Statistical sampling in tax filings: new confirmation from the IRS.

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.

[ILLUSTRATION OMITTED]

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.

[ILLUSTRATION OMITTED]

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.

The M&E revenue procedure offers some relief from the sampling penalty of the lower limit. Relative precision is one of several ways that we can measure sampling variability. Smaller relative precision is better than larger. If the relative precision of the M&E statistical sample is 10 percent or smaller, based on the estimate of the amount of the expenses that are 100-percent deductible but were erroneously classified as subject to the 50-percent limitation, the revenue procedure allows the use of the point estimate rather than the lower limit. There is always a trade-off between the cost associated with increasing the sample size to achieve better precision and the benefit associated with better precision. This becomes even more important when there is the effect of dropping off a cliff as soon as the 10-percent precision is exceeded, even by a very small amount.

Relative Precision Calculation. Another requirement of the revenue procedure is that the certainty stratum and strata with high sampling rates (greater than 80 percent) are to be excluded from the calculation of relative precision. This is an unusual requirement that is not consistent with standard statistical practice. Without going into the technical details of the relative precision calculation, (2) the exclusion of these items from the relative precision calculation combined with the requirement to base the precision on the amount that moves from 50-percent to 100-percent deductible rather than the total deductible amount, makes it much more difficult to achieve the 10-percent precision target needed to avoid the haircut of the lower limit. For example, if a sample of size 300 achieves 10-percent relative precision on the 100-percent deductible amount using standard statistical estimates, the sample size might jump to 800 or 1,000 to achieve 10-percent relative precision, calculated as specified in the revenue procedure on the amount that moves to 100-percent deductible.

Other Sampling Provisions. The revenue procedure explicitly prohibits the use of judgment samples. Judgment samples are those that are not randomly selected from the entire population of interest. (3) They are often constructed in an attempt to make them representative of the population but deliberate choice rather than the laws of chance governs the selection of elements into the sample. While judgment samples have been accepted for filings and also used by the IRS during their audits, they are not allowed under the provisions of the revenue procedure.

Another provision of the revenue procedure is that taxpayers can only apply the results to the years included in the sample. This precludes the application of a deductible rate determined from the sample to other years going forward or back.

Other sampling provisions of the revenue procedure relate primarily to technical details of the sample design and estimation and the documentation requirements and are not addressed here. In addition, the revenue procedure goes into some detail about how de minimis fringe expenses are to be handled but, in general, their treatment as part of a sample is not different from their treatment in an entire population review.

M&E Safe Harbor Sampling Implications

The revenue procedure on M&E sampling formalizes practices the IRS has already been following. Its positive effect is the recognition of the acceptability of statistical sampling for M&E tax filings and of multi-year samples. Another positive element is the recognition that, if the sample estimates are sufficiently precise (in the sense of having relatively low sampling variability), the IRS will allow the use of the standard statistical point estimate. This positive indicator, however, must be weighed against the practical difficulties of reviewing large enough samples to meet the IRS requirements. The negative effect of the sampling specified in the revenue procedure is the requirement to use the lower limit of the confidence interval rather than the standard statistical estimate.

Extensions of the M&E Sampling Rules

Sampling for M&E is among the more basic and straightforward of tax sampling situations. The issuance of Revenue procedure 2004-29, while issued specifically for M&E, can be viewed as an indicator of what might eventually become acceptable in other, more difficult, tax sampling situations. The extension of multi-year sampling to other settings would be the most beneficial expansion of the sampling logic of the revenue procedure.

One of the most difficult sampling situations is the determination of research expenditures that qualify for the research and experimentation (R&E) tax credit. It is difficult because the population tends to be highly variable, requiring a larger sample to drive the sampling variability to anywhere near 10 percent and it is expensive and intrusive to make a determination about the qualifying activity for each sampled project or employee, making it costly to achieve large samples. The acceptance of multi-year samples in R&E would make it less costly and less disruptive of their business activities for companies engaged in research and experimentation activities to claim the tax credit. The resulting reduction in sample size would also make it easier for the IRS to audit the sample. As it stands, if three years of annual R&E samples are large enough to meet the 10-percent relative precision goal, it is doubtful that the IRS would be able to dedicate the resources needed to complete the audit in a reasonable time. A multi-year approach to R&E samples would be a win for both companies and the IRS.

The other positive extension of the sampling logic included in the revenue procedure is the relaxation of the requirement to use the lower limit of the confidence interval when the sample is sufficiently precise. It is easy to understand the IRS's fear of bad samples by taxpayers that motivates the lower limit requirement just as it is easy to understand a corresponding fear by taxpayers that the IRS would design bad samples and use the results against them. There are better solutions to avoiding bad samples, however, than a blanket requirement to use the most adverse limit of the confidence interval. The recognition that for some low level of sampling variability, all sides can live with the point estimate is a good beginning. Nevertheless,, the specified method of dropping the certainty stratum and strata with high sampling rates from the denominator of the calculation does not represent good statistics and may even provide an incentive for bad sample design by discouraging some of the best methods of control of sampling variability, namely larger certainty and high sampling rate strata. Another approach to controlling the risk of bad samples might be to use a joint process to reach an agreed-upon sample design and sample size with an agreement to use the point estimate in a pre-filing context.

Conclusion

The issuance of Rev. Proc. 2004-29 is a step forward in providing taxpayers the flexibility to claim M&E deductions they might not otherwise be able to claim. While it includes some less than optimal sampling provisions, there is much to like in this document, beginning with the recognition of the appropriateness of statistical sampling for estimating M&E deductions, the explicit allowance of multi-year samples, and the recognition that the IRS safe harbor requirement to use the lower limit of the confidence interval may be waived when the sample is sufficiently precise. Although directed at M&E, these rules developed by the IRS statistical team with input from outside practitioners is a public statement of the IRS's latest thinking about the appropriate use of statistical sampling and is an indicator of rules that might apply to cost segregation, inventory, R&E credits, and other tax sampling areas.

(1) For additional information about the Field Directive, see Mary Batcher, "Statistical Sampling: A Potential Win for Business Taxpayers," 53 Tax Executive 464-66 (2001).

(2) There are almost always items in the population that are likely to result in large changes in the estimates, depending on whether they happen to be selected for the sample or not. These are often the items with the highest recorded value. To minimize the negative effect of these items on the sampling variability, they are often taken into the sample with certainty--that is to say, with 100-percent probability of selection. During estimation, they represent only themselves and are not inflated to represent other items in the population. There are additional items in the population that are not large enough to require sampling with certainty but are large enough that they are selected with greater frequency because of their importance in reducing sampling variability. The revenue procedure requires taxpayers to estimate the amount that moves from a 50-percent limitation to 100-percent deductible excluding strata where 80 percent or more of the population was sampled and use that in the denominator of the calculation of relative precision, even though these strata are part of the sample and the sampled items in them are reviewed. Since these are typically the highest dollar items, their exclusion from the denominator of the relative precision calculation makes the relative precision percentage higher than it would be if standard statistical procedures were followed and makes it much harder to achieve the 10 percent needed to avoid the penalty of taking the lower limit of the estimated deductible amount.

(3) A probability or statistical sample is one in which every element of the population has a known, non-zero, chance of being selected into the sample. Judgment samples, by contrast, are often selected to include certain elements thought to make the sample representative. There is no way, however, to quantify the selection probabilities associated with the different elements of the population and, thus, no way to objectively measure the merits of the sample.

MARY BATCHER is the National Director for Statistics and Sampling for Ernst & Young LLP. She has successfully directed many sampling studies for tax filing purposes. She was formerly employed by the Internal Revenue Service. She holds a Ph.D. in statistics from the University of Maryland.