B. Sensitivity Analysis
5. Conclusion
Recent literature has emphasized that interactions with the broader fiscal system can importantly affect the costs of environmental (and other regulatory) policies. This paper extends this literature to account for certain specific features of electricity generation, which is a major contributor to local and global pollution. These features include (a) the distinction between dirty (coal) technologies, which are assumed to be marginal only in off-peak periods, and clean (gas) technologies, which are assumed to be marginal in peak periods and (b) non-competitive pricing. The analysis is applied to current and proposed controls on utility emissions of SO2, carbon, and NOx.
The paper shows that allowing for these features significantly diminishes welfare losses from the tax-interaction effectthat is, the exacerbation of labor tax distortions due to the effect of regulations on raising product prices and reducing real household wages. The results are reasonably robust to a wide range of scenarios, such as full price deregulation, the extent of imperfect competition in the deregulated sector, and the extent of dispersion in marginal production costs across time of day. Results are most striking in the case of carbon where proposed proportionate emissions reductions are the most moderate.
For example, the costs of reducing carbon emissions by 10% under grandfathered permits and revenue-neutral auctioned permits are computed at $2.7 and −$0.5 billion in the present model in the benchmark case; in contrast, with a single, constant returns technology model with competitive pricing, the costs of these policies are computed at $5.2 and $1.7 billion, respectively.
One limitation is that we use a highly aggregated model of both the electricity market and labor market. In practice labor supply elasticities may vary across regions, and certainly the relative burden of
emissions mitigation costs varies across regions with different emissions intensities of production. If these factors are positively (or negatively) correlated, the aggregate costs of fiscal interactions will be larger (or smaller) than predicted above.
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Appendix
Deriving (2.13)
Using (2.1), (2.2) and duality, the household optimization problem can be expressed:
(B1) z
{
pMP,
pMO,
pRP, π ,
G,
t,
u}
=where z(.) is the expenditure function, λ is a Lagrange multiplier, u is a given (optimized) level of utility, and we have defined utility gross of environmental benefits. The first order conditions yield the compensated demand and labor supply functions:
(B2)Xij
=
Xij(
piP,
piO,
t)
;Y=
Y(
piP,
piO,
t)
;L=
L(
piP,
piO,
t)
These functions are independent of π and G as any income effects are implicitly neutralized in the expenditure function.
The welfare cost of emissions permits is given by:
(B4)W
≡
z{
pMP,
pMO,
pR, π ,
G,
t,
u} −
z{
p0MP,
p0MO,
p0R, π
0,
G0,
t0,
u}
That is, the compensation that must be paid to households to keep utility constant at u following the policy change. Here we look at the case when t adjusts to maintain government budget balance (G is fixed)the derivation is similar when G rather than t is adjusted.
From a second order Taylor series expansion of (B4) (with G fixed):
(B5)
(B6) p L t
From the government budget constraint (2.8), and equating ex ante and ex post tax revenues, we can obtain:
From (B6) and (B8) we can obtain, after some manipulation:
(B9)W ≈ΣijX0ij∆pij +Σij∆Xij∆pij /2
− ( 1 − β ) τ
E+
t0(
L0−
L) − ∆ π
(here we have ignored a term in ∆
π
∆t and in∆
t2, because ∆t is very small).Using (2.5), (2.10) and (2.12), the change in profits is:
(B10)∆
π
=[ΣijpijXij −Σi(α
C +aC)XCiP −Σij(α
D1 +α
D2XDij /2+aD)XDij +βτ
E]Using (2.10) we can obtain, after some manipulation:
(B11)∆
π
=Σij(pij − p0ij)Xij −(p0ij −MC0ij)(X0ij −Xij)−[kD{.}XD +kC{.}XC]For the case when t adjusts to maintain budget balance (θ = 1), equating ex ante and ex post tax
(C1)t0
(
L0+ π
0) = (
t0+ ∆
t)(
L0+ ∆
L+ π ) + ( 1 − β ) τ
ESubstituting (B7) in (C1) and canceling terms we obtain, after some manipulation:
(C2)
∂ π
, because electricity profits are very small relative to total labor income inthe economy. Substituting (B7) and (C2) in
−
t0(
L0−
L)
, and using this approximation, we can obtain leisure from an incremental increase in the price of leisure (1– t). When X is (initially) an average substitute for leisure:Substituting (D1) and (D2) in the formula for the tax-interaction effect in (2.14), and using the definition of M, we can obtain (2.15a).
Tables
Parameter Benchmark Value
Baseline electricity parameters and initial values
Total electricity output, million MWh 4,105
fraction of output by dirty plants 0.54
fraction of output by clean plants 0.46
average generation price, $/MWH 40
fraction of firms in regulated sector 0.5
economy-wide marginal production cost, $MWh 45
fraction of production in off-peak period 0.10
marginal production cost in off-peak period, $MWh 9.0 marginal production cost in peak period, $MWh 48.8
average cost, $MWh 35
own price elasticity of demand for electricity -0.3
Environmental parameters SO2 Carbon NOX
Unregulated emissions, million tons 16 689 5.9
fraction of total initial emissions at dirty plants 1.0 0.86 0.95
emissions cap, million tons 9.0 620 1.8
permit price at cap (auctioned permits), $/ton 290 52 900
slope of MAC at dirty plants 91,835
∞
489,521slope of MAC at clean plants
∞ ∞ ∞
marginal benefit from abatement $/ton 3,500 50 1000
Fiscal parameters
Marginal excess burden of labor taxation 0.25
Income tax 0.4
Table 1. Parameter Values for Benchmark Simulations
grand-
output-fathered revenue- lump-sum based
permits neutral replacement allocation
Single technology model
abatement costs 999 999 999 1,013
output effects 12 12 12 1
revenue-recycling effect
permit sales 0 -648 0 0
profits -259 0 0 0
tax-interaction effect 902 902 902 253
total cost 1,654 1,265 1,913 1,267
Benefits - costs 22,842 23,231 22,583 23,245
Multiple technology model
abatement costs 975 976 976 976
output effects -58 -155 -155 34
revenue-recycling effect
permit sales 0 -638 0 0
profits 19 148 148 145
tax-interaction effect 192 496 496 -111
total cost 1,127 827 1,465 1,043
relative cost 0.68 0.65 0.77 0.82
Benefits - costs 23,365 23,678 23,040 23,454
auctioned permits Table 2. Costs of SO2 Emissions Reduction
($ million)
grand-
output-fathered revenue- lump-sum based
permits neutral replacement allocation Single technology model
abatement costs 698 698 698 2,123
output effects 576 576 576 4
revenue-recycling effect
permit sales 0 -5,814 0 0
profits -2,326 0 0 0
tax-interaction effect 6,276 6,276 6,276 533
total cost 5,225 1,737 7,550 2,660
Benefits - costs -1,783 1,706 -4,108 791
Multiple technology model
abatement costs 1,413 1,155 1,155 1,720
output effects -270 -541 -541 420
revenue-recycling effect
permit sales 0 -8,064 0 0
profits -759 987 987 1,221
tax-interaction effect 2,327 6,001 4,801 -2,289
total cost 2,711 -462 6,401 1,071
relative cost 0.52 -0.27 0.85 0.40
Benefits - costs 758 3,897 -2,967 2,384
auctioned permits
grand-
output-fathered revenue- lump-sum based
permits neutral replacement allocation Single technology model
abatement costs 1,837 1,837 1,837 1,841
output effects 11 11 11 3
revenue-recycling effect
permit sales 0 -404 0 0
profits -161 0 0 0
tax-interaction effect 865 865 692 460
total cost 2,552 2,310 2,540 2,304
Benefits - costs 1,551 1,793 1,562 1,797
Multiple technology model
abatement costs 1,827 1,828 1,828 1,827
output effects -89 -152 -152 -30
revenue-recycling effect
permit sales 0 -405 0 0
profits 16 99 99 95
tax-interaction effect 294 489 391 98
total cost 2,048 1,859 2,166 1,991
relative cost 0.80 0.80 0.85 0.86
Benefits - costs 2,052 2,242 1,935 2,107
Table 4. Costs of NOX Emissions Reduction ($ million)
auctioned permits
grand-
output-fathered revenue- lump-sum based
permits neutral replacement allocation SO2
abatement costs 975 975 975 975
output effects 0 0 0 -3
revenue-recycling effect
permit sales 0 -638 0 0
profits 37 292 292 286
tax-interaction effect 154 154 154 -467
total cost 1,165 783 1,421 791
relative cost 0.70 0.62 0.74 0.63
Carbon
abatement costs 899 900 900 1,403
output effects 162 170 170 367
revenue-recycling effect
permit sales 0 -7,294 0 0
profits -1,131 1,756 1,756 2,229
tax-interaction effect 3,211 3,284 3,284 -4,831
total cost 3,141 -1,184 6,109 -833
relative cost 0.60 -0.68 0.81 -0.31
NOx
abatement costs 1,792 1,792 1,792 1,792
output effects 1 1 1 0
revenue-recycling effect
permit sales 0 -402 0 0
profits 35 194 194 186
tax-interaction effect 255 259 259 -132
total cost 2,082 1,844 2,246 1,846
relative cost 0.82 0.80 0.86 0.80
auctioned permits Table 5. Sensitivity with respect to Full Price Deregulation
(absolute costs from the multi-technology model)
Emissions
abatement grandfathered auctioned grandfathered auctioned
level (%) permits permits permits permits
Carbon
5 7.07 1.36 3.35 -1.30
10 4.10 1.36 2.13 0.84
20 2.59 1.36 1.45 1.23
SO2
20 2.45 1.25 1.19 0.78
45 1.64 1.25 1.14 1.01
70 1.38 1.25 1.13 1.09
NOx
20 2.45 1.25 0.83 -0.66
45 1.62 1.25 1.27 0.89
70 1.38 1.25 1.13 1.05
single technology model multi-technology model (Overall costs relative to combined abatement costs and output effects in single-technology model)
Table 6. Sensitivity With Respect to Extent of Abatement
Initial price-MC
ratio in peak period price output price output
constant constant constant constant
SO2
1.1 0.65 0.76 0.61 0.77
1.4 0.56 0.76 0.49 0.77
grandfathered permits auctioned permits Table 7. Sensitivity with respect to Market Power in the Deregulated Sector
(ratio of costs in multi-technology model to costs in single-technology model)
grand-
output-fathered revenue- lump-sum based
permits neutral replacement allocation
Benchmark 0.68 0.65 0.77 0.82
1. Dispersion in marginal costs across periods relative size of Dispersion in
off-peak period marginal cost
benchmark maximized 0.68 0.71 0.80 0.80
minimized 0.70 0.66 0.78 0.84
halved maximized 0.67 0.64 0.76 0.80
minimized 0.68 0.65 0.77 0.82
increased to size maximized 0.69 0.66 0.78 0.83
of peak period minimized 0.72 0.69 0.80 0.88
2. Difference between (mean) marginal cost and average cost
$20/MWh 0.65 0.57 0.71 0.83
$0/MWh 0.70 0.72 0.82 0.81
-$10/MWh 0.72 0.78 0.86 0.81
3. Slope of marginal abatement cost curve
reduced 25% 0.69 0.66 0.81 0.83
increased 25% 0.67 0.64 0.80 0.81
4. Electricity demand elasticity
η = -.2 0.69 0.68 0.79 0.81
η = -.7 0.66 0.56 0.71 0.84
5. Marginal excess burden
M = .15 0.75 0.70 0.79 0.88
M = .4 0.61 0.58 0.75 0.75
auctioned permits Table 8. Sensitivity with respect to Other Parameters
(ratio of costs in multi-technology model to costs in single-technology model for SO2)