Statistical sampling in tax filings: new confirmation from the IRS

Tax Executive, The, May-June, 2004 by Mary Batcher

Statistical sampling is playing an increasingly important role in identifying deductions and credits for federal income tax purposes. The Internal Revenue Service has been responsive to questions about the appropriateness of and requirements for the use of statistical sampling in tax determinations. The creation of territory sampling coordinator positions and the issuance of a new revenue procedure addressing the use of statistical sampling in determining meals and entertainment (M&E) deductions are welcome efforts to be more responsive to the needs of the business community. Recently, the IRS released Revenue Procedure 2004-29, which "provides the statistical sampling methodology that a taxpayer may use in establishing the amount of substantiated meal and entertainment expenses excepted from the 50% deduction disallowance of section 274(n)(1)...."

The revenue procedure builds on the requirements outlined in the Large and Mid-Size Business Division's March 2002 IRS Field Directive on the Use of Probability Samples by Taxpayers (2002 Field Directive). (1) The M&E revenue procedure adds two new sampling provisions, which make it easier for business filers to use statistical sampling to estimate their M&E deductions and, by extension, other deductions and credits. The first of these provisions is the allowance of the use of a single sample taken from up to three years combined rather than the requirement of three separate annual samples; the provision results in a great reduction in sample size over the combined years. The second is the ability to use the standard statistical estimate without incurring a reduction for sampling variability if the estimate is sufficiently precise. Both of these provisions are described in this article.

Sampling Provisions of the M&E Revenue Procedure

Rev. Proc. 2004-29 includes many of the same provisions specified in the 2002 Field Directive.

Allowance of Multi-Year Samples. The revenue procedure states that up to three years can be combined into a single sample. This is a great help to taxpayers using statistical samples for tax filings. Samples are designed to achieve specified confidence and precision criteria, which determine sample size. Three separate annual samples require approximately three times as many sample selections to achieve the design criteria as would be required for one sample that covers three years. Therefore, the cost and effort associated with a sampling project are greatly reduced if multiple years can be combined into a single sample. While the IRS has in practice informally allowed multi-year samples for meals and entertainment, the M&E revenue procedure is the first explicit acknowledgement of their acceptability for tax filings.

Conditions for Use of the Point Estimate. The IRS position on statistical samples as described in the 2002 Field Directive and repeated in the M&E revenue procedure is that the most adverse limit of the confidence limit should be used rather than the conventional statistical estimate. The M&E revenue procedure, however, describes exceptions where the reduction to the estimated value is not required.

When an estimate is made using a statistical sample, the estimated value would be expected to be different if a different sample selection was taken from the same population using exactly the same type of sample design and the same sample size. To reflect the inherent variability, a statistical estimate will customarily be presented with an associated range, called the confidence interval, within which we expect the true population value to fall. In the example below, the standard statistical estimate called the point estimate is $1.5 million. The width of the confidence interval is $300,000, which is the plus/minus factor, called the margin-of-error, that is applied to the estimate to create the confidence interval. Our estimate is $1.5 million but the true value could be as high as $1.8 million or as low as $1.2 million in this example.

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If we are interested in ensuring that we do not overestimate the deductible amount and we do not care about underestimation, we can construct a one-sided confidence interval where we put all of the margin-of-error on one side of the estimate. The graphic below illustrates a one-sided confidence interval. The IRS safe harbor position is that the taxpayer should claim the least advantageous lower bound rather than the conventional point estimate. As illustrated in the graphics, the lower bound for the 90-percent two-sided confidence interval is the same as the lower bound for the 95-percent one-sided interval.

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Consistent with other IRS guidance and practice, the M&E revenue procedure requires the taxpayer to use the lower limit of the confidence interval rather than the statistically best single estimate. Thus, it is important to keep the interval as narrow as possible. The width of the interval is determined by many factors, but the size of the sample is one of the most important. Increasing the sample size narrows the width of the interval. Therefore, the control of the size of the "penalty" inherent in the IRS requirement to use the lower limit of the confidence interval is best achieved by increasing the sample size.