Leasing, Learning, and Oil Field Development

Thomas J. Holmes, Boyoung Seo, and Matthew H. Shapiro

November 10, 2014

Introduction

The North Dakota oil boom, driven by high oil prices and innovations in the horizontal

drilling and hydraulic fracturing (fracking) of shale oil deposits, has, along with Texas, been

significant enough to lead to an unprecedented decline in U.S. oil imports. Despite the

rush to drill in the Bakken over the past six to seven years, companies in the region have

developed the oil fields in a strikingly methodical pattern. Generally, a single well is first

drilled on a two-square mile rectangular plot of land, called a spacing unit. Sometime later,

a second round of drilling begins on the spacing unit, and at this point multiple wells are

drilled. Figure 1 illustrates the pattern in an example oil field through a snapshot taken

each year from 2008 through 2013. The two-by-one mile spacing units are illustrated by the

red rectangles and the black lines trace out the footprints of individual horizontal wells. We

can see a pattern where first single well is drilled. Then there is additional development of

as many as six more wells. As each well costs about 8 million dollars or more to complete,

the overall investment on a single two-square mile spacing unit is on the order of a fifty

million dollars or more.

There is a standard contract term in mineral rights leases that provides a strong incentive

for firms to develop along the pattern described. Specifically, once oil starts flowing from the

first well it means the lease is held-by-production, which locks in contract terms, including

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those applicable to future wells in the spacing unit. If an oil company fails to get the first

well in before an the existing lease expires, the firm will have to negotiate a new lease and

potentially incur millions of dollars in additional costs (call bonus payments) to obtain a new

lease. This paper develops a model of oil field development that incorporates both learning

and leasing. The paper examines detailed data on the timing of well drilling in individual

spacing units. The main focus of the paper is to understand how this contract term affects

the timing of spacing unit development.

We also note that learning provides an alternative explanation. Firms might choose to

first drill one well on a spacing unit because of the opportunity to learn from this initial

well. The firm can then come back at a later time to drill other wells using the information

obtained from the initial well. For example, the drilling process yields detailed informaiton

about the geological formaiton of the spacing unit. A firm can also see how particular

fracking techniques worked, and whether they should be tweaked int he future. Covert (2014)

documents firm experimentation with different fracking inputs over time and learning about

the highest yield methods.

Since both channels impact the pattern of field development, policy interventions that

affect leasing also affect learning. That is, there is an interesting interaction between leasing

and learning. Spacing unit size is governed by state regulation. If the state makes spacing

units bigger, then more wells can fit on a given spacing unit. This accentuates the leasing

incentive to drill the first well, because the option value of drilling wells later scales up when

more land area is covered under the option. With enhanced incentives to drill, marginal

wells are completed earlier than they otherwise would. In turn, learning about marginal

plots also occurs earlier. Therefore, zoning large spacing units jump starts both drilling

and learning. In fact, regulators in North Dakota actually did set relatively large spacing

units compared to some other states. The role of North Dakota’s policy in promoting the

development of the oil fields is one of the key topics considered in this paper.

We employ two strategies to disentangle the role of leasing in accounting for the evolution

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of the industry. The first strategy exploits the fact that as of the beginning of the current

fracking boom, at some locations there were pre-existing conventional wells continuing to

produce oil and holding land by production through leases signed decades ago. Because the

old conventional wells draw from a different oil formation and a shallower depth than current

horizontal wells, the presence of these old wells does not affect the learning incentive to drill

a first horizontal well. However, the leasing incentive to drill is eliminated, because the land

is already held by the production of the old wells. We show in the data that: (1) on land

with a preexisting conventional well, the first horizontal well tends to be drilled significantly

later than otherwise, but (2) there still tends to still be a gap between the first and later

wells. Fact 1 implies that the leasing incentive matters (because without it the first well

comes later). Fact 2 implies the learning incentive also matters, because the leasing induced

delay of the first well also leads to a delay of later wells.

Our second strategy uses lease information to examine how lease expirations affect the

timing of the drilling decision. We estimate the bonus prices firms would pay if they delay

drilling and quantify these effect. The results from this work are extremely preliminary but

clear patterns motivate their significance.

In summary, this paper seeks to address three broad questions. First, what are the roles

of leasing arrangements and zoning in the timing of the first well. Second, to what extent

does the rush to drill a first well impact the rest of the development process. Finally, what,

if any, are the cost distortions of incentives that speed up the drilling of this first well. This

paper is preliminary start to answering these questions and quantifying the role of policy in

these immense development cases.

Related Literature (to be completed)

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1 Background and Discussion of Data

1.1 General Background

The current boom in North Dakota targets a shale oil formation known as the Bakken. The

land area containing the Bakken oil fields is a region in the northwest corner of the state

containing 15,600 square miles or about 10 million acres. As the region is comprised of ten

counties, we refer to it as the Ten-County Area , depicted in Figure 2.

Bakken wells are major investments on the order of seven to ten million dollars in upfront

costs to complete. Because the Bakken formation is deep, thin, and highly impermeable,

the drilling procedure features three extensive steps. The first step in is to drill vertically a

depth of two miles to reach the Bakken formation. The second step is to drill horizontally

for typically a mile to two miles. The well is finally completed by a fracking process that

stimulates oil production. Water is pumped into the well at high pressure to fracture the

shale. Millions of pounds of sand are pumped down into the well to keep fractures open

and oil flowing.

The first horizontal, fracture-stimulated, Bakken wells were completed in 2004. (The

appendix details how the data is constructed and lists sources.) As shown in Table 1, only

six wells were completed that year, but in each subsequent years the rate of development

rapidly increased until recently. In 2013, 1,968 new Bakken wells were completed, an

investment of approximately 14 billion dollars. Over the entire ten year period, 2004-2013,

7,011 Bakken wells were completed in the 10-County Area, and their footprints are mapped

in Figure 2. The average total depth of the wells (the horizontal plus vertical components) is

approximately 19,000 feet. As it is about 10,000 feet to the Bakken formation, the horizontal

portion averages 9,000 feet. More recent wells tend to be longer.

Even accounting for longer wells individual well production has also increased remarkably

over time. Early wells produced less than 10,000 barrels in the first 90 days (see Table 1).

By 2010, 90-day output of new wells increased to over 30,000 barrels. Part of this increase

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may be attributable to drilling in areas with higher potential geography. Covert (2014),

however, studies how firms learned to increase well output through changes in the fracking

process, including adding more inputs of sand and water. The second to last column of Table

1 reports total oil output of the Bakken by year. The 287.6 million barrels produced in 2013

exceeds the output of every state besides Texas. The last column shows oil production in

North Dakota other than the Bakken; averaging about 30 million barrels annually over the

period. Bakken output now dwarfs the rest of the state.

The oil industry is heavily regulated in North Dakota, and development of oil fields

follow specific rules. As part of the permitting process for a well, there is a regulatory

hearing to determine the spacing unit for the well. Ownership rights in a spacing unit are

pooled together in a compulsory fashion. For example, suppose a spacing unit is a two-mile

rectangle. Typically, such a unit is composed of two sections. Sections are one-mile square

mile units that were delineated by the Public Land Survey System in the 19th century

and partition the state into what looks like a checkerboard. Oil produced by wells in a

spacing unit is shared on a pro rata basis proportionate to land ownership. For example, an

individual owning the mineral rights of a quarter section of the spacing unit, or 1/8 of the

two combined section, is allocated 1/8 of the oil produced on any well in the spacing unit,

regardless of the specific location in the spacing unit.

Leases follow standard patterns of the oil industry and differ in acquisition between

government and private lands. Leases for government lands, both federal and state, are

obtained in a more uniform fashion, and we begin with them. The state of North Dakota

owns the mineral rights on 754,000 acres in the Ten-County Area, or 7.5 percent of the

total. An unleased tract of state-owned land becomes leased through the following steps.

First, a firm or individual nominates the tract to be included in the next oil lease auction,

which occur once a quarter, and the tract is allocated to the highest bidder in an ascending

auction. The bid is a bonus price per acre, which is an up front payment to buy the lease.

The lease specifies a fixed royalty rate of 18.75 percent of oil and gas revenues from the area

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it covers. The lease holder then has five years to begin drilling before the lease expires. If

the holder fails to hold the lease tract by production during this term, the tract is then free

to be nominated for a subsequent auction. If a well is drilled before the term completes,

however, the lease extends indefinitely while wells on the tract produce oil. The lease is said

to be held by production. In fact, currently 10,000 state-owned acres in the area are held by

production based on leases signed in 1948 and 1949. Leases on federal land have a similar

form but different parameters: the initial lease term is 10 years, and the royalty rate is 12.5

percent.

The leasing contracts for private land also have the form of (1) an up front bonus payment

per acre, (2) a fixed royalty rate, (3) a fixed initial lease term, (4) the hold-by-production

clause. There are two key differences between private and government land. First, private

land lease terms are determined by negotiation rather than auction. Second, for private

land it is possible to renegotiate extensions before the initial lease term ends.

1.2 Fact about Drilling: One Well First, More Later

Figure 1 in the introduction illustrates the pervasive pattern of drilling one well first, followed

by more at a later time. Table 2 demonstrates the same finding for the full set of data in

the Ten-County Area. For each of the 7,011 Bakken wells, we use mapping information

to determine which one-mile square sections each well cuts through horizontally. Typically

each well covers two sections. There are 15,612 sections in the area of interest. For each

section we count how many Bakken wells have arrived as of the end of 2013, summarized in

the second column. 7,266 sections have one well, 2,609 have two wells, and so forth.

The third column demonstrates a “bunching” pattern of drilling after the first well is

drilled. Each number represents the share of sections with at least n wells that also have

n+ 1 or more wells. For example, for n = 0, 47 percent get to n = 1, and have one well. Of

those with at least one well, 36 percent have at least two wells. Given there are at least two

wells, 62 percent have at least three. And these conditional shares are all 50 or 60 percent

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until sections with 7 wells. These data given a section has at least two wells it is more likely

to have many as compared to the likelihood of a section with only one well.

Next we consider the timing pattern. We calculate the median and mean time for the

next well, given that there is a next well. Conditioning on getting two wells or more, the

median duration between completion of well number 1 and well number two is 1.45 years.

Conditioning on getting three wells, the median time is .05 years. This table illustrates in

stark terms the pattern that initially one well is drilled and, if there are additional wells

drilled later, subsequent wells tend to be drilled almost simultaneously.

1.3 Facts about Leases

The final key set of facts links leases to drilling patterns. For each well drilled in the region,

we have the spacing unit information down to the geographic detail of 1/16 of a section, a

40-acre unit (This is a quarter of a quarter section, often called a quarter quarter.). The

7,011 Bakken wells we have discussed so far generally have spacing units defined at the

section level. However, vertical wells drilled in earlier periods typically have spacing units

that are smaller than a section, sometimes as small as a 1/16th. Some of these wells are still

producing, and thus holding old leases by production.

Table 3 shows the share of land held by production in each year. We calculate this value

by determining which wells produced positive amounts of oil in a given year and assign the

land in the corresponding spacing units as held by production. In 2004, 6.3 percent of the

land area was held by production, primarily by old vertical wells targeting formations other

than the Bakken. Calculating the same share as far back as 2000 would show nearly the

same number. Subsequent to 2004, the share of land held by production grew rapidly, and

by 2013 just over half of the land is held by production. The next column in Table 4 focuses

specifically on the 7011 Bakken wells and shows the share of land (calculated by 1/16th level)

with a Bakken spacing unit. Virtually all of the increase in acreage under lease since 2004

can be accounted for by Bakken wells. The last column shows the share of sections that

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contain the spacing unit of at least one Bakken well. Because there are some cases where

the spacing unit of a Bakken well only intersects part of a section, the last columns’ values

can be higher than the second to last. However, the differences are negligible. Therefore,

for most of our analysis we treat Bakken well spacing at the level of sections.

Land has not been indiscriminately leased in this land grab. In particular higher quality

land, i.e. land with higher output potential, is more likely to be held. We construct an

estimate of land quality based on the oil output of the Bakken wells already in production.

We restrict attention to wells drilled in 2009 and after because of significant technological

change over the full time period, though 90 percent of the wells are drilled after 2009 in any

case (6299 wells). We take the first 90 days of output of each well and regress it on a quartic

polynomial of longitude and latitude, and a quartic on the date the well was first drilled.

The R2 of this regression is .23. Note that in addition to differences in geology, over space,

a particular well might be drilled with more inputs, e.g. more sand, and this adds variation

that we don’t take into account here. There is also some variation in output across wells

even on the same spacing unit even after accounting for all observables. With this crude

measure, however, we can break sections into quartiles based on land quality. Figure 3A

plots the percent of land held by production conditional on quality quartile. In 2003, the

held-by-production share was less than 8 percent for all quartiles. We can see that as of

2013, the top quartile land is mostly all held by production (84%). The second quartile is

59% held, the third 56% held, and the bottom quartile is only 13 percent held.

Because state lease data is the cleanest to work with, we focus further study on this subset

of the data. Another useful feature of the state land is its relatively uniform distribution over

the Ten-County Area. The Public Land Survey System aggregates sections into six-by-six

mile units called townships, made up of 36 sections. The state owns section 16 and section

36 of most townships, which was a grant from the federal government at North Dakota’s

statehood. Surface rights have generally been sold off since then, but the state has generally

maintained ownership of the mineral rights below the surface. Table 4 reports the evolution

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of the leasing status of the 754,000 acres of state land. Note that as of 2004 6.9 percent

of acreage was held by production and increased to 52.4 percent by 2013. These figures are

very similar to the 6.3 to 50.4 percent of the entirety of the 10-County Area reported in

Table 3.

Next note the share of state land under lease in Table 4. From 2001 to 2004 30 percent

was leased. In 2004 the successful completion of the first horizontal Bakken wells precipitated

a land rush, demonstrable by the state lease information. In 2004 29 percent of the entire

state land stock was auctioned off and the share of leased land jumped to 53 percent. Over

the next couple of years most of the remaining land became leased, and the leased share has

been approximately 90 percent since 2008. Figure 3B illustrates the same pattern.

State leases have not been static since 2008, however. The last column of Table 4 reports

the share of state acreage in tracts that expired in each year. Note the big jump that

occurs in 2009, where 20.9 percent of the state acreage had lease expirations. This wave

of expiration is a consequence of the fact that in 2004 29 percent of the land was leased

and hit their 5-year expiration date in 2009. This land was all rapidly re-leased through

new auctions. There was another wave of expirations in 2011, following a big year of lease

auctions in 2006. A key take-away point here is that there is actually a substantial amount

of lease expiration. Thus one margin that we focus on, drill or let a lease expire, is empirically

interesting.

The last important fact to is the variation in bonus prices over the period. Figure 4 links

them to oil prices since 2004. Bonus prices (in red) were negligible from 2004 through 2008,

averaging less than $100 per acre, or less $128,000 dollars for a standard spacing unit of

1280 acres. Oils prices initially were also low, at only $30 a barrel in 2004, and productivity

of wells was also low as shown in Table 1. Oil prices climbed over $100 a barrel before

collapsing during the crisis, and then recovering. Notice the sharp uptick in bonus prices at

the end of 2009. Since then, bonus prices have averaged more than $1500 an acre, and some

parcels have sold for as much as $21,000 an acre. Bonus prices of this magnitude obviously

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provide a significant incentive to drill rather than risk losing a lease and incurring this cost.

2 The Theory

2.1 Description of the Model

Assume horizontal wells have a standard length ` (e.g. 2 miles long) and suppose each well

drains oil a distance $ on both sides, so it draws from a total area of awell ≡ 2× `× w. A

spacing unit is an amount of land that can exactly accommodate n wells, i.e., spacing unit

area equals aspacing ≡ n× awell. Assume the size of spacing units is set by state regulators.

Let spacing units be indexed by i.

We define a well on a spacing unit as exploratory if no previous horizontal well has been

drilled on the spacing unit before it. Define later wells on the spacing unit as development

wells. Let zet′(i, t) denote the oil output (in barrels of oil) at time t′ of an exploratory well

drilled on spacing unit i at time t′. Using discount factor β < 0, the discounted physical

output of the oil production over the life of the well is given by

qeit ≡∞∑t=t′

β(t′−t)zet′(i, t).

Analogously, for development wells define zdt′(i, t) as per-period output, and qdit as the dis-

counted present value of output. Assume the following

qeit = γtφi,

qdit = λγtφi,

for γ ≥ 1 and λ ≥ 1. The parameter φi will be referred to as the base-level quality of a

well in spacing i. It is the (discounted) quantity of oil produced by an exploratory well

drilled at time t = 0. The parameter γ determines the extent of technological progress in

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well productivity from period to period. Assume βγ < 1, which implies that discounting

more than offsets productivity growth. The parameter λ determines how learning from an

exploratory well affects productivity of development wells drilled later. The parameter λ

satisfies λ > 1 if drilling the exploratory well yields information about the geology of the

spacing unit that might be useful for later wells, or if it the experience makes it possible to

fine-tune the fracking technique employed.

Assume the exact underlying quality φi of spacing i is unknown before an exploratory

well is drilled. There is a public signal φsi of the quality. Assume the actual quality φi, given

the signal φsi , is distributed according to F (φi;φsi ), with density f(φi;φ

si ) with support [φ,φ̄].

Once an exploratory well is drilled on spacing unit i, the actual quality φi of the spacing

unit is immediately revealed.

The cost to drill a well at time t on spacing unit i is given by

cit = ω + εit.

The well cost shock εit captures idiosyncratic reasons why it might be costly or cheap to

drill a well at spacing i at time t. Assume ε has a continuous density g(ε) on support [0,ε̄].

Assume the cost shock is i.i.d. For example, costs depend on availability of a drilling rig. If

a particular rig has just completed a job at a nearby spacing unit at time t, we expect to

have a low value of εit.

Let pt be the price of oil in time t. Oil prices follow a stationary Markov process.

Formally, at time t, the distribution of pt+1 is given by H(pt+1|pt). Assume that once a well

is drilled, the entire present value of the oil is sold at the current price pt. There is a state

tax on oil revenue equal to ψ. In addition, we assume a fixed royalty rate of ρ. Hence, an

exploratory well drilled at time t on spacing i yields a discounted profit

πeit = pt (1− ψ) (1− ρ) qeit − cit

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and the formula for the profit πdit of a development well drilled at t is analogous.

The last thing to explain is leasing. Let t = 0 be the initial period in the model. Assume

that prior to t = 0, no horizontal wells have ever been drilled. In particular, all the discussion

about drilling and oil production above refers to a new formation that has not previously

been targeted. However, some spacing units may have pre-existing wells drilled before t = 0

at a shallower level. For such spacing units, mineral rights have already been leased. For

leased land, the description of the environment is complete, as the firm decides when to drill,

taking as fixed it has to pay taxes of τ and royalties of ρ.

For other spacing units, the land is unleased at t = 0, and there is a process by which

land becomes leased, as we now explain. For unleased land, assume that firms compete

to obtain a lease on a spacing unit from the original mineral rights owners. For simplicity

assume that competing firms are ex ante identical. Firms compete in a Bertrand fashion in

their choice of offer of a bonus payment per acre of land. This is a lump sum payment to

mineral rights owners called a bonus payment. Let bit denote the bonus payment per acre

on spacing i if paid at time t. Both the royalty rate ρ and the lease term m̄ is taken as

fixed. Finally, assume the winner must also incur a leasing transaction cost of τ per acre to

finalize the deal. This would include title searches, for example. If a well is drilled before

expiration, i.e., within m̄ periods, the lease on the spacing unit becomes held by production

and extends indefinitely.

In the case that the lease expires without a well having been drilled, we allow for two

possibilities. In both cases we model the incumbent leaseholder as having an advantage

of competing firms, and the difference is the degree. In case one, there is a renewal of

Bertrand competition to lease the spacing unit. If a new firm wins the auction, it must

repay the transaction cost τ per acre, while if the incumbent wins, it need not pay this cost

a second time. In case two, the incumbent has an even stronger advantage, as it is able to

obtain a lease extension at negligible cost, for simplicity taken to be zero. We refer to this

as the incumbent monopoly case. Assume that with probability ξ, at lease expiration the

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incumbent monopoly case is realized, while with probability 1− ξ, the Bertrand competition

outcome is obtained. Thus these two parameters, τ and ξ, govern the strength of the

incumbent leaseholder advantage.

2.2 Equilibrium in the Model

Let xit denote the cumulative number of horizontal wells drilled previous to time t in spacing

i. In this subsection we focus on equilibrium in a particular spacing unit i and to ease the

notation burden we leave i implicit. We drop the t subscript as well and treat x as the

number of wells drilled prior to the current period. Let x′ denote the well count at the

beginning of next period. If x = n, then spacing unit is completely full of wells. If x ≥ 1,

an exploratory well has been drilled, so the actual spacing quality φ is known. If instead

x = 0, no wells have been drilled and knowledge of spacing quality is given by the signal

φs. Other state variables observed at the beginning of period t are the price p and the cost

shock ε to drill a well in the current period.

The final state variable to describe is the leasing status ` of the spacing unit at the

beginning of the current period. We let ` = ∅ indicate the land is unleased. If the spacing

unit is leased, but currently has no producing well, let ` = m ≤ m̄ indicate the number of

periods until lease expiration. If ` = 0, a preexisting lease has just expired as of the current

period. Finally, ` = HBP indicates the land is leased and held by production. Note that

if x ≥ 1, then ` = HBP necessarily holds. If x = 0, there are no previous horizontal wells,

but it still may be that ` = HBP if prior conventional wells are holding by production a

lease on the spacing unit.

Consider first the case where x ≥ 1, so an exploratory well has been drilled. The lease

is held by production, and any uncertainty about spacing unit quality φ is now resolved.

Define y as the choice of how many development wells to drill in the current period. The

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firm’s value function is the following:

v(x, φ, p, ε, t) = maxy≤(n−x)

y[p (1− ψ) (1− ρ)λγtφ− ω − ε

]+ βEp′,ε′ [v(x+ y, φ, p′, ε′, t+ 1)] .

(1)

Note the value depends upon time t through the productivity growth γ term. The first

term in the objective function is the profit from drilling y wells in the current period. The

second term is the expected profit of going into the next period having drilled x+ y wells in

total.

Next consider the case where x = 0, and the land is leased with m ≥ 1 periods to

expiration. The firm owning the lease makes its drilling decision based on the signal φs of

well quality, as well as the current oil price p and the shock ε to drilling cost. We can write

the expected value of the firm’s problem as

u(m,φs, p, ε, t) = max{unot drill(m,φs, p, t), udrill(φs, p, ε, t)

},

where

unot drill(m,φs, p, t) = βEp′,ε′u(m− 1, φs, p′, ε′, t)

and

udrill(φs, p, ε, t) = maxy≥1

∫ φ̄

φ

[y[p (1− ψ) (1− ρ) γtφ− ω − ε

]+ βEp′,ε′v(x, φ, p′, ε′, t)

]dF (φ|φs).

(2)

Next consider the case where there is an incumbent leaseholder and the lease has just

expired, i.e., m = 0. Recall there are two possibilities. With probability ξ, the incumbent

will be able to renew the lease at zero cost, the incumbent monopoly outcome is the result.

With probability 1 − ξ the lease goes out to auction, but even here the incumbent has an

advantage as a new leaseholder must pay a transaction cost of τ per acre that the incumbent

has already incurred. The total cost advantage τaspacing of the incumbent will be the

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resulting profit from Bertrand competition, unless the value of owning a new lease is less

than this cost advantage, in which case the return is the value of the new lease. Formally,

u(0, φs, p, ε, t) = ξu(m̄, φs, p, ε, t) + (1− ξ) min {τaspacing, u(m̄, φs, p, ε, t)} .

If the spacing unit goes out to a Bertrand auction, the bonus payment per acre must

equal

b(p, φs, t) =

{Eεu(m̄, φs, p, ε, t)

aspacing− τ, 0

}. (3)

We are assuming here that bonus payments cannot be negative. If there is an incumbent

leaseholder on an expiring lease, it will always be willing to obtain a lease at a zero bonus.

If the spacing unit is unleased and if

Eεu(m̄, φs, p, ε, t)

aspacing< τ ,

it will remain unleased, because even at a zero bonus payment it is not economical to do the

paperwork to obtain the lease.

The last case to consider is that no horizontal wells have yet been drilled, x = 0, but

the spacing unit is nevertheless held by production because of conventional wells in a prior

period. Let the value to the leaseholder at the beginning of the period be equal to

uHBP (φs, p, ε, t) = max{βEp′,ε′u

HBP (φs, p′, ε′, t), udrill(φs, p, ε, t)}

.

This is the maximum of two returns. The first is to wait, and go into period t+ 1 and take

new draws of p′ and ε′ (and retain HBP status). The second is to drill and the return is the

maximum over all drilling choices yt ≥ 1.

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2.3 Analysis of the Model

Our characterization of the solution begins with the following lemma.

Lemma 1. (i) Suppose in the current period, no previous well has been drilled, x = 0, so

only the signal φs about land quality is observed. For any value of (φs, p, ε, t), the optimal

optimal is either drill none, y = 0, drill one, y = 1, or drill all, y = n.

(ii). Suppose at least one well has been previously drilled, x ≥ 1 so that the actual well

quality φ is revealed. For any value of (φ, p, ε) and time t, the optimal number of wells to

drill in the current period is either drill none, y = 0, or drill all remaining wells, y = n− x.

Proof. See appendix.

The result is an immediate consequence of the linearity of the objective function where

the returns to drilling the second well at the spacing unit are the same as the returns to

drilling the j-th well, for j ≥ 3. Note from inspection of (2) and (1) it is immediate that the

drilling decisions take the form of a cutoff rules on the current well cost shock ε such that

drilling at a particular level either takes place or does not, depending upon whether the cost

shock realization is below or about the cutoff.

Specifically, using Lemma 1 we can focus on the following set of cutoffs. Starting with

the case where no well has been drilled, x = 0, let ε̂10(p, φs, t, `) cutoff for drilling one well;

i.e. if ε < ε̂10(p, φs, t, `), at least one well is drilled. Note we allow the cutoff to depend

upon the leasing state ` in the current period. Analogously let ε̂n0 (p, φs, t, `) be the cutoff

for drilling all n wells in the current period given none have previously been drilled. Next

suppose at least one well has been drilled. Define ε̂n1 (p, φ, t) to be the cutoff for drilling

all the remaining wells. Note we have replace φ with φs because spacing quality has been

revealed by drilling the first well in a prior period. Also, for simplicity, we drop the leasing

state ` because drilling one well means the spacing unit is necessarily held by production.

Proposition 1. Assume (a) either φ< φ̄ or λ > 1 or both; (b) ξ < 1; and (c) τ = 0.

Then

(i) ε̂10(p, φs, t,m) strictly decreases in the periods m to expiration of a lease not held by

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production.

(ii) ε̂10(p, φs, t, m̄) > ε̂1

0(p, φs, t, HBP )

(iii) ε̂n0 (p, φs, t, `) is the same for all leasing states and can be written ε̂n0 (p, φs, t), and it

satisfies ε̂10(p, φs, t, HBP ) > ε̂n0 (p, φs, t).

Proof. See appendix.

Condition (a) assumes some kind of learning, with φ< φ̄ implying uncertainty about

well quality and λ > 1 implying learning by doing. Under either case ε̂10(p, φs, t, HBP ) >

ε̂n0 (p, φs, t), that is, for cost draws in the interval bounded by these two cutoffs, if land were

held by production it would be optimal to drill one well and wait until later to drill additional

wells.

Conditions (b) and (c) put leasing into play. Condition (b) sets ξ < 1 because otherwise

in the limiting case of ξ = 1, the incumbent can renew for free and the analysis is the

same as if the spacing unit was held by production. The condition τ = 0 shuts down

incumbent advantage in Bertrand competition upon renewal. We assume τ = 0 here only

for tractability, as otherwise we have more cases to work through. Below we consider a

simpler version of the setup and there we will allow τ to be positive.

Following proposition 1, the theory implies the pattern of oil field development illustrated

in Figure 1, where one well is initially drilled, and the oil company comes back later to do

the rest. The firm drills a single well when

ε̂n0 (p, φs, t) < ε < ε̂10(p, φs, t, `)

Note, it is possible for all the wells to be drilled at one, as this happens if ε < ε̂n0 (p, φs, t).

However, a low level such as this may be relatively unlikely.

In Proposition 1, we take the full model where we incorporate both learning and leasing

into the drilling decision. Proposition 2 reports the results of limiting cases:

Proposition 2. (i) Pure Learning Case: Assume (a) either φ< φ̄ or λ > 1; and (b) ξ = 1.

17

Then ε̂10(p, φs, t,m) = ε̂1

0(p, φs, t, HBP ) for all lease expirations m and ε̂10(p, φs, t, HBP ) >

ε̂n0 (p, φs, t).

(ii) Pure Leasing Case: Assume (a) φ= φ̄ or λ = 1, and (b) ξ < 1, and (c) τ = 0. Then

ε̂10(p, φs, t, HBP ) = ε̂n0 (p, φs, t), while ε̂1

0(p, φs, t,m) > ε̂n0 (p, φs, t) for any lease expiration m.

In the pure learning case, firms can renew leases at minimal cost, so lease expirations

are irrelevant. If land is already held by production from conventional wells, it will be no

less likely to get a well than leased land not held by production. In the pure leasing case,

learning is irrelevant Land held by production with old conventional wells will not get an

exploratory well. Rather it will go into the development phase whenever the first horizontal

well is drilled.

Our third result connects the effect of leasing on drilling to bonus price levels for lease

renewal. For this result, it is convenient to simplify the model to eliminate learning, i.e.

γ = 1 and φ= φ̄. We also shut down productivity growth, γ = 1, and assume price p is a

constant over time, to make the problem stationary. The discounted profit of a well, net of

royalties and taxes and the cost of the well is given by

α ≡ pq (1− ψ) (1− ρ)− ω,

which includes everything except for the random cost shock ε which must be subtracted off

from α. Here we allow the incumbent advantage to arise through the per acre transactions

cost τ that the incumbent need not pay again, but a new leaseholder has to pay. With the

simplifications we have made, the value of land that is held by production has has a spot for

single well equals

uHBP (ε) = max{α− ε, βEε′uHBP (ε′)

}.

The firm can take α− ε now by drilling in the current period or wait until next period and

18

hope for a better draw of ε′. The ε cutoff for drilling land held by production is then

ε̂HBP = α− βEuHBP ;

the cutoff equals the payout from drilling today, minus the opportunity cost of waiting until

tomorrow. To examine leased land not held by production, assume for simplicity that lease

terms are a period m̄ = 1. Then when the spacing unit holds n wells, the cutoff for drilling

a single equal equals

ε̂1n = α + β (n− 1)EuHBP − βτnawell.

This cutoff equals the payout of the one well today, plus the value of having the remaining

n− 1 well slots held by production going into next period, less the opportunity cost of not

drilling. This opportunity cost is that by not drilling the lease will expire, and the firm goes

into Bertrand competition with a cost advantage of τ per acre of the spacing unit. The

next result provides a characterization of the equilibrium and how it depends upon α, which

is a summary statistic of well profitability. In the result, there is a critical value of α̇ defined

by the α such that

EuHBP (α̇) ≡ τawell,

i.e. the expected profit of a well site held by production exactly equals the transactions cost

to get it. Our result is

Proposition 3. At the critical level α = α̇,

ε̂HBP = ε̂1n, for any n ≥ 1.

This is, the drilling decision for held by production land is identical to leased land, regardless

of the size of the spacing unit. For α < α̇, unleased land will remain unleased, and bonus

19

prices are zero. For α ≥ α̇,

dε̂HBP

dα<dε̂1

1

dα<dε̂1

2

dα< ... <

dε̂1n

dα,

that is, higher spacing quality α has a bigger effect on drilling on land not held by production,

and the effect is bigger the bigger the spacing unit. The equilibrium bonus price bn(α) = 0

at α = α̇, for all n, and is strictly increasing in α and n, for α > α̇.

Proof. See appendix.

The proposition is illustrated in Figure 5, for a numerical example in which the ε is

uniform on [0, 1]. We assume the transaction cost τ is set so that α̇ = .2. For α < α̇, the

land quality is too poor for anyone to lease it because of the transactions cost barriers. But

if this cost has already been incurred, the land might be drilled. Note at the critical point,

if the land is leased but not held by production, the drilling probability is no different than

when it is held by production. The intuition is very simple here. The land quality is not

high and bonus prices are close to zero. A firm with a lease will not pay much attention to

whether the lease is about to expire, because the firm can get it back cheaply. Contrast this

with what happens when land quality or oil prices are high. Now the probabilities of drilling

for land with leases not held by production go up relative to the land held by production

(and it goes up more the larger the number of wells in the spacing unit.) Note also the

bonus price is also high (and is higher, on a per acre basis, the more wells in the spacing

unit).

The last result examines the effect of a policy changing the spacing unit size. Suppose

we begin with the model of a single spacing unit as originally described. In changing the

spacing unit size, we want to preserve the underlying technological and information structure.

Hence, assume the land characteristics are the same as before, as applying to a spacing unit

with n wells. This is now divided into two spacing units with n2

slots for wells. For

expositional purposes, we call one the “east unit,” and the other the “west unit.” Learning

20

works as before, so if either spacing unit is drilled, then the underlying quality of wells in

both of the east and west units is revealed. Also, the productivity bump λ for subsequent

wells applies to both of the adjacent spacing units, if an exploratory well on either is drilled.

Because of the externality connecting the two adjacent units, it is immediate that it will

be worth more for a buyer to initially acquire the two units together. There are two new

considerations to work out in studying the firm’s problem. First, there is the issue a firm

might drill one well in the east unit, which will hold it by production, but not get around

to drilling a well in the west unit before the lease expires. In this case, we go into the lease

renewal process with the uncertainty realized (price depends on actual quality φ rather than

the signal of quality φs), and the wells on the west unit have have the productivity bump

λ ≥ 1 from the knowledge gained from drilling the well in the east unit. Second, the are

more possible choices for drilling that need to be considered. In particular, a firm initially

acquiring the leases on both the east and west units will have the following cutoff rules:

ε̂1,00,0(p, φs, t, `): cutoff to a well on one spacing unit (say the east unit), given no wells

drilled on either

ε̂1,10,0(p, φs, t, `): cut-off to drill one well on both units.

ε̂n22,n22

0,0 (p, φs, t, `): cut-off to drill out both units.

We can also calculate a cutoff rule for ε̂0,11,0(p, φ, t, `) for drilling the first well on the west

unit, given there is one well on the east. (Again, note uncertainty has been realized.)

Our result imposes the same assumptions as in Proposition 1.

Proposition 4. Assume (a) either φ< φ̄ or λ > 1 or both; (b) ξ < 1; and (c) τ = 0.

Assume γ = 1 (so no systematic productivity growth). Then

(i) ε̂1,00,0(p, φs, t,m) < ε̂1

0(p, φs, t,m), that is, the expected time to drill the one well on

either the east or west sides is strictly higher when the spacing is split in two.

(ii) Suppose we have learning by doing only, λ > 1 and φ= φ̄. Suppose n2≥ 2. The

expected time to completion where all the wells are drilled out is strictly higher when the

spacing is split into two.

21

Proof. See appendix.

There are a several forces at work in Proposition 4, and all go in the same direction.

To see how the result works, consider first the case with no learning. Then for the special

case considered in Proposition 3, we already have from Proposition 3 the result that the

first well is drilled sooner with a larger spacing unit covering more wells. Now consider

what happens when we include learning. Now in the decision to drill a single well on one

spacing unit, there is an externality, which was internalized before because drilling just one

well brought both the east and west sides into HBP status. Now if the firm drills east, and

west expires before it gets drilled, the benefits spill over to the competing firms in ensuing

Bertrand competition. This externality is the second reason that drilling of the first well is

later.

Finally, the entire spacing unit is more likely to be drilled out if an exploratory well

has been drilled in the past. So the sooner we get an exploratory well, the sooner we get

development wells.

Note we impose γ = 1 in the proposition for technical convenience in the proof. This

allows us to not have to keep track of time in the value function. We conjecture that similar

results would hold if γ > 1.

3 Evidence on the Role of Leasing: Matched Pairs

We are interested in understanding how lease expirations affect the incentive to drill. We

begin with a direct approach. Recall that in 2004, 6.3 percent of the 10-County Area

acreage was already held-by production by earlier leases, some ongoing since 1948. A key

point is that these earlier wells target different formations than the Bakken, and are unrelated

geologically. In particular, suppose we compare two sections, such that as of 2003, one is held

by production by continuing production of old wells, and the other section has no currently

producing well. In terms of drilling for the Bakken, the land will tend to be very similar.

22

Proximity matters here in two ways. First, geologically they will be similar. Second, there

are scale economies in moving rigs around and oil companies drill nearby wells at the same

time. So by taking pairs of adjacent sections, we are holding fixed the potential for scale

economies. In terms of leasing, of course, they are very different. On the one section that

is not held by production, there is an incentive to drill to obtain that status. On the other

there is no such incentive because hold by production status is already obtained.

We identified 368 sections in the Ten-County Area that for which the acreage of the

entire section was held by production in 2003 that were directly adjacent, in sharing a side,

or meeting diagonally in a corner with another well in which zero percent of land was held by

production in 2003. A given hold-by-production section may have more than one neighbor

and we identified 1228 matched pairs. The matched pairs are illustrated in Figure [XXX].

In Table 5 we report the share of sections that have at least one Bakken well by year,

comparing sections initially held by production, with their matched pair section not initially

held by production. There is a clear pattern that the neighboring section not held by

production is substantially more likely to get a well. In particular, beginning with 2009,

the differences are large. For example, by 2011, 25.2 percent of sections not initially held

by production are drilled, but only 14.3 percent of sections initially held by production are

drilled. The t-statistic for equality of these means is 6.9, so the hypothesis of equality can

be rejected with a high degree of confidence.

The theory highlights how the effect of HBP interacts with land quality. In particular,

as illustrated in Figure 5, the difference in the probability of drilling between HBP status

and non-HBP increases in land quality.

We use the measure of quality described in section 1.3 to break up the sample of matched

pairs. For each matched pair we take the difference in outcome between the HBP and non-

HBP side, where difHBPnonHBP,t ∈ {−1, 0, 1}. It equals −1 if the non-HBP has a well while the

HBP side does not. It equals 1 in the reverse case. It equals 0 if the outcome is the same

on both sides. Table 1 reports the mean value. The mean of this variable is the difference

23

between the two columns of Table 5 and is reported in the first column of Table 6. Again,

there is a significant difference in these probabilities. The next part of Table 6 conditions

on the land quality for the matched pairs. We first split the sample into below and above

the median. We can see that the difference between the HBP and non-HBP case tends

to be greater with higher land quality, consistent with the prediction of Figure 4. Last,

regress difHBPnonHBP,t on land quality for each year. The standard deviation of the quality

measure (log of 90-day oil) equals .49. So one standard deviation increase in land quality is

associated with an increase in the difference in well probability between HBP and non-HBP

of 8 percentage points.

Next we examine the timing of the second well on this subset of sections. We redo

Table 2, conditioning on sections where the first well has a spacing unit that is already held

by production as of 2003. There are 67 such sections. Here we are requiring that the entire

spacing unit be held by production. If we require instead that at least 75 percent is already

held by production, there are 112 cases. Given that a second well as added, the median

time is just about 3 years, demonstrating the time gap between the first and later wells even

without the incentive to drill to hold by production.

4 Costs and the Decision of When to Drill

The previous results show that leasing affects drilling incentives. In this section we explore

how the timing decisions of when to drill are related to variations in costs over time. When

a lease expires, a bonus payment must be paid to renew it. We can infer from the decision

to let a lease expire that a firm obtains some benefit from doing this.

To study this decision we need to first need to estimate what bonus payments will be to

renew a lease, and we discuss how we do this in the first subsection. The second step is to

study the choice behavior.

Note in this preliminary version, we only examine expirations of state leases. Because

24

the firm with the drilling decition will be paying attention to expiration dates of all its leases,

not just the state leases, this is a simplification. In many cases, however, state leases make

up at least half of a spacing unit given their distribution through the Public land Survey

System. In the next version of the paper, we will incorporate private leases.

4.1 Bonus Prices

Bonus prices depend not only on land quality, but also upon the expectation of when the

land will be drilled. In our decision problem we focus on the case of land that is far along in

development, where the decision is whether to drill now or in the near future. In particular

this analysis focuses on land that has already been permitted for a well.

We start with a sample of 2165 state leases that are held by production, but then narrow

down to a subsample of 142 leases with the following characteristics: (1) the permit of the

well was issued before the date of the auction. (2) the well was drilled in 2009 or after; (3)

the well is completed no later than one year after the auction; and (4) the well is spud no

earlier than one year before the auction (note there are cases where the state allows drilling

before the land is leased).

For our sample we regress log bonus price on (1) spot oil price (West Texas crude in-

termediate) as of the day before the auction, (2) our land quality measure, (3) the first 90

days of actual output of the first well on the lease, (4) the count of wells drilled on other

leases within a five mile radius of the land being leased, (5) elapsed time between January

1, 2009 and the date of the auction. Note we include the actual output of the first well as a

proxy for additional information that market particpants may have about the land quality.

The count of proximal wells ideally proxies as the method by which firms might learn more

about the quality of their own spacing unit by nearby production, but it may also pick up

an area that is focal point for development beyond explanations in our theory.

The results of this regression are reported in Table 8. The first specification uses only

our fitted values of 90-day oil production based on projecting on a quartic in longitude and

25

latitude. The coefficient equals 1.25. A coefficient above one is expected because the fixed

cost of the well means a doubling of oil output more than doubles profitability. Analogously,

the coefficient on the oil price is also significantly above one. The second specification also

includes actual 90-day production of the well drilled on the section. More weight is placed

on the expected output rather than the actual output. The sum of the two coefficients

remains above one. Finally, we add in log of counts of neighboring wells, which raises the

R2 to .44. The sum of the coefficients on the three quality measures is 1.22.

We used these estimates to construct predicted values of bonus prices if hypothetically

land was leased at auction on the day a well is first spud (the first day of drilling). A

summary of these results is in Table 9. Note we calculate this on all land, not just land that

is actually state land. We first calculate this for the first well in the spacing unit (the HBP

well). We also calculate this fitted value for development wells. This statistic is a prediction

of what the bonus would be on this land at this time, if the the particular development

well were actually the hold by production well. Note that that the fitted bonus prices for

development wells are significantly higher than for exploratory wells. This result follows

because exploratory wells tend to be drilled on higher quality land than exploratory wells

being drilled at the same time.

4.2 The Timing of Drilling

We narrow attention to the choice of whether to drill in the current period, t = 0, or the

next period t = 1, when a porition of the lease is set to expire. In the theoretical model,

we assumed all the leases in a given spacing unit have synchronized terms. Now we relax

that assumption and allow for the possibility that in period t = 1, aexp1 acres of lease will

expire but that this is only part of the land under lease. Let bt be the bonus price per acre.

Additionally, we assume that assume this is part of the process, and that at t = 0 the well

is permitted.

26

Suppose the cost of drilling is

ct = c+ εt

in period t. For simplicity, assume oil prices are invariant between the periods, the net

revenue is r in both periods. Assume that the firm sees both ε0 and ε1 when it makes

its drilling decision at t = 0. Finally, assume for simplicity that if the firm waits, it is

committing to drill in period 1. We are focusing on short term incentives to drill.

Let r be the value of a well when drilled in period 0 or 1. Ignoring discounting over this

short period of time, the firm waits if and only if

r − c− b1aexp1 − ε1 ≥ r − c− ε0,

which is optimal if

ε0 − ε1 ≥ b1aexp1 . (4)

The left-hand side is the difference in drilling costs from waiting. The right hand side is the

bonus payment penalty of waiting. If we parameterize the distribution of the ε0 − ε1, we

can use observations on the choice of when to let leases expire to estimate the distribution.

We have experimented by estimating this distribution with data on state lease expirations.

We condition on all state leases that have been drilled and are held production. We examine

those leases drilled in the first year and treat these as the choice of “wait,” as virtually all

lease drilled in the first year follow a previous lease that expired. These are treated as

satisfying condition (4), so waiting is optimal. We examine leases drilled in the fifth year

of the lease as “not wait,” so (4) is not satisfied.

For the empirical exercise we focus on wells drilled 2010 when bonus prices were significant

enough to likely enter into calculus of whether to let a lease expire. Addiitionally, we assume

that εt are type 1 extreme value so that the difference follows a logit model. The parameter

to be estimated is the variance of εt , as well as a constant term. The estimates are in Table

10. The estimates in the first two rows are derived from logit regression of waiting decision on

27

constant and bonus payment penalty of waiting. Given the estimates, the location and scale

of logit distribution for difference in cost shock are derived. The bonus payment penalty of

waiting is predicted from Table 8 and measured in $1, 000. The estimated standard deviation

of εt is about $1.5 million dollars.

These tentative results yield an estimate of the variance of εt that is extremely high.

Given the variation in ε0 and ε1, if the firm were exogenously not permitted to wait, expected

drilling costs would be $1.4 million dollars higher than if it could optimally decide whether

to wait or not. These preliminary results imply costs differences that are implausibly high.

Table 11 describes simulated extra costs when there is no option of waiting, E[ε0 − ε1 −

b1aexp1 | ε0 − ε1 − b1a

exp1 ≥ 0]. That is the expectation of the extra cost incurred by forcing

a firm to drill early conditional on waiting (and letting the lease expire) actually being the

optimal choice.

28

Figure 1: Evolution of wells (black) in a location over four time periods. Spacing unitsdesignated by red outlines.

29

Map of Bakken Wells(7011 Wells Completed 2004-2013)

Figure 2: Bakken Wells (black) in the Ten-County Area

30

Table 1 Summary Statistics of Bakken Wells 2004-2013

Time Period New Wells

Completed Depth New

Wells (Horz. + Vert.) (Mean in 1,000

feet)

First 90 Days of Production

(Mean in 1,000 barrels)

Oil Production (million barrels)

Bakken Wells

Rest of North Dakota

2004-2013 7,011 19.3 33.3 805.9 305.8

By Year 2004 6 15.8 7.9 0.1 30.7 2005 32 15.4 9.2 0.5 34.8 2006 73 16.7 11.9 1.8 37.8 2007 166 17.4 19.8 7.0 37.8 2008 435 17.7 29.4 26.8 35.5 2009 477 17.9 28.4 49.4 30.0 2010 778 18.6 34.3 85.6 27.0 2011 1,264 19.6 33.9 128.4 24.0 2012 1,811 19.9 33.7 218.8 23.5 2013 1,969 20.1 36.6 287.6 24.6

Table 2 n (Number of Wells Completed)

Count of Sections with n or More Wells

Share Getting at Least One More

Well

Time to Next Well (years) Given Get One

Median Mean 0 15,612 0.47

1 7,266 0.36 1.45 1.72 2 2,609 0.62 0.05 0.56 3 1,605 0.51 0.03 0.28 4 825 0.55 0.03 0.26 5 453 0.61 0.02 0.12 6 277 0.52 0.02 0.11 7 145 0.30 0.01 0.12 8 44 0.39 0.01 0.02 9 17 0.71 0.01 0.01

10 12 0.83 0.02 0.02 11 10 0.80 0.00 0.00 12 8 0.50 0.00 0.00 13 4 1.00 0.01 0.01 14 4 0.00

Table 3

Year Share of Land Held by

Production

Share of Land With Bakken Spacing

Unit

Share of Sections With Bakken Spacing Unit

2004 6.3 0.0 0.1 2005 6.8 0.3 0.4 2006 7.9 1.1 1.1 2007 9.7 3.1 3.2 2008 13.5 7.1 7.2 2009 17.5 11.4 11.5 2010 23.5 17.7 17.9 2011 33.6 28.3 28.4 2012 45.7 41.1 41.2 2013 50.4 46.5 46.6

   

Table 4 Evolution of Lease Status of State Acreage in Ten-County Area

Share of Land

Year

Share Held by

Production

Share under Lease

Share New

Lease

Share Expired Lease

2001 5.4 29.4 8.4 2002 5.5 31.6 3.5 6.7

2003 5.6 28.9 6.7 3.3 2004 5.9 53.5 29.0 1.5 2005 6.5 64.8 14.6 5.8 2006 8.2 82.7 30.8 4.6 2007 10.4 83.3 8.6 2.0 2008 15.2 86.3 13.8 3.4 2009 20.9 89.1 18.3 20.9 2010 26.6 92.4 21.9 7.5 2011 36.2 93.5 11.6 18.7 2012 48.0 86.7 14.1 2.4 2013 52.4 90.9 13.8 4.0

     

 Table 5

Year Share of Sections with a Bakken Well

HBP Not HBP 2005 0.007 0.008 2006 0.008 0.017 2007 0.024 0.030 2008 0.045 0.067 2009 0.065 0.103 2010 0.091 0.155 2011 0.143 0.252 2012 0.219 0.333 2013 0.275 0.382

     

Table 6 Differenced Probabilities HBP less non-HBP

Difference in Probability Bakken Well HBP less non-HBP

Difference in Outcome Regressed on Fitted

Section Quality Slope Coefficient

(std. err.)

All Pairs Section Quality

Year Below Median

Above Median

2009 -0.037 -0.036 -0.039 -0.009 (0.018)

2010 -0.064 -0.039 -0.088 -0.057 (0.018)

2011 -0.110 -0.088 -0.132 -0.096 (0.025)

2012 -0.114 -0.101 -0.127 -0.069 (0.027)

2013 -0.107 -0.086 -0.127 -0.083 (.025)

     

Table 7 Sections Where First Well’s Spacing Unit Was Held by Production in 2003

n (Number of Wells Completed)

Count of Sections with n or More Wells

Share Getting at Least One More

Well

Time to Next Well (years) Given Get One

Median Mean 1 67 0.48 2.92 3.16 2 32 0.38 0.01 0.63 3 12 0.42 0.01 0.39 4 5 0.20 0.08 0.08 5 1 1.00 0.06 0.06 6 1 1.00 0.12 0.12 7 1 0.00

 Table 8

Estimates of Bonus Price Function for State Land Conditional on Land Already Permitted

Variables Specification 1 Specification 2 Specification 3 Intercept -1.99

(3.05) -3.41 (3.02)

-3.11 (2.91)

Time .88 (.36)

.71 (.36)

.83 (.34)

Time2 -.16 (.06)

-.14 (.06)

-.17 (.06)

Log Day Before Oil Price 1.25 (.75)

1.58 (.74)

1.50 (.71)

Log Predicted 90-day oil 1.25 (.22)

.78 (.26)

.60 (.27)

Log Actual 90-day oil x .42 (.15)

.47 (.15)

Log Count of neighboring Wells

x x .15 (.08)

R2 .35 .38 .44 Number of Observations 141 141 141

                     

Table 9 Predicted Values of Bonus Prices

Conditional on Land Being Auctioned on Date a Well is Spudded ($1,000 per acre) Year Median 90th Percentile

HBP Well Development

Well HBP Well Development

Well 2009 540 1,565 1,775 3,150 2010 1,988 3,162 3,473 4,656 2011 2,868 4,584 5,172 7,112 2012 2,294 3,805 4,300 5,791 2013 1,488 2,881 2,452 4,126

 Table 10

Estimated Variance of Cost Shock Estimate Constant 0.5420 (0.1458) Penalty of Waiting -0.00084 (0.000257)

Loc of Diff Cost Shock -645.24 Scale of Diff Cost Shock 1,190.48 Std of Cost Shock 1,526.85 N Wait 255 Drill 215

Bonus payment penalty of waiting is predicted from Table 8 and measured in $1,000.

Table 11 Simulated Cost when Option of Waiting is Not Permitted

Spud Year Count Mean Median Std 2010 303 1,419.35 1,427.96 61.91 2011 421 1,387.07 1,411.26 81.52 2012 356 1,394.56 1,418.08 86.80 2013 113 1,432.52 1,450.58 53.32 Total 1193 1,401.81 1,419.55 77.99

Given estimates of location and scale of logit distribution for difference in cost shock in Table 10, the difference in cost shocks are simulated with 1,000 draws. Costs are measured in $1,000.

   

 Figure 3A

Share of Land Held By Production By Year and Land Quality Quartile

     

Figure 3B Plot of Lease Status Shares for State Land by Year

   

     

   

0  

0.1  

0.2  

0.3  

0.4  

0.5  

0.6  

0.7  

0.8  

0.9  

2003   2005   2007   2009   2011   2013  

Quar1le  1  

Quar1le  2  

Quar1le  3  

Quar1le  4  

0  10  20  30  40  50  60  70  80  90  100  

2001   2006   2011   2016  

Share  Held  by  Produc1on  

Share  Leased  

Figure 4: Oil and Bonus prices  

     

0  

20  

40  

60  

80  

100  

120  

140  

0  

500  

1000  

1500  

2000  

2500  

3000  

3500  

4000  

2/1/2004   10/28/2006   7/24/2009   4/19/2012  Oil  Price  in  Dollars  per  Barrel  

Bonu

s  Pric

e  in  Dollars  Per  Acre  

Bonus  per  Acre  (mean)  

Oil  Price    

Figure 5

Probability of Drilling by Land Quality and Lease Status                                    

 Bonus Price by Land Quality

Figure 6: “Matched Pair” Sections. Pink sections are held by production before 2003.

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