This section reports our estimation results for the TV and QL specifications of the average finding cost functions over the period 1967-90.⁽¹⁸⁾,⁽¹⁹⁾ The results for nonassociated natural gas are shown in Table 2; those for crude oil are in Table 3. Three different estimation techniques are considered: ordinary least squares (OLS) and instrumental variables (IV) regressions, which are discussed in this section, and a cointegration approach, discussed in Section IV.

Each model was first estimated using OLS. Residual autocorrelation and partial autocorrelation functions, and Ljung-Box statistics for serial correlation up to order 10, were then examined to identify a parsimonious ARMA specification for the error process. Each model was re-estimated allowing for the ARMA error process.

The OLS estimates are potentially vulnerable to simultaneous equation bias. Presumably average cost and the quantity of reserve additions are jointly determined. Moreover, the stochastic nature of discoveries implies that output in (2) is really expected output. By including actual reserve additions as a regressor in the average cost function, there is sure to be an errors-in-variables or measurement bias problem. One might also argue that the adoption of new technologies is jointly determined with cost and quantity. The opposing argument that technology in widespread use is largely predetermined because it takes time to put the new techniques in place also seems plausible a priori.

To address potential simultaneity bias in the OLS estimates, instrumental variables (IV) estimates are also shown in Tables 2 and 3. The instruments include the current and lagged values of the log of the real price of natural gas or oil [in Tables 2 and 3, respectively],⁽²⁰⁾ and lagged values of the dependent and all right-hand-side variables. Cumulative past reserve additions is also used as an instrument, as it is predetermined.

First, some general comments on the regression diagnostics in Tables 2 and 3. In all cases, the Ljung-Box Q statistics are statistically insignificant for various joint hypotheses involving serial correlation regardless of the number of lags chosen. This reflects the fact that error processes were modeled carefully to eliminate any serial correlation in the residuals. We report only the Ljung-Box Q(6) case to save space. To assess whether the resulting innovations in the error process are normally distributed, the Jarque-Bera statistics are reported. Generally speaking the innovations in the QL models appear to be normally distributed, while those in the TV specifications do not.⁽²¹⁾ All estimated equations reported have reasonable goodness of fit, with adjusted R-squared statistics ranging from .71 to .79.⁽²²⁾

Turing to the parameter estimates for the various average finding cost functions for natural gas in Table 2, columns 2 and 3 show the OLS and IV estimates for the TV model. Although the technology variable, lnN, has the expected negative regardless of the estimation method, it is not statistically significant. The IV estimate of the coefficient on LnQ is significantly negative, while the OLS estimate is statistically insignificant. The estimated depletion effect in the TV model is more problematic, being statistically insignificant and having the "wrong" sign in the OLS case.⁽²³⁾ In short, the TV model for natural gas does not fit the U.S. data well over the post-1966 period.

The estimated coefficients in the QL model are considerably better. Signs of the estimated coefficients are those predicted by the theory. There is a significant resource depletion effect, implying that higher past discoveries shift the current average cost function upward. Most interestingly, our technology variable (N) is highly significant in the QL model, regardless of estimation technique. Improvements in technology are associated with reductions in average finding costs for natural gas, as one would expect a priori.⁽²⁴⁾

Table 3 replicates the foregoing econometric analysis for crude oil. Because of a huge spike in the reserve additions series in 1970, reflecting the Prudhoe Bay find, a dummy variable that equals one in 1970 and zero otherwise (DUM1970), was included in the regressions. The estimated coefficients on the technology variables (N or LnN) are negative throughout, but insignificant. In the TV model, the cumulative depletion effect is insignificant and has the "wrong" sign. As was the case for natural gas, the residuals in the TV specification fail the Jarque-Bera normality test. Discouragingly, the bulk of the explanatory power of the equation is attributable to the AR(1) error process and DUM1970, not to the regressors suggested by (the TV variant of) the resource theory. In the QL model, in contrast, the depletion effect has the expected positive sign, but is statistically significant only at the 10% level.

The Impact of Technology in Offsetting Increased Scarcity

It is a common conjecture in the resource literature that ongoing technological improvements have largely, or at least partially, offset increasing resource scarcity. This hypothesis can be addressed for natural gas and crude oil, in turn, by carrying out some simple dynamic simulations using the models estimated in Tables 2 and 3. Given the superiority of the QL model relative to the TV model, we focus on the IV estimates of that model.

First consider natural gas. Suppose that the time path of annual reserve additions ("output") followed its historical pattern over the 1967-1990 sample period and then remained constant at its median level⁽²⁵⁾ through the year 2010. This hypothesized pattern of discoveries, of course, implies a calculable resource depletion effect as the "cumulative past production" variable rises. Two scenarios for technological change are compared. In the first denoted "with ongoing tech. change," diffusions are assumed to occur at their actual rate in-sample through 1990 and are then constant at their historical median rate of four diffusions/year through the year 2010. In the second scenario, labeled "with no tech. change after 1973", technology rises along its historical time path until 1973 and then is constant thereafter (by setting NEWTECH=0).

The "no tech. change" scenario must be interpreted carefully. Without technological improvements, reserve additions might have followed a very different time path than the historical series. Theory suggests that reserve additions could be higher or lower under a scenario with no technological progress!⁽²⁶⁾ To avoid these difficulties due to the endogeneity of the production of reserve additions, our simulations keep this 'output' (lnQ) on its historical path and ask: what would the average finding cost have been to prove up reserves in a way that matched the historical time path, but without any technological improvements?

Fig.3 shows simulated time paths for average cost based on the QL model for the with-tech and no-tech scenarios, respectively, from 1973 to 2010, as well as historical series for average cost over the 1967-90 period. The model predicts an ongoing decline in average finding cost of natural gas from the mid-1980s through the year 2010 if both technological improvements and discoveries (LnQ) continue at their historical rates. In the scenario where there is no technological progress after 1973, the model simulation shows steadily rising average finding costs.

What was the net impact of ongoing technological change on the average finding cost for natural gas? Over the 1970-89 period (omitting the sharp drop in 1990), actual average costs rose at an average annual rate of 2.3% percent in real terms. The with-tech simulation predicts a slightly higher average growth rate of 2.7% per year. In contrast, the no-tech scenario predicts that average finding costs would have had to rise at an average rate of 22.1% per year to prove up reserves at the historical rate without technological change. Clearly, this supports the conjecture in the resource literature that technological change has been instrumental in ameliorating the effects of increasing resource scarcity over time.

Fig.4 reports analogous "with tech" and "no-tech" simulations for crude oil. The average finding cost of crude oil bounces around with little perceptible trend under the two scenarios. From 1969 to 1988, the average finding cost rose at an average rate of 0.7% per year in real terms. The model simulation for crude oil in the with-tech case predicts a slight decline of  -0.4%/year on average. In the no-tech case, however, the simulation predicts a rise in average finding costs of +0.7% per year.

Comparing Figs. 3 and 4, an interesting conclusion emerges: technological change appears to have had a more significant impact reducing the E&D costs for natural gas than it has had for crude oil.⁽²⁷⁾

A priori, one would not expect average finding cost, C_t /P_t Q_t , to be stationary over time if it depends on a diminishing stock of an exhaustible natural resource. Of course, technological improvement can have a countervailing effect, but it would be a fluke indeed if ongoing resource depletion and technological change just offset each other period after period. In short, average finding cost is likely to be a nonstationary variable.

Variables capturing the cumulative depletion effect and the level of technology are almost certain to contain unit roots as well. Typical proxies for the depletion effect are cumulative past drilling effort or cumulative past reserve additions (see, e.g., Livernois (1988), Pindyck (1978), Uhler (1979)). Suppose drilling effort in period t equals X_t. Then cumulative past drilling effort, by definition, is:

The variable capturing the cumulative level of technology in (2) has the same feature. If the new diffusions series, NEWTECH, is mean stationary, the cumulation of such diffusions, N_t , will almost surely have a unit root. Technically, this may or may not be the case for lnN_t , the log transformation of the technology variable used in the TV model (because it is not a linear transformation). Nevertheless, an empirical test may be unable to reject the unit root hypothesis for lnN_t if it roughly approximates N_t .

Table 4 reports augmented Dickey-Fuller (ADF) tests for the presence of a unit root in each of our series. I(1) indicates integrated of order one; none of the series had more than one unit root. In all ADF regressions, the general-to-specific (GTS) methodology was to determine (i) the number of lags of the dependent variable included in the ADF regressions⁽²⁹⁾ and (ii) whether to include a deterministic time trend, a constant, or both (neither). The ADF tests confirm that the logs of real average finding costs for both gas and oil (LRACGN and LRACO) are nonstationary, as the intuition above suggested. The unit root results on reserve additions and cumulative reserve additions are at odds with the theoretical predictions above. In particular, the cumulative reserve additions series for both gas and oil seem to be better characterized as trend stationary processes rather than unit root with drift.⁽³⁰⁾ This is inconsistent with the reserve additions series being I(0), which is the case for gas, or borderline I(1), as for oil. Consistent with the finding that NEWTECH is I(0), the ADF tests do confirm that the cumulative technology variable, whether in levels or log-levels, is I(1).

While the presence of nonstationary variables calls into question past estimates of finding costs in the resource literature, it also represents an opportunity. If there is a long-run relationship of the form in (11) or (13), the variables in these relationships should be cointegrated. Moreover, using Johansen's vector error correction specification, it will be possible to get consistent estimates of the long-run equilibrium relationship (the cointegrating equation (CE)), and capture short-run dynamic interactions among the variables. Given the highly uncertain nature of the discovery and technology adoption processes, this flexibility is especially valuable. The approach also produces consistent estimates of standard errors, thereby permitting hypothesis testing when the underlying data are I(1) series.

The ECM has an additional advantage: it treats all of the variables considered as potentially endogenous. There is no need to use instrumental variables estimation to cope with the simultaneity bias (discussed in Section III) that would be an issue if all variables were stationary. (See Hamilton (1994, p.-.))

We carried out Johansen trace tests for cointegration using the vectors of four variables in the TV and QL models, respectively, i.e., y [LnAC, LnN, LnQ, Ln(sumQ] or y [LnAC, N, LnQ, Ln(sumQ]. This was done for both natural gas and crude oil. In all four cases (TV-Gas, QL-Gas, TV-Oil, QL-Oil), the null hypothesis of no cointegration is easily rejected at the 1 percent significance level.⁽³¹⁾ The following ECM was then estimated (with either N or LnN, depending on the model):

Recall that y_t in the ECM in (16) is a vector. Thus, the four-equation system includes separate dynamic error correction equations for the change in the log of average finding costs, changes in discoveries, changes in the depletion variable, and changes in technology. As mentioned above, the ECM treats all variables as potentially endogenous. When using the ECM to forecast, it provides time paths for all four variables. We focus on the ECM forecasts -- in-sample forecasts from 1973 and out-of-sample forecasts from 1991-- of the log of real average finding costs and the (log or level) of the technology variable. Such forecasts are called "with tech. change from 1973 [1991]" in Figures 5-8.

To examine the impact of technological change on average finding costs, these forecasted time paths are compared to a scenario with "no tech. change from 1973 [1991]" where the change in technology equation from the ECM is replaced by: D(LnN_t) = 0 or D(N_t) = 0. This change in specification for the technology equation then affects the forecasted time path for average finding costs, both directly and indirectly through the change in discoveries and depletion equations in the ECM. Thus, using the ECM for counter-factual simulations, it is no longer necessary to consider scenarios where the annual level of discoveries remains unchanged, as assumed in Section III.

Figures 5 and 6 show the impact of ongoing technological change on the average real finding cost for nonassociated natural gas using the QL and TV models, respectively. Four scenarios (plus the historical series) appear on each graph: (1) ongoing (ECM-forecasted) technological change from 1973 versus (2) the simulation with "no tech. change after 1973"; and (3) ongoing (ECM-forecasted) technological change from 1991 versus (4) the corresponding "no tech. change from 1990" scenario. See Panel A in the Figures for the alternative time paths for technology; panel B shows the consequences for long-run average finding costs.

Figures 7 and 8 replicate the exercise for crude oil. Notice that the forecasted technology paths are very quite similar regardless of whether they are obtained from the gas or oil ECMs. This is reassuring. (Compare the forecasts for N_t in Fig. 5A (gas) to Fig. 7A (oil), or those for lnN_t in Fig. 6A (gas) to Fig. 8A (oil).) Comparison of the corresponding with and without technological change scenarios shows the extent of technology's impact on finding costs: i.e., (1) vs. (2), or (3) vs. (4). The favorable impact of ongoing technological change on the average finding costs is larger for gas than oil for the U.S. industry, especially if the TV model estimates are used. This is consistent with the results in Section III.

1. CONCLUSIONS

This study provides arguably the first analysis of the extent to which ongoing technological change has offset the effect of ongoing depletion on the costs of finding additional reserves of natural gas and crude oil. In the process, a new index of technological change for exploration and development (E&D) activities was developed. The approach identifies largely successful technological developments at the time they come into widespread use, unlike other proxies for technological change such as R&D spending or patent activity. Technological diffusions in each year provides a measure of the rate of technological advance. Their cumulative total is a proxy for the level of technology.

Using this measure of technology in estimating average finding cost functions for additional natural gas and crude oil reserves, the effects of depletion and technological advance are isolated. Counter-factual "no technological change" simulations based on the cost functions suggest that technological change played a major role in allaying what would otherwise have been a sharp rise in the finding cost of additional natural gas reserves. The impact of technological change on finding costs for crude oil is more modest. In sum, our analysis provides empirical evidence of the common (but untested) claim in the natural resource literature that technology has largely offset increasing resource scarcity -- at least for the U.S. petroleum industry studied here.

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The approach to developing a series of technology diffusions (described in greater detail in Moss (1993)) was to collect information from reliable and reputable industry sources and focus on the identity and dates of technological developments that fit the selection criteria. Readily available technical and trade literature was relied on for this purpose. Although access to the full range of technical literature that would support the NPC-type study was impossible, literature reviewed included, in particular, the Oil and Gas Journal (O&GJ) and Petroleum Engineer International (PEI). O&GJ and PEI consistently track technological developments through technical articles, interviews with industry experts and general reporting.

Developing the series of technology diffusions consisted of four steps: (i) data collection; (ii) sorting collected materials by category; (iii) compiling chronologies from sorted materials; and (iv) dating the diffusions. In the first step, we located articles (by title or, when titles were not useful, by abstract, introduction, or conclusion) in weekly and monthly issues of O&GJ and PEI, respectively, pertaining to new equipment, techniques or methods, mathematical models, effects of technology on costs, or research and development efforts. As our focus was on exploration and development (E&D), articles on production, processing, or transportation technology were excluded from the search. In identifying articles in the data collection process, we reviewed journals in chronological order to detect sequences of reports on technological developments. This practice enhanced the probability of collecting information that would be useful in sketching out histories of technologies.

The second step was to sort and code the resulting collection of articles, first by year, then by technology type, including: equipment, methods and techniques, R&D and general. The next sort identified and arranged in chronological order articles for various categories of discovery technology. These categories included, for example: drill bits, seismology, deep drilling feasibility, fixed (i.e., bottom-supported) drilling structures, floating drilling structures, measurement while drilling, pipe handling equipment, horizontal drilling and underwater wellheads.

In the third step, chronologically arrayed articles for each category of technology were used to record the date and description of the developments contained therein. An important objective of this task was to record key phrase descriptions of developments to be able to piece together the history of a particular technology (if possible) and to determine the identity and dates of developments that qualified as new diffusions more accurately. Key phrases tended to recur consistently in articles, including, for example: funding for experimental (prototype) technology programs; initiation or results of an experimental technology program; field testing of an experimental technology; first commercial use of a technique, process, or piece of equipment; the date a process or piece of equipment became economical or came into full commercial application; trends in the use of and development of equipment or techniques; forecasts regarding the replacement of existing equipment or techniques with new methods; proposals to develop particular technologies; introduction of new techniques or equipment; and improvement in existing technologies.

In general, we erred on the side of including too much information (i.e., redundant articles) in the chronologies. At the same time, however, articles that were not helpful in developing a picture of the advancements that occurred in each category of E&D technology were discarded.

The final step was to use each of the chronologies developed in the third step to select those technologies that appeared to be in the diffusion stage. Fixing the date when a given technology had reached the diffusion stage resulted from conservative judgement--i.e., technologies that had no previous reference were excluded unless a summary article specifically discussed the history of that development. Generally, the date when various technologies were coming into widespread use in the industry could be identified, although pinpointing the exact year was not always possible. In those cases, we used our best judgement and erred on the side of setting the date later, as opposed to earlier in time.

Not for Publication; Available on Request

APPENDIX II:

CALCULATING CRUDE OIL AND NATURAL GAS FINDING COSTS

Finding costs are measured either as total cost or average per thousand cubic feet (mcf) of added natural gas reserves and average per barrel of added crude oil reserves. American Petroleum Institute (API) data on E&D expenditures for the U.S. petroleum industry are the starting point for deriving finding costs. API has historically reported annual capital and operating expenditures for E&D and production. Expenditures common to both E&D include drilling and equipping wells, acquiring acreage (undeveloped in the exploration stage and producing in the development stage), and overhead and general and administrative. Exploration expenditures also include land department leasing and scouting; geological and geophysical; lease rental and test hole contributions. Development expenditures also include improved recovery programs and lease equipment.

Some of the expenditures mentioned above are not strictly associated with the finding process and are excluded from total finding expenditures. For example, improved recovery programs focus primarily on recovering more oil from existing reservoirs through steam-, water- or gas-flooding. As such, improved recovery is better considered part of producing petroleum reserves.

Total E&D spending is allocated to oil and gas using, respectively, the proportion of gas and oil well completion costs attributable to oil and the proportion of gas and oil well completion costs attributable to gas, as in Adelman (1991). This approach has the advantage of implicitly allocating dry hole expenditures proportionately to gas or oil. Allocating observed exploration expenditures between gas and oil exploration is necessarily somewhat arbitrary. For alternatives to the approach used here, see Livernois and Ryan (1989).⁽³²⁾

Reserve additions are available from the American Gas Association (AGA) for the period 1959 to 1980 and the Energy Information Administration (EIA) from 1981 to 1990.⁽³³⁾ Reserve additions prior to 1966, however, are reported differently than those after 1966. First, reserve additions for natural gas prior to 1966 are reported for the sum of associated and nonassociated gas. We know of no good method for allocating total gas reserve additions between associated and nonassociated gas. Second, as discussed below (see also footnote 17) we exclude "revisions"--one of the four components of reserve additions--from total reserve additions in calculating finding costs. Prior to 1966, however, reserve revisions are not reported individually but are aggregated with "extensions," another category of reserve additions. We know of no good method for disaggregating revisions from the data prior to 1966. As a result of these data limitations, reserve additions data prior to 1966 are excluded.

Reserve additions for crude oil and natural gas accrue from four different sources: extensions to existing fields, discoveries of new fields, discoveries of new reservoirs in old fields, and net revisions of previously estimated reserves.⁽³⁴⁾ The last of these components--reserve revisions--requires some explanation. Reserve revisions (increases and decreases) in a given year reflect corrections associated with the difference between estimated production for the previous year and actual production in that year due to changes in gas and oil prices (i.e., post-production information) (API (June 1970)). Reserve revisions also result from new information gleaned from development drilling and improved recovery techniques.

Including (or not including) net revisions in total reserve additions is a possible source of measurement error in calculating finding costs. For example, revisions stemming from improved knowledge gained through development drilling are a legitimate product of the finding process and should be included in reserve additions. But revisions stemming from changes in prices do not result from finding activities, so it would be incorrect to include them. The same reasoning applies to revisions from improved recovery programs, which are not a part of the finding process.⁽³⁵⁾ Because information on the magnitude of the two components of revisions is lacking, potential measurement error cannot be eliminated. We can test, however, for relationships that would indicate the prevalence of a particular component.

For example, revisions associated with post-production information are probably strongly correlated with demand in any given year.⁽³⁶⁾ Therefore, a correlation (albeit weaker) between total net revisions and demand might indicate the relatively greater influence of revisions attributable to post-production information. In our initial work on natural gas, for example, we obtained a correlation coefficient between net revisions of natural gas and gas consumption over the period 1966 to 1991 of -.64. That consumption and net revisions are correlated does not establish a "bright line" for deciding to include or exclude net revisions; but it supports the notion that revisions stemming from post-production information may account for a relatively larger percentage of total net revisions. On this basis, net revisions are excluded from total reserve additions.

Table 1A presents average finding costs for nonassociated natural gas and crude oil in columns 7 and 9, respectively. It also reports the breakdown of petroleum E&D expenditures into drilling (column 2) and geological and geophysical (G&G) (column 3). A number of things are worth noting. First, spending for drilling comprises the bulk of total finding expenditures.⁽³⁷⁾ This is noteworthy because drilling activities are one of the most technology-intensive areas of the finding process, so the effects of technological progress in this area strongly influences finding costs. For example, the petroleum industry made significant advances in drilling techniques and materials, particularly after 1960. While G&G accounts for a much smaller percentage of total E&D expenditures, notable technological advances (e.g., seismic technology) have likely had significant effects on E&D productivity and cost.

Second, average finding costs for natural gas and display the effects of the drilling "boom" in the late 1970s and early 1980s. Costs increased during this period as a result of rising prices for seismic and drilling services, drilling materials and rig rentals. This was due largely to intensive exploratory activity spurred-on by high regulated prices for natural gas (particularly for deep gas) under the Natural Gas Regulatory Policy Act (NGPA) of 1978. This is important because for constant levels of E&D spending, higher prices will yield more reserves, since changes in reserves are, in part, a function of price--an effect observed from about 1977 to 1985. Finally, the familiar run-up in oil finding costs due to international oil market and related gas market dynamics can also be observed during the late 1970s and into the 1980s.

Figures 5A and 5B:

Nonassociated Natural Gas: Quality Ladders Model

Figures 6A and 6B:

Nonassociated Natural Gas: Technology Varieties Model

Figures 7A and 7B:

Crude Oil: Quality Ladders Model

Figures 8A and 8B:

Crude Oil: Technology Varieties Model

1. Epple (1975, pp. 63-65; see especially equation 5-4) shows that, more generally, the theory predicts that price minus marginal cost rises at the rate of interest.

2. Our analysis considers only reserve additions of nonassociated gas (i.e., gas not occurring in association with oil) to avoid the problem of joint costs.

3. Proved reserves are, by definition, the portion of the identifiable resource base that can be economically extracted using current technology.

4. Survey evidence suggests that firms in the majority of R&D-intensive industries view patents as relatively ineffective in "capturing and protecting the competitive advantages of new and improved production processes." (Levin (1986)).

5. For example, computer technologies that precipitated the development of 3-D seismic--a technique that reveals more about subsurface geology and potential hydrocarbon reservoirs--has probably had a relatively greater impact on productivity than other, smaller developments. Improved seismic techniques steer firms toward drilling in areas with a higher probability of containing petroleum and away from more risky investments that might have been made had advanced technology been unavailable. Other technological developments also reduce costs, but at a later, less risky stage in the finding process.

6. Exploration gravity measurements are a method for detecting the local variations in the earth's general gravitational field produced by the subsurface geology. The composition of rocks affects the gravitational field, i.e., the less compact the rock, the less its effect. Variations or anomalies are contoured on a map and provide evidence of geologic structures such as faults or other reservoir traps.

7. Past studies of technological activity have found clustering effects in technological developments over time (Schmookler (1966) and Sahal (1983)).

8. The results for the 1970-1990 period, which for data availability reasons is used in estimating cost functions in Section III, are very similar.

9. Chapters 1 and 2 of Uhler's (1979) well-known study detail this approach. He cautions, however, that "the use of crew-weeks as a measure of geophysical effort contains some severe limitations. In view of the advances in geophysical technology, which increasingly makes use of electronic and computer equipment, a crew-week of geophysics today is not the same as a crew-week twenty years ago...An improved measure of geophysics input would involve technology-adjusted crew weeks but since data on technological change in this activity are not available such an adjustment cannot be made so that in this study unadjusted crew-weeks will be used." (p.27) In effect, our study has done what Uhler suggests as the desired strategy: it accounts separately for the quantities of crew effort and drilling effort and the improvements in the efficiency of these inputs due to technological advances.

10. The new technological processes are presumably designed and produced by a profit-maximizing research and development firm (as in Romer (1990). As the list of computer technologies in Table 1 suggests, some of the new technologies result from R&D within the petroleum sector; others come from other sectors of the economy.

11. In the non-resource literature on cost and/or production functions, a similar variable is often used to capture the "learning-by-doing" or "learning curve" effect. Thus, one might want to think of the cumulative past output variable in (2) as picking up the net impact of two separate effects: (i) the "resource depletion" effect, which should impact output negatively, and (ii) the "learning curve" effect, which should impact output positively.⁽¹²⁾

12. /On the former, see Pindyck (1978); on the latter, Berndt (1991, Ch. 3).

13. This specification embodies the expectation that reserves will be discovered in order of their quality and ease of accessibility.

14. See Grossman and Helpman (1991, Chapters 3 and 4).

15. Although this assumption is standard in theoretical work, it appears hard to defend (except for the absence of workable alternatives) when one looks at the heterogeneity of actual technological diffusions.

16. Following Uhler (1979), total exploratory drilling costs are divided by footage drilled to get the unit cost of drilling p_Dt ; total G&G expenditures are divided by crew-months of G&G activity to get p_Gt .

17. This statement of the quality ladders model is adapted from Kortum and Lach (1995).

18. The estimation period is unfortunately limited because reserve additions data prior to 1966 do not disaggregate reserve "revisions" from the other components of reserve additions. Revisions and 'extensions' are lumped together. While to some extent revisions reflect information gained through development drilling, they also reflect, in large part, a reassessment of the economic viability of already discovered reserves as market prices change. This component of revisions does not reflect "output" from the E&D process and supports the notion that reserve revisions should be excluded from the remaining components of reserve additions, as is done for the post 1966 data we use (see Appendix II).

19. Natural gas wellhead prices in the U.S. were regulated from 1954 through the early 1990s. The Natural Gas Policy Act (NGPA) of 1978, which was in effect through 1984, put into place a new regime of price controls that provided incentives for drilling for deep, expensive gas. Increased drilling activity resulted, which presumably put upward pressure on factor costs (e.g. rental rates on drilling rigs increased). In principle, cost functions can be estimated -- as we do in this paper -- even when output prices are controlled. The activity variable in the cost function picks up possible (dis)economies of scale, while the producer price index captures changes in factor costs. There is a potential problem, however, to the extent that controls alter the optimal mix of outputs (e.g. deep vs. shallow gas). Models in Table 2 were also estimated including a level-shift dummy for the 1978-84 period. The dummy, however, was statistically insignificant.

20. A reviewer argued that "oil and gas prices would seem nature candidates for instruments since they influence E&D efforts, but there would likely be very little reverse effect since reserve additions in a given year are sufficiently modest relative to the existing stock that they will likely have little contemporaneous effect on price." Incidently, the same argument applies to the endogeneity of technology resulting from the adoption of new techniques.

21. Adding an MA(5) component to the ARMA process in the TV model for natural gas produced residuals that passed the normality test. Although the goodness of fit improved modestly, the regressors were still statistically insignificant like those shown in columns 2 and 3 of Table 2. Details are available on request.

22. The standard error of regression, the standard error of the dependent variable and the adjusted R2 for the ECM are not comparable to those from the OLS and IV regressions, because the dependent variable in the ECM is the change in the dependent variable not its (log) level.

23. The low t values on the coefficients associated with the technology and depletion variables [lnN and ln(sumQ)] may, in principle, reflect high multicollinearity between the two variables. To assess this possibility, tests for joint significance of these two variables in the TV specifications were carried out. For both the OLS and IV estimates, however, the joint hypothesis that both variables have zero coefficients could not be rejected.

24. One might ask whether industry-specific knowledge about the major technological innovations sheds light on the relative merits of the two specifications of the technology index. Looking back over the list of diffusions for the period 1967 to 1990, we estimate that perhaps three-quarters of the major technological changes seem to be best characterized as quality improvements rather than the addition of new varieties of technology. Good examples of quality improvements are the supplanting of one- and two-dimensional seismic imaging with three-dimensional seismic; improvements in the strength and corrosion-resistance of tubular goods; and improvements in downhole drilling equipment. This is not to say that the addition of new varieties of technology are unimportant. For example, different environments (e.g., deep versus shallow water, hard versus soft rock formations) arguably require the application of different "varieties" of specialized technologies. However, within each general "variety" of technology, there have been dramatic quality improvements. In future research, we hope to carefully categorize all diffusions as variety enhancements or quality improvements, and then develop a more general analytical model that allows for both types of technolgical advances.

25. The median was 9,747,264 million cubic feet per year. The mean was slightly higher at 10,219,230 mcf per year.

26. There are opposing effects. Without technological improvements, the average finding cost curve would undoubtedly shift upward, tending to cause the profit-maximizing 'supply' of reserve additions each period to fall. On the other hand, without technology the probability of actually finding additional reserves when E&D activity is undertaken will be lower. Thus, without technological improvements the 'demand' for reserves by firms upstream in the petrochemical industry, say, will be higher. A priori, either effect could dominate. Thus, actual reserve additions may rise or fall in the counter-factual "no tech. change" scenario relative to the historical series.

27. These results are consistent with Adelman's (1991) observations about oil and gas supply development costs over the period 1984-1989. He argues that natural gas development costs decreased as a result of a downward shift in the cost curve while development costs for oil decreased as a result of movement down the curve.

28. If the variables are cointegrated, the parameter estimates in Tables 2 and 3 are superconsistent, but standard errors are invalid, preventing hypothesis testing based on standard asymptotic distribution theory. If the variables are not cointegrated, the regression results -- and presumably all earlier ones in the literature, as well -- are spurious.

29. See Ng and Perron (1995) and Hall (1994) for Monte Carlo evidence supporting the use of the GTS procedure relative to the Schwarz or Akaike criteria for choosing lag length.

30. Note, however, that trend stationarity is the limiting case of a difference stationary process where the variance in the unit root part of the process takes the limiting value of zero. The sample is apparently too short to distinguish these alternative specifications.

31. In several cases, there was more than one significant cointegrating vector (as determined by the number of eigenvalues in the dynamic system that were statistically different from zero). It is well-known that adding a stationary variable, like lnQ_t, to a collection of cointegrated I(1) variables will increase the number of cointegrating vectors by one. In all cases, therefore, the ECM was estimated assuming a single cointegrating vector, so that the estimated long-run finding cost function will include lnQ_t, as well as the three I(1) variables.

32. Livernois (1988) approaches the problem by estimating a multiple-output exploration cost function, which is then used to calculate the predicted values of marginal finding costs for oil and gas.

33. ^{There is an overlap in AGA and EIA data for the years 1978 to 1980. Given the longer time for which the AGA series is available relative to EIA data, we use the former until 1980.}

34. These are standard categories for petroleum (i.e., crude oil, associated and nonassociated natural gas) reserve additions used by API, AGA and EIA.

35. Revisions through improved recovery are likely to be small for nonassociated natural gas. Most improved recovery programs are directed at crude oil.

36. Net revisions may actually lag changes in demand by one year.

37. Overhead and the remainder of non-land acquisition and non-improved recovery expenditures are allocated proportionately to drilling and G&G.