not distinguish trend movements from cyclical relationships.

- Preferred approach: distinguish trends and cycles in both emissions and output via two equations:
  - Cyclical relationship (equation (2)):
    - e_t^c = β^c y_t^c + ε_t^c
    - e_t^c and y_t^c are the cyclical components of log emissions and log real output; β^c is the cyclical elasticity.
  - Trend relationship (equation (3)):
    - e_t^τ = β^τ y_t^τ + γ + ε_t^τ
    - e_t^τ and y_t^τ are the trend components of the logs of emissions and real output; β^τ is the trend elasticity; γ is an intercept to capture different initial levels across countries.
  - The estimates of β^τ (trend elasticities) are the focus of the paper as they measure long-run co-movement of emissions and output.

### Extraction of trend and cyclical components
- Hodrick-Prescott (HP) filter used to extract trend and cyclical components.
  - The HP filter minimizes the function shown in equation (4) for x_t ∈ {e_t, y_t}.
  - x_t^τ denotes the trend component, x_t^c denotes the cyclical component (x_t − x_t^τ).
  - The smoothing parameter λ is set at 100 (common practice with annual data).

### Tests for cointegration and robustness
- Cointegration tests used: Augmented Dickey Fuller, Philipps-Perron, Kwiatkowski–Phillips–Schmidt–Shin.
  - For the 1990-2014 period, residuals were found stationary in the vast majority of cases.
  - For longer time series, early years were characterized by larger residuals.
- Instrumental variable (IV) approach to address endogeneity of output:
  - Real output instrumented by trade-weighted real output of trading partners (constructed from bilateral UN COMTRADE data, top 20 trading partners weighted by export share).
  - First-stage F-statistic (or robust Kleinberger-Papp rk Wald statistic) exceeded Stock and Yogo (2005) thresholds.
  - IV vs OLS: only two cases where IV trend elasticity differs from OLS — Italy and Ukraine.
  - Overall correlation between IV and OLS estimates is 0.9.
- Additional robustness:
  - Bivariate VAR model estimated; greater evidence for causality from output to emissions than vice versa.

---

### Decomposition examples (illustrative)
- Figure 2 decomposes emissions and output into cyclical and trend components for selected advanced and emerging market economies (1990-2014).
  - Left charts: cyclical components (Cycle (HP)).
  - Right charts: trend components (Trend (HP)).
  - Observations summarized in text:
    - In almost all countries, emissions cycles track output cycles (peaks and troughs match), though relationship is somewhat weak for Germany and Brazil.
    - Trend behavior differs across groups:
      - Advanced economies: downward trend in emissions in Germany and the UK over full period; Italy and the US show downward trend in emissions since the mid-2000s.
      - Emerging markets: strong upward trend in emissions matching upward trend in output.

- Figure 3 compares trend components of production-based and consumption-based emissions for six countries:
  - Advanced economies: consumption-based emissions are higher than production-based emissions.
  - Emerging markets: production-based emissions are higher than consumption-based emissions (Brazil is a small recent exception).
  - Germany: both measures trended down over sample period.
  - Italy and US: consumption-based emissions started trending down only since mid-2000s.
  - Emerging markets: both measures trend upward and differences are small.

---

### 4. Results

### 4.1 Cyclical and trend elasticities — key findings
- Cyclical elasticities (β^c) using production-based emissions for 20 countries (Figure 4):
  - In all cases, estimates are positive: emissions are procyclical.
  - Average cyclical elasticity is 0.5.
  - Estimates are statistically significant in all but four cases: Australia, Saudi Arabia, Germany and Brazil.
  - Average elasticity by group:
    - Advanced economies: 0.6
    - Emerging markets: 0.4
  - Note: cyclical elasticities using consumption-based emissions are higher than production-based cyclical elasticities for most countries (left for future work).

- Trend elasticities (β^τ) for all countries (Figure 5):
  - Average trend elasticity is 0.4.
  - Trend elasticity is significantly positive for 14 countries.
  - For most of these 14 countries, elasticity is well below 1 (termed "relative decoupling").
  - Differences between groups:
    - Advanced economies: average trend elasticity close to 0.
    - Emerging markets: average trend elasticity nearly 0.7.
  - Six countries with non-significant or significantly negative trend elasticities (interpreted as absolute decoupling):
    - Not significantly different from zero: Italy, Russia, Ukraine.
    - Significantly negative: France, Germany, UK.
    - These countries are identified as having reduced or stabilized trend emissions and are noted as having implemented national decarbonization policies.

- Production-based vs consumption-based trend elasticities (Figures 6a and 6b):
  - Average consumption-based trend elasticity is 0.6 (higher than production-based average of 0.4).
  - Group averages:
    - Advanced economies: consumption-based average increases to 0.5 from production-based zero.
    - Emerging markets: consumption-based average remains about 0.7 (essentially unchanged).
  - Notable country differences:
    - Germany: consumption-based elasticity = -0.4; production-based elasticity = -0.8.
    - France and Italy: consumption-based elasticity positive while production-based elasticity negative.
    - Ukraine: notable exception among emerging markets with larger differences.

### 4.2 Determinants of cross-country differences
- Aggregate patterns:
  - Average trend elasticities summarized by group and emissions type (Figure 7):
    - Advanced Economy average Trend Elasticity (Production) = 0.0 (visual from text: "average elasticity is close to 0 for the former")
    - Emerging Market average Trend Elasticity (Production) ≈ 0.7 (text: "nearly 0.7 for the latter")
    - Advanced Economy average Trend Elasticity (Consumption) ≈ 0.5 (text: "increases to 0.5 from zero")
    - Emerging Market average Trend Elasticity (Consumption) ≈ 0.7
  - Trend elasticities tend to decline with per capita income; Figure 8 shows some support for an inverted-U shape when plotting trend elasticities against Real GDP per Capita (PPP, 2011).

- Sectoral composition:
  - Trend elasticities are positively correlated with the share of agriculture or industry relative to services in value added (Figure 9):
    - Countries with larger agriculture-to-services or industry-to-services ratios have higher trend elasticities.
    - Relationship stronger for production-based than consumption-based emissions.
  - Correlation coefficients reported in Figure 9 panels:
    - Ratio of Agriculture VA to Services VA vs Trend Elasticity (Production): Correlation coef. = 0.315
    - Ratio of Agriculture VA to Services VA vs Trend Elasticity (Consumption): Correlation coef. = 0.165
    - Ratio of Industry VA to Services VA vs Trend Elasticity (Production): Correlation coef. = 0.535
    - Ratio of Industry VA to Services VA vs Trend Elasticity (Consumption): Correlation coef. = 0.289

- Climate-related policy indices:
  - Trend elasticities are negatively correlated with indices capturing climate policy effort (higher index values → lower trend elasticities) (Figure 10).
    - Policy indicators are averages over the 2006-14 period.
    - Correlation coefficients reported:
      - Trend Elasticity and G's CCPI (Production): Correlation coef. = -0.579
      - Trend Elasticity and G's CCPI (Consumption): Correlation coef. = -0.480
      - Trend Elasticity and EY's RECAI (Production): Correlation coef. = -0.273
      - Trend Elasticity and EY's RECAI (Consumption): Correlation coef. = -0.237
  - Simple regressions of trend elasticities (production or consumption-based) on policy indices, real GDP per capita and sectoral ratios confirm a negative and statistically significant influence of policy indices on long-run emissions.
  - Authors caution small sample size: regressions are suggestive and further work is needed.

### 4.3 Changes in trend elasticities over time — two exercises
- Exercise 1: Compare post-WWII period (1946-1982) with Great Moderation (post-1983) for 20 countries (Table 2):
  - Trend Elasticity (average, 20 countries):
    - Post-WWII period (1946-1982): 1.11
    - Great Moderation (post-1983): 0.66
  - Cyclical Elasticity (average, 20 countries):
    - Post-WWII period (1946-1982): 0.64
    - Great Moderation (post-1983): 0.65
  - Interpretation:
    - Post-WWII period had high elasticities (rapid energy demand growth, mostly oil).
    - Trend elasticities declined significantly in later period, averaging 0.7.
    - Possible contributors: Kyoto protocol, slowdown in energy consumption (notably coal until 2001).
    - China’s trend elasticity more than halved between the two periods.

- Exercise 2: Compare long-period elasticities with post-1990 estimates for 16 countries with historical data (Table 3).
  - Table 3 reports, for each country: Initial date, Full Period trend elasticity, Since 1990 trend elasticity.
  - Selected country values (preserve exactly):
    - Advanced economies:
      - Australia: Initial Date 1860 — Full Period 1.4 — Since 1990 0.7
      - Canada: Initial Date 1870 — Full Period 1.0 — Since 1990 0.5
      - France: Initial Date 1850 — Full Period 0.7 — Since 1990 0.1
      - Germany: Initial Date 1850 — Full Period 0.9 — Since 1990 -0.6
      - Italy: Initial Date 1860 — Full Period 1.5 — Since 1990 0.6
      - Japan: Initial Date 1950 — Full Period 0.9 — Since 1990 0.7
      - Korea: Initial Date 1911 — Full Period 1.4 — Since 1990 0.7
      - U.K.: Initial Date 1850 — Full Period 0.4 — Since 1990 -0.2
      - U.S.A: Initial Date 1850 — Full Period 1.0 — Since 1990 0.3
    - Emerging markets:
      - Brazil: Initial Date 1901 — Full Period 1.2 — Since 1990 1.2
      - China: Initial Date 1950 — Full Period 1.0 — Since 1990 0.6
      - India: Initial Date 1884 — Full Period 1.8 — Since 1990 0.8
      - Indonesia: Initial Date 1889 — Full Period 1.7 — Since 1990 1.2
      - Mexico: Initial Date 1900 — Full Period 1.1 — Since 1990 0.8
      - South Africa: Initial Date 1950 — Full Period 0.9 — Since 1990 0.7
      - Turkey: Initial Date 1923 — Full Period 1.3 — Since 1990 1.0
  - Averages reported:
    - Average (all countries): Full Period 1.1 — Since 1990 0.6
    - Advanced (average): Full Period 1.0 — Since 1990 0.3
    - Emerging (average): Full Period 1.3 — Since 1990 0.9
  - Interpretation:
    - For all countries except Brazil, trend elasticities for the later period are much lower than for the full sample.
    - Reduction is more striking for advanced economies (average 0.3 in recent period vs 1 over full sample); emerging markets also show progress (recent average 0.9 vs 1.3 over full sample).

---

*Source: wp1856 - 3.2 Econometric framework (excerpt) — IMF working paper content provided.*

### 5. Conclusions

### 5. Conclusions

### Framework and approach
- Proposed a simple but comprehensive framework—the trend/cycle decomposition—that is widely used in many other fields in economics to investigate the decoupling of emissions and growth.

### Key empirical findings
- For the twenty largest emitters, the average trend elasticity, viz. the response of trend emissions to a 1 percent change in trend GDP, is 0.4.
- For the advanced economies within this group, the elasticity averages zero; some countries have negative elasticities, suggesting that they had made progress in decoupling their trend emissions from trend GDP.
- Taking account of consumption-based emissions weakens the case for progress but does not overturn it.
- Suggestive evidence that trend elasticities can be lowered through policy efforts on the part of countries.
- Historical investigation shows that elasticities in recent decades are considerably lower than in previous decades.

### Implications for policy and analysis
- The trend/cycle decomposition provides a practical framework to separate long-run (trend) relationships from short-run (cycle) co-movements when assessing decoupling.
- Policy efforts appear capable of reducing trend elasticities, implying that targeted policy can contribute to long-run decoupling even when consumption-based accounting moderates measured progress.

*Source: 5. Conclusions, wp1856.*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp1856.pdf_