Published in Energy Economics 30 (2), 303-320
6. Estimation and testing
As described in Section 5, our econometric model consists of two parts. First, we have the long-term structural relation between drilling efforts and the
model. Our choice of oil price denomination also secures consistency of measurement in our econometric model – as the left-hand variable is a true volume term.
19 This resource estimate has been subject to revisions (including re-statements), due to technological progress, new information and changes in economic conditions. However, the NPD does not provide detailed historical information on these revisions. We therefore have to
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explanatory variables, as represented by Equation (6). Second, we have the econometric specification of the error-correction model, to capture short-term dynamics and sluggishness. This approach allows a separation between temporary and persistent (structural) effects, as well as an explicit representation for the adjustment process towards the structural equilibrium.
All estimations are performed with fixed-effects panel data procedures, whereby regional dummy variables are included and suppressed through normalisation around sample means (DVLS).20 Further, our estimation strategy follows a general-to-specific approach, starting out with a full-blown model, including all explanatory variables. We have tested for a variety of lag specifications, and have retained variables and lags that could justify a position in the model based on estimated coefficient qualities and more general model diagnostics.
Before we present the estimates for the structural and dynamic models, we include a note of caution with respect to co-integration. Our hypothesis is that the structural equilibrium of our exploration model can be described as a cointegrating vector, and we would like to specify a dynamic representation of the relationship as an error-correction model. A critical requirement in this respect is that our structural equilibrium is indeed characterised by co-integration.
Strictly speaking, our data set is a panel – consisting of three time series over 40 years. A consensus is yet to be reached on how to test for co-integration in heterogeneous panel data. Some tests have been developed (e.g., Levin and Lin 1993; Banerjee 1999) for balanced panels, but challenges remain unsettled for our data set due to varying starting points for our time series, as well as several gaps.21 We have therefore tested the stationarity properties of all our explanatory variables separately for each of the three regions, applying both Dickey-Fuller and Phillips-Perron procedures and test statistics.22
20 Our approach is a dynamic econometric model for a panel data set, with large T and small N.
Modern estimation procedures for dynamic panel data models often involves the GMM estimators introduced by Arellano and Bond (1991). However, as pointed out by Bond (2002), fixed-effects least squares estimates are consistent in the case of large T panels.
21 For the first 15 years of our data period (1965-1979), regular drilling took place only in the North Sea. In the Norwegian Sea, exploration wells have been drilled every year since the opening of the area in 1980. The Barents Sea was also opened in 1980, but since 1994, exploration activities in this northern region have been interrupted by both voluntary and regulated interludes (cf. upper right-hand pan in Figure 3).
22 Dickey and Fuller (1981) introduced a popular procedure to test that a variable follows a unit-root process. The null hypothesis is that the variable is contains a unit root, with a stationary data-generating process as the alternative. With the augmented Dickey-Fuller test, a
Detailed results from these stationarity tests are presented in Appendix 2, including results also for the aggregate series for the total NCS. The null of non-stationarity is rejected on a 99 per cent significance level for all dependent variables (well categories) in all the three regions, as well as for the respective aggregate series for the total NCS. Non-stationarity is also rejected for the explanatory variables, on a 99 per cent significance level in 11 out of 12 cases. These results suggest that we have the necessary support for our specification of error-correction models for NCS exploration efforts.
We now regress the change in drilling activity (∆lndt) against the change in the oil price (∆lnpt), lagged discoveries (∆lnrest), lagged changes in available exploration acreage (∆lnacrt), as well as lagged levels of all explanatory variables (cf. Equation [7]). Full-blown estimated versions of Equation [7]
with all explanatory variables are presented in Appendix 3. A time trend was also included in our initial estimations (cf. Appendix 3). However, a position for this variable could not be justified in our preferred models.23
In our general-to-specific estimation approach, the models have been narrowed down, based on parameter inference and general model diagnostics.
Preferred estimates for the error-correction models are presented in Table 1, with p-values of the respective estimates in brackets. Parameter inference is
regression is run of the differenced variable on its lagged level, as well as its lagged differences (sometimes also with a time trend):
t j t j j t
t x x v
x = + +∑ +
∆ γ0 γ1 −1 γ2 − .
A significant negative parameter estimate for γ1 will be supportive of stationarity in ∆xt, implying that the variable expressed in levels (xt) is integrated of degree 1 (I(1)). The Dickey-Fuller test accounts for serial correlation by use of additional lags of the first-difference variable. Phillips and Perron (1988) introduced a modified variant of this test, whereby a non-parametric correction of the standard errors is applied to capture serial correlation of the above regression.
23 Various categories of seismic surveying activity have also been tested as proxy variables for technological progress in our drilling equations – without success. As argued by a number of authors (e.g, Forbes and Zampelli 2000, 2002; Managi et al. 2005), technological progress clearly plays an important role for the productivity of oil and exploration. The development of new technologies and competence has contributed to more efficient exploration efforts, also on the NCS. New technologies have enabled the companies to drill deeper and more advanced wells, increasing their reach and precision. To this end, technological progress has also caused NCS success rates to increase over the years. However, the focus of our econometric model is not on productivity (success), but on activity (effort). The absence of a time trend in our estimated drilling equations is therefore not an argument that technological progress is
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based on robust standard errors, to adjust for the potential bias arising from heteroskedasticity or remaining serial correlation in the residuals.24
When Phillips Petroleum discovered the first huge oil field (Ekofisk) on the NCS back in 1969, estimates for recoverable oil and gas reserves on the Norwegian Continental Shelf were multiplied 15 times from one year to another. With the log of cumulative discoveries as one of our explanatory variables, the Ekofisk discovery creates a disturbing outlier in our data set.
We have therefore introduced a dummy variable (Dt
res) that takes the value 0 for years before 1970, and 1 for all years after 1970. The change in this variable takes a highly significant parameter estimated in our models, and improves the quality both on the parameter estimates and the general model diagnostics.
Table 1 shows significant short-term effects on drilling efforts from all our explanatory variables, whereas longer-term effects are restricted to the oil price and cumulative oil and gas discoveries. According to R2, our models account for 50-64 per cent of the variation in the data set.25 Test statistics for joint parameter significance are robust, and the null hypothesis that all parameters equal zero is rejected on a 99 per cent significance level for all three models. Observe that that the error-correction coefficient is highly significant for all models, lending additional support to our hypothesis of co-integration in NCS exploration efforts. The estimated error-correction coefficients also suggest a very rapid adjustment process, as they indicate that 84 to 89 per cent of last year’s deviation from the structural equilibrium is eliminated every year. Short-term oil price effects are significant only for appraisal wells, whereas a significant persistent oil price effect is detected also for wildcat wells.
24 Estimated standard errors are based on the so-called Huber-White or Sandwich ariance estimator (Huber 1967; White 1984).
25 This may not seem very impressive. However, NCS activity is very volatile, both over time and across our three regions. According to rig count data from Baker Hughes over the last 25 years, average NCS rig activity is below 50 per cent of corresponding activity on the UKCS, and less than 15 per cent of the corresponding activity in the Gulf of Mexico. These larger provinces also show less relative variation in drilling and rig activity. It is therefore no big surprise that the explanatory power is lower for our models on NCS data set than for some of the previous time series studies on US and UKCS data.
Table 1. Estimated error-correction models for NCS exploration efforts
E&A wells Exploration wells Appraisal wells Estimated coefficients a)
Intercept 0.51*
Derived structural coefficients (cf. Equation [9])
ln pt 0.25**
Efforts and efficiency in oil and gas exploration