AN IRS PRODUCTION FUNCTION WILLIAM J. HUNTER * & MICHAEL A. NELSON **

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1 AN IRS PRODUCTION FUNCTION WILLIAM J. HUNTER * & MICHAEL A. NELSON ** Abstract - The effectiveness of the Internal Revenue Service (IRS) is assessed by estimating a production function for the years We provide estimates of the contribution of various factor inputs to output, including labor and capital at both the field and national office level. Output is measured by the value of additional individual income taxes and penalties assessed. We determine that several technological innovations introduced by the IRS in recent years have produced positive effects on production. However, we also find that the IRS can produce additional tax revenues at no additional cost if it were to alter its mix of inputs. INTRODUCTION Tax evasion has been an issue of longstanding concern to policymakers, and recent evidence suggests that the problem is especially serious today. The General Accounting Office (1994), for instance, estimates that the Internal * Department of Economics, Marquette University, Milwaukee, WI ** Department of Economics, Illinois State University, Normal, IL Revenue Service (IRS) failed to collect $127 billion in taxes in 1992, almost one-fifth of what taxpayers owed the government. Treasury officials point to lack of funding as an important contributing factor to the problem, 1 while oversight agencies such as the GAO have from time to time questioned (e.g., GAO, 1976, 1993, 1994) whether the IRS has used the resources it controls in the most effective manner. Interestingly, IRS efficiency tends to be overlooked in most of the analysis of tax evasion, and there has been little work directly related to the behavior of tax enforcement agencies. 2 Issues of IRS production and efficiency are further obscured by the fact that efficiency has been measured in a number of different ways, including revenue maximization and social efficiency. Should the IRS mission be to maximize federal government revenues, then efficiency would require the IRS to expend resources up to the point where the marginal cost of enforcement is equal to marginal tax revenue (Toma and Toma, 1986). From a social perspective, IRS enforcement is efficient when the marginal cost of additional enforcement effort is equal to the marginal social benefit of reduced evasion. Since taxation and tax evasion both involve social costs which exceed 105

2 NATIONAL TAX JOURNAL VOL. XLIX NO. 1 tax revenues, IRS efficiency implies that the marginal tax yield from increased enforcement should exceed the IRS s marginal cost of enforcement (Sandmo, 1981; Slemrod and Yitzhaki, 1987). For the purpose of this study, the target function of the IRS is taken to be the maximization of net revenue collections. A necessary condition for this is that the IRS allocates the resources at its disposal in a cost-effective manner. It is this issue that has been recently called into question (Beron, Tauchen, and Witte, 1992; GAO, 1993), and it is this issue that is of concern here. Specifically, we assess the effectiveness of the IRS in the enforcement of the individual income tax by estimating an IRS production function. In so doing, we provide estimates of the contribution of various factor inputs to IRS output. In addition, the model allows for factor-neutral technical progress to be incorporated into the estimation. IRS output is measured by the value of additional taxes and penalties assessed through IRS audits, and the model is estimated using annual data for the years We determine that several technological innovations introduced by the IRS in recent years have produced positive effects on production. However, we also find that the IRS can produce additional tax revenues at no additional cost if it were to alter its mix of inputs. THE ORGANIZATION OF IRS TAX ENFORCEMENT ACTIVITIES The tax enforcement activities are overseen by the national office in Washington, D.C., and are carried out by offices in the field. Included in the latter are 7 regional offices, 63 district offices, and 10 service centers. The service centers process tax returns and conduct certain audits through correspondence with taxpayers. District offices operate under the direction of the national and regional offices and carry out programs for selecting and auditing tax returns. These offices, most of which have boundaries that are contiguous with individual state borders, are responsible for the direct interaction between the IRS and taxpayers through the divisions of collection, examination, taxpayer services, etc. The national office houses a planning division, human resource and support divisions, information system development divisions, and a variety of computer services. Included under the computer service umbrella are the tax systems division, the compliance services division, and two large computing centers in Detroit, Michigan, and Martinsburg, West Virginia. IRS employment of both labor and capital has generally increased in the national office relative to the field over the past four decades. Figure 1 indicates the number of national and field office employees on a taxpayer adjusted basis for the years Beginning in 1955, the IRS employed national office workers for every ten thousand taxpayers. By 1990, national office employment per ten thousand taxpayers rose to 0.741, for an increase of about 61 percent. Field office employment also rose over the same period, albeit at a much slower rate. In 1955, it stood at workers per ten thousand taxpayers and increased to workers by 1990, an increase of approximately 20 percent. Figure 2 illustrates the amount of national office capital stock and its share of total IRS capital stock. During the early to mid-1960s, national office capital stock more than quadrupled, 106

3 FIGURE 1. IRS Employment per 10,000 Taxpayers, Source: IRS, Annual Reports. rising from just under $14 million in 1962 to $55 million by 1965 (1982 dollars). Perhaps more significant, this growth corresponded with a shift of capital resources away from the field offices 1 and to the national office. Prior to 1963, the national office share remained below 25 percent. Following the growth during the 1960s, the share rose 1 to 50 percent, and, except for the mid 1970s, the national office share of capital has fluctuated within a percent share band over the remainder of the period. This change in the allocation of resources between the national and field offices is coincidental with several important technological changes which have had a significant impact on tax enforcement. These changes will be discussed in the next section. THE SELECTION OF TAX RETURNS FOR AUDIT IRS audit activity demonstrated spectacular variation over these four decades. For example, as indicated in Figure 3, the percent of returns audited steadily increased during the 1950s, peaking at almost 5.55 percent in Then, starting in 1964, audit rates began a steady decline, with the exception of a slight rise in audit rates in the mid-1970s. By 1990, less than one percent of all individual income tax returns were audited by the IRS. The general decline in audit activity over this period coincides with a number of technological initiatives undertaken by the IRS during the 1960s. In 1962, the IRS instituted the first computerized 107

4 NATIONAL TAX JOURNAL VOL. XLIX NO. 1 FIGURE 2. IRS National Office Capital Stock, Source: IRS, Annual Reports. audit selection system. This system constituted an improvement over the manual process of audit selection used earlier, but was still inadequate because it realized only marginal improvements in identifying returns with high audit potential (GAO, 1976, p. 13). Two programs launched later in the decade had a much more significant impact on tax enforcement and agency productivity. The first, the Taxpayer Compliance Measurement Program (TCMP), began in 1964 with a statistical review of 1963 delinquent accounts and returns. The TCMP expanded throughout the 1960s, first with detailed field audits of individual returns in 1964 and then with specialized audits and analysis through 1967 (IRS, 1966). From the TCMP data, the IRS developed an additional compliance tool, the selection of returns for audit by discriminant function, DIF. The discriminant function analysis is a computerized selection process of individual and corporate returns for audit. The selection criteria are a set of individual tax items, all of which are weighted for probability of error or evasion. The first set of audits based on the DIF analysis occurred in 1969 in which a subset of income classes were reviewed. Additional income classes were added in 1970 and further refinements to the DIF system were made in subsequent years (GAO, 1976). Throughout the 1980s, the IRS further enhanced the audit process with computerized matching of third party documents and computer scanning for mathematical accuracy (Dubin, Graetz, and Wilde, 1990). The DIF technique seems to have enhanced audit efficiency by permitting the IRS to focus its audit efforts on 108

5 FIGURE 3. Percent of Individual Income Tax Returns Audited, Source: IRS, Annual Reports. those individuals with the highest probability of underpayment of taxes. As a consequence, audit productivity improved as measured by two standards. The first is the percentage of audits resulting in no tax change. 3 This percentage dropped from 43 percent in 1968 to 23 percent by 1975 and continued to decline at a more gradual rate through the 1980s. By 1990, it stood at 11 percent (IRS, ). The second measure, illustrated in Figure 4, is additional taxes and penalties assessed. In 1963, the additional taxes and penalties assessed by the IRS amounted to about $700 (1982 dollars) per return audited. This amount increased to just over $1,000 per audit following the introduction of the TCMP process and rose to a high in excess of $4,500 in In 1990, the average stood at $4,400. THE IRS PRODUCTION FUNCTION While the IRS has undergone a number of resource and technological changes in the last 30 years that have improved its ability to enforce the tax code, it is not certain that it has allocated the resources at its disposal in a costeffective manner. This requires that the IRS allocate its resources such that the marginal output, marginal delinquent taxes assessed (MTR), equals the marginal factor cost (MC) for all inputs: 109

6 NATIONAL TAX JOURNAL VOL. XLIX NO. 1 FIGURE 4. Additional Taxes and Penalties per Audit, (1982 dollars) Source: IRS, Annual Reports. 1 MTR l MC l = MTR k MC k. For example, equation 1 indicates that an additional dollar spent on labor (l ) should generate the same amount of marginal taxes as an additional dollar spent on capital (k). Consequently, if labor produced a larger marginal return per dollar than capital, the IRS would be better served if it were to divert resources away from capital and hire additional units of labor. To assess the relative contribution of national and field office inputs to IRS output, a production function for this agency is estimated. In this analysis, it is assumed that the output (P) is tax enforcement and that such enforcement can be adequately measured by the additional taxes and penalties assessed by the IRS in conjunction with the personal income tax. 4 Our measure of output is consistent with how the agency itself evaluates its performance in its Annual Reports. However, we acknowledge that cost-effective tax enforcement is not the only possible performance measure that could be used to evaluate this agency. Other goals, such as ensuring the administration of the tax code yields outcomes that are consistent with societal norms of horizontal and vertical equity, are also important. In addition, our cost measures are limited to agency costs; other 110

7 social costs associated with compliance with the income tax (including taxpayer audit costs) are not considered. 5 The factors of production are taken to include labor (L), capital (K), and travel (T). Separate inputs are utilized for the field and national offices and are designated by the subscripts f and n, respectively. The production function may therefore be written as 2 P = f ( L f, L n, K f, K n, T f, T n ). Assuming Cobb Douglas technology, and allowing for factor-neutral technical progress, the production function may be expressed in log form as 4 dp dl f w f Since the coefficients of equation 3 are output elasticities (e.g., α 3 = dp/dl f l f / p), the numerator of equation 4 can be expressed as a function of these coefficients. Substituting these expressions into equation 5 and simplifying yields 5 dp dp = dl n = dk f = r = w n dp dt f = l dp dt n. l dp dk n r 3 p = α 1 + α 2 b(τ) + α 3 l f + α 4 l n + α 5 k f + α 6 k n + α 7 t f + α 8 t n α 3 α 4 α 5 = = = w f l f w n l n rk f α 7 α = = 8 t f t. n α 6 rk n where the logarithms of the variables are denoted in lowercase letters, α 1 is a constant term, α 2 represents the influence of the technological change measure on output, b(τ) is a measure of technical change at time period τ, and variables α 3 α 8 represent the output elasticities. In the empirical analysis below, technical change is modeled as a time trend variable designed to capture the influence of the computerization of the audit selection process and other innovations discussed above. Assuming that the IRS cost of capital is the same between the field offices and the national office, cost efficiency requires That is, cost efficiency requires that the estimated coefficient for each input, weighted by the total cost of that input, be equal across inputs. DATA Equation 3 is estimated with annual data for the years All data are taken from the Annual Report of the IRS, and nominal variables are converted into real terms using the GNP deflator (1982 = 100). A further description of the data, including descriptive statistics, can be found in the Appendix. The real capital stock variables used in this analysis are constructed from IRS equipment expenditure data. The 111

8 NATIONAL TAX JOURNAL VOL. XLIX NO. 1 technique employed to estimate capital stock follows Browne, Mieszkowski, and Syron (1980). For any given year, capital stock is calculated by adding that year s real capital expenditures to the depreciated, cumulative capital expenditures from previous years. Investment in this sector is assumed to depreciate throughout the period of analysis at the rate of per year, the estimated depreciation rate for office, computing, and accounting machinery (Hulten and Wykoff, 1981). The expenditure data are deflated by the producer price index for finished capital equipment goods. 6 We considered a number of different approaches to assess the influence of technical change on IRS productivity. First, we entertained the possibility that the introduction of the DIF system is best characterized as a once-and-for-all, step-function innovation in technology. To test for this, we divided the sample at various points, beginning with 1969 and proceeding year-by-year until 1975, and performed the Chow test for model stability. For each year where the sample was divided, an F test did not reject the constrained hypothesis that the model was stable over the entire period. Second, we added several alternative time trend variables to the basic estimating equation to model technical change as a learning process over the period. 7 One specification was simply a time trend variable for the entire period of the analysis, another took on a value of zero before 1970 and incremented by one through 1975, and a third was defined similarly except that the value increased by one throughout the period. 8 Of the three, the last had the highest degree of statistical significance and is included in the estimation of equation 3 reported below. EMPIRICAL RESULTS The ordinary least-squares results are reported in Table 1. 9 Overall, the model performs well when judged by the adjusted R square and the F statistic. The findings for the individual righthand-side input variables indicate that IRS employment of capital stock in the national office and labor in the field have contributed positively to IRS output. National office travel also exhibits a positive association with the amount of taxes and penalties assessed. TABLE 1 IRS PRODUCTION FUNCTION ESTIMATES Dependent variable: real taxes and penalties recommended Independent variable: Labor national office (l n ) * (4.65) Labor field office (l f ) (1.64) Capital stock national office (k n ) * (4.05) Capital stock field office (k f ) ** (2.24) Travel national office (t n ) * (5.29) Travel field office (t f ) (1.07) Technical change (b(τ)) * (4.87) Constant (4.07) R squared adjusted 0.99 Standard error of the estimate Number of observations 36 * Significant at the 1 percent level. ** Significant at the 5 percent level. Notes: All variables are expressed in log form prior to estimation. Absolute values of t statistics are in parentheses. 112

9 The positive and significant coefficient for the technical change variable indicates that following the introduction of the DIF audit selection system (and subsequent refinements), IRS productivity was enhanced each year thereafter. 10 The DIF analysis is modified with the periodic introduction of additional statistical techniques and with new information generated through subsequent TCMP audits. The contribution of the expansion of national capital equipment and the concurrent technological changes has had a significant and positive impact on the detection of unreported taxes over a time period when the IRS significantly reduced its audit activity. While these results are not inconsistent with the view that the IRS operates in a cost-efficient manner, the evidence for the other inputs in the model calls this into question. Specifically, the marginal products of national office employment and field office capital stock are both negative. 11 The negative marginal output elasticity of national office labor is especially interesting in light of the large increases in its levels of employment over the period of study. It is conceivable that the number of employees has expanded well beyond its efficient level. Further, the finding is consistent with the conclusion drawn by the GAO (1976, 1993) that the IRS has had difficulties in allocating labor resources to their most productive uses during this time period. Although the GAO has primarily focused on staffing imbalances among the field offices, our result points to the possibility that the national office is overstaffed. Indeed, the evidence presented here suggests that the IRS is operating on the negative portion of the marginal productivity curve of national office employment. The negative coefficient for field equipment capital stock is, perhaps, more puzzling. It could, for example, reflect inadequate training of employees to an ever-changing technology. Alternatively, it may represent information overload. IRS employees might have access to so much data that search time for individual taxpayer information (e.g., interest and dividend income reported to another regional office) actually increases as does the complexity of their data analysis. Overall, our results support the GAO contention that significant output gains could be realized by the IRS if it were to reallocate some of its resources. For example, our output elasticity estimates indicate that a one million dollar increase in national office equipment would increase the amount the IRS assesses in additional taxes and penalties by nearly $77 million (1982 dollars), in the first year alone. 12 If this investment were financed through a reduction in national office staff, even greater gains would be achieved. Conclusions Concerns over tax evasion and the growing tax gap have heightened the call for greater enforcement effort on the part of tax authorities. To this end, the IRS has consistently requested additional resources to meet the noncompliance challenge. However, it is not altogether clear that improvements in IRS detection necessarily require a larger budget. Our estimates of the IRS production function point to considerable room for improvement in tax enforcement, not through increased resources, but rather through a more judicious use of resources currently at hand. 113

10 NATIONAL TAX JOURNAL VOL. XLIX NO. 1 Our estimates indicate that the marginal product on IRS inputs varies considerably. One particularly disturbing finding is that labor in the national office is characterized by a negative marginal product. Simply stated, the current levels of national office staffing may actually impede the process of tax enforcement. Therefore, productivity could be enhanced without additional resources through a reduction in national office labor. A reduced work force would free up funds that could be used to increase capital in that office so as to take greater advantage of computer technology. Alternatively, and in particular, if institutional barriers preclude a shrinkage of the total labor force, employees in that national office could be reassigned to the field where their marginal product is positive. In summary, this paper has raised a number of questions about the allocation of resources under the control of the IRS. Our findings, in combination with the concerns raised by the GAO, point to the very real possibility that IRS effectiveness could be enhanced without any additional resources. In any event, further study is warranted, particularly if the impact of IRS enforcement on noncompliance remains an important policy concern. A more sophisticated model of IRS production might shed additional light on these issues. ENDNOTES The authors wish to thank Peter Toumanoff, Farrokh Nourzad, James Alm, Mark Toma, two anonymous referees, and the editor of this journal for comments on earlier versions of this paper. The usual caveat applies. 1 This seems to be an issue of concern for recent IRS commissioners, as virtually all have claimed that an additional budgetary dollar would yield several dollars in marginal revenue to the treasury (Slemrod, 1990). See also Malanga (1986) and Toma and Toma (1986). 2 Noteworthy exceptions include Toma and Toma (1986), Congleton (1986), Yitzhaki and Vakneen (1989), and Hunter and Nelson (1995). 3 See GAO (1976), especially chs. 3 and 4, for a more complete discussion of the DIF audit selection system and its effectiveness. 4 Obviously, an important aspect of enforcement is deterrence from tax evasion as well as detection of evasion. While our measure of output (P) pertains to the latter, it can be argued that detection and deterrence are directly related. Indeed, this is assumed in much of the theoretical literature on tax evasion. 5 We thank an anonymous referee for making this point. 6 Due to a lack of data, real capital expenditures (field and national) are assumed to be at constant 1955 levels for all years prior to As discussed in the preceding section a number of innovations were introduced over the decades of the 1970s and 1980s, including occasional updates and improvements in the DIF system and, more recently, computerized matching of third party documents and scanning for mathematical accuracy. We thank an anonymous referee for the insight that technical change is most appropriately modeled as a learning process on the part of the IRS. 8 A referee suggested that the technical change variable should start in the mid-1960s, the beginning of the large increase in national capital stock. In response, we estimated the empirical model with a number of different beginning points for the technical trend variable starting with These variables were never significant and the overall explanatory power of the model was reduced. Our finding of no significant technical change prior to 1970 is consistent with IRS reports of efficiency gains beginning that year. 9 The Durbin Watson test indicated no need to correct for first-order autocorrelation. 10 The conclusions regarding the influence of the capital, labor, and travel inputs on IRS output are not affected by whether the technical change variable is included in the model. 11 The interpretation of these results, however, should be approached with some caution due to the simplicity of the model and relatively high level of aggregation of the inputs. 12 This calculation is based on sample means and the estimated elasticities for the model where the dependent variable is defined on a total basis, i.e., national capital stock elasticity of REFERENCES Beron, Kurt J., Helen V. Tauchen, and Ann Dryden Witte. The Effect of Audits and Socioeconomic Variables on Compliance. In 114

11 Why People Pay Taxes: Tax Compliance and Enforcement, edited by Joel Slemrod, Ann Arbor: The University of Michigan Press, Browne, Lynn E., Peter Mieszkowski, and Richard F. Syron. Regional Investment Patterns. New England Economic Review (July/ August, 1980): Congleton, Roger. The Allocation of Tax Enforcement Effort. George Mason University. Mimeo, Dubin, Jeffrey A., Michael J. Graetz, and Louis L. Wilde. The Effect of Audit Rates on the Federal Individual Income Tax, National Tax Journal 43 No. 4 (December, 1990): Hulten, Charles R., and Frank C. Wykoff. The Measurement of Economic Depreciation. In Depreciation, Inflation, and the Taxation of Income from Capital, edited by Charles R. Hulten, Washington, D.C.: The Urban Institute Press, Hunter, William, and Michael Nelson. Tax Enforcement: A Public Choice Perspective. Public Choice 82 (January, 1995): Malanga, Frank. The Relationship between IRS Enforcement and Tax Yield. National Tax Journal 39 No. 3 (September, 1986): Sandmo, Agnar. Income Tax Evasion, Labour Supply, and the Equity-Efficiency Tradeoff. Journal of Public Economics 16 No. 3 (December, 1981): Slemrod, Joel. Optimal Taxation and Optimal Tax Systems. Journal of Economic Perspectives 4 No. 1 (Winter, 1990): Slemrod, Joel, and Shlomo Yitzhaki. The Optimal Size of a Tax Collection Agency. Scandinavian Journal of Economics 89 No. 2 (1987): Toma, Eugenia F., and Mark Toma. Congressional Control Model of Treasury Revenue Collection. Southern Economic Journal 52 (July, 1986): U.S. General Accounting Office. How the Internal Revenue Service Selects Individual Income Tax Returns for Audit. Washington, D.C.: Government Printing Office, U.S. General Accounting Office. Improved Staffing of IRS Collection Function Would Increase Productivity. Washington, D.C.: Government Printing Office, U.S. General Accounting Office. Tax Gap: Many Actions Taken, But a Cohesive Compliance Strategy Needed. Washington, D.C.: Government Printing Office, U.S. Treasury, Internal Revenue Service (IRS). Annual Report. Washington, D.C.: Government Printing Office, Yitzhaki, Shlomo, and Yitzhak Vankeen. On the Shadow Price of a Tax Inspector. Public Finance 44 No. 3 (1989): APPENDIX DESCRIPTIVE STATISTICS OF VARIABLES USED IN THE MODEL a Sample Mean Name Description (Standard Deviation) P real additional taxes and penalties recommended after examination 1,731,500,000 individual income tax (2,219,500,000) National Office Field Offices L IRS personnel number of employees at close of year 4, ,513 (1,478.4) (19,525) K Estimate of the real capital stock b 72,856,000 54,950,000 (37,673,000) (41,327,000) T Real IRS costs, travel 5,656,200 36,705,000 (9,904,900) (45,166,000) a Unless otherwise noted, all data are taken from the Annual Reports of the IRS, With the exception of the capital stock variables, all nominal data are deflated by the GNP deflator (1982 = 100). Capital stock estimates are deflated by the producer price index for finished capital goods (1982 = 100) taken from the 1993 Economic Report to the President, p b See the text for a discussion of how this variable is constructed. 115