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Reporting import tariffs (and other taxes)

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Abstract

This paper derives the implications for compliance and fiscal revenues of a tax base that is the product of several factors. For instance, in the case of import tariffs, the tax base is the product of quantity and unit value, both reported to, and during an audit assessed by, the custom authority. Import tariffs are particularly interesting as custom receipts represent an important share of government revenues in many developing countries and there has recently been a surge in empirical studies showing how evasion in this field is a pervasive phenomenon. I show that, with a multiplicative tax base, when the fiscal authority has an imperfect detection technology a greater declaration in one dimension actually increases the fine when evasion in the other dimension is detected. Therefore, there is an additional incentive for the taxpayer to underdeclare and a multiplicative tax base is subject to more evasion, compared to a tax base that can be assessed directly. As a result, fiscal revenues decrease with the dimensionality of the tax base. Also, voluntary compliance and fiscal revenues may be higher when the importer is required to declare only the total value of imports instead of quantity and unit value separately.

This paper provides an argument in favour of uniform or specific tariffs and a reason for why a flat tax may improve compliance.

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Notes

  1. Tariff receipts accounted for 22 % of total tax receipts in low-income countries over the period 2001–2006. The figure is 18.1 % for middle-income countries and 2.5 % for high-income ones (Baunsgaard and Keen 2010; Jean and Mitaritonna 2010).

  2. They also report the results of several studies showing how in many African countries collection of custom duties is very poor (the worst reported case is the Democratic Republic of Congo, with “80 % of custom taxes not being collected”). Van Dunem and Arndt (2009) estimate that the average level of evasion in Mozambique is nearly 36 % of total recorded imports.

  3. Evidence of tariff evasion has been found also for developed countries with a low level of corruption. See, for instance, the study by Stoyanov (2012) on trade between Canada and the US in 1989.

  4. Quantities are often indicated for information only (Jean and Mitaritonna 2010) and the unit of measurements reported by different statistical agencies may be non-convertible, e.g. units vs. kilograms (Stoyanov 2012). See also Rozanski and Yeats (1994) for a comprehensive analysis of the reliability of trade statistics.

  5. The empirical studies by Feinstein (1991) and Erard (1997) show that non-detection is indeed a serious issue even in the US context. Feldman and Slemrod (2007) cite an IRS study that found that “for every dollar of under-reported income detected by TCMP [Taxpayer Compliance Measurement Program] examiners without the aid of third-party information documents, another $2.28 went undetected”. The issue of imperfect detection is plausibly even more relevant for developing countries, where administrative capacity is generally low.

  6. There is a related literature considering the implications of the fact that the tax base is not perfectly observed. See Slemrod and Traxler (2010) for a recent contribution.

  7. “Fishers may fail to report their harvest, or misreport its weight. When a report is filed, they may attempt to report the species taken as some other species with a lower quota value.” (Johnson 1995)

  8. See also Tonin (2011).

  9. The case of a fine proportional to the undeclared amount, as in Allingham and Sandmo (1972), is discussed in Sect. 5.

  10. An optimizing custom authority could also condition its auditing on the observed declaration xy, as is usually assumed in the literature on optimal auditing (see Reinganum and Wilde 1985, for an early contribution). The optimal auditing strategy is, however, beyond the scope of this paper.

  11. An equivalent narrative is that in an audit, the custom authority may find no evidence at all of evasion with probability G(x), which is increasing as the liability declared to the authorities increases. Conditional on detection taking place, the density for any given fraction of import value \(\hat{x}\in[ x,1]\) being discovered is given by \(g( \hat{x}) /[ 1-G( x)]\).

  12. Notice that for this to be the case, it is not necessary that the two random variables are independent. Suppose, for instance, we are in the plausible situation such that \(\hat{x}_{1}\) and \(\hat{x}_{2}\) are positively correlated. Then the probability that either \(\hat{x}_{1}<x_{1}\) and \(\hat{x}_{2}>x_{2}\), or \(\hat{x}_{1}>x_{1}\) and \(\hat{x}_{2}<x_{2}\), is strictly positive for any pair (x 1,x 2), unless \(\hat{x}_{1}\) and \(\hat{x}_{2}\) are perfectly correlated, in which case the two-dimensional problem reduces to an uni-dimensional one.

  13. Clearly, mislabelling is better modelled as a discrete rather than continuous choice. This would require some more cumbersome notation, but would not change the results in a significant way.

References

  • Aizenman, J., & Jinjarak, Y. (2009). Globalisation and developing countries—a shrinking tax base? Journal of Development Studies, 45(5), 653–671.

    Article  Google Scholar 

  • Allingham, M. G., & Sandmo, A. (1972). Income tax evasion: a theoretical analysis. Journal of Public Economics, 1(3–4), 323–338.

    Article  Google Scholar 

  • Andreoni, J., Erard, B., & Feinstein, J. (1998). Tax compliance. Journal of Economic Literature, 36, 818–860.

    Google Scholar 

  • Bahl, R., Martinez-Vazquez, J., & Youngman, J. (2008). The property tax in practice. In R. Bahl, J. Martinez-Vazquez, & J. Youngman (Eds.), Making the property tax work. Cambridge: Lincoln Institute of Land Policy.

    Google Scholar 

  • Baunsgaard, T., & Keen, M. (2010). Tax revenue and (or?) trade liberalization. Journal of Public Economics, 94(9–10), 563–577.

    Article  Google Scholar 

  • Burgess, R., & Stern, N. (1993). Taxation and development. Journal of Economic Literature, 31(2), 762–830.

    Google Scholar 

  • Erard, B. (1997). Self-selection with measurement errors. A microeconometric analysis of the decision to seek tax assistance and its implications for tax compliance. Journal of Econometrics, 81, 319–356.

    Article  Google Scholar 

  • Feinstein, J. (1991). An econometric analysis of income tax evasion and its detection. RAND Journal of Economics, 22, 14–35.

    Article  Google Scholar 

  • Feldman, N., & Slemrod, J. (2007). Estimating tax noncompliance with evidence from unaudited tax returns. The Economic Journal, 117(518), 327–352.

    Article  Google Scholar 

  • Fisman, R., & Wei, S. (2004). Tax rates and tax evasion: evidence from “Missing imports” in China. Journal of Political Economy, 112(2), 471–496.

    Article  Google Scholar 

  • Gordon, J. (1989). Individual morality and reputation costs as deterrents to tax evasion. European Economic Review, 33(4), 797–805.

    Article  Google Scholar 

  • Gordon, R., & Li, W. (2009). Tax structures in developing countries: many puzzles and a possible explanation. Journal of Public Economics, 93(7–8), 855–866.

    Article  Google Scholar 

  • Gordon, R., & Slemrod, J. (2000). Are ‘Real’ responses to taxes simply income shifting between corporate and personal tax bases? In J. Slemrod (Ed.), Does atlas shrug? The economic consequences of taxing the rich (pp. 240–280). Cambridge: Russell Sage Foundation/Harvard University Press.

    Google Scholar 

  • Gorodnichenko, Y., Martinez-Vazquez, J., & Sabirianova Peter, K. (2009). Myth and reality of flat tax reform: micro estimates of tax evasion response and welfare effects in Russia. The Journal of Political Economy, 117(3), 504–554.

    Article  Google Scholar 

  • Hindriks, J., Keen, M., & Muthoo, A. (1999). Corruption, extortion, and evasion. Journal of Public Economics, 74, 395–430.

    Article  Google Scholar 

  • Javorcik, B., & Narciso, G. (2008). Differentiated products and evasion of import tariffs. Journal of International Economics, 76, 208–222.

    Article  Google Scholar 

  • Jean, S., & Mitaritonna, C. (2010). Determinants and pervasiveness of the evasion of custom duties (Mimeo).

  • Johnson, R. (1995). Implications of taxing quota value in an individual transferable quota fishery. Marine Resource Economics, 10, 327–340.

    Google Scholar 

  • Keen, M., Kim, Y., & Varsano, R. (2008). The “flat tax(es)”: principles and experience. International Tax and Public Finance, 15(6), 712–751.

    Article  Google Scholar 

  • Mishra, P., Subramanian, A., & Topalova, P. (2008). Tariffs, enforcement, and customs evasion: evidence from India. Journal of Public Economics, 92(10–11), 1907–1925.

    Article  Google Scholar 

  • Rauch, J. (1999). Networks versus markets in international trade. Journal of International Economics, 48, 7–35.

    Article  Google Scholar 

  • Reinganum, J. F., & Wilde, L. L. (1985). Income tax compliance in a principal-agent framework. Journal of Public Economics, 26(1), 1–18.

    Article  Google Scholar 

  • Rozanski, J., & Yeats, A. (1994). On the (in)accuracy of economic observations: an assessment of trends in the reliability of international trade statistics. Journal of Development Economics, 44(1), 103–130.

    Article  Google Scholar 

  • Scotchmer, S. (1987). Audit classes and tax enforcement policy. American Economic Review Papers and Proceedings, 77(2), 229–233.

    Google Scholar 

  • Slemrod, J. (2007). Cheating ourselves: the economics of tax evasion. The Journal of Economic Perspectives, 21(1), 25–48.

    Article  Google Scholar 

  • Slemrod, J., & Traxler, C. (2010). Optimal observability in a linear income tax. Economics Letters, 108, 105–108.

    Article  Google Scholar 

  • Slemrod, J., & Yitzhaki, S. (2002). Tax avoidance, evasion, and administration. In A. Auerbach & M. Feldstein (Eds.), Handbook of public economics (Vol. III). Amsterdam: Elsevier.

    Google Scholar 

  • Stoyanov, A. (2012). Tariff evasion and rules of origin violations under the Canada-U.S. free trade agreement. Canadian Journal of Economics/Revue canadienne d’économique, 45(3), 879–902.

    Article  Google Scholar 

  • Tonin, M. (2011). Minimum wage and tax evasion: theory and evidence. Journal of Public Economics, 95(11–12), 1635–1651.

    Article  Google Scholar 

  • Van Dunem, J. E., & Arndt, C. (2009). Estimating border tax evasion in Mozambique. Journal of Development Studies, 45(6), 1010–1025.

    Article  Google Scholar 

  • Yitzhaki, S. (1974). A note on ‘Income tax evasion: a theoretical analysis.’. Journal of Public Economics, 3, 201–202.

    Article  Google Scholar 

Download references

Acknowledgements

I thank the Institute of Economics at the Hungarian Academy of Sciences, where part of this research was conducted, for its hospitality. I would like to thank the editor, Eckhard Janeba, and two anonymous referees for invaluable suggestions.

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Correspondence to Mirco Tonin.

Appendix

Appendix

Unitary tax base: derivation of the first-order condition

Take the first derivative with respect to x of

$$y-\gamma t\theta y \int_{x}^{1} (\hat{x}-x)g(\hat{x})\,d\hat{x}-tyx $$

to get

$$-\gamma\theta ty\frac{d}{dx} \int_{x}^{1} ( \hat{x}-x)g(\hat{x})\,d\hat{x}-ty. $$

Using Leibniz integral rule,

$$\frac{d}{dx} \int_{x}^{1} (\hat{x}-x)g( \hat{x})\,d\hat{x}= \int_{x}^{1} \frac{d}{dx}( \hat{x}-x)g(\hat{x})\,d\hat{x}= \int_{x}^{1} -g( \hat{x})\,d\hat{x}=-1+G(x). $$

Then the f.o.c. is

Multiplicative tax base: derivation of the first-order condition

Considering (7), the two first order conditions are given by

To derive \(\frac{\partial f}{\partial x_{1}}\), rewrite the first term within square brackets in (6) as

$$\int_{x_{1}}^{1} \int_{x_{2}}^{1} ( \hat{x}_{1}\hat{x}_{2} ) g_{\hat{x}_{2}}( \hat{x}_{2})g_{\hat {x}_{1}}(\hat{x}_{1})\,d \hat{x}_{2}\,d\hat{x}_{1}- ( x_{1}x_{2} ) \int_{x_{1}}^{1} g_{\hat{x}_{1}}(\hat{x}_{1}) \int_{x_{2}}^{1} g_{\hat{x}_{2}}(\hat{x}_{2}) \,d\hat{x}_{2}\,d\hat{x}_{1} $$

or

$$\int_{x_{1}}^{1} \hat{x}_{1}g_{\hat{x}_{1}}( \hat{x}_{1}) \biggl[ \int_{x_{2}}^{1} \hat{x}_{2}g_{\hat{x}_{2}}(\hat{x}_{2})\,d \hat{x}_{2} \biggr] \,d\hat{x}_{1}- ( x_{1}x_{2} ) \bigl[ 1-G_{\hat{x}_{2}} ( x_{2} ) \bigr] \bigl[ 1-G_{\hat{x}_{1}} ( x_{1} ) \bigr] . $$

Applying the Leibniz integral rule to the first term, the derivative with respect to x 1 is given by

$$ -x_{1}g_{\hat{x}_{1}}(x_{1}) \biggl[ \int _{x_{2}}^{1} \hat{x}_{2}g_{\hat{x}_{2}}( \hat{x}_{2})\,d\hat{x}_{2} \biggr] -x_{2} \bigl[ 1-G_{\hat{x}_{2}} ( x_{2} ) \bigr] \bigl[ 1-G_{\hat{x}_{1} } ( x_{1} ) -x_{1}g_{\hat{x}_{1}} ( x_{1} ) \bigr]. $$
(12)

Then apply the Leibniz integral rule to the second term in (6) to get the derivative with respect to x 1

$$ x_{2}G_{\hat{x}_{2}}(x_{2})\bigl[ G_{\hat{x}_{1}}(x_{1})-1\bigr] , $$
(13)

while, for the third term in (6) the derivative with respect to x 1 is given by

$$ \bigl[ G_{\hat{x}_{1}}(x_{1})+x_{1}g_{\hat{x}_{1}}(x_{1}) \bigr] \int_{x_{2}}^{1} ( \hat{x}_{2}-x_{2}) g_{\hat{x}_{2}}(\hat{x}_{2})\,d\hat{x}_{2}. $$
(14)

Putting together (12), (13), and (14) and simplifying, we get the expression for the derivative of the fine with respect to x 1.

$$\frac{d{f}}{dx_{1}}=y_{1}y_{2}t\theta \biggl[ G_{\hat {x}_{1}}(x_{1}) \int_{x_{2}}^{1} \hat{x}_{2}g_{\hat{x}_{2}}(\hat{x}_{2})\,d \hat{x}_{2}-x_{2}+x_{2}G_{\hat {x}_{2}}(x_{2})G_{\hat{x}_{1}}(x_{1}) \biggr]. $$

The same steps can be done to obtain the derivative with respect to x 2. Then the two first-order conditions are given by

Then \(x_{1}^{\ast}\) and \(x_{2}^{\ast}\) have to simultaneously satisfy

$$ \begin{array} {@{}l} \displaystyle x_{1}^{\ast} =G_{\hat{x}_{1}}^{-1} \biggl( \frac{ ( 1-\alpha ) }{ [ G_{\hat{x}_{2}}(x_{2}^{\ast})+\frac{1}{x_{2}^{\ast}} \int_{x_{2}^{\ast}}^{1} \hat{x}_{2}g_{\hat{x}_{2}}(\hat{x}_{2})\,d\hat{x}_{2} ] } \biggr), \\[6mm] \displaystyle x_{2}^{\ast} =G_{\hat{x}_{2}}^{-1} \biggl( \frac{ ( 1-\alpha ) }{ [ G_{\hat{x}_{1}}(x_{1}^{\ast})+\frac{1}{x_{1}^{\ast}} \int_{x_{1}^{\ast}}^{1} \hat{x}_{1}g_{\hat{x}_{1}}(\hat{x}_{1})\,d\hat{x}_{1} ] } \biggr). \end{array} $$
(15)

Proof of Proposition 1

Recall from (4) that an interior solution in the uni-dimensional case is characterized by

$$x^{\ast}=G^{-1}(1-\alpha) $$

where G is an increasing function. Then G −1 is also an increasing function. The solution in the bi-dimensional case is characterized by (15). To compare the uni- and bi-dimensional cases, the assumption is that the distribution of the probability of detection in one of the two dimensions, say \(\hat{x}_{1}\), is the same as for the uni-dimensional case, i.e. \(G=G_{\hat{x}_{1}}\), and enforcement is also the same in the two environments. Then

Using the fact that

$$\bigl[ 1-G_{\hat{x}_{2}}\bigl(x_{2}^{\ast}\bigr) \bigr] = \int _{x_{2}^{\ast}}^{1} g_{\hat{x}_{2}}(\hat{x}_{2})\,d \hat{x}_{2}, $$

the condition reduces to

$$\Leftrightarrow\quad \int_{x_{2}^{\ast}}^{1} \bigl( \hat{x}_{2}-x_{2}^{\ast} \bigr) g_{\hat{x}_{2}}( \hat{x}_{2})\,d\hat {x}_{2}>0 $$

that is always satisfied. As \(x^{\ast}>x_{1}^{\ast}\) and \(x_{2}^{\ast} \in( 0,1) \), then \(x^{\ast}>x_{1}^{\ast}x_{2}^{\ast}\). □

Proof of Proposition 2

Using the expression for \(x_{1}^{\ast}\) in (15), we have that

As \(G_{\hat{x}_{1}}^{-1}\) is an increasing function, it follows that as \(x_{2}^{\ast}\) increases, \(x_{1}^{\ast}\) also increases. □

Derivation of expressions for unitary and multiplicative cases in Sect.  4 and comparison

Unitary tax base

For an unitary tax base, the expression for the expected fine (1) when g(⋅) is uniform in the support [0,1], i.e. \(\hat {x}\thicksim U_{[0,1]}\), becomes

$$ \gamma f=\gamma t\theta y(1-x)^{2}/2. $$
(16)

The optimal reporting behavior given by (4) becomes

$$ x^{\ast}=1-\alpha. $$
(17)

So, the model implies that what is revealed to the authorities is a fraction of the true import value that depends on the enforcement parameters. Using (16), the expected fine is given in equilibrium by

$$ \gamma f^{\ast}=yt\alpha/2 $$
(18)

and thus, substituting (17) and (18) into (5), I get the equilibrium expected profits

$$ \varPi^{\ast}=y(1-t+t\alpha/2). $$
(19)

Multiplicative tax base

For a multiplicative tax base, the expression for the expected fine (6) when the probabilities of detection are uniformly distributed over the relevant intervals, so that \(g_{\hat{x}_{1}}(\hat {x}_{1})=1\) and \(g_{\hat{x}_{2}}(\hat{x}_{2})=1\), becomes

$$ \gamma f=t\gamma\theta y_{1}y_{2} \bigl[ ( 1-x_{1}x_{2} )^{2}+ ( x_{1}-x_{2} )^{2} \bigr] \big/4, $$
(20)

where it is evident how the fine depends on the total share of the tax base that is evaded, (1−x 1 x 2), and on the difference between the share of evasion in the two dimensions, (x 1x 2). Given the total amount of evasion, it is evident from (20) and (7) that the only effect of declaring an unequal portion along the two dimensions is to increase the expected fine and, therefore, the optimal behaviour is to equalize them. The first-order conditions are indeed simultaneously satisfied if and only if

$$ x_{1}^{\ast}=x_{2}^{\ast}=\sqrt[2]{1-2\alpha}. $$
(21)

The expected fine is then given by

$$ \gamma f^{\ast}=y_{1}y_{2}t\alpha, $$
(22)

giving expected profits of

$$ \varPi^{\ast}=y_{1}y_{2}(1-t+t\alpha). $$
(23)

As underlined in the previous sections, with a multiplicative tax base there is an additional incentive to underreport along one dimension as a higher declaration increases the fine when evasion in the other dimension is detected. To see how this is indeed the case, consider what would happen if the taxpayer disregarded the fact that the two dimensions of the tax base are linked and instead considered them in isolation. Then evasion along each dimension would equal evasion in the unitary case, giving a total declaration of (1−α)2 y 1 y 2. As (1−α)2>1−2α, it is evident that taking into account the fact that the two dimensions are related increases under-reporting.

Table 1 summarizes the comparison between the two cases. The proportion of the tax liability that is declared, the voluntary compliance rate, is clearly higher in case of an unitary tax base. The proportion of tax liability that is paid through enforcement, the fine rate, is instead higher for a multiplicative tax base. This does not imply that a multiplicative tax base is easier to detect than an unitary one, maybe because two parameters instead of one have to be reported to the tax authority. Actually, the opposite is true. In the unitary case, from (16), we have

$$\frac{f}{y}=\frac{t\theta}{2} ( 1-x )^{2}. $$

Compare it with (20) when the same proportion is evaded along the two dimensions

$$\frac{f}{y_{1}y_{2}}=\frac{t\theta}{4} ( 1-x_{1}x_{2} )^{2}. $$

It is evident that for any given proportion of undeclared income, more is uncovered in the unitary case compared to the multiplicative one. The higher fine rate in the multiplicative case is simply due to higher evasion. Taking both voluntary compliance and enforcement into account, a taxpayer manages to reduce total payments to the fiscal authority more effectively with a multiplicative tax base than with an unitary one. Indeed, with a multiplicative tax base, the taxpayer succeeds through tax evasion to reduce the proportion of the tax base that is paid to fiscal authorities, the effective tax rate, by a factor of α compared to what he should have paid, the statutory tax rate. In the unitary case, this reduction is only by a factor of α/2.

Table 1 Comparison

Unitary declaration: expression for fine

Using (10), an equivalent expression for the fine is

Using this expression for the fine in (2) gives rise to the following expression for the first-order condition, where y 1 y 2 has been replaced by y,

Unitary tax base vs. unitary declaration of a multiplicative tax base

Recall from (17) that in case of an unitary tax base x=(1−α). As −x(lnx)>0, then the solution to (11) has to be strictly smaller than (1−α).

Multiplicative tax base vs. unitary declaration of a multiplicative tax base

Indicate the solution to (11) as x ∗∗ and notice how the left-hand side of expression (11) is increasing in x at a decreasing rate. Recall that in case of a standard two-dimensional tax base x=1−2α. To know how this compare to x ∗∗, we can calculate the value of the left-hand side of expression (11) when x=1−2α and see if it is smaller or bigger than (1−α). If it is smaller, it means that x ∗∗>1−2α, if it is bigger it means that x ∗∗<1−2α. The comparison

$$1-2\alpha- ( 1-2\alpha ) \ln ( 1-2\alpha ) >1-\alpha $$

gives the following condition:

$$\alpha<- ( 1-2\alpha ) \ln ( 1-2\alpha ). $$

In Fig. 2, the two sides are plotted.

Fig. 2
figure 2

Comparison to a multiplicative tax base

Let us indicate as α ≃0.36 the point on the x-axis corresponding to the intersection between the two curves. Then

$$\begin{array}{@{}l@{\quad}l}x^{\ast\ast}<1-2\alpha& \mbox{if}\ \alpha<\alpha^{\ast},\\[1mm] x^{\ast\ast}\geq1-2\alpha& \mbox{if}\ \alpha\geq\alpha^{\ast}. \end{array} $$

Fine proportional to the undeclared amount

A fine proportional to the undeclared amount would imply the removal of t from expressions (1), (6), and (10). Equivalently, we could consider the same expressions for the fine and replace γ′=γ/t. Then all the derivations for the first-order conditions presented in this Appendix holds, with α=1/(γθ)=t/(γθ).

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Tonin, M. Reporting import tariffs (and other taxes). Int Tax Public Finance 21, 153–173 (2014). https://doi.org/10.1007/s10797-012-9262-8

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