Endogenous Security, Third-Party Trade, and Interstate Disputes: A Conflict-Theoretic Analysis: Defence and Peace Economics: Vol 34 , No 2

ABSTRACT

This paper examines third-party trade and its implications for conflicts between hostile countries not engaging in trade. We present a conflict-theoretic model to analyze two adversaries’ endogenous arming decisions when they separately establish a free trade agreement (FTA) with a neutral third-party state. We contrast this multiple FTAs regime with a single FTA regime between one adversary and the third-party state, which excludes the other adversary as a non-member. In our analysis, the benchmark case is a protectionist regime when the bilateral trade between the third-party state and each of the adversaries is a tariff war. Among the three trade regimes, we show that the two adversaries’ aggregate arming is the lowest under multiple FTAs but is the highest under a single FTA. These results suggest that, despite no trade between two adversary countries, multiple FTAs through third-party trade have the pacifying or appeasing effect of lowering overall military buildups in interstate conflicts.

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Disclosure statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Nor do the authors have any financial and personal relationships with other organizations or people that could inappropriately influence or bias their work.

A-4. Decomposing the welfare effect of arming for each adversary country

Under the assumption of symmetry, we look at the welfare effect of country A’s arming and show that the effect contains three different components. Country A’s overall welfare under the protectionist regime is: $S W^{A, P R} = C S^{A, P R} + P S^{A, P R} + T R^{A, P R},$

which implies that

S W^{A, P R} = \frac{1}{2 β} [(Q_{a}^{A, P R})^{2} + (A P P_{b})^{2} + (Q_{c}^{A, P R})^{2}] + P_{a}^{A, P R} X_{a}^{A, P R} + P_{b}^{A, P R} A P P_{b} + τ_{c}^{A, P R} Q_{c}^{A, P R},

noting that $A P P_{b}$ represents the amount of good b that country A appropriates from its rival for domestic consumption. Taking the derivative of $S W^{A, P R}$ with respect to $G^{A}$ yields:

\begin{aligned} \frac{\partial S W^{A, P R}}{\partial G^{A}} = \frac{1}{β} (\frac{\partial Q_{a}^{A, P R}}{\partial G^{A}} Q_{a}^{A, P R} + \frac{\partial A P P_{b}}{\partial G^{A}} A P P_{b} + \frac{\partial Q_{c}^{A, P R}}{\partial G^{A}} Q_{c}^{A, P R}) + (\frac{\partial P_{a}^{A, P R}}{\partial G^{A}} X_{a}^{A, P R} + \frac{\partial X_{a}^{A, P R}}{\partial G^{A}} P_{a}^{A, P R}) \\ + (P_{b}^{A, P R} \frac{\partial A P P_{b}}{\partial G^{A}} + A P P_{b} \frac{\partial P_{b}^{A, P R}}{\partial G^{A}}) + (τ_{c}^{A, P R} \frac{\partial Q_{c}^{A, P R}}{\partial G^{A}} + \frac{\partial τ_{c}^{A, P R}}{\partial G^{A}} Q_{c}^{A, P R}) . \end{aligned}

For several terms on the right-hand side of the above equation, we note the following:

(i) $\frac{\partial Q_{a}^{A, P R}}{\partial G^{A}} = - β \frac{\partial P_{a}^{A, P R}}{\partial G^{A}}$ ;

(ii) $\frac{\partial (τ_{c}^{A, P R} Q_{c}^{A, P R})}{\partial G^{A}} = \frac{\partial τ_{c}^{A, P R}}{\partial G^{A}} Q_{c}^{A, P R} + τ_{c}^{A, P R} \frac{\partial Q_{c}^{A, P R}}{\partial G^{A}} = 0$ since both $τ_{c}^{A, P R}$ and $Q_{c}^{A, P R}$ areindependent of $G^{A}$ ;

(iii) $\frac{\partial P_{b}^{A, P R}}{\partial G^{A}} = - \frac{1}{β} \frac{\partial A P P_{b}}{\partial G^{A}}$ Since $P_{b}^{A, P R} = \frac{1}{β} [α - \frac{G^{A}}{G^{A} + G^{B}} (R - G^{B})]$ and

A P P_{B} = \frac{G^{A}}{G^{A} + G^{B}} (R - G^{B}) .

Taking into account the conditions (i)-(iii), we simplify the derivative of $S W^{A, P R}$ with respect to $G^{A}$ into three terms:

\frac{\partial S W^{A, P R}}{\partial G^{A}} = \frac{\partial P_{a}^{A, P R}}{\partial G^{A}} (X_{a}^{A, P R} - Q_{a}^{A, P R}) + \frac{\partial A P P_{b}}{\partial G^{A}} P_{b}^{A, P R} + \frac{\partial X_{a}^{A, P R}}{\partial G^{A}} P_{a}^{A, P R} .

The impact that arming has on overall welfare has three different effects:

(1) The first term, $\frac{\partial P_{a}^{A, P R}}{\partial G^{A}} (X_{a}^{A} - Q_{a}^{A, P R}),$ shows the export-revenue effect of arming;

(2) The second term, $\frac{\partial A P P_{b}}{\partial G^{A}} P_{b}^{A, P R},$ is the resource-appropriation effect of arming;

(3) The third term, $\frac{\partial X_{a}^{A, P R}}{\partial G^{A}} P_{a}^{A, P R},$ is the output-distortion effect of arming.

A-5. Optimal arming is lower under multiple FTAs than under the protectionism regime

We adopt the approach by evaluating the slope of the $S W^{A, M}$ when there are multiple FTAs at the equilibrium arming allocations under the protectionist regime. The slope of the $S W^{A, M}$ is:

\frac{\partial S W^{A, M}}{\partial G^{A}} = \frac{\partial P_{a}^{A, M}}{\partial G^{A}} (X_{a}^{A, M} - Q_{a}^{A, M}) + \frac{\partial A P P_{b}}{\partial G^{A}} P_{b}^{A, M} + \frac{\partial X_{a}^{A, M}}{\partial G^{A}} P_{a}^{A, M} .

We then conduct a comparison for each effect (that is, each term) separately as follows:

(i) Comparing the export-revenue effect of arming

We evaluate the following expression:

(a.21)

[\frac{\partial P_{a}^{A, M}}{\partial G^{A}} (X_{a}^{A, M} - Q_{a}^{A, M}) - \frac{\partial P_{a}^{A, P R}}{\partial G^{A}} (X_{a}^{A, P R} - Q_{a}^{A, P R})]

(a.21)

at the point where $G^{A, P R} = G^{B, P R} = G,$ noting the following:

(a.22)

P_{a}^{A, P R} = \frac{G^{A} (2 G^{A} - 2 R + 3 α) + 3 α G^{B} + 2 D^{A} (G^{A} + G^{B})}{3 β (G^{A} + G^{B})},

(a.22)

(a.23)

P_{a}^{A, M} = \frac{2 α - (\frac{G^{A}}{G^{A} + G^{B}}) (R - G^{A}) - D^{A}}{2 β},

(a.23)

$\frac{\partial P_{a}^{A, M}}{\partial G^{A}} = \frac{{(G^{A})}^{2} + G^{B} (2 G^{A} - R)}{2 β {(G^{A} + G^{B})}^{2}},$ $\frac{\partial P_{a}^{A, P R}}{\partial G^{A}} = \frac{2 [G^{A} (G^{A} + 2 G^{B}) - R G^{B}]}{3 β {(G^{A} + G^{B})}^{2}} .$

After substituting (a.22) and (a.23) back into (a.21), we have:

(a.24)

[\frac{\partial P_{a}^{A, M}}{\partial G^{A}} (X_{a}^{A, M} - Q_{a}^{A, M}) - \frac{\partial P_{a}^{A, P R}}{\partial G^{A}} (X_{a}^{A, P R} - Q_{a}^{A, P R})] = \frac{(R - 3 G) (G + 2 D - R)}{288 G β} > 0.

(a.24)

(ii) Comparing the resource- appropriation effect of arming

We evaluate the following expression:

(a.25)

[\frac{\partial A P P_{B}}{\partial G^{A}} (P_{b}^{A, M} - P_{b}^{A, P R})]

(a.25)

at the point where $G^{A, P R} = G^{B, P R} = G$ . Since

P_{b}^{A, M} = P_{b}^{A, P R} = \frac{1}{β} (α - \frac{G^{A}}{G^{A} + G^{B}} (R - G^{B}))

we have from (a.5) that

(a.26)

\frac{\partial A P P_{B}}{\partial G^{A}} (P_{b}^{A, M} - P_{b}^{A, P R}) = 0.

(a.26)

(iii) Comparing the output-distortion effect of arming

We evaluate the following expression:

(a.27)

[\frac{\partial X_{a}^{A}}{\partial G^{A}} (P_{a}^{A, M} - P_{a}^{A, P R})]

(a.27)

at the point where $G^{A, P R} = G^{B, P R} = G,$ noting that

\frac{\partial X_{a}^{A}}{\partial G^{A}} = \frac{\partial (\frac{G^{A}}{G^{A} + G^{B}} (R - G^{A}) - D^{A})}{\partial G^{A}} = - \frac{G^{A} (G^{A} + 2 G^{B}) - R G^{B}}{{(G^{A} + G^{B})}^{2}} .

Substituting the results from (a.22) and (a.23) into (a.27), taking into account the above derivative, we have:

(a.28)

[\frac{\partial X_{a}^{A}}{\partial G^{A}} (P_{a}^{A, M} - P_{a}^{A, P R})] = \frac{(R - 3 G) (G + 2 D - R)}{48 G β} < 0

(a.28)

Taking the summation of the differences in the three effects as shown in (a.24), (a.26), and (a.28) yields:

\frac{(R - 3 G) (G + 2 D - R)}{288 G β} + \frac{(R - 3 G) (G + 2 D - R)}{48 G β} = \frac{5 (R - 3 G) (G + 2 D - 5)}{288 G β} < 0

That is,

\frac{\partial S W^{A, M}}{\partial G^{A}} |_{G^{A} = G^{B} = G^{A, P R} = G^{B, P R} = G} < 0.

The strict concavity of the welfare function implies that $G^{A, M} < G^{A, P R}$ . Thus, a move from the protectionism regime to the multiple FTAs regime induces both adversary countries to reduce their arming. This result arises since the sum of the export-revenue effect and the resource-predation effect, which measures the marginal revenue of arming, exceeds the output-distortion effect, which measures the marginal cost of arming.

A-6. Conflict intensity under single FTAs exceeds that under multiple FTAs

We evaluate the slope of $S W^{B, S}$ when there is a single FTA, at the equilibrium arming allocations under multiple FTAs. Between the two alternative regimes, we then conduct a comparison for each effect separately as follows:

(i) Comparing the export-revenue effect of arming

We evaluate the following expression:

(a.29)

[\frac{\partial P_{b}^{B, S}}{\partial G^{B}} (X_{b}^{B, S} - Q_{b}^{B, S}) - \frac{\partial P_{b}^{B, M}}{\partial G^{B}} (X_{b}^{B, M} - Q_{b}^{B, M})]

(a.29)

at the point where $G^{B, M} = G^{A, M} = G$ , noting the following:

P_{b}^{B, M} = \frac{1}{2 β} [2 α - (\frac{G^{B}}{G^{A} + G^{B}} (R - G^{B}) - D^{B})],

$\frac{\partial P_{b}^{B, M}}{\partial G^{B}} = \frac{G^{B} (2 G^{A} + G^{B}) - R G^{A}}{2 β {(G^{A} + G^{B})}^{2}},$ $τ_{b}^{C, S} = \frac{1}{3 β} [(\frac{G^{B}}{G^{A} + G^{B}} (R - G^{B}) - D^{B})],$

P_{b}^{B, S} = \frac{2 α - (\frac{G^{B}}{G^{A} + G^{B}} (R - G^{B}) - D^{B}) - β τ_{b}^{C, S}}{2 β},

\frac{\partial P_{b}^{B, S}}{\partial G^{B}} = \frac{G^{B} (2 G^{A} + G^{B}) - R G^{A}}{3 β {(G^{A} + G^{B})}^{2}} .

After substituting the above equations into (a.29), after rearranging terms, we have the following result:

(a.30)

[\frac{\partial P_{b}^{B, S}}{\partial G^{B}} (X_{b}^{B, S} - Q_{b}^{B, S}) - \frac{\partial P_{b}^{B, M}}{\partial G^{B}} (X_{b}^{B, M} - Q_{b}^{B, M})] = - \frac{5 (R - 3 G) (G + 2 D - R)}{288 G β} .

(a.30)

(ii) Comparing the resource-appropriation effect of arming:

We evaluate the following expression:

(a.31)

[\frac{\partial A P P_{a}}{\partial G^{B}} (P_{a}^{B, S} - P_{a}^{B, M})]

(a.31)

at the point where $G^{A, P R} = G^{B, P R} = G$ . Given that

P_{a}^{B, M} = P_{a}^{B, S} = \frac{1}{β} (α - \frac{G^{B}}{G^{A} + G^{B}} (R - G^{A}))

we have from (a.31) that

(a.32)

\frac{\partial A P P_{a}}{\partial G^{B}} (P_{a}^{B, S} - P_{a}^{B, M}) = 0.

(a.32)

(iii) Comparing the output-distortion effect of arming:

We evaluate the following expression:

(a.33)

[\frac{\partial X_{b}^{B}}{\partial G^{B}} (P_{b}^{B, S} - P_{b}^{B, M})]

(a.33)

at the point where $G^{A, M} = G^{B, M} = G,$ noting that

\frac{\partial X_{b}^{B}}{\partial G^{B}} = \frac{\partial (\frac{G^{B}}{G^{A} + G^{B}} (R - G^{B}) - D^{B})}{\partial G^{B}} = - \frac{G^{B} (G^{B} + 2 G^{A}) - R G^{A}}{{(G^{A} + G^{B})}^{2}} .

Substituting the above equation into (a.33), we have the following result:

(a.34)

[\frac{\partial X_{b}^{B}}{\partial G^{B}} (P_{b}^{B, S} - P_{b}^{B, M})] = \frac{(R - 3 G) (G + 2 D - R)}{48 β G} .

(a.34)

The summation of the differences in the three effects as shown in (a.30), (a.32), and (a.34) leads to

- \frac{5 (R - 3 G) (G + 2 D - R)}{288 G β} + \frac{(R - 3 G) (G + 2 D - R)}{48 β G} = \frac{5 (R - 3 G) (G + 2 D - R)}{288 β G} > 0

That is,

\frac{\partial S W^{B, S}}{\partial G^{A}} |_{G^{A} = G^{B} = G^{A, M} = G^{B, M} = G} > 0.

The positive sign indicates that

G^{B, S} > G^{B, M}

A move from the multiple FTAs to the single FTA induces the non-member adversary (Country B) to increase its arming since the sum of the export-revenue effect plus the resource-predation effect, which is the marginal revenue of arming, dominates the output distortion effect, which is the marginal cost of arming.

Notes

1. See, e.g. The Global Risks Report of 2018, World Economic Forum.

2. Bagwell, Bown, and Staiger (Citation2016) present a systematic review of issues related to preferential trade agreements, as well as on the perils and promise facing the world trading system.

3. An example of the move is the United Kingdom’s decision to leave the European Union.

4. Some third-party interventions have the objective of conflict management (i.e. United Nations peacekeeping missions). Such an ideal motivation may not drive all third-party actions. Regan (Citation1998) links interventions by external powers to their national interests and considers it the ‘paradigm of realism’ and the dominant philosophy in international politics. For other studies on third-party interventions see, e.g. Cetinyan (Citation2002), Rowlands and Carment (Citation2006), Chang and Sanders (Citation2009), Grigorian (Citation2010), Sanders and Walia (Citation2014), Sawyer, Cunningham, and Reed (Citation2015), Chang et al., (Citation2015), Cunningham (Citation2016), and Chang, Luo, and Zhang (Citation2018).

5. For studies that analyze the correlation between trade and conflict, see, e.g. Polachek (Citation1980), Mansfield and Pollins (Citation2001), Reuveny (Citation2002), Polachek and Seiglie (Citation2007), and Glick and Taylor (Citation2010). Polachek (Citation1980) shows that strengthening the extent of trade openness between contending countries is conflict-reducing. This result is echoed by Oneal and Russett (Citation1999). Kim and Rousseau (Citation2005) find that the pacifying effect of greater trade openness can be neutral. Other studies, such as Barbieri (Citation1996), find that extensive links through trade may increase armed conflicts. Barbieri and Levy (Citation1999) show that war does not significantly impact trade between adversaries. There is no consensus on the trade-conflict nexus. See Copeland (Citation2015) for a systematic survey of the literature on trade and conflict in international relations.

6. See, e.g. Gowa (Citation1995) and Copeland (Citation2015). For example, Israel and most Arab countries do not trade; Saudi Arabia and Iran do not trade, nor do Morocco and Algeria.

7. For studies on the Arab-Israel Conflict see, e.g. the book edited by Fawcett (Citation2016).

8. For studies on economic integration through establishing FTAs without resource conflicts see, e.g. Bhagwati and Panagariya (Citation1996), Bagwell and Staiger (Citation1997, Citation1999), Baier and Bergstrand (Citation2004, Citation2007), Egger and Larch (Citation2008), Chang and Xiao (Citation2013, Citation2015), and Braymen, Chang, and Luo (Citation2016).

9. This differs from the small open economy assumption in the traditional international economic analysis that stresses trade between ‘small’ countries who cannot affect their exportables’ world prices. The international trade models developed by Bagwell and Staiger (Citation1997, Citation1999) are examples of trade between large open economies. Chang and Sellak (Citation2019) analyze the behavior of conflict over external territories between two ‘large’ countries whose arming decisions affect the world prices of their exportable products.

10. Polachek (Citation1980) is among the first to contend that conflict is supposed to affect terms of trade between nations.

11. See, e.g. Amegashie and Kutsoati (Citation2007), Garfinkel, Skaperdas, and Syropoulos (Citation2008), Sanders and Walia (Citation2014), Chang and Luo (Citation2017), McGuire (Citation2020), and Garfinkel, Syropoulos, and Yotov (Citation2020).

12. As in Garfinkel, Syropoulos, and Zylkin (Citation2020), we assume that the destruction cost parameter is constant. We also impose the conditions that destruction costs are not too high such that the amounts of civilian goods produced (net of arming and those amounts being appropriated) by two adversaries are positive.

13. Similar to the analysis in Bagwell and Staiger (Citation1997, Citation1999), we assume away income effects in demand for each good and substitutability between traded goods. There is implicitly a freely traded numeraire good that leads to the derivation of linear demands. The linear demand assumptions make it tractable to derive optimal arming and Nash tariffs under resource predation possibilities for the symmetric cases. We do not attempt to present a general analysis due to its complexity. After solving the trade-conflict equilibrium in Section 2.2, we show in Appendix A-3 that the partial equilibrium analysis can be closed by introducing a traded numeraire good and that the trade balance conditions will not qualitatively alter this paper’s primary results.

14. See $X_{a}^{A}$ in (2a) for country A and $X_{b}^{B}$ in (2b) for country B.

15. In adopting the sequential-move game structure where arming allocations are determined before setting Nash tariffs, we adopt the plausible assumption that two enemy countries’ arming decisions prioritize tariff policies in their decision-making under the shadow of conflict. An alternative approach is a game where Nash tariffs are set before arming allocations. This game structure is analytically unsolvable due to its complexity.

16. In our analysis of welfare decomposition, arming induces a terms-of-trade improvement in that it causes export prices and revenues to go up. This incentivizes a further increase in arming. This result parallels the positive effect that greater counterterror effort has on the relative price of manufactured goods (i.e. a terms-of-trade externality), which may cause counterterror effort to be excessive, as shown by Bandyopadhyay, Sandler, and Younas (Citation2020).

17. Note that we assign some plausible values for $K (i . e ., K = 0.2)$ , $R = 1$ in evaluating the derivative.

18. See also Garfinkel, Skaperdas, and Syropoulos (Citation2008). In their footnote 13, the authors indicate ‘the intensity of conflict as reflected in the production of guns.’

19. We show in Appendix A-5 the detailed derivations of the results.

20. Note that we assign some plausible values for $K (i . e ., K = 0.2)$ , and $R = 1$ in evaluating the derivative.

Endogenous Security, Third-Party Trade, and Interstate Disputes: A Conflict-Theoretic Analysis

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Endogenous Security, Third-Party Trade, and Interstate Disputes: A Conflict-Theoretic Analysis

ABSTRACT

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A-4. Decomposing the welfare effect of arming for each adversary country

A-5. Optimal arming is lower under multiple FTAs than under the protectionism regime

A-6. Conflict intensity under single FTAs exceeds that under multiple FTAs

Notes

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