Appellant Harold H. Uchimura (“Uchimu-ra”) appeals his conviction for filing a materially false tax return in violation of 26 U.S.C. § 7206(1). The question presented is whether the trial court committed reversible error by ruling that “materiality” in the context of 26 U.S.C. § 7206(1) is a question of law for the court. We have jurisdiction pursuant to 28 U.S.C. § 1291 and we reverse.1
FACTS AND PROCEEDINGS BELOW
Until his retirement in 1991, Appellant was a police officer with the Honolulu Police Department. From 1983 to 1991, he worked in the Narcotics Vice Division, and in 1988 he began selling cocaine and crystal methamphetamine with two drug dealers he had arrested. On his 1990 tax return, Uchimura reported a 1990 joint taxable income of $32,-416. Based on his expenditures, though, the IRS calculated Uchimura’s true 1990 joint taxable income as $136,163.
Uchimura was charged with, among other things, filing a materially false tax return (count 8) in violation of 26 U.S.C. § 7206(1). On June 9, 1994, the jury found him guilty, and on November 28,1994, he was sentenced to 36 months for count 8 and longer concurrent terms for the other counts. Uchimura timely appealed.2
DISCUSSION
I. Materiality
Section 7206(1) makes it a crime for a person to file a tax return “which he does not believe to be true and correct as to every material matter.” Uchimura argues that the district court erred by refusing to submit materiality to the jury. As of June 1994, when the jury was charged, whether a statement on a tax return was a “material matter” was a question of law for the court. U.S. v. Flake, 746 F.2d 535, 537 (9th Cir.1984), cert. denied, 469 U.S. 1225, 105 S.Ct. 1220, 84 L.Ed.2d 360 (1985). After trial, however, the Ninth Circuit decided U.S. v. Gaudin, 28 F.3d 943 (9th Cir.1994) (en banc), which was affirmed by the Supreme Court on June 19, 1995. — U.S. —, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995). Gaudin holds that materiality in the context of 18 U.S.C. § 1001 is a mixed question of law and fact for the jury to decide. — U.S. at —, 115 S.Ct. at 2320; 28 F.3d at 951. The application of Gaudin in this context is a question of first impression in this Circuit.
A. Gaudin
In Gaudin, the defendant had been convicted of making false statements on Department of Housing and Urban Development loan documents, in violation of 18 U.S.C. § 1001. The trial court, as in the instant case, instructed the jury that materiality was a question of law for the court. The Supreme Court, in rejecting this holding, employed the following syllogism:
The Constitution gives a criminal defendant the right to demand that a jury find him guilty of all the elements of the crime with which he is charged; one of the elements in the present case is materiality; [the defendant] therefore had a right to have the jury decide materiality.
— U.S. at—, 115 S.Ct. at 2314. Materiality is also one of the essential elements of 26 U.S.C. § 7206(1). U.S. v. Marabelles, 724 F.2d 1374, 1380 (9th Cir.1984). Uchimura therefore also had a right to have a jury decide materiality.
Indeed, the Supreme Court’s reasoning applies with equal potency to every crime of which materiality is an element. Accordingly, in every post-Gaudin perjury-type case where we have reached the issue this Court has ruled that materiality, if an element, *-261must be submitted to the jury. U.S. v. Keys, 95 F.3d 874, 880 (9th Cir.1996) (en banc) (18 U.S.C. § 1628 (Perjury)); Fecht v. Price Company, 70 F.3d 1078, 1080 (9th Cir.1995), cert. denied, — U.S.—, 116 S.Ct. 1422, 134 L.Ed.2d 547 (1996) (15 U.S.C. § 78j(b) (Civil Securities Fraud)); U.S. v. Nash, 76 F.3d 282, 285 (9th Cir.1996) (18 U.S.C. § 1014 (False Statement to FDIC)). But see Hervey v. Estes, 65 F.3d 784, 789 n. 4 (9th Cir.1995) (Gaudin not applicable to civil cases). We have also limited Gaudin to its syllogism; if materiality is not an element of the crime charged, then the jury need not consider it. U.S. v. Taylor, 66 F.3d 254, 255 (9th Cir.1995) (18 U.S.C. § 287 (False Claims Against the U.S.)).
B. Materiality — A Mixed Question of Law and Fact
The government nonetheless argues that Gaudin is distinguishable because the respective défínitions of materiality in 18 U.S.C. § 1001 and 26 U.S.C. § 7206(1) are different; “material” in 18 U.S.C. § 1001 means having “a natural tendency to influence, or [be] capable of influencing, the decision of the decisionmaking body to which it was addressed.” Gaudin, 28 F.3d at 948 (quotation omitted). Such a definition “almost always necessitates a factual inquiry.” Appellee Br. at 30. By contrast, argues the government, the test for materiality in the present case was so clearly met that materiality was established as a matter of law.
This argument is, at first glance, beside the point. The Supreme Court’s syllogism renders the fact/law distinction irrelevant-the only pertinent inquiry is whether materiality is an essential element of the crime. Gaudin, — U.S. at —, 115 S.Ct. at 2314. Nevertheless, two other Circuits have reached this issue and have split on,its resolution.3 U.S. v. DiRico, 78 F.3d 732, 736 (1st Cir.1996) (using the Gaudin definition of “material” in Section 7206(1) cases, materiality is a mixed question of law and fact for the jury to decide); U.S. v. Klausner, 80 F.3d 55, 60-61 (2d Cir.1996) (“material” means “essential to the accurate computation of ... taxes;” under such a definition, “no ... factual questions needed to be resolved by the jury in the present case”).4 In addition, this Court addressed the same argument when we applied Gaudin to the perjury statute, 18 U.S.C. § 1623. Keys, 95 F.3d at 878 (the Supreme Court’s syllogism applies “because materiality contains a ‘factual component’” (quoting Gaudin, 28 F.3d at 949)). We must therefore determine whether materiality has a factual component in this case, as well.
This Circuit has never explicitly defined “material” in § 7206(1), although our Model Jury Instructions for § 7206(2) define it as “something necessary to a determination of whether income tax was owed.” Ninth Circuit Model Jury Instructions: Criminal 9.06E (1995). The definitions applied by other Circuits, and by at least one of our Districts, have similar language. Klausner, 80 F.3d at 60 (“essential to the accurate computation of ... taxes”); Aramony, 88 F.3d at 1384 (“in order that the taxpayer estimate and' compute his tax correctly”); U.S. v. Warden, 545 F.2d 32, 37 (7th Cir.1976) (same); U.S. v. Rayor, 204 F.Supp. 486, 491 (S.D.Cal.1962) (same).
Despite our adoption of a materiality definition similar to the one in Klausner, we cannot agree with the Second Circuit. The logic that must be employed (whether by a judge or by a jury) to deduce that a false *-260statement is material renders materiality a “mixed question of law and fact.” Under 18 U.S.C. § 1001, deciding whether a statement is material requires the determination of “at least two subsidiary questions of purely historical fact: (a) Vhat statement was made?’; and (b) “what decision was the agency trying to make?’.” Gaudin, — U.S. at —, 115 S.Ct. at 2314. Under 26 U.S.C. § 7206(1), deciding whether a statement is material surely requires a similar determination of (a) “what statement was made?”; and (b) “what information was necessary in this case to a determination of whether income tax was owed?”.
The government correctly notes that the answer to (b) is spelled out in detail in the Internal Revenue Code and Regulations. Appellee Br. at 31. The answer to (b) in Section 7206 cases is therefore not “purely” a matter of historical fact. But each case is different, and the answer to (b) in each case is necessarily different. For example, a taxpayer is required to report her Social Security number on her tax return. But willfully falsifying one’s Social Security number, while it may hinder the IRS’ record keeping, normally does not affect a determination of whether income tax is owed. As a more cogent example, if one’s legitimate deductions exceed one’s true gross income, taxable income will be zero. Failure to report all income will thus have no effect on taxes owed, at least for that year, and unreported income will not be necessary to a determination of whether income tax is owed.
Under most circumstances, this Court’s pre-Gaudin statement that “any failure to report income is material” is one with which most juries would agree, since any failure to report income usually affects a determination of whether tax is owed. U.S. v. Holland, 880 F.2d 1091, 1096 (9th Cir.1989). But just because a jury usually would agree with such a statement does not mean that a jury must agree with it, as a matter of law. Even if any failure to report income is material in most circumstances, it is not necessarily material in all circumstances, since the materiality of an underreporting of income necessarily depends on the facts of each case. The materiality of other false statements on a tax return, such as deductions, is surely just as fact-dependent. For this reason, we cannot agree with the Klausner court’s observation that a false statement is “material” merely because it renders the return “inaccurate.” Klausner, 80 F.3d at 61.5
C. Materiality Should Have Been Submitted to the Jury
In short, we conclude that Gaudin overturns our holding in Flake, and that materiality under 26 U.S.C. § 7206(1) is a mixed question of law and fact that must be submitted to the jury. Our holding today is based on a fact-sensitive definition of materiality, but even so, the Supreme Court’s syllogism is inescapable. Indeed, the Supreme Court has held, in contexts other than 18 U.S.C. § 1001, that materiality is not a purely “legal” question. Gaudin, — U.S. at — - —, 115 S.Ct. at 2314-15 (citing TSC Industries, Inc. v. Northway, Inc., 426 U.S. 438, 450, 96 S.Ct. 2126, 2132-33, 48 L.Ed.2d 757 (1976) (securities fraud), and McLanahan v. Universal Ins. Co., 26 U.S. (1 Pet.) 170, 188-89, 191, 7 L.Ed. 98 (1828) (false statements in insurance applications)). Because Uehimura is entitled to the benefit of the law prevailing at the time of his appeal, including new rules such as this one, the district court’s instruction removing the element of materiality from the jury’s consideration was erroneous. Griffith v. Kentucky, 479 U.S. 314, 328, 107 S.Ct. 708, 716, 93 L.Ed.2d 649 (1987); Keys, 95 F.3d at 877.
II. Harmless Error
Because he did not object to this instruction at the time of trial, we would normally review for plain error, a highly prejudicial error affecting substantial rights. U.S. v. Payne, 944 F.2d 1458, 1463 (9th Cir.1991), *-259cert. denied, 503 U.S. 975, 112 S.Ct. 1598, 118 L.Ed.2d 313 (1992). In this case, though, Uchimura was faced at trial with a “solid wall of circuit authority” holding that materiality was a question of law. Flake, 746 F.2d at 537; Keys, 95 F.3d at 878. As a result, review for plain error “would be unconscionable,” and we instead review for harmless error.6 Keys, 95 F.3d at 879-80; Fed.R.Crim.P. 52(a).
Under Rule 52(a), any “error, defect, irregularity or variance which does not affect substantial rights shall be disregarded.” Because the instructional error here is of constitutional dimension, to be disregarded it must be harmless beyond a reasonable doubt. Keys, 95 F.3d at 880. We apply two different harmlessness tests, depending on the circumstances of the case. Where the trial court “ ‘simply fails to alert the jurors they must consider’ ” materiality, as in Keys, the omission is harmless “only if review of the facts found by the jury establishes [beyond a reasonable doubt] that the jury necessarily found the omitted element.” Id. (quoting Roy v. Gomez, 81 F.3d 863, 866-67 (9th Cir.1996) (en bane) (emphasis omitted)).7 Where the trial court instead removes proof of an element from the jury’s determination, thus precluding the jury from considering whether the element existed at all, the error is “structural” and cannot be “harmless,” since there can be no inquiry into what evidence the jury considered to establish that element. Keys, 95 F.3d at 880.
This case is of the latter type. The trial court charged the jury as follows:
The question of the materiality of the allegedly false statements made in connection with the subscribing or signing of a tax return is a question of law for the court.
The Court instructs you that if you find that the defendant understated the joint taxable income reported on his joint return then I instruct you that the understatement of joint taxable income is a material matter as contemplated by Section 7206(1).
Jury Instruction 35. The false statement of which Uchimura was accused was his understatement of joint taxable income. Indictment, Count 8. Under this instruction, the jury therefore had two options. First, they could find that he had made a false statement (i.e., he had understated his joint taxable income) in which case the false statement was automatically material. Second, they could find that he had not made a false statement, in which ease he would have been acquitted.
The jury in this ease obviously chose the first option. But because the judge instructed the jurors that if they found Uchimura had made a false statement then they need not separately consider the statement’s materiality, the jurors clearly were “precluded from considering whether the element existed at all.” Keys, 95 F.3d at 880 (quoting Gaudin, 28 F.3d at 951). Accordingly, the error in Uchimura’s Section 7206(1) materiality instruction was not harmless beyond a reasonable doubt, and his conviction for making a false statement on his tax return is
REVERSED.
. In a separate, unpublished memorandum we affirm Uchimura's conviction and sentence for counts of conspiracy, distribution of drugs, and unlawful structuring of currency transactions.
. We deferred submission of Uchimura’s appeal pending this Court’s en banc rehearing of U.S. v. Keys, 67 F.3d 801 (9th Cir.1995). See infra Part II.
. Five Circuits altogether have heard post-Gati-din Section 7206(1) cases. The Fourth Circuit did not reach the issue of whether materiality should go to the jury. U.S. v. Aramony, 88 F.3d 1369, 1383 (4th Cir.1996) (assuming that materiality is a matter for the jury, reversal inappropriate because error was harmless). The Fifth and Seventh Circuits held that materiality is a matter for the jury, but did not address the question of whether Section 7206 materiality is fundamentally different from 18 U.S.C. § 1001 materiality. U.S. v. McGuire, 99 F.3d 671, 672 (5th Cir.1996) (en banc) (materiality should have been submitted to the jury, but no harm since defendant acquitted of Section 7206 charge); U.S. v. DiDomenico, 78 F.3d 294, 303 (7th Cir.), cert. denied, —U.S.—, 117 S.Ct. 507, 136 L.Ed.2d 398 (1996) (materiality should have been submitted to the jury, but conviction affirmed since error was not plain).
. Klausner is actually about Section 7206(2), but the Second Circuit uses the same definition of materiality for Section 7206(1). Klausner, 80 F.3d at 60 n. 4.
. The Second Circuit also noted that "the determination of materiality in the present case involved purely a question of law and was suitable for resolution by the district court ... [because] no ... factual questions needed to be resolved by the jury." Klausner, 80 F.3d at 60-61 (emphasis added). This reasoning bears upon plain error analysis, but it is inappropriate in determining whether materiality should be submitted to the jury. Case-by-case determinations of whether materiality is a question of law or fact are clearly foreclosed by Gaudin.
. After this Court decided Keys, the Supreme Court granted certiorari in U.S. v. Johnson, 82 F.3d 429 (11th Cir.) (unpublished), cert. granted, —U.S.—, 117 S.Ct. 451, 136 L.Ed.2d 346 (1996). One question presented is the proper standard of review of Gaudin-type cases on direct appeal at the time Gaudin was decided. Petitioner's Opening Brief at i, Johnson (No. 96-203), 1996 WL 741434 (U.S. Dec. 30, 1996). The Circuits have split on this issue, a split noted both by this Court in Keys and the petitioner in Johnson. Id. at 25; Keys, 95 F.3d at 880 n. 7. Although the Supreme Court's decision in Johnson will likely affect the ultimate disposition of the instant case, we are not yet persuaded that our approach in Keys is incorrect.
. The Supreme Court vacated and remanded Roy after this Court decided Keys, ruling that the proper harmless error standard in this first type of case is the standard enunciated in O’Neal v. McAninch, 513 U.S. 432, 115 S.Ct. 992, 130 L.Ed.2d 947 (1995), and Brecht v. Abrahamson, 507 U.S. 619, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). California v. Roy, — U.S. —, —, 117 S.Ct. 337, 339, 136 L.Ed.2d 266 (1996). Since the Supreme Court nonetheless continued to recognize the distinction between the two types of harmless error cases, and we conclude below that the present case involves "structural'' enror, which was not at issue in Roy, it is clear that California v. Roy does not affect the instant case. Roy, —U.S. at—, 117 S.Ct. at 338-39.