## Time-Varying Impacts of Government Spending on CO2 Emissions

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### Model framework and objectives
- Empirical model: factor-augmented interacted vector autoregressive framework purified of expectations (FAIVAR-X), building on Caggiano et al. (2017), Di Serio et al. (2021), and Di Serio et al. (2024).
- Objective: identify the exogenous variation of government spending, Gt, while capturing links with other endogenous variables and allowing nonlinear, interaction-driven state dependence.
- Reduced-form specification:
  - Yt = c + sum_{k=1}^p Ak Yt−k + sum_{k=1}^p sum_{j=1}^n Ajk Gt−k ◊ Xjt−k + Vf(t|t−1) + ut.
  - t = 1, ..., T denotes time dimension.
  - p denotes number of lags; n denotes number of interaction terms.
  - Yt is the vector of endogenous variables; Gt−k ◊ Xjt−k are interaction terms where Xjt−k are endogenous variables in a subset of Yt.
  - f(t|t−1) is treated as an exogenous variable.
  - Ak are autoregressive coefficient matrices; Ajk capture coefficients for interaction terms.
  - ut is a vector of normally distributed residuals with mean zero and covariance matrix À.
- Lag structure restricted to a two-quarter lag:
  - Rationale: increasing the number of lags leads to pervasive instability due to a rapid increase in interaction terms and parameters.

### Key methodological features and advantages
- Interaction terms:
  - Allow capturing nonlinearities and estimating responses conditional on proxies for theoretical channels.
  - Interaction variables are endogenized and react to shocks and other variables in the system.
- Factor augmentation:
  - Principal components from a broad set of macroeconomic variables mitigate limited-information problems; factors act as proxies for unobserved influences (two-step estimation as in Bernanke et al., 2005).
  - Bai and Ng (2007) ICp2 selects three factors.
- Purging anticipated fiscal shocks:
  - Including forecasts of government spending formed over the quarter as an exogenous variable f(t|t−1) purges anticipated components of government spending shocks, mitigating fiscal foresight concerns.

### Dataset, timing, and estimation choices
- Sample period: 1981Q1-2019Q1 (dictated by availability of the news-based environmental and climate policy index by Noailly et al. (2024)).
- Lag choice: two-quarter lag structure is used.
- Factor extraction: principal components; three factors selected.
- Exogenous variable:
  - f(t|t−1) is the forecast of time-t growth of real government spending over the past three months based on the Survey of Professional Forecasters (SPF).
  - Computation of forecast: f(t|t≠1) = [ (C3 Ge t|t≠1 / Ge t≠1|t≠1)^4 − 1 ] × 100, where Ge t|t≠1 and Ge t≠1|t≠1 are the sum of the forecasts for RFEDGOV and RSLGOV.

### Endogenous variables (vector Yt)
- Yt = [ Gt, GDPt, Tt, COP2,t, COC2,t, EPt, ECt, πt, Rt, Ft, SERVt, ENVPt, PGt ]′
  - Gt: real government purchases (sum of government gross fixed capital formation and government consumption), included in per-capita terms.
  - GDPt: real gross domestic product (per-capita terms).
  - Tt: real net taxes (per-capita terms).
  - COP2,t: production-generated CO2 emissions (per-capita terms).
  - COC2,t: consumption-generated CO2 emissions (per-capita terms).
  - EPt: year-on-year growth rate of the oil price (proxy for energy prices).
  - ECt: energy consumption (per capita total energy consumed across residential, commercial, industrial, and transportation sectors).
  - πt: year-on-year CPI inflation rate.
  - Rt: one-year government bond rate.
  - Ft: common factors extracted from a broad macro dataset (three factors).
  - SERVt: share of service providers over total number of government and private employees.
  - ENVPt: news-based environmental and climate policy index (Noailly et al., 2024).
  - PGt: share of government spending on public goods (education, housing, income security, health, recreation).

### Interaction channels and their proxies
- Four interaction channels (Gt−k ◊ Xjt−k) endogenized within the generalized impulse response framework:
  - Income: proxied by real per capita GDP (GDPt). Linked to the Environmental Kuznets Curve (EKC).
  - Tertiarization: proxied by the share of service workers (SERVt).
  - Environmental regulation: proxied by the environmental and climate policy index (ENVPt).
  - Spending composition: proxied by the share of government spending on public goods (PGt).

### Additional modeling notes
- CO2 definitions:
  - Production-generated CO2 emissions include Total Industrial Sector CO2 Emissions.
  - Consumption-generated CO2 emissions are constructed as the sum between Total Energy Residential Sector CO2 Emissions and Total Energy Transportation Sector CO2 Emissions.
- Energy variables:
  - EPt and ECt included because energy prices and consumption are important determinants of emissions; ECt is noted to Granger-cause long-term pollution from CO2 in the U.S. context.
- Monetary policy:
  - Rt is the one-year government bond rate preferred over the federal funds rate as it incorporates forward guidance effects.
- FAIVAR-X advantage:
  - Allows conditioning shock propagation across a continuum of regimes, unlike threshold VARs which estimate separate coefficients per regime.

### Inference, identification, and computation of cumulated CO2 elasticities
- Estimation approach:
  - FAIVARX model estimated using a Bayesian strategy with Minnesota prior for the coefficients; variance-covariance matrix set to its OLS estimate.
  - Hierarchical Minnesota priors: hyperparameters optimized via grid search maximizing the model’s marginal likelihood.
- Generalized impulse response functions (GIRFs):
  - Derived following Koop et al. (1996) and Caggiano et al. (2017), endogenizing variables in interaction terms.
  - GIRF simulation design highlights:
    - Initial condition chosen as Ê_{t≠1}.
    - Residual series simulated from empirical distribution ̃u_{r,t+h}.
    - For each residual simulation r, recover paths E[y_{t+h}|Ê_{t≠1}]_r and E[y_{t+h}|",Ê_{t≠1}]_r.
    - Government spending shock identified using a Cholesky decomposition (government spending ordered first as in Blanchard and Perotti (2002)).
    - Average GIRF across R = 500 simulations to obtain consistent estimates.
  - Posterior sampling:
    - Step 2 repeated for 10,000 draws from the posterior distribution.
    - Median IRFs across the 10,000 parameter draws reported.
    - Parameter uncertainty summarized by saving the 16th and 84th percentiles as an error band.
- Cumulative CO2 elasticities E_h:
  - E_h = (sum_{h=0}^H dlnCO2(h)) / (sum_{h=0}^H dlnG(h)) for horizons h = 0, 1, ..., H.

### Key empirical findings on cumulative CO2 elasticities (1982–2019)
- Horizons reported: H = {4, 12, 20} (one, three, and five years).
- Consumption-generated CO2 emissions:
  - Generally rise in response to a positive government spending shock.
  - Cumulative effect grows stronger over the medium term compared to the short term.
  - Decline over time: at a five-year horizon, elasticity declined from nearly 0.5 in the early 1980s to about 0.1 in 2019.
- Production-generated CO2 emissions:
  - Larger absolute magnitudes at longer horizons.
  - Time evolution: early 1980s a positive response (around 0.4 at five years), weakening and reversing by the 1990s; by end of sample the five-year cumulative elasticity is approximately −0.5.
- Subsample averages (cut at year 2000) — five-year averages from Table 1:
  - Consumption-generated: Pre-2000q3 = 0.35; Post-2000q3 = 0.10; Prob([B]<[A]) = 0.78.
  - Production-generated: Pre-2000q3 = 0.12; Post-2000q3 = −0.14; Prob([B]<[A]) = 0.94.
- Bayesian-compatible inference on subsample differences:
  - Consumption-generated emissions: probability of a negative difference increases from 47 percent at a one-year horizon to 78 percent at a five-year horizon.
  - Production-generated emissions: probability of a negative difference remains above 90 percent across all horizons.
  - Inference based on 10,000 posterior draws with 68 percent credible sets reported.

### Drivers of CO2 emission elasticities — partial-correlation evidence
- Method: Ten-year rolling windows of partial correlations between elasticities and each interaction variable (controlling for the other three) from 1992Q1 to 2019Q1.
- Consumption-generated elasticities (partial-correlation patterns):
  - Negative relationship with environmental protection index (ENVPt).
  - Negative relationship with share of workers in service-providing activities (SERVt).
  - Relation with GDP tends to be positive but not uniform.
  - Relation with share of public goods (PGt) switches signs across subperiods.
- Production-generated elasticities (partial-correlation patterns):
  - Consistently negative correlations with ENVPt and SERVt.
  - GDP level generally shows a positive association (with some windows of negative association).
  - Share of public goods mostly negatively correlated, though the negative association weakens at times.

### Cumulated CO2 elasticities by spending composition — consumption vs. investment
- Government consumption:
  - Consumption-generated elasticities mirror total government expenditure elasticities.
  - Consumption-generated elasticities begin about 0.3–0.5, trend downward but remain positive; five years after a shock a one percent rise in government consumption raises household emissions by roughly 0.1–0.2 percent toward the end of the sample.
  - Production-generated elasticities tied to government consumption shift sign around the early 1990s: mildly positive through the 1980s, flipping negative from the mid-1990s onward, reaching –0.3 to –0.5 in the late 2000s.
  - Table 2 summary probabilities:
    - Consumption-generated Prob([B]<[A]) ranges between 0.59 and 0.81 across horizons.
    - Production-generated Prob([B]<[A]) at least 0.95 at every horizon.
- Government investment:
  - Cyclical pattern: rise sharply in early 1980s, fall through the 1990s, rebound in early 2000s, dip after global financial crisis, edge upward toward end of sample.
  - Production-generated elasticities decline on average after 2000 Q3 but remain on average positive with short-lived drops below zero.
  - Consumption-generated elasticities for government investment show no significant change across the 2000 Q3 breakpoint, ranging between 0.1–0.4 regardless of horizon.
  - Table 3 summary probabilities:
    - Consumption-generated Prob([B]<[A]) ranges between 0.12 and 0.48 across horizons.
    - Production-generated Prob([B]<[A]) ranges between 0.45 and 0.74 across horizons.
- Aggregate interpretation:
  - Government consumption is chiefly responsible for the gradual reduction in consumption-generated CO2 elasticities to government spending and for the post-1990 shift of production-generated elasticities from positive to negative.
  - Government investment plays a lesser role in the decline in consumption-generated elasticities and is not the primary driver of the production-generated sign change in the recent sample.

### Conclusions — policy-relevant implications and recommendations
- Main empirical conclusions:
  - Government spending had heterogeneous and time-varying effects on U.S. carbon emissions over 1981–2019.
  - Consumption-generated CO2 emissions responded positively to fiscal expansions throughout 1981–2019, but the medium-term elasticity declined substantially (e.g., five-year elasticity from roughly 0.5 in early 1980s to about 0.1 in 2019).
  - Production-generated CO2 emissions: positive responses in the early 1980s flipped to negative by the 1990s and remained negative into the most recent decade (five-year elasticity from around 0.4 at the start to approximately −0.5 at the end).
  - Subsample comparisons (pre- and post-2000q3) and Bayesian-compatible inference indicate high probability that elasticities have declined over time, particularly for production-generated emissions.
- Drivers consistent with evidence:
  - Strong negative roles for environmental regulation (ENVPt) and tertiarization (SERVt) in moderating fiscal expansions’ carbon impacts.
  - GDP level generally positively associated with emission elasticities unless counteracted by regulation or technology.
  - Government consumption—more than investment—explains much of the long-run decline in elasticities and the sign reversal for production-generated emissions.
- Policy recommendations:
  - Greening of procurement standards to reduce emissions associated with government purchases.
  - Expansion of public investment in clean infrastructure to strengthen downward pressure on emissions.
  - Tightening of environmental regulation to further reduce both household and industrial emissions.
  - Emphasis on spending composition and regulatory context when designing fiscal measures for environmental objectives.

*Source — wpiea2025132-print-pdf*

### 2.1  Empirical Model  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

### 2.1  Empirical Model

### Model framework and objectives
- The empirical model is a factor-augmented interacted vector autoregressive framework purified of expectations (FAIVAR-X), building on Caggiano et al. (2017), Di Serio et al. (2021), and Di Serio et al. (2024).
- Objective: identify the exogenous variation of government spending, Gt, while capturing links with other endogenous variables and allowing nonlinear, interaction-driven state dependence.
- The reduced-form specification:
  Yt = c + sum_{k=1}^p Ak Yt−k + sum_{k=1}^p sum_{j=1}^n Ajk Gt−k ◊ Xjt−k + Vf(t|t−1) + ut.
  - t = 1, ..., T denotes time dimension.
  - p denotes number of lags; n denotes number of interaction terms.
  - Yt is the vector of endogenous variables; Gt−k ◊ Xjt−k are interaction terms where Xjt−k are endogenous variables in a subset of Yt.
  - f(t|t−1) is treated as an exogenous variable.
  - Ak are autoregressive coefficient matrices; Ajk capture coefficients for interaction terms.
  - ut is a vector of normally distributed residuals with mean zero and covariance matrix À.
- The specification restricts analysis to a two-quarter lag structure.
  - Rationale: increasing the number of lags leads to pervasive instability due to a rapid increase in interaction terms and parameters.

### Key methodological features and advantages
- Interaction terms allow capturing nonlinearities and estimating responses conditional on proxies for theoretical channels; interaction variables are endogenized and react to shocks and other variables in the system.
- Augmentation with factors from a broad set of macroeconomic variables mitigates limited-information problems; factors act as proxies for unobserved influences (two-step estimation as in Bernanke et al., 2005).
- Including forecasts of government spending formed over the quarter as an exogenous variable purges anticipated components of government spending shocks, mitigating fiscal foresight concerns.

### Dataset, timing, and estimation choices
- Sample period: 1981Q1-2019Q1 (dictated by availability of the news-based environmental and climate policy index by Noailly et al. (2024)).
- Lag choice: two-quarter lag structure is used.
- Factor extraction: principal components from a large set of macroeconomic series; Bai and Ng (2007) ICp2 selects three factors.
- Exogenous variable: f(t|t−1) is the forecast of time-t growth of real government spending over the past three months based on the Survey of Professional Forecasters (SPF).

### Endogenous variables (vector Yt)
- Yt = [ Gt, GDPt, Tt, COP2,t, COC2,t, EPt, ECt, πt, Rt, Ft, SERVt, ENVPt, PGt ]′
  - Gt: real government purchases (sum of government gross fixed capital formation and government consumption), included in per-capita terms.
  - GDPt: real gross domestic product (per-capita terms).
  - Tt: real net taxes (per-capita terms).
  - COP2,t: production-generated CO2 emissions (per-capita terms).
  - COC2,t: consumption-generated CO2 emissions (per-capita terms).
  - EPt: year-on-year growth rate of the oil price (proxy for energy prices).
  - ECt: energy consumption (per capita total energy consumed across residential, commercial, industrial, and transportation sectors).
  - πt: year-on-year CPI inflation rate.
  - Rt: one-year government bond rate.
  - Ft: common factors extracted from a broad macro dataset (three factors).
  - SERVt: share of service providers over total number of government and private employees.
  - ENVPt: news-based environmental and climate policy index (Noailly et al., 2024).
  - PGt: share of government spending on public goods (education, housing, income security, health, recreation).

### Interaction channels and their proxies
- Four key channels govern how government spending may influence CO2 emissions; each is proxied and interacts with government spending:
  - Income: proxied by real per capita GDP (GDPt). Linked to the Environmental Kuznets Curve (EKC).
  - Tertiarization: proxied by the share of service workers (SERVt). Captures shifts toward service-oriented activities.
  - Environmental regulation: proxied by the environmental and climate policy index (ENVPt).
  - Spending composition: proxied by the share of government spending on public goods (PGt).
- Interaction terms are of the form Gt−k ◊ Xjt−k, and all interaction variables are endogenized within the generalized impulse response framework.

### Additional modeling notes
- Production- and consumption-generated CO2 emissions definitions:
  - Production-generated CO2 emissions include Total Industrial Sector CO2 Emissions.
  - Consumption-generated CO2 emissions are constructed as the sum between Total Energy Residential Sector CO2 Emissions and Total Energy Transportation Sector CO2 Emissions (per U.S. Environmental Protection Agency data).
- Energy price and consumption inclusion rationale: energy prices (EPt) and energy consumption (ECt) are important determinants of emissions; ECt is noted to Granger-cause long-term pollution from CO2 in the U.S. context.
- Monetary policy capture: Rt is the one-year government bond rate preferred over the federal funds rate as it incorporates forward guidance effects.
- The FAIVAR-X with interaction terms allows conditioning shock propagation across a continuum of regimes, in contrast to threshold VARs which estimate separate coefficients per regime.

*Source: wpiea2025132-print-pdf - 2.1  Empirical Model (excerpt)*

### 2.3  Inference, Identification, and Computation of Cumulated CO

### 2.3  Inference, Identification, and Computation of Cumulated CO2 Elasticities

### Estimation and Identification Procedure
- Model estimated: FAIVARX model (equation (1)).
- Bayesian strategy with Minnesota prior for the coefficients; variance-covariance matrix set to its OLS estimate.
- Hierarchical approach for Minnesota priors: hyperparameters optimized via grid search maximizing the model’s marginal likelihood.
- Generalized impulse response functions (GIRFs) derived following Koop et al. (1996) and Caggiano et al. (2017), endogenizing variables in interaction terms and conditioning responses on their evolution.
- GIRF computation highlights and simulation design:
  - Initial condition chosen as Ê_{t≠1}.
  - Residual series simulated from empirical distribution ̃u_{r,t+h}.
  - For each residual simulation r, recover paths E[y_{t+h}|Ê_{t≠1}]_r and E[y_{t+h}|",Ê_{t≠1}]_r.
  - Government spending shock identified using a Cholesky decomposition (government spending ordered first as in Blanchard and Perotti (2002)).
  - Average GIRF across R = 500 simulations to obtain consistent estimates.
- Posterior sampling and uncertainty:
  - Step 2 repeated for 10,000 draws from the posterior distribution.
  - Median IRFs across the 10,000 parameter draws reported.
  - Parameter uncertainty summarized by saving the 16th and 84th percentiles as an error band.
- Cumulative CO2 emissions elasticities E_h computed analogously to cumulative fiscal multipliers:
  - E_h = (sum_{h=0}^H dlnCO2(h)) / (sum_{h=0}^H dlnG(h)) for horizons h = 0, 1, ..., H (Equation (4)).

### 3.1 Cumulative CO2 Elasticities to Government Spending — Key Findings
- Sample and horizons:
  - Impulse responses computed quarter-by-quarter for the estimation sample spanning 1982 to 2019 (after adjusting for the lag structure).
  - Reported horizons H = {4, 12, 20} (i.e., one, three, and five years).
- Consumption-generated CO2 emissions:
  - Generally rise in response to a positive government spending shock.
  - Cumulative effect grows stronger over the medium term compared to the short term.
  - Decline over time: at a five-year horizon, elasticity declined from nearly 0.5 in the early 1980s to about 0.1 in 2019.
- Production-generated CO2 emissions:
  - Also show larger absolute magnitudes at longer horizons.
  - Time evolution differs: early 1980s a positive response (around 0.4 at five years), weakening and reversing by the 1990s; by end of sample the five-year cumulative elasticity is approximately ≠0.5.
- Subsample averages (cut at year 2000) — summary from Table 1:
  - Consumption-generated five-year average: Pre-2000q3 = 0.35; Post-2000q3 = 0.10; Prob([B]<[A]) = 0.78.
  - Production-generated five-year average: Pre-2000q3 = 0.12; Post-2000q3 = ≠0.14; Prob([B]<[A]) = 0.94.
- Bayesian-compatible inference on subsample differences:
  - For consumption-generated emissions, probability of a negative difference increases from 47 percent at a one-year horizon to 78 percent at a five-year horizon.
  - For production-generated emissions, probability of a negative difference remains above 90 percent across all horizons.
  - Across draws (10,000), distributions of differences shown with 68 percent credible sets.

### 3.2 Drivers of CO2 Emission Elasticities — Partial-Correlation Evidence
- Method: Ten-year rolling windows of partial correlations between elasticities and each interaction variable (controlling for the other three) from 1992Q1 to 2019Q1.
- Interaction variables examined: real GDP per capita level, share of service-providing workers, environmental regulation (environmental protection index), and spending composition (share of public goods).
- Consumption-generated elasticities (Figure 4) — partial-correlation patterns:
  - Negative relationship with environmental protection index.
  - Negative relationship with share of workers in service-providing activities.
  - Relation with GDP tends to be positive but not uniform.
  - Relation with share of public goods switches signs across subperiods (nuanced).
- Production-generated elasticities (Figure 5) — partial-correlation patterns:
  - Consistently negative correlations with environmental protection index and share of workers in service activities.
  - GDP level generally shows a positive association (with some windows of negative association noted).
  - Share of public goods mostly negatively correlated (consistent with a “technique effect”), though the negative association weakens at times.

### 3.3 Cumulated CO2 Elasticities by Spending Composition — Consumption vs. Investment
- Government consumption:
  - Consumption-generated elasticities mirror total government expenditure elasticities.
  - Consumption-generated elasticities begin about 0.3–0.5, trend downward but remain positive; five years after a shock a one percent rise in government consumption raises household emissions by roughly 0.1–0.2 percent toward the end of the sample.
  - Production-generated elasticities tied to government consumption shift sign around the early 1990s: mildly positive through the 1980s, flipping negative from the mid-1990s onward, reaching –0.3 to –0.5 in the late 2000s.
  - Table 2 summary probabilities:
    - Consumption-generated Prob([B]<[A]) ranges between 0.59 and 0.81 across horizons.
    - Production-generated Prob([B]<[A]) at least 0.95 at every horizon.
- Government investment:
  - Cyclical pattern: rise sharply in early 1980s, fall through the 1990s, rebound in early 2000s, dip after global financial crisis, edge upward toward end of sample.
  - Production-generated elasticities decline on average after 2000 Q3 but remain on average positive with short-lived drops below zero.
  - Consumption-generated elasticities for government investment show no significant change across the 2000 Q3 breakpoint, ranging between 0.1–0.4 regardless of horizon.
  - Table 3 summary probabilities:
    - Consumption-generated Prob([B]<[A]) ranges between 0.12 and 0.48 across horizons.
    - Production-generated Prob([B]<[A]) ranges between 0.45 and 0.74 across horizons.
- Aggregate interpretation:
  - Government consumption is chiefly responsible for the gradual reduction in consumption-generated CO2 elasticities to government spending and for the post-1990 shift of production-generated elasticities from positive to negative.
  - Government investment plays a lesser role in the decline in consumption-generated elasticities and is not the primary driver of the production-generated sign change in the recent sample.

### 4 Conclusions — Summary of Main Results
- Government spending had heterogeneous and time-varying effects on U.S. carbon emissions over 1981–2019.
- Consumption-generated CO2 emissions responded positively to fiscal expansions throughout 1981–2019, but the medium-term elasticity declined substantially (e.g., five-year elasticity from roughly 0.5 in early 1980s to about 0.1 in 2019).
- Production-generated CO2 emissions: positive responses in the early 1980s flipped to negative by the 1990s and remained negative into the most recent decade (five-year elasticity from around 0.4 at the start to approximately ≠0.5 at the end).
- Subsample comparisons (pre- and post-2000q3) and Bayesian-compatible inference indicate high probability that elasticities have declined over time, particularly for production-generated emissions.
- Drivers consistent with evidence:
  - Strong negative roles for environmental regulation and tertiarization (share of service-providing workers) in moderating fiscal expansions’ carbon impacts.
  - GDP level generally positively associated with emission elasticities unless counteracted by regulation or technology.
  - Government consumption—more than investment—explains much of the long-run decline in elasticities and the sign reversal for production-generated emissions.

*Italic: Source — wpiea2025132-print-pdf - 2.3  Inference, Identification, and Computation of Cumulated CO2 Elasticities*

### 0.5 to 0.1. Production-generated emissions, by contrast, moved from an elasticity close to

### Time-Varying Impacts of Government Spending on CO2 Emissions

### Key empirical findings
- Consumption-generated emission elasticities moved from 0.5 to 0.1.
- Production-generated emissions moved from an elasticity close to 0.4 in the early 1980s to about –0.5 by the late 2010s.
- Rolling correlations with structural and policy indicators reveal:
  - The income effect may have prevalently contributed positively to emissions.
  - Stricter environmental regulation shows a negative association with emissions.
  - A rising service share shows a negative association with emissions.
  - Greater allocations to public goods show a negative association with emissions.
- Decomposing outlays highlights the pivotal role of government consumption:
  - Government consumption accounted for most of the downward trend in consumption-generated elasticities.
  - Government consumption drives the post-1990 sign switch on the production-generated side.
  - Government investment contributed only marginally to the trends.

### Mechanisms and interpretation
- The elasticity of emissions is highly state dependent, reconciling seemingly conflicting empirical results reported earlier in the literature.
- The environmental impact of fiscal policy is shaped by:
  - Spending composition (notably government consumption versus government investment).
  - Regulatory context (environmental regulation and climate policy).
  - Structure of production (service share and industrial composition).

### Policy recommendations
- Greening of procurement standards to reduce emissions associated with government purchases.
- Expansion of public investment in clean infrastructure to strengthen downward pressure on emissions.
- Tightening of environmental regulation to further reduce both household and industrial emissions.
- Emphasis on spending composition and regulatory context when designing fiscal measures for environmental objectives.

### Directions for future research
- Extend the framework to other greenhouse gases.
- Explore alternative tax-spending mixes.
- Apply the framework in cross-country settings.

### Data and methodology (summary)
- Sample: quarterly U.S. data from 1981Q1 to 2019Q1.
- Baseline endogenous variables:
  - Gt: real per capita government consumption expenditures and gross investment;
  - GDPt: real per capita gross domestic product;
  - Tt: real per capita government current tax receipts, constructed as the sum of real per capita federal government current tax receipts and real per capita state and local government current tax receipts;
  - COP2,t: per capita production-generated CO2 emissions, measured as per capita Total Industrial Sector CO2 Emissions;
  - COC2,t: per capita consumption-generated CO2 emissions, constructed as the sum between per capita total energy residential sector CO2 emissions and per capita total energy transportation sector CO2 emissions;
  - EPt: yearly real oil price growth rate (real crude oil domestic first purchase price);
  - ECt: per capita total energy consumed by residential, commercial, industrial, transportation sectors;
  - fit: year-on-year CPI inflation rate;
  - Rt: market yield on U.S. Treasury securities at 1-year constant maturity;
  - SERVt: share of service-providing employees over total government and private employees;
  - ENVPt: environmental and climate policy news-based index, developed by Noailly et al. (2024);
  - PGt: share of government spending in education, housing, income security, health, recreation.
- Data sources:
  - Gt, GDPt, Tt, fit, PGt downloaded from the U.S. Bureau of Economic Analysis (BEA).
  - COP2,t, COC2,t, EPt, ECt downloaded from the U.S. Energy Information Administration (EIA).
  - Rt retrieved from the Federal Reserve Bank of St. Louis database (FRED).
  - SERVt constructed using U.S. Bureau of Labor Statistics (BLS) data.
- Exogenous variable:
  - The exogenous variable is the forecast of time-t growth of real government spending over the past three months based on the Survey of Professional Forecasters (SPF) available from Federal Reserve Bank of Philadelphia.
  - As in Auerbach and Gorodnichenko (2012b,a), the annualized growth rate of real government purchases forecast for timetat timet≠1 is computed as f(t|t≠1) = [ (C3 Ge t|t≠1 / Ge t≠1|t≠1)^4 − 1 ] × 100, where Ge t|t≠1 and Ge t≠1|t≠1 are the sum of the forecasts for the Real Federal Government Consumption Expenditures & Gross Investment (RFEDGOV) and Real State and Local Government Consumption Expenditures & Gross Investment (RSLGOV).
- Informational dataset:
  - The informational dataset used to extract common factors is composed by 64 series downloaded from the Federal Reserve Bank of St. Louis database, covering National Account, Government Statistics, Output and income, Employment and hours, Money and credit quantity aggregates, Interest Rates, and Prices.
  - Where appropriate variables were differenced to guarantee stationarity tested by the Dickey and Fuller (1979) and Kwiatkowski et al. (1992) tests.

*Time-Varying Impacts of Government Spending on CO2 Emissions. Working Paper No. WP/2025/132*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025132-print-pdf.pdf_