LIBRARY
OF THE
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SiBFtARtBS
W/ISS. INST. TECH.
JAN
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMEN"
THE REGULATORY POLICY IMPLICATIONS OF
THREE ALTERNATIVE ECONOMETRIC SUPPLY MODELS
OF NATURAL GAS"^
by
Paul W. MacAvoy*
'^
690-73
Robert
S.
Pindyck**
December, 1973
7
197^
M/l?S.
SEP ;^3l975
n
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453S
introduction
The shortage of natural gas in the United States has grown sub-
stantially in the last few years and is now at the level where it probably
exceeds ten percent of total demands.
Prior discovery of the lowest cost,
highest volume reservoirs has been given as one reason for this state of
affairs
— the
argument being that exploratory companies had found most of
the high-productivity reservoirs by the early 1960's.
But this is not a
sufficient explanation, since rising resource costs alone would have
resulted in relative price increases in natural gas and not in a large and
systematic shortage.
The additional condition is that the Federal Power
Commission in the early 1960 's set limits on field prices for new production
approximate to the unregulated prices of the late 1950' s, and then held these
prices for most of the decade.
2
The combination of rising resource costs,
general inflation, and frozen gas prices must have provided strong incentives
for increased demands but no incentives for increased discoveries and production.
The shortage, and this rationale for the shortage, has resulted in wide-
spread and concerted efforts to deregulate field prices.
Increased prices
resulting from deregulation, it is generally expected, would add to reserves
and result in more production each year out of reserves; at the same time,
demands for production would be dampened as users of boiler fuel replaced
the more expensive gas with oil products or coal.
But the question has been
asked as to whether the tendency to clear markets of excess demand is sufficient reason for deregulation.
If the increase in reserves resulted only
2
Stephen Breyer and Paul W. MacAvoy, "The Natural Gas Shortage and the
Regulation of Natural Gas Producers," Harvard Law Review , Vol. 86, No.
April, 1973.
6,
,
2
in payments of rents to owners of the source
(land) resources, then many of
the proponents of deregulation would likely be less enthusiastic.
Deregulation, if it were to take place, would not be accomplished in
an afternoon.
The 1973-1974 proposals of the Nixon Administration call for a
series of substantial price increases, to be administered by one or the other
agency, as regulation winds down over the rest of the decade.
The opposition
in the Senate has proposed new procedures for the Federal Power Commission to
use in allowing price increases; if these procedures were to be put into effect,
the resulting prices would probably be only a few cents per Mcf greater than
on new contracts signed this year.
A few cents, rather than doubling of new
contract prices, may be sufficient to clear the market of excess demand.
The
choice of the proper "interim" policy for the next few years depends on the
effect of the price increase on the levels of additional production.
The size of the response of reserve accumulations and production to
price changes is thus critical in policy determination for the next few
years.
Estimates of the response have been made by a number of sources,
some on the basis of experience in the industry
more formal modelling exercises.
evaluate these estimates.
4
and others on the basis of
An attempt should be made at this time to
This attempt is made below.
3
Paul W. MacAvoy and Robert S. Pindyck, Alternative Regulatory Policies for
Dealing with the Natural Gas Shortage," Bell Journal of Economics and
Management Science Vol. 4, No. 2, Autumn, 1973.
,
4
National Petroleum Council, United States_Energy Outlook
December, 1972.
,
Washington, D.C.
J. D. Khazzoom, "The FPC Staff's Econometric Model of Natural Gas Supply in
the United States," Bell Journal of E_conomics and Management Science Vol. 2,
1, Spring, 1971, and E. Erickson and R. Spann, "Supply Response in a
Regulated Industry: The Case of Natural Gas," Bell Journal of Economics and
Management Science Vol. 2, No. 2, Spring, 1971
,
No.
,
2.
Background for This Work
For the past year and one-half a research group at MIT has been developing
an econometric model of the natural gas industry, to be used in studying the
effects of alternative regulatory policies on the wellhead price of gas.
That model is a set of within-module simultaneous equations.
a
The supply module,
regional basis, has equations for drilling activity (in response to price
and cost variables), and for new discoveries, extensions, and revisions for
either oil-associated or non-associated gas (also in response to price variables,
in response to drilling
levels
end to costs).
This makes up reserve supply;
under conditions of Federal Power Commission regulations (resulting in depressed
prices and excess reserve demand)
,
quantities of new reserves are determined
by inserting the exogenous wellhead price of gas in the appropriate equations
in any year.
Production of gas out of reserves is determined in the
model by assuming exogenous prices equal to marginal costs and by then relating
marginal costs to actual reserve levels and to production levels.
The model
also contains a set of regional wholesale demand equations that relate demand
to the size of final retail or wholesale markets, wholesale prices of gas, and
prices of alternative fuels.
Wholesale and field markets are linked together
in the model by a set of pipeline price mark-up equations together with an
input/output table that determines the distribution of gas from production
regions to wholesale consumption regions.
This model was developed under National Science Foundation Grant //GI-34936,
described in detail in P. W. MacAvoy and R.S. Pindyck "Alternative
Regulatory Policies for Dealing with the Natural Gas Shortage," The Bell
Journal .oj^ Economics and Management Science Vol. 4, No. 2, Autumn, 1973,
It is
,
4
The part of the model which Is probably most open to controversy is the
set of equations that explain reserve additions.
exploration and discovery process
— about
Little is known about the
the incentives for further exploration,
the opportunities for significant finds (dependent on how much undiscovered
gas remains under the ground in the United States) and the relation between
a priori opportunities and a posteriori finds.
The MIT research project ap-
proached the problem by specifying equations that offered an intuitive explanation for drilling activity, and then fitting these equations as best as one could
the available data.
Our approach began by assuming that drilling can be divided
into two modes of behavior, depending on whether it is done extensively or
intensively
.
The first reaches out into new areas, with the supposed result
that the ratio of successful wells declines but the size of find per successful
well increases; the second results in a higher success ratio but smaller finds.
However as a result of data aggregation, it is impossible to determine ex post
o
whether drilling has been done in the extensive or intensive mode.
Regression
equations fitted ex post had a tendency to show increasing size of finds on
higher gas prices for non-associated gas, but decreasing size on associated gas.
Other econometric models have been developed for natural gas exploration
and discovery.
Two in particular have received some attention and use very
In extensive drilling, few wells are drilled, but those that are drilled
usually go out beyond the frontiers of recent discoveries to open up new
geographical locations or previously neglected deeper strata at old locations.
This might include drilling farther off-shore or on-shore but at very great
depth.
Here the probability of discovering gas is rather small, but the
When drilling is done intensively
size of discovery may be comparatively large.
many wells are drilled in an area that has already proven itself to be a
source for gas discovery.
Here the probability of discovering gas is larger
but the size of discovery is likely to be very small.
g
See M. Subrahmanyam and K. Challa, "The Oil and Natural Gas Exploratory
Process in the United States: A Framework for Analysis," unpublished
research memorandum, October, 1973.
5
different formulations than that which was used in the MIT model.
The first
Q
of these, developed by Khazzoom for the Federal Power Commission,
relates
new discoveries, extensions and revisions to a distributed lag of past ceiling
prices, oil prices, and prices of natural gas liquids.
The model can be
thought of as a set of reduced form equations (or equivalently a "black box")
because it does not specify explicitly any structural relationships between
prices, drilling activity, and discoveries. This is not to fault the model,
since it is not at all clear what a correct specification for a structural
form model of exploration and discovery would be, and the reduced form specification of Khazzoom' s model is appropriate to a variety of "reasonable" structural
forms.
The second alternative supply model is that of Erickson and Spann,
a more structural model which contains
logarithmic equations.
The first equatic
relates wildcattlng activity to prices, previous success ratios, and other
geographical and geological variables.
The second relates the success ratio
to prices and geological variables, and the last two relate average oil dis-
covery size and gas discovery size respectively to prices and geological
variables.
Extensions and revisions are not covered by the model, but new
discoveries are explained with more structural detail than is the case in
the MacAvoy-Pindyck model.
Supply in the United States," The Bell_Joumal of Economics and Management
Science , Vol. 2, No. 1, Spring, 1971.
E. W. Erickson and R. M. Spann, "Supply Response in a Regulated Industry:
The Case of Natural Gas," The Bell Journal of Economics and Management
Science , Vol. 2, No. 1, Spring, 1971.
The MacAvoy-Pindyck model has an equation for total exploratory drilling,
and then equations that relate average discovery size to attempted wells
whether or not those wells are successful. Thus it lacks a description of
the success ratio and could be thought of as a semi-reduced form or a variation on the Erickson and Spann model.
In this paper we re-estimate the Khazzoom and Erickson-Spann models using
the same data as for the exploration and discovery part of the MacAvov-Pindyck
model.
12
Each of these models for exploration and discovery will then be
simulated as a module of the MacAvoy-Pindyck overall model.
We will thus
produce three alternative sets of simulation results for natural gas reserves,
production, and demand the first using the original exploration and discovery
equations that were part of that model, the second using Khazzoom's equations
for exploration and discovery, and the third the Erickson-Spann formulation
for exploration and discovery.
Each of the three models for exploration and
discovery has a different degree of structural detail.
By comparing the three
sets of simulations, we will attempt to assess the appropriateness of the
degree of detail
— or
the extent to which structural theory is helpful in ex-
plaining and predicting gas reserves.
In the next section we describe the Khazzoom and Erickson-Spann models
for exploration and discovery, and then present the re-estimated form of those
models.
The fourth section of the paper presents the different simulation
results used in the three alternative exploration and discovery formulations.
Historical simulations will be performed first (in order to compare the fit
of the three models)
,
and then forecasts are made of natural gas production
demand and supply through 1980 so that the long-mn implications of these
alternative formulations can be compared.
Finally, the paper provides some
speculation on the econometrics of natural gas exploration and discovery.
12
As we will see in the next section some minor re-specification of those
models is necessary in order to make the variables consistent with the data
used in the MacAvoy-Plndyck model.
.
3.
Alternative Formulations of Natural Gas Exploration and discovery
The "base case" for comparisons will be the exploration and discovery
equations of the MacAvoy-Pindyck gas model.
These equations were estimated
using pooled data over 18 FPC production districts for the years 1964 through
1971.
The exploration and discovery sub-model begins with an equation for
total exploratory wells drilled for any district in any year as a function of
previous revenues (REVD), previous average cost (ATCD)
,
as measured by the variance of previous success rates.
and average risk (RISKV)
The equation, with
regional dummy variables DDA, DDB, and DDC, is shown below with t-statistics
in parentheses:
WXT = 439.39 + 934.53DDA + 83.75DDB + 137.48DDC
(9.17)
(3.81)
(0.40)
(1)
(3.24)
+3.156xlO"'^REVD _ -4.43x10"\tCD
^ ^
(2.22)
(4.79) J,'^
-2.13x10 RISKV
(-2.74)
R^ = 0.495
F = 17.2
S.E. = 193.6
DW
= 0.36
Equations are estimated for average discovery size of pools and fields of
non-associated gas (SIZEDN) and for average discovery size of associated gas
(SIZEDA).
These variables thought to affect size are the past prices of gas
and oil, past drilling costs, and the cumulative number of wells drilled (CWXT)
The relationship of discovery size ot cumulative wells drilled is hypothesized
to be negative because of depletion effects that occur over time in a reservoir
region in which mnay wells are drilled.
on the following page.
The estimated equations are shown
:
SIZEDN = 815.62 - 600.69DDA + 189.70DDB + 825.43DDC + 28.89(PG
+ PG „ + PC „)y
^'^
^'^
""^
(-2.78)
(-0.9A)
(0.63)
(6.52)
(2.05)
+ 0.0131(ATCD
(5.86)
+ ATCD
^
^
+ATCD
^-^
F = 29.9
„)/3 - 0.301CWXT ,
^-^
^"^
(-3.18)
DW = 0.74
S.E.= 578.3
SIZEDA = 50.60 + 106.96DDA + 48.3ADDB + 30.02DDC - 14,30(PO
(1.64)
+
(2.65)
3. 138x10"'^
(2.67)
(ATCD
^
(2.24)
^
(4.02)
^'^
+ PO
+ ATCD^ „+ ATCD^ _)/3 - 4.590xlO~^CTXT
^-^
^
^
F = 26.3
R^ = 0.601
(-1.64)
(-1.84)
S.E. = 34.6
DW
(2)
+ PO _^)/3
^"^
^
"^
^'^,
= 1.06
(3;
New discoveries of associated gas and non-associated gas (NDA,NDNA) are thus
given by:
NDNA = SIZEDN
•
WXT
(4)
NDA
•
WXT
(5)
= SIZEDA
Separate equations are estimated for non-associated and associated extensions
and revisions.
Non-associated and associated extensions depend on exploratory
drilling activity as well as previous non-associated and associated new discoveries:
XN = 2.20x10^ + 1.33xlO^DDA + 1.56xlO^DDB + 3,639xl0^DDC + 237.1WXT
(0.430)
R^ = 0.725
(5.63)
(0.55)
(11.04)
F = 67.6
S.E. = 3.2x10^
DW
(1,24)
= 0.87
XA = -1054.93 + 2.323xlO^DDA + 1.205xlO^DDB - 1947.44DDC + 48.00 WXT
(2.11)
(-0.11)
(0.17)
(4.44)
(5.20)
F = 57.7
S.E. = 5.8x10^
+ 0.137NDNA
(1.93)
(6)
+ 0.722NDNi
^
DW = 1.60
(2.53)
(7)
Associated and non-associated revisions, on the other hand, depend largely on
the previous year's change in reserves
(AR)
RN = 6.87x10
(1.19)
+ 1.138x1oSdA - 6.864xlO%DB + 3.438xlo'^DDC + 0.239AR
(-3.60)
(5.95)
S£
F = 18.2
RA
=
(0.373)
= 4.5x10
(4.
963)*^~-'-
DW = 1.65
(8)
-2234.90 + 4.863xl0^DDA + 3.240xlO^DDB + 3.550xl0'^DDC + 0.106AR
(-0.07)
(4.56)
R^ = 0.289
(3.04)
F = 11.2
(0.69)
S£.
= 2.5x10^
(3.94)
^
^
DW = 1.71
(9)
Noto that district dummy variables are used in all of these equations, and
the same district dummies will be used in the Khazzoom and Erikson-Spann models.
to
Finally,
additions/ reserves are given by total new discoveries plus extensions
and revisions:
DR = NDNA
+NDA+XN+XA+RN+RA
(10)
This reserve accounting identity excludes, of course, losses and changes in
underground storage.
The Khazzoom model relates aggregated new discoveries (ND = NDNA + NDA)
to the price of gas
liquids,
(PL).
(PG)
,
the price of oil (PC) and the price of natural gas
(Since we had no data available for natural gas liquids, this
variable had to be omitted from our version of the Khazzoom model.)
The
district dummy variables used by Khazzoom were the same as those used in the
MacAvoy-Pindyck model, and these include DBA for Louisana South, DB for the
Permian producing region, DDC for Kansas, Oklahoma, and Texas Railroad ComWe estimated Khazzoom's discovery
the
equation over the same 18 production districts and /years 1965-1969 as in the
mission districts
1,
2,
3,
4
and 10.
10
M/P model.
The resulting equation is given below:
ND = -42463 + 1.647xlO^DDA + 7.862xlO^DDB + 3.401x1oSdC
(-0.38) (1.41)
(1.14)
(0.92)
+ 1086.3(PG_
+ PG_ )/2 + 10844(PO_
+ P0_ )/2 + 0.685ND_
"-
(0.23)
^
(0.25)
^
DW = 2.05
F = 100.5
S.E. = 1.23x10^
R^ = .895
(11.99)
(11)
Our version of Khazzoom's extensions and revisions equation is shown below,
again using the price of gas, the price of oil, previous new discoveries and
lagged extensions plus revisions.
XR = -16252 + 2.209xlO^DDA + 1.201x1oSdB - 1.653xl0^DDC - 946.0 PG + 3.209xlO^PO
(-.03)
(2.283)
+ 0.645ND
(2.77)
^
_
(2.55)
(0.17)
+ 0.325XR
(2.72)
DW
F = 56.2
S.E. = 6.11x10^
R^ = .814
(-0.04)
(1.06)
= 1.48
(12)
Note that the price variables (PG and PC) are statistically insignificant in
both equations.
This is a change in results
a significant fit for t^-a price of gas
t-statistic greater than 2).
— Khazzoom's
own estimates showed
(which in both of his equations had a
Since it was not possible to use the original
equations in our simulation foremat, the alternatives were
and 12
(2)
(1)
use equations 11
change the basic form of Khazzoom's equations to produce higher
t-statistics for price.
The first seemed preferable, in order to preserve the
essential nature of Khazzoom's approach.
The reader might wonder why our estimated version of Khazzoom's equations
differ considerably from Khazzoom's original estimates; in particular why the
price terms have become insignificant.
We have, of course, estimated Khazzoom's
equations over a somewhat shorter time period than he did originally (1964-1969
versus 1961-1969), and one might suspect that by truncating the estimation period
11
we have eliminated just those years (1961-1963) over which prices and discoveries
had their greatest variance.
If this was the case,
than it would account for the
loss of significance in the price terms in our estimates of Khazzoom's equations.
In Table A we show,
for eight representative production districts around the
country, new contract prices for the years 1952 to 1969, and new discoveries and
extensions and revisions for 1956 to 1969 (data on these latter variables was not
available before 1956).
Note that between 1960 and 1969 discoveries dropped al-
most consistently in Louisana South, Mississippi, Kansas, Texas 6, and Texas 10.
New contract prices also dropped in those districts between 1960 and 1963, then
rose between 1963 and 1969, so that the elimination of the 1961 to 1963 period
(at least for those districts)
tween price and discoveries.
would indeed reduce the positive correlation beIn Texas 3 and Texas 4 discoveries increased from
1960 to 1967 and then decreased from 1967 to 1969, while prices showed some de-
crease between 1960 and 1963 and then increased thereafter.
Thus eliminating
the 1961 to 1963 years from the estimation period should for these two districts
improve the positive correlation between price and discoveries.
Of course our
regressions are also picking up cross-sectional variance between price and discoveries, but this does not change much from year to year.
Putting this toget-
her, it would be reasonable to expect that decreasing prices in the majority of
districts between 1960 and 1963 contributed to the significance of the Khazzoom's
price terms when his equations were estimated over the longer time period.
There is another problem with Khazzoom's formulation however, and that Is
that both of his equations contain a lagged dependent variable.
In the new
discoveries equation this variable accounts for most of the explained variance,
12
so that in fact the equation represents little more than a simple first
order autoregressive model for a random process.
If the errors are serially
correlated (and there is no reason to believe that they are not) than his
estimates of the price coefficients are inconsistent in any case.
The model constructed by Erickson and Spann seeks first to explain total
wildcatting activity.
In order to make their structural format consistent
with our data base, some reformulation was necessary,
For example, we reformu-
lated the drilling equation to include all exploratory wells drilled instead
of just new pool and new field wildcats.
The average depth of drilling variable
thus also applies to all exploratory wells and not just wildcats,
Erickson and
Spann use two variables relating to past drilling activity, the first of these
is wildcats drilled by major companies in a given district in a given year as
a percent of total U.
S.
wildcats drilled by all companies in that year, and
the second is wildcats drilled by major companies in a given district in a
given year as a percent of total U.
that year.
S.
wildcats drilled by those companies in
We did not have access to this data and therefore used a single
variable (WRATIO)
,
which is the relative fraction of total exploratory wells
drilled in a particular district in a particular year as a fraction of total
exploratory wells drilled in the entire United States.
Finally, the variables
used by Erickson and Spann for Texas shutdown days were omitted from our version
of their model since data for them was xmavailable.
13
Our version of the Erlckson and Spann wildcatting equation Is shown
below, using the same logarithmic form as Erlckson and Spann do, but
relating total exploratory wells drilled to deflated gas prices (PGD)
and deflated oil prices (POD)
,
previous success ratios (SR)
,
average
footage (AFX), and the activity variable (WRATIO) mentioned above:
log WXT = 9.018 + 1.577xlO~^DDA
(45.83)
(0.01)
.0029DDB
(-0.09)
,0172DDC - 0.033 log PGD
(-1.13)
(-0,98)
(14)
+ 0.065 log POD - 0.0067 log SR
(-0.44)
(1.02)
-0.0061 log AFX
R^ = .995
+ 1.006 log WRATIO
^~
(00.36)
S.E. = 0.063
(121.63)
F = 2497
DW = 1.98
Next, our version of the Erlckson and Spann success ratio equation
relates that variable to the deflated price of gas and the deflated price
of oil, again in logarithmic form:
log SR = -4.869 - 0.148DDA + 0.554DDB + 0.121DDC
(1.22)
(2.67)
(-0.70)
(-7.91)
+ 0.570 log PGD + 1.419 log POD
(2.51)
.274
(3.68)
S.E. = 0.443
F = 6.93
DW = 0.72
Finally, an average gas discovery size equation (for both non-
associated and associated gas) is given, relating that variable to
deflated oil and gas prices, and the previous period's success ratio;
(15)
(16)
log SIZE = 0.80A + 2.693DDA + 1.464DDB
(1.92)
(3.61)
(0.28)
+ 1.564DDC + 1.826 log PGD + 0.348 log POD
(0.24)
(2.20)
(4.43)
-0.309 log SR
(-0.81)
R^ = .268
S.E. = 1.568
F = 5.57
DW = 0.65
While the fit of this model leaves something to be desired, particularly
for the success ratio and size equations, what is most startling is that the
results, including the signs of several of the coefficients, differ considerably
from Erickson and Spann's original results.
For example, one sees reversals
in the signs of the coefficients of the price of gas and average footage in
the wells equation,
and in the price of gas and the price of oil in the
success ratio equation.
Most important, the price elasticities that result
from our estimates of these equations are very different from those implied
by the original estimates.
example,
is
The own price elasticity of gas discoveries,
for
2.36 (the sum of the elasticities of -.033 for wildcat drilling,
.570 for the success ratio,
and 1.826 for the average size), as compared with
0.69 for Erickson and Spann's original estimates.
Certainly simulations of
this model are likely to show a much greater response to price stimulation
than was the case when the original estimates were used, but what is disturbing
is
that these elasticities changed so dramatically when the model was estimated
over a different time period.
Erickson and Spann estimated their original equations over the period
1946 to 1959, while we have re-estimated them over the period 1964 to 1969.
As can be seen from Table A, new contract prices in all districts showed
15
much greater percentage increases from 1952 to 1958 than they did from 1960
to 1969.
New discoveries, on the other hand, did not show such
percentage increase over the earlier period.
a
dramatic
Thus it is very reasonable to
expect that Erickson and Spann's model would show much smaller price elasticities
when estimated over the earlier period.
While that explains why the elasticities
are greater when the model is estimated over the later time period, their
model nonetheless seems to be considerably over-estimating the price elasticity.
The problem may be in their average size equation, which indicates (according
to the estimated price elasticity of 1.826)
that small price increases tend
to result in very large increases in discovery size.
The equation has a low R
2
and an F-statistic of only 5.6, so that most of the variance in average size
is
unexplained and the significance of the equation as a whole is questionable.
Since Erickson and Spann's three equations are logarithmic, the price elasticities
add across equations, so that a spurious elasticity in the size equation becomes
reflected in the overall price elasticity for discoveries.
(
16
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4.
Simulations of the Three Models
The three formulations for exploration and discovery estimated above
can now be simulated as part of the complete supply-demand gas model in
order to determine their alternative impacts on production, supply, demand,
and excess demand.
We begin by performing an historical simulation - a
"backcast"- of each model over the period 1965 through 1971,
Some ex-
planation is needed for how these simulations are performed.
The Khazzoom model predicts both new discoveries and extensions and
revisions, so that the two equations of that model can simply be sub-
stituted for the seven equations of the MacAvoy-Pindyck model that predict
wells, discoveries, extensions, and revivsions.
The Erickson-Spann model,
however, predicts only new discoveries, so that a method was needed to
generate extensions and revisions.
We chose to substitute the three
Erickson-Spann exploration and discovery equations in place of the equations
of the MacAvoy-Pindyck that also predict new discoveries, but to retain
the four extensions and revisions equations of that model.
In performing
the historical simulation we used the actual values for associated and
non-associated new discoveries as inputs to the extensions and revisions
equations rather than the predicted values generated by the Erickson-Spann
discovery equations.
In a sense this gives some "benefit of doubt" to the
Erickson-Spann formulation, since it prevents accumulated errors in new
discoveries from affecting extensions and revisions.
It is important to point out that simulated demand for production will
be slightly different for each model formulation, even though the only
difference between the models are in the exploration and discovery equations.
The reason for this is that demand for production depends on the wholesale
19
price (either for sales for resales or for mainline sales).
The whole-
sale price in turn is based on a pipeline mark-^up over an average "rolled
in" wellhead price.
The average "rolled in" price is computed separately
for each production region, and depends on the current period's production
level in that region (since in computing rolled-in prices, new contract
*
prices are weighted proportionately to new production)
Production out
.
of reserves, on the other hand, is itself a function of the average rolledin price and year-end reserves, which means that the rolled-in price and
production out of reserves are determined simultaneously, each one depending on the other and on year-end reserves.
Thus new reserves and new
production, which differ between models, will lead to different prices
at the field and wholesale level
— and
ultimately to different demands at
wholesale.
The results of these simulations are shown in table 2, together with the
root-mean-square (RMS) and mean simulation errors for each variable.
Note
that over this seven year time range the MacAvoy-Pindyck formulation performs
best in terms of new discoveries, with an RMS simulation error of 1.19x10
versus 1.49x10
for the Khazzoom formulation and 1.70x10
Spann formulation.
for the Erickson-
The Khazzoom formulation has the lowest RMS error for
additions to reserves, since the aggregated extensions plus revisions
equations of that model "tracks" the historical data more closely than do
the disaggregated MacAvoy-Pindyck equations.
It is questionable how mean-
ingful this is, however, since (a) the Khazzoom extensions and revisions
equation depends on new discoveries, which are being underpredicted^
— so
that if Khazzoom' s new discoveries tracked better his extensions and revisions
For a more detailed description of how rolled-in prices are computed,
see footnote 11, page 462, of MacAvoy and Pindyck, op.cit
.
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24
would track more poorly; and
(b)
the autoregressive component of Khazzoom's
equation is helping it pick up trend, but what is allowing the model to pick
up trend may prevent it from picking up turning points.
What we are really
after is a tool for analyzing the impacts of alternative regulatory price policies
and the autoregressive nature of Khazzoom's model is likely to prevent it from
being useful for this purpose.
The Erickson-Spann formulation has the largest RMS error for additions to
reserves; but this is entirely a result of its underpredicting new discoveries,
(since it is being simulated using the extenions and revisions equation of the
M-P model, with actual values of new discoveries as Inputs to those equations).
The Erickson-Spann model also has the largest underprediction of the supply of
production out of reserves, again because it underpredicts new discoveries,
Finally, the simulated values for the demand for production out of reserves is
roughly the same in all three formulations; again the differences are attributable
to the different predicted rolled-in prices that result from different supply
predictions, but these differences are not substantial on this side of the model.
It is also informative to simulate the three formulations over a future
time horizon in order to compare their long run djmamic behavior.
We performed
forecast simulations over the time period 1971 through 1980, using three alter-
native sets of assumptions about regulatory policy for each model simulated.
The first policy is called "cost of service" regulation. Since it requires
historical average cost pricing of the FPC probably it; implies wellhead price
increases of Ic per mcf per annum on new contracts.
The second policy, which
we call a "status quo" policy, assumes that FPC regulatory policy of 1970
through 1972 is continued by allowing wellhead price increases on new con-
tracts of about 3C per mcf per annum.
Finally, a "deregulation" policy
is simulated in which new contract prices are allowed to rise by 150 in
1974 and then an additional
3(?
per annum after 1974^
.
(For a detailed
_
description of these three alternative policies, see MacAvoy and Pindyck,
op.clt.
)
.
In all of the forecasts, exogenous variables (such as the price of
as
oil, per capita GNP) were assumed to follow the "medium" growth paths
described in that article.
Tables 2A, 2B, and 2C show the forecasts results using the Khazzoom
exploration and discovery equations.
Those results reflect the lack of price
sensitivity in the Khazzoom equations, as there is almost no response in
reserve additions to increases in the wellhead price (compare the "deregulation" case with the "cost of service" case).
Thus, even under the "deregula-
tion" policy, excess demand grows steadily and reaches a level of more than
seven trillion cubic feet by 1980.
Forecasts results using the Erickson-Spann exploration and discovery
equations are shown in Tables 3A, 3B and 3C.
What we find is that the
model is extremely sensitive to price, so that under "deregulation" new
discoveries increase about ten fold between 1971 and 1980, production out of
reserves more than doubles in that time period, and we have excess supplies
of about 18 trillion cubic feet by 1980.
Again, this is because of vary large supply elasticities for new
discoveries with respect to oil and gas prices in the Erickson-Spann formulation.
Since the equations are logarithmic, we can add the supply elasticities
of well drilled, success ratios and size.
If we do this we find that the
26
elasticity of total discoveries with respect to the deflated gas price is
equal to about 2.36, and the elasticity of total discoveries with respect to
the deflated oil price is equal to about 1.83.
These elasticities apply only
to new discoveries and not total additions to reserve;
the elasticities for
additions to reserves are about twice as large since new discoveries contribute
to extensions and revisions.
Thus a doubling of the wellhead price (under the
"regulation" policy) can result in a ten-fold increase in discoveries.
The M-P model shows (in Tables 4A, B, and C) excess demands of about ten trillion cubic feet in 1980 under "cost of service"
6
regulation, excess demand of about
trillion feet in 1980 under "status quo" regulation, and Che elimination of
excess demand by 1979 under the "deregulation" policy.
calling "deregulation" is not really deregulation
— we
Remember that what we are
are not permitting com-
plete decontrol of the wellhead price, but simply allowing price to increase
by a specified amount.
We picked a price increase of 15c per mcf in 1974 (with
further price increases of 3c per annum) because that came close to doubling
the wholesale price by the end of the decade,
with policies of the Cost of Living Council).
is whether that price increase is too small
(and as such would be "in line"
Now the question, of course,
(as suggested by the Khazzoom
formulation) or is too large (as suggested by the Erickson-Spann formulation).
In order to have market clearing
by 1980 with the Khazzoom formulation, it
would be necessary to have a price increase in 1974 of something closer to 50c
per mcf.
in order to have markets just clear by 1980
(with little or no
excess supply) with the Erickson-Spann fonnulation, an additional price increase
in 1974 of
sufficient.
2
or 3c (beyond the 3c per annum price increase) would probably be
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5.
Conclusion
Clearly then, policy proposals for dealing with the natural gas
shortage are very sensitive to the particular model that is used for
exploration and discovery.
The three alternative formulations for ex-
ploration and discovery that we have examined in this paper suggest
very different price policies for dealing with the shortage.
Our own
priors would favor the 15C price increase as being the most reasonable,
but it is at least clear that the whole question of the dynamics of
exploration and discovery is crucial to the design of regulatory policy.
REFERENCES
1.
S.
G. Breyer and P. W. MacAvoy, "The Natural Gas Shortage and the
Regulation of Natural Gas Producers," Harvard Law Review Vol. 86,
No. 6, April, 1973.
,
2.
E.
Erickson and R. Spann, "Supply Response in a Regulated Industry:
The Case of Natural Gas," Bell Journal of Economics and Management
Science Vol. 2, No. 1, Spring, 1971
,
3.
J.
D. Khazzoom, "The FPC Staff's Econometric Model of Natural Gas
Supply in the United States," Bell Journal of Economics and
Management Science Vol. 2, No. 1, Spring, 1971.
,
MacAvoy and R. S. Plndyck, "Alternative Regulatory Policies
for Dealing with the Natural Gas Shortage," Bell Journal of
Economics and Management Science Vol. 4, No. 2, Autumn, 19 73.
W.
4.
P.
5.
National Petroleum Council, United States Energy Outlook
December, 1972.
6.
M.
,
,
Washington, D.C.
Subrahmanyam and K. Challa, "The Oil and Natural Gas Exploratory
Process in the United States: A Framework for Analysis," unpublished
research memorandum, October, 1973.
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