THE ECONOMETRICS OF MACROECONOMIC MODELLING

Comparison with the wage-curve NAIRU

In Chapter 5 we saw that the model with bargained wages and price-setting firms defined a certain level of unemployment denoted uw at which the con­flicting real wage claims were reconciled. Moreover, if there is no wedge term in wage-setting, theory implies that uw depends only of factors in wage - and price-setting.

Recall first that the two long-term relationships are

wage-setting Wq, t = mb + iat + upq, t — wut + ecmb, t, E[ecmb, t] = 0,

price-setting wq, t = mf + at + dut + ecmf, t, E[ecmf, t] = 0.

The counterpart to uw is derived by taking the (unconditional) expectation on both sides of (5.11) and (5.14) and solving for the rate of unemployment:

We add a time subscript to Uw, since the mean of productivity, a non-stationary variable, enters on the right-hand side of the expression. Remember that at in wage-setting is essential for the framework to accommodate the integration properties of the wage and price data. However, in the case of i =1 (full pass through of productivity on real wages) and ш = 0 (no wedge) the expression of the wage curve NAIRU simplifies to

mb — mf (d + w)

which corresponds to the fundamental supply-side determined NAIRU of the static incomplete competition model (see equation (5.8)).

In Section 6.4 we established the general result that ut ^ uss = uw, which contradicts ICM though we build on the same long-run wage and price equations. The difference is that we model the implied equilibrium correction behaviour of wages and prices. Thus, there is in general no correspondence between the wage curve NAIRU and the steady state of the wage-price system (the correspondence principle of Samuelson (1941) appears to be violated).

Interestingly, elimination of ‘money illusion’, by imposing фwp + фwq = 1 (workers) and фqw + фф = 1 (firms), is not enough to establish dynamic cor­respondence between uw and uss, see Section 6.4.2. Instead, to formulate a

dynamic model that captures the heuristic dynamics of the static wage curve model, we invoke the following set of restrictions:

(1) Eliminate the wedge in the long-run wage equation, ш = 0, but maintain

ew > 0.

(2) Impose short-run homogeneity of the particular form фqw = фwq = 1, and hence фwp = фqi =0.

The implication of (1) and (2) is that (6.3) and (6.5) are two conflicting equa­tions of the product real wage wq, t. Essentially, all nominal rigidity is eliminated from the model. The assumption of an exogenously determined rate of unem­ployment can no longer be reconciled with dynamic stability.[43] Instead, we argue (heuristically) that unemployment has to converge to the level necessary to rec­oncile the ‘battle of markups’ incarnated in two conflicting real wage equations. Formally, the system that determines the time paths of wqt and ut becomes

A'wq, t — kw 0w wut-1 0 ww q, t-1 + 0w 1at-1 + ^w, t, (6.39)

A'wq, t = kq + 0q $ut—1 0q wq, t-1 + 0q at—1 + ^q, t• (6.40)

Consistency with cointegration implies that 0q and/or 0w are strictly positive, and the roots of (6.39) and (6.40) are therefore within the unit circle. Hence, in a situation where all shocks are switched off, ut ^ Uw:

where the second term on the right-hand side reflects that the model (6.39)-(6.40) is a dynamic generalisation of the conventional static ICM.

Figure 6.1 illustrates the different equilibria. The upward sloping line repre­sents firms’ price-setting and the downward sloping line represents wage-setting (they define a phase diagram). According to the wage curve model, the only possible equilibrium is where the two line cross, hence the NAIRU uw is also the dynamic equilibrium. It is not surprising to find that the natural rate property is equivalent to having a wage-price system that is free of any form of nominal rigidity, but the restrictions needed to secure nominal neut­rality are seldom acknowledged: neither long-term nor dynamic homogeneity are sufficient, instead the full set of restrictions in conditions (1) and (2) is required. There is no logical or practical reason which forces these restrictions on the dynamic wage-price system, and without them, a rate of unemployment like uss is fully consistent with a steady-state rate growth of the real wage, and a stationary wage share, cf. Section 6.4.

On the other hand, there is nothing that says that (1) and (2) cannot hold, and econometric specification and testing of wage-price systems should investigate that possibility.