Working Paper. Trade Policy Coordination and Food Price Volatility. Highlights. Christophe Gouel

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1 No December Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty Chrstophe Gouel Hghlghts The countercyclcal adjustments of trade polces wth food prces are an mportant contrbuton to the volatlty of food prce. We study n a theoretcal model the features of an nternatonal agreement to dscplne ther use. Even n cooperaton, t s not possble to exclude devaton from free trade as ncentve to devate from cooperaton could become too hgh n free trade n case of large shocks. Gven that the dstrbuton of staple food prces s postvely skewed, food exporter wll occasonally face large ncentve to devate from free trade, thus, dscplnng export taxes wll be more dffcult than tarffs n trade agreements.

2 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty Abstract Many countres adjust ther trade polces countercyclcally wth food prces, to the extent that the use by numerous food exporters of export restrctons has occasonally threatened the food securty of food mportng countres. These trade polces are nconsstent wth the terms-of-trade motvaton often retaned to characterze the payoff fronter of self-enforcng trade agreements, as they can worsen the terms of trade of the countres that apply them. Ths paper analyzes trade polcy coordnaton when trade polces are drven by terms-of-trade effects and a desre to reduce domestc food prce volatlty. Ths framework mples that mportng and exportng countres have ncentves to devate from cooperaton at dfferent perods: the latter when prces are hgh and the former when prces are low. Snce staple food prces tend to have asymmetrc dstrbutons, wth more prces below than above the mean but wth occasonal spkes, a self-enforcng agreement generates asymmetrc outcomes. Wthout cooperaton, an mportng country uses more frequently ts trade polcy because of the concentraton of prces below the mean, but an exportng country has a greater ncentve to devate from a cooperatve trade polcy because postve devatons from the mean prce are larger than negatve ones. Thus, the asymmetry of the dstrbuton of commodty prces can make t more dffcult to dscplne export taxes than tarffs n trade agreements. Keywords Commodty prce stablzaton, export restrctons, repeated game, WTO. JEL F13, Q17, Q18. Workng Paper CEPII (Centre d Etudes Prospectves et d Informatons Internatonales) s a French nsttute dedcated to producng ndependent, polcyorented economc research helpful to understand the nternatonal economc envronment and challenges n the areas of trade polcy, compettveness, macroeconomcs, nternatonal fnance and growth. CEPII Workng Paper Contrbutng to research n nternatonal economcs CEPII, PARIS, 014 All rghts reserved. Opnons expressed n ths publcaton are those of the author(s) alone. Edtoral Drector: Sébasten Jean Producton: Laure Bovn No ISSN: CEPII 113, rue de Grenelle Pars Press contact: presse@cep.fr

3 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty Trade Polcy Coordnaton and Food Prce Volatlty 1 Chrstophe Gouel 1. Introducton Durng food prce spkes, food exportng countres frequently use export restrctons to nsulate ther domestc markets from hgh prces on the world market. Ther use can be so wdespread that the hgh levels reached by nternatonal prces could be seen as a consequence of these nterventons (Dawe and Slayton, 011), and the restrctons can be so strngent that they can lead to the near dsappearance of the world market as happened to the rce market over nne months n 1973 (Tmmer, 010). Food mportng countres also do not reman nactve: they decrease ther tarffs to protect ther consumers. When world prces are low, the stuaton s reversed: mporters rase ther mport duty. In summary, n food markets countres routnely adjust ther trade barrers to nsulate ther domestc markets from nternatonal prce varablty (Anderson and Nelgen, 01). The lack of commtment to leavng borders open can reduce trust n the world trade system and lead to costly polces. Importng countres that expect food exporters to restrct ther exports n tmes of scarcty wll move away from a specalzaton consstent wth ther comparatve advantages, to ensure a hgher self-suffcency, or wll carry expensve publc stocks. For example, the current large-scale publc nterventons n the Asan countres, through whch many countres attempt to acheve self-suffcency n major staples, can be explaned largely by ther experence of the 197/73 food crss (Rashd et al., 008). The wdespread use of export restrctons n the 007/08 food prces spke, and the Russan ban on exports n 010 after a devastatng drought, spurred call for World Trade Organzaton (WTO) dscplnes on export restrctons (FAO et al., 011, HLPE, 011, Bouët and Laborde, 01). These proposals receved a cold recepton from several food-exportng developng countres (Mtra and Joslng, 009), and were not consdered n the agreement reached at the 9 th WTO Mnsteral Conference held n Bal (WTO, 013). 3 So far, accordng to agrcultural draft modaltes (WTO, 1 The author thanks Antone Bouët, Jean-Marc Bourgeon, Quy-Toan Do, Lonel Fontagné, Sébasten Jean, and Wll Martn for helpful comments. Ths research was generously supported by the Knowledge for Change Program (KCP), and by the European Unon s Seventh Framework Programme FP7/ under Grant Agreements no FOODSECURE. The author only s responsble for any omssons or defcences. The European Unon and European Commsson are not accountable for the content of the paper. INRA, Économe Publque, and CEPII (chrstophe.gouel@grgnon.nra.fr) In a survey of country responses to the food securty crss, Demeke et al. (009) show that 5 developng and emergng countres n a panel of 81 restrcted or banned exports. 3 Ths was not a new ssue as proposals to regulate export restrctons were rejected by many member countres at the begnnng of the Doha Round negotatons (WTO, 004). 3

4 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty 008), n the case of another agreement there would not be any sgnfcant strengthenng of the dscplnes on export restrctons. Gven the mportance of export restrctons for nfluencng trust n world markets, and thus food polces n the long run, t s essental to understand what s preventng a trade agreement on ths ssue. Ths paper contrbutes to understandng of what trade agreements would be acceptable wth respect to trade polces that are countercyclcal wth food prces. Usng some concepts of game theory, t explores the possblty of cooperaton through a self-enforcng trade agreement between countres whch, on ther own, would try to decrease the volatlty of ther domestc food prces va trade polces. A formal treatment of countercyclcal trade polces, and the extent to whch self-enforcng agreements can dscplne countercyclcal trade polces are proposed n Bagwell and Stager (1990, 003). An agreement s self-enforcng when cooperaton s sustaned by the threat of future punshment f cooperaton s volated, wthout the need for an external enforcement mechansm. Bagwell and Stager (1990, 003) show that the threat of a return to a non-cooperatve stuaton s suffcent to obtan tact cooperaton among countres nvolved n repeated nteractons. However, ths cooperaton s not necessarly synonymous wth free trade, because when trade shocks are large enough the ncentve to devate from cooperaton would become too hgh n free trade. The papers by Bagwell and Stager focus on trade polces motvated by terms-of-trade gans, and explan changes n trade polces by changes n potental terms-of-trade gans arsng from dosyncratc supply shocks. For food products, terms-of-trade theory may not be suffcent to explan the behavor of trade barrers. Examples of devatons from ths theory are the export bans mposed by many countres durng the recent food crss that precluded any gans from trade, and the export subsdes appled by wealthy countres n perods of low prces whch deterorate the terms of trade of the countres usng them. In addton, terms-of-trade theory relates trade polcy adjustments to trade volume rather than to the world prce, because trade volume characterzes the potental gans from manpulatng terms of trade. However, Anderson and Nelgen (01, Table 1) show that protecton of food products s negatvely correlated wth devatons from trend n the nternatonal prce of the products n queston. So to account for the extent of trade polcy adjustments n food products, and to characterze the payoff fronter of self-enforcng trade agreements, we need a model where governments are not just motvated by terms-of-trade gans, but want also to stablze domestc prces. Our startng pont s the two-country partal equlbrum model proposed by Bagwell and Stager (1990). There are two features that dstngush our model from Bagwell and Stager s. Frstly, to nvestgate the mpact of prce fluctuatons on trade polcy coordnaton, a partcular structure must be placed upon the socal welfare functon snce explotaton of the terms of trade s not suffcent to explan the offsettng of nternatonal prce varatons by trade polces. To ntroduce the observed reacton of trade polces to the world prce, t s necessary to consder other economc and poltcal-economy motvatons. Countercyclcal trade polces can be ratonalzed as nsurance nstruments when accountng for market falures n rsk management (Eaton and Grossman, 1985, Cassng et al., 1986, Gouel and Jean, forthcomng). Ther exstence mght also be explaned by poltcal-economy consderatons. For example, the loss-averson framework 4

5 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty of Freund and Özden (008) and Tovar (009) was appled by Gordan et al. (014) to account for prce-nsulatng trade polces. Gven the varety of potental motvatons for these polces (Swnnen, 010, Anderson et al., 013), and the focus of the present paper on the strategc nteractons of countres, we adopt a tractable reduced-form socal welfare functon that accounts for the economc and poltcal-economy motvatons descrbed above. Secondly, n contrast to Bagwell and Stager s model whch was concerned only wth dosyncratc rsk, we ntroduce aggregate uncertanty, whch s crucal to add world prce volatlty to the model. The resultng model s used to characterze the statc Nash equlbra and the nature of a self-enforcng agreement on tme-varyng trade polces. The combnaton of the reduced-form socal welfare functon wth aggregate uncertanty mples that n tact cooperaton equlbra, mportng and exportng countres have ncentves to devate from cooperaton at dfferent perods: exporters when prces are hgh and mporters when prces are low. In addton to contrbutng to the theoretcal lterature on self-enforcng trade agreements, ths paper contrbutes to the polcy dscussons on export restrctons. Despte the potental usefulness of dscplnes on export restrctons, a few papers have ponted out that they are unlkely to be achevable n the WTO framework. For Abbott (01), ths s because polcy makers wll not agree to renounce ther rght to stablze ther markets. For Cardwell and Kerr (014), the dspute settlement system cannot enforce such dscplnes because export restrctons are of short duraton compared to the tme taken to settle dsputes, and because complanant countres may not be n a poston to retalate owng to nsuffcent blateral trade levels. In the present paper, dscplnes on export restrctons are also proved dffcult to acheve. Snce staple food prces tend to have postvely-skewed dstrbutons (Deaton and Laroque, 199), wth more prces below the mean than above t, but wth occasonal spkes, a self-enforcng agreement generates asymmetrc outcomes. Although an mportng country suffers less n trade war than an exportng country, the latter has a greater ncentve to devate from a cooperatve trade polcy because postve devatons from the mean prce wll be larger than negatve ones. Thus, due to the asymmetry of the dstrbuton of commodty prces, t may be more dffcult to dscplne export taxes n trade agreements, than tarffs. The remander of the paper s organzed as follows. Secton presents the model under free trade and equlbrum under gven trade polces. Secton 3 characterzes the socal welfare functons and solves the statc Nash equlbra resultng from each country s socal welfare maxmzaton. The nteror Nash equlbrum s used subsequently as a credble punshment n the dynamc game. Secton 4 characterzes analytcally the tact cooperatve equlbrum, and secton 5 llustrates numercally the results under symmetrc and asymmetrc prce dstrbutons. Secton 6 concludes.. Model setup Consder a partal equlbrum model of a global cereal market. There are two countres (Home and Foregn) wth dentcal demand schedules. Foregn s ndcated by the superscrpt. Producton s assumed to be nelastc and s represented by two stochastc shocks, ε and ε, whch are drawn 5

6 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty from known probablty dstrbutons defned on bounded supports and whch are not serally correlated. Producton shocks are perfectly observable. They are such that n free trade Home s always n a poston to export to Foregn, so to ensure ε ε the dstrbuton of ε s assumed to domnate absolutely the dstrbuton of ε. Demand s represented by an nverse demand functon D(P) assumed to be lnear and dentcal n both countres D(P) = a bp and D (P ) = a bp. Domestc prces clear the markets: ε = D(P) +V and ε = D (P ) V, where V refers to the volume of trade. Countres can apply specfc trade taxes: τ and τ. When trade takes place, domestc prces are defned by combnng the world prce, P w, wth trade polces: P = P w + τ and P = P w + τ. (1) Ths defnton mples that when Home exports, a negatve τ s an export tax; conversely, when Foregn mports, a postve τ s an mport tax. By combnng the above equatons, we can characterze the volume of trade: V = ε ε + b(τ τ ). () From (), the free-trade trade volume s defned as V f (ε ε )/. Trade s strctly postve for τ τ > ε ε b or τ τ < V f b. (3) When (3) holds, world prce s gven by P w = a (ε + ε )/ b τ + τ. (4) In a stuaton of free trade, the world prce would be P f a/b (ε + ε )/(b). Let s be the state of the world. It s defned by the two supply shocks ε and ε. Another equvalent defnton of the state of the world that proves useful later n the paper s the aggregate rsk, ε + ε and the dfference n dosyncratc rsks, ε ε, whch can also be represented by the free-trade world prce, P f, and the free-trade trade volume, V f. 3. The statc game In ths secton, we characterze the Nash equlbra of the statc game n whch each country apples the trade taxes maxmzng a socal welfare functon whch, n addton to the usual measures of surplus, accounts for the polcy-makers preference for food prce stablty. The resultng nteror trade polces are costly for both countres and wll serve as punshments n the repeated game. 6

7 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty 3.1. Socal welfare functon Gven that ths paper focuses on the strategc nteractons of countres that nsulate ther markets, we adopt a tractable reduced-form socal welfare functon able to account for varous economc and poltcal-economy motvatons and whch allows trade polces to vary countercyclcally wth the world prce accordng to the stylzed facts (Anderson and Nelgen, 01). We assume that governments maxmze ther country s welfare whch s defned as the sum of the producer s surplus, the consumer s surplus, and the tarff revenue to whch a quadratc term n the domestc prce s added to account for the polcy-makers preference for food prce stablty. Home and Foregn welfare functons are defned as functons of the state of the world and the trade polces by W (s,τ,τ ) W (s,τ,τ ) a/b P(s,τ,τ ) a/b P (s,τ,τ ) D(p) dp + P(s,τ,τ )ε τv (s,τ,τ ) K [P(s,τ,τ ) P], (5) D (p) dp + P (s,τ,τ )ε + τ V (s,τ,τ ) K [P (s,τ,τ ) P], (6) where K 0 s a parameter characterzng the preference for prce stablty and P s a target prce around whch polcy-makers want prces to be stablzed. P s taken as the steady-state, free-trade prce, or the prce when shocks are equal to ther expectatons, and when countres do not use trade polces. Gven the lnearty of the model, the steady-state, free-trade prce s equal also to the average prce wthout nterventon. For smplcty, the preference for prce stablty and the target prce are assumed to be dentcal n both countres. 3.. Trade polces as functon of world prce Before consderng the Nash equlbrum, we analyze how trade polces react to the world prce when countres maxmze ther socal welfare functon as defned above. To get the optmal reacton to world prce changes, we maxmze W (s,τ,τ ) over τ 0 and W (s,τ,τ ) over τ 0. The welfare functons are strctly concave wth respect to ther domestc trade polcy, so the optmal trade polces are gven by the frst-order condtons, whch f (3) holds leads to: Smoothng [ {}}{ K ( P P w ) τ = mn 0, K + b and to a smlar expresson for Foregn trade polcy. Market power {}}{ (ε a + bp w ) ], (7) Ths trade polcy has two components. The frst component obeys a smoothng motve. It s countercyclcal and wll tend to mpose export subsdes when prces are below the target prce, and export taxes when prces are above the target prce. The second component explots the country s market power. It leads to the use of export taxes to explot market power over world 7

8 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty prce, and as s clear from the equaton, ths component s proportonal to the trade volume at the border prce (ε D(P w )). For K = 0, ths s the only ratonale for nterventon The nteror Nash equlbrum Next, we characterze the nteror Nash equlbrum and express all results as functons of P f and V f. From equaton (7), best-response correspondences are gven by [ τ R (s,τ ) = mn 0, K ( P P f ) ] V f + K + b K + 3b K + 3b τ, (8) [ τr (s,τ) = max 0, K ( P P f ) ] +V f + K + b K + 3b K + 3b τ. (9) For each country, the nteror Nash trade polces present three possble regmes. For suffcently low prces (P f P bv f /K (K + b)), the unconstraned polcy for the exporter would be to subsdze ts exports. Because ts polcy s constraned to be a tax, t does not mpose any trade barrer. In ths case, the mporter polcy s set by (9) wth τ = 0. The opposte s true for suffcently hgh prces (P f P + bv f /K (K + b)): no trade polcy on the mporter sde, and exporter trade polcy determned by (8). For ntermedate prces, trade polces n each country account for the nterventon n the other country. Ths s summarzed by the followng expressons: 0 f P f < P bv f K(K+b), K( τ N (s) = P P f ) b V f K+b f P P f bv f K(K+b), (10) K( P P f ) V f K+3b f P f > P + bv f K(K+b), K( P P f )+V f K+3b f P f < P bv f K(K+b), τn (s) = K( P P f ) b + V f K+b f P P f bv f K(K+b), (11) 0 f P f > P + bv f K(K+b), where the subscrpt N desgnates varables on the Nash equlbrum. Agan we fnd n these expressons the two components of smoothng and market power. Terms proportonal to P P f relate to smoothng, and terms proportonal to V f relate to market power. They behave very dfferently. 4 Wth a small country, the optmal trade polcy would be τ = mn[0,k ( P P w )/(K + b)]. Ths s smlar but slghtly dfferent from the smoothng component of (7). Wth respect to the smoothng objectve, a small country reacts more to world prce change than a bg country, for whch the use of countercyclcal trade polces amplfes world prce movement and so hurts ts smoothng objectve. However, when accountng for the terms-of-trade motvaton, a bg country adjusts more ts trade polcy wth world prce changes than a small country, because the rato of the slopes of the trade polcy rules wth respect to world prce s K (K + b)/(k + b), whch s always nferor to 1. 8

9 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty The market power components have opposte sgns n the two countres. Gven the world prce equaton (4), ths means that for ntermedate world prce levels, when polces are unconstraned, these components do not change the world prce. The exporter tends to tax exports, and the mporter tends to tax mports. It reduces trade levels, leaves the world prce unchanged, reduces prces n the exporter, and ncreases prces n the mporter. In contrast, for ntermedate world prce levels, the component of trade polcy motvated by smoothng s equal across countres and does not affect the domestc prce. Each country tres to bd more for the same commodty. In a stuaton of scarcty, the exporter ncreases ts export tax, and the mporter decreases ts tarff by the same amount, so the quanttes allocated are the same. The terms of trade of the exporter mprove at the expense of the mporter, thus, a transfer has taken place from the mportng to the exportng country. In a stuaton of glut, the stuaton s reversed: the exporter decreases ts export tax and the mporter ncreases ts tarff, so ths smoothng component leads to transfers from the exportng to the mportng country. These polcy adjustments perfectly offset each other, and so are neffcent. Ths neffcency of countercyclcal trade polces at the global level s hghlghted n Bgman and Karp (1993) and Martn and Anderson (01). Martn and Anderson (01) compare ths neffcency of the countercyclcal component of trade polces to the collectve-acton problem whch arses when a crowd stands up n a stadum to get a better vew: when everybody s standng then standng up does not result n a better vew, but remanng seated s no longer an opton. In our framework, ths zone of compensaton does not justfy an nternatonal cooperatve agreement wth respect to the smoothng motvaton, because the only aggregate welfare cost s related to the terms-of-trade part of the nterventon. Snce the smoothng parts of trade polces compensate each other, they do not affect domestc prces but create ncome transfers assocated wth the terms-of-trade changes. Across tme, these transfers compensate because the target prce s also the average prce. In our welfare framework, gven the absence of averson to ncome rsk, ths volatlty of ncome s not costly. The smoothng motvaton for trade polces opens the possblty for a trade agreement precsely when polces do not compensate: for a low or hgh free-trade world prce when one country s constraned n ts trade polcy. Ths s what motvates here restrctng trade polces to be taxes. In the model, trade polces are constraned to be taxes to prevent a subsdy n one country to perfectly offset the effect of a tax n the other country. Wthout ths restrcton, the smoothng component of trade polces would not generate any aggregate welfare losses because of the perfect compensaton of subsdes by taxes. Ths s not to deny the actual use of subsdes, but to account that for varous reasons, ncludng fscal reasons, ther use s unlkely to be as extensve as the use of trade taxes. The results n ths paper would be smlar, f nstead of assumng that countres are constraned to use trade taxes, they were constraned to not exceed a certan level of subsdes. Such a constrant would mantan the exstence of states of the world n whch the smoothng components of trade polces do not offset each other. 9

10 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty Gven the use by the two countres of these Nash trade polces, the world prce s gven by K(P f P)+V f K+3b f P f < P bv f K(K+b), PN w = P f K(P + f P) b f P P f bv f K(K+b), (1) K(P f P) V f K+3b f P f > P + bv f K(K+b). These trade polces amplfy the movements n the free-trade prce and ths amplfcaton depends on K. A hgher preference for domestc prce stablty entals a hgher volatlty of the world prce (see also Gordan et al., 014, for an n-depth analyss of ths multpler effect of trade polcy). Wth respect to free trade, the world prce wll be ncreased by trade polces f the free-trade prce s above the target prce, and decreased when t s below (see fgure 1). The world prce equals the free-trade prce only when the free-trade prce equals the target prce. These trade polces ncrease the world prce varance wth respect to the free-trade stuaton. Ths ncreased varance s caused by the smoothng motvaton (the world prce varance would be the same as n free trade f K equal 0). The model has two exogenous varables that defne ts state: the free-trade world prce, P f, and the free-trade trade volume, V f (or equvalently ε and ε ). The free-trade world prce represents the aggregate rsk as t s determned by the overall producton level, that s the sum of producton shocks n the two countres. In free trade, for the same world prce, there can be dfferent levels of trade volume dependng how producton s dvded between the countres, thus, the free-trade trade volume represents the dosyncratc rsk. Focusng on the two specal cases of pure aggregate rsk and pure dosyncratc rsk presents nterestng contrasts that contrbute to our analyss of these polces. Pure aggregate rsk In a stuaton where ε ε s a constant, there s an aggregate supply rsk only, and no dosyncratc rsk. Ths leads to a constant free-trade trade volume but a volatle free-trade prce, and accordng to (10) and (11), changes n trade polcy are explaned only by the smoothng motvaton. However, strategc nteractons and market power consderatons are present. For ntermedate world prces, the slope of the trade polcy rule wth respect to the free-trade prce s K/b, whle t would be smaller at K/(K + b) n a small country. Indeed n the Nash equlbrum, larger countres adjust ther trade polces more to the world prce than would a small country n an attempt to compensate for ther partner s trade polcy when ths latter s actve. Pure dosyncratc rsk If ε + ε s a constant, there s no aggregate rsk, only dosyncratc rsk (ths s the stuaton analyzed n Newbery and Stgltz, 1984, and Bagwell and Stager, 1990). The free-trade prce and the smoothng component of trade polces are constant. In ths stuaton, the change n trade polces stemmng from the terms-of-trade motvaton appears 10

11 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty Nash world prce wth a low free trade trade volume hgh free trade trade volume Nash world prce (P N w ) P Free trade world prce bv f bv f P K(K + b) P P + K(K + b) Free trade world prce (P f ) Fgure 1 Interor Nash world prce (P w N ) as a functon of free-trade world prce (P f ) for two levels of free-trade trade volume (V f ) to be n conflct wth the desre for smoothng. Wthout trade polcy nterventon, the world prce would be constant but potental terms-of-trade gans compel countres to ntervene. Ths creates a trade-off between the smoothng and terms-of-trade motvatons. Ths s shown n equatons (10) and (11) n the slope of trade polcy wth respect to the free-trade trade volume: for an ntermedate world prce, wthout the smoothng motvaton n the socal welfare functon, the slope would be 1/b, whereas t s actually 1/(K +b). The slope s reduced by the smoothng motve, snce pursut of terms-of-trade gans goes aganst t. One ntuton about trade polces motvated by prce smoothng s that they may hnder nternatonal sharng of agrcultural producton rsk. Agrcultural producton s much more volatle at the country than at the world level, because the poolng of all dosyncratc weather shocks leads to much more stable aggregate producton. The two extreme cases analyzed above show that the smoothng component of trade polces does not try to prevent rsk sharng, and t s equal to zero when only dosyncratc rsk s present. Smoothng-related trade polces are 11

12 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty motvated only by aggregate shocks The autarky equlbra We now turn to the Nash equlbra that correspond to autarky. If τ V f /b or τ V f /b then, whatever the value of the other country s trade polcy, condton (3) does not hold and autarky prevals. So there s a set of Nash equlbra wthout trade for any trade tax par n whch one of the taxes, n absolute value, exceeds V f /b Effcent trade polces The trade polces that maxmze jont welfare, W (s,τ,τ ) +W (s,τ,τ ), are defned by τ = τ, (13) whch, consderng trade polces constraned to be taxes, s compatble only wth free trade. So the nteror Nash equlbrum s neffcent, because t features too lttle trade and too much prce volatlty. 4. Internatonal cooperatve agreement We now consder that the countres nteract repettvely whch enables them to coordnate on more cooperatve polces. In ths dynamc game, based on the observed state varables, countres decde ther trade polcy at each perod. They can coordnate on lower protecton levels than n the statc game, because cooperaton s enforced by the threat of forever revertng to the nteror Nash equlbrum f one country devates from cooperaton. 5 Snce we want to analyze what would be best and most credbly acheved by such coordnaton, we consder trade polces that are subgame perfect. Even n cooperaton, free trade may not always be sustanable, because the long-run gans from cooperaton may not exceed the short-run gans from devaton when world prce s very hgh or very low. To understand when countres could be susceptble to defectng from cooperaton, we characterze ther ncentves to do so. The short-run gans of devatng from the cooperatve trade polces {τ c,τ c } are represented by Ω(s,τ c,τ c ) W D (s,τ c ) W (s,τ c,τ c ) and Ω ( s t,τ c,t,τ c,t) W D (s,τ c ) W (s,τ c,τ c ), where W D (s,τ c ) = max τ 0 W (s,τ,τ c ) s the welfare n case of devaton, that s, when the country s trade polcy s gven by ts best-response correspondence (8). 5 Revertng forever to the nteror Nash equlbrum s not renegotaton proof. A renegotaton-proof agreement would have to nclude a return to cooperaton after the punshment. Ths would make the analyss of the dynamc game more complex wthout affectng substantally the results. A renegotaton-proof agreement would mply less severe punshments followng a devaton, and so could not sustan the same level of cooperaton as sustaned by the threat of forever revertng to the Nash. 1

13 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty Usng the envelope theorem, we can characterze the behavor of the statc gans from defecton wth respect to the state varables. Wth respect to the free-trade trade volume we have dω(s,τ c,τ c )/dv f = [τ R (s,τ c ) τ c ]/ and dω (s,τ c,τ c )/dv f = [τ R (s,τ c) τ c ]/. As n Bagwell and Stager (1990), provded that the trade polcy under devaton s farther from free trade than the cooperatve polces (.e., τ R (s,τ c ) < τ c and τ R (s,τ c) > τ c ), the statc gan from devaton ncreases wth the trade volume, because the potental terms-of-trade gans are larger wth a larger volume of trade. For the behavor of the short-run gans from defecton wth respect to the free-trade world prce we have dω(s,τ c,τ c )/dp f = K [ τ R (s,τ c ) τ c ] / and dω (s,τ c,τ c )/dp f = K [τ R (s,τ c) τ c ]/. Provded that the trade polcy under devaton s farther from free trade than the cooperatve polces, the ncentves to defect are asymmetrcal. The exportng country has more ncentves to defect when the world prce s hgh, whle the mportng country has more ncentves to defect when the world prce s low. Snce we focus on subgame perfect trade polces, the cooperatve trade polces are functons only of the payoff-relevant varables whch are the current state varables, not past hstory: τ c = τ c (s) and τc = τc (s). Gven that trade polces are functons only of state varables, and state varables have no ntrnsc dynamcs (the state varables, ε and ε, are not serally correlated), beyond current perod we can defne the expected future welfare gan from cooperaton by ω (τ c ( ),τc ( )) E s [W (s,τ c (s),τc (s)) W (s,τ N (s),τn (s))] and smlarly for Foregn. For each country, there s a trade-off between the short-run gans from devaton and the long-run losses from returnng to the Nash equlbrum. To ensure that countres have no ncentve to devate, the followng partcpaton constrants have to be respected for all states s: Ω(s,τ c (s),τc (s)) β 1 β ω (τ c ( ),τc ( )), (14) Ω (s,τ c (s),τ c (s)) β 1 β ω (τ c ( ),τ c ( )), (15) where β [0, 1) s the dscount factor. These partcpaton constrants convey the lack of commtment of each country. They do not commt to respect cooperatve polces whatever the stuaton. Cooperaton s possble as long as n any stuaton the cooperatve polcy s such that t satsfes these constrants. The equlbrum has to be self-enforcng. The set of trade polces satsfyng the partcpaton constrants s not empty snce Nash trade polces always satsfy them. We can show also that f the dscount factor s suffcently hgh, free trade s sustanable. Let us defne L(s,β) Ω(s,0,0) ω (0,0)β/(1 β), the dscounted future loss of Home from devatng from free trade. We have L(s,0) > 0 and lm β 1 L(s,β) =, so by the contnuty of L(s,β) n β there exsts β (0,1) such that L(s,β) 0 f β β. The same apples to Foregn. Correspondng to the partcpaton constrant of Home, the threshold parameter s the dscount 13

14 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty factor such that Ω(s,0,0) ω (0,0)β/(1 β) = 0, where s s the state of the world that maxmzes Ω(s,0,0). Gven that Ω ncreases wth P f and ncreases wth V f, s corresponds to a stuaton of hgh trade volume and hgh prce. Ths s smlar for the Foregn partcpaton constrant, except that snce Ω decreases wth P f, the threshold dscount factor parameter wll be determned by the maxmum value of Ω, whch wll be a low prce combned wth a hgh trade volume. Except when the dstrbutons of producton shocks are symmetrc, they are unlkely to be equal and the threshold parameter for both constrants s just the maxmum over each one: [ β = max Ω(s,0,0) Ω(s,0,0) + ω (0,0), Ω (s,0,0) Ω (s,0,0) + ω (0,0) ]. (16) When the dscount factor falls strctly below β, free trade s not sustanable, but there s an nfnty of trade polces that satsfy these constrants. We focus on the most cooperatve subgame perfect Nash equlbrum, the trade polces that maxmze ntertemporal jont welfare whle satsfyng partcpaton constrants. Another way to see ths problem s to consder that t s the problem of a planner that tres to fnd the tme-consstent trade polces that maxmze jont welfare whle satsfyng the countres partcpaton constrants. Ths amounts to solvng at each perod t the followng maxmzaton problem: maxw (s t,τ t,τ τ t 0,τt t ) +W (s t,τ t,τt ) + β 0 1 β E s [W (s,τ c (s),τc (s)) +W (s,τ c (s),τc (s))] (17) subject to the partcpaton constrants, (14) and (15). Gven that the problem has no ntrnsc dynamcs and that we are focusng on the subgame perfect equlbrum, all expectatons terms are n fact constants whch are functons of the optmal cooperatve polces. Constranng trade polces to be taxes and assocatng postve Lagrange multplers, µ t and µ t, to equatons (14) and (15), the above problem gves the followng frst-order necessary condtons: (1 + µ t ) W (s t,τ t,τt ) + (1 + µ t ) W (s t,τ t,τt ) µ t τ t τ t (1 + µ t ) W (s t,τ t,τt ) τt + (1 + µ t ) W (s t,τ t,τt ) τt W D (s t,τ t ) τ t 0, = 0 f τ t < 0, (18) µ t W D (s t,τ t ) τ t 0, = 0 f τ t > 0, (19) Ω(s t,τ t,τt ) β 1 β ω (τ c ( ),τc ( )) 0, = 0 f µ t > 0, (0) Ω (s t,τ t,τt ) β 1 β ω (τ c ( ),τc ( )) 0, = 0 f µ t > 0. (1) The frst-order condtons characterze the trade polces τ t and τt only as functons of the cooperatve trade polcy functons τ c ( ) and τc ( ) whch defne the expected future welfare gans 14

15 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty from cooperaton n equatons (0) and (1). The most cooperatve subgame perfect trade polces are those that for every t satsfy the frst-order condtons (18) (1) and τ t = τ c (s t ) and τ t = τ c (s t ). () Equaton () enforces ratonal expectatons about future perods by ensurng that the appled trade polces derve from the same polcy functons that wll be appled subsequently. When the dscount factor falls below β, gven that Nash trade polces and best-response functons present several knks, and that polces may occasonally be constraned to be taxes, a complete analytcal characterzaton of the polces, ncludng a proof of ther exstence, s out of reach. 6 Below, we provde an nterpretaton of these equatons n varous stuatons dependng on whch constrant s bndng, and we later rely on numercal smulatons to provde further nsghts on the soluton. The frst-order condtons can be nterpreted as follows. µ and µ play the role of the relatve weghtng of countres n world welfare. It may change at each perod dependng on whch partcpaton constrant s bndng. When one country s partcpaton constrant s bndng, ts welfare weght becomes postve justfyng ts devaton from the frst-best trade polcy (.e., from free trade). No bndng partcpaton constrant Wth µ t = µ t = 0, equatons (18) and (19) are dentcal to what they would be were the maxmzaton not subject to the partcpaton constrants, that s to globally effcent trade polces. Equaton (18) gves τt τ t 0, = 0 f τ t 0, whch s only compatble wth τ t = τt = 0. Thus, when no partcpaton constrant s bndng, the cooperatve polcy s free trade. Note, however, that ths s a consequence of restrctng the analyss to tax polces. Wthout ths restrcton, the soluton would be τ t = τt, whch s compatble wth free trade and also wth countercyclcal trade polces that perfectly offset each other. Bndng partcpaton constrants For a dscount factor below β, the effcent trade polcy does not satsfy the partcpaton constrants for all possble shocks, so the cooperatve trade polces must nclude some devaton from free trade. These devatons from free trade are governed n the frst-order condtons by the Lagrange multplers that play the role of state-contngent welfare weghts: they ensure that trade polces always satsfy the partcpaton constrants. There are three possble stuatons: partcpaton constrant bndng for Home, for Foregn, or for both countres. Ths contrasts wth Bagwell and Stager (1990) where the stuaton of both partcpaton constrants bndng was the only possble one, because the only motvaton for trade polces was the terms-of-trade gans whch smlarly affect the temptaton to devate n the two countres. In ths paper, we also have the smoothng motvaton whch has asymmetrc effects. 6 See Bagwell and Stager (1990) for the analytcal characterzaton of a smlar but smpler problem. 15

16 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty The temptaton to devate wll be hgher for exporters n perods of hgh prces and for mporters n perods of low prces. If both welfare weghts are strctly postve, the terms WD (s t,τ t )/ τ t and W D (s t,τt )/ τt n equatons (18) and (19) may matter. They account for the fact that when a country changes ts trade polcy, ths changes ts partner s ncentves to devate. Ths concern about the partner s ncentve to devate exsts only f the partner s partcpaton constrant s bndng. If not, the country does not have to worry about ts partner s ncentve untl t becomes bndng. Gven the behavor n Nash, n cooperaton, we could expect the partcpaton constrants to be both bndng for ntermedate free-trade prce levels and a suffcently hgh free-trade trade volume. For a hgh (low) free-trade prce, the devaton wll come from the exporter (mporter). For an ntermedate prce level, ths s the terms-of-trade motvaton that wll compel both countres to devate at the same tme (as n Bagwell and Stager, 1990). 5. Numercal smulatons In ths secton, we analyze cooperatve behavor further by conductng numercal smulatons. Gven the absence of endogenous state varables, t s easy to calculate a numercal soluton to ths problem. It s the soluton to a set of complementarty equatons defned over a grd of carefully chosen producton shocks (through a Gaussan quadrature) whch wll allow us to calculate the terms n expectatons. The equatons are the frst-order condtons, (18) (1), and the equatons ensurng that the same cooperatve trade polces are appled n subsequent perods (.e., expectatons are ratonal), (). See the appendx for detals of the numercal methods. We focus the dscusson of numercal results on the stuaton of pure aggregate rsk, n whch the smoothng motvaton for trade nterventon s domnant. Snce n ths case free-trade prce summarzes the state of the system, ths facltates the nterpretaton of results by allowng dagrammatc representatons. In the alternatve confguraton of pure dosyncratc rsk, the results are very close to Bagwell and Stager (1990), the only dfference beng that our statc level of protecton s less mportant because the smoothng objectve goes aganst the explotaton of terms-of-trade gans. In that case, trade polces are of equal ntensty but wth opposte sgns. In a repeated game, for a suffcently hgh dscount factor, the threat of retalatons allows coordnaton on free trade. For a lower dscount factor, devatons from free trade cannot be excluded. They occur at the same moment for both countres when free-trade volume s hgh, because a hgher free-trade volume ncreases the potental terms-of-trade gans and the ncentve to devate. To choose relevant values for K, the parameter of preference for prce stablty, we note that although the quadratc term n the socal welfare functons s merely a means of ntroducng (n a tractable way) addtonal concavty nto the socal welfare functon, t can also be gven some mcro-foundatons by beng nterpreted as the dfference between the second-order approxmaton to the equvalent varaton of a rsk-averse consumers and ts surplus, so t would be the welfare 16

17 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty term accountng for non-zero rsk averson and ncome elastcty. Followng Turnovsky et al. (1980), K would n ths case be equal to γ (R ν)d( P)/ P, where γ, R, and ν are values at steady-state of the commodty budget share, relatve rsk averson to ncome, and ncome elastcty. K would be postve f rsk averson s hgher than ncome elastcty, whch seems reasonable for staple food products. Ths would represent an approxmaton of socal welfare for an ncomplete-markets economy n whch rsk-averse consumers cannot nsure aganst food prce rsk (see Gouel and Jean, forthcomng, for such a stuaton). We assume K = 0.3, whch could correspond to a 15% budget share, a relatve rsk averson equal to, and a null ncome elastcty. The other parameters are chosen such that at steady state n both countres demand s equal to 1 and trade to 0.. The steady-state prce s taken to be 1 and demand elastcty 0.. In what follows, results wll dffer n the assumed dstrbutons for the producton shocks. Producton shocks are assumed to be ether symmetrc or skewed. Snce we focus on a stuaton of aggregate rsk where V f s constant, ε s defned from ε and s equal to ε 0.4. ε s assumed to follow a beta dstrbuton. The dstrbuton s translated and rescaled for ε to have a mean of 1. and a standard devaton of Wth ths choce of parameters and dstrbuton of producton shocks, the coeffcent of varaton of the free-trade prce s equal to 30%. For the symmetrc case, the beta dstrbuton has shape parameters 3 and 3. For the asymmetrc cases, the second parameter s mantaned at 3, whle the frst s adjusted to change the skewness (the locaton and scale parameters are also adjusted to mantan the mean and standard devaton constant) Cooperaton under a symmetrc prce dstrbuton Ths example llustrates the extent of trade polcy coordnaton when the free-trade prce dstrbuton s symmetrc around the steady-state prce. Fgure dsplays the cooperatve and non-cooperatve trade polces for varous dscount factors. At a dstance of the steady-state prce, the non-cooperatve Nash polces (dash-dotted curves) are constraned by ther restrcton to beng taxes. For hgh world prces, the mportng country would lke to apply an mport subsdy. When ths constrant bnds, the slope of the exportng country trade polcy decreases wth respect to the world prce, because t does not need to react so strongly to the world prce snce ts polcy s no longer offset by ts partner. Ths change n slope when only one country s usng ts trade polcy occurs n repeated games also. When the game s repeated, polces that are more cooperatve are sustanable, although t s not possble always to exclude devatons from free trade for hgh and low free-trade prces. Cooperatve polces are represented n fgure for varous dscount factors, n sold lnes. There are three possble regmes. () For a suffcently hgh dscount factor, β β = 0.80, free trade can be sustaned by the threat of retalaton whatever the level of stochastc shocks. () For a lower value of the dscount factor, partcpaton constrants start to bnd for low and hgh world prces. However, they are not bndng at the same tme; each country s allowed to devate from free trade at dfferent moments. The exporter devates when the world prce s hgh by taxng 17

18 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty 1.0 Importng country Nash polcy τ Trade polcy τ * Repeated game (varous dscount factors) Exportng country Free trade world prce (P f ) Fgure Cooperatve and non-cooperatve trade polces under a symmetrc prce dstrbuton exports, and the mporter devates when the world prce s low by taxng mports. Outsde the regons where partcpaton constrants are bndng, the cooperatve trade polcy s free trade. These trade polces affect the dstrbuton of world prce wth respect to free trade. The world prce wll be dentcal to the free-trade prce when ths latter s close to the steady state. But far from the steady state, when the ncentves to devate from free trade are too hgh to make t sustanable n cooperaton, the world prce wll be above (below) the free-trade prce f the free-trade prce s above (below) ts steady state. Cooperaton reduces the volatlty of world prce, but manly close to steady state, and less for low and hgh world prces. () For lower values of the dscount factor, partcpaton constrants bnd more often, and can be bndng at the same tme. Ths stuaton s qualtatvely closer to the Nash stuaton than the two others. Note that the dscount factor should be nterpreted not as a market dscount factor but as the dscount factor of polcy-makers for whch the future may not extend much farther than the next electon. 5.. Cooperaton under an asymmetrc prce dstrbuton Some of the prevous results are a consequence of the symmetry of the problem. Beyond the perfect symmetry of the countres, what seems crucal s the symmetry of the prce dstrbuton, whch tself s an outcome of many assumptons. In realty, commodty prces are postvely 18

19 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty skewed (Deaton and Laroque, 199), a feature often explaned by storage, whch would have been too challengng to ntegrate n a repeated-game approach. Prce skewness can also be explaned n other ways. A convex demand functon, for example, could create skewness n the prce dstrbuton. Ths s precsely the effect of storage, whch convexfes demand by addng to fnal demand, demand for stocks at low prces (Wrght and Wllams, 198). Postve prce skewness could also arse from a negatvely skewed yeld. The lack of symmetry of the prce dstrbuton could be crucal because t affects the dstrbuton of welfare between the two countres, and consequently, what could be expected from cooperaton ensured by the threat of retalaton. To analyze ths we ntroduce an asymmetry by assumng that yelds are negatvely skewed. Ths does not nvolve any change n the equatons. They hold equally for symmetrc and asymmetrc shocks. Results wll be symmetrc wth postvely-skewed yelds; but negatvely-skewed yelds mply postvely-skewed prces, as observed n the prce data. Below, ε s assumed to follow a beta dstrbuton wth shape parameters 30 and 3 whch results n a skewness of the free-trade prce equal to 0.95, a value comparable to that observed for staple food markets (Deaton and Laroque, 199). The asymmetry affects the respectve costs of the trade war between the exportng and the mportng countres. In the statc game (0 dscount factor n fgure 3), the nteror Nash equlbrum s more costly for the exportng than the mportng country. Ths s explaned by the prce dstrbuton (see fgure 4). Upward prce spkes are more common than downward prce spkes, so we more often observe large trade polcy nterventons from the exporter compared to the mporter. However, much of the prce dstrbuton s concentrated n prces below the target prce, wth a sgnfcant share n the regon where the exportng country does not apply export restrctons. So, on average, the exportng country suffers more from the trade war, because t s more often constraned n ts trade polces. In a repeated game, these lower losses for the mportng country hold for a low to medum dscount factor (untl β 0.51), because cooperaton does not change the fact that the exportng country s more often constraned n ts trade polces. However, the relatonshp between the dscount factor and the dfference between expected welfare under coordnaton and under free trade s not monotonc. For a hgh enough dscount factor, nether country uses trade polces and ther welfare s equal to the free-trade value. However, before reachng the frst-best welfare there s an nterval over the dscount factor for whch exportng country welfare exceeds free-trade welfare and most of the welfare ncreases are captured by the exportng country. For these ntermedate dscount factor values, the threat of revertng to a trade war exceeds the short-run gans from devaton for most of the free-trade world prce, and free trade prevals for most supply shocks. In partcular, for the mportng country, the gans from devaton are never very hgh snce the free-trade world prce does not reach very low values. On the contrary, for the exportng country, the gans from devaton can occasonally be hgh because of the possblty of hgh world prces. In these cases, when the dscount factor s not too hgh, the partcpaton constrant of the exporter s bndng and compels t to devate from the frst best. Ths stuaton 19

20 CEPII Workng Paper Trade Polcy Coordnaton and Food Prce Volatlty Welfare dfference Exportng country Importng country Dscount factor (β) Fgure 3 Dfference between expected welfare under coordnaton and free trade under an asymmetrc prce dstrbuton, E s [W (s,τ c (s),τ c (s)) W (s,0,0)] (as a percentage of the steady-state budget spent by consumers on ths commodty) s asymmetrcal as shown n fgure 4 when β = 0.8: the dscount factor s hgh enough to deter any devaton from frst best for the mporter, but not suffcently hgh for the exporter gven that the prce dstrbuton s skewed. Snce the exporter occasonally apples trade polces, whle the mporter does not, the former enjoys a welfare level above what t could acheve from free trade at the expense of ts partner. Despte the exportng country beng the country wth more to gan from cooperaton snce t suffers more n the nteror Nash equlbrum, t s also the more reluctant to cooperate gven that the occasonal prce spkes compel t to mantan some devaton from free trade. The role of prce skewness can also be analyzed n relaton to ts effect on the threshold dscount factor. The threshold dscount factor above whch free trade can be sustaned n cooperaton s defned (equaton (16)) as the maxmum between the dscount factor that makes the partcpaton constrant of the exportng country hold wth an equalty at the hghest prce, and the dscount factor that makes the partcpaton constrant of the mportng country hold wth an equalty at the lowest prce. For a symmetrc prce dstrbuton, these two parameters are dentcal but f the dstrbuton becomes postvely skewed, they wll start to dffer (fgure 5). The threshold dscount factor correspondng to the exportng country ncreases wth prce skewness as the maxmum prce gets further away from the target prce. The threshold dscount factor correspondng to the mportng country decreases wth prce skewness as the mnmum prce gets closer to the target. Ths behavor holds f, nstead of usng the dscount factor sustanng free trade n all states, we use the dscount factor sustanng free trade n all states except the 1% lowest and hghest prces. So, n ths settng where producton shocks are governed by a beta dstrbuton, ncreasng skewness whle keepng the frst two moments constant makes free trade more dffcult 0