America’s unreported economy: measuring the size, growth and determinants of income tax evasion in the U.S.

Abstract

This study empirically investigates the extent of noncompliance with the tax code and examines the determinants of federal income tax evasion in the U.S. Employing a refined version of Feige’s (Staff Papers, International Monetary Fund 33(4):768–881, 1986, 1989) General Currency Ratio (GCR) model to estimate a time series of unreported income as our measure of tax evasion, we find that 18–23% of total reportable income may not properly be reported to the IRS. This gives rise to a 2009 “tax gap” in the range of $390–$540 billion. As regards the determinants of tax noncompliance, we find that federal income tax evasion is an increasing function of the average effective federal income tax rate, the unemployment rate, the nominal interest rate, and per capita real GDP, and a decreasing function of the IRS audit rate. Despite important refinements of the traditional currency ratio approach for estimating the aggregate size and growth of unreported economies, we conclude that the sensitivity of the results to different benchmarks, imperfect data sources and alternative specifying assumptions precludes obtaining results of sufficient accuracy and reliability to serve as effective policy guides.

Appendices

Appendix A: The general currency ratio (GCR) model

The General Currency Ratio (GCR) model as described in Feige [28, 29] is a heuristic framework capable of representing a variety of common monetary approaches for obtaining time series estimates of the “unobserved” sector of the economy.

Let:

o:

subscript to denote the observed sector

u:

subscript to denote the unobserved sector

C:

actual currency stock

D:

actual stock of checkable deposits

Y_o :

observed income

k_o :

ratio of domestic currency to checkable deposits in the observed sector

k_u :

ratio of domestic currency to checkable deposits in the unobserved sector

V_o :

observed sector income velocity

V_u :

unobserved sector income velocity

When the object of analysis is to estimate unreported income on federal income tax returns, the empirical counterpart to observed income is the IRS measure of adjusted gross income (AGI). The unobserved sector now is measured by Y_u, namely unreported adjusted gross income.²⁷ The GCR model specifies the following:

$$ {\text{C}} = {{\text{C}}_{\text{o}}} + {{\text{C}}_{\text{u}}} $$

(A:1)

$$ {\text{D}} = {{\text{D}}_{\text{o}}} + {{\text{D}}_{\text{u}}} $$

(A:2)

$$ {{\text{k}}_{\text{o}}} = {{\text{C}}_{\text{o}}}/{{\text{D}}_{\text{o}}} $$

(A:3)

$$ {{\text{k}}_{\text{u}}} = {{\text{C}}_{\text{u}}}/{{\text{D}}_{\text{u}}} $$

(A:4)

$$ {{\text{V}}_{\text{o}}} = {{\text{Y}}_{\text{o}}}/{{\text{C}}_{\text{o}}} + {{\text{D}}_{\text{o}}} $$

(A:5)

$$ {{\text{V}}_{\text{u}}} = {{\text{Y}}_{\text{u}}}/{{\text{C}}_{\text{u}}} + {{\text{D}}_{\text{u}}} $$

(A:6)

$$ \beta = {{\text{V}}_{\text{o}}}/{{\text{V}}_{\text{u}}} $$

(A:7)

Equations (A:1) and (A: 2) decompose the actual stocks of currency and checkable deposits into their reported and unreported components. Equations (A: 3) and (A: 4) are definitions of the terms k_o and k_u which can be specified either as constants or functions. Similarly, (A: 5) and (A: 6) define income velocity in the two sectors. To solve the model for unreported income (Y_u), we must evaluate (A: 6) in terms of the models observable variables namely, C, D and Y_o. Repeated substitution and rearrangement of terms yields the general solution:

$$ {Y_{{ut}}} = \frac{1}{\beta }{Y_{{ot}}}\frac{{(ku + 1)({C_t} - ko\,{D_t})}}{{(ko + 1)(ku\,{D_t} - {C_t})}} $$

(A:8)

The most restrictive variants of the GCR model impose the following assumptions²⁸:

• a) The entire stock of currency is held domestically.

• b) Currency is the exclusive medium of exchange for unreported transactions. (D_u → 0; k_u → ∞)

• c) The income velocities in the reported and unreported sectors are identical. (β = 1)

• d) The ratio of currency to checkable deposits in the observed sector is constant over time. (k_ot = constant for all t)

Imposing these assumptions on Eq. 8 yields the restrictive form of the GCR model,

$$ {Y_{{ut}}} = {Y_{{ot}}}\left\{ {\frac{{{C_t} - {k_o}{D_t}}}{{({k_o} + 1){D_t}}}} \right\} $$

(A:9)

Empirical estimates of unreported income (Y _ut ) require an estimate of the parameter k _o which Cagan [15] and Gutmann [40] assumed could be approximated as follows:

$$ {k_o} = \left( {\frac{{{C_o}}}{{{D_o}}}} \right)_{1940} = \left( {\frac{C}{D}} \right)_{1940} $$

(e)

The 1940 benchmark assumption implied that prior to World War II, income tax evasion was zero.²⁹ The restrictive assumptions represented by (a….e) give rise to what is commonly known as the “simple currency ratio” model. Given a value of k_o, obtained via assumption (e), Eq. A: 9 expresses the unknown unreported income as a simple function of observed variables.

In principle, any year t for which we have an independent estimate of both reported and unreported income can serve as “benchmark” year for estimating the GCR model. Given ${\alpha_t} = \frac{{{Y_{{ut}}}}}{{{Y_{{ot}}}}}$, we can solve Eq. 9 for k_ot:

$$ {k_{{ot}}} = \frac{{{C_t} - {\alpha_t}{D_t}}}{{{\alpha_t}{D_t} + {D_t}}} = \frac{{(1 - {\eta_t}){C_t}}}{{{D_t}}} - {\eta_t} $$

(A:10)

where η_t is the noncompliance rate. If k_ot = k_o for all t, it is possible to generate a temporal path of the noncompliance rate from Eq. A: 9.

If we have independent knowledge concerning the values of the parameters, β and k_u, assumptions (b) and (c) can be discarded and Eq. A: 8 can be employed to directly solve for Y_ut.

Appendix B

Table B:2 Data for dependent variable, U _AGI /R _AGI , by Year, 1960–2008

Table 1 Empirical estimates (dependent variable: (U _AGI /R _AGI )

Table B:3 Correlation matrix for explanatory variables, 1970–2008