A political economy of tax havens

Abstract

The welfare effect of the existence of tax havens on high-tax countries has not been conclusive in the theoretical literature. Some papers show that the existence of tax havens is harmful to high-tax countries, while other studies argue that the opposite could occur. We aim to address a question: Do these welfare-reducing or welfare-enhancing properties still hold in the presence of lobbying? We find that the welfare-enhancing property does not hold, provided that the policy-maker attaches a sufficiently large weight to the political contribution received. Moreover, we point out that the cooperation among high-tax countries in restricting the international tax planning activity can lead to a lower level of social welfare in all high-tax countries.

Appendices

Appendix 1: Derivation of (11) without the global-truthfulness assumption

According to Grossman and Helpman (1994), $t^{e}$is a sub-game-perfect Nash equilibrium of the lobbying game, if (i) $t^{e}$ maximizes $\theta m^{k}(t)+W(t)$ and (ii) $t^{e}$ maximizes $W^{k}(t)-m^{k}(t)+[\theta m^{k}(t)+W(t)]$. Condition (i) stipulates that, given the contribution schedule provided by the lobbyists, the policy-maker chooses $t$ to maximize his own welfare. Condition (ii) states that the equilibrium tax rate should maximize the joint welfare of the lobbyists and the policy-maker. If this condition is violated, then the lobbyists could reformulate the political contribution schedule to induce the policy-maker to choose the jointly optimal policy.

Condition (i) implies that

$$\begin{aligned} \theta \frac{\partial m^{k}(t^{e})}{\partial t}+\frac{\partial W(t^{e})}{\partial t}=0 \end{aligned}$$

(22)

and condition (ii) implies that

$$\begin{aligned} \frac{\partial W^{k}(t^{e})}{\partial t}-\frac{\partial m^{k}(t^{e})}{\partial t}+\left[ {\theta \frac{\partial m^{k}(t^{e})}{\partial t}+\frac{\partial W(t^{e})}{\partial t}} \right] =0 \end{aligned}$$

(23)

Taken together, the two conditions ensure that

$$\begin{aligned} \frac{\partial m^{k}(t^{e})}{\partial t}=\frac{\partial W^{k}(t^{e})}{\partial t} \end{aligned}$$

(24)

This condition shows that the contribution schedule is locally truthful around the equilibrium $t$; i.e., the lobbying group sets its contribution schedule so that the marginal change in the contribution for a small change in the tax rate fits the effect of the change in $t$ on the lobbying group’s gross welfare.

Then by inserting (24) into (22), we obtain (11), which is the same as the first-order condition with the global-truthfulness assumption. Thus, the equilibrium policy under the global-truthfulness assumption is the same as that without the assumption. The workers’ and pensioners’ lobbying can be obtained by a similar approach, and so we do not repeat it here.

Appendix 2: Derivation of (15)

We first derive the effects of the capital tax and tax planning on the social welfare by using (8) and (9a)–(9f):

$$\begin{aligned}&\frac{\partial W}{\partial t}=-n^{k}h\psi -n^{k}(1+h)(1-\psi )+(1+\beta )\left[ {n^{k}(1-\psi +h)+(1-\psi )^{2}\frac{t}{{f}''}} \right] \nonumber \\ \end{aligned}$$

(25)

$$\begin{aligned}&\frac{\partial W}{\partial \psi }=-n^{k}ht+n^{k}(1+h)t+(1+\beta )t\left[ {-(1-\psi )\frac{t}{{f}''}-n^{k}} \right] \end{aligned}$$

(26)

Supposing the economy is initially in equilibrium, we can then substitute (12) into (25) and (26), and further substitute them into (14), which gives:

$$\begin{aligned}&\frac{dW}{d\psi }=\frac{\partial W}{\partial t}\frac{dt}{d\psi }+\frac{\partial W}{\partial \psi }=\frac{-n^{k2}h\psi {f}''\theta }{(1+\beta )(1-\psi )^{3}}(\beta -\beta \psi +2\beta h-h\psi \theta -h\theta )\\&\quad -\frac{n^{k2}{f}''}{(1+\beta )(1-\psi )^{3}}(\beta h-h\psi \theta )\beta (1-\psi +h-h\psi \theta ). \end{aligned}$$

By rearranging the above equation, we can obtain (15) in the main text.

Appendix 3: Proof of Proposition 3

From (14), we see that

$$\begin{aligned} \frac{dW}{d\psi }\frac{>}{<}0\Leftrightarrow -\psi h\theta ^{2}+(1-\psi +h)\beta ^{2}\frac{>}{<}0. \end{aligned}$$

Rearranging the above equation yields

$$\begin{aligned} \frac{dW}{d\psi }\frac{>}{<}0\Leftrightarrow \theta ^{2}\frac{<}{>}\frac{(1-\psi +h)\beta ^{2}}{h\psi }, \end{aligned}$$

and since $\theta$ and $\beta$ are non-negative, we have proved Proposition 3.

Appendix 4: Derivation of (17)

The change in each country’s welfare in response to $\hat{{\psi }}$ can be expressed as:

$$\begin{aligned} \frac{dW}{d\hat{{\psi }}}=\frac{\partial W}{\partial t}\frac{dt}{d\hat{{\psi }}}+\frac{\partial W}{\partial \hat{{\psi }}}. \end{aligned}$$

(27)

First, we use the conditions $\partial W^{k}/\partial \hat{{\psi }}=n^{k}t,\, \partial W^{l}/\partial \hat{{\psi }}=0$ and $\partial W^{p}/\partial \hat{{\psi }}=-n^{k}t$ to obtain $\partial W/\partial \hat{{\psi }}=-\beta n^{k}t$. Substituting this condition and (25) into (27) gives:

$$\begin{aligned} \frac{dW}{d\hat{{\psi }}}=\frac{-n^{k2}h\psi {f}''\theta }{(1+\beta )(1-\psi )^{3}}(\beta -\beta \psi +2\beta h-h\psi \theta -h\theta )-\beta n^{k}t. \end{aligned}$$

(28)

Now we insert the initial equilibrium tax rate (12) into (28):

$$\begin{aligned} \frac{dW}{d\hat{{\psi }}}&= \frac{-n^{k2}h\psi {f}''\theta }{(1+\beta )(1-\psi )^{3}}(\beta -\beta \psi +2\beta h-h\psi \theta -h\theta ) \\&+\,\beta n^{k}\frac{n^{k}{f}''}{(1+\beta )(1-\psi )^{2}}\left[ {\beta (1-\psi +h)-h\psi \theta } \right] \\&= \frac{n^{k2}{f}''\left\{ {\beta (1-\psi )\left[ {\beta (1-\psi +h)-h\psi \theta } \right] -(\beta -\beta \psi +2\beta h-h\psi \theta -h\theta )h\psi \theta } \right\} }{(1+\beta )(1-\psi )^{3}} \\ \end{aligned}$$

After some algebra we can obtain (17) in the main text.

Appendix 5: Proof of Proposition 5

Let us define the function

$$\begin{aligned} \Omega (\theta )=-h^{2}\psi (1+\psi )\theta ^{2}+2h\beta \theta (1-\psi +h)-\beta ^{2}(1-\psi +h)(1-\psi ), \end{aligned}$$

and let $D$ be the discriminant of $\Omega (\theta )=0$. Thus, we have:

$$\begin{aligned} D=4h^{2}\beta ^{2}(1-\psi +h)\psi (\psi +h\psi -1). \end{aligned}$$

From (17), it can obviously be seen that $\partial W/\partial \hat{{\psi }}$ and $\Omega (\theta )$ share the same sign. If $(\psi +h\psi -1)<0$, then $D<0,\, \Omega (\theta )<0$ so that $\partial W/\partial \hat{{\psi }}<0$. However, if $(\psi +h\psi -1)>0$, $\Omega (\theta )$ can be rewritten as:

$$\begin{aligned} \Omega (\theta )&= \left[ {\theta -\frac{\psi (1-\psi +h)+\sqrt{(1-\psi +h)\psi (\psi +h\psi -1)}}{(1+\psi )h\psi }\beta } \right] \nonumber \\&\; \times \left[ {\theta -\frac{\psi (1-\psi +h)-\sqrt{(1-\psi +h)\psi (\psi +h\psi -1)}}{(1+\psi )h\psi }\beta } \right] . \end{aligned}$$

(29)

Thus, we have proved that, under the condition $(\psi +h\psi -1)>0$, $\partial W/\partial \hat{{\psi }}$ is positive if $\theta$ lies within a positive interval.

Appendix 6: Worker’s lobbying

We first replace $(\theta , \beta )$ in (15) by $(\Theta , B)$ to derive the condition:

$$\begin{aligned} \frac{dW}{d\psi }\frac{>}{<}0\;if\;\left[ {-\psi h\Theta ^{2}+(1-\psi +h)B^{2}} \right] \frac{>}{<}0. \end{aligned}$$

Hence, we see that $dW/d\psi$ is more likely to be negative if $|\Theta |$ is larger, that is, if the difference between $\theta$ and $\delta$ is larger. Next, by replacing $(\theta , \beta )$ in (29) by $(\Theta , B)$, we can show that, under the condition $(\psi +h\psi -1)>0$, $\partial W/\partial \hat{{\psi }}$ will be positive, if $\theta$ lies within the following interval:

$$\begin{aligned} \frac{\psi (1-\psi +h)-\Gamma }{(1+\psi )h\psi }(\beta -\delta )+\delta <\theta <\frac{\psi (1-\psi +h)+\Gamma }{(1+\psi )h\psi }(\beta -\delta )+\delta , \end{aligned}$$

where $\Gamma =\sqrt{(1-\psi +h)\psi (\psi +h\psi -1)}$.