POSNER, Circuit Judge.

The plaintiffs brought suit for a refund of federal income taxes, had a jury trial that resulted in a verdict for the government, and appeal, complaining about the jury instructions and the exclusion of much of their evidence.

The plaintiffs, husband and wife, own three retail stores in Hammond, Indiana. The stores operate under the name "Nick's Liquor" but sell cigarettes, beer, wine, soft drinks, potato chips, and other snack food as well as hard liquor. Most sales are cash sales; the stores do not accept credit cards. Nick Kikalos, the husband, does the bookkeeping. He testified that at the close of business each day he determines the total receipts of each store from the cash-register tape — the "Z" tape, as it is called — records the total in a log book, then destroys the tape. The total receipts shown in the log book are the amount that Kikalos reports to his accountant for use in preparing the plaintiffs' tax return. Kikalos's stubborn refusal to retain the Z tapes has engendered a protracted struggle with the Internal Revenue Service. See Kikalos v. Commissioner, 190 F.3d 791 (7th Cir. 1999); Kikalos v. Commissioner, Tax Memo 2004-82, 87 T.C.M. (CCH) 1146 (2004); Kikalos v. Commissioner, T.C. Memo 1998-92, 75 T.C.M. (CCH) 1924 (1998).

The plaintiffs acknowledge that the Z tapes are the best evidence of the stores' receipts. The tapes record the actual transactions with the customers, and, because they are marked sequentially by the cash register, underreporting of sales is often revealed just by gaps in the numbering. Kikalos's log book is a human copy that could deliberately or accidentally underreport the totals on the Z tapes. Taxpayers are required to maintain such "permanent books of account or records, including inventories, as are sufficient to establish the amount of gross income, deductions, credits, or other matters required to be shown by such person in any return of such tax or information." 26 C.F.R. § 1.6001-1(a). The records must "include the taxpayer's regular books of account and such other records and data as may be necessary to support the entries on his books of account and on his return. . . ." § 1.446-1(a)(4) (emphasis added). Given the simple alternative of retaining the Z tapes and the inherently greater reliability of the tapes, the plaintiffs' records do not comply with the requirement that we have italicized. E.g., Merritt v. Commissioner, 301 F.2d 484, 485-86 (5th Cir. 1962); Schwarzkopf v. Commissioner, 246 F.2d 731, 732-34 (3d Cir. 1957); Varjabedian v. United States, 339 F.Supp.2d 140, 158-59 (D.Mass. 2004); 2121 Arlington Heights Corp. v. United States, 1996 WL 435051, at *2 (N.D.Ill. July 31, 1996), affirmed under the name 2121 Arlington Heights Corp. v. IRS, 109 F.3d 1221 (7th Cir. 1997); Edgmon v. Commissioner, T.C. Memo 1993-486, 66 T.C.M. (CCH) 1093 (1993). The government was therefore entitled to estimate the plaintiffs' total receipts and the income that those receipts yielded (gross receipts minus cost of goods sold) indirectly. Mendelson v. Commissioner, 305 F.2d 519 (7th Cir. 1962); Choi v. Commissioner, 379 F.3d 638, 640 (9th Cir. 2004); Stuart v. United States, 337 F.3d 31, 35 (1st Cir. 2003). To determine net taxable income, other costs — overhead costs like rent and salary — would have to be deducted,

26 U.S.C. §§ 162(a)(1), (3); 26 C.F.R. § 1.162-1(a), but that computation is not in issue.

Employing the "percentage markup" method of estimation, commonly used in cases involving retailers, Cebollero v. Commissioner, 967 F.2d 986, 989 (4th Cir. 1992); Lambaiso v. Commissioner, T.C. Memo 1999-343, 78 T.C.M. (CCH) 593 (1999); Rataiczak v. Commissioner, T.C. Memo 1999-285, 78 T.C.M. (CCH) 362 (1999), the government assessed deficiencies, including penalties and interest, against the plaintiffs for 1988 and 1989 of some $900,000. (The plaintiffs paid, and brought this refund suit under 28 U.S.C. § 1346(a)(1) and 26 U.S.C. § 7422(a).) At trial, the government's economic expert witness explained how he had applied the percentage markup method. He had first estimated from the stores' purchase invoices the total amount and cost of the goods that the plaintiffs had purchased. Those goods that the stores advertised at stated prices he assumed were sold to customers at those prices, and he determined the markup on those sales by first subtracting the cost of the goods (that is, what the plaintiffs had paid for them) from the advertised price to yield an average percentage markup and then multiplying the number of sales of price-advertised goods by that percentage. He estimated on the basis of the stores' total cost of goods sold and other data that only about 20 percent of sales were made at advertised prices. The markup on other sales would be higher because stores tend to advertise their best bargains; he estimated the markup from data concerning stores similar to the plaintiffs' stores.

The plaintiffs, while not doubting that the percentage markup method is one of the methods legitimately used to estimate taxable income indirectly, wanted to be allowed to present their own expert testimony. Their expert would have testified that the application to the plaintiffs' business of two other common methods of estimating taxable income indirectly — the bank-deposits method, whereby receipts are estimated from the bank deposits made by the taxpayer, Estate of Kanter v. Commissioner, 337 F.3d 833, 859 (7th Cir. 2003) (per curiam), reversed in part on other grounds, Ballard v. Commissioner, ___ U.S. ___, 125 S.Ct. 1270, 161 L.Ed.2d 227 (2005); Choi v. Commissioner, supra, 379 F.3d at 639-40, and the net-worth method, whereby income in a given period is inferred from the increase in the taxpayer's net worth between the beginning and the end of the period, United States v. Marrinson, 832 F.2d 1465, 1469-70 (7th Cir. 1987); United States v. Shetty, 130 F.3d 1324, 1332 (9th Cir. 1997); Estate of Spear v. Commissioner, 41 F.3d 103, 105 (3d Cir. 1994) — would produce a more accurate estimate of the stores' income. The two methods, bank deposits and net worth, yield similar estimates of the plaintiffs' taxable income; and this concordance, the expert opined, demonstrated the superior robustness of the methods. We note that these are methods used by the government to estimate a taxpayer's income; their use by a taxpayer's expert witness is highly questionable (and is not supported by any of the cited cases) since the expert will perforce base his calculations only on the documentation concerning banks, expenditures, etc. that the taxpayer chooses to show him.

The district judge excluded the expert testimony not on grounds of unreliability, however, but on the ground that the government's choice of the method of indirect estimation to use in a particular case is conclusive, 313 F.Supp.2d 876 (N.D.Ind. 2003). He excluded Kikalos's log books on the same ground. He further ruled that the plaintiffs could prevail only by proving that the government's assessment of deficiencies was arbitrary. And so he instructed the jury that the plaintiffs had the burden of proving not only "the amount of the refund to which they are entitled" but also "that the assessment by the Internal Revenue Service was arbitrary." He defined "arbitrary" for the jury as meaning "without any rational basis" and he further instructed the jury that "the question is not whether the IRS assessment was accurate, but whether the IRS assessment was without a rational basis or was arbitrary." (No wonder the plaintiffs lost.)

These instructions were incorrect (as well as confusing — what would a term like "without any rational basis" mean to the average juror? Cf. Gehring v. Case Corp., 43 F.3d 340, 343-45 (7th Cir. 1994); Gordon v. New York City Board of Education, 232 F.3d 111, 118 (2d Cir. 2000)). The judge was telling the jury that it was not enough for the plaintiffs to prove that the government's estimate of their tax deficiencies was incorrect. They had to prove that it was irrational. In so ruling, the judge added an element to the statutory entitlement to a refund. All the statute requires is that the taxpayer prove that he overpaid his taxes. It doesn't require him to prove that the government's assessment was not only inaccurate but irrational. Suppose Nick Kikalos was a highly credible witness and the jury believed he'd been scrupulous about transferring the data in the Z tapes to his log book, a belief the jury might find corroborated by the results of the alternative indirect methods used by the plaintiffs' expert. We do not see on what basis a jury would be required to disbelieve Kikalos's testimony in favor of a rough method of estimation, just because the estimation could not be deemed irrational. There is nothing in the Internal Revenue Code or its implementing regulations to suggest the imposition of so insuperable a burden on a refund plaintiff.

The district judge was misled by statements in refund cases that the method of indirect estimation chosen by the government is not to be rejected just because it enables only a rough estimate, when it is the taxpayer, by having, whether willfully or not, destroyed the best evidence of his taxable income, that has forced the government to rely on a rough estimate. E.g., Mendelson v. Commissioner, supra, 305 F.2d at 523; Stuart v. United States, supra, 337 F.3d at 35. The courts don't mean that the results yielded by the particular method chosen by the government are conclusive on the jury's decision (or the Tax Court, when it is the trier of fact), but only that a method doesn't have to have a high degree of accuracy to be admissible. For while the cases disparage the taxpayers' criticisms of the government's rough methods, they don't rule the taxpayers' alternative methods of computation inadmissible because irrelevant (they might of course rule them inadmissible on some other ground). E.g., Bradford v. Commissioner, 796 F.2d 303, 305-07 (9th Cir. 1986); cf. Zuhone v. Commissioner, 883 F.2d 1317, 1327-28 (7th Cir. 1989); Choi v. Commissioner, supra, 379 F.3d at 640-41.

Analogous are cases in which the defendant's conduct has made it difficult for the plaintiff to determine his damages. In an antitrust case, for example, if the defendant destroyed the plaintiff's business in its infancy, before it had a track record from which expected profits could be inferred with confidence, the jury is instructed that a rough estimate will satisfy the plaintiff's burden of production. J. Truett Payne Co. v. Chrysler Motors Corp., 451 U.S. 557, 565-67, 101 S.Ct. 1923, 68 L.Ed.2d 442 (1981); Bigelow v. RKO Radio Pictures, 327 U.S. 251, 264-66, 66 S.Ct. 574, 90 L.Ed. 652 (1946); Locklin v. Day-Glo Color Corp., 429 F.2d 873, 879-80 (7th Cir. 1970); Home Placement Service, Inc. v. Providence Journal Co., 819 F.2d 1199, 1205-06 (1st Cir. 1987). The courts don't mean that the rough estimate is conclusive evidence and the defendant can't present his own estimate.

The analogy is not perfect. Because the government's tax assessment carries a presumption of correctness, Helvering v. Taylor, 293 U.S. 507, 514, 55 S.Ct. 287, 79 L.Ed. 623 (1935); Sherwin-Williams Co. v. United States, 403 F.3d 793, 796 (6th Cir. 2005), the taxpayer who has failed to maintain adequate records has a deep row to hoe in order to upset the government's method, rough as it necessarily is, of assessment in such a case. See, e.g., Pittman v. Commissioner, 100 F.3d 1308, 1313-14 (7th Cir. 1996); Zuhone v. Commissioner, supra, 883 F.2d at 1327; Mendelson v. Commissioner, supra, 305 F.2d at 522; Page v. Commissioner, 58 F.3d 1342, 1347-48 (8th Cir. 1995); Jones v. Commissioner, 903 F.2d 1301, 1303-04 (10th Cir. 1990). A self-reporting system of taxation would founder if taxpayers, who have the best access to all relevant information, could exploit the uncertainty created by their defiance, willful or inadvertent, of the Tax Code's record-keeping requirements. But it is one thing to shift the burden of persuasion to the taxpayer who fails to keep adequate records; it is another to require him to prove that the government's assessment was not only inaccurate but downright irrational. There is no statutory basis for shifting the burden that far.

However, the district judge excluded from evidence both the testimony of the plaintiffs' expert and the log books, and if those rulings stand the plaintiffs cannot prevail at a trial and the judge's error regarding the plaintiffs' burden was harmless. The judge excluded both bodies of evidence as irrelevant, as indeed they would have been had the judge been correct that the government's chosen method of indirect estimation cannot be challenged. He can still, on remand, exclude them from evidence if they are inadmissible under the federal rules of evidence; they merely are not inadmissible as a matter of tax law. It might seem that they fall within the hearsay exception for business records and therefore are clearly admissible. Fed.R.Evid. 803(6). They are indeed business records in the literal sense; but when the record keeper, rather than being a clerical or professional employee, is a principal with a strong motive to falsify the records, the district judge may deem them so unreliable as to be unworthy of consideration by the jury; in the language of the rule, they are to be excluded if "the method or circumstances of preparation indicate lack of trustworthiness." See Wheeler v. Sims, 951 F.2d 796, 802 (7th Cir. 1992); Bracey v. Herringa, 466 F.2d 702, 704-05 (7th Cir. 1972); Romano v. Howarth, 998 F.2d 101, 108 (2d Cir. 1993). The judge will have to determine whether this is such a case.

Concerning the admissibility of the plaintiffs' expert testimony, the judge will have to make the usual Daubert determination, Fed.R.Evid. 702; Kumho Tire Co. v. Carmichael, 526 U.S. 137, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999); Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), with due regard for the concern we expressed earlier about a taxpayer's use of the bank-deposit and net-worth methods of income estimation.

REVERSED AND REMANDED.