On ad valorem taxation of nonrenewable resource production

RESOURCE ELSEVIER

and ENERGY ECONOMICS Resource and Energy Economics 19 (1997) 221-239

On ad valorem taxation of nonrenewable resource production John Rowse Department of Economics, The University of Calgary, Calgary, Alta., T2N 1N4, Canada Received 1 January 1996; accepted 1 September 1996

Abstract Taxing a nonrenewable resource typically shifts production through time, compresses the economically recoverable resource base and shrinks social welfare. But by how much? In this paper a computational model of natural gas use, representing numerous demand and supply features believed important for shaping efficient intertemporal allocations, is utilized to answer this question under different ad valorem royalty taxes on wellhead production. Proportionate social welfare losses from fixed royalties up to 30% are found to be small and the excess burden stands at less than 6.5% for a 30% royalty. This result replicates findings of several earlier studies and points to a general conclusion. © 1997 Elsevier Science B.V. JEL classification: H21 ; Q31 Keywords: Ad valorem taxation; Nonrenewable resource production

1. Introduction Since the mid-1980s, simulation methods have been used to study issues in nonrenewable resource taxation, e.g. Slade (1984), Gamponia and Mendelsohn (1985), Blankenship and Weimer (1985), Yucel (1986, 1988, 1989), Deacon (1993) and Ward and Kerkvliet (1993). Except for the latter, each study employs a model exhibiting relatively little complexity in demand or supply whereas most allocation problems exhibit much complexity. In addition, citing arguments of Livernois and Uhler (1987), a few studies utilizing particular extraction costs are misspecified, e.g. Yucel (1986, 1988, 1989). Some studies also find small effi0928-7655/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 0 9 2 8 - 7 6 5 5 ( 9 6 ) 0 0 0 1 4 - 0

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J. Rowse / Resource and Energy Economics 19 (1997) 221-239

ciency losses for certain taxes; see Gamponia and Mendelsohn (1985), Yucel (1986), Deacon (1993) and Ward and Kerkvliet (1993). Given these observations, it is natural to ask what results might emerge from a simulation model which represents substantial demand and supply complexity and is not misspecified according to Livernois and Uhler. It is also natural to ask if the finding of small efficiency losses for certain taxes appears general. This paper focuses on natural gas royalty taxation and asks: How does taxation reallocate production over time, shrink the economically recoverable resource base and social welfare, and what results seem general? To address these questions a computational model of natural gas allocation for the Canadian province of British Columbia is formulated and solved under different wellhead royalties. Model features include representation of domestic demands and exports; separation of domestic demand into fixed demand and flexible demand; segregation of the resource base into proved reserves and new reserves; representation of natural gas production profiles; incorporation of exponentially-rising unit capital costs; distinction between the domestic price and the wellhead price, upon which the royalty is levied; and representation of a royalty formula linking higher ad valorem royalty rates with higher wellhead prices. Unique to this work is the simultaneous determination in a complex dynamic model of efficient price and production time paths and endogenous wellhead royalties satisfying the royalty formula. Numerical results are determined first with no tax, then the royalty rate is varied from 15% to 90%. Proportionate social welfare losses from all royalty rates up to about 30% are small, with the excess burden ranging upward to less than 6.5%. This finding is similar to that of other studies and is explained in several ways. It is then argued that this result is general. The paper is organized as follows. First, the model is presented, then the results are set forth and explained. Sensitivity analyses and the behaviour of tax revenues are discussed subsequently. Next, comparisons are drawn with previous findings. Concluding remarks follow.

2. The computational model Analysis is performed with a model of natural gas allocation for the Canadian province of British Columbia (BC). Earlier versions of the model are used by Rowse (1986, 1990); several major modifications underpin this work. Only skeletal model details are provided; see Rowse (1996) for full details. The time frame is 1990-2064 (75 years) and each period is one year long. 2.1. Variables and constraints

For year t the choice variables are: U~, production from proved reserves; St, deliverable gas from proved reserves which is not produced; X t, resource commit-

J. Rowse / Resource and Energy Economics 19 (1997) 221-239

223

ment (see Chao, 1981, and the discussion below); B t, backstop supply; Q t , total domestic gas consumption, one part of which is Q R t, t h e price-responsive domestic consumption; E t, gas exports; and Yt, gas reserves committed for supply. All variables are non-negative. The first constraints equate demands to supplies: t (l+e)Qt+(l+v)E,=Ut+

~.,at_l,+lXk+Bt, k=l

/ = 1 . . . . . T,

(1)

where T = 75. Gas demands consist of domestic consumption and prospective exports, where the parameters • = 0.023 and v = 0.030 augment Qt and E t , respectively, to account for gas used as intraprovincial pipeline fuel. Gas supplies can come from proved reserves, new reserves and the backstop source. Production from proved reserves satisfies (2) below. Production from new reserves follows a thirty-year recovery profile specified by a 1, a z, a 3 . . . . . a T, which assumes 10% annual decline prior to abandonment. The profile embodies geologic, engineering and economic factors which stretch production over many years. The parameter a I = 1, and thus the resource commitment variable X t represents the capacity of new reservoirs which first produce during t. The summation in (1) represents supplies from capacities of years t and earlier. Backstop supplies could come from several different high-cost sources. All sources are aggregated to form one backstop category costing $7.50 per gigajoule (GJ) in 1990 dollars, a cost specified by Canada's National Energy Board henceforth NEB - in NEB (1991, p. 41). Gas supplies from proved reserves satisfy: U 1 +S 1 =

BO~

U2 + 82 =

BO2 + 0-1SI

U3 + $3 =

B O 3 A¢- 0-251 -1- O-182

Ur + S r =

B O r + O-r- I $1 + ° r - 2 $2 + " " " + °'1Sr

(2) 1

Nonproduced gas can augment future production, but only in a way consistent with the characteristics of producing reservoirs and installed capacity. The parameters 0-1, 0-2, " ' " , 0-r specify the profile for nonproduced or shut-in gas, which assumes 10% annual recovery of shut-in volumes. Productive capacities from proved reserves are specified by parameters B O 1. . . . . B O T. Together constraints (1) and (2) are important, in part because they permit the model to mimic reality by allowing gas supplies in each year to come from capacities of many different vintages and three different sources. Supplies from new reserves are limited by exogenous bounds BNt: t

Eat_ k=l

+lX

<-BN,,

t = 1 . . . . . 7".

(3)

J. Rowse / Resource and Energy Economics 19 (1997) 221-239

224

These bounds allow inclusion of expert opinions on how rapidly new capacity can be installed. Straitjacketing the supply response is undesirable, however, and hence the bounds BNt are taken so large that they never bind. Gas reserves associated with resource commitments are: Yt=

a k X t,

(4)

t = l . . . . . T.

Aggregate new gas reserves cannot exceed the exogenous stock R: T

Er,_
(5)

t=l

Included for completeness, this constraint is redundant because costs will rise sufficiently to choke off reserve development prior to stock exhaustion. Exports are constrained as follows: Et
(6)

t=l ..... T

In each period exports are allowed at a prespecified price up to ceiling Er Other ways of modelling exports are possible but, given massive uncertainty about the development of export markets, none seems unambiguously better. BC demand Qt consists of fixed demand and price flexible demand QRt: Qt

=

~ttQo -4- QR,,

(7)

t = 1 . . . . . T.

Initial consumption Q0 is exogenous and, because 0 < ~O< 1, fixed demand ~OtQ0 declines at a constant annual rate. Flexible demand QR t = o~tPt t~, where /3 is the (absolute) long-run price elasticity. Consequently, over time, as fixed demand shrinks, QR t gains in importance for determining Qt. 2.2. The objective function without taxation

When a royalty tax is absent, the objective function is the private sector present-valued sum of consumer surplus (CS) and producer surplus ( P S ) arising from gas production, domestic consumption and exports: T

- EStxtXtt=l

T

E6tPBB,--

T

T

/ -]

(8)

?k(r,,r2," ,rr) /

t=l

where 6 t is the discount factor 1/(1 + r) t and r is the real discount rate (5%). All costs and benefits are measured in 1990 dollars and discounting is to 1989. Define the terms in (8) as follows: /2 -= A + B + C - D - E - F - G. The term A is present-valued gross domestic consumer surplus, with the delivered price of backstop gas forming a choke price for computing CS. B

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J. Rowse / Resource and Energy Economics 19 (1997) 221-239

consists of discounted export revenues, with e t the exogenous export price. C is the salvage value of gas from proved reserves not produced by 2065. The remaining entries represent real resource costs. D represents supply costs for proved reserves, with u t measuring the unit variable costs of extraction, processing and transport. Capital costs of proved reserves are sunk and hence excluded. E measures the supply costs of new reserves, with x t capturing the same costs as u t but also the recovery profile and any salvage value. F consists of backstop costs. G measures the capital costs of new reserves. Unit capital costs rise exponentially: k ( W ) = kl ek2w, where W is cumulative reserve additions. Letting &(W) represent the integral of k ( W ) from 0 to W, in a static f r a m e w o r k the social supply costs would be: qb( W ) = k,ee2W/ k 2 + k 3,

(9)

where k 3 is chosen to satisfy 4)(0) = 0. By contrast, in a multiperiodframework, postponing capital expenditures shrinks discounted costs. Letting W, = E~ = 1Yk and substituting into ~b, the discounted social costs of supply are: 4a(Y,,Y2 . . . . . Yr) = 614'(Y,) + 8214'(Y1 + I12) - 4'(r,11 + . . - ]

(~-1)]

[ (~) + 8 r 4) , ]1' - 4 ) ,--~]Y'

.

(10,

2.3. Base case assumptions

Domestic demand functions are specified by Q0, ~/', fl and the a r Q0 is 1989 consumption of 225.6 petajoules (PJ) and, assuming that 4% of the gas-using capital stock is retired annually, the annual survival rate 0 is 0.96. Price elasticity /3 = 1.25. Exogenous pairs (Q,, Pt) anchor the demand functions QR r The Qt r e s t on the assumption that at a constant price fit of $2.50 per gigajoule (GJ) (1990), ceteris paribus, demand grows at 3% annually. Export price e t is assumed to be $2.50/GJ in 1990 Canadian dollars at the US border, for all t. Export ceilings are E 1 = 100 PJ, ff7z = 130 PJ, and if7t = 160 PJ, for t = 3, . . . ,T. Many alternative assumptions are plausible. The principal supply assumptions are as follows. For all proved (and new) reserves operating costs are $0.60/GJ (1990) and intraprovincial transport costs are $0.30/GJ. The parameters BO 1, BO 2 . . . . . BO r are computed from data underlying projections of BC productive capacity in NEB (1991, p. 407). The unit capital cost function for new reserves k ( W ) passes through (0.0 EJ, $0.50/GJ) and (24.0 EJ, $6.60/GJ), where EJ denotes an exajoule, or 103 PJ. 2.4. Royalty taxation and modifications to the objective function

After 1987 BC gas royalties followed one formula for conservation gas and a second for nonassociated gas (O'Dell et al., 1991, pp. 64-66). Conservation gas is

226

J. Rowse / Resource and Energy Economics 19 (1997) 221-239

produced with crude oil and is not of interest because it is reinjected into the reservoir after production. Hence the following percentage royalty formula for nonassociated gas production at the wellhead is used: R = R ( P ) = [750 + 25( P - 5 0 ) ] / P = 25 - 5 0 0 / P ,

(11)

where P is the wellhead price in $ / 1 0 3 m 3 and m 3 denotes a cubic meter. This formula has an asymptotic maximum of 25%. There is also a 15% floor on R. Royalties apply only to conventional gas, not to backstop gas. Because gas is measured in heat units, a volume/heat conversion factor is needed. Utilizing data on BC conversion factors from NEB (1991, p. 318), all BC gas is assumed to have a heat content of 39.1 M J / m 3. Utilizing the royalty formula poses a problem. To specify the royalty rate, the price must be known. But to compute the price, the royalty rate must be known. Hence, to solve for intertemporal allocations, the time paths of royalties and prices must be determined simultaneously and endogenously. With royalties included, the model still simulates competitive outcomes. A specific tax (in $ / G J ) simply augments production costs but an ad valorem tax is more complicated. The Kuhn-Tucker optimality conditions equate net-of-tax wellhead prices to the sum of marginal factor costs and user costs. To satisfy these conditions, when the ad valorem rate is fixed at ~-, the gross CS t e r m s A t are multiplied by (1 - ~-), as are export prices e t. However, because the tax is levied on the wellhead price, not the market price, and the price exceeds the tax by transport cost, a credit of (1 - r ) times the intraprovincial transport cost must be added to 12 through the U, and X t variables. With these alterations the correct marginal conditions are satisfied when the model is solved but 12 no longer measures private surplus. Thus CS is computed after model solution. Rowse (1996, note 15) discusses a final, minor complication.

3. Base case findings

Four price and production profiles are graphed in Figs. 1 and 2. The no-royalty price path rises to the delivered price ($7.67/GJ) of backstop gas in 2056, with noteworthy behaviour only around 2000. For the first decade price rises toward the spatial equilibrium price between the domestic and export markets, which is attained in 2001 and 2002. In these years the marginal profit of delivering gas to the export market is equated to that of the domestic market. Prior to 2001 the export market is more lucrative and is supplied to the maximum; after 2002 it is less profitable and thus abandoned. From Fig. 2, production rises after 1990, tracking maximum allowed exports, then contracts as exports collapse. Production climbs slowly thereafter until the domestic price stabilizes in 2056, then grows at a constant rate. The formula-royalty price profile generally lies above the no-royalty profile, but not always. Noteworthy about the former is the slight upward turn prior to

227

J. Rowse / Resource and Energy Economics 19 (1997) 221-239

j, r

75% Royalty \ \ \ \

\

f

j-

/-

~/J

50% Royalty

Formula Royalty i

~

\,

No Royalty

i

2000

2010

2620

20'30

~0'40

L

2o'50

20'60

Fig. 1. Base case price profiles.

F--Ro lty

500

400

20111

50% Royalty

100[

10~

75% Royalty

i

2000

t

2010

20~20

20130

I

2040

Fig. 2. Base case production profiles.

/

1990 2000 2010 2020

1990 2000 2010 2020

1990 2000 2010 2020

Consumer surplus (B$): (undiscounted)

Wellhead royalty ($/GJ):

Royalty revenues (B$): (undiscounted) 0.000 0.000 0.000 0.000

0.00 0.00 0.00 0.00

1.348 1.173 1.062 0.953

0.087 0.153 0. t46 0.190

0.22 0.30 0.44 0.56

1.322 1.200 0.980 0.866

1.81 2.36 3.34 4.11

1990 2000 2010 2020

Domestic price ($/GJ): 1.70 2.45 3.09 3.86

15%

Performance measure\wellhead royalty: None

0.099 0.191 0.204 0.275

0.23 0.38 0.64 0.83

1.327 1.199 0.950 0.825

1.79 2.37 3.43 4.23

Formula

Table 1 Performance measures for several different royalty rates: base case

0.151 0.257 0.247 0.317

0.39 0.53 0.79 0.98

1.296 1.170 0.921 0.804

1.92 2.46 3.53 4.30

25%

0.185 0.206 0.298 0.381

0.49 0.65 0.97 1.20

1.282 1.149 0.890 0.773

1.98 2.52 3.63 4.40

30%

0.259 0.283 0.404 0.511

0.71 0.93 1.40 1.70

1.246 1.103 0.817 0.697

2.13 2.67 3.88 4.65

40%

0.345 0.365 0.516 0.642

0.98 1.25 1.90 2.26

1.201 1.049 0.734 0.615

2.32 2.86 4.19 4.94

50%

0.318 0.459 0.611 0.778

1.34 1.65 2.16 2.98

1.136 0.975 0.787 0.493

2.60 3.12 3.99 5.40

60%

0.447 0.580 0.736 0.926

1.91 2.27 2.86 4.05

1.020 0.845 0.657 0.295

3.10 3.62 4.49 6.23

70%

0.541 0.657 0.807 1.008

2.33 2.70 3.31 4.78

0.933 0.756 0.574 0.167

3.48 3.99 4.82 6.82

75%

0.675 0.757 0.889 1.096

2.93 3.30 3.91 5.64

0.805 0.631 0.462 0.030

4.05 4.53 5.31 7.51

80%

1.255 1.114 1.109 1.223

5.54 5.65 5.81 6.09

0.235 0.179 0.137 0.085

6.61 6.72 6.92 7.23

90%

t~

ixa t,a

oo

2056 1.802 2002 27.221 11.419 0.450 11.869 21.121 11.567 0.000 32.688

First year of backstop prodn

Aggregate exports (EJ) Last year of exports

Aggregate domestic cons (EJ)

Aggregate conv gas costs (B$) Aggregate backstop costs (B$) Aggregate supply costs (B$)

Aggregate consumer surplus (B$) Aggregate producer surplus (B$) Aggregate royalties (B$) Aggregate social welfare (B$)

Aggregate deadweight loss (B$) Aggregate excess burden (%)

2004 19.548

First year of new conv gas prodn Aggregate new conv gas prodn (EJ)

0.069 2.205

20.138 9.349 3.132 32.619

10.552 0.567 11.119

26.229

1.815 2002

2054

2004 18.090

0.160 3.778

19.808 8.491 4.229 32.528

10.137 0.675 10.812

25.783

1.772 2001

2053

2004 17.183

0.240 4.614

19.347 7.896 5.205 32.448

9.804 0.657 10.461

25.547

1.670 2000

2053

2005 16.916

0.392 6.319

18.924 7.166 6.207 32.296

9.350 0.705 10.055

25.213

1.510 1999

2053

2006 16.247

0.832 10.194

17.954 5.741 8.161 31.856

8.425 0.834 9.259

24.474

1.190 1997

2052

2007 14.732

1.692 17.289

16.878 4.331 9.787 30.996

7.185 0.995 8.180

23.742

0.550 1993

2050

2009 12.851

2.966 26.399

15.405 3.083 11.234 29.722

5.921 1.307 7.228

22.824

0.000

2047

2012 10.455

4.465 33.718

12.917 2.063 13.243 28.223

5.010 2.131 7.141

21.587

0.000

2041

2016 7.092

5.719 40.630

11.342 1.551 14.076 26.969

4.450 3.065 7.515

21.015

0.000

2035

2017 4.683

8.001 55.998

9.317 1.084 14.287 24.688

3.653 5.178 8.832

20.507

0.000

2024

2019 1.366

10.169 51.819

2.765 0.129 19.625 22.519

3.077 5.845 8.922

19.746

0.000

2022

0.000

b,a

I

b,a

t~

2052 3.406 2006 20.210 11.348 0.774 12.122 24.864 16.877 0.000 41.741

First year of backstop prodn

Aggregate exports (EJ) Last year of exports

Aggregate domestic cons (EJ)

Aggregate conv gas costs (B$) Aggregate backstop costs (B$) Aggregate supply costs (B$)

Aggregate consumer surplus (B$) Aggregate producer surplus (B$) Aggregate royalties (B$) Aggregate social welfare (B$)

Aggregate deadweight loss (B$) Aggregate excess burden (%)

1999 12.677

1999 13.608

First year of new conv gas prodn Aggregate new conv gas prodn (EJ)

0.094 2.460

24.216 13.608 3.824 41.647

10.182 0.822 11.005

19.865

2.964 2004

2051

15%

Performance measure\wellhead royalty:None

0.195 3.609

23.888 12.255 5.403 41.546

9.715 0.910 10.625

19.608

2.858 2004

2050

1999 12.082

Formula

30%

0.278 4.406

23.598 11.566 6.299 41.464

9.381 0.868 10.250

19.561

2.679 2003

2051

0.367 4.837

23.209 10.587 7.579 41.375

9.134 0.928 10.062

19.322

2.686 2003

2050

Sensitivity Analysis I 2005 2005 11.956 11.570

25%

Table 2 Performance measures for several different royalty rates, two sensitivity analyses

0.648 6.377

22.285 8.653 10.156 41.094

8.581 1.068 9.649

18.810

2.663 2002

2049

2005 10.690

40%

1.215 9.670

21.295 6.667 12.564 40.526

7.816 1.217 9.033

18.336

2.391 2000

2047

2007 9.606

50%

2.332 15.991

20.098 4.729 14.582 39.410

6.754 1.378 8.132

17.875

1.785 1997

2046

2009 8.217

60%

4.596 30.079

19.111 2.752 15.281 37.145

5.266 1.613 6.879

17.522

0.633 1993

2044

2015 6.326

70%

6.378 41.905

18.185 1.957 15.221 35.363

4.384 1.862 6.247

17.264

0.000

2042

2018 5.055

75%

7.691 46.283

16.018 1.415 16.617 34.050

3.935 2.573 6.507

16.705

0.000

2037

2021 3.382

80%

11.573 54.660

8.656 0.339 21.173 30.168

3.020 4.925 7.945

15.785

0.000

2025

0.000

90%

k,a

I

60

t~

t~

12.554 5.682 2.354 20.590 0.075 3.169

16.413 5.283 0.016 5.299 12.608 6.232 1.787 20.628 00.037 2.060

16.953 5.779 0.015 5.795 12.932 7.733 0.000 20.664

Aggregate domestic cons (F_.J)

Aggregate conv gas costs (B$) Aggregate backstop costs (B$) Aggregate supply costs (B$)

Aggregate deadweight loss (B$) Aggregate excess burden (%)

Aggregate consumer surplus (B$) Aggregate producer surplus (B$) Aggregate royalties (B$) Aggregate social welfare (B$)

3.828 2008

4.153 2009

Aggregate exports (E J) Last year of exports

5.097 0.018 5.115

16.119

3.648 2007

2052

2053

2053

1998 10.537

First year of backstop prodn

1998 11.144

1997 12.087

First year of new conv gas prodn Aggregate new conv gas prodn (EJ)

0.124 4.216

12.357 5.250 2.934 20.541

4.893 0.017 4.909

16.041

0.191 5.456

12.210 4.772 3.492 20.474

4.690 0.017 4.708

15.821

0.413 9.135

11.922 3.811 4.519 20.251

4.215 0.018 4.233

15.416

2053 2053 2053 Sensitivity Analysis II 3.511 3.354 2.883 2007 2006 2004

Sensitivity Analysis II 1998 1999 1999 10.406 9.997 9.068

0.578 10.243

11.551 2.888 5.647 20.086

3.969 0.022 3.990

14.629

2.829 2004

2051

2006 7.992

0.787 11.483

11.038 1.981 6.857 19.877

3.765 0.030 3.794

13.652

2.878 2004

2049

2007 6.643

1.271 15.818

10.258 1.103 8.033 19.394

3.446 0.045 3.492

12.612

2.689 2001

2045

2010 4.787

1.761 20.953

9.855 0.646 8.402 18.904

3.196 0.063 3.259

12.273

2.265 1999

2042

2016 3.523

5.031 87.035

9.677 0.176 5.781 15.633

1.894 0.083 1.977

13.025

0.000

2039

2026 1.833

7.039 82.543

5.081 0.016 8.528 13.625

1.398 0.099 1.497

11.317

0.000

2038

0.000

tuo

7"

t.,a

232

J. Rowse/ Resource and Energy Economics 19 (1997) 221-239

2004, when new gas arrives. This behaviour is not observed for the no-royalty case but is observed in accentuated form for the 50%-royalty and 75%-royalty cases. For the 50% royalty no spatial price equilibrium exists, even though exports occur. For the 75% royalty, exports never occur. Fig. 2 depicts the earlier contraction in exports for the 50% royalty and the absence of exports for the 75% royalty. The post-2005 dip in these production profiles accompanies the upward jog in the domestic price. Table 1 provides further solution details. Twelve cases are examined, including 10 for fixed percentage royalties. Provided in the top half of the table are four (snapshot) time profiles, yielding information on the domestic price, consumer surplus, wellhead royalty and tax revenues. All prices climb to the delivered price of backstop gas, but very different approaches occur. Price rises monotonically, and the price for a given year tends (generally but not universally) to rise with the royalty. CS for each year, in undiscounted billions of dollars (B$), depends upon the demand function and the choke price. The behaviour of CS relative to the previous year depends upon the price rise, the shift of the demand function and the demand price elasticity, and hence CS may rise or fall. In contrast, the wellhead royalty (in $ / G J ) shows much regularity. For 10 cases the percentage royalty is constant but its absolute size changes with the wellhead price. Royalty revenues (in B$, undiscounted) are less regular, but generally rise with the royalty rate. Because of the relatively high actual gas prices of the mid-to-late 1980s, in 1990 there was a surplus of gas beyond contracted amounts. Hence, in the no-royalty case, additional supplies are needed only by 2004. Levying a royalty and raising the rate tends to increase prices, slowing consumption growth and development of new supplies, and reduces the profitability of production, rendering uneconomic increasing amounts of new reserves. The price thus rises faster to the delivered price of backstop gas. In the no-royalty case backstop gas enters in 2056 and sooner with a higher royalty. Remarkably, even with a 50% royalty, backstop supplies enter only six years earlier. But a 90% royalty renders all new conventional production uneconomic and advances backstop supply by more than three decades. A rising royalty rate also erodes exports. The export price is fixed at $2.50/GJ and as the absolute royalty increases and the domestic price rises, exports lose their appeal. A 60% royalty eliminates exports. Aggregate domestic consumption, namely Etv=l Qt, adjusts similarly. With exceptions, the whole price profile rises with the royalty rate, less new conventional gas becomes economic and backstop gas enters sooner. The aggregate discounted costs of conventional gas and of backstop gas are also listed. Higher royalties shrink new conventional supplies (and their discounted costs) and increase backstop supplies (and their discounted costs). Together these costs decline to a minimum at a 70% royalty rate, then rise. Except for excess burden, all remaining measures are present-valued using a 5% discount rate. (A similar comment applies to Table 2 below.) In general, CS

J. Rowse/ Resource and EnergyEconomics 19 (1997) 221-239

233

and PS shrink as the royalty rises. Tax revenues climb, but this outcome depends on demand growth, price elasticities and the discount rate. Aggregate social welfare (SW), defined as C S + P S + royalty revenues, is largest with no tax (namely 32.688 B$) and shrinks as the tax increases. The dead weight loss (DWL) starts at nil, rises relatively slowly and then accelerates. As a proportion of aggregate SW, DWL is small through rates of 50% or less (no figures are listed). Aggregate excess burden, namely the (percentage) ratio of DWL to royalty revenues, behaves similarly. It rises only to about 6.3% for a 30% rate, a surprisingly small excess burden. Although DWL and excess burden are small for royalty rates at or below 30%, producers would likely complain bitterly. For instance, the 30% royalty redistributes PS over time and shrinks it by 4.4 B$, or 38%. CS behaves somewhat similarly. Hence the issue of intertemporal equity arises: different generations of consumers bear the tax differently through higher prices and reduced CS. Whether such redistribution is socially preferred is unknown. Distributional issues are only represented through SW, and it is unlikely that this measure fully captures society's preferences.

4. Sensitivity analysis For Sensitivity Analysis I, the backstop cost is increased to $10.00/GJ and th(W) is altered to pass through (0.0 EJ, $0.50/GJ) and (16.0 EJ, $9.10/GJ), making the costs of new reserves rise faster and eliminating more than one-third of the conventional gas available at the old backstop cost. The export price is also increased to $3.50/GJ and all export limits are raised by 50%. The principal findings are listed under Sensitivity Analysis I in Table 2. For brevity, the snapshot profiles are suppressed. The patterns replicate those found earlier. In particular, DWL and excess burden are small for rates through 30% and excess burden is below 10% for a 50% royalty. For Sensitivy Analysis II, all assumptions of Analysis I apply but ~b is lowered to 0.90 and /3 is raised to 1.5, giving price changes a more rapid and pronounced influence on consumption. A 10% discount rate is also used. Less new reserves are economic, exports increase and domestic consumption shrinks. DWL and excess burden behave similarly to Analysis I save for a few differences. The principal Base Case patterns are replicated by these analyses and the excess burden is under 6.5% for rates through 30%. Most results seem to reflect general tendencies and hence further analyses do not appear warranted.

5. On aggregate royalty revenues Aggregate royalty revenues peak for high royalty rates and increase monotonically in the Base Case, but not in the sensitivity analyses. Why?

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Semitivity Analysis II

50

55

60

65

70

75

80

85

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Royalty Rate (%) Fig. 3. Three tax revenue functions.

Raising the royalty far enough eliminates all gas production and all revenues. Hence a 'Laffer curve' for tax revenues (as defined by Yucel, 1986, p. 216)) exists and thus at least one tax-revenue-maximizing tax rate (TRMTR) exists. To understand TRMTR, it is useful to derive the knife-edge rate which nearly eliminates all production from proved reserves. The wellhead price including tax must not exceed the Base Case backstop cost of $7.50/GJ less the intraprovincial transport cost of $0.30/GJ, namely $7.20/GJ. Further, the price net of tax must cover operating costs of $0.60/GJ. Hence the knife-edge rate r satisfies (1 - ~-) $7.20/GJ = $0.60/GJ, or ~-= 11/12 = 0.91667 or 91.667%. Numerical experimentation reveals the Base Case TRMTR to be 0.91662 or 91.662% (with revenues of 22.058 B$), a whisker below the knife-edge rate. Thus TRMTR boosts the tax-augmented cost of gas from proved reserves to just below the backstop cost so that all gas from proved reserves remains economic. The whole price profile thus approaches the delivered price of backstop gas. The Analysis I TRMTR is found to be 0.93811 (with revenues of 28.842 B$), just below the knife-edge rate of 0.93814. The Analysis II TRMTR is found to be 0.93808 (with revenues of 11.957 B$), again just below the knife-edge rate. To examine the nonmonotonic behaviour of aggregate royalties, tax revenues were found for royalty rates varying from 50% through 91% in unit percentage increments. Fig. 3 displays the revenue functions found. Each function exhibits at least one local maximum different from the TRMTR. The single local maximum for the Base Case (78%) and for Analysis II (75%) are easily explained. Revenues first rise with the tax rate, but economically viable production shrinks. Thus, as the rate rises, revenues peak and then decline. But revenues eventually rise again with the tax because, as long as it lies slightly below the knife-edge rate, proved

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reserves continue producing and the rising tax rate extracts more surplus from consumers and producers. Four local maxima exist for Analysis I. These maxima cluster (63%, 65%, 69% and 71%) and yield very similar revenues. Although unusual, these maxima do not contradict economic theory: the price paths for rates from 60% through 75% cross and recross irregularly and domestic demands exhibit different elasticities at the different efficient prices. Interestingly, the four local maxima of Analysis I shrink to one local maximum for Analysis II. The increased price responsiveness of demands and a higher discount rate account for this occurrence. Three conclusions emerge. First, the behaviour of tax revenues can be complex and does not seem predictable a priori. Secondly, TRMTR may depend upon the backstop cost, which is likely to be conjectural. Finally, tax revenues may depend strongly upon the discount rate, demands and price elasticities, the latter of which - for the distant future - are likely to be conjectural.

6. T h e results in perspective

6.1. Findings by other researchers

Four studies appear particularly relevant as predecessors. In this section their approaches and a few of their findings are discussed. Gamponia and Mendelsohn (1985) utilize a model (of no specific resource) with constant marginal extraction cost, exogenous stock, and stationary demand with constant price elasticity, to compare a yield (ad valorem) tax, property tax, unit (specific) tax and windfall profits tax. Results are found for various combinations of yield tax: 10%, 20%, 40%; price elasticity: - 0 . 5 , - 1 . 0 , - 2 . 0 ; discount rate: 1%, 2%, 4%; stock size: 2000, 4000, 8000 units; and unit cost: $0, $1, $5. Time-to-exhaustion varies from 37 years to 590 years. In their base case, the excess burdens of the yield tax vary from 0.001% to 3.47% and the excess burdens of the unit tax vary from 0.303% to 14.98%. Results are robust with respect to the discount rate, stock size and extraction cost. In general, moderate ad valorem taxes (up to 20%) give rise to very small to small excess burdens for the yield and unit taxes. All tax burdens fall primarily upon resource owners. Focusing on ad valorem severance taxation, Yucel (1986) simulates efficient crude oil allocation with a model allowing for stock additions, utilizing one Cobb-Douglas function for output and a second for exploration outcomes, time horizons of 50 years and 90 years, a 5% discount rate and a nonstationary demand function linear in price and income. Yucel finds that in general DWL is low, the tax burden is absorbed by producers through lower rents, and deadweight losses are 1.1%, 5.2% and 17.5% for tax rates of 5%, 20% and 50%, respectively. Yucel reports a TRMTR of 88% and that it always exceeds 80% for different demand

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specifications. But Livernois and Uhler (1987) implicitly call these results into question: Yucel's extraction cost function exhibits marginal extraction costs that (implausibly) decline with reserve additions. Deacon (1993) adopts some aspects of Yucel's approach to compare a property tax, an ad valorem severance tax and a corporate income tax on petroleum production in the Lower-48 US states. The major assumptions are: cumulative reserve additions vary exponentially with cumulative drilling, drilling costs vary quadratically with drilling, production costs follow a constant-returns-to-scale Cobb-Douglas function, the discount rate is 5%, the tax rate is 15%, the final year of production is set at 61 years and wellhead prices are exogenous. Deacon notes that the Livernois and Uhler criticism applies to his work but argues that data limitations prevent his estimating a cost function not subject to this criticism. He finds that the severance tax shifts output toward the future but the dominant effect (p. 173) is "high-grading, however; resources that would otherwise be explored, added to reserves, and produced are rendered sub-economic by the severance tax". Average DWL (or excess burden) is found to be 4.52%. Findings are quite robust over his sensitivity analyses. Further (pp. 172-173): "the simulation program inherits a sizeable reserve in the initial period. Because the cost of acquiring this reserve is sunk, the corporate levy can tax the return to this initial capital stock with no penalty for reduced efficiency". His reasoning applies to the corporate tax, but it is also relevant for this work. Ward and Kerkvliet (1993) utilize a complex nonlinear programming model of the linked coal and electricity markets of New Mexico to examine the effects of different severance taxes over a six-decade time frame. Unit taxes of $1.05/ton (the prevailing tax) through $11.50/ton are simulated, and the private discount rate is 10%. Coal demands are endogenously determined by demands for electrical energy. Coal supplies come from an eight-step coal supply function, the last step comprising the backstop source. Finally, the last year of New Mexico coal production is endogenous. They report the following results. Of their simulated tax rates, TRMTR is $11/ton or $11.50/ton, much above $1.05/ton. Higher taxes also produce a 'high grading' effect, and the reduction to present-valued PS + CS for all taxes is proportionately small. Although excess burdens are not computed (and cannot be computed from their results), they must be relatively small because the DWL has little impact upon CS + PS. The DWL size is mentioned but not explained. 6.2. On the excess burden of severance~royalty taxation

The preceding studies employ very different models but reach similar conclusions: for relatively low severance taxes the tax rate has little impact on measured social surplus. This outcome warrants discussion. The excess burdens reported certainly seem relatively small. For instance,

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Ballard et al. (1985) examine the marginal welfare costs of taxes in the United States using a general equilibrium model and find (p. 128): that the marginal excess burden of taxes in the United States is large. The welfare loss from a 1 percent increase in all distortionary tax rates is in the range of 17 to 56 cents per dollar of extra revenue, when we use elasticity assumptions that we consider to be plausible. In contrast, the excess burdens found above, for ad valorem taxes in ranges actually observed, are less than 6.5%. Can these small sizes be explained? Three explanations seem possible. First, Ballard et al. use a model which represents several taxes simultaneously. Hence, raising a single tax in the presence of several distortionary taxes may compound the distortions and lead to a higher DWL than when only a single tax is represented and raised. A second explanation stems from observations of previous studies regarding the inherited or initial stock. For most resources there is a known (or well estimated) stock of proved reserves, the capital costs of which are sunk. Most resource products are capital intensive, especially hydrocarbons, and thus the noncapital costs constitute only a fraction of total costs. The bulk of proved reserves can usually be recovered only for the noncapital costs. Thus a severance tax can expropriate most quasi-rents for the proved reserves without much affecting supplies, and it will discourage only certain increments to proved reserves. Because these increments tend to appear in large amounts one or more decades in the future, discounting shrinks the surplus losses associated with discouraged increments. Thus, proved reserves tend to provide supplies inelastically for prices not much above the noncapital costs, and it is only several years after the imposing or raising of a royalty (severance) tax that the supply response becomes more elastic. A third explanation draws in part upon the second but is more general. Rowse (1988) argues that a nonrenewable resource has many near-optimal depletion paths. Applying his results here, a moderate royalty - for instance the formula royalty - shifts allocations away from the optimal path, but at relatively little cost in terms of excess burden (less than 4%).

7. Concluding remarks This work appears to be the first simulation study of an ad valorem tax on wellhead production of a nonrenewable resource in a model exhibiting much demand and supply complexity. The following general (but not universal) tendencies are observed: a rising royalty raises the price profile, depresses the production profile and total conventional production, advances backstop supplies, shrinks domestic consumption plus exports, squeezes aggregate domestic supply costs and

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compresses the sum of consumer surplus, producer surplus and tax revenues. A high royalty rate also maximizes tax revenues. A central finding is that moderate royalties generate relatively small excess burdens. This outcome may stem from considering only a single tax and could change with several distortionary taxes. Alternatively, the royalty may bear largely upon quasi-rents accruing to the initial resource stock and exert little influence upon incremental supplies until one or more decades later, allowing discounting to mute the effects of the tax on social welfare. Finally, many depletion paths appear near optimal for a nonrenewable resource and taxation may simply shift the optimal allocation to one of these paths. The relatively small excess burdens may appear to make ad valorem taxation attractive. Yet the analysis is performed only with a single tax and in a deterministic framework. In reality, producers must contend with several taxes simultaneously and much supply uncertainty. Moreover, this work is silent on the issue of intertemporal equity among consumers (and producers) and on regional or macroeconomic stabilization objectives to be furthered by tax policy. To promote these other objectives, governments may properly place less weight on taxation than this study might suggest. More generally, this work supports the following assertions:- For tax policy analysis of nonrenewable resources it is possible to utilize simulation models which can represent much demand and supply complexity. • Results of tax policy simulation models must be interpreted with care. Nonrenewable resource models require horizons of half a century or more and hence demands, supply capabilities, imports, exports and technical advances must be projected into the distant future. Given the uncertainties of such projections, only broad insights into tax implications seem possible. • Even if industry data is accessible, data limitations may still pose serious difficulties. For example, in the petroleum industry the heterogeneity of the resource base and probable technical progress in reducing production costs likely make any aggregation of pools/fields questionable. Technical advances could also unlock large nonconventional hydrocarbon reserves. Moreover, gradual reserve exhaustion may move prices into ranges not previously seen, inducing economic behaviour never before observed.. This work replicates findings of several earlier studies. For example, certain findings by Yucel (1986), who utilizes a model misspecified according to Livernois and Uhler (1987), and by Deacon (1993), whose approach is similar to Yucel's but who discusses the misspecification, are supported by this work. In particular, small efficiency losses (and excess burdens) for 'moderate' ad valorem taxes are found. This result appears general. • The tax rate which maximizes tax revenues (TRMTR) appears large and the tax revenue function may be complex. But TRMTR may depend upon the backstop availability and cost and distant-future demand and supply elasticities and export/import prospects, making its size uncertain. Further, even if a large TRMTR could be quantified with confidence, imposing it would likely be unwise. Monopoly behaviour by a private resource producer would rightfully be faulted on

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efficiency grounds, and government taxation leading to a similar outcome would have to be viewed the same way. Finally, serious equity issues could arise with heavy taxation of a resource such as natural gas or crude oil.

Acknowledgements Financial support for this work has been provided by the Social Sciences and Humanities Research Council of Canada. I have benefited from numerous helpful comments offered by Robert Deacon, Joe Kerkvliet and Alan MacFadyen. Suggestions by two reviewers and Charles Kolstad have also led to improvements. I thank these individuals but append the usual disclaimer.

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