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A combined decline-curve and price analysis of US crude oil production, 1968–1976
A combined decline-curve and price analysis of US crude oil production, 1968-76 Anthony E. Bopp An approach combining decline-curve and price analysis is used to model US oil production over the period I968- 76. The decline curve characteristics of US oil production are captured with time series analysis. Regression analysis is then used to adjust the time series estimates in order to account for price changes. Significant but small price effects are shown to exist in the short run and policy implications of the analytical findings are explored.
A major problem in modelling energy markets and in designing energy policies based on those models is the lack of policy-oriented short-term crude oil production forecasting methodologies. Time series analysis can be used to provide short-term forecasts but such methods are particularly policy insensitive. Econometric models can be constructed but such models rely on notions of equilibrium and long-term adjustments, they can provide less than satisfactory short-term forecasts. The purpose of this paper is to outline and demonstrate a methodology that overcomes these problems: the methodology presented here produces accurate short-term forecasts and is policy sensitive.
Literature A number of studies have dealt with petroleum production. Griffin and Adams* developed an econometrlc/llnear programming model of refineries, modelled in the fashion of the Bonner and Moore refinery representation.* Those studies assume a given level of crude oil as an input to the refinery but make no attempt to forecast production levels. The author is with the Department of Economics, James Madison University, Harrisonburg, VA 22807, USA. Support for this project was provided by the Federal Energy Administration, Office of Oil and Gas, Modeling and Forecasting Division. Of course, errors and opinions are the property of the author, not the Federal Energy Administration or James Madison University. Final manuscript
received 26 June 1978.
0140.9883/80/02011
l-04 802.00
Kennedy,3 the Federal Energy Adrnlnistration,4 and Data Resources I~c,~ have all developed and reported on world and US long-term equilibrium crude oil supply forecasts. These forecasts depend heavily upon price assumptions and hence are policy sensitive. However, they also depend upon achieving an equilibrium in energy markets and are of little vahre ln predicting short-term disequilibrium petroleum production levels. The model presented here is both policy sensitive and predicts well in short-term disequilibrium situations. To accomplish this it relies on the methods of both time series analysis and of econometrics. In one sense it follows Bergmar& in the use of ‘prepared’ time series forecasts. Bergmann prepared regression variables through the use of a simulation model. The present study also uses time series results to prepare an economic regression. Uri7 has tested this procedure in predicting the peak demand for electricity and found it superior to a pure time series approach and to a pure econometric approach. The time series/econometric methodology is shown here to be superior to a pure time series approach in the oil production case, even ignoring the limitations of the time series approach in policy. areas. Further, no shortterm econometric model exists for comparisons ln the case of oil. There are no econometric models for shortterm forecasts because in the short term non-economic variables overwhelmingly account for crude oil production variations and levels, and specifying the nature of the role of the economic variables in an empirically meaningful way is difficult, if not impossible, for reasons explained below.
0 1980 IPC Business Press
A combined declinecurve and price analysis of US crude oil production: A. E. Bopp
A decline-curve based analysis of short-term petroleum production
Table 1. Reel whole&e price index for US crude oil and US domeetic crude oil production levets.
The rationale for using an eclectic. approach to modelling short-term oil production relies on the fact that in the 1970s over 60% of US oil production came from ‘old’ fields, that is, fields producing oil prior to December 1973. Those fields can be expected to produce oil following an engineering decline path, illustrated in Figure 1, at constant prices. Many fields peaked in the 1970-73 period - precisely at the time of higher real prices. Table 1 presents the real wholesale price index for crude oil for the period 196876, and the corresponding production level. The idea developed here is to estimate oil production using time series analysis applied to 1968-73 monthly data in order to estimate a constant price production path. This model is then used to predict monthly oil production over the period 1974-76. Residuals - differences between actual oil production levels and time series predictions - are then used as the dependent variable in a regression with crude oil prices as the independent variable. The rationale for this step is that even in disequilibrium or under regulation higher prices should positively affect production rates - whatever the decline characteristics of the producing fields. In short periods of higher prices production should slightly exceed the time series forecast. Stripper well producers, that is those producing 10 barrels per day or less, and other small producers who do not make long-term production plans will respond to price changes as far as possible. The regression equation captures these marginal short-term production adjustments due to changing prices. Large fields follow programmed production schedules established to meet the long-term objectives of the large integrated oil company. Production rates in these fields do change in response to economic changes but less so in the short run. For forecasting purposes the procedure is reversed. First, crude oil price forecasts are used to estimate residuals - the adjustments to the basic time series forecast. Then the estimated residuals are used to adjust the time series forecast, which is based on constant oil prices.
2
P %
~9.6 eFd 1973pficeIevel declinecurve
.Y
%
,, 1970
1968 1969 1970 1961 1972 1973 1974 1975 1976
0.98 0.99 0.96 1.00 0.96 0.94 1.32 1.41 1.39
9.1 9.2 9.6 9.5 9.4 9.2 8.8 8.6 8.1
The model Box and Jenkinsa indicate that a series such as that shown in Figure 1 can be modelled with a first- or seconddifference process. Following their procedures, first and second differences were performed and autocorrelation functions were computed for each. Since each autocorrelation function quickly died out, a stationary process was indicated in each case. The first-difference model was then pursued on the grounds of simplicity. An inspection of the autocorrelation and partial autocorrelation functions of the first-difference model revealed an autoregressive process since the autocorrelation function of the firstdifference process tailed off and the partial autocorrelation function had a spike at the first lag and was then cut off. A first-differenced autoregressive process was estimated and its autocorrelation function was inspected. The lag corresponding to the last non-zero autocorrelation occurred at lag one indicating a moving average process. Consequently a mixed autoregressive moving average, ARIMA (1 ,l ,l), was estimated.9 Seasonal components were not found to be significant. Although a total of 72 observations were used, there were only 6 observations for each month. This may not be enough to reveal significant seasonality. Thus, the model: (1 - $B)Z, = (1 - BB)u,
_
Parameter 9 e
(1)
Estimate 0.10242 0.09745
1973
Figure 1. Engineering decline curve for US domestic oil production at constant oil prices and actual decline curve.
112
Domestic oil production (million bbl/dey)
was estimated using a maximum likelihood procedure where # is the autoregressive parameter, 8 is the moving average one, B is the backshift operator, Z, is monthly crude oil production, 1968/l to 1973/12, and at is an assumed vector of white noise residuals. The same model with a constant term was also estimated but the constant was not found to be significant. The estimates of the parameters were:
t
g
B(
Y&W
Wholeeele price index of US-produced crude oil/ wholetale price index
f-value 2.84 3.12
The residuals from this model were observed to be very flat. The estimated residuals can be used to calculate the Box-Pierce statistic which is distributed x2 under the
ENERGY
ECONOMICS April 1980
A combined declinecurve and price analysis of US cnuie oil production: A. E. Bopp maintained hypothesis of white noise. A computed ROX-Pierce statistic was 13.9 which was less than the critical x* (22) value of 33.9.rOThus the hypothesis of white noise could not be rejected. By itself this time series model accounted for 93% of the variation in crude oil production over the period 1974-76. As noted elsewhere,‘* Box-Jenkins models can be used to generate excellent forecasts in the short term and excehent explanations of past variations in a given series. The residuals were then used in a second round of estimation where the following equation was estimated: Res=A
+B.Pwd,+e
(2)
where Res is the vector of residuals of first differences of the time series model, A and B are regression parameters, Pcrudeis the Bureau of Labor Statistics index of the wholesale price of crude oil, and e is a vector of regression errors, also assumed to be white noise. Since my aim is to forecast US national crude oil production, only a national crude oil price is appropriate. However, the wholesale price index for crude oil is simply an index of a particular type of Olkahoma crude. Indexation problems here could be severe as Oklahoma crude becomes less typical of national oil, and more importantly, as old oilnew oil ratios of the Oklahoma product deviate from national old-new ratios. Old oil is controlled, while undar the controls new oil can sell at world prices. In 1975,5 million bbl of the US production of 8 million bbl/day were controlled. The regression estimates for Equation (2) are as follows: Parameter A B
Estimate 28.3 -19.4
t-statistic 0.933 -1.39
F statistics on the equation = 3.45 DW= 1.8 Recall that the residuals are actual first differences minus predicted first differences from a time series model. Further recall that the time series model is expected to under predict (see Figure 1) in periods of higher prices. Economic theory suggests that the sign on the price term of this regression equation should be negative - that is, predicted production levels will be adjusted upwards if predicted residuals are adjusted downwards. The above regression bears out economic theory. The value of the Durbin-Watson statistic further bears out the white noise assumption. When the adjusted residuals are used to recompute predicted production values for 1974-76, the new estimated production series accounts for 99% of the variation in crude oil production, and as an estimating equation it can be used to assess policy options in the short run. Ail of the short-run analysis which accompanied President Ford’s 1975 proposals12 and President Carter’s 1977 proposals13 on the energy supply side were constructed only to be consistent with long-term studies. No analytical device was employed except that reported figures for 1976-79 were to be consistent with studies reporting on 1980 and 1985. Consistency in this sense
ENERGY ECONOMICS April 1980
Table 2. US oil production 1966-73. 1974-76, Constant
fwels (thousand
bbl/day).
average average
9369 6623
price time series forecast,
Time series/econometric prices, 1974-76
1974-76
forecast accounting
8693 for higher
Time series/econometric forecast assuming 10% higher than actual prices, 1974- 76
8619
8 624
means that small but positive price effects be demonstrated. The methodology reported here is also consistent in this sense but is based on analytical procedures that take into account short-term nuances of economic and engineering importance.
Forecast results and policy implications Table 2 presents the 1968-73 average US oil production level, the 1974-76 average US oil production level, and some of the results from the foregoing analysis. A number of issues are now explicable. The 1974-76 production level would have been less than the 1968-73 levels almost irrespective of any price increase due to the physical decline characteristics of old fields. The price rises increased production relative to where it would have been at constant prices, not absolutely. Higher prices raised production in the period 1974-76 to an average of 26 thousand bbl/day above what it would have been at constant prices. The computed short-term supply elasticity from this analysis is +0.006. The policy implications of this analysis are crucial. The results show that prices do matter, even in the short run, but that short-term responsiveness is small. Policy makers are prone to look for quick and substantial results from their actions, yet on the oil supply side price response is neither quick nor substantial in the short run. However, long-term results can still be expected to be significant. These points are important since Congress often reviews its acts one or two years after implementation and demands results. Alternatively Congress considers the expected consequences of its acts only two years ahead. This study shows that price policies will have a positive effect on oil production in the near term but that they will not be substantial. Such plans must be judged in terms of their long-term implications. It has, however, been shown analytically that in the short term there are small but positive production effects.
Conclusions Two or three years can elapse between the decision to explore for, drill and eventually produce oil. Large fields face established production schedules based on long-term corporate needs. Hence, a considerable lag exists between
113
A combined declinexurve
and price analysis of US crude oil production:
oil price changes and substantial changes in oil production. Further, existing oil fields face decline curves relating the amount of oil produced to the age of the field. In the short term the decline characteristics of an oil field overwhelm price changes for established fields. This analysis has accounted for the above institutional characteristics of oil production and for the quantum leap in domestic oil prices by modelling oil production in two stages. The first stage captured the decline characteristics of oil fields by applying time series analysis to the 1968-73 stable price period. The second stage used regression analysis to capture the price effects of the 1974-76 period. Positive but small price effects have been demonstrated in the short term. The importance of this demonstration is relevant for US decision makers - Congress - who expect significant effects to rapidly follow their actions. This analysis shows that price effects will increase production in the short run from constant price levels, but not substantially. Long-term programmes should not be cancelJed because they do not ‘appear’ to be working in the short run. Refinements in the analysis could be achieved by applying it to more disaggregated data. Decline characteristics of individual fields could be captured, as well as detailed cost specifications, to enhance the policy sensitivity of the model. This work demonstrates the viability of the eclectic approach and shows that price does matter even in short-run oil production, although not substantially. It also represents a first step in the development of a short-term oil supply model.
114
A. E. Bopp
References 1 J. M. Griffin and F. G. Adams. ‘An econometrilinear programming model of the US petroleum refining industrv’. Journal of the American StatisticaZ Association. Vol67, No 339, September 1972, pp 5422551. 2 Bonner and Moore Associates, US Motor Gasoline Economics, American Petroleum Institute, Washington, DC, 1967. 3 M. Kennedy, ‘An economic model of the world oil market’, The Bell Journal of Economics, Vol 5, No 2. Autumn 1974. pp 540-577. 4 Federal Energy Admiuistration, National Energy Outlook. US Government Printing Office. Washington, DC, 1976. Data Resources Inc, DRI Energy Bulletin, 1975 and 1976. B. Bergmann, ‘Microsimulation and regression’, Econometrica, Vo13, May 1974, pp 948-963. Noel Uri, ‘Forecasting: a hybrid approach’, Omega, the International Journal of Management Science, Vol5, No 4, 1977, pp 463-472. 8 G. Box and G. Jenkins, Time Series Analysis, HoldenDay, San Francisco, 1970, p 178. 9 Charles Nelson, Applied Time Series Analysis, HoldenDay, San Francisco, 1975, p 89. Ibid, p 107. 1’: I. Ibahim and T. Otsuki. ‘Forecasting GNP components using the method of Box-Jenkins’, Southern Economics Journal, Vo142, No 3, January 1976, pp 46 l-470. National Petroleum 12 Federal Energy Administration, Product Susulv and Demand: 1975. US Government Printing Office, Washington, DC, 1975. 13 Executive Office of the President, Energy Policy and Planning, The National Energy Plan, US Government Printing Office, Washington, DC, 1977.
ENERGY
ECONOMICS
April
1980
A major problem in modelling energy markets and in designing energy policies based on those models is the lack of policy-oriented short-term crude oil production forecasting methodologies. Time series analysis can be used to provide short-term forecasts but such methods are particularly policy insensitive. Econometric models can be constructed but such models rely on notions of equilibrium and long-term adjustments, they can provide less than satisfactory short-term forecasts. The purpose of this paper is to outline and demonstrate a methodology that overcomes these problems: the methodology presented here produces accurate short-term forecasts and is policy sensitive.
Literature A number of studies have dealt with petroleum production. Griffin and Adams* developed an econometrlc/llnear programming model of refineries, modelled in the fashion of the Bonner and Moore refinery representation.* Those studies assume a given level of crude oil as an input to the refinery but make no attempt to forecast production levels. The author is with the Department of Economics, James Madison University, Harrisonburg, VA 22807, USA. Support for this project was provided by the Federal Energy Administration, Office of Oil and Gas, Modeling and Forecasting Division. Of course, errors and opinions are the property of the author, not the Federal Energy Administration or James Madison University. Final manuscript
received 26 June 1978.
0140.9883/80/02011
l-04 802.00
Kennedy,3 the Federal Energy Adrnlnistration,4 and Data Resources I~c,~ have all developed and reported on world and US long-term equilibrium crude oil supply forecasts. These forecasts depend heavily upon price assumptions and hence are policy sensitive. However, they also depend upon achieving an equilibrium in energy markets and are of little vahre ln predicting short-term disequilibrium petroleum production levels. The model presented here is both policy sensitive and predicts well in short-term disequilibrium situations. To accomplish this it relies on the methods of both time series analysis and of econometrics. In one sense it follows Bergmar& in the use of ‘prepared’ time series forecasts. Bergmann prepared regression variables through the use of a simulation model. The present study also uses time series results to prepare an economic regression. Uri7 has tested this procedure in predicting the peak demand for electricity and found it superior to a pure time series approach and to a pure econometric approach. The time series/econometric methodology is shown here to be superior to a pure time series approach in the oil production case, even ignoring the limitations of the time series approach in policy. areas. Further, no shortterm econometric model exists for comparisons ln the case of oil. There are no econometric models for shortterm forecasts because in the short term non-economic variables overwhelmingly account for crude oil production variations and levels, and specifying the nature of the role of the economic variables in an empirically meaningful way is difficult, if not impossible, for reasons explained below.
0 1980 IPC Business Press
A combined declinecurve and price analysis of US crude oil production: A. E. Bopp
A decline-curve based analysis of short-term petroleum production
Table 1. Reel whole&e price index for US crude oil and US domeetic crude oil production levets.
The rationale for using an eclectic. approach to modelling short-term oil production relies on the fact that in the 1970s over 60% of US oil production came from ‘old’ fields, that is, fields producing oil prior to December 1973. Those fields can be expected to produce oil following an engineering decline path, illustrated in Figure 1, at constant prices. Many fields peaked in the 1970-73 period - precisely at the time of higher real prices. Table 1 presents the real wholesale price index for crude oil for the period 196876, and the corresponding production level. The idea developed here is to estimate oil production using time series analysis applied to 1968-73 monthly data in order to estimate a constant price production path. This model is then used to predict monthly oil production over the period 1974-76. Residuals - differences between actual oil production levels and time series predictions - are then used as the dependent variable in a regression with crude oil prices as the independent variable. The rationale for this step is that even in disequilibrium or under regulation higher prices should positively affect production rates - whatever the decline characteristics of the producing fields. In short periods of higher prices production should slightly exceed the time series forecast. Stripper well producers, that is those producing 10 barrels per day or less, and other small producers who do not make long-term production plans will respond to price changes as far as possible. The regression equation captures these marginal short-term production adjustments due to changing prices. Large fields follow programmed production schedules established to meet the long-term objectives of the large integrated oil company. Production rates in these fields do change in response to economic changes but less so in the short run. For forecasting purposes the procedure is reversed. First, crude oil price forecasts are used to estimate residuals - the adjustments to the basic time series forecast. Then the estimated residuals are used to adjust the time series forecast, which is based on constant oil prices.
2
P %
~9.6 eFd 1973pficeIevel declinecurve
.Y
%
,, 1970
1968 1969 1970 1961 1972 1973 1974 1975 1976
0.98 0.99 0.96 1.00 0.96 0.94 1.32 1.41 1.39
9.1 9.2 9.6 9.5 9.4 9.2 8.8 8.6 8.1
The model Box and Jenkinsa indicate that a series such as that shown in Figure 1 can be modelled with a first- or seconddifference process. Following their procedures, first and second differences were performed and autocorrelation functions were computed for each. Since each autocorrelation function quickly died out, a stationary process was indicated in each case. The first-difference model was then pursued on the grounds of simplicity. An inspection of the autocorrelation and partial autocorrelation functions of the first-difference model revealed an autoregressive process since the autocorrelation function of the firstdifference process tailed off and the partial autocorrelation function had a spike at the first lag and was then cut off. A first-differenced autoregressive process was estimated and its autocorrelation function was inspected. The lag corresponding to the last non-zero autocorrelation occurred at lag one indicating a moving average process. Consequently a mixed autoregressive moving average, ARIMA (1 ,l ,l), was estimated.9 Seasonal components were not found to be significant. Although a total of 72 observations were used, there were only 6 observations for each month. This may not be enough to reveal significant seasonality. Thus, the model: (1 - $B)Z, = (1 - BB)u,
_
Parameter 9 e
(1)
Estimate 0.10242 0.09745
1973
Figure 1. Engineering decline curve for US domestic oil production at constant oil prices and actual decline curve.
112
Domestic oil production (million bbl/dey)
was estimated using a maximum likelihood procedure where # is the autoregressive parameter, 8 is the moving average one, B is the backshift operator, Z, is monthly crude oil production, 1968/l to 1973/12, and at is an assumed vector of white noise residuals. The same model with a constant term was also estimated but the constant was not found to be significant. The estimates of the parameters were:
t
g
B(
Y&W
Wholeeele price index of US-produced crude oil/ wholetale price index
f-value 2.84 3.12
The residuals from this model were observed to be very flat. The estimated residuals can be used to calculate the Box-Pierce statistic which is distributed x2 under the
ENERGY
ECONOMICS April 1980
A combined declinecurve and price analysis of US cnuie oil production: A. E. Bopp maintained hypothesis of white noise. A computed ROX-Pierce statistic was 13.9 which was less than the critical x* (22) value of 33.9.rOThus the hypothesis of white noise could not be rejected. By itself this time series model accounted for 93% of the variation in crude oil production over the period 1974-76. As noted elsewhere,‘* Box-Jenkins models can be used to generate excellent forecasts in the short term and excehent explanations of past variations in a given series. The residuals were then used in a second round of estimation where the following equation was estimated: Res=A
+B.Pwd,+e
(2)
where Res is the vector of residuals of first differences of the time series model, A and B are regression parameters, Pcrudeis the Bureau of Labor Statistics index of the wholesale price of crude oil, and e is a vector of regression errors, also assumed to be white noise. Since my aim is to forecast US national crude oil production, only a national crude oil price is appropriate. However, the wholesale price index for crude oil is simply an index of a particular type of Olkahoma crude. Indexation problems here could be severe as Oklahoma crude becomes less typical of national oil, and more importantly, as old oilnew oil ratios of the Oklahoma product deviate from national old-new ratios. Old oil is controlled, while undar the controls new oil can sell at world prices. In 1975,5 million bbl of the US production of 8 million bbl/day were controlled. The regression estimates for Equation (2) are as follows: Parameter A B
Estimate 28.3 -19.4
t-statistic 0.933 -1.39
F statistics on the equation = 3.45 DW= 1.8 Recall that the residuals are actual first differences minus predicted first differences from a time series model. Further recall that the time series model is expected to under predict (see Figure 1) in periods of higher prices. Economic theory suggests that the sign on the price term of this regression equation should be negative - that is, predicted production levels will be adjusted upwards if predicted residuals are adjusted downwards. The above regression bears out economic theory. The value of the Durbin-Watson statistic further bears out the white noise assumption. When the adjusted residuals are used to recompute predicted production values for 1974-76, the new estimated production series accounts for 99% of the variation in crude oil production, and as an estimating equation it can be used to assess policy options in the short run. Ail of the short-run analysis which accompanied President Ford’s 1975 proposals12 and President Carter’s 1977 proposals13 on the energy supply side were constructed only to be consistent with long-term studies. No analytical device was employed except that reported figures for 1976-79 were to be consistent with studies reporting on 1980 and 1985. Consistency in this sense
ENERGY ECONOMICS April 1980
Table 2. US oil production 1966-73. 1974-76, Constant
fwels (thousand
bbl/day).
average average
9369 6623
price time series forecast,
Time series/econometric prices, 1974-76
1974-76
forecast accounting
8693 for higher
Time series/econometric forecast assuming 10% higher than actual prices, 1974- 76
8619
8 624
means that small but positive price effects be demonstrated. The methodology reported here is also consistent in this sense but is based on analytical procedures that take into account short-term nuances of economic and engineering importance.
Forecast results and policy implications Table 2 presents the 1968-73 average US oil production level, the 1974-76 average US oil production level, and some of the results from the foregoing analysis. A number of issues are now explicable. The 1974-76 production level would have been less than the 1968-73 levels almost irrespective of any price increase due to the physical decline characteristics of old fields. The price rises increased production relative to where it would have been at constant prices, not absolutely. Higher prices raised production in the period 1974-76 to an average of 26 thousand bbl/day above what it would have been at constant prices. The computed short-term supply elasticity from this analysis is +0.006. The policy implications of this analysis are crucial. The results show that prices do matter, even in the short run, but that short-term responsiveness is small. Policy makers are prone to look for quick and substantial results from their actions, yet on the oil supply side price response is neither quick nor substantial in the short run. However, long-term results can still be expected to be significant. These points are important since Congress often reviews its acts one or two years after implementation and demands results. Alternatively Congress considers the expected consequences of its acts only two years ahead. This study shows that price policies will have a positive effect on oil production in the near term but that they will not be substantial. Such plans must be judged in terms of their long-term implications. It has, however, been shown analytically that in the short term there are small but positive production effects.
Conclusions Two or three years can elapse between the decision to explore for, drill and eventually produce oil. Large fields face established production schedules based on long-term corporate needs. Hence, a considerable lag exists between
113
A combined declinexurve
and price analysis of US crude oil production:
oil price changes and substantial changes in oil production. Further, existing oil fields face decline curves relating the amount of oil produced to the age of the field. In the short term the decline characteristics of an oil field overwhelm price changes for established fields. This analysis has accounted for the above institutional characteristics of oil production and for the quantum leap in domestic oil prices by modelling oil production in two stages. The first stage captured the decline characteristics of oil fields by applying time series analysis to the 1968-73 stable price period. The second stage used regression analysis to capture the price effects of the 1974-76 period. Positive but small price effects have been demonstrated in the short term. The importance of this demonstration is relevant for US decision makers - Congress - who expect significant effects to rapidly follow their actions. This analysis shows that price effects will increase production in the short run from constant price levels, but not substantially. Long-term programmes should not be cancelJed because they do not ‘appear’ to be working in the short run. Refinements in the analysis could be achieved by applying it to more disaggregated data. Decline characteristics of individual fields could be captured, as well as detailed cost specifications, to enhance the policy sensitivity of the model. This work demonstrates the viability of the eclectic approach and shows that price does matter even in short-run oil production, although not substantially. It also represents a first step in the development of a short-term oil supply model.
114
A. E. Bopp
References 1 J. M. Griffin and F. G. Adams. ‘An econometrilinear programming model of the US petroleum refining industrv’. Journal of the American StatisticaZ Association. Vol67, No 339, September 1972, pp 5422551. 2 Bonner and Moore Associates, US Motor Gasoline Economics, American Petroleum Institute, Washington, DC, 1967. 3 M. Kennedy, ‘An economic model of the world oil market’, The Bell Journal of Economics, Vol 5, No 2. Autumn 1974. pp 540-577. 4 Federal Energy Admiuistration, National Energy Outlook. US Government Printing Office. Washington, DC, 1976. Data Resources Inc, DRI Energy Bulletin, 1975 and 1976. B. Bergmann, ‘Microsimulation and regression’, Econometrica, Vo13, May 1974, pp 948-963. Noel Uri, ‘Forecasting: a hybrid approach’, Omega, the International Journal of Management Science, Vol5, No 4, 1977, pp 463-472. 8 G. Box and G. Jenkins, Time Series Analysis, HoldenDay, San Francisco, 1970, p 178. 9 Charles Nelson, Applied Time Series Analysis, HoldenDay, San Francisco, 1975, p 89. Ibid, p 107. 1’: I. Ibahim and T. Otsuki. ‘Forecasting GNP components using the method of Box-Jenkins’, Southern Economics Journal, Vo142, No 3, January 1976, pp 46 l-470. National Petroleum 12 Federal Energy Administration, Product Susulv and Demand: 1975. US Government Printing Office, Washington, DC, 1975. 13 Executive Office of the President, Energy Policy and Planning, The National Energy Plan, US Government Printing Office, Washington, DC, 1977.
ENERGY
ECONOMICS
April
1980