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1 Department of Economcs Workng Paper Seres Do Labor Issues Matter n the Determnaton of U.S. Trade Polcy? An Emprcal Reevaluaton Xena Matschke Unversty of Connectcut Shane M. Sherlund Federal Reserve Board Workng Paper November Mansfeld Road, Unt 1063 Storrs, CT Phone: (860) Fax: (860)

2 Abstract Some recent emprcal studes, motvated by Grossman and Helpman s (1994) protecton for sale model, suggest that very few factors (none of them laborrelated) determne trade protecton. Ths paper reexamnes the roles that labor ssues play n the determnaton of trade polcy. We ntroduce collectve barganng, dfferences n labor moblty across ndustres, and trade unon lobbyng nto the protecton-for-sale model and show that the equlbrum protecton rate n our model depends upon these labor market varables. In partcular, our model predcts that trade protecton s structurally hgher than n the orgnal protectonfor-sale model f the trade unon of a sector lobbes but captal owners do not, because unon workers collect part of the protecton rents; equlbrum protecton s lower f captal owners lobby but the trade unon does not, because part of the protecton rents s dsspated to workers. Usng data from U.S. manufacturng, we fnd that collectve barganng, dfferences n labor moblty across ndustres, and trade unon lobbyng ndeed play mportant roles n the determnaton of U.S. trade polcy. Journal of Economc Lterature Classfcaton: F13, F16 Keywords: Trade protecton, protecton for sale, labor market We thank the edtor Davd Card and two anonymous referees for helpful comments that greatly mproved ths paper. We also thank Scott Taylor for hs valuable comments and advce and Kshore Gawande and Danel Trefler for provdng data. We are grateful to Bruce Hansen, Bob Stager, and Gautam Trpath for for ther helpful comments and suggestons and to Ellen Dykes and Jonas Robson for ther help wth edtng the language and grammar. Xena Matschke gratefully acknowledges fnancal support from a Deutsche Forschungsgemenschaft research fellowshp. Ths paper represents the vews of the authors and does not necessarly represent the vews of the Federal Reserve System, ts members, or ts staff.

3 2 MATSCHKE AND SHERLUND 1. Introducton Lobbysts for trade and other ndustral polces represent dfferent nterest groups n socety. In partcular, dstngushng between labor and captal lobbes s common. Labor nterests, usually represented by trade unons, often lobby for trade protecton. For example, U.S. trade unons strongly opposed NAFTA n the 1990s because of fears that freer trade would decrease domestc employment and wage levels. Further, accordng to Baldwn (1985) and Baldwn and Magee (2000), trade unon contrbutons are postvely correlated wth the probablty that a U.S. congressman votes aganst trade lberalzaton. The protecton for sale model of Grossman and Helpman (1994), however, suggests that very few factors none of them labor-related determne trade protecton. In the protecton-for-sale model, wages are fxed and equal across ndustres, and there s full employment. Only captal owners are allowed to lobby for trade polcy, but even f workers, too, were allowed to lobby, they would want mport subsdes n order to beneft from lower product prces. Hence, the GH model cannot explan why trade unons lobby for trade protecton so as to secure hgher wage and employment levels. The GH model s also at odds wth the older emprcal trade protecton lterature (Rodrk, 1995, provdes an overvew) that fnds that labor market consderatons are an mportant trade polcy determnant. However, more-recent emprcal studes (for example, Goldberg and Magg, 1999; Gawande and Bandyopadhyay, 2000; Echer and Osang, 2002) fnd strong support for the protecton-for-sale model. Some of these studes also test whether labor market varables have addtonal explanatory power and fnd them to be statstcally nsgnfcant. Ths paper shows that the concluson that labor market varables do not nfluence trade protecton s msleadng. The earler papers that estmate the GH model employ the nonlnear form of protecton suggested by that model for estmaton. 1 But snce the GH model has nothng to say about labor market varables, the ncluson of these varables n emprcal studes thus far has been ad hoc. The man contrbuton of ths paper s to show that, once labor market varables have been approprately controlled for, statstcal methods strongly reject the null hypothess that labor market varables are rrelevant to trade protecton. To ths end, we construct a model n the same sprt as GH but relax assumptons about the labor market. In partcular, we allow for (1) ndustry-specfc trade unons that bargan wth captal owners over unon wages and employment, (2) dfferences n labor moblty across ndustres, and (3) actve lobbyng by trade unons. Our model predcts 1 For example, n the GH model, mport protecton decreases wth mport penetraton rato and mport demand elastcty when captal owners lobby, but t ncreases wth these two varables when captal owners do not lobby.

4 that trade protecton s structurally hgher than n the GH model f the trade unon of an ndustry lobbes but captal owners do not, because unon workers collect part of the protecton rents. However, equlbrum protecton s lower f captal owners lobby but the trade unon does not, because workers receve part of the protecton rents. Moreover, as long as trade protecton ncreases the wages of at least some non-unonzed workers, equlbrum protecton s lower than n the GH model even f both the captal owners and the trade unon of an ndustry lobby. In contrast to the protecton-for-sale model wthout trade unon actvty, the equlbrum protecton rate n our model depends upon sectoral wage and employment elastctes that, n turn, vary accordng to the moblty of workers across ndustres. We test our model predctons usng 1983 data from U.S. manufacturng. Snce our framework nests the GH model, we can test the statstcal valdty of the GH restrctons. Our major fndng s that we can reject the GH model n favor of our labor-augmented model. Consstent wth our theory, we fnd that, compared wth the GH predctons, trade protecton s ndeed hgher when trade unons lobby and captal owners do not, but lower when captal owners lobby. Not only does trade protecton vary accordng to whether captal owners of an ndustry lobby, but t also depends on trade unon actvty and dfferences n labor moblty across ndustres. Moreover, our labor-augmented model delvers consderably lower estmates of the percentage of lobbes n the populaton and the weght of contrbutons n the governmental welfare functon, both of whch had been found to be unreasonably hgh n prevous tests of the GH model. The remander of ths paper s organzed as follows. In Secton 2, we derve the equlbrum tarffs for ndustres wth moble and mmoble labor when trade unons bargan wth frms over wages and employment and are also allowed to lobby for trade protecton. We present the econometrc model and ts predctons n Secton 3. In Secton 4, we descrbe the data, and we proceed wth estmaton and testng n Secton 5. Fnally, n Secton 6, we conclude the paper and make suggestons for future research The Model 2.1. Model Bascs. In the followng, we augment the GH model to allow for labor market consderatons. Consder a small country wth n + 1 ndustres, each producng a sngle good. The country has fxed endowments of labor, L, and ndustry-specfc captal, K, where = 1,...,n. Each worker (captal owner) nelastcally supples one unt of labor (ndustry-specfc captal). On the consumpton sde, all ndvduals, h = 1,...,H, have dentcal quaslnear preferences of the form U h = x h 0 + n =1 u(xh ), where xh denotes h s consumpton of good and u s strctly concave and ncreasng n x h. If each ndvdual has enough ncome to

5 4 MATSCHKE AND SHERLUND consume all goods, quaslnearty of preferences ensures that demand of a good = 1,...,n depends only on ts own prce. Let I = {0, 1, 2,...,n} denote the set of all ndustres. The numerare ndustry, = 0, uses only labor for producton accordng to F 0 = L 0. The world prce of good 0 s fxed at p 0, and no trade barrers are mposed on t. Each non-numerare ndustry, = 1,...,n, conssts of two sectors A, whch s unonzed, and B, whch s non-unonzed wth dentcal producton functons. Frms n these ndustres employ three producton factors: captal, labor, and the numerare good 0 as an ntermedate nput. 2 Each unt of the fnal good requres a fxed (but dfferng wth ) amount of good 0 (Leontef technology). To keep notaton smple, we denote the prce of the amount of good 0 requred for one unt of good by q and then wrte (p q )F (K, L ) as value added. Unlke the ntermedate good 0, captal and labor are substtutable n the producton functon. Captal employed n the sectors of any non-numerare ndustry namely, K A n the unonzed sector A and K B = K K A n the non-unonzed sector B s mmoble. In contrast, labor may or may not be moble across ndustres as dscussed n the next paragraph. The reduced producton functon F (K, L ) s lnearly homogeneous and weakly concave, where FLL < 0, FKK < 0, and F KL > 0.3 We allow for dfferences n the nterndustry moblty of labor. For smplcty, we assume that non-unon workers are ether completely moble between certan ndustres or that they cannot ext ther ndustry and workers from other ndustres cannot enter. If ndustry I M, ts labor pool potentally conssts of all laborers n the moble subset of ndustres. If we assume that 0 I M, the compettve wage must be w = p 0 for I M. Unon workers may swtch ndustres f I M ; however, they cannot be employed n the unonzed sectors of ndustres other than tself. 4 If ndustry I I, where I M I I = I and I M I I =, ndustry s workers are mmoble and can work only n ndustry. In the unonzed sector A, the captal owners bargan wth the -specfc trade unon, whch has N members, over wages and employment. 5 In the non-unonzed sector B, 2 To keep the analyss focused on the nfluence of labor ssues on trade protecton, the modelng of ntermedate goods as nputs s kept as smple as possble. We ntroduce them only to take nto account that frms and unons bargan over value added, not the entre value of shpments. Wthout ths adjustment, we would substantally and systematcally underestmate unon barganng strength. 3 We omt the ntermedate nput as an argument n the producton functon. Because good 0 s a Leontef nput, we must adjust the amount of good 0 proportonally wth F when captal or labor nputs vary. 4 Ths assumpton mantans the de facto partal equlbrum structure of the GH model, whch would be destroyed f the ndustry-specfc trade unons also had to take nto account that ther members mght fnd employment n unonzed sectors elsewhere. 5 Assumng barganng over both wages and employment (effcent barganng) restrcts the effect of unonfrm barganng to redstrbutve ssues. Effcent barganng seems a justfable assumpton because emprcal tests between ths model and the competng rght-to-manage model ether have been nconclusve or have

6 employment s chosen by frms. As s commonly observed n practce, unon workers do not work exclusvely n the unonzed sector, and non-unon workers are not confned to work n the non-unonzed sector. Employment of unon workers n sector A s measured as a fracton α of the N unon members, whereas the share of covered non-unon workers n the non-unon worker labor pool for ndustry s δ α (where δ 0). The unon wage pad n sector A s denoted by w. 6 In sector B, the wage s equal ether to p 0 (f I M ) or to the wage that equates resdual labor supply and labor demand (f I I ). In some of the ndustres (but not the numerare ndustry 0), ether captal owners or the trade unon or both are actve lobbes that solct trade protecton from the domestc government. In the frst (lobbyng) stage, each lobby offers the government a schedule that lsts ts contrbutons as a functon of the domestc prce vector. The domestc prce, p, may dffer from the world prce, p, f the domestc government mposes a vector t of specfc mport tarffs (or mport subsdes) or export taxes (or export subsdes) at ths stage. In the second (producton) stage, frms and unons take goods prces as gven when they determne wages and employment. If good s an mport good, t > 0 (t < 0) mples that an mport tarff (mport subsdy) s mposed. In contrast, f good s an export good, t > 0 (t < 0) mples an export subsdy (export tax). To facltate the descrpton, we focus on mport goods when descrbng the determnaton of the equlbrum trade polcy Second Stage: Employment and Wage Determnaton. To fnd the subgameperfect Nash equlbrum, we start wth the producton stage and then consder the lobbyng stage. At the producton stage, we assume that frms maxmze profts and that the unon maxmzes the wage bll of unon workers Industres wth moble labor. In sector B, the frms choose the number of workers L B such that the frst-order condton of proft maxmzaton, (p q )F L(K B, L B ) = p 0, (2.1) holds. The wage w s predetermned by p 0 so that L B adjusts to ensure that (2.1) holds. Any labor not employed n the non-numerare ndustres s absorbed by ndustry 0. We assume that n sector A frms and unon bargan over wages and employment jontly and splt the surplus accordng to the generalzed Nash barganng soluton. If barganng s successful, the wage bll for unon workers equals α w N + (1 α ) p 0 N, that s, α N unon workers work n sector A and receve unon wage w, and (1 α )N unon workers work for the compettve wage n any of the non-unonzed sectors wthn I M. We assume that f a worker s member of unon N, he cannot receve a unon wage n any produced (weak) evdence n favor of the effcent barganng model (MaCurdy and Pencavel, 1986). Matschke (2004) dscusses how employng the rght-to-manage model of unon-frm barganng alters these results. 6 In secton 2.2, we dscuss how α and w are determned. 5

7 6 MATSCHKE AND SHERLUND ndustry apart from. If N = I M N, the profts that reman for captalsts n sector A amount to Π A = (p q )F (K A, α [N + δ (L M N)]) w α [N + δ (L M N)], where L M denotes the total labor pool for all ndustres n I M and L M N s the pool of nonunon members wthn L M. If barganng fals, all workers have to fnd employment n the non-unonzed sectors of the ndustres n I M, and the expected wage bll reduces to p 0 N. If we assume that the unon succeeds n nterruptng producton n sector A, profts drop to zero. The generalzed Nash barganng soluton thus maxmzes {α ( w p 0 )N } s {(p q )F (K A, α [N +δ (L M N)]) w α [N +δ (L M N)]} 1 s, (2.2) where s and 1 s denote the relatve barganng strength of ndustry s trade unon and ndustry frms (both are assumed to be exogenously gven). Maxmzng (2.2) wth respect to α and w leads to two equatons. The frst equaton, (p q )F L(K A, α [N + δ (L M N)]) = p 0, (2.3) whch mrrors (2.1), says that producton s effcent. The second equaton, w = s (p q )F A L A + (1 s ) p 0, (2.4) descrbes how the unon wage serves to dstrbute the barganng surplus between the unon and the captal owners. It s straghtforward to show the followng comparatve statcs: Proposton 2.1. If ndustry I M, the compettve wage does not depend on p ( dw = 0), employment n the unonzed sector s ncreasng n p ( dα α = p 0 > 0), and (p q ) 2 L A FLL A the unon wage weghted by the probablty of a worker s recevng t s also ncreasng n p ( d(α w ) = s F A N +δ (L M N) + p 0 dα > 0). Proof. dw = 0 by constructon of the numerare ndustry producton structure. The other results follow from comparatve statcs on (2.3) and (2.4) Industres wth mmoble labor. When labor s mmoble between ndustres, equlbrum labor n sector B has to equal the resdual labor supply of the ndustry L α [N + δ (L N )], that s, all labor not employed n sector A of. Hence the compettve wage must adjust. From proft maxmzaton and labor market clearng, we have (p q )F L(K B, L α [N + δ (L N )]) = w. (2.5) In sector A, frms and unon splt the surplus accordng to the generalzed Nash barganng soluton. If barganng s successful, the wage bll for unon workers equals α w N + (1 α )w N. The profts earned by captal owners n sector A equal Π A = (p q )F (K A, α [N + δ (L N )]) w α [N + δ (L N )]. If barganng fals, all workers must fnd employment n the non-unonzed sector B of ndustry, n whch case the wage bll reduces to w N, where w = (p q )F L (K B, L ). Moreover, the unon

8 succeeds n nterruptng producton n sector A, so that profts are zero. The generalzed Nash barganng soluton thus maxmzes {α w N + (1 α )w N w N } s (2.6) { (p q )F (K A, α [N + δ (L N )]) w α [N + δ (L N )] } 1 s. Maxmzng (2.6) wth respect to α and w leads to two equatons. The employment share α s determned by F A L = F B L + (1 α )[N + δ (L N )]F B LL. (2.7) Ths equaton shows that f I I, the margnal product of labor across the sectors of s usually not equalzed because unons and frms realze that the compettve wage depends on ther employment choce. Furthermore, (2.5) and (2.7) suggest that dα = 0. 7 Therefore, we fnd that, n contrast to the case of moble labor, prce changes are reflected solely n wage changes when labor s mmoble. 8 The unon wage s determned by w = s (p q )F A L A (p Snce w > w, the unon wage s smaller than w = s q )F A L A comparatve statcs hold: + (1 s ) w (1 α )w α. (2.8) + (1 s )w. The followng 7 Proposton 2.2. If ndustry I I, employment n the sectors does not depend on p ( dα = 0), whereas unon and compettve wages are both ncreasng n p ( d w = w p q > 0, dw = w p q > 0). Proof. The result follows from comparatve statcs on (2.5), (2.7), and (2.8). We showed above that dα = 0 solves (2.7); the results for the wage changes easly follow Frst Stage: Lobbyng. In ths stage, trade unon and captal owner lobbes present the domestc government wth menus that map all possble tarff vectors, t, nto contrbutons that a lobby would pay n case a certan t s chosen (common-agency model of Bernhem and Whnston, 1986). The government takes these menus as gven and chooses the t that maxmzes the weghted sum of total contrbutons and aggregate gross welfare (that s, the sum of producton value, tarff revenue, and consumer surplus), where the weght on aggregate welfare s denoted by a and contrbutons receve weght 1. The equlbrum tarff vector t s defned by the followng condtons (Grossman and Helpman, 1994): It maxmzes the government s utlty functon, and t maxmzes the sum of governmental utlty and the utlty of any lobby. 7 Ths soluton need not be unque, but wthout further assumptons about F LL, the exstence of other solutons s not guaranteed. 8 Ths fndng assumes flexble wages. Wth nflexble wages, unemployment s lkely (see Matschke, 2004).

9 8 MATSCHKE AND SHERLUND The common-agency framework n whch lobbes confront the government wth an nfnte lstng of tarff vectors and contrbutons attached to them clearly looks qute dfferent from real-world lobbyng. Lobbes typcally tell the government what protecton they want (or they provde selectve nformaton from whch the government can nfer these wshes). The government then takes a weghted average of the wshes of the dfferent lobbes and ts own deas of what the optmal tarff would look lke to determne the equlbrum tarff. Matschke (2004) reconcles these two alternatve vews of lobbyng. She defnes the unlaterally optmal tarff as the tarff that a group would set (f t could do so) to maxmze ts own welfare. Let t N j and t K j denote the unlaterally optmal tarffs of groups N j and K j. Also, let t G denote the domestc welfare-maxmzng tarff. Ths s the tarff that the government would set f no lobbes exsted, and t can thus also be nterpreted as a unlaterally optmal tarff. Matschke then shows that the equlbrum tarff for ndustry n the lobbyng game can be wrtten as the weghted average of the unlaterally optmal tarffs for the dfferent players of the lobbyng game: Lemma 2.1 (Matschke 2004). The equlbrum tarff for ndustry s gven by t = atg (t ) a + Θ + θ Kj t K j (t ) a + Θ + θ Nj t N j (t ) a + Θ, (2.9) K j Ω N j Ω where θ gj denotes the populaton share of group g j and Ω s the set of all lobbes. Therefore, t can be determned by frst calculatng the unlaterally optmal tarffs and then usng Lemma Player Interests and the Equlbrum Tarff General results. To understand the players nterests, we calculate ther unlaterally optmal tarffs frst. The natural startng pont s the welfare-maxmzng tarff t G, that s, the tarff that the government would mpose wthout lobby nfluence. The government maxmzes domestc welfare (omttng parts that do not depend on p ) W G = (p q )F A + (p q )F B + p 0 F 0 + (L + n k=1 K k)v + t M by choosng p, where (L + n k=1 K k)v s the consumer surplus from good. If I M, the government can use a tarff to ncrease producton n (at the expense of producton n the numerare ndustry), but because the margnal value added s the same across all ndustres, the government has no ncentve to do so. If I I, the margnal value added of labor s equal nether across ndustres nor across sectors of an ndustry. However, employment s ndependent of the product prce, 9 Here, the t g j are functons of t. Ths does not dmnsh the usefulness of Lemma 2.1 because the equlbrum tarff predctons n the orgnal GH model are also gven only as mplct functons where t appears on both sdes of the equlbrum tarff equaton.

10 and therefore labor cannot be shfted to ndustres or sectors wth hgher margnal value added. Hence, free trade s welfare-maxmzng n both cases. Thus, t G = 0. (2.10) For lobbes g j outsde ndustry, the desre to drve a wedge between the domestc prce and the world prce for product stems from two sources. Frst, as consumers, the lobby wants as low a prce as possble. Second, as a recpent of tarff revenue, the lobby desres a strctly postve tarff. Formally, the lobby maxmzes W g j θ gj (L + n k=1 K k)v + θ gj t M, where j. Maxmzng W g j t g j 9 = by choce of t, we obtan = F M. (2.11) Because consumer surplus consderatons outwegh tarff revenue consderatons, lobby g j would lke to mpose an mport subsdy on good j. Fnally, we consder the nterests of lobby groups nsde ndustry. Captal owners maxmze the sum of profts, consumer surplus, and tarff revenue share, that s, W K = (p q )F A +(p q )F B w L A w L B +θ K (L + n k=1 K k)v +θ K t M. The captalsts unlaterally optmal tarff s gven by t K = 1 θ K M [ (1 θ K )F + ( w (p q )FL A ) dl A d w dw + L A + L B ]. (2.12) We see that t K conssts of four components. The frst component s also present n the orgnal GH model. Captal owners are nterested n a postve tarff for ther ndustry because such a tarff ncreases sales revenues and leads to hgher tarff revenues, but they also take nto account that they consume ther own good. Thus t K n the orgnal GH model would be (1 θ K )F θ K. However, when labor market nfluences are present, the captal owners M realze that a hgher tarff may lead to hgher wages n sectors A and B and may dstort producton toward the unonzed sector A, where workers receve wages above the margnal value added of labor. These nfluences decrease t K. The trade unon of ndustry maxmzes the sum of the wage bll, consumer surplus, and tarff revenue share accrung to unon members, that s, W N = α w N +(1 α )w N + θ N (L + n k=1 K k) V + θ N t M. The unlaterally optmal tarff for the trade unon n ndustry s t N = 1 θ N M [ ] θ N F dα d w dw ( w w )N α N (1 α )N. (2.13) In the orgnal GH model, unon workers, lke all consumers who own no captal, desre an mport subsdy for good because consumer nterests more than offset tarff revenue consderatons. However, once we allow for labor market mperfectons, three addtonal components appear that may make the unon of ndustry prefer a postve mport tarff

11 10 MATSCHKE AND SHERLUND for ts good. Not only may unon workers obtan hgher wages when the domestc prce of good ncreases, but more unon workers may fnd employment n the unonzed sector A, where rents can be earned because w > w Tarff predctons when labor s moble. To facltate comparablty wth the expressons gven by Grossman and Helpman (1994), we rewrte the optmal tarff equaton n terms of the equvalent ad valorem tarff τ. Notce that τ 1+τ = t p. Lettng e denote the absolute value of the mport demand elastcty, M p M, the followng proposton results: Proposton 2.3. If ndustry I M, the equlbrum ad valorem tarff τ of the lobbyng game s gven by τ 1 + τ = Θ F Θ+a e M Θ F Θ+a e M + 1 Θ+a 1 Θ F Θ+a e M 1 Θ+a s F A e M 1 Θ F Θ+a e M 1 Θ+a α N L A s F A e M ( ) 1 α N F L A s A e M f nobody n lobbes, f only the unon n lobbes, f only captalsts n lobby, f all n lobby. Proof. Because w = w 0 = p 0, the result follows from substtutng (2.10) (2.13) nto Lemma 2.1, usng the expressons for dw, dα, and d(α w ) from proposton 2.1. Not surprsngly, the equlbrum tarff equals the tarff of the orgnal GH model when nobody n ndustry lobbes. When both the unon and captal owners of ndustry lobby, the tarff would also be the same as n the orgnal GH model f unon wages were pad only to unon workers. Ths follows because effcent unon wage barganng then redstrbutes ncome only between the two lobbes. However, as long as non-unon workers, too, beneft from hgher unon wages, protecton benefts are dspersed from a lobby (the captal owners) to a populaton group that does not lobby (the non-unon workers), and therefore the equlbrum tarff τ wll be structurally lower than n the GH model. Protecton may be even further reduced f captal owners decde that lobbyng s not worthwhle snce rent dsperson to workers lowers the protecton rents that they could capture. Fnally, f one of the two groups n ndustry does not lobby, τ n our model s dstnct from τ n the GH model. The reason for ths result les n the proft sharng due to unon wage barganng. If captal owners lobby, they take nto account that they cannot capture all the protecton rents and are therefore less nterested n tarff protecton for ther product. The resultng τ s hence lower by a dsperson component. If the trade unon lobbes, τ s now hgher than n the GH model by a collecton component because part of the protecton rents s captured by the trade unon, an actve lobby. The dscrepancy between the equlbrum tarffs found here and n the GH model s hgher the greater the share of unonzed producton n ndustry and the hgher the barganng strength of the trade unon. Only f w = w (.e., s = 0) would the results match the predctons of the GH model.

12 Tarff predctons when labor s mmoble. For ndustres wth mmoble labor, the followng equlbrum tarff structure emerges: Proposton 2.4. Let λ denote the labor force share n ndustry whch s covered by collectve barganng (that s, rewrte L A = λ L and L B = (1 λ )L ). If ndustry I I, the equlbrum ad valorem tarff τ of the lobbyng game s gven by Θ F Θ+a e M f nobody n lobbes, τ Θ F Θ+a e 1 + τ = M + 1 α w +(1 α )w Θ+a e (p q )M N f only the unon n lobbes, 1 Θ F Θ+a e M 1 λ w +(1 λ )w Θ+a e (p q )M L f only captalsts n lobby, 1 Θ F Θ+a e M 1 α δ w +(1 α δ )w Θ+a e (p q )M (L N ) f all n lobby. Proof. The result follows mmedately from substtutng (2.10) (2.13) nto Lemma 2.1, usng the expressons for dα, dw, and d w from proposton 2.2. If nobody n ndustry lobbes, τ wll be the same as n the orgnal GH model. But the tarff structure dffers as soon as ndustry lobbes enter the scene. As wth moble labor, the GH predctons are altered by a collecton component f the trade unon lobbes and captal owners do not, and by a dsperson component f captal owners lobby and the unon does not. And just as wth moble labor, a dsperson component arses even f both groups lobby. When labor s mmoble, however, ths dsperson component does not dsappear as δ goes to zero: Trade protecton ncreases the wages pad to workers even f no unonzed sector exsts. A hgher tarff ncreases labor demand that meets completely nelastc supply. The prce ncrease s thus accompaned by an ncrease n the compettve wage w. Ths wage ncrease n turn means that workers n the non-unonzed sector share n the protecton rents. Proft-sharng s even hgher n the unonzed sector because w > w. The unon nterest n a hgher wage partly counterbalances the dsperson effect when both captal owners and the unon lobby. The dsperson component s then caused only by wage ncreases that go to non-unon workers: Every non-unon worker n gets at least w, and α δ (L N ) non-unon workers get even more because they are employed n sector A and receve the hgher unon wage w. 3. The Econometrc Model To wrte the equlbrum tarff equaton to nclude both moble and mmoble labor, we defne the followng ndcator varables: k takes the value 1 when captalsts n ndustry lobby (0 otherwse), n equals 1 when trade unons n ndustry lobby (0 otherwse), and m equals 1 when labor n ndustry s moble (0 otherwse). Proposton 3.1. The equlbrum ad valorem tarff τ for ndustry s gven by τ 1 + τ F F = Θ + 1 Θ + a e M Θ + a k + 1 e M Θ + a 11 labvar e, (3.1)

13 12 MATSCHKE AND SHERLUND where labvar = ( α (1 k )n m N F L A s A F M k (1 n )m s A M k n m 1 α N L A ) s F A M +(1 k )n (1 m ) α w +(1 α )w (p q )M N k (1 n )(1 m ) λ w +(1 λ )w (p q )M L k n (1 m ) α δ w +(1 α δ )w (p q )M (L N ) Proof. Use k, n, and m to collapse propostons 2.3 and 2.4 nto one expresson. The varable labvar s postve f the trade unon of ndustry lobbes but captal owners do not, negatve f captal owners n lobby, and zero f nobody n lobbes. To obtan our man estmaton equaton, we start wth proposton 3.1, move e to the left sde, and ntroduce an addtve error term ε, where E[ε ] = 0 and E [ ε 2 ] = σ 2. Our estmaton equaton s thus. τ F F 1 + τ e = β 0 + β 1 + β 2 k + β 3 labvar + ε. (3.2) M M Accordng to our theory, β 0 = 0, β 1 = Θ Θ+a, and β 2 = β 3 = 1 Θ+a. A more parsmonous specfcaton results by lettng β 2 = β 3, as the theory predcts: τ F F 1 + τ e = β 0 + β 1 + β 2 (k ) + labvar + ε. (3.3) M M Ths strcter nterpretaton of our model n (3.3) facltates the analyss of the structural parameters a and Θ snce over-dentfcaton of a and Θ n (3.2) leads to two (potentally very dfferent) estmates per parameter. 4. The Data Followng earler lterature, we lmt our analyss to manufacturng ndustres n the Unted States durng The tme perod and ndustry range are the same as those used n the studes by Goldberg and Magg (1999), Gawande and Bandyopadhyay (2000), and Echer and Osang (2002), who all found that the basc GH model wthout labor market nfluences predcts U.S. trade polcy well. Ths data set has the major advantage of lettng us drectly nvestgate whether model msspecfcaton s responsble for the fndng that the ntroducton of extraneous labor market varables does not mprove the emprcal model ft. On the downsde, 1983 was a recesson year n the Unted States and therefore may be unrepresentatve of the lnk between economc data and U.S. trade polcy over a longer perod. On the other hand, the fact that the early 1980s were marked by a deep recesson may help explan why the protecton-for-sale model has been found to work well for 1983 U.S. data the government beng more sympathetc towards lobbes sufferng from the economc crss. But snce the queston we focus on s whether we can mprove upon the performance of the basc GH model wth our labor market augmentaton, data avalablty and comparablty wth the above-mentoned earler studes encourage the use of the 1983 data set.

14 To test our labor-augmented model, we need addtonal data compared wth prevous studes. We extract nformaton about wages and unonzaton from the 1983 Current Populaton Survey (CPS). These data are gven at the 3-dgt CIC level but are concorded to ther 3-dgt SIC counterparts. We keep the data set at the 4-dgt SIC level to retan as much nformaton as possble. Whenever varables are avalable only at the 3-dgt or even 2-dgt level, they are smply replcated for all 4-dgt SIC codes wthn the correspondng 3-dgt (or 2-dgt) classfcaton, 10 followng the study by Gawande and Bandyopadhyay (2000). After deletng ndustres for whch our data set was ncomplete, we are left wth 194 observatons. Descrptve statstcs and unts of measurement for key varables are provded n table 1. Lke the earler emprcal studes, we employ non-tarff barrer (NTB) coverage ratos as a measure for trade barrers. 11 Whle the use of NTBs n the protecton-for-sale model s problematc (Magg and Rodrguez-Clare, 2000), U.S. tarffs n 1983 were determned by multlateral (GATT) tarff negotatons, whereas the protecton-for-sale model assumes that a country has the power to set tarffs unlaterally, precludng the use of tarff data. The mport demand elastcty s ncluded as a component of the left-hand sde to reduce possble multcollnearty, but our results are not very senstve to ths choce (see Secton 5.3). 12 Apart from wages, unonzaton, and coverage measures, the explanatory varables n the trade protecton equaton are the mport penetraton rato and ndcator varables for unon and captal owner lobbyng and labor moblty. The mport penetraton rato s defned as value of gross mports dvded by the value of shpments. 13 To correct for the exstence of ntermedate nputs, we also use value added to substtute for (p q )F. As n Goldberg and Magg (1999) and Gawande and Bandyopadhyay (2000), estmates of who s organzed as a lobby are based on poltcal acton commttee (PAC) contrbutons data for congressonal electons , , , and (Gawande, 1995). Dvergng from prevous tests of the protecton-for-sale model, however, we use separate data for corporate PAC contrbutons and labor PAC contrbutons (for a descrpton, see Gawande, 1995) to dstngush between frm and unon lobby groups. The corporate PAC contrbutons are avalable at the 3-dgt SIC level, the labor PAC contrbutons at the 2-dgt level. To determne whether the captal owners of an ndustry lobby for trade protecton, we modfy the procedure n Gawande and Bandyopadhyay (2000): We regress corporate contrbutons dvded by profts aganst the mport penetraton rato nteracted wth 2-dgt We account for clusterng at the 3-dgt SIC level n the estmaton. 11 Gawande and Trefler provded these data. 12 Gawande provded the mport demand elastctes. The orgnal source for these elastctes s Shells, Stern, and Deardorff (1986), who based ther estmates on mport demand data for The correcton procedure to account for these varables beng generated regressors s descrbed n Gawande (1997). 13 These seres come from the NBER trade and mmgraton database.

15 14 MATSCHKE AND SHERLUND SIC dummes. Industres wth postve coeffcents are assumed to have an actve captal owner lobby. Smlarly, to determne whether trade unons n an ndustry lobby for trade protecton, we regress trade unon contrbutons dvded by wage blls aganst the mport penetraton rato nteracted wth 2-dgt SIC dummes. Industres wth postve coeffcents are assumed to have an actve trade unon lobby. In our senstvty analyss, we experment wth alternatve ways of determnng who lobbes. To obtan the remanng varables, we employ CPS data from One mportant aspect of these data s the percentage of unon workers. In the sample of manufacturng ndustres, 27.9% of workers were unon members n Unonzaton vares wdely across ndustres, wth percentages between 0 and nearly 100. Equally mportant for our model s the queston of how many workers are covered by collectve barganng agreements. Unfortunately, a major problem wth the CPS data s that, after workers n the outgong rotaton groups were asked whether they were unon members, only those workers who answered no were then asked whether they were covered by a collectve barganng agreement. The BLS assumed that unon workers were covered. For ths reason, the BLS s reported coverage ratos have always exceeded actual unonzaton rates. In fact, accordng to newer nformaton obtaned from the BLS, when unon workers were asked n 2001 whether they were covered by a collectve barganng agreement, only 85% of unon workers answered yes. It seems reasonable to assume that unon workers who dd not work at the tme of the CPS survey were not covered by a collectve barganng agreement. When ths assumpton s made, we fnd that 7.8% of the unon workers are not covered. Ths number can be vewed as a lower bound on the percentage of uncovered unon workers because at any tme there are also unon workers employed n frms that are not yet subject to collectve barganng. Unon and non-unon wages for the dfferent ndustres are calculated usng hourly wage data from the CPS, adjusted for worker characterstcs. These hourly wages are then adjusted by multplyng by annual work tme to obtan an annual wage bll per worker. To w calculate the unon barganng strength s, we use s = w from (2.4). 15 (p q )F A w L A We experment wth several approaches to decde whch ndustres have moble labor. We could wrte down the equlbrum tarff equaton wthout decdng whch ndustres have moble or mmoble labor, but then we would need sound estmates of wage and employment elastctes n the unonzed and non-unonzed sectors for the dfferent ndustres. Because we do not have such estmates, we adopt the approach of sortng ndustres nto moble and mmoble classes, but we perform extensve senstvty analyss to account for the arbtrarness of such sortng. In our basc specfcaton, we dentfy moble ndustres based on 14 From the NBER data dsk Current Populaton Survey: Merged Outgong Rotaton Groups In practce, s need not always le between 0 and 1 when calculated ths way. We therefore rescale s to mpose ths condton.

16 ndustry unemployment rates an ndustry s consdered moble f the unemployment rate does not exceed 10%. In our senstvty analyss, we explore alternatve methods of defnng moble ndustres. Table 2 reports means for several key varables across our captalst lobby, trade unon lobby, and labor moblty classfcatons. The man result s that trade protecton ( τ 1+τ ) depends not only upon our measure of captalst lobby actvty and the mport penetraton rato, but also upon our measures of trade unon actvty and labor moblty. As wth the earler emprcal studes, we use the same nstruments for the endogenous varables, plus the captal-labor rato and the relatve barganng strength of the trade unon. The nstruments nclude factor shares (defned as factor revenues dvded by producton value) for physcal captal, nventores, engneers and scentsts, whte-collar labor, sklled labor, semsklled labor, cropland, pasture, forest, coal, petroleum, and mnerals, as well as seller concentraton, seller number of frms, buyer concentraton, buyer number of frms, scale, captal stock, unonzaton, geographc concentraton, and tenure (see Trefler, 1993) Estmatng and Testng the Model 5.1. Methodology. We estmate and compare the GH specfcaton,.e., (3.2) wth β 3 = 0, to the labor-augmented full specfcaton (3.2) and the labor-augmented short specfcaton (3.3). Several complcatons arse n estmatng the econometrc model. Frst, our measure of trade protecton s censored, requrng the use of lmted dependent varable methods. Second, components of the explanatory varables are endogenously determned, thereby suggestng that we mplement nstrumental varables technques. To ths end, we use the approach of Smth and Blundell (1986) to estmate a Tobt model wth endogenous explanatory varables (Wooldrdge, 2001, provdes a dscusson). Last, certan components of our explanatory varables (k, n, and m ) are constructed. We therefore explore the senstvty of our results to dfferent varable formulatons. The frst step n mplementng the Smth and Blundell approach s to estmate the resduals from the nstrumental varable equatons. Lettng z denote the column vector of nstruments and x the column vector of (endogenous) explanatory varables for ndustry, the estmated resduals are gven by ˆv = x z ˆΠ, wth ˆΠ = (Z Z) 1 Z X (equaton-by-equaton OLS). The second step then nvolves estmatng the Tobt model τ 1+τ = max {0, x β + ˆv γ + ε } wth the estmated resduals as addtonal explanatory varables. We then need to adjust the usual Tobt varance-covarance matrx for the frst-stage estmaton (see Smth and Blundell, 1986, and Amemya, 1979, for the exact form). If γ 0 (where the test of weak exogenety uses the unadjusted Tobt varance-covarance matrx), we reject the null hypothess of weakly exogenous x s. Varous studes suggest that the mport penetraton rato n our model s an endogenous varable. That s, not only does mport penetraton affect trade protecton, but

17 16 MATSCHKE AND SHERLUND trade protecton n turn nfluences mport penetraton, hgher trade protecton leadng to lower mport penetraton. Furthermore, captalst and unon lobbyng are endogenously determned n the model. Wages, employment, and trade protecton per ndustry are ntrnscally lnked and thus endogenous. We therefore treat each of our explanatory varables as endogenous. 16 Our nstruments do a decent job of explanng varaton n our endogenous explanatory varables Results. Parameter estmates are reported n table 3. As shown, our labor market varable s ndeed an mportant determnant of trade protecton. We reject the null hypothess that the labor market has no effect on trade protecton (β 3 = γ 3 = 0), as evdenced by a Wald test score (p-value) of (.0012). Hence, our estmaton results favor the labor-augmented model, and so labor mmoblty ssues and trade unon lobbyng ndeed seem to nfluence trade polcy. Also, as table 1 shows, the redstrbutve labor market varable can be qute szable. Interestngly, the average labor market component n the sample s negatve, so that (wth fxed coeffcents) accountng for trade unon actvty and labor mmoblty reduces the average n-sample tarff predcton. Further, we fal to reject the null that β 2 = β 3 = γ 2 = γ 3 wth a Wald statstc of 4.31 (.1159). Thus, we cannot reject the short specfcaton n favor of the full specfcaton. For all three specfcatons, β 1 < 0 and β 2 > 0 to statstcally sgnfcant degrees, and β 0 = 0 cannot be rejected, all of whch s n accordance wth our theory. All three models explan a sgnfcant porton of the varance n our trade protecton measure because Wald tests reject the null hypothess that all the coeffcents are zero, that s, β = 0. We also reject the null hypothess of weakly exogenous explanatory varables (γ = 0). We margnally reject the null hypothess that β 1 + β 2 0 n the labor-augmented specfcatons, n contrast to the basc GH specfcaton n whch the pont estmate of β 1 + β 2 s negatve. Under the GH specfcaton, we estmate the structural parameters, Θ and a, to be 1.13 and 706. These estmates compare to estmates of 0.77 and 321 under the short specfcaton (and and n the full specfcaton). We cannot reject the null hypotheses that Θ [0, 1] and a 0 at any standard sgnfcance level level. 18 Thus, the government places much more weght on gross socal welfare around 99.7% of total weght than on poltcal contrbutons. Stll, our estmate of the weght on contrbutons n the domestc welfare functon s hgher than that found n the GH specfcaton. Also, we estmate the percentage of the populaton organzed as a lobby at about 77%, whch s 16 Contrary to the approach of Goldberg and Magg (1999), we treat entre explanatory varables as endogenous, not just components of the explanatory varables. In other words, we treat F F M, k M, and labvar as endogenous, nstead of F M, k, m, n, etc. In fact, n the 2SLS framework, one can show that a nonlnear functon of ftted values s not the same as ftted values of a nonlnear functon. 17 Frst-stage R 2 values range from 0.16 to 0.18, so that we reject the null of weak nstruments. 18 Standard errors are calculated usng the Delta method.

18 much lower and thus more realstc than n the basc GH specfcaton whch s subject to omtted varable bas. Most lkely, our structural parameter estmates are stll too hgh, but the labor augmentaton has brought down the estmates consderably. Together wth the fact that all the estmated coeffcents have the correct sgns and are sgnfcant, our results provde strong support for the labor-augmented protecton-for-sale model Senstvty Analyss. In table 4, we consder several alternatves to the varable formulatons used n table 3. We report results for the short specfcaton only, but also provde Wald test results of the restrctons mpled by the GH and short specfcatons. Overall, we fnd that our estmates are qute robust to these alternatves. We frst consder alternatves to our unemployment-based labor moblty ndcator varable moblty observed from the Panel Study of Income Dynamcs (PSID), moblty based on average worker tenure, complete labor mmoblty n all ndustres, and complete labor moblty n all ndustres. 19 For moblty based on the 1983 PSID, we treat any household that reports changng jobs and occupatons as moble. Alternatvely, any household that reports changng jobs but not occupatons or reports keepng the same job s treated as mmoble. 20 An ndustry s then classfed as moble f at least 40% of ts workers are moble. As a second measure usng the PSID, we compare ndustry classfcatons from 1983 to Household heads and spouses who report changng ndustres are consdered moble; those who report no change are treated as mmoble. An ndustry s then consdered moble f at least 55% of ts workers are moble. We also defne an alternatve labor moblty measure based on average worker tenure n an ndustry. If average tenure s below 5 years, we classfy labor of an ndustry as moble. In each alternatve specfcaton, the parameter estmates obtan the correct (statstcally sgnfcant) sgns. We reject the GH restrcton and fal to reject the restrcton mposed by the short specfcaton whenever labor s not completely moble, and the estmates of the structural parameters Θ and a are always consderably lower than n the GH specfcaton reported n table 3. Next, we examne the senstvty of our results to the defnton of actve captalst lobbyng. We consder two alternatves to our regresson-based approach: the ndustry organzaton ndcator from Gawande and Bandyopadhyay (2000) and the poltcally organzed ndcator from Goldberg and Magg (1999). Not surprsngly, the GB formulaton produces results very smlar to our orgnal specfcaton because our captalst lobby ndcator varable was constructed n much the same manner as GB s. GM s formulaton, however, yelds dfferent results. The parameter estmate for β 2 s only margnally statstcally sgnfcant, and the structural parameter estmates have far larger standard errors 19 We also consdered moblty based on nter-ndustry wage dfferentals and average worker age. These results, not reported here, are smlar to those n table The PSID collects ths nformaton only when a household head enters the sample. The response s then carred forward wth no updatng as long as the household head remans n the sample. 17

19 18 MATSCHKE AND SHERLUND than any results we have seen so far. We should note that the constructon of the GM poltcal organzaton dummy s based on a threshold of corporate contrbutons and does not reflect per-value-added nfluence or cost; sze probably matters here. We also explore dfferent defntons for actve trade unon lobbyng, based on contrbutons dvded by ndustry wage bll and contrbutons per unon worker. Agan, the parameter estmates have the correct (statstcally sgnfcant) sgns. In each case, we reject the restrcton mposed by the GH model and fal to reject the restrcton mpled by the short specfcaton. Moreover, the estmates of Θ and a are close to our orgnal results. We also compare our estmaton results wth results usng Gawande s corrected mport demand elastctes on the rght-hand sde of the estmatng equaton (as n Gawande and Bandyopadhyay, 2000). The parameter estmates for β 1 and β 2 have the rght sgns and are sgnfcant. We reject the GH specfcaton n favor of the full specfcaton, we cannot reject the short specfcaton n favor of the full specfcaton, and the structural parameter estmates each take on values smlar to those already reported. Overall, our estmaton results are qute robust to the choce of labor moblty measure and captalst and trade unon lobby measures. We also show that our results are nsenstve to how the mport demand elastcty s treated n estmaton. 6. Concluson In ths paper, we show how trade unon lobbyng, collectve barganng, and dfferences n labor moblty across ndustres can be ncorporated nto the protecton-for-sale model n a theoretcally consstent manner to generate emprcally verfable mplcatons. We demonstrate that, for tests of the mportance of varables beyond the ones n the basc protecton-for-sale model, prevous emprcal studes suffer from model msspecfcaton. We show that trade unon actvty leads to a redstrbuton of protecton rents between captal owners, unon workers, and non-unon workers whch ntroduces labor market varables nto the equlbrum tarff equaton. We test the predctons of our laboraugmented model aganst the GH model usng the same 1983 manufacturng data set, whch has been used extensvely n the lterature to test the protecton-for-sale model, and fnd that labor market varables have a sgnfcant mpact on trade polcy once they have been approprately controlled for. Moreover, we fnd that the estmated structural parameters of the protecton-for-sale model (percentage of populaton represented by lobbes and weght on domestc welfare n the governmental welfare functon) are lower and thus more realstc than n the GH model, although they probably stll le above ther true values. Addtonal augmentatons of the GH model may be needed to arrve at more realstc estmates. Ultmately, ths caveat asde, we fnd that trade unon actvty and labor moblty, n addton to the mport penetraton rato, mport demand elastcty, and captalst lobby actvty, ndeed play mportant roles n the determnaton of trade polcy.

20 Several mportant extensons of our work seem noteworthy. Frst, an applcaton usng more-recent data would be nterestng. Second, a theoretcal underpnnng mappng poltcal contrbutons to trade unon and captalst lobby actvty would be useful. Thrd, good estmates of wage and employment elastctes would elmnate the need to defne moble and mmoble ndustres. Last, our model seems partcularly well suted to those countres outsde the Unted States for whch collectve barganng, trade unon lobbyng, and labor moblty are sgnfcant ssues. 19

21 20 MATSCHKE AND SHERLUND Appendx A. Tables Table 1. Descrptve Statstcs Varable Name Unt Mean Medan Std. Dev. Mnmum Maxmum τ rato τ 1+τ none F M none , F k M none , labvar none , Annual w $1, Annual w $1, Import demand elastcty absolute value Imports $100 mllon Shpments $100 mllon , Unon shpments $100 mllon Value added $100 mllon Labor force thousands Covered unon percent Covered non-unon percent Covered percent Unonzed percent