Political-economic problems in trade capacity building

Abstract

Theoretically, trade capacity building should contribute to export-led growth and support liberal economic policies. Unfortunately, it often fails to meet this ideal due to resource misallocation, misplaced focus on existing obligations, and donor-driven implementation. This article presents a formal theory of political-economic problems in trade capacity building. I analyze trade liberalization as a repeated game with imperfect public monitoring between a developed and developing country. Modeling trade capacity building as an investment by the developed country, I show that it suffers from two problems. First, the need to enforce trade liberalization drives resource misallocation: costly projects are implemented only to build commitment capacity while others are not implemented because they encourage protectionism. Second, donor interests distort trade capacity building. Counterintuitively, if the donor can seek compensation from the recipient when it violates international trade law, it sometimes refuses to invest in low-cost trade capacity building while funding projects that hurt the recipient.

Appendix

1.1 Equilibrium in Symmetric Agreements

Assume the players have access to a public randomization device to convexify the payoff space. The equilibrium can be characterized as follows:

• 1. From time t = 0, play (C,C) every period as long as the public signal has been (C,C) in the past.

• 2. For signal (C,D) or (D,D), play the one-stage Nash equilibrium forever.

• 3. For signal (D,C) at time t, with some positive probability play the “punishment” (D,D) for T periods beginning at time t + 1; otherwise continue to play (C,C).

• 4. After the “punishment,” play (C,C) every period as long as the public signal has been (C,C) since the previous “punishment.”

Using equations (2) and (3), respectively, the following constraints must hold in equilibrium:

$$ V_{G}^{1}-V_{B}^{1}\geq\frac{1-\delta}{\delta}\frac{1}{p_{D\mid D}-p_{D\mid C}}(\beta_{1}-\alpha_{1}); $$

$$ V_{G}^{2}-V_{B}^{2}\geq\frac{1-\delta}{\delta}\frac{1}{1-p_{D\mid C}}(\beta_{2}-\alpha_{2}). $$

Since a defection by the developed country is detected with certainty, it is indeed optimal to punish the developed country through a permanent reversion to the one-stage equilibrium. Thus, it suffices to find out whether there is a punishment to enforce cooperation by the developing country that is compatible with the two constraints.

Assume this is the case. One can solve for maximal $V_{G}^{1}$ by setting

$$ V_{G}^{1}-V_{B}^{1}=\frac{1-\delta}{\delta}\frac{1}{p_{D\mid D}-p_{D\mid C}}(\beta_{1}-\alpha_{1}); $$

To see why, note that minimizing $V_{G}^{1}-V_{B}^{1}$ minimizes the punishment. Now,

$$ \begin{array}{lll} V_{G}^{1} & = & (1-\delta)\alpha_{1}+\delta\left((1-p_{D\mid C})V_{G}^{1}+p_{D\mid C}V_{B}^{1}\right)\Leftrightarrow\\[4pt] (1-\delta)V_{G}^{1} & = & (1-\delta)\alpha_{1}+\delta p_{D\mid C}\left(V_{B}^{1}-V_{G}^{1}\right)\Rightarrow\\[4pt] V_{G}^{1max} & = & \alpha_{1}-\frac{p_{D\mid C}}{p_{D\mid D}-p_{D\mid C}}(\beta_{1}-\alpha_{1}). \end{array} $$

To obtain maximal $V_{G}^{2}$, note that the payoffs at any time t are either (α ₁,α ₂) or (0,0), so the frequency of α ₁,α ₂ in equilibrium is identical. When country 1 loses α ₁, country 2 loses α ₂. Thus,

$$ V_{G}^{2max}=\alpha_{2}-\frac{\alpha_{2}}{\alpha_{1}}\frac{p_{D\mid C}}{p_{D\mid D}-p_{D\mid C}}(\beta_{1}-\alpha_{1}).$$

In the main text, I write $\lambda=\frac{p_{D\mid C}}{p_{D\mid D}-p_{D\mid C}}\frac{(\beta_{1}-\alpha_{1})}{\alpha_{1}}$

1.2 Equilibrium in Asymmetric Agreements

Assume the players have access to a public randomization device to convexify the payoff space. The equilibrium can be characterized as follows:

• 1. From time t = 0, play (C,C) every period as long as the public signal has been (C,C) in the past.

• 2. For public signals (C,D) or (D,D) at time t, play the one-stage Nash equilibrium forever.

• 3. For public signal (D,C) at time t, with positive probability play the “punishment” (C,D) for T periods beginning at time t + 1; otherwise play (C,C).

• 4. For signal (D,D) during the “punishment,” with positive probability set the number of remaining periods to T. Otherwise continue as if the signal was (C,D).

• 5. After the “punishment,” play (C,C) every period as long as the public signal has been (C,C) since the previous “punishment.”

Assuming the developed country can be induced to cooperate so that Eq. 9 holds, the maximum payoff $W_{G}^{1max}$ can be solved for exactly as in the case of symmetric agreements. If not $W_{G}^{1max}$ decreases as the developed country must be compensated more generously for cooperation through punishments of the developing country. The maximum payoff $W_{G}^{2max}$ is implicitly solved for in the main text. Note in particular that it depends on Eqs. 8 and 10, because the developing country obtains γ ₁ whenever the developed country obtains β ₂.

Proof of Proposition 1

It has to be shown that if trade liberalization is possible at x = (0,...,0), it is impossible at x ^* if and only if the conditions outlined in the proposition hold.

Consider first a symmetric agreement. Begin with sufficiency. Let $\beta_{i}(x^*)-\beta_{i}(x^0)$ be sufficiently large for some i = 1,2. The enforcement constraints are

$$ V_{G}^{1}-V_{B}^{1}\geq\frac{1-\delta}{\delta}\frac{1}{p_{D\mid D}(x^A)-p_{D\mid C}(x^A)}(\beta_{1}(x)-\alpha_{1}(x)); $$

$$ V_{G}^{2}-V_{B}^{2}\geq\frac{1-\delta}{\delta}\frac{1}{1-p_{D\mid C}(x^A)}(\beta_{2}(x)-\alpha_{2}(x)). $$

Since state i never obtains the payoff β _i (x) in equilibrium, it follows that for sufficiently large β _i (x), these conditions cannot hold.

Now consider necessity. Trade capacity building only effects a change in $\{\alpha_{i}(x),\beta_{i}(x),p_{D\mid C}(x^A),p_{D\mid D}\}(x^A)_{i=1,2}$, so it suffices to show that the changes from trade capacity building in $\{\alpha_{i}(x),p_{D\mid C}(x^A),p_{D\mid D}(x^A)\}_{i=1,2}$ cannot violate the enforcement constraints. Differentiate the enforcement constraints above with respect to α _i (x) to see that the right side decreases. Differentiate the enforcement constraints above with respect to $-p_{D\mid C}(x^A)$ (since trade capacity building has a reducing effect) to see that the right side decreases. Differentiate the enforcement constraints above with respect to $p_{D\mid D}(x^A)$ to see that the right side decreases.

Consider now an asymmetric agreement. The enforcement constraints are

$$ W_{G}^{1}-W_{B}^{1}\geq\frac{(1-\delta)}{\delta}\frac{1}{p_{D\mid D}(x^A)-p_{D\mid C}(x^A)}(\beta_{1}(x)-\alpha_{1}(x)); $$

$$ \left(1-p_{D\mid C}\left(x^A\right)\right)W_{G}^{2}+p_{D\mid C}\left(x^A\right)W_{B}^{2}\geq\frac{(1-\delta)}{\delta}(\beta_{2}(x)-\alpha_{2})(x); $$

$$ \frac{1-\delta}{\delta}\gamma_{1}\geq(p_{D\mid C}(x^A)-p_{D\mid D}(x^A))\left(W_{T}^{1}-W_{B1}^{1}\right). $$

To prove the first claim, let $\beta_{1}(x^*)-\beta_{1}(x^0)$ be large enough. The right side of the first equation is increasing in β ₁(x) while the left side is constant, so the claim follows.

To prove the second claim, it suffices to show that without an increase in β _i (x) or a decrease in $p_{D\mid C}(x^A)$, the enforcement constraints cannot be violated. Differentiate the three enforcement constraints with respect to $\{\alpha_{i}(x),p_{D\mid D}(x^A)\}_{i=1,2}$ to see that they cannot be violated. □

Proof of Proposition 2

To prove the first part, consider a symmetric agreement. The only payoffs that ether country i = 1,2 obtains at any time are {α _i (x),0} and the frequency of the higher payoff α _i (x) can be increased as $p_{D\mid C}(x^A)$ decreases.

Consider now an asymmetric agreement. The per-period payoffs for i = 1,2 are

$$ W_{G}^{i}=(1-\delta)\cdot\alpha_{i}(x)+\delta\cdot\left(\left(1-p_{D\mid C}\left(x^A\right)\right)\cdot W_{G}^{i}+p_{D\mid C}\left(x^A\right)W_{B}^{i}\right). $$

The enforcement constraints are

$$ W_{G}^{1}-W_{B}^{1}\geq\frac{(1-\delta)}{\delta}\frac{1}{p_{D\mid D}(x^A)-p_{D\mid C}(x^A)}(\beta_{1}(x)-\alpha_{1}(x)); $$

$$ \left(1-p_{D\mid C}\left(x^A\right)\right)W_{G}^{2}+p_{D\mid C}\left(x^A\right)W_{B}^{2}\geq\frac{(1-\delta)}{\delta}(\beta_{2}(x)-\alpha_{2}(x)); $$

$$ \frac{1-\delta}{\delta}\gamma_{1}\geq\left(p_{D\mid C}\left(x^A\right)-p_{D\mid D}\left(x^A\right)\right)\left(W_{T}^{1}-W_{B}^{1}\right). $$

Begin with the second part of the proposition. Any project x _j that increases β ₁(x) must be followed by an increase in the left side of the first constraint. If the third constraint, which is independent of β ₁(x), is binding with equality, this can only be achieved by increasing $W_{G}^{1}$. If x _j does not cause a large increase in one of $\{\alpha_{2}(x),\beta_{2}(x),-p_{D\mid C}(x^A),p_{D\mid D}(x^A)\}$, the claim follows, as $W_{G}^{2}$ must decrease when the frequency of β ₂(x) decreases relative to α ₂(x).

Consider now a project $x_{j}^{A}$ that decreases $p_{D\mid C}(x^A)$. Choose {α _i (x),β _i (x),γ _i , $p_{D\mid C}(x^A),p_{D\mid D}(x^A)\}_{i=1,2}$ such that, at $x_{j}^{A}$, for the asymmetric agreement that prompts the maximal payoff $W_{G}^{2max}$ to the developed country,

$$ W_{G}^{1}-W_{B1}^{1}>\frac{(1-\delta)}{\delta}\frac{1}{p_{D\mid D}(x^A)-p_{D\mid C}(x^A)}(\beta_{1}(x)-\alpha_{1}(x))$$

and the difference is very large while

$$ \frac{1-\delta}{\delta}\gamma_{1}=\left(p_{D\mid C}\left(x^A\right)-p_{D\mid D}\left(x^A\right)\right)\left(W_{T}^{1}-W_{B}^{1}\right). $$

This is clearly possible when β ₁(x) − α ₁(x) and $p_{D\mid C}(x^A)$ are small enough. To see why, observe that the second constraint sets a least upper bound for $W_{B}^{2}$ and the requirement that (C,C) prompts further cooperation with certainty sets a least upper bound for the frequency of punishments.

When $p_{D\mid C}(x^A)$ decreases, the first constraint continues to be met while the second constraint is no longer binding. It is in the interest of the developed country to choose the most severe punishment possible, so that the second constraint continues to bind with equality. This equality constraint determines a minimum for $W_{B}^{1}$, which in turn determines a maximum for $W_{B}^{2}$. For a sufficiently large decrease in $p_{D\mid C}(x^A)$, the maximal permissible increase in $W_{B}^{2}$ is not enough to prevent a decrease in $W_{G}^{2max}$.

Now consider the third part of the proposition. Choose a project $x_{j}^{A}$ that increases $p_{D\mid D}(x^A)$. Assume

$$ W_{G}^{1}-W_{B}^{1}=\frac{(1-\delta)}{\delta}\frac{1}{p_{D\mid D}(x^A)-p_{D\mid C}(x^A)}(\beta_{1}(x)-\alpha_{1}(x)).$$

This constraint is relaxed as $p_{D\mid D}(x^A)$ increases. Since changes in $p_{D\mid D}(x^A)$ are irrelevant on the equilibrium path, as the developing country never defects, it is thus possible to reduce $W_{B1}^{1}$, which in turn permits an increase in $W_{B}^{2}$ so that $W_{G}^{2max}$ increases.

To prove the last part of the proposition, simply let α ₂(x) increase rapidly enough relative to α ₁(x) and choose z(x) appropriately. □

Proof of Proposition 3

First, let $\frac{\partial\beta_{1}(\hat{x})}{\partial x_{j}^{I}}<\frac{\partial\alpha_{1}(\hat{x})}{\partial x_{j}^{I}}$. When trade liberalization is feasible for a sufficiently wide range of parameters, the maximal payoffs for the developing country can be written conveniently as

$$ V_{G}^{1max}=\alpha_{1}\left(x_{j}^{I}\right)-\frac{p_{D\mid C}}{p_{D\mid D}-p_{D\mid C}}\left(\beta_{1}\left(x_{j}^{I}\right)-\alpha_{1}\left(x_{j}^{I}\right)\right); $$

$$ W_{G}^{1max}=\alpha_{1}\left(x_{j}^{I}\right)-\frac{p_{D\mid C}}{p_{D\mid D}-p_{D\mid C}}\left(\beta_{1}\left(x_{j}^{I}\right)-\alpha_{1}\left(x_{j}^{I}\right)\right). $$

Differentiate these payoffs first with respect to $x_{j}^{I}$ and then with respect to − p _D|C or p _D|D. Note that the cross derivative is unambiguously positive.

Second, let $\frac{\partial\beta_{1}(\hat{x})}{\partial x_{j}^{I}}>\frac{\partial\alpha_{1}(\hat{x})}{\partial x_{j}^{I}}$. Proceed as above and note that the cross derivative is unambiguously negative. □

1.3 Impact of Trade Capacity Building on Incentive to Defect

A key assumption of the model is that trade capacity building can indeed increase the incentive to defect. International trade theory does not provide a compelling treatment of this issue, so I show here that even in the “least likely case” of a small economy without any market power, political decision-making can create this effect.

Consider the common agency model in Grossman and Helpman (1994), but assume a common iceberg transport cost g, where g ∈ (0,1). Now the domestic prices p ^* with free trade can be written as $p^{*}=\frac{p^{w}}{1-g}$, where p ^w represents the world prices without transport costs. Trade capacity building amounts to a decrease in g. I show that the gain from deviating from free trade can increase as g decreases.

First note that if the government in a small economy is only concerned with social welfare, it trivially follows that it has no incentive to deviate from free trade. It thus suffices to prove the converse, namely that sometimes a decrease in g can increase the profitability of deviation. To this end, first note that the marginal social cost of a tariff on any good is, as in equation (15) of Grossman and Helpman (1994),

$$ \frac{\partial W}{\partial p_{j}}=\left(p_{j}-p_{j}^{*}\right)m_{j}^{'}\left(p_{j}\right), $$

where W is social welfare and p _j is the domestic price with tariffs. Finally, $m_{j}^{'}=Nd'(p_{j})-y'(p_{j})<0$ is the marginal net import demand, where N is the population size, d(p _j ) is the demand function, and y(p _j ) is the derivative of the (convex) profit function. If y(p _j ) can be approximated by a first-order Taylor series expansion while d′′(p _j ) > 0 is sufficiently high everywhere, it follows that $\frac{\partial W}{\partial p_{j}}<0$ is decreasing in $p_{j}^{*}$ for a given $(p_{j}-p_{j}^{*})$. But $p^{*}=\frac{p^{w}}{1-g}$ implies that if p ^w is sufficiently low, the marginal social cost is arbitrarily high for sufficiently high g and arbitrarily low for sufficiently low g. Investigating equation (14) of Grossman and Helpman (1994), one similarly notes that the marginal bilateral surplus with the organized interest groups is increasing in p ^* for a given $(p_{j}-p_{j}^{*}).$ Thus, the incentive to deviate from the true domestic prices p ^* increases in g even in a small economy.