OPINION

REINHARDT, Circuit Judge:

Gerardo Sandoval-Gonzalez was convicted under 8 U.S.C. § 1326(a) for being an alien who reentered the United States after previously being deported. The jury at his trial, however, was not required to find beyond a reasonable doubt that Sandoval was an alien. Instead, the jury was told that "there is a presumption" of his alienage, and the burden of proof was shifted to Sandoval to establish that he had obtained American citizenship by having been born to a U.S. citizen father. We hold that this was error, and, moreover, a prejudicial error. Accordingly, we vacate his conviction and remand.

BACKGROUND

Sandoval's birth certificate states that he was born in 1957 in Tijuana, Mexico, to a Mexican mother and an American father. At the age of fourteen, he entered the United States without inspection. In 2006, over thirty years later, he was charged by the Department of Homeland Security (DHS) with being an alien unlawfully present in the country. Sandoval did not contest his removability, and he was deported in February 2006. In December 2006, Sandoval was again deported after having crossed back into the United States without the consent of the Attorney General.

In 2008, Sandoval was again discovered in the United States. He first told immigration officers that he was a U.S. citizen who had been born in Fresno, California, but then acknowledged that he had previously been deported and that he lacked any immigration documents allowing him to enter or remain in the United States. The government charged Sandoval with being an alien who was previously deported from the United States and then found in the country without permission, a crime under 8 U.S.C. § 1326.

At trial, the government played for the jury a recording of part of Sandoval's February 2006 deportation hearing in immigration court, to establish his alienage. The jury heard the following exchange between the immigration judge and Sandoval:

Through U.S. Border Patrol Agent Antonio Hernandez, the government also introduced into evidence Sandoval's Mexican birth certificate, which stated that he was born in Tijuana, his mother was a Mexican national, and his father was a national of the United States who was originally from Los Angeles, California.

On cross-examination, defense counsel began to ask Hernandez about the possibility of a foreign-born individual acquiring citizenship at birth through a U.S. citizen parent, known as "derivative citizenship." Upon the government's request for a side bar discussion, defense counsel explained that under our decision in United States v. Smith-Baltiher, 424 F.3d 913 (9th Cir. 2005), evidence of derivative citizenship may be used to cast doubt upon the government's allegation that a defendant is an alien, and that Sandoval's father's citizenship provided basis for such doubt. The government objected that derivative citizenship is an affirmative defense for which the defendant must make a prima facie showing of eligibility—namely, that he could meet the burden of establishing such citizenship: that he is "a person born outside the geographical limits of the United States ... of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States" for a period of ten years, at least five of which were after the age of fourteen.2

While the court initially allowed the defense to proceed with its questioning, when later discussing jury instructions with counsel it expressed doubts that a defendant bore no burden to establish his eligibility for derivative citizenship, because "for the government to disprove alienage[sic; presumably intended to be "citizenship"] is an almost impossible task because it requires that they prove a negative." The court concluded that it would provide the jury with the legal definition of derivative citizenship, but it would allow the government to "ask, well, have any of these other things [the requirements for derivative citizenship] been proven to your satisfaction ... ? Have you heard any evidence of that?"

The government accepted the court's invitation to do so. During its closing argument, the government explained that it had proven alienage by presenting Sandoval's statements in the recording from his deportation proceedings and evidence that he had previously been deported. It continued, "You've heard that there is a presumption that if someone is born outside of the United States, they are not considered a United States citizen." Sandoval's objection was overruled. The government then explained that the jury instruction on derivative citizenship provided "two elements that must be established"—(1) birth to one U.S. citizen parent, who (2) met the physical presence requirement prior to the person's birth—and argued that "the mere fact that the birth certificate lists the defendant's father as a national of the United States does not mean that the other elements have been established." Sandoval's objection was again overruled.

In response, defense counsel stressed to the jury that the government had not proven alienage beyond a reasonable doubt. Counsel explained that Sandoval's statements during his deportation proceedings were made in confusion over the difference between citizenship and permanent residence, as evidenced by the recording. Moreover, counsel argued, Sandoval's statement that he was a Mexican citizen was made out of a desire to leave custody, rather than as a conclusive statement of his citizenship.

Following closing arguments, the court denied Sandoval's motion to acquit under Federal Rule of Criminal Procedure 29. It concluded that a rational juror could find beyond a reasonable doubt that Sandoval was a deported alien in the United States, in light of his admissions and two prior deportations, and the fact that he had not demonstrated that he was entitled to derivative citizenship. The entire trial lasted around four hours. After seven hours of deliberation, the jury sent a note to the court expressing its inability to reach a decision. Following two more hours of deliberation the following morning, the jury returned a guilty verdict.3 Sandoval timely appealed.

ANALYSIS

I. Derivative Citizenship

The government reiterates its argument that derivative citizenship is an affirmative defense to a criminal charge under § 1326, for which the defendant must satisfy a burden of production before being permitted to mount the defense. Specifically, it believes that a defendant must be required to demonstrate that he meets the requirements for derivative citizenship under § 1401(g) before such a defense is allowed. We review this question de novo. United States v. Hernandez-Franco, 189 F.3d 1151, 1157 (9th Cir.1999). We conclude that a defendant does not face any such burden because he is attempting to negate an element of the offense for which the government bears the burden of proof beyond a reasonable doubt.

Section 1326(a) creates criminal liability for "any alien who . . . (1) has been denied admission, excluded, deported, or removed or has departed the United States while an order of exclusion, deportation, or removal is outstanding, and thereafter (2) enters, attempts to enter, or is at any time found in, the United States" without permission from the government. It is well-established that, by the statute's plain terms, alienage is a core element of the § 1326 offense. United States v. Meza-Soria, 935 F.2d 166, 168 (9th Cir. 1991); see also Smith-Baltiher, 424 F.3d at 921; United States v. Gracidas-Ulibarry, 231 F.3d 1188, 1196 (9th Cir.2000) (en banc); United States v. Ortiz-Lopez, 24 F.3d 53, 55 (9th Cir.1994). As such, "the government must prove alienage beyond a reasonable doubt," Meza-Soria, 935 F.2d at 171, and a defendant "is entitled to have the jury determine that question at trial." Smith-Baltiher, 424 F.3d at 921 (citing Apprendi v. New Jersey, 530 U.S. 466, 476-477, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000)).4

In Smith-Baltiher, we considered a claim of derivative citizenship made by a defendant contesting the alienage element of the offense. We held that "[b]ecause derivative citizenship would negate that element of the offense," a defendant "must be allowed to present that defense to the jury." 424 F.3d at 922. Seizing on the word "defense," the government now argues that derivative citizenship is an affirmative defense for which the defendant must first make out a prima facie case. The government reads too much into that term, however. We reversed the conviction in Smith-Baltiher because the defendant had been collaterally estopped from presenting any evidence that would support his claim of derivative citizenship.5 Id. at 917. It was in that context that we used the term "defense" to mean the defendant's "evidence of derivative citizenship" that he was not permitted to introduce, and the claim of United States citizenship that he was not allowed to make to the jury. Id. at 922. We did not require that a defendant make any preliminary showing before arguing against his alienage on the basis that he may have been born a U.S. citizen by virtue of derivative citizenship. To the contrary, we reaffirmed that it is the government that has the burden of proving alienage in a prosecution under § 1326, and therefore found that preventing Smith from attempting to negate that element "served to relieve the government of its obligation to establish Smith's guilt beyond a reasonable doubt." Id. at 923. Lest there be any further doubt, we now clarify that a criminal defendant faces no burden whatsoever regarding the issue of derivative citizenship in a prosecution for an offense of which alienage is an element.

Our conclusion that derivative citizenship is not an affirmative defense is confirmed by comparing it with actual affirmative defenses. Classic affirmative defenses are those, "such as self-defense and necessity, [that] do not negative any of the elements of the crime but instead go to show some matter of justification or excuse which is a bar to the imposition of criminal liability." 1 LaFave, Substantive Criminal Law § 1.8(c), at 82 (2d ed.2003); see also United States v. Davenport, 519 F.3d 940, 945 (9th Cir. 2008). For such defenses, a defendant may be held to a burden of production. Considering the defenses of "duress" and "necessity" to the charge of attempting to escape from prison, for example, the Supreme Court has held that defendants must first make a "threshold showing" of the defense before they may present it to a jury. United States v. Bailey, 444 U.S. 394, 416, 100 S.Ct. 624, 62 L.Ed.2d 575 (1980). Moreover, defendants often bear the burden of "prov[ing] the elements of [an] affirmative defense by a preponderance of the evidence." United States v. Beasley, 346 F.3d 930, 935 (9th Cir.2003) (self-defense); see also United States v. Dominguez-Mestas, 929 F.2d 1379, 1383 (9th Cir.1991) (per curiam) (duress).6 For some affirmative defenses, such as insanity, statutes prescribe an even higher burden of proof for the defendant. See 18 U.S.C. § 17(b) ("The defendant has the burden of proving the defense of insanity by clear and convincing evidence.").

Other "defenses," by contrast, are advanced simply to negate an element of the crime. Defendants are largely free to put on whatever relevant evidence they wish in an attempt to create reasonable doubt about an element of the offense in the mind of the jury, without meeting any burden of production or proof. For example, a defendant who testifies "I wasn't there!" need not establish his absence from the crime scene or his presence elsewhere; at all times the burden remains with the government to prove beyond a reasonable doubt that the defendant did, in fact, commit the alleged criminal act as charged. See LaFave, supra, at 86-87 ("[T]he burden of proof as to the `defense' of alibi may not be placed upon the defendant, for alibi of necessity negates [the] defendant's participation in the conduct defined as criminal."); see also United States v. Audett, 529 F.2d 569 (9th Cir.1976) (per curiam). A jury may nonetheless convict in such a case, of course, if it has no reasonable doubt that the government's evidence places the defendant at the scene of the crime, and that the defendant was lying or mistaken when he claimed otherwise.

Derivative citizenship is a "defense" in this latter sense. As we held in Smith-Baltiher, derivative citizenship is a fact that negates an element of the offense: alienage. 424 F.3d at 922. A defendant may assert that he has derivative citizenship just as readily as he may assert that he is a U.S.-born citizen, or that he has never before been excluded or deported from the country (and thus could not illegally re-enter). If he has evidence that has a tendency to make derivative citizenship more likely, it is relevant to the issue of alienage. Cf. United States v. Ibarra, 3 F.3d 1333, 1334-1335 & n. 3 (9th Cir.1993), overruled on other grounds by United States v. Alvarado-Delgado, 98 F.3d 492, 493 (9th Cir.1996) (en banc). It is for the government to persuade the jury that, notwithstanding the defendant's claims or evidence to the contrary, it has proven (1) alienage, (2) prior exclusion or deportation, and (3) improper reentry or attempted reentry. Cf. Meza-Soria, 935 F.2d at 168.

To be clear, the government does not have the burden of disproving each element of derivative citizenship; only "alienage" is among the elements of the crime, so only it must be proven. Indeed, as we discuss below in affirming the denial of Sandoval's motion to acquit, the government advanced sufficient evidence for a rational factfinder to conclude beyond a reasonable doubt that Sandoval is a Mexican citizen, even though the government did not disprove each criterion for derivative citizenship. The government could endeavor to disprove each requirement for derivative citizenship in an effort to eliminate all doubt—for example, by producing the defendants' parents' own immigration or residency records—but it need not do so. Either way, at all times the question for the jury is the same: whether the government's evidence of guilt so outweighs the defendant's evidence to the contrary as to eliminate reasonable doubt—not whether the defendant has met any required burden.

II. Burden Shifting

Having clarified that a defendant faces no burden to claim derivative citizenship in an effort to negate the government's charge that he is an alien, we consider whether such a burden was improperly imposed on Sandoval here, and if so, whether such error requires reversal.

A

It is clear enough that, consistent with its confusion over the "defense" of derivative citizenship, the district court permitted the government to shift the burden of proof to Sandoval with regard to alienage. In her closing argument, the prosecutor stated, "You've heard that there is a presumption that if someone is born outside of the United States, they are not considered a United States citizen." Following the court's earlier suggestion, she continued by explaining that the jury instruction on derivative citizenship provided "two elements that must be established" — (1) birth to one U.S. citizen parent, who (2) met the physical presence requirement prior to the alien's birth—and that "the mere fact that the birth certificate lists the defendant's father as a national of the United States does not mean that the other elements have been established." (Emphasis added.) The court erred in overruling Sandoval's objections to each of these two statements.

First, there is no presumption of alienage, regardless of a defendant's place of birth. To the contrary, as explained above, alienage is an element of the offense, as to which the defendant benefits from a presumption of innocence and the government bears the burden of proof. See Meza-Soria, 935 F.2d at 168; see also Estelle v. Williams, 425 U.S. 501, 503, 96 S.Ct. 1691, 48 L.Ed.2d 126 (1976) ("The presumption of innocence, although not articulated in the Constitution, is a basic component of a fair trial under our system of criminal justice.").

Second, there are no "elements" of derivative citizenship that "must be established" by a criminal defendant, as opposed to, for example, an applicant for a U.S. passport, see 22 C.F.R. § 51.43. The jury instruction on alienage described, correctly, two types of "natural born United States citizen[s]": a person "born in the United States," and a person who is born to a United States citizen parent "if, before the birth of that person, [the] United States citizen parent of that person was physically present in the United States for ten (10) years, at least five (5) of which were after the citizen parent reached the age of fourteen (14)." Sandoval raised the possibility that he fit the latter definition in an attempt to cast doubt on alienage.

The government could have argued that its proffered evidence overwhelmingly proved alienage, notwithstanding the American citizenship of Sandoval's father. Or it could have argued that if Sandoval were actually a citizen, he probably would have fought his prior deportation proceedings on that basis. There are many ways a prosecutor can try to convince a jury that it should have no reasonable doubt about an element of an offense, notwithstanding the defense's attempt to create one. What the government could not do, however, was what it did: suggest that Sandoval bore any responsibility for proving or "establish[ing]" his citizenship, derivative or otherwise. The prosecutor's statement was particularly egregious because she said that the jury had "heard" of such a presumption previously. Of course, it had not—not from counsel, not from a witness, and certainly not from the judge when he instructed the jury minutes earlier; the prosecutor simply misstated the record. Her closing statement, and the district court's rulings sustaining these comments, impermissibly shifted the burden of proof to Sandoval.

B

We must next determine whether these errors require reversal. Some errors "infect the entire trial process, and necessarily render a trial fundamentally unfair," such that automatic reversal is warranted. Neder v. United States, 527 U.S. 1, 8, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999) (internal quotation marks and citations omitted). Most constitutional errors, however, do not rise to that level, and instead do not require reversal if "the court[is] able to declare a belief that it was harmless beyond a reasonable doubt." Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967); see also United States v. Walters, 309 F.3d 589, 593 (9th Cir. 2002). A third category of errors—non-constitutional ones—do not require reversal if the government can show that "it is more probable than not that the error did not materially affect the verdict." United States v. Morales, 108 F.3d 1031, 1040 (9th Cir.1997) (en banc). Sandoval-Gonzalez and the government disagree on whether we should apply the "beyond a reasonable doubt" or "more probable than not" standard for harmless error. We need not decide this issue because the prosecutor's burden-shifting was prejudicial under either standard.

We have considered related errors in the past; this is not the first time a prosecutor has made a closing statement that seeks to shift the burden of proof by proposing a legal presumption in favor of the government. See, e.g., United States v. Segna, 555 F.2d 226, 230-232 (9th Cir. 1977) (prosecutor stated that presumption of sanity existed after defendant had mounted an insanity defense). The closest case to ours is United States v. Perlaza, 439 F.3d 1149 (9th Cir.2006). In the government's closing argument in that case, the prosecutor stated, "You're going to go back into that deliberation room and that presumption of innocence, that presumption of innocence that these men have all been cloaked with . . . [t]hat presumption, when you go back in the room right behind you, is going to vanish when you start deliberating. And that's when the presumption of guilt is going to take over you." Id. at 1169 (emphasis altered). The court overruled the defendant's objections, replying, "That's proper rebuttal. Go ahead. You are all right." Id. at 1170 (emphasis omitted). Later on, the court gave a curative instruction to explain that "[t]here is no such thing as a presumption of guilt in a criminal case." Id. We determined that this after-the-fact remedy was "inadequate to correct the district court's earlier error," which was so prejudicial that the government could not meet its burden to demonstrate harmlessness "under either test." Id. at 1171.

This case is virtually indistinguishable. The jury in Perlaza was told to presume guilt. Juries do not actually find guilt, of course; they find the particular elements of the charged offense. See Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979); In re Winship, 397 U.S. 358, 364, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970). The "presumption of guilt" in Perlaza is thus the same as a presumption that defendant committed each element of the charged offense. And if only one element of the offense is in question, then a presumption as to that element is just as harmful to defendant as a presumption of "guilt." That is what happened here: Alienage was the sole contested issue at trial, as there was no dispute that Sandoval reentered without permission after having been deported, and the jury was told erroneously that it could "presum[e]" the presence of that element because Sandoval was born in Mexico. If the jury followed the prosecutor's instruction and did presume alienage, it would have had little choice but to convict Sandoval. See 8 U.S.C. § 1326(a). The presumption of alienage likely had the same prejudicial effect as the presumption of "guilt" in Perlaza. The prosecutor's other false statement only made the presumption more powerful: By wrongly suggesting that Sandoval had not met his burden of "establish[ing]" derivative citizenship, the prosecutor undercut the only evidence Sandoval relied upon in an attempt to cast doubt on his own alienage.

As in Perlaza, the court's failures to correct the prosecutor's misstatements of law were reversible error under either standard of harmlessness. Even if the standard for nonconstitutional error applied, we could not say that it is "more likely than not" that the jury would have convicted absent the court's errors, notwithstanding the other evidence of alienage the government presented, because that error negated the only effort Sandoval made to raise a doubt about his guilt. Our doubt that the errors were harmless is heightened by the length of the jury's deliberations. "Longer jury deliberations `weigh against a finding of harmless error because lengthy deliberations suggest a difficult case.'" United States v. Velarde-Gomez, 269 F.3d 1023, 1036 (9th Cir.2001) (en banc) (quoting United States v. Varoudakis, 233 F.3d 113, 126 (1st Cir.2000)) (alterations omitted). Here, as the district court observed, the jury "deliberated longer than the case took to try"—twice as long, in fact—and the only contested element of the crime was alienage.

Perlaza explained how the district court could have corrected the prosecutor's misconduct. It could have sustained Sandoval's immediate objections during closing argument. See, e.g., United States v. Cox, 633 F.2d 871, 875 (9th Cir.1980) (affirming conviction where court sustained defendant's objection and "admonished the jurors that the defense had no burden in a criminal case"). Or it could have issued a curative instruction referring "specifically" to its overruling of Sandoval's two objections, confessing error, and "set[ting] forth the Government's proper burden of persuasion." Perlaza, 439 F.3d at 1171-1172 (emphasis omitted). But it did not do either. Because the district court failed entirely to correct both the prosecutor's burden-shifting presumption as to alienage and her description of Sandoval's burden to "establish[]" derivative citizenship, we are bound by Perlaza to vacate Sandoval's conviction. We therefore do not reach the question of whether, by ratifying the prosecutor's burden-shifting statements, the district court violated Sandoval's constitutional rights as well.

III. Motion to Acquit

Finally, Sandoval challenges the denial of his motion to acquit under Fed. R.Crim.P. 29, based on insufficiency of the evidence. We review de novo, United States v. Tucker, 133 F.3d 1208, 1214 (9th Cir.1998), and we affirm.

"We must determine `whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.'" United States v. Mosley, 465 F.3d 412, 415 (9th Cir.2006) (quoting Jackson, 443 U.S. at 319, 99 S.Ct. 2781). We believe that a rational trier of fact could find, beyond a reasonable doubt, that Sandoval is an alien, notwithstanding his father's American citizenship. Sandoval had previously been deported twice. While not conclusive, that Sandoval had been deported before, and that he had allowed himself to be deported twice without asserting American citizenship, is certainly probative. Moreover, he was born in Mexico, and he had previously admitted to being a Mexican citizen and entering the United States illegally. Although Sandoval characterizes his admission as "incredibly unreliable," given his confusion during the colloquy with the immigration judge, we find that this evidence would further support a determination that Sandoval is an alien, when viewing it in the light most favorable to the prosecution. It is entirely possible that a "rational trier of fact" could consider the evidence of Sandoval's father's citizenship, determine that Sandoval might meet the qualifications for derivative citizenship, but then conclude beyond a reasonable doubt that, based on his actions and admissions, Sandoval is not actually an American citizen. We affirm the denial of Sandoval's motion to acquit on this basis, and thus allow for the possibility of retrial on remand.

CONCLUSION

In some ways, our conclusion as to Sandoval's motion to acquit is the complement to our harmless error analysis. Absent the improper burden shifting, a rational juror might well have developed a reasonable doubt about Sandoval's alienage based on his father's citizenship, notwithstanding the other evidence of alienage. Another rational juror could just as easily view the other evidence as overcoming any possible doubt created by the father's citizenship. It would be reasonable to come out either way; that is why we leave essential questions of fact for juries to decide. We ensure that such decisions are kept consistent with constitutional guarantees, however, by requiring that juries be instructed to presume only the defendant's innocence—and nothing else—until the government proves each element of the offense beyond a reasonable doubt. We vacate Sandoval's conviction and remand to the district court for further proceedings consistent with this opinion.

VACATED and REMANDED.