THE ECONOMETRICS OF MACROECONOMIC MODELLING
Cointegration, long-run multipliers, and the steady state
There is a correspondence between the elasticities in the equations that describe the steady-state growth paths and the elasticities in the cointegrating relationships (5.11) and (5.14). However, care must be taken when mapping from one representation to the other. For example, since much applied work pays more attention to wage-setting (the bargaining model) than to price-setting, it is often implied that the coefficient of unemployment in the estimated cointegrating wage equation also measures how much the steady-state growth path of real wages changes as a result of a permanent shift in the rate of unemployment. In other words, the elasticity in the cointegrating equation is interpreted as the long-run multiplier of real wages with respect to the rate of unemployment. However, from (6.19) the general result (from the stable case) is that the long-run multiplier of the producer real wage wq is
r/° = $ > 0,
Comparing the multipliers for the two definitions of the real wage, it is evident that it is only the multiplier of the consumer real wage curve that has the conventional negative sign. However, also d(w — p)/du is a function of the elasticities from both cointegrating relationships (price and wage).
The one-to-one correspondence between the long-run multiplier and the unemployment elasticity in the ‘wage curve’ (5.11) requires additional assumptions. Consider, for example, the case of w = 1 and $ = 0, that is, only costs
of living (not product prices) play a role in wage bargaining, and domestic firms practice normal cost pricing. As argued in Section 5.4, this corresponds to the case of aggregate wage-price dynamics, and we obtain dwq/du = 0 and d(w — p)/du = —w. Thus, the long-run multiplier of the consumer real wage is identical to the elasticity of unemployment in the wage curve in this case.
