Market Integration and Strike Activity

Transcription

1 Market Integration and Strike Activity Ana Maleon FNRS and CEREC, Facltés Universitaires Saint-Lois; and CORE. Vincent Vannetelbosch FNRS and CORE, Université catholiqe de Lovain. April 2005 Abstract We consider a two-contry model o wage determination with private inormation in nionized imperectly competitive indstries. We investigate the eects o separated prodct markets opening p or competition as well as o rther market integration on the negotiated wage and the maximm delay in reaching an agreement. From an initial sitation o reciprocal intra-indstry trade, an increase in prodct market integration will decrease the maximal delay in reaching an agreement. However, markets opening p or competition have an ambigos eect on both the wage otcome and the maximm real delay time in reaching an agreement. Keywords: economic integration, prodct market competition, wage bargaining, strike activity. JEL Classiication: C78, F15, J50, J52, L13. Ana Maleon and Vincent Vannetelbosch are Research Associates o the National Fnd or Scientiic Research (FNRS), Belgim. Vincent Vannetelbosch is Associate Fellow o CEREC, Facltés Universitaires Saint-Lois. Corresponding athor address : CORE, Université catholiqe de Lovain, Voie d Roman ays 34, B Lovain-la-Neve, Belgim. vannetelbosch@core.cl.ac.be, Tel: , Fax:

2 1 Introdction The labor market implications o Eropean integration are o considerable importance. Since labor is not very mobile in Erope, the eects o international integration on labor markets are mostly indirect via prodct market integration. More competitive prodct markets wold redce the power in national labor markets, making them more competitive. Andersen, Haldrp and Sørensen (2000) have ond that integration gradally changes labor market strctres and indces wage convergences as well as stronger wage interdependencies in wage ormation among Eropean contries. 1 Empirical literatre sggests that indstry-speciic actors are key determinants o strike activity. Key determinants are, among others, the type o indstry, the indstry or market size, the indstry concentration, and the international competition. See e.g. Tracy (1986), Abowd and Tracy (1989), Cramton and Tracy (1994) who have stdied the determinants o U.S. labor disptes. Despite this evidence, the theoretical literatre on wage bargaining in indstries with market power has neglected the analysis o the relationship between strike activity and market integration. In the present paper we investigate the eects o separated prodct markets opening p or competition as well as o rther market integration on wages and strikes. 2 In order to do it, we consider a two-contry model o wage determination with private inormation in nionized imperectly competitive indstries. In the literatre, prodct market integration has been interpreted as a redction in costs associated with international trade: transport costs, taris, taxes, inormation costs abot oreign markets, etc. These costs cold be divided into ixed costs or start p costs associated with exporting, and variable costs proportional to the level o exports. Naylor (1998) has shown that a decrease in variable export costs may give rise to a higher wage since a monopoly nion responds by increasing the wage rate to the increased employment s demand. However, Hizinga (1993) and Sørensen (1993) have shown that a decrease in ixed costs, that implies the move rom atarchy to lly integrated markets, wold increase the degree o competition in the prodct market and, as Dowrick (1989) 1 Ctcher-Gersheneld, Kochan and Calhon-Wells (1998) have examined or the U.S. nion and management perceptions o actors heavily inlencing negotiations or the process in collective bargaining and its otcomes. The observations sggest that, beside other actors sch as alling real wages, ear o job loss, and increased domestic competition, the increased international competition is a central eatre motivating the parties to reach agreements. 2 Maleon and Vannetelbosch (2003) have analyzed in a closed oligopolistic indstry how prodct dierentiation and market competition aect the actal strike dration and the eiciency loss incrred dring wage negotiations. I bargaining takes place at the irm-level, strike activity is increasing with the degree o prodct dierentiation and is smaller nder Bertrand than nder Cornot competition. 1

3 predicted, wold redce wages. More recently, Mnch and Skaksen (2002) have shown that a redction in ixed costs leads to an nambigos decrease in wages, whereas a redction in variable trade costs has an ambigos eect on wages, de to the act that the introdction o international competition or some goods netralizes the eect on the employment s demand. Bt, all these previos papers have sed complete inormation models which predict eicient otcomes o the bargaining process. In particlar agreement is always settled immediately, so that strikes cannot occr at eqilibrim. 3 This is not the case once we introdce private inormation into the wage bargaining, in which the irst ronds o negotiation are sed or inormation transmission between the two negotiators. The main eatre o or model is that both the nion and the irm have private inormation. Or model enables s to stdy the impact o prodct markets opening p or competition as well as o rther market integration on wages and strikes. To describe the wage bargaining process, we adopt Rbinstein s (1982) alternating-oer bargaining model with two-sided incomplete inormation, which allows the occrrence o strikes at eqilibrim. From an initial sitation o reciprocal intra-indstry trade, we show that an increase in prodct market integration will have an ambigos eect on wages even in case o bargaining with complete inormation. In this case, i markets are weakly integrated, an increase in prodct market integration will decrease wages. However, i markets are strongly integrated, an increase in prodct market integration will increase wages. This ambigos relationship between wages and market integration is observed both when nions maximize the srpls as in Naylor (1998) or when nions simply maximize the wage. Naylor (1998) has shown that an increase in prodct market integration will nambigosly increase wages whenever only nions decide over wages. Ths, Naylor s reslts with a monopoly nion are not robst to a right-to-manage model where the nion and the irm negotiate over the wage. With respect to strike activity, we show that an increase in prodct market integration will decrease the maximal delay in reaching an agreement. We also compare the sitation where markets are separated to the one where markets are lly integrated. In case o bargaining with complete inormation, wages and prices will decrease while consmer srpls, proits and total qantities sold in each contry will increase. Bt, once the nion and the irm have private inormation, the wage otcome when markets are lly integrated is not necessarily smaller than the wage otcome when markets are separated. Moreover, markets opening p or competition have an ambigos eect on the maximm real delay time in reaching an agreement. Indeed, each nion-irm 3 Strikes data seem to have a signiicant impact on the wage-employment relationship or collective negotiations. See Kennan and Wilson (1989, 1993) or srveys o bargaining models with private inormation and their relation to strike data. See Kennan (1986) or a srvey o the empirical reslts on strike activity. 2

4 pair expects to be able to alter its relative wage position in order to gain a larger share o the prodct market in each contry. 4 This incentive is stronger the more integrated the markets are since now a wage decrease makes the nion-irm pair winning a more sbstantialmarketshareoitsrival. Thisexplainwhyitislikelythatmoreconcessionsand less conlicts in wage negotiations wold occr once markets become integrated. However, markets opening p raise the potential payos or the nion and the irm, and in expanding the payo set (or range o possible payos), also increase the scope or delay (longer strikes and lockots may be needed or screening the private inormation). The paper is organized as ollows. In Section 2, the model is presented. Section 3 describes the wage bargaining game and solves this game or the case o complete inormation. It also analyses the relationship between wages and market integration. Section 4 is devoted to the wage bargaining game with private inormation. Section 5 derives the maximal delay in reaching an agreement. Finally, Section 6 concldes. 2 The model Following Naylor (1998), we assme that there are two identical contries (A and B) and that in each contry there is one irm (irm 1 in contry A and irm 2 in contry B) prodcing some homogeneos good. We assme that prodct demand is linear: A = a b(x 1A + X 2A ), B = a b(x 1B + X 2B ), where i is the price o the homogeneos good in contry i, X 1A is prodction by irm 1 or consmption in contry A, X 2A is prodction by irm 2 or consmption in contry A, X 1B is prodction by irm 1 or consmption in contry B, X 2B is prodction by irm 2 or consmption in contry B. There is a constant cost o T per nit o the commodity exported. We interpret this cost as captring all costs associated with international trade, sch as transactions, transport and tari costs. Let T be the pper limit on T sch that or T T there is intra-indstry trade in which both X 1B > 0 and X 2A > 0. We will mainly ocs on three cases: markets are lly integrated (T =0), markets are integrated (T (0, T ]), or markets are separated (T = ). Each irm regards each contry as a separate market and chooses the proit-maximizing qantity or each market separately, and on the Cornot assmption that the other irm s otpt in each market is given. 4 Davidson (1988) and Horn and Wolinsky (1988) were irst to stdy the impact o wage spillover eects on the interaction o nion-irm bargaining and dopolistic qantity-setting. Dowrick (1989) has stdied how prodct market power and proitability are related to wages. 3

5 rodction technology exhibits constant retrns to scale with labor as the sole inpt and is normalized is sch a way that (X ia + X ib )=L i,wherel i is labor inpt. The total labor cost to irm i o prodcing qantity (X ia + X ib ) is (X ia + X ib ) W i,where W i is the wage in irm i. Ths, irm 1 s proits and irm 2 s proits can be, respectively, written as Π 1 = ( A W 1 )X 1A +( B W 1 T )X 1B, Π 2 = ( A W 2 T )X 2A +( B W 2 )X 2B, where T is the constant nit trade cost. Each irm is nionized and each nion is assmed to maximize the wage rate. The reservation wage is set eqal to zero in each contry. 5 Hence, U 1 = W 1 and U 2 = W 2. This wold imply that the nion places no weight on employment. Althogh this may seem implasible, the notion that, in negotiating wages, nions do not take into accont the employment conseqences o higher wages has a long tradition inclding the inlential work o Ross (1948), and is oten stated by nion leaders today (encavel, 1991). This assmption is made to obtain closed-orm soltions in order to carry ot the analysis nder incomplete inormation. Cramton and Tracy (2003) have conclded that disptes largely are motivated rom the presence o private inormation and the sharply conlicting interests o the nion and the irm over the wage. In the appendix we show that or reslts nder complete inormation are robst to an alternative speciication where nions maximize the economic rent L i W i. Moreover, Maleon and Vannetelbosch (2005) have shown that, i the nion is not too strong (in act, the range o nion bargaining power we will consider), it is optimal or the nion that maximizes the rents to send to the negotiation table delegates who maximize the wage. 6 Interactions between market integration and wage bargaining are analyzed according to the ollowing game strctre. In stage one, wages are negotiated at the irm-level in both contries. Within each contry the nion and the irm negotiates a wage taking as given the wage set in the other contry and taking into accont the irm s labor 5 It can be shown that all reslts are qalitatively robst to this assmption. 6 Maleon and Vannetelbosch (2005) have developed a model o wage determination with private inormation, in which the nion has the option to delegate the wage bargaining to either srpls-maximizing delegates or to wage-maximizing delegates (sch as senior nion members). Maleon and Vannetelbosch (2004) have considered a nionized dopoly model to analyze how nions aect the incentives or merger when srpls-maximizing nions have the option to delegate the wage bargaining to wage-maximizing delegates (sch as senior nion members). One o their reslts is that, in case o linear demands, the nion in each irm will choose a wage-maximizing delegate i and only i the nion bargaining power is not too strong, α.81. 4

6 demand nction. In stage two, each irm chooses its otpt (and hence employment) levels or the separate prodct markets, taking as given both (i) the otpt decisions o the other irm and (ii) the negotiated wages. The two-stage game makes the model an appropriate description o a sitation in which wages are determined or a relatively long period while prodction decisions are made or a relatively shorter period. The model is solved backwards. In the last stage o the game, the wage levels have already been determined. Both irms compete by choosing simltaneosly their otpts (and hence, employment) to maximize proits with price adjsting to clear the market. In case markets are integrated, the niqe Nash eqilibrim o this stage game yields: X 1A (T ) = max[ 0] a + T 2W1 + W 2,, 3b X 2A (T ) = max[ 0] a 2T 2W2 + W 1,, 3b X 1B (T ) = max[ 0] a 2T 2W1 + W 2,, 3b X 2B (T ) = max[ 0] a + T 2W2 + W 1,. 3b The Nash eqilibrim otpts o a irm (and hence, eqilibrim level o employment) are decreasing with its own wage, bt are increasing with the other irm s wage and total indstry demand. In case markets are lly separated, the niqe Nash eqilibrim o this stage game yields: X 1A (T = ) = max[ 0] a W1,, 2b X 2A (T = ) = 0, X 1B (T = ) = 0, X 2B (T = ) = max[ 0] a W2,. 2b 3 Wage bargaining with complete inormation Union-irm pairs condct simltaneos negotiations. Two assmptions are made. First, when one set o negotiations is taking place, the agents are naware o any proposals made (or settlement reached) in related negotiations. Second, the prodction and market competition occr only when either both irms have come to terms with their workers or when 5

7 one irm settles with its nion and the other nion decides to leave the bargaining table orever. Hence, each nion-irm pair takes the decisions o its rivals as given while condcting its own negotiation. Moreover, each nion-irm pair always correctly anticipates the eect o wages on the sbseqent market competition. Each negotiation proceeds as in Rbinstein s (1982) alternating-oer bargaining model. The irm and the nion make alternatively wage oers, with the irm making oers in oddnmbered periods and the nion making oers in even-nmbered periods. The length o each period is. The negotiation starts in period 0 andendswhenoneothenegotiators accepts an oer. No limit is placed on the time that may be expended in bargaining and perpetal disagreement is a possible otcome. The nion is assmed to be on strike in every period ntil an agreement is reached. Both the irm and the nion are assmed to be impatient. The irm and the nion have time preerences with constant discont rates r > 0 and r > 0, respectively. 7 To captre the notion that the time it takes to come to terms is small relative to the length o the contract, we assme that the time between periods is very small. This allows a stdy o the limiting sitations in which the bargaining procedre is essentially symmetric and the potential costs o delaying agreement by one period can be regarded as negligible. As the interval between oers and conteroers is short and shrinks to zero, the alternating-oer model has a niqe limiting sbgame perect eqilibrim, which approximates the Nash bargaining soltion to the bargaining problem (see Binmore, Rbinstein and Wolinsky, 1986). Ths the predicted wages are given by W SE 1 = argmax[ [ U1 U1]α 0 Π1 Π 0 1]1 α W SE 2 = argmax[ U2 U 0 2]α [ Π2 Π 0 2]1 α where Ui 0 =0and Π 0 i =0are, respectively, the disagreement payos o the nion and r the irm. The parameter α (0, 1) is the nion bargaining power which is eqal to r +r. When markets are integrated we shall restrict or attention to the case o symmetric pre strategy eqilibria associated with reciprocal intra-indstry trade in which both X 1B > 0 and X 2A > 0. The necessary and sicient condition or reciprocal intra-indstry trade is F(α, T) > 0, wheref(t,α)=4(2a T) 2 (2 α) 2 8(2a 2 2aT +5T 2 )α(4 3α). 7 Two versions o Rbinstein alternating-oer bargaining model captre dierent motives that indce parties to reach an agreement rather than to insist indeinitely on incompatible demands. In a irst version the parties incentive to agree lies in the act that they are impatient : player i is indierent between receiving x exp( r i ) today and x tomorrow, where r i > 0 is player i s discont rate. In a second version the parties are not impatient bt they ace a risk that i agreement is delayed then the opportnity they hope to exploit jointly may be lost : player i believes that at the end o each bargaining period there is a positive probability 1 exp( r i ) that the process will break down, r i > 0. So, r i can be interpreted either as player i s discont rate or as his estimate abot the probability o a breakdown o the negotiations. 6

8 Assmption 1 When markets are integrated, there is intra-indstry trade in which both X 1B > 0 and X 2A > 0. That is, F (α, T ) > 0. Ths, the pper limit T sch that or T T there is reciprocal intra-indstry trade is given by 4a(1 α) T(α) =. (2(1 α)+3 α(4 3α)) The assmption involves that, given tari costs T, the nion bargaining power is below some critical level α given by α(t )= 16a(a T )+22T 2 6T 4a(a T )+10T a(a T )+31T 2 Notice that as the demand parameter a becomes very large, α approaches 1. Then, the eqilibrim wages and nions tilities are That is, Wi SE (α, T) = 2(2a T )(2 α) F (α, T) = U i (α, T), i =1, 2. (1) 4(4 3α) Wi SE (r,r,t)= (2a T )(r +2r ) G(r,r,T) = U i (r,r,t), i =1, 2, (2) 2(r +4r ) where G(r,r,T)=16ar(a 2 T ) (9r 2 +36r r 4r)T 2 2.RemarkthatG(r,r,T) > 0 is the necessary and sicient condition or reciprocal intra-indstry trade when α is expressedintermsor and r.weobtainthat ( ) Wi SE (α, T ) > 0 T> 2a 3 10(α 2) 20(α 1) (1 α) T (α). T 5(4+α(31α 44)) We have that T (α) is decreasing with the nion bargaining power α and T (α) < T (α). The relation between wages and the level o market integration is depicted in Figre 1 with a =2. roposition 1 I markets are weakly integrated (T > T (α)) an increase in prodct market integration will decrease wages. However, i markets are strongly integrated (T < T (α)) an increase in prodct market integration will increase wages. This reslt is de to a tradeo between two eects. First, when markets are integrated, each nion-irm pair expects to be able to alter its relative wage position. Each nionirm pair has an incentive to lower wages in order to gain a larger share o the prodct market in each contry. Second, an increase in market integration indces that, or given 7

9 Wages Cost o trade T Figre 1: The relation between wages and prodct market integration. wages, irms ace lower costs when exporting goods, which in trn transorms into higher demand or labor. The nion then exploits the higher labor demand to obtain higher wages rom negotiations. Depending on the degree o market integration one eect will dominate the other one. In the appendix we show that this relationship is also observed nder an alternative speciication where nions maximize the srpls as in Naylor (1998). Ths, Naylor s reslts with a monopoly nion are not robst to a right-to-manage model. Naylor (1998) has shown that, i markets are integrated, an increase in prodct market integration will nambigosly increase wages. Eqilibrim otpts when markets are integrated are given by X1A(α, T ) = X2B(α, T )= 8a(1 α)+2t (10 7α)+ F(α, T ), 12(4 3α)b X1B(α, T ) = X2A(α, T) = 8a(1 α) T (28 22α)+ F(α, T ). 12(4 3α)b roits and prices are Π i (α, T )= (1 α)[16a 2 (1 α) 16aT (1 α)+2t 2 (38 29α)+(2a T ) F(α, T ) ], 9(4 3α)b 2 (3) or i =1, 2, and i (α, T )= 2a(8 5α)+4T (1 α)+ F(α, T ), i = A, B. 6(4 3α) Consmer srpls is eqal to )2 (4(2a T)(1 α)+ F (α, T) CS i (α, T) = 72(4 3α) 2 b 8, i = A, B.

10 The consmer srpls is increasing with an increase in prodct market integration. When markets are separated, eqilibrim wages and nions tilities are That is, W SE i (α, T = ) = α 2 α a = U i (α, T = ), i =1, 2. (4) W SE i (r,r,t = ) = Eqilibrim otpts when markets are separated are given by roits and prices are Consmer srpls is eqal to r r +2r a = U i (r,r,t = ), i =1, 2. (5) X 1A (α, T = ) = X2B(α, T = ) = a (1 α) b (2 α), X 1B (α, T = ) = X 2A (α, T = ) =0. Π i (α, T = ) = a2 (1 α) 2, i =1, 2. (6) b 2 (2 α) a i (α, T = ) =, i = A, B. (2 α) CS i (α, T = ) = (2a(1 α))2, i = A, B. 8(2 α) 2 b Comparing the sitation where markets are separated (T = ) to the one where markets are lly integrated (T =0) leads to the ollowing proposition. roposition 2 When separated markets become lly integrated, wages and prices will decrease while consmer srpls, proits and total qantities sold in each contry will increase. This is similar to the indings in Hizinga (1993) and Sørensen (1993). The nderlying reason or this reslts is that irms in the two contries start to compete in a common market. This rise in the degree o competition spills over to the labor market by increasing the elasticity o labor demand. The response by the negotiators is to set a lower wage. 4 Wage bargaining with private inormation The main eatre o the negotiations is that both negotiators have private inormation. Each negotiator does not know the impatience (or discont rate) o the other party. It is common knowledge that the irm s discont rate is inclded in the set [r ],where,ri 0 <r r I, and that the nion s discont rate is inclded in the set [r,r], I where 9

11 0 <r r I. The sperscripts I and identiy the most impatient and most patient types, respectively. The types are independently drawn rom the set [ri,ri i ] according to the probability distribtion p i,ori =,. We allow or general distribtions over discont [ [ r I + r ] 1 and α = r I r [ ] + r ] 1 I. The next assmption imposes that, given tari costs T 0, T, the pper bond on rates. This ncertainty implies bonds on the nion bargaining power which are denoted by α = r the nion bargaining power is below some critical level. This assmption garantees that, or all T [ 0, T ], there is intra-indstry trade (X1B > 0 and X 2A > 0) when bargaining is with private inormation. Assmption 2 α < α(t ). Lemma 1 Consider the wage bargaining with incomplete inormation in which the distribtions p and p are common knowledge, and in which the period length shrinks to zero. Assme each nion-irm pair takes the other wage settlement in the other contry as given dring the bargaining. For any perect Bayesian eqilibria (BE), the payo o the nion i belongs to [U i (α),u i (α)] and the payo o the irm i belongs to [Π i (α), Π i (α)]. The proo o this lemma as well as o Lemma 2 may be ond in Maleon and Vannetelbosch (2005). In Lemma 1, U i (α) and Π i (α) denote, respectively, the SE tility o the nion and the SE proit o the irm o the complete inormation game, when it is common knowledge that the nion s bargaining power is α = α. In case o integrated markets, then U i (α) and Π i (α) are given, respectively, by Expression (2) and Expression (3) with α = α. In case o separated markets, then U i (α) and Π i (α) are given, respectively, by Expression (5) and Expression (6) with α = α. Similarly or α = α. Lemma 1 ollows rom Watson s (1998) analysis o Rbinstein s alternating-oer bargaining model with two-sided incomplete inormation. 8 Lemma 1 is not a direct corollary to Watson (1998) Theorem 1 becase Watson s work ocses on linear preerences, bt the analysis can be modiied to handle the present case. Translating Watson (1998) Theorem 2 to or ramework completes the characterization o the BE payos. Lemma 2 Consider the wage bargaining with incomplete inormation in which the period length shrinks to zero. For any Ũ i [U i (α),u i (α)], Πi [Π i (α), Π i (α)], there exists distribtions p and p, and a BE sch that the BE payos are Ũ i and Πi. 8 Watson (1998) characterized the set o BE payos which may arise in Rbinstein s alternating-oer bargaining game and constrcted bonds (which are met) on the agreements that may be made. The bonds and the BE payos set are determined by the range o incomplete inormation and are easy to compte becase they correspond to the SE payos o two bargaining games o complete inormation. These two games are deined by matching one player s most impatient type with the opponent s most patient type. 10

12 In other words, whether or not all payos within the intervals given in Lemma 1 are possible depends on the distribtions over types. As Watson (1998) stated, Lemma 1 and Lemma 2 establish that each player will be no worse than he wold be in eqilibrim i it were common knowledge that he were his least patient type and the opponent were hismostpatienttype. Frthermore,eachplayerwillbenobetterthanhewoldbein eqilibrim with the roles reversed. Since we allow or general distribtions over types, mltiplicity o BE is not an exception. From Lemma 1 we obtain roposition 3 and roposition 4. roposition 3 For any distribtion over types, BE wage bargaining otcomes in case o integrated markets, W (α, α, T ), satisy the ollowing ineqalities (2a T )(r +2r I ) G(r I,r,T) 2(r +4r I ) W (α, α, T) (2a T )(r I +2r) G(r,rI,T). 2(r I +4r ) (7) Notice that each wage satisying these bonds can be the otcome by choosing appropriately the distribtion over types. The lower (pper) bond is the wage otcome o the complete inormation game, when it is common knowledge that the nion s type is r I (r ) and the irm s type is r (r I ) (and the nion bargaining power is α (α)). For many distribtions over types, there is a wide range o BE: there are BE in which the wage is close to the pper bond and there are BE in which the wage is close to the lower bond (see below or some intition). Expression (7) implies bonds on the irm s employment level, as well as on the irm s otpt, at eqilibrim. roposition 4 For any distribtion over types, BE wage bargaining otcomes in case o separated markets, W (α, α, T = ), satisy the ollowing ineqalities r r a W (α, α, T = ) a. (8) +2r I r I +2r r I In complete inormation, wages will decrease and consmer srpls will increase when markets open p or competition and become lly integrated. Bt once the nion and the irm have private inormation, these complete inormation reslts do not necessarily hold. Corollary 1 In case o nion-irm bargaining with private inormation, the wage otcome when markets are lly integrated is not necessarily smaller than the wage otcome when markets are separated. 11

13 The necessary and sicient condition to recover the complete inormation reslt that the wage otcome when markets are lly integrated is smaller (whatever the distribtion over types) than the wage otcome when markets are separated is α > α 2 α or 2r r >r I r I. (9) which is obtained by comparing the lower bond rom (8) with the pper bond rom (7) when T =0. The larger the amont o private inormation α α is, the less likely the necessary and sicient condition (9) will be satisied. Indeed, when the amont o private inormation is large enogh, one can always ind probability distribtions over types sch that there is a BE wage when markets are lly integrated which is higher than some BE wage when markets are separated. Ths, markets opening p or competition have an ambigos eect on wages. Nevertheless, the stronger the nion is (higher α), the more likely the contry s wage will decrease when markets open p or competition. The previos analysis establishes bonds on the BE payos, bt it says nothing abot the possible payo vectors inside the bonds. It wold be interesting to stdy the set o payos and the set o wages that are spported by perect Bayesian eqilibria in the wage bargaining game which is close to having complete inormation. Sppose there are three possible types or both the nion and the irm: ri, r i, ri i where r i <r i <ri I, or i =,. Sppose the distribtion over these types( i) r i,r i is (β,1 2β,β) or both,ri the nion and the irm; β is the probability that player i s discont rate is ri, 1 2β is the probability that player i s discont rate is r i,andβ is the probability that player i s discont rate is ri I. Then, we might wish to know how the set o BE payos or the wage otcomes change as β converges to zero, where there is only a slight chance that player i is either o type ri or type ri I. From Watson s (1998) Theorem 4 and Theorem 5, it ollows that, as β converges to zero, BE wage otcomes satisy the bonds in Expression (7) and Expression (8) with ri = r i. There are BE in which the wage is close to the pper bond W SE (r ) and there are BE in which the wage is close to the lower,ri bond W SE (r,r I ). Ths, BE wages do not converge to a single wage, despite that the distribtion over types converges to a point mass distribtion. 9 9 This lopsided convergence ollows rom the constrction o BE strategies, where players will pnish one another i they depart rom their eqilibrim strategies. An eective orm o pnishment in the bargaining game is that when a player takes some deviant action, belies abot him are pdated optimistically -ptting probability one on his weakest type. The existence o a very impatient type (a type near r I i as compared to r i ) allows the threat o sch a revision o belies, however small is the probability o the impatient type. The existence o a very patient type has little eect, since it wold not be sed in pnishing a player. 12

14 5 Maximaldelayinreachinganagreement Ineicient otcomes are possible, even as the period length shrinks to zero. While the scope o possible ineiciency is clear rom Lemma 1 and Lemma 2, what is not so obvios is the potential or delay. The wage bargaining game may involve delay (strikes or lock-ots), bt not perpetal disagreement, at eqilibrim (see Watson, 1998). 10 In act, delay is positively related to the distance between the discont rates o the most and least patient typesotheplayers. Itherangeotypesisredced,thenthisleadstoasmallerrange o possible payos and less delay. Delay can occr even when the game is close to one o complete inormation (as the type distribtions converge to point mass distribtions). We propose to identiy strike activity with the maximm delay time in reaching an agreement. Only in average this measre is a good proxy or actal strike dration. 11 It is not ncommon in the literatre on bargaining to analyze the maximm nmber o delay time that may be expended beore reaching an agreement. 12 In the appendix we compte the maximm delay in eqilibrim which shows that an agreement is reached in inite time and that delay time eqals zero as incomplete inormation vanishes (in that ri and ri I converge). In case o integrated markets, the maximm real delay )} time in reaching an agreement is given by D(T )=min{d (T ),D (T (10) 10 Watson (1998) has constrcted eqilibria with delay in which the types o each player behave identically (no inormation is revealed in eqilibrim), players se pre strategies, and players make non-serios oers ntil some appointed date. 11 In the literatre on strikes, three dierent measres o strike activity are sally proposed: the strike incidence, the strike dration, and the nmber o work days lost de to work stoppages. See Cheng and Davidson (1991), Kennan and Wilson (1989). Since we allow or general distribtions over types and we may have a mltiplicity o BE, we are nable to compte measres o strike activity as the ones jst mentioned. 12 Cramton (1992) has constrcted a seqential eqilibrim in a bargaining model with two-sided ncertainty, where types are revealed ater a maximm o two ronds, bt where delay is directly related to the types o the players. There is also a continm o other seqential eqilibria where types are not lly revealed. Unlike in Rbinstein s model in which the time between oers is ixed, in Cramton (1992) each player can delay making oers. This ability to delay oers enables each player to commit to not revising or rescinding an oer ntil a conter-oer is made. Cai (2003) has also analyzed the maximm nmber o delay periods bt in a mltilateral bargaining. His model has a inite nmber o Markov perect eqilibria, some o which exhibiting wastel delays. The maximm nmber o delay periods that can be spported in Markov perect eqilibria increases in the order o the sqare o the nmber o players. These reslts are robst to a relaxing o the Markov reqirements and to more general srpls nctions. Asbel, Cramton and Deneckere (2002) provide a recent srvey o bargaining models with incomplete inormation. 13

15 where D (T )= 1 r log ( 4r + r I 4r I + r ) (2a T )(r +2r I ) G(r I,r,T) (2a T )(r I +2r ) G(r,r I,T) (11) is the maximm real time the nion wold spend negotiating, and D (T ) = 1 r log[( r r I )( 4r I )2 + r (12) 4r + r I 8a(a T )r )T 2 +(2a T) G(r +(9rI +38r,T),rI 8a(a T )r I +(9r +38r I )T 2 +(2a T ) G(r,r I,T) is the maximm real time the irm wold spend negotiating. In act, D (T ) (D (T )) is the maximm real time the nion (irm) wold spend negotiating in any eqilibrim i the nion (irm) was o its most patient type. So, D (T ) (D (T )) is the pper bond on the maximm time the nion (irm) o type r (r ) wold spend negotiating; maximm time that is decreasing with type r (r ). So, the more patient a player is the greater the delay that may be observed. Since D (T ) and D (T ) are positive, inite nmbers, the maximm real delay in reaching an agreement in case o integrated markets is inite and converges to zero as ri I and r i become close, or i =,. In the appendix we show that D (T ) T > 0 and D (T) T roposition 5 From an initial sitation o reciprocal intra-indstry trade (i.e. markets are integrated), an increase in prodct market integration will decrease the maximal delay in reaching an agreement. When markets are integrated, each nion-irm pair expects to be able to alter its relative wage position. That is, each nion-irm pair has an incentive to lower wages in order to gain a larger share o the prodct market in each contry. This incentive is stronger the more integrated the markets are since now a wage decrease makes the nionirm pair winning a more sbstantial market share o its rival. This explain why it is likely that more concessions and less conlicts in wage negotiations wold occr once markets become more integrated. In case o separated markets, the maximm real delay time )} in reaching an agreement is given by D(T = ) =min{d (T = ),D (T = (13) > 0. where D (T = ) = 1 r log[( 2r + r I 2r I + r )( )] r (14) r I 14

16 is the maximm real time the nion wold spend negotiating, and D (T = ) = 1 r log[( 2r I + r 2r + ri )2( r r I )2] (15) is the maximm real time the irm wold spend negotiating. Since D (T = ) and D (T = ) are positive, inite nmbers, the maximm real delay in reaching an agreement in case o separated markets is inite and converges to zero as ri I and r i become close, or i =,. Let s compare the strike activity when markets go rom separated markets to lly integrated markets. We have D (T =0)>D (T = ). The maximm real time the nion wold spend negotiating is shorter when markets are separated. However, we have D (T =0)<D (T = ). The maximm real time the irm wold spend negotiating is shorter when markets are lly integrated. Let s assme that r = r = r and r I = =.Then, ri ri D(T = ) >D(T =0) D (T = ) >D (T =0) 22r r I (r ) 2 (r I ) 2 > 0. For instance, when r =0.01 and r I =0.1 we have D (T = ) >D (T =0),btwhen r =0.001 and r I =0.1 we have D (T = ) <D (T =0). Ths, the possibility o being o a very patient type (i.e. a relatively strong negotiator) makes strikes more likely when markets open p or competition and become lly integrated. Ths, markets opening p or competition have an ambigos eect on the maximm real delay time in reaching an agreement. When markets become open, each nion-irm pair has a stronger incentive to lower wages and to concede earlier in order to gain a larger share o the prodct market in each contry. However, markets opening p raise the potential payos or the nion and the irm, and in expanding the payo set (or range o possible payos), also increase the scope or delay (longer strikes and lockots may be needed or screening the private inormation). We provide now an example abot the maximm delay. In this example we let r = r = r, r I = ri = r I, r I =0.33 r with r [0.04, 0.16] and a =2. Table 1 gives s the integerpartothemaximmdelayordierentvalesotheparametert. 13 We observe that (i) D and D are increasing with the amont o private inormation i r i r I,(ii)D and D are slightly increasing with T or T T. Notice that real delay time in reaching an agreement is not negligible: many bargaining ronds may be needed at eqilibrim beore an agreement is reached. Reslts (i) and (ii) hold in general. 13 We can interpret r i as the annal discont rate and the nmbers in Table 1 as the maximm nmber o days needed to reach an agreement. Indeed, the integer part o the maximm delays or =1/365 are exactly the nmbers o Table 1. The data in Table 1 seem consistent with U.S. strike drations reported in Cramton and Tracy (1994). 15

17 6 Conclsion T =0 T = 1 8 T = 1 4 T = 1 2 T = r D D D D D D D D D D Table 1: Maximm delay in reaching an agreement We have considered a two-contry model o wage determination with private inormation in nionized imperectly competitive indstries. We have investigated the eects o separated prodct markets opening p or competition as well as o rther market integration on the negotiated wage and the maximm delay in reaching an agreement. From an initial sitation o reciprocal intra-indstry trade, an increase in prodct market integration will decrease the maximal delay in reaching an agreement. However, markets opening p or competition have an ambigos eect on both the wage otcome and the maximm real delay time in reaching an agreement. Ths, contrary to the reslts ond in the literatre with complete inormation, we have shown that, in presence o private inormation, a redction in ixed costs (the act that prodct markets open p or competition) has an ambigos impact on the negotiated wage. So, or model sggests that one shold be catios when making policy recommendations with respect to the impact o prodct market integration on wages and employment levels. Nevertheless, this ambigity does not prevent s to draw very interesting reslts. Indeed, we have shown that the stronger the nion is, the more likely the contry s wage will decrease when markets open p or competition. Finally, notice that the possibility o being o a very patient type (i.e. a relatively strong negotiator) makes 16

18 strikes more likely when markets open p or competition. Acknowledgments We wish to thank ierre icard or valable comments. Financial spport rom Spanish Ministerio de Ciencia y Tecnología nder the project BEC , spport o a SSTC grant rom the Belgian Federal government nder the IA contract 5/26 (FUSL), and spport rom the Belgian French Commnity s program Action de Recherches Concertée 03/ (UCL) are gratelly acknowledged. This paper presents research reslts o the Belgian rogram on Interniversity oles o Attraction initiated by the Belgian State, rime Minister s Oice, Science olicy rogramming. Appendix A Unions maximizing economic rents Sppose that each irm is nionized and each nion maximizes its economic rents. Hence, U 1 = L 1 (W 1,W 2 ) W 1 and U 2 = L 2 (W 1,W 2 ) W 2. In order to get a closed orm soltion rom the wage bargaining we need to ix the nion bargaining power. For instance, let assme that the irm and the nion have eqal bargaining power: α = 1. Then, we obtain Z) 2 that the eqilibrim wage otcome is Wi SE (T,α = 1 2 )= 1 (10a 5T 16a2 16aT 59T , i =1, 2, Z where Z =64a 3 96a 2 T +552aT 2 260T 3 +21T 256a 4 512a 3 T +528a 2 T 2 272aT T 4. The relation between wages and the level o market integration is very close to the one obtained assming that nions maximize wages and is depicted in Figre 2 with a =2. B Maximal delay The negotiation proceeds as in Rbinstein s (1982) alternating-oer bargaining model. The irm and the nion make alternatively wage oers, with the irm making oers in oddnmbered periods and the nion making oers in even-nmbered periods. The negotiation starts in period 0 and ends when one o the negotiators accepts an oer. No limit is placed 17

19 Wages Cost o trade T Figre 2: Unions maximizing rents and α = 1 2. on the time that may be expended in bargaining and perpetal disagreement is a possible otcome. The nion is assmed to be on strike in every period ntil an agreement is reached. Both the irm and the nion are assmed to be impatient. The irm and the nion have time preerences with constant discont actors δ (0, 1) and δ (0, 1), respectively. It is assmed that each nion-irm pair takes the other wage settlement as given dring the negotiation. For any wage bargaining which leads to an agreement W i at period n, δ n Π i(w i,l i (W i,w j )) and δ n U(W i,l i (W i,w j )) are, respectively, irm i s payo and nion i s payo. For any wage bargaining which leads to perpetal disagreement, disagreementpayosaresettozero. { From Binmore, Rbinstein and Wolinsky (1986), the SE wage otcome is sch that Πi (T,W i,l i (W i,w j )) = δ Π i (T,W i,l i (W i,w j )) U i (T,W i,l i (W i,w j )) = δ U(T,W i,l i (W i,w j )) where W i is the SE wage otcome i the nion makes the irst wage oer, and W i is the SE wage otcome i the irm makes the irst oer. Let H(T,δ,δ )=4(1+δ 2δ δ ) 2 (2a T ) 2 8(1 δ )((1 δ (1 δ ) 2 )(2a 2 2aT +5T 2 ). Since the nion makes the irst oer, the niqe symmetric SE wages in case o integrated markets are given by W SE 4(1 δ (1 2δ ) 2 ) i (T,δ,δ )= 2(1 + δ (1 2δ ))(2a T ) H(T,δ,δ ) rom which we get the SE proits and the SE nions payos,, i =1, 2, U i (T,δ,δ ) = 2(1 + δ (1 2δ ))(2a T ) H(T,δ,δ ) Π i (T,δ,δ ) = 4(1 δ 2[, i =1, 2, (1 2δ ) 2 ) δ (1 δ ) 2(4a 2 (1 + δ 9b(1 δ (1 2δ ) 2 (1 2δ ) 2 )(1 δ ) )] )(a T )+(1+ ) 8δ + δ (1 2δ ) 2 (1 10δ ))T 2 ) (1 2δ )(2a T H(T,δ,δ. 18

20 { Similarly, the niqe symmetric SE wages in case o separated markets are given by Πi (T =,W i,l i (W i,w j )) = δ Π i (T =,W i,l i (W i,w j )) U i (T =,W i,l i (W i,w j )) = δ U(T =,W i,l i (W i,w j )) where W i is the SE wage otcome i the nion makes the irst wage oer, and W i is the SE wage otcome i the irm makes the irst oer. Since the nion makes the irst oer, the SE wage is W SE (T =,δ i,δ )= 1 δ 1 a, i =1, 2, δ δ rom which we get the SE proits and the SE nions payos, U i (T =,δ,δ )= (1 δ )a 1, i =1, 2, δ δ Π i (T =,δ,δ )= δ (1 δ ) 2 a 2 4(1, i =1, 2. δ δ ) 2 b The players have private inormation. They are ncertain abot each others discont actors. layer i s discont actor is inclded in the set[ i] δ I i,δ,where0 <δ I i δ i < 1, or i =,. We allow or general probability distribtions over discont actors. From Watson (1998), we have that: (i) in case o integrated markets, or any BE, the payo o the nion belongs to [U i,δ (T,δI ),U i (T,δ,δ I )] and the payo o the irm belongs to [Π i ), (T,δ,δI Π i )]; (ii) in case o separated markets, or any BE, the payo o (T,δI,δ the nion belongs to [U i (T =,δ,δi ),U i (T =,δ,δ I )] and the payo o the irm belongs to [Π i (T =,δ,δ I), Π i (T =,δ,δi )]. In case o integrated markets, the maximm nmber o bargaining periods the nion wold spend negotiating, I (m (T )), isgivenby rom which we obtain m (T )= U i (T,δ I,δ )=( δ )m (T ) U i (T,δ,δ I ), 1 log( 2(1 + δ (1 2δ I ))(2a T ) H(T,δ I,δ δ ) log ) (1 2(1 + δ H(T,δ (1 δi 2δ )2 ). I(1 ))(2a T ) 2δ ) (1 δ (1,δI ) 2δI 2 ) Notice that I (m (T )) is simply the integer part o m (T ). It is cstomary to express the players discont actors in terms o discont rates, r and r, and the length o the bargaining period,, according to ormla δ i =exp( r i ), ori =,. With this interpretation, player i s type is identiied with his discont rate r i,wherer i [ri,ri i ]. We ths have that δ I i =exp( ri I ) and δ i =exp( ri ), ori =,. Note that ri i r i since greater patience implies a lower discont rate. As approaches zero, we have (sing l Hopital s rle): (i) (1 δ I (1 2δ ) 2 )/(1 δ ) 2 ) converges to (4r (1 2δI +r I )/(4rI +r ), 19

21 (ii) (2(1+δ (1 2δI ))(2a T ) H(T,δ I,δ ))/(2(1+δI (1 2δ ))(2a T ) H(T,δ,δ I )) converges to ((2a T )(r +2r I ) G(r,r I,T))/((2a T )(ri +2r ) G(r,r I,T)), and (iii) / log(δ ) converges to ).Theseactsimplythat ( 1/r D (T )= lim (m (T ) ) = 1 0 r log ( 4r + r I 4r I + r ) (2a T )(r +2r I ) G(r I,r,T) (2a T )(r I +2r ) G(r,rI,T), which is a positive, inite nmber. Notice that D (T ) converges to zero as ri and ri I become close, or i =,. We have D (T ) 9aT r +2r I = + T r (2a 2 2aT +5T 2 ) G(r ri +2r,r G(r I,T),r I,T) The sign o the expression is the sign o the expression (r I r I + r r )( +2r r I r G(r I + +2r, G(r I,T),r,T),rI 16a(a T )+40T 2) + r I r ( 64(a T )+160T 2), which is always positive. Ths, it ollows that D (T)/ T > 0. The maximm nmber o bargaining periods the irm wold spend negotiating, I(m (T)), is given by rom which we obtain Π i (T,δ,δ I )=(δ (T ) ) m Π i (T,δ I,δ ), [ ] 1 Π m (T )= log(δ ) log i (T,δ,δ I ) Π i,δ (T,δI ), and as approaches zero, D (T ) = lim 0(m (T ) ) = 1 r log[( r r I )( 4r I )2 + r 4r + r I 8a(a T )r +(9r I +38r )T 2 +(2a T) G(r,r I,T) 8a(a T )r I +(9r +38r I )T 2 +(2a T ) G(r I,r,T). which is a positive, inite nmber. Notice that D (T ) converges to zero as ri close, or i =,. We have and r I i become 20

22 D (T ) T = The sign o the expression a r (2a2 2aT +5T 2 )T 8a(a T )r I +(2r I 9r )T 2 + G(r,r I,T) 8a(a T )ri +(2r I 9r )T 2 + G(r,r I,T) is the sign o the expression 8a 2 (a T ) 2 +22a(a T )T 2 +5T 4) r I r ( 8a(a T)r +(2r 9r I)T 2. G(r,r I,T) 8a(a T )r +(2r 9r I)T 2, G(r,r I,T) 36a(a T )T 2 +90T 4), (r I ri + r r )( which is always positive since α< α. Ths, it ollows that D (T )/ T > 0. Themaximm real delay time beore reaching an agreement is given by D(T )=min{d (T ),D (T )}. In case o separated markets, the maximm nmber o bargaining periods the nion wold spend negotiating, I (m (T = )), isgivenby rom which we obtain U i (T =,δ I,δ )= ( δ )m (T = ) U i (T =,δ,δ I ), m (T = ) = and as approaches zero 1 log( δ ) log δ 1 1 δ I D (T = ) = lim (m (T = ) ) = 1 0 r 1 δ δ I, 1 δ I δ log[( 2r + r I 2r I + r )( )] r, r I which is a positive, inite nmber. Notice that D (T = ) converges to zero as ri and ri I become close, or i =,. Similarly, the maximm nmber o bargaining periods the irm wold spend negotiating, I(m (T = )), isgivenby rom which we obtain Π i (T =,δ,δi )=(δ )m (T = ) Π i (T =,δi,δ ), m (T = ) = ( ) 2( )2 1 log(δ ) log δ I 1 δ I δ 1 δ, 1 δ 1 δ δ I I δ 21

23 and as approaches zero, D (T = ) = lim 0(m (T = ) ) = 1 r log[( 2r I + r 2r + r I )2( )2] r. r I Then, the maximm real delay time beore reaching an agreement is given by D(T = ) =min{d (T = ),D (T = )}. Reerences [1] Abowd, J.M. and J.S. Tracy, 1989, Market Strctre, Strike Activity, and Union Wage Settlements, Indstrial Relations 28, [2] Andersen, T.M., N. Haldrp and J.R. Sørensen, 2000, EU Labor Markets: Eects o Greater rodct Market Integration, Economic olicy 30, [3] Asbel, L.M.,.C. Cramton and R.J. Deneckere, 2002, Bargaining with Incomplete Inormation, in R.J. Amann and S. Hart (eds.), Handbook o Game Theory, Vol.3, (Amsterdam: Elsevier Science blishers). [4] Binmore, K.G., A. Rbinstein, and A. Wolinsky, 1986, The Nash Bargaining Soltion in Economic Modelling, Rand Jornal o Economics 17, [5] Cai, H., 2003, Ineicient Markov erect Eqilibria in Mltilateral Bargaining, Economic Theory 22, [6] Cheng, F.K. and C. Davidson, 1991, Bargaining Strctre and Strike Activity, Canadian Jornal o Economics 24, [7] Cramton,.C., 1992, Strategic Delay in Bargaining with Two-Sided Uncertainty, Review o Economic Stdies 59, [8] Cramton,.C. and J.S. Tracy, 1994, The Determinants o U.S. Labor Disptes, Jornal o Labor Economics 12, [9] Cramton,.C. and J.S. Tracy, 2003, Unions, Bargaining and Strikes, in J.T. Addison and C. Schnabel (eds.), International Handbook o Trade Unions, Chapter 3, (Cheltenham, UK: Edward Elgar). [10] Ctcher-Gersheneld, J., Kochan, T. and J. Calhon-Wells, 1998, How Do Labor and Management View Collective Bargaining, Monthly Labor Review 121(Oct.),

24 [11] Davidson, C., 1988, Mltinit Bargaining in Oligopolistic Indstries, Jornal o Labor Economics 6, [12] Dowrick, S., 1989, Union-Oligopoly Bargaining, TheEconomicJornal99, [13] Horn, H., and A. Wolinsky, 1988, Bilateral Monopolies and Incentives or Merger, Rand Jornal o Economics 19, [14] Hizinga, H., 1993, International Market Integration and Union Wage Bargaining, Scandinavian Jornal o Economics 95, [15] Kennan, J., 1986, The Economics o Strikes, in O. Ashenelter and R. Layard (eds.), Handbook o Labor Economics, Vol.2, (Amsterdam: Elsevier Science blishers). [16] Kennan, J. and R. Wilson, 1989, Strategic Bargaining Models and Interpretation o Strike Data, Jornal o Applied Econometrics 4, S87-S130. [17] Kennan, J. and R. Wilson, 1993, Bargaining with rivate Inormation, Jornal o Economic Literatre 31, [18] Maleon, A. and V. Vannetelbosch, 2003, Market Competition and Strike Activity, International Jornal o Indstrial Organization 21(5), [19] Maleon, A. and V. Vannetelbosch, 2004, Strategic Union Delegation and Incentives or Merger, orthcoming in Applied Economics Letters. [20] Maleon, A. and V. Vannetelbosch, 2005, Strategic Union Delegation and Strike Activity, Canadian Jornal o Economics 38(1), [21] Mnch,J.R. and J.R. Skaksen, 2002, rodct Market Integration and Wages in Unionized Contries, Scandinavian Jornal o Economics104, [22] Naylor, R., 1998, International Trade and Economic Integration when Labor Markets are Generally Unionised, Eropean Economic Review 42, [23] encavel, J., 1991, Labor Markets nder Trade Unionism: Employment, Wages, and Hors (Oxord: Basil Blackwell). [24] Ross, A.M., 1948, Trade Union Wage olicy (University o Caliornia ress, Berkeley, CA). 23