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Productivity, indexation and macroeconomic outcomes: The implications of goods market competition and wage bargaining structure
Journal of Economics and Business 58 (2006) 465–479
Productivity, indexation and macroeconomic outcomes: The implications of goods market competition and wage bargaining structure Jonathan G. James, Phillip Lawler ∗ Department of Economics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom
Abstract One strand of the macroeconomics literature explores the extent to which the indexation of nominal wages to a variable in addition to the price level can improve macroeconomic performance. The present paper contributes to this literature by developing a model in which the nominal wage is indexed not only to the price level but also to productivity. Two key features of the framework are a monopolistically competitive goods market and a unionized labor market in which wages are determined by a finite number of unions. A significant finding is that the multiparameter indexation scheme generally outperforms full-information wage setting. © 2006 Elsevier Inc. All rights reserved. JEL classification: E24; J51 Keywords: Unions; Indexation; Goods market competition; Externalities
1. Introduction A key theme of the wage indexation literature stemming from Gray’s (1976) seminal contribution is the degree to which indexation schemes can approximate full-information macroeconomic outcomes. Given short-term nominal rigidities associated with contractual wage setting, Gray’s own study examines the potential stabilizing role that indexation of nominal wages to the price level might play in the presence of unforeseen shocks. Although indexation dampens the variations in output and employment associated with monetary disturbances, it amplifies the impact of real shocks. Accordingly, Gray demonstrates the optimal degree of indexation to lie between zero and one, with its precise value dependent on the stochastic structure of the economy, in ∗
Corresponding author. Fax: +44 1792 295 872. E-mail address: [email protected] (P. Lawler).
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particular the relative prevalence of nominal and real disturbances. The compromise nature of optimal indexation is reflected in the fact that it achieves only partial stabilization of output and employment in response to either type of shock. In an important subsequent paper, Ball (1988) argues that identification of the optimal degree of wage indexation does not, in itself, imply that the optimal scheme will inevitably result from decentralized decision making by individual agents. In making this point, he recognizes that market failure can potentially lead to a departure of the equilibrium degree of indexation from its efficient (i.e. optimal) value. To explore this issue, Ball modifies Gray’s framework by introducing a monopolistically competitive goods market and considering the possibility of indexation costs. The optimal degree of indexation implied by Ball’s model is closely related to that found by Gray1 . Moreover, in the absence of indexation costs this efficient outcome is attained by the uncoordinated choices of wage setters within individual firms. However, when indexation is costly, not all firms choose to index and the indexation decisions of those firms which do index impose externalities on those which do not. The consequence is a departure of the equilibrium degree of indexation from its optimal value. The present paper takes up Ball’s theme of indexation externalities and applies it to another vein of literature which derives from Gray, namely that concerned with multiparameter indexation schemes. Several studies have argued that superior macroeconomic outcomes can be achieved by such schemes, which index nominal wages not only to the price level, but also to one or more additional variables. An early exploration of this idea is due to Blanchard (1979), who investigates the circumstances under which contract wages might be indexed both to the price of a composite consumption good and a price index for material inputs to production. Blanchard’s key point is that a multiparameter indexation scheme can reduce employment and output deviations from their market-clearing levels by exploiting an additional source of information regarding stochastic disturbances. This idea of optimal information exploitation is also central to the insightful paper of Karni (1983), which provides a more direct adaptation of Gray’s framework. Karni considers a scheme which indexes nominal wages to output as well as to the price level and shows that the optimal indexation formula, which involves full indexation to prices and partial indexation to movements in output,2 replicates full-information outcomes. The relatively sparse literature on multiparameter indexation subsequent to Karni has pursued this theme of information exploitation. It has departed from Karni, however, by taking the view that contractual provisions for productivity-related bonuses and profit-sharing can be modeled by assuming the wage is indexed not only to the expectational error in respect of the price level but also, directly or indirectly, to the actual realization of the productivity shock. This is the approach adopted in Duca and VanHoose (1991, 1998), and Drudi and Giordano (2000). Duca and VanHoose (1991) consider a two-sector model based on Duca (1987), in which each sector produces a single good under perfect competition. The two sectors face sector-specific productivity shocks and are characterized by different labor market structures, with one sector having wage contracts, and the other a spot labor market. The study finds that optimal indexation involves partial indexation to the two goods’ prices, together with partial indexation to the productivity shocks. Crucially, this optimal indexation scheme can achieve market-clearing outcomes in a manner which is reminiscent of Karni. This conclusion is also a feature of Duca and VanHoose (1998), which extends the framework of their earlier paper to incorporate monopolistically-competitive firms. 1 Minor differences arise as a result of different assumptions with regard to labor supply and the elasticity of aggregate demand with respect to real money balances. 2 Though with full indexation to output when labor supply is completely inelastic.
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Finally, in a very different repeated-game framework, Drudi and Giordano (2000) investigate the interplay between multiparameter wage indexation and the reputation of the monetary policymaker when bargaining between firms and unions over the base nominal wage potentially generates an inflation bias. They find that indexing the wage to productivity can lower the bias, in that the resulting greater employment stability reduces the temptation facing a weak policymaker to spring inflation surprises.3 The following analysis combines the study of indexation externalities and multiparameter indexation within a model of a unionized economy. The focus is on the relationship between the equilibrium multiparameter indexation scheme and the economy’s wage bargaining structure. To consider this issue, a framework is developed which allows analysis of the strategic indexation choices of a finite number of unions, each representing a non-negligible fraction of the economy’s total labor force, but which also encompasses both the possibility of a single economy-wide union and that of a continuum of atomistic unions as limiting cases. A substantial body of work concerned with the macroeconomic implications of strategic behavior by non-atomistic unions now exists: see, for example, Skott (1997), Cukierman and Lippi (1999), Lawler (2000, 2001), Soskice and Iversen (2000), Lippi (2003), Holden (2005), and Coricelli, Cukierman, and Dalmazzo, (2006). The focus of this literature has, however, been almost exclusively on the consequences of the interaction between union wage setting and the conduct of monetary policy for optimal policy design. While the analysis of equilibrium indexation in the context of a unionized labor market is not uncommon, previous work has tended to assume one or other of the extreme cases of wage bargaining structure, i.e. an all-encompassing monopoly union (as in De Bruyne, 1997, and Hutchison & Walsh, 1998, for example) or, alternatively, an atomistic union structure (e.g. Nishimura, 1989, and Calmfors & Johansson, 2006), thus abstracting from strategic interaction among unions. In analyzing the equilibrium multiparameter indexation scheme, it is assumed that each union chooses the indexation parameters and base nominal wage to minimize an objective function which has both the real wage and employment as arguments. As in the aforementioned papers by Duca and VanHoose (1991, 1998) and Drudi and Giordano (2000) productivity-related pay is modeled by assuming the nominal wage to be indexed directly to the productivity shock as well as to the price level. A further significant feature of the model is the assumption of a monopolistically competitive goods market, as in Ball (1988) and Duca and VanHoose (1998). As will become clear, this characterization of the goods market, in combination with union wage setting behavior, plays a central role in generating the paper’s key results. In evaluating the performance of the multiparameter indexation scheme, we take as the natural reference point the equilibrium achieved under full information, where unions have complete knowledge of the actual values of macroeconomic disturbances before wages are set. We demonstrate that for the limiting cases of wage bargaining structure the equilibrium multiparameter indexation scheme exactly replicates the corresponding full-information outcomes. However, our principal finding is the surprising conclusion that for intermediate degrees of centralization of wage-bargaining, the multiparameter indexation scheme outperforms full-information wage setting when evaluated in terms of the union objective function. The key to this counterintuitive result is a negative externality associated with union wage setting and which, outside the case of a single economy-wide union, leads to a departure from the efficient equilibrium. This externality arises
3 In Drudi and Giordano, policymakers are of two types: a strong type which only cares about inflation, and a weak type which also cares about employment.
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from the impact of wage outcomes on the price level and aggregate demand, the consequences of which for employment elsewhere in the economy are disregarded by individual unions when making their own wage decisions. Although this externality is present both in the full-information case and under the indexation scheme, the latter mitigates its effects relative to the former case and leads the macroeconomic response to productivity shocks to approximate more closely the efficient outcome. The structure of the remainder of the paper is as follows. Section 2 provides an outline of the main features of the model. The properties of macroeconomic equilibrium in the reference case of fully-informed wage setting are then analyzed in Section 3. Section 4 considers the multiparameter indexation scheme, identifying its consequences for the behavior of the macroeconomy and examining its implications for union welfare by comparison with the full-information case. Finally, Section 5 summarizes the conclusions that can be drawn from our analysis. 2. The model The framework builds on Ball’s (1988) indexation model. There is a continuum of monopolistically competitive firms, uniformly distributed over the unit interval. Each firm shares a common production technology which transforms the sole variable input, labor, into its respective differentiated product. For firm i, the relationship between output4 , yi , and employment, li , is described by: yi = α li + θ
0<α<1
(1)
where θ ∼ N(0, σθ2 ) represents a random productivity shock common to all firms. Integrating individual firm outputs and their respective product prices, pi over the unit interval gives aggregate output, y, and the price level, p. Aggregate demand is determined by the real money stock, i.e., the nominal money supply, m, deflated by the price level, subject to a stochastic disturbance, φ ∼ N(0, σφ2 ), which is independent of the productivity shock: 1 y = γ(m − p + φ),
where y =
1 yi di, p =
i=0
pi di
(2)
i=0
where γ identifies the elasticity of aggregate demand with respect to real money balances. The analysis is confined to the case of purely passive monetary policy, in which the monetary authorities refrain from adjusting the money stock, m, in response to the shocks. An alternative interpretation is that the authorities do not possess any information about the realizations of the shocks at the time m is set. Given these assumptions, it follows that m is a constant, and for convenience, and without loss of generality, we normalize it at zero.5 Demand for firm i’s output as a proportion of aggregate demand is determined by its relative price: yi − y = −ε(pi − p), 4
ε>1
(3)
All variables are expressed as logarithms. A possible interpretation of φ, of course, is that it represents a random movement in the money stock itself, in which case m is to be thought of as the mean value of the money supply. 5
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where ε denotes the relative price elasticity of product demand. The limiting case of perfect goods market competition arises as ε → ∞. More generally, ε can be interpreted as measuring the degree of product market competition. Combining (2) and (3) yields firm i’s product demand. Given our normalization of m at zero: yi = γ(φ − p) − ε(pi − p)
(4)
The individual firm’s profit-maximizing labor demand is:6 lid =
γ(φ − p) − ε(wi − p) + (ε − 1)θ α + ε(1 − α)
(5)
where wi is the nominal wage at firm i. The economy’s labor force is organized into n identical unions, indexed by j (j = 1, . . ., n), with each union acting as a monopoly supplier of labor to a fraction, 1/n, of the totality of firms. Labor is assumed to be immobile between unions, with desired labor supply by union j members, ljs , perfectly inelastic.7 For convenience, normalizing membership of each union at zero: ljs = 0
(6)
Indexing firms so that all those whose employees belong to union j lie within the contiguous subinterval [(j − 1)/n, j/n], the demand for union j labor is: j/n d (j−1)/n li di (7) ljd = j/n (j−1)/n di The wage agreement arrived at by union j imposes a common nominal wage, wj , across the firms to which it supplies labor. Our reference point of full-information wage setting assumes that each union (and all firms) has complete knowledge of the realized values of the supply and aggregate demand shocks, θ and φ, respectively, when wages are determined. By comparison, the multiparameter indexation scheme (which provides the main focus of our analysis) assumes that the wage contract is agreed before the values of the disturbances are observed. This scheme specifies a base wage, together with indexation parameters relating movements in the actual nominal wage to unexpected movements in the price level and to realizations of the supply shock. As under the standard monopoly union approach, unions have the power to choose the remuneration terms of the contract, and the firm has the ‘right to manage’ in the sense that employment is determined by its demand for labor. The objective function of the individual union is assumed to contain both employment and the real wage as arguments: Ωj = lj2 + cu (wj − p)2
(8)
6 An unimportant constant has been suppressed from (5). Derivation of (5) involves combining the versions in levels of Eqs. (1) and (4) with the profit function i = Pi Yi −Wi Li , where capital letters denote the counterparts in levels of the variables which occur in the text. Maximizing i by choice of Pi , substituting the log of the resulting optimal price into (4) to determine the associated (log) product demand for firm i, and combining that product demand with (1) allows the individual firm’s (log) labor demand to be solved for as (5). 7 Allowing for a positive elasticity of labor supply with respect to the real wage would not alter the conclusions to be derived from the model.
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with cu identifying the relative weight attached by each union to the real wage compared to employment. This specification is widely used in the literature featuring union wage setting (see, for example: Herrendorf & Lockwood, 1997; Bratsiotis & Martin, 1999; Holden, 2005) with a microeconomic justification provided by Oswald (1985). The desired employment level of each union implicit in (8) is zero, reflecting the specification of labor supply given by Eq. (6). The implicit target real wage is also zero, which, given Eqs. (6), (5) and (7), is the value of the real wage associated with labor market clearing when the disturbance terms take their expected values of zero. Although it would be straightforward to incorporate a target real wage in excess of the market-clearing value, this modification would have no substantive implications for our analysis or results.8 The key implication of (8) in the stochastic framework of this paper is that unions are averse to variability of both employment and the real wage. Because productivity shocks imply that at least one of employment or the real wage will depart from its mean value, each union faces a trade-off between the two arguments of its objective function when specifying its wage contract. As will become clear, the fact that unions are faced with such a trade-off is central to the results derived in what follows. 3. Equilibrium with full-information wage setting In order to provide a reference point for evaluating the performance of the multiparameter indexation scheme, we first examine the nature of the macroeconomic equilibrium which arises when unions have complete knowledge of the actual realizations of the aggregate demand and productivity shocks before wages are set. The full-information case is a natural point of comparison, given Karni’s (1983) insight that an appropriately-designed multiparameter indexation scheme is capable of reproducing the full-information equilibrium. However, we note that unlike Karni, who focuses purely on the existence of such an indexation scheme, our interest lies in whether the uncoordinated indexation choices of individual agents (i.e., unions) will invariably lead to an equilibrium which replicates the full-information outcome. This distinction between the nature of the issues investigated and some significant differences in model specification (a monopolistically-competitive goods market and the wage setters’ objectives) can give rise to results which, under some cases, differ from those of Karni.9 As a preliminary stage we determine the price level as a function of the average nominal wage w ≡ (1/n) nj=1 wj , and the realizations of the productivity and demand shocks. Using (5) in combination with (1), integrating over firms within union sector j, and then aggregating over all union sectors yields aggregate output as a function of w, p, θ and φ. Using this expression in combination with the aggregate demand relationship (2) allows us to solve for p: p=
αw + γ(1 − α)φ − θ α + γ(1 − α)
(9)
We now consider the individual union’s optimization problem. With perfect knowledge of the realizations of θ and φ, union j chooses wj to minimize Ωj taking the nominal wages of all other 8 Such a modification might be significant in a discretionary policy context, since it would lead steady-state employment to lie below the market-clearing level and potentially give rise to an inflation bias, as in the aforementioned paper by Herrendorf and Lockwood. Of course, the relationship between wage indexation and the inflation bias has been explored extensively elsewhere (by Waller & VanHoose, 1992, and Crosby, 1995, for example). 9 We note that some special cases of the model yield outcomes consistent with Karni’s findings.
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unions as given, but recognizing the impact which its choice may have on aggregate variables. Using (5) in combination with (7) to substitute for lj , and (9) to substitute for p in (8) and minimizing over wj , noting ∂w/∂wj = 1/n and ∂p/∂wj = (∂p/∂w)(∂w/∂wj ), allows us to solve for wj as a function of φ, θ and w. With each union facing the same decision problem and with the realized values of the shocks common knowledge, the first order condition of each union is identical. Imposing wj = w, ∀j we find the symmetric Nash equilibrium nominal wage under full information, which we denote by w* , to be: 1 (αγ + Λε)(1 − γ) + Λcu [α + ε(1 − α)] θ (10) w∗ = φ − γ (αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)] where ≡ (n − 1)α + nγ(1 − α). With all firms facing the same nominal wage, firm, union sector and aggregate variables take the same value. Hence we can use Eqs. (9) and (10) in combination with (5) to determine aggregate employment under full information, l* , while the former two equations together identify directly the corresponding real wage (w − p)* : Λcu [α + ε(1 − α)] l∗ = θ (11) αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)] αγ + Λε θ (12) (w − p)∗ = αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)] It is evident from (11) and (12) that the aggregate nominal wage response to any non-zero value of the aggregate demand shock prevents any impact on either employment or the real wage. By raising its nominal wage exactly in line with the value of the disturbance, each union completely insulates both arguments of its objective function from the shock. The consequences of productivity disturbances, however, are rather more complex reflecting the fact that, following a non-zero realization of θ, greater employment stability can be achieved only at the expense of a greater variation in the real wage. Thus, when choosing their nominal wage response, unions face a tradeoff between the two arguments of their objective function and choose wages to achieve an optimal combination of real wage and employment stability, given the perceived trade-off between these two objectives. The aggregate outcome of individual union wage decisions, and thus their consequence for employment and the real wage, depends both on the extent to which wage bargaining is decentralized, as reflected in n,10 and on the degree of product market competition, as represented by ε. Using Eqs. (11) and (12), it is straightforward to demonstrate that, for any non-zero value of the productivity shock, the resulting deviation of employment from its mean value is larger, while the corresponding adjustment of the real wage is smaller, the more decentralized is wage bargaining, i.e., the larger is n, and the less the degree of competition in the product market, i.e., the smaller is ε. The influence of n and ε on employment and real wage behavior is reflected in the expected union loss associated with fully-informed wage setting, E(Ω* ), found by using Eqs. (11) and (12) in combination with (8): E(Ω∗ ) =
cu {(αγ + Λε)2 + Λ2 cu [α + ε(1 − α)]2 }σθ2 {αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)]}2
(13)
10 In identifying the influence of the extent to which wage bargaining is decentralized on equilibrium outcomes, it is important to recognize the dependence of Λ on n.
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Differentiating this expression with respect to ε and n (noting the dependence of Λ on n) allows two important properties of E(Ω* ) to be identified, as summarized in the following Proposition: Proposition 1. With full-information wage setting, the expected union loss is: (a) strictly increasing in n for 1 < ε < ∞, (b) strictly decreasing in ε for 1 < n. The findings of Proposition 1 result from an externality which is present in union wage setting, and which leads to an inefficient aggregate wage response to productivity shocks. As discussed, given any non-zero realization of the productivity shock, the individual union’s nominal wage choice is directed at achieving the optimal combination of employment and real wage stability. However, the union only partially internalizes the implications of its decision for the price level and, through (2), aggregate demand. Hence it disregards the impact of any induced change in the price level on employment in other sectors, with the consequence that the overall employment cost of limiting a departure of the real wage from its desired value is underestimated at the level of the individual union. The result is a suboptimally low degree of real wage adjustment and an inefficiently large change in aggregate employment. The more centralized is wage bargaining (the smaller is n) the greater the extent to which the externality resulting from the individual union’s wage decision is internalized. Hence the response of the real wage to productivity shocks is greater, implying correspondingly smaller variations in employment. In the limiting case in which wage setting is perfectly coordinated by a single monopoly union (n = 1), the efficiency losses associated with the externality are eliminated completely and the expected union loss achieves its minimum value. The significance of the degree of product market competition (ε) derives from the fact that the extent of the externality is larger the greater is the capacity of firms within an individual union sector to raise their own product price above the prevailing average value. Thus, the larger is ε, and the smaller the scope for an individual firm’s price to deviate from p, the closer the equilibrium which results from individual union wage decisions lies to the efficient outcome. Because the inefficiency which characterizes equilibrium has its source in the divergence of each union’s perceived trade-off between employment and the real wage from the corresponding aggregate trade-off, this inefficiency would disappear if unions had only a single objective. If, for example, unions were concerned only with employment stability, in which case cu = 0, fullyinformed wage setting would achieve the optimal outcome and maintain employment constant following any non-zero realization of θ. Alternatively, if stabilization of the real wage was the only objective of unions, an eventuality represented in our framework as the limiting case associated with cu → ∞, then the wage decisions of individual unions would be consistent with this aim and completely insulate the real wage from the potential impact of productivity shocks. The factors which underlie the equilibrium which results when unions have full information also play an important role in determining the equilibrium associated with the multiparameter indexation scheme. We now turn to analyze the nature of this equilibrium. 4. Multiparameter indexation and macroeconomic equilibrium In contrast to the preceding analysis of full-information wage setting, it is now assumed that contracts are set when neither firms nor workers possess any information about the realizations of ¯ j and indexation the aggregate demand and productivity shocks. Contracts specify a base wage w
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parameters, xj and bj , relating the actual nominal wage, wj , to unexpected movements in the price level and the level of productivity: ¯ j + xj (p − Ep) + bj θ wj = w
(14)
We follow Drudi and Giordano (2000) in assuming that the contract wage is directly indexed to the shock. A possible objection is that real-world employment contracts generally do not index nominal wages either to productivity or to the marginal product of labor. While this objection has some force, realism also argues against the complete omission of a productivity-related term from the nominal wage equation, since employment contracts frequently contain profit-sharing clauses which indirectly link workers’ remuneration (including deferred remuneration in the form of pensions) to productivity. The modeling strategy adopted here can therefore be justified as a convenient and straightforward means of capturing the widespread linking of contract wages to productivity-related outcomes.11 ¯ j such that Given its objective function, each union minimizes its expected loss by setting w E(lj ) = 0. From (5), this implies: ¯j = w
(ε − γ) Ep ε
(15)
Following the derivation of Eq. (9), Eqs. (14) and (15) can be used with (2) and (5) to find the following expression for the price level:12 [γ(1 − α)φ − (1 − αb)θ] (16) [γ(1 − α) + α(1 − x)] where x = (1/n) nj=1 xj , b = (1/n) nj=1 bj . The individual union’s optimal choice of indexation parameters solves the two simultaneous first-order conditions, ∂E(Ω)/∂xj = 0 and ∂E(Ω)/∂bj = 0, taking the indexation decisions of all other unions as given, but accounting for the consequences of its own choice for the aggregate parameters x and b and, thereby, for aggregate variables. Combining Eqs. (14)–(16) provides an expression for union j’s real wage, which, together with (5), can be substituted into Eq. (8) to determine the individual union’s expected loss. Differentiating this expression with respect to xj , then with respect to bj , yields the two first-order conditions expressed in terms of the model’s structural parameters, as well as xj , bj , x and b. Imposing xj = x and bj = b then determines the ˆ 13 symmetric Nash equilibrium parameter values, xˆ and b: p=
xˆ = 1 bˆ =
[α + nε(1 − α)] {α + nε(1 − α) + ncu (1 − α)2 [α + ε(1 − α)]}
(17a) (17b)
Several aspects of (17) are noteworthy. First, as in other macroeconomic studies of multiparameter wage indexation, the relative variances of the two shocks do not help determine the equilibrium 11 Qualitatively very similar results are obtained in a version of our model which features indexation of the nominal wage to both the price level and aggregate output (as advocated by Karni), or alternatively to the price level and aggregate employment. 12 Note this expression implies Ep = 0, hence w ¯ j = 0. 13 In the limiting cases which arise for n = 1 and as n → ∞, it is straightforward to demonstrate that the solution described by (17) is unique: for the general case of 1 < n < ∞, no alternative solution to that described by (17) can be identified.
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degree of indexation to either the price level or the productivity shock. This result contrasts with a general finding of the literature following Gray (1976) on indexing of the wage solely to the price level, namely that individual agents’ equilibrium indexation choices will depend on the relative variances of the two disturbances. The reason for this difference between the two veins of literature is that with two shocks, two (or more) indexation instruments allow the desirable degree of neutralization of aggregate demand disturbances14 to be achieved by an appropriate setting of one parameter, allowing the other parameter to be directed at achieving the optimal wage response to productivity shocks. Because our model assumes, like Karni (1983), that every firm employs labor under contracts, and omits a second sector with spot-market labor hiring which is central to Duca and VanHoose (1991, 1998), it is optimal for each union to index fully to the price level. The second significant feature of (17) is that the equilibrium degree of indexation to the producˆ u < 0. tivity shock depends on the weight, cu , placed by unions on real wage stability, with ∂b/∂c Hence, as in a full-information environment, the equilibrium nominal wage is influenced by the relative significance attached by unions to their two objectives, where this influence reflects the trade-off facing unions in the presence of productivity shocks. With xj = 1, setting bj closer to zero (given the indexation choices of all other unions) allows the individual union to achieve a more stable real wage, but at the expense of greater employment variability. Thus, if real wage stability was the sole objective of unions, captured in our framework as the limiting case arising as cu → ∞, (17b) indicates bˆ = 0 and, with xˆ = 1, the real wage would be completely rigid. Conversely, if unions were concerned only with stabilizing employment (in which case cu = 0), then bˆ = 1 and the nominal wage would be fully indexed to the productivity shock. In fact, this latter finding is closely related to Karni’s implicit result that, given a perfectly inelastic labor supply, fully indexing the nominal wage to the price level and aggregate output completely stabilizes employment at its market-clearing level. The influence of wage bargaining structure (n) and the degree of product market competition ˆ (ε) on bˆ is also evident from (17b). It is straightforward to establish that ∂b/∂n < 0 for 1 < ε < ∞, ˆ while ∂b/∂ε > 0 for n > 1. This dependence of the responsiveness of the nominal wage to productivity shocks on these structural parameters reflects the operation of an externality arising from union indexation choices which parallels that present with full-information wage setting. To directly compare this nominal wage with that occurring when unions are fully informed about the realizations of φ and θ before wages are set, and to establish whether the multiparameter indexation scheme replicates the full-information outcome, we use (17) to substitute for x and b in (14). Additionally, using (16) to substitute for p, we determine the nominal wage associated with the equilibrium multiparameter indexation scheme, which we denote by wMI : 1 [α + nε(1 − α)](1 − γ) + n(1 − α)cu [α + ε(1 − α)] θ (18) wMI = φ − γ α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)] Comparing Eqs. (10) and (18), it is apparent that the nominal wage response to productivity shocks under the multiparameter indexation scheme in general differs from that under fullyinformed wage setting.15 It follows that employment and real wage outcomes will also diverge.
14 Complete neutralization if every firm has labor contracts, as in Karni (1983), partial neutralization if some firms employ labor in a spot market, so that cross-sectoral spillovers arise, as in Duca and VanHoose (1998). 15 Note that one particular pair of values for x and b replicates the equilibrium outcome under full-information wage ˆ setting, namely x = 1, b = b ≡ (αγ + Λε)/{αγ + Λε + Λ(1 − ␣)cu [α + ε(1 − α)]}. For 1 < n < ∞, we find that b < b.
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Using (18), together with (5), (16) and (17a) allows us to identify the values of employment and the real wage under the multiparameter indexation scheme: n(1 − α)cu [α + ε(1 − α)] θ (19) lMI = α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)] α + nε(1 − α) θ (20) (w − p)MI = α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)] It is straightforward to demonstrate that the impact of productivity shocks on employment increases in (absolute) magnitude, while that on the real wage diminishes, the larger is n and the smaller is ε. Thus, the externality which results from individual union indexation choices operates in the same direction as in the full-information case. Significantly, however, comparison of (19) with (11) and of (20) with (12), establishes that, for given values of n and ε, the adjustment in employment associated with any non-zero realization of θ is generally smaller while that in the real wage is larger under the multiparameter indexation scheme than under fully-informed wage setting. The expected union loss, E(ΩMI ), to which these movements in employment and the real wage give rise is described by: E(ΩMI ) =
cu {[α + nε(1 − α)]2 + n2 (1 − α)2 cu [α + ε(1 − α)]2 }σθ2 2
{α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)]}
(21)
The following Proposition identifies the key properties of E(ΩMI ): Proposition 2. Given the multiparameter indexation scheme described by (14), with the equilibrium values of x and b identified by (17), the expected union loss, E(ΩMI ) is: (a) strictly increasing in n for 1 < ε < ∞, (b) strictly decreasing in ε for 1 < n, (c) strictly less than E(Ω* ) for 1 < ε < ∞, 1 < n < ∞.16 As is evident from parts (a) and (b) of Proposition 2, the qualitative influence of both wage bargaining structure and the degree of product market competition on the expected union loss is the same as that arising under fully informed wage setting. This congruence reflects the similarity of the externality in the two cases. Despite this similarity, the macroeconomic outcomes differ in the two scenarios, and part (c) of Proposition 2 identifies a surprising and noteworthy result: the expected union loss associated with the equilibrium multiparameter indexation scheme is generally smaller than in the full-information case.17 This finding is particularly significant, 16 The following is a proof. Equating (13) and (21) and solving for n, the only admissible finite solution value (i.e. the only n ≥ 1) to the equation E(Ω* ) = E(ΩMI ), is found to be n = 1. Since it has already been established that the equilibrium expected loss, as a function of n, is minimized in both scenarios when n = 1, we examine the second derivatives with respect to n of these loss expressions evaluated at n = 1. Since ∂2 E(Ω∗ )/∂n2 |n=1 = 3 2cu2 α2 [α + γ(1 − α)]2 σθ2 /γ 2 [α + ε(1 − α)]2 [1 + cu (1 − α)2 ] > ∂2 E(ΩMI )/∂n2 |n=1 = 2cu2 α2 (1 − α)2 σθ2 /[α + ε(1−α)]2 3
[1 + cu (1 − α)2 ] , it follows that E(Ω* ) > E(ΩMI ) for all finite n > 1. 17 Note that if we consider a standard expected social loss function E(Γ ) = E(l2 + δπ 2 ), where π ≡ p − p −1 (and with p−1 conveniently normalized at zero), we find that E(Γ )|x=1,b=bˆ < E(Γ ∗ ) for 1 < n < ∞.Thus, when the economy features multiple non-atomistic unions, not only the expected loss of unions, but also the expected social loss, is lower in equilibrium under multiparameter indexation than under full-information wage setting.
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given that the criterion by which indexation schemes are typically evaluated is their ability to approximate full-information outcomes. This counterintuitive result arises because under the multiparameter indexation scheme, full indexation of the nominal wage to the price level increases the sensitivity of the latter to nominal wage adjustments resulting directly from non-zero realizations of θ.18 This greater responsiveness of the price level translates into a larger impact on aggregate demand and, hence, on employment within each union sector. As a consequence, when making its choice of bj , each union perceives a less favorable trade-off between employment and real wage stability than under full-information wage setting: specifically, under the multiparameter indexation scheme, the union discerns the employment-variability cost of achieving a more stable real wage to be higher. Hence the perceived trade-off at the level of the individual union approximates more closely the actual tradeoff at the aggregate level.19 Reflecting this, each union’s choice of bj leads, in aggregate, to a smaller efficiency loss than that which arises in the full-information case. The exceptions to this general superiority of the equilibrium multiparameter indexation scheme are provided by the two extreme cases of wage bargaining structure. Because a single economywide union fully internalizes the consequences of its decisions for aggregate demand, both fullyinformed wage setting and the multiparameter indexation scheme are equally capable of achieving the efficient nominal wage response to non-zero realizations of θ. The expected union loss in the two cases is thus identical and is described by: E(ΩMI )|n=1 = E(Ω∗ )|n=1 =
cu σθ2 1 + cu (1 − α)2
(22)
In the opposite limiting case of atomistic unions, each union views the impact of its choice variable, whether wj or bj , on the price level as negligible with the implication that the greater sensitivity of the price level to nominal wage adjustments under the multiparameter indexation scheme is irrelevant. As a result, the perceived trade-off between employment and real wage stability in the two scenarios is identical. Consequently, individual union decisions give rise to the same nominal wage response to productivity shocks under the multiparameter indexation scheme as under full-information wage setting and thus the expected union loss in the two cases is the same: lim E(ΩMI ) = lim E(Ω∗ ) =
n→∞
n→∞
cu {ε2 + cu [α + ε(1 − α)]2 }σθ2 {ε + cu (1 − α)[α + ε(1 − α)]}2
(23)
Viewing the findings represented by Eqs. (22) and (23) against the perspective of part (c) of Proposition 2 highlights an important implication for evaluating indexation schemes in the presence of externalities. That is, models which focus on only one or other of the extreme cases of wage bargaining structure may, when externalities are present, arrive at conclusions whose validity is specific to that particular case. Furthermore, intermediate degrees of wage-bargaining centralization potentially give rise to rather different results. Our findings are summarized in Table 1, which also identifies the crucial role played by union objectives in generating the key results of this paper.
18
This can be seen by comparing (16), with x set to unity, with (9). The relationship between the individual union’s perceived trade-off between employment and real wage stability under both full-information wage setting and the multiparameter indexation scheme, and the aggregate trade-off is explicitly identified in an Appendix which is available from the authors upon request. 19
Table 1 Key findings and the role of union objectives Equilibrium value of indexation parameters
Influence of degree of product market competition and wage bargaining structure on equilibrium degree of indexation to productivity shocks
Influence of degree of product market competition and wage bargaining structure on expected union loss with multiparameter indexation
Expected union loss associated with multiparameter indexation scheme compared to full information outcome
Further remarks
General case: 0 < cu < ∞
ˆ where x = 1, b = b, 0 < bˆ < 1
ˆ 0 < ∂b/∂ε for ˆ 1 < n, ∂b/∂n < 0 for 1<ε<∞
∂E(ΩMI )/∂ε < 0 for 1 < n, ∂E(ΩMI )/∂n > 0 for 1<ε<∞
E(ΩMI ) < E(Ω* ) for 1 < ε < ∞ and 1 < n < ∞
Union objectives relate solely to employment stability: cu = 0
x = 1, b = 1
No effect
No effect
E(ΩMI )|cu =0 = E(Ω∗ )|cu =0
Union objectives relate solely to real wage stability: cu → ∞
x = 1, b = 0
No effect
No effect
E(ΩMI )|cu →∞ = E(Ω∗ )|cu →∞
Despite efficiency losses multiparameter indexation achieves superior outcomes to those attained by indexation of nominal wages only to price level. Replicates Karni’s (1983)a findings. Constraining b to zero, with indexation only to prices, reproduces Gray’s (1976)a and Ball’s (1988)b results. Multiparameter indexation achieves superior outcomes. Multiparameter indexation redundant: unions choose to index nominal wages only to the price level.
a b
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Relative weight placed on real wage stability by unions
With perfectly inelastic labor supply. Absent indexation costs. 477
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5. Concluding remarks This paper extends the analysis of multiparameter indexation to consider the macroeconomic implications of such a scheme for an economy characterized by a monopolistically competitive goods market and in which wage contracts are set strategically by non-atomistic unions. Assuming nominal wages can be indexed to both the price level and the productivity shock, the indexation choices of individual unions were analyzed and the characteristics of the resulting equilibrium identified. The equilibrium degree of indexation to productivity shocks depends on both the degree of product market competition and the economy’s wage bargaining structure. Underlying this result is the presence of an externality in union indexation decisions which parallels that found to operate under full-information wage setting. Comparing the macroeconomic outcomes under the multiparameter indexation scheme with those in the case of fully-informed wage setting yields two particularly significant findings. First, outside the two extreme cases of one or an infinite number of unions, the equilibrium differs between the scenarios. Second, when evaluated in terms of the union objective function, the multiparameter indexation scheme delivers superior outcomes. In the light of this latter finding, it appears that the early literature’s emphasis on the informationexploiting properties of multiparameter indexation schemes was well founded. Indeed, such schemes may work better than the original contributors to their analysis might have imagined. Our findings suggest that when the underlying economic structure gives rise to negative externalities, the information regarding stochastic shocks embodied in aggregate variables may be exploited more efficiently under endogenous indexation than when full information regarding such shocks is available at the time wages are determined. Acknowledgements The authors gratefully acknowledge helpful comments from two anonymous referees and the editors. References Ball, L. (1988). Is equilibrium indexation efficient? Quarterly Journal of Economics, 103(2), 299–311. Blanchard, O. J. (1979). Wage indexing rules and the behavior of the economy. Journal of Political Economy, 87(4), 798–815. Bratsiotis, G., & Martin, C. (1999). Stabilization, policy targets, and unemployment in imperfectly competitive economies. Scandinavian Journal of Economics, 101(2), 241–256. Calmfors, L., & Johansson, A. (2006). Nominal wage flexibility, wage indexation and monetary union. Economic Journal, 116, 283–308. Coricelli, F., Cukierman, A., & Dalmazzo, A. (2006). Monetary institutions, monopolistic competition, unionized labor markets and economic performance. Scandinavian Journal of Economics, 108(1), 39–63. Crosby, M. (1995). Wage indexation and the time consistency of government policy. Scandinavian Journal of Economics, 97(1), 105–121. Cukierman, A., & Lippi, F. (1999). Central bank independence, centralization of wage bargaining, inflation and unemployment. European Economic Review, 43(7), 1395–1434. De Bruyne, G. (1997). Wage indexation and the exchange rate regime: A strategic analysis. Journal of Macroeconomics, 19(3), 571–589, Summer. Drudi, F., & Giordano, R. (2000). Wage indexation, employment and inflation. Scandinavian Journal of Economics, 102(4), 645–668. Duca, J. V. (1987). The spillover effects of nominal wage rigidity in a multisector economy. Journal of Money, Credit and Banking, 19(1), 117–121.
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Duca, J. V., & VanHoose, D. D. (1991). Optimal wage indexation in a multisector economy. International Economic Review, 32(4), 859–867. Duca, J. V., & VanHoose, D. D. (1998). Goods-market competition and profit sharing: A multisector macro approach. Journal of Economics and Business, 50(6), 525–534. Gray, J. A. (1976). Wage indexation: A macroeconomic approach. Journal of Monetary Economics, 2(2), 221–235. Herrendorf, B., & Lockwood, B. (1997). Rogoff’s “conservative” central banker restored. Journal of Money, Credit and Banking, 29(4), 476–495. Holden, S. (2005). Monetary regimes and the co-ordination of wage-setting. European Economic Review, 49(4), 833–843. Hutchison, M. M., & Walsh, C. E. (1998). The output-inflation tradeoff and central bank reform: Evidence from New Zealand. Economic Journal, 108, 703–725. Lawler, P. (2000). Centralized wage setting, inflation contracts and the optimal choice of central banker. Economic Journal, 110, 559–575. Lawler, P. (2001). Monetary policy, central bank objectives, and social welfare with strategic wage setting. Oxford Economic Papers, 53(1), 94–113. Lippi, F. (2003). Strategic monetary policy with non-atomistic wage setters. Review of Economic Studies, 70(4), 909–919. Karni, E. (1983). On optimal wage indexation. Journal of Political Economy, 91(2), 282–292. Nishimura, K. G. (1989). Indexation and monopolistic competition in labor markets. European Economic Review, 33(8), 1605–1623. Oswald, A. J. (1985). The economic theory of trade unions: An introductory survey. Scandinavian Journal of Economics, 87(2), 160–193. Skott, P. (1997). Stagflationary consequences of prudent monetary policy in a unionized economy. Oxford Economic Papers, 49(4), 609–622. Soskice, D., & Iversen, T. (2000). The non-neutrality of monetary policy with large price or wage setters. Quarterly Journal of Economics, 115(1), 265–284. Waller, C. J., & VanHoose, D. D. (1992). Discretionary monetary policy and socially efficient wage indexation. Quarterly Journal of Economics, 107(4), 1451–1460.
Productivity, indexation and macroeconomic outcomes: The implications of goods market competition and wage bargaining structure Jonathan G. James, Phillip Lawler ∗ Department of Economics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom
Abstract One strand of the macroeconomics literature explores the extent to which the indexation of nominal wages to a variable in addition to the price level can improve macroeconomic performance. The present paper contributes to this literature by developing a model in which the nominal wage is indexed not only to the price level but also to productivity. Two key features of the framework are a monopolistically competitive goods market and a unionized labor market in which wages are determined by a finite number of unions. A significant finding is that the multiparameter indexation scheme generally outperforms full-information wage setting. © 2006 Elsevier Inc. All rights reserved. JEL classification: E24; J51 Keywords: Unions; Indexation; Goods market competition; Externalities
1. Introduction A key theme of the wage indexation literature stemming from Gray’s (1976) seminal contribution is the degree to which indexation schemes can approximate full-information macroeconomic outcomes. Given short-term nominal rigidities associated with contractual wage setting, Gray’s own study examines the potential stabilizing role that indexation of nominal wages to the price level might play in the presence of unforeseen shocks. Although indexation dampens the variations in output and employment associated with monetary disturbances, it amplifies the impact of real shocks. Accordingly, Gray demonstrates the optimal degree of indexation to lie between zero and one, with its precise value dependent on the stochastic structure of the economy, in ∗
Corresponding author. Fax: +44 1792 295 872. E-mail address: [email protected] (P. Lawler).
0148-6195/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jeconbus.2006.06.005
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particular the relative prevalence of nominal and real disturbances. The compromise nature of optimal indexation is reflected in the fact that it achieves only partial stabilization of output and employment in response to either type of shock. In an important subsequent paper, Ball (1988) argues that identification of the optimal degree of wage indexation does not, in itself, imply that the optimal scheme will inevitably result from decentralized decision making by individual agents. In making this point, he recognizes that market failure can potentially lead to a departure of the equilibrium degree of indexation from its efficient (i.e. optimal) value. To explore this issue, Ball modifies Gray’s framework by introducing a monopolistically competitive goods market and considering the possibility of indexation costs. The optimal degree of indexation implied by Ball’s model is closely related to that found by Gray1 . Moreover, in the absence of indexation costs this efficient outcome is attained by the uncoordinated choices of wage setters within individual firms. However, when indexation is costly, not all firms choose to index and the indexation decisions of those firms which do index impose externalities on those which do not. The consequence is a departure of the equilibrium degree of indexation from its optimal value. The present paper takes up Ball’s theme of indexation externalities and applies it to another vein of literature which derives from Gray, namely that concerned with multiparameter indexation schemes. Several studies have argued that superior macroeconomic outcomes can be achieved by such schemes, which index nominal wages not only to the price level, but also to one or more additional variables. An early exploration of this idea is due to Blanchard (1979), who investigates the circumstances under which contract wages might be indexed both to the price of a composite consumption good and a price index for material inputs to production. Blanchard’s key point is that a multiparameter indexation scheme can reduce employment and output deviations from their market-clearing levels by exploiting an additional source of information regarding stochastic disturbances. This idea of optimal information exploitation is also central to the insightful paper of Karni (1983), which provides a more direct adaptation of Gray’s framework. Karni considers a scheme which indexes nominal wages to output as well as to the price level and shows that the optimal indexation formula, which involves full indexation to prices and partial indexation to movements in output,2 replicates full-information outcomes. The relatively sparse literature on multiparameter indexation subsequent to Karni has pursued this theme of information exploitation. It has departed from Karni, however, by taking the view that contractual provisions for productivity-related bonuses and profit-sharing can be modeled by assuming the wage is indexed not only to the expectational error in respect of the price level but also, directly or indirectly, to the actual realization of the productivity shock. This is the approach adopted in Duca and VanHoose (1991, 1998), and Drudi and Giordano (2000). Duca and VanHoose (1991) consider a two-sector model based on Duca (1987), in which each sector produces a single good under perfect competition. The two sectors face sector-specific productivity shocks and are characterized by different labor market structures, with one sector having wage contracts, and the other a spot labor market. The study finds that optimal indexation involves partial indexation to the two goods’ prices, together with partial indexation to the productivity shocks. Crucially, this optimal indexation scheme can achieve market-clearing outcomes in a manner which is reminiscent of Karni. This conclusion is also a feature of Duca and VanHoose (1998), which extends the framework of their earlier paper to incorporate monopolistically-competitive firms. 1 Minor differences arise as a result of different assumptions with regard to labor supply and the elasticity of aggregate demand with respect to real money balances. 2 Though with full indexation to output when labor supply is completely inelastic.
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Finally, in a very different repeated-game framework, Drudi and Giordano (2000) investigate the interplay between multiparameter wage indexation and the reputation of the monetary policymaker when bargaining between firms and unions over the base nominal wage potentially generates an inflation bias. They find that indexing the wage to productivity can lower the bias, in that the resulting greater employment stability reduces the temptation facing a weak policymaker to spring inflation surprises.3 The following analysis combines the study of indexation externalities and multiparameter indexation within a model of a unionized economy. The focus is on the relationship between the equilibrium multiparameter indexation scheme and the economy’s wage bargaining structure. To consider this issue, a framework is developed which allows analysis of the strategic indexation choices of a finite number of unions, each representing a non-negligible fraction of the economy’s total labor force, but which also encompasses both the possibility of a single economy-wide union and that of a continuum of atomistic unions as limiting cases. A substantial body of work concerned with the macroeconomic implications of strategic behavior by non-atomistic unions now exists: see, for example, Skott (1997), Cukierman and Lippi (1999), Lawler (2000, 2001), Soskice and Iversen (2000), Lippi (2003), Holden (2005), and Coricelli, Cukierman, and Dalmazzo, (2006). The focus of this literature has, however, been almost exclusively on the consequences of the interaction between union wage setting and the conduct of monetary policy for optimal policy design. While the analysis of equilibrium indexation in the context of a unionized labor market is not uncommon, previous work has tended to assume one or other of the extreme cases of wage bargaining structure, i.e. an all-encompassing monopoly union (as in De Bruyne, 1997, and Hutchison & Walsh, 1998, for example) or, alternatively, an atomistic union structure (e.g. Nishimura, 1989, and Calmfors & Johansson, 2006), thus abstracting from strategic interaction among unions. In analyzing the equilibrium multiparameter indexation scheme, it is assumed that each union chooses the indexation parameters and base nominal wage to minimize an objective function which has both the real wage and employment as arguments. As in the aforementioned papers by Duca and VanHoose (1991, 1998) and Drudi and Giordano (2000) productivity-related pay is modeled by assuming the nominal wage to be indexed directly to the productivity shock as well as to the price level. A further significant feature of the model is the assumption of a monopolistically competitive goods market, as in Ball (1988) and Duca and VanHoose (1998). As will become clear, this characterization of the goods market, in combination with union wage setting behavior, plays a central role in generating the paper’s key results. In evaluating the performance of the multiparameter indexation scheme, we take as the natural reference point the equilibrium achieved under full information, where unions have complete knowledge of the actual values of macroeconomic disturbances before wages are set. We demonstrate that for the limiting cases of wage bargaining structure the equilibrium multiparameter indexation scheme exactly replicates the corresponding full-information outcomes. However, our principal finding is the surprising conclusion that for intermediate degrees of centralization of wage-bargaining, the multiparameter indexation scheme outperforms full-information wage setting when evaluated in terms of the union objective function. The key to this counterintuitive result is a negative externality associated with union wage setting and which, outside the case of a single economy-wide union, leads to a departure from the efficient equilibrium. This externality arises
3 In Drudi and Giordano, policymakers are of two types: a strong type which only cares about inflation, and a weak type which also cares about employment.
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from the impact of wage outcomes on the price level and aggregate demand, the consequences of which for employment elsewhere in the economy are disregarded by individual unions when making their own wage decisions. Although this externality is present both in the full-information case and under the indexation scheme, the latter mitigates its effects relative to the former case and leads the macroeconomic response to productivity shocks to approximate more closely the efficient outcome. The structure of the remainder of the paper is as follows. Section 2 provides an outline of the main features of the model. The properties of macroeconomic equilibrium in the reference case of fully-informed wage setting are then analyzed in Section 3. Section 4 considers the multiparameter indexation scheme, identifying its consequences for the behavior of the macroeconomy and examining its implications for union welfare by comparison with the full-information case. Finally, Section 5 summarizes the conclusions that can be drawn from our analysis. 2. The model The framework builds on Ball’s (1988) indexation model. There is a continuum of monopolistically competitive firms, uniformly distributed over the unit interval. Each firm shares a common production technology which transforms the sole variable input, labor, into its respective differentiated product. For firm i, the relationship between output4 , yi , and employment, li , is described by: yi = α li + θ
0<α<1
(1)
where θ ∼ N(0, σθ2 ) represents a random productivity shock common to all firms. Integrating individual firm outputs and their respective product prices, pi over the unit interval gives aggregate output, y, and the price level, p. Aggregate demand is determined by the real money stock, i.e., the nominal money supply, m, deflated by the price level, subject to a stochastic disturbance, φ ∼ N(0, σφ2 ), which is independent of the productivity shock: 1 y = γ(m − p + φ),
where y =
1 yi di, p =
i=0
pi di
(2)
i=0
where γ identifies the elasticity of aggregate demand with respect to real money balances. The analysis is confined to the case of purely passive monetary policy, in which the monetary authorities refrain from adjusting the money stock, m, in response to the shocks. An alternative interpretation is that the authorities do not possess any information about the realizations of the shocks at the time m is set. Given these assumptions, it follows that m is a constant, and for convenience, and without loss of generality, we normalize it at zero.5 Demand for firm i’s output as a proportion of aggregate demand is determined by its relative price: yi − y = −ε(pi − p), 4
ε>1
(3)
All variables are expressed as logarithms. A possible interpretation of φ, of course, is that it represents a random movement in the money stock itself, in which case m is to be thought of as the mean value of the money supply. 5
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where ε denotes the relative price elasticity of product demand. The limiting case of perfect goods market competition arises as ε → ∞. More generally, ε can be interpreted as measuring the degree of product market competition. Combining (2) and (3) yields firm i’s product demand. Given our normalization of m at zero: yi = γ(φ − p) − ε(pi − p)
(4)
The individual firm’s profit-maximizing labor demand is:6 lid =
γ(φ − p) − ε(wi − p) + (ε − 1)θ α + ε(1 − α)
(5)
where wi is the nominal wage at firm i. The economy’s labor force is organized into n identical unions, indexed by j (j = 1, . . ., n), with each union acting as a monopoly supplier of labor to a fraction, 1/n, of the totality of firms. Labor is assumed to be immobile between unions, with desired labor supply by union j members, ljs , perfectly inelastic.7 For convenience, normalizing membership of each union at zero: ljs = 0
(6)
Indexing firms so that all those whose employees belong to union j lie within the contiguous subinterval [(j − 1)/n, j/n], the demand for union j labor is: j/n d (j−1)/n li di (7) ljd = j/n (j−1)/n di The wage agreement arrived at by union j imposes a common nominal wage, wj , across the firms to which it supplies labor. Our reference point of full-information wage setting assumes that each union (and all firms) has complete knowledge of the realized values of the supply and aggregate demand shocks, θ and φ, respectively, when wages are determined. By comparison, the multiparameter indexation scheme (which provides the main focus of our analysis) assumes that the wage contract is agreed before the values of the disturbances are observed. This scheme specifies a base wage, together with indexation parameters relating movements in the actual nominal wage to unexpected movements in the price level and to realizations of the supply shock. As under the standard monopoly union approach, unions have the power to choose the remuneration terms of the contract, and the firm has the ‘right to manage’ in the sense that employment is determined by its demand for labor. The objective function of the individual union is assumed to contain both employment and the real wage as arguments: Ωj = lj2 + cu (wj − p)2
(8)
6 An unimportant constant has been suppressed from (5). Derivation of (5) involves combining the versions in levels of Eqs. (1) and (4) with the profit function i = Pi Yi −Wi Li , where capital letters denote the counterparts in levels of the variables which occur in the text. Maximizing i by choice of Pi , substituting the log of the resulting optimal price into (4) to determine the associated (log) product demand for firm i, and combining that product demand with (1) allows the individual firm’s (log) labor demand to be solved for as (5). 7 Allowing for a positive elasticity of labor supply with respect to the real wage would not alter the conclusions to be derived from the model.
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with cu identifying the relative weight attached by each union to the real wage compared to employment. This specification is widely used in the literature featuring union wage setting (see, for example: Herrendorf & Lockwood, 1997; Bratsiotis & Martin, 1999; Holden, 2005) with a microeconomic justification provided by Oswald (1985). The desired employment level of each union implicit in (8) is zero, reflecting the specification of labor supply given by Eq. (6). The implicit target real wage is also zero, which, given Eqs. (6), (5) and (7), is the value of the real wage associated with labor market clearing when the disturbance terms take their expected values of zero. Although it would be straightforward to incorporate a target real wage in excess of the market-clearing value, this modification would have no substantive implications for our analysis or results.8 The key implication of (8) in the stochastic framework of this paper is that unions are averse to variability of both employment and the real wage. Because productivity shocks imply that at least one of employment or the real wage will depart from its mean value, each union faces a trade-off between the two arguments of its objective function when specifying its wage contract. As will become clear, the fact that unions are faced with such a trade-off is central to the results derived in what follows. 3. Equilibrium with full-information wage setting In order to provide a reference point for evaluating the performance of the multiparameter indexation scheme, we first examine the nature of the macroeconomic equilibrium which arises when unions have complete knowledge of the actual realizations of the aggregate demand and productivity shocks before wages are set. The full-information case is a natural point of comparison, given Karni’s (1983) insight that an appropriately-designed multiparameter indexation scheme is capable of reproducing the full-information equilibrium. However, we note that unlike Karni, who focuses purely on the existence of such an indexation scheme, our interest lies in whether the uncoordinated indexation choices of individual agents (i.e., unions) will invariably lead to an equilibrium which replicates the full-information outcome. This distinction between the nature of the issues investigated and some significant differences in model specification (a monopolistically-competitive goods market and the wage setters’ objectives) can give rise to results which, under some cases, differ from those of Karni.9 As a preliminary stage we determine the price level as a function of the average nominal wage w ≡ (1/n) nj=1 wj , and the realizations of the productivity and demand shocks. Using (5) in combination with (1), integrating over firms within union sector j, and then aggregating over all union sectors yields aggregate output as a function of w, p, θ and φ. Using this expression in combination with the aggregate demand relationship (2) allows us to solve for p: p=
αw + γ(1 − α)φ − θ α + γ(1 − α)
(9)
We now consider the individual union’s optimization problem. With perfect knowledge of the realizations of θ and φ, union j chooses wj to minimize Ωj taking the nominal wages of all other 8 Such a modification might be significant in a discretionary policy context, since it would lead steady-state employment to lie below the market-clearing level and potentially give rise to an inflation bias, as in the aforementioned paper by Herrendorf and Lockwood. Of course, the relationship between wage indexation and the inflation bias has been explored extensively elsewhere (by Waller & VanHoose, 1992, and Crosby, 1995, for example). 9 We note that some special cases of the model yield outcomes consistent with Karni’s findings.
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unions as given, but recognizing the impact which its choice may have on aggregate variables. Using (5) in combination with (7) to substitute for lj , and (9) to substitute for p in (8) and minimizing over wj , noting ∂w/∂wj = 1/n and ∂p/∂wj = (∂p/∂w)(∂w/∂wj ), allows us to solve for wj as a function of φ, θ and w. With each union facing the same decision problem and with the realized values of the shocks common knowledge, the first order condition of each union is identical. Imposing wj = w, ∀j we find the symmetric Nash equilibrium nominal wage under full information, which we denote by w* , to be: 1 (αγ + Λε)(1 − γ) + Λcu [α + ε(1 − α)] θ (10) w∗ = φ − γ (αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)] where ≡ (n − 1)α + nγ(1 − α). With all firms facing the same nominal wage, firm, union sector and aggregate variables take the same value. Hence we can use Eqs. (9) and (10) in combination with (5) to determine aggregate employment under full information, l* , while the former two equations together identify directly the corresponding real wage (w − p)* : Λcu [α + ε(1 − α)] l∗ = θ (11) αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)] αγ + Λε θ (12) (w − p)∗ = αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)] It is evident from (11) and (12) that the aggregate nominal wage response to any non-zero value of the aggregate demand shock prevents any impact on either employment or the real wage. By raising its nominal wage exactly in line with the value of the disturbance, each union completely insulates both arguments of its objective function from the shock. The consequences of productivity disturbances, however, are rather more complex reflecting the fact that, following a non-zero realization of θ, greater employment stability can be achieved only at the expense of a greater variation in the real wage. Thus, when choosing their nominal wage response, unions face a tradeoff between the two arguments of their objective function and choose wages to achieve an optimal combination of real wage and employment stability, given the perceived trade-off between these two objectives. The aggregate outcome of individual union wage decisions, and thus their consequence for employment and the real wage, depends both on the extent to which wage bargaining is decentralized, as reflected in n,10 and on the degree of product market competition, as represented by ε. Using Eqs. (11) and (12), it is straightforward to demonstrate that, for any non-zero value of the productivity shock, the resulting deviation of employment from its mean value is larger, while the corresponding adjustment of the real wage is smaller, the more decentralized is wage bargaining, i.e., the larger is n, and the less the degree of competition in the product market, i.e., the smaller is ε. The influence of n and ε on employment and real wage behavior is reflected in the expected union loss associated with fully-informed wage setting, E(Ω* ), found by using Eqs. (11) and (12) in combination with (8): E(Ω∗ ) =
cu {(αγ + Λε)2 + Λ2 cu [α + ε(1 − α)]2 }σθ2 {αγ + Λε + Λ(1 − α)cu [α + ε(1 − α)]}2
(13)
10 In identifying the influence of the extent to which wage bargaining is decentralized on equilibrium outcomes, it is important to recognize the dependence of Λ on n.
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Differentiating this expression with respect to ε and n (noting the dependence of Λ on n) allows two important properties of E(Ω* ) to be identified, as summarized in the following Proposition: Proposition 1. With full-information wage setting, the expected union loss is: (a) strictly increasing in n for 1 < ε < ∞, (b) strictly decreasing in ε for 1 < n. The findings of Proposition 1 result from an externality which is present in union wage setting, and which leads to an inefficient aggregate wage response to productivity shocks. As discussed, given any non-zero realization of the productivity shock, the individual union’s nominal wage choice is directed at achieving the optimal combination of employment and real wage stability. However, the union only partially internalizes the implications of its decision for the price level and, through (2), aggregate demand. Hence it disregards the impact of any induced change in the price level on employment in other sectors, with the consequence that the overall employment cost of limiting a departure of the real wage from its desired value is underestimated at the level of the individual union. The result is a suboptimally low degree of real wage adjustment and an inefficiently large change in aggregate employment. The more centralized is wage bargaining (the smaller is n) the greater the extent to which the externality resulting from the individual union’s wage decision is internalized. Hence the response of the real wage to productivity shocks is greater, implying correspondingly smaller variations in employment. In the limiting case in which wage setting is perfectly coordinated by a single monopoly union (n = 1), the efficiency losses associated with the externality are eliminated completely and the expected union loss achieves its minimum value. The significance of the degree of product market competition (ε) derives from the fact that the extent of the externality is larger the greater is the capacity of firms within an individual union sector to raise their own product price above the prevailing average value. Thus, the larger is ε, and the smaller the scope for an individual firm’s price to deviate from p, the closer the equilibrium which results from individual union wage decisions lies to the efficient outcome. Because the inefficiency which characterizes equilibrium has its source in the divergence of each union’s perceived trade-off between employment and the real wage from the corresponding aggregate trade-off, this inefficiency would disappear if unions had only a single objective. If, for example, unions were concerned only with employment stability, in which case cu = 0, fullyinformed wage setting would achieve the optimal outcome and maintain employment constant following any non-zero realization of θ. Alternatively, if stabilization of the real wage was the only objective of unions, an eventuality represented in our framework as the limiting case associated with cu → ∞, then the wage decisions of individual unions would be consistent with this aim and completely insulate the real wage from the potential impact of productivity shocks. The factors which underlie the equilibrium which results when unions have full information also play an important role in determining the equilibrium associated with the multiparameter indexation scheme. We now turn to analyze the nature of this equilibrium. 4. Multiparameter indexation and macroeconomic equilibrium In contrast to the preceding analysis of full-information wage setting, it is now assumed that contracts are set when neither firms nor workers possess any information about the realizations of ¯ j and indexation the aggregate demand and productivity shocks. Contracts specify a base wage w
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parameters, xj and bj , relating the actual nominal wage, wj , to unexpected movements in the price level and the level of productivity: ¯ j + xj (p − Ep) + bj θ wj = w
(14)
We follow Drudi and Giordano (2000) in assuming that the contract wage is directly indexed to the shock. A possible objection is that real-world employment contracts generally do not index nominal wages either to productivity or to the marginal product of labor. While this objection has some force, realism also argues against the complete omission of a productivity-related term from the nominal wage equation, since employment contracts frequently contain profit-sharing clauses which indirectly link workers’ remuneration (including deferred remuneration in the form of pensions) to productivity. The modeling strategy adopted here can therefore be justified as a convenient and straightforward means of capturing the widespread linking of contract wages to productivity-related outcomes.11 ¯ j such that Given its objective function, each union minimizes its expected loss by setting w E(lj ) = 0. From (5), this implies: ¯j = w
(ε − γ) Ep ε
(15)
Following the derivation of Eq. (9), Eqs. (14) and (15) can be used with (2) and (5) to find the following expression for the price level:12 [γ(1 − α)φ − (1 − αb)θ] (16) [γ(1 − α) + α(1 − x)] where x = (1/n) nj=1 xj , b = (1/n) nj=1 bj . The individual union’s optimal choice of indexation parameters solves the two simultaneous first-order conditions, ∂E(Ω)/∂xj = 0 and ∂E(Ω)/∂bj = 0, taking the indexation decisions of all other unions as given, but accounting for the consequences of its own choice for the aggregate parameters x and b and, thereby, for aggregate variables. Combining Eqs. (14)–(16) provides an expression for union j’s real wage, which, together with (5), can be substituted into Eq. (8) to determine the individual union’s expected loss. Differentiating this expression with respect to xj , then with respect to bj , yields the two first-order conditions expressed in terms of the model’s structural parameters, as well as xj , bj , x and b. Imposing xj = x and bj = b then determines the ˆ 13 symmetric Nash equilibrium parameter values, xˆ and b: p=
xˆ = 1 bˆ =
[α + nε(1 − α)] {α + nε(1 − α) + ncu (1 − α)2 [α + ε(1 − α)]}
(17a) (17b)
Several aspects of (17) are noteworthy. First, as in other macroeconomic studies of multiparameter wage indexation, the relative variances of the two shocks do not help determine the equilibrium 11 Qualitatively very similar results are obtained in a version of our model which features indexation of the nominal wage to both the price level and aggregate output (as advocated by Karni), or alternatively to the price level and aggregate employment. 12 Note this expression implies Ep = 0, hence w ¯ j = 0. 13 In the limiting cases which arise for n = 1 and as n → ∞, it is straightforward to demonstrate that the solution described by (17) is unique: for the general case of 1 < n < ∞, no alternative solution to that described by (17) can be identified.
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degree of indexation to either the price level or the productivity shock. This result contrasts with a general finding of the literature following Gray (1976) on indexing of the wage solely to the price level, namely that individual agents’ equilibrium indexation choices will depend on the relative variances of the two disturbances. The reason for this difference between the two veins of literature is that with two shocks, two (or more) indexation instruments allow the desirable degree of neutralization of aggregate demand disturbances14 to be achieved by an appropriate setting of one parameter, allowing the other parameter to be directed at achieving the optimal wage response to productivity shocks. Because our model assumes, like Karni (1983), that every firm employs labor under contracts, and omits a second sector with spot-market labor hiring which is central to Duca and VanHoose (1991, 1998), it is optimal for each union to index fully to the price level. The second significant feature of (17) is that the equilibrium degree of indexation to the producˆ u < 0. tivity shock depends on the weight, cu , placed by unions on real wage stability, with ∂b/∂c Hence, as in a full-information environment, the equilibrium nominal wage is influenced by the relative significance attached by unions to their two objectives, where this influence reflects the trade-off facing unions in the presence of productivity shocks. With xj = 1, setting bj closer to zero (given the indexation choices of all other unions) allows the individual union to achieve a more stable real wage, but at the expense of greater employment variability. Thus, if real wage stability was the sole objective of unions, captured in our framework as the limiting case arising as cu → ∞, (17b) indicates bˆ = 0 and, with xˆ = 1, the real wage would be completely rigid. Conversely, if unions were concerned only with stabilizing employment (in which case cu = 0), then bˆ = 1 and the nominal wage would be fully indexed to the productivity shock. In fact, this latter finding is closely related to Karni’s implicit result that, given a perfectly inelastic labor supply, fully indexing the nominal wage to the price level and aggregate output completely stabilizes employment at its market-clearing level. The influence of wage bargaining structure (n) and the degree of product market competition ˆ (ε) on bˆ is also evident from (17b). It is straightforward to establish that ∂b/∂n < 0 for 1 < ε < ∞, ˆ while ∂b/∂ε > 0 for n > 1. This dependence of the responsiveness of the nominal wage to productivity shocks on these structural parameters reflects the operation of an externality arising from union indexation choices which parallels that present with full-information wage setting. To directly compare this nominal wage with that occurring when unions are fully informed about the realizations of φ and θ before wages are set, and to establish whether the multiparameter indexation scheme replicates the full-information outcome, we use (17) to substitute for x and b in (14). Additionally, using (16) to substitute for p, we determine the nominal wage associated with the equilibrium multiparameter indexation scheme, which we denote by wMI : 1 [α + nε(1 − α)](1 − γ) + n(1 − α)cu [α + ε(1 − α)] θ (18) wMI = φ − γ α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)] Comparing Eqs. (10) and (18), it is apparent that the nominal wage response to productivity shocks under the multiparameter indexation scheme in general differs from that under fullyinformed wage setting.15 It follows that employment and real wage outcomes will also diverge.
14 Complete neutralization if every firm has labor contracts, as in Karni (1983), partial neutralization if some firms employ labor in a spot market, so that cross-sectoral spillovers arise, as in Duca and VanHoose (1998). 15 Note that one particular pair of values for x and b replicates the equilibrium outcome under full-information wage ˆ setting, namely x = 1, b = b ≡ (αγ + Λε)/{αγ + Λε + Λ(1 − ␣)cu [α + ε(1 − α)]}. For 1 < n < ∞, we find that b < b.
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Using (18), together with (5), (16) and (17a) allows us to identify the values of employment and the real wage under the multiparameter indexation scheme: n(1 − α)cu [α + ε(1 − α)] θ (19) lMI = α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)] α + nε(1 − α) θ (20) (w − p)MI = α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)] It is straightforward to demonstrate that the impact of productivity shocks on employment increases in (absolute) magnitude, while that on the real wage diminishes, the larger is n and the smaller is ε. Thus, the externality which results from individual union indexation choices operates in the same direction as in the full-information case. Significantly, however, comparison of (19) with (11) and of (20) with (12), establishes that, for given values of n and ε, the adjustment in employment associated with any non-zero realization of θ is generally smaller while that in the real wage is larger under the multiparameter indexation scheme than under fully-informed wage setting. The expected union loss, E(ΩMI ), to which these movements in employment and the real wage give rise is described by: E(ΩMI ) =
cu {[α + nε(1 − α)]2 + n2 (1 − α)2 cu [α + ε(1 − α)]2 }σθ2 2
{α + nε(1 − α) + n(1 − α)2 cu [α + ε(1 − α)]}
(21)
The following Proposition identifies the key properties of E(ΩMI ): Proposition 2. Given the multiparameter indexation scheme described by (14), with the equilibrium values of x and b identified by (17), the expected union loss, E(ΩMI ) is: (a) strictly increasing in n for 1 < ε < ∞, (b) strictly decreasing in ε for 1 < n, (c) strictly less than E(Ω* ) for 1 < ε < ∞, 1 < n < ∞.16 As is evident from parts (a) and (b) of Proposition 2, the qualitative influence of both wage bargaining structure and the degree of product market competition on the expected union loss is the same as that arising under fully informed wage setting. This congruence reflects the similarity of the externality in the two cases. Despite this similarity, the macroeconomic outcomes differ in the two scenarios, and part (c) of Proposition 2 identifies a surprising and noteworthy result: the expected union loss associated with the equilibrium multiparameter indexation scheme is generally smaller than in the full-information case.17 This finding is particularly significant, 16 The following is a proof. Equating (13) and (21) and solving for n, the only admissible finite solution value (i.e. the only n ≥ 1) to the equation E(Ω* ) = E(ΩMI ), is found to be n = 1. Since it has already been established that the equilibrium expected loss, as a function of n, is minimized in both scenarios when n = 1, we examine the second derivatives with respect to n of these loss expressions evaluated at n = 1. Since ∂2 E(Ω∗ )/∂n2 |n=1 = 3 2cu2 α2 [α + γ(1 − α)]2 σθ2 /γ 2 [α + ε(1 − α)]2 [1 + cu (1 − α)2 ] > ∂2 E(ΩMI )/∂n2 |n=1 = 2cu2 α2 (1 − α)2 σθ2 /[α + ε(1−α)]2 3
[1 + cu (1 − α)2 ] , it follows that E(Ω* ) > E(ΩMI ) for all finite n > 1. 17 Note that if we consider a standard expected social loss function E(Γ ) = E(l2 + δπ 2 ), where π ≡ p − p −1 (and with p−1 conveniently normalized at zero), we find that E(Γ )|x=1,b=bˆ < E(Γ ∗ ) for 1 < n < ∞.Thus, when the economy features multiple non-atomistic unions, not only the expected loss of unions, but also the expected social loss, is lower in equilibrium under multiparameter indexation than under full-information wage setting.
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given that the criterion by which indexation schemes are typically evaluated is their ability to approximate full-information outcomes. This counterintuitive result arises because under the multiparameter indexation scheme, full indexation of the nominal wage to the price level increases the sensitivity of the latter to nominal wage adjustments resulting directly from non-zero realizations of θ.18 This greater responsiveness of the price level translates into a larger impact on aggregate demand and, hence, on employment within each union sector. As a consequence, when making its choice of bj , each union perceives a less favorable trade-off between employment and real wage stability than under full-information wage setting: specifically, under the multiparameter indexation scheme, the union discerns the employment-variability cost of achieving a more stable real wage to be higher. Hence the perceived trade-off at the level of the individual union approximates more closely the actual tradeoff at the aggregate level.19 Reflecting this, each union’s choice of bj leads, in aggregate, to a smaller efficiency loss than that which arises in the full-information case. The exceptions to this general superiority of the equilibrium multiparameter indexation scheme are provided by the two extreme cases of wage bargaining structure. Because a single economywide union fully internalizes the consequences of its decisions for aggregate demand, both fullyinformed wage setting and the multiparameter indexation scheme are equally capable of achieving the efficient nominal wage response to non-zero realizations of θ. The expected union loss in the two cases is thus identical and is described by: E(ΩMI )|n=1 = E(Ω∗ )|n=1 =
cu σθ2 1 + cu (1 − α)2
(22)
In the opposite limiting case of atomistic unions, each union views the impact of its choice variable, whether wj or bj , on the price level as negligible with the implication that the greater sensitivity of the price level to nominal wage adjustments under the multiparameter indexation scheme is irrelevant. As a result, the perceived trade-off between employment and real wage stability in the two scenarios is identical. Consequently, individual union decisions give rise to the same nominal wage response to productivity shocks under the multiparameter indexation scheme as under full-information wage setting and thus the expected union loss in the two cases is the same: lim E(ΩMI ) = lim E(Ω∗ ) =
n→∞
n→∞
cu {ε2 + cu [α + ε(1 − α)]2 }σθ2 {ε + cu (1 − α)[α + ε(1 − α)]}2
(23)
Viewing the findings represented by Eqs. (22) and (23) against the perspective of part (c) of Proposition 2 highlights an important implication for evaluating indexation schemes in the presence of externalities. That is, models which focus on only one or other of the extreme cases of wage bargaining structure may, when externalities are present, arrive at conclusions whose validity is specific to that particular case. Furthermore, intermediate degrees of wage-bargaining centralization potentially give rise to rather different results. Our findings are summarized in Table 1, which also identifies the crucial role played by union objectives in generating the key results of this paper.
18
This can be seen by comparing (16), with x set to unity, with (9). The relationship between the individual union’s perceived trade-off between employment and real wage stability under both full-information wage setting and the multiparameter indexation scheme, and the aggregate trade-off is explicitly identified in an Appendix which is available from the authors upon request. 19
Table 1 Key findings and the role of union objectives Equilibrium value of indexation parameters
Influence of degree of product market competition and wage bargaining structure on equilibrium degree of indexation to productivity shocks
Influence of degree of product market competition and wage bargaining structure on expected union loss with multiparameter indexation
Expected union loss associated with multiparameter indexation scheme compared to full information outcome
Further remarks
General case: 0 < cu < ∞
ˆ where x = 1, b = b, 0 < bˆ < 1
ˆ 0 < ∂b/∂ε for ˆ 1 < n, ∂b/∂n < 0 for 1<ε<∞
∂E(ΩMI )/∂ε < 0 for 1 < n, ∂E(ΩMI )/∂n > 0 for 1<ε<∞
E(ΩMI ) < E(Ω* ) for 1 < ε < ∞ and 1 < n < ∞
Union objectives relate solely to employment stability: cu = 0
x = 1, b = 1
No effect
No effect
E(ΩMI )|cu =0 = E(Ω∗ )|cu =0
Union objectives relate solely to real wage stability: cu → ∞
x = 1, b = 0
No effect
No effect
E(ΩMI )|cu →∞ = E(Ω∗ )|cu →∞
Despite efficiency losses multiparameter indexation achieves superior outcomes to those attained by indexation of nominal wages only to price level. Replicates Karni’s (1983)a findings. Constraining b to zero, with indexation only to prices, reproduces Gray’s (1976)a and Ball’s (1988)b results. Multiparameter indexation achieves superior outcomes. Multiparameter indexation redundant: unions choose to index nominal wages only to the price level.
a b
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Relative weight placed on real wage stability by unions
With perfectly inelastic labor supply. Absent indexation costs. 477
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5. Concluding remarks This paper extends the analysis of multiparameter indexation to consider the macroeconomic implications of such a scheme for an economy characterized by a monopolistically competitive goods market and in which wage contracts are set strategically by non-atomistic unions. Assuming nominal wages can be indexed to both the price level and the productivity shock, the indexation choices of individual unions were analyzed and the characteristics of the resulting equilibrium identified. The equilibrium degree of indexation to productivity shocks depends on both the degree of product market competition and the economy’s wage bargaining structure. Underlying this result is the presence of an externality in union indexation decisions which parallels that found to operate under full-information wage setting. Comparing the macroeconomic outcomes under the multiparameter indexation scheme with those in the case of fully-informed wage setting yields two particularly significant findings. First, outside the two extreme cases of one or an infinite number of unions, the equilibrium differs between the scenarios. Second, when evaluated in terms of the union objective function, the multiparameter indexation scheme delivers superior outcomes. In the light of this latter finding, it appears that the early literature’s emphasis on the informationexploiting properties of multiparameter indexation schemes was well founded. Indeed, such schemes may work better than the original contributors to their analysis might have imagined. Our findings suggest that when the underlying economic structure gives rise to negative externalities, the information regarding stochastic shocks embodied in aggregate variables may be exploited more efficiently under endogenous indexation than when full information regarding such shocks is available at the time wages are determined. Acknowledgements The authors gratefully acknowledge helpful comments from two anonymous referees and the editors. References Ball, L. (1988). Is equilibrium indexation efficient? Quarterly Journal of Economics, 103(2), 299–311. Blanchard, O. J. (1979). Wage indexing rules and the behavior of the economy. Journal of Political Economy, 87(4), 798–815. Bratsiotis, G., & Martin, C. (1999). Stabilization, policy targets, and unemployment in imperfectly competitive economies. Scandinavian Journal of Economics, 101(2), 241–256. Calmfors, L., & Johansson, A. (2006). Nominal wage flexibility, wage indexation and monetary union. Economic Journal, 116, 283–308. Coricelli, F., Cukierman, A., & Dalmazzo, A. (2006). Monetary institutions, monopolistic competition, unionized labor markets and economic performance. Scandinavian Journal of Economics, 108(1), 39–63. Crosby, M. (1995). Wage indexation and the time consistency of government policy. Scandinavian Journal of Economics, 97(1), 105–121. Cukierman, A., & Lippi, F. (1999). Central bank independence, centralization of wage bargaining, inflation and unemployment. European Economic Review, 43(7), 1395–1434. De Bruyne, G. (1997). Wage indexation and the exchange rate regime: A strategic analysis. Journal of Macroeconomics, 19(3), 571–589, Summer. Drudi, F., & Giordano, R. (2000). Wage indexation, employment and inflation. Scandinavian Journal of Economics, 102(4), 645–668. Duca, J. V. (1987). The spillover effects of nominal wage rigidity in a multisector economy. Journal of Money, Credit and Banking, 19(1), 117–121.
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