THE ECONOMETRICS OF MACROECONOMIC MODELLING

# Is the Phillips curve consistent with persistent changes in unemployment?

In the expressions for the main-course NAIRU (4.5) and (4.10), wphl1 depends on parameters of the wage Phillips curve (4.1) and exogenous growth rates. The coefficients of the unemployment equation do not enter into the natural rate NAIRU expression. In the other version of the Phillips curve, the expression for the NAIRU depends on parameters of price-setting as well as wage-setting, that is, the model is specified as a price Phillips curve rather than a wage Phillips curve. But the NAIRU expression from a price Phillips curve remains independent of parameters from equation (4.2) (or its counterpart in other specifications).

The fact that an important system property (the equilibrium of unem­ployment) can be estimated from a single equation goes some way towards explaining the popularity of the Phillips curve model. Nevertheless, results based on analysis of the incomplete system gives limited information. In par­ticular, a single-equation analysis gives insufficient information of the dynamic properties of the system. First, unless the Phillips curve is estimated jointly with equation (4.2), dynamic stability cannot be tested, and the correspond­ence between wphl1 and the steady state of the system cannot be asserted. Thus, single equation estimates of the NAIRU are subject to the critique that the correspondence principle may be violated (see Samuelson 1941). Second, even if one is convinced a priori that wphl1 corresponds to the steady state of the system, the speed of adjustment towards the steady state is clearly of interest and requires estimation of equation (4.2) as well as of the Phillips curve (4.1).

During the last 20-25 years of the previous century, European rates of unemployment rose sharply and showed no sign of reverting to the levels of the 1960s and 1970s. Understanding the stubbornly high unemployment called for models that (1) allow for long adjustments lags around a constant natural rate, or (2) allow the equilibrium to change. A combination of the two is of course also possible.

Simply by virtue of being a dynamic system, the Phillips curve model accommodates slow dynamics. In principle, the adjustment coefficient ви1 in the unemployment equation (4.2) can be arbitrarily small—as long as it is not zero the wphl1 formally corresponds to the steady state of the system. However, there is a question of how slow the speed of adjustment can be before the concept of equilibrium becomes undermined ‘from within’. According to the arguments of Phelps and Friedman, the natural rate ought to be quite stable, and it should be a strong attractor of the actual rate of unemployment (see Phelps 1995). However, the experience of the 1980s and 1990s has taught us that the natural rate is at best a weak attractor. There are important practical aspects of this issue too: policy makers, pondering the prospects after a nega­tive shock to the economy, will find small comfort in learning that eventually the rate of unemployment will return to its natural rate, but only after 40 years or more! In Section 4.6 we show how this kind of internal inconsistency arises in an otherwise quite respectable empirical version of the Phillips curve system (4.1) and (4.2).

Moreover, the Phillips curve framework offers only limited scope for an eco­nomic explanation of the regime shifts that sometimes occur in the mean of the rate of unemployment. True, expression (4.10) contains a long-run Okun’s law type relationship between the rate of unemployment and the rate of produc­tivity growth. However, it seems somewhat incredible that changes in the real growth rate ga alone should account for the sharp and persistent rises in the rate of unemployment experienced in Europe. A nominal growth rate like gf can of course undergo sharp and large rises, but for those changes to have an impact on the equilibrium rate requires a downward sloping long-run Phillips curve—which many macroeconomists will not accept.

Thus, the Phillips curve is better adapted to a stable regime characterised by a modest adjustment lag around a fairly stable mean rate of unemploy­ment, than to the regime shift in European unemployment of the 1980s and 1990s. This is the background against which the appearance of new models in the 1980s must be seen, that is, models that promised to be able to explain the shifts in the equilibrium rate of unemployment (see Backhouse 2000), and there is now a range of specifications of how the structural characteristics of labour and commodity markets affect the equilibrium paths of unemployment (see Nickell 1993 for a survey and Chapter 5 of this book). Arguably how­ever, none of the new models have reached the status of being an undisputed consensus model that once was the role of the Phillips curve.

So far we have discussed permanent changes in unemployment as being due to large deterministic shifts that occur intermittently, in line with our maintained view of the rate of unemployment as I(0) but subject to (infrequent) structural breaks. An alternative view, which has become influential in the United States, is the so-called time varying NAIRU: cf. Gordon (1997), Gruen et al. (1999), and Staiger et al. (1997). The basic idea is that the NAIRU reacts to small supply-side shocks that occur frequently. The following modifications of equation (4.3) defines the time varying NAIRU

= —fiw1(ut — Ut) + Pw2^at + + 8wt: (4.11)

Ut = ut-l + £u, t - (4.12)

The telling difference is that the natural rate U is no longer a time-independent parameter, but a stochastic parameter that follows the random walk (4.12), and a disturbance £u, t which in this model represents small supply-side shocks. When estimating this pair of equations (by the Kalman filter) the standard error of eu, t typically is limited at the outset, otherwise ut will jump up and down and soak up all the variation in Awt left unexplained by the conventional explanatory variables. Hence, time varying NAIRU estimates tend to reflect how much variability a researcher accepts and finds possible to communicate. Logically, the methodology implies a unit root, both in the observed rate of unemployment and in the NAIRU itself. Finally, the practical relevance of this framework seems to be limited to the United States, where there are few big and lasting shifts in the rate of unemployment.

Related to the time varying NAIRU is the concept of hysteresis. Following Blanchard and Summers (1986), economists have invoked the term unemploy­ment ‘hysteresis’ for the case of a unit root in the rate of unemployment, in which case the equilibrium rate might be said to become identical to the lagged rate of unemployment. However, Rped (1994) instructively draws the distinc­tion between genuine hysteresis as a non-linear and multiple equilibrium phe­nomenon, and the linear property of a unit root. Moreover, Cross (1995) have convincingly shown that ‘hysteresis’ is not actually hysteresis (in its true mean­ing, as a non-linear phenomenon), and that proper hysteresis creates a time path for unemployment which is inconsistent with the natural rate hypothesis.

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