OPINION OF THE COURT
RENDELL, Circuit Judge.Edmond N. Gaudelli, Jr. appeals his conviction for perjury in violation of 18 U.S.C. § 1621, based on statements he made in a deposition in a civil action that he initiated against his employer, the City of Pittsburgh, and Chief of Police Robert McNeilly. Gaudelli maintains that the statements he made do not satisfy the materiality requirement necessary for a perjury conviction, and also, that the government’s decision not to grant immunity to a defense witness who invoked the Fifth Amendment denied him a fair trial and his constitutional right to call witnesses. Our jurisdiction over this appeal from a final decision of the District Court is pursuant to 28 U.S.C. § 1291. For the reasons set out below, we will affirm.
I.
In June 1999, Gaudelli, a police officer with the City of Pittsburgh, filed a civil action against his employer and several police officers in his department alleging that after he had responded to a domestic violence call at the home of McNeilly, he was told by his superiors to expunge the call from his records. Gaudelli claimed that when he tried to “[speak] out about *365police misconduct and harassment and other matters of public concern,” the department and its officers retaliated against him in violation of his First Amendment right to free speech.
At his deposition in the case, Gaudelli elaborately detailed responding to a domestic violence call at the McNeilly residence on September 28, 1996. He stated that a fellow officer instructed him not to log the response in his record and that other officers confided with him about similar encounters at the McNeilly home. Evidence was produced, however, contradicting Gaudelli’s claims. McNeilly provided documentation that on the day of the alleged call, he and his family were vacationing in Florida. Several officers that Gaudelli referenced in his story denied his allegations. There was no record of such an event in the department’s record-keeping system, and the individual who created the system stated that a record could not have been expunged from it. In light of this evidence, Gaudelli voluntarily dismissed the case.
Subsequently, Gaudelli was tried for perjury in violation of 18 U.S.C. § 1621. At trial, the government presented evidence that the statements Gaudelli made during his deposition were false. McNeilly testified that he was in Florida on the day that Gaudelli claimed to have responded to a call at his home. Several officers testified that Gaudelli had fabricated conversations he had alleged in his deposition testimony. Gaudelli presented several officers and dispatchers who testified that a call did come from the McNeilly residence on some unknown date. Ultimately, the jury convicted Gaudelli.
II.
Gaudelli makes two arguments on appeal. First, he asserts that the statements that he made during his deposition for which he was convicted do not satisfy the materiality requirement of the offense of perjury. Additionally, Gaudelli argues that the government’s decision not to grant immunity to a defense witness who invoked her Fifth Amendment privilege denied Gaudelli a fair trial and his constitutional right to call witnesses.
Perjury consists of four elements: (1) a false statement; (2) given under oath; (3) made knowingly and willfully; (4) that concerns a material matter. See 18 U.S.C. § 1621. A false statement is material if it has “a natural tendency to influence, or [is] capable of influencing, the decision of the decisionmaking body to which it is addressed.” United States v. Gaudin, 515 U.S. 506, 509, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995) (quoting Kungys v. United States, 485 U.S. 759, 770, 108 S.Ct. 1537, 99 L.Ed.2d 839 (1988)). “The Constitution gives a criminal defendant the right to have a jury determine, beyond a reasonable doubt, his guilt of every element of the crime with which he is charged.” Id. at 522-23, 115 S.Ct. 2310.
The determination of whether Gaudelli’s statements concerned a material matter was committed to the jury at trial. We consider whether there is sufficient evidence, viewed in the light most favorable to the government, to uphold the jury’s decision. United States v. Dent, 149 F.3d 180, 187 (3d Cir.2003). “Our review of the sufficiency of the evidence after a guilty verdict is ‘highly deferential’ ” to the government as the verdict winner. United States v. Hodge, 321 F.3d 429, 439 (3d Cir.2003) (quoting United States v. Hart, 273 F.3d 363, 371 (3d Cir.2001)). We will sustain the verdict if “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Voigt, 89 F.3d 1050, 1080 (3d Cir.1996) (citing Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)).
*366III.
Gaudelli argues that the allegedly false statements that he made at his deposition were not material essentially because his claims lacked merit. He cites the testimony of his expert witness, who stated that his claims would not survive a motion to dismiss. Therefore, Gaudelli argues that the allegedly false statements could not have influenced a decisionmaker and, consequently, were not material. We disagree. The allegations that Gaudelli made in his deposition, that is, that he responded to a domestic violence call at the McNeilly residence and that his superiors told him to cover up the call, were the basis for his claims that the police department retaliated against him. He claims that they were irrelevant and extraneous to the claims advanced in the civil lawsuit, but, to the contrary, they were at the heart of his retaliation claim.
In the alternative, Gaudelli argues that because he voluntarily withdrew his suit, the allegedly false statements could not have influenced the decision maker and were therefore not material. But, a false statement’s capacity to influence a fact finder is judged at the time the statement was made. See United States v. Sarihifard, 155 F.3d 301, 307 (4th Cir.1998); United States v. Gremillion, 464 F.2d 901, 904-05 (5th Cir.1972). The statements Gaudelli made in his deposition had the potential of influencing an eventual fact finder. That the statements were never presented to a fact finder is irrelevant.1
In short, viewed in the light most favorable to the government, Gaudelli’s arguments aimed at the elements of the perjury conviction must fail.
IV.
Gaudelli also argues that the District Court erred when it denied his motion for judgment of acquittal based on the government’s refusal to grant immunity to Gail Elliott, a defense witness who invoked the Fifth Amendment. We review the refusal to immunize a witness for abuse of discretion. United States v. Perez, 280 F.3d 318, 348 (3d Cir.2002) (citing United States v. Herman, 589 F.2d 1191, 1203 (3d Cir.1978)). The District Court’s factual findings regarding the likely effect of undisclosed information are reviewed for clear error. Id. (citing United States v. Pelullo, 173 F.3d 131, 135 (3d Cir.1999)).
Elliott is a former dispatcher at the City of Pittsburgh’s 911 center, who, Gaudelli maintains, would have testified to taking a call for a domestic violence incident at McNeilly’s home sometime between 1993 and 1999. On the day she was scheduled to testify, Elliott informed defense counsel that she would invoke the Fifth Amendment if she were called as a witness, a decision defense counsel alleged was the product of conversations she had with FBI Agent Larry Juliano. The District Court then called both Elliott and Juliano to testify in camera about their conversations.
Elliott testified that she had engaged in several conversations with Juliano over the course of the investigation and trial. A week before the trial was to begin, Elliott initiated a meeting with Juliano to discuss *367her testimony, during which Elliott expressed a reluctance to testify. Juliano told Elliott there were no records to support her story about receiving a call from the McNeilly home and that “she should be aware of the consequences” of testifying. When questioned by the District Court, “Did Mr. Juliano specifically threaten you or intimidate you or specifically say that if you testified, you would be prosecuted or anything like that?” Elliott responded, “No. It was from the way that he told me about the records is the way I take it.”
The District Court denied defense counsel’s request that it direct the government to guarantee immunity to Elliott, finding that because Elliott herself initiated the conversations with Juliano and Juliano’s statements to Elliott never explicitly accused her of lying or threatened her with prosecution, the government’s conduct did not require the court to demand immunity for Elliott. In addition, the District Court found that Elliott’s testimony would be cumulative and not exculpatory.
Under 18 U.S.C. § 6003, a court may grant immunity to a defense witness generally only “upon the request of the United States attorney for such district.” Nevertheless, despite “our governmental system’s strong tradition of deference to prosecutorial discretion” in granting statutory immunity, this Court has recognized two instances in which due process requires that a defense witness be guaranteed prosecutorial immunity. Herman, 589 F.2d at 1203. First, if the court finds prosecutorial misconduct in the form of “the government’s deliberate intent to disrupt the fact finding process,” the court should order the government to grant the defense witness statutory immunity or face a judgment of acquittal. Gov’t of Virgin Islands v. Smith, 615 F.2d 964, 974 (3d Cir.1980); Herman, 589 F.2d at 1204. Second, even in the absence of prosecutorial misconduct, the court has the inherent power to grant a witness immunity where a defendant is deprived of testimony that is “essential to an effective defense,” that is, where the witness can offer testimony “which is clearly exculpatory and essential to the defense case and when the government has no strong interest in withholding use immunity.” Smith, 615 F.2d at 974. “[Wjhether judicial immunity is warranted is a matter to be determined by the district court in the first instance.” Id.
In United States v. Morrison, we found that due process demanded that the government grant immunity to a defense witness “when prosecutorial misconduct caused the defendant’s principal witness to withhold out of fear of self-incrimination testimony which would otherwise allegedly have been available to the defendant.” 535 F.2d 223, 229 (3d Cir.1976). Gaudelli argues that because the government engaged in prosecutorial misconduct, Morrison requires that the District Court have granted Elliott immunity. We disagree.
In Morrison, under the pressure of a “barrage of warnings” from the government that she was liable to be prosecuted for perjury and drug charges if she testified, the defense witness invoked the Fifth Amendment. Id. at 226. Because “the pressure brought to bear on [the witness] by the Assistant United States Attorney ... infringed on defendant’s constitutional right to have [the witness’s] freely-given testimony,” we ordered the District Court to enter a judgment of acquittal if on remand the government refused to grant immunity to the witness when she invoked the Fifth Amendment. Id. at 228, 229.
In the case at bar, however, there was no “barrage” of “repeated warnings” or intimidation of Elliott. It was Elliott who initiated conversations with Juliano and declared her reluctance to testify. While testifying in camera, Elliott indicated that *368Juliano never threatened or intimidated her with prosecution if she testified.
Gaudelli urges that Morrison held that the good faith of the government is not relevant to the inquiry whether the witness should have been granted immunity and that the effect of the prosecutorial misconduct, not the intent, is determinative. We stated in Herman, however, that a defendant asserting a Morrison claim of prosecutorial misconduct bears the substantial burden of showing that “the government’s decisions were made with the deliberate intention of distorting the judicial fact finding process.” Herman, 589 F.2d at 1204. “[Ajbsent this type of prosecutorial misconduct, a defendant is foreclosed from insisting that statutory immunity be granted his witnesses.” Smith, 615 F.2d at 968.
In Smith, we further defined a court’s inherent power to grant immunity to a defense witness. We stated that a court’s ability to require immunity is triggered “not by prosecutorial misconduct or intentional distortion of the trial process, but by the fact that the defendant is prevented from presenting exculpatory evidence which is crucial to his case.” Smith, 615 F.2d at 969. Justification for this authority arises from the “due process right to have clearly exculpatory evidence presented to the jury, at least when there is no strong countervailing systemic interest which justifies its exclusion.” Herman, 589 F.2d at 1204. However, we have said that immunity “will be denied if the proffered testimony is found to be ambiguous, not clearly exculpatory, cumulative, or if it is found to relate only to the credibility of the government’s witness.” Smith, 615 F.2d at 973.
Gaudelli maintains that Elliott’s testimony was both exculpatory and essential to his defense, but we cannot agree. Whereas the testimony of the witnesses in Morrison and Smith would have exonerated the defendants, Elliott’s testimony likely would not have exonerated Gaudelli. See Morrison, 535 F.2d at 225 (witness would have accepted responsibility for the offense for which defendant was charged); United States v. Lowell, 649 F.2d 950, 965 (3d Cir.1981) (immunity for a witness is not required when the witness’s testimony on its own will not exonerate the defendant). Gaudelli anticipated that Elliott would testify that at some unknown date between 1993 and 1999 she received a domestic violence call from the McNeilly residence. However, because several other defense witnesses testified to receiving a call from the McNeilly home at an unknown date, Elliott’s testimony would have been cumulative. Also, Elliott has stated that she is certain that McNeilly was Commissioner, not Chief of Police, at the time she received the call, further diminishing the probative value of her testimony and any likelihood of Gaudelli’s acquittal if Elliott’s testimony had been provided to the jury. In light of these circumstances, we conclude that Elliott’s testimony was neither exculpatory nor essential to Gaudelli’s defense, and the District Court did not abuse its discretion when it refused to grant Elliott immunity.
Accordingly, we will AFFIRM the Judgment and Commitment Order of the District Court.
. We also reject Gaudelli’s contention that the allegedly false statements were not material because the statements were made in a deposition, not in a formal court proceeding. Clearly, the perjury statute does not require that the false statement be made in a formal court proceeding. Section 1621 only requires that the statement have been made "before a competent tribunal, officer, or person” with the authority to place the individual under oath and applies to “any written testimony, declaration, deposition, or certificate” that the individual has sworn to be true. 18 U.S.C. § 1621.