POSNER, Circuit Judge.

The defendants were convicted of violating, and conspiring to violate, 18 U.S.C. § 1014, which criminalizes "knowingly mak[ing] any false statement ... for the purpose of influencing in any way the action of" any specified private and public entity that provides, or regulates the provision of, financial services; among the entities are federally insured banks. The defendants were each sentenced to two months' imprisonment plus three years of supervised release and they were ordered to pay (along with Brian Bowling, of whom more shortly) nearly $90,000 in restitution to successors in interest to the bank they were convicted of having made false statements to. A panel of this court affirmed the judgment, 688 F.3d 802 (7th Cir.2012), over the dissent of one of the panel members. The full court granted rehearing en banc to clarify the elements of the crime and their application to charges of mortgage fraud, which have mushroomed in the wake of the collapse of the housing and credit bubbles in the period 2006 to 2008. We try in this opinion to clarify the meaning of "knowingly" making a false statement "for the purpose of influencing in any way" the action of the bank or other covered entity in response to the false statement.

Lacey Phillips and Erin Hall are a couple. Phillips is a hairdresser, Hall a barber. In the spring of 2006, just as — unbeknownst to them — the housing bubble was deflating, they found a house they wanted to buy priced slightly below $250,000. Like countless American couples during the housing bubble they mistakenly believed they could afford the house they wanted. They had never owned a house, had only a high-school education (Hall had some college but no degree), and were financially unsophisticated.

They applied to Associated Bank for a mortgage. The bank turned down their application because Hall had a recent bankruptcy and because the bank deemed the couple's joint monthly income of $3,800 too meager to justify the loan of more than $200,000 that they needed. After this rebuff Hall turned to a mortgage broker named Brian Bowling whom he knew and admired (Hall had been Bowling's barber) for help in obtaining a mortgage loan. Bowling — a crook who brokered fraudulent loans (but there is no indication that either Phillips or Hall knew or suspected that he was a crook) — steered the couple to a federally insured bank of dubious ethics named Fremont Investment & Loan. Had Fremont been the bank that had turned the defendants down the first time, this might have shown that they realized they didn't meet the bank's criteria for a loan and so would be able to obtain a loan only by lying. But it was of course a different bank that had previously turned them down.

Associated Bank was a reputable bank. Fremont was not. See Commonwealth v. Fremont Investment & Loan, 452 Mass. 733, 897 N.E.2d 548, 551-55 (2008); In re Fremont Investment & Loan, Docket No. FDIC-07-035b (FDIC Order to Cease and Desist, Mar. 7, 2007), www.fdic.gov/bank/individual/enforcement/2007-03-00.pdf; "U.S. Regulators Order Fremont Investment & Loan to Tighten Its Loan Policies and Operations," New York Times, Mar. 8, 2007, www.nytimes.com/2007/03/08/ business/worldbusiness/08iht-mortgage.4840813.html (both websites were visited on September 3, 2013). Fremont's specialty was making "stated income" loans — known to the knowing as "liars' loans" because in a stated-income loan the lender accepts the borrower's statement of his income without trying to verify it. Such loans, which played a significant role in the financial collapse of September 2008 — the doleful consequences of which continue to plague the U.S. and world economies — were profitable despite the high risk of default because lenders sold them as soon as they'd made them. Many of the loans were repackaged by the buyers into ill-fated mortgage-backed securities whose holders lost their shirts. This was musical-chairs financing.

Fremont went broke when the music stopped in June 2008. Its collapse was a harbinger of the worldwide financial collapse that occurred three months later when Lehman Brothers suddenly declared bankruptcy. "[The] very terms [of Fremont's loans] — short-term interest rates followed by payment shock, plus high loan-to-value and high debt-to-income ratios — were likely to lead to default and foreclosure." Megan Woolhouse, "Lender Settles with State for $10m," Boston Globe, Business, p. 7, June 10, 2009, www.boston.com/business/articles/2009/06/10/subprime_lender_settles_suit_with_mass_for_10m/ (visited Sept. 3, 2013) (quoting Attorney General of Massachusetts).

The defendants soon lost their home, being unable — despite valiant efforts to keep up their mortgage payments by working second jobs — to make the monthly payments of principal and interest required by the terms of the mortgage. The interest rate was adjustable; it reset automatically after two years, doubtless at a higher rate. "A large majority of Fremont's subprime loans [the loan to the defendants was subprime] were adjustable rate mortgage (ARM) loans, which bore a fixed interest rate for the first two or three years, and then adjusted every six months to a considerably higher variable rate for the remaining period of what was generally a thirty-year loan." Commonwealth v. Fremont Investment & Loan, supra, 897 N.E.2d at 552. Though hapless victims of Bowling, the defendants were convicted in part on the basis of his testimony; for he turned state's evidence and was rewarded for helping to convict his victims by being given a big slice off his sentence.

At the government's urging, the trial judge excluded, as irrelevant, evidence that might have persuaded the jury that the defendants either had not made statements they knew to be false or, though knowing the statements to be false, hadn't made them for the purpose of influencing the bank's action on their mortgage application. The district judge ruled erroneously that if mortgage applicants "sign something and they send it in, they're attempting to influence the bank.... They didn't sign these papers just to put them up on their wall. They signed these papers with the idea they would go in to whoever and they would get a mortgage.... [If defendant Phillips, who signed the mortgage application to Fremont] just took the papers and went home, we would not have a crime. But by sending them in to the mortgage company, she's met the requirements of [section] 1014."

The implication of the passage we just quoted is that making a statement that is false and influences a bank is a crime. It isn't. The statement must be knowingly false. The judge excluded evidence that if believed might have convinced a jury that any false statements the defendants made were not made knowingly — that is, not known by them to be false. The evidence if believed might also have rebutted an inference of intent to influence the bank. Not that the jury was erroneously instructed. But the judge may have been led by a misunderstanding of section 1014 to exclude evidence that if admitted might have exonerated the defendants.

We take up the issue of influencing first, and then the issue of knowing falsehoods. Suppose you're an actress and you habitually subtract three years from your true age because you're worried about movie producers' discriminating against aging actresses. You're 40 but pretend to be 37. You know the bank doesn't care whether you're 40 or 37 — you're wealthy and the bank is eager to have you as a customer — but you don't like your true age to appear on any document; a bank employee might read it and discover the lie and post his discovery on Facebook or Twitter, and within hours the whole world would be privy to your secret. You would have made a knowingly false statement on your bank application by listing your age as 37, and rather than just pinning the application to your wall you had submitted it to the bank. Under the district judge's interpretation of section 1014 — an erroneous interpretation that warped the trial in this case — you would be guilty of a felony punishable by a prison sentence of up to 30 years and a maximum fine of up to $1,000,000.

What is true is that if you make a knowingly false statement intending to influence a bank, it's no defense that you didn't succeed in influencing it or even that you couldn't have succeeded. Materiality is not an element of the offense punished by section 1014. United States v. Wells, 519 U.S. 482, 484, 117 S.Ct. 921, 137 L.Ed.2d 107 (1997); United States v. Lane, 323 F.3d 568, 582-83 (7th Cir.2003). But it is relevant. If the loan applicant doesn't think his falsehood would influence the bank it is unlikely that in making it he intended to influence the bank; as in our example of the actress, he would have had a different motive. As the Supreme Court explained in Wells, "a statement made `for the purpose of influencing' a bank will not usually be about something a banker would regard as trivial, and `it will be relatively rare that the Government will be able to prove that' a false statement `was... made with the subjective intent' of influencing a decision unless it could first prove that the statement has `the natural tendency to influence the decision.' Hence the literal reading of the statute will not normally take the scope of § 1014 beyond the limit that a materiality requirement would impose." United States v. Wells, supra, 519 U.S. at 499, 117 S.Ct. 921 (emphasis added), quoting Kungys v. United States, 485 U.S. 759, 780-81, 108 S.Ct. 1537, 99 L.Ed.2d 839 (1988).

Wells declined to read a requirement of proving materiality into the statute not because materiality is irrelevant but because "the literal reading of the statute" — the reading that excludes materiality as an element of the offense — nevertheless allows immateriality to be used as evidence that the false statement was not intended to influence the bank.

If the defendants believed that all the bank cared about was that the applicant for a loan have a decent credit rating, as did Phillips, who alone signed the application as borrower, they wouldn't have thought the statement of income would influence the bank's decision any more than pinning Phillips's baby pictures to the application would have done so. And if one believes the defendants' version of what their mortgage broker told them — a version they were forbidden to present to the jury — they didn't think that including in the space for "borrower's income" a non-borrower's income would affect the bank's decision, as all the bank cared about was the total income available to service the loan — and the non-borrower was the applicant's "significant other" and future spouse. What can it mean to intend to influence a bank by telling it something you're confident won't influence it?

The defendants wanted but were forbidden by the district judge to testify that Bowling had told them, first, that Phillips should be the only applicant for the stated-income loan because her credit history was good while Hall's was bad because of his recent bankruptcy; second that Hall's income should be added to hers on the line in the application that asked for the borrower's gross monthly income; and third that this was proper in the case of a stated-income loan because what the bank was asking for was the total income from which the loan would be repaid rather than just the borrower's income. Phillips and Hall were a couple (they have since married) and so both their incomes would be available to contribute to the mortgage payments. And nowadays of course many unmarried couples live together indefinitely in a state functionally equivalent to marriage, sharing joint expenses, such as mortgage expenses, as a married couple would do.

The judge forbade the defendants to testify to these things because she didn't see the relevance of such testimony. The government adds that it would have been hearsay. Not so (a surprising mistake for a Justice Department lawyer to make); the defendants were offering the testimony about Bowling's alleged statements not to prove that a stated-income loan does permit what Bowling told them it did, but to explain what they had heard him tell them (and that they believed what he told them) when they made the application. It is not hearsay to testify to what someone told you and what you thought the person meant, as long as you're not insisting on "the truth of the matter asserted in the [out-of-court] statement." Fed.R.Evid. 801(c)(2); Talmage v. Harris, 486 F.3d 968, 975 (7th Cir.2007); United States v. Hanson, 994 F.2d 403, 406-07 (7th Cir.1993); United States v. Thompson, 279 F.3d 1043, 1047 (D.C.Cir.2002). The defendants wanted to testify not that Bowling had told them the truth but that his lies, undetected by them, had made them misunderstand the meaning of "borrower's income" in an application for a stated-income loan.

The evidence they were prevented from giving was pertinent both to whether they had knowingly made a false statement and to whether, if so, their intention had been to influence the bank to grant them a mortgage. They wanted to testify that Bowling had told them that in a stated-income loan the line for the borrower's income on the application form really means the borrower's income plus the income of a spouse, or parent, or a person one is cohabiting with in a committed relationship whether marital or nonmarital, or anyone else whose income will be an additional source of repayment of the mortgage. On this interpretation, which financial naïfs like these defendants could well believe, they weren't trying to influence the bank by means of a false statement, because on that interpretation what the bank was asking for in the line for borrower's income was the total income out of which the mortgage would be repaid. The defendants must have known that in a literal sense Hall's income was not part of the borrower's, Phillips's, income. But literal meanings are not the only true meanings of phrases or sentences or other linguistic units. If Phillips told Hall that she had a toothache that was killing her, it would not have been an intelligent response for Hall to call 911 for an ambulance. Or if she had told him that he was a "cool cat," this would not be a lie just because he lacks whiskers and a nictitating membrane.

These examples illustrate, what should be obvious, that even the simplest sentences require interpretation. Francis Lieber gave the following example almost two centuries ago in his celebrated book Legal and Political Hermeneutics, Or, Principles of Interpretation and Construction in Law and Politics: With Remarks on Precedents and Authorities 28-30 (1839): "Suppose a housekeeper says to a domestic: `Fetch some soupmeat,' accompanying the act with giving some money to the latter." That sounds straightforward, but Lieber explains that the domestic

It is for a jury to determine what the defendants understood to be the meaning that Bowling attached to "borrower's income." In finance as in law, words and phrases in everyday use often bear a specialized meaning of which ordinary people are ignorant. Won't the typical reader of a typical mortgage application form (such as "Uniform Residential Loan Application," https://www.fanniemae.com/content/guide_form/1003rev.pdf (visited Sept. 3, 2013)) sense that such words as "liquid," "delinquent," "delinquency," "successors," "title," "discount," "vested interest," and "improvements" are not being used in their everyday sense? Couldn't a loan applicant believe — if told by a professional whom the applicant has reason to trust — that "borrower's income" on such a form also may not bear its everyday meaning?

Indeed the bank, given its business model, may have been asking for either an individual's income or a combined income, rather than just for the former. If Phillips was trying to influence the bank not by concealing the existence of Hall (with his bad credit record) but by reporting an income from which the mortgage would be repaid that was large enough to persuade the bank that the loan would not be unduly risky, and she thought the loan application asked for that measure of income, she was trying to influence the bank by saying something she believed to be true.

An FBI agent who interviewed Hall quoted him as saying that "Bowling mentioned that [Phillips] would need to change her [job] title to make her income look a little better." (So on the loan application she was listed as a "sales manager," which was false.) But there was also evidence, consistent with Fremont's business model, that the bank didn't give a fig about the couple's ability to repay the loan. It planned to sell the loan, which would then be folded with many other loans into a mortgage-backed security that would be sliced and the slices sold around the world, the premise being that the security would be safe because of diversification — the mortgages bundled into the security would be on properties scattered across the United States. A nationwide collapse of the housing market was not foreseen.

It's true that even if the bank didn't care what was on the loan application, the defendants could have thought they were influencing the bank — and a purpose to influence is an element of the crime (though, to repeat, only if the influence is exerted through knowingly false statements). But a jury could find that the defendants believed the bank had approved the loan to the couple, and was telling them through Bowling what to put on the loan application, or what he should put on it in their name, and that in complying with his directives the defendants were not trying to influence the bank because they knew the bank had already made up its mind to make the loan and were just following Bowling's directions, which they may not have understood. What if he told them that the bank wouldn't even read their application, that all it cared about was having a signed application? Then in authorizing Bowling to fill in the application the defendants would not have been trying to influence the bank.

The jury rendered a general verdict, simply finding the defendants guilty of both counts of the indictment (the second being the conspiracy count). The verdict did not reveal what false statements the jury attributed to the defendants. For all we can know, the only false statement to the bank that the jury found that Phillips and Hall had known to be false (given that Hall hadn't signed the application and that neither of the defendants may have read it) was the statement of income in the borrower's line on the form — for they admitted to having known their incomes would be combined on that line, while denying knowledge of the other falsities charged — those they attributed to Bowling. Had they been allowed to testify to what Bowling had told them the phrase "borrower's income" meant, the jury might well have concluded that the couple had believed that combining their income on the "borrower's income" line of the loan application was precisely what the application called for.

It's true that the combined income was inflated on the application and that Phillips's job was falsely listed as that of a sales manager rather than a hairdresser in order to make the income figure more credible. Phillips testified, however, that the application was filled out by Bowling and that neither she nor Hall read it or was aware of the inaccuracies in it. Bowling had told them he would add Hall's income to Philipps's in the line for the borrower's income but not that he would inflate their combined income.

The jury may well have believed the FBI agent's testimony that Hall had acknowledged having been told by Bowling that Phillips's job title would be inflated on the application. But alternatively the jury may not even have considered the agent's testimony; the judge's evidentiary ruling left the jury with little choice but to convict the defendants on the basis of the (literal) meaning of "borrower's income" alone.

The government does not argue that by signing the form Phillips adopted the false statements in it that she was unaware of. Nor would that be a plausible reading of a criminal statute that forbids only false statements made "knowingly." It is careless to sign a document without reading it, but it is a knowing adoption of its contents only if the signer is playing the ostrich game ("willful blindness"), that is, not reading it because of what she knows or suspects is in it. In re Aimster Copyright Litigation, 334 F.3d 643, 650 (7th Cir.2003); United States v. Azubike, 564 F.3d 59, 66-67 (1st Cir.2009); United States v. Aina-Marshall, 336 F.3d 167, 170-71 (2d Cir.2003).

Because Hall didn't sign the application form, the bank could not have sought a deficiency judgment against him when the mortgage was defaulted. But there is no evidence that Hall was kept off the application form in order to avoid being potentially subject to a deficiency judgment. It would be highly implausible. Deficiency judgments are rarely sought in Wisconsin because Wisconsin law allows mortgagees to foreclose six months after obtaining a default judgment if they waive their right to a deficiency judgment. Wis. Stat. 846.101(2). Otherwise they must wait a year. Id., 846.10. Anyway what bank would think it worth the expense of suing to obtain a deficiency judgment against a barber? And remember that Fremont's business model involved selling the mortgages it issued, not servicing and if necessary foreclosing on them.

But the district court's key error was forbidding the defendants to testify to what Bowling told them when he instructed Phillips to sign the application for the mortgage loan. He may have said to them: "Your application isn't illegal." Or: "Whatever you write on it won't affect the bank's lending decision because it doesn't read the applications — they're just window dressing." Or: "combining your income isn't a misstatement under Fremont's stated-income loan program." The first statement would not have helped the defendants because mistake of law is rarely allowed as a defense to a criminal charge, Cheek v. United States, 498 U.S. 192, 199, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991); United States v. Dimitrov, 546 F.3d 409, 414 (7th Cir.2008); United States v. Allen, 670 F.3d 12, 18 (1st Cir.2012), and we are given no reason to think that 18 U.S.C. § 1014 is an exception. The second statement, however, would have helped negate the element of intent to influence. And the third if believed would have refuted the prosecution's claim that the defendants had knowingly made a false statement to the bank, unless the jury believed that other false statements on the application were made by the defendants or (as may have been the case with the change in Phillips's job title) with their knowledge, rather than by Bowling without his telling them. Had the jury believed either that the defendants lacked the intent to influence the bank or that they did not make any knowingly false statements, it would have acquitted them.

The erroneous exclusion of evidence favorable to the defendants could thus have been decisive in the jury's decision to convict. The judgment is therefore reversed and the case remanded for a new trial.

REVERSED, AND REMANDED WITH INSTRUCTIONS.

EASTERBROOK, Chief Judge, with whom BAUER, Circuit Judge, joins, dissenting.

Lacey Phillips and Erin Hall decided to buy a house together. After one bank turned them down because their income was inadequate, Brian Bowling, a loan broker, told them that they could get a loan by changing what they told the potential lender. Bowling prepared an application that omitted Hall's name (avoiding a credit check that would have revealed his bankruptcy), attributed the combined income of Hall and Phillips to Phillips alone, doubled that combined income, and falsely claimed that Phillips was a sales manager at a satellite TV business. (Bowling knew that the $90,000 annual income Phillips claimed to earn needed to match the job she claimed to hold; actually she was a hairstylist at J.C. Penney, with an annual income less than $24,000.) Phillips signed the application and an employment verification form. Fremont Investment & Loan extended credit, and the couple bought their home. But they could not keep up the payments, and the mortgage holder foreclosed. A jury convicted them of violating 18 U.S.C. § 1014.

Section 1014 is a simple statute. It reads: "Whoever knowingly makes any false statement ... for the purpose of influencing in any way the action of [any of a long list of entities, including federally insured lenders] shall be fined not more than $1,000,000 or imprisoned not more than 30 years, or both." There are just three elements: (1) knowingly making a false statement; (2) to one of the listed entities; (3) for the purpose of influencing that entity. Phillips and Hall concede that the documents contain many false statements, and the jury found that they knew the documents' contents to be false. The instructions told the jury to acquit defendants if they thought the statements to be true. Defendants concede that Fremont was among the entities listed in § 1014. That leaves "for the purpose of influencing in any way the action" of the lender. The bank fraud statute, 18 U.S.C. § 1344, requires proof of intent to defraud; § 1014 is a different animal, requiring only proof of intent to influence. See United States v. Wells, 519 U.S. 482, 117 S.Ct. 921, 137 L.Ed.2d 107 (1997); United States v. Lane, 323 F.3d 568, 582-85 (7th Cir.2003).

Much of the majority opinion reads as if there were an open issue about whether defendants knew that the application contained false representations. Yet Bowling's testimony would have been irrelevant to that subject, which the jury resolved against defendants on instructions they do not contest. Although the jury did not return a special verdict telling us which falsehoods it had found, there's no need for special verdicts in criminal cases. See Black v. United States, 561 U.S. 465, 130 S.Ct. 2963, 177 L.Ed.2d 695 (2010). It is enough if the evidence supports any of the ways in which the defendants could have committed the offense. See Griffin v. United States, 502 U.S. 46, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991). The evidence shows that defendants' income was combined (even though Hall's income would have been unavailable to the lender) and then doubled, and that Phillips's occupation was misrepresented in order to make the asserted income look plausible. Defendants argue that (a) Bowling told them that it was OK to combine their income, and (b) they did not read the application and thus did not know about the doubling, which Bowling added without telling them (presumably after Phillips signed the form). The jury necessarily rejected proposition (b), which supports the conviction without regard to what Bowling may have said about the propriety of combining incomes.

Bowling's proposed testimony would have been relevant if the only lie in the application were combining the couple's income while omitting Hall's name. Most of the majority's opinion treats this as the only lie. But it wasn't. The combined income was doubled and Phillips's occupation misstated. Given Griffin we must resolve this appeal on the assumption that the jury found that defendants knew about the doubling.

In asking whether the doubling was "for the purpose of influencing" the lender, it is helpful to distinguish two things that Bowling might have said. First, he might have told the defendants that banks do not care whether applicants disclose any income. That is to say Bowling might have said that applicants can leave the "income" line blank and still get a loan. Or he might have told them that banks do not care about the truth of the stated income. Banks that syndicate their loans do not lose if the borrowers default — that's why some didn't run credit checks on potential borrowers, and why the phrase "liars' loans" developed — but they do care about the representation that the income is high enough. Without the representation that the income is sufficient, the loan can't be syndicated, the original bank would remain on the hook, and the loan therefore would not be made. The distinction I am drawing is between a belief about whether the statement would influence the bank, and whether the truth of the statement would influence the bank.

If Bowling told defendants that banks would make loans with the income line left blank, then his testimony would have been relevant, because it would have tended to show that the defendants did not have "the purpose of influencing" the lender when they put a number, any number, in the income blank. But if Bowling told the defendants only that the bank did not care about the truth of the claimed income, that would not have aided the defense. To the contrary, it would have supported the prosecution by showing that defendants knew that the stated income was vital to the success of the application.

I could not find any suggestion by defense counsel in the district court that Bowling would have testified that he told defendants that Fremont would loan money to applicants who left the income line blank. Everything that happened in the district court is consistent with the second understanding: defendants wanted to show that, although they knew that banks respond to the income stated on the form, they thought that banks don't care whether the statements are true. Indeed, the whole idea of a "stated-income loan program" is that the statements matter, even if banks don't verify their truth. A belief in the propriety of lying is a mistake-of-law defense that a district court may (indeed must) rebuff. All § 1014 requires is proof that the defendants lied in order to influence a bank. And as a proposition of fact the sort of testimony they wanted to offer would have demonstrated the very purpose needed to convict them. They were not prejudiced by its exclusion.

My colleagues see three possibilities:

Opinion at 656 (bracketed numbers added). Possibility (1) would be a forbidden mistake-of-law defense, just as the majority says. Possibility (3) would be a genuine defense if the application accurately stated the couple's combined income, but because it doubled the income (and given Griffin we must assume that the verdict reflects a finding that defendants knew this) does not assist defendants. And possibility (2) neglects the vital distinction I have mentioned — the difference between a lender not caring whether there is a number in the income blank, and a lender not caring whether that number is true.

If the lender cares about the level represented as the would-be borrower's income — as Fremont surely did, in order to syndicate the loan — then the representation is made for the purpose of influencing the lender. Had defendants told the truth, they wouldn't have received the loan. And Bowling's testimony, as counsel described it to the district court, would have shown that defendants knew that banks care how much they claim to earn, even if they thought banks don't care about whether the claim is true. The upshot of my colleagues' contrary conclusion is that crooked brokers such as Bowling can confer on clients a legal entitlement to obtain loans by deceit. That's bad economics as well as bad law. It makes it harder to extirpate liars' loans programs, and it raises the rate of interest that will be charged to honest applicants. These convictions should be affirmed.