## 4. Pollution Damage Calculations for Santiago

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---

### Introduction and objective
- Purpose: compile rough estimates of automobile and commercial truck externalities for Chile (with focus on Santiago) by combining local data with extrapolations from U.S. literature to derive (second-best) corrective gasoline and diesel fuel taxes.
- Key contextual benchmarks:
  - Corrective gasoline tax (benchmark): $2.35 per gallon (year 2006 dollars), about 60 percent greater than the prevailing fuel tax.
  - Corrective diesel tax (benchmark): $2.09 per gallon (year 2006 dollars).
- Main caveat: estimates depend on judgment where data are limited; valuation of fatality risks (VSL) is the most important source of uncertainty.

### Conceptual framework for corrective fuel taxes
- Separate treatment for gasoline (passenger vehicles) and diesel (commercial trucks).
- Externalities accounted:
  - Proportional to fuel use (eG, dollars per gallon): e.g., CO2, a share of local tailpipe emissions.
  - Proportional to vehicle miles (eM, dollars per vehicle mile): e.g., accidents, congestion, a share of local tailpipe emissions.
- Corrective gasoline tax (long run, simplified):
  - CGt = eG + β · g eM
  - eG and eM denote marginal external costs from gasoline use and mileage; g is fuel per mile (inverse of fuel economy); β is fraction of incremental reduction in gasoline use coming from reduced miles driven.
- Corrective diesel tax (analogous):
  - CFt = eF + α · f eT
  - eF and eT denote marginal external costs from diesel use and truck miles; f is diesel fuel per mile; α is fraction of incremental fuel reduction from reduced truck mileage.

### Parameter compilation (benchmark assumptions, year 2006)
- Fuel, vehicle, and tax data (exact values):
  - Initial fuel consumption, million gallons: Automobiles 819.02, Trucks 898.28
  - Initial fuel economy, miles/gallon: Automobiles 30.00, Trucks 8.00
  - Vehicle miles, billion: Automobiles 24.57, Trucks 7.19
  - Initial retail fuel price, $/gallon: Gasoline $4.27, Diesel $3.17
  - Initial fuel tax, $/gallon: Gasoline $1.46, Diesel $0.37
  - Fuel tax revenue, $billion: Gasoline $1.19, Diesel $0.33
- Externalities from fuel combustion, $/gallon:
  - Local tailpipe emissions: Gasoline $0.29, Diesel $0.18
  - Carbon: Gasoline $0.18, Diesel $0.21
- Externalities from driving, $/vehicle mile:
  - Local tailpipe emissions: Automobiles $0.02, Trucks $0.07
  - Congestion: Automobiles $0.04, Trucks $0.10
  - Accidents: Automobiles $0.06, Trucks $0.07
  - Noise: Automobiles $0.00, Trucks $0.01
  - Road damage: Automobiles $0.00, Trucks $0.08
- Elasticities:
  - Fuel demand elasticity: Automobiles -0.50, Trucks -0.50
  - Mileage to fuel price elasticity: Automobiles 0.50, Trucks 0.60
  - Fuel economy elasticity: Automobiles 0.25, Trucks 0.20
- Additional parameter notes:
  - Fleet fuel economy assumptions: passenger vehicles 30 miles per gallon; heavy trucks 8 miles per gallon.
  - Local emissions apportionment: automobiles two-thirds of local emissions vary with mileage and one-third with fuel combustion; trucks one-third proportional to fuel combustion and two-thirds to miles driven.
  - CO2 emissions per gallon: gasoline 0.009 tons, diesel 0.010 tons.
  - Central social cost of carbon: $21 per ton (year 2007 dollars), sensitivity low/high: $5 and $65 per ton.
  - Marginal delay for Santiago: 0.035 hours per auto mile (average across time of day); nationwide weighted marginal delay: 0.022 hours per mile.
  - Central value of travel time (VOT): $2.7 per hour, range $1.5–$4.5 per hour.
  - Marginal external congestion cost (preferred nationwide, after scaling): $0.04 per mile.
  - Truck mile contributes 2.5 times congestion of an auto mile.
  - Local pollution nationwide: $0.03 per mile average (Santiago $0.06 per mile); apportioned two-thirds to mileage and one-third to fuel use.
  - Automobile local pollution external cost outside Santiago: $0.007 per mile (based on VSL $1.6 million extrapolation).
  - Accident externalities: car external cost $0.06 per mile (pedestrian/cyclist fatalities account for ~three-quarters); truck external cost $0.07 per mile (assumed 25 percent greater than cars).
  - Road damage for trucks: $0.08 per mile; noise for trucks: $0.01 per mile.

### Benchmark corrective tax results and impacts
- Corrective taxes (year 2006 dollars):
  - Gasoline corrective tax: $2.35 per gallon
  - Diesel corrective tax: $2.09 per gallon
- Contribution breakdown (per gallon):
  - Gasoline (dollars per gallon):
    - Local tailpipe emissions: $0.60
    - Carbon: $0.18
    - Congestion: $0.63
    - Accidents: $0.94
    - Noise: $0.00
    - Road damage: $0.00
  - Diesel (dollars per gallon):
    - Local tailpipe emissions: $0.53
    - Carbon: $0.21
    - Congestion: $0.52
    - Accidents: $0.39
    - Noise: $0.03
    - Road damage: $0.40
- Impacts of raising taxes from 2006 levels to corrective levels (long-run):
  - Percent reduction in fuel use: Gasoline 9.0 percent, Diesel 19.5 percent
  - Percent increase in fuel economy: Gasoline 4.9 percent, Diesel 9.1 percent
  - Percent increase in tax revenue: Gasoline 46.8 percent, Diesel 352.3 percent
  - Welfare gain (annual), $ million: Gasoline $33.2 million, Diesel $150.2 million
- Counterfactual relative to zero initial tax:
  - Percent reduction in fuel use: Gasoline 26.2 percent, Diesel 24.4 percent
  - Welfare gain, $ million: Gasoline $229.3 million, Diesel $222.3 million

### Sensitivity analysis — key scenarios and numerical outcomes
- Corrective taxes under alternative parameter values ($/gallon):
  - Benchmark case: Gasoline $2.35, Diesel $2.09
  - VSL = $0.8 million: Gasoline $1.53, Diesel $1.60
  - VSL = $3.1 million: Gasoline $4.00, Diesel $3.02
  - Social cost of carbon = $5 per ton: Gasoline $2.20, Diesel $1.91
  - Social cost of carbon = $65 per ton: Gasoline $2.78, Diesel $2.57
  - Initial fuel economy 36 miles per gallon: Gasoline $2.51, Diesel $2.31
  - Initial fuel economy 24 miles per gallon: Gasoline $2.20, Diesel $1.87
  - Local pollution increased 50 percent: Gasoline $2.69, Diesel $2.37
  - Local pollution decreased 50 percent: Gasoline $2.02, Diesel $1.81
  - Travel delay increased 50 percent: Gasoline $2.71, Diesel $2.37
  - Travel delay decreased 50 percent: Gasoline $2.01, Diesel $1.81
  - VOT = $1.5 per hour: Gasoline $2.05, Diesel $1.84
  - VOT = $4.5 per hour: Gasoline $2.83, Diesel $2.46
  - Accident externalities increased 50 percent: Gasoline $2.88, Diesel $2.30
  - Accident externalities decreased 50 percent: Gasoline $1.85, Diesel $1.88
  - Road damage increased 50 percent: Gasoline $2.35, Diesel $2.30
  - Road damage decreased 50 percent: Gasoline $2.35, Diesel $1.88
  - Fuel price elasticity increased 50 percent: Gasoline $2.41, Diesel $2.17
  - Fuel price elasticity decreased 50 percent: Gasoline $2.31, Diesel $2.01
  - Fraction of fuel price elasticity due to reduced mileage:
    - Gasoline 0.65, diesel 0.75: Gasoline $2.93, Diesel $2.46
    - Gasoline 0.35, diesel 0.45: Gasoline $1.76, Diesel $1.67
- Principal sensitivity finding: VSL assumptions produce the largest variation in corrective taxes; other parameters (emission rates, fuel economy, behavioral responses, marginal travel delays) have relatively smaller impacts.
- Additional sensitivity notes (from alternate truck fuel economy cases and parameter variation):
  - Changing truck fuel economy to 6.4 and 9.6 miles per gallon causes corrective taxes to vary by about + or –6 percent for cars and + or –10 percent for trucks.
  - Increasing/decreasing local pollution damages by up to 50 percent causes corrective taxes to vary by up to about + or –14 percent.
  - Increasing/decreasing marginal travel delay by up to 50 percent causes corrective taxes to vary by up to about + or –15 percent.
  - Using VOT = $1.50 instead of $2.70 per hour decreases both corrective taxes by about 12 percent.
  - Varying accident externalities by + and –50 percent causes corrective gasoline tax to vary by about + and –20 percent, and corrective diesel tax to vary between about + and –10 percent.
  - Results are fairly insensitive to varying own-price fuel elasticities if mileage and fuel economy elasticities change in the same proportion.
  - For given overall fuel price elasticity, the split between reduced mileage and improved fuel economy (β and α) materially affects corrective tax estimates.

### Key qualitative conclusions and policy interpretation
- Under benchmark assumptions, fuels in Chile are under-taxed from an externality perspective, especially diesel.
- Diesel’s lighter taxation relative to gasoline is not justified by external cost considerations given significant road damage and per-mile externalities from trucks.
- The most important uncertainty is the valuation of fatality risks (VSL); policy conclusions about whether fuels are under- or over-taxed are robust to plausible alternative assumptions for most other parameters.
- More efficient instruments than fuel taxes exist for some externalities:
  - Congestion: better addressed through per mile tolls on congested roads that rise and fall during rush hour.
  - Accidents: can be efficiently reduced through pay-as-you-drive auto insurance (insurance payment = annual miles driven × per mile charge depending on risk factor).
- Until congestion and accident externalities are comprehensively internalized through other instruments, including them in fuel tax assessment is appropriate.
- The analysis abstracts from linkages between fuel taxes and the broader fiscal system:
  - Potential efficiency gain from using fuel tax revenues to reduce distortionary taxes or fund socially productive projects.
  - Potential efficiency loss if higher transportation prices cause contraction in economic activity and labor supply.
- Distributional considerations:
  - CASEN (2006): in 2006 only 9.4 percent of households in the bottom income decile owned a car, compared with 72.7 percent for the top-income decile.
  - Holding down fuel taxes to benefit the poor is inefficient because it benefits all households; distributional goals are better met through targeted provisions in the tax and benefit system, education policy, housing policy, and so on.

### Analytical derivations (Appendix I) — highlights
- Corrective gasoline tax derived from household first-order conditions and government budget constraint; incorporation of β (fraction of gasoline use reduction due to reduced mileage) yields corrective tax formula in equation (2a).
- Welfare gains from tax reform derived and integrated to give total welfare gain (equation (4)).
- Corrective diesel tax derived similarly, accounting for effects on producer optimization and the price of trucked goods, yielding formulas in (6a) and (6b).

### External cost assessment (Appendix II) — pollution, congestion, accidents, road damage, and noise
- Pollution (outside Santiago):
  - U.S. NRC (2009) estimate for gasoline vehicle: $0.008 per vehicle mile (year 2005, in year 2007 dollars); mortality effects for sensitive groups ~three-quarters.
  - VSL extrapolation formula: VSLChile = VSLUS × (IChile/IUS)^(η), with income ratio 0.27.
  - Plausible VSL range for Chile: $0.8 million to $3.1 million, benchmark $1.6 million (elasticity = 1).
  - Assumption on emission rates: Chilean auto emission rates same as U.S. 1992, or three times current U.S. rates.
  - Central adjusted damage outside Santiago: $0.0065 per vehicle mile.
- Pollution (Santiago):
  - Rizzi (2008a) estimates adjusted downward by one-third; monetized with central VSL and Rizzi unit costs produce aggregate figures (tables in source) including:
    - Total pollution cost entries: $640.6 million (automobiles) and $536.4 million (trucks).
    - Pollution cost, US$/mile: $0.10 for automobiles and $0.2 for trucks (using distances automobiles 11,474 million miles, trucks 2,853 million miles).
- Congestion and travel time:
  - Santiago travel speeds: peak 21.2, off-peak 24.5, free-flow 28.5 miles per hour.
  - Peak-period average delay: 0.012 hours per mile.
  - Off-peak average delay: 0.006 hours per mile.
  - Time-weighted average delay (50 percent peak, 50 percent off-peak): 0.009 hours per mile.
  - Functional form for travel time per mile: T = Tf {1 + α V^θ } (formula in source); typical θ range: 2.5–5.0; with α = 0.15 and θ = 4.0 (Bureau of Public Roads formula).
  - Marginal delay equals θ times average delay; with θ = 4 marginal delay = 0.035 hours per mile for Santiago.
  - Nationwide marginal delay (weighted by mileage shares): 0.022 hours per mile (Santiago ~50 percent of car mileage; other urban areas 40 percent; rural 10 percent).
  - Recommended Chile VOT: $2.7 per hour (extrapolated from U.S. VOT using income ratio); sensitivity range $1.5–$4.5 per hour.
- Accidents: fatalities, injuries, and monetized external costs
  - Police-reported road deaths in Chile in 2006: 1,652.
    - Pedestrians/cyclists: 55 percent of deaths.
    - Car/truck occupants: 41 percent of deaths.
  - Externality classification assumptions yield external fatalities count: 1,078.
  - Monetized external fatalities (central VSL) cost: $1.72 billion.
  - Police-reported nonfatal injuries in 2006:
    - Serious injuries: 6,515.
    - Less-serious injuries: 4,400.
    - Light injuries: 36,020.
  - Assumption: 32 percent of non-fatal injuries are external.
  - Personal suffering costs per injury (Parry (2004) scaled by Chile/U.S. VSL 0.27):
    - Serious: $0.023 million.
    - Less-serious: $0.005 million.
    - Light: $0.004 million.
  - Monetized external non-fatal injuries (first method): $0.10 billion.
  - Alternative non-fatal injury valuation (Rizzi (2008b) combined medical + personal injury costs) yields alternative external non-fatal injury cost: $0.18 billion.
  - Preferred external cost for non-fatal injuries (split the difference): $0.14 billion.
  - External medical cost (85 percent of non-fatal injuries external): additional external medical cost $0.09 billion (split between methods).
  - Property damage external costs: $0.04 billion (assumptions: 50 percent externality, number of property-damage-only accidents equals light injuries).
  - Total external accident cost (sum of components): approximately $2 billion.
  - Truck externality assumption: external accident cost per truck mile = 1.25 times that for a car mile.
  - Average external cost per mile:
    - Cars: $0.06 per mile.
    - Trucks: $0.07 per mile.
- Road damage and noise
  - Road maintenance spending (central and local government) in Chile in 2006: $0.85 billion.
  - Allocation assumptions produce damage cost per truck mile: $0.08 per truck mile.
  - Damage-per-axle-weight assumption (Porter (1999)): damage per truck mile = 1000 times car damage or twice bus mile damage.
  - Vehicle noise costs for heavy trucks (U.S. FHWA (2000)): urban $0.027 per mile, rural $0.002 per mile; transferred to Chile by income ratio 0.27 and weighted by mileage share urban/rural (0.87/0.13) yields nationwide external noise cost: $0.006 per mile.

*Source: _wp11168 - 4. Pollution Damage Calculations for Santiago (chapter/section text).*

### References .............................................................................................................

### References

### Tables
- 1. Benchmark Data and Parameter Assumptions .....................................................................10
- 2. Corrective Tax Computations: Benchmark Parameter Values ............................................11
- 3. Corrective Tax Calculations: Alternative Parameter Values ...............................................17

### Figures
- 1. Excise Taxes on Gasoline and Diesel in OECD Countries in Year 2010 ..............................4

### Appendixes
- I. Analytical Derivations ..........................................................................................................21
- II. Additional Details on External Cost Assessment ................................................................24

- Appendix Tables

*Source: _wp11168 - References .............................................................................................................*

### 4. Pollution Damage Calculations for Santiago .......................................................................25

### _wp11168 - 4. Pollution Damage Calculations for Santiago .......................................................................25

### Introduction and objective
- Purpose: compile rough estimates of automobile and commercial truck externalities for Chile (with focus on Santiago) by combining local data with extrapolations from U.S. literature to derive (second-best) corrective gasoline and diesel fuel taxes.
- Key context:
  - Gasoline tax benchmark: corrective gasoline tax for Chile is $2.35 per gallon (year 2006 dollars), about 60 percent greater than the prevailing fuel tax.
  - Diesel benchmark: corrective diesel tax is $2.09 per gallon (year 2006 dollars).
- Main caveat: estimates depend on judgment where data are limited; valuation of fatality risks is the most important source of uncertainty.

### Conceptual framework for corrective fuel taxes
- Gasoline (passenger vehicles) and diesel (commercial trucks) are treated separately; corrective taxes account for:
  - Externalities proportional to fuel use (eG, dollars per gallon) — e.g., CO2, a share of local tailpipe emissions.
  - Externalities proportional to vehicle miles (eM, dollars per vehicle mile) — e.g., accidents, congestion, a share of local tailpipe emissions.
- Corrective gasoline tax formula (long run, simplified):
  - CGt = eG + β · geM
  - eG and eM denote marginal external costs from gasoline use and mileage; g is fuel per mile (inverse of fuel economy); β is fraction of incremental reduction in gasoline use coming from reduced miles driven.
- Corrective diesel tax formula (analogous):
  - CFt = eF + α · feT
  - eF and eT denote marginal external costs from diesel use and truck miles; f is diesel fuel per mile; α is fraction of incremental fuel reduction from reduced truck mileage.

### Parameter compilation (benchmark assumptions, year 2006)
- Fuel, vehicle, and tax data (selected exact values):
  - Initial fuel consumption, million gallons: Automobiles 819.02, Trucks 898.28
  - Initial fuel economy, miles/gallon: Automobiles 30.00, Trucks 8.00
  - Vehicle miles, billion: Automobiles 24.57, Trucks 7.19
  - Initial retail fuel price, $/gallon: Gasoline $4.27, Diesel $3.17
  - Initial fuel tax, $/gallon: Gasoline $1.46, Diesel $0.37
  - Fuel tax revenue, $billion: Gasoline $1.19, Diesel $0.33
- Externalities from fuel combustion, $/gallon:
  - Local tailpipe emissions (varying with fuel use): Gasoline $0.29, Diesel $0.18
  - Carbon: Gasoline $0.18, Diesel $0.21
- Externalities from driving, $/vehicle mile:
  - Local tailpipe emissions (varying with mileage): Automobiles $0.02, Trucks $0.07
  - Congestion: Automobiles $0.04, Trucks $0.10
  - Accidents: Automobiles $0.06, Trucks $0.07
  - Noise: Automobiles $0.00, Trucks $0.01
  - Road damage: Automobiles $0.00, Trucks $0.08
- Elasticities:
  - Fuel demand elasticity: Automobiles -0.50, Trucks -0.50
  - Mileage to fuel price elasticity: Automobiles 0.50, Trucks 0.60
  - Fuel economy elasticity: Automobiles 0.25, Trucks 0.20
- Additional parameter notes:
  - For passenger vehicles in Chile, assumed fleet fuel economy = 30 miles per gallon; heavy trucks = 8 miles per gallon.
  - For local emissions apportionment: automobiles assumed two-thirds of local emissions vary with mileage and one-third with fuel combustion; similar but for trucks one-third proportional to fuel combustion and two-thirds to miles driven (for trucks emissions per mile standards assumed).
  - CO2 emissions per gallon: gasoline 0.009 tons, diesel 0.010 tons.
  - Central social cost of carbon used: $21 per ton (year 2007 dollars), with low/high cases $5 and $65 per ton for sensitivity.
  - Marginal delay for Santiago: 0.035 hours per auto mile (average across time of day); nationwide weighted marginal delay: 0.022 hours per mile.
  - Central value of travel time (VOT): $2.7 per hour, range $1.5–$4.5 per hour for sensitivity.
  - Marginal external congestion cost (preferred nationwide, after scaling): $0.04 per mile.
  - Truck mile contributes 2.5 times congestion of an auto mile.
  - Local pollution nationwide: $0.03 per mile average (Santiago $0.06 per mile, rest of country lower); apportioned two-thirds to mileage and one-third to fuel use.
  - Automobile local pollution external cost outside Santiago: $0.007 per mile (based on VSL $1.6 million extrapolation).
  - Accident externalities: car external cost $0.06 per mile (pedestrian/cyclist fatalities account for ~three-quarters); truck external cost $0.07 per mile (assumed 25 percent greater than cars).
  - Road damage for trucks: $0.08 per mile; noise for trucks: $0.01 per mile.

### Benchmark corrective tax results and impacts
- Corrective taxes (year 2006 dollars):
  - Gasoline corrective tax: $2.35 per gallon
  - Diesel corrective tax: $2.09 per gallon
- Contribution breakdown (per gallon):
  - Gasoline contribution components (dollars per gallon):
    - Local tailpipe emissions: $0.60
    - Carbon: $0.18
    - Congestion: $0.63
    - Accidents: $0.94
    - Noise: $0.00
    - Road damage: $0.00
  - Diesel contribution components (dollars per gallon):
    - Local tailpipe emissions: $0.53
    - Carbon: $0.21
    - Congestion: $0.52
    - Accidents: $0.39
    - Noise: $0.03
    - Road damage: $0.40
- Impacts of raising taxes from 2006 levels to corrective levels (long-run):
  - Percent reduction in fuel use: Gasoline 9.0 percent, Diesel 19.5 percent
  - Percent increase in fuel economy: Gasoline 4.9 percent, Diesel 9.1 percent
  - Percent increase in tax revenue: Gasoline 46.8 percent, Diesel 352.3 percent
  - Welfare gain (annual), $ million: Gasoline $33.2 million, Diesel $150.2 million
- Counterfactual relative to zero initial tax:
  - Percent reduction in fuel use: Gasoline 26.2 percent, Diesel 24.4 percent
  - Welfare gain, $ million: Gasoline $229.3 million, Diesel $222.3 million

### Sensitivity analysis — key scenarios and numerical outcomes
- Corrective gasoline and diesel taxes under alternative parameter values (selected cases, $/gallon):
  - Benchmark case: Gasoline $2.35, Diesel $2.09
  - Value of statistical life (VSL) = $0.8 million: Gasoline $1.53, Diesel $1.60
  - VSL = $3.1 million: Gasoline $4.00, Diesel $3.02
  - Social cost of carbon = $5 per ton: Gasoline $2.20, Diesel $1.91
  - Social cost of carbon = $65 per ton: Gasoline $2.78, Diesel $2.57
  - Initial fuel economy 36 miles per gallon: Gasoline $2.51, Diesel $2.31
  - Initial fuel economy 24 miles per gallon: Gasoline $2.20, Diesel $1.87
  - Local pollution increased 50 percent: Gasoline $2.69, Diesel $2.37
  - Local pollution decreased 50 percent: Gasoline $2.02, Diesel $1.81
  - Travel delay increased 50 percent: Gasoline $2.71, Diesel $2.37
  - Travel delay decreased 50 percent: Gasoline $2.01, Diesel $1.81
  - VOT = $1.5 per hour: Gasoline $2.05, Diesel $1.84
  - VOT = $4.5 per hour: Gasoline $2.83, Diesel $2.46
  - Accident externalities increased 50 percent: Gasoline $2.88, Diesel $2.30
  - Accident externalities decreased 50 percent: Gasoline $1.85, Diesel $1.88
  - Road damage increased 50 percent: Gasoline $2.35, Diesel $2.30
  - Road damage decreased 50 percent: Gasoline $2.35, Diesel $1.88
  - Fuel price elasticity increased 50 percent: Gasoline $2.41, Diesel $2.17
  - Fuel price elasticity decreased 50 percent: Gasoline $2.31, Diesel $2.01
  - Fraction of fuel price elasticity due to reduced mileage:
    - Gasoline 0.65, diesel 0.75: Gasoline $2.93, Diesel $2.46
    - Gasoline 0.35, diesel 0.45: Gasoline $1.76, Diesel $1.67
- Principal sensitivity finding: VSL assumptions produce the largest variation in corrective taxes; other parameters (emission rates, fuel economy, behavioral responses, marginal travel delays) have relatively smaller impacts.

### Key qualitative conclusions
- Under benchmark assumptions, fuels in Chile are under-taxed from an externality perspective, especially diesel.
- Diesel’s lighter taxation relative to gasoline is not justified by external cost considerations given the significant road damage and per-mile externalities from trucks.
- The most important uncertainty is the valuation of fatality risks (VSL); policy conclusions about whether fuels are under- or over-taxed are robust to plausible alternative assumptions for most other parameters.
- The analysis does not explore non-tax instruments (e.g., peak-period congestion pricing) nor linkages between fuel taxes and the broader fiscal system; these are noted limitations.

*Source: _wp11168 - 4. Pollution Damage Calculations for Santiago (chapter/section text).*

### 6.4 and 9.6 miles per gallon for trucks. This causes the corrective fuel taxes to vary by

### _wp11168 - 6.4 and 9.6 miles per gallon for trucks. This causes the corrective fuel taxes to vary by

### Sensitivity analysis of corrective fuel taxes
- Changing fuel economy assumptions (6.4 and 9.6 miles per gallon for trucks) causes the corrective fuel taxes to vary by about + or –6 percent for cars and + or –10 percent for trucks as higher (lower) fuel economy magnifies (dampens) the contribution of mileage-related externalities.
- Increasing and decreasing local pollution damages by up to 50 percent causes the corrective fuel taxes to vary by up to about + or –14 percent.
- Increasing and decreasing marginal travel delay by up to 50 percent causes corrective taxes to vary by up to about + or –15 percent.
- Using the smaller value for the VOT ($1.50 instead of $2.70 per hour) decreases both corrective taxes by about 12 percent.
- Varying accident externalities by + and –50 percent causes:
  - corrective gasoline tax to vary by about + and –20 percent, and
  - corrective diesel tax to vary between about + and –10 percent.
- Varying road damage + and –50 percent causes the corrective diesel tax to vary between + and –10 percent.
- Results are fairly insensitive to varying own-price fuel elasticities, since mileage and fuel economy elasticities change in the same proportion.
- For a given overall fuel price elasticity, the relative price responsiveness of mileage and fuel economy (which determines β and α in equations (2) and (6)) is important:
  - Varying the fraction of the gasoline elasticity that is due to reduced mileage from 0.35 to 0.65 causes the corrective gasoline tax to vary between about + and –25 percent.
  - Varying the fraction of the diesel fuel price elasticity due to mileage between 0.45 and 0.75 causes the corrective diesel tax to vary between approximately + and –20 percent.

### Key benchmark corrective tax estimates for Chile
- Corrective gasoline tax (benchmark case): $2.35 per gallon.
- Corrective diesel tax (benchmark case): $2.09 per gallon.
- Comparative context: these benchmark taxes are higher than typical tax rates prevailing in Western Hemisphere countries, but lower than typical rates in Western Europe.
- Despite lower valuations of health risks and travel delays, corrective fuel tax estimates for Chile are larger than comparable estimates for the United States due to:
  - higher incidence of pedestrian fatalities in Chile, and
  - high proportion of population residing and driving in the metropolitan Santiago region, where pollution formation and road congestion are pronounced.

### Policy interpretation and caveats
- The analysis provides a methodology and a first-pass assessment for compiling parameters to assess corrective motor fuel taxes for a middle-income country, illustrated using Chile.
- There is scope for parameter improvement with better data; aside from the (contentious) valuation of mortality risk, refinements are conjectured to have a non-dramatic impact on corrective fuel tax estimates.
- More efficient instruments than fuel taxes exist for some externalities:
  - Traffic congestion is better addressed through per mile tolls on congested roads that rise and fall during rush hour (examples cited).
  - Accident externalities can be efficiently reduced through a transition to pay-as-you-drive auto insurance (insurance payment = annual miles driven × per mile charge depending on risk factor).
  - Until congestion and accident externalities are comprehensively internalized through other instruments, including them in fuel tax assessment is appropriate.
- The analysis abstracts from linkages between fuel taxes and the broader fiscal system, including:
  - potential efficiency gain from using fuel tax revenues to reduce distortionary taxes or fund socially productive projects, and
  - potential efficiency loss if higher transportation prices cause a contraction in economic activity and labor supply.
- Distributional considerations:
  - According to CASEN (2006), in 2006 only 9.4 percent of households in the bottom income decile owned a car, compared with 72.7 percent for the top-income decile, calling into question a simple distributional argument against higher fuel taxes.
  - Holding down fuel taxes to benefit the poor is inefficient because it benefits all households; distributional goals are better met through targeted provisions in the tax and benefit system, education policy, housing policy, and so on.

### Analytical derivations (Appendix I) — highlights
- Deriving the corrective gasoline tax:
  - First-order conditions from household optimization are presented (equations summarized in (A1)).
  - Total differential of the household’s indirect utility with respect to the gasoline tax leads to (A2).
  - Government budget constraint differentiated gives (A3).
  - Equating welfare differential to zero and substituting budget constraint yields (A4) and, after incorporating the fraction β of gasoline use reduction due to reduced mileage (A6), the corrective tax formula in equation (2a).
- Welfare gains from tax reform:
  - Expression (A2) divided by λ and substitution yields (A7).
  - Definitions of CGt and β produce (A8); integrating over the tax rise gives total welfare gain in equation (4).
- Deriving the corrective diesel tax:
  - First-order conditions for household and producer optimization are given ((A9), (A10)).
  - Differentiating indirect utility and government budget constraint and accounting for impact of fuel tax on the price of trucked goods ((A11)–(A13)) yields the corrective diesel tax formulas in (6a) and (6b).

### External cost assessment (Appendix II) — Pollution and congestion details
- Pollution (outside Santiago):
  - U.S. consensus: NRC (2009), Table 3.3, estimated about $0.008 per vehicle mile for a gasoline vehicle for year 2005 (in year 2007 dollars); mortality effects for sensitive groups account for about three-quarters of these estimates.
  - VSL extrapolation formula used: VSLChile = VSLUS × (IChile/IUS)^(η), with USChile II/ = ($13,000/$48,150=) 0.27.
  - Empirical VSL/income elasticity estimates vary between about 0.5 and 1.5; plausible VSL range for Chile: $0.8 million to $3.1 million, with benchmark $1.6 million when elasticity is unity.
  - Assumption: current auto emission rates in Chile are the same as those applying in the United States in 1992, or three times the current U.S. rates.
  - Applying central adjustments for VSL and emission rates yields a damage of $0.0065 per vehicle mile (outside Santiago).
- Pollution (Santiago):
  - Rizzi (2008a) estimates of mortality and morbidity for year 2001 attributed to trucks and automobiles are adjusted downward by one-third (per Luis Cifuentes) to reflect concave dose-response evidence.
  - Monetizing with central VSL and valuing morbidity by Rizzi (2008a) unit costs:
    - Total annual health costs: $0.49 or $0.84 billion for automobiles, $0.42 billion or $0.72 billion for trucks (table presents ranges).
    - Materials damage: $85.0 million and $73.0 million for automobiles and trucks respectively (table upper shows $85.0 and $73.0 million).
    - Total pollution cost: $640.6 million (automobiles) and $536.4 million (trucks) in aggregate table entries.
    - Fraction of cost due to mortality: 0.8 and 0.8.
    - Pollution cost, US$/mile: $0.10 for automobiles and $0.2 for trucks (derived by dividing total damages by distance travelled).
  - Distances used for division: automobiles 11,474 million miles, trucks 2,853 million miles.
- Congestion (Santiago):
  - Travel speeds for Santiago obtained from the ESTRAUS model.
  - Average automobile travel speeds under peak, off-peak, and free-flow traffic conditions in the Santiago metropolitan area are 21.2, 24.5 and [text truncated in source].

*Source: _wp11168 (excerpts) — IMF working paper content provided in the supplied PDF content.*

### 28.5 miles per hour, respectively. Inverting these figures, and comparing actual and free-flow

### _wp11168 - 28.5 miles per hour, respectively. Inverting these figures, and comparing actual and free-flow

### Congestion delays and marginal vs. average delay
- Peak-period average delay due to congestion: 0.012 hours per mile.
- Off-peak (including weekends) average delay due to congestion: 0.006 hours per mile.
- Time-weighted average delay (50 percent peak, 50 percent off-peak): 0.009 hours per mile.
- Functional form relating travel time per mile (T) to traffic volume (V) given in the source as:
  - (C2) }1{  VTT f 
- Typical exponent θ range cited: 2.55.0.
- With α = 0.15 and θ = 4.0, equation (C2) is the Bureau of Public Roads formula.
- Delay per vehicle mile due to congestion (average delay) derived from (C2): 1 VT f .
- Marginal delay per vehicle mile (derivative) from (C2): 1 VT f .
- Ratio of marginal to average delay equals θ; with θ = 4, marginal delay = 4 × average delay.
- Quadrupling average delay gives a marginal delay of 0.035 hours per mile.

### Nationwide aggregation of marginal delay
- Santiago accounts for about half of nationwide car mileage.
- Other urban areas account for a further 40 percent of nationwide car mileage.
- Rural areas account for 10 percent of nationwide car mileage (Sii, 2008).
- Assumption: no congestion in rural areas.
- Simulations of the ESTRAUS model imply average (and hence marginal) delays in other urban areas are 32 percent of those for Santiago as a whole.
- Nationwide marginal delay (weighted by mileage shares): 0.022 hours per mile.

### Value of travel time (VOT)
- Recommended U.S. VOT for peak-period auto travel: about half the market wage.
- Based on average urban wage rates in BLS (2006), Table 1, implied U.S. VOT: $10 per hour.
- Extrapolation to Chile: multiply by Chile/U.S. income ratio 0.27 raised to the power of the VOT/income elasticity.
- Typical VOT/income elasticity for high-income countries: around unity, yielding Chile VOT: $2.7 per hour.
- Sensitivity analysis VOT range considered: $1.5 to $4.5 per hour.
- Note: Jara-Díaz et al. (2008) estimate a VOT of $2.9 per hour (general travel) using Chilean data.
- Note: Current government practice in Chile cited as around $1.5 per hour; other unpublished estimates over $4.4 per hour cited by personal communication.

### Accidents: fatalities, injuries, and monetized external costs
- Police-reported road deaths in Chile in 2006: 1,652.
  - Pedestrians/cyclists accounted for 55 percent of deaths.
  - Car/truck occupants accounted for 41 percent of deaths.
- Assumptions on externality classification:
  - All pedestrian/cyclist deaths treated as external.
  - Of vehicle occupant deaths, half of these are in single-vehicle accidents and treated as internalized risks.
  - For remaining multi-vehicle collision deaths, half are treated as external (following Parry (2004) medium scenario).
- External fatalities count: 1,078.
- External fatalities monetized using central VSL produces a cost of $1.72 billion.
- Police-reported nonfatal injuries in 2006:
  - Serious injuries: 6,515.
  - Less-serious injuries: 4,400.
  - Light injuries: 36,020.
- Assumption: 32 percent of non-fatal injuries are external (compared with 65 percent for fatalities).
- Personal suffering costs per injury (Parry (2004) scaled by Chile/U.S. VSL 0.27):
  - Serious: $0.023 million.
  - Less-serious: $0.005 million.
  - Light: $0.004 million.
- Monetized external non-fatal injuries (first method): $0.10 billion.
- Alternative injury valuations from Rizzi (2008b) (combined medical + personal injury costs):
  - Serious: $0.074 million.
  - Less-serious: $0.018 million.
  - Light: $0.004 million.
- Using Parry (2004) decomposition (medical costs 20 percent, personal injury costs 80 percent) and Rizzi figures yields alternative external non-fatal injury cost: $0.18 billion.
- Preferred external cost for non-fatal injuries (split the difference): $0.14 billion.
- Medical costs for all non-fatal injuries: assume 85 percent are external.
  - Valuing 85 percent of non-fatal injuries using medical costs implied by Parry (2004) and Rizzi (2008b), then splitting the difference, produces additional external medical cost: $0.09 billion.
- Property damage costs:
  - Assume 50 percent of property damage costs are external (borne by insurance companies).
  - Assume number of accidents involving property damage only equals number involving light injuries.
  - External costs from property damage computed at $0.04 billion.
- Total external accident cost (summing components): approximately $2 billion.
- Truck externality assumption: external accident cost per truck mile is 1.25 times that for a car mile (de Palma and others (2008), Parry (2008), U.S. FHWA (2000)).
- Average external cost per mile:
  - Cars: $0.06 per mile.
  - Trucks: $0.07 per mile.
  - (Average external cost per car mile obtained by dividing total cost by car miles plus 1.25 times truck miles from Table 1 in source.)

### Road damage and noise
- Road maintenance spending (central and local government) in Chile in 2006: $0.85 billion.
- Assumptions on allocation of road maintenance to vehicle driving:
  - All road maintenance in Santiago (21 percent of total) attributed to vehicle driving.
  - Two-thirds of road maintenance in the rest of Chile attributed to vehicle driving.
  - Remaining maintenance attributed to weather, erosion, falling rocks, etc.
- After allocating portions to buses and cars, resulting damage cost per truck mile: $0.08 per truck mile.
- Damage-per-axle-weight assumption: following Porter (1999), damage per truck mile is 1000 times the damage from a car or twice the damage from a bus mile.
- Vehicle noise costs for heavy trucks (U.S. FHWA (2000), Table 13):
  - Urban truck driving: $0.027 per mile.
  - Rural truck driving: $0.002 per mile.
- Transfer to Chile: multiply U.S. figures by Chile/U.S. real income ratio 0.27.
- Weight by share of mileage in urban and rural areas (0.87 and 0.13 respectively) to obtain nationwide external noise cost: $0.006/mile.

*Source: _wp11168 - 28.5 miles per hour, respectively. Inverting these figures, and comparing actual and free-flow*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11168.pdf_