The Spillover Effects of Good Governance in a Tax Competition Framework with a Negative Environmental Externality

Abstract

We investigate the impact of a political regime shift affecting consumers, business interests and lobby contributions when countries engage in tax competition in capital and a polluting resource. When consumers have more influence than resource owners, the resource tax rate and public spending rise while environmental damages, lobbying contribution, and the capital tax rate fall. This response can spillover to other countries leading to lower welfare. Capital tax harmonization improves welfare of consumers and resource owners. Resource tax harmonization and governance harmonization both reduce the influence of lobbying and improve consumer welfare but resource owners are worse off.

Appendix 1: Proof of Propositions

1.1 Proposition 1: Optimal Policy Rules

1.1.1 Policy Rules

Lemma

If (a) $1-\frac{\theta M_q }{m}>0$ and (b) $1+\tau \frac{K_r}{k}>0$, at an interior solution to the government’s decision problem, then an increase in either tax rate raises more revenue, given factor prices.

Proof

Differentiate the government’s budget constraint to obtain, $\frac{\partial g}{\partial \theta }=m-\theta M_q =m\left( {1-\frac{\theta M_q }{m}} \right)$ and $\frac{\partial g}{\partial \tau }=k+\tau K_r =k\left( {1+\frac{\tau K_r }{k}} \right)$.

To derive the optimal policy rules we solve the model backward. For the resource owner, $M\left( {q-\theta } \right) =\left( {q-\theta } \right) /d$ solves their decision problem, with $M_q =\frac{dm}{dq}=1/d$. For the representative consumption good firm, we have the demand for capital per worker and demand for the resource per worker, respectively, $K\left( {r+\tau ,q} \right)$ and $N\left( {r+\tau ,q} \right)$, which solve their decision problem. The government chooses its policy to maximize its objective function Eq. (1), taking into account that the responses of the firms and the response of the payment function, $b\left( \theta \right)$. The first order conditions are

$$\begin{aligned} {\Lambda }_\tau= & {} \alpha \left( {(k+\tau K_r } \right) U_g -kU_c )=0. \end{aligned}$$

(12)

$$\begin{aligned} {\Lambda }_\theta= & {} \alpha \left( {\left( {m-\theta M_q } \right) U_g -U_D D_M M_q } \right) -\beta m-\upphi \left( {\frac{\hbox {db}}{\hbox {d}\uptheta }} \right) =0, \end{aligned}$$

(13)

$\square$

Equation (12) yields Eq. (8) of Proposition 1. To obtain Eq. (9) we need to consider the lobby’s choice for $db/d\theta$.

The lobby chooses the resource tax rate to maximize aggregate industry profit net of the political payment, ${\Pi }-b$, subject to the participation constraint, Eq. (3). The first order condition with respect to the resource tax rate is $-m-\frac{\partial b}{\partial \theta }+\eta {\Lambda }_\theta =0$, where $\eta$ is a Lagrange multiplier for the participation constraint. When the government optimizes on the resource tax rate, ${\Lambda }_\theta =0$. These two conditions imply that $\frac{\partial b}{\partial \theta }=-m$. Use Eq. (13) and the truthfulness condition to obtain Eq. (9). Combining (8) and (9) implies (10).

If we assume $u_D =-1,D=\delta m^{2}/2,$ and $C=dm^{2}/2,$ then we obtain the special case of Eq. (9) given by,

$$\begin{aligned} U_g =\left( {1-\frac{\theta }{q-\theta }} \right) ^{-1}\left( {\frac{\beta +\phi }{\alpha }-\frac{\delta }{d}} \right) , \end{aligned}$$

which is Eq. (11), where $\frac{\left( {q-\theta } \right) M_q }{m}=1,$ hence $1-\frac{\theta M_q }{m}=1-\frac{\theta }{q-\theta }>0$. This is positive if the lemma holds.

Combine (12) and (13), and simplify,

$$\begin{aligned}&\left( {1-\frac{\theta }{q-\theta }\frac{\left( {q-\theta } \right) M_q }{m}} \right) =\left( {1+\frac{\tau }{r+\tau }\frac{\left( {r+\tau } \right) K_r }{k}} \right) \\&\quad \times \,\left( {U_D \frac{mD_M }{D}\frac{D}{\theta m}\frac{\theta }{q-\theta }\frac{\left( {q-\theta } \right) M_q }{m}+\frac{\beta +\phi }{\alpha }} \right) , \end{aligned}$$

which simplifies to the special case of Corollary 1 given by Eq. (13),

$$\begin{aligned} \left( {1-\frac{\theta }{q-\theta }} \right) =\left( {1-\frac{\tau }{r+\tau }\varepsilon } \right) \left( {\frac{1}{U_c }} \right) \left( {\frac{\beta +\phi }{\alpha }-\frac{\delta }{d}} \right) , \end{aligned}$$

since $\frac{\left( {q-\theta } \right) M_q }{m}=1$, and where $\varepsilon =-\frac{\left( {r+\tau } \right) K_r }{k}>0$ is the own price elasticity for the demand for capital.

1.2 Transboundary Pollution

Suppose there are pollution spillovers and to simplify assume that all pollution created by resource extraction spills over everywhere. Damage at each location is then given by $D=\delta \left( {\sum m^{j}} \right) ^{2}/2.$ The government in country i chooses the resource tax rate according to,

$$\begin{aligned} \frac{\partial }{\partial \theta }=\alpha \left[ {u_g \left( {m-\theta M_q } \right) -\delta \left( {\sum m^{j}} \right) M_q } \right] -\beta m+\phi \left( {db/d\theta } \right) =0. \end{aligned}$$

(14)

The equation for the lobby’s choice is almost the same as well. When combined,

$$\begin{aligned} \left( {\frac{db}{d\theta }} \right) =-m. \end{aligned}$$

Using this in (14), we have instead,

$$\begin{aligned} U_g \left( {1-{\Theta \xi }} \right) =\frac{\beta +\phi }{a}-\frac{\delta }{d}\frac{\sum m^{j}}{m^{i}}. \end{aligned}$$

The resource lobby’s payment to the local government is still determined in the same manner. The only impact of the pollution spillovers on the policy rules occurs in the term $\frac{\sum m^{j}}{m^{i}}>1$, which magnifies the impact of $\frac{\delta }{d}.$ So the inclusion of the transboundary externality is similar to an increase in the damage parameter $\delta$; an increase in this term due to $\frac{\sum m^{j}}{m^{i}}>1$ leads to an increase in public spending, an increase in the resource tax rate, and a decrease in the capital tax rate, relative to not including the transboundary externality.

1.3 Proposition 2: Policy Responses

1.3.1 Policy Responses to a Shift Toward Consumer Welfare

We also require the second order conditions hold, ${\Lambda }_{\theta \theta } \le 0,{\Lambda }_{\tau \tau } \le 0,$and $\Lambda ={\Lambda }_{\theta \theta } {\Lambda }_{\tau \tau } -{\Lambda }_{\theta \tau } {\Lambda }_{\tau \theta } >0$ is the determinant of the Hessian, where these second derivatives are given by,

$$\begin{aligned} {\Lambda }_{\theta \theta }= & {} \alpha \left( {m-\theta M_q } \right) ^{2}U_{gg} -\alpha U_g \left( {1+{\Theta }} \right) M_q <0,\\ {\Lambda }_{\tau \tau }= & {} \left( {k+\tau K_r } \right) ^{2}U_{gg} +k^{2}U_{cc} +K_r \left( {k+\tau K_r } \right) U_g <0,\\ {\Lambda }_{\tau \theta }= & {} \left( {k+\tau K_r } \right) \left( {m-\theta M_q } \right) U_{gg} , \end{aligned}$$

for an interior solution, where ${\Lambda }_{\tau \theta } <0$ if the lemma holds, and where we have used the policy rules to simplify.¹⁹

To obtain the response of the representative government to an increase in the parameter $\alpha$ when factor prices are fixed totally differentiate Eqs. (12) and (13),

$$\begin{aligned} {\Lambda }_{\theta \theta } d\theta +{\Lambda }_{\theta \tau } d\tau= & {} -\frac{m}{\alpha }d\alpha +m\left( {d\beta +d\phi -\left( {\frac{\alpha }{d}} \right) d\delta } \right) ,\\ {\Lambda }_{\tau \theta } d\theta +{\Lambda }_{\tau \tau } d\tau= & {} 0, \end{aligned}$$

and solve,

$$\begin{aligned} \frac{\partial \theta }{\partial \alpha }= & {} -\frac{{\Lambda }_{\theta \alpha } {\Lambda }_{\tau \tau } }{{\Delta }}>0, \end{aligned}$$

(15)

$$\begin{aligned} \frac{\partial \tau }{\partial \alpha }= & {} \frac{{\Lambda }_{\theta \alpha } {\Lambda }_{\tau \theta } }{{\Delta }}<0, \end{aligned}$$

(16)

under the lemma, where ${\Lambda }_{\theta \alpha } =\frac{m}{\alpha }>0$. The response of government spending is,

$$\begin{aligned} \frac{\partial g}{\partial \alpha }=\left( {1-\theta M_q } \right) \left( {\frac{\partial \theta }{\partial \alpha }} \right) +\left( {1+\tau K_r } \right) \left( {\frac{\partial \tau }{\partial \alpha }} \right) . \end{aligned}$$

Use (15) and (16),

$$\begin{aligned} \frac{\partial g}{\partial \alpha }=-\frac{m}{\alpha }^{2}\frac{\left( {1-\frac{\theta }{q-\theta }\xi } \right) \left( {k^{2}U_{cc} +\left( {1+\frac{\tau }{r+\tau }\varepsilon } \right) U_g K_r } \right) }{\Delta }, \end{aligned}$$

where $\xi =\frac{\left( {q-\theta } \right) M_q }{m}=1$ is the own price elasticity of demand for the resource. Since ${\Delta }\ge 0$ and $k^{2}U_{cc} +\left( {1+\frac{\tau }{r+\tau }\varepsilon } \right) U_g K_r <0$, government spending is increasing in the parameter $\alpha$ when the resource tax rate satisfies (b) of the lemma.

Following the same procedure, the resource tax rate is decreasing in $\beta$ and $\phi$, the capital tax rate is increasing in $\beta$ and $\phi$, and government spending is decreasing in $\beta$ and $\phi$, if part a of the Lemma holds. Finally, the impact of $\delta$ on the equilibrium policy is the same as that of $\alpha$, given prices; an increase in the damage parameter causes the resource tax rate and public spending to increase, and the capital tax rate to fall.

1.3.2 Response of Prices to an Increase in the Resource Tax Rate in One Country

Suppose the resource tax rate increases in country i in response to an increase in $\alpha$ in that country, for example. And suppose that the tax rates in non-reform countries are fixed, but government spending responds to changes in the tax base in those countries. Differentiate the equilibrium conditions and solve to obtain,

$$\begin{aligned} \frac{\partial q}{\partial \theta ^{i}}= & {} M_q^i \sum \nolimits _j \frac{K_r^j }{H}>0,\\ \frac{\partial r}{\partial \theta ^{i}}= & {} M_q^i \sum \nolimits _j \frac{K_q^j }{H}, \end{aligned}$$

where $H=\mathop \sum \nolimits _j \left( {M_q^j -N_q^j } \right) \mathop \sum \nolimits _j K_r^j -\mathop \sum \nolimits _j N_r^j \mathop \sum \nolimits _j K_q^j <0.$ This is essentially the response of prices to $\alpha$ in country i. An increase in $\alpha$ in country i that raises the resource tax rate in that country will cause the resource price to increase and this will spillover to other countries. If $f_{kn} >\left( < \right) 0,$ and hence $K_q^j <\left( > \right) 0,$ then the return on capital decreases (increases) with the resource tax rate in the reform country.

1.4 Policy Reform Analysis

Differentiate the indirect utility function of the representative consumer,

$$\begin{aligned} \hbox {dV}= & {} \left[ (\hbox {m}-\theta M_q )U_g -U_D D_M M_q \right] {d\theta +}\left[ \left( {k+tK_r } \right) U_g -kU_c \right] dt\\&+ \left[ U_g \left( {\frac{dR}{dq}} \right) +U_c \frac{dw}{dq}+U_D D_M M_q\right] {dq+} \left[ \left( {s-k} \right) U_c +U_g \frac{dR}{dr}\right] dr, \end{aligned}$$

where $\frac{dR}{dq}=\theta M_q +tK_q$ is the response of tax revenue to q, $\frac{dW}{dq}=-n$, and so on. Use the rules for the tax rates in the lobby equilibrium to simplify,

$$\begin{aligned} \hbox {dV} = \left[ {\frac{\beta +\phi }{\alpha }} \right] d\theta {+}\left[ \left( {\frac{dR}{dq}} \right) U_g {+}\frac{dw}{dq}U_c +U_D D_M M_q \right] {dq+} \left[ \left( {s-k} \right) U_c +U_g \frac{dR}{dr}\right] dr.\nonumber \\ \end{aligned}$$

(17)

Next, differentiate the profit equation,

$$\begin{aligned} d{\Pi }=m\left( {dq-d\theta } \right) . \end{aligned}$$

(18)

Next, to obtain the response of society’s welfare to a parameter, calculate $\alpha dV+\beta d{\Pi }+Vd\alpha +{\Pi }d\beta$ to get,

$$\begin{aligned} d{\Lambda }=Vd\alpha +{\Pi }d\beta +\phi md\theta +\left[ {\alpha A_1 +\beta m} \right] dq+\alpha A_2 dr, \end{aligned}$$

(19)

where $A_1 =\left( {\frac{dR}{dq}} \right) U_g +\frac{dw}{dq}U_c +U_D D_M M_q$ and $A_2 =\left( {s-k} \right) U_c +U_g \frac{dR}{dr}$.

Equation (17) governs the welfare effects for consumers of any change in parameters, (18) governs the response of profit, and (19) governs society’s welfare, a combination of (17) and (18). Unfortunately, each equation is ambiguous. For example, the second and third expressions are ambiguous. The first expression in (17) captures the impact of the resource tax rate as it affects public spending and environmental damage. The second and third expressions capture the impact of relative prices on welfare, which are both ambiguous. From Eq. (18), resource profit is increasing in the net resource price.