Further Thoughts on Strategic Trade Policy under Asymmetric Information

We study the informational impacts of multilateral voluntary export restraints (henceforth VERs) in an international trade model with differentiated products [1]. We first show that with competing mechanisms, the two firms’ lying intentions are strategic complements and will increase with the degree of product differentiation. Next, we show that each government will design their VERs menus to allow for only partial revelation. Contrary to the single intervention case [2], a separating equilibrium where each country’s domestic firm truthfully reveals its private information does not exist under multilateral policy interventions. Finally, we demonstrate that trade retaliation, when the two governments’ VERs are positively related, will happen when the government believes that its domestic firm is more likely to be inefficient.


Introduction
It is now well known that government intervention can shift rents by providing a strategic advantage to the domestic firm.In particular, the pioneering work by Brander and Spencer [3] showed that under Cournot competition, an export subsidy enables the domestic firm to be a Stackelberg leader, and thus it increases the domestic welfare at the expense of the foreign firm.Subsequently, Eaton and Grossman [4] demonstrated that the optimal policy will be an export tax, when the domestic firm competes with a foreign firm in prices 1 .This indicates that the type of export policy is sensitive to the form of competition.In addition, the literature has also noticed that information can also crucial in determining the appropriate policy.For example, Wong [5] demonstrated that in the Brander-Spencer model with asymmetric information (about cost), the optimal export subsidy scheme derived from the full information case is no longer incentive compatible.Collie and Hviid [6] and Qiu [2] examined the use of strategic trade policy as a signalling device when the informational asymmetry is between domestic and foreign firms.
With incomplete information, the Principal-Agent model can best describe the leader-follower relation between uninformed government and informed firm.By applying the Revelation Principle, the uninformed government can adopt a direct mechanism by offering a menu of policies and letting the informed domestic firm self-select the intended policy.When domestic firm is competing with foreign firms, this "self-selection" process becomes more informative.In Qiu's [2] words, "it is a mix of screening and signalling problems"; by choosing among the menu of policies, the domestic firm also signals its private information to the rival firms [6].The task of the government is then to trade off between the inefficiency from asymmetric information and the strategic advantage from trade policy; whether to have the informed domestic firm truly reveal its information, or to hide and enjoy the strategic benefit from asymmetric information?Qiu [2] showed that under Cournot competition the uniformed government will choose a policy menu to truly reveal its cost information (separating equilibrium).
While the analysis on unilateral policy intervention has proved to be powerful to describe the dilemma encountered by the uninformed government, in reality we often see bilateral or multilateral policy interventions instead of unilateral policy.If we adopt a direct mechanism for these multiple contracting cases, will there be a separating equilibrium?If not, how much information can be revealed?How does the degree of information revelation relate to the market structure?Will there be trade retaliation?
In this paper, we provide answers to these questions by studying an incomplete information VERs game in an intra-industry trade model.The model we consider is an international trade model with differentiated products [1].There are two countries and each country has only one producer, which sells its products to two countries.In order to capture intra-industry trade of this kind, we employ the differentiated product framework by Dixit [10] and Singh and Vives [11].There are three reasons to study an incomplete information VERs game of this form.First, there have been many discussions on the informational impacts of taxes, subsidies or tariffs; we hope to complement the literature by investigating the informational impacts of VERs, which are seen as equally important strategic tools.Second, although we are aware that both the choice of policy instrument and the degree of information revelation can be sensitive to the form of competition (Cournot or Bertrand), since our focus is on the information aspects of multilateral interventions, we adopt a quantity competition setup to better handle the impacts from VERs.
Third and most interestingly, we will show that in the complete information benchmark case, each government's VER decision is as efficient as in the single government case.There is no direct interaction between the two governments, so the policy efficiency can be retained even with bilateral interventions.The question of concern is: now that there is no game between the two governments, can we apply the revelation principle directly and look for a truth-telling direct mechanism in the incomplete information VERs game?Unfortunately, the answer is no, as we will demonstrate that the "signaling effect" of menu selection will change the rival firm's perception about domestic firm's private information.Consequently, each firm's intention of information revelation will be related to the rival firm's intention, and thus the two governments are no longer "independent" from each other.
Our paper starts with the complete information benchmark case, where we show that, by using VER each government gains a first mover advantage in the rival country [12][13][14].However, when considering incomplete information, we first demonstrate that with competing mechanisms, each firm's intention to lie is positively related to the rival firm's lying intention.The two firms' lying intentions are strategic complements and will increase with the degree of product differentiation.Impor-tantly, we show that each government will design their VERs menus to allow for only partial revelation.Contrary to the single intervention case [2], a separating equilibrium where each country's domestic firm truthfully reveals its private information does not exist with multilateral policy interventions.Finally, we demonstrate that trade retaliation, when the two governments' VERs are positively related, will happen when the government believes that its domestic firm is more likely to be inefficient.This result partly reflects the result by Martina and Vergoted [15], who discussed the role of retaliation in trade agreements and showed that retaliation is a necessary feature of any efficient equilibrium.
The issues on "competing mechanisms" have received many discussions.Peck [16] and Martimort and Stole [17] first illustrated apparent failures of the standard revelation principle with competing mechanisms.Since there is no obvious way to deal with these problems, the literature has responded by imposing ad hoc restrictions on the set of mechanisms from which Principals can choose [18][19][20][21][22].This is the reason why we stick to direct mechanisms in this current paper.Next, our paper investigates ex-post information revelation under bilateral government interventions.This is different from ex-ante information revelation such as Creane and Miyagiwa [23], where duopoly firms make their revelation decisions before they observe their own private information.From the information content, our model is closed to Collie and Hviid [6] and Qiu [2], but they mainly assumed unilateral policy design.Brainard and Martimort [21] considered bilateral government interventions but restricted to truth-telling equilibria 2 .Finally, our results conclude that trade retaliation happens when the government believes that its domestic firm is more likely to be inefficient.This partly coincides with Martina and Vergoted's [15] results.They showed that in the presence of private information, retaliation can always be used to increase the welfare derived from such agreements by the participating governments.In particular, it is shown that retaliation is a necessary feature of any efficient equilibrium.
The remainder of the paper is organized as follows.Section 2 discusses the complete information VERs game as a benchmark of comparison.We demonstrate that, by using VER, each government gains a first mover advantage in the rival country.Section 3 characterizes the equilibrium in the incomplete information VERs game.In equilibrium, each government will only implement partial revelation from its domestic firm, and there can be trade retaliation when the government believes that its C. Y. FU, S. J. HO 698 domestic firm is more likely to be inefficient.Section 4 concludes the paper with some suggestions on further research.

The Model
Specifically, let the superscript , index the two countries.Country 's demand for firm 1 and firm 2's products are given by where subscript , indexes firm .and denote firm i 's price and output in country k .The coefficients  and  denote the own price effect and cross price effects, respectively.We assume    to reflect that the own price effect is higher than the cross effects.Notice that the level of  can be seen as a mea- sure for the substitution between the two products; When    0 the two products are almost homogenous; when   the two products are almost differentiated.
The reason we have considered a quantity instead of price competition model is because we can handle the quantity restraints easily.We are aware that the form of competitionmight changes the policy insights [4].Since our focus is on the informational impacts of VERs, we will stick to this simple framework for a neat presentation.Finally, since our focus is on the informational impacts of government interventions, we assume zero transportation cost for simplification.Each firm's marginal production is assumed to be .
i Each firm's profit is thus given by where i and i denote firm 's revenue in domestic   and foreign countries, respectively.
We consider that the government of each country will choose a VER , to maximize social welfare i .Each country's social welfare is the overall utility deducted by foreign firm's revenue, added by domestic firm's revenue in the foreign country, and minus the domestic firm's total production cost.That is, , j i q i j  SW   , for 1, 2, and .
This setup is firstly given by Singh and Vives [11], which assumed that The advantage of this setup is: since in differentiated product models, we cannot use the area under demand function to measure the consumer surplus.The setup of can help us easily measure the consumer surplus.
Also, we can easily derive the country 's demand function by partial differentiating with respect to .

Complete Information VERs Game
As a benchmark of comparison, Section 2 discusses the complete information VERs game where both firms' production costs are publicly known.We will show that, under complete information, each government's VER decision will be as efficient as in the single government case.However, this policy efficiency will disappear when we consider incomplete information in Section 3.
Not only because there is information rent in the VERs contract, but also because the two governments' competing mechanisms will increase firms' strategic incentives to lie.The complete information VERs game proceeds as follows.First, government 1 and government 2 set their VERs, , and simultaneously.After observing the VER decisions, both firm 1 and firm 2 compete in the product markets of the two countries.By backward induction, we first solve the market equilibrium, given the two governments' VER decisions, and then determine each government's optimal VER. 2 1 q 1 2 q Market Equilibrium Given the two governments' VER decisions, and firm 1 and firm 2 maximize their profits simultaneously.
Each firm's best reply to the rival government's VER is given by Optimal VERs Now, given the two firms' best replies in (1), each government chooses its VER to maximize its social welfare.In the case of country 1, the structural form of is: 1 .2

SW
q q q q q q q q q q c c q From the first order condition of maximization: Similarly, we can calculate government 2's optimal VER: We will later refer 2 1 q and 1 2 q as the efficient VERs, as each government's VER decision is as efficient as in the single government case.
Accordingly, substitute , Here we make two remarks on these efficient VERs.First, we can compare j i q to the outputs in the free trade case, where each firm choose both and to maximize The free trade outputs in domestic and foreign markets are 2 shows that The VER is higher than the foreign output in the free trade case.The advantage of using VER is that, by pre-committing to j i q , the government gains the po- sition of a leader in the rival country, and in output competition, there will be a first mover advantage.
This strategic advantage is first mentioned by Harris [12], who analyzed the impacts of VERs in a Bertrand model.Rosendorff [25] explained why governments prefer VERs to tariff in a Cournot model.Also, Ishikawa [26] studied the effect of VERs on profit, market share, consumer surplus and welfare in a Cournot model.Berry, et al. [27] evaluated VERs that was initially placed on automobiles exports from Japan in 1980's.They found that VERs had increased both prices and the profits of domestic firms, while leaving consumer welfare worse off.Feenstra and Lewis [28] considered a domestic government with political pressure to negotiate over the volume of trade and the transfer of rents.They characterized the globally optimal, incentive-compatible trade policies, in which the domestic government has no incentive to overstate (or understate) the pressure for protection.De Santis [14] studied the impact of VERs on exporting countries.He showed that VERs at the free-trade level would favour the concentration of industry, and raise the price mark-up in the domestic market.However, the impact on welfare is indeterminate depending upon the effect on global efficiency.
Second, j i q in (2) tells us something about the moti- vation of mimicking.Notice that j i q is decreasing in i , and this indicates that a more efficient firm will have a higher VER.In particular, if i has two possible values: . This, however, does not imply that the less efficient firm will mimic the efficient firm.Actually, since i  is concave in , and by the definition of maximization, the less efficient firm In the words of Spence [29], the inefficient firm does not envy the efficient firm.This means that when we consider incomplete information in a unilateral intervention case, a separating equilibrium where each type of i chooses its intended VER   j i i q c i might exist.Hence, our model would suggest the same result as Qiu [2] in the unilateral intervention case.In the next section, we will show that with multiple mechanisms, a separating equilibrium does not exist.

Incomplete Information VERs Game
Section 3 discusses the incomplete information VERs game where i c is only privately known by firm .Neither government nor government i j or firm j knows this value.To simplify the analysis, we assume a binary type set,

 
, We have shown that with complete information, each government's VER decision is as efficient as in the single government case.There is no direct interaction between the two governments, so the policy efficiency can be retained even with bilateral interventions.With incomplete information, we will show that the "signaling effect" of menu selection will change the rival firm's perception about domestic firm's private information.Consequently, each firm's intention of information revelation will be related to the rival firm's intention, and the two governments are no longer "independent" from each other.
The incomplete information VERs game proceeds as follows.First, each government announces a VERs i menu independently.Second, each firm self selects a VER from the menu, and this choice is publicly observed.Third, according to the observed policy choices, the two firms update their beliefs about the rival firm's production cost, and then compete in the product markets of the two countries.By backward induction, we first solve the market equilibrium given the two firms' menu selection.Then we characterize the two firms' menu selection equilibrium.Finally, we determine each government's VERs menu.
i Before proceeding with the derivation of market equilibrium, we define more notations for the prior and posterior beliefs on i .First, as said, we assume that

 
, .After observing the rival firm's menu selection strategy, each firm i can update its belief on ., the selection strategy for type L c of firm i is , and for type . In particular, denotes the separating strategy where each type of firm selects its intended VER.As an- denotes the hybrid strategy where type L c of firm i selects its intended VER, while type H c of firm i randomly selects between with a probability i  .

Market Equilibrium
Belief Updating We now solve the market equilibrium given the two firms' menu selection.After observing firm 's selection strategy, firm i j can update its belief on i .That is, according to the Bayes' rule, given the observation c i  , the on-equilibrium path belief is given by:   For simplification, we assume that the off-equilibrium path belief will be the same as the prior  . If  .In particular, for the separating strategy i i , we have . As another example, for the hybrid strategy   denote country 's VER associated with selection strategy i i  .Since each firm's profit will be affected by their selection strategies, we rewrite the profits as , where . c q q q q Eq q c q q In the case of , there is an expected term Eq  .The reason for the expectation form is because firm 1 cannot observe 2 c , and by observing 2  , firm 1 will guess firm 2'sVER as: ,  , and the probability that can be explained similarly.In the product market, each firm chooses to maximize , will be determined by the menu selection strategy.By the first order condition of maximization 4 , we have This is similar to (1) in the complete information case, except that the expected VERs will be determined in the menu selection game.
Substitute the two best replies in ( 6) to ( 4) and ( 5), we can rewrite Eq c c q E c q Eq c c q 4 The second order condition of maximization is satisfied.


In the case of , notice that there is a posterior expected cost term .From (6), we know useful for equilibrium characterization.
Lemma 1 . The similar argument applies to firm 2.

Menu Selection
.■ First, recall that in the complete information case, we conclude that type H c is better off choosing q c .In the unilateral intervention case, a separating equilibrium where each type of i chooses its intended VER c   j H q c i might exist.Hence, to simplify the discussion, we restrict the selection strategy to be , given the best replies in (6).That is, for  and , 7) is rewritten as (see Equation ( 11) ): That is, we assume that type L c will take the intended VER, while type .With this restriction, will indicate the separating strategy where each type chooses its intended VER, and 1 i   denotes the pooling strategy where both types L c and H c choose , type L c will take the intended VER, and type H c will mimic type L c by taking a mixed strategy . So in (11), we have replaced . Also in (12), we have replaced . Also, we have replaced with the definitions given in ( 9) and (10).The similar argument applies to firm 2. ( 7) and ( 8) can be rewritten accordingly.
We need to show that for , 1, 2 i  1 (11), if we require 1  to be best reply for type L c , the intended VER must be set at the following level Lemma 1 concludes a preliminary result which will be , 2 which is obtained by differentiating (11) with respect to L q s set to be (13), then c 1 1 L   will be best reply.

Next, for type
That is, given 2  , the first order condition of maximization for ( 12) is: i .
Similarly, we can calculate firm 2's best reply to where This indicates that 1  and 2  are strategic complements.Since the level of i  denotes the degree that type H c of firm i will mi ic type m L c the more that type H c of firm i lies will trigger H c type of the rival firm to lie more.Next, recall that the level of  measures the degree of substitution, and the smaller  indicates a higher degree of product differentiation.If we take the partial differentiation of with respect to   , we know that the degree of strategic complements is positively related to the degree of product differentiation.
Lemma 2 1  and 2  are strategic complements, and Second, it is interesting to know if t he separating equilibrium exists.That is, in the case of firm 1, we ask if 1 0   is a best reply to 2 0   in (14).To find out, substitute 2 0   in ( 14), so we have Compare this level to the efficient VER . We can conc  13).We the ore have the , q c e truth, no words, given the , which will induce each type of m 1 to tell th matter what the rival will do.In fir other menu , the dominant strategy for each type of firm 1 is to tell the truth and pick the intended VER.
Lemma 3 1) Given the menu , the dominant strategy for each type of firm 1 is to tell the 2) The efficient V truth and pick the intended VER.
ERs can indeed induce a truth-telling equilibrium but only when 2

L c c
 .In the incomplete information VERs game, the "sig-naling o effect" f menu selection will change the rival fir ary results.m's perception about domestic firm's private information.Consequently, each firm's intention of information revelation will be related to the rival firm's intention.The question of concern is whether the government will find it optimal to induce truthtelling, no matter how the rival firms might lie.Will it be better off for the government to induce a certain degree of lying in equilibrium?How will this degree relate to the market structure?We will provide answers to these questions shortly in next subsection.
Finally, it can be calculated from ( 14) for the following prelimin ed in Figur creasin As illustrat e 1, in g   indicates that th smalle   e r  is, the m best re ore the ply of 1  will shift outward.In other words, when the two pr ucts become more differenti-od ated, the more likely that type H c will lie.Intuitively, when the two products are more differentiated, each firm will hope to increase their actual e port to counteract the demand reduction from a smaller x  .Since we are restricting , type H c of each firm has more intention to lie and hence 1  becomes higher.

Equilibrium VERs
Given the market equilibriu tion equilibrium determined m in (6) and the menu selecby ( 14) and ( 15), we now The same argument can apply to firm left with the determination on 2. Hence we are   j L i q c .As mentioned in Lemma 3 that the menu 13) and ( 16)) can induce 1 0   fo level of 2 r any  .The question of concern is whe ent will find it optimal to induce truth-telling from its own f rm, no matter how the rival firms might lie.
To answer the question, we first calculate the first or der condition of maximization: The expected social welfare is: . Since the structural or the detailed deri-rms are complicated, we omitted vation of   and move the be f 1 st reply o  inward to decrease both f 1 o  and 2  in equilibrium.

Mart
Vergoted [15] discussed the role of retaliation in trade ag ements.They showed that ina and re in the presence of private information, retaliation can always be used to increase the welfare derived from such agreements by the participating governments.In particular, it is shown that retaliation is a necessary feature of any efficient equilibrium.Our results show that retaliation can only happen when *    .
Proposition 6 Given any level of j  , it is optimal for the government to i en mplem t 0 i   .e In the case of firm 1, to see wheth it is optimal for government 1 to choose r      2 2 1 1 q    (from (13)   , L H q c c 0 and ( 15)) to implement 1   , we substitute   , we ca de that givenany level of 1 2 n conclu  , it is optimal for government 1 to implement 1  .

Concluding Remarksss 4.
We study the informational impa untary export restraints in a he f mu nou Brander and Krugman's [30] international trade model.Similar to the unilateral intervention case such as Qiu [2] and Collie and Hviid [6], we ask if separating equilibrium where each country's domestic firm truthfully reveals its private information still exists.If not, how much information can be revealed?How does information revelation relate to market structure?Will there be trade retaliation?
To these questions, we first showed that with competing mechani gic complements and will increase with the degree of product differentiation.Next, we showed that each government will design their VERs menus to allow for only partial revelation.Contrary to the single intervention case [2], a separating equilibrium where each country's domestic firm truthfully reveals its private information does not exist with multilateral interventions.Finally, we demonstrated that trade retaliation, when the two governments' VERs are positively related, will happen when the government believes that its domestic firm is more likely to be inefficient.
As mentioned, we have restricted our discussion on the VERs game to an intra alytical convenience and for complementation to the literature.It is also interesting to extend our model to discuss other policy instruments such as subsidies or taxes, and in another form of competition such as Cournot and Bertrand models.The literature has shown that the type of export policy is sensitive to the form of competition.In the case of subsidies or taxes, the informational impacts will not be as surprising as in VERs game, as the two governments are already related to each other with complete information.We will leave these interesting issues for further research.
complicated, we derive the following proper the menu selection equilibrium.First, from(14), it can be calculated that ties on of which can tell us wether the two policies are strategic i H j q c  , the sign complements or substitutes.Finally, we check whether it is dominant for government 1 to choose of prior belief  .In the case of government 1, if she thinks that the domestic more likely to be efficient (i.e., , the best reply of two firms' lying intentions are strate -industry trade model, for both an ENCES [1] H. H. Wang, C iffication and Welfare in a Diff e World Economy, only privately known by firm i .All other players (including government , government i j , and firm j ) have common prior beliefs that the prob- H c is 1   j