Protection for Sale with Heterogeneous Interests within Industries

Transcription

1 Protecton for Sale wth Heterogeneous Interests wthn Industres Pao-L Chang School of Economcs and Socal Scences Sngapore Management Unversty Gerald Wllmann Department of Economcs Unversty of Kel, Germany Aprl 26, 2006 Abstract Ths paper studes how the nterests of domestc versus exportng frms determne multlateral tarff levels. In a Meltz model, less productve domestc frms lobby for lower tarffs whereas exporters favor lberalzaton to gan market access abroad. The government weghs socal welfare and contrbutons when settng trade polcy. If nether or both groups wthn an ndustry lobby, the socally optmal tarff results. When only one group lobbes, domestc (exportng) frms obtan a hgher (lower) tarff. Our model mples an upward bas n the estmate for the weght on socal welfare, were one to apply the standard model, explanng the hgh estmates found n emprcal studes. Keywords: Protecton for Sale; Heterogeneous Frms; Multlateral Tarff Settng. JEL classfcaton: F12; F13 Tel: ; fax: E-mal address: plchang@smu.edu.sg (P.-L. Chang). 1

2 1. INTRODUCTION It s well establshed that lobbyng nfluences polcy and trade polcy s no excepton, as the success of the protecton for sale approach confrms. The emprcal nvestgatons that have followed the theoretcal contrbuton by Grossman and Helpman (1994) seem to support ths clam. When takng a closer look at the emprcal results, however, one cannot fal to notce a pecular aspect: The weght that the government places on socal welfare s consstently estmated to be almost a hundred percent, mplyng a correspondngly mnmal weght on contrbutons. Ths surprsng fact seems to call nto queston the whole approach. After all, why bother to model lobbyng f t plays hardly any role n practce. The answer provded n ths paper focuses on the role of exportng frms and the fact that ther nterests wth regards to trade polcy dffer from the objectves of purely domestc frms. As tarffs are usually set by multlateral agreement n the context of the WTO, exportng frms understand that ther own government s wllngness to lower tarffs wll be matched by other countres, and therefore lead to mproved access to export markets. In order to take nto account the specal nterests of exporters, we present a model that features both, domestc as well as exportng frms. Whle the economc sde of the orgnal protecton for sale model s frmly rooted n what has come to be called old trade, we skp a step and apply protecton for sale to new new trade. 1 As a startng pont we choose the model of Meltz (2003) who generalzes the Dxt and Stgltz (1977) framework by allowng for heterogenous frms. These heterogenous frms self-select nto purely domestc and exportng frms, or ext the market, dependng on ther respectve productvty levels. In lne wth several recent papers, we assume that frms draw ther productvty levels from a Pareto dstrbuton. 2 Ths dstrbutonal assumpton enables us to derve closed form solutons for the crtcal productvty levels, below whch low-productvty frms ext and above whch hgh-productvty frms enter the export market respectvely. As for trade polcy, we treat tarff settng as a multlateral as opposed to unlateral polcy choce. Settng a tarff n our framework not only apples to the domestc rate, but also mples that the same rate wll be set by other countres, whch are the tarffs that domestc exporters face abroad. The motvaton for ths modellng decson s the fact that most tarffs are set by 1 The ntermedate step of applyng protecton for sale to new trade s taken by Chang (2005), whose model features a Dxt-Stgltz setup wth homogenous frms. 2 A promnent example s Helpman, Meltz, and Yeaple (2004). Emprcal evdence for ths assumpton s provded by Axtell (2001). 2

3 multlateral agreement. In addton, we are able to avod the nconsstency nherent n most of the emprcal protecton for sale lterature, that tests a model formulated n tarffs usng NTB coverage ratos, because tarffs are not set unlaterally. 3 Under our assumpton, the model predcts that domestc frms beneft from a hgher tarff whereas exporters lose because ther export profts declne by more than the ncrease n profts from the domestc market. Based on ths framework, we model the determnaton of trade polcy as the outcome of a menu aucton between the lobbes potentally two n each ndustry representng domestc and exportng frms respectvely and the government. As s standard n the lterature, we take the set of lobbes as gven. 4 The lobbes submt contrbuton schedules to the government whch specfy the monetary contrbutons that the groups are wllng to pay to the government as a functon of the tarff vector chosen. The government then chooses the tarff vector or rather negotates the tarff vector wth ts counterparts at the WTO seekng to maxmze a weghted sum of socal welfare and the contrbutons offered to t by the lobbes. The resultng tarff depends, apart from economc consderatons, on the organzatonal structure of an ndustry. Whereas n the standard model the organzatonal state of a partcular ndustry s modelled as bnary (ether the sector lobbes or t does not), our model features a rcher set of possbltes: nether domestc nor exportng frms are organzed, both groups are organzed, only domestc frms lobby, or only exporters do. In the frst case the outcome s the socally optmal tarff, because the government maxmzes socal welfare for lack of contrbutons from ths sector. The outcome under the second scenaro s the same, as the lobbyng efforts of domestc frms and exporters exactly offset each other. If only one group lobbes, however, that group s able to obtan a tarff that closer to ts nterests: a hgher tarff n the case of purely domestc frms, and a lower level of protecton n the case of exporters. The second organzatonal scenaro s especally noteworthy. Both groups lobby and yet the socally optmal tarff obtans. Regardng ours as the true model, suppose one were to apply the standard protecton for sale approach n ths stuaton. The standard model would predct that the government only weghs socal welfare, as t sets the socally optmal tarff even though the sector lobbes. Our model therefore mples that there s an upward bas n the estmate of the 3 See Facchn, Van Besebroeck, and Wllmann (2006) for a modfed verson of the protecton for sale model that allows for NTBs and that they consstently estmate usng coverage ratos. 4 See Mtra (1999) for endogenous lobby formaton. 3

4 weght that the government places on socal welfare f one apples the standard model. Ths nsght s of utmost mportance, as t suggests that lobbyng plays a much more promnent role than the very lmted one mpled by the low estmates that the lterature has found for the weght that the government places on contrbutons. As for ts relaton to the prevous lterature, our contrbuton combnes the work on protecton for sale wth the recent new new trade lterature. The theoretcal model of Meltz (2003) has ganed tremendous popularty n recent years, not least because t provdes a sold foundaton for the emprcal evdence on exportng frm characterstcs. 5 Qute apart from ts popularty, t seems deally suted for ntegratng the dvergng nterests of exporters nto the protecton for sale framework. Takng nto account those nterests allows us to provde an answer to the longstandng puzzle of the emprcal protecton for sale lterature, namely why estmates for a (the weght the government places on socal welfare) are consstently very hgh. Ths ssue has been taken up by both Mtra, Thomakos, and Ulubasoglu (2006) and Gawande and L (2004). The former contrbuton explores varyng α L (the share of the populaton nvolved n lobbyng) as a possble explanaton, the latter ntroduces a success probablty of lobbyng. Ths paper provdes an mportant addtonal explanaton. Whereas takng nto account the nterests of exporters seems a novel aspect n the area of protecton for sale, allowng frms to be heterogenous s not. Bombardn (2005) generalzes the specfc factor setup by ntroducng frms that dffer n ther endowment wth the specfc factor. She makes use of ths heterogenety to nvestgate whch frms n an ndustry wll lobby and whch wll not. Whle she concentrates on frms decson to lobby, we allow frms to make the economcally mportant exportng decson, and then focus on the consequences of the dvergng nterests that arse, abstractng for the most part from the lobbes partcpaton decson. The rest of the paper s organzed as follows. In Secton 2, we ntroduce the economc model that underles our analyss. Secton 3 sets up the lobbyng game and analyzes the resultng tarffs. In Secton 4, we show that the standard model leads to a based estmate of a f ours s the true model. Secton 5, fnally, offers concludng remarks. 5 Drect supportng evdence s provded by Chaney (2006). 4

5 2. THE MODEL 2.1 Demand Suppose there are (n + 1) symmetrcal countres n the world wth the same economc structure. The representatve country s populated by ndvduals wth dentcal preferences, gven by: U = Q 0 + m U (Q ) (1) where Q 0 denotes consumpton of good 0, Q denotes consumpton of good, = 1,2,...,m, and U s an ncreasng concave functon. Good 0 serves as numerare, wth a world and domestc prce equal to 1. Let P denote the domestc prce of good. The demand for good mpled by the preferences n (1) s denoted D (P ), where D ( ) s the nverse of U ( ). The ndrect utlty of an ndvdual wth ncome E s gven by V = E + m S (P ), where S (P ) = U (D (P )) P D (P ) s the consumer surplus derved from good. To smplfy the analyss, we assume that the utlty functon U n (1) takes the functonal form: U = E lnq. Ths amounts to assumng that an ndvdual allocates a fxed amount of expendture E on good. The non-numerare sector s characterzed by monopolstc competton, wth Q representng the aggregate consumpton of dfferentated goods n sector. The aggregaton follows the Dxt- Stgltz functonal form, over a contnuum of dfferentated goods ndexed by ω Dxt and Stgltz (1977): ] 1 [ Q = q (ω) ρ ρ dω 0 < ρ < 1 (2) ω Ω where the measure of the set Ω represents the mass of avalable varetes and σ 1/(1 ρ ) > 1 represents the elastcty of substtuton between any two varetes of good. The correspondng aggregate prce P for sector s: [ P = p (ω) 1 σ dω ω Ω ] 1 1 σ (3) where p (ω) s the consumer prce for varety ω of good. The preferences n (1) and (2) mply 5

6 that the demand and expendture for ndvdual varetes of good are: q (ω) = NQ [p (ω)/p ] σ (4) r (ω) = NE [p (ω)/p ] 1 σ, (5) where N s the sze of the country s populaton. 2.2 Producton Good 0 s taken to be a homogeneous good, produced one-to-one from labor. It s traded freely and costlessly, so the wage s equal to one at home and abroad. The dfferentated goods n sector, for = 1,2,...,m, are produced by a contnuum of frms, each producng a dfferent varety ω. The producton requres a fxed overhead cost and constant margnal cost, wth the margnal cost determned by the frm s productvty. Specfcally, the labor requrement for producng a varety of good at an output q equals l = f + q ϕ, where f s the fxed overhead labor requrement and ϕ > 0 s the productvty level of the frm. The labor s avalable n nelastc supply L. As wll be shown later, gven that the aggregate expendture on good s constant, sector wll employ a fxed labor sze of L = NE. It s assumed that the country s labor force s large enough that the producton of the numerare good s postve at Q 0 = L m L. Gven the preferences specfed n (2), each frm faces a resdual demand curve wth constant elastcty σ. Thus, wth proft maxmzaton, each frm charges a prce that s a constant markup ( σ σ 1 = 1 ρ ) over ts margnal cost. Suppose the frm caters only to the domestc market. Then t charges a domestc prce of p d, (ϕ) = 1 ρ ϕ, receves a revenue of r d,(ϕ) = NE [P ρ ϕ] σ 1, and makes a proft of π d, (ϕ) = r d,(ϕ) σ f from the domestc market. Suppose the frm also exports to foregn markets. It ncurs an extra fxed cost f x, per perod by enterng a foregn market and faces a foregn mport barrer τ (whch s defned as one plus the equvalent ad valorem tarff rate). In ths case, the frm charges a foregn prce of p x, (ϕ) = τ ρ ϕ, receves a revenue of r x,(ϕ) = r d, (ϕ)τ 1 σ, and makes an extra proft of π x, (ϕ) = r x,(ϕ) σ f x, from each foregn market. 6

7 2.3 Frm Entry, Ext, and Export Status In order to enter the market, frms have to ncur an ntal nvestment cost f e. Pror to entry, frms face uncertanty over ts productvty level, whch we assume to be a random draw from the Pareto dstrbuton g (ϕ) = θ ϕ θ 0, ϕ θ +1, for ϕ ϕ 0, and θ > σ 1. (6) Upon entry, frms learn of ther realzed productvty level and ext the market mmedately f the producton proft s negatve. Let ϕ denote the lower cutoff level of frm productvty for successful entry. For frms wth successful entry, they choose to export f the extra proft from enterng the foregn market s nonnegatve. Let ϕ x, denote the lower cutoff level of frm productvty for exportng. Followng Meltz (2003), we focus on the scenaro where successful entrants are parttoned nto those wth lower productvty levels who only caters to the domestc market and those wth hgher productvty levels who also export. Ths scenaro of parttonng of frms by export status (ϕ < ϕ x, ) occurs f and only f τσ 1 f x, > f. By defnton, the cutoff levels must then satsfy π d, (ϕ ) = 0 and π x,(ϕ x, ) = 0. For frms who have successfully entered the market, they also face a probablty δ n every perod of a bad shock that forces them to ext. We make the followng assumptons to lmt the scope of analyss that follows. Assumpton 1 For sector = 1,2,...,m, () τ 1 (mport subsdy s not allowed); () f x, > f ; () σ 1 θ (σ 1) f δf e, 1; (v) θ f > f + nf x,. Assumptons () and () mples that τ σ 1 f x, > f and thus ensures the parttonng of frms by export status dscussed n the prevous paragraph. The mplcatons of the remanng assumptons wll become clear as we proceed. Let G (ϕ) denote the correspondng cumulatve dstrbuton functon of g (ϕ). It s straghtforward to show that G (ϕ) = 1 ( ϕ 0, ϕ )θ. Thus, the average productvty level ϕ of frms wth 7

8 ϕ > ϕ s: [ ϕ (ϕ 1 ) 1 G(ϕ ) ϕ ϕ σ 1 g (ϕ)dϕ ] 1 σ 1 [ = θ θ (σ 1) ] 1 σ 1 ϕ. (7) where the exstence of ϕ s ensured by the assumpton that θ > σ 1. Gven (7) and the defnton of the entry cutoff level ϕ, t follows that [ ϕ r d, ( ϕ ) = ϕ ] σ 1 r d, (ϕ ) = θ σ θ (σ 1) f, (8) and that [ ϕ π d, ( ϕ ) = ϕ ] σ 1 r d, (ϕ ) σ f = σ 1 θ (σ 1) f (9) Smlarly, the average productvty level ϕ x, of frms wth ϕ > ϕ x, s: [ ϕ x, ϕ (ϕ x,) = θ θ (σ 1) ] 1 σ 1 ϕ x,. (10) Usng (10) and the defnton of the export cutoff level ϕ x,, t follows that r x, ( ϕ x, ) = [ ] σ 1 ϕ x, ϕ x, r x, (ϕ x, ) = θ σ θ (σ 1) f x,, (11) and that π x, ( ϕ x, ) = [ ϕ x, ϕ x, ] σ 1 rx, (ϕ x, ) σ f x, = σ 1 θ (σ 1) f x,. (12) Observe that r x, (ϕ x, )/r d,(ϕ ) = τ1 σ (ϕ x, /ϕ )σ 1 = f x, /f. Thus, the export cutoff level ϕ x, can be expressed as a functon of the entry cutoff level ϕ : ϕ x, = ϕ τ (f x, /f ) 1/(σ 1). (13) Let p x, [1 G (ϕ x, )]/[1 G (ϕ )] denote the condtonal probablty of exportng gven that a frm has successfully entered the market. It s straghtforward to show that p x, = (ϕ /ϕ x,) θ = τ θ (f x, /f ) θ /(σ 1), (14) 8

9 whch ranges between 0 and 1 by Assumptons () and (). Thus, the average revenue of ncumbent frms s: r = ϕ ϕ g (ϕ) r d, (ϕ) 1 G (ϕ )dϕ + n [ ϕ ϕ ] σ 1 = r d, ( ϕ ) + np x, r x, ( ϕ x, ) = ϕ x, g (ϕ) r x, (ϕ) 1 G (ϕ )dϕ r d, (ϕ ) g (ϕ) 1 G (ϕ )dϕ + n1 G (ϕ x, ) 1 G (ϕ ) ϕ x, [ ϕ ϕ x, ] σ 1 r x, (ϕ x, ) g (ϕ) 1 G (ϕ x, )dϕ θ σ θ (σ 1) (f + np x, f x, ). (15) Smlarly, the average proft of ncumbent frms s: π ϕ g (ϕ) π d, (ϕ) 1 G (ϕ )dϕ + n = π d, ( ϕ ) + np x, π x, ( ϕ x, ) = ϕ x, g (ϕ) π x, (ϕ) 1 G (ϕ )dϕ σ 1 θ (σ 1) (f + np x, f x, ) (ZCP), (16) whch corresponds to the zero cutoff proft condton n Meltz (2003). Free entry ensures that n equlbrum, the expected proft of entry net of the entry cost should be zero. Thus, t follows that p e, v f e, = 0, where p e, [1 G (ϕ )] s the probablty of successful entry, and v t=0 (1 δ)t π = π /δ s the sum of future profts wth successful entry, dscounted by the probablty of ext as a result of bad shocks. Ths yelds: π = δf e, /p e, = δf e, [ϕ /ϕ 0,] θ (FE), (17) whch corresponds to the free entry equlbrum condton n Meltz (2003). Equatons (16) and (17) together determne the equlbrum entry cutoff level ϕ : { ϕ = σ 1 θ (σ 1) } f + np x, f 1/θ x, ϕ 0,. (18) δf e, Assumpton () ensures that ϕ ϕ 0, so that an nteror soluton for ϕ exsts. The equlbrum 9

10 export cutoff level ϕ x, s n turn determned by (13). that: It s straghtforward to show that dp x, /dτ = θ /τ p x, < 0. Gven ths, we can further show dϕ np x,f x, ϕ = < 0. (19) dτ f + np x, f x, τ Thus, a tarff reducton wll rase the equlbrum entry cutoff level: the least productve frms wll be drven out of the market wth a tarff reducton. On the other hand, we can show that: dϕ x, dτ = f f + np x, f x, ϕ x, τ > 0. (20) Thus, the equlbrum export cutoff level falls wth the tarff: proportonally more ncumbent frms wll enter the export market when the tarff s lower. In summary, the condtonal probablty of ncumbent frms exportng wll ncrease wth a tarff reducton. Each country by lowerng the tarff wll experence a hgher degree of mport penetraton, n return for a freer access to foregn markets and a hgher volume of exports. 2.4 Aggregate Equlbrum and Welfare Suppose the mass of ncumbent frms s M n sector and the mass of new entrants n every perod s M e,. Then, n a statonary equlbrum, the mass of successful entrants should equal the mass of ncumbents who ext: p e, M e, = δm, so that the aggregate varables reman constant over tme. Let R = NE = M r denote the aggregate frm revenue of sector, Π = M π the aggregate frm proft of sector. Also let L p, and L e, denote the aggregate labor used for frm producton and entry nvestment, respectvely. By defnton, aggregate frm profts are what remans of aggregate revenue after payng for workers used n producton: Π R L p,. Use the statonary condton p e, M e, = δm and the free entry condton (17). It follows that Π = M π = M e, f e, = L e,. Thus, the aggregate revenue of sector equals the aggregate labor payment (employment) n sector : R = Π +L p, = L e, +L p, = L. Gven ths, the equlbrum mass of ncumbent frms s determned by: L M = R = θ (σ 1), (21) r θ σ f + np x, f x, 10

11 where L = NE. Usng (21), the zero cutoff proft condton (16), and the fact that σ 1 σ = ρ, we obtan the equlbrum aggregate proft as: Π = M π = R r π = ρ θ L, (22) whch turns out to be ndependent of the trade polcy τ. Next, the equlbrum tarff revenue from sector s: g (ϕ) TR = (τ 1)np x, M r x, (ϕ) 1 G (ϕ x, )dϕ ϕ x, = (τ 1)np x, M r x, ( ϕ x, ) = (τ 1) np x,f x, L f + np x, f x,, (23) where we have used (11) and (21) n the last equalty. Recall that the condtonal probablty of frm exportng, p x,, decreases as the tarff ncreases. Thus, a tarff ncrease rases the unt tarff revenue (the frst term n (23)), but at the same tme lowers the aggregate mport value (the second term n (23)). The net effect on the total tarff revenue depends on the parameters and the tarff level. Snce the expendture E by an ndvdual on good s constant by assumpton, the consumer surplus S U (Q ) P Q = U (Q ) E vares only wth U (Q ). Note also that q d, (ϕ) = r d,(ϕ) p d, (ϕ) = ( ϕ ϕ ) σ 1 σ f (ρ ϕ) = ( ϕ ϕ ) σ 1 (σ 1)f ϕ and that q x, (ϕ) = r x,(ϕ) p x, (ϕ) = ( ϕ ϕ ) σ 1 σ f x, (ρ ϕτ 1 ) = x, ( ϕ ϕ ) σ 1 (σ 1) f x, x, τ ϕ. Thus, at equlbrum, the utlty derved from consumng good by an ndvdual s: ( Z Z U (Q ) = M q d, (ϕ) ρ g (ϕ) + ϕ 1 G (ϕ npx,m q x,(ϕ) ρ g (ϕ) )dϕ ϕ 1 G x, (ϕ x, )dϕ ( Z» = M ( ϕ ρ Z g(ϕ)» ) σ 1 (σ ϕ ϕ 1)f ϕ + 1 G (ϕ npx,m ( ϕ ρ ) σ 1 (σ )dϕ ϕ ϕ 1) fx, g(ϕ) ϕ x, x, τ 1 G (ϕ x, )dϕ ( M f ρ Z = (σ 1) ϕ σ 1 g (ϕ) ϕ (σ 1)ρ ϕ 1 G (ϕ )dϕ + M f ρ Z ) 1 ρ npx, x, τ ρ ϕ σ 1 g (ϕ) ϕ x, (σ 1)ρ ϕ 1 G x, (ϕ x, )dϕ ( ) M f ρ ϕ σ 1 M f ρ 1 x, = (σ 1) + np ϕσ 1 ρ x, ϕ (σ x, 1)ρ τ ρ ϕ x, (σ 1)ρ ) 1 ρ ) 1 ρ «1/ρ L = (σ 1)f ϕ, σ f (24) where the last equalty follows from (7), (10), and (13). As the entry cutoff level ϕ rses wth a 11

12 lower tarff, a tarff reducton mproves the consumer surplus. Summng ndrect utltes over all ndvduals, and notng that aggregate ncome s the sum of labor ncome, profts, and tarff revenue, one obtans the aggregate welfare: W = NE + N = (L = L + m S m L ) + m (L p, + Π ) + m TR + N m TR + N m m S. (25) Gven (23), t s straghtforward to show that dtr = np ] x,f x, L [f dτ (f + np x, f x, ) 2 + np x, f x, + ( 1τ 1)θ f, (26) S where the expresson n the bracket s a decreasng functon of τ for τ 1. Thus, gven Assumpton (v), there exsts a tarff-maxmzng tarff ˆτ > 1 such that dtr dτ for τ ˆτ. = 0 for τ = ˆτ and dtr dτ 0 Gven (24), t s also straghtforward to show that np x,f x, du = (σ 1)f dτ f + np x, f x, ( L σ f ) 1/ρ ϕ τ < 0, (27) and that d2 U > 0. Thus, U dτ 2 s a decreasng convex functon of τ. Gven (26) and (27), we have dw dτ τ =1 = dtr dτ τ =1 + N du dτ τ =1 np x,f x, = np x,f x, L N (σ 1)f f + np x, f x, f + np x, f x, [ = np ( x,f x, N L E (σ 1)f f + np x, f x, σ f ( L ) 1/ρ ϕ ) 1/ρ ϕ σ f ]. (28) Gven the defnton of ϕ n (18) and the defnton of p x, n (14), t follows that dw dτ τ =1 = 0 f 12

13 and only f { } 1/θ θ (σ 1) δf e, E ϕ 0, = σ 1 f + n (f x, /f ) θ /(σ 1) ( ) f 1/ρ. (29) x, (σ 1)f L σ f We wll assume that the underlyng economc parameters satsfy ths necessary condton for free trade to be the welfare-maxmzng polcy. To ensure that free trade s the welfare-maxmzng polcy, t s suffcent that dw dτ < 0 for all τ > 1. Ths condton s apparently satsfed for τ ˆτ, where dtr dτ 0 and du dτ < 0. For 1 < τ < ˆτ, there s ncentve to ncrease tarff arsng from tarff-revenue consderaton; on the other hand, there s also dsncentve to ncrease tarff because of loss n consumer surplus. In general, we have that dw = dtr + N du dτ dτ dτ [ = np x,f x, N E + E ( 1 ( ) ] θ f 1/ρ L ϕ 1) (σ 1)f f + np x, f x, τ f + np x, f x, σ f τ = np [ x,f x, N E + E ( 1 θ f 1) E ( 1 ] f + np x, f x, ) f + np x, f x, τ f + np x, f x, τ f + n(f x, /f ) θ /(σ 1) f x, = np [ x,f x, NE 1 (1 1 θ f ) ( 1 ] f + np x, f x, ) f + np x, f x, τ f + np x, f x, τ f + n(f x, /f ) θ /(σ 1), f x, (30) where n the thrd equalty, we have used the condton (29) for ϕ 0, n the defnton of ϕ. We can show that for suffcently large θ, the expresson n the bracket s negatve for τ > 1 (to be double-checked agan!!). Thus, we wll take t to be the case that the underlyng parameter θ for = 1,2,...,m s suffcently large, so that dw dτ < 0 for τ > 1 and for = 1,2,...,m. Ths ensures that the aggregate welfare functon s a monotoncally decreasng functon of τ for τ > THE LOBBYING GAME 3.1 Group Interests We consder a lobbyng game as n the orgnal protecton for sale model. However, we now have dfferent nterests wthn each ndustry. Profts from sellng to the domestc market amount to π d (ϕ) = (ϕ/ϕ ) σ 1 f f and profts from sellng to a foregn market are π x (ϕ) = τ 1 σ (ϕ/ϕ ) σ 1 f 13

14 f x. It s straghtforward to show that: dπ d (ϕ) dτ = (σ 1)f τ np x f x f + np x f x ( ) ϕ σ 1 ϕ > 0, (31) and that: dπ x (ϕ) dτ (σ 1)f = τ σ f f + np x f x ( ) ϕ σ 1 ϕ < 0. (32) Thus frms wth ϕ < ϕ x that serve only the domestc market beneft from an ncrease n the tarff (lose from a tarff reducton). Frms wth ϕ > ϕ x, on the other hand, whch export n addton to supplyng the domestc market make a hgher proft n the domestc market yet lose profts abroad. Further dervatons show that: dπ d (ϕ) dτ + n dπ x(ϕ) dτ = (σ 1)f τ np x f x f + np x f x ( ) ϕ σ 1 ( ) θ (σ 1) 1 ϕ τ σ 1f σ 1 x < 0, (33) f where the last nequalty follows from our earler assumpton that τ σ 1 f x, > f. Thus, exportng frms wth ϕ > ϕ x are worse off (better off) overall when the world-wde tarff rate ncreases (decreases) because ths restrcts (facltates) market access n other countres. The export cut-off productvty level ϕ therefore separates frms wthn each sector nto two camps of conflctng nterests: Let group l denote the group of lower productvty frms wth ϕ < ϕ and group h the group of hgher productvty frms wth ϕ > ϕ. The combned proft of the former group amounts to: ϕ x g(ϕ) Π l = M π d (ϕ) ϕ 1 G(ϕ ) dϕ = M p e { [ (ϕ0 ) = M θ θ θ (σ 1) f ϕ ( ϕ0 ϕ x ϕ x ϕ π d (ϕ)g(ϕ)dϕ ) θ ( ϕ x ϕ ) ] [ σ 1 (ϕ0 ) θ f ϕ ( ϕ0 ϕ x ) θ ]}, (34) 14

15 and the aggregate proft of the hgher productvty frms s: Π h = M ϕ x g(ϕ) π d (ϕ) 1 G(ϕ dϕ + nm ) { = M π d (ϕ)g(ϕ)dϕ + n p e = M ( ϕ0 ϕ x ϕ x ϕ x ϕ x g(ϕ) π x (ϕ) 1 G(ϕ ) dϕ } π x (ϕ)g(ϕ)dϕ ) θ { } 1 + nτ 1 θ θ (σ 1) θf ϕ x ϕ f nf x, (35) where M M p e = Π πp e = Π δf e does not depend on τ, and from (31) and (33) t follows that dπ l /dτ > 0 and dπ h /dτ < 0. Furthermore, t follows from d Π/dτ = 0 that dπ l /dτ = dπ h /dτ. Havng analyzed the profts of the two groups wthn each ndustry, we can wrte ther respectve gross pay-off functons as follows: W,g (τ) = Π,g + α,g (CS + TR) g {l,h} (36) To nfluence the government, each group f organzed offers a contrbuton schedule C,l (τ) and C,h (τ) to the government, whch specfes how much the nterest group wll pay the government condtonal on the tarff vector chosen. Faced wth the contrbuton schedules, the government sets a tarff vector that maxmzes the followng weghted sum of socal welfare and contrbutons: n n G(τ) = aw + I,l C,l (τ) + I,h C,h (τ), (37) where the parameter a represents the relatve weght the government places on socal welfare and the Is are ndcator functons that take a value of one f that partcular group s organzed and zero otherwse. Note that there are four possble organzatonal scenaros n each ndustry: nether group s organzed, both groups are, only domestc frms lobby, or only exporters do. 3.2 Solvng the Lobbyng Game In solvng the lobbyng game outlned above, we look for a subgame perfect Nash equlbrum defned as follows: 15

16 Defnton 1 The collecton ({C,l 0 (τ) : L l}, {C,h 0 (τ) : L h},τ 0 ) s a subgame perfect Nash equlbrum of the lobbyng game f C,g 0 s feasble for all (,g) L l L h, τ 0 maxmzes G(τ), and, gven {Cj 0(τ)} j L\, no lobby has an alternatve feasble strategy C (τ) that would yeld a hgher (net) payoff. To fnd such an equlbrum, we make use of of Lemma 2 n Bernhem and Whnston (1986). The followng proposton restates ther lemma usng our notaton: Proposton 1 ({C 0,l (τ) : L l}, {C 0,h (τ) : L h},τ 0 ) s a subgame perfect Nash equlbrum for the lobbyng game f and only f: ) C 0,g (τ) s feasble (,g) L l L h, ) τ 0 arg max G(τ), ) τ 0 arg max G(τ) + W,g (τ) C,g (τ) L l L h, v) (,g) L l L h, τ,g R n that maxmzes G(τ) such that C 0,g (τ,g ) = 0. Assumng the usual dfferentablty of the contrbutons schedules, and combnng condton ) and ) above, we obtan the followng mplct equaton for the equlbrum tarff rates: a W τ j + n I,l W,l τ j + n I,h W,h τ j = 0 j N. (38) Recall the composton of W and W,g and note that aggregate profts do not depend on τ and ndustry profts do only depend on ther own tarff. Ths allows us to rewrte the prevous equaton as follows: ( CS (a + α L ) + TR ) Π j,l (τ j ) Π j,h (τ j ) + I j,l + I j,h = 0 j N. (39) τ j τ j τ j τ j The very frst term represents the welfare cost of a tarff: the loss n consumer surplus net of tarff revenue weghted by a, that s, by how much weght the government places on socal welfare. The second term represents the consumer and revenue nterests of all groups that lobby. The thrd term s the postve effect of a tarff on the profts off the domestc subgroups, provded they lobby, and the last term stands for the detrmental effect on exporters profts. In order to dscuss the tarffs 16

17 mpled by ths equaton, recall the four organzatonal possbltes for each ndustry mentoned above: (1) nether subgroup of an ndustry s organzed, (2) both subgroups are organzed, (3) only domestc frms lobby, and (4) only exporters do. We analyze these four cases n turn. The scenaro where nether low-productvty domestc frms nor hgh-productvty exporters are organzed s easly understood. Snce both I j,l as well as I j,h are zero, equaton (39) reduces to: ( CS (a + α L ) + TR ) = 0. (40) τ j τ j It s straghtforward to see that ths corresponds to choosng the socally optmal tarff, as maxmzng W = Π + CS + T R also mples that CS/ τ + T R/ τ = 0. Ths result s qute ntutve: f the ndustry does not lobby the government chooses the socally optmal polcy vs-à-vs the sector. Consder now the case where both groups wthn ndustry j are organzed,.e. I j,l = I j,h I j,h = 1. Equaton (39) then becomes: ( CS (a + α L ) + TR ) + Π j,l(τ j ) + Π j,h(τ j ) = 0. (41) τ j τ j τ j τ j Recallng that Π j,l / τ j = Π j,h / τ j, we see that n ths case the effects of both groups lobbyng efforts cancel and the government agan chooses the socally optmal tarff. Under the thrd scenaro, only low-proftablty domestc frms lobby. Equaton (39) thus takes the form: ( CS (a + α L ) + TR ) + Π j,l(τ j ) = 0. (42) τ j τ j τ j From the government s perspectve, the cost n terms of welfare and lobbes consumer (and revenue) nterests the frst two terms now stands aganst the beneft to the domestc producers whch s conveyed to the government va lobbyng. The government thus chooses to set the tarff hgher than ts socally optmal level to satsfy the specal nterest of the domestc producers. Note that the extent of ths dstorton depends on the weght the government places on socal welfare and the aggregate degree of organzaton. The fourth and fnal case has only hgh-productvty exportng frms lobbyng. Equaton (39) becomes: ( CS (a + α L ) + TR ) + Π j,h(τ j ) = 0. (43) τ j τ j τ j 17

18 Under ths scenaro, t s the exporters who convey ther nterests n a lower tarff va lobbyng. The government takes ths nterest nto account agan dependng on the weght t places on welfare and aggregate lobbes consumer and revenue nterests and lowers the tarff compared to ts socally optmal level. 4. BIAS OF THE STANDARD MODEL Whle the standard protecton for sale model has generally found support n the data, there remans one mportant unresolved puzzle: all emprcal studes we are aware of fnd very hgh values usually well above 95 percent for the weght the government places on socal welfare. Such hgh values for socal welfare n turn mply that the government places correspondngly lttle weght on monetary contrbutons,.e. less than 5 percent. If one beleved these fndngs to be correct, one would be forced to serously queston the whole approach; after all, why model lobbyng f t hardly plays any role. The problem s well known, of course, and t seems that many share our pror that perfectly benevolent governments are too good to be true. In response, two mportant contrbutons by two of the top scholars n the feld have nvestgated possble routes of obtanng more reasonable values for the weght the government places on socal welfare. Mtra, Thomakos, and Ulubasoglu (2006) explore varyng α L (the share of the populaton nvolved n lobbyng) as a possble way of lowerng the estmate for a. Gawande and L (2004) ntroduce a success probablty of lobbyng that, f smaller than one, also leads to lower values for the weght on socal welfare. The explanaton we propose n ths paper s complementary and reles crucally on the nterests of exporters, as formally ntroduced above. If our model s correct, then exporters nterests n market access abroad go aganst the more conventonal desre of purely domestc frms for protecton. If both groups are organzed and lobby the government to take nto account ther respectve nterests, then ths gves rse to the followng scenaro: the sector lobbes (ndeed, both subgroups do) and nevertheless the government sets the socally optmal tarff, even f t does place a hgh value on contrbutons, that s, has a low a. Suppose we approach ths stuaton from the perspectve of the standard protecton for sale model. The sector s organzed but does not obtan a tarff, despte ts lobbyng efforts. Wthn the context of the standard model ths mples that the government must be maxmzng socal welfare only and places no weght on contrbutons. We conclude that 18

19 the standard model gves rse to an upward bas n the estmate for a, consstent wth the hgh values found n the emprcal lterature, that many of us regard wth suspcon. Our model s thus provdes one possble soluton to ths longstandng puzzle. 5. CONCLUSION In ths paper we propose a new model of endogenous trade protecton that apples the protecton for sale style lobbyng game to a new new trade model wth heterogenous frms à la Meltz (2003). Our model has two mportant features: The nterests of purely domestc and of exportng frms dffer wth regards to trade polcy. Secondly, we treat sectoral tarff levels as a multlateral polcy choce. Usng ths setup, we can show that purely domestc frms favor protecton n the conventonal way, whereas exporters beneft from lower tarff levels because lberalzaton facltates access to export markets. Snce our framework features two subgroups n each ndustry, t allows for a rch set of four organzatonal possbltes n each sector: both groups can be organzed, nether group lobbes, or only exporters or purely domestc frms do. As the government maxmzes a weghted sum of socal welfare and contrbutons, the case wthout lobbyng clearly leads to the socally optmal polcy, because contrbutons are zero n ths case. Interestngly, the case where both subgroups lobby also leads to the same polcy outcome, namely the socally optmal tarff, because both subgroups lobbyng efforts neutralze each other. However, the government does receve contrbutons n ths case. As for the assymmetrc scenaros, each subgroup, f lobbyng alone, s able to dvert the government s polcy choce towards ts preferred trade polcy: a hgher tarff n the case of purely domestc frms and lower protecton for exporters. One mportant aspect of our model s ts ablty to explan the very hgh values for the weght on socal welfare found n the emprcal protecton for sale lterature. The possblty that the government sets the socally optmal polcy even when the sector lobbes can be explaned wthn the standard model only f the government does not value contrbutons and exclusvely maxmzes socal welfare. Our model, on the other hand, can account for ths possblty when both subgroups wthn a sector are poltcally actve. Ths mples an upward bas n the estmate for the weght the government places on socal welfare when applyng the standard model, offerng a soluton to 19

20 ths long-standng puzzle n the emprcal protecton for sale lterature. As for future work, smulatons wll shed lght on the exact determnants of tarffs n our model. Generatng smulated data wll also allow us to evaluate more precsely the bas that s caused when applyng the standard model. Another ntestng extenson s the ncluson of endogenous lobby formaton, as proposed by Mtra (1999) n the context of the standard model. Fnally, our model can be tested emprcally to see f the export orentaton of ndustres does play a role n explanng sectoral varatons n tarff levels. REFERENCES Axtell, R. L. (2001). Zpf dstrbuton of u.s. frm szes. Scence 293(5536), Bernhem, B. D. and M. D. Whnston (1986). Menu auctons, resource allocaton, and economc nfluence. Quarterly Journal of Economcs 101, Bombardn, M. (2005). Frm heterogenety and lobby partcpaton. Mmeo, UBC. Chaney, T. (2006). Dstorted gravty: Heterogenous frms, market structure and the geography of nternatonal trade. Mmeo, Unversty of Chcago. Chang, P.-L. (2005). Protecton for sale under monopolstc competton. Journal of Internatonal Economcs 66(2), Dxt, A. K. and J. E. Stgltz (1977). Monopolstc competton and optmum product dversty. Amercan Economc Revew 67(3), Facchn, G., J. Van Besebroeck, and G. Wllmann (2006). Protecton for sale wth mperfect rent capturng. Canadan Journal of Economcs 39(3). Gawande, K. and H. L (2004). The case of the mssng contrbutons. Mmeo. Grossman, G. M. and E. Helpman (1994). Protecton for sale. Amercan Economc Revew 84, Helpman, E., M. J. Meltz, and S. R. Yeaple (2004). Export versus fd wth heterogenous frms. Amercan Economc Revew 94(1), Meltz, M. J. (2003). The mpact of trade on ntra-ndustry reallocatons and aggregate ndustry productvty. Econometrca 71(6),

21 Mtra, D. (1999). Endogenous lobby formaton and endogenous protecton: A long run model of trade polcy determnaton. Amercan Economc Revew 89(5), Mtra, D., D. Thomakos, and M. Ulubasoglu (2006). Can we obtan realstc parameter estmates for the protecton for sale model? Canadan Journal of Economcs 39(1). 21