Inter-governmental political relations in a federation and illegal mining of natural resources

Abstract

The paper studies the impact of inter-governmental political relations on illegal resource extraction in a federal setup. In a stylized model, a corruptible sub-national politician accepts bribes from a private miner to allow under-reporting of mineral extraction and evasion of royalty payment. The probability that a mine is audited by a national audit agency increases with the extent of illegal mining. In addition, when the audit agency is politicized, the probability of audit declines with the political weight of the politician in the ruling national coalition government. We find that there is an endogenous threshold political weight beyond (below) which greater politicization of the audit agency leads to higher (lower) illegal mining. The threshold weight increases with the rate of fine on royalty evasion but decreases with the rate of royalty itself. The model also suggests that there is no unambiguous relationship between economic distortions in the form of illegal mining and the degree of rent extraction through bribes. As the audit agency becomes more politicized, the possibility of higher illegal mining but lower bribes or lower illegal mining but higher bribes cannot be ruled out.

Appendices

Appendix 1 Second-order conditions

Case 2: Illegal mining when the politician is corrupt

The levels of the bribe and reported extraction are determined through the Nash Product ($\Psi =M*P$) where as defined in Eqs. (4) and (5),

$$\begin{aligned} M &= pQ-C[Q]- rpR - \lambda fI - B - \Pi ^*, \quad \hbox {and} \\ P &= B+ a(\Pi - B + G[rpR]) \\ &\quad -\lambda K - (\Pi ^* + G^*[rpR^*]) \end{aligned}.$$

It is straightforward to see that $\Psi _B =-P+(1-a)M$ and $\Psi _{BB}= -2(1-a)<0$. Similarly, $\Psi _R =PM_{RR}+MP_{RR}+2M_RP_R$, and by using the first-order conditions, Eqs. (7) and (8), it can be shown that $\Psi _{RR}= M(-2\lambda _If +aG''(rp)^2)-2(M_R)^2 \frac{P}{M}<0$. Similarly, it can shown that $\Psi _{BB}*\Psi _{RR}=-2(1-a)M(-2\lambda _If +aG''(rp)^2) +4(1-a)^2(M_R)^2 > 4(1-a)^2(M_R)^2 = \Psi _{BR}*\Psi _{RB}$

In the second stage of the game, it can be shown that $M_{QQ}=-C''-2\lambda _If(1-R_Q)<0$. This follows from the concavity of the cost function and $R_Q <1$. The latter can be derived from Eq. (8) using the implicit function rule as follows:

$$\begin{aligned} 0< R^s_Q = \left[ \frac{-2\lambda 'f}{-2\lambda 'f +aG''(rp)^2}\right] < 1 \quad {\text { given that }}G''<0 \end{aligned}.$$

Appendix 2 Comparing illegal mining in Case 1 versus Case 2

Totally differentiating (11) and (12), with respect to S, we get the following simultaneous set of equations in matrix notation:

$$\begin{aligned} \left| \begin{array}{ll} -2& \frac{2\lambda _If -a\xi G''(rp)^2}{\lambda _If}\\ -C''& \xi aG''(rp)^2 \end{array} \right| = \left| \begin{array}{l} \frac{{\mathrm{d}}Q}{{\mathrm{d}}\xi }\\ \frac{{\mathrm{d}}R}{{\mathrm{d}}\xi } \end{array} \right| = \left| \begin{array}{l} \frac{aG'rp + \lambda _IK}{\lambda _If}\\ -aG'rp \end{array} \right| \end{aligned}.$$

(20)

Using Cramer’s rule, it can be shown that $\frac{{\mathrm{d}}Q}{{\mathrm{d}}\xi }= \frac{J_1}{J} >0$ and $\frac{{\mathrm{d}}R}{{\mathrm{d}}\xi }= \frac{J_2}{J} >0$, where J is the determinant of the coefficient matrix and is given by $-2\xi aG''(rp)^2 +C''\frac{2\lambda _If-a\xi G''(rp)^2}{\lambda _If} > 0$. $J_1$ is the determinant of the matrix obtained by replacing the first column of the coefficient matrix with the r.h.s of (20) and can be solved into $\left( \xi aG''(rp)^2\frac{g}{f}+2aG'rp \right)$ which can be assumed to $>0$ if the first-order effect dominates. Similarly, $J_2$ is the determinant of the matrix obtained by replacing the second column of the coefficient matrix with the r.h.s of (20) and can be solved into $\left( 2aG'(rp)+ C'' \frac{aG'rp +\lambda _IK}{\lambda _If}\right) >0$. Finally, using these results, it can be shown that $\frac{{\rm d}I}{{\rm d}\xi }=\frac{{\rm d}Q}{{\rm d}\xi }-\frac{{\rm d}R}{{\rm d}\xi } = \frac{1}{J}\left[ a\xi G''(rp)^2\frac{g}{f} -(aG'rp +\lambda _IK)\frac{C''}{\lambda _If}\right] <0 .$

Appendix 3 Comparative statics with respect to the degree of politicization of the audit agency

Totally differentiating Eqs. (15), (14), and (13), with respect to the parameter $\beta$, we get the following system of equations in matrix notation,

$$\begin{aligned} \left| \begin{array}{lll} 1 & -\beta i_IK & aG'rp+\beta i_IK \\ 0 & -2 & \frac{2\beta i_If -aG''(rp)^2}{\beta i_If}\\ 0& -C'' & aG''(rp)^2 \end{array} \right| = \left| \begin{array}{l} \frac{{\rm d}B}{{\rm d}\beta }\\ \frac{{\rm d}R}{{\rm d}\beta }\\ \frac{{\rm d}Q}{{\rm d}\beta } \end{array} \right| = \left| \begin{array}{l} \frac{K(i-1+w)- (1-2a)(Q-R)(i-1+w)}{2(1-a)} \\ \frac{-(1-w)f +rp(1-aG')}{\beta ^2 i_If}\\ 0 \end{array} \right| \end{aligned}.$$

(21)

Using Cramer’s rule, it can be shown that $\frac{{\rm d}Q}{{\rm d}\beta }= \frac{J_2}{J}\lessgtr 0$, depending on $w \gtrless \bar{w}$, and $\frac{{\rm d}R}{{\rm d}\beta }= \frac{J_3}{J}\gtrless 0$ depending on $w \gtrless \bar{w}$, where

• $\bar{w}= 1- \frac{rp(1-aG')}{f}.$

• J is the determinant of the coefficient matrix and is given by $-2aG''(rp)^2 + C''(2\beta i_If - a G''(rp)^2) > 0.$

• $J_2$ is the determinant of the matrix obtained by replacing the second column of the coefficient matrix with the r.h.s of (21) and can be solved into $aG''(rp)^2 \frac{-(1-w)f +rp(1-aG')}{\beta ^2 i_If}.$

• $J_3$ is the determinant of the matrix obtained by replacing the third column of the coefficient matrix with the r.h.s of (21) and can be solved into $C'' \frac{-(1-w)f +rp(1-aG')}{\beta ^2 i_If}.$