
    BURLINGTON NORTHERN INC. v. The UNITED STATES.
    No. 30-72.
    United States Court of Claims.
    March 10, 1982.
    
      Robert A. Klayman, Washington, D. C., atty., of record, for plaintiff; Daniel B. Rosenbaum and Caplin & Drysdale, Washington, D. C., of counsel.
    George L. Squires, with whom was Acting Asst. Atty. Gen., John F. Murray, Washington, D. C., for defendant; Theodore D. Peyser, Washington, D. C., of counsel.
    Before NICHOLS, KASHIWA and BENNETT, Judges.
   OPINION

BENNETT, Judge:

This action by taxpayer is for the recovery of federal income taxes alleged to have been erroneously assessed and collected for the calendar years 1956, 1957 and 1958. The aggregate recovery sought is $9,369,-081.64, plus statutory interest.

The case is now before the court on the exceptions of plaintiff to the findings of fact and recommended opinion of Trial Judge George Willi. All other issues having been resolved by agreement before trial, the only question presented for decision is whether, for the years in suit, plaintiff is entitled, under section 167(a) of the Internal Revenue Code of 1954, to ratable depreciation deductions with respect to the costs incurred to install railroad grading and tunnel bores. The availability of such deductions depends on whether such properties can be shown to have a reasonably ascertainable useful life in the taxpayer’s trade or business. Under the regulations on depreciation, a useful life capable of being estimated is indispensable for the institution of a system of depreciation. Treas.Reg. § 1.167(a)-l(b) (1964); Harrah’s Club v. United States, 229 Ct.Cl.-,-, 661 F.2d 203, 207 (1981).

We have duly considered the briefs and oral argument of counsel and have given appropriate attention to the findings of fact and conclusion of law of the trial judge. We hold that plaintiff has herein failed to demonstrate a reasonable useful life for its railroad grading and tunnel bores. While our decision comports with the conclusion reached by the trial judge, we have chosen to present our own discussion of the issues in this case.

I. BACKGROUND

A. Facts

Plaintiff is successor in interest to the Northern Pacific Railway Company. Northern Pacific was a land grant railroad largely constructed in the latter part of the 19th century beginning at St. Paul and traversing the western plains of Minnesota, North Dakota and eastern Montana, across the Rockies in western Montana and Idaho, through the plains of eastern Washington, over the Cascade Mountains and into the Puget Sound area. By the period in suit its rail system covered about 6,500 route miles with approximately 9,900 miles of track. As of December 31, 1956, Northern Pacific had installed grading at a total cost of $121,894,149 and had installed, beginning in 1883, 61 tunnel bores at a total cost of $4,962,022.

Railroad grading is the contoured surface prepared by man to receive the track structure (j.e., ballast, ties, rail, switches and associated track materials) on which rolling stock moves. It is the cost of creating this contoured surface, or roadbed, that is involved in this litigation.

A tunnel bore is the horizontal passageway that is made through a hill or mountain in order to accommodate the placement of a roadbed through the same. Although the construction of a railroad tunnel ordinarily includes the cost of (1) a lining, (2) ventilation and drainage systems, (3) portals and (4) lighting, it is only the cost of creating the airspace of the passageway with which this litigation is concerned.

Railroad grading and tunnels are subject to deterioration from severe weather conditions and seasonal change. Maintenance ordinarily can restore grading and tunnels which have been adversely affected by the elements, but the cost of such maintenance can be high. With proper maintenance, neither grading nor tunnel bores are susceptible to physical exhaustion through use or otherwise.

Historically, railroads could capitalize the costs of their grading and tunnel bores but were unable to depreciate those items because of the uncertainties as to the length of their useful life. For these assets, railroads followed the retirement-replacement method of accounting which generally produced deductions only when an asset was retired or replaced. In 1969, Congress provided railroads with the option to amortize their grading and tunnel bores first placed in service after 1968 on the basis of a 50-year average life. This provision was amended in 1976 to permit similar amortization of grading and tunnel bores, the original use of which had commenced prior to 1969. However, this has never been the exclusive means by which grading and tunnel bores placed in service before 1969 could be depreciated. Taxpayers have been permitted to depreciate these items whenever they have been able to satisfy the strict requirements of section 167.

B. The Actuarial Method

At trial, plaintiff attempted to establish a reasonably ascertainable useful life for its grading and tunnel bores by means of “the actuarial method of life analysis.”

The “actuarial method” purports to analyze the past retirement experience of depreciable assets for purposes of estimating their future service life and represents the application to industrial property of statistical procedures developed in the life insurance field for analyzing data on human mortality. The fundamental principle of the actuarial method is that groups of similar assets possess, on the average, similar service life characteristics. The goal of this statistical approach for determining the useful life of an asset is to generate a survivor curve for the particular asset and then to analyze that curve to determine that asset’s useful life. Application of the actuarial method involves three phases: data gathering and mathematical calculations, life analysis and life estimation.

In the first phase, data is collected on the annual volume of additions to and retirements from the group of assets under study, and also on the age in years of each asset at the time of its retirement and the age of all the surviving assets. These assets, both those retired and those surviving, are then assigned to appropriate “age intervals,” each'interval representing a single year. Next, a determination as to the annual rate at which property was retired from each of these age interval groups is made. Under this procedure, the annual retirement rate is equal to retirements during an age interval divided by the total number of assets in that age interval. The survivor rate for that interval is equal to 100 percent minus the retirement rate. The survivor rate is then used to determine the percentage of property in each age interval which survives until the beginning of the next age interval. By multiplying the survivor rate for the first age interval by the survivor rate for the second age interval, and so on through all age intervals for which data is available, the percentage surviving at the end of each age interval on a cumulative basis is determined. The resulting sequence of percentages is then plotted on a graph. The horizontal axis of this graph represents the property age in years, while the vertical axis represents the percentage of all assets surviving. This plotted data is then smoothed to form the observed survivor curve which is characteristic of the property group studied during the years for which data was available. Where, as here, the historical data are insufficient to produce a complete survivor curve, an incomplete curve, or “stub” curve, results. Since an average useful life of an asset cannot be determined without a complete survivor curve, it is necessary to complete and smooth the rough curve artificially. While there are a number of acceptable methods of smoothing and extending this stub curve, the method used herein involves the matching of the stub curve with one of the 18 “Iowa curves." These are predetermined full-length survivor curves derived from empirical studies of numerous types of industrial properties, which through repeated application and testing have come to be regarded as generalized models of retirement behavior.

The second phase of the actuarial method, life analysis, involves the selection of the Iowa curve which appears most compatible with the stub survivor curve. Selection can be done mathematically or, most commonly, visually. The analyst’s judgment also contributes to the choice of the appropriate Iowa curve since selection of the curve which best represents a reasonable portrayal beyond the original data points is based, in part, on his familiarity with the property under study. Thus, the Iowa curve chosen may provide an indication of the property’s probable average service life, based upon past retirement experience.

In the life estimation phase, the analyst evaluates the cause of past retirements and applies his judgment as to whether such causes may be expected to continue in the future. He also considers the impact of anticipated future developments. Any necessary adjustments or refinements are then made to the average service life reflected by the Iowa curve.

C. Prior Cases

Use of the actuarial method was first sanctioned by this court in the cases of Pennsylvania Power & Light Co. v. United States, 188 Ct.Cl. 76, 411 F.2d 1300 (1969) (hereinafter PP&L), and Virginia Electric & Power Co. v. United States, 188 Ct.Cl. 120, 411 F.2d 1314 (1969) (hereinafter VEP-CO), wherein depreciation deductions were allowed for right-of-way easements, assets previously regarded as nondepreciable.

In PP&L, plaintiff’s expert witnesses calculated the useful lives of the assets in issue by applying both the actuarial method as previously described, employing the Iowa curves, and a “geometric mean” method to available data. At the outset, the court concluded that the right-of-way easements were intangible assets the useful lives of which extended beyond the lives of the power lines constructed thereon. After careful review of the proffered testimony, and stressing the fact that the government had presented no expert witness in rebuttal, this court accepted plaintiff’s estimates and allowed the desired deductions:

Despite the impreciseness of taxpayer’s estimates of useful lives, they are reasonable, and their application will result in spreading the recapture of the pertinent capital costs over the very substantial periods of time above-stated. The fact that taxpayer has not established a useful life for each of its easements and for each item of initial clearing costs, but rather a useful life for the mass properties in each of the pertinent accounts, does not detract from the reasonableness of its estimates. [188 Ct.Cl. at 88, 411 F.2d at 1307.]

Similar, but more extensive, proof was offered in VEPCO. As in PP&L, the plaintiff’s useful life estimates were derived from historical statistical studies using the actuarial and geometric mean methods in conjunction with the Iowa curves. However, in addition thereto, these initial mathematical projections were refined by further testimony providing reasonable predictions of probable future developments in plaintiff’s business. Consequently, this court, again noting the defendant’s failure to rebut the expert’s predictions, granted the claim for depreciation, but reached a different conclusion as to the length of the useful life for these easements in this taxpayer’s trade or business. 188 Ct.Cl. at 127-28, 411 F.2d at 1317-18. Subsequently, the Internal Revenue Service acquiesced in the decisions in those cases. Rev.Rul. 72-403, 1972-2 C.B. 102.

Relying on these decisions for guidance, the Tax Court first extended the use of the actuarial method to a case involving railroad grading and tunnel bores. Chesapeake & Ohio Ry. v. Commissioner, 64 T.C. 352 (1975) (hereinafter C&O). Identifying the critical inquiry as whether the taxpayer had demonstrated with adequate proof that its claimed deductions embodied sufficiently “accurate estimation[s]” of the useful lives of the properties in question so as to render the resultant allocations meaningful, the court was persuaded that the petitioner therein had established reasonably ascertainable useful lives for both its grading and tunnel bores:

Without here addressing ourselves to the relative bearing of all of the considerable amount of evidence before us, we think, on the basis of the entire record, that the actuarial method of life analysis is, in the circumstances of this case, an acceptable means by which to extrapolate from petitioner’s relevant experience with retirements. While we are acutely aware of the limitations of such a statistical approach as well as the critical importance of applying informed judgment to its results, we are nonetheless inclined to accept the explanations and conclusions of petitioner’s highly qualified expert witnesses. Thus petitioner has presented a reasonable case, soundly based upon the 80 or more years of its carefully recorded retirement experience. And notwithstanding the borderline character of the reliability of an extrapolation in such circumstances we conclude, albeit without strong confidence, that the statistical studies of the sort presented here may form the basis for making acceptable predictions of future retirements. [64 T.C. at 380.]

In reaching its decision, the court was moved both by our holdings in PP&L and VEPCO and by the admission at trial by the government’s expert witness that the lives therein were more determinable than the lives in the utility cases because of the completeness of the petitioner’s data. However, the Tax Court was careful to limit the extent of its holding:

The decision we have reached here is based solely on the particular facts and circumstances of the record before us and is in no way intended to foreclose a different decision on the basis of a different record. Thus, while we recognize the possibility that the analytic means employed here, or some variant thereof, may be brought to bear theoretically in respect of some other class of business property, our decision here is not to be considered a binding precedent in connection with the applicability of life studies with respect to other types of property which have hitherto been regarded as nondepreciable assets. In particular we wish to correct any possible impression that by the result herein we have endorsed a general rule in respect of the depreciability of other railroads’ grading and tunnel bores. That question must await resolution in light of the pertinent facts and circumstances of each taxpayer. [64 T.C. at 383-84.]

Later decisions of the Tax Court have maintained this case-by-case approach. In Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497 (1980) (hereinafter Southern Pacific), the evidence presented, which included a life analysis, was held to be sufficiently similar to that presented in the C&O case to warrant a similar result. Again the court gave a cautionary warning that its decision was not to be construed as establishing a general rule. 75 T.C. at 801. And in Kansas City Southern Ry. v. Commissioner, 76 T.C. 1067, 1152-56 (1981) (hereinafter Kansas City Southern), ratable depreciation deductions were allowed for a taxpayer’s railroad grading upon a showing of a reasonably determinable useful life through use of the actuarial method. By contrast, depreciation deductions were denied where the taxpayer failed to carry his burden of proof as to useful life because he presented virtually no evidence on that question. Spartanburg Terminal Co. v. Commissioner, 66 T.C. 916, 928-32 (1976).

It is with this history in mind that we turn to examine the evidence presented by plaintiff in the present case.

II. DISCUSSION

A. Statute and Regulations

The statutory authority for allowance of depreciation for the taxable years 1956, 1957 and 1958 is section 167(a). This Code section provides that there shall be allowed as a depreciation deduction a reasonable allowance for the exhaustion, wear and tear of property used in a trade or business, including a reasonable allowance for obsolescence.

The pertinent regulations provide as follows:

Sec. 1.167(a)-l. Depreciation in general. (a) Reasonable allowance. Section 167(a) provides that a reasonable allowance for the exhaustion, wear and tear, and obsolescence of property used in the trade or business or of property held by the taxpayer for the production of income shall be allowed as a depreciation deduction. The allowance is that amount which should be set aside for the taxable year in accordance with a reasonably consistent plan (not necessarily at a uniform rate), so that the aggregate of the amounts set aside, plus the salvage value, will, at the end of the estimated useful life of the depreciable property, equal the cost or other basis of the property as provided in section 167(g) and § 1.167(g)-1.
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(b) Useful life. For the purpose of section 167 the estimated useful life of an asset is not necessarily the useful life inherent in the asset but is the period over which the asset may reasonably be expected to be useful to the taxpayer in his trade or business or in the production of his income. This period shall be determined by reference to his experience with similar property taking into account present conditions and probable future developments. Some of the factors to be considered in determining this period are (1) wear and tear and decay or decline from natural causes, (2) the normal progress of the art, economic changes, inventions, and current developments within the industry and the taxpayer’s trade or business, (3) the climatic and other local conditions peculiar to the taxpayer’s trade or business, and (4) the taxpayer’s policy as to repairs, renewals, and replacements. * * * If the taxpayer’s experience is inadequate, the general experience in the industry may be used until such time as the taxpayer’s own experience forms an adequate basis for making the determination. The estimated remaining useful life may be subject to modification by reason of conditions known to exist at the end of the taxable year and shall be redetermined when necessary regardless of the method of computing depreciation. However, estimated remaining useful life shall be redetermined only when the change in the useful life is significant and there is a clear and convincing basis for the redetermination. For rules covering agreements with respect to useful life, see section 167(d) and § 1.167(d) — 1.

A useful life for depreciation purposes need not be established with certainty. Indeed, only a “reasonable approximation” or even a “rough estimate” need be shown. Burnet v. Niagara Brewing Co., 282 U.S. 648, 655, 51 S.Ct. 262, 265, 75 L.Ed. 594 (1931); United States v. Ludey, 274 U.S. 295, 302, 47 S.Ct. 608, 610, 71 L.Ed. 1054 (1927). However, since it is the primary purpose of depreciation accounting to further the integrity of periodic income statements, a meaningful allocation of the cost entailed in the use of the asset to the periods to which it contributes must be made. Massey Motors, Inc. v. United States, 364 U.S. 92, 104, 80 S.Ct. 1411, 1418, 4 L.Ed.2d 1592 (1960); See Coca-Cola Bottling Co. v. United States, 203 Ct.Cl. 18, 28-29, 487 F.2d 528, 534 (1973).

Under the statute, a depreciation deduction is allowed for the physical exhaustion and obsolescence of property. “Wear and tear” refers to physical deterioration of an asset which is not offset by repairs. See United States v. Ludey, 274 U.S. at 300-01, 47 S.Ct. at 610. As previously stated, railroad grading and tunnel bores may be kept in service indefinitely by means of proper maintenance. Thus, the predominant reason for the retirement of these assets is obsolescence.

Obsolescence is covered by Treas.Reg. § 1.167(a)-9 (1960), which provides in pertinent part: .

The depreciation allowance includes an allowance for normal obsolescence which should be taken into account to the extent that the expected useful life of property will be shortened by reason thereof. Obsolescence may render an asset economically useless to the taxpayer regardless of its physical condition. Obsolescence is attributable to many causes, including technological improvements and reasonably foreseeable economic changes. Among these causes are normal progress of the arts and sciences, supersession or inadequacy brought about by developments in the industry, products, methods, markets, sources of supply, and other like changes, and legislative or regulatory action. In any case in which the taxpayer shows that the estimated useful life previously used should be shortened by reason of obsolescence greater than had been assumed in computing such estimated useful life, a change to a new and shorter estimated useful life computed in accordance with such showing will be permitted. No such change will be permitted merely because in the unsupported opinion of the taxpayer the property may become obsolete.

“Obsolescence may arise from changes in the art, shifting of business centers, loss of trade, inadequacy, supersession, prohibitory laws, and other things which, apart from physical deterioration, operate to cause plant elements or the plant as a whole to suffer diminution in value.” U. S. Cartridge Co. v. United States, 284 U.S. 511, 516, 52 S.Ct. 243, 245, 76 L.Ed. 431 (1932). As pointed out by the Tax Court in C&O:

Unlike physical exhaustion through use which more readily lends itself to empirical study and follows more predictable patterns, exhaustion through obsolescence often defies observation while in progress, succumbing to certainty only in retrospect. This is in part a reflection of the fact that obsolescence is to some extent a function of managerial policy rather than a physical phenomenon. [64 T.C. at 379.]

Consequently, a determination of useful life, whether based on physical exhaustion or on obsolescence, is one of fact. Zimmerman v. Commissioner, 67 T.C. 94, 106 (1976); Radio Station WBIR, Inc. v. Commissioner, 31 T.C. 803, 817 (1959).

B. Evidence Presented

The thrust of plaintiff’s position is that the outcome of this case is governed by our decisions in PP&L and VEPCO. As plaintiff understands those cases, where there is presented a body of historical retirement experience and if there is testimony in the record detailing why such retirements occurred and that those retirements will continue to occur in the future, with either the same or greater frequency, then an appropriate case has been made for application of the actuarial method in conjunction with the Iowa curves. Characterizing this as the correct “legal standard” set forth by those decisions, plaintiff seeks to have that standard applied to the facts herein.

At trial, plaintiff presented a substantial body of material to document its useful life estimates. Plaintiff presented evidence of the retirement history for Northern Pacific grading and tunnel bores. Plaintiff further presented evidence by engineering, operations and executive personnel, and introduced into evidence voluminous documentary materials, explaining the reasons that these retirements had occurred. Plaintiff admitted that regular maintenance completely offset the wear and tear for its railroad grading, and that obsolescence was the principal cause of retirements of Northern Pacific grading and tunnel bores. ■ Furthermore, plaintiff contended that this evidence showed that, for the years in issue, the same reasons were expected to result in additional retirements in the future with even greater frequency. It employed Robley Winfrey and John J. Reilly, expert witnesses who, individually or together, had testified previously in PP&L, VEPCO, C&O and Kansas City Southern. These experts, using the data and other information compiled by plaintiff and applying the actuarial method of life analysis, formulated detailed estimates of the useful lives of Northern Pacific grading and tunnel bores.

Plaintiff claims that the data base from which the opinions of its experts were derived is superior to that available in the earlier cases. Relying on the similarity of its proof to that of the earlier cases, plaintiff asserts that it too is entitled to an allowance for depreciation.

Undaunted by its past defeats, the government has continued to contest the propriety of the claimed deductions. However, defendant’s strategy has apparently shifted from whether or not grading and tunnel bores are depreciable properties per se to whether or not plaintiff’s method of estimating the useful lives of these properties is valid. While defendant still denies the depreciability of these items, the brunt of its attack focuses on the actuarial method itself. Defendant states that this is the first litigation in which, when confronted by a taxpayer’s reliance on the actuarial method in conjunction with the Iowa curves, it has undertaken a thorough analysis into and exposition of the methodology’s character and composition.

Generally, defendant has asserted that plaintiff’s application of the actuarial method was improper because this methodology assumes, without itself proving, that plaintiff’s major contention is true: i.e., that Northern Pacific grading and tunnel bores are depreciable properties. Specifically, defendant assails plaintiff’s efforts with respect to the data gathering phase and life analysis phase of the method.

According to the defendant, plaintiff’s analyst improperly based his estimates in part on retirement data which is inappropriate in a study of useful life. In particular, defendant maintains that, contrary to the regulations, plaintiff’s experts relied on hindsight information, retirement data for the years 1957 through 1973, in formulating their estimates; that the data base itself improperly included retirements which did not constitute actual permanent retirements from service, such as daylighted tunnels, condemnations and other like-kind exchanges and sales of assets for continued service; and that plaintiff’s use of percentages of dollars invested in grading and tunnel bores surviving over a series of age intervals to develop a stub survivor curve was less efficient than plotting retirement ratios over a series of age intervals.

As to the life analysis phase of plaintiff’s study, defendant contends that use of the Iowa curves was fundamentally inappropriate since plaintiff’s analyst failed to follow the procedures set forth in Bulletin 125, the study from which the Iowa curves were developed. Defendant alleges that the analyst ignored all retirement data except that for the 1957-73 period in selecting a curve, failed to consider any of the curves other than the ones ultimately chosen and, thus, failed to select the Iowa curves which best fit the retirement data in this case. Most importantly, in the view of defendant, since implicit in the Iowa curves is the assumption that as property ages, the rate of retirement increases, plaintiff’s methodology was inapplicable because the retirement experience of Northern Pacific grading and tunnel bores did not reflect this characteristic. Defendant points out that the property groups underlying the Iowa curves did not include railroad grading and tunnel bores. Moreover, defendant continues, plaintiff’s description of its process for completing the life analysis phase of the actuarial method, that is, selecting the proper Iowa curve, disclosed no clear procedure for the analyst to follow, but rather relied largely on the individual’s subjective judgment.

Finally, defendant complains that use of the method was invalid because plaintiff failed to apply probability theory to, or measure the standard for error in, its conclusions.

C. Deficiencies in Plaintiff’s Proof

Our task in this case is essentially factual in nature: to decide whether plaintiff’s grading and tunnel bores have reasonably determinable useful lives, as required by the regulations, such that a reasonable annual allowance for depreciation may thereupon be computed. As the trial judge astutely recognized, the present controversy concerns only the timing, and not the allow-ability of expense deductions related to these assets. In other words, the issue is whether this expense is to be charged rat-ably over the life of the assets as plaintiff contends or, as the government maintains, only in lump sum whenever the assets are actually retired from service. See Chicago, Burlington & Quincy R.R. v. United States, 197 Ct.Cl. 264, 284-87, 455 F.2d 993, 1005-07, rev’d on other grounds, 412 U.S. 401, 93 S.Ct. 2169, 37 L.Ed.2d 30 (1972).

As previously mentioned, plaintiff’s assets are virtually immune to physical decay; that is, they are largely unaffected by the mere passage of time. In our opinion, the grading and tunnel bores herein are akin to the intangible assets involved in PP&L and VEPCO. Thus, in order for plaintiff to meet its burden of proof as to the incorrectness of the government’s determination denying depreciation deductions, Welch v. Helvering, 290 U.S. 111, 115, 54 S.Ct. 8, 9, 78 L.Ed. 212 (1933), it must establish that obsolescence will cause its assets to be retired from service and it must further show when this will reasonably occur. PP&L, 188 Ct.Cl. at 82, 411 F.2d at 1304.

We first direct our attention to the latter portion of this requirement. A careful examination of the useful life estimates offered by plaintiff as evidence of when retirement of its assets could reasonably be expected to occur leads us to question the use of the actuarial method herein. To be more precise, it is not the use of the actuarial method as a general proposition that concerns us. Rather, we are principally interested in the manner in which this methodology was applied in the present case.

In his report, plaintiff’s expert witness, Mr. Reilly, explained the means by which he selected the Iowa curves from which he derived his conclusions as to service life:

The actuarial method, as applied by me in this study, involves the statistical procedure known as the “annual rate method” of analysis. This procedure relates the retirements during each age interval to the exposures at the beginning of that interval, the ratio of these being the annual retirement ratio. Subtracting each retirement ratio from unity yields a sequence of annual survival ratios from which a survivor or mortality curve can be determined. The length of this curve depends primarily upon the number of years of experience available. Normally, an incomplete or stub survivor curve results. While there are a number of acceptable methods of smoothing and extending this stub survivor curve in order to define the area under it from which the average life is determined, the well-known Iowa Type Curve Method was used in this study. The selection of the appropriate type curve and average life is accomplished by plotting the stub curve on transparent graph paper and superimposing it on Iowa curves of the various types and of various average lives drawn to the same scale, and then determining by judgment which Iowa type curve best suits the stub. This gives an indication of average life as experienced in the past. The final step in estimating an appropriate average life is to evaluate the average service lives derived from past experience to determine whether they are appropriate for application in the foreseeable future. [Emphasis added.]

Using this approach, he concluded that Northern Pacific grading had an average service life of 100 years and that it followed the retirement characteristics of an R-l Iowa curve. He also concluded that Northern Pacific tunnel bores had an average service life of 80 years and followed the mortality characteristics of an R-2 Iowa curve.

Bulletin 125 includes a table in which each of the 176 property groups studied are listed, with a description of the property and its particular mortality experience and resulting Iowa curve classification set forth. For all R-l and R-2 curves shown, that table reflects:

Plaintiff’s exhibit No. 60, R. Winfrey, Statistical Analyses of Industrial Property Retirements (1935) at 142-49.

Upon consideration of the details of this approach, we are hesitant to overturn the determination of the Internal Revenue Service disallowing plaintiff’s claim for refund. First, we are concerned with the propriety of the execution of the second phase of the actuarial method under the facts of this case. We are not convinced that the particular curves used by Mr. Reilly in making his life analysis were relevant to the task at hand. These curves seem inappropriate as devices to describe the exponential retirement patterns and probable service lives for the assets herein when the properties underlying the curves were subject to few, if any, of the retirement factors affecting assets such as plaintiff’s. See footnote 26, supra. Try as we might, we fail to see the relevancy of curves reflecting the mortality characteristics of such diverse properties as submarine cable and railroad boxcars in estimating the probable retirement patterns of railroad grading and tunnel bores.

Mr. Reilly testified that in his opinion the R-l and R-2 Iowa curves reflected the life characteristics of railroad grading and tunnel bores. In other words, in his subjective judgment, the Iowa curves selected were the ones most appropriately suited to a projection of the likely future retirement behavior of the properties under consideration. At no time did he provide a logical explanation for the comparability of the retirement factors affecting the assets underlying the R-l and R-2 curves and those affecting grading and tunnel bores.

It is axiomatic that expert testimony is not binding on the court. Norfolk Dredging Co. v. United States, 175 Ct.Cl. 594, 621, 360 F.2d 619, 634 (1966). And it is certainly within the discretion of the court to decide whether or not an analyst has correctly exercised his judgment at each point during the employment of the actuarial method. See Southern Pacific, 75 T.C. at 794-96.

After careful scrutiny of the record, we find that plaintiff has failed to show that it exercised its judgment properly in selecting the Iowa curves used in its analysis. Where selected from among the available Iowa curves by an altogether visual perception of contour similarities, the results of which are then modified by the injection of the analyst’s subjective judgment, we are not satisfied that the results yielded by the extrapolation of the curves are reliable absent a showing of a reasonable relationship between the mortality characteristics of the properties underlying the curves selected and the mortality characteristics of the property under consideration.

The problems with plaintiff’s present procedure are dramatically illustrated by the testimony of Mr. Winfrey, another of plaintiff’s witnesses. Quite independent of Mr. Reilly, he matched each of the Iowa curves to the plaintiff’s grading retirement data for the period 1868 through 1956 and concluded that the S-0 curve fit best, resulting in a 220-year average service life. By contrast, Mr. Reilly selected an R-l curve with a 175-year average life for grading for the same period. And one of defendant’s expert witnesses, Ronald Bartyczak, attempting to track Mr. Reilly’s findings, concluded that the best R-l curve indicated a useful life of 225 years.

Given the disparity in the results reached by these experts, we are understandably reluctant to permit this type of unsubstantiated proof, particularly in light of the “borderline character of the reliability of an extrapolation in such circumstances.” C&O, 64 T.C. at 380. In sum, we do not feel that plaintiff has demonstrated with adequate proof a means for selecting an Iowa curve sufficiently dependable so as to provide an estimation of useful life such as to assure the “meaningful allocation of cost” envisioned by the statute.

We are not persuaded by plaintiff’s efforts to verify the accuracy of its curve selections through studies conducted on retirement patterns for periods subsequent to 1958. Absent some showing of relevancy, these results are as likely a product of coincidence as they are of quantitative similarity. Moreover, the reasonableness of any claim for depreciation must be determined upon the basis of conditions known to exist at the end of the period for which the claim is made. Treas.Reg. § 1.167(b)-0(a) (1956); Missouri Pac. R.R. v. United States, 204 Ct.Cl. 837, 859, 497 F.2d 1386, 1399 (1974); Johnson v. Commissioner, 302 F.2d 86, 88 (4th Cir.), cert. denied, 371 U.S. 904, 83 S.Ct. 206, 9 L.Ed.2d 164 (1962). Such evidence as presented herein is clearly unsatisfactory to establish that the Iowa curve selected to project an historical data base will produce a realistic forecast of the asset’s retirement pattern.

We are also troubled by plaintiff’s failure to corroborate its useful life estimates by any objective means. This is not to say that results obtained by the proper application of the actuarial method must be verified through the use of specific principles of mathematical statistics. Section 167(a) does not mandate such a requirement. But where, as here, a taxpayer necessarily attempts to fix the useful life of an admittedly long-lived asset through projections founded on studies of assets with decidedly shorter whole lives, evidence establishing a reliable statistical trend would assure confidence in any proffered results. To be sure, such information would have reduced the uncertainty inherent in the extrapolations presented in this case.

Moreover, it would appear logical that a user of a statistical method of proof such as the actuarial method, would apply statistical procedures to gauge the accuracy of its results. In the statistical discipline, the generally recognized method for determining the configuration of the curve that best fits observation points in a data base is the “least square” procedure. A companion test used to determine the reliability of the results indicated by the “least squares” method is the standard error of deviation. Neither of these procedures, nor to our knowledge any other, were used by plaintiff to minimize the risk of error in its projections. To our way of thinking, under the particular facts of this case, plaintiff’s failure to include some type of statistical verification in its proof does not demonstrate the application of informed judgment to the results to be obtained from the proper use of the actuarial method. Given the general difficulty of showing exhaustion wholly the result of obsolescence, Real Estate Title Co. v. United States, 309 U.S. 13, 15-17, 60 S.Ct. 371, 372-373, 84 L.Ed. 542 (1940); C&O, 64 T.C. at 379, such a showing would certainly reduce the degree of doubt in any proffered results to a reasonable level.

The result we reach with respect to the present case is not foreclosed by any of the prior decisions which have permitted the use of the actuarial method. In neither of the instances in which this method of proof was offered before this court did the government present any expert testimony on the subject. PP&L, 188 Ct.Cl. at 86, 411 F.2d at 1306; VEPCO, 188 Ct.Cl. at 127, 411 F.2d at 1318. Thus, a full and thorough consideration of taxpayers’ proof was precluded. Moreover, each of those decisions clearly indicated that the results reached were limited to the circumstances therein and the proof before the court. 188 Ct.Cl. at 87, 89, 411 F.2d at 1307-08; 188 Ct.Cl. at 123, 129-30, 411 F.2d at 1315, 1319.

Nor has the Tax Court stated a rule of general application regarding the use of life studies. Each time that court has examined the question of the depreciability of railroad grading and tunnel bores, it has been careful expressly to limit the ramifications of its decision. Southern Pacific, 75 T.C. at 801; C&O, 64 T.C. at 383-84. See also Kansas City Southern, 76 T.C. at 1153; Spartanburg Terminal Co. v. Commissioner, 66 T.C. 916, 928 (1976). Quite clearly that court has stated that the depreciability of railroad grading and tunnel bores, and concomitantly the propriety of using the actuarial method to achieve that result, must be determined in light of the pertinent facts and circumstances of each taxpayer.

We do not intend that our decision today be viewed as a disapproval of the actuarial method itself. Indeed, as the heretofore-mentioned decisions have shown, the statutory scheme of section 167 is sufficiently flexible to permit the use of statistical methods to establish a reasonably determinable useful life for an asset. We are confident that “with proper application and with the exercise of informed judgment, [the actuarial method] is capable of producing an acceptable estimate of asset life.” Southern Pacific, 75 T.C. at 796.

III. CONCLUSION

In summary, we hold that plaintiff has failed to demonstrate a reasonably ascertainable useful life for its railroad grading and tunnel bores so as to entitle it to depreciation deductions under section 167(a). Accordingly, as a matter of law, plaintiff cannot recover on its refund claims and its petition is dismissed.

NICHOLS, Judge,

concurring:

Everything that Judge Bennett says about the case is perfectly valid by my lights and I join in it, yet the overall effect I find somewhat unsettling. The reason for this may be the appearance of excessive respect for the so-called “actuarial method” of estimating useful life. Certainly by Judge Bennett’s showing it is, as used in this case, an example of the pompous pseudo-science that so often goes down readily with courts and lawyers. He had to write so as to avoid appearing disrespectful to our prior precedent decisions, and yet it appears reasonable to suppose that defendant might have achieved the same result in the prior cases, as here, if it had attacked the technique in the same vigorous manner. We lawyers are by occupational myopia incapable of seeing that the emperor has no clothes, until somebody tells us. Such a technique as plaintiff attempted here is never frozen into law, as plaintiff argued, merely by approved use in prior court cases, and the prior cases themselves make that clear. The most the precedents can do is to establish that testimony is admissible. How much weight, if any, it will have is for the trier of fact. Techniques of estimating useful life, like techniques to estimate fair market values or reasonable profits, are just techniques, not rules of law except where made so by statute or regulation. The careful trier of fact will, if he can, use two or three to test against a tentative conclusion and apply or abandon them to the extent he finds them useful or the reverse. Leesona v. United States, 220 Ct.Cl. 234, 259, 599 F.2d 958, 973 cert. denied, 444 U.S. 991, 100 S.Ct. 522, 62 L.Ed.2d 420 (1979).

Common sense suggests that the useful life of the gradings and tunnel bores of a line of railroad cannot exceed the useful life of the line of which they are a part. In this country a number of economically marginal railroad lines were built which with all the changes in transportation economics, have become financial disasters to their owners and have had to be abandoned. Naturally the gradings and tunnel bores along these lines were abandoned too. A good many of the retirements here involved were of that character. With regard to the main or “heart” line, some portions of the rights-of-way have been condemned, e.g., for reservoir flowage, and substitute rights-of-way obtained. The gradings and tunnel bores on the original rights-of-way also figure as retirements here, though such transactions can hardly be placed in any relationship to the obsolescence of such facilities. A third category has been the “daylighting” of tunnel bores, i.e., cutting them open overhead to eliminate tunnel ventilation problems. It is not surprising that as a matter of actual experience to 1956, or from then to date of trial, the likelihood of one of these kinds of retirements bore no discoverable relationship to the age of the facility. The “actuarial method,” as developed by plaintiff, required of the court a great and beautiful faith that such a relationship would somehow develop in the future, as the plotted curve dipped down.

As, in general, on uneconomic branch lines, the useful life of the gradings and tunnel bores ended with the economic useful life of the lines, so, conversely, the continued and vigorous useful life of the main line dictates some abandonments there because tracks must be straightened and grades reduced. To some extent abandonments are the result of obsolescence of the line; to some extent the result of the reverse of its obsolescence. The predictable obsolescence and wear and tear that we encounter with buildings and many kinds of transportation equipment and machinery, making estimates of useful life possible, have such diverse and disparate effects here that any estimate of useful life appears to me a ehimaera, conjured up for forensic purposes only. I question whether anyone trained in the difficult and demanding science of the actuary would acknowledge as his own the “actuarial method” as used herein.

KASHIWA, Judge,

dissenting:

I dissent.

There is no dispute here whether these assets, railroad gradings and tunnel bores, will physically wear out. It is agreed they will not. It is equally clear that despite their physical durability, these assets will someday be retired by plaintiff from service. Although Code § 167 is usually associated with annual allowances for the physical wasting of an asset, the statute by its express terms extends to annual allowances for anticipated obsolescence. According to Treas.Reg. § 1.167(a)-9, obsolescence may occur for a variety of reasons:

* * * Obsolescence is attributable to many causes, including technological improvements and reasonably foreseeable economic changes. Among these causes are normal progress of the arts and sciences, supersession or inadequacy brought about by developments in the industry, products, methods, markets, sources of supply, and other like changes, and legislative or regulatory action. * * *

Anticipation of obsolescence, of course, is required before the asset’s useful life to the business can be estimated. But an estimate is just that and need only be reasonable: mathematical certainty is not and has never been required when deriving useful life. See Treas.Reg. § 1.167(a)-l(b); Burnet v. Niagara Falls Brewing Co., 282 U.S. 648, 654-655, 51 S.Ct. 262, 264-265, 75 L.Ed. 594 (1931); United States v. Ludey, 274 U.S. 295, 302, 47 S.Ct. 608, 610, 71 L.Ed. 1054 (1927). See also Massey Motors, Inc. v. United States, 364 U.S. 92, 105, 80 S.Ct. 1411, 1418-1419, 4 L.Ed.2d 1592 (1960). Long ago, the Treasury implicitly recognized the uncertainties of anticipating obsolescence when Bulletin F approximated round-numbered useful lives for certain extremely durable assets, such as dams, tunnels, grading, and roads. See Bulletin F (revised January 1942) 58, 59, 61, 66, 67, reprinted in [1981] Index CCH Stand. Fed.Tax Rep. ¶¶ 310 et seq.

The majority discusses in great length how this taxpayer’s industrial depreciation experts derived the useful lives of its railroad gradings and tunnel bores. I perceive no need to repeat that discussion. It suffices to say the methodology consists of three steps: (1) the depiction of available retirement experience on partial or “stub surviv- or” curves; (2) the approximation of a useful life for the entire asset class based on a comparison of the stub curves and the 18 standard full-length survivor curves developed in industrial studies at Iowa State College (now Iowa State University); and (3) the evaluation and concomitant refinement of that approximate useful life in light of present conditions and anticipated developments within the industry. This methodology has been employed for almost 50 years in financial and regulatory accounting and has been endorsed (as the majority concedes) by several recent court decisions for purposes of the federal income tax. I find none of defendant’s arguments against the application of the methodology to these facts persuasive.

For example, defendant argues that the Iowa standard curves can be used only if the data on actual retirements clearly demonstrate retirements will increase as the asset class ages. That argument is inherently flawed and the majority apparently agrees with me that the argument should be ignored. Plaintiff’s experts on industrial depreciation included the civil engineer who developed the Iowa curves after extensive study. His testimony (and that of plaintiff’s other depreciation expert) is clear that because'the retirement rate for any industrial property will eventually increase, the Iowa curves are applicable to all industrial property. Defendant offered no contrary expert testimony on this point. Moreover, nothing within common sense dictates that the increasing retirement rate will be equally apparent at all times while the assets are in use. Industrial retirement experience simply does not always fall into neat arithmetic progressions. To hold plaintiff to such a standard ignores reality.

It is critical to point out that the Iowa curves were the result of specific studies, done over a period of years, to approximate the useful lives for particularly long-lived assets. These studies catalogued retirements, including those attributable solely to obsolescence, of the assets within 176 broad classifications. The 18 Iowa standard full-length curves were derived from the full-length curves of the 176 asset classes when it was found those 176 curves fell into 18 discrete patterns.

Recognizing the value of the empirical studies from which the Iowa standard curves are derived, and further recognizing that only a reasonable estimate of useful life need be made under Treas.Reg. § 1.167(a)-l(b), supra, this court has previously endorsed the methodology the present taxpayer employs. In Pennsylvania Power & Light Co. v. United States, 188 Ct.Cl. 76, 411 F.2d 1300 (1969), and Virginia Electric and Power Co. v. United States, 188 Ct.Cl. 120, 411 F.2d 1314 (1969), the taxpayers sought an allowance under Code § 167 for the anticipated obsolescence of real property easements and certain related costs. In those cases, as in the present one, recovery was premised on useful lives derived by John J. Reilly, a long-recognized expert on industrial depreciation, through the Iowa curves. There, as here, Mr. Reilly testified in exhaustive detail as to how his projections were obtained. In allowing the Pennsylvania Power and Virginia Electric plaintiffs recovery, we plainly embraced the methodology and I dissent because the majority fails to apply that methodology today.

The majority argues against the application of the Iowa curve methodology for two basic reasons. One is concern that the Iowa methodology, either in general or as applied here, is not statistically precise. But the Code requires not precision but rather reasonableness for an obsolescence allowance to be proper under section 167. Given the broad band of empirical experience underlying the Iowa curves, as well as the curves’ widespread acceptance for other accounting purposes, I have little trouble concluding that useful life projections based on the Iowa curves satisfy the reasonableness requirement of Code § 167.

The majority’s second reason for not accepting the useful lives projected from the Iowa curves is that the asset groups which underlie the particular Iowa curves plaintiff’s experts selected consist of boxcars and submarine cables, rather than other railroad gradings and tunnel bores. But that argument surely proves too much, for just as there are no assets underlying the Iowa curves precisely identical with railroad gradings and tunnel bores, neither were there assets within the Iowa study that had even a slight resemblance to the easements present in Pennsylvania Power, supra, and Virginia Electric, supra. Yet this court had little problem in those cases accepting useful lives derived from the Iowa curves. Moreover, by requiring that physically similar property underlie the particular Iowa curve that is selected, the majority disregards the very nature of the Iowa studies. The premise underlying the Iowa curves is that the retirement experience of all industrial properties, regardless of physical characteristics, will conform to one of the 18 standard curves. It follows from this premise that only the available retirement experience, i.e., the stub survivor curve, and not physical characteristics need be compared to project useful life. A taxpayer has always been free, notwithstanding the Iowa curves, to project useful life from that of physically similar property. Like property, however, cannot always be found and it is where no similar property exists that the alternate methodology of the Iowa curves was uniquely significant.

The tax practitioner is, I think, left after today’s majority opinion with two options when projecting. the useful life of an extremely durable asset. One option is to rely on those Iowa curves which contain at least in part the retirement experience of physically similar assets. For railroad gradings and tunnel bores, I imagine the likely candidates will be the Iowa curves reflecting the retirements of stone culverts or of various paving types. Those assets, like railroad gradings and tunnel bores, are particularly long lived and are inseparable physically from the realty they improve. This taxpayer might well have prevailed had those Iowa curves been selected.

A more likely option for the practitioner is to ignore the Iowa curves as a method of projection. If one must compare the retirement experience of like properties and anticipate technological developments whether the Iowa curves are used or not, the standard curves become at best a subtle refinement of, and merely cumulative to, an expert’s judgment. Such refinements are often lost, in this court as elsewhere, to the pragmatics of cost-conscious litigation. Given the widespread acceptance of the Iowa curves for financial and regulatory accounting, and further given the previous acceptance of the curves for tax accounting, I can only view that result as unfortunate. To repeat, I dissent. 
      
      . The trial judge’s recommended decision and conclusion of law were filed on November 6, 1980, in accordance with Rule 134(h).
     
      
      . All statutory references herein pertain to the Internal Revenue Code of 1954, as amended, unless otherwise indicated.
     
      
      . Plaintiff is a Delaware corporation formed on March 2, 1970, as a result of a merger of the Northern Pacific Railway Company, the Great Northern Railway Company, the Chicago, Burlington & Quincy Railroad Company and the Pacific Coast Railroad Company. Plaintiff has, by operation of law, succeeded to the entire interest of the Northern Pacific Railway Company.
     
      
      . By December 31, 1956, $10,321,715, or 8.5 percent, of this grading, and 19 tunnel bores costing $759,472, or 15.3 percent, had been retired for all causes.
     
      
      . For federal tax purposes, Northern Pacific claimed and was allowed current deductions for all such maintenance expenses.
     
      
      . Northern Pacific was, and plaintiff is, a rail carrier regulated by the Interstate Commerce Commission. The I.C.C. has established a Uniform System of Accounts for Railroad Companies (49 C.F.R., Part 1201 et seq.) which prescribes that investment in right-of-way land, grading, tunnels and the track elements be charged to separate accounts, each with its own instructions. Amounts paid or accrued are capitalized and accounted for in the rail carrier’s books and records in Account 3, to which is charged the cost of clearing and grading and roadbed and constructing protection for the roadbed, and in Account 5, to which is charged the cost of constructing tunnels, including the cutting of the bore and the placing of portals at the entrances to and lining within the tunnels. Historically, the I.C.C. (and the Internal Revenue Service) have treated these accounts as consisting of both “depreciable” and “nondepreciable” portions.
     
      
      . S.Rep.No.91-552, 91st Cong., 1st Sess. (1969), reprinted in [1969] U.S.Code Cong. & Ad.News 1645, 2027, 2291 and in 1969-3 C.B. 423, 584; Conf.Rep.No.91-782, 91st Cong., 1st Sess. (1969), reprinted in [1969] U.S.Code Cong. & Ad.News 2392, 2442 and in 1969-3 C.B. 644, 674.
     
      
      . See Rev.Rul. 67-22, 1967-1 C.B. 52. Throughout its history, Northern Pacific had always capitalized additions of grading and tunnel bores, and deducted from income these capitalized amounts on actual retirement without replacement.
     
      
      . 26 U.S.C. § 185 (Supp. V 1965-1969), Tax Reform Act of 1969, Pub.L.No.91-172, § 705(a), 83 Stat. 487, 672-73.
     
      
      . 26 U.S.C. § 185(d)-(e) (1976), Tax Reform Act of 1976, Pub.L.No.94 — 455, § 1702(a), 90 Stat. 1525, 1760.
     
      
      . See Chesapeake & Ohio Ry. v. Commissioner, 64 T.C. 352 (1975); S.Rep.No.94-938, 94th Cong., 2d Sess. (1976), reprinted in [1976] U.S. Code Cong. & Ad.News 3439, 3911 and in 1976-3 C.B. (Vol.3) 49,522.
     
      
      . See Kansas City Southern Ry. v. Commissioner, 76 T.C. 1067 (1981); Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497 (1980); Chesapeake & Ohio Ry. v. Commissioner, 64 T.C. 352 (1975). But see Rev.Rul. 69-87, 1969-1 C.B. 57.
     
      
      . An exhaustive explanation of the actuarial method is presented by Judge Raum in Chesapeake & Ohio Ry. v. Commissioner, 64 T.C. 352, 372-75 (1975). See also Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497, 783-86 (1980); Comment, Determination of the Useful Life of a Taxpayer’s Asset for Purposes of the Federal Income Tax Deduction for Depreciation Using Statistical Methods to Analyze the Facts and Circumstances, 21 Vill.L.Rev. 674 (1975-76).
     
      
      . A survivor curve is a curve which indicates the percentage of some particular type of property which is still in service from the time when that property is first put in service until the time when the last unit is retired.
     
      
      . The term “actuarial method” is used generically to denote the various methods used to compile retirement data for the construction of survivor curves. The actuarial method, as applied in this case, involved the statistical procedure known as the "annual rate” or “retirement rate” method of analysis. See plaintiffs exhibit No. 86, Depreciation Study of Grading and Tunnel Costs for Burlington Northern, Inc., April 1976. This method of analysis is more fully described in the text hereafter. Other methods of developing survivor curves include the “original group” method, which uses only data concerning the retirements of a group of assets put in service in a particular year, and the “individual unit” method, which uses only data of assets which have been actually retired.
     
      
      . Data accumulated on these assets may be stated in terms of units of property or in terms of dollars of investment.
     
      
      . Other methods of smoothing and extending survivor curves range from visual extension by an expert to statistical curve fitting involving complicated mathematical procedures.
     
      
      . Neither railroad grading nor tunnel bores were among the properties studied.
     
      
      . The Iowa curves are set forth in R. Winfrey, Statistical Analyses of Industrial Property Retirements (generally known as Bulletin 125), published in 1935 and republished in 1967 by the Iowa Engineering Experiment Station at Iowa State College. Bulletin 125 contains the results compiled from historical studies made on 176 distinct types of agricultural and industrial property. Retirement curves developed from these studies were then grouped into 18 different patterns which reflect the retirement characteristics of all 176 property types.
     
      
      . The deductions included the acquisition costs of easements which were used for construction, maintenance and operation of transmission and distribution lines, and initial clearing costs.
     
      
      . The “geometric mean” method is an accepted form of the “turnover” method of analyzing historical retirement data. The two most widely accepted methods for determining the useful lives of mass property accounts are the actuarial method and the turnover method. The basic difference between the two methods is that the turnover method employs only gross additions and gross retirements and thus does not generate a survivor curve because ages of the retirements are not used, while the actuarial method identifies the actual age of property retired and property surviving. Consequently, the actuarial method provides a more detailed, and more reliable, analysis of past retirement experience.
     
      
      . For other decisions allowing the depreciation of utility easements and related clearing costs, see Southern Natural Gas Co. v. United States, 188 Ct.Cl. 302, 412 F.2d 1222 (1969); Texas-New Mexico Pipe Line Co. v. United States, 185 Ct.Cl. 570, 401 F.2d 796 (1968); Badger Pipe Line Co. v. United States, 185 Ct.Cl. 547, 401 F.2d 799 (1968): Commonwealth Natural Gas Corp. v. United States, 395 F.2d 493 (4th Cir. 1968); Northern Natural Gas Co. v. O’Malley, 277 F.2d 128 (8th Cir. 1960); Union Electric Co. v. Commissioner, 177 F.2d 269 (8th Cir. 1949); Tenneco, Inc. v. United States, 301 F.Supp. 598 (S.D.Tex.1969); Consumers Power Co. v. United States, 299 F.Supp. 1180 (E.D.Mich.1969), affd and rev’d on other grounds, 427 F.2d 78 (6th Cir.), cert. denied, 400 U.S. 925, 91 S.Ct. 186, 27 L.Ed.2d 185 (1970); Great Lakes Pipe Line Co. v. United States, 293 F.Supp. 1073 (W.D.Mo.1968); Oklahoma Gas & Electric Co. v. United States, 289 F.Supp. 98 (W.D.Okl.1968); Shell Pipe Line Corp. v. United States, 267 F.Supp. 1014 (S.D. Tex. 1967).
     
      
      . 26 U.S.C. § 167(a) (Supp. II 1952 ed.), Pub. L.No.591, ch. 736, 68A Stat. 3, 51 (1954).
     
      
      . Even with substantial stipulation of documented facts, the trial transcript exceeded 3,200 pages and was augmented by numerous exhibits.
     
      
      . Plaintiffs witnesses testified at trial that wear and tear was a cause of retirement only to the extent that in a given situation maintenance costs would be so excessive in relation to the benefits to be derived from continued operation that a management decision would be made to discontinue use of a particular piece of property.
     
      
      . Federal tax law has recognized two distinct categories of obsolescence: (1) “Extraordinary” obsolescence or the sudden loss of utility and (2) “normal” obsolescence or the gradual loss of usefulness due to the normal progress of the arts, invention, technological improvements and legislation. Coors Porcelain Co. v. Commissioner, 52 T.C. 682, 689 (1969), aff’d, 429 F.2d 1 (10th Cir. 1970). It is into this second category that plaintiffs retirements fall. Northern Pacific decisions to retire its grading and tunnel bores were influenced by factors such as competition from other railroads and other modes of transportation, the desirability of reducing or eliminating safety hazards, the desirability of reducing maintenance costs and other costs of operation, the progress of construction technology, the aim of accommodating the line to developing railroad technology, changes in business locations and traffic patterns, the requirements of public authorities, the action of the elements and the possibility of eliminating duplicate facilities through mergers or agreements to coordinate with other lines. Generally, a decision to retire grading or a tunnel would be a product of a combination of several of these factors.
     
      
      . Mr. Winfrey was offered as an expert in the field of estimating the useful lives of industrial properties. Mr. Reilly was offered as an expert on the estimation of service lives of industrial property and particularly public utility property.
     
      
      . Plaintiff claims that by reason of certain erroneous evidentiary rulings at trial, the record of this case does not contain a full indication as to how its data were both quantitatively and qualitatively superior to the data available in PP&L and VEPCO.
      
     
      
      . However, we note the extensive arguments made by the government with respect to the actuarial method and the estimates resulting therefrom in Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497, 791, 793-99 (1980), and the government’s reliance on a mathematical statistician for rebuttal purposes in Kansas City Southern Ry. v. Commissioner, 76 T.C. 1067, 1148, 1151, 1154 (1981).
     
      
      . Treas.Reg. § 1.167(b)-0(a) (1956); see Missouri Pac. R.R. v. United States, 204 Ct.CI. 837, 859, 497 F.2d 1386, 1399 (1974).
     
      
      . Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497, 798-99 (1980). But see Chesapeake & Ohio Ry. v. Commissioner, 64 T.C. 352, 371 (1975).
     
      
      . Defendant contends that the amorphous and elusive criteria forming the basis of this judgment are best evidenced by the disclosure at trial that the analyst is not supposed to fit the actual stub curve to one of the Iowa curves, but rather is to fit an Iowa curve to the retirement pattern which he expects that he would have found if the assets under study had experienced a complete life cycle.
     
      
      . Plaintiff’s exhibit No. 86, Depreciation Study of Grading and Tunnel Costs for Burlington Northern, Inc. (April 1976) at 3.
     
      
      . He was influenced in his selection by his experience that the pattern of an R-type curve is characteristic of property that is retired primarily for reasons of obsolescence, that R-type curves were appropriate for smoothing and extending the stub survivor curves of the assets involved in the utility and other railroad cases and that the stub survivor curves in the shorter, more recent experience bands in this case appeared clearly to follow the retirement pattern of the R-type curve.
     
      
      . The fact that the principal basis for plaintiffs claims is obsolescence, a factor not predominant in the exhaustion of the assets underlying the Iowa curves, does not go unnoticed.
     
      
      . His final estimate of a 100-year average useful life for grading was reached after an assessment of conditions allegedly anticipated by Northern Pacific as of 1956 to cause an increase in future retirements. He concluded that a reduction of the useful life estimate by 75 years was warranted by these conditions.
     
      
      . Mr. Bartyczak used the mathematical “least squares” method of analysis. More accurately this method is described as the least sum of the squared differences. It is a mathematical measure of the differences between the hypothesized line (the curve being fit) and the observed data for the purpose of determining how closely the hypothesized line describes the data. In this exercise the linear area (distance) between the hypothesized line and each of the data points is squared in order to give greater weight to large, rather than to small, deviations.
     
      
      . We are mindful that Mr. Reilly selected curves for several different experience bands of years in making his analysis. The problems we outline above are also inherent in those selections.
     
      
      . Nor do we intend to imply that a purely mechanical approach to estimating a useful life is necessarily correct. Obviously, mathematics can, in certain instances, yield absurd results, as demonstrated by the figures arrived at by defendant’s expert witnesses: an average useful life of 466 years for Northern Pacific grading for the period 1868-1972 and an average useful life of 463 years for Northern Pacific tunnel bores for the period 1883-1972. Such figures acutely emphasize the need for informed judgment in estimating a reasonable useful life for depreciable property.
     
      
      . In his report, Mr. Reilly described the actuarial method of life analysis as a “statistical method.” See plaintiffs exhibit No. 86, Depreciation Study of Grading and Tunnel Costs for Burlington Northern, Inc. (April 1976) at 2,3, 5. Additionally, the courts having approved the use of the actuarial method have each characterized the method as a statistical method. See Pennsylvania Power & Light Co. v. United States, 188 Ct.Cl. 76, 118-19 (findings of fact), 411 F.2d 1300 (1969); Virginia Electric & Power Co. v. United States, 188 Ct.Cl. 120, 123-24, 138-40 (findings of fact), 411 F.2d 1314, 1315 (1969); Kansas City Southern Ry. v. Commissioner, 76 T.C. 1067, 1146, 1153 (1981); Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497, 783-86, 793 (1980); Chesapeake & Ohio Ry. v. Commissioner, 64 T.C. 352, 372-76, 378, 380 (1975).
     
      
      . For a description of this mathematical procedure, see footnote 37.
     
      
      . The purpose of this procedure is to inform the observer of the degree of probability that his impression of the fidelity of the curve that he has selected is correct. A standard error is derived by taking the square root of the sum of the linear area between each item of data and the average or mean path of all of the data, dividing the resulting figure by the number of data and adding 1 to that result. If the curve falls within one standard error, the most generally used measure of reliability, the observer may assume that the chances are two out of three that the curve selected correctly describes the data observations to which it has been fitted. Falling within two standard errors (j.e., twice the latitude for mistake) the confidence level rises to a 95-percent likelihood of correctness.
     
      
      . Statistical verification might also be appropriate in determining the reliability of the stub survivor curve plotted from accumulated historical data. Information from which these stub curves are generated varies in form and accuracy according to the character of the assets, the number of assets, the character of service rendered, management policy, maintenance care, and economic conditions, as well as the methods by which such information is compiled. Thus, depending on the data available for collection and plotting, the smoothed stub curve may or may not reflect an accurate portrayal of an asset’s retirement history. If the stub survivor curve is not reliable, further doubt is cast on the complete survivor curve selected to provide a reasonable whole life projection. An estimate made from a short curve is likely to be less accurate than one made from a long or approximately complete curve. Moreover, the resulting stub curve may possess irregularities because of small numbers of assets or infrequent or irregular observations, or both. While such poorly shaped curves can be made useful by the initial smoothing process, where there exists doubt as to the location of the stub curve through the known but scattered data points, there exists doubt as to the accuracy of the extension. See R. Winfrey, Statistical Analyses of Industrial Property Retirements (1935) at 37, 86.
     
      
      . By comparison, expert witnesses in other cases have confirmed their conclusions by analyzing the available data using various statistical approaches. Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497, 783-86, 797 (1980).
     
      
      . The equivocal character of useful life estimates derived from survivor curves reflecting data on retirements largely predicated on obsolescence is confirmed by Bulletin 125:
      [I]f the future retirements of the remaining units follow a natural law, the extension of the stub survivor curve by the type-curve method is apt to be more reliable than if the remaining units are retired by sudden changes in policy, an unusual development in the art of manufacture of the units, a change in the character of service required, or unusual economic conditions which affect the rate and regularity of retirement.
      R. Winfrey, Statistical Analyses of Industñái Property Retirements (1935) at 86.
     
      
      . Plaintiff’s efforts to manufacture a “legal standard” from these decisions are for naught. Such a contention assumes the matter in dispute; that is, whether, under the facts of this case, use of the actuarial method in conjunction with the Iowa curves is an appropriate means for ascertaining the useful life of railroad grading and tunnel bores is precisely what we have been called upon to decide.
     
      
      . Nor is this decision intended to require a higher level of proof in cases involving depreciation claims predicated on obsolescence. By our holding we are merely acknowledging that the nature of the proof needed to support the claimed deductions may necessarily vary in each case. In some instances, a claim for depreciation may require the presentation of specific facts to establish obsolescence. See, e.g., Zimmerman v. Commissioner, 67 T.C. 94, 107-09 (1976); Dunn v. Commissioner, 42 T.C. 490, 495 (1964). On the other hand, in evaluating certain obsolescence claims, facts which may not otherwise be susceptible to reasonable prediction can be given greater credence when supported by a reliable statistical study. Southern Pac. Transp. Co. v. Commissioner, 75 T.C. 497, 793 (1980). As we have discussed, the particular study conducted herein has not been found to be reliable.
     
      
      . The government has maintained throughout that an analysis of future developments without the use of the Iowa curves (and, apparently, without the use of the actuarial method) would produce just as, if not more, accurate or reliable results than an analysis of future developments in conjunction with the use of the Iowa curves. In fact, government counsel contended at oral argument that, based on the evidence in the record, plaintiff could establish useful lives for its assets on a far more rational basis than that used in this case. Such a showing would entail, in defendant’s view, an extrapolation of adequate historical retirement data on the basis of substantiated future projections. Factors important to sustaining these future projections would include testimony from corporate executives showing management intent during the years involved with respect to future retirements, relevant studies, analyses and expert testimony documenting the impact of probable future developments in the areas of engineering, technology, economics, financing, management policy and other miscellany and evidence of any special circumstances that might cause the premature retirement of property as a result of physical exhaustion or obsolescence.
     