THE ECONOMETRICS OF MACROECONOMIC MODELLING

An important unstable solution: the ‘no wedge’ case

Real-wage resistance is an inherent aspect of the stable solution, as 6wu = 0 is one of the conditions for the stability of the wage-price system, cf. equation (6.15). However, as we have discussed earlier, the existence or otherwise of wedge effects remains unsettled, both theoretically and empirically, and it is of interest to investigate the behaviour of the system in the absence of real wage resistance, that is, 6wш = 0 due to ш = 0.

Inspection of (6.9) and (6.12) shows that in this case, the system partitions into a stable real wage equation

Wq, t = $t + £Apit + KWq, t-1 - nut-1, (6.28)

and an unstable equation for the real exchange rate

Apiq, t = - dt + eApit - kwq, t-1 + nut-1. (6.29)

Thus, in the same way as in the stable case of ш > 0, the real wage follows a stationary autoregressive process around the productivity trend which is included in St. However, from (6.29), the real exchange rate is seen to follow a unit root process, albeit with wq, t-1, ut-1, and a (suppressed) disturbance term as I(0) variables on the right-hand side.[41]

The steady-state real-wage path is given by:

Unlike the real wage given by (6.19), the coefficients of the long-run real wage in (6.30) contain parameters from both sides of the bargain, not only price-setting. The expression for the long-run multiplier with respect to the unemployment rate, dwq, ss/duss, shows interesting differences from the stable case in Section 6.4:

dwq, ss [^0w(1 '0qw) dq$(1 Фwq ФwpФ)]

duss [dw(1 Фqw) + dq(1 Фwq ФwpФ)

The multiplier is now a weighted sum of the two coefficients w (wage curve) and $ (price-setting). With normal cost pricing $ = 0, the long-run multiplier is seen to be negative.

The long-run elasticity of wq, ss with respect to productivity becomes

dwq, ss 1 + (@q/@w X1 фwq фwpФ') / (1 фqw)

da 1 + (0q/0w)(1 фwq фwpФ)/(1 фqw)

Hence, in the case of 1 _ 1 in the cointegrating wage equation, the long-run multiplier implies that the product real-wage will increase by 1% as a result of a 1% permanent increase in productivity. Thus, the steady-state wage share is again without a deterministic trend.

The steady-state rate of inflation in the no-wedge case is obtained by sub­stituting the solution for the real wage (6.30) back into the two equilibrium correction equations (6.3), imposing ш _ 0, and (6.5), and then using the definition of consumer prices in (5.9). The resulting steady-state rate of infla­tion can be shown to depend on the unemployment rate and on import price growth, that is, Ap _ Api in the equilibrium associated with the ‘no wedge’ case (ш _ 0). Instead, the derived long-run Phillips curve is downward-sloping provided that n > 0.

Finally we note that, unlike the static wage curve of Chapter 5, the ‘no wedge’ restriction (ш _ 0) in itself does not imply a supply-side deter­mined equilibrium rate of unemployment.[42] The restrictions that are sufficient for the model to imply a purely supply-side determined equilibrium rate of unemployment is considered in Section 6.5.