concurring.
I join the court’s opinion. However, I wish to offer a few additional thoughts about the limitation of Edelson’s testimony, a question that the district court described as “very close.” (R. 145, Nov. 25, 1991 Tr. at 7; see also id. at 5.)1
I agree that the district court did not abuse its discretion when it barred Edelson from opining that VHS must have incurred substantial unreported costs. This testimony might have lent some support to the theory that Brinson and Price were not skimming undisclosed corporate income but instead merely were reimbursing themselves for undocumented costs that they had covered personally. Like my brothers, however, I am convinced that Edelson’s hypothesis was not sufficiently grounded in the particular facts of this case to be admissible.
*733Had the government premised its case on the simple hypothesis that because the company’s reported receipts were low compared to other firms in the industry, VHS must have earned additional income that was tunneled into defendants’ pockets, fair play might have required an opportunity for the defense to respond in kind. But the government’s ease did not rest on such speculation. The government documented large sums that VHS took in but did not report during the relevant tax years: $821,160.72 in 1982, $760,020.72 in 1983, $421,717.07 in 1984, and $781,361.22 in 1985. (See Tr. at 1272, 1280, 1282, 1285.) The government also identified each payment that Brinson and Price had received in these years that it deemed taxable income as opposed to reimbursement for costs incurred on behalf of VHS. These were not paltry sums either: by the IRS’ calculation, Brinson had received undisclosed income of $567,972.90 in 1983, $268,855.22 in 1984, and $157,736.75 in 1985 (Tr. at 825-26; Gov. Ex. Griffin 2, App. B), whereas Price had received unreported income of $228,-752.00 in 1983, $205,917.94 in 1984, and $138,-598.09 in 1985 (Tr. at 864; Gov. Ex. Griffin 3, App. C).
Notably, the government did not attempt to prove that all unreported payments to Brinson and Price amounted to taxable income, but focused only on payments received under circumstances suggesting that they were income rather than reimbursement. (See Tr. at 791-92, 801, 822, 823-24, 829.)2 For example, a number of the payments that the government deemed income to Brinson were payments that he had attempted to disguise as reimbursements with falsified invoices and canceled checks. (See Gov. Ex. Griffin 2, Schedule 15; Tr. at 796-801.) The government also counted as taxable income payments associated with defendants’ purely personal expenses, such as the purchase of limousines, boats, or work done on a defendant’s private residence (e.g., Tr. at 806, 810, 811, 832-33, 838, 844, 855-56, 856-59), as well as payments deposited into or negotiated through defendants’ personal accounts (Tr. at 804, 808-09, 825, 828-29, 834, 835-36, 838-44.)3 Finally, many of the payments deemed income to Price took the form of cashier’s checks payable to Price that Brinson had' purchased with funds drawn, directly or indirectly, from various VHS accounts. (Tr. at 831-64.)
Given the specificity with which the government documented the sums that both VHS and defendants had received, the excluded portion of Edelson’s testimony had only marginal probative value. ‘ I do not mean to suggest that Edelson was required to show that the government had miseharae-terized a particular payment as taxable income. (See ante at 5-6; Tr. at 1325, 1433, 1434.) After all, the defendants premised' their ease on the notion that VHS’ records were in such disarray that many costs simply were not documented. That theory suggests that Edelson would have been hard pressed to demonstrate that a given payment to defendants constituted reimbursement for an undocumented company expense. But the flaw in Edelson’s opinion was much deeper, for his theory piled inference upon inference: based upon statistical data that was of questionable relevance to VHS, he hypothesized that VHS must have incurred unreported costs and that those costs must in turn have been paid by Brinson and Price. Without any basis in the facts of the case, ■ Edelson’s testimony was mere speculation. Had Edel-son been able to identify one or more kinds of expenses that VHS in fact incurred but did not record in its books, his opinion might have had a firmer basis in the evidence.4 But given the substantial methodological flaws the court has already identified (not the least of which being Edelson’s use of data for producers of baked goods rather than mail order distributors of these and other types of *734products), Edelson’s reliance upon nothing more than industry data to support his hypothesis proved fatal to his testimony.
Moreover, Judge Hart carefully exercised his discretion here. Before limiting Edel-son’s testimony, he listened to Edelson’s analysis on voir dire and entertained argument from both sides as to its propriety. Given the nature of the government’s proof and the shortcomings in Edelson’s methodology, I agree that the district judge was well within his discretion in excluding Edelson’s proffered analysis.
Even if Edelson’s opinion was wrongfully excluded, the error was surely harmless. The record contains overwhelming evidence against Brinson and Price. As I have already noted, the government meticulously established both that VHS receipts had been grossly understated on the corporate tax returns (see, e.g., Tr. at 1272, 1280, 1282, 1285) and that Brinson and Price had received large sums of money from VHS that were not disclosed on their personal tax returns— sums that dwarfed their reported income (see Gov. Ex. Griffith 2, 3; see also, e.g., Tr. at 825-26, 864, 1245, 1249, 1255-56, 1257). The evidence revealed that much of this money passed through VHS-affiliated accounts that were not reflected on the company’s books and that in a number of instances were closed shortly after defendants were apprised of the government’s investigation. (See Tr. at 646-48, 656-60, 680-93, 1140-42.)
At the same time, the evidence belied each of the explanations defendants offered for the unreported payments. More than half a dozen individuals testified that the invoices and cheeks Brinson had submitted as proof of his cash outlays on behalf of VHS reflected fictional purchases of goods and services. One after another, these witnesses testified that the invoices appeared to have been doctored and that their own company records did not reflect the transactions indi-eated. (Tr. at 242-48, 259-60, 274-76, 281-89, 346-47, 365-75, 393-94, 408-11, 429, 493-97, 554-59, 574-76, 579-80; see also id. at 733-35.)5 Indeed, more than one testified that his or her firm did not even sell the types of goods or services reflected on the invoices. (Tr. at 347, 355, 409-10, 429-30, 557-58.) All testified that it was not their firms’ practice to accept large cash payments, which contradicted defendants’ representation that they customarily paid cash because their vendors preferred it. (Compare Tr. at 663, 664-65, 668, 994, 999 with id. at 236-37, 285-86, 348, 369-70, 394, 410-12, 430-32, 496, 560.)6 In addition, the evidence disclosed that Price had received hundreds of thousands of dollars from corporate accounts through Brinson from 1983 through 1985. This contradicted Price’s claim that Brinson had bought him out of business in 1982 for $5,000 and that he did not even work for the company for more than a year between 1983 and 1984. (See Tr. at 52, 643, 651-52, 1149, 1571.) Although Price contended that the payments were reimbursement for the $30,-000 he had loaned to the corporation at its inception (see Tr. at 53, 1580-82), he ultimately received well over half a million dollars in unreported disbursements. (See Gov. Ex. Griffith 3, App. C.)
In short, although there is no dispute that VHS’ bookkeeping was exceedingly deficient (Tr. at 155, 198, 1396), the evidence revealed not just an inadvertent failure to report the sums paid to Brinson and Price, but a purposeful effort to disguise the nature of those payments. For that reason, I am certain that the verdicts would have been the same even if the jury had been allowed to hear Edelson’s opinion. (See Tr. at 1445,1446-47, 1471-72.)
. All transcript cites that follow are to the trial transcript.
. The district court itself described the government's analysis as painstaking. (Tr. at 1452.)
. Of course, the government considered defendants' reported compensation and amounts received in payment of actual loans to the company in calculating their unreported income. (See Tr. at 1236-39, 1253.)
.Of course, even with this kind of factual support, Edelson’s reasoning still would have required the inference that if there were unreported costs, Brinson and Price must have paid them.
. Some of the businesses reflected on the invoices and checks did not even appear to exist. (See Tr. at 705-08, 735-41.)
. Defendants asserted that McCarty typically used cash to purchase goods and services for VHS. (See Tr. at 668, 994, 999, 1001-02, 1027-28, 1079, 1565-66.) Although a number of the invoices that Brinson supplied to the IRS had McCarty’s name on them, it was consistently misspelled "McCarthy.” (Tr. at 668-70.) Moreover, when shown a copy of an invoice that McCarty purportedly had initialled, his widow observed not only that his name was misspelled, but also that the initials were not in his handwriting. (Tr. at 514-15.)