# Revisiting the reportedly weak value relevance of oil and gas asset present values: the roles of measurement error, model misspecification, and time-period idiosyncrasy.

I. INTRODUCTIONAccounting use of fair value measures is increasing, and with it the use of present value as an estimate of fair value. For example, 11 of the 32 financial reporting standards the Financial Accounting Standards Board (FASB) issued between December 1990 and December 1999 required firms to measure present values (FASB 2000, paragraph 4). (1) Yet despite this increase, our understanding of when and why such measures are relevant and reliable is limited. My study adds to our understanding of the relevance and reliability of present value measures by investigating three possible alternative explanations for the reportedly weak value relevance of oil and gas asset present values documented in prior research: measurement error, model misspecification, and time-period idiosyncrasy.

Firms have disclosed present value estimates of oil and gas asset fair values for two decades, pursuant to Accounting Securities Release (ASR) No. 253 and later Statement of Financial Accounting Standards (SFAS) No. 69. Prior research based on 1979-1988 data has concluded that, at best, these present value disclosures have only weak explanatory power for stock prices (e.g., Magliolo 1986; Harris and Ohlson 1987; Shaw and Wier 1993) and stock returns (Doran et al. 1988; Alciatore 1993). The apparently weak value relevance of these disclosures is puzzling because the economic character of oil and gas assets suggests that their present values should be no less value relevant than are other types of operating assets. Prior research has speculated that the weak association between these present value estimates and stock prices/returns is attributable to measurement error in the present value measure (Harris and Ohlson 1987; Magliolo 1986; Lys 1986; Clinch and Magliolo 1992). Measurement error seemed a plausible explanation because of alleged defects in the method SFAS No. 69 prescribed to assign value to reserve quantities, and because reserve quantities themselves are difficult to estimate accurately. This explanation now appears less plausible in light of recent evidence of a fairly consistent association between stock prices and fair value estimates not only of financial assets (e.g., Landsman 1986; Barth 1991, 1994; Barth et al. 1996; Eccher et al. 1996; Venkatachalam 1996; Nelson 1996), but also of long-lived operating assets with substantial firm-specific value for which fair values are difficult to estimate accurately (i.e., intangible assets and property and equipment; see Easton et al. 1993; Amir et al. 1993; Barth and Clinch 1998; Aboody et al. 1999). In contrast to these firm-specific operating assets, oil and gas assets trade in active markets; these assets have little firm-specific value, and thus their fair values should be accurately estimable. Since measurement error is insufficient to generate statistical insignificance in tests of value relevance of the hard-to-measure fair values of long-lived assets, (2) it seems unlikely that measurement error accounts for the generally insignificant association between stock prices and the more easily measured present value of oil and gas assets. Thus, prior research's weak evidence that present values of oil and gas assets are value relevant presents an unsolved puzzle. I test measurement error, model misspecification, and time-period idiosyncrasy as three explanations for the reportedly weak value relevance of oil and gas asset present values.

I am able to replicate the findings of prior research when estimating annual, imputed value models similar to those estimated in the studies. In particular, during 1984-88, the years common to both my study and prior studies, the present value measure of oil and gas assets exhibits significantly less explanatory power for stock prices than the corresponding historical cost measure. However, specification tests reject the annual, imputed value model in favor of an unrestricted, fixed-effects balance-sheet valuation model. In the unrestricted, fixed-effects model, oil and gas assets measured at present value exhibit significantly more explanatory power for stock prices than the corresponding historical cost measure, both in the full 1984-1996 period and in the 1984-88 subperiod.

Consistent with the valuation analysis, I also find evidence that measurement error in the present value measure of oil and gas assets is less than in the corresponding historical cost measure, both in the 1984-1996 period and the 1984-88 subperiod that corresponds to the period examined in prior research. Analysis of across-firm and across-time variation in measurement-error variance reveals that present value measurement-error variance increases both as revisions in reserve quantity estimates increase and as firm-specific discount rates deviate from the uniform 10 percent rate SFAS No. 69 requires in calculating present values.

Overall, the evidence suggests that model misspecification, rather than measurement error or time-period idiosyncrasy, most likely explains the weak value relevance of oil and gas present values reported in prior research. These results help resolve an anomaly in the literature, and demonstrate that present value offers a viable means of obtaining reliable fair value estimates for oil and gas assets--nonfinancial assets that have little firm-specific value and are traded in active markets.

I have organized the remainder of the paper as follows: Section II provides institutional detail concerning oil and gas accounting, discusses related prior research, and develops the three hypotheses. Section III develops the research design, while Section IV discusses the sample selection criteria and characteristics of the sample. Section V discusses test results, and synthesis and conclusions follow in Section VI.

II. BACKGROUND, PRIOR RESEARCH, AND HYPOTHESES

Background and Prior Research

Firms engaged in oil and gas exploration and production can use either the full cost or the successful efforts method to account for their oil and gas activities. The two methods differ in the accounting for the cost of drilling nonproductive wells. The successful efforts method expenses these costs when the well is deemed nonproductive, whereas the full cost method capitalizes and amortizes these costs under the rationale that the cost incurred to discover producing wells necessarily includes the cost of drilling nonproductive wells. Thus, full cost accounting leads to higher historical cost of oil and gas assets than does successful efforts accounting. Because required asset impairment tests effectively limit an asset's depreciated cost to no more than current value, a higher oil and gas asset cost is closer to fair value than a lower cost.

Critics allege that full cost and successful efforts methods, both based on historical cost accounting, are inappropriate for firms in the oil and gas industry (U.S. Securities and Exchange Commission [SEC] 1978). Companies often discover oil and gas assets with substantial value at relatively nominal cost, so the cost of obtaining these assets is often not a fair measure of the value obtained at the time of acquisition. Critics argue that this violation of the fundamental premise underlying historical cost accounting renders historical cost inappropriate.

Because of this limitation, the SEC in 1978 sought to replace historical cost accounting for oil and gas activities with reserve recognition accounting (SEC 1978) based on present value rather than historical cost asset measurement. The SEC, facing stiff opposition based on concerns that the present value measure lacked reliability, eventually abandoned the proposal (SEC 1981). The FASB, however, made this present value measure the centerpiece of the supplemental disclosures required by SFAS No. 69 (FASB 1982). SFAS No. 69 requires firms to estimate oil and gas asset fair values by discounting at a 10 percent rate of interest the net revenue from estimated future extraction and sale of "proved" reserves.

Prior research concludes that present value estimates of oil and gas asset fair values prepared pursuant to SFAS No. 69 are, at best, weakly value relevant. Magliolo (1986) finds that while the present value measure of oil and gas assets is associated with stock prices during the period 1979-1983, the association is weaker than that based on a competing proprietary estimate of reserve values prepared by financial analysts. Magliolo (1986) speculates, as does Lys (1986), that the present value measure of oil and gas assets may contain substantial measurement error. Harris and Ohlson (1987) find that during the period 1979-1983, the historical cost measure of oil and gas assets is more strongly associated with stock prices than is the present value measure, leading them also to speculate that the present value measure suffers from measurement error. Using a returns-type design and data obtained from 1979-1984, Doran et al. (1988) find little association between stock returns and changes in the SFAS No. 69 measure, while Alciatore (1993) finds that selected components of the change in the SFAS No. 69 measure are associated with stock returns during the period 1982-84. Shaw and Wier (1993) find little evidence of an association between stock prices and the SFAS No. 69 present value measure during the period 1985-88. As I elaborate below, I investigate three possible explanations for the weak value relevance: measurement error, model misspecification, and time-period idiosyncrasy hypotheses.

Measurement Error Hypothesis

Barth and Landsman (1995) note that market imperfections create a divergence among asset entry value (i.e., replacement cost), exit value (i.e., the price at which an asset can be sold to a third party), and value-in-use (i.e., the incremental firm value attributable to an asset). Value-in-use differs from exit value if a firm's unique skill in exploiting the asset creates firm-specific value that is not transferable to a buyer. Barth and Landsman (1995) further note that it is particularly difficult to accurately estimate fair values for assets that are not traded in active markets and that have substantial firm-specific value. Oil and gas assets are actively traded in established markets and have little firm-specific value. Thus, present value estimates of oil and gas asset fair values should exhibit less measurement error than fair value estimates of intangible assets and property and equipment that are not traded in established markets and that contain substantial firm-specific value. On the other hand, the SFAS No. 69 present value measure may be subject to severe measurement error because (1) reserve quantity estimates underlying the valuation disclosures may contain substantial error, and (2) the valuation model used to attach value to those reserve quantities may be flawed (Clinch and Magliolo 1992).

Studies conclude that estimates of reserve quantities do contain substantial error. For example, the annual revision of the previous year's reserve quantity estimate as a percentage of beginning reserve quantities ranges from -82 percent to 37 percent with a standard deviation of 17 percent around a mean of -3.9 percent (Porter 1980; King 1982; Kahn et al. 1983). Furthermore, this annual revision of reserve estimates varies across firms and across time in a pattern suggesting that petroleum firms use reserve estimates to manage earnings (Hall and Stammerjohan 1997). Thus, noise in reserve quantity estimates, whether from estimation error or purposeful manipulation, may introduce measurement error into oil and gas asset present values. Ceteris paribus, firms that tend to report large annual revisions to the previous year's reserve quantity estimates should have greater present value measurement error. Moreover, present value measurement error may also depend upon whether internal or external petroleum engineers prepare the reserve estimates. External petroleum engineers may prepare more reliable reserve estimates if they constrain managers' abilities to bias reserve estimates, but they may prepare less reliable reserve estimates if internal engineers possess private information they would otherwise use in estimating reserve quantities.

In addition to estimation error in reserve quantities, the SFAS No. 69 valuation model may also introduce measurement error into oil and gas asset present values. Adams et al. (1994) criticize the SFAS No. 69 valuation model because (1) it estimates future cash flows by multiplying the projected future production volumes times current oil and gas prices (i.e., the spot price on the balance sheet date) rather than expected future oil and gas prices, and (2) it discounts estimated future cash flows at a uniform rate of 10 percent rather than at a firm-specific discount rate. SFAS No. 69 effectively assumes that oil and gas prices do not change and that the appropriate discount rate neither varies across firms as a function of risk nor across time as a function of changes in market-wide interest rates. SFAS No. 69 thus mandates a present value model inconsistent with SFAC No. 7, which advocates explicitly recognizing uncertainty about the amount and timing of future cash flows by discounting the expected value of those cash flows at a firm-specific discount rate that reflects the risk associated with those cash flows as well as prevailing market rates of interest (FASB 2000, paras. 39, 40, 62-71).

These shortcomings of the SFAS No. 69 valuation model suggest that measurement error in the oil and gas present values varies across firm-years as a function of oil-price volatility and the deviation in firm-specific discount rates from 10 percent. Volatile spot prices increase the probability that prices will temporarily rest at an extreme value on the balance sheet date. If investors' expectations of future oil and gas prices are weakly related to spot prices on the balance sheet date, then the reported oil and gas present values are likely to differ from investors' implicit valuation of oil and gas assets, leading to greater measurement error in the present value estimates. In contrast, if investors' expectations of future oil and gas prices are strongly related to spot prices, then the measurement error in historical cost will be higher relative to the measurement error in present value because historical costs remain fixed while present values, a function of spot prices, move in synchrony with investors' implicit valuation of oil and gas assets. Therefore, oil and gas price volatility may lead to differential measurement error, but the direction is unclear ex ante. With respect to measurement error induced by the uniform 10 percent discount rate, the present value measure is more likely to deviate from the value investors assign oil and gas assets when the firm-specific discount rate differs from 10 percent. Based on the preceding discussion, I propose the following measurement error hypotheses (alternative form):

H1: Present value measurement error variance differs from historical cost measurement error variance in oil and gas assets.

H1a: Present value measurement error variance will be larger in firms that, on average, report larger annual revisions to the previous year's reserve quantity estimates than in firms that, on average, report smaller annual revisions.

H1b: Present value measurement error variance in firms employing independent (external) petroleum engineers to estimate reserve quantities will differ from present value measurement error variance in firms using internal petroleum engineers.

H1c: Present value measurement error variance when oil prices are volatile will differ from present value measurement error variance when oil prices are less volatile. (3)

H1d: Present value measurement error variance will be greater when firm-specific discount rates substantially differ from 10 percent than when close to 10 percent.

Model Misspecification Hypothesis

Magliolo (1986), Harris and Ohlson (1987), and Shaw and Wier (1993) rely on annual, cross-sectional estimates of an "imputed value" regression model that is a restricted form of the standard balance sheet valuation model. This model imputes the value of oil and gas assets as total market value of equity less the book value of non-oil-and-gas assets and liabilities (when liabilities are defined as negative values). The imputed value is then regressed on the accounting measure of oil and gas assets (either historical cost or present value). This specification restricts the coefficients on liabilities and non-oil-and-gas assets to 1 and the intercept to be constant across firms. The reportedly weak association between stock prices and present value (relative to historical cost) oil and gas asset measures may arise, in part, from model misspecification if the restrictions in the imputed value model are invalid--for example, when market value differs from book value of non-oil-and-and-gas assets and liabilities. I thus propose the following hypothesis:

H2: Specification err in the imputed value model contributes to the weak association between stock prices and oil and gas asset present values documented in prior research.

Time-Period Hypothesis

Prior studies (i.e., Magliolo 1986; Harris and Ohlson 1987; Doran et al. 1988; Alciatore 1993; Shaw and Wier 1993) are based on data from 1979-1988, suggesting that time-period idiosyncrasies may have been responsible for the reported weak value relevance of oil and gas present values. Thus, weak value relevance may not generalize to more recent years. This leads to my final hypothesis:

H3: The weak association between stock prices and oil and gas present values does not generalize to more recent years.

III. RESEARCH DESIGN

Test of H1

I assume a conventional cross-sectional valuation framework (Landsman 1986; Barth 1991, 1994) in which the market value of equity equals the difference between the summed market value of assets and liabilities, where market values are defined as the amounts investors implicitly assign to assets and liabilities when they value the firm:

(1) MVE = OTHER_MV + OG_MV + LIAB_MV

MVE is market value of equity, OTHER_MV is market value of all non-oil-and-gas assets, OG_MV is market value of oil and gas assets, and LIAB_MV is market value of liabilities (I consider liabilities negative values). (4)

Financial statements and related disclosures measure the market values of assets and liabilities with error:

(2) OTHER_HC = OTHER_MV + [u.sub.1] OG_i = [S.sub.i] x (OG_MV + [u.sub.2i]) LIAB_HC = LIAB_MV + [u.sub.3]

where:

OTHER_HC = the (historical cost) book value of non-oil-and-gas assets;

OTHER_MV = the value that investors implicitly assign to non-oil-and-gas assets;

OG_i = the accounting measure of oil and gas assets (either historical cost book value as denoted by i = HC, or the SFAS No. 69 present value measure as denoted by i = PV);

OG_MV = the value that investors implicitly assign to oil and gas assets;

LIAB_HC = the (historical cost) book value of liabilities multiplied by - 1;

LIAB_MV = the value that investors implicitly assign to liabilities multiplied by - 1;

[u.sub.1], [u.sub.2i], and [u.sub.3] - error in the accounting measure of the related market value construct; and

[S.sub.i] = a parameter reflecting the difference in scale between OG_HC and OG_PV.

Each error term, [u.sub.x], is a random variable with variance [[sigma].sup.2.sub.x] so the smaller the measurement error variance the more reliable the measure. Covariance between [u.sub.x] and [u.sub.y] is denoted [[sigma].sub.x,y]. Equation (2) includes a scale factor [S.sub.i] because OG_HC is systematically smaller than OG_PV. Empirically, OG_PV is 1.30 to 1.40 times larger than OG_HC (see Table 1, discussed later).

Measurement error, as defined by Equation (2), arises when accounting values and market values become misaligned. Historical costs and market values become misaligned because interest rate shocks or cash flow shocks after initial acquisition cause market values to change, while historical cost metrics remain largely fixed at initial acquisition price or at depreciated costs that approximate market value only by coincidence. The misalignment should be more severe in OG_HC because historical cost does not equal fair value, even at initial acquisition. However, because full cost accounting yields asset measures that are less severely understated than does successful efforts accounting, there should be less misalignment between OG_HC and OG_MV under full cost accounting.

Misalignment between market values and SFAS No. 69 present values also occurs, but the misalignment arises principally from interest rate effects (i.e., firm-specific discount rates that differ from 10 percent) rather than cash flow effects because petroleum firms update OG_PV at each balance sheet date to reflect changes in expected future cash flows. However, misalignment from cash flow shocks can arise if investors' expectations of future cash flows differ from the SFAS No. 69 expected amount, which might occur if, for example, investors suspect error in estimating reserve quantities, or if investors' expectations of future oil and gas prices differ from the spot prices at the balance sheet date SFAS No. 69 uses to value future oil and gas production. The Appendix provides greater detail about the nature of the measurement error terms.

Empirical estimation of Equation (1) with accounting values substituted for the unobservable market values yields the following errors-in-variables regression model:

(3) MVE = [[gamma].sub.0] + [[gamma].sub.1] OTHER_HC + [[gamma].sub.2]OG_i + [[gamma].sub.3]LIAB_HC + HC + [xi]

where [xi] = [[gamma].sub.1] [u.sub.1] - [[gamma].sub.2] [S.sub.i] [u.sub.2i] - [[gamma].sub.3] [u.sub.3]. Absent error in the accounting measures, the intercept in Equation (3) should be 0 and the slope coefficients on the regressors should be 1. With measurement error the expected value of the [[gamma].sub.k] coefficients is not 1, but is 1 - [B.sub.k] where [B.sub.k] is the magnitude of bias in the coefficient. As the Appendix shows, the degree of bias [B.sub.k] depends upon the variance/covariance structure in the accounting measurement error terms [u.sub.x].

I exploit this bias to structure a test of H1. Intuitively, my approach, based on Barth (1991) and Choi et al. (1997), involves first estimating the model in Equation (3) with OG_i defined as OG_PV and then again with OG_i defined as OG_HC. I then use the extent of observed bias in each estimation and a specification of the determinants of that bias to draw inferences about the relative magnitude of measurement error in the two alternative measures. As discussed in the Appendix, I implement this approach through a two-stage estimation technique. Coefficients estimated in the second stage form the basis for a statistical test of H1. The second stage model is:

(4) MVEI * = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

MVE2 * = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The parameters [[phi].sub.j], [[phi].sub.t], [[delta].sub.j], and [[delta].sub.t] in Equation (4) denote firm ([[phi].sub.j], [[delta].sub.j]) and year ([[phi].sub.t], [[delta].sub.t]) fixed effects. FC and SE are 0,1 variables indicating the full cost or successful efforts method. The FC and SE variables allow the slope coefficients to differ between accounting methods because, as previously noted, the misalignment between OG_HC and OG_MV should be less severe under full cost than successful efforts accounting. MVE1* equals MVE - (OTHER_HC + OG_PV + LIAB_HC) and MVE2* equals MVE - (OTHER_HC + (([S.sub.PV]/[S.sub.HC]) x OG_HC) + LIAB_HC). The Z regressors are orthogonal values of OTHER_HC, (([S.sub.PV]/[S.sub.HC]) x OG_HC), OG_PV, and LIAB_HC obtained from the first-stage regressions.

[Sp.sub.pv]/[S.sub.HC] is a rescaling factor that controls for test bias due to a systematic scale difference between OG_HC and OG_PV. I calculate it by dividing the mean value of OG_PV by the mean value of OG_HC. Scale differences between OG_PV and OG_HC would confound comparisons of measurement error variance because variance is a function of scale (i.e., Var(sx) = [s.sup.2]Var(x)). Multiplying OG_HC by [S.sub.PV]/[S.sub.HC] transforms [u.sub.2HC] to be of the same scale as [u.sub.2PV], and thus facilitates a scale-free comparison of measurement error variance between OG_HC and OG_PV (see the Appendix). (5) Consequently, I ran all measurement error regressions after substituting ([S.sub.PV]/[S.sub.HC]) x OG_HC in place of OG_HC.

I estimate the model in Equation (4) as a seemingly unrelated regression, deflating each variable by barrel-of-oil equivalent units (BOE) to avoid size-related coefficient bias and mitigate heteroskedasticity. (6) I pool observations across firms and years to increase statistical power, but I control for year-specific and firm-specific fixed effects. I also present annual cross-sectional regressions for comparison.

Subtracting [[delta].sub.i] from [[phi].sub.i] in Equation (4) and rearranging yields the following expression containing the two terms of interest, [[sigma].sup.2.sub.u.sub.2PV] and [[sigma].sup.2.sub.u.sub.2HC]:

(5) [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi].sub.1] + [[phi.sub.2] - [[phi].sub.3] = [[sigma].sup.2.sub.u.sub.2PV] - [[sigma].sup.2.sub.u.sub.2PV] - [[sigma].sup.2.sub.u.sub.2HC] + [[sigma].sub.OTHER_MV.sub.u.sub.2HC] - [[sigma].sub.OTHER_MV.sub.u.sub.2PV] + [[sigma].sub.OG_MV,sub.u.sub.2PV] - [[sigma].sub.OG_MV,sub.u.sub.2HC] + [[sigma].sub.LIAB_MV,sub.u.sub.2HC] - [[sigma].sub.LIAB_MV,sub.u.sub.2PV])

A statistical test of H1, that [[sigma].sup.2.sub.u.sub.2HC], based on Equation (5), is [H.sub.0]: [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi].sub.1] + [[phi].sub.2] - [[phi].sub.3] = 0. As detailed in the Appendix, the nature of historical cost in relation to present value asset measurement permits me to make plausible assumptions about the net signed value of the covariance terms in parentheses in Equation (5). In particular, I expect a positive, net value for the parenthetical covariance terms, and thus the coefficient function [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi.sub.1] - [[phi].sub.2] - [[phi.sub.3] is biased toward a positive value under the null hypothesis that measurement error variance in OG_PV and OG_HC are the same (i.e., [H.sub.0]: [[sigma].sup.2.sub.u.sub.2PV] = [[sigma].sup.2.sub.u.sub.2HC]). Consequently, a statistically significant negative value for the coefficient function in Equation (5) constitutes strong evidence to reject the null hypothesis that [[sigma].sup.2.sub.u.sub.2PV] equals [[sigma].sup.2.sub.u.sub.2HC] in favor of the alternative that [[sigma].sup.2.sub.u.sub.2PV] is less than [[sigma].sup.2.sub.u.sub.2HC]. However, a statistically significant positive value for the coefficient function provides weak evidence to reject the null hypothesis, because the positive value of the function could be attributable either to [[sigma].sup.u.sub.2PV] > [[sigma].sup.2.sub.u.sub.2HC] or to the positive values of the covariance difference terms.

Tests of H1a-H1d

Hypotheses 1a-1d predict across-firm and across-time variation in present value measurement error based on hypothesized causal factors. I test these hypotheses by evaluating whether the coefficient function [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi.sub.1] + [[phi.sub.2] - [[phi.sub.3] differs between data subsets partitioned based on these factors.

I partition the data by adding to Equation (4) a dummy variable, D, both as a main effect and as an interaction term. D assumes a value of 1 or 0 depending upon the values of the partitioning variables EST_ERROR, INSIDE, OIL_VOLATILITY, and RATE, defined as follows.

EST_ERROR = proxy for the magnitude of the error in estimating reserve quantities, calculated as the absolute value of the coefficient of variation in a firm's revision to the beginning-of-year measure of OG_PV. I calculate this firm-specific measure using reserve revisions across the period 1984-1996. D = 1 if the value of EST_ERROR is above its pooled sample median value, and 0 otherwise;

INSIDE = binary variable assigned a value of 1 if the firm relied on its own petroleum engineering staff to prepare reserve quantity estimates; 0 otherwise. D = 1 if INSIDE = 1, and 0 otherwise;

OIL_VOLATILITY = annualized standard deviation in the natural logarithm of the oil price relative, calculated as [sigma] [square root of 250], where [sigma] is the estimated standard deviation of the log-transformed ratio of day t to day t - 1 spot price of oil. It is calculated across days 0 to -59 where day 0 corresponds to the balance sheet date. D = 1 if the value of OIL_VOLATILITY is above its pooled sample median value, and 0 otherwise; and

RATE = proxy for the degree of distortion in OG_PV introduced by the uniform 10 percent discount rate, calculated as |r - 0.10|, where r is the pension settlement rate the firm uses in accounting for defined benefit pension costs. D = 1 if the value of RATE is above its pooled sample median value, and 0 otherwise.

Test of H2

I base tests of H2 on Equations (6A) and (6B), which differ only in terms of the oil and gas measures (OG_PV vs. OG_HC). [[alpha].sub.j] and [[alpha].sub.t] in Equations (6A) and (6B) denote firm and time fixed effects. All other variables in Equations (6A) and (6B) have been previously defined.

(6A) MVE = [[alpha].sub.j] + [[alpha].sub.t] + [[gamma].sub.1t,FC] (OTHER_HC x FC) + [[gamma].sub.2t,FC] (OG_PV x FC) + [[gamma].sub.3t,FC] (LIAB_HC x FC) + [[gamma].sub.1t,SE] (OTHER_HC x SE) + [[gamma].sub.2t,SE) (OG_PV x SE) + [[gamma].sub.3t,SE] (LIAB_HC x SE) + [[epsilon].sub.1]

(6B) MVE = [[alpha].sub.j] + [[alpha].sub.t] + [[gamma].sub.1t,FC] (OTHER_HC x FC) + [[gamma].sub.2t,FC] (OG_PV x FC) + [[gamma].sub.3t,FC] (LIAB_HC x FC) + [[gamma].sub.1t,SE] (OTHER_HC x SE) + [[gamma].sub.2t,SE) (OG_HC x SE) + [[gamma].sub.3t,SE] (LIAB_HC x SE) + [[epsilon].sub.1]

Prior research estimated both Equations (6A) and (6B) as annual cross-sectional regressions, subject to the restriction that [[gamma].sub.1t] = [[gamma].sub.3t] = 1. Researchers also restricted the OG_PV coefficient to be the same for full cost and successful efforts firms--that is, they restricted [[gamma].sub.2t,FC] = [[gamma].sub.2t,SE] in models corresponding to Equation (6A).

As a test of H2, I estimate Equations (6A) and (6B) and evaluate both the appropriateness of these coefficient restrictions and their impact on the explanatory power of the models. To facilitate comparison with prior research, I base the analysis on data for the 1984-88 subperiod, which are the years common to both my study and prior studies.

Test of H3

I test H3 by comparing the results obtained for the 1984-1996 full period to those for the 1984-88 subperiod that overlaps the period used in prior research and the 1989-1996 subperiod subsequent to prior research.

IV. SAMPLE SELECTION AND DATA

I merged the 1997 Compustat PC Plus database, the 1997 CRSP database, and the Arthur Andersen Oil and Gas Disclosures Database for the years 1988 (containing data for 1984-88), 1993 (containing data for 1989-1993), and 1996 (containing data for the years 1994-96), and retained all firm-years with nonmissing data. (7) The final sample includes 745 firm-year observations from 111, SIC 1311 exploration and production firms. I exclude integrated/diversified petroleum firms in SIC 2911 to ensure a homogenous group of firms for which oil and gas assets comprise a substantial portion of firm value.

Table 1 presents descriptive statistics for all regression variables, expressed in dollars per barrel-of-oil equivalent units (BOE). The table also presents supplementary statistics on total market value of equity (SIZE), systematic risk (BETA), and the deflator (BOE). These results are consistent with prior research (Malmquist 1990; Deakin 1979) in that successful efforts firms (1) are larger than full cost firms (SIZE and BOE are larger in successful efforts firms) and (2) report lower capitalized oil and gas asset costs (OG_HC is smaller in successful efforts firms). Successful efforts firms also own less-valuable reserves (OG_PV is smaller in successful efforts firms) and rely less on debt financing than do full cost firms (absolute value of mean LIAB_HC is smaller in successful efforts firms).

Oil and gas assets comprise a large fraction of total assets (i.e., OG_PV/[OTHER_HC + OG_PV] is 70 percent in the successful efforts group and 72 percent in the full cost group). Thus, oil and gas assets are large enough to affect cross-sectional variation and stock prices. Moreover, OG_PV is systematically larger than OG_HC in both groups. The mean difference (OG_PV - OG_HC) is $0.52 per barrel-of-oil-equivalent unit in the successful efforts group and $0.42 per barrel-of-oil-equivalent unit in the full cost group. The mean ratio OG_PV/OG_HC exceeds 1 in both the successful efforts group (1.39) and in the full cost group (1.31), reflecting the scale-related differences between OG_HC and OG_PV.

V. EMPIRICAL RESULTS

Test of H1 Based on Measurement Error Model

Table 2 reports tests of H1 based on direct estimates of measurement error variance. Panel A reports the details of the parameter estimates of the measurement error model. Of greater interest, Panel B reports the key tests of the coefficient function [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi].sub.1] + [[phi].sub.2] - [[phi].sub.3]. For full cost firms and successful efforts firms, the values of the coefficient functions are -1.52 and -0.83, respectively, both significantly negative (Z = -12.01 and Z = -6.16). The significantly negative coefficient function suggests that present value measures of oil and gas assets suffer from less measurement error variance than do historical cost measures (i.e., [[sigma.sup.2.sub.u.sub.2PV] < [[sigma].sup.2.sub.u.sub.2HC]). This evidence is particularly compelling because, as already noted, the value of the coefficient function is biased toward a positive value.

The value of the coefficient function is significantly more negative for the full cost firms (-1.52) than for the successful efforts firms (-0.83) (p < 0.001 in an untabulated test). This result suggests that historical cost is less reliable relative to present value for the full cost firms than for the successful efforts firms. This result is surprising because, as noted above, successful efforts understates oil and gas asset historical costs more severely than does the full cost method, which suggests that the successful efforts method should suffer from more historical cost measurement error. One possible explanation is that successful efforts firms also have large present value measurement error variance, which may obscure the conjectured large historical cost measurement error variance. Table 1 reports evidence consistent with this speculation, as successful efforts firms have significantly greater reserve quantity estimation error (EST_ERROR) than do full cost firms (5.35 vs. 4.16, significant at the 0.08 level). Tests of H1a, discussed in the following subsection, document that firms with more reserve quantity estimation error suffer from larger measurement error in their present values.

In annual cross-sectional estimates, the mean value of the coefficient function is -0.34 and -0.51 for full cost and successful efforts firms, respectively (third column in Table 2, Panel B). The coefficient function is significantly negative in seven of the 13 annual tests for the full cost firms and in nine of the 13 annual tests for the successful efforts firms (last column of Panel B). The mean Z-statistics from these annual tests ([bar]Z = -1.48 and -2.03 in the third column of Panel B) are significantly negative (tests based on Z1* and Z2* statistics in Panel B). (8) Consequently, these annual cross-sectional estimates also indicate that present value oil and gas measures suffer from less measurement error than do historical cost measures.

In summary, the evidence in Table 2, from both pooled, fixed-effects regressions and from annual regressions, consistently supports HI. The results indicate that historical cost oil and gas asset measures are noisier (less reliable) than present value measures.

Tests of H1a-H1d Based on Measurement Error Model

Table 3 summarizes tests of H1a-H1d based on the measurement error model, augmented with the variable D added both as a main effect and as an interaction term. For brevity, I suppress the individual coefficient estimates. A test that the coefficient function [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi].sub.1] + [[phi].sub.2] - [[phi].sub.3] differs between partitions is [H.sub.0]: [[delta].sub.4] - [[delta].sub.5] + [[delta].sub.6] - [[phi].sub.4] + [[phi].sub.5] - [[phi].sub.6] = 0. A negative value for [[delta].sub.4] - [[delta].sub.5] + [[delta].sub.6] - [[phi].sub.4] + [[phi].sub.5] - [[phi].sub.6] implies less present-value measurement error variance in the D = 1 group relative to the D = 0 group, and a positive value implies the opposite.

Panel A summarizes test results for full cost firms and Panel B summarizes the results for successful efforts firms. In Panel A, the significantly positive value of the coefficient function [[delta].sub.4] - [[delta].sub.5] + [[delta].sub.6] - [[phi].sub.4] + [[phi].sub.5] - [[phi].sub.6] in the "EST_ERROR" column indicates that present value measures suffer from more measurement error in firms that routinely report larger annual revisions to the previous year's reserve quantity estimates. Similarly, the significantly positive value of the coefficient function in the "RATE" column indicates that present value measures suffer from more measurement error when firm-specific discount rates differ substantially from the required, uniform 10 percent discount rate than when rates are close to 10 percent. The coefficient function is not significantly different from 0 for full cost firms in the "INSIDE" column (test of H1b) or the "OIL_VOLATILITY" column (test of H1c). Thus, there is no evidence that present value measurement error variance is related to use of external petroleum engineers or to oil price volatility. Finally, the coefficient function is not significantly different from 0 in successful efforts firms for any of the partitioning variables (Panel B).

In summary, although there is no evidence that present value measures of oil and gas assets are significantly noisier when internal engineers prepare the reserve estimates or when oil prices are more volatile, evidence does indicate that present value measures are noisier in full cost firms (1) experiencing large reserve estimate revisions and (2) when firm-specific discount rates are substantially different from the SFAS No. 69 uniform 10 percent discount rate. Thus, tests support H1a and H1d, but only in full cost firms.

Tests of H2

Table 4 presents specification tests of Equations (6A) (present value model) and (6B) (historical cost model) for the years 1984-88, which are the years that overlap prior research sample periods. Consistent with prior research, the "Restricted Model" restricts the slope coefficients on OG_PV to be the same ([[gamma].sub.2tFC] = [[gamma].sub.2t,SE]) in Equation (6A) only, and restricts the slope coefficients on LIAB_HC and OTHER_HC to a value of 1 in both Equations (6A) and (6B) ([[gamma].sub.1t] = [[gamma].sub.3t] = 1) (Magliolo 1986; Harris and Ohlson 1987; Shaw and Wier 1993).

The most general specification, Model 1, provides for fixed time and firm effects and allows slope coefficients [[gamma].sub.k,t] to vary across years. In unrestricted estimates of Model 1, the present value specification's [R.sup.2] significantly exceeds the historical cost specification's [R.sup.2] (0.83 > 0.81, p = 0.07). In restricted estimates of Model 1, the [R.sup.2] is not significantly different between the present value and historical cost models. The right-hand columns of Table 4 show that the restrictions are inappropriate and that the unrestricted Model 1 has significantly greater explanatory power than the restricted Model 1 in both the present value and historical cost models (p [less than or equal to] 0.001). Results are similar in Model 2 that holds coefficients constant across years.

Results differ markedly, however, in specifications without firm fixed effects, Models 3-8, that correspond to specifications estimated in prior research. Model 3 differs from Models 4-8 only in that Model 3 constrains the variance of the disturbance terms to be temporally constant, whereas the variance is free to vary across years in Models 4-8. In unrestricted estimates of Model 3, the [R.sup.2] is not significantly different between historical cost and present value specifications. In restricted estimates of Model 3 (the specification used in prior studies), the historical cost specification's [R.sup.2] significantly exceeds the present value specification's [R.sup.2] (p < 0.05). This finding replicates results reported in Harris and Ohlson (1987) and Shaw and Wier (1993). Importantly, however, the right-hand columns of Table 4 show that the restrictions are inappropriate and that the unrestricted version of Model 3 has significantly greater explanatory power than the restricted version in both present value and historical cost specifications (p < 0.001).

In annual unrestricted estimates of Models 4-8, the differences in [R.sup.2] values are not significant in Vuong (1989) tests. In annual restricted estimates of Models 4-8, the present value specification's [R.sup.2] is significantly less than the historical cost specification's [R.sup.2] in 1986 and 1987, and marginally so in 1988. As in Model 3, these findings confirm prior research. Also as in Model 3, however, tests of the restricted vs. unrestricted specifications of Models 4-8 (reported in the right-hand columns of Table 4) reveal that the restrictions are inappropriate in 1986, 1987, and 1988 in the historical cost model, and in 1985-88 in the present value model.

A test of Model 1 vs. Model 2 (bottom of Table 4) cannot reject the hypothesis of temporal stability in slope coefficients. In contrast, a test of Model 1 vs. Model 3 rejects the hypothesis of no firm fixed effects in all specifications at the 0.001 level. Thus, specification tests indicate that unrestricted Models 1 and 2 are better specified than the competing Models 3-8 that do not allow firm fixed effects.

In summary, restricted versions of Models 3, 5, 6, 7, and 8 that correspond to the models used in prior research replicate prior research's reportedly weak association between stock prices and present value (relative to historical cost) oil and gas asset measures. However, specification tests reject these misspecified models in favor of unrestricted forms of Model 1 or Model 2 that: (1) allow for firm fixed effects and (2) do not constrain the slope coefficients on LIAB_HC and OTHER_HC to equal 1, nor do they constrain OG_PV to be the same for full cost and successful efforts firms. In the more appropriately specified Models 1 and 2, present value measures of oil and gas assets have significantly greater explanatory power for stock prices than do historical cost measures. Thus, the weak association between stock prices and present value (relative to historical cost) oil and gas asset measures during the period 1984-88 seems to be attributable to model misspecification that disappears when the specification error is corrected. In brief, evidence obtained from model specification tests supports H2.

Why do the coefficient restrictions imposed in annual, cross-sectional imputed value models so severely diminish the association between stock prices and the present value measures of oil and gas assets, and why do pooled, fixed-effect regressions attenuate this effect? Although I leave it to future research to answer this question, I offer two conjectures. First, measurement error in the present value measure may be correlated with measurement error in the non-oil-and-gas assets and liabilities, causing the slope coefficients on non-oil-and-gas assets and liabilities to deviate from their theoretical expected value of 1. In this case, the effect of measurement error in non-oil-and-gas assets and liabilities, although by itself perhaps weak, may be exacerbated by covariance with present value measurement error. The weak results from the restricted annual valuation estimates may thus be attributable to a defect in the present value measure that is offset either by relaxing the coefficient restriction or by estimating a fixed-effect specification. Alternatively, if error in the present value measure is independent of error in the measure of non-oil-and-gas assets and liabilities, then error in measuring non-oil-and-gas assets and liabilities alone accounts for the weak explanatory power of present value in the restricted annual estimates. In this case, relaxing the coefficient restrictions or estimating a fixed-effect specification compensates, in effect, for defects in the measurement of non-oil-and-gas assets and liabilities.

Test of H3

Hypothesis 3 proposes that the weak value relevance of oil and gas present values as documented in prior research does not generalize to more recent years. The tests of H2 reported in Table 4 reveal that the weak value relevance of oil and gas present values in 1984-88 disappears after I correct apparent model misspecification. Nonetheless, for the sake of completeness, I estimate (in unrestricted form) Equations (6A) and (6B) using data for the 1984-1996 full period, the 1984-88 subperiod, and the 1989-1996 subperiod. In each period, the present value specification's [R.sup.2] significantly exceeds the historical cost specification's [R.sup.2] (p < 0.10 in untabulated tests). Thus, results that hold for the full period 1984-1996 also hold for the 1984-88 and the 1989-1996 subperiods, so the data do not support H3.

Additional Analysis

Because the measurement error analysis requires strong and untestable assumptions, I provide corroborative evidence from alternative supplementary tests of measurement error based on Re comparisons. Assuming measurement error reduces Re in addition to causing coefficient bias, I interpret model specifications with the smaller Re as suffering from more measurement error. I compare the Re from Equation (6A) (present value model) to the Re from Equation (6B) (historical cost model) using Vuong's (1989) likelihood ratio test. This supplementary analysis of [R.sup.2] differs from the pooled analysis of Re reported in Table 4 in that: (1) the period examined is longer (1984-1996 vs. 1984-1988 in Table 4) and (2) the data are partitioned by factors expected to influence the across-firm and across-time reliability of the present value measure.

One should interpret the Re comparisons cautiously, however, because [R.sup.2] values do not perfectly rank order alternative accounting metrics according to relative measurement-error variance unless one of the compared models is measured without error and the measurement error is independent of the true value (Barth 1989). This assumption is not strictly met here because I assume that all accounting metrics are noisy measures of market values, and I do not assume independence between measurement error and market values. Thus, these results are only suggestive.

Test of H1 Based on [R.sup.2] Comparisons

Table 5 presents the supplementary tests of H1 based on [R.sup.2] comparisons. In the unrestricted fixed-effects model (Model 2 from Table 4), the present value specification's [R.sup.2] (0.68) is significantly higher than the historical cost specification's [R.sup.2] (0.66) per the Vuong (1989) tests (p = 0.08 level). This additional evidence that the present value specification suffers from less measurement error than the historical cost specification confirms the main tests of H1.

Similarly, in annual cross-sectional estimates, the mean [R.sup.2] from the present value specification is 0.36 and the mean [R.sup.2] from the historical cost specification is 0.32. Vuong tests based on annual estimates reject [H.sub.0]: [R.sup.2.sub.PV] = [R.sup.2.sub.HC] in 3 out of the 13 years (untabulated). The mean Z-statistic obtained from these annual Vuong tests is [bar]Z= 0.53 (untabulated), which is significant in a test based on Z1* (p = 0.06), but not in a test based on Z2* (p = 0.12). (9) Because Z2* is a more robust test than Z1* (albeit a weaker test), the insignificance of Z2* does cast some doubt over the significance of the results obtained with Z1*.

In summary, [R.sup.2] comparisons based on the pooled, fixed-effects model and based on the aggregated annual cross-sectional tests derived from Z1* weakly confirm results from the main test of H1.

Tests of H1a-H1d Based on [R.sup.2] Comparisons

Table 5 also presents the supplementary tests of H1a-H1d based on [R.sup.2] comparisons for various data partitions. Not surprisingly, the [R.sup.2] comparisons in the partitioned analysis are weaker than those based on the pooled analysis, most likely because of the lower statistical power arising from the data partitioning. The [R.sup.2] values are significantly different only in the high OIL_VOLATILITY partition where the present value specification's [R.sup.2] is greater than that of the historical cost specification's [R.sup.2] (0.71 > 0.67, p < .001). The higher [R.sup.2] in the present value specification (relative to the [R.sup.2] in the historical cost specification) when oil prices are volatile supports H1c, suggesting that measurement error variance is lower in present value relative to historical costs when oil prices are volatile, perhaps because investors' expectations of future oil prices are related to spot prices.

Sensitivity Analysis

I evaluate the sensitivity of the reported results by repeating the analysis after eliminating observations that standard outlier diagnostic techniques identify as potentially influential (i.e., Belsley et al. 1980). I also estimate change-form specifications of the models. (10) The overall tenor of the results is similar to those reported.

To assess whether the inferences are sensitive to goodwill and other unrecognized assets that could potentially represent correlated omitted variables, I probe for possible effects of unrecognized assets. Harris and Ohlson (1987) argue that aggressive exploration creates goodwill. Because firms with aggressive exploration effort replace a larger percentage of reserves, I use the percentage of reserves added in the current year as a proxy for goodwill. I repeat the analysis adding this variable as another regressor, and the inferences drawn from the tests are unaffected.

In two-stage estimation, one typically uses parameters estimated in the first-stage regression to generate regressors used in the second-stage regression. Because the parameters estimated in the first-stage regression are themselves random variables rather than fixed values, one risks understating the second-stage standard errors if in the second stage the values of the generated regressors are treated as fixed values rather than as random variables estimated with error (Pagan 1984; Murphy and Topel 1985). The results I report treat the first-stage estimates as fixed values; therefore, the second-stage standard errors potentially are understated. To assess whether any such understatement influences my inferences, I use the procedure outlined in Murphy and Topel (1985) to adjust the second-stage standard errors and repeat the test of H1. Intuitively, the Murphy and Topel (1985) adjustment transforms the second-stage standard errors by a function of the first-stage standard errors. The second-stage-adjusted standard errors are indeed larger, but inferences are qualitatively unchanged, remaining significant at the 0.01 level or stronger.

Finally, estimation error in the deflator BOE could bias the measurement error tests. Both BOE and OG_PV are functions of reserve quantities, so any estimation error in reserve quantities affects both measures. Deflating oil and gas asset present values by barrel-of-oil equivalent units offsets errors in reserve quantity estimates in both the numerator and denominator, so the deflated present value measure of oil and gas assets may manifest less measurement error variance than the undeflated measure. OG_HC, not a function of reserve quantities, is unaffected by error in estimating reserve quantities, so when deflated it may exhibit more measurement error variance. That is, deflating by barrel-of-oil equivalent units may dampen measurement error variance in deflated oil and gas asset present values but amplify it in deflated oil and gas asset historical costs. I address this concern in three ways. First, I purge barrel-of-oil equivalent units of measurement error by regressing it on oil and gas sales revenue (a size variable highly correlated with barrel-of-oil equivalent units but unlikely to have substantial measurement error), retain the resulting fitted values, and repeat the analyses after deflating by the fitted value of barrel-of-oil equivalent units. The results were virtually identical to those reported.

Second, I repeat the analyses using undeflated variables and base statistical inferences on a heteroskedasticity-consistent covariance matrix, because diagnostic tests indicate heteroskedasticity (White 1980). The undeflated analysis led to similar but significantly weaker results than the deflated analysis. I interpret the weaker significance levels as attributable to loss in estimation efficiency arising from the heteroskedasticity in the undeflated model.

Third, I simulate the effect of measurement error in barrel-of-oil equivalent units on the Type I error rate in a test of measurement error variance in deflated oil and gas asset present values and historical costs when the null hypothesis of equal variances is true in the undeflated variables. Simulation results indicate that for plausible ranges of measurement error in the deflator and the oil and gas asset measures, deflating inflates the Type I error rate by only 0.30 of 1 percent due to a simultaneous dampening of measurement error in deflated oil and gas asset present values and an amplifying of measurement error in deflated oil and gas asset historical costs. (11) Based on (1) the instrumental variable analysis, (2) the similarity of deflated and undeflated results, and (3) the simulation analysis, I conclude that noise in the deflator is unlikely to have influenced my inferences.

VI. INTERPRETATION AND CONCLUDING COMMENTS

I am able to replicate the findings of prior research when I estimate annual, imputed value models similar to the models these prior studies used (Magliolo 1986; Harris and Ohlson 1987; Shaw and Wier 1993). In particular, during 1984-88 (the years common to both my study and prior studies) the present value measure of oil and gas assets exhibits significantly less explanatory power for stock prices than the corresponding historical cost measure when I use the restricted model specifications from prior research. However, specification tests show that these annual, imputed value models are misspecified, and reject this approach in favor of an unrestricted, fixed-effects balance sheet valuation model. In the unrestricted, fixed-effects model, oil and gas assets measured at present value exhibit significantly more explanatory power for stock prices than the corresponding historical cost measure, both in the 1984-1996 full period and in the 1984-88 subperiod.

Consistent with the valuation analysis, I find that measurement error variance in the present value measure of oil and gas assets is less than in the corresponding historical cost measure, in both the 1984-1996 full period and the 1984-88 subperiod that corresponds to the period examined in prior research. Analysis of across-firm and across-time variation in present value measurement error variance reveals that the measurement error increases in full cost firms as revisions in reserve quantity estimates increase and as firm-specific discount rates deviate from the uniform 10 percent rate that SFAS No. 69 requires. There is weak evidence that present value measurement error variance decreases when oil price volatility is high, and no evidence that present value measurement error variance is different when firms employ an external petroleum engineer to estimate reserve volumes rather than relying on their own internal engineers.

Overall, the evidence suggests that model misspecification, rather than measurement error or time-period idiosyncrasy, most likely explains the weak value relevance of present value measures of oil and gas assets reported in prior research. My findings are important because (1) they help resolve an anomaly in the literature, and (2) they demonstrate that present value offers a viable means of obtaining reliable fair value estimates for oil and gas assets--nonfinancial assets that have little firm-specific value and are traded in active markets. Of course, I cannot rule out that sampling difference contributes to the differences between my results and those reported in prior research, nor can I eliminate the possibility that time-period idiosyncratic factors unique to the period 1979-1983 (i.e., the period examined in prior research that I do not examine) accounts for the weak association between stock prices and the oil and gas asset present value measure as reported in Magliolo (1986) and Harris and Ohlson (1987).

One should interpret the results in this paper in light of the study's limitations. First, the measurement error analysis assumes that investors' implicit assessed value of assets and liabilities provides a meaningful benchmark for assessing measurement error. If stock prices deviate from "intrinsic value," then investor-assessed values provide noisy benchmarks that, in turn, could affect my inferences. Second, because my selection criteria limit the sample to large firms (i.e., firms on Compustat and CRSP) that can arguably devote more expertise and resources to preparing present value estimates, it is not clear whether the present value measure of oil and gas assets would have greater explanatory power and less measurement error in a sample of smaller firms. Finally, I interpret the measurement error tests under a maintained hypothesis about certain aspects of the measurement error structure as detailed in the Appendix. Although the assumptions that form the maintained hypothesis follow logically from an analysis of differences in recognition and measurement under reserve recognition vs. historical cost accounting for oil and gas operations, I cannot test the descriptive validity of these assumptions.

APPENDIX MEASUREMENT ERROR MODEL DETAILS

Financial statements and related disclosures measure the market values of assets and liabilities with error as Equation (2) in the body of the paper shows:

(2) OTHER_HC = OTHER_MV + [u.sub.1] OG_i = [S.sub.i] x (OG_MV + [u.sub.2i]) LIAB_HC = LIAB_MV + [u.sub.3]

Each error term, [u.sub.x], is a random variable with variance [[sigma].sup.2.sub.x]. Covariance between x and y is denoted [[sigma].sub.x,y]. [S.sub.i] is a parameter reflecting the difference in scale between OG_HC and OG_PV. Measurement error as defined by Equation (2) arises when accounting values and market values become misaligned.

Rao (1973), Garber and Klepper (1980), Barth (1989, 1991) and Choi et al. (1997) show that measurement error in least squares regressors causes biased coefficient estimates. Their findings suggest that a least squares regression of the theoretical valuation model (specified as Equation [1] in the body of the paper) estimated using measured-with-error accounting values as proxies for the unobservable market values will yield coefficient bias as specified in Equations (A1) and (A2) when OG_MV is proxied by OG_PV and OG_HC, respectively.

(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[[phi].sub.i] in Equation (A1) and [[delta].sub.i] in Equation (A2) measure the variances/covariances among the measurement error terms ([u.sub.1], [u.sub.2i], and [u.sub.3]). [[alpha].sub.ij] in Equation (A1) measures the partial correlations among the accounting measures when OG_PV proxies for OG_MV, and is operationally defined as the slope coefficients obtained from the regression specified in Equation (A3):

(A3) OTHER_HC = [[alpha].sub.10] + [[alpha].sub.12]OG_PV + [[alpha].sub.13]LIAB_HC + [e.sub.1] OG_PV = [[alpha].sub.20] + [[alpha].sub.21]OTHER_HC + [[alpha].sub.23]LIAB_HC + [e.sub.2] LIAB_HC = [[alpha].sub.30] + [[alpha].sub.31]OTHER_HC + [[alpha].sub.32]OG_PV + [e.sub.3]

[[beta].sub.ij] measures the partial correlations among the accounting measures when OG_HC proxies for OG_MV and is operationally defined as the slope coefficients obtained from the regression in Equation (A4):

(A4) OTHER_HC = [[beta].sub.10] + [[beta].sub.12]OG_HC + [[beta].sub.13]LIAB_HC + [e.sup.*.sub.1] OG_PV = [[beta].sub.20] + [[beta].sub.21]OTHER_HC + [[beta].sub.23]LIAB_HC + [e.sup.*.sub.2] LIAB_HC = [[beta].sub.30] + [[beta].sub.31]OTHER_HC + [[beta].sub.32]OG_PV + [e.sup.*.sub.3]

Choi et al. (1997) show that Equations (A1) and (A2) can be re-expressed as shown in Equations (A5) and (A6), respectively:

(A5) [MVE1.sup.*] = [[phi].sub.0] + [[phi].sub.1][Z1.sub.OTHER_HC] + [[phi].sub.2][Z1.sub.OG_PV] + [[phi].sub.3][Z1.sub.LIAB_HC] + [[epsilon].sub.1]

(A6) [MVE2.sup.*] = [[delta].sub.0] + [[delta].sub.1][Z2.sub.OTHER_HC] + [[delta].sub.2][Z2.sub.OG_HC] + [[delta].sub.3][Z2.sub.LIAB_HC] + [[epsilon].sub.2]

where:

(A7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[MVE1.sup.*] equals MVE - (OTHER_HC + OG_PV + LIAB_HC) and [MVE2.sup.*] equals MVE - (OTHER_HC + OG_HC + LIAB_HC).

Subtracting from [[delta].sub.i] from [[phi].sub.i] cancels common covariance terms, yielding:

(A8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Rearranging Equation (A8) yields Equation (5) in the body of the paper:

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The parentheses below the covariance difference terms in Equation (5) identify the expected sign of the expression based on the posited sign of and relationship among the covariance difference terms as discussed next.

Because measurement error is defined as misalignment between accounting and market values, any factor causing market values to increase (decrease) relative to accounting values also creates a negative (positive) realized value for the measurement error term. Thus, by definition, measurement error terms and market values must move in opposite directions, implying negative covariance, or [[sigma].sub.OTHER_MV,u.sub.1] < 0, [[sigma].sub.OG_MV,u.sub.2i] < 0, and [[sigma].sub.LIAB_MV,u.sub.3] < 0. Furthermore, the measurement error terms will not be independent, because interest rate shocks should trigger simultaneous misalignment between accounting and market values of all assets and liabilities. Because, first, measurement error terms are not independent and, second, measurement error and market values have negative covariance, it follows that measurement error in oil and gas assets will have negative covariance with OTHER_MV and positive covariance with LIAB_MV, or [[sigma].sub.OTHER_MV,u.sub.2i] < 0 and [[sigma].sub.LIAB_MV,u.sub.2i] > 0.

Moreover, because the same set of common factors (changes in interest rates and expected cash flows) creates measurement error in OTHER_HC, LIAB_HC, and OG_HC whereas only one of these factors (changes in interest rates) creates measurement error in OG_PV, measurement error in OG_HC as compared to OG_PV should be more strongly associated with measurement error in OTHER_HC and LIAB_HC, and their market values. Consequently, measurement error covariance in OG_PV ([[sigma].sub.x,u.sub.2PV]) will be of the same sign yet smaller in absolute value (i.e., weaker) than measurement error covariance in OG_HC ([[sigma].sub.x,u.sub.2HC]). That is, [absolute value of [[sigma].sub.x,u.sub.2HC]] > [absolute value of [[sigma].sub.x,u.sub.2PV]]. Based on the chain of logic that [[sigma].sub.OG_MV,u.sub.2i] < 0, [[sigma].sub.OTHER_MV,u.sub.2i] < 0, [[sigma].sub.LIAB_MV,u.sub.2i] > 0 and [absolute value of [[sigma].sub.x,u.sub.2HC]] > [absolute value of [[sigma].sub.x,u.sub.2PV]], I conclude that the covariance difference terms in Equation (5) will have the following signed values: [[sigma].sub.OTHER_MV,u.sub.2HC] - [[sigma].sub.OTHER_MV,u.sub.2HC] < 0, [[sigma].sub.OG_MV,u.sub.2PV] - [[sigma].sub.OG_MV,u.sub.2HC] > 0, and [[sigma].sub.LIAB_MV,u.sub.2HC] - [[sigma].sub.LIAB_MV,u.sub.2PV] > 0. This line of logic shows that two of the three covariance difference terms should be positive. Additionally, because the magnitude of OG_MV is larger than OTHER_MV (because oil and gas firms invest the largest fraction of their total assets in oil and gas assets), and because covariance is a magnitude-sensitive metric, I expect the negative covariance difference term, [[sigma].sub.OTHER_MV,u.sub.2HC] -- [[sigma].sub.OTHER_MV,u.sub.2PV], to be smaller in absolute value than the positive covariance difference term, [[sigma].sub.OG_MV,u.sub.2PV] -- [[sigma].sub.OG_MV,u.sub.2HC]. As a result, I expect the covariance terms in Equation (5) to net to a positive signed value.

A statistical test of H1, that [[sigma].sup.2.sub.u.sub.2PV] = [[sigma].sup.2.sub.u.sub.2HC], based on Equation (5) is: [H.sub.0]: [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi].sub.1] + [[sigma].sub.2] - [[phi].sub.3] = 0. Because the covariance terms in Equation (5) should net to a positive value, the coefficient function [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi].sub.1] + [[phi].sub.2] - [[phi].sub.3] is biased toward a positive value under the null hypothesis that measurement error variance in OG_PV and OG_HC are the same (i.e.,[H.sub.0]: [[sigma].sup.2.sub.u.sub.2PV] = [[sigma].sup.2.sub.u.sub.2PV] = [[sigma].sup.2.sub.u.sub.2HC]. Finally, Appendix Table A1 summarizes the covariance structure that I posit based on the measurement differences between OG_HC and OG_PV.

Control for Scale Effects

The role of scale is evident when I re-express the specification of OG_PV and OG_HC in Equation (2) as:

(A9) OG_PV = [S.sub.PV] x (OG_MV + [u.sub.2PV]) and OG_HC = [S.sub.HC] x (OG_MV + [u.sub.2HC])

where [S.sub.PV] and [S.sub.HC] are scale factors. In this revised specification, the variance of measurement error in OG_PV is [S.sup.2.sub.PV] x [[sigma].sup.2.sub.u.sub.2PV] and the variance of OG_HC is [S.sup.2.sub.HC] x [[sigma].sup.2.sub.u.sub.2HC]. Thus, one cannot reliably test [H.sub.0]: [[sigma].sup.2.sub.u.sub.2PV] = [[sigma].sup.2.sub.u.sub.2HC] unless [S.sub.PV] = [S.sub.HC]. Multiplying OG_HC by [S.sub.PV]/[S.sub.HC] transforms [u.sub.2HC] to the same scale as [u.sub.2PV], and thus facilitates a scale-free test of [H.sub.0]: [[sigma].sup.2.sub.u.sub.2PV] = [[sigma].sup.2.sub.u.sub.2HC]. Consequently, I ran all measurement error regressions after substituting ([S.sub.PV] /[S.sub.HC]) x OG_HC in place of OG_HC. I estimate [S.sub.PV]/[S.sub.HC] by dividing the mean of OG_PV by the mean OG_HC.

TABLE A1 Posited Signs of and Relations among Covariances Covariance Reasoning [[sigma].sub.OTHER_MV,u.sub.t] < 0 Measurement error is defined [[sigma].sub.OG_MV,u.sub.2i] < 0 as misalignment between LIAB_[MV,u.sub.3] accounting and market values. Any factor causing market values to increase (decrease) relative to accounting values creates a negative (positive) realized measurement error. Thus, by definition, measurement error terms and market values must move in opposite directions, implying negative covariance. [[sigma].sub.u.sub.1.u.sub.2i] > 0 Asset and liability values [[sigma].sub.u.sub.1.u.sub.3] < 0 are sensitive to similar [[sigma].sub.u.sub.2i.u.sub.3] < 0 factors, implying a positive covariance between asset market values and a negative covariance between asset market values and liability market values (the covariance is negative since liabilities are defined as negative values). Since these changes in asset and liability values cause changes of the opposite sign in their related accounting measurement error terms, the error terms [u.sub.1] and [u.sub.2i] will exhibit positive covariance while [u.sub.3] will exhibit negative covariance with [u.sub.1] and [u.sub.2i]. [[sigma].sub.OTHER_MV,u.sub.2t] < 0 Implied by the positive [[sigma].sub.OG_MV,u.sub.1] < 0 covariance in asset measurement error terms ([[sigma].sub.u.sub.1.u.sub. 2i] > 0) and the negative covariance with asset values ([[sigma].sub.OTHER_MV,u.sub.1] < 0 and [sigma.sub.OG_MV, u.sub.2i] [[sigma].sub.LIAB_MV,u.sub.1] > 0 Implied by the negative [[sigma].sub.LIAB_MV,u.sub.2i] > 0 covariance between asset and liability measurement error ([[sigma].sub.u.sub.1.u.sub.3] < 0 and [[sigma].sub.u.sub.2i.u.sub.3] < 0) and the negative covariance between liability values and measurement error ([[sigma].sub.LIAB_MV,u.sub.3] < 0). [[sigma].sub.OTHER_MV,u.sub.3] > 0 Implied by the negative [[sigma].sub.OG_MV,u.sub.3] > 0 covariance between asset measurement error ([[sigma].sub.OTHER_MV,u.sub.1] < 0 and [[sigma].sub.OG_MV, u.sub.2i] < 0) and the negative covariance in asset and liability measurement error ([[sigma].sub.u.sub.1.u. sub.3] < 0 and ([[sigma].sub.u.sub.1.u.sub.3] < 0). [[sigma].sub.u.sub.1.u.sub.2HC] > OG_PV is updated at each [[sigma].sub.u.sub.1.u.sub.2PV] balance sheet date to reflect [[sigma].sub.OTHER_MV,u.sub.2HC] changing expectations of < [[sigma].sub.OTHER_MV,u.sub.2PV] future cash flows. OTHER_HC [[sigma].sub.OG_MVu.sub.2HC] and OG_HC are not similarly < [[sigma].sub.OG_MV,u.sub.2PV] updated. The same set of common factors (changes in interest rates and changes in expected future cash flows) creates measurement error in both OTHER_HC and OG_HC, while only one of these common factors (changes in interest rates) creates measurement error in OG_PV. Thus, I expect the positive covariance between measurement error in OTHER_HC and OG_HC to be stronger than the positive covariance of measurement error between OTHER_HC and OG_PV. Similar reasoning leads to the conclusion that asset market values covary more negatively with the measurement error in OG_HC than with the measurement error in OG_PV. [[sigma].sub.u.sub.2HC.u.sub.3] < Same reasoning as above [[sigma].sub.u.sub.2PV.u.sub.3] except the negative [[sigma].sub.LIAB_MV,u.sub.2HC] covariance between > [[sigma].sub.LIAB_MV,u.sub.2PV] [u.sub.2i] and [u.sub.3] and the positive covariance between LIAB_MV and [u.sub.2i] will be weaker in OG_PV than in OG_HC. TABLE 1 Sample Descriptive Statistics and Tests for Differences in Means across Successful Efforts and Full Cost Firms (a,b) Successful Efforts Firms n Mean Std. Dev. Median MVE 370 4.48 2.52 4.06 OTHER_HC 370 2.11 2.17 1.27 OG_HC 370 3.47 1.27 3.43 OG_PV 370 3.98 3.99 3.78 LIAB_HC 370 -2.91 2.12 -2.61 OG_PV OTHER_HC + OG_PV 370 0.70 0.18 0.73 SIZE 370 836.41 1,723.43 136.47 BETA 370 0.76 0.70 0.78 BOE 370 191.40 384.14 29.25 OG_PV - OG_HC 370 0.52 1.42 0.40 OG_PV/OG_HC 370 1.39 1.32 1.12 EST_ERROR 370 5.35 129.65 2.45 INSIDE 370 0.21 0.41 0.00 OIL_VOLATILITY 370 13.99 11.36 12.75 RATE 132 0.04 0.03 0.03 Significance Level from Two-Tailed Test for Difference in Means between Full Cost Firms Successful Efforts and Std. Full Cost n Mean Dev. Median Firms MVE 375 5.31 4.05 4.13 0.00 OTHER_HC 375 2.28 2.79 1.43 0.36 OG_HC 375 4.15 1.77 4.10 0.00 OG_PV 375 4.57 1.68 4.30 0.00 LIAB_HC 375 -3.27 2.55 -2.64 0.04 OG_PV OTHER_HC + OG_PV 375 0.72 0.17 0.75 0.11 SIZE 375 217.86 454.19 57.84 0.00 BETA 375 0.79 0.82 0.76 0.51 BOE 375 42.03 78.82 14.99 0.00 OG_PV - OG_HC 375 0.42 1.67 0.25 0.42 OG_PV/OG_HC 375 1.31 0.91 1.07 0.31 EST_ERROR 375 4.16 52.27 2.39 0.08 INSIDE 375 0.11 0.31 0.00 0.00 OIL_VOLATILITY 375 16.21 15.27 12.75 0.03 RATE 106 0.07 0.04 0.10 0.00 (a) n denotes number of firm-year observations. (b) Variable definitions: MVE = price per share of common stock (measured as of the first trading day 90 days after fiscal year-end) multiplied by numbers of shares outstanding, deflated by ending oil and gas reserves measured in barrel-of-oil equivalent units; OTHER_HC = the amortized historical cost (book value) of assets excluding oil and gas properties, deflated by ending oil and gas reserves measured in barrel-of-oil equivalent units; OG_HC = the amortized historical cost (book value) measure of oil and gas assets, deflated by ending oil and gas reserves measured in barrel-of-oil equivalent units; OG_PV = the SFAS No. 69 discounted present value of oil and gas assets, deflated by ending oil and gas reserves measured in barrel-of-oil equivalent units; LIAB_HC = the amortized historical cost (book value) of liabilities multiplied by - 1, deflated by ending oil and gas reserves measured in barrel-of-oil equivalent units; SIZE = price per share of common stock (measured as of the first trading day 90 days after fiscal year-end) multiplied by shares outstanding (in millions); BETA = systematic risk estimated using weekly returns across the one-year period before the balance sheet date; BOE = barrel-of-oil equivalent units (in millions), calculated by summing the physical units of oil (measured in barrels) and one-sixth of the physical units of natural gas (measured in thousands of cubic feet); EST_ERROR = proxy for the magnitude of the error in estimating reserve quantities, and is the absolute value of coefficient of variation in a firm's revision to the beginning of year measure of OG_PV. It is a firm-specific measure calculated using the firm's reserve revisions across the period 1984-1996; INSIDE = a binary variable assigned a value of 1 if the firm relied on its own petroleum engineering staff to prepare reserve quantity estimates, and 0 otherwise; OIL_VOLATILITY = the annualized standard deviation in the natural logarithm of the oil price relative. It is calculated as [sigma] [square root of 250], where [sigma] is the estimated standard deviation of the natural logarithm of the ratio of the spot price of oil on day t to the spot price of oil on day t - 1 calculated across days 0 to -59, where day 0 corresponds to the balance sheet date; and RATE = a proxy for the degree of distortion in OG_PV introduced by the uniform 10 percent discount rate, and is calculated as |r - 0.10|, where r is the pension settlement rate the firm uses in accounting for defined benefit pension costs. TABLE 2 Pooled Fixed-Effects and Annual Regression Estimates of Measurement Error Model and Related Tests of the Reliability of the Present Value Measure of Oil and Gas Assets as Compared to the Reliability of the Historical Cost Measure of Oil and Gas Assets: 1984-1996 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Panel A: Estimates of Measurement Error Model Pooled Two-Way Fixed- Effects Variable Coefficient Estimation FC x [Z1.sub.OTHERASSETS_HC] [[phi].sub.1,FC] 2.11 (4.34) *** FC x [Z1.sub.0&GASSETS_PV] [[phi].sub.2,FC] 2.80 (23.61) *** FC x [Z1.sub.LIAB_HC] [[phi].sub.3,FC] -1.30 (-2.84) *** SE x [Z1.sub.OTHERASSETS_HC] [[phi].sub.1,SE] -0.87 (-1.67) * SE x [Z1.sub.O&GASSETS_PV] [[phi].sub.2,SE] 1.64 (26.93) *** SE x [Z1.sub.LIAB_HC] [[phi].sub.3,SE] 1.01 (1.90) * FC x [Z2.sub.OTHERASSETS_HC] [[delta].sub.1,FC] 3.25 (6.57) *** FC x [Z2.sub.O&GASSETS_HC] [[delta].sub.2,FC] 3.76 (16.73) *** FC x [Z2.sub.LIAB_HC] [[delta].sub.3,FC] -2.99 (-6.44) *** SE x [Z2.sub.OTHERASSETS_HC] [[delta].sub.1,SE] -0.49 (-0.92) SE x [Z2.sub.O&GASSETS_HC] [[delta].sub.2,SE] 1.85 (11.52) *** SE x [Z2.sub.LIAB_HC] [[delta].sub.3,SE] 0.01 (0.02) Annual Cross-Sectional Estimation Mean of Annual Variable Estimates Z1 (b) Z2 (b) FC x [Z1.sub.OTHERASSETS_HC] -3.40 -3.37 *** -1.49 (-0.94) FC x [Z1.sub.0&GASSETS_PV] 1.87 26.50 *** 5.30 *** (7.35) FC x [Z1.sub.LIAB_HC] 3.55 5.76 *** 3.23 *** (1.60) SE x [Z1.sub.OTHERASSETS_HC] -0.56 -0.60 -0.40 (-0.17) SE x [Z1.sub.O&GASSETS_PV] 1.63 148.15 *** 14.17 *** (41.09) SE x [Z1.sub.LIAB_HC] 1.83 5.55 *** 6.76 *** (1.54) FC x [Z2.sub.OTHERASSETS_HC] -2.26 -0.74 -0.29 (-0.21) FC x [Z2.sub.O&GASSETS_HC] 1.66 11.73 *** 3.87 *** (3.25) FC x [Z2.sub.LIAB_HC] 1.86 1.68 * 0.84 (0.47) SE x [Z2.sub.OTHERASSETS_HC] -0.18 0.61 0.39 (0.17) SE x [Z2.sub.O&GASSETS_HC] 1.52 18.75 *** 10.74 *** (5.20) SE x [Z2.sub.LIAB_HC] 0.83 2.20 ** 2.55 *** (0.61) Annual Cross-Sectional Estimation Siginificantly Different from 0 at [less than or equal to] 0.10 Level Variable Num. > 0 Num. < 0 FC x [Z1.sub.OTHERASSETS_HC] 2 5 FC x [Z1.sub.0&GASSETS_PV] 11 0 FC x [Z1.sub.LIAB_HC] 7 0 SE x [Z1.sub.OTHERASSETS_HC] 1 1 SE x [Z1.sub.O&GASSETS_PV] 13 0 SE x [Z1.sub.LIAB_HC] 5 0 FC x [Z2.sub.OTHERASSETS_HC] 3 5 FC x [Z2.sub.O&GASSETS_HC] 9 1 FC x [Z2.sub.LIAB_HC] 3 3 SE x [Z2.sub.OTHERASSETS_HC] 2 1 SE x [Z2.sub.O&GASSETS_HC] 13 0 SE x [Z2.sub.LIAB_HC] 3 0 Panel B: Test of HI, Specified in Null Form as [[delta].sub.1] - [[delta].sub.2] + [[delta].sub.3] - [[phi].sub.1] + [[phi].sub.2] - [[phi].sub.3] = 0 Annual Cross-Sectional Pooled Estimation Two-Way Fixed- Mean of Effects Annual Description Estimation Estimates Z1 * [c] Value of [[delta].sub.1,FC] - [[delta].sub.2,FC] + [[delta].sub.3,FC - [[phi].sub.1,FC] + [[phi].sub.2,FC] - [[phi].sub.3,FC] -1.52 -0.34 Z-statistic testing the null hypothesis in FC firms -12.01 *** -1.48 -5.33 *** Value of [[delta].sub.1,FC] - [[delta].sub.2,SE] + [[delta].sub.3,SE] - [[phi].sub.1,SE] + [[phi].sub.2,SE] - [[phi].sub.3,SE] -0.83 -0.51 Z-statistic testing the null hypothesis in SE firms -6.16 *** -2.03 -7.32 *** Annual Cross-Sectional Estimation Significantly Different from 0 at [less than or equal to] 0.10 Level Description Z2 * [c] Num. > 0 Num. < 0 Value of [[delta].sub.1,FC] - [[delta].sub.2,SE] + [[delta].sub.3,FC - [[phi].sub.1,FC] + [[phi].sub.2,FC] - [[phi].sub.3,FC] Z-statistic testing the null hypothesis in FC firms -2.32 *** 2 7 Value of [[delta].sub.1,FC] - [[delta].sub.2,SE] + [[delta].sub.3,SE] - [[phi].sub.1,SE] + [[phi].sub.2,SE] - [[phi].sub.3,SE] Z-statistic testing the null hypothesis in SE firms -6.41 *** 0 9 *,**,*** Denote significance in two-tailed tests at the 0.10, 0.05, and 0.01 levels, respectively. (a) In the fixed-effects estimation, the parameters [[phi].sub.j] and [[delta].sub.j] denote firm fixed effects and [[phi].sub.t] and [[delta].sub.t] are year fixed effects. In the annual cross-sectional estimation, [[phi].sub.j] and [[delta].sub.j] denote separate intercepts for firms in the full cost and successful efforts groups. For brevity, the estimated values of these parameters are not reported. FC and SE are dummy variables assigned a value of 1 if the firm uses the full cost or successful efforts method, respectively, and 0 otherwise. The Z regressors are orthogonal values of OTHER_HC, OG_PV, OG_HC, and LIAB_HC obtained from first-stage regressions as shown in the Appendix. All variables are deflated by barrel-of-oil equivalent units, MVE1 * equals MVE - (OTHER_HC + OG_PV + LIAB_HC) and MVE2 * equals MVE - (OTHER_HC + ([[S.sub.PV]/[S.sub.HC]] x OG_HC) + LIAB_HC). All other variables are defined in Table 1. (b) Z1 and Z2 statistics test whether the time-series mean asymptotic t-statistic equals 0. Z1 equals 1/[square root of N] [[SIGMA]].sup.N.sub.i=1] [t.sub.j]/[square root of [k.sub.j]/ ([k.sub.j] - 2)] where [t.sub.j] is the asymptotic t-statistic for year j, [k.sub.j] is the degrees of freedom for year j, and N is the number of years. Z2 equals [bar]t/(stddev(t)/[square root of(N - 1))]. (c) Z1 * and Z2 * statistics test whether the time-series mean Z-statistic equals 0. Z1 * equals [bar]z [square root of N] and Z2 * equals [bar]z/(stddev(z)/[square root of (N - 1))]. The tests reported in Panel B are based on a [chi square] statistic with 1 degree of freedom obtained from a Wald test. I convert the [chi square] statistic to an equivalent Z-statistic (z = [square root of [chi square](1 df))] to construct the Z1 * and Z2 * statistics. TABLE 3 Pooled Fixed-Effects Test for Differences in the Reliability of Oil and Gas Assets Measured at Present Value as Compared to the Reliability When Measured at Historical Cost--For Data Partitioned Based on Factors Expected to Influence the Across-Firm and Across-Time Reliability of the Present Value Measure: 1984-1996 (a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Panel A: Tests for Full Cost Firms Positioning Variable EST_ ERROR INSIDE (Test of (Test of H1a) H1b) Test for a difference between D = 1 and D = 0 in reliability of oil and gas assets measured at present value as compared to reliability when measured at historical cost. Test specified as: [[delta].sub.4,FC] - [[delta].sub.5,FC] + [[delta].sub.6,FRC] - [[phi].sub.4,FC] + [[phi].sub.5,FC] - [[phi].sub.6,FC = 0 Value of coefficient function 1.26 0.27 [chi square] statistic from a Wald test of null hypothesis 25.27 *** 0.27 POSITIONING VARIABLE OIL_VOLATILITY RATE (Test of H1c) (Test of H1d) Test for a difference between D = 1 and D = 0 in reliability of oil and gas assets measured at present value as compared to reliability when measured at historical cost. Test specified as: [[delta].sub.4,FC] - [[delta].sub.5,FC] + [[delta].sub.6,FRC] - [[phi].sub.4,FC] + [[phi].sub.5,FC] - [[phi].sub.6,FC] = 0 Value of coefficient function 0.15 0.89 [chi square] statistic from a Wald test of null hypothesis 0.79 3.34 ** Panel B: Tests for Successful Efforts Firms Positioning Variable EST_ ERROR INSIDE (Test of (Test of H1a) H1b) Test for a difference between D = 1 and D = 0 in reliability of oil and gas assets measured at present value as compared to reliability when measured at historical cost. Test specified as: [[delta].sub.4,SE] - [[delta].sub.5,SE] + [[delta].sub.6,SE] - [[phi].sub.4,SE] + [[phi].sub.5,SE] - [[phi].sub.6,SE] = 0 Value of coefficient function -0.03 0.16 [chi square] statistic from a Wald test of null hypothesis 0.01 0.30 POSITIONING VARIABLE OIL_VOLATILITY RATE (Test of H1c) (Test of H1d) Test for a difference between D = 1 and D = 0 in reliability of oil and gas assets measured at present value as compared to reliability when measured at historical cost. Test specified as: [[delta].sub.4,SE] - [[delta].sub.5,SE] + [[delta].sub.6,SE] - [[phi].sub.4,SE] + [[phi].sub.5,SE] - [[phi].sub.6,SE] = 0 Value of coefficient function 0.07 0.12 [chi square] statistic from a Wald test of null hypothesis 0.28 0.11 (a) *,**,*** Denote significance at the 0.10, 0.05, and 0.01 levels, respectively, in a nondirectional test. The parameters [[phi].sub.j] and [[delta].sub.j] denote firm fixed effects and [[phi].sub.t] and [[delta].sub.t] are year fixed effects. D is a binary partitioning variable that is assigned a value of 1 or 0. [[phi].sub.0] and [[delta].sub.0] represent the main effect (intercept shift) associated with firm-years in the D = 1 condition of the partitioning variable. The partitioning variables are EST_ERROR, INSIDE, OIL_VOLATILITY, and RATE. EST_ERROR = 1 when the absolute value of the coefficient of variation of reserve revisions is above the sample median, and 0 otherwise. INSIDE = 1 when the company's own petroleum engineering staff estimate reserve quantities and 0 when an outside petroleum engineering firm estimates reserve quantities. OIL_VOLATILITY = 1 when oil price volatility is above the sample median, and zero otherwise. RATE = 1 when the distortion induced by a uniform 10 percent discount rate is above the sample median, 0 otherwise. FC and SE are dummy variables assigned a value of 1 if the firm uses the full cost or successful efforts method, respectively, and 0 otherwise. All other variables are defined in Table 1. A positive value for the coefficient function [[delta].sub.4] - [[delta].sub.5] + [[delta].sub.6] - [[phi].sub.4] + [[phi].sub.5] - [[phi].sub.6] means that high values of the partitioning variable are associated with more measurement error in the present value of oil and gas assets. TABLE 4 Tests of Model Specification, 1984-88 Present Value Model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Historical Cost Model: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Unrestricted Model (a) [R.sup.2] [R.sup.2] Present Historical Value Cost Model Description Model Model 1 Pooled with firm and time fixed effects and time-varying slopes 0.83 0.81 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 2 Pooled with firm and time fixed effects but slopes held constant across time 0.77 0.74 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] = [[gamma].sub.k,t+1]) 3 Pooled with time-varying slopes and time fixed effects but no firm fixed effects 0.45 0.42 ([[alpha].sub.j] = [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 4 1984 cross-sectional 0.49 0.29 5 1985 cross-sectional 0.81 0.77 6 1986 cross-sectional 0.36 0.18 7 1987 cross-sectional 0.55 0.50 8 1988 cross-sectional 0.25 0.34 Unrestricted Model (a) Restricted Model (a) Significance Levels from [R.sup.2] Vuong Test of Present [R.sup.2.sub.PV Value Model Description = [R.sup.2.sub.H Model 1 Pooled with firm and time fixed effects and time-varying slopes 0.07 0.74 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 2 Pooled with firm and time fixed effects but slopes held constant across time 0.11 0.74 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] = [[gamma].sub.k,t+1]) 3 Pooled with time-varying slopes and time fixed effects but no firm fixed effects 0.58 0.17 ([[alpha].sub.j] = [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 4 1984 cross-sectional 0.50 0.53 5 1985 cross-sectional 0.55 0.54 6 1986 cross-sectional 0.32 0.02 7 1987 cross-sectional 0.39 0.02 8 1988 cross-sectional 0.26 0.02 Restricted Model (a) [R.sup.2] Significance Historical Levels from Cost Vuong Test of Model Description Model [R.sup.2.sub.PV] = [R.sup.2.sub.HC] 1 Pooled with firm and time fixed effects and time-varying slopes 0.73 0.97 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 2 Pooled with firm and time fixed effects but slopes held constant across time 0.71 0.18 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] = [[gamma].sub.k,t+1]) 3 Pooled with time-varying slopes and time fixed effects but no firm fixed effects 0.28 0.05 ([[alpha].sub.j] = [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 4 1984 cross-sectional 0.34 0.42 5 1985 cross-sectional 0.62 0.52 6 1986 cross-sectional 0.19 0.07 7 1987 cross-sectional 0.21 0.10 8 1988 cross-sectional 0.22 0.12 Significance Level from Test of Restricted vs. Unrestricted Model (a) Present Hist. Value Cost Model Description Model Model 1 Pooled with firm and time fixed effects and time-varying slopes 0.00 0.00 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 2 Pooled with firm and time fixed effects but slopes held constant across time 0.01 0.08 ([[alpha].sub.j] [not equal to] [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] = [[gamma].sub.k,t+1]) 3 Pooled with time-varying slopes and time fixed effects but no firm fixed effects 0.00 0.00 ([[alpha].sub.j] = [[alpha].sub.t] [not equal to] [[alpha].sub.t+1]; [[gamma].sub.k,t] [not equal to] [[gamma].sub.k,t+1]) 4 1984 cross-sectional 0.55 0.51 5 1985 cross-sectional 0.02 0.20 6 1986 cross-sectional 0.00 0.09 7 1987 cross-sectional 0.00 0.01 8 1988 cross-sectional 0.03 0.08 Significance Levels Significance Levels from Model from Model Comparisons Comparisons Model Comparisons PV HC PV HC 1 vs. 2 0.22 0.67 0.21 0.13 1 vs. 3 0.00 0.00 0.00 0.00 (a) The parameters aj and % denote firm and year fixed effects; [[gamma].sub.kt] denotes slope coefficients free to vary by year. Consistent with prior research, the restricted model requires [[gamma].sub.1t] = [[gamma].sub.3t] = 1 in both the historical cost and present value models and [[gamma].sub.2t,FC] = [[gamma].sub.2t,SE] in the present value model. (b) Test based on following F-statistic: F[J, n - K] = [([SSE.sub.R] - [SSE.sub.UR])/J]/[[SSE.sub.UR]/(n - K)]. SSE denotes sum of squared residuals for restricted (R) and unrestricted (UR) models, J denotes the number of restrictions, K is the number of parameters, and n is the number of observations. TABLE 5 Alternative Tests of Hypothesis 1 Based on Differences in the Explanatory Power of Oil and Gas Assets Measured at Present Value Versus Historical Cost--Analysis Based on Pooled Data and Data Partitioned Based on Factors Expected to Influence the Across-Firm and Across-Time Reliability of the Present Value Measure: 1984-1996 Present Value Model: MVE = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Historical Cost Model: MVE = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Significance Levels from Present Historical Vuong Tests Value Cost for Equal Model Model [R.sup.2]s Test of H1 [R.sup.2] from a pooled 0.68 0.66 0.08 fixed-effects regression (b) Mean [R.sup.2] from annual 0.36 0.32 0.06 (d) cross-sectional 0.12 (e) regressions (c) Test of H1a [R.sup.2] from a pooled 0.73 0.71 0.19 fixed-effects regression that includes only firm-years with EST_ERROR below pooled median [R.sup.2] from a pooled 0.63 0.61 0.37 fixed-effects regression that includes only firm-years with EST_ERROR at or above pooled median Test of H1b [R.sup.2] from a pooled 0.67 0.65 0.17 fixed-effects regression that includes only firm-years with INSIDE = 0 [R.sup.2] from a pooled 0.83 0.82 0.57 fixed-effects regression that includes only firm-years with INSIDE = 1 Test of H1c [R.sup.2] from a pooled 0.69 0.69 0.80 fixed-effects regression that includes only firm-years with OIL_VOLATILITY below pooled median [R.sup.2] from a pooled 0.71 0.67 0.00 fixed-effects regression that includes only firm-years with OIL_VOLATILITY at or above pooled median Test of H1d [R.sup.2] from a pooled 0.67 0.65 0.18 fixed-effects regression that includes only firm-years with RATE below pooled median [R.sup.2] from a pooled 0.73 0.71 0.27 fixed effects regression that includes only firm-years with RATE at or above pooled median *, **, *** Denote significance at the 0.10, 0.05, and 0.01 levels, respectively, in a two-tailed test. (a) The parameters [[alpha].sub.j] and [[alpha].sub.t] denote firm and year fixed effects. FC and SE are dummy variables assigned a value of 1 if the firm uses the full cost or successful efforts method, respectively, and 0 otherwise. All other variables are defined in Table 1. (b) The pooled fixed-effects specification corresponds to unrestricted Model 2 in Table 4. (c) The annual cross-sectional specification corresponds to unrestricted Models 4-8 in Table 4. (d) Test of whether the time-series mean Vuong z-statistic equals 0, based on Z1 * = z [square root of N]. (e) Test of whether the time-series mean Vuong z-statistic equals 0, based on Z2 * = z/stddev(z)/[square root of (N - 1)].

I appreciate helpful comments by Mary Barth (the associate editor), Charles Boynton, and two anonymous reviewers. Funding for much of this project was provided by the Institute of Petroleum Accounting at the University of North Texas.

Submitted February 2000

Accepted July 2001

(1) The FASB issued Statement of Financial Accounting Concepts (SFAC) No. 7 in February 2000 to provide conceptual guidance on the accounting use of present values.

(2) I use the term value relevance to mean a statistically significant association with stock prices or stock returns in the predicted direction.

(3) I do not propose a similar hypothesis for gas price volatility because I was unable to obtain natural-gas spot prices for much of my sample.

(4) I do not assume that market values implicit in share prices are unbiased or error-free measures of economic assets or liabilities. Rather, they represent benchmarks against which I assess measurement error.

(5) I repeated the tests without the [S.sub.PV]/[S.sub.HC] rescaling factor. Results were qualitatively unchanged.

(6) Barrel-of-oil equivalent units (BOE), the deflator commonly used in prior oil and gas valuation studies, is a measure of the oil-equivalent energy content of oil and gas reserves. One calculates it by summing the physical units of oil (measured in barrels) and one-sixth of the physical units of natural gas (measured in thousands of cubic feet). (The thermal energy content of one thousand cubic feet of natural gas is approximately one-sixth the energy content of a barrel of oil.)

(7) To retain a reasonable sample size, I do not exclude observations with missing values for the pension discount settlement rate. Thus, analysis of RATE partitions is based on the subset of 238 firm-year observations with available discount settlement rate data.

(8) Z1* equals [bar]z [square root of N] and Z2* equals [bar]z/(stddev(z)/[square root of (N - 1))]. Z1* assumes independence in the annual Z-statistics, whereas Z2* corrects for potential lack of independence (Healy et al. 1987; Christie 1990; Barth 1994).

(9) Z1* equals [bar]z [square root of N] and Z2* equals [bar]z/(stddev(z)/[square root of (N - 1))]. Z1* assumes independence in the annual Z-statistics, whereas Z2* corrects for potential lack of independence.

(10) I performed two types of change-form analysis. One involved simply first-differencing the transformed explanatory variables (i.e., the Z variables) used in estimating the models reported. This approach provides some insight into whether the measurement error results are influenced by omitted variables that are correlated with MVE1* and MVE2*. The other involved first-differencing the "raw" explanatory variables before running the first-stage regressions and then calculating the transformed explanatory variables from the first-differenced raw variables. Because changes in successive balance sheets articulate through the income statement (plus transactions with shareholders), this second approach examines whether measurement error differs between historical cost and reserve recognition earnings. Both approaches yielded similar results.

(11) The intuition behind this result is simple. If oil reserves estimates are off by 1 barrel of oil, then this will induce 1 unit of measurement error in BOE but will induce (p - x)/[(1 + .10).sup.n] units of measurement error in OG_PV, where p is the current price of oil, x is the current cost of extracting that barrel of oil, and n is the number of years until that barrel will be extracted. In most cases, (p - x)/[(1 + .10).sup.n] substantially exceeds 1. Thus, the dampening of measurement error in deflated OG_PV is minor.

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Jeff P. Boone Mississippi State University

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Author: | Boone, Jeff P. |
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Publication: | Accounting Review |

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Date: | Jan 1, 2002 |

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