
    DULUTH, MISSABE & IRON RANGE RAILWAY COMPANY, Duluth, Winnipeg & Pacific Railway Company, Escanaba & Lake Superior Railroad Company, Fox Valley & Western Limited, Nicolet Badger Northern Railroad Company, Soo Line Railroad Company, Wisconsin Central Limited, Wisconsin & Calumet Railroad Company, and Wisconsin & Southern Railroad Company, Plaintiffs-Appellants, v. STATE OF WISCONSIN, Department of Revenue, Defendant-Appellee.
    No. 95-3619.
    United States Court of Appeals, Seventh Circuit.
    Argued April 18, 1996.
    Decided Nov. 13, 1996.
    Ann Ustad Smith, Michael, Best & Fried-rich, Madison, WI, James W. McBride (argued), Anne M. Stolee, Baker, Donelson, Bearman & Caldwell, Washington, DC, for Plaintiffs-Appellants.
    Peter C. Anderson (argued), Office of the Attorney General, Wisconsin Department of Justice, Madison, WI, for Defendant-Appel-lee.
    Before CUDAHY, RIPPLE and KANNE, Circuit Judges.
   CUDAHY, Circuit Judge.

The state of Wisconsin imposes an ad valo-rem tax on property, both real and personal. A group of railroads that own property in Wisconsin believe that, for tax purposes, the state assesses their real, and personal property at its fall market value while it assesses the real and personal property of other commercial and industrial entities at much less than its full market value. According to the former 49 U.S.C. § 11503, a state may not discriminate against railroads in its tax assessments. Relying on this statute, the railroads went to the district court and attempted to prove that Wisconsin engaged in such illegal discrimination against them. Their proof consisted almost entirely of a report by an economist who estimated the fair market value of nonrailroad personal property in Wisconsin. After a bench trial, the district court found that this report was not ultimately persuasive, and it ruled for the state. The railroads appeal, arguing that the district court’s finding is clearly erroneous because it does not reflect a reasoned analysis of the evidence in the ease. We disagree with this characterization of the district court’s fact-finding and affirm its judgment.

I.

When it enacted the Railroad Revitalization and Regulatory Reform Act of 1976 (4-R Act), Pub.L. 94-210, 90 Stat. 31, Congress sought to restore the financial stability of American railroads. Department of Revenue of Oregon v. ACF Indus., Inc., 510 U.S. 332, 336, 114 S.Ct. 843, 846, 127 L.Ed.2d 165 (1994). One threat to the financial stability of the rail system came from discriminatory state taxation. Congress recognized that the railroads “ ‘are easy prey for State and local tax assessors’ in that they are ‘nonvoting, often nonresident, targets for local taxation’ who cannot easily remove themselves from the locality.” Western Air Lines, Inc. v. Board of Equalization, 480 U.S. 123, 131, 107 S.Ct. 1038, 1043, 94 L.Ed.2d 112 (1987) (quoting S.Rep. No. 91630, p. 3 (1969)). As a result of this recognition, § 306 of the 4-R Act, codified at 49 U.S.C. § 11503, prohibits states and localities from discriminating against railroads in the levying of state taxes. In particular, § 11503 makes it illegal for states to

assess rail transportation property at a value that has a higher ratio to the true market value of the rail transportation property than the ratio that the assessed value of other commercial and industrial property in the same assessment jurisdiction has to the true market value of the other commercial and industrial property.

49 U.S.C. § 11503(b)(1). Railroads may bring federal lawsuits under this subsection, but they may not obtain relief unless the ratio of assessed value to true market value of rail transportation property exceeds, by at least five percent, the ratio of assessed value to-true market value of other commercial and industrial property in the same assessment jurisdiction. 49 U.S.C. § 11503(c).

Wisconsin levies taxes on all general property in the state, which includes real and personal property. Wis.Stat. §§ 70.01, 70.02, 70.03, 70.04. But the state also exempts significant amounts of property from taxation. E.g., Wis.Stat. §§ 70.11, 70.111. For the most part, taxable real property and taxable personal property are assessed by different methods. See Wis.Stat. §§ 70.32, 70.34. Although real property is assessed in terms of its value at a private sale, personal property is assessed according to the value reported by its owner in a tax return. Tax assessors verify these returns by making their own independent assessment of personal property. This independent assessment is based upon the assessors’ “actual view” of personal property made in visits to the taxpayers, Wis.Stat. § 70.34, and it is based upon a comparison of returns made by similarly situated taxpayers. If the property value claimed in one taxpayer’s return seems incommensurate with the claimed values of comparable property listed on other returns, the assessor will correct the return with something ominously described as a “doom-age assessment.” See Wis.Stat. § 70.34. Taxable railroad property is assessed through a different method. Instead of making a separate assessment of the real and personal property owned by railroads, state assessors estimate the value of all rail property as a single unit. Wis.Stat. § 76.03(1).

The railroads here claim that Wisconsin’s system of property taxation has a discriminatory effect upon them. They note that all of their property was assessed at its full market value, and they acknowledged that the real property owned by other commercial and industrial entities was assessed at its full market value. But they contend that the non-railroad personal property was assessed at such a low level that the entire system of property assessment was unfair to them and violated federal law. They made this claim in a suit filed under 49 U.S.C. § 11503(b)(1).

Proving the underassessment of non-railroad personalty in Wisconsin is a difficult task. The primary source of empirical evidence about the value of personal property in the state comes from the official assessments. These data, of course, only lend themselves to one interpretation: that all Wisconsin personalty is assessed at its full market value because the official assessments are made on that basis.

Because they could not look to the assessors’ reports, the railroads had to find other data. Hiring their own qualified assessors to canvass the state and value all of the non-railroad personal property would have been practically impossible. So the railroads turned to an economist for assistance, Dr. Roy Bahl, a professor at Georgia State University. Dr. Bahl estimated the market value of nonrailroad commercial and industrial personal property in Wisconsin by analyzing data about the aggregate value of all of the capital stock used in business and industry in the United States. These data primarily came from the Bureau of Economic Analysis of the United States Department of Commerce (BEA), and were published in a report entitled Fixed Reproducible Tangible Wealth in the United States, 1925-89. Dr. Bahl described his method for analyzing the BEA data and articulated his conclusions in a report submitted to the district court. According to Dr. Bahl’s report, non-railroad personalty in Wisconsin was assessed at no more than three-quarters of its full market value. The railroads contended that this disparity in the assessment of personal property was enough to show that all of the non-railroad commercial and industrial property in Wisconsin was illegally underassessed for the purposes of § 11503.

Dr. Bahl’s method was the subject of extensive scrutiny in the district court. His method ultimately depended upon the BEA’s own analysis of its data. Although the BEA did not provide state-by-state estimates of the value of “fixed reproducible tangible wealth,” it did analyze its data by breaking them down into categories. The BEA classified all business and industry into various categories, listed the assets typically used in each category and, after accounting for depreciation, estimated the aggregate value of all the assets used in each category.

Dr. Bahl allocated part of this value to Wisconsin to obtain his estimate of the true market value of all taxable non-railroad personalty in the state. The first step in this allocation involved the determination of which nonrailroad asset categories contained personal property that would be taxable in Wisconsin. For each of these categories that contained taxable personalty, he then calculated, on a nationwide basis, a capital/labor ratio. That is, he divided the value of the assets in each category by the number of people who were employed by every business in the nation included in that category. This capital/labor ratio represented the value of the capital stock associated with each person employed in each of the categories of industry and business. This capital/labor- ratio was at the center of Bahl’s method for allocation. After determining this ratio for each relevant category; Dr. Bahl identified the number of people in Wisconsin who were employed in each of these categories. He completed his allocation by multiplying the capital/labor ratio for each category by the number of Wisconsin employees in that category; and he added all of the resulting products together. This left him with his final estimate of the value of non-railroad personalty in Wisconsin.

Dr. Bahl’s estimate was crucial to the railroads’ case at trial. To prove that Wisconsin discriminated' against railroads in its assessment of real and personal property, the railroads attempted to show that non-railroad personal property was assessed far below its market value; and Dr. Bahl’s estimate was the only evidence that the railroads offered about the market value of non-railroad personalty. During the railroads’ case-in-chief, Dr. Bahl testified about his estimates and the method by which he arrived at them, and another witness buttressed that testimony. Dr. Donald Nichols, a professor of economics and public policy at the University of Wisconsin, testified .that Dr. Bahl’s methods and the data he employed were the kinds of methods and data typically relied upon by economists.

The state’s case was largely negative. As an initial matter, the state suggested that the railroads’ .evidence was simply insufficient to prove its claim. In the state’s view, the railroads could not show that all commercial and industrial property in the state was un-derassessed by showing that the personal property in commerce and industry was un-derassessed. If personal property constituted a small proportion of all of the property owned by commercial and industrial entities, even a gross underassessment of commercial and industrial personal property might create only a negligible underassessment of commercial and industrial property as a whole.

The state did not, however, rely solely on this argument about the meaning of the railroads’ evidence. Indeed this argument was a relatively minor aspect of its case. At trial, the state tried to show that the railroads lacked any credible evidence showing that non-railroad personalty was underassessed. The state made this effort by raising a series of questions about Dr. Bahl’s method.

In its cross-examination of Dr. Bahl, the state made a systematic attack on the fundamental aspects of his method for analyzing the BEA data. The state did this by challenging Dr. Bahl’s assumption that the BEA data could be reliably applied to Wisconsin. The attorney representing the state noted that Wisconsin differed significantly from the national norms upon which the BEA data were based, and he asked Dr. Bahl to account for these differences. One such difference pertained to Dr. Bahl’s reliance on capital/labor ratios. Dr. Bahl presumed that he could apply national capital/labor ratios to Wisconsin. But the state’s lawyer pointed out that labor costs in Wisconsin are below the national average. He therefore suggested that Wisconsin enterprises might achieve the same results as their competitors in other states by using less capital and more labor. On the basis of this suggestion, he asked Dr. Bahl to explain why the capital/labor ratios drawn from BEA data should apply to Wisconsin. The state’s lawyer raised similar questions about the differences between Wisconsin and the rest, of the nation in the use of depreciation schedules and in the distribution of assets across categories of industry and business. All of these questions reflected on the reliability of the eapi-tal/labor ratios at the center of Dr. Bahl’s report.

The state also attacked Dr. Bahl’s estimate of the value of non-railroad personalty by suggesting that the method produced inconsistent results when applied to the valuation of different kinds of property. When Dr. Bahl’s method was used to estimate the value of manufacturing property alone, it led to the conclusion that Wisconsin assessed such property at more than twice its market value. In light of this fact, the state’s lawyer pursued an additional line of questioning, asking Dr. Bahl to explain how Wisconsin could so dramatically overassess manufacturing personal property while so drastically underas-sessing other commercial personal property.

The state further pursued this line of attack by submitting the testimony of Rebecca Boldt, an analyst for the Wisconsin Department of Revenue. As an experiment, Ms. Boldt had applied Dr. Bahl’s method to the valuation of railroad personal property. This application led to the conclusion that railroad personalty was underassessed to an even greater degree than non-railroad personalty. The state cross-examination of Dr. Bahl on these matters and its presentation of Boldt’s testimony were all designed to suggest that the use of BEA data would lead to inconsistent conclusions about the value of personal property in Wisconsin.

Finally, the state tried to show that Dr. Bahl’s estimates were simply implausible on their face. If those estimates were accurate, Wisconsin assessors must have dramatically underassessed non-railroad personal property, or they must have entirely overlooked a large segment of that property. To show that errors of such magnitude were inconceivable, the state offered the testimony of several assessors (at trial and in depositions), all of whom declared that their assessments were thorough and accurate. In essence, they testified that they were able to find all of the taxable personalty in their jurisdictions through their practice of making an “actual view” of such property; and they asserted that they would not be fooled by attempts to underreport the value of property. Because they could compare one taxpayer’s return with the return of another taxpayer who owned similar property, the assessors claimed that they could be sure that no meaningful underreporting occurred.

After raising all of these questions about Dr. Bahl’s method, and after introducing the testimony about the assessors’ abilities, the state argued that the assessors, and not Dr. Bahl, provided the most accurate and rehable estimate of the value of non-railroad personalty. According to this estimate, of course, the state’s assessment of railroad property was not discriminatory.

The district court quickly reached its decision and made an oral report of its factual findings. The court’s recitation of its findings suggested that it had concluded that Dr. Bahl had not effectively responded to the state’s questions about his method. The court therefore found that Dr. Bahl’s estimate of the value of non-railroad personal property was not as credible as the estimate made by the assessors and that the railroads had not established that Wisconsin’s property . tax assessments discriminated against them. Although the court’s oral decision was relatively brief, it did explain some of its reasons for disbelieving Dr. Bahl. Those reasons generally corresponded with the state’s challenges to his report. The court acknowledged that Dr. Bahl was an able economist and a competent analyst, but it expressed doubts that BEA data could be reliably used in the way that Dr. Bahl sought to use them.

II.

In their challenge to the district court’s factual findings, the railroads argue that the district court clearly erred in discounting Dr. Bahl’s testimony. They point to a few statements in the district court’s oral recitation of its findings, and they contend that these statements reflect a complete misunderstanding of the evidence in the case. Because they believe that the district court so utterly misinterpreted the evidence, they believe that it did not have a rational basis for assessing the credibility of Dr. Bahl’s report.

In our review of factfinding by a district court, we give marked deference to the district court’s credibility determinations. Anderson v. City of Bessemer City, North Carolina, 470 U.S. 564, 574-75, 105 S.Ct. 1504, 1511-12, 84 L.Ed.2d 518 (1985). Of course, we give great deference to all credibility determinations made at a trial, whether made by the judge or the jury. But judges’ credibility determinations sometimes depend on documents or other objective evidence. In those cases, if the district court’s evaluation of the extrinsic evidence is clearly erroneous, we will not defer. Id. Here, the railroads effectively argue that the district court’s credibility determinations cannot be sustained because they depend upon profoundly mistaken factual findings. We will set aside a district court’s findings of fact if our review of the record leads us to the definite and firm conviction that those findings are mistaken and do not represent a permissible view of the evidence. Id.

The railroads first argue that the district court relied on faulty reasoning to discount Dr. Bahl’s estimate. They find this reliance in the following statement:

The Court can understand the plaintiffs’ concern where it believes it has set forth the best data available, the best expert testimony available, and yet is unable to prevail, the Court believing that the standardized procedures as followed by local assessors and the opinions of those local assessors that the tax level of personal property that is being missed would be less than five percent of the total value of all personal property. From the Court’s examination of the depositions in this matter and that testimony which it is allowed to consider as set forth in the uncontested facts of the pretrial report, that although the defendant has no burden to prove an affirmative defense or the values thereof is better than that expertise and those, that expert, data as presented by the plaintiff.

As the railroads read it, this passage indicates that the district court disbelieved Dr. Bahl because it concluded that the assessors did not overlook more than five percent of the taxable personal property in their jurisdictions. If this reading fairly represents the district court’s analysis of the evidence, then there is something to the suggestion that the district court fundamentally misunderstood the evidence. A finding that state officials made a tax assessment of more than ninety-five percent of the'property in their jurisdictions does not ineluctably lead to the finding that non-railroad personalty was assessed at full market value. If the railroads are right, clear error would undermine the judge’s credibility determination.

Although we find the district court’s statement rather obscure, we conclude that the railroads have not accurately described the reasoning behind it. The district court was not concluding that the all of the personal property was assessed at full market value because all of .the personal property was assessed. The district court’s statement seems to be a reference to the state’s contention at trial that Dr. Bahl’s estimate was implausible because it implied monumental incompetence hr corruption by the tax assessors. In this connection, the statement can be seen as a general expression of the opinion that the assessors were accurate in their valuation of personal property.

The railroads also contend that the district court made a finding that the railroads’ personal property was underassessed. They believe that there was no credible evidence to support this finding and that this finding was essential to the district court’s evaluation of Dr. Bahl’s report. They locate this finding in the following statement by the district court:

Well, I do believe that [Dr. Bahl’s] methodology is shown to be inherently inaccurate when using the railroad property to be subjected thereto.
We talk about unfairness. Certainly it would be unfair to use any type of methodology when looking at that particular property. The Court believes it’s just as unfair to use it as it concerns the other than railroad property which is under discussion here. The — It is almost three times the amount allocated for the allocation for the total railroad equipment under the methodology employed by the plaintiff in the Department of Revenue value.
The Court is of the opinion that any underassessment of the Wisconsin commercial property is certainly less than any underassessment of rail property.

When considered in isolation, the last sentence in the quotation above could seem to be a finding that the railroads’ personal property was underassessed. And the railroads are certainly correct to point out that there was no evidence in the record to support such a finding; the parties agreed that all railroad property was assessed at its full market value. When we consider this sentence in the context of the remarks that preceded it, however, we come to the conclusion that the court was not making this particular finding. In this part of its discussion of the evidence, the court commented on the way in which Ms. Boldt’s testimony reflected on the. reha-bility of Dr. Bahl’s method. Ms. Boldt’s testimony involved a kind of reductio ad absurdwm; the state tried to use this testimony to show that the use of Dr. Bahl’s method could lead to ridiculous or mutually inconsistent conclusions. The district court’s statement here is reasonably understood as the expression of agreement with the state’s challenge to Dr. Bahl’s method.

Finally, the railroads argue that the district court erred when it found that Dr. Bahl’s estimate was not persuasive. The district court said:

The witness Bahl was persuasive and convincing as a witness but the data he provided the Court is not as persuasive and convincing as that which would allow the plaintiff to recover. The presumption that national figures can accurately be applied to Wisconsin commercial entities has not been established by a preponderance of the evidence, either by the testimony of Mr. Bahl or Mr. Nichols. The service fives which have [been] applied by this method are suspect even as adjusted. All you do is shorten them up and the more you shorten them up, the more that apparently under this examination the true value would then adequately be set forth by the assessment method which has been provided by local assessors.

Here again, the railroads believe that the district court’s reasoning was suspect. They believe that it discounted Dr. Bahl’s estimate because it thought that his data were faulty. But they think that this conclusion is untenable because the data were not faulty, and they point to the testimony of Dr. Nichols who noted that economists everywhere regularly rely on the BEA for accurate data.

Of course, data may be reliable for one purpose but not another. The quotation above demonstrates that the district court did not assail the BEA or its data in general terms; rather the district court concluded that the BEA’s data about the value of the capital stock of the entire nation were not a reliable basis for determining the value of taxable personal property in Wisconsin. In fight of all of the evidence in the ease, this was certainly a permissible conclusion about the BEA’s data and Dr. Bahl’s report.

In the end, the district court’s findings in this case were quite simple. It found that Dr. Bahl’s report proved little about the value of non-railroad personal property in Wisconsin, and that Wisconsin’s own tax assessors had a better idea of that value than Dr. Bahl did. Thus it concluded that the railroads had not proven, that they were subject to discriminatory assessments in violation of 49 U.S.C. § 11503(b)(1).

But these simple findings and clear conclusions only emerged after the parties and the district court had sifted through a large body of complicated, highly abstract analysis. Given the welter of evidence that was relevant to the dispositive issues here, the district court would have been well-advised to explain its findings and conclusions in a written opinion. Instead, the court chose to announce its findings from the bench in an often elliptical expression of its evidentiary analysis. The obscurity of this expression makes it very difficult to understand how and why the district court reached its decision, and we are not surprised that the railroads still seem a little uncertain about why they lost. Nevertheless, when we review the record in its entirety, we conclude that the district court’s findings and conclusions are firmly rooted in the evidence, even if they are not clearly expressed in prose.

For these reasons, the judgment of the district court is

AFFIRMED. 
      
      . Congress omitted this section in its general revision of this subtitle. ICC Termination Act, Pub.L. 104-88, Title I, § 102(a), Dec. 29, 1995, 109 Stat. 843-44. A slightly revised text now appears at 49 U.S.C. § 11501.
     
      
      . The railroads' complaint also included another claim. They alleged that other commercial and industrial entities effectively paid no personal property tax at all because Wisconsin provided so many exemptions to the personal property tax. Because they did not benefit so extensively from these exemptions, they believed that they were subject to a discriminatory tax (as distinct from a discriminatory assessment), and they sued trader 49 U.S.C. § 11503(b)(4), which generally prohibits state taxes that discriminate against railroads. The district court granted summary judgment to the state, and we affirmed, noting that the Supreme Court had recently held that such claims are not cognizable under § 11503. Burlington Northern R.R. Co. v. Wisconsin Department of Revenue, 59 F.3d 55 (7th Cir.1995) (relying on Oregon Department of Revenue v. ACF Industries, 510 U.S. 332, 114 S.Ct. 843, 127 L.Ed.2d 165 (1994)).
     
      
      . Dr. Bahl arrived at two different estimates of the full market value of non-railroad personalty in Wisconsin, each based upon a different assumption of the service lives of personal property used in industry. According to one estimate, non-railroad personalty was assessed at 63.5 percent of its fair market value; according to the other, this assessment was 74.6 percent of market value.
     