Imperfect Detection of Tax Evasion in a Corrupt Tax Administration

Abstract

This article models the imperfect detection of tax evasion motivated by the existence of a corrupt tax administration. Consistent with previous literature, fines and audit probabilities both have a positive effect on compliance. Moreover, the model shows that they have a negative effect on the bribes paid to corrupt tax officials. More corruption decreases compliance levels, giving honest auditors incentives to work harder to detect evasion. Giving inspectors a share of the detected evasion (tax farming) makes auditors work harder; however, increasing their wages reduces their exerted effort to discover evasion. Higher compliance can as well be achieved by hiring more efficient inspectors.

Appendix

From the Implicit Function Theorem: $\partial D/\partial b = - \frac{{\partial G/\partial b}}{{\partial G/\partial D}}$, $\partial D/\partial {a_h} = - \frac{{\partial G/\partial {a_h}}}{{\partial G/\partial D}}$, and $\partial D/\partial {a_c} = - \frac{{\partial G/\partial {a_c}}}{{\partial G/\partial D}}$. G is given in Eq. 9 and

$$ \begin{array}{*{20}{c}} {\frac{{\partial G}}{{\partial b}} = - tpks\left\{ {U''(X)\left[ {1 + sb\left( {\frac{{\partial \varphi ({a_c})}}{{\partial D}} - 1} \right)} \right]\left( {\varphi ({a_c}) - D} \right) + U'(X)\left[ {\frac{{\partial \varphi ({a_c})}}{{\partial D}} - 1} \right]} \right\}} \\ {\frac{{\partial G}}{{\partial {a_c}}} = - tpksb\left\{ {U''(X)\left[ {1 + sb\left( {\frac{{\partial \varphi ({a_c})}}{{\partial D}} - 1} \right)} \right]\left( {\frac{{\partial \varphi ({a_c})}}{{\partial {a_c}}}} \right) + U'(X)\left[ {\frac{{{\partial^2}\varphi ({a_c})}}{{\partial {D^2}}}\frac{{\partial D}}{{\partial {a_c}}}} \right]} \right\}} \\ {\frac{{\partial G}}{{\partial {a_h}}} = - tp(1 - k)s\left\{ {U''(Z)\left[ {1 + s\left( {\frac{{\partial \varphi ({a_h})}}{{\partial D}} - 1} \right)} \right]\left( {\frac{{\partial \varphi ({a_h})}}{{\partial {a_h}}}} \right) + U'(Z)\left[ {\frac{{{\partial^2}\varphi ({a_h})}}{{\partial {D^2}}}\frac{{\partial D}}{{\partial {a_h}}}} \right]} \right\}} \\ {\frac{{\partial G}}{{\partial D}} = {t^2}\left\{ \begin{gathered} (1 - p)U''(W) + pk\left\{ {U''(X){{\left[ {1 + sb\left( {\frac{{\partial ({a_c})}}{{\partial D}} - 1} \right)} \right]}^2} - \frac{{sb}}{t}U'(X)\left[ {\frac{{{\partial^2}\varphi ({a_c})}}{{\partial {D^2}}}} \right]} \right\} \hfill \\ + p(1 - k)\left\{ {U''(Z){{\left[ {1 + s\left( {\frac{{\partial ({a_h})}}{{\partial D}} - 1} \right)} \right]}^2} - \frac{s}{t}U'(Z)\left[ {\frac{{{\partial^2}\varphi ({a_h})}}{{\partial {D^2}}}} \right]} \right\} \hfill \\ \end{gathered} \right\}} \\ \end{array} $$