THE ECONOMETRICS OF MACROECONOMIC MODELLING
Nominal rigidity despite dynamic homogeneity
At first sight, one might suspect that the result that uss is undetermined by the wage - and price-setting equations has to do with dynamic inhomogeneity, or ‘monetary illusion’. For example, this is the case for the Phillips curve model where the steady-state rate of unemployment corresponds to the natural rate whenever the long-run Phillips curve is vertical, which in turn requires that dynamic homogeneity is fulfilled. Matters are different in the model in this section, though. As explained above, the property of dynamic homogeneity requires that we impose фqw + фqi = 1 in the equation representing price formation, and фwq + ф^ = 1 in the dynamic wage curve. It is seen directly from (6.18) that the model is asymptotically stable even when made subject to these two restrictions. Thus the equilibrium conditioned on a level of unemployment uss determined outside the system, does not require dynamic inhomogeneity. Put differently, the two restrictions, фqw + фф = 1 and фwq + ф^ = 1 (dynamic homogeneity) do not remove nominal rigidity from the system.
The stable solution even applies to the case of фqw = 1 (ф^ = 0), in which case the coefficients of the reduced form equation for wq, t reduce to
St = (Cq 0q mf 0q at-1)?
Є = 0,
X = 0, (6.26)
К = 1 — 0q,
V = — gq,
while the coefficients (6.13) of the reduced form equation (6.12) for piq become
d = [(Cq — 0q mf — 0 q at-l) + (Cw + 0W mb + Mt-l)j /l^wp(1 — Ф),
e = 0,
l = 1 — 0w ^/^wV, (6.27)
k =(0q — 0w )/^wP(1 — Ф)), n = (gw + gq )/^wP(1 — Ф)).
Since X = 0 in (6.26), there is no effect of the real exchange rate in the reduced-form equation for real wages, hence the solution for real wages can be obtained from equation (6.9) alone. Note also how all coefficients of the real wage equation (6.9) depend only on parameters from the firms’ price-setting, whereas the competitiveness equation (6.12) still amalgamates parameters from both sides of the wage bargain, as is seen from the coefficients in (6.27).
The steady state is given by (6.19) and (6.20) as before. The expressions for and n0 are unchanged, but £0 = e0 = 0 as a result of dynamic homogeneity, hence we obtain the expected result that the steady-state real exchange rate and the real wage are both unaffected by the rate of international inflation.
