THE ECONOMETRICS OF MACROECONOMIC MODELLING

Beyond the natural rate doctrine: unemployment-inflation dynamics

In this section, we relax the assumption, made early in the section, of exo­genously determined unemployment which, after all, was made for a specific purpose, namely for showing that under reasonable assumptions about price - and wage-setting, there exist a steady-state rate of inflation, and a steady - state growth rate for real wages for a given long-run mean of the rate of unemployment. Thus, the truism that a steady state requires that the rate of unemployment simultaneously converges to the NAIRU has been refuted. Moreover, we have investigated special cases where the natural doctrine rep­resents the only logically possible equilibrium, and have discussed how the empirical relevance of those special cases can be asserted.

6.9.1 A complete system

Equations (6.51)-(6.57) are a distilled version of an interdependent system for real wages, the real exchange rate and unemployment that we expect to encounter in practical situations.

Awq, t = 5t + £Apit + ( - 1)wq, t-1 + piq, t-L - VUt-1 + £wq, t, (6.51)

Apiq, t = - dt + e Apit - kwq, t-1 + ( - 1) piq, t-1 + ПЩ-1 + £piq, t,

(6.52)

Aut = (3u0 - (1 - (3u1)ut-1 + fin2wq, t-1 + (3u3at-1

+ [du4piq, t — 1 [du5zut + £u, t: (6.53)

Apit = gpi + £pi, t, (6.54)

Aqt = Apit - Apiq t, (6.55)

Awt = Awq, t + Aqt, (6.56)

Apt = bp1(Awt - Aat) + bp2Apit + £p, t - (6.57)

Equations (6.51) and (6.52) are identical to equations (6.9) and (6.12) of Section 6.3, where the coefficients were defined. Note that the two intercepts have time subscripts since they include the (exogenous) labour productivity at, cf. (6.10) and (6.13). The two equations are the reduced forms of the theoretical
model that combines wage bargaining and monopolistic price-setting with equi­librium correction dynamics. Long-run dynamic homogeneity is incorporated, but the system is characterised by nominal rigidity. Moreover, as explained above, not even dynamic homogeneity in wage - and price-setting is in general sufficient to remove nominal rigidity as a system property.

A relationship equivalent to (6.53) was introduced already in Section 4.2, in order to close the open economy Phillips curve model. However there are two differences as a result of the more detailed modelling of wages and prices: first, since the real exchange rate is endogenous in the general model of wage price dynamics, we now include piq, t-1 with non-negative coefficient (fiu,4 > 0).[51] Second, since we maintain the assumption about stationarity of the rate of unemployment (in the absence of structural break), that is, @u1 < 1, we include at-1 unrestricted, in order to balance the productivity effects on real wages and/or the real exchange rate. In the same way as in the section on the Phillips curve system, zut represents a vector consisting of I(0) stochastic variables, as well as deterministic explanatory variables.

Equation (6.54) restates the assumption of random walk behaviour of import prices made at the start of the section, and the following two equations are definitions that back out the nominal growth rates of the product price and nominal wage costs. The last equation of the system, (6.57), is a hybrid equation for the rate of inflation that has normal cost pricing in the non-tradeables sector built into it.[52]

The essential difference from the wage-price model of Section 6.2 is of course equation (6.53) for the rate of unemployment. Unless (3u2 = (3u3 = 0, the stability analysis of Section 6.4 no longer applies, and it becomes impractical to map the conditions for stable roots back to the parameters. However, for estimated versions of (6.51)-(6.57) the stability or otherwise is checked from the eigenvalues of the associated companion matrix (as demonstrated in the next paragraph). Subject to stationarity, the steady-state solution is easily obtained from (6.51)-(6.53) by setting Awqt = ga, Apiqt = 0, Auss = 0, and solving for wq, ss, piq, ss, and uss. In general, all three steady-state variables become functions of the steady states of the variables in the vector zu, t, the conditioning variables in the third unemployment equation, in particular

f (zu, ss) ■

Note that while the real wage is fundamentally influenced by productiv­ity, ut ~ I(0) implies that equilibrium unemployment uss is unaffected by the level of productivity. Is this equilibrium rate of unemployment a ‘natural rate’? If we think of the economic interpretation of (6.53) this seems unlikely: equation (6.53) is a reduced form consisting of labour supply, and the labour demand of private firms as well as of government employment. Thus, one can
think of several factors in zu, t that stem from domestic demand, as well as from the foreign sector. At the end of the day, the justification of the spe­cific terms included in zu, ss and evaluation of the relative strength of demand - and supply-side factors, must be made with reference to the institutional and historical characteristics of the data.

In the next section, we give an empirical example of (6.51)-(6.57), and Chapters 9 and 10 present operational macroeconomic models with a core wage-price model, and where (6.51) is replaced by a system of equations describing output, domestic demand, and financial markets.