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Threat Effects and Trade: Wage Discipline through Product Market Competition

Arindrajit Dube and Sanjay G. Reddy


We present a model of the effect of heightened product market competition induced by trade liberalization on the distribution of income between profits and wages. Integration increases the employment cost of wage demands, thereby decreasing bargained wages and the share of rents accruing to workers. This effect is amplified because of the existence of strategic complementarities which bring about a race to the bottom. Wage discipline induced by trade liberalization reduces the negative impact of increased competition on firm rents, and may even raise profits.

JEL Codes: F12; F15; F16; D31; D33; J3; J5

Corresponding author: Arindrajit Dube, Department of Economics, Thompson Hall, University of Massachusetts, Amherst, MA 01002, USA, e-mail:

Appendix: Proofs of Propositions

Proposition 1: For a given average wage faced by its competitors, w˜i, labor demand at firm i becomes more elastic with respect to its own wage with scale of integration, k.

Proof. First, we define the average wage of competitors


Substituting w˜i into expression (6) produces


Own wage elasticity of labor demand is defined as η=ni(wi,w˜i)wiwini,

which in turn is equal to fkwi(a+(1fk)wi+(fk1)w˜i)=fkwi(w˜iwi)+((aw˜i+wi)fk).

Differentiating η with respect to k produces


The denominator is positive, and the non-negativity condition on firm profits requires that (aw˜i)0, implying that the numerator is negative, and that dηdk<0. In other words, demand becomes more elastic as k rises.   □

Proposition 2: Workers’ share of the surplus, σ, and hence the equilibrium bargained wage, w*, fall with the level of integration k, i.e., dwdk<0

Proof. Differentiating (10) with respect to k, we obtain:

dwdk=((aw0)f[(fkϕλ+fk+(θγ)fθfk+1)]2)(ϕλ+1θ), which is negative as long as a>w0, and is always true in the economically relevant region (i.e., when production is profitable). Further differentiating dwdk shows that d2wdw0dk>0,d2wdadk<0, and d2wdk2>0.   □

Proposition 3: Profits eventually fall with integration, k. Moreover, profits rise with k for sufficiently small values of k (although possibly for the economically irrelevant case of k<1). There exist cases in which profits rise between k=1 and k=2.

Proof. The first statement follows from the fact that the cubic term of the derivative, with respect to k, is negative, and this dominates other terms for a large enough k. The second statement follows from the fact that the derivative at k=0 is equal to 2–λ+λβ>0. Finally, it can be shown that profits rise between k=1 and k=2 iff f2((21/2–4)+(21/2–4)ϕ+2θ+(2–21/2)γ)+f(21/2–4)+(21/2–2)ϕ+θ+(1–21/2)γ)+(21/2–1)>0. There exist admissible values of the parameters for which the statement is true.

Proposition 4: For the case of complete organization, real wage wp is a U shape function of the total number of firms in all regions, F=fk, there exists a critical value F^, such that:


Proof. Differentiating the real wage expression with respect to F, we find that dwpdF=(a+F(a+δa)+F2δw0)(a+δw0+2Fδw0)(a+F(a+δw0)+F2δw0)(a+δa+2Fδw0)=a2δ+aF2δ2w0+aδw0F2δ2w02=F2(aδ2w02δ2w02)+(aδw0a2δ).

Note that δ>0, i.e., βλ+2>2λ, as λ≤1, and β>0. It then follows that dwpdF<0 if x2δw0(aw0)+a(w0a)<0 which is equivalent to the condition F2δw0a=F2[2+βλ2]w0a<0, i.e., F<F^=a(2λ2+β)w0. Moreover, dwpdF>0 when F>F^=a(2λ2+β)w0.   □

Proposition 5: In the short run, integration of a sufficient number of regions k raises real wages as trade increases competition and reduces prices. However, for k less than a critical value k^, real wages decline with integration. This range where real wages fall with integration may be economically irrelevant if k^<2.

Proof. In the short run, f is fixed. Substituting F=fk, we can rewrite the cutoff in terms of level of integration, k. A sufficient condition for the real wage to fall when moving from integration level k to k+1 is that dwpdx<0 at k+1. Rewriting F^=a(2λ2+β)w0 in terms of a cutoff k^, we derive the sufficient condition:


Note that this is a sufficient condition in light of the integer constraint. As a continuous function of F, the real wage wp may fall when going from k to k+1 sometimes when dwpdF>0 at k+1, but dwpdF<0 at k.   □

Proposition 6: In the long run, with free entry by firms and an entry cost proportional to production (cn), the real wage wp(k) is constant across different degrees of integration, k (up to integer constraints).

Proof. As equation (27) shows, the total number of firms F* is invariant to the level of integration k. Additionally, equation (25) shows that the real wage wp is only a function of level of x*. As a result, wp is invariant to k.   □

  1. 1

    Organized workers exist whenever coalitions form within firms and exercise a degree of power. These organized workers may act as if exhibiting concern both for their own wages and for the level of employment of their fellow workers. In this sense, the “workers’ objectives” might be thought of as a reduced form behavioral response which could reside in internal labor markets, norms, etc. The use of “organized workers” rather than “unions” through much of the paper is meant to assert that workers can have bargaining power within the firm even in the absence of unionization but it is not meant to deny that formal unions may be an especially important vehicle for workers to achieve their goals.

  2. 2

    In the Dixit-Stiglitz model, profit maximization implies that the markup depends only on consumers’ elasticity of substitution between differentiated products. This in turn implies that the labor demand of a particular firm is not directly dependent on the wage bargains struck elsewhere and therefore there is no strategic complementarity in wage-setting between unions.

  3. 3

    This observation goes back to Dunlop (1950) and Slichter (1950), but has also received more recent support. It has been observed, for example, that in two different segments of the trucking industry in the United States (namely that for “full truckloads” and that for “less-than-truckloads”) which have very different degrees of competitiveness (in the latter the largest four carriers accounted for 11% of revenues and in the former they accounted for 37%) the level of union wages was dramatically different (28.4 cents per mile vs. 35.8 cents per mile, and a union to non-union wage ratio of 1.23 vs. 1.34, respectively) [Belzer (1998, 1995), Ehrenberg and Smith (1997)]. An independent example involving the trucking industry is that deregulation is reported to have led to “substantial relative wage reductions for union truckers and much less wage response for non-union truckers following deregulation,” a view that is interpreted as “consistent” with the judgment that wages respond to increased product market competition [Freeman and Katz (1991), see also Rose (1987)]. Similarly, when deregulation of the airline industry in the United States increased competition on many routes after 1978, there were substantial reductions in the wages of unionized pilots, as a result of requests for concessions by airlines which were accepted by unions. By 1987, the real earnings of pilots had fallen 17% below the levels in 1978, and the real earnings of airline mechanics had fallen by 13% [Card (1986, 1989), Johnson (1991)]. Abowd and Lemieux (1993) find that, instrumenting quasi-rents by import competition shocks, firm-level wage bargains are considerably influenced by product market competition. Blanchflower et al. (1996), using an un-balanced panel from the US manufacturing sector, find strong evidence of a rise in a sector’s profitability leading to an increase in the level of wages in that sector over time. Blanchflower and Machin (1996) find limited support from establishment-level data for an impact of product market competition on wages in Britain and Australia. Christofides and Oswald (1992) find from Canadian labor contract data that real wages are an increasing function of profitability in an industry. Nickell et al. (1994) similarly find evidence from a large sample of British manufacturing firms that a firm’s market power has a positive impact on wages, which is however not dependent on union status, suggesting that the sharing of rents is not dependent on unionization as such.

  4. 4

    This view is contrary to that presented by Lawrence and Lawrence (1985). Their so-called “end-game” interpretation describes the possibility of unions in a declining industry, who see little future for it, seeking to maximize their extraction of surplus in the short run, and therefore raising wages.

  5. 5

    However, trade related measures appear to incompletely explain this rise.

  6. 6

    The more general case of uniformly convex or concave demand curves is considered by Reddy (2000). It is argued there that liberalization induced reductions in bargained wages and in workers’ share of available rents can arise in such a context if the the derived labor demand curves of firms are “not too convex to the origin in the region of the wage adjustment.”

  7. 7

    The assumption of rent maximizing worker-collective behavior has been widely justified on the grounds that it has plausible “micro-foundations.” Specifically, risk-neutral workers can under specific assumptions be expected to form rent-maximizing worker-collectives [see, for example, Oswald (1982)]. However, some empirical evidence suggests that unions pursue employment objectives to a larger extent than suggested by the “rent maximization” model [see Macurdy and Pencavel (1986), McDonald and Solow (1981), etc.]. As well alternative theories which assign a greater decision making role to older and more senior employee (who for example would be likely to prevail in a median voter model of worker-collective behavior) would suggest that worker-collectives pursue wage objectives to a larger extent than suggested by the “rent maximization” model. The characterization of worker-collective objectives here is meant to accommodate all of these possibilities. It does however have the feature of suggesting that the interests of the unemployed are at least partially taken account of in worker-collective decision making. This view, consonant with McDonald and Solow (1981) is disputed by, among others, Layard et al. (1991). An alternative rationalization is that “union bosses” have employment as an objective as it is a component of total rent, or alternatively of derived social or political power.

  8. 8

    A straightforward way to generalize these assumptions is to parametrize the degree of competition or collusion by using a conjectural variations model. The central result that we derive – in which decreases in bargained wages and in the share of rents accruing to workers (perhaps sufficient to cause profit increases) are a result of increased integration – can be derived in this more general case. Under Bertrand competition among firms, wages are generally set at the competitive level and no such consequences arise.

  9. 9

    The central conclusion of our analysis – that integration results in decreases in bargained wages as a result of a diminished share of available rents for workers, possibly sufficient to raise profits – can be derived in a model in which intra-firm bargaining is efficient (because it is over wages and employment jointly). Reddy (2000) demonstrates that our results can be arrived at when the outside options of the parties are endogenous by considering a model in which non-unionized workers threaten to unionize if they are not provided with at least as high an increment to total compensation as they would receive if they were unionized and engaged in the bargaining game described in this paper. The meaning of “unionization” here is simply the imposition upon the firm of the non-cooperative game in which bargaining is inefficient. Product market competition can, by shifting the labor demand curve that would be made recourse to in the event that the threat was realized, lead to changes in the distribution of surplus. These changes arise even though the threat is never realized in equilibrium. This form of efficient bargaining is of the same general form as the “Separate Spheres” bargaining model described by Lundberg and Pollak (1993). Chapter two of Reddy (2000) identifies further cases in which changes in bargained shares can result from changes in product market competition even when outside options are not endogenous. See also Mezzetti and Dinopoulos (1991).

  10. 10

    Layard et al. (1991) state that “employment is almost never bargained over as such.” Moreover they report that US contracts typically include a “management rights” clause, asserting “that the company ‘will determine the extent of any required force adjustments’.” Further, strike in pursuit of an employment objective is in the US typically illegal, in the sense that doing so risks loss of protection of collective bargaining under the National Labor Relations Board. They also report the results of Oswald (1982) to the effect that only five out of 120 British and American unions surveyed reported that they “normally negotiate over the number of jobs as well as over wages and conditions.” Hall and Lilien (1979) also find that firms often set employment unilaterally.

  11. 11

    In this model, the form of product demand, bargaining and the Cournot-Nash competition lead to a unique equilibrium in spite of the presence of strategic complementarity. This is evident from the linearity of the reaction function in equation (8). In an extended model, the strategic complementarity could be stronger and lead to multiple self-fulfilling equilibria. These possibilities are explored in Reddy (2000).

  12. 12

    We refer to unions rather than worker collectives in this section and the next section as it is realistic to assume a degree of formality of worker organization when worker are organized at a level beyond the individual enterprise.


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Published Online: 2014-3-8

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