WCERE Thematic Session on Shale
Strategic Interactions between Regulators and Firms:
Unconventional Shale Gas Industry in Pennsylvania
Arie Beresteanu,
University of Pittsburgh
(arie@pitt.edu)
Shanti Gamper-Rabindran,
University of Pittsburgh
(shanti1@pitt.edu)
Keywords: Regulatory Inspections, Bayesian Games, Sample Selection
1. Strategic Interactions between Regulators and Firms: Unconventional Shale Gas Industry
in Pennsylvania
Inspections by regulatory agencies are an important instrument to incentivize firms to internalize
environmental costs. Effective inspection strategies are important because both inspections and
environmental damages, when violations are not deterred, are costly. Our paper builds a novel
estimation model, which allows us to analyze whether the regulator’s reallocation of inspection
resources from one set of firms to another, based on firms’ observed discrete characteristics, can
potentially improve the regulators’ inspection strategy. For example, if violation rates of new
entrants are far higher than those of experienced firms, but inspections rates are much higher for
the latter, at the margin, the reallocation of inspection resources towards the new entrants would
improve the regulators’ inspection strategy. We model the strategic interactions between the
regulator and the firms as a Bayesian game, yielding a system of simultaneous equation: one
equation on the regulator’s probability of inspections, and one equation on the firms’ probability
of violation. These equations are functions of firms’ characteristics, costs of inspections,
penalties when inspections detect violations, and firms’ benefit from violations (e.g. not having
to pay for the abatement costs). The equilibrium condition of this Bayesian game yields a unique
solution. We recover parameter estimates using the likelihood function for the sample in which
the operators’ characteristics and violation/non-violation of regulations are observed only when
the firm is inspected.
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We implement this estimation strategy to the inspections in the unconventional shale gas (UGD)
industry in Pennsylvania (PA). UGD inflicts water and air contamination if gas well operators
fail to take sufficient preventative measures, such the proper construction of well-casing and
storage pits, the proper disposal of wastewater, and prevention of surface spills (Vidic et al.,
2013; Vengosh et al., 2014) The PA Department of Environmental Protection (DEP) undertakes
inspections of the operators of gas wells and notes operators’ violations of the environmental
regulations. Despite recognition by Secretary of Energy Advisory Board (2013) that the
regulatory regime, including inspections, plays a critical role in incentivizing firms to reduce
their environmental footprint in the UGD industry, few studies have examined this issue. We
construct a novel database using data from the DEP and auxiliary data. Our method is applicable
to the broader issue of analyzing the effectiveness of inspections in reducing violations. Previous
reduced form estimation, correlating violations with lagged inspection and applying a
questionable instrument for lagged inspections, are biased against finding that inspections reduce
violations. Violations are observed only when inspections occur, and regulators selective target
inspections on firms that are more likely to violate regulations, based on characteristics
unobserved to the researcher.
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Unconventional shale gas industry in Marcellus Shale in PA
The UGD industry began around 2005 in PA, growing rapidly by 2009, and by 2014,
Pennsylvania has become the second largest producer of shale gas in the US, behind Texas. By
the end of the 4th quarter of 2013, there were 2883 pads in PA, which are operated by more than
100 distinct firms. The operator, which operates a well pad containing one or more wells,
ultimately responsible for environmental compliance at the well pad. In order to drill a well, the
operator needs an approved permit from the DEP. The data indicates that there is a 1 in 4 chance
that a pad is inspected in a given quarter. The DEP stated goals are to inspect the well pad from
the time significant activity occurs at the well pad, including its construction of the well pad, the
drilling of the wellbore and so on. We treat a well pad as inspectable after the earliest spud date
of any well on the pad. The spud date denotes when the drill bit breaks the surface. This
definition of inspectable avoids the period of no-activity on site between permit approval and the
start of construction of the well pad, but it has the disadvantage of overstating the inspection
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frequency by treating the period between well pad construction and the first spud date as a noninspectable period. The start date on well pad construction is not available.
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Game representation
Suppose each well pad, p, is characterized by a discrete characteristic rR={R1,R2,…Rn} and a
vector of other characteristics xX. Consider the following 2x2 Bayesian game played between
the monitoring agency (DEP) and the well owners. The actions available to the DEP are 𝐴𝐷𝐸𝑃 =
{𝐼𝑛𝑠𝑝𝑒𝑐𝑡, 𝐷𝑜 𝑛𝑜𝑡 𝑖𝑛𝑠𝑝𝑒𝑐𝑡} and the actions available to the well owner are 𝐴𝑊𝑒𝑙𝑙 =
{𝑉𝑖𝑜𝑙𝑎𝑡𝑒, 𝐷𝑜 𝑛𝑜𝑡 𝑣𝑖𝑜𝑙𝑎𝑡𝑒}.
For
each
(𝑎1 , 𝑎2 ) ∈ 𝐴𝐷𝐸𝑃 × 𝐴𝑊𝑒𝑙𝑙
let
𝑈𝐷𝐸𝑃 (𝑎1 , 𝑎2 )
and
𝑈𝑊𝑒𝑙𝑙 (𝑎1 , 𝑎2 ) denote the payoffs for player 1 (the DEP) and player 2 (well owner) respectively.
The table below makes the payoff functions explicit.
Well
DEP
Violate
Do not violate
Inspect
(−𝑐, 𝑣̅ (𝑟) − 𝜉 − 𝑗)
(−𝑐, 0)
Do not inspect
(−𝑥 ′ 𝛽 + 𝜀 , 𝑣̅ (𝑟) − 𝜉)
(0,0)
We assume that the parameters 𝜃 = (𝑟, 𝑥, 𝑗, 𝑐, 𝛽, {𝑣 ̅(𝑟)}𝑟∈𝑅 ) are known to the players but
ξ is the well owner’s private information and ε is the DEP’s private information. We assume that
players have correct common prior 𝐹𝜉,𝜀 for the joint distribution of (𝜉, 𝜀). Let Ξ × ℰ be the
support of (𝜉, 𝜀). A pure strategy for the DEP in the above Bayesian game is a map 𝑡𝐷𝐸𝑃 : ℰ →
{𝐼𝑛𝑠𝑝𝑒𝑐𝑡, 𝐷𝑜 𝑛𝑜𝑡 𝑖𝑛𝑠𝑝𝑒𝑐𝑡}. Let 𝑇𝐷𝐸𝑃 be the set of all these maps. Similarly, a strategy for a well
owner is 𝑡𝑊𝑒𝑙𝑙 : Ξ → {𝑉𝑖𝑜𝑙𝑎𝑡𝑒, 𝐷𝑜 𝑛𝑜𝑡 𝑣𝑖𝑜𝑙𝑎𝑡𝑒}. Let 𝑇𝑊𝑒𝑙𝑙 be the set of all these maps.
Definition: In the above game, a pair of pure strategy Bayesian Nash Equilibrium (PSBNE)
∗
∗
strategies are two maps 𝑡𝐷𝐸𝑃
∈ 𝑇𝐷𝐸𝑃 and 𝑡𝑊𝑒𝑙𝑙
∈ 𝑇𝑊𝑒𝑙𝑙 Such that
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i.
∗
∗
∗
(𝜀), 𝑡𝑊𝑒𝑙𝑙
(𝜉)) 𝑑𝐹𝜉|𝜀 ≥ ∫ 𝑈𝐷𝐸𝑃 (𝑡(𝜀), 𝑡𝑊𝑒𝑙𝑙
(𝜉)) 𝑑𝐹𝜉|𝜀 ,∀𝑡 ∈ 𝐴𝐷𝐸𝑃 and ∀𝜀 ∈ ℰ.
∫ 𝑈𝐷𝐸𝑃 (𝑡𝐷𝐸𝑃
ii.
∗
∗
∗
(𝜀), 𝑡𝑊𝑒𝑙𝑙
(𝜉)) 𝑑𝐹𝜀|𝜉 ≥ ∫ 𝑈𝐷𝐸𝑃 (𝑡𝐷𝐸𝑃
(𝜀), 𝑡(𝜉)) 𝑑𝐹𝜀|𝜉 ,∀𝑡 ∈ 𝐴𝑊𝑒𝑙𝑙 and ∀𝜉 ∈ Ξ.
∫ 𝑈𝑊𝑒𝑙𝑙 (𝑡𝐷𝐸𝑃
Using the payoffs in the above game we can show that both players employ threshold crossing
strategy. In other words for 𝜀 ≤ 𝜀̅ the DEP chooses to inspect and for 𝜉 ≤ 𝜉 ̅ the well owner
chooses to violate. Both 𝜀̅ and 𝜉 ̅ depend on the parameter 𝜃. As a result of this threshold crossing
strategy we can write the probability that the DEP inspect and that the well owner violate:
The probability of inspection in the group (r,x) is 𝜌𝑟,𝑥 . Penalty imposed if inspection finds a
penalty is 𝑗. The expected utility of a well pad from committing a violation is 𝑣 − 𝜌𝑟,𝑥 ∙ 𝑗. We
assume that 𝑣 = 𝑣̅ (𝑟) − 𝜉 where 𝑣̅ (𝑟) is the average utility from violations that depends only on
rR.
(1) 𝜑𝑟,𝑥 = 𝑃𝑟(𝑣𝑖𝑜 = 1|𝑟, 𝑥) = 𝑃𝑟(𝜉 < 𝑣̅ (𝑟) − 𝜌𝑟,𝑥 ∙ 𝑗) = 𝐹𝜉 (𝑣̅ (𝑟) − 𝜌𝑟,𝑥 ∙ 𝑗).
The expected benefit to the inspection agency from an inspection of a well pad with
characteristics (r,x) is (𝑥′𝛽 − 𝜀)𝜑𝑟,𝑥 − 𝑐 where c>0 is the cost per inspection and 𝜀 is an
unobserved characteristic. We normalize the utility from not inspecting a well to be zero.
Therefore, we can write
𝑐
𝑐
𝑟,𝑥
𝑟,𝑥
(2) 𝜌𝑟,𝑥 = Pr(𝐼𝑛𝑠𝑝 = 1|𝑟, 𝑥) = Pr (𝜀 < 𝑥 ′ 𝛽 − 𝜑 ) = 𝐹𝜀 (𝑥 ′ 𝛽 − 𝜑 ).
Equations (1) and (2) need to be jointly satisfied in equilibrium. Given that both 𝜉 and 𝜀 have
continuous and strictly increasing distribution functions, the solution to the above system exist
and is unique. Denote by (𝜑 ∗ , 𝜌∗ |𝑟, 𝑥; 𝜃) the solution to the system (1) and (2) for a given value
of the covariates (r,x) and a value of the parameters 𝜃. Note that the distribution functions 𝐹𝜉 and
𝐹𝜀 could potentially be part of the parameter vector 𝜃 but we are taking a parametric approach
here and assume that they have a known distribution with no parameters (e.g. standard normal or
logistic). This is done to simplify our estimation. Next we write down the likelihood of a sample
in which we observe r,x,a1 and a2 only observed if a1=Inspect.
𝐿(𝜃) = ∏ Pr(𝑖𝑛𝑠𝑝 = 0) ∏ Pr(𝑣𝑖𝑜 = 1|𝑖𝑛𝑠𝑝 = 1) ∙ Pr(𝑖𝑛𝑠𝑝 = 1)
0
1
such that (1) and (2) above are satisfied.
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4 Estimates of Factors influencing a Regulator’s Probability of Inspecting a Well Pad
We consulted three inspectors from the DEP about factors that influence the DEP’s probability
of inspecting a pad. A new inspection at the pad is either (i) initiated by the DEP, based on the
operators’ reports on the activities at the well (e.g. critical stages such as drilling and cementing)
or on errors at the pads (e.g. spills), or (ii) is undertaken by the DEP in response to complaints
from members of the public. Inspectors note that to avoid environmental damage, the critical
stages in the well’s lifecycle drilling, well construction and cementing, while the production
stage of the well is less critical. Inspectors describe sharing their knowledge with other
colleagues on operators’ violation history, suggesting that operator’s characteristics and their
violation record matter for the probability of inspections. In our preliminary work, we estimate a
reduced form panel logit with random effects relating inspections at a pad with the characteristics
of the pad, operator and neighboring pads. The observations are pad p that is inspectable in
quarter t (1st quarter 2007 to 4th quarter 2013). The dependent variable is a binary variable on the
presence of inspection at well pad p at quarter t. The explanatory variables are time invariant
characteristics that are related to the environmental or public health sensitivity of the well pad
location and socioeconomics of the well pad location, (ii) well pad characteristics, (iii) operator
characteristic and (iv) characteristics of other pads in the vicinity (10km) These characteristics
include inspection and violation history, and counts of wells that have spudded, producing gas,
or producing waste, respectively. The mean probability of inspection for a pad at any given
quarter is 0.26.
4.1
Results
Factors that influence the probability of inspections include factors that are related to the
ecological characteristics or public health implications of the location and the violation history of
the operator.
Ecology or Public Health
Compared to a pad in a location relying on public water supply, typically piped water, those pads
is in a location that relies on private water wells has twice the probability of inspection. Pads that
are located closer to high value streams are more likely to be inspected. A decline in distance
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between a pad and a high value stream by 1 km raises the probability of inspection by 0.015, i.e.,
6% of the mean probability of inspection. Pads located in areas with lower population density are
more likely to be inspected, while the average income at the census tract where the pad is located
does not influence the likelihood of inspections.
Operator violation history
One violation in the operator’s other pads in the previous quarter, accounting for the counts of
inspections at the operators other pads, and its counts of total pads in the previous quarter, raises
the likelihood of inspections by 0.07. This increase in the probability of inspections is about 27%
of the mean probability of inspection.
Neighboring pad history
We find an increase in the probability of inspection at a pad if its neighbor was inspected in the
previous period. But only in some specifications, do we find an increase in this likelihood of
inspection if its neighbor was found to have a violation in the previous period.
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MLE Structural Estimation
This section is in progress.
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