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The Pedagogy of Tax Evasion: Its Extent and Its Determinants.

CHRIS PAUL [*]

This pedagogical note develops a model of individual choice and a comprehensible and functionally realistic framework that explains how the size of the underground economy or the extent of aggregate income tax evasion can be estimated. It also describes three models for estimating the size of the underground economy for the U.S. and provides a formal but easily understood analytical model of determinants of the extent of aggregate income tax evasion. The latter model is useful in serving as the basis for empirical estimates of determinants of income tax evasion and is useful in enhancing student understanding economic behavior through student projects. (JEL A23, H26)

Introduction

Income tax evasion presents several characteristics that make it an effective subject for teaching economic concepts and tools. First, it offers the opportunity to apply marginal analysis and demonstrate the use of the equimarginal principle in the choice calculus of economic agents. Second, the illegal nature of tax evasion allows the incorporation of risk and ethical considerations into the individual's choice calculus. Third, income tax evasion is illegal and by its very nature leaves no directly observable data. Thus, its magnitude must be inferred, that is, estimated from secondary sources. This means that alternative methods of measurement may be applied and their results compared. This exercise exposes the student to techniques of national income accounting and deductive logic. Fourth, it demonstrates the use of empirical methods and results of estimating income tax evasion by applying methods of measurement.

There is extensive literature addressing the determinants of tax evasion behavior or, alternatively stated, the size of the underground economy. Aside from a variety of principally theoretical models of tax evasion behavior (see, for example, Falkinger [1988], Allingham and Sandmo [1972], Klepper et al. [1991], Das-Gupta [1994], and Pestieau et al. [1994]), there are a number of studies on such behavior using questionnaires or experiments [Spicer and Lundstedt, 1976; Friedland, 1982; Spicer and Thomas, 1982; Benjamini and Maital, 1985; Alm et al., 1992; Baldry, 1987; De Juan, 1989; Thurman, 1991] or, in a few cases, what De Juan et al. [1994] refer to as official data [Clotfelter, 1983; Slemrod, 1985; Pommerehne and Weck-Hannemann, 1989; Erard and Feinstein, 1994] such as audit and income tax data. Indeed, the issue of the size of the underground economy as measured by the extent of income tax evasion, which consists essentially of economic transactions that are not reported or are underreported to the gover nment tax collection authority, was the subject of an entire issue of Public Finance/Finances Publiques [1994].

In order to comprehensively cover the economic issues associated with tax evasion, the first section of this study presents an individual choice model of income tax evasion which incorporates expected net monetary value of avoiding taxes, risk preferences, and guilt as arguments in the choice function. The second section offers a model of aggregate income tax evasion. The third section discusses the three primary methods used to estimate the extent of income tax evasion and presents selected estimates of tax evasion applying each model. The fourth section provides concluding remarks.

A Choice Model of Tax Evasion

Here, a simple analytical model is developed to explain the choice to evade income taxes. It should be emphasized to the student that the choice of reporting or not reporting income is subject to the same principles as other economic choices. Individuals make decisions based on the relationship between marginal benefits and marginal costs. Consequently, the methodology developed here is applicable in general form to a vast array of other individual choice issues. Students may be assigned the task of identifying and modeling other choice behaviors, such as the decisions to vote or to migrate.

We begin by assuming the economic agents are risk-neutral utility maximizers, who generate economic value in the form of income. The economic agents have a choice of whether or not to report their income to the tax-collecting authority, as reported income creates a tax liability. In this simple model, the choice to evade taxes is a function of the utility (U) generated by the monetary gain (M) and the disutility associated with the guilt (G) of cheating:

U = f(M, G). (1)

In the more specific formulation, the arguments are the marginal tax rate, the probability of discovery and the form and magnitude of punishment if discovered, and the guilt or shame resulting from evading taxes. For simplicity, the exposition of the income effects of tax evasion is addressed first.

It is generally accepted that the size of the underground economy is affected by income tax rates [Clotfelter, 1983; Slemrod, 1985; Pommerehne and Weck-Hannemann, 1989; Feige, 1994]. Higher marginal tax rates increase the benefit, in terms of a reduced tax liability, of not reporting taxable income. In application, Clotfelter's [1983] simulations based on actual audited individual tax returns show that tax bills resulting in marginal tax rate reductions are expected to decrease tax evasion.

Economic agents are able to reduce their tax liability, that is, increase their net after-tax income, by not reporting or by underreporting income. The following discussion is based on the model presented by Rice [1992]. This benefit can be presented in equation form:

eb = G - tR, (2)

where G is gross before tax income, t is the marginal tax rate, and R is unreported income. From this simple formulation, net benefits of tax evasion are positively related to the marginal tax rate and the level of unreported income. The expected cost of tax evasion is given by:

ec = [(ftU) + FC] P(U), (3)

where f is the fine associated with tax evasion, EC is the fixed cost of an audit, and P is the probability of an audit (which is a function of the level of unreported income). It is assumed that [P.sub.U] [greater than] 0 and [P.sub.UU] [less than] 0.

Agents will choose to either not report or underreport their taxable income based on the net benefits of the choice [Friedland, 1982; Spicer and Thomas, 1985; De Juan, 1989]. Combining (2) and (3) yields the net monetary benefit function:

E(N) = G - tR{[(ftu)+FC]P(U)}. (4)

The first order condition is given by:

U = [l/f + P(U)[[P.sup.-1].sub.U]]- (FC1ft). (5)

From (5), if U has a large effect on P and FC is relatively small, it can be seen that the size of unreported income, R, is an increasing function of t and f and a decreasing function of FC.

Two additional considerations may be presented to students to enrich the presentation. First, the foregoing discussion addresses the income/wealth calculus for evading taxes by underreporting income. Implicit in this treatment is the assumption of risk neutrality on the part of the decision maker. The incorporation of risk into the analysis offers an opportunity to present and discuss how decisions are affected by the presence of risk. Second, the discussion has been free of any ethical or moral considerations. Following is a brief presentation of how these topics can be introduced into the discussion.

The Consideration of Risk

First, note that a risk-neutral individual will always select the alternative with the highest expected value, and will be indifferent to alternatives with the same expected value. He will place the same value on a 0.5 chance of winning $2.00 and receiving $1.00 with certainty. Hence, a risk-neutral decision maker will evade taxes as long as there is a positive expected value.

Alternatively, the risk-averse individual, given a choice of alternatives with the same expected value, will prefer the certain outcome to the risky one. This results in the risk-averse individual requiring a premium of return to undertake tax evasion. Hence, they will require a greater expected net benefit from tax evasion before choosing to evade taxes. The effect of risk-taking behavior has the converse result.

Ethical Considerations

From an ethical perspective, the manner in which the individual decision maker views the activity of evading taxes will affect the decision to engage in the evasion. Thus, the belief that evasion is unethical will generate feelings of guilt, which will result in a reduction of utility. Any information or rationalization that reduces feelings of guilt will induce more tax evasion.

Akerlof and Dickens [1982, p. 307] construct a model of cognitive dissonance wherein individuals, "can manipulate their own beliefs by selecting sources of information likely to confirm 'desired' beliefs." The implication is that individuals desiring to evade taxes can use filtered observations on the behavior of government and government officials to support or rationalize their decision.

Thus, either unpopular policies or political malfeasance will reduce the cognitive dissonance of tax evasion and increase the degree of tax evasion. The argument is that dissatisfaction with government reduces the guilt or shame associated with tax avoidance and leads the individual to more closely follow the economic calculus in making the choice to underpay taxes.

A Model of Aggregate Income Tax Evasion

An aggregate model can be constructed based on the proceeding choice model. From an aggregate perspective, the relative probability that the representative economic agent will not report his taxable income to the tax authority is an increasing function of the expected gross benefits to the agent of not reporting income, eb, and a decreasing function of the expected gross costs to the agent of not reporting income, ec.

Thus, the ratio of the probability of not reporting income, pnr, to the probability of reporting income, (1 - pnr), is described for the representative economic agent by:

pnr/(1 - pnr) = f(eb - ec) , (6)

where the probability of underreporting income increases as the net expected benefits from doing so, eb - ec, increases.

The expected gross benefits from not reporting income are anticipated to be an increasing function of the income tax rate [Cagan, 1958; Bawley, 1982; Tanzi, 1982, 1983; Clotfelter, 1983; Slemrod, 1985; Pyle, 1989; Feige, 1994]. In the U.S., the income tax rate may take a number of forms, including the personal income tax rate (PT), the social security tax rate (ST), and the corporate income tax rate (CT), where eb is directly related to PT, ST, and CT.

As an exercise, students can be asked to determine the effect of inflation on the incidence of tax evasion and the implications of the Tax Reform Act of 1986. In particular, for the U.S. prior to inflation indexing as introduced under provisions of the Tax Reform Act of 1986, it might well be expected that inflation would push many income earners into higher tax brackets, a phenomenon known as "bracket creep. Whereas this consideration may well have contributed to tax evasion in the past [McLeod, 1997], there is little reason to believe it still remains an issue of significance.

Additionally, as previously presented, it can be hypothesized that a higher level of public dissatisfaction with the performance or actions of government or a higher level of public distrust and resentment toward government may contribute to the size of the underground economy. In other words, the greater the public's dissatisfaction with government (D), the greater the utility people may derive from underreporting their income to the tax collection authority. In general functional form, eb is given by:

eb = h(PT, ST, CT, D), (7)

where eb is also directly related to D. For simplicity, (4) can be rewritten in linear form as:

eb = [g.sub.0] + [g.sub.1]PT + [g.sub.2]ST + [g.sub.3]CT. (8)

The expected gross costs of not reporting income are an increasing function of the risks thereof, which include penalties (PEN) imposed by the tax collection authority on detected unreported income [Friedland, 1982; Pestieau et al., 1994]. In the U.S., penalties can be as much as 20 percent of the amount of detected unpaid income tax liabilities and can also include interest on unpaid past tax liabilities and penalties. Table 1 provides the percentage interest rate assessments applied by the Internal Revenue Service (IRS) on detected unpaid taxes (and penalties) for the period of October 1988 through April 1999. Moreover, these risks are presumably enhanced by an increase in AUDIT, the percentage of income tax returns that are audited by the government tax collection authority. IRS audit rates, expressed as a percent of filed tax returns, for the 1988-97 period also appear in Table 1.

In any case, the expected costs of underreporting income may be expressed as:

ec = h(AUDIT, PEN), (9)

where ec is directly related to both AUDIT and PEN. Equation (6) can be rewritten simply in linear form as:

ec = [h.sub.0] + [h.sub.1] AUDIT + [h.sub.2] PEN. (10)

Substituting from (5) and (7) into (3) yields:

Pnr/(1 - pnr) = ([g.sub.0] - [h.sub.0]) + [g.sub.1] PT + [g.sub.2]ST + [g.sub.3]CT - [h.sub.1]AUDIT - [h.sub.2]PEN. (11)

In order to formulate an empirical measure of the probability of evading taxes, let AGI represent the true value of the total actual adjusted gross income in the economy, that is, AGI = UGE + RAGI, where UGE is the dollar size of the underground economy, that is, the dollar size of the unreported AGI, and RAGI is the dollar size of the reported AGI. It reasonably follows that:

UGE = [(pnr).sup.*] AGI, (12)

and

RAGI = [(1 - pnr).sup.*] AGI. (13)

It then follows that:

UGE / RAGI = [(pnr).sup.*] AGI / [(1 - pnr).sup.*] AGI = (pnr) / (1 - pnr). (14)

From (8) and (11), we obtain:

UGE / RAGI ([g.sub.0] - [h.sub.0]) + [g.sub.1]PT + [g.sub.2]ST + [g.sub.3]CT - [h.sub.1]AUDIT - [h.sub.2]PEN. (15)

Measuring the Extent of Income Tax Evasion

Presented here are three alternative methods for estimating the size of the underground economy and resulting income tax evasion. Each is useful in developing an understanding of the macroeconomy. Each model can be presented with students discussing the differences and relative merits of each.

Among the well-known contributions to estimating the size of the underground economy for U.S. are those by Tanzi [1982, 1983], Feige [1989, 1994], Bawley [1982], Carson [1984], Pozo [1996], and Pyle [1989]. Researchers have traditionally adopted one of three major models:

1) the AGI gap approach;

2) the taxpayer compliance measurement program (TCMP); and

3) currency ratio (CR) models, including the general currency ratio (GCR) model.

The first two models are known as discrepancy models. This means that the difference or discrepancy between two observed or computed values measures the value of the unobserved variable.

The AGI Gap Approach

The AGI gap approach, compiled by the Bureau of Economic Analysis [1993], computes the discrepancy between the aggregate AGI reported to the IRS and an independent estimate of the aggregate AGI derived from the National Income and Product Accounts' estimate of aggregate personal income. Several researchers, including Carson [1984] and Feige [1989], argue that the AGI gap approach is a reasonable indicator of the lower bound of the size of the underground economy. The accuracy of this method depends on the accuracy of the two component measures.

A Gap Approach Using Sampling

The second discrepancy measure of the underground economy is that prepared by the IRS on the basis of its TCMP, and it is a sample method. In each year when the TCMP is prepared, a sample of approximately 55,000 tax filers is subjected to a detailed examination by IRS auditors, who attempt to determine the amounts of income that should have been reported as opposed to the amounts that were in fact reported. Final estimates of unreported income of filers for those years were obtained by combining audits, information returns, and special surveys. The IRS estimates were based on the office of Management and Budget forecasts of personal income combined with an assumption of constant rates of noncompliance between 1982 and 1992. The discrepancy (or gap) indicates the extent of the underreporting of income that is estimated to occur. Final estimates of unreported income of filers and nonfilers for those years were obtained by combining information from audits, information returns, and special surveys. The IRS esti mates for the period 1985 to 1992, which were based on the Office of Management and Budget forecasts of personal income, were combined with an assumption of constant rates of no compliance between 1982 and 1992.

The Currency Ratio Model

The third common methodology for estimating the size of unreported income relies on some variant of the GCR model. [1] This model takes several different forms. In its simplest and most restrictive form, the CR model assumes that:

1) currency is the exclusive medium of exchange for unreported transactions;

2) the ratio of currency to checkable deposits is only affected by the growth of unreported domestic transactions;

3) the income velocities of reported and unreported transactions are equal; and

4) in some base period, unreported income was zero so that the observed currency to deposit ratio (as a percent) in that base period serves as a proxy for the desired currency ratio in the official economy.

As the observed currency to checkable deposit ratio rises and falls over time, so does the estimated ratio of unreported income to reported income.

All of the simple currency ratio model estimates are predicated on the assumption that U.S. currency is exclusively used to affect domestic transactions in either the official or the underground economy. This assumption ignores the increased use of U.S. currency as a medium of exchange in foreign countries. Both the magnitude and variation in foreign holdings of U.S. currency will result in an overstatement of the size of the domestic underground economy by the currency ratio model.

In the simple CR model, the ratio of unreported income ([Y.sub.u]) to reported income ([Y.sub.o]) is:

[Y.sub.u]/[Y.sub.o] = (C - [k.sub.o]D)/([k.sub.o] + 1)D, (16)

where C is currency, D is checkable deposits, and [k.sub.o] = [C.sub.o]/[D.sub.o] is reported cash to checkable deposits ratio. In the GCR model, currency need no longer be the exclusive medium of exchange for unreported transactions, and any year for which an independent estimate of unreported income is available can serve as a benchmark, such that:

[Y.sub.u]/[Y.sub.o] = ([k.sub.o] + 1)(C - [k.sub.o]D)/( [k.sub.o] + 1)([k.sub.u]D - C), (17)

where [k.sub.u] and [k.sub.o] are the currency to deposit ratios in the unreported and reported economies, respectively.

However, it should be noted that Sprenkle [1993] reports that surveys commissioned in 1984 and 1986 by the Federal Reserve showed aggregate household demand for currency to be $23.3 billion while business holdings summed to approximately $5 billion. In 1986, the currency in circulation was $177 billion, so household plus business demand constituted $28 billion or less than 16 percent of total currency in circulation. There are three possible holders of the 84 percent of currency outstanding: the underground economy, children under 18, and foreign holdings.

Estimates of Income Tax Evasion

The variety of models employed to estimate the incidence of income tax evasion allows the comparison of results and their implications for the relative variance in each measure. Given the variety of approaches to estimating the extent of tax evasion, it should come as no surprise that these various approaches produce differing estimates. The time series data provided in Table 2 illustrates the relative size of the underground economy, measured by Feige [1989, 1994]. He provides estimates of unreported adjusted gross income (UAGI) as a percentage of RAGI. As shown in Table 2, the degree of tax evasion can change dramatically over time. Table 3 illustrates that the estimated size of the underground economy differs dramatically, depending upon the approach adopted. For example, in Table 3, the size of the underground ranges from as little as 4.5 percent of gross national product (GNP) to as much as more than 28 percent of GNP.

The volatile nature of the RAGI measure brings into question its accuracy. It can be questioned whether the size of the underground economy fluctuates wildly from one year to the next.

Concluding Remarks

This brief pedagogical note has attempted to provide a comprehensible, useful, and functionally realistic framework that explains how the size of the underground economy, especially in the U.S., can be estimated, provides a variety of actual estimates of the size of the underground economy in the U.S., and provides a formal but easily understood analytical model, as summarized in (12), of determinants of the size of the underground economy, and especially the tax evasion component thereof. The latter model may be useful, with suitable adaptations for different economic environments, in serving as the basis for empirical estimations of determinants of income tax evasion behavior. Moreover, the model may also be useful in enhancing student understanding of tax evasion behavior through student projects.

(*.) Armstrong Atlantic State University and Georgia Southern University--U.S.A.

Footnotes

(1.) For a description of the GCR model, see Feige [1994, PP. 123-5, 134].

References

Akerlof, G.; Dickens, W. "The Economics Consequences of Cognitive Dissonance," American Economic Review, 72, 1982, pp. 307-19.

Allingham, M. G.; Sandmo, A. "Income Tax Evasion," Journal of Public Economics, 1, 1972, pp. 323-38.

Alm, J.; Jackson, B.; McKee, M. "Institutional Uncertainty and Taxpayer Compliance," American Economic Review, 82, 1992, pp. 1018-26.

Baldry, J. C. "Income Tax Evasion and the Tax Schedule: Some Experimental Results," Public Finance/Finances Publiques, 42, 1987, pp. 357-83.

Bawley, D. The Subterranean Economy, New York, NY: McGraw-Hill, 1982.

Benjamini, Y.; Maital, S. "Optimal Tax Evasion and Optimal Tax Evasion Policy: Behavioral Aspects," in W. Gaertner; A. Wenig, eds., The Economics of the Shadow Economy, Berlin, Germany: Springer-Verlag, 1985, pp. 140-58.

Bureau of Economic Analysis. Unreported Income, Washington, DC: U.S. Government Printing Office, 1993.

Cagan, P. "The Demand for Currency Relative to the Total Money Supply," Journal of Political Economy, 66, 1958, pp. 303-28.

Carson, C. "The Underground Economy: An Introduction," Survey of Current Business , 64, 1984, pp. 24-35.

Clotfelter, C. T. "Tax Evasion and Tax Rates: An Analysis of Individual Returns," Review of Economics and Statistics, 65, 1983, pp. 363-73.

Das-Gupta, A. "A Theory of Hard-to-Tax Groups," Public Finance/Finances Publiques, 49, 1994, pp. 28-39.

De Juan, A. Fiscal Attitudes and Behavior: A Study of 16-35 Year Old Swedish Citizens, Stockholm, Sweden: Stockholm School of Economics, 1989.

De Juan, A.; Lasheras, M. A.; Mayo, R. "Voluntary Tax Compliant Behavior of Spanish Taxpayers," Public Finance/Finances Publiques, 49, 1994, pp. 90-105.

Erard, B; Feinstein, J. S. "The Role of Moral Sentiments and Audit Perceptions in Tax Compliance," Public Finance/Finances Publiques, 49, 1994, pp. 70-89.

Falkinger, J. "Tax Evasion and Equity: A Theroetical Analysis," Public Finance/Finances Publiques, 43, 1988, pp. 388-95.

Federal Reserve Bank of Philadelphia. Underground Activity, Philadelphia, PA: Federal Reserve Bank of Philadelphia, 1993.

Feige, E. L. The Underground Economies: Tax Evasion and Information Distortion, Cambridge, MA: Cambridge University Press, 1989.

___. "The Underground Economy and the Currency Enigma," Public Finance/Finances Publiques, 49, 1994, pp. 119-36.

Friedland, N. "A Note on Tax Evasion as a Function of the Quality of Information about the Credibility of Threatened Fines: Some Preliminary Research," Journal of Applied Social Psychology, 12, 1982, pp. 54-9.

Internal Revenue Service. Annual Report of the Commissioner and Chief Counsel of the Internal Revenue Service, Washington, DC: U.S. Government Printing Office, various.

___. Interest Penalties on Unpaid Taxes, Atlanta, GA: IRS, Atlanta Service Center, 1999.

Klepper, S.; Nagin, D.; Spurr, S. "Tax Rates, Tax Compliance, and the Reporting of Long-Term Capital Gains," Public Finance/Finances Publiques, 46, 1991, pp. 236-51.

McLeod, J. "Inflation and the Size of the Underground Economy: Analysis for 1962-1980 with the Tanzi Data," Academy of Economics and Finance Proceedings, 21, 1997, pp. 407-10.

Pestieau, P; Possen, U.; Slutsky, S. "Optimal Differential Taxes and Penalties," Public Finance/Finances Publiques, 49, 1994, pp. 15-27.

Pommerehne, W. W.; H. Weck-Hannemann, H. "Tax Rates, Tax Administration and Income Tax Evasion in Switzerland," paper presented at the Conference of the Applied Econometrics Association, 1989.

Pozo, S. Exploring the Underground Economy, Kalamazoo, MI: Upjohn, 1996.

Public Finance/Finances Publiques. Supplement, 49, 1994.

Pyle, D. Tax Evasion and the Black Economy, New York, NY: St. Martin's Press, 1989.

Rice, E. M. "The Corporate Tax Gap: Evidence on Tax Compliance by Small Corporations," in J. Slemrod, ed., Why People Pay Taxes: Tax Compliance and Enforcement, Ann Arbor, MI: University of Michigan Press, 1992, pp. 125-61.

Slemrod, J. B. "An Empirical Test for Tax Evasion," Review of Economics and Statistics, 67, 1985, pp. 232-67.

Spicer, M. W.; Lundstedt, S. B. "Understanding Tax Evasion," Public Finance/Finances Publiques, 31, 1976, pp. 295-305.

Spicer, M. W.; Thomas, J. E. "Audit Probabilities and the Tax Evasion Decision: An Experimental Approach," Journal of Economic Psychology, 2, 1982, pp. 241-5.

Sprenkle, B. "Currency Holdings in the U.S.," Public Finance/Finances Publiques, 48, 1993, pp. 301-10.

Tanzi, V. The Underground Economy in the United States and Abroad, Lexington, MA: Lexington Books, 1982.

___. "The Underground Economy in the United States: Annual Estimates, 1930-1980," International Monetary Fund Staff Papers, 30, 1983, pp. 283-305.

Thurman, Q. C. "Taxpayer Noncompliance and General Prevention: An Expansion of the Deterrence Model," Public Finance/Finances Publiques, 46, 1991, pp. 289-98.

U.S. Department of Labor. Estimating Underground Activity, Washington, DC: U.S. Government Printing Office, 1992.
                   Interest Rates Applied by the IRS to
                    Unpaid Taxes and the IRS Audit Rate
Effective Date  Interest Rate (PEN) Audit Rate (AUDIT)
October 1, 1988         11                 1.1
April 1, 1989           12                 1.1
October 1, 1989         11                 1.1
April 1, 1991           10                 0.9
January 1, 1992          9                 0.8
April 1, 1992            8                 0.8
October 1, 1992  7 0.8
July 1, 1994     8 0.93
October 1, 1994  9 0.93
April 1, 1995   10 1.38
July 1, 1995     9 1.38
April 1, 1996    8 1.38
July 1, 1996     9 1.38
April 1, 1998    8  NA
January 1, 1999  7  NA
April 1, 1999    8  NA
Notes: NA denotes not currently available.
Source: IRS [various]; IRS [1999].
                   UAGI as a Percentage of RAGI: 1973-77
Year UAGI/RAGI
1973   14.84
1974   18.21
1975   20.87
1976   24.17
1977   26.20
1978   26.90
1979   28.36
1980   30.04
1981   29.04
1982   27.95
1983   26.01
1984   26.56
1985   25.39
1986   21.99
1987   20.03
1988   21.73
1989   24.20
1990   25.08
1991   24.77
1992   21.46
1993   19.79
1994   20.71
1995   18.80
1996   18.00
1997   18.03
Notes: Figures are in percentages.
Source: Feige [1989, 1994].
                       Various Estimates of the Size
                        of the Underground Economy
                                      Estimate       Estimate
                                   in Billions of  in Percentage
Study                              Current Dollars    of GNP     Year
IRS [various]                            145            8.0      1976
Feige [1989, 1994]                      600+            28+      1979
Tanzi [1982, 1983]                     118-159        4.5-6.0    1980
Bureau of Economic Analysis [1993]       184            5.4      1983
U.S. Dept. of Labor [1992]               500           10.0      1992
Source: Federal Reserve Bank of Philadelphia [1993].
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