THE ECONOMETRICS OF MACROECONOMIC MODELLING

Wage bargaining and monopolistic competition

There is a number of specialised models of ‘non-competitive’ wage-setting; see, for example, Layard et al. (1991: ch. 7). Our aim in this section is to rep­resent the common features of these approaches in a theoretical model of wage bargaining and monopolistic competition, building on Rpdseth (2000: ch. 5.9) and Nymoen and Rpdseth (2003). We start with the assumption of a large number of firms, each facing downward-sloping demand functions. The firms are price setters and equate marginal revenue to marginal costs. With labour being the only variable factor of production (and constant returns to scale) we obtain the following price-setting relationship:

EIqY Wi
EIqY - 1 Ai ’

where Ai = Yi/Ni is average labour productivity, Yi is output, and Ni is labour input. EIqY > 1 denotes the absolute value of the elasticity of demand facing each firm i with respect to the firm’s own price. In general EIqY is a func­tion of relative prices, which provides a rationale for inclusion of, for example, the real exchange rate in aggregate price equations. However, it is a common simplification to assume that the elasticity is independent of other firms’ prices and is identical for all firms. With constant returns technology aggregation is no problem, but for simplicity we assume that average labour productivity is the same for all firms and that the aggregate price equation is given by

eiq y w eiqy -1 A'

The expression for real profits (n) is therefore

We assume that the wage W is settled by maximising the Nash product:

(v - vofn1-U, (5.2)

where v denotes union utility and v0 denotes the fall-back utility or reference utility. The corresponding break-point utility for the firms has already been set to zero in (5.2), but for unions the utility during a conflict (e. g. strike or work-to-rule) is non-zero because of compensation from strike funds. Finally О represents the relative bargaining power of unions.

Union utility depends on the consumer real wage of an employed worker and the aggregate rate of unemployment, thus v(W/P, U, Zv) where P denotes the consumer price index (CPI).2 The partial derivative with respect to wages is positive, and negative with respect to unemployment (vW > 0 and v'v < 0). Zv represents other factors in union preferences. The fall-back or reference utility of the union depends on the overall real-wage level and the rate of unemployment, hence v0 = v0 (W/P, U) where W is the average level of nominal wages which is one of the factors determining the size of strike funds. If the aggregate rate of unemployment is high, strike funds may run low in which case the partial derivative of v0 with respect to U is negative (v0и < 0). However, there are other factors working in the other direction, for example, that the probability of entering a labour market programme, which gives laid-off workers higher utility than open unemployment, is positively related to U. Thus, the sign of v'0и is difficult to determine from theory alone. However, we assume in the following that vU — v0и < 0.

We abstract from income taxes.

With these specifications of utility and break-points, the Nash product, denoted N, can be written as

where Wq = W/Q is the producer real wage and Pq = P/Q is the wedge between the consumer and producer real wage. The first-order condition for a maximum is given by Nw = 0 or

75_____ vW(Wq/Pq, U, Zg)__________ = (і _ 7?) 1/A (5 3)

V (Wq/Pq, U,ZV) - Vo(W/P, U) У l - Wq/A) '

In a symmetric equilibrium, W = IT, leading to Wq/Pq = W/P in equation (5.3), and the aggregate bargained real wage W^ is defined implicitly as

Wb = F (Pq ,A,7,U). (5.4)

A log linearisation of (5.4), with subscript t for time period added, gives

w t = mb, t + ^pq, t — ttut, 0 < ш < 1, w > 0. (5.5)

mb, t in (5.5) depends on A, 7, and Zv, and any one of these factors can of course change over time.

As noted above, the term pq, t = (p — q)t is referred to as the wedge between the consumer real wage and the producer real wage. The role of the wedge as a source of wage pressure is contested in the literature. In part, this is because theory fails to produce general implications about the wedge coefficient ш—it can be shown to depend on the exact specification of the utility functions v and v0 (see, for example, Rpdseth 2000: ch. 8.5 for an exposition). We follow custom and restrict the elasticity ш of the wedge to be non-negative. The role of the wedge may also depend on the level of aggregation of the analysis. In the traded goods sector (‘exposed’ in the terminology of the main-course model of Chapter 3) it may be reasonable to assume that ability to pay and profitability are the main long-term determinants of wages, hence ш = 0. However, in the sheltered sector, negotiated wages may be linked to the general domestic price level. Depending on the relative size of the two sectors, the implied weight on the consumer price may then become relatively large in an aggregate wage equation.

Equation (5.5) is a general proposition about the bargaining outcome and its determinants, and can serve as a starting point for describing wage forma­tion in any sector or level of aggregation of the economy. In the rest of this section we view equation (5.5) as a model of the aggregate wage in the economy,

which gives the most direct route to the predicted equilibrium outcome for real wages and for the rate of unemployment. However, in Section 5.4 we consider another frequently made interpretation, namely that equation (5.5) applies to the manufacturing sector.

The impact of the rate of unemployment on the bargained wage is given by the elasticity w, which is a key parameter of interest in the wage curve literature. w may vary between countries according to different wage-setting systems. For example, a high degree of coordination, especially on the employer side, and centralisation of bargaining is expected to induce more responsiveness to unemployment (a higher w) than uncoordinated systems that give little incentives to solidarity in bargaining. At least this is the view expressed by authors who build on multi-country regressions; see, for example, Alogoskoufis and Manning (1988) and Layard et al. (1991: ch. 9). However, this view is not always shared by economists with detailed knowledge of, for example, the Swedish system of centralised bargaining (see Lindbeck 1993: ch. 8).

Figure 5.1 also motivates why the magnitude of w plays such an important role in the wage curve literature. The horizontal line in the figure is consist­ent with the equation for price-setting in (5.1), under the assumption that productivity is independent of unemployment (‘normal cost pricing’). The two downward sloping lines labelled ‘low’ and ‘high’ (wage responsiveness), repres­ent different states of wage-setting, namely ‘low’ and ‘high’ w. Point (i) in the figure represents a situation in which firm’s wage-setting and the bargain­ing outcome are consistent in both countries—we can think of this as a low unemployment equilibrium. Next, assume that the two economies are hit by a supply-side shock, that shifts the firm-side real wage down to the dotted line. The Layard-Nickell model implies that the economy with the least real-wage responsiveness w will experience the highest rise in the rate of unemployment, (ii) in the figure, while the economy with more flexible real wages ends up in point (iii) in the figure.

A slight generalisation of the price-setting equation (5.1) is to let the price markup on average cost depend on demand relative to capacity. If we in addition invoke an Okun’s law relationship to replace capacity utilisation with the rate of unemployment, the real wage consistent with firms’ price-setting, wf, can be written in terms of log of the variables as

wf t = mf, t + dut, d > 0. (5.6)

mf, t depends on the determinants of the product demand elasticity EIqY and average labour productivity at.