International tax competition with endogenous sequencing

Abstract

This paper examines endogenous timing in an international tax competition model. Unlike existing studies, governments are assumed to decide not only tax rates but also whether they are set early or late. The Nash equilibrium provides four conclusions for alternative double tax allowances. First, tax deductions cause simultaneous tax competition, whereas tax credits yield sequential tax competition. Second, any double taxation relief would generate capital trade. Third, a credit system could maximize one country’s economic welfare but would lower another country’s economic welfare more than a deduction regime. Fourth, a home country’s government would choose credit regimes under a maximax rule, but select deduction methods under minimax and maximin rules, while all double tax allowances are indifferent to a host country. The findings resolve the question raised by Bond and Samuelson (Economic Journal 99:1099–1111, 1989) of why governments choose tax credits when tax deductions are clearly better. Namely, this paper shows that one country is better off but another is worse off with credits rather than deductions. Accordingly, we cannot clearly specify whether governments choose credit systems or deduction regimes. The possible double tax allowances employed by the governments depend on their own decision criterion.

Appendix

This appendix extends the pure strategy to include the mixed strategy with respect to the timing of setting tax rates. The analytical method follows Gibbons (1992). Suppose that the home country’s government believes that the foreign country’s government will play first with probability f∈[0,1] and second with probability (1−f). That is, the home country’s government believes that the foreign country’s government will play the mixed strategy {f,1−f}. Let {h,1−h} denote the mixed strategy in which the home country’s government chooses first with probability h∈[0,1]. For each value of f between zero and one, we now compute the value of h, denoted $\hat{h}(f)$, such that {h,1−h} is the best response for the home country’s government to {f,1−f} by the foreign country’s government.

We will begin with the analysis of DED. The home government’s expected payoff from playing {h,1−h} when the foreign country’s government play {f,1−f} is

$$ h\bigl[(Y_{\mathit{DH}} - Y_{\mathit{DS}}) - f\bigl\{ (Y_{\mathit{DH}} - Y_{\mathit{DS}}) - (Y_{\mathit{DS}} - Y_{\mathit{DF}})\bigr\} \bigr] + \bigl[fY_{\mathit{DF}} + (1 - f)Y_{\mathit{DS}}\bigr], $$

(16)

where both (Y _DH −Y _DS ) and (Y _DS −Y _DF ) are positive from Lemma 3. Accordingly, (16) is increasing in h, because f is between zero and one. This result means that the home government’s best response is h=1 (i.e., first) for any value of f between zero and one. An analogous discussion would indicate that the foreign government’s best response is f=1 (i.e., first) for any value of h between zero and one. Consequently, only DED would cause an equilibrium (i.e., h=1 and f=1). That is, both governments select first in the equilibrium under DED.

Next, let us examine the case of CRE. The result is summarized in Fig. 3. The home government’s expected payoff from playing {h,1−h} when the foreign country’s government is playing {f,1−f} is

$$ h\bigl[(Y_{\mathit{CH}} - Y_{\mathit{CS}}) - f\bigl\{ (Y_{\mathit{CH}} - Y_{\mathit{CS}}) + (Y_{\mathit{CF}} - Y_{\mathit{CS}})\bigr\} \bigr] + \bigl[fY_{\mathit{CF}} + (1 - f)Y_{\mathit{CS}}\bigr], $$

(17)

where both (Y _CH −Y _CS ) and (Y _CF −Y _CS ) are positive from Lemma 4. Letting ϕ ^∗ denote (Y _CH −Y _CS )/{(Y _CH −Y _CS )+(Y _CF −Y _CS )}, (17) is increasing in h as f<ϕ ^∗, and is independent of h as f=ϕ ^∗, as well as decreasing in h as f>ϕ ^∗. Accordingly, the home government’s best response is h=1 (i.e., first) if f<ϕ ^∗ and h=0 (i.e., second) if f>ϕ ^∗, as indicated by the two horizontal segments of $\hat{h}(f)$, or AD and BE in Fig. 3.

Fig. 3

Mixed strategy equilibria with tax credits

On the other hand, the home government’s expected payoff (17) is independent of h when f=ϕ ^∗. In this case, the home country’s government is indifferent among all the mixed strategies {h,1−h}. That is, when f=ϕ ^∗ the mixed strategies {h,1−h} are a best response to {f,1−f} for any value of h between zero and one. Thus, $\hat{h}(\phi^{*})$ is the entire interval [0,1], as indicated by the vertical segment of $\hat{h}(f)$, or DE in Fig. 3. Similar reasoning can derive the value of f, denoted $\hat{f}(h)$, such that {f,1−f} is a best response for the foreign country’s government to {h,1−h} by the home country’s government. This result is illustrated as the kinked segments AFCGB in Fig. 3.

When the tax rule is CRE, therefore, the equilibria can occur at three intersections of $\hat{h}(f)$ and $\hat{f}(h)$ in Fig. 3. The first equilibrium (i.e., h=1 and f=0) corresponds to point A, and the second equilibrium (i.e., h=0 and f=1) coincides with point B. In the two equilibria, one country’s government chooses first, and another country’s government selects second. Moreover, the third equilibrium (h=ϕ and f=ϕ ^∗) occurs at point C. It means that the home country’s government chooses first with probability ϕ where ϕ denotes $(Y_{\mathit{CF}}^{*} - Y_{\mathit{CS}}^{*})/\{(Y_{\mathit{CF}}^{*} - Y_{\mathit{CS}}^{*})+ (Y_{\mathit{CH}}^{*} - Y_{\mathit{CS}}^{*})\}$. Meanwhile, the foreign country’s government selects first with probability ϕ ^∗.

According to Lemma 4, the home and the foreign payoffs are, respectively, Y _CH and $Y_{\mathit{CH}}^{*}$ in the first equilibrium (i.e., h=1 and f=0) and Y _CF and $Y_{\mathit{CF}}^{*}$ in the second equilibrium (i.e., h=0 and f=1). In these cases, one country’s government could maximize its national income, while the other one could avoid the greatest damage. When we compare the two equilibria, hence, we cannot say that one dominates the other. In the third equilibrium (i.e., h=ϕ and f=ϕ ^∗), both governments would gain the expected payoffs where the weights are the probabilities (ϕ,ϕ ^∗). Because the expected payoffs of the home and foreign countries include, respectively, Y _CS and $Y_{\mathit{CS}}^{*}$, i.e., the lowest level of their own national incomes, the third equilibrium cannot allow both countries to be better off than the other. Even if we consider the risk-dominance criteria as defined by Harsanyi and Selten (1988), it is ambiguous whether the third equilibrium is dominant and plausible. Therefore, it is impossible to select a convincing equilibrium under CRE.