Welfare implications of upstream subsidy in the presence of countervailing duties under limited verifiability

Abstract

This paper examines how a politically biased strategic export subsidy influences social welfare when an importing country imposes countervailing duties on imported goods if the subsidy is verified. Based on a simple model that integrates the political contribution provided by exporting firms and the verifiability problem of an export subsidy for the upstream firms within a vertically fragmented production process, this paper demonstrates that politically biased strategic export policies can deteriorate social welfare. Moreover, when it is more difficult to identify hidden government subsidies, welfare loss due to politically biased subsidy is increased. Interestingly, an importing country is not motivated to fully countervail the politically biased export subsidies when it is concerned about social welfare, including consumer surplus. These results provide an answer on why the conflicts over hidden subsidies are increasing with deepening fragmentation of exporting firms’ production processes. In addition, the results imply that it is imperative to make further efforts to enhance the verifiability of the hidden subsidies in order to reduce the welfare deterioration caused by the politically biased strategic trade policies.

Appendices

Appendix A

Proof of Proposition 1

Proof is straightforwardly given as follows:

$$ \begin{aligned} s_{\text{c}}^{*} (\mu ) & = \frac{{a(1331 - 1276\mu + 288\mu^{2} )}}{(11 - 4\mu )(121 + 12\mu )} = \frac{a(121 - 72\mu )}{(121 + 12\mu )} \\ \frac{{\partial s_{\text{c}}^{*} (\mu )}}{\partial \mu } & = - \frac{{10{,}164a}}{{(121 + 12\mu )^{2} }} < 0,\frac{{\partial E[u(s_{\text{c}}^{*} (\mu ))]}}{\partial \mu } = \frac{5082a}{{(121 + 12\mu )^{2} }} > 0,\frac{{\partial E[f^{*} (\mu )]}}{\partial \mu } = - \frac{{88{,}704a}}{{(121 + 12\mu )^{3} }} < 0 \\ \frac{{\partial {\text{SW}}_{1} }}{\partial \mu } & = - \frac{{a^{2} (11 - 4\mu )(275 + 12\mu )}}{2(121 + 12\mu )} < 0,\frac{{\partial {\text{SW}}_{2} }}{\partial \mu } = \frac{{a^{2} (11 - 4\mu )(27951 - 4\mu (1441 + 4\mu (263 + 12\mu )))}}{{4(121 + 12\mu )^{3} }} > 0. \\ \end{aligned} $$

Proof of Proposition 2

Proof is straightforwardly given as follows:

$\frac{{\partial s_{\text{p}}^{*} (\mu ,\theta )}}{\partial \mu } = - \frac{{10{,}164a\theta }}{{(363 - 132\mu - 2\theta (121 - 72\mu ))^{2} }} < 0$, $\frac{{\partial E[m(s_{\text{p}}^{*} (\theta ,\mu ))]}}{\partial \mu } = \frac{5082a\theta }{{(363 - 132\mu - 2\theta (121 - 72\mu ))^{2} }} > 0$, $\frac{{\partial E[f(s_{\text{p}}^{*} (\theta ,\mu ))]}}{\partial \mu } = - \frac{1848a\theta }{{(363 - 132\mu - 2\theta (121 - 72\mu ))^{2} }} < 0$, $\frac{{\partial SW_{1} (s_{\text{p}}^{*} (\theta ,\mu ))}}{\partial \mu } = - \frac{{a^{2} (11 - 4\mu )(A - 32\theta^{2} B + 8\theta C)}}{{4(363 - 132\mu - 2\theta (121 - 72\mu ))^{3} }} > 0$ since $A = - 33(11 - 4\mu )^{2} (79 + 4\mu )$, $B = (1331 - 2970\mu + 1296\mu^{2} )$, and $C = (41261 - 37840\mu + 9472\mu^{2} + 288\mu^{3} )$ where the condition in the denominator, $363 - 132\mu - 2\theta \left( {121 - 72\mu } \right) > 0$, should be required for the nonnegative demand condition for firms in both countries.

We obtain $\frac{{s_{\text{p}}^{*} (\theta ,\mu )}}{{s_{\text{c}}^{*} (\mu )}} = \frac{\theta (121 + 12\mu )}{363 - 132\mu - 2\theta (121 - 72\mu )} \ge 1$ that the equilibrium subsidy provided to the upstream firm is higher when the government of the exporting country receives political contributions than when it does not. We obtain the intermediate good price in each model as: $E[m(s_{\text{c}}^{*} (\mu ))] = a/4 - s_{\text{c}}^{*} (\mu )/2$ and $E[m(s_{\text{p}}^{*} (\theta ,\mu ))] = a/4 - s_{\text{p}}^{*} (\theta ,\mu )/2$. Then,$E[m(s_{\text{p}}^{*} (\theta ,\mu ))] < E[m(s_{\text{c}}^{*} (\mu ))]$ since $s_{\text{p}}^{*} (\theta ,\mu ) > s_{\text{c}}^{*} (\mu )$.

Proof of Lemma 3

• (a) $E[\pi_{1} (s_{\text{p}}^{*} (\theta ,\mu )] - C_{\text{p}}$ is increasing in $\theta$ while $E[\pi_{1} (s_{\text{c}}^{*} (\mu )]$ is unrelated to $\theta$. $E[\pi_{1} (s_{\text{p}}^{*} (\theta ,\mu )] - C_{\text{p}} = E[\pi_{1} (s_{\text{c}}^{*} (\mu )]$ if $\theta = 1$. If $\theta > 1$, $E[\pi_{1} (s_{\text{p}}^{*} (\theta ,\mu )] - C_{\text{p}} > E[\pi_{1} (s_{\text{c}}^{*} (\mu )]$ always holds.

• (b) $E[\pi_{2} (s_{\text{p}}^{*} (\theta ,\mu )]$ is decreasing in $\theta$ while $E[\pi_{2} (s_{\text{c}}^{*} (\mu )]$ is unrelated to $\theta$. $E[\pi_{2} (s_{\text{p}}^{*} (\theta ,\mu )] = E[\pi_{2} (s_{\text{c}}^{*} (\mu )]$ if $\theta = 1$. If $\theta > 1$, $E[\pi_{2} (s_{\text{p}}^{*} (\theta ,\mu )] < E[\pi_{2} (s_{\text{c}}^{*} (\mu )]$ always holds.

• (c) $E[\pi_{\text{u}} (s_{\text{p}}^{*} (\theta ,\mu )]$ is increasing in $\theta$ while $E[\pi_{\text{u}} (s_{\text{c}}^{*} (\mu )]$ is unrelated to $\theta$. $E[\pi_{\text{u}} (s_{\text{p}}^{*} (\theta ,\mu )] = E[\pi_{\text{u}} (s_{\text{c}}^{*} (\mu )]$ if $\theta = 1$. If $\theta > 1$, $E[\pi_{\text{u}} (s_{\text{p}}^{*} (\theta ,\mu )] > E[\pi_{\text{u}} (s_{\text{c}}^{*} (\mu )]$ always holds.

• (d) The result is definite since $s_{\text{p}}^{*} (\theta ,\mu ) > s_{\text{c}}^{*} (\mu )$ and $E[q_{1} (s_{\text{p}}^{*} (\theta ,\mu )] > E[q_{1} (s_{\text{c}}^{*} (\mu )]$ when $\theta > 1$.

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Appendix B

Proof of Proposition 3

• (a) In the equilibrium, the participation constraint of the government will be binding as: ${\text{SW}}_{1} (s_{\text{p}}^{*} (\theta ,\mu )){ + (}\theta - 1)C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu )) = {\text{SW}}_{1}^{*} (s_{\text{c}}^{*} (\mu ))$. Thus, ${\text{SW}}_{1} (s_{\text{p}}^{*} (\theta ,\mu )) - C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu )) < {\text{SW}}_{1}^{*} (s_{\text{c}}^{*} (\mu ))$ always holds. Specifically, according to Lemma 3, ${\text{SW}}_{1} (s_{\text{p}}^{*} (\theta ,\mu )) - C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu )) - {\text{SW}}_{1}^{*} (s_{\text{c}}^{*} (\mu )) < 0$. This follows from the fact as:

  

• (b) In addition, in the equilibrium, we obtain the value of the politically weighted social welfare ${\text{SW}}_{1} (s_{\text{p}}^{*} (\theta ,\mu )){ + (}\theta - 1)C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu )) = a^{2} (11 - 4\mu )^{2} /(968 + 96\mu )$. Taking the first derivative of it with respect to $\theta$ must be zero, as follows:

$$ \frac{{\partial {\text{SW}}_{1} (s_{\text{p}}^{*} (\theta ,\mu ))}}{\partial \theta }{ + (}\theta - 1)\frac{{\partial C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu ))}}{\partial \theta }{ + }C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu )) = 0 $$

Rearranging it, since $C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu ))$ is increasing in $\theta$, we have

$$ \frac{{\partial {\text{SW}}_{1} (s_{\text{p}}^{*} (\theta ,\mu ))}}{\partial \theta } - \frac{{\partial C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu ))}}{\partial \theta } = - \,C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu )) - \theta \frac{{\partial C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu ))}}{\partial \theta } < 0 $$

Thus, the net social welfare of the exporting country ${\text{SW}}_{1} (s_{\text{p}}^{*} (\theta ,\mu )) - C_{\text{p}} (s_{\text{p}}^{*} (\theta ,\mu ))$ is decreasing in $\theta$.□

Proof of Proposition 4

From Eq. (9), defining the social welfare of the foreign country, we compare the social welfare in the presence of the political contribution with the one in the absence of the contribution as:

$$ \begin{aligned} & {\text{SW}}_{2} (s_{\text{p}}^{*} (\theta ,\mu )) - {\text{SW}}_{2} (s_{\text{c}}^{*} (\mu )) \\ & \quad = \frac{{a^{2} (\theta - 1)(11 - 4\mu )^{2} (121 - 72\mu )(20\mu (1331 + 8(5 - 6\mu )\mu ) - \theta (121 - 72\mu )(121 - 8\mu (7 + 2\mu )))}}{{8(121 + 72\mu )^{2} (363 - 132\mu - 2\theta (121 - 72\mu ))^{2} }} > 0 \\ \end{aligned} $$

Then, we examine how the political parameter affects the social welfare of the importing country as:

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Proof of Proposition 5

$\partial s_{\text{p}}^{*} (\theta ,\mu )/\partial \mu < 0$ and $\partial f(s_{\text{p}}^{*} (\theta ,\mu ))/\partial \mu < 0$, $\left| {\partial s_{\text{p}}^{*} (\theta ,\mu )/\partial \mu } \right| \, > \, \left| {\partial f(s_{\text{p}}^{*} (\theta ,\mu ))/\partial \mu } \right|$.

In addition, $\left. {\partial s_{\text{p}}^{*} (\theta ,\mu )/\partial \mu } \right|_{\mu = 1} \, > \, \left. {\partial f(s_{\text{p}}^{*} (\theta ,\mu ))/\partial \mu } \right|_{\mu = 1}$. Therefore, $s_{\text{p}}^{*} (\theta ,\mu ) > \, f(s_{\text{p}}^{*} (\theta ,\mu ))$.□

Appendix C: the strategic interaction and the welfare loss due to the politically biased subsidies

The politically biased strategic trade policies were diagnosed as worsening social welfare mainly because of the increase in the socially wasteful expenditure on the political contribution in the earlier literature including Kagitani (2009). Even when the political contribution is considered to be a simple transfer of the income from the corporate sector to the government sector, the politically biased trade policies would worsen the social welfare by means of price distortion, as demonstrated by Grossman and Helpman (1994). The introduction of the limited verifiability of a hidden subsidy in this paper enables the theoretical evaluation of the increasing international tensions over the hidden subsidies to the export industries with complicated vertical production processes.

Kagitani (2009) focused on the welfare effect of the different patterns of the oligopolistic competition under the political economic structure of trade policies without considering the strategic interactions initiated by the importing country’s subsidy–countervailing measures. This paper, on the other hand, examines the strategic interactions between trading countries by introducing subsidy–countervailing measures of the importing country, which depend on the probabilistic features of subsidy verifiability. The limited verifiability of the hidden subsidies helped to inflate strategic subsidies via the increased amount of equilibrium political contributions. In that context, the limited verifiability of the subsidies aggravates the distortion caused by the politically biased strategic trade policies.

Another feature of this study that was not considered in the earlier literature, including Kagitani (2009), is examining how the politically biased strategic trade policies affect the importing country’s welfare. By means of this study, we provide another answer to the question of how the current WTO subsidy–countervailing rules might work properly to fully offset the prohibited export subsidies. We show that the politically biased export subsidies might improve the consumer surplus of the importing country significantly, reducing the importing country’s policy incentive to fully countervail the subsidies. In addition, we share the same feature with Grossman and Helpman (1994), in that a single monopoly lobby extracts all the rents, as defined in the following binding participation condition of the policymaker:

$$ {\text{SW}}_{1} (s){ + (}\theta - 1)C_{\text{p}} \ge {\text{SW}}_{1}^{*} \, $$

If we substitute the binding participation condition of the policymaker for the objective function of the single monopoly lobby, the equilibrium subsidy is supposed to satisfy the following first-order condition of the single lobby, which extracts all the rents:

$$ (1 - \mu )\frac{{{\text{d}}E[\pi_{1n} (s)]}}{{{\text{d}}s}} + \mu \frac{{{\text{d}}E[\pi_{1v} (s)]}}{{{\text{d}}s}} + \frac{1}{\theta - 1}\frac{{{\text{dSW}}_{1} (s)}}{{{\text{d}}s}} = 0 $$

The equilibrium subsidy derived from the above first-order condition shows that the lower verifiability of the hidden subsidy, represented by the lower value of $\mu$, increases the socially wasteful political contributions, which distorts the subsidy levels upward and eventually reduces the social welfare of the exporting country that provides more politically biased subsidies.

The introduction of the strategic response of the importing by means of a countervailing duty, which is dependent on the limited verifiability of the subsidy because of the complicated vertically fragmented production processes, is a novel feature of this study that was not tried in the earlier literature, including Kagitani (2009). This new approach produced a strong policy implication emphasizing the importance of improving policy transparency in order to increase the verifiability of the hidden subsidies.

Moreover, to focus on the strategic effects of politically biased export subsidies facing the possible countervailing measures of the importing country, this paper considers consumer surplus only in the importing country. The change in the producer surplus of the exporting country is composed of two parts: (1) increased profits of the upstream firm because of the direct effect of cost reduction by the subsidies, and (2) increased profits of the downstream firm because of the decreased price of the intermediate inputs, which can be interpreted also as the transfer of the corporate surplus from the importing country.