United States v. Richard Stadtmauer ( 2010 )


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  •                                       PRECEDENTIAL
    UNITED STATES COURT OF APPEALS
    FOR THE THIRD CIRCUIT
    No. 09-1575
    UNITED STATES OF AMERICA
    v.
    RICHARD STADTMAUER,
    Appellant
    Appeal from the United States District Court
    for the District of New Jersey
    (D.C. Criminal Action No. 2-05-cr-00249-003)
    District Judge: Honorable Jose L. Linares
    Argued November 17, 2009
    Before: AMBRO, ALDISERT, and ROTH, Circuit Judges
    (Opinion filed September 9, 2010)
    David Debold, Esquire
    Miquel A. Estrada, Esquire (Argued)
    Scott P. Martin, Esquire
    Gibson, Dunn & Crutcher LLP
    1050 Connecticut Avenue, N.W.
    9th Floor
    Washington, DC 20036-0000
    Robert S. Fink, Esquire
    Kostelanetz & Fink, LLP
    7 World Trade Center
    34th Floor
    New York, NY 10007
    David M. Zinn, Esquire
    Williams & Connolly LLP
    725 12th Street, N. W.
    Washington, D.C. 20005
    Counsel for Appellant
    Ralph J. Marra, Jr.
    Acting United States Attorney
    George S. Leone
    Chief, Appeals Division
    Steven G. Sanders (Argued)
    Assistant U.S. Attorney
    Office of the United States Attorney
    970 Broad Street, Room 700
    2
    Newark, NJ 07102-0000
    Counsel for Appellee
    OPINION OF THE COURT
    AMBRO, Circuit Judge
    Table of Contents
    I. Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
    A. Richard Stadtmauer and the Kushner Companies. 5
    B. The Other Players. . . . . . . . . . . . . . . . . . . . . . . . . . 7
    C. The Alleged Conspiracy. . . . . . . . . . . . . . . . . . . . . 8
    1. The General Ledgers.. . . . . . . . . . . . . . . . . 11
    i. Charitable Contributions. . . . . . . . . 11
    ii. “Non-Property” Expenses. . . . . . . . 12
    iii. Capital Expenditures. . . . . . . . . . 13
    iv. Gift and Entertainment Expenses. . 15
    2. KC’s Internal Financial Statements. . . . . . 15
    3. SSMB’s Preparation of the Partnerships’
    Tax Returns.. . . . . . . . . . . . . . . . . . . . . 16
    D. Evidence of Stadtmauer’s Knowledge. . . . . . . . . 19
    1. “Thursday Meetings” . . . . . . . . . . . . . . . . . 21
    2. “Richard Specials” and Other Special
    Financial Statements.. . . . . . . . . . . . . . 23
    3. Other Circumstantial Evidence of
    Stadtmauer’s Knowledge of Tax Law
    3
    and Consciousness of Guilt. . . . . . . . . 26
    i. Rationale for Private School Tuition
    Payments .. . . . . . . . . . . . . . . . . 26
    ii. The 1996 IRS Audit. . . . . . . . . . . . 26
    iii. Dissenting Limited Partners and
    Executives. . . . . . . . . . . . . . . . 27
    E. The Verdict and Stadtmauer’s Post-Verdict
    Motions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
    II. Jurisdiction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
    III. Discussion.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
    A. Willful Blindness. . . . . . . . . . . . . . . . . . . . . . . . . 32
    1. Whether the District Court’s Willful
    Blindness Instruction Applied to
    Stadtmauer’s Knowledge of the Law. . 33
    2. Willful Blindness and Cheek. . . . . . . . . . . 38
    3. Whether the District Court’s Willful
    Blindness Instruction Applied
    to the Element of Specific Intent. . . . . 46
    4. Whether Trial Evidence Warranted the
    Willful Blindness Instruction. . . . . . . . 50
    B. Lay Opinion Testimony.. . . . . . . . . . . . . . . . . . . . 52
    1. Background.. . . . . . . . . . . . . . . . . . . . . . . . 52
    2. Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 59
    C. Prosecutorial Misconduct. . . . . . . . . . . . . . . . . . . 71
    D. Expert Testimony. . . . . . . . . . . . . . . . . . . . . . . . . 76
    E. Restrictions on Cross-Examination. . . . . . . . . . . . 82
    Following a two-month jury trial in the District Court for
    the District of New Jersey, Richard Stadtmauer was convicted
    of one count of conspiracy to defraud the United States (in
    4
    violation of 
    18 U.S.C. § 371
    ), and nine counts of willfully aiding
    in the filing of materially false or fraudulent tax returns (in
    violation of 
    26 U.S.C. § 7206
    (2)). On appeal, Stadtmauer raises
    many challenges to these convictions. We deal principally with
    the issue Stadtmauer raises last: whether the District Court erred
    in giving a willful blindness instruction in this case, including
    whether the Supreme Court’s decision in Cheek v. United States,
    
    498 U.S. 192
     (1991), forecloses the possibility that willful
    blindness may satisfy the legal knowledge component of the
    “willfulness” element of criminal tax offenses. We join our
    sister circuit courts in concluding that Cheek does not prohibit
    a willful blindness instruction that applies to a defendant’s
    knowledge of relevant tax law. We reject also Stadtmauer’s
    other claims of error, and thus affirm.
    I.       Background 1
    A.    Richard Stadtmauer and the Kushner Companies
    This criminal case stemmed from an investigation of
    Charles Kushner, a prominent real estate entrepreneur, political
    fundraiser, and philanthropist in New Jersey. Kushner controls
    hundreds of limited partnerships, each of which owns and
    manages a single commercial or residential property. Kushner
    1
    “As required when reviewing convictions, we recite the
    relevant facts in the light most favorable to the [G]overnment.”
    United States v. Leo, 
    941 F.2d 181
    , 185 (3d Cir. 1991).
    5
    is the general partner of each partnership and, for most, his
    siblings (including his brother, Murray Kushner 2 ) and their
    children are the other limited partners. These partnerships have
    collectively operated under the name “Kushner Companies”
    (“KC”). KC is not a registered entity and does not own any
    properties.3
    In the mid-1990s, Charles and Murray Kushner accused
    each other of taking more than his fair share out of their
    common businesses. During the course of the ensuing civil
    litigation, Murray alerted federal authorities to potential
    misconduct by his brother and KC. Following an investigation,
    Kushner pled guilty in 2004 to, among other things, assisting in
    the filing of false partnership tax returns and federal campaign
    contribution offenses.
    During the course of its investigation of Kushner, the
    Government indicted several other individuals, including
    Stadtmauer—a Certified Public Accountant, a law school
    graduate, and Kushner’s brother-in-law. He became an
    employee of KC in 1985, and eventually rose to become an
    executive vice president. In this role, Stadtmauer oversaw the
    2
    We use “Kushner” throughout this opinion to refer only to
    Charles Kushner.
    3
    For descriptive purposes, however, we refer to KC hereafter
    as if it were an entity.
    6
    operations of KC’s residential and commercial properties.
    Stadtmauer also held a small stake (between 1% and 7%) in
    many of KC’s partnerships. Stadtmauer and Kushner held equal
    interests (50% each) in Westminster Management, an entity
    which collected management fees from the other partnerships.
    B.     The Other Players
    Several former KC executives testified against
    Stadtmauer at trial, including: (1) Chief Financial Officer
    (“CFO”) Stanley Bentzlin; (2) Chief Operations Officer
    (“COO”) Scott Zecher; and (3) Alan Lefkowitz, who succeeded
    Bentzlin as CFO in 2000. Of these three, only Zecher was
    indicted.4
    KC employed the accounting firm of Schonbraun, Safris,
    McCann, Bekritsky & Company, LLC (“SSMB”) as its main
    “outside” accountant. The lead SSMB accountant for KC
    matters was Marci Plotkin, who served as KC’s CFO in the early
    1990s before returning to SSMB.5 Though Plotkin was
    4
    He pled guilty to conspiring to defraud the United States.
    5
    In the late 1990s, Kushner briefly replaced SSMB with the
    accounting firm of Richard Eisner & Company. Kushner agreed
    to hire Eisner & Company on the condition that it hire Plotkin
    as its lead accountant for KC matters. Eisner & Company
    agreed to hire Plotkin, but shortly thereafter Kushner decided to
    7
    technically an employee of SSMB, KC reimbursed SSMB for
    yearly bonuses it paid to Plotkin 6 and certain of Plotkin’s salary
    increases, and reimbursed Plotkin for the cost of her son’s
    private school tuition. Kushner did not heed Bentzlin’s warning
    that paying Plotkin a bonus would impair her independence and
    preclude SSMB from issuing financial statements on behalf of
    KC partnerships.
    Marci Plotkin was assisted by (among others) SSMB
    partner Stanley Bekritsky and Anne Amici, a staff accountant
    who worked almost exclusively on KC matters. Plotkin,
    Bekritsky, and Amici were indicted along with Stadtmauer and
    each pled guilty to conspiring to defraud the United States. Of
    these three, only Bekritsky testified at Stadtmauer’s trial.
    C.     The Alleged Conspiracy
    The Government charged that Stadtmauer, Bekritsky,
    Plotkin, and Amici conspired to file false or fraudulent tax
    returns for the 1998-2001 tax years for Westminster
    Management and eleven other KC limited partnerships:
    “Oakwood Garden Developers,” “Elmwood Village
    re-hire SSMB (after SSMB agreed to re-hire Plotkin).
    6
    KC funneled to Plotkin (through SSMB) bonus payments of
    $15,000 in 1996, $20,000 in 1997, and $25,000 in 1998. (App.
    2823–24.)
    8
    Associates,” “Pheasant Hollow,” “QEM,” “Mt. Arlington,” and
    six partnerships with variations of the name “Quail Ridge.” The
    Government alleged that these partnerships fraudulently claimed
    four categories of expenditures as fully deductible business
    expenses 7 on their tax returns 8 : (1) charitable contributions,
    7
    The Internal Revenue Code provides that an expenditure is
    fully deductible as a business expense if it: “(1) was paid or
    incurred during the taxable year; (2) was for carrying on a trade
    or business; (3) was an expense; (4) was a necessary expense;
    and (5) was an ordinary expense.” Neonatology Assocs., P.A. v.
    Comm’r, 
    299 F.3d 221
    , 228 (3d Cir. 2002) (citing I.R.C.
    § 162(a)).
    8
    A partnership does not, itself, pay taxes. “Instead, the
    partners claim a pro-rata share of the partnership’s profits and
    losses and each pays tax on his share.” Kantor v. Comm’r, 
    998 F.2d 1514
    , 1517 n.1 (9th Cir. 1993). However, partnerships are
    still required to file income tax returns.
    [F]or the purpose of computing income and
    deductions, “the partnership is regarded as an
    independently recognizable entity apart from the
    aggregate of its partners.” It is only once the
    partnership’s income and deductions are
    ascertained and reported that its existence may be
    disregarded and the partnership becomes a
    conduit through which the taxpaying obligation
    passes to the individual partners.
    9
    which generally are not deductible as business expenses; (2)
    expenditures incurred by one partnership but paid by a different
    partnership (known as “non-property” expenses); (3) capital
    expenditures, which generally must be amortized and
    depreciated over the life of the relevant asset (and thus are not
    immediately deductible in full); and (4) gift and entertainment
    expenses, which generally are not fully deductible as business
    expenses.
    The Government’s theory was that these four types of
    expenditures were fraudulently deducted in full as ordinary
    business expenses on the partnerships’ tax returns through a
    three-step process. First, the expenses were logged in each
    limited partnership’s general ledger via a computer-based
    accounting program that broke down all revenue and expenses
    into categories called “accounts.” Second, KC used the general
    ledgers to prepare internal financial statements that
    automatically categorized these four types of expenditures as
    “expenses.” Finally, SSMB used the general ledgers and
    internal financial statements to prepare external financial
    statements and tax returns for each partnership that falsely
    claimed these four categories of expenditures as fully deductible
    business expenses.
    To illustrate, below we discuss primarily the 2000 tax
    Brannen v. Comm’r, 
    722 F.2d 695
    , 703 (11th Cir. 1984)
    (quoting United States v. Basye, 
    410 U.S. 441
    , 448 (1973)).
    10
    return for one of the limited partnerships, Elmwood Village
    Associates (“Elmwood Village”).
    1.     The General Ledgers
    i.     Charitable Contributions
    Kushner and Stadtmauer frequently directed that
    charitable contributions be paid out of partnership funds, which
    were logged into the general ledger under the “contributions”
    account. In 2000, Elmwood Village paid approximately
    $186,000 to various charitable organizations, including
    donations to the Suburban Torah Center—the “personal
    synagogue” of Kushner and Stadtmauer—and to the Center’s
    Rabbi, Stadtmauer’s “rabbinical advisor.” (App. 2846–47.)
    Also logged under the “contributions” account were
    donations made to various political campaigns and political
    action committees, and $25,384 in private school tuition
    payments for Zecher’s and Plotkin’s children. Because the latter
    payments were logged as partnership expenses (rather than
    entered into the payroll system as taxable income), no taxes
    were withheld and no Form 1099 was issued to Zecher or
    Plotkin. Zecher testified that he generally left the descriptions
    blank on the checks for tuition payments because “[t]here was
    nothing [he] really could write. It was not an appropriate
    business expense.” (Id. at 2817.)
    11
    ii.    “Non-Property” Expenses
    Whenever a particular KC partnership incurred an
    expense that it could not satisfy out of its current funds, Kushner
    would direct that a different partnership pay the expense. He
    referred to this practice as “losing a bill,” and it was a regular
    agenda item for upper-level management meetings held every
    Tuesday (referred to as “Tuesday Meetings” or “Cash
    Meetings”). Typically, either Kushner, the CFO, or the
    controller chose the source of payment; in other instances,
    Kushner directed Stadtmauer to choose which partnership would
    pay the expense. Zecher testified that it was Kushner’s view
    that an expense could be paid by any partnership that he
    controlled. Sometimes Kushner would tell Zecher that the
    partnership actually paying the expense “didn’t matter because
    it was all family.” (Id. at 3116.)
    For example, in 1998 various KC partnerships paid more
    than $1 million in expenses associated with the renovation of
    KC’s central office building in Florham Park, New Jersey.9
    Kushner directed Bentzlin to have several different partnerships,
    on a rolling basis, pay portions of the total expenses incurred as
    a result of the renovations. These expenditures were logged in
    the partnerships’ respective general ledgers under the “repairs
    and maintenance” account. Eventually, Kushner instructed
    9
    The building is owned by “Florham Park Associates,” a
    limited partnership controlled by Kushner and his children.
    12
    Bentzlin to review with Stadtmauer the list of all bills due for
    the renovation work, and directed Stadtmauer to “instruct
    [Bentzlin] on how to lose it,” i.e., to choose “what entity to pay
    it out of.” (Id. at 2130.)
    In addition to one partnership paying another
    partnership’s expenses, KC partnerships also paid for expenses
    that had no relation to any partnership’s business. In 2000,
    Elmwood Village paid approximately $30,000 in “non-property”
    expenses that were booked to various general ledger accounts,
    including “advertising,” “seminars,” “legal fee-other,” and
    “other professional fees.” This amount included (among other
    things): (1) $10,000 paid to a consulting firm to research the
    viability of a comeback by then-former Israeli Prime Minister
    Benjamin Netanyahu; (2) $10,000 toward a $100,000 fee to pay
    Mr. Netanyahu to speak at a breakfast sponsored by NorCrown
    Bank (an entity not affiliated with KC in which Kushner held an
    interest); and (3) $3,815 toward a $50,000 fee to pay former
    Chairman of the Federal Reserve Paul Volcker to speak at
    another NorCrown Bank event.
    iii.   Capital Expenditures
    From 1998 through 2001, various KC partnerships
    purchased capital assets and made capital improvements to their
    properties. In general, these expenses were logged in the
    partnerships’ general ledgers under the “repairs and
    maintenance” account rather than the capital expenditures
    13
    account. As Lefkowitz explained at trial, “[t]here [were] a few
    instances where things might have been capitalized, but as a
    general rule . . . everything went through expenses.” (Id. at
    2604.) Bentzlin explained that, although each general ledger
    had a capital improvement “account,” capitalizing assets
    “wasn’t the way it was done at Kushner Companies.” He added
    that
    [w]e regularly and routinely expensed [capital
    assets] under one of the repairs and maintenance
    or capital improvement accounts . . . [;] that was
    the way they were doing it upon my arrival, and it
    didn’t change throughout my tenure with a
    few—just with a few exceptions.
    ...
    . . . You didn’t question it. You know, it
    was ruled with an iron fist. They controlled pretty
    much everything.
    (Id. at 2190.)
    In 2000, Elmwood Village spent $269,323 on
    improvements that allegedly should have been capitalized,
    which included adding new bathrooms and kitchens to
    apartments—including new cabinets and $49,318.40 worth of
    new appliances (such as washers and dryers)—and a new truck
    14
    (for $25,126). All of these expenses were logged in the
    partnership’s general ledger under the “repairs and
    maintenance” general ledger account rather than a capital
    account.
    iv.    Gift and Entertainment Expenses
    Kushner and Stadtmauer frequently directed various
    partnerships to pay gift and entertainment expenditures that had
    no specific connection with the partnership paying the expense.
    In 2000, Elmwood Village paid: (1) $12,640 to cater a brunch
    at the New Jersey Performing Arts Center; (2) $7,027 to a wine
    store for alcohol delivered to Kushner’s and Stadtmauer’s
    private homes during the holidays; (3) $5,905.23 to cater a
    fundraiser for former New Jersey Governor Jon Corzine; and (4)
    thousands of dollars for New York Yankees, New York Mets,
    and New Jersey Nets season tickets. Each of these expenditures
    was logged in Elmwood Village’s general ledger under a
    “miscellaneous,” “gifts/entertainment,” or “travel” account.
    2.     KC’s Internal Financial Statements
    KC used the general ledgers to generate internal financial
    statements for each partnership. The accounting template (or
    “skeleton”) used to produce these statements automatically
    grouped certain accounts from the general ledgers—including
    the “contributions,” “gifts/entertainment,” “miscellaneous,” and
    “seminars” accounts—under the category of “office expenses.”
    15
    In addition, the “legal fee-other” and “other professional fees”
    accounts were grouped under the category of “payroll and
    related expenses.” Each of these categories—in addition to the
    “advertising ” an d “repairs and maintenance”10
    categories—were, in turn, grouped under the general category
    of “expenses,” and thus deducted in full from the partnership’s
    revenue on the internal financial statement.11 This violated
    applicable accounting standards, which required the
    partnerships’ financial statements to be prepared on an income
    tax basis.
    3.      SSMB’s Preparation of the Partnerships’
    Tax Returns
    SSMB used KC’s general ledgers and internal financial
    statements to prepare external financial statements for each
    partnership. KC would submit a “Management Representation
    Letter” to SSMB along with its financial statements, in which
    10
    Included in the “repairs and maintenance” group were the
    “apartment renovations” and “building improvement” accounts
    which, as Zecher explained, included, respectively, “capital
    improvements made to apartments” and “capital improvements
    made to the general property, [e.g.,] the outside of the buildings,
    the roofs, paving parking lots, things like that.” (Id. at 2923.)
    11
    Bentzlin and Bekritsky believed that Plotkin had
    configured the software before she left KC, but neither was sure.
    (Id. at 2341, 3292.)
    16
    KC management certified that “[t]here are no material
    transactions that have not been properly reflected in the financial
    statements.” Stadtmauer signed most of these representation
    letters. KC also provided SSMB with the template it used to
    prepare its internal financial statements.
    In preparing the partnerships’ external financial
    statements and tax returns, SSMB used the groupings applied by
    KC’s internal accounting software. Thus, the 2000 internal and
    external financial statements for Elmwood Village reflected
    virtually identical amounts for “office expenses” and “repairs
    and maintenance.” As Bekritsky testified, the tax returns were
    prepared “on the same basis” as the partnerships’ financial
    statements, meaning that “if [something is] deducted on the
    financial statement, it is deducted on the tax return and produces
    income or increases the loss of the partnership.” (Id. at 3218.)
    Elmwood Village’s 2000 tax return deducted a total of
    $496,713 in ordinary and necessary business expenses (on lines
    3 through 15 of Form 8825, entitled “Rental Real Estate
    expenses”). Included in this amount was $211,885 in charitable
    contributions, political donations, and tuition payments (for,
    among others, Plotkin’s and Zecher’s children). (Line 8 of
    Schedule K to the return—where partnerships are required to list
    charitable contributions—was left blank.) The “non-property,”
    and gift and entertainment, expenses incurred by Elmwood
    Village in 2000 were similarly claimed as fully deductible
    business expenses (instead of listed separately as required on
    17
    Schedule M-1). Finally, Elmwood Village reported no increase
    in capital assets in 2000. Rather, $269,323 in alleged capital
    expenditures were included in the $347,939 reported as
    “repairs” (on line 10 of Form 8825), while other alleged capital
    expenditures were spread among various items in Statement 10
    of Schedule M-2 (entitled “Other Rental Expenses”).12
    Around March or April of each year, Stadtmauer met
    with KC’s CFO and someone from SSMB—usually Plotkin, and
    infrequently Bekritsky—to review and sign the KC partnerships’
    tax returns. During these sessions, Stadtmauer sometimes
    reviewed SSMB’s financial statements for the partnerships;
    indeed, he refused to “sign a tax return unless he had the
    financial statements next to him.” (Id. at 2958.) He would “flip
    through” each return, “look at certain things, and then sign it.”
    (Id. at 2194.) Stadtmauer only occasionally asked questions
    about the returns, and typically spent “30 seconds to a minute”
    on each. (Id. at 2283.) However, he spent more time on KC’s
    major properties, particularly those that had large annual
    increases in “repairs and maintenance” expenses. (Id. at 2958.)
    Stadtmauer reviewed and signed as many as 800 tax
    12
    Bekritsky explained that this was done so that amounts
    reported for repairs and maintenance “wouldn’t stick out on the
    return[s].” (Id. at 3261.) Bekritsky admitted that he knowingly
    prepared and filed false tax returns on behalf of KC partnerships
    to avoid losing a valuable account. (Id. at 3352.)
    18
    returns in a given day. Stadtmauer signed each of the
    partnerships’ tax returns below a legend declaring, “[u]nder
    penalties of perjury,” that he had “examined th[e] return,
    including accompanying schedules and statements,” and that, to
    the best of his knowledge, the return was “true, correct, and
    complete.” (E.g., Supp. App. 937.) Stadtmauer signed each
    return in his capacity as Vice-President of the corporate general
    partner; as Bentzlin and Zecher testified, Stadtmauer believed
    that by doing so he would protect himself from personal
    liability. (App. 2209, 2903.)
    The Government alleged that, from 1998 through 2001,
    the twelve KC partnerships identified in the indictment claimed
    more than $6 million in improper deductions. Capital
    expenditures that were deducted in full the year they were
    incurred accounted for more than half of this amount.
    D.    Evidence of Stadtmauer’s Knowledge
    To establish that Stadtmauer “willfully” aided in the
    preparation of materially false or fraudulent tax returns—as
    required for a violation of 
    26 U.S.C. § 7206
    (2) 13 —the
    13
    
    26 U.S.C. § 7206
    (2) makes it a crime to
    [w]illfully aid[] or assist[] in, or procure[],
    counsel[], or advise[] the preparation or
    presentation under, or in connection with any
    19
    Government was required to prove beyond a reasonable doubt
    that he voluntarily and intentionally violated “a known legal
    duty.” United States v. Pomponio, 
    429 U.S. 10
    , 12 (1976).
    Whether Stadtmauer had knowledge that the deductions claimed
    on the partnerships’ tax returns were materially false or
    fraudulent was the critical issue at trial.
    At trial, Bentzlin, Zecher, and Bekritsky each testified
    that they never discussed with Stadtmauer the falsity of any
    particular deduction or tax return. Accordingly, the Government
    sought to meet its burden of proving that Stadtmauer acted
    “willfully” through various forms of circumstantial evidence
    (some of which have already been discussed), including: (1)
    evidence of Stadtmauer’s intimate familiarity with the
    partnerships and how their general ledgers were maintained; (2)
    evidence that Stadtmauer made decisions on how to treat
    partnership expenses in the past with tax consequences in mind;
    and (3) other evidence suggestive of a consciousness of guilt,
    e.g., evidence that Stadtmauer was aware that the partnerships
    were making improper expenditures.
    matter arising under, the internal revenue laws, of
    a return, affidavit, claim, or other document,
    which is fraudulent or is false as to any material
    matter, whether or not such falsity or fraud is with
    the knowledge or consent of the person authorized
    or required to present such return, affidavit, claim,
    or document[.]
    20
    1.     “Thursday Meetings”
    In addition to the “Tuesday Meetings” that Stadtmauer
    regularly attended, for many years he ran weekly “Thursday
    Meetings” with the limited partnerships’ property managers, as
    well as KC’s in-house counsel, controller, Bentzlin, and
    sometimes Plotkin.14 The purpose of each meeting was to
    conduct an in-depth review of one or two KC properties. The
    managers prepared presentation packages that showed the
    partnerships’ actual expenses to date. Stadtmauer went through
    the presentations “line by line,” and asked “specific” questions
    about each. (App. 2641.) According to Zecher, “there was
    nothing [Stadtmauer] didn’t see fit to get involved with in
    property management,” and he was “one of the brightest people
    [that Zecher had] ever met.” (Id. at 2836.)
    In 1996, certain property managers started using special
    letter codes on their general ledgers to identify “non-property”
    expenses paid for by their respective partnerships. The codes
    allowed property managers to identify those expenses more
    easily and exclude them from their Thursday Meeting
    presentations. According to Bentzlin, the property managers
    were hesitant to answer Stadtmauer’s questions about such
    expenses during Thursday Meetings (previously listed as
    “miscellaneous” expenses on the presentations), because they
    14
    Stadtmauer led these meetings until early 1999, when
    another KC executive began running them. (App. 2701.)
    21
    knew the expenses were for expenses “paid out of other
    properties,” and “didn’t want to blurt it out in front of a roomful
    of people.” (Id. at 2150.)
    Stadtmauer was “quite unhappy” when he learned of the
    codes, and directed his subordinates to end the practice. (Id. at
    2186.) Stadtmauer and Bentzlin ultimately decided to lump
    non-property expenses together under a category called “other.”
    Doing so obviated the need for Stadtmauer to “interrogate or
    continue to question the property manager as to the nature of
    those expenditures” during Thursday Meetings, and made it
    easier during Tuesday Meetings to “figure out [how] the
    apartment complex on its own was really operating.” (Id. at
    2185–86.)      In addition, Stadtmauer directed that KC’s
    accounting software be modified “to allow somebody to go in
    and change [existing] descriptions within the general ledger.”
    (Id. at 2187.)
    Stadtmauer also frequently instructed his subordinates to
    omit descriptions in check requests to avoid leaving a “trail”
    when KC “used one property to pay another property’s
    expenses.” (Id. at 2628.) He admonished Zecher to “never put
    the descriptions in,” because he “d[idn’t] want the descriptions
    [to show up] in the ledger.” (Id. at 2855.) Stadtmauer also
    “reminded [Zecher,] over and over, [to] be careful what [he] put
    in emails. Emails never disappear.” (Id. at 2858.)
    22
    2.     “Richard Specials” and Other Special
    Financial Statements
    In certain circumstances, Stadtmauer directed that special
    financial statements for the partnerships be prepared for banks
    and other entities. These were known as “Richard Specials.”
    These special financial statements were often prepared when KC
    wanted to reduce outstanding letters of credit on particular
    properties. Stadtmauer would direct that “negative items” that
    tended to depress the partnership’s profitability be removed
    from these statements, such as capital expenditures (that had
    been logged as “repair and maintenance” expenses) and “non-
    property” expenses. (Id. at 2077–78.) To prepare these
    statements, Stadtmauer was given a “detailed report” of the
    partnership’s general ledger, which he would go through line by
    line and indicate the items to be removed for the financial
    statement. (Id. at 2077.) KC prepared both internal and external
    versions of every “Richard Special”; the internal version
    revealed the adjustments made, while the external version
    showed only the final numbers after adjustments. (Id. at 2225.)
    The first time Stadtmauer asked Bentzlin to create a
    “Richard Special,” Bentzlin objected and told Stadtmauer that
    he “didn’t think it was the right thing to do” because they
    “would be sending different financials out other than the ones
    prepared by the accountant.” (Id. at 2079.) Stadtmauer argued
    it would be proper because they would call it a “statement from
    operations” (as opposed to a “statement of operations”),
    23
    supposedly making clear that it wasn’t a true financial statement.
    (Id. (emphasis added).) Bentzlin told Stadtmauer he thought the
    justification was “ridiculous,” and though Bentzlin ultimately
    agreed to prepare the “Richard Specials,” he “didn’t want [them]
    ever to go out with [his] name on [them].” 15 (Id.)
    Similar to “Richard Specials,” on several occasions KC
    prepared special financial statements in connection with
    potential acquisitions and joint ventures. For example, in 1995
    certain lenders agreed to finance KC’s acquisition of Elmwood
    Village, provided that KC would commit to making $1.5 million
    in capital improvements to the property and secure a $1.6
    million letter of credit. These expenditures were entered, as
    usual, under non-capital accounts on the partnership’s general
    ledger. At the end of the year, however, KC decided to
    15
    Similar to the “Richard Specials,” SSMB often prepared
    special supplemental schedules, listing various non-property
    expenses and capital improvements, that were attached to the
    partnerships’ financial statements.        These supplemental
    schedules were called “Schedules of Non-Recurring Expenses,”
    but were unofficially referred to as “Schonbraun Specials.”
    However, as Bentzlin explained at trial, these “non-recurring”
    expenses were essentially “non-recurring every year,” and he
    feared that KC was “giving the Government a road map” on
    how to discover, in the event of an audit, expenses that were
    being improperly deducted on the tax returns. (App. 3255.)
    After Bekritsky raised his concerns to Plotkin, SSMB ended the
    practice. (Id.)
    24
    capitalize the items on the partnership’s financial statement “to
    get the letter of credit cancelled.” (Id. at 2348.) This decision
    was made during a Tuesday “Cash Meeting” in which
    Stadtmauer participated.
    Elmwood Village’s 1996 tax return accurately reported
    almost $1 million in capital improvements. After the letter of
    credit was cancelled, however, KC “went back to the usual
    procedures of expensing those types of expenditures.” (Id. at
    2210.) Elmwood Village did not capitalize any expenditures
    after 1996, and its post-1996 returns treated the 1996
    renovations that had been capitalized as fully deductible repairs.
    Similarly, in 2000 KC paid $280 million to acquire a
    company called WNY, which owned approximately 40
    properties in New Jersey, Pennsylvania, Maryland, and
    Delaware. KC was required to obtain a $40 million letter of
    credit in connection with the acquisition. Stadtmauer, Plotkin,
    and Zecher had a “very detailed meeting” on how they would
    “do the accounting for the WNY properties.” (Id. at 2967.)
    They agreed that they would “capitalize everything and anything
    [they] could, instead of expensing it, like [they] always did in
    the other properties.” (Id.) Zecher testified that Stadtmauer was
    “convinced, because the transaction was so large, and the $40
    million [in] letters of credit were so unusual for [KC], that the
    banks were going to come in and look at not only the tax returns,
    but . . . the actual books and records.” (Id.)
    25
    When the letters of credit were removed, Plotkin asked
    whether she should expense the capitalized items. Zecher
    responded that he and Stadtmauer had determined that the
    financial statements would “look very weird” if they stopped
    capitalizing. (Id. at 2970–71.)
    3.      Other Circumstantial Evidence of
    Stadtmauer’s Knowledge of Tax Law and
    Consciousness of Guilt
    i.     Rationale for Private        School
    Tuition Payments
    As noted, for several years KC paid the private school
    tuition for, among other KC employees, Plotkin’s and Zecher’s
    children. Zecher testified that Stadtmauer came up with the idea
    of paying the tuition directly to the school instead of increasing
    Zecher’s year-end bonus by that amount. (Id. at 2824.)
    Stadtmauer told Zecher that he was “trying to be nice” by paying
    the tuition directly to the school, which would allow Zecher to
    avoid thousands of dollars in additional income taxes. (Id.)
    ii.    The 1996 IRS Audit
    In 1996, the Internal Revenue Service (“IRS”) audited the
    tax returns for two KC partnerships, focusing on the large
    deductions taken for repairs (including $850,000 to reconstruct
    a building’s facade, which was deducted in full as a business
    26
    expense). The IRS ultimately issued “no change” letters.
    Following the audit, however, Plotkin sent a letter to
    Bentzlin—on which Stadtmauer was copied—instructing
    Bentzlin to change the word “improvements” to “repairs” in the
    “tenant improvements,” “apartment renovations,” and “building
    improvements” general ledger accounts. (Id. at 2269–70.)
    Bentzlin believed the purpose was to make these categories
    appear as if they contained repair and maintenance expenditures
    rather than “potentially a capital improvement type item.” (Id.
    at 2270.)
    iii.   Dissenting Limited Partners and
    Executives
    In addition to the Kushner family and Stadtmauer, there
    were other individuals who held interests in various KC
    partnerships. As Zecher testified at trial, many of these
    individuals made repeated requests for information regarding the
    financial state of their partnership interests. In many instances,
    Stadtmauer and Kushner ordered Zecher to refuse those
    requests.
    In one instance, a partner of a KC partnership named “K
    & F Clinton” inquired as to certain political contributions made
    by that partnership and attributed to him. (Id. at 2891.) The
    partner denied he had ever authorized the contributions, and
    noted that, “had [he] been informed of the intention to make
    political contributions, [he] would have advised that such
    27
    political contributions were inappropriate and [he] would have
    demanded that they not be made from K & F” funds. (Id. at
    2892.) He further noted that “[n]othing in the partnership
    agreement authorized the disbursement of K & F funds for any
    unrelated purpose.” (Id. at 2892–93.) Zecher got similar
    responses from several other partners. (Id. at 2893.)
    Another           limited        partner—Stanley
    Greenberg—“constantly” had difficulty obtaining annual
    financial statements for the partnerships in which he had an
    interest. (Id. at 3356.) When he finally obtained and examined
    the partnerships’ financial statements for a prior three-year
    period,16 “it was obvious [to him] that the expenses [claimed
    for] run[ning] the[] properties were way out of line.” (Id.)
    Among other things, Greenberg noticed that the partnerships in
    which he had an interest had treated capital expenditures as
    ordinary expenses, and had made numerous charitable
    contributions to Kushner’s and Stadtmauer’s synagogues, as
    well as political contributions. (Id. at 3363.)
    When Greenberg expressed his concerns to Kushner, the
    latter told him that “if you don’t like it, I will give you your
    money back.” (Id. at 3358.) Greenberg also had conversations
    with Stadtmauer, both in person and by phone, regarding the
    improper expenses being paid by the partnerships, and asked
    16
    Though Greenberg also requested the partnerships’ general
    ledgers, he never received any. (Id. at 3358.)
    28
    Stadtmauer to “stop [KC from] doing what they were doing.”
    (Id.) Though he offered no “excuse . . . or any explanation” for
    the expenses, Stadtmauer rejected Greenberg’s request,
    explaining that “that was the way they did business.” (Id.)
    Following these conversations, KC attempted to buy out
    Greenberg’s interests in the partnerships.
    In addition to these dissenting limited partners, the
    Government also introduced testimony that KC executives were
    expected not to challenge KC’s accounting practices. As
    Bentzlin explained, “[y]ou had to do pretty much as you were
    told [at KC]. [Stadtmauer] and [Kushner] often would throw
    tirades at any number of the meetings on a regular routine basis
    or in the office, you know, that you really didn’t have latitude to
    make any changes.” (Id. at 2190.)
    Former CFO Alan Lefkowitz learned this lesson the hard
    way. In early 2001, he emailed Kushner to ask whether he
    should follow the past practice of paying a bill for a Mikvah (a
    Jewish ritual) with funds from one of the partnerships. Kushner
    was furious, and admonished Lefkowitz that he “should never
    write something like th[at] down.” (Id. at 2613.) According to
    Zecher, Kushner was angry that Lefkowitz had “put[] in an
    email in writing that [KC was] paying bills for a . . . not-for-
    profit project out of . . . for-profit properties.” (Id. at 2858.)
    Kushner printed out the email and hand-wrote: “This guy is a
    definite Moron. We must deal with the situation.” Kushner
    forwarded a copy of the email (bearing his hand-written note) to
    29
    Stadtmauer, and it was later discussed among upper-level
    management. Stadtmauer later told Zecher: “This is a stupid
    thing to do and you better make sure this guy doesn’t do it
    again.” (Id.)
    Lefkowitz was eventually barred from Tuesday Meetings
    and later resigned. He believed that management (including
    Stadtmauer) had concluded that he was not a “team . . . player,”
    i.e., was “not willing to go along with what they want[ed] to
    do.” (Id. at 2613.)
    E.    The Verdict and Stadtmauer’s Post-Verdict
    Motions
    Following a two-month trial,17 the jury convicted
    Stadtmauer of one count of conspiracy and nine counts of aiding
    in the willful filing of materially false or fraudulent partnership
    tax returns.18 The District Court denied Stadtmauer’s motions
    17
    We note that Stadtmauer chose not to put on a defense.
    18
    The jury acquitted Stadtmauer of six counts of aiding in the
    willful filing of false or fraudulent tax returns (Counts Six
    through Eleven), which corresponded to the 1999–2000 tax
    returns for three of the Quail Ridge partnerships. As the
    Government notes, a question asked by the jury during its
    deliberations suggests that it acquitted Stadtmauer on these
    counts because it was unable to locate a piece of evidence
    explaining how expenses from Quail Ridge’s unitary general
    30
    for a judgment of acquittal and to dismiss the indictment.19 In
    February 2009, the District Court sentenced him to 38 months’
    imprisonment. He timely appealed.
    II.        Jurisdiction
    The District Court had jurisdiction under 
    18 U.S.C. § 3231
    . We have appellate jurisdiction under 
    28 U.S.C. § 1291
    .
    III.       Discussion
    Stadtmauer contends that (1) the District Court erred in
    giving a willful blindness instruction to the jury; (2) the Court
    improperly admitted prejudicial lay opinion testimony by a
    Government witness; (3) the prosecutor violated his obligation
    to correct false testimony by a Government witness; (4) the
    ledger were apportioned among the three specific Quail Ridge
    partnerships (i.e., “8 Quail Ridge,” “9 Quail Ridge,” and “10
    Quail Ridge”).
    19
    Stadtmauer moved before trial to dismiss the indictment to
    the extent it was based on the failure to capitalize expenditures,
    arguing that the law on capitalization is vague and uncertain.
    The District Court deferred ruling on the motion, concluding
    that “[a] determination of whether the tax laws in question are
    vague and uncertain necessarily involves a fact sensitive
    analysis.” (Id. at 86.) The Court denied the motion after trial,
    and Stadtmauer does not challenge that ruling on appeal.
    31
    Court improperly allowed an IRS agent to testify as an expert
    witness; and (5) the Court violated the Federal Rules of
    Evidence and his Sixth Amendment rights by restricting the
    scope of his cross-examination of Government witnesses. We
    address each claim in turn.
    A.     Willful Blindness
    Stadtmauer argues that the District Court erred in giving
    a willful blindness instruction to the jury for three reasons.
    Relying on Cheek v. United States, 
    498 U.S. 192
     (1991), he first
    argues that the “willfulness” element of criminal tax
    offenses—which “requires the Government to prove that the law
    imposed a duty on the defendant, [and] that the defendant knew
    of th[at] duty,” 
    id.
     at 201—can never be satisfied by willful
    blindness. Second, he contends that the Court improperly
    instructed the jury that the element of intent could be satisfied
    through proof of willful blindness, by analogy in violation of our
    recent en banc decision in Pierre v. Attorney General, 
    528 F.3d 180
     (3d Cir. 2008) (en banc). He finally argues that the trial
    evidence did not warrant a willful blindness instruction.
    We exercise plenary review over whether a willful
    blindness instruction properly stated the law. United States v.
    Khorozian, 
    333 F.3d 498
    , 507–08 (3d Cir. 2003); see also
    United States v. Wert-Ruiz, 
    228 F.3d 250
    , 255 (3d Cir. 2000).
    We review a district court’s determination that the trial evidence
    32
    justified the instruction for abuse of discretion, United States v.
    Flores, 
    454 F.3d 149
    , 156 (3d Cir. 2006), and “view the
    evidence and the inferences drawn therefrom in the light most
    favorable to the [G]overnment,” Wert-Ruiz, 
    228 F.3d at 255
    .
    1.     Whether the District Court’s Willful
    B lindness Instruction A pplied to
    Stadtmauer’s Knowledge of the Law
    Before turning to Stadtmauer’s first challenge to the
    District Court’s willful blindness instruction, we address the
    Government’s contention that the Court’s instruction applied
    only to Stadtmauer’s knowledge of facts, not his knowledge of
    the law.
    The Government’s initial proposed willful blindness
    instruction plainly applied to Stadtmauer’s knowledge of the
    law. The final sentence of that instruction stated: “You may
    find that [the] defendant acted knowingly . . . if you find either
    that the defendant actually knew about the applicable IRS
    requirements for the prosecution years, or that the defendant
    deliberately closed his . . . eyes to what he . . . had every reason
    to believe.” (Supp. App. 60.) Stadtmauer submitted a brief
    objecting to this instruction. Though he conceded that willful
    blindness may be appropriate to establish knowledge of facts, he
    argued that, under Cheek, “willfulness” requires actual
    knowledge of the law, which cannot be satisfied through
    deliberate ignorance.
    33
    At the charging conference, the Government submitted
    a revised instruction that omitted the reference to Stadtmauer’s
    knowledge of “applicable IRS requirements.” It instead
    instructed the jury that the “element of knowledge” would be
    satisfied if the Government proved beyond a reasonable doubt
    “a conscious purpose by the defendant to avoid knowledge [that]
    the tax returns at issue were false or fraudulent as to a material
    matter.” (App. at 3973–74.) Though the Government revised
    its charge to address Stadtmauer’s objections, it nonetheless
    made explicit its position that willful blindness could cover both
    knowledge of the law and knowledge of facts, arguing that “it
    is a little difficult to say that it can’t [apply to] legal
    [knowledge] at all[,] because it’s really kind of a mixed question
    of law and fact[] in many [tax] cases.” 20 (Id. at 3905.)
    20
    Stadtmauer contends that the Government sought a willful
    blindness instruction solely (and improperly) as a “preemptive
    measure.” (Appellant’s Br. at 76.) He notes that when then the
    Government requested the instruction, it stated: “[w]e believe
    [Stadtmauer] has actual knowledge, but we would like to
    preserve the right to argue willful blindness depending on what
    we hear from the other side” in closing arguments. (App. 3906.)
    We disagree with this contention. As our precedent
    makes clear, there is nothing improper with the Government
    seeking a willful blindness instruction while also contending
    that there is sufficient evidence of actual knowledge. See, e.g.,
    Wert-Ruiz, 
    228 F.3d at 255
     (“[I]t is not inconsistent for a court
    to give a charge on both willful blindness and actual knowledge,
    34
    In its final instructions, the District Court gave a willful
    blindness instruction consistent with the Government’s revised
    instruction. In relevant part, the Court instructed the jury as
    follows:
    The element of knowledge on the part of the
    defendant may be satisfied by inferences drawn
    from proof that the defendant closed his eyes to
    what would otherwise have been obvious to the
    defendant. A finding beyond a reasonable doubt
    of a conscious purpose by the defendant to avoid
    knowledge that the tax returns at issue were false
    or fraudulent as to a material matter would
    permit an inference that he had such knowledge.
    Stated another way, the defendant’s
    knowledge of a fact or circumstance may be
    inferred from his willful blindness to the
    existence of that fact and circumstance.
    for if the jury does not find the existence of actual knowledge,
    it might still find willful blindness.”). Moreover, though
    Stadtmauer argued in his summation that the number of tax
    returns he signed at a time, coupled with the brief amount of
    time he spent reviewing each, proved that he lacked actual
    knowledge of their contents (App. 4082, 4135), the Government
    did not make arguments based on a willful blindness theory in
    its summation.
    35
    No one can avoid responsibility for a crime
    by deliberately ignoring what is obvious. Thus,
    you may find that the defendant knew that the tax
    returns at issue were false or fraudulent as to a
    material fact based on evidence that you find
    exists that proves beyond a reasonable doubt that
    the defendant was aware of a high probability
    that the tax returns at issue were false or
    fraudulent as to a material matter; and two, that
    defendant consciously and deliberately tried to
    avoid learning about this fact or circumstance.
    (App. 3973–74 (emphases added).) Thus, though the Court’s
    willful blindness instruction referred to Stadtmauer’s
    “knowledge of a fact or circumstance,” it also instructed the jury
    that the Government could satisfy its burden of proof on “the
    element of knowledge” by proving that Stadtmauer consciously
    avoided learning that the returns were “false or fraudulent as to
    a material matter,” using language that tracks the applicable
    statute. See 
    26 U.S.C. § 7206
    (2).
    The Government argues that the Court’s reference to
    Stadtmauer’s knowledge that the tax returns were “false or
    fraudulent as to a material matter” was merely “addressed to
    Stadtmauer’s knowledge of the contents of the returns.”
    (Appellee’s Br. at 77.) The Government notes, for example, that
    regardless of Stadtmauer’s knowledge of the relevant tax laws,
    he could have consciously avoided learning of “the fact that an
    36
    expenditure from one partnership was falsely represented as a
    deduction of another partnership,” a question of fact that did not
    require proof of Stadtmauer’s knowledge of tax law. (Id. at 79.)
    We disagree.
    The Government’s charges in this case were not limited
    to improper deductions for “non-property” expenses (i.e.,
    expenses paid by a partnership different than the one that
    actually incurred the expense). Indeed, the bulk of the allegedly
    improper deductions were for expenditures that should have
    been capitalized, and it was undisputed that these amounts were
    paid for work that was actually performed. Rather, for this
    category of deductions (and others), the Government’s theory
    was that legitimate expenditures were deducted in a fraudulent
    manner on the partnerships’ tax returns.
    To prove that Stadtmauer knew the partnership tax
    returns were “false or fraudulent as to a material matter” with
    respect to these deductions, the Government needed to establish
    two “facts” beyond a reasonable doubt: (1) that Stadtmauer
    knew that these expenditures were claimed as fully deductible
    business expenses; and (2) that he knew those deductions were
    impermissible under the relevant tax laws (i.e., that they
    rendered the tax returns “false or fraudulent as to a material
    matter”). Cf. United States v. Schiff, 
    801 F.2d 108
    , 113 (2d Cir.
    1986) (noting that in a criminal tax case the defendant’s
    “knowledge of tax law [is], itself, a fact to be proved as part of
    the government’s case”) (emphasis in original). In that light, we
    37
    believe a reasonable juror could have interpreted the District
    Court’s willful blindness instruction as applying not only to
    Stadtmauer’s knowledge of facts (i.e., which expenditures were
    claimed as deductible business expenses on the tax returns), but
    also his knowledge of the law (i.e., whether those deductions
    were materially “false or fraudulent” under the Tax Code).
    Accordingly, we turn to Stadtmauer’s argument that the Court’s
    instruction incorrectly stated the law in that regard.
    2.      Willful Blindness and Cheek
    Stadtmauer argues that a willful blindness charge that
    applies to a defendant’s knowledge of the law is “categorically
    and unequivocally” inappropriate in a criminal tax case in light
    of the Supreme Court’s decision in Cheek. (Appellant’s Br. at
    69.) We disagree.
    We begin with the facts of Cheek. The defendant there
    stopped filing federal income tax returns in 1980 and was
    charged with (1) willfully failing to file federal income tax
    returns and (2) willfully attempting to evade income taxes. 
    498 U.S. at 194
    . Cheek’s defense at trial was that, as a result of
    “indoctrination” he received as a member of a group that
    believed the federal tax system is unconstitutional, he “sincerely
    believed that the tax laws were being unconstitutionally
    enforced and that his actions . . . were lawful,” and thus had
    “acted without the willfulness required” for the offenses
    charged. 
    Id. at 196
    .
    38
    The trial court instructed the jury that, to satisfy the
    element of “willfulness,” the Government was required to
    “prove the voluntary and intentional violation of a known legal
    duty, a burden that could not be proved by showing mistake,
    ignorance, or negligence.” 
    Id.
     However, the court also
    instructed the jury that only “an objectively reasonable good-
    faith misunderstanding of the law would negate willfulness.”
    
    Id.
     (emphasis added). The Seventh Circuit Court affirmed
    Cheek’s conviction, holding that “even actual ignorance is not
    a defense unless the defendant’s ignorance was itself objectively
    reasonable.” 
    Id. at 198
    .
    The Supreme Court reversed. It first reaffirmed that the
    term “willfully,” as used in criminal tax statutes, “carv[es] out
    an exception to the traditional rule” that ignorance of the law is
    not a defense to criminal liability. 
    Id. at 200
    . Second, it
    reaffirmed its prior decisions establishing that “the standard for
    the statutory willfulness requirement is the ‘voluntary,
    intentional violation of a known legal duty.’” 
    Id. at 201
     (quoting
    Pomponio, 
    429 U.S. at 12
    ); see also United States v. Bishop,
    
    412 U.S. 346
    , 360 (1973).
    Turning to the jury instruction given in Cheek’s trial, the
    Court concluded that the trial judge erred in instructing the jury
    that “a claimed good-faith belief must be objectively
    reasonable” to “negat[e] . . . evidence purporting to show a
    defendant’s awareness of the legal duty at issue.” 
    498 U.S. at 203
    . The Court explained that, in proving that a defendant had
    39
    “actual knowledge” of the legal duty imposed on him by the tax
    laws, the Government must also
    negat[e] a defendant’s claim of ignorance of the
    law or a claim that because of a misunderstanding
    of the law, he had a good-faith belief that he was
    not violating any of the provisions of the tax laws.
    This is so because one cannot be aware that the
    law imposes a duty upon him and yet be ignorant
    of it, misunderstand the law, or believe that the
    duty does not exist. In the end, the issue is
    whether, based on all the evidence, the
    Government has proved that the defendant was
    aware of the duty at issue, which cannot be true if
    the jury credits a good-faith misunderstanding and
    belief submission, whether or not the claimed
    belief or misunderstanding is objectively
    reasonable.
    
    Id. at 202
    . The Court thus distinguished between two types of
    persons: (1) a person with “actual knowledge” of a legal duty,
    and (2) a person who, in good faith, is ignorant of the duty,
    misunderstands it, or believes that it does not exist. It held that
    criminal tax liability could not attach to a person in the latter
    category.
    Stadtmauer’s attempt to equate a person who deliberately
    avoids learning of a legal duty with a person falling within the
    40
    latter category (e.g., one who is ignorant of that duty by virtue
    of a good-faith belief or misunderstanding) is not persuasive.
    The willful blindness charge, also known as a “deliberate
    ignorance” charge, originates from the Ninth Circuit Court’s
    decision in United States v. Jewell, 
    532 F.2d 697
     (9th Cir.
    1975). See United States v. Caminos, 
    770 F.2d 361
    , 365 (3d
    Cir. 1985). Jewell explained that
    [t]he substantive justification for the [charge] is
    that deliberate ignorance and positive knowledge
    are equally culpable. The textual justification is
    that in common understanding one “knows” facts
    of which he is less than absolutely certain. To act
    “knowingly,” therefore, is not necessarily to act
    only with positive knowledge, but also to act with
    an awareness of the high probability of the
    existence of the fact in question. When such
    awareness is present, “positive” knowledge is not
    required.
    Jewell, 532 F.2d at 700 (emphasis added). Thus, willful
    blindness is a “subjective state of mind that is deemed to satisfy
    a scienter requirement of knowledge,” United States v. One
    1973 Rolls Royce, 
    43 F.3d 794
    , 808 (3d Cir. 1994), and “cannot
    become a safe harbor for culpable conduct,” Wert-Ruiz, 
    228 F.3d at 258
    .
    We see nothing in Cheek—which did not involve a
    41
    willful blindness instruction—that suggests the Supreme Court
    intended to exempt criminal tax prosecutions from this general
    rule. Cf. United States v. Bussey, 
    942 F.2d 1241
    , 1249 (8th Cir.
    1991) (defendant’s reliance on Cheek in challenging willful
    blindness instruction in criminal tax trial was “seriously
    misplaced” because “Cheek did not involve a willful blindness
    instruction”). The justification for requiring knowledge of the
    relevant tax laws is that, “in our complex tax system, uncertainty
    often arises even among taxpayers who earnestly wish to follow
    the law, and it is not the purpose of the law to penalize frank
    difference[s] of opinion or innocent errors made despite the
    exercise of reasonable care.” Cheek, 
    498 U.S. at 205
     (internal
    quotation marks and citation omitted); see also Bryan v. United
    States, 
    524 U.S. 184
    , 195 (1998) (explaining that “[t]he danger
    of convicting individuals engaged in apparently innocent
    activity” is what “motivated [the Court’s] decision[]” in Cheek);
    United States v. Murdock, 
    290 U.S. 389
    , 396 (1933) (“Congress
    did not intend that a person, by reason of a bona fide
    misunderstanding . . . , should become a criminal by his mere
    failure to measure up to the prescribed standard of conduct.”),
    overruled on other grounds by Murphy v. Waterfront Comm’n,
    
    378 U.S. 52
     (1964). By definition, one who intentionally avoids
    learning of his tax obligations is not a taxpayer who “earnestly
    wish[es] to follow the law,” or fails to do so as a result of an
    “innocent error[] made despite the exercise of reasonable care.”
    Cheek, 
    498 U.S. at 205
     (internal quotation marks and citation
    omitted). Rather, a person who deliberately evades learning his
    legal duties has a subjectively culpable state of mind that goes
    42
    beyond mere negligence, a good faith misunderstanding, or even
    recklessness. Cf. Wert-Ruiz, 
    228 F.3d at 237
     (“Willful blindness
    is not to be equated with negligence or lack of due care, for
    willful blindness is a subjective state of mind that is deemed to
    satisfy a scienter requirement of knowledge.” (internal quotation
    marks and citation omitted)); see also 1973 Rolls Royce, 43 F.3d
    at 808 (describing the “mainstream conception of willful
    blindness as a state of mind of much greater culpability than
    simple negligence or recklessness, and more akin to
    knowledge”).
    Several of our sister circuit courts have similarly
    concluded that a willful blindness instruction that applies to a
    defendant’s knowledge of tax law does not run afoul of Cheek.
    See United States v. Anthony, 
    545 F.3d 60
    , 64–65 (1st Cir.
    2008); United States v. Dean, 
    487 F.3d 840
    , 851 (11th Cir.
    2007); Bussey, 
    942 F.2d at
    1248–49.21 The First and Eleventh
    21
    The Fifth and Seventh Circuit Courts have also approved
    of a willful blindness instruction that applies to a defendant’s
    knowledge of the law, though those Courts did not specifically
    discuss Cheek. See United States v. Hauert, 
    40 F.3d 197
    , 203
    n.7 (7th Cir. 1994) (affirming conviction for tax evasion where
    the facts “support[ed] the inference that the defendant was
    aware of a high probability of the existence of the fact in
    question [tax liability] and purposefully contrived to avoid
    learning all of the facts” (internal quotation marks and citation
    omitted; second alteration in original)); United States v.
    43
    Circuit Courts have interpreted Cheek as counseling that, though
    a belief that one is complying with the tax laws need not be
    “objectively reasonable” to constitute a defense, it nonetheless
    must be “held in good faith.” Anthony, 
    545 F.3d at 65
    ; see also
    Dean, 
    487 F.3d at 851
     (reasoning that the Cheek Court had,
    “albeit, not in so many words,” held that “the law would not
    countenance” willful blindness to one’s tax obligations).
    Accordingly, “the defense that the accused did not know of his
    [legal] duty fails if he came by his ignorance through deliberate
    avoidance of materials that would have apprised him of his duty,
    as such avoidance undermines the claim of good faith.”
    Anthony, 
    545 F.3d at 65
    ; see also Dean, 
    487 F.3d at 851
     (“A
    willful blindness instruction is entirely appropriate where the
    evidence supports a finding that a defendant intentionally
    insulated himself from knowledge of his tax obligations.”).
    We agree with the reasoning of these Courts and join
    them in concluding that a willful blindness instruction that
    applies to a defendant’s knowledge of the law in a criminal tax
    case (such as the instruction at issue here) does not run afoul of
    Cheek.
    Wisenbaker, 
    14 F.3d 1022
    , 1027–28 (5th Cir. 1994) (willful
    blindness instruction was appropriate in tax evasion case in light
    of the defense theory, i.e., that the defendant “belie[ved] that he
    was not responsible for . . . taxes,” and evidence that he failed
    to file tax returns even after his accountants “brought to his
    attention his duty to do so”).
    44
    The District Court’s willful blindness instruction in this
    case also adhered to our precedent requiring that such an
    instruction “‘make clear that the defendant himself was
    subjectively aware of the high probability of the fact in question,
    and not merely that a reasonable man would have been aware of
    the probability.’” Wert-Ruiz, 
    228 F.3d at 255
     (quoting Caminos,
    
    770 F.2d at 365
    ). The Court instructed the jury that it must find
    beyond a reasonable doubt that Stadtmauer (1) “was aware of a
    high probability that the tax returns at issue were false or
    fraudulent as to a material matter,” and (2) “consciously and
    deliberately tried to avoid learning about this fact.” (App.
    3974.) The Court told the jury that it could not find the element
    of knowledge satisfied if it found only that Stadtmauer “should
    have known that the tax returns at issue were false as to a
    material matter[,] or that a reasonable person would have known
    of a high probability of that fact.” (Id. (emphases added).)
    Finally, the Court stressed that it was insufficient that
    Stadtmauer “may have been stupid or foolish or may have acted
    out of inadvertence or accident. A showing of negligence or of
    a good-faith mistake of law is not . . . sufficient to support a
    finding of . . . knowledge.” (Id.)
    The instruction as a whole thus belies Stadtmauer’s
    claims that the District Court “allowed the jury to substitute a
    failure to inquire for evidence of actual knowledge of the tax
    laws”; allowed the jury to convict him simply for being
    “ignorant of” or “for misunderstanding” the law; and instructed
    the jury to apply an “objective test[]” in determining whether he
    45
    had knowledge of the law.22 (Appellant’s Br. at 70–71.)
    Accordingly, we conclude that the Court’s willful blindness
    instruction correctly stated the law.
    3.     Whether the District Court’s Willful
    Blindness Instruction Applied to the
    Element of Specific Intent
    22
    Stadtmauer suggests that permitting willful blindness to
    satisfy the element of legal knowledge will “surely alarm the
    many thousands of taxpayers who provide records to their
    accountants, let the accountants prepare the returns, and then
    sign them. . . without flyspecking the tax professionals’ work.”
    (Appellant’s Reply Br. at 39 n.23.) We cannot agree. Such a
    taxpayer cannot be said (without more) to be “‘subjectively
    aware of [a] high probability’” that the returns being prepared
    on his behalf are false or fraudulent. Wert-Ruiz, 
    228 F.3d at 255
    (quoting Caminos, 
    770 F.2d at 365
    ). Rather, to prove
    willfulness beyond a reasonable doubt, the Government would
    have to negate the taxpayer’s claim that he relied in good faith
    on the advice of his accountant. Cf. Cheek, 
    498 U.S. at 202
    ;
    Anthony, 
    545 F.3d at
    65 n.6; see also United States v. Moran,
    
    493 F.3d 1002
    , 1013 (9th Cir. 2007) (noting that “[t]he burden
    is on the government to negate the defendant’s claim that he had
    a good faith belief that he was not violating the tax law,” and
    “[g]ood faith reliance on a qualified accountant has long been a
    defense to willfulness in cases of tax fraud” (internal quotation
    marks and citation omitted)).
    46
    Though we agree with Stadtmauer that the District
    Court’s willful blindness instruction could be interpreted as
    applying to his knowledge of the law, we reject his argument
    that the instruction also (and impermissibly) applied to the
    element of intent.
    In addition to requiring a “known legal duty,” Cheek
    requires proof that the defendant “voluntarily and intentionally
    violated that duty.” 
    498 U.S. at 201
    . “Willfulness” thus
    requires more than a general intent to accomplish an act; it
    requires proof that the act was done with the specific intent to do
    something that the law forbids. See 
    id.
     at 200–01; Pomponio,
    
    429 U.S. at
    12–13; Murdock, 290 U.S. at 394–95; see also
    Carter v. United States, 
    530 U.S. 255
    , 268 (2000) (explaining
    that general intent (as opposed to specific intent) requires “that
    the defendant possessed knowledge [only] with respect to the
    actus reus of the crime”).
    The penultimate paragraph of the District Court’s willful
    blindness instruction stated:
    [Y]ou may find that the defendant acted
    knowingly and willfully if you find beyond a
    reasonable doubt either that the defendant actually
    knew that the tax returns were false or fraudulent
    as to a material matter or that the defendant
    deliberately closed his eyes to what he had every
    reason to believe.
    47
    (App. 3974.) Stadtmauer argues that the Court’s instruction that
    the jury could find that Stadtmauer “acted knowingly and
    willfully” if he “deliberately closed his eyes to what he had every
    reason to believe” improperly substituted willful blindness for
    proof of a specific intent, as the element of “willfulness”
    encompasses both a knowledge and intent component. In that
    light, Stadtmauer argues that the Court’s instruction by analogy
    ran afoul of Pierre, where we held that, although “[w]illful
    blindness can be used to establish knowledge,” it “does not
    satisfy the specific intent requirement” under the Convention
    Against Torture (“CAT”). 23 
    528 F.3d at 190
    .
    Even assuming that the inclusion of these two words
    (“and willfully”) in the District Court’s willful blindness
    instruction was technically an incorrect statement of the law,24
    23
    In Pierre, our Court rejected the petitioner’s argument that
    he could show that he was more likely than not to be tortured if
    removed to Haiti through evidence that pain and suffering
    would be the “practically certain result” of his confinement by
    Haitian authorities upon returning. 
    Id. at 189
    . In so holding, we
    rejected a dictum in an earlier precedent suggesting that
    “specific intent could be proven through ‘evidence of willful
    blindness.’” 
    Id. at 188, 190
     (quoting Lavira v. Att’y Gen., 
    478 F.3d 158
    , 188 (3d Cir. 2007)).
    24
    The Government suggests that we should review this claim
    for plain error, as Stadtmauer did not raise a challenge specific
    to the inclusion of the words “and willfully” in the
    48
    we conclude that the Court’s “instructions, taken as a whole,
    properly instructed the jury as to the proof required” for the
    element of intent. United States v. Leahy, 
    445 F.3d 634
    , 650 (3d
    Cir. 2006). The Court’s instructions made clear that willful
    blindness applied only to the element of knowledge. See App.
    3973 (“The element of knowledge on the part of the defendant
    may be satisfied by inferences drawn from proof that the
    defendant closed his eyes to what would otherwise have been
    obvious to him.” (emphasis added)). Indeed, aside from two
    isolated instances where the Court mentioned the words
    “willfully” or “willfulness,” 25 its eight-paragraph instruction
    referred only to the “element of knowledge,” Stadtmauer’s
    “knowledge that the tax returns at issue were false or
    fraudulent,” or his “knowledge of a fact or circumstance.” It
    never mentioned “intent,” “purpose,” or any other language that
    could be reasonably interpreted as applying to the element of
    Government’s proposed instruction. (Appellee’s Br. at 82 &
    n.28.) We need not decide this issue because, as explained
    below, we would affirm regardless of the standard of review.
    25
    In the second instance, not quoted previously, the Court
    stated: “[A] showing of negligence or of a good-faith mistake of
    law is not . . . sufficient to support a finding of willfulness or of
    knowledge.” (Id. at 3974 (emphasis added).) This was, in fact,
    a correct statement of the law. As discussed, the element of
    “willfulness” encompasses a legal knowledge component, see
    infra Part III.A.1, which cannot be satisfied by negligence or a
    good-faith mistake of law, see infra Part III.A.2.
    49
    intent.
    In this context, we cannot agree that a reasonable juror
    would have concluded from the District Court’s instructions that
    a finding of willful blindness may also satisfy the element of
    specific intent. See United States v. Gurary, 
    860 F.2d 521
    , 527
    n.6 (2d Cir. 1988) (though the trial court “also mentioned
    conscious avoidance in connection with willfulness, the
    components of which are knowledge and intent, a fair reading
    of . . . the charge as a whole indicate[d] that conscious
    avoidance was to be used only in connection with the knowledge
    component”). Accordingly, we reject Stadtmauer’s contention
    that the Court’s willful blindness instruction improperly charged
    the jury as to the element of intent.
    4.      Whether Trial Evidence Warranted the
    Willful Blindness Instruction
    Stadtmauer finally argues that the trial evidence did not
    warrant a willful blindness instruction, noting simply that “[n]ot
    one” of the Government’s witnesses directly claimed that he
    “deliberately tried to shield himself from learning any fact about
    the tax returns.” (Appellant’s Br. at 75.) We disagree. The
    Government need not present direct evidence of conscious
    avoidance to justify a willful blindness instruction. E.g., United
    States v. Singh, 
    222 F.3d 6
    , 11 (1st Cir. 2000). In any event, the
    District Court did not err in concluding that the instruction was
    warranted in this case.
    50
    At trial, there was abundant evidence that Stadtmauer
    was intimately involved with the operations of the partnerships
    and was aware of how the partnerships characterized capital
    expenditures, charitable contributions, gift and entertainment
    expenses, and “non-property” expenses in the general ledgers
    and financial statements. There was also evidence that, despite
    this knowledge—and despite the logical inference that, as
    Bentzlin described, “if there is garbage in, [there’s] garbage out”
    (App. 2281)—Stadtmauer spent very little time reviewing the
    partnerships’ tax returns, and never asked questions of SSMB as
    to the propriety of the expenses deducted therein. One possible
    inference from this is what Stadtmauer asked the jury to draw:
    that he relied in good faith on his accountants to prepare the tax
    returns consistent with applicable law (and thus had no need to
    review them closely). However, another possible inference is
    that Stadtmauer deliberately avoided “ask[ing] the natural
    follow-up question[s]”—e.g., whether the deductions claimed in
    the tax returns were consistent with how expenses were falsely
    characterized in the general ledgers and reported on the financial
    statements—despite his awareness of a high probability of that
    fact. Wert-Ruiz, 
    228 F.3d at 257
    ; United States v. Brodie, 
    403 F.3d 123
    , 158 (3d Cir. 2005); see also United States v. Stewart,
    
    185 F.3d 112
    , 126 (3d Cir. 1999) (evidence justified willful
    blindness instruction in mail fraud and money laundering trial,
    where the defendant maintained that he “lacked the intent to
    defraud because he relied upon the findings of solvency reported
    in state examinations and audit reports,” and where the jury
    reasonably could have concluded that the defendant “recognized
    51
    the likelihood of insolvency yet deliberately avoided learning
    the true facts”).
    In this context, we conclude that the Court did not abuse
    its discretion in giving a willful blindness instruction.26
    B.     Lay Opinion Testimony
    Stadtmauer next contends that the District Court admitted
    impermissible lay opinion testimony as to his knowledge of the
    falseness of the partnerships’ tax returns by SSMB partner
    Stanley Bekritsky. We review the admission of lay opinion
    testimony for abuse of discretion. United States v. Hoffecker,
    
    530 F.3d 137
    , 170 (3d Cir. 2008).
    1.      Background
    About one month into trial, the Government informed
    defense counsel that, during a recent interview in preparation for
    his testimony, Bekritsky had recalled a tax return signing session
    26
    Even assuming the trial evidence did not support a finding
    of willful blindness, we believe that any resulting error was
    harmless, given that “the instruction itself contained the proper
    legal standard,” and in light of the “ample evidence” of
    Stadtmauer’s “actual knowledge” of the falsity of the tax
    returns. Leahy, 
    445 F.3d at
    654 n.15 (collecting cases). See
    infra Part III.B.2.
    52
    during which Stadtmauer asked him “whether the returns were
    okay to sign.” The Government disclosed that Bekritsky (1)
    “understood [Stadtmauer’s] question [to be] about whether the
    IRS would be likely to detect the problems with the returns,”
    and (2) stated “I signed them” in response to Stadtmauer’s
    question. (Supp. App. 1049.)
    Stadtmauer filed a motion in limine to prevent Bekritsky
    from testifying as to his “‘understanding’ of Mr. Stadtmauer’s
    intended meaning of the question that Mr. Stadtmauer posed to
    Mr. Bekritsky.” (Id. at 1051.) Stadtmauer argued that such
    testimony would be impermissible lay opinion testimony under
    Federal Rule of Evidence 701. The Government opposed the
    motion, arguing that, as a participant in the conversation,
    Bekritsky should be permitted under Rule 701 to testify as to his
    understanding of what Stadtmauer was attempting to convey to
    him. The Government further noted that, unless Bekritsky was
    permitted to testify as to that understanding, Stadtmauer’s
    question could be interpreted as having an exculpatory meaning
    (i.e., that he was seeking Bekritsky’s confirmation that the tax
    returns were accurate 27 ). (Id. at 1057.)
    27
    This potential exculpatory interpretation of Stadtmauer’s
    question is what prompted the Government—“[i]n furtherance
    of [its] Brady obligations”—to disclose Bekritsky’s anticipated
    testimony to Stadtmauer. (Id. at 1049.) Indeed, Stadtmauer
    contended in his motion in limine that the “more plausibl[e]”
    meaning of his question was that he “relied on Mr. Bekritsky to
    53
    The District Court granted the motion in limine,
    reasoning that the jurors could “come to their own conclusions
    [about] what Mr. Stadtmauer meant” by the question. (App.
    3217.) The Court nonetheless made clear that the Government
    was authorized to ask Bekritsky “what . . . he mean[t] when he
    said, ‘I signed it[.]’” (Id.)
    At trial, Bekritsky testified on direct examination as
    follows:
    Q.     Did [Stadtmauer] ever ask you generally about the
    returns?
    ...
    A.     Yes.
    Q.     What did he ask you?
    A.     On one occasion, he asked me if he could—if he
    should sign the returns—if the returns were okay,
    and—
    ...
    prepare the tax returns and trusted Mr. Bekritsky to advise him
    of any concerns.” (Id. at 1052.)
    54
    A.    —and I said, I signed the returns.
    Q.    What did he 28 mean by that?
    ...
    [Defense Counsel]: Objection.
    ...
    THE COURT: I don’t want you to tell us what you
    thought Mr. Stadtmauer [meant] by asking you the
    question[.] You can testify, however, as to what you
    meant by your answer.
    ...
    28
    Stadtmauer contends that the prosecutor violated the
    District Court’s order granting Stadtmauer’s motion in limine by
    asking Bekritsky what Stadtmauer meant by his question. The
    Government maintains that the court reporter mis-transcribed
    the prosecutor’s question, which actually asked, “What did you
    mean by that?” (Appellee’s Br. at 52 n.18 (emphasis added).)
    This dispute is beside the point, as the Court immediately
    interceded and rephrased the question to make clear that
    Bekritsky was not to opine on what he thought Stadtmauer
    meant by the question.
    55
    A.     What I meant by my answer was that I knew that
    there were problems with these tax returns, and
    based upon my understanding of Richard’s
    involvement, Richard knew—
    [Defense Counsel]: Objection.
    (Id. at 3262–63 (emphases added).)
    The parties then went to sidebar, where defense counsel
    objected to Bekritsky “testifying to what [Stadtmauer] knew or
    didn’t know.” (Id. at 3263.) Counsel argued that Bekritsky
    testifying about “what [Stadtmauer] knew” was “the basis for
    [the] motion” in limine. (Id.)
    The District Court disagreed:
    I disagree with you that was the basis of the
    Court’s ruling. The basis was his interpretation of
    a statement by Mr. Stadtmauer as to what
    Stadtmauer’s statement meant, because those
    words, in my view, did not need interpretation to
    help the jury.
    That is different than this witness testifying
    about what, based on his perception, he believed
    Mr. Stadtmauer knew or didn’t know, so I will
    allow it.
    56
    (Id.) Bekritsky’s testimony then resumed:
    THE COURT: . . . [You] said, what I meant by my
    answer was that I knew there were problems with these
    tax returns, and based on my understanding of Richard’s
    involvement. What did you mean by that?
    A.     Richard was involved with the details of the
    operations of the partnerships. He knew that
    professional expenses of one entity were being
    paid by another entity.
    [Defense Counsel]: Same objection to his testimony as to
    what [Stadtmauer] knew or didn’t know.
    THE COURT: . . . Overruled.
    ...
    THE COURT: . . . What did you intend to convey when
    you said you signed it?
    A.     What I intended to convey was there were
    problems that we both knew that existed in the
    returns. The returns were prepared in a way that
    I thought that they would get by the Government
    and questions would not be raised.
    57
    (Id. at 3264 (emphasis added).)
    Defense counsel then moved to strike Bekritsky’s
    statement as to what Stadtmauer “knew”; in the alternative, he
    moved for a mistrial. Defense counsel argued that Bekritsky’s
    testimony was “incredibly prejudicial,” had no “probative value
    at all,” and lacked a foundation. (Id. at 3264–65.) The District
    Court denied Stadtmauer’s motions, reasoning that (1)
    Bekritsky’s perception of Stadtmauer’s involvement in and
    knowledge of the partnerships provided a sufficient foundation
    for his testimony as to what Stadtmauer knew; and (2) in
    testifying that Stadtmauer “knew that things were being
    expensed that shouldn’t have been,” Bekritsky was merely
    “explaining what he meant when he said . . . ‘I signed it.’” (Id.
    at 3266.)
    At the close of its summation, the Government quoted
    Bekritsky’s testimony and emphasized that, instead of asking
    whether the returns were “accurate” or “a hundred percent
    correct,” Stadtmauer had asked whether they were “okay to
    sign.” (Id. at 4060.) In that context—and in light of Bekritsky’s
    testimony regarding what he intended to convey by his answer,
    “I signed [them]”—the Government argued that Stadtmauer’s
    goal was not to file “accurate[,] true returns,” but to file returns
    that would not raise “flags . . . with the IRS.” 29 (Id.)
    29
    The prosecutor who gave the rebuttal argument on behalf
    of the Government also referenced Bekritsky’s testimony, and
    58
    By contrast, defense counsel urged the jury to draw the
    opposite inference from Bekritsky’s testimony. Counsel argued
    in summation that “any reasonable person” would have
    interpreted Stadtmauer’s question to “mean[] the returns are
    okay to sign, meaning that they are correct.” (Id. at 4062.) In
    that light, defense counsel contended that “Bekritsky’s
    testimony [as a] whole . . . exonerate[d]” Stadtmauer. (Id.)
    2.      Analysis
    Stadtmauer argues that Bekritsky’s testimony that
    Stadtmauer “knew” there were “problems” with the tax returns
    was inadmissible under Federal Rule of Evidence 701. In
    relevant part, it limits lay testimony “in the form of opinions or
    inferences” to those “which are (a) rationally based on the
    perception of the witness, [and] (b) helpful to a clear
    understanding of the witness’ testimony or the determination of
    a fact in issue[.]” Fed. R. Evid. 701.
    Rule 701 represents “a movement away from . . . courts’
    historically skeptical view of lay opinion evidence,” and is
    argued that Stadtmauer’s question itself was suggestive of a
    consciousness of guilt. See id. at 4148 (“If he didn’t think there
    was anything to worry about, why did he ask?”). However, this
    prosecutor did not quote the portion of Bekritsky’s testimony
    that Stadtmauer challenges on appeal (i.e., that Stadtmauer
    “knew” there were “problems” with the returns).
    59
    “rooted in the modern trend away from fine distinctions between
    fact and opinion and toward greater admissibility.” Asplundh
    Mfg. Div. v. Benton Harbor Eng’g, 
    57 F.3d 1190
    , 1195 (3d Cir.
    1995); see also Teen-Ed, Inc. v. Kimball Int’l, Inc., 
    620 F.2d 399
    , 403 (3d Cir. 1980). The Rule is nonetheless designed to
    exclude lay opinion testimony that “amount[s] to little more than
    choosing up sides,” Fed. R. Evid. 701 advisory committee’s
    note, or that “‘merely tell[s] the jury what result to reach,’”
    United States v. Rea, 
    958 F.2d 1206
    , 1215–16 (2d Cir. 1992)
    (quoting Fed. R. Evid. 704 advisory committee’s note on 1972
    Proposed Rules). Lay testimony in the form of an opinion about
    what a defendant did or did not know often comes dangerously
    close to doing just this. Though “we have never held that lay
    opinion evidence concerning the knowledge of a third party is
    per se inadmissible,” 30 we have explained that “this kind of
    evidence [is] difficult to admit” under either prong of Rule 701:
    If the witness fails to describe the opinion’s basis,
    in the form of descriptions of specific incidents,
    the opinion testimony [should] be rejected on the
    ground that it is not based on the witness’s
    30
    We note that the mere fact that Bekritsky’s testimony
    related to an ultimate issue to be decided by the jury—i.e.,
    whether Stadtmauer had knowledge that the tax returns he
    signed were false or fraudulent as to a material matter—does not
    alone render Bekritsky’s testimony inadmissible. See Fed. R.
    Evid. 704(a).
    60
    perceptions. To the extent the witness describes
    the basis of his or her opinion, that testimony
    [should] be rejected on the ground that it is not
    helpful because the fact finder is able to reach his
    or her own conclusion, making the opinion
    testimony irrelevant.
    United States v. Polishan, 
    336 F.3d 234
    , 242 (3d Cir. 2003)
    (internal citation omitted).
    In our case, Stadtmauer primarily argues that Bekritsky’s
    testimony was inadmissible under the first prong of Rule 701.
    Bekritsky’s opinion that Stadtmauer “knew” there were
    “problems” in the tax returns was not, according to Stadtmauer,
    “rationally based” on Bekritsky’s perceptions because he never
    discussed with Stadtmauer the falseness of any specific tax
    return (or any deduction claimed on a return). (Appellant’s Br.
    at 49.) We do not follow this path.
    Rule 701’s “rationally based” requirement is essentially
    a restatement of the personal knowledge requirement necessary
    for all lay witness testimony. See Fed. R. Evid. 701 advisory
    committee’s note; see also Christopher B. Mueller & Laird C.
    Kirkpatrick, Federal Evidence § 7:3, at 751 (3d ed. 2007). We
    agree with the District Court that Bekritsky’s testimony that
    Stadtmauer “knew” there were “problems” with the partnership
    tax returns—specifically, that certain partnerships were claiming
    deductions for expenses paid on behalf of other partnerships
    61
    (“non-property” expenses)—was at least “rationally based” on
    his perception of Stadtmauer’s (1) involvement with and control
    over the operations of the partnerships, (2) knowledge of how
    certain kinds of expenditures were characterized in the
    partnerships’ general ledgers and financial statements, and (3)
    knowledge that those materials were used to prepare the
    partnerships’ tax returns. Cf. Polishan, 
    336 F.3d at 242
     (“Lay
    opinion testimony may be based on the witness’s own
    perceptions and ‘knowledge and participation in the day-to-day
    affairs of [the] business.’” (alteration in original) (quoting
    Lightning Lube, Inc. v. Witco Corp., 
    4 F.3d 1153
    , 1175 (3d Cir.
    1993)); Rea, 
    958 F.2d at 1216
     (“[T]here are a number of
    objective factual bases from which it is possible to infer . . . that
    a person knows a given fact,” including what the person “was in
    a position to see or hear . . . , conduct in which he engaged, and
    what his background and experience were.”).
    Indeed, our Court (and other circuit courts) have held far
    more prejudicial statements to satisfy this Rule 701 requirement
    (even where such statements violated Rule 701’s helpfulness
    requirement). See United States v. Anderskow, 
    88 F.3d 245
    , 250
    (3d Cir. 1996) (lay witness’s testimony that defendant “must
    have known” of loan fraud scheme satisfied the “rationally
    based” requirement of Rule 701, as the testimony was based on
    the witness’s “first-hand knowledge” of the defendant’s frequent
    exposure to fraudulent loan schedules); see also United States
    v. Wantuch, 
    525 F.3d 505
    , 512–14 (7th Cir. 2008) (lay witness’s
    testimony that defendant “knew all the time that everything that
    62
    he was doing was illegal” satisfied the “rationally based”
    requirement of Rule 701, as the witness was “deeply involved
    in” the fraudulent scheme and was the defendant’s “contact
    every step of the way”); Rea, 
    958 F.2d at 1217, 1219
     (lay
    witness’s testimony that defendant “had to” have known of
    scheme to evade taxes satisfied the “rationally based”
    requirement of Rule 701, as the witness testified that he
    repeatedly told the defendant that he lacked a license that would
    exempt their transactions from federal excise taxes).
    Whether Bekritsky’s testimony violated the helpfulness
    prong of Rule 701 requires closer attention.31 At first blush,
    31
    We reach this issue only by construing Stadtmauer’s
    opening brief as liberally as possible. Though he analogizes
    Bekritsky’s testimony to the testimony we ruled impermissible
    in Anderskow in his opening brief, his argument appears to be
    limited to the first requirement of Rule 701 (a prong we held
    was satisfied in Anderskow).          (Appellant’s Br. at 49.)
    Stadtmauer first makes an argument specific to the helpfulness
    prong in his Reply Brief. But “an issue is waived unless a party
    raises it in its opening brief, and for those purposes a passing
    reference to an issue will not suffice . . . .” Skretvedt v. E.I.
    DuPont De Nemours, 
    372 F.3d 193
    , 202–03 (3d Cir. 2004)
    (internal quotation marks and citation omitted).
    Moreover, plain error review is arguably appropriate in
    these circumstances. Though Stadtmauer claimed in his motion
    in limine that allowing Bekritsky to testify as to what
    Stadtmauer meant by his question would violate Rule 701’s
    63
    Bekritsky’s testimony that Stadtmauer “knew” there were
    “problems” with the returns seems unhelpful because the basis
    for Bekritsky’s opinion—e.g., Stadtmauer’s intimate knowledge
    of the partnerships’ operations and how their books and records
    were maintained—was already in evidence. Cf. Rea, 
    958 F.2d at 1216
     (“[W]hen a witness has fully described what a defendant
    was in a position to observe, what the defendant was told, and
    what the defendant said or did, the witness’s opinion as to the
    defendant’s knowledge will often not be ‘helpful’ . . . because
    the jury will be in as good a position as the witness to draw the
    inference as to whether or not the defendant knew.”).
    Bekritsky’s testimony is nonetheless different in
    important respects from the lay opinion testimony we found
    helpfulness prong, he raised different arguments in support of
    his motion to strike Bekritsky’s testimony as to what he meant
    by his answer to Stadtmauer’s question (e.g., that the statement
    was unfairly prejudicial). See Fed. R. Evid. 103(a)(1) (an
    objection to the admission of evidence must “stat[e] the specific
    ground of objection”); see also United States v. Gomez-Norena,
    
    908 F.2d 497
    , 500 (9th Cir. 1990) (“[A] party fails to preserve
    an evidentiary issue for appeal not only by failing to make a
    specific objection, but also by making the wrong specific
    objection.” (internal citations omitted) (emphasis in original)).
    However, the Government does not argue waiver or
    forfeiture, and, as we explain below, we would affirm in any
    event because any error in admitting Bekritsky’s testimony was
    harmless.
    64
    inadmissible in Anderskow, the principal case on which
    Stadtmauer relies. In that case, a cooperating conspirator in a
    loan fraud conspiracy testified that he provided one of the
    defendants, Donald Anchors, with fraudulent loan schedules to
    be passed along to borrowers. 
    88 F.3d at 249
    . On direct
    examination, the Government asked the witness whether
    Anchors would have been “deceived by the information that [the
    witness was] sending him.” 
    Id.
     The witness responded:
    Donald Anchors had probably 20 or 30 borrowers,
    maybe more for all I know, who had been
    promised millions of dollars for a long time, some
    as long as a year. He had never seen one dime
    funded or loaned, and he kept on with the
    business at hand. I had no reason to believe that
    he wasn’t fully aware of what was occurring, as
    long as he was getting paid.
    
    Id. at 250
     (emphasis added). We held that this testimony was
    inadmissible under Rule 701’s helpfulness prong, reasoning that
    “a witness’ subjective belief that a defendant ‘must have known’
    [of the object of a conspiracy] is [not] helpful to a factfinder that
    has before it the very circumstantial evidence upon which the
    subjective opinion is based.” 
    Id. at 251
    . Stated another way, the
    witness’s testimony was not helpful—and thus inadmissible
    under Rule 701—because the jury was in just as good a position
    as the witness to infer what Anchors “must have known.”
    65
    However, unlike the witness in Anderskow, Bekritsky did
    not offer his opinion as to what Stadtmauer “knew” in a
    vacuum. Rather, Bekritsky was responding to a question asking
    him to explain what he meant by his ambiguous answer (“I
    signed them”) to Stadtmauer’s equally ambiguous questions
    (whether “he should sign the returns,” and whether “the returns
    were okay”). Rather than opining as to what Stadtmauer “must
    have known,” Bekritsky more specifically testified as to what he
    believed Stadtmauer knew at the time of this conversation (in
    the context of explaining why he answered Stadtmauer’s
    questions the way he did). In that light, even if Bekritsky’s
    opinion regarding what Stadtmauer “knew” was unhelpful to
    “the determination of a fact in issue” (i.e., whether Stadtmauer
    had guilty knowledge), it arguably was helpful to “a clear
    understanding of [Bekritsky’s] testimony.” Fed. R. Evid. 701.
    Cf. United States v. De Peri, 
    778 F.2d 963
    , 977 (3d Cir. 1985)
    (lay witness’s testimony was helpful to a clear understanding of
    conversations consisting of “unfinished sentences and
    punctuated with ambiguous references to events that [were] only
    clear to [the participants]”); see also United States v. Urlacher,
    
    979 F.2d 935
    , 939 (2d Cir. 1992) (lay witness’s testimony was
    helpful to a clear understanding of “statements or words
    [recorded] on the tape that would be ambiguous or unclear to
    someone who was not a participant in the conversation”); United
    States v. Awan, 
    966 F.2d 1415
    , 1430 (11th Cir. 1992) (same).32
    32
    We are not asked to determine whether the District Court
    was correct in barring Bekritsky from testifying as to what he
    66
    This question is close. However, even assuming that the
    believed Stadtmauer intended to convey by his questions. We
    note, however, that other courts have upheld the admission of
    testimony by a participant in a conversation as to what another
    participant intended to convey. See, e.g., United States v.
    Kozinski, 
    16 F.3d 795
    , 809 (7th Cir. 1994) (witness was
    permitted under Rule 701 to testify “about the context and
    meaning of conversations to which he was a party,” including
    his “understanding of the thoughts that were being
    communicated to him”). As Professors Mueller and Kirkpatrick
    explain:
    [F]irsthand observers often understand the mental
    state of another in ways not captured in literal
    meanings of words spoken by the other, nor
    readily conveyed in close analytical accounts of
    what exactly transpired. The old adage that “you
    had to be there” makes this point, and witnesses
    asked to give “factual” accounts of what another
    said or did may be confounded by their
    knowledge that doing so would be misleading,
    and that the surface of the words carries little of
    their real meaning. In everyday life, personal
    interaction is nuanced and nonliteral, . . . and
    knowledgeable witnesses can easily satisfy the
    rational basis and helpfulness criteria [of Rule
    701] in providing interpretive opinions on the
    mental states of others.
    Mueller & Kirkpatrick, Federal Evidence § 7:5, at 775.
    67
    District Court erred in refusing to strike Bekritsky’s testimony,33
    we conclude that any error was harmless. A non-constitutional
    error at trial does not warrant reversal where “it is highly
    probable that the error did not contribute to the judgment.”
    United States v. Helbling, 
    209 F.3d 226
    , 241 (3d Cir. 2000)
    (internal quotation marks and citation omitted); see also
    Kotteakos v. United States, 
    328 U.S. 750
    , 764–65 (1946). This
    “high probability” standard “requires that we have a sure
    conviction that the error did not prejudice the defendant[]”;
    however, “we may be firmly convinced that the error was
    harmless without disproving every ‘reasonable possibility’ of
    prejudice.” United States v. Jannotti, 
    729 F.2d 213
    , 220 n.2 (3d
    Cir. 1984).
    When Bekritsky’s testimony is viewed in the context of
    the record as a whole, we conclude that it is highly probable that
    any error in admitting that testimony did not prejudice
    Stadtmauer. See, e.g., United States v. Zehrbach, 
    47 F.3d 1252
    ,
    33
    We note that even if testimony similar to Bekritsky’s
    could satisfy the requirements of Rule 701, it may be
    inadmissible on other grounds, e.g., because its probative value
    (and helpfulness) are substantially outweighed by the potential
    for unfair prejudice. Fed. R. Evid. 403; see also Rea, 
    958 F.2d at 1216
    . Because Stadtmauer does not raise such an argument
    on appeal, we express no opinion on whether Bekritsky’s
    testimony should have been struck under Rule 403 (assuming it
    satisfied the Rule 701 requirements).
    68
    1265 (3d Cir. 1995) (“The harmless error doctrine requires that
    the court consider an error in light of the record as a whole
    . . . .”). Though Stadtmauer challenges Bekritsky’s testimony
    that Stadtmauer “knew” there were “problems” with the returns,
    he does not challenge Bekritsky’s testimony that, by his answer
    (“I signed them”), he intended to convey that (1) “there were
    problems . . . that existed in the returns”; and (2) “[t]he returns
    were prepared in a way that [Bekritsky] thought that they would
    get by the Government and questions would not be raised.”
    (App. 3264.) The plain and unmistakable implication of these
    unchallenged portions of Bekritsky’s testimony is that he
    believed Stadtmauer also “knew” that there were “problems”
    with the return. Otherwise, Bekritsky’s explanation of what he
    intended to convey by answering “I signed [them]” would be
    nonsensical.34
    34
    This conclusion is bolstered when Bekritsky’s statement is
    viewed in light of the even more damaging testimony that
    defense counsel elicited during cross-examination of
    Bentzlin—who testified before Bekritsky—regarding why
    Bentzlin similarly told Stadtmauer to “just sign” the returns:
    Q:     Isn’t it a fact that you didn’t tell
    [Stadtmauer] . . . that the returns were in
    any way incorrect?
    A.     I didn’t need to tell Mr. Stadtmauer,
    because he was fully aware between the
    Richard Specials and the Tuesday signing,
    69
    Moreover, any error in refusing to strike Bekritsky’s
    testimony regarding what he believed Stadtmauer “knew” was
    harmless in light of the “mountain of circumstantial evidence
    supporting the inference that” Stadtmauer knew that improper
    deductions were claimed in the partnerships’ tax returns,
    Anderskow, 
    88 F.3d at 251
    , including evidence that Stadtmauer:
    (1) was intimately familiar with how the partnerships operated
    and maintained their general ledgers; (2) was involved in
    and the [practice of “losing” bills] and the
    Thursday presentations and signing the
    checks for all the entities, he was fully
    aware of the type of information that was
    in there, so I didn’t see that there was any
    need to tell [him]. He was a very
    accomplished financial leader. He was
    familiar with the tax returns. So, no, I
    didn’t feel the need to tell him, just sign it
    or not.
    ...
    I kn[ew] the nature of the stuff that
    was in the tax returns. If you have repair
    and maintenance items processed on a
    regular basis through various entities all
    over the place, . . . logic would dictate that
    that stuff is reflected somewhere in the tax
    return.
    (Id. at 2478–79 (emphases added).)
    70
    deciding which partnerships would pay certain expenditures; (3)
    was aware that certain expenditures were falsely characterized
    as expenses in the ledgers and financial statements; (4)
    mischaracterized expenditures in the partnerships’ financial
    statements when expedient; and (5) made all of these decisions
    with awareness of their tax consequences (e.g., the tuition
    payments for Zecher’s children, and the decision to continue
    appreciating capital expenditures for the partnerships involved
    in the WNY transaction). In that light, we are conviced that,
    regardless of Bekritsky’s testimony, the jury would have
    rejected Stadtmauer’s defense that he genuinely believed that
    SSMB—led by Plotkin, to whom KC was funneling yearly
    bonuses and private school tuition payments—was, for purposes
    of the partnerships’ tax returns, correcting the extensive mis-
    characterizations of expenditures as reflected in the
    partnerships’ general ledgers and financial statements.
    In sum, any error in admitting Bekritsky’s testimony is
    harmless and thus does not require reversal.
    C.     Prosecutorial Misconduct
    Stadtmauer claims that the Government violated his due
    process rights by “improperly standing silent” when one of its
    witnesses, former COO Scott Zecher, made several statements
    during cross-examination that the lead prosecutor knew to be
    false. (Appellant’s Br. at 41.) To succeed on this claim,
    Stadtmauer bears the burden of establishing that: (1) Zecher
    71
    committed perjury; (2) the Government knew or should have
    known that Zecher committed perjury but failed to correct his
    testimony; and (3) there is a reasonable likelihood that the false
    testimony could have affected the verdict. See Hoffecker, 
    530 F.3d at 183
    . Because Stadtmauer cannot meet his burden as to
    the first two of these elements, we need not address the third.
    In 2005, Zecher was interviewed several times by FBI
    agents and prosecutors (including one of the prosecutors that
    tried Stadtmauer’s case). During trial, defense counsel sought
    to impeach Zecher with his statements during these interviews,
    as recorded in summaries prepared by the FBI agents present
    (known as “Form 302s”). To take one example, defense counsel
    asked Zecher during cross-examination whether he recalled
    telling investigators that Kushner, and not Stadtmauer, had
    raised the idea of paying Zecher’s children’s private school
    tuition “rather than paying [Zecher] a bonus.” (App. 3045.)
    Zecher first stated that he did not recall making the statement,
    and then denied that he made such a statement. Defense counsel
    then showed Zecher the Form 302 to refresh his recollection,
    which stated:
    ZECHER stated when he was hired KUSHNER
    told him that he could not pay ZECHER the salary
    he wanted, but instead would make up the
    difference in bonuses in June and December. KC
    normally issues bonuses to employees in
    December, but does not issue bonuses in June.
    72
    ZECHER stated that because no bonuses were
    paid in June, KUSHNER would pay ZECHER’s
    . . . school tuition rather than paying him a bonus.
    (Id. at 567.) Zecher denied that the Form 302 refreshed his
    recollection, and was adamant that the only conversations he had
    regarding the issue were with Stadtmauer. (Id. at 3045.)
    Though the District Court permitted Stadtmauer to cross-
    examine Zecher on the content of his statements, it refused on
    several occasions to admit the Form 302s themselves as prior
    inconsistent statements, rulings, we note, that Stadtmauer does
    not challenge. The Court’s reasoning was that the Form 302s
    contained the FBI’s characterizations of what Zecher said
    (which Zecher had not adopted).35
    After both sides rested, defense counsel moved for a
    35
    Federal Rule of Evidence 613 permits a party to examine
    “a witness concerning a prior statement made by the witness,
    whether written or oral,” Fed. R. Evid. 613(a) (emphasis added),
    and permits a party to introduce “extrinsic evidence” of a
    witness’s prior inconsistent statement as long as “the witness is
    afforded an opportunity to explain or deny” it, id. 613(b).
    Several of our sister circuit courts have affirmed the exclusion,
    under Rule 613, of interview memoranda prepared by law
    enforcement that the witness had not adopted. See, e.g., United
    States v. Adames, 
    56 F.3d 737
    , 744–45 (7th Cir. 1995); United
    States v. Saget, 
    991 F.2d 702
    , 710 (11th Cir. 1993); United
    States v. Almonte, 
    956 F.2d 27
    , 29 (2d Cir. 1992).
    73
    mistrial based on “the perjured testimony of Scott Zecher and .
    . . the Government’s failure to correct that testimony.” (Id. at
    3731.) Defense counsel argued that, when considered in light
    of the totality of Zecher’s testimony—which included numerous
    instances where Zecher testified that he could not recall certain
    events and conversations—there was enough for the District
    Court to determine that Zecher’s testimony was demonstrably
    false. The Court denied the motion, explaining that it could not
    find that Zecher’s “apparent lack of recollection in some
    instances . . . was due to confusion or mistake or faulty memory
    or a willful lie.” (Id. at 3871.)
    We review a district court’s factual finding that a
    witness’s testimony was not false for clear error, and “will not
    disturb that finding unless it is wholly unsupported by the
    evidence.” Hoffecker, 
    530 F.3d at 183
    . We have little trouble
    concluding that the District Court’s finding in this case was not
    clearly erroneous. As the Court noted, other than the
    inconsistencies between the FBI agent’s notes and Zecher’s
    recollection of his statements, there was no other evidence that
    Zecher perjured himself. Cf. United States v. Dunnigan, 
    507 U.S. 87
    , 94 (1993) (a witness does not commit perjury if his
    false testimony is the “result of confusion, mistake, or faulty
    memory”).
    Even assuming the District Court clearly erred in finding
    that Zecher’s testimony was not false, Stadtmauer has not
    demonstrated that the Government knew or should have known
    74
    that Zecher’s testimony was false. See Hoffecker, 
    530 F.3d at 183
    . Stadtmauer relies on United States v. Harris, 
    498 F.2d 1164
     (3d Cir. 1974), where the Government failed to correct a
    witness who falsely testified during cross-examination that
    prosecutors had made no promises to help her achieve a reduced
    sentence on pending state charges in exchange for her testimony
    against the defendant. In concluding the Government had
    violated its “duty to disclose a promise made to a Government
    witness,” 
    id. at 1169
    , we first noted that the witness arguably
    had not committed perjury by her responses because she may
    have “believed in good faith” that the questions posed to her
    “only referred to specific promises concerning her sentence,”
    which the Government did not (and could not) make. 
    Id. at 1168
    . We reasoned, however, that the prosecution’s duty to
    disclose false testimony should not be “narrowly and technically
    limited to those situations where the prosecutor knows that the
    witness is guilty of the crime of perjury.” 
    Id. at 1169
    . Rather,
    “when it should be obvious to the Government that the witness’
    answer, although made in good faith, is untrue,” it has an
    obligation to correct that testimony. 
    Id.
    The circumstances of Zecher’s testimony are far afield
    from the witness’s testimony in Harris, where it was undisputed
    that the prosecutor had personal knowledge that the witness’s
    answers were not correct. See 
    id. at 1168
     (prosecutor admitted
    that he had promised the cooperating witness that the
    Government would do “whatever [it] could” to get her state
    sentence reduced). Here, there was no way for the prosecutor to
    75
    know whether Zecher was giving false testimony when he
    denied—or could not recall—making certain statements during
    the 2005 interviews. Thus, Stadtmauer’s assertion that the
    Government’s counsel refused “to speak up when he knew for
    a fact that Zecher had made” false statements is simply
    unsupported by the record. Cf. Tapia v. Tansy, 
    926 F.2d 1554
    ,
    1563 (10th Cir. 1991) (“Contradictions and changes in a
    witness’s testimony alone do not constitute perjury and do not
    create an inference, let alone prove, that the prosecution
    knowingly presented perjured testimony.”).
    D.     Expert Testimony
    Over Stadtmauer’s objection, the District Court permitted
    IRS Agent Susan Grant to testify as an expert (and summary)
    witness. See Fed. R. Evid. 702, 703. Stadtmauer argues that the
    Court erred in admitting Agent Grant’s testimony because she
    “opined, with insufficient factual or legal foundation, that the
    [KC] partnership returns were false and fraudulent.”
    (Appellant’s Br. at 51.) We review a district court’s admission
    of expert testimony for abuse of discretion. Estate of Schneider
    v. Fried, 
    320 F.3d 396
    , 404 (3d Cir. 2003).
    Prior to trial, the Government disclosed the expert
    testimony that Agent Grant intended to provide and produced to
    defense counsel a set of her summary charts. Stadtmauer moved
    in limine to preclude Grant from testifying, arguing that her
    proposed testimony would improperly bear on the ultimate legal
    76
    issues in the case, and would be unhelpful and unreliable. The
    District Court denied Stadtmauer’s motion, finding that Grant’s
    testimony had “sufficient indicia of reliability and relation to the
    facts of this case.” (App. 89–92.)
    In her direct testimony, Grant described how a
    partnership tax return is prepared, and explained where on the
    return different categories of deductions were reported. Grant
    explained how she totaled the expenses she determined were
    improperly deducted from each partnership return, and carried
    them through to a summary chart for each partnership for each
    tax year, illustrating how the total amount of improper
    deductions affected the net income reported to the IRS. Defense
    counsel vigorously cross-examined Grant for two days,
    including questions on many specific deductions, and nearly
    every category of deductions, she determined were improperly
    claimed.
    Our sister circuit courts that have addressed the issue are
    unanimous that “expert testimony by an IRS agent which
    expresses an opinion as to the proper tax consequences of a
    transaction is admissible evidence.”          United States v.
    Mikutowicz, 
    365 F.3d 65
    , 72 (1st Cir. 2004) (internal quotation
    marks and citation omitted); see, e.g., United States v. Bedford,
    
    536 F.3d 1148
    , 1158 (10th Cir. 2008); United States v. Pree,
    
    408 F.3d 855
    , 870 (7th Cir. 2005); United States v. Sabino, 
    274 F.3d 1053
    , 1067 (6th Cir. 2001), modified on other grounds, 
    307 F.3d 446
     (6th Cir. 2002); United States v. Duncan, 
    42 F.3d 97
    ,
    77
    101–02 (2d Cir. 1994); United States v. Moore, 
    997 F.2d 55
    ,
    58–59 (5th Cir. 1993). The “primary limitation” on such
    testimony is that the expert “may not testify about the
    defendant’s state of mind when the challenged deductions were
    claimed.” Mikutowicz, 
    365 F.3d at 72
    ; see Fed. R. Evid. 704(b)
    (an expert witness may not opine “as to whether the defendant
    did or did not have the mental state or condition constituting an
    element of the crime charged”); see also Sabino, 
    274 F.3d at 1067
    .
    In our case, it is undisputed that Grant did not opine on
    Stadtmauer’s knowledge or intent. Stadtmauer nonetheless
    argues that the District Court impermissibly allowed her to
    “interpret the tax laws” and “add her unreliable and otherwise
    inadmissible opinion that the tax returns were false and
    fraudulent.” (Appellant’s Br. at 51.) Stadtmauer seeks to
    compare Grant’s testimony to expert testimony the Second
    Circuit Court found objectionable in United States v. Scop, 
    846 F.2d 135
     (2d Cir. 1988). There an investigator from the
    Securities and Exchange Commission testified as an expert in
    securities trading practices, and opined, drawing “directly upon
    the language of the statute,” that the defendants’ scheme of
    buying and selling securities to create artificial price levels
    constituted market “manipulation” and “fraud.” 
    Id. at 140
    . The
    Second Circuit Court determined that, through this testimony,
    the expert had “invade[d] the province of the court to determine
    the applicable law and to instruct the jury as to that law.” 
    Id.
    (internal quotation marks and citation omitted). In addition, the
    78
    expert conceded on cross-examination that his opinion was
    largely based not on his expertise in securities trading, but on his
    “positive assessment of the trustworthiness and accuracy of the
    testimony of the government’s witnesses.” 
    Id. at 142
    .
    Agent Grant’s testimony is far from the expert testimony
    deemed objectionable in Scop. She never used the words “false”
    or “fraudulent” to describe any of the deductions she concluded
    were improper, and did not base any portion of her testimony on
    her assessment of the credibility of other witnesses.
    Accordingly, Scop is unavailing to Stadtmauer. Cf. Hoffecker,
    
    530 F.3d at 171
     (distinguishing the testimony in Scop from
    testimony that defendant’s commodities investment program
    was a “scam,” where the witness “did not couch his view . . . on
    the language of the mail fraud statute, and did not base his
    opinion on the credibility or testimony of others”); see also
    Duncan, 
    42 F.3d at
    101–02 (distinguishing the testimony in
    Scop from IRS agent’s testimony that did not “use any legally
    specialized terms” and was “based on [the agent’s] own
    investigation of the facts and review of the records”).
    Stadtmauer also contends that the District Court erred in
    admitting Grant’s testimony because she made “out-and-out
    mischaracterizations” and “bald assertions” of the law in
    explaining her opinions. (Appellant’s Br. at 53, 55.) The record
    79
    belies these assertions.36 In any event, all expert testimony as to
    the “proper tax consequences of a transaction” is bound to touch
    on the law to some extent, Mikutowicz, 
    365 F.3d at 72
    , and we
    have little trouble concluding that Grant’s testimony did not
    improperly invade the province of the Court. Indeed, the Court
    not only gave extensive instructions on the applicable tax laws,
    and during Grant’s testimony emphasized to the jury that it was
    “bound to follow the law as [the Court] tell[s] you it applies in
    this case.” (App. 3434.) The Court emphasized that only it, and
    36
    To take one example, Stadtmauer contends that Grant
    erroneously testified that “only 50% of entertainment expenses
    may ever be deducted” by a business, id. at 53, despite the fact
    that entertainment expenses may be deducted in full when,
    among other things, they are made for “recreational, social, or
    similar activity . . . primarily for the benefit of [the taxpayer’s]
    employees generally.” 
    26 C.F.R. § 1.274-2
    (f)(2)(v). Contrary
    to Stadtmauer’s characterization, Grant never testified that there
    is a per se rule that such expenses are only deductible up to
    50%. Rather, in the portion of her testimony that Stadtmauer
    cites, Grant simply: (1) identified the line on the tax return
    where “travel and entertainment” expenses must be recorded
    (Line 4B); and (2) testified that this line was “for the 50 percent
    of travel and entertainment [expenses] that [are] . . . not
    deductible by the partnership.” (App. 3411.) Moreover, Grant
    agreed during cross-examination that the 50% rule “has
    exceptions,” 
    id.
     at 3548–49; see also 
    id. at 3422
    , and the District
    Court specifically instructed the jury as to four types of
    exceptions to the general rule, 
    id. at 3969
    .
    80
    not Grant, was authorized to instruct the jury as to the law. See
    
    id. at 3411
     (for example, instructing the jury that “to the extent
    that [Agent Grant] use[s] the word ‘Law,’ I will instruct you as
    to the law at the end of the case. [Agent Grant] can certainly
    testify as to what her understanding based on her experience as
    a tax expert is [and] to what the IRS’ view of things is”).
    In sum, to the extent there were (as Stadtmauer contends)
    shortcomings in the IRS Agent’s conclusions as to the propriety
    of specific deductions, they were “raised properly on cross-
    examination and went to the credibility, not the admissibility, of
    [her] testimony,” Kannankeril v. Terminix Int’l, Inc., 
    128 F.3d 802
    , 809 (3d Cir. 1997), and the record in this case confirms that
    defense counsel had ample opportunity to cross-examine Grant
    on her specific conclusions, methodology, and assumptions.37
    Accordingly, we conclude that the District Court did not abuse
    37
    Indeed, over the Government’s objections, the District
    Court allowed defense counsel to cross-examine Grant regarding
    her knowledge of specific provisions of the Tax Code, the IRS’s
    field manual, and federal court and Tax Court decisions. This
    went far beyond what other courts have permitted. Cf.
    Mikutowicz, 
    365 F.3d at 72
     (holding that trial court did not
    violate defendant’s confrontation rights by refusing to allow
    defense counsel to question the Government’s tax expert, an IRS
    agent, “about various judicial opinions, which [the defendant]
    claim[ed] would have established that the deductions were
    properly taken”).
    81
    its discretion in admitting Agent Grant’s testimony.38
    E.     Restrictions on Cross-Examination
    We end with the argument that Stadtmauer raises first:
    that the District Court improperly barred him from affirmatively
    admitting certain exhibits into evidence during cross-
    examination of Government witnesses. We review a district
    court’s rulings on the scope of cross-examination for abuse of
    discretion, United States v. Casoni, 
    950 F.2d 893
    , 902 (3d Cir.
    1991), “but to the extent the district court’s ruling turns on an
    interpretation of a Federal Rule of Evidence[,] our review is
    38
    Stadtmauer also challenges the District Court’s decision to
    allow the Government to admit summary charts prepared by
    Grant, arguing that they impermissibly summarized her “pre-
    trial conclusions.” (Appellant’s Br. at 56 (emphasis in
    original).) This argument fails outright. Agent Grant—who
    also served as a summary witness (based on her participation in
    the Government’s investigation of KC’s partnerships)—testified
    that she reached her conclusions (reflected in her summary
    charts) based on the voluminous documentary evidence the
    Government introduced during trial. Cf. United States v. West,
    
    58 F.3d 133
    , 140 (5th Cir. 1995) (district court did not abuse its
    discretion in permitting IRS agent to testify as an expert
    summary witness where her “specialized training and experience
    . . . made her adequately suited to assist the jury in
    understanding the large amount of documentary evidence
    presented by the [G]overnment and the tax implications”).
    82
    plenary,” United States v. Velasquez, 
    64 F.3d 844
    , 848 (3d Cir.
    1995) (internal quotation marks and citation omitted).
    Stadtmauer contends that the District Court erroneously
    barred him from admitting several categories of exhibits during
    defense counsel’s cross-examination of Bentzlin, Zecher, and
    Bekritsky. For example, during cross-examination of Zecher,
    defense counsel sought to introduce hundreds of advertisements
    bearing the name “Kushner Companies” (instead of the name of
    an individual partnership). Defense counsel sought to introduce
    the concept of “branding” through these exhibits, and thus to
    offer an exculpatory explanation for why expenses incurred by
    one partnership were frequently paid by a different partnership.39
    The District Court prevented Stadtmauer from admitting
    these documents because they were “case-in-chief materials”
    39
    The general rule is that a taxpayer may not deduct expenses
    incurred on behalf of another taxpayer’s business. See, e.g.,
    Deputy v. du Pont, 
    308 U.S. 488
    , 494 (1940). An exception to
    this rule is where a taxpayer’s payment of the business expenses
    of another serves to “protect or promote” his own business. See,
    e.g., Lohrke v. Comm’r, 
    48 T.C. 679
    , 684–85 (1967). Through
    the “branding” theory, Stadtmauer sought to argue that the “non-
    property” expenses deducted by the partnerships qualified under
    this exception.
    83
    rather than “impeachment materials.” 40 See, e.g., App. 2405
    (excluding proposed defense exhibits during cross-examination
    because they were “not really specifically impeachment
    material,” but “more akin to case-in-chief type evidence”); 
    id.
     at
    3002–03 (excluding proposed defense exhibits during cross-
    examination because Stadtmauer was limited to “impeachment
    material, not case-in-chief material”). Stadtmauer contends that
    the District Court thereby violated Federal Rule of Evidence
    611(b), which provides that cross-examination “should be
    limited” to (1) “the subject matter of the direct examination,”
    and (2) “matters affecting the credibility of the witness.” Fed.
    R. Evid. 611(b). He argues that the Court erroneously barred
    him from admitting the documents on the grounds that they (1)
    did not “impeach” the witness (even though they pertained to the
    “subject matter” of the witness’s direct testimony), and (2) could
    be introduced in Stadtmauer’s case-in-chief. Cf. United States
    40
    The Government contends that the District Court actually
    excluded all of the documents defense counsel sought to
    introduce during cross-examination because Stadtmauer had
    failed to comply with the Court’s pre-trial order requiring the
    reciprocal exchange of trial exhibits. (Appellee’s Br. at 29–30.)
    We see little in the record to support that blanket assertion.
    Though the Court sometimes noted in ruling on Stadtmauer’s
    requests to introduce exhibits during cross-examination that it
    “could” bar their admission because they had not been produced
    to the Government before trial, e.g., App. 2353–54, the record
    reveals that the Court’s rulings were ultimately not based on any
    violation of its pre-trial discovery order.
    84
    v. Segal, 
    534 F.2d 578
    , 582–83 (3d Cir. 1976) (“the fact that
    some of the points which defendant sought to explore could
    have been introduced in the defense case is not determinative”
    of whether the evidence is within the “subject matter” of the
    Government’s direct examination).
    From our review of the record, however, it is apparent
    that the District Court was using the terms “case-in-chief
    materials” and “impeachment materials” as shorthand to
    describe those documents that it would (or would not) permit
    Stadtmauer to introduce during cross-examination so as to
    manage effectively the presentation of evidence. The Court did
    not rely on Rule 611(b) in its rulings, and, as it later described,
    the question was not the admissibility of these exhibits but “the
    timing of the[ir] introduction.” App. 3570; see also 
    id. at 3322
    (agreeing that proposed defense exhibit was “within the subject
    matter” of the Government’s direct examination, but excluding
    it because it was more akin to a “case-in-chief document[]”).
    In that light, the more pertinent provision of Rule 611 is
    subsection (a), which grants district courts broad discretion to
    “exercise reasonable control over the mode and order of
    interrogating witnesses and presenting evidence.” Fed. R. Evid.
    611(a); see also 28 Charles A. Wright & Victor J. Gold, Federal
    Practice and Procedure § 6162, at 338 (1993) (Rule 611(a)
    “gives trial courts broad powers to control the ‘mode and order’
    of what is otherwise admissible evidence”). In our case, we
    have little trouble concluding that the District Court did not
    85
    abuse its discretion in postponing the admission of Stadtmauer’s
    proposed exhibits, even if they were technically within the
    “subject matter” of the Government’s direct examination. See,
    e.g., United States v. Lambert, 
    580 F.2d 740
    , 747 (5th Cir. 1978)
    (district court did not abuse its discretion under Rule 611(a) by
    excluding defendant’s “proffers of voluminous documentary
    evidence” during cross-examination); United States v. Ellison,
    
    557 F.2d 128
    , 135 (7th Cir. 1977) (district court did not abuse
    its discretion by excluding proposed defense exhibits during
    cross-examination, even assuming the documents “would have
    been relevant rebuttal evidence if offered during the presentation
    of [the defendant’s] own case”).
    Finally, even assuming that the District Court relied on
    an erroneous interpretation of Rule 611(b) in excluding
    Stadtmauer’s proposed exhibits, the error was harmless. For
    example, though the Court did not permit Stadtmauer to
    introduce the KC advertisements themselves, it nonetheless gave
    defense counsel broad leeway to use them in cross-examining
    Zecher. The Court allowed defense counsel to show Zecher
    approximately 20 advertisements, and he agreed that they
    refreshed his recollection that KC placed advertisements in
    “newspapers and professional journals” and “spent money
    advertising the Kushner name.” (App. 3010–11.) He also
    agreed that management used the name “Kushner Companies”
    in a “generic sense,” rather than “listing all 100 or 200
    partnerships” on corporate materials. (Id. at 2999.) Through
    this testimony, defense counsel was able to establish the same
    86
    basic point: that the partnerships often did business under the
    name “Kushner Companies” (rather than names of individual
    partnerships).41 In this context, we conclude that any error in
    excluding the exhibits during defense counsel’s cross-
    examination of the Government’s witnesses did not prejudice
    Stadtmauer.42
    *    *   *    *    *
    41
    Moreover, these advertisements were only tangentially
    relevant to the broader theory that defense counsel sought to
    establish: that non-property expenses and charitable
    contributions were properly paid by various partnerships
    because they collectively benefitted from using the KC “brand.”
    Even if Stadtmauer were permitted to introduce these exhibits,
    we fail to see how they would have meaningfully rebutted the
    testimony of Bentzlin, Lefkowitz, and Zecher that they never
    discussed the concept of “branding” as a justification for certain
    partnerships paying the expenses of other partnerships. (Id. at
    2224, 2608, 2841.)
    42
    For these reasons, we also reject Stadtmauer’s claim that
    the District Court’s exclusion of these exhibits violated his Sixth
    Amendment right of confrontation. See Delaware v. Van
    Arsdall, 
    475 U.S. 673
    , 679 (1986) (though the Sixth
    Amendment “guarantees an opportunity for effective cross-
    examination,” it does not guarantee “cross-examination that is
    effective in whatever way, and to whatever extent, the defense
    might wish” (internal quotation marks and citation omitted)
    (emphasis in original)).
    87
    In summary, we conclude that a willful blindness
    instruction may, where warranted by the trial evidence in a
    criminal tax case, properly apply to a defendant’s knowledge of
    his legal duties. The District Court did not abuse its discretion
    in giving such an instruction in this case, and we disagree with
    Stadtmauer’s contention that the instruction also impermissibly
    applied to the element of specific intent.
    Though the question whether Bekritsky’s lay opinion
    testimony was admissible under Rule 701 is close, we conclude
    that an error here, if any, was harmless. In addition, we reject
    Stadtmauer’s prosecutorial misconduct claim based on the
    Government’s supposed failure to “correct” Zecher’s testimony
    that he could not recall statements he purportedly made to FBI
    agents (with Government counsel present) during investigatory
    interviews. Finally, we conclude that the District Court did not
    abuse its discretion in (1) admitting the expert testimony of an
    IRS agent in this complicated tax fraud case, and (2) preventing
    Stadtmauer from affirmatively admitting certain categories of
    exhibits into evidence during defense counsel’s cross-
    examination of Government witnesses.
    For these reasons, we affirm the District Court’s
    judgment of conviction.
    88