THE ECONOMETRICS OF MACROECONOMIC MODELLING

An empirical open economy Phillips curve system

In this section, we first specify and then evaluate an open economy Phillips curve for the Norwegian manufacturing sector. We use an annual data set for the period 1965-98, which is used again in later sections where competing models are estimated. In the choice of explanatory variables and of data trans­formations, we build on existing studies of the Phillips curve in Norway, cf. Stplen (1990, l993). The variables are in log scale (unless otherwise stated) and are defined as follows:

wct = hourly wage cost in manufacturing; qt = index of producer prices (value added deflator); pt = the official consumer price index (CPI); at = average labour productivity;

tut = rate of total unemployment (i. e. unemployment includes participants in active labour market programmes); rprt = the replacement ratio;

ht = the length of the ‘normal’ working day in manufacturing; t1 t = the manufacturing industry payroll tax-rate (not log).

Equation (4.42) shows the estimation results of a manufacturing sector Phillips curve which is as general as the number of observations allows. Arguably the use of OLS estimation may be defended by invoking the main - course theory (remembering that we model wages of an exposed industry), but the main reason here is plain simplicity, and we return to the estimation of the Phillips curve by system methods below.

The model is a straightforward application of the theoretical Phillips curve in (4.1): we include two lags in Aqt and Aat, and, as discussed ear­lier, it is a necessary concession to realism to also include a lag polynomial of the consumer price inflation rate, Apt. w We use only one lag of the unemploy­ment rate, since previous work on this data set gives no indication of any need to include a second lag of this variable.

Awct — Apt_i = — 0.0287 + 0.133Apt — 0.716Apt_1 — 0.287Apt_2

(0.0192) (0.182) (0.169) (0.163)

+ 0.0988Aat + 0.204Aat_1 — 0.00168Aat_2 (0.159) (0.153) (0.136)

+ 0.189Aqt + 0.317Aqt_1 + 0.177Aqt_2 — 0.0156 tut (0.0867) (0.0901) (0.0832) (0.0128)

— 0.00558 tut_1 + 0.796At1t + 0.0464 rprt_1

(0.0162) (0.531) (0.0448)

— 0.467Aht + 0.0293 i1967t — 0.0624IPt (4.42)

(0.269) (0.0201) (0.0146)

OLS, T = 34 (1965-98)

The last five explanatory variables in (4.42) represent two categories; these are, first, the theoretically motivated variables: the change in the payroll tax rate (At1t) and a measure of the generosity of the unemployment insurance system (the replacement ratio, rprt_1); and second, variables that capture the impact of changes in the institutional aspects of wage-setting in Norway. As indicated by its name, *1967t is an impulse dummy and is 1 in 1967 and zero elsewhere. It covers the potential impact of changes in legislation and indir­ect taxation in connection with the build up of the national insurance system in the late 1960s. Aht captures the short-run impact of income compensation in connection with the reforms in the length of the working week in 1964, 1968, and 1987 (see Nymoen 19896). Finally, IPt is a composite dummy representing a wage - and price-freeze in 1979 and centralised bargaining in 1988 and 1989: it is 1 in 1979 and 0.5 in 1980, 1 again in 1988 and 0.5 in 1989—zero elsewhere. The exact ‘weighting’ scheme is imported from Bardsen and Nymoen (2003).[25] [26]

The left-hand side variable in (4.42) is Awct — Apt-1, since our earlier experience with this data set (see, for example, Bardsen and Nymoen 2003, and Section 6.9.2), shows that the lagged rate of inflation is an important predictor of this year’s nominal wage increase. Note, however, that the transformation on the left-hand side does not represent a restriction in (4.42) since Apt-1 is also present on the right-hand side of the equation.

The general model (4.42) contains coefficient estimates together with con­ventionally computed standard errors (in brackets). Below the equation we report estimation statistics (T, number of observations; the residual sum of squares, RSS; the residual standard error <r, R2, and F^uii the probab­ility of observing an F value as large or larger as the one we observe, given the null of ‘no relationship’), and a set of mis-specification tests for the general unrestricted model (GUM): F-distributed tests of residual auto­correlation (FAr(1_2)), heteroskedasticity (Fhet®2), autoregressive conditional heteroskedasticity (Farch(i-i)) and the Doornik and Hansen (1994) Chi-square test of residual non-normality (x2ormaiity). The last two diagnostics reported are two tests of parameter constancy based on Chow (1960). The first is a mid­sample split (Fchow(1982)) and the second is an end-of-sample split (Fchow(1995)). For each diagnostic test, the numbers in square brackets are p-values for the respective null hypotheses; they show that none of the tests are significant.

Automatised general to specific model selection using PcGets (see Hendry and Krolzig 2001), resulted in the Phillips curve in (4.43).

Awct — Apt-i = — 0.0683 — 0.743Apt-i + 0.203Aqt (0.0139) (0.105) (0.0851)

+ 0.29Aqt-1 — 0.0316 tut — 0.0647IPt (4.43)

(0.0851) (0.00431) (0.0103)

OLS, T = 34 (1965-98)

RSS = 0.005608 a = 0.01415

Fgum = 1.462[0.23] Far(i-2) = 3.49[0.05]

Farch(i-i) = 0.157[0.90] x2ormaiity = 4.907[0.09]

Fchow(i982) = 0.575[0.85] Fchow(i995) = 0.394[0.76]

Whereas the GUM in (4.42) contains 16 explanatory variables, the final model (4.43) keeps only 5: the lagged rate of inflation, the current and lagged changes in the product price index, the rate of unemployment, and the com­posite incomes policy dummy. The test of the joint significance of the 11 restrictions is reported as Fgum below the equation, with a p-value of 0.23, showing that the increase in residual standard error from 1.3% to 1.4% is sta­tistically insignificant. The diagnostic tests confirm that the reduction process is valid, that is, only the test of 2. Order autocorrelation is marginally significant at the 5% level.

coefficients in earlier studies on both annual and quarterly data (see, for example, Johansen

1995a).

As discussed earlier, a key parameter of interest in the Phillips curve model is the equilibrium rate of unemployment, that is, wphl1 in (4.10). Using the coefficient estimates in (4.43), and setting the growth rate of prices (gf) and productivity growth equal to their sample means of 0.06 and 0.027, we obtain wphl1 = 0.0305, which is nearly identical to the sample mean of the rate of unemployment (0.0313).

In this section and throughout the book, figures often appear as panels of graphs, with each graph in a panel labelled sequentially by a suffix a, b,c,..., row by row. In Figure 4.2, the graphs numbered (a)-(f) show the recursively estimated coefficients in equation (4.43), together with ±2 estimated standard errors over the period 1976-98 (denoted в and ±2a in the graphs). The last row with graphs in Figure 4.2 shows the sequence of 1-step residuals (with ±2 residual standard errors denoted ±2se), the 1-step Chow statistics and lastly the sequence of ‘break-point’ Chow statistics. Overall, the graphs show a considerable degree of stability over the period 1976-98. However, Constant (a) and the unemployment elasticity (e) are both imprecisely estimated on samples that end before 1986, and there is also instability in the coefficient estimates (for Constant, there is a shift in sign from 1981 to 1982). These results will affect the natural rate estimate, since wphl1 depends on the ratio between Constant and the unemployment elasticity, cf. equation (4.5).

The period from 1984 to 1998 was a turbulent period for the Norwegian economy, and the manufacturing industry in particular. The rate of unem­ployment fell from 4.3% in 1984 to 2.6% in 1987, but already in 1989 it had risen to 5.4% and reached an 8.2% peak in 1989, before falling back to 3% in

1998.[27] An aspect of this was a marked fall in manufacturing profitability in the late 1980s. Institutions also changed (see Barkbu et al. 2003), as Norway (like Sweden) embarked upon less coordinated wage settlements in the begin­ning of the 1980s. The decentralisation was reversed during the late 1980s. The revitalisation of coordination in Norway has continued in the 1990s. However, according to (4.43), the abundance of changes have had only limited impact on wage-setting, that is, the effect is limited to two shifts in the intercept in 1988 and 1989 as IPt then takes the value of 1 and 0.05 as explained above. The stability of the slope coefficients in Figure 4.2 over (say) the period 1984-98 therefore invalidates a Lucas supply curve interpretation of the estimated rela­tionship in equation (4.43). On the contrary, given the stability of (4.43) and the list of recorded changes, we are led to predict that the inverted regression will be unstable over the 1980s and 1990s. Figure 4.3 confirms this interpretation of the evidence.

Given the non-invertibility of the Phillips curve, we can investigate more closely the stability of the implied estimate for the equilibrium rate of unem­ployment. We simplify the Phillips curve (4.43) further by imposing dynamic homogeneity (F(1,28) = 4.71[0.04]), since under that restriction wphl1 is
independent of the nominal growth rate (gf). Non-linear estimation of the Phillips curve (4.43), under the extra restriction that the elasticities of the three price growth rates sum to zero, gives

Awct — Apt-i — 0.027 = — 0.668415Apt-i + 0.301663Agt + 0.289924Agt-i

(0.1077) (0.07761) (—)

—0.0266204 (tut — log(0.033)) — 0.072 IPt (0.003936) (0.00376) (0.01047)

(4.44)

NLS, T = 34 (1965-98)

RSS = 0.00655087875 а = 0.0152957

FAR(1-2) = 3.5071[0.0448] FHETx2 = 0.18178[0.9907]

Farch(i-i) = 0.021262[0.8852] xLmaiity = 0.85344[0.6526]

The left-hand side has been adjusted for mean productivity growth (0.027) and the unemployment term has the interpretation: (tut — uphl1). Thus, the full sample estimate obtained of uphl1 obtained from non-linear estimation is 0.033 with a significant ‘t-value’ of 8.8. A short sample, like, for example, 1965-75 gives a very high, but also uncertain, uphl1 estimate. This is as one would expect from Figure 4.2(a) and (e). However, once 1982 is included in the sample the estimates stabilise, and Figure 4.4 shows the sequence of uphl1 estimates for the remaining samples, together with ±2 estimated standard errors and the actual unemployment rate for comparison. The figure shows that the estimated equilibrium rate of unemployment is relatively stable, and that it appears to be quite well determined. The years 1990 and 1991 are exceptions, where uphl1

Table 4.1

Confidence intervals for the Norwegian wage Phillips curve NAIRU

NAIRU 95% confidence interval for NAIRU

Wald Fieller and LR

Full sample: 1965-98 0.0330 [0.0253 ; 0.0407] [0.0258 ; 0.0460]

Sub sample: 1965-91 0.0440 [0.0169 ; 0.063l] [0.0255 ; 0.2600]

Sub sample: 1965-87 0.0282 [0.0182 ; 0.0383] [0.0210 ; 0.0775]

Note: The Fieller method is applied to equation (4.43), with homogeneity imposed. The confidence intervals derived from the Wald and LR statistics are based on equation (4.44).

increases to 0.033 and 0.040 from 0.028 in 1989. However, compared to con­fidence interval for 1989, the estimated NAIRU increased significantly in 1991, which represents an internal inconsistency since one of the assumptions of this model is that wphl1 is a time invariant parameter.

However, any judgement about the significance of jumps and drift in the estimated NAIRU assumes that the confidence regions in Figure 4.4 are approx­imately correct. As explained in Section 4.4, the confidence intervals are based on the Wald principle and may give a misleading impression of the uncertainty of the estimated NAIRU. In Table 4.1 we therefore compare the Wald interval with the Fieller (and Likelihood Ratio) confidence interval. Over the full sample the difference is not large, although the Wald method appears to underestimate the interval by 0.5%.

The two sub-samples end in 1987 (before the rise in unemployment), and in 1991 (when the rise is fully represented in the sample). On the 1965-87 sample, the Wald method underestimates the width of the interval by more than 3%; the upper limit being most affected. Hypothetically therefore, a decision maker who in 1987 was equipped with the Wald interval, might be excused for not considering the possibility of a rise in the NAIRU to 4% over the next couple of years. The Fieller method shows that such a development was in fact not unlikely. Over the sample that ends in 1991, the Wald method underestimates the uncertainty of the NAIRU even more dramatically; the Fieller method gives an interval from 2.6% to 26%.

A final point of interest in Figure 4.4 is how few times the actual rate of unemployment crosses the line for the estimated equilibrium rate. This sug­gests very sluggish adjustment of actual unemployment to the purportedly constant equilibrium rate. In order to investigate the dynamics formally, we graft the Phillips curve equation (4.43) into a system that also contains the rate of unemployment as an endogenous variable, that is, an empirical coun­terpart to equation (4.2) in the theory of the main-course Phillips curve. As noted, the endogeneity of the rate of unemployment is just an integral part of the Phillips curve framework as the wage Phillips curve itself, since without the ‘unemployment equation’ in place one cannot show that the equilibrium rate of unemployment obtained from the Phillips curve corresponds to a steady state of the system.

In the following, we model a three equation system similar to the theoret­ical setup in equations (4.7)-(4.9). The model explains the manufacturing sector wage, consumer price inflation and the rate of unemployment, conditional on incomes policy, average productivity and product price. In order to model Apt and tut we also need a larger set of explanatory variables, namely the GDP growth rate (Aygdp, t), and an import price index (pit). In particular, the inclu­sion of Aygdpt in the conditioning information set is important for consistency with our initial assumption about no unit roots in tut. It is shown by Nymoen (2002) that (1) conventional Dickey-Fuller tests do not reject the null of a unit root in the rate of unemployment, but (2) regressing tut on Aygdp, t-1 (which in turn is not Granger caused by tut) turns that around, and establishes that tut is without a unit-root and non-stationary due to structural changes outside the labour market.

The first equation in Table 4.2 shows the Phillips curve (4.43), this time with full information maximum likelihood (FIML) coefficient estimates. There are only minor changes from the OLS results. The second equation mod­els the change in the rate of unemployment, and corresponds to equation (4.2) in the theoretical model in Section 4.2.[28] The coefficient of the lagged unem­ployment rate is —0.147, and the t-value of —4.41 confirms that tut can be regarded as a I(0) series on the present information set, which includes Aygdp, t and its lag as important conditioning variables (i. e. zt in (4.2)). In terms of eco­nomic theory, Aygdpt represents an Okun’s law type relationship. The elasticity of the lagged wage share is positive which corresponds to the sign restriction bu2 > 0 in equation (4.2). However, the estimate 0.65 is not significantly differ­ent from zero, so it is arguable whether equilibrium correction is strong enough to validate identification between the estimated uphl1 and the true steady-state unemployment rate. Moreover, the stability issue cannot be settled from inspec­tion of the first two equations alone, since the third equation shows that the rate of CPI inflation is a function of both ut-1 and wct-1 —qt-1 —at-1. However, the characteristic roots of the companion matrix of the system

0.1381 0 0.1381

0.9404 0.1335 0.9498

0.9404 —0.1335 0.9498

show that the model is dynamically stable (i. e. has a unique stationary solution for given initial conditions). That said, the large magnitude of the complex root implies that adjustment speeds are low. Thus, after a shock to the system,

Table 4.2

FIML results for a Norwegian Phillips curve model

Awct — Apt-i = — 0.0627 — 0.7449Apt-i + 0.3367Aqt-i

(0.0146) (0.104) (0.0826)

— 0.06265IPt + 0.234Aqt — 0.02874tut (0.00994) (0.0832) (0.00449)

Atut = — 0.1547tut-i — 7.216Aygdp, t — 1.055Aygdp, t-i (0.0302) (1.47) (0.333)

+ 1.055(wc — q — a)t-1 + 0.366i1989t — 2.188A2pit (0.333) (0.139) (0.443)

Apt = 0.06023 + 0.2038Apt-i — 0.009452tut-i + 0.2096(wc — q — a)t-i (0.0203) (0.0992) (0.00366) (0.0564)

+ 0.2275A2pit — 0.05303i1979t +0.04903 i1970t (0.0313) (0.0116) (0.0104)

wct — qt — at = wct-i — qt-i — a-i + Awct — Aat — Aqt; tu = tut-i + Atut;

0

Figure 4.5. Dynamic simulation of the Phillips curve model in Table 4.2.
Panels (a-d) Actual and simulated values (dotted line). Panels (e-f):
multipliers of a one point increase in the rate of unemployment

As discussed at the end of Section 4.2, the belief in the empirical basis of the Phillips curve natural rate of unemployment was damaged by the remorseless rise in European unemployment in the 1980s, and the ensuing discovery of great instability of the estimated natural rates. Thus, Solow (1986), commenting on the large within country variation between different three-year sub-periods in OECD estimates of the natural rate, concludes that

A natural rate that hops around from one triennium to another under the influence of unspecified forces, including past unemployment, is not ‘natural’ at all. (Solow 1986, p. 33)

In that perspective, the variations in the Norwegian natural rate estimates in Figure 4.4 are quite modest, and may pass as relatively acceptable as a first-order approximation of the attainable level of unemployment. However, the econometric system showed that equilibrium correction is very weak. After a shock to the system, the rate of unemployment is predicted to drift away from the natural rate for a very long period of time. Hence, the natural rate thesis of asymptotical stability is not validated.

There are several responses to this result. First, one might try to patch up the estimated unemployment equation, and try to find ways to recover
a stronger relationship between the real wage and the unemployment rate. In the following we focus instead on the other end of the problem, namely the Phillips curve itself. In Section 6.9.2 we show that when the Phillips curve framework is replaced with a wage model that allows equilibrium correction to any given rate of unemployment, rather than to the ‘natural rate’ only, all the inconsistencies are resolved. However, that kind of wage equation is first anchored in the economic theory of Chapters 5 and 6.

4.6.1 Summary

The Phillips curve ranges as the dominant approach to wage and price modelling in macroeconomics. In the United States, in particular, it retains its role as the operational framework for both inflation forecasting and for estimating of the NAIRU. In this chapter we have shown that the Phillips curve is consistent with cointegration between prices, wages and productivity, and a stationary rate of unemployment, and hence there is a common ground between the Phillips curve and the Norwegian model of inflation of the previous chapter. However, unlike the Norwegian model, the Phillips curve framework specifies a single equilibrating mechanism which supports cointegration—in the simplest case with fixed and exogenous labour supply, the equilibrium correc­tion is due to a downward sloping labour demand schedule. The specificity of the equilibrating mechanism of the Phillips curve is not always recognised. In the context of macroeconomic models with a large number of equations, it has the somewhat paradoxical implication that the stationary value of the rate of unemployment can be estimated from a single equation.

We have also argued that the Phillips curve framework is consistent with a stable autoregressive process for the rate of unemployment, subject only to a few regime shifts that can be identified with structural breaks in the operation of labour markets. The development of European unemployment rates since the early 1980s is difficult to fit into this framework, and model builders started to look for alternative models. Interestingly, already in 1984 one review of the United Kingdom macroeconomic models concluded that ‘developments in wage equations have led to the virtual demise of the Phillips curve as the standard wage relationship in macro models’.[29] These developments are the themes of the following two chapters.