INVESTIGATING TAX DISTORTIONS: AN APPLIED MODEL OF PETROLEUM EXPLORATION AND EXTRACTION DECISIONS

Abstract

Abstract A numerical model is proposed for the testing of distortions caused by petroleum fiscal systems on the exploration and extraction activities of a profit-maximizing firm. Traditional models have not been capable of testing for the distortions caused by the complex tax structures most often used by governments. Two tax combinations, as well as certain other taxes, are analyzed for distortions in the model. The model is parameterized using generic data because specific jurisdictions are not considered. The distortions due to rentals and royalties are as expected by theory. Property taxes show a new distortion result where production tilting is ambiguous.

1. Introduction. 

Taxation is an important factor affecting our petroleum supply, but the effects of the complex fiscal systems actually used by governments are not well understood. Many studies have looked at the distortions introduced by frequently used, individual fiscal instruments, on production and exploration decisions using mathematical models. However, governments use an assortment of taxes in combination, interacting with each other in complex ways. Thus far, no model has been proposed to test for the distortion effects of tax combinations. This paper introduces one such model.

The literature dealing with the effects of petroleum taxation may be separated into two broad categories for the purposes of this paper. The first category is the traditional literature looking at the impact of taxation on the optimal path of extraction, on the levels of uneconomic resources left in situ (the "high-grading" effect) and on the life of the mine. The problem was apparently first addressed by Gray [1914], but the paper by Hotelling [1931] is the cornerstone for this body of work, including, but not limited to, the work of Burness [1976], Uhler [1979], Dasgupta et al. [1980], Heaps [1985], Heaps and Helliwell [1985], Gamponia and Mendelsohn [1985], Yucel [1986] and Deacon [1993]. These researchers test the economic efficiency of a single fiscal device, never more than one device at a time, on the extractive and exploratory effort of a firm or a competitive industry.

The second category of petroleum taxation literature is the applied research, which focuses on the practical analysis of actual fiscal regimes, as pioneered by Kemp and his associates in the 1980s, for example, Kemp and Rose [1985] and Kemp [1987]. These studies involved testing full fiscal systems using a suite of generic oil fields. The central concept relating economic efficiency to the results of the empirical analysis was the idea that the more accurately a fiscal system targeted economic rent, the more efficient the fiscal regime would be. This type of generic oil field fiscal testing led to benchmarking studies of petroleum fiscal systems, as done by, for example, Van Meurs [1997] and Johnston [2001].¹

Thus, complex tax scenarios, which include taxes in combination, have not been directly tested for distortionary incentives. Although the traditional literature sought to directly investigate the resource allocation effects of individual taxes, Kemp's work could only, by an indirect route, compare the efficiencies of full fiscal systems. The advantage of Kemp's empirical methodology was that actual complex fiscal systems could be analyzed, thus allowing practical policy advice to be formulated. The disadvantage is that the impact of fiscal systems on extractive and exploratory effort could not be determined. The methodology used in the theoretical literature, mainly optimal control theory, could not be applied to complex tax scenarios.

This paper seeks to bridge the gap between the theoretical and applied literature by proposing a model, which may be used to test for the distortionary effects of complex tax scenarios. Therefore, the complicated fiscal devices that are used by governments, such as production sharing arrangements, as well as combinations of taxes, may be analyzed for their incentive effects. The proposed model is a sequential basin model, similar to that of Nilssen and Nystad [1986], with two decision variables: exploratory effort and initial production.²

In Section 2, the model is described and its features are discussed. In Section 3, the results of including certain tax instruments into the model are compared to the results in the received literature. Section 4 reports on the results for two tax combinations while Section 5 concludes.

2. The model 

2.1. Model description. 

A profit-maximizing firm is assumed to sequentially explore and exploit crude oil in a basin³ by expending exploratory effort instantaneously in year t_E, then developing the discoveries in year t_D, so that crude oil production starts subsequently in year t_p. A petroleum-producing basin contains a variety of oil fields of differing sizes. If there are n field size classes, the field discovery function used to describe the returns to exploratory activity, as proposed by Arps and Roberts [1958], is

• (1)

where F_n(W) is the number of discoveries in field size class n; F_n(∞) is the ultimate, or original, number of fields in class n; A_n is the average areal extent of each field in class n; B is the total area of the basin; c_n is the efficiency of exploration for fields in class n and W is the exploratory effort. The number of wells drilled is used, herein, as the measure of exploratory effort. A common alternative formulation of this discovery function is

• (2)

where γ is related to the efficiency of exploration. The formulation in equation (1) is chosen because the data used for the parameterization of the model is given in this format. This exploration model, sometimes called a finding rate function, is commonly used in geological assessments by the United States Geological Survey (USGS), for example, by Attanasi and Bird [1995] and Attanasi and Freeman [2005].

The exploration costs are assumed to be proportional to exploratory effort as

• (3)

where C_E is the total exploration costs for the basin, and β is the average exploration well cost. This proportional cost model, where marginal costs are constant, assumes that the markets for the inputs to exploratory effort are competitive, and that any amount of exploratory effort may be “purchased” with no change in the price. This exploration cost function is often assumed by analysts, for example, Uhler [1979].

Development and production of the discovered fields take place after the exploration stage. Each field's production is assumed to follow exponential decline. This is a conventional assumption in the petroleum industry.⁴ As Hannesson [1998] points out, production decline is rarely smooth, but exponential production is a good approximation “…particularly when calculating present values of future income streams; deviations from the curve will cancel each other out.” So, production is described by

• (4)

where is the instantaneous production at time t for fields in class n. q_i,n is the initial output for fields in class n. a_n is the decline rate for fields in class n. a_n is related to q_i,n by

• (5)

where R_n is the technically recoverable reserves for field size class n and is the parameter used to define field size in each class. R_n is defined by

• (6)

The economically recoverable reserves, R_E,n, for fields in class n, is calculated as

• (7)

T_n is the time of production cut-off for fields in size class n, which occurs when production revenues decline so that they become equal to production costs. T_n is determined later.

Development investment, which occurs at time t_D, is proposed to be dependent on the desired level of initial production capacity. So, the development expenditure for fields in size class n, C_D,n, is defined by

• (8)

where a_D and b_D are parameters: a_D is a measure of the cost environment, whereas b_D indicates the presence of economies of scale when 0 < b_D <1. A similar function is proposed by Nilssen and Nystad [1986].

Operating costs for fields in size class n, C_O,n, are assumed to be proportional to the development expenditure as

• (9)

where f_n is the proportionality factor relating development and operating costs for fields in size class n. This is the so-called factor method of estimating operating costs, as discussed by Kaiser [2006]. T_n may now be determined by equating production revenues and costs

• (10)

where p_t is the crude oil price at time t. Substituting for q_i,n and T_n in the above equation and rearranging yields

• (11)

where T_n may be uniquely defined by the above equation depending on the price and operating cost assumptions. Herein, prices and operating costs are both assumed to be constant.

The firm's objective, the profit function, may now be defined. However, because this model must be solved by numerical simulation, a discrete time formulation of the objective function is presented. For the discrete and continuous formulations to be consistent, the production in discrete time is defined by

• (12)

So q_t,n is crude oil production, in discrete time, at time t for fields of class n. The firm's objective function for the basin is thus

• (13)

where Π is the basin profits before taxes, r is the discount rate and N is the total number of field size classes. The task of the firm is to maximize the profit function given the decision variables, q_i,n and W, namely,

• 

subject to the non-negativity constraints

• 

There are (N+1) decision variables. If there are three field size classes: 1, 2, and 3, then there will be four choice variables: q_i,1, q_i,2, q_i,3, and W. In order for the model to be verifiably optimized by allowing for the graphing of the objective function,⁵ only one field size class will be analyzed at a time. The implications of using one field size class are discussed in Section 2.3. Therefore, dropping n from the nomenclature so that just one field size class is being considered, the objective function becomes

• (14)

Thus, there are only two decision variables, q_i and W, representing the production and exploration decisions of the firm. All other variables are exogenous (including t_E, t_D, and t_p). Note that the production decision variable is endogenous for the initial production in an otherwise exogenously specified exponential production decline curve. This differs from most conventional studies (of the first category specified in the introduction) where production is fully endogenous.

Two types of distortions may be tested using the above model, exploration distortions, and production distortions, resulting in changes to the basin value. The distortions and the basin value changes are defined as

• (15)

• (16)

• (17)

where W* is the optimal exploratory effort before taxes are imposed and is the after tax optimal exploratory effort. is the optimal initial production before taxes whereas is the after tax optimal initial production. Π* is the optimal basin profits of the firm before the imposition of taxes, and is the optimal basin profits of the firm after taxes. GT is the government take from the imposition of taxes.

2.2. Empirical scenarios. 

The empirical scenarios developed herein are generic in nature because specific tax jurisdictions are not being tested. Instead, as described later, the distortionary effects of three frequently used tax instruments, as well as two generic tax combinations, are analyzed relative to the received theory. Jurisdiction-specific case studies may then be developed in later work. The data used for the parameterization of the model is presented in Table 1. The model was implemented in Excel and the optima found using Solver.

Table 1.  Model parameterization.

Variable	Onshore	Offshore	Description
B	100	47.50099	Basin area (thousand square miles)
F 1(∞)	13	17	Ultimate number of large fields
F 2(∞)	10	25.8	Ultimate number of medium fields
F 3(∞)	27.2	50.7	Ultimate number of small fields
A 1	27.5	17.17	Area of fields in large field class (sq miles)
A 2	21	10.91	Area of fields in medium field class (sq miles)
A 3	15	6.93	Area of fields in small field class (sq miles)
c 1	3.15	5.64	Exploration efficiency for large fields
c 2	3.15	4.89	Exploration efficiency for medium fields
c 3	3.15	4.15	Exploration efficiency for small fields
R 1	291.45	291.45	Technical reserves for large fields (MMBOE)
R 2	145.75	145.75	Technical reserves for medium fields (MMBOE)
R 3	72.9	72.9	Technical reserves for small fields (MMBOE)
β	1.3	24.2	Average exploration well cost (millions USD)
a D	0.1708	0.48264	Cost “environment” parameter for development costs
b D	0.844	0.702	Economies of scale for development costs
f 1	0.052	0.039	Operating cost factor for large fields
f 2	0.054	0.044	Operating cost factor for medium fields
f 3	0.059	0.054	Operating cost factor for small fields
t E	0	0	Exploration expenditure instantaneous time
t D	1	1	Development expenditure instantaneous time
t p	2	2	Production start time

Twelve empirical scenarios were created using one onshore and one offshore basin, three field size classes (“Small”, “Medium,” and “Large”), and two price scenarios. The basin data for each field size class are used to parameterize the exploration model. The onshore basin data is based on the Permian Basin in the United States, and is taken from Attanasi et al. [1981]. The offshore basin is based on the Miocene–Pliocene trend of the Western Gulf of Mexico and the data is taken from Attanasi and Haynes [1984].⁶ A global average offshore exploration well cost estimate for 2008 was gleaned from Smith [2008], and an estimate was calculated for the global average onshore well cost from Blake [2010]. Flat prices of $100/bbl (the 2008 average price) and $50/bbl were used as the price scenarios.⁷

The development expenditure function was parameterized using a development cost database for onshore and offshore projects. The development cost database was created from reports in Platts Oilgram News during the period 2005–2008, and adjusted to 2008 dollars where necessary by using the IHS/CERA Upstream Capital Cost Index. The operating cost “f” factors were such that larger fields had smaller factors, but all the factors averaged to 5%, a common industry rule of thumb, as Adelman [1993] indicates. A discount rate of 15% is assumed throughout and inflation is ignored (0%).

2.3. Depletion features. 

Bohi and Toman [1984], in discussing the theory of nonrenewable supply behavior, point out that “The core of the theory is a formal representation of depletion effects in the supply process and of how these effects influence the behavior of the firm”. In the proposed model, depletion is portrayed by the decreasing returns to effort for exploration and extraction, constrained by inherent finiteness, as shown in Figure 1.⁸

Figure 1. Diminishing returns to extraction and exploration.

Increasing q_i requires an increase in development expenditure, which, when 0 < b_D < 1, increases the economically recoverable reserves through the assumed relationship with operating costs. This model feature captures the so-called “geological distribution effect” of Nystad [1988], which is a known occurrence in the petroleum industry where development investment serves not only to bring reserves into production, but also adds to reserves with increasing development intensity, for example, by increasing the number of wells, the number of platforms and enhanced oil recovery projects. In the present model, there are decreasing returns of R_E to q_i (and C_D) such that the limit is R. On the other hand, the exploration model is limited by the ultimate number of fields in the basin. Decreasing returns to exploratory effort have been empirically observed in petroleum basins.

This representation of depletion effects is unconventional when compared to the theoretical literature where these effects are traditionally represented by increasing “extraction costs” as the level of reserves is reduced, for example, as discussed by Deacon [1993]. Furthermore, the supply process in traditional models is often characterized by completely endogenous production. In this conventional conceptualization, the effect of increasing extraction costs is a limiting factor on output, as well as an incentive to explore.

Livernois and Uhler [1987], however, have argued that the relationship between extraction costs and the reserves level is ambiguous in an aggregate setting. The idea that extraction costs decrease when reserves are added is incompatible with the expectation that a rational explorer will target more favorable exploration targets first. Livernois and Uhler [1987] do acknowledge that within a single deposit, extraction costs may increase with declining reserves. The present model looks at the problem from a different perspective: development expenditure affects the recovery of reserves in each field, and not vice versa.

In concluding this section, we note that the assumption of just one field size class per basin ignores heterogeneity. Therefore, the behavior of the rational explorer who exploits better quality reserves first, is not modeled.⁹ This is an important depletion effect because this behavior will cause costs to rise over time. This type of exploration behavior by oil companies is not observed in reality, as Krautkraemer and Toman [2003] point out, although the long run discovery pattern of basins causes this type of search to be approximated. One reason for this lack of “rational” behavior by oil companies is due to the randomness of the exploration process.

Nevertheless, the present model would be improved if more than one field size class were to be included in a basin. As mentioned earlier, this would cause the model to become practically difficult to solve. As a partial solution, different field size classes are separately tested in the model. So, the small, medium, and large field size classes are separately applied to the basins being modeled. One advantage of this methodology is that it serves as a sensitivity test, and may be viewed as testing different basins with differing levels of prospectivity. In this context, the field size class tested is the long run average expectation of the returns to exploratory activity.

3. Theory versus model results. 

Three frequently analyzed and commonly used taxes are examined in this section: royalties, rentals, and property taxes. Royalties, or severance taxes in the United States with equivalent distortion effects, are the most frequently analyzed of the fiscal devices, with many authors, from Gray [1914] to Rowse [1997], considering their effects. Examined herein is an ad valorem royalty where the discount rate rises faster than the royalty rate (which is constant) as well as prices (also constant). The theoretical expectation is for this royalty to cause the future tilting of production.

Also considered here are rentals, akin to the “franchise taxes” or “license fees” considered by Burness [1976], Heaps [1985] and Heaps and Helliwell [1985]. Rentals are formulated herein to be flat annual payments as in the previous papers, but with a slight refinement in the calculation: the final rentals payment is prorated. So, if the final year's production terminates halfway through the year, then half of the usual rental is liable. This is done so that the objective function surface remains smooth. Prorating the final year rental payment also occurs in practice. Rentals are expected to present tilt production.

Finally, a property tax based on the value of reserves is considered. Property taxes have been considered by many authors, including Deacon [1993]. The consensus is that these taxes cause a present tilting of production.

Previous authors using simulation models have often compared different taxes by using one benchmark level of government take, for example, Deacon [1993] and Gamponia and Mendelsohn [1985]. Yucel [1986] looked solely at royalties, but considered different royalty rates, as did Rowse [1997]. On the basis of the work of Yucel [1986] and Rowse [1997], distortions introduced by a non-neutral tax are expected to vary with government take as illustrated in Figure 2. For the tax scenarios considered in this paper, the distortions are calculated over a range of government take levels (by varying the rates of taxation) up to the government take limit.

Figure 2. Expected relationship between government take and distortions.

3.1. Royalties. 

Including royalties in the model altered the objective function, equation (14), to

• (18)

where Π_τ is the after tax basin profits accruing to the firm. ROY_t is the royalty liability in year t for each field, and is always non-negative. Royalties are included in the production cut-off calculation so that T is now defined as

• (19)

where τ_ROY is the flat, non-negative, royalty rate, so

• (20)

In all the scenarios tested, royalties caused decreases in the optimal level of initial production, which, in this exponentially declining model of production, is equivalent to the future tilting of production. Exploration is impaired in all scenarios and the basin value is reduced. The graphs in Figures 3, 4 and 5 are typical.

Figure 3. Royalty production distortions: offshore basin, large fields, $100/bbl.

Figure 4. Royalty exploration distortions: offshore basin, large fields, $100/bbl.

Figure 5. Royalty basin value changes: offshore basin, large fields, $100/bbl.

3.2. Rentals. 

Imposing rentals causes the firm's objective function to become

• (21)

where RN_t is the rentals paid in year t for a field and is always non-negative. Rentals are paid for the entire period of exploitation and are not included in the production cut-off calculation.

The model's results for rentals, as far as the theory goes, are as expected. In every scenario, rentals resulted in increases in the optimal level of initial production, thus causing the present tilting of production. In all cases, exploration is impaired and the basin loses value.

However, in the production distortions versus government take graphs, there are discontinuities. Figure 6 shows an example of a graph with two discontinuities. On examining the points around the discontinuities, they are observed to occur whenever a new production period is lost (or added).

Figure 6. Rentals production distortions: onshore basin, small fields, $100/bbl.

Because rentals are not included in the production cut-off calculation, the later years near the end of production show negative cash flows when rentals are imposed. So while the firm's response to rentals is to withdraw production from later years to the earlier years, as this reduces the rentals liability, the presence of negative cash flows in later periods, and the increasing levels of government take, provides an added incentive for getting rid of entire periods of production. The discontinuities in the graphs disappear if rentals are included in the cut-off calculation, thus avoiding the terminal negative cash flows.

The exploration distortions versus government take graphs are as expected while the basin value graphs show kinks where the production discontinuities occur. Figures 7 and 8 are typical.

Figure 7. Rentals exploration distortions: offshore basin, large fields, $100/bbl.

Figure 8. Rentals basin value changes: offshore basin, large fields, $100/bbl.

3.3. Property taxes. 

The property tax is modeled as a value tax where the tax base is the present value of the net cash flow from each field, similar to the representations of Burness [1976] and Heaps [1985]. Exploration costs are assumed sunk in all assessment periods, because exploration was assumed to take place instantaneously at time 0. The property value is defined as

• (22)

where V_i is the property value assessed in period i for each field, and is always non-negative. The upper equation is used when the tax assessment period is before development (t_D≥i), and the lower equation for postdevelopment (t_D < i). The firm's objective function becomes

• (23)

where τ_PT is the flat, non-negative property tax rate.

The results for property taxes were not as expected. In all but one of the scenarios, the expected production distortion, where production is present tilted, was obtained by an increase in the optimal level of initial production. In the scenario using the onshore basin with small fields at $50/bbl, the optimal level of initial production was reduced so that production was future tilted. Figure 9 shows the typical production distortions versus government take graph, as would be expected by theory. Figure 10 shows the atypical scenario.

Figure 9. Property tax production distortions: onshore basin, small fields, $100/bbl.

Figure 10. Property tax production distortions: onshore basin, small fields, $50/bbl.

The reason for the unusual result is due to the model. In the traditional theoretical models, the only method available to the firm for reducing the level of reserves, thereby lowering the property tax liability, is to produce those reserves faster than in the pretax situation. However, in the present model, the reserves level is also dependent on the level of development intensity. So in the scenario using the onshore basin with small fields at $50/bbl, the level of recoverable reserves were decreased by reducing the level of development investment, so the optimal level of initial production was reduced.

However, why is this incentive to lower development intensity only seen in the scenario using the onshore basin with small fields at $50/bbl? The reason lies in the fact that this scenario has by far the smallest optimal level of pretax initial output. All the other scenarios have pretax optimal levels of initial production which are, at the very least, more than double that of the atypical scenario and, in many cases, many orders of magnitude greater. This is as a result of the data used to parameterize the scenario, particularly the lower level of b_D for the onshore basin, and the fact that small fields are being developed at a relatively low price. Consequently, the scenario is faced with the least favorable economies of scale from development investment and operating costs, and thus has the lowest optimal levels of initial production.

The low pretax optimal level of initial production in the atypical scenario means that accelerating production is no longer the best method of reducing the property tax liability for two reasons. First, the present value of the property tax liability is not as sensitive to changes in the reserves levels further out into the future. When accelerating production, the reserves at the end of the project are reduced relative to the pretax situation. The second reason is due to the increased sensitivity of changes in recoverable reserves at the start of the project when reducing an already low level of investment, compared to reducing higher levels of investment, as a result of the diminishing returns to extractive effort (see Figure 1).

The exploration distortion and basin value graphs are as expected. Figures 11 and 12 are typical.

Figure 11. Property tax exploration distortions: onshore basin, small fields, $100/bbl.

Figure 12. Property tax basin value changes: onshore basin, small fields, $100/bbl.

4. Tax combinations. 

Two tax scenarios are presented in this section, a combination of royalties and rentals, and a combination of income taxes, royalties, and rentals. Combining royalties and rentals has been suggested by Burness [1976] and Osmundsen [1998] and is an interesting case due to the possibility of the production distortions, which move in opposite directions, canceling each other out. The combination of income taxes, royalties, and rentals is one of the most common combinations being used by governments that employ the tax/royalty category of petroleum fiscal system, see Blake [2010].

To keep matters simple, the tax combinations are tested in the model such that each fiscal instrument in the combination would garner an equal share of the overall government take. This is neither a realistic assumption nor a valid policy goal. However, this assumption removes the distribution of government take within the combinations tested as a complicating factor in our analysis of the results.

4.1. Royalties + Rentals. 

The objective function for the firm under this combination of taxes becomes

• (24)

In combining these two instruments, the most interesting aspect is the resulting production distortions. In all the economic scenarios tested, the final direction of the production distortion could be predicted by taking the average (arithmetic mean) of the production distortion graphs before the instruments are combined. In other words, the dominant instrument with the larger absolute production distortion at each level of government take determined the final direction of the production distortion. Figure 13 illustrates these observations for one scenario.

Figure 13. Rentals + Royalties combined vs. average production distortions: onshore basin, large fields, $50/bbl.

When the production periods change, rentals discontinuities were observed. However, these discontinuities do not show up in the exploration distortion or basin value graphs, which were as expected for all scenarios.

The combined production distortions do show significant cancellation effects, and the resulting improvements affect the exploration distortions and basin values. For most scenarios, the exploration distortions and basin value losses are lower than either of the original instruments. In those scenarios where the combination did not result in an improvement over the original instruments, the absolute level of the average production distortion was greater than one of the original instruments.

4.2. Income Taxes + Royalties + Rentals. 

The income tax used in this fiscal combination is defined such that there is no limit on the carry forward of losses, there are expensed exploration costs, 5-year straight line depreciation for development costs, and all costs are ring-fenced on a field basis, even though the firm maximizes basin profits. The basin exploration costs are allocated in equal shares to all the fields in the basin for the income tax calculation.

The income tax base, when not in combination with any other instrument, is defined as

• (25)

where TB_t is the income tax base in year t. TD_t is the total allowable capital deductions in year t (excluding LCF_t–1). LCF_t–1 represents the losses carried forward from year t–1 and depends on the tax base of the previous year such that

• (26)

The losses carried forward, LCF_t–1, are defined before the cut-off date, T, because losses may not be carried forward beyond T. The income taxes due are therefore

• (27)

where IT_t represents the income taxes due in year t, and are always non-negative. The objective function for the firm therefore becomes

• (28)

The papers by Gaudet and Lasserre [1986] and Deacon [1993] contain examples of income taxes resulting in production distortion effects. Gaudet and Lasserre [1986] looked at income taxes in the United States and Canada and found that the extraction path under these taxes depended on the parameters used in defining the tax. Deacon [1993] considered a version of the US income tax and found that it did not introduce large deadweight losses, and that it caused the future tilting of production. In the present model, the income tax on its own also caused the future tilting of production in all the economic scenarios tested, as well as introducing, in most scenarios, smaller basin value losses compared to the other instruments considered herein.

In combining the income tax with royalties and rentals, the income tax calculation is changed so that royalties and rentals are both deductible. Therefore, the income tax base becomes

• (29)

The objective function of the combination is

• (30)

The production distortions caused by this combination were, as one might expect, much more complicated than that of the previous combination. The average of the individual production distortions predicted the final direction of the combination's production distortions in scenarios where production is tilted unambiguously, regardless of the level of government take, but not in scenarios where production tilting is ambiguous. Even so, the average was a perfect predictor in an ordinal analysis, ranking the absolute combined distortions versus that of the original elements. In other words, the average predicted whether the tax combinations would show greater or lesser absolute levels of production distortions compared to the noncombined tax instruments.

In many of the production distortion graphs for the combination, as expected, rentals discontinuities were observed. However, a new set of features were also observed: kinks and peaks in the graphs that are due to ad hoc production adjustments which serve to avoid the carrying forward of losses in the income tax calculation. The firm is able to manipulate production so that enough revenues are available in periods that are in danger of having to carry forward losses, thereby avoiding a reduction in the value of these write-offs. Figure 14 shows rentals discontinuities as well as the ad hoc production adjustments due to the income tax.

Figure 14. Income Tax + Rentals + Royalties production distortions: offshore basin, large fields, $100/bbl.

The exploration distortion and basin value graphs, for most of the scenarios, are as expected. In a few instances, slight kinks may be seen resulting from production distortion features being passed on. In the majority of scenarios, the combination is an improvement on both royalties and rentals, but not on the income tax.

5. Conclusions. 

The proposed model was deliberately kept as simple as possible, while at the same time describing the essential trade-offs that petroleum firms are faced with. Simplicity considerations meant that uncertainty, reservoir-specific effects, and other more realistic descriptions of the petroleum supply process, needed to be ignored. However, the model allows for the analysis of complicated tax scenarios. More complex models fail because they quickly become intractable to optimization algorithms when multitax scenarios are included.

The model compares well with theoretical results except in the case of the property tax where a novel distortionary phenomenon is observed. The intuition for this property tax distortion is simple: greater levels of reserves additions increase the property tax base, so by reducing investment in reserves the firm reduces the property tax burden. In the proposed model, reducing development intensity and accelerating production are mutually adverse strategies. In defense of this feature, we note that actual investments in production acceleration are often associated with the addition of reserves. For example, investments in development drilling, “workovers” which stimulate well production, enhanced oil recovery techniques and infill drilling campaigns often result in reserves additions as well as production acceleration.

In this brief consideration of tax combinations, the average distortion of the individual tax components seems to be an important benchmark for predicting the combined distortion level. Furthermore, there is some evidence that combining certain taxes may create fewer distortionary incentives than the original instruments due to countervailing production incentives.

ENDNOTES

• 1

  There is a third category of petroleum taxation analysts who consider uncertainty by using financial valuation concepts, particularly contingent claims valuation derived from options valuation theory, to test for the efficiency of taxes. The seminal paper is by Ball and Bowers [1982]. Some authors in this category have studied the distortionary effects of full fiscal systems under uncertainty, starting with Lund [1992] and continued by Blake and Roberts [2006]. However, the tax impacts on extraction and exploration activities are not estimated by these authors.

• 2

  The model herein and the model by Nilssen and Nystad [1986] both describe a supply process where exploration, development, and production occur in sequence. However, the production profile used by Nilssen and Nystad [1986] plateaus before declining exponentially and their exploration cost function is quadratic instead of proportional. Their model has three decision variables: exploration effort, exploration time, and the production plateau rate-reserves ratio. Neither model can be solved analytically and must therefore be solved using numerical techniques. However, the model by Nilssen and Nystad [1986] is not suitable for the present analysis because it requires global optimization numerical techniques to solve, which are not fully reliable. For the reliability problems associated with global optimizers, see, for example, Neumaier et al. [2005]. Unfortunately, having three or more decision variables precludes graphical verification of the solutions provided by global optimizers. The model proposed herein has two decision variables, allowing the objective function to be graphed, and thereby ensuring that global maxima may be found using local optimization numerical techniques.

• 3

  The exploration submodel defines the area to which the model applies. The exploration model may be applied to a play, a basin, or even to a “province”, but a basin is the chosen unit for the present work.

• 4

  This convention has been challenged by a number of authors, for example, Kemp and Kasim [2005]

• 5

  Supra note 2.

• 6

  Field size classes 15 (“Small”), 16 (“Medium”) and 17 (“Large”) in the publications were chosen for both basins. In Table 1 these field size classes are referred to as 1, 2, and 3 for small, medium, and large.

• 7

  The offshore basin with small fields at $50/bbl was run in the pretax model, but left out of the posttax analysis because its profits were minimal and the scenario would not bear much tax liability.

• 8

  The relationship between q_i and R_E may be derived as

  • 

   R is an asymptote, > 0 and < 0 for 0 < b_D < 1. If b_D > 1, R_E decreases with increasing q_i. As shown in Table 1, 0 < b_D < 1. The relationship between W and F(W) is derived from equation (1).

• 9

  This behavior of the rational explorer has been the conventional wisdom, although the idea has been challenged, for example, by Slade [1998].

Acknowledgments

This paper is drawn from the University of Dundee doctoral dissertation “Petroleum Taxes and the Distortions in Upstream Activities.” I would like to thank Philip Andrews-Speed and Xiaoyi Mu for their invaluable comments and advice. I would also like to thank the anonymous referees for their excellent recommendations.