In
United States v. Ukwu, 2013 U.S. App. LEXIS 23513 (4th Cir. 2013),
here, the Fourth Circuit affirmed a tax loss calculation based on what it viewed as a proper statistical inference from a sample of the population. I want to address that issue in this blog.
The cases where this type of statistical inference is drawn as to the tax loss usually appear in tax return preparer prosecutions. In these cases, the IRS discovers a pattern of errors in some number of returns prepared by the target of the investigation. It will do some level of investigation and determine that some percentage of the errors -- usually a very high percentage -- represent the preparer's fraud. The IRS will then project that percentage over the universe of returns prepared by the preparer to determine, by statistical inference, the tax loss. This type of inference is usually not presented in the trial to determine guilt or innocence because a more exacting standard of proof than mere inference is required but rather is presented at sentencing to determine the relevant conduct (which can include noncharged years or returns, acquitted years or returns, etc.). From a statistical perspective, the initial inquiry is whether the sample size is adequate. See generally the Wikipedia entry on Sampling (Statistics),
here. Let's say, for example, that the preparer prepared 1,000 returns, that the IRS audited 10 and that 9 out of 10 claimed fraudulent deductions or credits resulting in average underpaid tax of $1,000. Can a fair inference be drawn that 90% of the remaining unaudited 990 returns not only contained fraudulent deductions but that their average amount of fraudulent deductions was $1,00? What if the number audited were 100, with similar percentages and amounts? What if the number audited were 200? 300? Would it be important that the taxpayers audited were randomly drawn? And what does randomly drawn mean?
I can't write a book on statistics, but there are any number of scholarly books and articles on the subject. One popular book is Nate Silver,
The Signal and the Noise (2012),
here. I will mention Silver again below, although I can't resist saying that Silver was the "gold standard" in projecting the outcome of the 2012 presidential elections. See Nate Silver's Wikipedia entry
here. I mention also Charles Whelan,
Naked Statistics: Stripping the Dread from the Data (2012),
here.
Let's see what the Fourth Circuit did in its statistical exegesis in
Ukwu. I note at the outset that opinion is an unpublished per curiam opinion. I won't go into a rant about unpublished opinions, not to mention unattributed per curiam opinions. I have done that elsewhere and, besides, nobody is or should be interested in my opinions on such opinions. I do say that it is some type of "junior" opinion deemed to be of less significance than published opinions in terms of adding to the law. (Perhaps this could be compared to the difference between Memorandum and Regular Tax Court Opinions.) Let's get right to to opinion:
The Court gave us the key background (but not the details) as follows:
After Mr. Ukwu's jury conviction, the government estimated how much money Mr. Ukwu took from federal and state coffers. It concluded that Mr. Ukwu's criminal behavior created tax losses of $2.1 million, which corresponds to a base offense level of 22 under § 2T4.1 of the United States Sentencing Guidelines Manual.
On appeal, Mr. Ukwu takes issue with the $2.1 million estimate, arguing that a preponderance of the evidence shows that his ill-gotten gains amounted to less than $1 million. Specifically, he argues that the district court's method of estimating the tax shortfall was unsound because it used a small, flawed sample of tax returns to make inferences about another 1000 returns that he prepared. Based in part on its estimate, the district court sentenced Mr. Ukwu to 51 months in prison. Mr. Ukwu filed a timely appeal.
