ALARCON, Circuit Judge:

Jay Flake appeals from his conviction for two counts of making and subscribing false income tax returns in violation of 26 U.S.C. § 7206(1).

I

Flake seeks reversal on the following grounds:

One. The district court erred in treating materiality of the alleged false statement as a matter of law.

Two. The district court erred in failing to dismiss the indictment because it was based on perjured testimony. Three. The prosecutor committed prejudicial misconduct by vouching for the credibility of a key government witness.

Four. The prosecutor committed other acts of misconduct in failing to advise the grand jury that a witness had committed perjury in denying that the government intervened on his behalf in a parole matter, by attempting to establish that Flake was an unethical lawyer, and by arguing outside the record.

Five. The district court erred by refusing to permit defense counsel to argue that the prosecution had changed its theory of the case.

Six. The district court erred in instructing that a jury may find an accused not guilty of underreporting his income where there is an honest disagreement among experts about the tax consequences of a particular transaction.

We conclude that each of these contentions lacks merit and affirm.

We discuss each issue and the facts pertinent thereto under separate headings.

II

MATERIALITY AS A MATTER OF LAW

Flake contends that the materiality of alleged false statements, made in violation of 26 U.S.C. § 7206(1), is a question of fact which should have been submitted to the jury for resolution. The only case cited by Flake in support of this proposition is United States v. Valdez, 594 F.2d 725 (9th Cir. 1979). Valdez is neither dispositive nor applicable. In Valdez, we held that "[m]ateriality is an essential element of the offense prohibited by 18 U.S.C. § 1001." Id. at 728. Under § 1001, a statement is not material unless "the falsification is calculated to induce action or reliance by an agency of the United States . . . ." United States v. East, 416 F.2d 351, 353 (9th Cir. 1969). In Valdez, we agreed with the appellant's contention that "the materiality issue should have been submitted to the jury." 594 F.2d at 729. We also concluded, however, that "the failure to do so was not reversible error." Id.

In the matter before us, we are concerned with a different statute. This court has not been called upon to decide whether the materiality of a false statement which violates 26 U.S.C. § 7206(1) is a matter of law, or is an element of the offense. Other circuits have considered this precise issue. Each has held materiality under § 7206(1) is a question of law.

The issue before us was squarely presented to the Fifth Circuit in Hoover v. United States, 358 F.2d 87 (5th Cir.), cert. denied, 385 U.S. 822, 87 S.Ct. 50, 17 L.Ed.2d 59 (1966), in a prosecution for a violation of § 7206(1). Relying on its earlier opinion in Blackmon v. United States, 108 F.2d 572 (5th Cir. 1940), the court stated "[o]n the basis of the reasoning employed in the perjury cases, the trial court could . . . have decided that the subject matter was material as a matter of law . . ." Id. at 89.

For example, in United States v. Taylor, 574 F.2d 232 (5th Cir.), cert. denied, 439 U.S. 893, 99 S.Ct. 251, 58 L.Ed.2d 239 (1978), the Fifth Circuit stated:

The trial judge did not err in deciding the question of materiality as a matter of law rather than submitting it to the jury. We have long held that in a prosecution for perjury the materiality of the alleged false statement is a question of law. Blackmon v. United States, 108 F.2d 572, 574 (5th Cir. 1940). The rule applies to prosecutions under section 7206(1).

Id. at 235.

In United States v. Strand, 617 F.2d 571, 574 (10th Cir.), cert. denied, 449 U.S. 841, 101 S.Ct. 120, 66 L.Ed.2d 48 (1980), the Tenth Circuit adopted the rule of the Fifth Circuit in United States v. Taylor, 574 F.2d 232, in a § 7206(1) prosecution.

In United States v. Romanow, 509 F.2d 26 (1st Cir. 1975), the First Circuit found "no error" in the trial court's ruling that materiality is a question of law under § 7206(1). Id. at 28.

It is also the law of this circuit that the materiality of an alleged false statement in a prosecution for perjury is a question of law. United States v. Dipp, 581 F.2d 1323, 1328 (9th Cir. 1978), cert. denied, 439 U.S. 1071, 99 S.Ct. 841, 59 L.Ed.2d 37 (1979); United States v. Sisack, 527 F.2d 917, 920 (9th Cir. 1975); Vitello v. United States, 425 F.2d 416, 423 (9th Cir.), cert. denied, 400 U.S. 822, 91 S.Ct. 43, 27 L.Ed.2d 50 (1970). We see no compelling reason to carve out a different rule for false statements in violation of § 7206(1).

The trial court did not err in instructing the jury on materiality as a matter of law.

III [15] DENIAL OF FLAKE'S MOTION TO DISMISS THE INDICTMENT

Flake contends that we must reverse because the district court denied his motion to dismiss the indictment in spite of evidence in the record that the government's witness, Church, lied to the grand jury. He argues that he is entitled to a new trial notwithstanding "the unwillingness of the prosecutor to acknowledge the obvious, i.e. that Church unquestionably lied to the grand jury on material matters and also probably lied during the trial." Flake claims that a review of United States v. Basurto, 497 F.2d 781 (9th Cir. 1974) and Mesarosh v. United States, 352 U.S. 1, 77 S.Ct. 1, 1 L.Ed.2d 1 (1956) "demonstrates that the motion should be granted."

Neither of these cases is applicable to the facts in this record. In Basurto, the prosecutor was advised by a government witness that "he had committed perjury before the grand jury in important respects. In particular, he told the prosecutor that all his grand jury testimony relating to his knowledge of appellants' activities in the conspiracy prior to May 1, 1971, was untrue." United States v. Basurto, 497 F.2d at 784. In the instant matter, the record shows that Church denied committing perjury before the grand jury. Our review of the record convinces us that any misstatements or inconsistencies in Church's testimony did not relate to any fact that was material to the offenses under investigation. Our holding in Basurto was carefully and narrowly drawn. We stated:

We hold that the Due Process Clause of the Fifth Amendment is violated when a defendant has to stand trial on an indictment which the government knows is based partially on perjured testimony, when the perjured testimony is material, and when jeopardy has not attached. Whenever the prosecutor learns of any perjury committed before the grand jury, he is under a duty to immediately inform the court and opposing counsel — and, if the perjury may be material, also the grand jury — in order that appropriate action may be taken.

Id. at 785-86. Flake has failed to demonstrate that the prosecutor in this matter violated the requirements of Basurto in any respect.

In Mesarosh, 352 U.S. 1, 77 S.Ct. 1, 1 L.Ed.2d 1 "[t]he Solicitor General of the United States moved to remand the case to the trial court for further proceedings because of untruthful testimony given . . . by Joseph D. Mazzei, a Government witness . . . ." Id. at 3, 77 S.Ct. at 2. Stating that "[t]he dignity of the United States Government will not permit the conviction of any person on tainted testimony," id. at 9, 77 S.Ct. at 5, the court ordered a new trial.

In this matter, the government has advised this court that "[t]here is absolutely no evidence that Church made a false statement or intended to deceive the grand jury in any way." Mesarosh offers no support for Flake's argument on this issue. The district court did not abuse its discretion in denying Flake's motion to suppress the indictment.

The essence of Flake's argument is that perjury occurred before the grand jury and tainted his indictment. In order for a defendant to obtain a dismissal of his indictment based on inconsistent testimony by a witness, he must show that the witness committed "knowing perjury relating to a material matter . . . ." United States v. Kennedy, 564 F.2d 1329, 1338 (9th Cir. 1977), cert. denied, 435 U.S. 944, 98 S.Ct. 1526, 55 L.Ed.2d 541 (1978). Flake made no such showing. Although Flake demonstrated inconsistencies in Church's testimony, inconsistency is not tantamount to perjury absent a showing of knowing falsehood. If knowing falsehood is not shown, dismissal of an indictment is improper. See United States v. Noti, 731 F.2d 610, 613-14 (9th Cir. 1984).

Moreover, the alleged inconsistencies are not material to Flake's indictment. Church's inconsistent testimony did not bear on the tax charge against Flake, but only reflected potential misconduct by Church. Therefore, the alleged perjury, even if it was intentional, was material to Flake's indictment only to the extent that it artificially inflated the grand jurors' opinion of Church's credibility and not the guilt of the accused, and when the petit jurors have an independent opportunity to assess the witness' credibility, an indictment should not be dismissed. See United States v. Bracy, 566 F.2d 649, 654-56 (9th Cir. 1977), cert. denied, 439 U.S. 818, 99 S.Ct. 79, 58 L.Ed.2d 109 (1979).

IV [23] PROSECUTION MISCONDUCT — VOUCHING

Flake claims that the prosecutor committed prejudicial misconduct in his rebuttal argument "in response to a predictable attack on his star witness." Flake argues that the prosecutor vouched for the credibility of the witness, Church, by "placing the prestige of the government behind the witness" and by "[indicating] that information not presented to the jury supported the witness' testimony."

In order to evaluate this contention, it is necessary to review the argument made by Flake's trial counsel. The following excerpts show that Flake's lawyer not only discussed the credibility of the prosecutor's witness but also attacked the government officers who prosecuted this matter.

Let me talk to you about Mr. Church and his motives. And why would he lie? And in that connection let me talk to you about the plaintiff in this case, the United States of America, our country, the government.

You remember Mr. Church said several times `I have no immunity, no immunity from prosecution, no deal.' And that is what you are being told here, no deal with Mr. Church, right?

Now, let's look at that statement in terms of the credibility of the Government of the United States as the plaintiff in this lawsuit. Do you want to believe the plaintiff's theory of this case, the plaintiff's theory being that Jay Flake is guilty? Do you want to believe that? This fellow Church got on that witness stand in this courtroom and he admitted that on six or seven or eight or nine — and it doesn't make any difference how many, just a bunch — he lied, committed perjury in the bankruptcy proceeding, in a court of the United States of America, a serious crime. We know that, all of us know that you can't intentionally lie on a document that you file with the bankruptcy court. You get indicted for that kind of business.

. . . Is it just our Government fell asleep at the switch, they forgot to fire the gun, they forgot to go in front of the grand jury and indict him? Nah, they didn't forget. This is an intentional act. This is the Government deciding that they wanted this fellow to keep testifying for them and ain't ever going to indict him, and when he tells you there ain't no immunity, that is hooey. They are trying to sell you something that isn't real when they tell you there isn't any immunity in this case.

Now, what do you think of the credibility of the plaintiff in this case now? Do you want to believe their theory of the case? Do you want to believe Jay Flake is guilty while they stand there and sit there and tell you `We don't have a deal with this guy Church'?

And how come they are telling us that? How come Church is telling us that `We don't have a deal'? Well. because if you — if there was writing, a written deal, then I would be able to stand here and argue `Take a look at what they gave this guy, they gave him immunity. They saved him from 150 years of incarceration and whatever the fines might be.' But there isn't any piece of paper, so it comes out kind of slick. You don't have to worry about Green having that piece of paper to talk to the jury. Instead, we've got this fairy godmother tale, this nursery rhyme: Church sits up there and says `I don't have any immunity, I'm just not being prosecuted.'

And then to get to the real bottom line about the credibility of our Government in terms of whether or not there is or isn't immunity in the case, he sat up there and told you about income tax returns. This is an income tax case, folks. That's what my client is charged with. And Church said on the witness stand, he said `I don't have any immunity. They just decided not to prosecute me', I guess for not filing income tax returns. Nah, that ain't what happened.

What happened is this is the carrot and stick. You behave, Mr. Church, the way you think we want you to behave and we won't indict you. And you behave differently than that and we'll crack the whip.

That's what's going on and you — I keep asking you throughout the course of the closing argument, how come he keeps lying? Well, remember what he said when I asked him. I said `You'd do anything to stay out of jail, wouldn't you?' and he said `Yes, sir, I'd do anything.'

And that's what he's been doing, anything he thinks the Government wants him to do, that's what he's doing, sitting there lying, not because a Government agent or a Government lawyer wants him to lie. I'm not suggesting to you that these folks are perjurers or suborn perjury or anything like that, but take a look at the way he testifies. Watch his answers. Think back about the way he did these things, slipping and sliding and changing his story, and he remembers Jones wasn't there because he saw some document.

No, he's getting a perception in his mind: that ain't what the Government wants me to say; okay, well, we'll say it a different way.

And they've got him dancing on the string of: Don't play it our way, we'll just indict you. That's what's going on.

Now, do you believe your Government? Can you believe in the same breath, when they tell you `We have proved our case beyond a reasonable doubt' and in the same breath they are telling you `We didn't give that guy immunity, we ain't got a deal'?

The government responded to these remarks as follows:

Now, in the face of that evidence, the argument has been made to you that you cannot believe that, you just can't believe that, just — just using your common sense, you can't believe that. If you accept that argument, then you have to accept two other things. First of all, in spite of Mr. Church's testimony, you have to believe that because the questions asked of him on redirect examination were precise and direct and all-encompassing, you have to believe that Mr. Church perjured himself intentionally and willfully on the stand. And more than that, you have to believe the Government of the United States, in the person of the prosecutor standing before you, the agents who have been at the table and the people of the United States Attorney's office have suborned that perjury, that they have allowed that witness to testify in that perjurious way, they have elicited that perjury from him intentionally to deceive you and mislead you.

In order to accept the argument made to you by the defense, you have to accept that, as well.

I suggest to you, ladies and gentlemen, that there is no evidence, no evidence before you — and that is the basis on which you should make your decision — no evidence that there has been any deal made of any kind in connection with Mr. Church's testimony.

These comments were clearly invited by Flake's closing argument to the jury. Flake's attorney directly attacked "the credibility of the Government of the United States." He inferred that the prosecution was suborning perjury and making false statements to the jury by stating "[t]hey are trying to sell you something that isn't real when they tell you there isn't any immunity in this case."

The prosecutor's comments merely pointed out to the jury that Flake's attorney had asked them to conclude that Church committed perjury, that the prosecution intentionally presented evidence concerning the alleged promise of immunity which was false. This was an accurate summary of the defense counsel's remarks.

Flake's reliance on United States v. Roberts, 618 F.2d 530 (9th Cir. 1980) is misplaced. The prosecutor here did not "place the prestige of the government behind the witness or . . . indicate that information not presented to the jury supports the witness's testimony." Id. at 533. Instead, in self-defense, he asked the jury to disregard defense counsel's insinuation that the government had intentionally deceived the jury in producing testimony that immunity had not been granted. Under these circumstances, the prosecutor's argument was proper.

V [30] OTHER ALLEGED ACTS OF PROSECUTORIAL MISCONDUCT

A. Failure to Advise Grand Jury of Alleged Perjury

Flake argues that the prosecutor failed to advise the grand jury that a letter had been sent to a parole agency in Nevada by another government lawyer, after Church had denied that the United States had done anything "to interfere or affect in any way" his prison sentence.

There is no evidence in the record that any prosecutor connected with the grand jury investigation had any knowledge of the existence of the letter at the time the question was asked concerning governmental assistance. However, assuming that the prosecutor who presented the evidence to the grand jury was charged with knowledge of the letter sent by his fellow government agent, Flake has failed to demonstrate that the witness' statement was false. Church has explained that he gave a negative answer to the grand jury because the letter did not have any effect on his sentence. The question "[a]nd has the United States Government done anything to interfere or affect in any way your sentence in Las Vegas" was not only ambiguous and compound but also called for a conclusion and hearsay. The explanation of the witness that he received no benefit from the letter is uncontradicted. Thus, his answer to that part of the question directed at the "affect" of the governmental interference was not shown to be untruthful. Prosecutorial misconduct will justify a reversal if it appears more probable than not that the alleged misconduct effected the jury's verdict. United States v. Tham, 665 F.2d 855, 860 (9th Cir. 1981), cert. denied, 456 U.S. 944, 102 S.Ct. 2010, 72 L.Ed.2d 466 (1982). We must defer to the district court's determination of the impact of a claim of misconduct on the outcome of a criminal prosecution, because the trial judges are in a better position to evaluate its impact. United States v. Nadler, 698 F.2d 995, 1001 (9th Cir. 1983).

The district court did not abuse its discretion in refusing to dismiss the indictment for the failure to disclose the existence of the letter.

B. Questions Concerning Flake's Ethics

Flake asserts that the prosecutor was guilty of misconduct by asking him if he had taken an ethics course in law school. Flake is an attorney. During cross-examination, Flake denied knowing the practice in the profession concerning the handling of trust accounts. The prosecutor then inquired whether the subject had been discussed in his law school ethics course. Flake's attorney objected on the ground that this was not a disciplinary proceeding. After a sidebar discussion, the prosecutor agreed to avoid asking questions concerning ethics. The prosecutor dropped this line of inquiry.

Flake has failed to explain how he was prejudiced by the unanswered question. "To warrant a new trial prosecutorial misconduct in the form of improper comment or questioning `must be so pronounced and persistent that it permeated the entire atmosphere of the trial.'" United States v. Lichenstein, 610 F.2d 1272, 1281 (5th Cir.), cert. denied, 447 U.S. 907, 100 S.Ct. 2991, 64 L.Ed.2d 856 (1980) ( quoting United States v. Blevins, 555 F.2d 1236, 1240 (5th Cir. 1977), cert. denied, 434 U.S. 1016, 98 S.Ct. 733, 54 L.Ed.2d 761 (1978)). Assuming that the question was improper, it does not demonstrate "pronounced and persistent" prejudicial misconduct.

C. Argument Outside The Record

Flake correctly points out that during argument, the prosecutor asked the jury to speculate as to the consequences which would have occurred if an agreement between Flake and Church had been enforced. Flake's attorney objected to this argument as being outside the record and, in a sidebar conference, requested that the jury be admonished to disregard it. The trial court agreed and admonished the jury as follows:

Ladies and gentlemen, the last argument by Mr. Lyons is not supported by any evidence or any testimony in this case either as to fact or law, so you will disregard that argument and I admonish you to completely disregard it in your considerations and deliberations.

It was entirely improper argument because it is not supported by any evidence. There is no testimony to support the legal conclusion he was attempting to assert.

Following this special instruction, the prosecutor told the jury: "Ladies and gentlemen, I apologize to you for making such an argument and I wish you to follow the Court's — admonition of the court."

Before this court, Flake argues that the prosecutor's argument "was the genesis of a question later asked by the jury." The jury's question was as follows: "We, the jury, have a question. If a mutual agreement is made between the parties whereby one receives a transfer of property, is that a taxable event to the receiver?"

We are told that this question demonstrates that "the jury ignored the District Court's admonition to disregard the groundless argument of the prosecution." Flake has failed to demonstrate any factual basis for this fanciful speculation. Improprieties in counsel's argument to the jury do not require a new trial unless they "are `so gross as probably to prejudice the defendant,' and any resulting prejudice is not `neutralized' by the court's instructions." United States v. Crenshaw, 698 F.2d 1060, 1063 (9th Cir. 1983) ( quoting United States v. Potter, 616 F.2d 384, 392 (9th Cir. 1979), cert. denied, 449 U.S. 832, 101 S.Ct. 101, 66 L.Ed.2d 37 (1980)).

While the prosecutor's comments were confusing and speculative, they were not "gross." They were swiftly followed by the court's admonition and the prosecutor's apology and personal request that the jury heed the court's instruction. Under these circumstances, while the prosecutor's comments were improper, they did not constitute prejudicial misconduct.

VI [44] RESTRICTION ON DEFENSE ARGUMENT AS TO LEGAL THEORY

The district court ordered Flake's trial attorney not to argue that the government changed its legal theory prior to this trial. Flake contends that "this admonition unfairly hindered the presentation of his case and diminished his right to the assistance of counsel." Flake cites no authority which suggests that defense counsel may argue a matter concerning a pretrial change in the government's legal theory. Nor has our attention been directed to any evidence or testimony in the record which would support such an argument.

The district court did not abuse its discretion by refusing to permit counsel to argue matters which were outside the record in this case.

VII [47] ALLEGED INSTRUCTIONAL ERROR

Flake's final complaint concerns the fact that the district court used the word "may" in instructing the jury what they could find if they concluded that there was an honest disagreement among the tax experts. Flake now argues that the court was required to instruct that the jury "should," not "may," make a finding favorable to the defendant under such circumstances. This contention is frivolous. No objection was made to the giving of the challenged instruction. After the court instructed the jury and before it was excused to commence its deliberations, counsel were asked: "Do either of you have any objections other than what you have already made to the instructions as read?" Flake's attorney replied: "No, sir."

The failure to object to an instruction before the trial court is a bar to any challenge before this court in the absence of a showing of plain error. Henderson v. Kibbe, 431 U.S. 145, 154, 97 S.Ct. 1730, 1736, 52 L.Ed.2d 203 (1977); United States v. Krasn, 614 F.2d 1229, 1235 (9th Cir. 1980). Flake has not attempted to excuse the failure of his attorney to object to the instruction nor has he made a showing that would justify an application of the plain error rule. Finally, we note with dismay and despair that in his opening brief, Flake concedes that the language he now characterizes as "an erroneous statement of the law" "was a variation of an instruction proposed by Appellant" which also would have advised the jury what they "may" do if they concluded that there was an honest disagreement among experts.

The judgment is AFFIRMED.