Safeguarding Free Trade in Recessions

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Safeguarding Free Trade in Recessions

- A Game-Theoretic Interpretation of the Multilateral

Policy Response to the 2008 Crisis

Carl Johan von Seth Bachelor thesis

Department of Economics, Uppsala University

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Abstract

In this paper, I propose a simple approach to trade cooperation in economic shocks. A two-country, two-good trade model provides a stage setting which yields numeric Nash equilibria. In a dynamic model, international demand for traded goods is allowed to be subject to sudden shocks. Numerical simulations predict that negative, sustained demand shocks may spark trade wars. Negative demand shocks that are short relative to the period it takes for governments to detect violations render instead incentives in free trade agreements more robust. I nd that the multilateral policy response to the 2008 crisis may have worked to strengthen this eect.

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List of Figures

1 World export 1980-2010. Source: IMF, WEO Database . . . 19

2 Lower-bound discount factor (δ) in negative demand shocks. . . 21

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4 Lower-bound discount factor, δ, in negative demand shocks and increased

monitoring. . . 24

List of Tables

1 Game I . . . 15

2 Game II (when governments are motivated by political economy). . . 15

3 Lower-bound discount factor under limited retaliation k . . . 17

4 Specication of timing in the recession-extended game . . . 19

5 Payo values from extreme game outcome without political bias . . . 34

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1 Introduction

In 2008, global trade volumes where subject to a collapse unprecedented since the Great Depression. The G20, a group of nance ministers and central bank governors from 20 economies, committed to keep protectionism at bay. On the G20' reqest, international bodies have closely monitored the developments in trade policy1_{. They have done so} seemingly with some success as countries have not yet adopted protectionist measures to a great extent during the crisis, as opposed to previous extraordinary economic downturns. In this paper, I aim to explain why protectionism has not, at least yet, rised during the crisis. In particular, I nd a theoretic interpretation of the countercyclically enhanced monitoring of trade policy that has been carried out.

I adopt as approach the terms-of-trade theory of trade cooperation. This theoretic literature nds a rationale for trade agreements in the trade taxation externality, which creates a classic Prisoners' Dilemma in trade cooperation. The terms-of-trade framework has also explained why taris historically have been higher during recessions and lower during economic booms (Bagwell and Staiger, 2003a). Behind this nding lies a straightforward intuition. In a repeated Prisoners' Dilemma game where payos vary over time, the strategies vary, too. In the face of a sustained downturn in payos, such as in a recession, cheating becomes more attractive since the punishment for cheating is decreasing relative to the immediate gain.

Typically, the applied game-theoretic literature explores most-cooperative levels of strategies (whether they are prices in oligopolies or taris in trade) using enforcement incentive contraints. In this paper, I solve for lower-bound discount factors that will yield a cooperative outcome in the game. I characterize the cooperative outcomes as self-enforcing free trade agreements and non-cooperative outcomes as trade wars.

The remainder of the introduction will describe the international institutional framework of trade cooperation and some of the policy responses to the crisis. I will in section 2 review the literature on trade cooperation and game theory. In section 3, I set up a model of trade cooperation in the presence of uctuating demand for traded goods. Section 5 provides numerical simulations and an interpretation of the model.

1_{Yi (2009) and Baldwin and Evenett (2009) describe the collapse in global trade and the multilateral}

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The World Trading System

The international institutional framework of trade cooperation has its foundation in the World Trade Organization. Its predecessor the General Agreement on Taris and Trade (GATT), was created in 1949 at the UN Conference on Trade and Employment. As an outcome of the seventh round of negotiations, the World Trade Organization (WTO) was created in 1994, an organization with now some 150 member countries.

During and between negotiations, the WTO serves as facilitator in settling disputes and interpreting agreed rules. It acts to monitor, gather information and ensure transparency in policy. The WTO enforces agreed rules through a Dispute Settlement Procedure. A dispute arises when a member country submit to the WTO secretariat a complaint toward any disputable trade-related measure implemented by another member. If countries cannot by themselves reach a mutually acceptable solution within two months, the Dispute Settlement Body installs a panel of three or ve experts on the relevant subject. The GATT of 1994 stipulates a proceeding of the panel stage in which a number of deadlines for hearings, rebuttals, draft of reports and reviews are given. Subsequent to this proceeding, the Dispute Settlement Body adopts a report prepared by the panel which includes a case ruling. If the panel rules the disputable measure incompatible with the responding country's commitments, the report will recommend that country to conform its measure to agreed rules. The stage from initiation of a complaint to the case ruling should take no longer than one year (WTO, 2010a).

If the responding country is unwilling to comply with the panel ruling within a time period, the complaining country may submit a request to retaliate. Primarily, the complaining country is admitted retaliation in the sector subject to dispute. The Dispute Settlement Body will specify a proportionate measure of retaliation, which can be sustained as long as the responding country is unwilling to conform its disputable measure, however, no longer than that (WTO, 2010a).

Global Policy Responses to the Crisis

Even though trade was not the main focus of its discussions, the G20 in the rst summits in November 2008 took stock of concerns in global trade.2 _{Primarily, participants agreed} to refrain from raising new barriers to trade and investment. OECD, WTO and UNCTAD were given the task to monitor the development in international trade policy. These

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bodies now regularly prepare reports to the G20. The WTO reports point to that around two percent of global trade ows have so far been aected by new policies (WTO, 2010b) (they do not assert that new trade-distorting measures account for two percent of the decrease in global trade ows). According to Bown (2010), antidumping3 _{measures make} up for a signicant share of examples of new trade protection (see also WTO, 2010b). When compared to the the fourth quarter of 2008, the same period in 2009 resulted in an increase of 37.5 percent in antidumping measures employed by WTO members. Nontari barriers are in particular increasing in the automotive sector, agricultural sector and the textiles sector (WTO, 2010b).

Even though it is not hard to nd examples of some new trade-distorting policies rising in the wake of the crisis, this paper's starting point is that protectionism has not been as prevailing as one would have expected (see for example Crean, 2009).

Evidence of the Countercyclical Pattern of Taris

Previous macroeconomic shocks have had measurable impact on trade policy. A prominent anectodtal piece of evidence would of course be the trade wars during and in the wake of the Great Depression 4_{. What is more, evidence of the counter-cyclical} behavior of taris extend to other periods. This issue has been investigated in numerous works, one of them being Bohara and Kaempfer (1991). The authors consider GNP, unemployment rate and the trade balance in the United States, during a period spanning from the 1890's throughout the 1970's. This study points to the fact that unemployment, GNP and the price level have moderate causal eects on average taris. They show that taris in the US are countercyclical and that unemployment seems to feed higher protection. The reverse is true for high ination. As regards the generality of these ndings, Bohara and Kaempfer note that their test is performed for a relatively trade-independent economy and that they therefore expect the apparent eects to be higher in other economies.

3_{Antidumping refers to a legal term which, essentially, allows for suspending tari concessions for}

goods that can be proven to be imported below market prices. See, for example, Messerlin (1990).

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2 Review of Theory

This section will provide a brief description of the concepts I will employ in the theoretical approach to trade wars. I will rst turn to the literature on the economic theory of international trade cooperation. The main points made in the traditional economic literature on this topic, following Johnson (1953-54), will be reviewed. In the ensuing subsection, I will turn briey to the literature on business-cycles in repeated games.

2.1 The Economic Approach to Trade Cooperation

The neoclassical rationale for engaging in international trade cooperation derives from a trade taxation externality, as it is typically considered that governments are self interested in the sense that they do not take into account the cost of a tari that travels through world prices. Johnson (1953-54) rst described this setting, assuming that governments are national-income maximizers who exercise their power to manipulate world prices through domestic taris, under the possibility of retaliation. Mayer (1981), Dixit (1987) and Bagwell and Staiger (1990) further formalized this model in a contemporary game-theoretic environment.

A strategic setting of possible retaliation and counter retaliation yields that Nash equilibrium will not correspond to free trade (Bagwell and Staiger, 2002). Governments will have an incentive to beggar their neighbour through taxing trade ows, causing a downward shift in the world price. The lower (at-the-border) price for imported goods will improve the country's export-import relationship, its terms of trade. This outcome is arguably Pareto-inecient.

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today against payos in the future.

Bagwell and Staiger (1999) consider that governments' may have preferences for distribution, e.g. between exporting sectors and import competing industries. Under this assumption, the authors specify how a trade agreements can also remedy the ineciencies that such political objectives may cause. In this political-economy augmented framework, authors conclude that the Nash equilibrium is still inecient. Governments' beggar-thy-neighbour incentives persist since they may still pass costs of their taris onto another through world prices. Consequently, the ecient solution of this game is negotiating reciprocal tari cuts. As opposed to the non-political case, it is considered that the most-ecient tari level needs not to be zero. The authors nd, however, that there are no additional political ineciencies that can explain international trade cooperation besides the terms of trade.

2.2 Theory of Fluctuating Demand and Pricing in Oligopolies

Rotemberg and Saloner (1986) propose a framework in which oligopolies respond to uctuations in demand for their goods. In a setting of rms engaging in an implicitly collusive oligopoly, rms strategically choose prices to maximize prots. In order for rms to maintain a self-policing oligopoly, they are assumed to punish cheating through competitive outcomes for a number of periods. Rotemberg and Saloner argue that a boom in demand will inuence cheating and price-competitive behavior. The intuition behind this conclusion is that in times of high demand, a rm's benet from price undercutting is greater. Assuming that demand follows a boom-and-bust cycle that is perfectly detectable among rms, expected retaliation in the future becomes less painful as the present value of prot is decreasing. The authors conclude that when demand is increasing, the higher will the equilibrium output be and the lower the equilibrium price. Oligopolies will hence respond to uctuation in demand by pricing countercyclical.

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strategy will make rms respond to depression in demand by acting competitive and oligopolies will, hence, price procyclical.

2.3 Theory of Countercyclical Trade Protection

In the paper Protection and the Business Cycle Bagwell and Staiger (2003a) attract their attention to explain the countercyclical regularities observed in trade protection.

In order to bring compliance, a self-enforcing trade agreement must oer a balance between short-term incentives to cheat and the long-term costs of a trade war. We can expect this balance to be upset in times of demand shocks, provided that trade ows are procyclical. In modeling the implications of business cycle, the authors consider a two-phase international economy with booms and recessions. They set up a model with persistent movements, transitory shocks and stochastic turning points under the assumption of independent and identically distributed random variables.

The authors conclude that most-cooperative taris are countercyclical.

2.4 An Explicit Stage Game of Trade Cooperation

This subsection will outline a static game and follow the model formulated in Bagwell and Staiger (2003a). In order to discuss the role of political-economy sources of changes in trade cooperation, I will supplement the framework with some formulations in Bagwell and Staiger (2003b). This setting deviates from other settings used in the literature in that it can yield numeric solutions for best-response and equilibrium taris. The full derivation of the model and Nash equilibria is relegated to the Appendix.

Here, a two-country, two-good general equilibrium economy is considered in which country A is endowed with an abundant good and a scarce good. Country B is endowed with the same goods, however, in reversed abundance so that countries desire trade with each other. The endowment of each good is 3/2 for the abundant good and 1/2 for the scarce good, in each country respectively. The abundant good is the respective country's natural export good. The scarce good is its natural import good.

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cleared in the world market and countries accept whatever price and quantity of goods. We assume that all goods are normal goods traded at zero costs.

2.4.1 Demand Functions, Taris and Market Clearing Prices

Countries demand for each of the goods in the world economy is given by D(P ) = 3/2−P . Governments can choose negative or positive taris either to restrict or promote trade in any direction, for all its traded goods. τA

x denotes export policy in country A, where taxation corresponds to positive values and subsidies correspond to negative values. τA m denotes its import policy. τB

x characterizes, in turn, the export policy for country B and τ_mB that country's import policy.

For any good, P represents the price. The natural export good of country A, trades at price PA

x in country A and price PmB in country B. Import prices are set to be determined by export prices in the exporting country, export taris in the exporting country and import taris in the importing country:

P_mB = P_xA+ τ_xA+ τ_mB (1)

P_mA= P_xB+ τ_xB+ τ_mA (2)

A material balance constraint can be set to require that total world demand must equal 3/2 + 1/2 = 2. Drawing from the general demand function D(P ) = 3/2 − P , we obtain the following material balance constraints:

2 = [3/2 − P_xA] + [3/2 − P_mB] (3)

2 = [3/2 − P_xB] + [3/2 − P_mA] (4)

2.4.2 Governments' Objective Functions and Best-Response Taris

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γx equal to unity represents no bias. γm 6= 1 and/or γx 6= 1 will have two separate implications. First, any bias ratio, γx

γm 6= 1 will determine the government's political-economy bias between the import-competing and the exporting sectors. Second, any bias may also determine the government's bias between consumers and rms.

In making a government's objectives explicit, total surplus W becomes a function of the importing country's import tari and the exporting country's export tari, such that WA

x(τxA, τmB)and WyA(τmA, τxB)represent the surpluses in country A, from its natural export and import goods respectively. This characterization of governments' preferences admits a three term representation of the function WA_{. The rst term (the integral} of D(P ) = 3/2 − P from the market clearing export price to the maximum price 3/2) represents the consumer surplus from a good at market clearing price. The second term, either 3/2 or 1/2 times the market clearing price of a good, represents the rms' surplus. We can attach to this term the political bias, γm or γx . The third and last term represents the policy makers' surplus. This term captures the net income from trade policy, whether it is taxation or subsidies. Subsequently, we can obtain the following total surplus functions:

WA(τ_xB, τ_mB, τ_mA, τ_xA) =

Consumer surplus from good x

z }| { 3/2 Z [1−(τA x+τmB)]/2 3 2 − P dP +

Firms' surplus from good x

z }| {

γA_x3 2[1 − (τ

A

x + τmB)]/2

Policy maker's surplus from taxing good x

z }| {

+τ_xA[1 − (τ_xA+ τ_mB)]/2

+

Consumer surplus from good m

z }| { 3/2 Z [1+(τA m+τxB)]/2 3 2− P dP +

Firms' surplus from good m

z }| {

γ_mA1 2[1 − (τ

A

m+ τxB)]/2

Policy makers' surplus from taxing good m

z }| {

−τ_mA[1 − (τ_mA+ τ_xB)]/2 ,

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+ 3/2 Z [1+(τA x+τmB)]/2 3 2 − P dP + γ_xA1 2[1 − (τ A x + τmB)]/2 + τxA[1 − (τxA+ τmB)]/2 (6) In order to explore governments' behavior in face of the above specied objective functions, conventional game theory suggests best-response functions. Best-response functions for export and import policy of country A are obtained by maximizing WA under the rst order condition with respect to τA

m and τxA, separately. WB is maximized under the rst order condition with respect to τB

x and τmB. The following functions are obtained:

(γ_mA− 1)/2 + MA( ˆP_mA) = τ_mA (7)

MB( ˆP_mB) − 3(γ_xA− 1)/2 = τ_xA (8)

(γ_mB− 1)/2 + MB( ˆP_mB) = τ_mB (9)

MA( ˆP_mA) − 3(γB_x − 1)/2 = τ_xB (10) The full derivation is relegated to the Appendix.

2.4.3 Nash Equilibrium

Having obtained country A and B's respective reaction functions, we can solve for Nash equilibrium. Assuming symmetry in equilibrium, Nash Equilibrum tari pairs are τN m and τN

x . This solution method yields that equation (7) = (9) and (8) = (10), eliminating half of the unknowns so that we can obtain the following symmetric equilibria:

ˆ

τ_mN = (3γx+ 3γm− 4)/8 (11)

and

ˆ

τ_xN = (12 − 9γx− γm)/8 (12)

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3 Dynamic Models of Trade Cooperation

Trade cooperation in reality can best be characterized as an innitely repeated game in which countries can respond to defective behavior by tit-for-tat retaliation, either constrained under the Dispute Settlement Procedure in the WTO, or, illegally. In this section, I move on to a dynamic setting of trade cooperation. The essential distinction between the static game in section 2.4 and a repeated game is the presence of future strategic choices and payos. Formally, it is considered that retaliation takes the form of Nash equilibrium outcomes (a trade war) in a number of periods following defection. In the following subsection, I will rst consider that countries choose a grim trigger strategy, which implies that a defection will result in an innite trade war. In the next subsection I will consider the case when countries choose limited punishment, which corresponds to a type of formalized tit-for-tat strategy.

I solve the dynamic games based on the stage game in section 2.4, following the solution method proposed by Osborne (2004). In subsection 3.4, I extend the method with a recession factor.

3.1 Assumptions

Before solving the dynamic games, I make the following complementary assumptions about countries' strategies and objectives in the stage game. Countries strategies will be restricted so they have just two choices: Either, they choose unrestricted trade, or restricted trade. Unrestricted trade corresponds to τx= τm= 0. I derive restricted trade (R) from the Nash equilibrium equations (11) - (12), such that if countries choose to tax trade, they will set τx= τm= 1₄ provided they are not inuenced by political economy. If governments are inuenced by political economy such that they value import-competing rms' surplus 1/5 more than other agents' surplus, they will set τx = ₄₀9 and τm = 13₄₀ when they choose to tax trade.

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Table 1: Game I

Country A

Unrestricted Restricted

Country B

Unrestricted_Restricted _{2.08, 1.89}2, 2 1.89, 2.08_{1.96, 1.96} Table 2: Game II (when governments are motivated by political economy)

Country A

Unrestricted Restricted

Country B

Unrestricted_Restricted _{2.146, 1.944}2.05, 2.05 1.944, 2.146_{2.003, 2.003}

From the game matrices 1 and 2 we can make the following conclusions. Both tari games resemble a classic Prisoner's Dilemma, as they are non-zero sum game with unique equilibria that are Pareto-inecient. The strategy to restrict trade strictly dominates the other strategy. Hence, the equilibrium in both games are for countries to choose restricted trade.

In a dynamic (repeated game) setting, countries may be able to sustain cooperation and persue a free trade agreement if they are able to present a credible threat to retaliate against violations. The countries' free trade agreement must - since there is still no "police" of world trade with power to put violators in jail - be self-enforcing. Consequently, governments' patience, their discount factor, becomes important.

This setting admits for solving for a lower-bound discount factor, which I call δ. δ belongs to (0, 1) and I assume that it is the same in both countries. I denote payos a and consider it a function of one player's strategy given the counterpart's. a belongs to {q, c, z}, where q denotes the immediate payo from cheating, c denotes the payo from cooperating and z the future payo from cheating.

3.2 Solution under Grim Trigger

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trade agreement. Their respective total payos are composed of the one payo from cooperating in t = 1 and the discounted stream of payos in the future. Making use of the specied notation, the sum of payos can be expressed as:

(1 − δ) ∞ X t=1

aδt−1

Where (1 − δ) yields average payos.

I want to characterize countries' best-responses, assuming they are both playing grim trigger. Following the specied notation in which q denotes the immediate payo from cheating, c the payo from cooperating and z the future payo from cheating in every period, the payo from cheating is given by:

(1 − δ)[q + δz + δ2z + δ2z + ...] = (1 − δ)[q + δz(1 + δ + δ2+ ...)]

= (1 − δ)[q + δz

(1 − δ)] (13)

Similarly, the payo from cooperating is given by:

(1 − δ)[c + δc + δ2c + δ2c + ...] = (1 − δ)[c + δc(1 + δ + δ2+ ...)]

= (1 − δ)[ c

(1 − δ)] = c (14)

The solution method I employ is to determine the lower bound of the discounting factor δ that will yield a cooperative outcome. I set up the inequality (13) ≤ (14) and consider rst the payos in game I:

2.08(1 − δ) + δ1.96 ≤ 2

⇐⇒ δ ≥ 2

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Solving for δ, I nd that countries' best-response will be to sustain a free trade agreement when the discounting factor is greater than 2

3. If governments' discount factor is smaller than 2

3, the free trade agreement will not be self-enforcing.

We can also see that the lower-bound discount factor is greater in Game II than in Game I:

2 − (2.08(1 − δ) + δ1.96) ≈ 0.6667 < 0.6713 ≈ 2.05 − (2.146(1 − δ) + δ2.003)

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3.3 Solution under Limited Punishment

Under limited punishment, countries implement retaliation in a nite number of k periods. Their tari strategies thus become dependent on k. In the limited punishment strategy, countries have negotiated and implemented a free trade agreement in period t = 1. In period t = 1, players may choose to violate the agreement. In response to a violation, the other player will choose to violate it in t = 1 + 1 throughout period t + k + 1, regardless of what the defective player does. When period t+k +1 has ended, the retaliating player returns to cooperation.

The limited retaliation mechanism alters the relevant stream of payos so it will be the following sum:

(1 − δ) 1+k+1

X t=1

aδt−1

The payos from cheating in t = 1 + 1 is:

q(1 − δ) + δz(1 − δk) (16)

And the payo from cooperating throughout the same period:

c(1 − δk+1) (17)

Employing the same solution method as in section 3.2, I solve the inequality (16) ≤ (17) considering Game I:

2.08(1 − δ) + δ1.96(1 − δk) ≤ 2(1 − δk+1),

or, in its simplest form, 0.08 − 0.12δ + 0.04δk+1_{≤ 0}_{. If 0.080.12δ + 0.04δ}k+1 _{= 0}_{, solving} for δ will yield a lower bound discount factor that can produce a self-enforcing trade agreement. Table 3 presents a number of lower-bound discount factors.

Table 3: Lower-bound discount factor under limited retaliation k

k 2 3 4 6 50

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We can observe from table 3 that the lower-bound discount factor is decreasing with the length of the punishment period. That is, countries must be more patient in order to sustain a self-enforcing trade agreement if they perpetrate a strategy which involves shorter punishment periods. If the punishment period is set to 50 periods, the lower-bound discount factor is close to the one obtained under the grim trigger strategy.

3.4 A Recession-Extended Repeated Game of Trade

In the following subsection, I add demand shocks to the setting described in subsection 3.2. Here, the business cycle is modeled to capture the governments' short run expectations on demand. Typically, trade volume follows a pattern best described as a number of years of high growth followed by a number of years of slower growth. Danthine and Donaldsson (1993) show that exports and imports are procyclical, and more variable than output. Figure 1 illustrates the growth in world exports and output since 1980 and provides a rather clear visualization of the conventional notion of trade volumes and the business cycle. From this picture it is also evident, however, that the normal description of the business cycle is unsuitable when considering the present crisis. The extraordinary shock in trade between 2008 and 2010 motivates me to model the business cycle in a rudimentary, scewed "V"-shaped way. Below, I attempt an approach to the demand shock factor, which I call t.

If Gtis the growth rate of demand, twill be equal to _1−G1 _t so that t> 1corresponds to positive growth and t< 1corresponds to negative growth. I consider an international business cycle, so t will take the same value in both countries. The basic chronology of the game is specied as follows. Before t = 1, governments have negotiated a free trade agreement. Having implemented a self-enforcing, reciprocal free trade agreement, governments observe in time t = 1 an international demand shock. Governments automatically assume that the shock is going to last for r years.

I assume governments will anticipate the demand to return to its initial state after r periods of growth corresponding to t to the power of t. I specify t the following way:

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Figure 1: World export 1980-2010. Source: IMF, WEO Database 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 100 150 200 250 300 350 400 450 500 550 -15 -10 -5 0 5 10 15

Trade volume Yearly growth in trade volume

Trade volume,index year=1980 (left y-axis) Year-to-year percent growth in trade (right y-axis)

*

*The two second quarters 2010 are IMF staffestimates.

A Simple Geometric-Progression Approach

This specication implies that if governments in t = 1 observe a 10 percent decline in demand, they assume that t will be approximately 0.9 to the power of t for r periods. With this primitive forecast at hand, governments evaluate their respective gain from cooperation in t = 1 throughout t = r, given the imminent demand shock. Table 3.4 illustrates the game timing.

Table 4: Specication of timing in the recession-extended game

Time Demand Factor

t = 1 t _{Demand for traded goods experiences a shock.}

Govern-ments anticipate that the present growth level will last for rperiods.

t = r r Governments anticipate the demand to be at its lowest level in the last period of the shock.

t = r + 1 0 _{Governments assume demand for traded goods will return}

to its initial level.

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governments choose to play grim trigger. If country A defects in the face of a demand shock, country B will retaliate forever. B will do the same if A defects. Here I add tin line with the above specication. Derivations are relegated to the Appendix.

The payos from cheating today and the stream of payos in the future from cheating are given by:

q + r X t=2 zδt−1t+ ∞ X t=r+1 zδt−1

Which is equal to:

q + z(δ + 2δ2+ ... + r−1δr−1) + (zδr+ zδr+1+ ...) I obtain: q + zδ(1 − r−1_δr−1₎ 1 − δ + zδr 1 − δ = q + zδ − (δ) r 1 − δ + zδr 1 − δ (18)

The payos from cooperating is given by: c + r X t=2 cδt−1t+ ∞ X t=r+1 cδt−1

Which is equal to:

c + c(δ + 2δ2+ ... + r−1δr−1) + (cδr+ zδr+1+ ...) I obtain: c + cδ(1 − r−1_δr−1₎ 1 − δ + cδr 1 − δ = c 1 − (δ) r 1 − δ + cδ r 1 − δ (19)

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4 Solution and Interpretation of the Model

4.1 Solutions to the Geometric-Progression Approach

The models in section 3.4 allows for solving for the lower-bound discount factor (δ) when parameters r and are specied. I rst consider shock levels () between 0.95 and 0.8 which correspond to negative growth between 5.2 and 25 percent.

Figure 2: Lower-bound discount factor (δ) in negative demand shocks.

1 2 3 4 5 0,56 0,58 0,6 0,62 0,64 0,66 0,68 0,7 0,72 0,74 = 1 ε = 0.95 ε = 0.9 ε = 0.85 ε = 0.8 ε Duration of shock D is co un t fa ct or

Countercyclical region Procyclical region

Figure 2 illustrates the lower-bound discount factor under a number of negative shock levels, lasting up to ve periods. When the non-growth case (i.e. when t = 1) is the benchmark, we observe two regions. In sustained shocks, the lower-bound discount factor is countercyclical (observed in the right hand region of the gure). In short shocks, however, the lower-bound discount factor is procyclical (observed in the left hand region of the gure) .

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governments expect the shock to last for more than approximately two and a half periods, the agreement will no longer be self-enforcing and they will, rationally, start a trade war. The intuition behind this predicition is robust. As countries experience a demand shock in traded goods, they expect the gain from violating the trade agreement to outweigh the costs of a future trade war if and only if the shock is suciently long to decrease the payos in the punishment period relative the initial gain. When the shock is suciently short, merely the gain from violating is decreasing - the pains from the trade war are instead, relatively, increasing.

The relationship between the procyclical and the countercyclical region is driven by the assumption that countries may gain from cheating as a result from their counterpart being able to detect and respond to the defection after one period. That is, the defecting country's gain from cheating will last just one period. The assumption can be interpreted such that a government's information about other's choices and its own opportunity to retaliate has a lag of one period. If information increases and governments' choices become more exible, the number of periods in the game increases.

Figure 3 illustrates the lower-bound discount factor in surges of demand. For positive shocks, the result is reversed compared to negative shocks. From gures 2 and 3 we can assert that when the shock coincides with the point in time where cheating is punished, the incentives in the free trade agreement is at its most procyclical level.

4.2 Extended Interpretation

The results obtained here admits the following interpretation of the multilateral trade policy response to the 2008 crisis. First, we can establish that negotiating or renegotiating trade agreements are associated with certain costs. Governments should therefore be willing to avoid that an existing free trade agreement suddenly becomes non-self enforcing, compelling them to either forgo the benets from cooperation or to invest in a new negotiation. Arguably, they will be willing to protect the existing free trade agreement to any cost lower than or equal to the costs associated with renegotiation. This is possible, provided that governments have the opportunity to regulate the time it takes to for them to discover cheating and retaliate, by putting more or less resources into monitoring trade.

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lower-Figure 3: Lower-bound discount factor, δ, in positive demand shocks. 1 2 3 4 5 0,53 0,55 0,57 0,59 0,61 0,63 0,65 0,67 0,69 0,71 0,73 = 1 ε = 1,05 ε = 1.11 ε = 1.18 ε = 1.25 ε Duration of shock D is co un t fa ct or Procyclical region Countercyclical region

bound discount factor. To illustrate the interpretation of countercyclical monitoring, I assume that governments increase the frequence of monitoring of trade so that it takes them 0.05 periods less to retaliate against cheating. This modication of the model has one straightforward implication to the solution: Only the rst term of equation (18) will be modied so instead of q, governments receive 0.95(q) + 0.05(z) in the rst period. This is illustrated in Figure 4, where the downward shift in the lowe-bound discount factor produces a regulation of the procylical region. The increase in the procyclical region lies in the vicinity of two and a half and four (marked with double-distance crosshatches).

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Figure 4: Lower-bound discount factor, δ, in negative demand shocks and increased monitoring. 1 2 3 4 5 0,58 0,6 0,62 0,64 0,66 0,68 0,7 0,72 = 1 ε = 0.9 (when ε monitoring is increased) = 0.9 ε Duration of shock D is co un t fa ct or Countercyclical region Procyclical region

factor. Countercyclical monitoring will therefore have the same eect as for "Game I"; Countercyclical monitoring will shift the lower-bound discount curve downwards and increase the procyclical region. This holds as long as governments are not politically motivated to the extent that the game no longer resembles a Prisoners' Dilemma and becomes a zero-sum game.

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5 Conclusions

In contrast to previous periods of extraordinary collapse in trade, rather few signs point to that the world is experiencing an extraordinary rise in protectionism in the wake of the 2008 crisis. In this paper, I have persued an explanation of the absence of trade wars in the light of the multilateral response taken by the G20. Primarily, the multilateral policy response has been to strengthen the information mechanisms of the global trading system.

This paper's framework is composed of a strategic, terms-of-trade-theoretic environ-ment in which governenviron-ments are allowed to expect negative growth in demand for traded goods for short periods.

The main result is that the conventional notion of trade wars in recessions holds only when economic downturns are sustained. If negative shocks are suciently short, they work to make incentives in free trade agreements more robust.

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References

[1] Bagwell, Kyle and Robert W. Staiger (1990), "A Theory of Managed Trade." American Economic Review, September, 779-95.

[2] Bagwell, Kyle and Robert W. Staiger (1999), "An Economic Theory of GATT" American Economic Review, March, 215-248.

[3] Bagwell, Kyle and Robert W. Staiger (2002), The Economics of the World Trading Systsem, Cambridge, MA: The MIT Press,

[4] Bagwell, Kyle and Robert W. Staiger (2003a), "Protection and the Business Cycle", Advances in Economic Analysis and Policy Vol. 3, No. 1, Article 3, 1-43.

[5] Bagwell, Kyle and Robert W. Staiger (2003b), "Protection and the Business Cycle", Unpublished manuscript.

[6] Baldwin, Richard and Simon J. Evenett.(2009) The collapse of global trade, murky protectionism, and the crisis: Recommendations for the G20 A Vox EU Publication, March, 2009.

[7] Crean, E. Simon. (2009) "Protectionism and the global economic crisis - the role of trade in the response", in The collapse of global trade, murky protectionism, and the crisis: Recommendations for the G20, edited by Richard Baldwin and Simon J. Evenett. A Vox EU Publication, March, 2009.

[8] Danthine, J.P. and J.B Donaldsson (1993), "Methodological and Empirical Issues in Real Business Cycle Theory", European Economic Review, 37 January, 1-35. [9] Dixit, Avinash (1987), "Strategic Aspects of Trade Policy", in Truman F. Bewley ed.,

Advances in Economic Theory: Fifth World Congress. Cambridge, MA: Cambridge University Press, 329-62.

[10] Johnson, Harry G. (1953-54) "Optimum Taris and Retaliation", Review of Economic Studies, 142-53.

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[12] Maggi, Giovanni (1999), "The Role of Multilateral Institutions in International Trade Cooperation", American Economic Review, March, 190-214.

[13] Mayer, Wolfgang (1981), "Theoretic Considerations on Negotiated Tari Adjust-ments", Oxford Economic Papers, March, vol. 33 (1), 135-53.

[14] Messerlin, Patrick A. (1990), "Antidumping Regulations or Pro-Cartel Law? The EC Chemical Cases.", World Economy, December, 456-92.

[15] Osborne M. J. (2004), An Introduction to Game Theory, Oxford Univ. Press, 2004. [16] Rotemberg, J.J. and Saloner, G. (1986), "A Supergane-Theoretic Model of Price

Wars during Booms", American Economic Review, June, 390-407.

[17] World Trade Organization (2010a). Understanding the WTO, Geneva, the World Trade Organization, Fifth edition.

[18] Zedillo, Ernesto. (2009) "The multilateral trading system: a response to its challengers", in The collapse of global trade, murky protectionism, and the crisis: Recommendations for the G20, edited by Richard Baldwin and Simon J. Evenett. A Vox EU Publication, March, 2009.

Online resources:

[19] Bown, Chad (2010), "Antidumping, safeguard and protectionosm during the crisis: Two new insights from 4th quarter 2009", www.voxeu.org, 18 February, retreived 2010-11-28.

[20] World Trade Organization (2010b). "Report to the Trade Policy Review Body From Director-General on Trade-Related Developments", www.wto.org, June, retreived 2010-11-28.

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A Appendix

A.1 Derivation of Best-response Taris

Prices for each import good is given by the following identities:

P_mB = P_xA+ τ_xA+ τ_mB (21)

P_mA= P_xB+ τ_xB+ τ_mA (22)

From the assumed endowment of 3/2 and 1/2 units of each goods, I derive a material balance constraint which require total world demand must equal 3/2+1/2 = 2. Drawing from the general demand function D(P ) = 3/2 − P , I obtain:

2 = [3/2 − P_xA] + [3/2 − P_mB] (23)

2 = [3/2 − P_xB] + [3/2 − P_mA] (24)

Where the demand for good each good is determined by the price of the good in each country and where demand must in total be equal to 2. From (23)-(26), we solve for each market clearing price and import volume:

2P_xA= 3/2 + 3/2 − 2 − (τ_xA] + τ_mB = 1 − (τ_xA+ τ_mB) (25)

ˆ

P_xA= [1 − (τ_xA+ τ_mB)]/2 (26)

Market clearing import volumes are in turn given by M(PA

m) = D( ˆPmA) − 1/2 and MB( ˆP_xA) = D( ˆP_mB) − 1/2. When solving for each price and import volume, I obtain

ˆ

P_xA= [1 − (τ_xA+ τ_mB)]/2 ; ˆP_mB= [1 + (τ_mA+ τ_xB)]/2 (27)

ˆ

P_xB= [1 − (τ_mA+ τ_xB)]/2 ; ˆP_mA= [1 + (τ_mA+ τ_xB)]/2 (28)

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At free trade, i.e. when τB

x = τmA = τxA = τmB = 0, the price for any export good is (1 − 0 − 0)/2 = 1/2 and (1 + 0 + 0)/2 = 1/2 is the price for any import good. Each country's equilibrium import volume is (1 − 0 − 0)/2 = 1/2, so that they will import 1/2 of their natural import good and export 1/2 of their natural export good.

Note also that there is a level of tari for each good, that will prohibit trade entirely: M (P ) = 0

M (P ) = [1 − (τ_mA+ τ_xB)]/2

and solve for (τA m+ τxB)

1/2 = (τ_mA+ τ_xB)]/2

(τ_mA+ τ_xB) = 1

Consequently, I have that trade policy will prohibit trade when (τA

m+ τxB) ≥ 1.

It is now straightforward to set up the following total surplus function for country A: WA(τ_xB, τ_mB, τ_mA, τ_xA) = 3/2 Z [1−(τA x+τmB)]/2 3 2− P dP + γ_xA3 2[1 − (τ A x + τmB)]/2 + τxA[1 − (τxA+ τmB)]/2 + 3/2 Z [1+(τA m+τxB)]/2 3 2− P dP + γ_mA1 2[1 + (τ A m+ τxB)]/2 + τmA[1 − (τmA+ τxB)]/2 (30) The assumed symmetry yields a reversed function for country B (see equation 6). To explore the reaction functions for export and import policy of country A, I maximize WA under the rst order condition with respect to τA

m and τxA separately. I employ Leibniz integral rule for consumer surplus and take the derivative of WA _{with respect to τ}A

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= dW A dτA m = 1 2 γy 2 − 3 2 + 1 2+ τ_mA 2 + τ_xB 2 +(1 − [τ A m+ τxB]) 2 − τ_mA 2 = 0 = dW A dτA m = γy 4 − τ_xB 4 − 3τ_mA 4 = 0 Solving for τA m, I obtain: γy 4 − τ_xB 4 = 3τ_mA 4 = τ_mA= γy 3 − τ_xB 3 = τ_mA= γy− 1 2 + M ( ˆP A m) (31)

Maximizing WA _{under FOC with respect to τ}A

x and solving for τxAI obtain:

τ_xA= M ( ˆP_mA) −3(γx− 1)

2 (32)

I assume symmetry in equilibrium, so that τA

m = τmB and τxA= τxB, which I call τm and τx respectively. This denition allows for the following rewriting of (30) and (31):

τm = γm− 1 2 + (1 − [τm+ τx]) 2 = τm = 1 3γm − 1 3τx (33) τx= 4 3 − 1 3τm − γx (34)

Solving for Nash equilbrium import taris τN

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= τ_mN = 3 8γm + 3 8γx − 1 2 = τ_mN = 3(γm+ γx) − 4 8 (35)

Solving for Nash equilibrium export taris τN

x , I obtain:

τ_mN = 12 − 9γx− γm

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A.2 Payos in the Stage Game

To obtain total surpluses, let us recall the market-clearing prices and import volume. Given the symmetry, these equations suce:

ˆ

Px= [1 − (τm+ τx)]/2

ˆ

Pm= [1 + (τm+ τx)]/2

M ( ˆPm) = [1 − (τm+ τx)]/2; M ( ˆPm) = [1 − (τm+ τx)]/2

Total surpluses are obtained from (i) consumers: 3/2 Z [1−(τm+τx)]/2 3 2 − P dP ; 3/2 Z [1+(τm+τx)]/2 3 2 − P dP,

from the export good and import good respectively. Firms' payo is given by 3

2Pˆx and 1

2Pˆm. The policy makers' surplus is given by the tari rate times the market-clearing import volume.

A.2.1 Payos without political bias

Following the assumptions in section 3.4, taris will be either 0 or 1

4 and the same for import and export.

Payos from reciprocal unrestricted trade

Market clearing price for each good: [1+0+0)]/2 = [1+0+0)]/2 = 1/2. Market clearing import volume: [1 + (0 + 0)]/2 = 1/2. Consumer surplus from the export good will be: 1/2. Firms' surplus from the export good will be 3/2 ∗ 1/2 = 3/4. The policy makers' surplus will be zero, as they do not tax trade.

Turning to surpluses from the import good, consumers surplus will 1/2. Firms' surplus from the export good will be 1/2 ∗ 1/2 = 1/4. The policy makers' surplus will be zero.

Payos from unilateral restricted trade

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consider that country A chooses restricted trade when B is perpetrating unrestricted trade. Given the symmetry, the reversed case will correspond to the same payo values. Market-clearing price for the import good in both countries will be: [1+1/4+0)]/2 = 5/8. Market-clearing price for the export good in both countries will be: [1−1/4−0)]/2 = 3/8. Market-clearing import volume in both countries will be: [1 − 1/4 − 0)]/2 = 3/8.

Consumer surplus from the import good will be: 49/128. Consumer surplus from the export good will be: 81/128. Firms' surplus from the export good will be 3/2∗1/4 = 9/16. Firms' surplus from the import good will be 1/2 ∗ 5/8 = 5/16.

The policy makers' surplus in country B will be zero, as they do not tax trade. The policy makers' surplus in country A will be: 1/4[1 − 1/4 + 0)]/2 = 3/32 from the import good and 1/4[1 − 1/4 − 0)]/2 = 3/32 from the export good.

Payos from reciprocal restricted trade

Drawing from the assumptions in section 3.4, countries will in equilibrium tax trade by 1/4. The local price for each export good in a state of reciprocal restricted trade will be [1−(1/4+1/4)]/2 = 1/4. The local price for the import good will be [1+(1/4+1/4)]/2 = 3/4. Import volume will be equal to 1/4 in both countries.

Total surpluses in country A and B will be the following. Consumer surplus from the import good will be: 9/32. Consumer surplus from the export good will be: 25/32.

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Table 5: Payo values from extreme game outcome without political bias

A restrict., B unrestrict. Both restricted Both unrestricted

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A.2.2 Payos with political bias

This section presents values in extreme outcomes of the game when governments are inuenced by political economy. Specically, I assume that governments value the import-competing industry's surplus 1/5 as much as anyone else's surplus. Hence, I set γm = 6/5. Taris will be τm= 13/40 and τx= 9/40, from the Nash equilbrium equations.

Payos from reciprocal unrestricted trade

Payos in reciprocal free trade will be the same as in the non political-bias case, expect for the the rms' surplus. Firms' surplus from the import good in both countries will be 6/5 ∗ 1/2 ∗ 1/2 = 3/10.

Payos from unilateral restricted trade

As in the previous section, unilateral restricted trade corresponds to either country A or B responding to its counterpart's unrestricted trade strategy by choosing restricted trade. I will consider that country A chooses restricted trade when B is perpetrating unrestricted trade. Country B responding to country A's unrestricted strategy will yield the reversed payo values.

Market-clearing price for the import good in country A will be: [1 + 13/40 + 0)]/2 = 53/80. Market-clearing price for the export good in country A will be: [1−9/40−0)]/2 = 31/80. Market-clearing price for the import good in country B will be: [1+9/40+0)]/2 = 49/80.

Market-clearing price for the export good in country B will be: [1 − 13/40 − 0)]/2 = 27/80. Market-clearing import volume in countriy A will be: [1 − 13/40 − 0)]/2 = 27/80. Market-clearing import volume in countriy B will be: [1 − 9/40 − 0)]/2 = 31/80.

Consumer surplus from the import good in country A will be approximately 0.351. Consumer surplus from the export good in country A will be approximately 0.619.

Consumer surplus from the import good in country B will be approximately 0.394. Consumer surplus from the export good in country B will be approximately 0.676.

Firms' surplus from the import good in country A will be 6/5 ∗ 1/2 ∗ 53/80 ≈ 0.398. Firms' surplus from the export good in country A will be 3/2 ∗ 31/80 ≈ 0.581.

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The policy makers' surplus in country B will be zero, as they do not tax trade. The policy makers' surplus in country A will be: 13/40[1 − 13/40 + 0)]/2 ≈ 0.11 from the import good and 9/40[1 − 9/40 − 0)]/2 ≈ 0.087 from the export good.

Payos from reciprocal restricted trade

Market-clearing price for the import good in both countries will be: [1 + (13/40 + 9/40)]/2 = 31/40. Market-clearing price for the export good in both countries will be: [1 − (9/40 + 13/40)]/2 = 9/40. Market-clearing import volume in both countries will be: [1 − (13/40 + 9/50)]/2 = 9/40.

Total surpluses in country A and B will be the following. Consumer surplus from the import good will be approximately 0.263. Consumer surplus from the export good will be approximately 0.813.

Firms' surplus from the export good will be 3/2 ∗ 9/40 = 27/80. Firms' surplus from the import good will be 6/5 ∗ 1/2 ∗ 31/40 ≈ 0.465. The policy makers' surplus from the import good will be 13/40[1−(9/40+13/40)]/2 ≈ 0.073 and 9/40[1−(9/40+13/40)]/2 ≈ 0.051 for the export good.

Table 6: Payo values from extreme game outcome with political bias

A restrict., B unrestrict. Both restricted Both unrestricted

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A.3 Geometric-progression solution X = c + c(δ + 2δ2+ ... + r−1δr−1) + (cδr+ zδr+1+ ...) Is equal to: −c − (c)X= δ + 2δ2+ ... + r−1δr−1+ cδ r 1 − δ multiply by (1 − δ): −c − (c)(1 − δ)X= (1 − δ)(δ + 2δ2+ ... + r−1δr−1) + cδ r 1 − δ,

all intermediate terms cancel each other out:

−c − (c)(1 − δ)X= (δ − rδr) + cδ r 1 − δ,

Safeguarding Free Trade in Recessions