inflation, unemployment and the nairu in australia

The Australian Economic Review, vol. 31, no. 2, pp. 117–29

The University of Melbourne, Melbourne Institute of Applied Economic and Social Research 1998Published by Blackwell Publishers Ltd, 108 Cowley Road, Oxford OX4 1JF, UK and

350 Main Street, Malden, MA 02148, USA

* We would like to thank two referees, John Creedy, earlyrisers at the University of Melbourne Macroeconomicsbreakfasts, and seminar participants at the University ofAdelaide and the Australasian meeting of the EconometricSociety in Melbourne for helpful comments. Any errorsare our own.

Abstract

In this paper we investigate the relationshipbetween inflation and unemployment in Aus-tralia, post 1959. Our approach is based onidentification of the time series components ofthe data. Evidence is found of significant cor-relations between the non-trend frequencies ofinflation and unemployment and these correla-tions are exploited to estimate a simple fore-casting model that does not suffer from theinstability normally associated with the Phil-lips Curve. Estimates of the NAIRU are alsoprovided and these range from as low as 2.3per cent to as high as 9.2 per cent over this pe-riod, but these estimates are quite imprecise.Reasons for this imprecision are discussed.

1. Introduction

In this paper we investigate the relationship be-tween inflation and unemployment in Austra-lia, since 1959. Interest in the relationshipbetween inflation and unemployment goesback to Phillips (1958), who found a system-atic, negative relationship between unemploy-ment and money wage growth in UK data.Studies that confirmed this finding for othercountries soon followed. When combined witha mark-up pricing model, the Phillips Curvecan be written as a negative relationship be-tween inflation and unemployment. This rela-tionship appeared to become unstable in manycountries in the 1970s. However, we show thatthe Phillips Curve is still informative aboutmacroeconomic relationships in Australia ifthe time series characteristics of the data arecarefully identified. In Sections 2 and 3, wepresent evidence that the relationship betweenunemployment and inflation exhibits little evi-dence of instability once trend movements areremoved from the data. By focusing on thehigher frequency movements in the data, muchcan be learned about the relationship betweenunemployment and inflation. In particular, inSection 2 we identify correlations between thevariables that exist at the business cycle fre-quency. Since these correlations do not extendto the trend components of the data, in Section3 we investigate the unemployment–inflationrelationship using vector autoregressions(VARs) specified in the first differences of thevariables. We find no evidence of instability inthe bivariate VAR, and forecast errors over any

Inflation, Unemployment and the NAIRU in Australia

Mark Crosby and Nilss Olekalns*Department of Economics The University of Melbourne

118 The Australian Economic Review June 1998

The University of Melbourne, Melbourne Institute of Applied Economic and Social Research

1959 1963 1967 1971 1975 1979 1983 1987 1991 1995

-2.5

0

2.5

5

7.5

10

12.5

15

17.5INF UE

subperiod do not depend on the estimationperiod. We also find evidence that changes inunemployment Granger cause changes in infla-tion, but that the opposite is not true. The ab-sence of significant correlations in the trendcomponents of inflation and unemployment isconsistent with the natural rate hypothesis and,in Section 4, we build on our previous results toestimate a key component of that hypothesis,the non-accelerating inflation rate of unem-ployment (NAIRU). The NAIRU proves to bedifficult to measure with any precision but theindications are that it has increased steadilyover the last two decades.

2. Correlations between Inflation and Unemployment

In this section we summarise the data by pre-senting correlations between the two series. Itis shown that correlations between the raw in-flation and unemployment series appear tohave changed since the mid 1970s, but correla-tions between the detrended series are stable. Inother words, inflation and unemployment havefollowed quite different trend paths since theearly 1970s, but fluctuations in the two seriesaround these two trends are negatively corre-lated. In Figure 1 we plot the unemploymentrate (the dashed line) and the inflation rate(four-quarter change in the CPI) for the period

since 1959.

1

The two series do not appear toshare a common trend, and there appears to besome (inverse) correlation between these twovariables over business cycles in this period.While unemployment drifts upward over theentire period, inflation appears to have jumpedupward in the mid 1970s and has little obviousdrift. The inverse correlation during businesscycles is most clearly evident when unemploy-ment rose and inflation fell in the late 1970s,early 1980s and in the period 1991 to 1993.However, the correlation between inflation andunemployment over the entire period is zero—the correlation at the business cycle frequencyis offset by the correlation in trends.

2

This com-pares with a correlation among annual inflationand unemployment data of –0.48 for the period1901 to 1974.

3

This correlation is of the signtraditionally associated with Phillips Curves,and significantly different from zero. The lackof a negative correlation over the period sincethe mid 1970s has led many macroeconomiststo the view that the Phillips Curve is uninfor-mative about the relationship between inflationand unemployment. Indeed Lucas and Sargent(1978) argued that this zero correlation was ev-idence that the Phillips Curve was ‘economet-ric failure on a grand scale’. In contrast, wefind that there are still key correlations betweeninflation and unemployment, particularly overbusiness cycles.

per cent

Figure 1 Inflation and Unemployment, Australia, 1959–1997

year

Source

: See endnote 1.

Crosby & Olekalns: Inflation, Unemployment and the NAIRU 119


1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 19921962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

CPIF UEF

1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992

0

2

4

6

8

10

12

CPIF UEF

Figure 3 Trends in Inflation and Unemployment, Australia, 1959–1997

per cent

year

To explore the correlation at the businesscycle frequency between inflation and unem-ployment, we begin by filtering the data. Fig-ure 2 presents unemployment (the dashed line)

and inflation filtered so that both the trends andthe high frequency movements in the series areremoved (we have used the band pass filter de-scribed in Baxter and King (1995) to do this),

Figure 2 Cyclical Components of Inflation and Unemployment, Australia, 1959–1997

per cent

year

Table 1 Inflation and Unemployment Correlations

Sample period Raw data Trend components Cyclical componentsHigh frequency

components

1959–1995 –0.00 0.15 –0.48* –0.06

1959–1973 –0.15 0.84* –0.74* –0.04

1974–1984 –0.46* –0.94* –0.41* –0.06

1984–1995 –0.68* –0.87* –0.62* –0.16

Note

: * indicates significantly different from zero at the 5 per cent significance level.

Source

: See endnote 1.

Source

: See endnote 1.



so that only the cyclical components of the se-ries remain.

4

A negative correlation is apparentfrom the figure. The correlation over the entiresample is –0.48, while over the period prior to1973 it is –0.74, and since 1984 it is –0.62 (Ta-ble 1).

5

All these correlations are significantlydifferent from zero at the 5 per cent signifi-cance level, and of the sign conventionally as-sociated with the Phillips Curve. This suggeststhat when unemployment is above trend, infla-tion tends to be below trend, and vice versawhen unemployment is below trend. This rela-tionship does not appear to have been affectedby the stagflation of the 1970s.

Figure 3 presents the trends in the data,where the trend is calculated using a filterwhich eliminates all movements having fre-quency higher than eight years. The correlationamong the trends is 0.15 over the entire sample,but 0.84 before 1973 and –0.87 since 1984. Be-fore 1974 both variables drifted up, while since1974 inflation has reversed this trend and un-employment has not. The variables are highlynegatively correlated at all frequencies since1974. The final column of Table 1 shows thatthe high frequency correlations between infla-tion and unemployment are negative, but insig-nificantly different from zero. The highfrequency parts of the series are what is leftafter the trends and the cycles have been re-moved.

This analysis suggests that uncovering a sta-ble relationship between inflation and unem-ployment in Australia requires removal oftrends in the series and a focus on the higherfrequency movements in the data. In the nextsection we explore this issue using bivariateVAR models in an attempt to uncover any fore-casting relationship between these two vari-ables.

3. Forecasting Inflation and Unemployment

In the previous section we found that the trendsin inflation and unemployment do not appear tobe systematically related in any way, but thatfluctuations over the business cycle might berelated. In this section we explore this issuefurther using VAR models. Before continuing,

it is useful to state what an expectations aug-mented Phillips Curve implies about the rela-tionship between inflation and unemployment.The expectations augmented Phillips Curvesuggests that there will be no long-run relation-ship between inflation and unemployment, butthat unanticipated movements in inflation canaffect real wages and cause unemployment tomove away from the NAIRU. If we interpretthe trend in inflation as the anticipated compo-nent of inflation, then movements around trendin inflation will cause unemployment to moveaway from trend, but movements in the trend ininflation will not be related to unemployment.In a statistical sense, this implies that the lowfrequency (trend) movements in the series willnot be correlated, while the non-trend move-ments should be inversely correlated. Some ev-idence on the lack of a relationship between thetrends in the two series was presented in theprevious section, where it was found that therewas little correlation between the trends. Amore formal test is to see if the two series arecointegrated using the Engle-Granger two stepprocedure (Engle & Granger 1987). Firstly, wetest the individual inflation and unemploymentseries to see if they contain unit roots. We usethe augmented Dickey-Fuller test, with fourlags of the dependent variable (see Davidsonand MacKinnon (1993) for details of this test),and find evidence that both the inflation rateand the unemployment rate contain unit roots(the t-statistic for the null hypothesis of a unitroot is –2.31 for the inflation equation, and–1.45 for the unemployment equation, whichcompares with a 10 per cent critical value of–2.57). We then run the regression of the infla-tion rate on the unemployment rate, and test forunit roots in the residuals in this regression (thefinding that the residuals from this regressiondo not contain a unit root is consistent withthese two variables being cointegrated). Wefind that the residuals from this regression docontain a unit root (the t-statistic is –1.43), andso we conclude that inflation and unemploy-ment both contain unit roots, but are notcointegrated

6

. In other words, inflation and un-employment both contain trends which are sto-chastic, but these trends are not related. This isconsistent with both the empirical evidence in



the previous section and with macroeconomictheory.

Our findings thus far suggest that inflationand unemployment may be related, but notthrough trends in the series. In order to find anyrelationship between these two variables weneed to remove their trends. We have chosen todetrend by first differencing the two variables,and we then use VAR techniques to examinethe nature of any causal relationships betweeninflation and unemployment. We justify this bynoting that this is consistent with our findingthat both series contain unit roots. As long aswe include enough lags in our VAR, we oughtto pick up both high frequency and mediumfrequency (business cycle) relationships be-tween inflation and unemployment. Further-more, by including lags of inflation in theinflation equation, we hope to be incorporatinginflationary expectations into our model. Ourestimating equation is the unrestricted bivariateVAR given by:

∆π

t

=

α

1

+

β

i

∆π

t – i

+

γ

i

∆µ

t – i

+

e

1

t

∆µ

t

=

α

2

+

η

i

∆π

t – i

+

δ

i

∆µ

t – i

+

e

2

t

(1)

where

π

t

is the quarterly inflation rate,

µ

t

is theunemployment rate,

∆

is the first difference op-erator,

e

t

are error terms, and the lag length,

q

,is selected by minimising the Schwarz Baye-sian Information Criterion, with the maximumpossible lag length set to four periods.

7

We can relate our estimate of the inflationequation in (1) to standard estimates of thePhillips Curve in the following way. The stan-dard representation of the Phillips Curve is:

π

t

= +

β

( )

where are inflationary expectations and isthe natural rate of unemployment. The difficul-

ties in estimating this equation are, firstly, thatinflation expectations and the natural rate arenot observed and, secondly, that unemploy-ment and inflation are likely to be jointly deter-mined. Our solutions to these estimationdifficulties are, firstly, to assume that lags ofinflation are useful predictors of inflation. Thisis consistent with adaptive expectations, butalso with rational expectations when the infla-tion process is persistent, so that current infla-tion provides a good forecast of near futureinflation.

8

The equation estimated in (1) is alsoconsistent with a number of different models ofthe natural rate.

9

For example, if:

=

δµ

t –

1

=

π

t –

1

then the equation for the Phillips Curve be-comes nested in (1) with appropriate restric-tions on the coefficients of the VAR. If

δ

= 1(complete hysteresis), for example, then thePhillips Curve becomes:

∆π

t

=

β∆µ

t

which is the inflation equation in (1) when nolags of inflation are included, and when laggedunemployment is used as an instrument for

µ

t

.Hence we think of equation (1) as nesting anumber of plausible Phillips Curve relationswhen appropriate coefficient restrictions areimposed. Rather than prior imposition of theserestrictions we estimate the general model, (1).

Granger causality is used to analyse the na-ture of any predictability between the variablesin (1). Table 2 reports the results, and theseshow that past values of unemployment havepredictive power for inflation but that past in-flation has no information concerning futurechanges to the unemployment rate. Causationfrom unemployment to inflation is consistentwith cost-push explanations of inflation in

i 1=

q

∑i 1=

q

∑

i 1=

q

∑i 1=

q

∑

πte µt µt–

πte µ

µt

πte

Table 2 Granger Causality Tests

Sample period Causality F-test P-value Lag length

1960:3–1995:3

∆π

→

∆µ

1.239 0.293 2

∆µ

→

∆π

5.128 0.007



which short-run labour market pressures leadto upward movement in prices. Indeed, this isthe traditional Phillips Curve story about la-bour market pressures leading to wage andprice pressure. The

R

2

for these regressionssuggest that the VAR explains around 40 percent of the variation in the change in inflation.In addition, the sum of the coefficients on un-employment equals –0.661 which is consistentwith the negative correlation noted in the pre-vious section.

A potential problem with these estimates isthat there may be some instability in the PhillipsCurve that translates to these short-run forecast-ing relations. It has often been suggested thatPhillips Curves became unstable around themiddle of the 1970s. We can test for instabilityin our estimating equations using structuralbreak tests based on the familiar split-sample F-tests (Chow tests) for parameter instability. Intesting for structural breaks it is possible tochoose a break point a priori, and test for astructural break conditional on the chosen date.Alternatively, we can search over a range ofdates for structural breaks. We have chosen thelatter procedure, keeping in mind that correctcritical values also need to be calculated. To in-vestigate the possibility of structural breaks, weuse Quandt’s (1960) Sup-F test to detect an un-known structural break point. This test requiresa priori specification of the earliest and latestpossible break points;

10

we choose, respec-tively, 1970:1 and 1985:1. Included within thistime interval are possible sources of instabilitysuch as the first and second oil price shocks,two wages explosions, and financial deregula-tion. The results are in Table 3.

The Sup-F statistics are calculated by takingthe largest Chow F-statistics from a series ofsplit-sample regressions, with the break pointscommencing in 1970:1 and increasing by onequarter thereafter until 1985:1. The null hy-pothesis is parameter stability. The dates re-

ported in the table, 1976:1 and 1976:3, are thebreak points corresponding to the largest of theF-statistics and the significance levels are thosefound from the F-distribution. However, giventhat the choice of break point is data dependent,the Sup-F test will not have the standard F-distribution. Bootstrapping is used to calculatethe correct empirical significance levels andthese indicate that, for both equations, we can-not reject the null of parameter stability.

11

The null hypothesis of the Chow test utilisedabove is that the equations of the model are sta-ble. A problem with this is that if the model isvery poorly fitting (all of the coefficients closeto zero for example) then we may be unable toreject the null even when the coefficients of themodel change by a large absolute amount, lead-ing to large changes in the forecasts from thesemodels. One way to see if this is the case is toexamine the out-of-sample forecasting perfor-mance of the model. A second problem withthe Sup-F test is that it assumes the existence ofonly one break point in the sample. However, itcould be argued that the sample divides natu-rally into three separate subsamples based onincidents that might have had some impact onthe Phillips Curve; the first, 1959:3 to 1973:4,covers the period of Keynesian macroeco-nomic demand management; the second,1974:1 to 1983:4, encompasses the oil priceand wages shocks that are often held to be thereasons for the perceived breakdown in thePhillips Curve; the third, 1984:1 to 1995:3,marks the period of financial deregulation inAustralia as well as the introduction of an in-comes policy, the prices and wages Accord.Once again, out-of-sample forecasting shouldbe poor if the coefficients of the model changedrastically over these three subperiods. Table 4reports the results of a forecasting exercise inwhich separate VARs are run for each of thesubperiods and then used to generate out-of-sample forecasts. Should parameter instability

Table 3 Sup-F Tests

Dependent variable Sup-F Date SignificanceBootstrapped significance

∆π

1.764 1976:1 0.125 0.580

∆µ

1.986 1976:3 0.082 0.456



be significant, we would expect a deteriorationin the forecasting performance of the model ifthe parameter estimates from one period wereused to generate forecasts for another period.

The root mean square errors reported in thetable do not show any obvious parameter insta-bility. As regards the forecasting performanceof the equations, it makes little difference fromwhich period the parameter estimates are de-rived. These results also show that it is moredifficult to forecast changes to inflation than itis to forecast changes to the unemployment ratedespite the fact that unemployment Grangercauses inflation. The other interesting featureof the table is the relative increase in difficultyin obtaining accurate forecasts for either vari-able during the period 1974:1 to 1983:4.

As a final check for instability, dummy vari-ables corresponding to each of the three sub-periods were introduced into the VAR and theirjoint significance tested using the likelihoodratio statistic. The test statistic has a value of3.04 which, when compared to the

χ

2

distribu-tion with two degrees of freedom, has a signif-icance value of 22 per cent. This is furtherconfirmation of the hypothesis that the VAR isstable.

We interpret these findings as consistentwith the existence of a short-run PhillipsCurve, where changes in unemployment leadus to predict short- to medium-run movementsin inflation in the opposite direction. The find-ing of no cointegration between inflation and

unemployment is consistent with no long-runrelationship between trends in the two vari-ables. It appears that these equations are quitestable, as long as one considers higher fre-quency movements in the variables, rather thantrend movements in the variables.

4. Estimating the NAIRU

The results in the previous sections of the papershow that medium to high frequency variationsin unemployment and inflation are systemati-cally related and can be used for the purposesof forecasting. As argued above, this is consis-tent with the natural rate hypothesis (althoughthese results should not be interpreted as apowerful test of that theory). We now turn ourattention to a key component of the natural ratehypothesis, the NAIRU. Having a view aboutthe level of the NAIRU is an important compo-nent in the design of monetary policy. Yet de-termining this level with any degree ofprecision has proven to be extremely difficult(one economist recently described attempts tomeasure the NAIRU as a ‘professional embar-rassment’ (Galbraith 1997, p. 108)). In this sec-tion, we provide an estimate of the NAIRU forAustralia. As with other studies, our estimateof the NAIRU proves to be extremely impre-cise. It seems most unlikely, for reasons we dis-cuss, that the difficulties involved in measuringthe NAIRU can be resolved and this raises se-rious questions about the practical usefulness

Table 4 Root Mean Squared Errors

(one quarter ahead forecasts)

Forecast period—Dependent variable:

∆π

t

Estimation period 1960:3–1995:3 1960:3–1973:4 1974:1–1983:4 1984:1–1995:3

1960:3–1995:3 1.001 0.658 1.455 0.815

1960:3–1973:4 1.006 0.658 1.458 0.836

1974:1–1983:4 1.004 0.661 1.455 0.822

1984:1–1995:3 1.002 0.661 1.460 0.799

Forecast period—Dependent variable:

∆µ

t

Estimation period 1960:3–1995:3 1960:3–1973:4 1974:1–1983:4 1984:1–1995:3

1960:3–1995:3 0.374 0.305 0.467 0.347

1960:3–1973:4 0.374 0.302 0.475 0.347

1974:1–1983:4 0.392 0.339 0.446 0.393

1984:1–1995:3 0.382 0.310 0.495 0.334



of the concept for guiding Australian monetarypolicy.

A preliminary, non-parametric examinationof the data suggests that the concept of aNAIRU may not be all that relevant for Austra-lia. Suppose that the NAIRU in Australia hasalways been between 5 per cent and 7 per cent.Since 1960 unemployment has been below 5per cent in 68 quarters. In 37 of these quartersinflation fell, and in only 31 quarters did infla-tion rise. In other words, more often than notinflation has been falling in Australia when un-employment has been below 5 per cent. If welook at unemployment above 7 per cent, infla-tion has been falling in 25 quarters, but also ris-ing in 20 quarters. This is hardly powerfulevidence of a NAIRU of between 5 per centand 7 per cent. A different choice of theNAIRU, or splitting the sample, does not seemto help in this kind of exercise. In our view thiskind of evidence suggests that unemployment

levels

tell us little about movements in infla-tion. It should be noted that this does not pre-clude the possibility of a well-defined ‘natural’or average rate of unemployment determined inthe labour market.

12

It simply suggests thatsuch a natural rate is not particularly useful inan inflation equation, or alternately that an in-flation equation may not be very helpful inidentifying the natural rate. We offer three pos-sible explanations for this evidence, all ofwhich cast doubt on the relevance of a uniqueNAIRU for Australia.

• Although, as we argued above, there is a sys-tematic inverse relation between the first dif-ferences of inflation and unemployment, itmay be the case that movements in inflationhave not been systematically related to the

level

of unemployment in Australia. For ex-ample, Australia’s history of unique wage-setting institutions, such as the Accord, mayhave led to the uncoupling of wages (andhence prices) from the level of excess de-mand in the labour market.

• It may also be the case that the NAIRU haschanged significantly since 1960, a viewconsistent with the idea that there is hystere-sis in unemployment, so that the NAIRU

may always be close to the current level ofunemployment (see Blanchard and Katz(1997) for a discussion of hysteresis and theNAIRU). This implies that only changes inunemployment will affect inflation, andthere may be no relationship between thelevel of unemployment and inflation.

• Finally, we note recent theoretical work thatsuggests there could be a range of equilib-rium unemployment rates consistent withnon-accelerating inflation (McDonald1990).

All of these explanations imply that the econo-metric identification of a unique NAIRU isgoing to be difficult.

Several pieces of previous work relate to ourattempt to estimate Australia’s NAIRU. Pissar-ides (1991) examined the relationship betweenunemployment and real wages in Australia,with the aim of establishing whether incomespolicies had any effect on unemployment. Hesuggests that unemployment rose in the 1970sdue to rising tax rates and unemployment ben-efits, and rises in unemployment in the 1980swere due to changes in investment and aggre-gate demand. Hence the NAIRU should be ris-ing throughout this period. Gregory (1986), inhis study of the relationship between wagespolicy and unemployment, also argues that thenatural rate of unemployment increased in the1970s. Trivedi and Baker (1985) estimate aPhillips Curve, and try to explain the resultingestimates of the natural rate. They find thatnone of their proposed explanatory variablesadequately captures movements in their esti-mates of the natural rate.

Setterfield, Gordon and Osberg (1992) forCanada, and Rea (1983) and Motley (1990) forthe United States, find that the NAIRU is diffi-cult to measure with much precision. In addi-tion, Setterfield, Gordon and Osberg (1992)find that estimates of the NAIRU differ consid-erably across different sample periods. Thissuggests that the NAIRU in these two countriesalso comprises a time-varying element. King,Stock and Watson (1995) estimate the NAIRUin the United States, using an estimation tech-nique that explicitly allows the NAIRU to vary



over time. They find evidence that the NAIRUhas fluctuated considerably in the UnitedStates over the last forty years, though theirpoint estimates suggest that the NAIRU in1994 is little different from that in 1954.

The equation that we use to estimate theNAIRU is the following:

∆π

t

=

β

i

(

µ

t – i

– ) +

γ

i

∆π

t – i

+

φ

t

(2)

where is the NAIRU and

φ

t

is an error term.Equation (2) relates changes in inflation to thedifference between the level of unemploymentand the NAIRU; the lags in the unemploymentterm capture any inertia in the adjustment ofprices to labour market pressures while laggedinflation changes are used to proxy expecta-tions formation. This equation differs from theinflation equation in the VAR in (1) since ituses levels of unemployment rather than differ-ences, and this helps to explain why estimatesof derived from equations such as (2) maybe very imprecise. To see this, note that equa-tion (2) can be derived from the inflation equa-tion in the VAR if the sum of the

β

i

coefficientsequals zero and if there is consistency in the laglengths used in the respective equations.

13 Thiscreates an identification problem since en-ters (2) as βi , so when βi = 0,equation (2) cannot identify the NAIRU. Inother words, if it is only changes in unemploy-ment that forecast changes in inflation, ratherthan the level of unemployment, then theNAIRU will be difficult to pin down with anyprecision. Indeed, if it is only changes in unem-ployment that are related to inflation, then theNAIRU today is simply yesterday’s unemploy-ment rate!

In Section 3 we argued that inflation and un-employment were not cointegrated, indicatingthe absence of a relationship between the re-

spective trends of the two series. The correla-tions between the band-pass filtered data thatwe identified and the Granger causality resultsindicate that the variables are related at thehigher frequencies. This suggests that (1) is thecorrect specification. Nonetheless, equation (2)can be used to recover a rough estimate of since in practice β will be only approxi-mately equal to zero. However, there will be alarge standard error on our estimate of and,as a result, a wide confidence interval if (1) isthe correct model.

Equation (2) can be estimated using non-linear least squares. Table 5 shows the resultsfrom estimating (2) over the entire sample pe-riod, and over various subperiods of the data.

In each regression three lags of unemploy-ment and two of the inflation variable are in-cluded in the estimation of (2), consistent withthe evidence of the previous section and the re-marks above. The table presents the estimate ofthe NAIRU for each subperiod, followed by thestandard error of this estimate, the average un-employment rate over the relevant period, andthe R2 for the estimated equation. The firstpoint to note is that the estimate of the NAIRUover the entire sample is not estimated veryprecisely. This is consistent with overseas evi-dence cited above, but may also be due to pos-sible misspecification due to the sum of the βcoefficients being close to zero.14 Interestingly,estimates of the NAIRU estimated over varioussubsamples are estimated more precisely,though standard errors are still uncomfortablylarge. The estimate over the 1984–1997 periodsuggests that a 95 per cent confidence intervalfor the NAIRU would range from 6.4 per centto 12.0 per cent. Bearing these comments inmind, the point estimates of the NAIRU areconsistent with the results of Gregory (1986)and Pissarides (1991) who found the NAIRUincreasing over time in Australia. This can be

i 1=

p

∑ µi 1=

k

∑

µ

µt

µΣi 1=

p µ Σi 1=p

µΣi 1=

p

µ

Table 5 NAIRU Estimates

Sample period NAIRU Standard error Average UE R2

1959–1995 6.19 (2.99) 5.23 0.39

1959–1973 2.31 (1.07) 2.00 0.42

1974–1984 5.04 (1.65) 5.93 0.48

1984–1997 9.18 (1.38) 8.61 0.30



contrasted with results for the United States forexample, where King, Stock and Watson(1995) found the NAIRU to be quite similar in1995 to their NAIRU estimate for 1954(around 6.3 per cent) using similar regressionsto those used above. Interestingly, the periodover which the NAIRU is most difficult to esti-mate is the period since 1984. This is consistentwith the idea that the uncoupling of the labourmarket from demand pressures because of theAccord over most of this period makes the es-timation of the natural rate from (2) very diffi-cult.

The large standard errors in our NAIRU esti-mates are consistent with the non-parametricfindings outlined above. In short, we shouldnot be too confident that any unemploymentrate in Australia is consistent with inflation ris-ing, or with it falling. In the previous sectionwe found that changes in unemployment pre-dict changes in inflation. The same does not ap-pear to be true for deviations in unemploymentfrom an estimated NAIRU. These results haveinteresting interpretations for monetary policy.If the NAIRU is close to (or equal to) the cur-rent unemployment rate, then low unemploy-ment will not lead to high inflation. However,if falls in unemployment do occur from currenthigh levels, our models suggest that we mightexpect inflation to rise. Fortunately there are atleast two reasons why this might not be thecase. Firstly, the root mean squared forecast er-rors in our out-of-sample forecasts suggestconsiderable unpredictability in inflation, sothat we can reasonably hope that unemploy-ment falls will not lead to rises in inflation.Secondly, structural changes in the Australianand in other economies seem to be leading tolow inflation regardless of the unemploymentrate.

5. Conclusion

In this paper we have suggested that Australianinflation and unemployment data reveal thatthe Phillips Curve still describes some impor-tant empirical relationships in the macroecon-omy. However, the change in the trend ininflation in the mid 1970s needs to be ad-dressed in any model linking inflation and un-

employment. When this is done, it is possibleto construct stable bivariate forecasting mod-els. These models suggest that unemploymentGranger causes inflation, but not vice versa.We have also estimated the NAIRU in Austra-lia and we find that our point estimate of theNAIRU has risen significantly over the 1980s,to a level of around 9.2 per cent. Consistentwith other studies, however, we find that theNAIRU is difficult to measure with precision,and it may be that it is changes in unemploy-ment that affect inflation, rather than devia-tions in unemployment from a NAIRU. For thisreason we argue that in Australia it seems thatinflation equations may not be very useful inidentifying the natural rate of unemployment.

First version received August 1997;final version accepted March 1998 (Eds).

Appendix 1: Band Pass Filters

In the second section of the paper two filterswere used to extract the business cycle andtrend components from the raw unemploymentand inflation series. In this appendix these fil-ters are briefly discussed.15 The first filter, theband pass filter (BP632), is designed to isolatefluctuations in the data which persist for peri-ods of eighteen months (6 quarters) through toeight years (32 quarters). Hence high fre-quency noise in the data is removed, as are anylow frequency trends in the data. Among thedesirable properties of the filter are, firstly, thatno phase change in the series is induced (that is,the series is not moved backward or forward intime) and, secondly, that any series lower thanI(2) is rendered stationary. The actual filterused is simply a symmetric two-sided moving-average filter. Baxter and King (1995) showthat the ideal filter involves applying an infiniteorder moving average to the data, and that theoptimal approximating filter for a given maxi-mum lag length, K, is constructed by simplytruncating the ideal filter’s weights at lag K. Toensure stationarity, the truncated band pass fil-ter weights are adjusted so that the weights sumto zero. In Section 2, K was set equal to 12.

The optimal lower pass filter (LP32) extractsfrom the data any movements in the data which



persist for longer than eight years. For a com-parison with other detrending methods, such asthe Hodrick-Prescott filter, see Baxter andKing (1995). Once again, to use the filter, asymmetric two-sided moving average is ap-plied to the data. Again, the optimal filter is aninfinite order moving average, and the trun-cated filter weights are constructed by truncat-ing the ideal filter weights at lag K. Again, inthe text, K was set equal to 12 (using K equal to8 gives the same qualitative results as thosepresented in Section 2). To ensure that the fil-tered series places unit weight at the zero fre-quency (so that, for example, it has the samemean as the unfiltered data) the weights are ad-justed so that the weights sum to one. Theweights used in this paper are reproduced inTable A1. It should be noted that filtering thedata leads to the loss of the first and last K ob-servations, so that Figures 2 and 3 present re-sults only from 1962 to 1994.

Endnotes

1. The data are taken from the NIF-10S data-base in DX. Unemployment is the total unem-ployment rate for each quarter from 1959:3 to1997:2 (variable VNEQ.AN_RNU), while theCPI is the weighted average for eight capitalcities series (variable VNEQ.UI90_PCPI). Wehave also experimented with using the underly-

ing inflation rate, series GCPITURQF, withsimilar results to those reported using the ac-tual CPI.

2. This is the correlation between unemploy-ment and the quarter on quarter change in theCPI. The correlation rises to 0.60 when thefour-quarter change in the CPI is used.

3. The data are taken from the Reserve Bank ofAustralia’s Preliminary Annual Database.

4. Specifically, we have used an optimal bandpass filter which removes frequencies lowerthan 32 quarters, and higher than 6 quarters,from the data. Frequencies between these twowere defined as business cycle frequencies byBurns and Mitchell (1946). See Appendix 1 forfurther details. Baxter and King (1995) alsodiscuss how the band pass filter is related toother detrending methods. It turns out that theband pass filter is close to the Hodrick-Prescott(HP) filter described in Hodrick and Prescott(1997). However, the HP filter does not allowfor the removal of specific frequencies fromthe series of interest—for example, it is notpossible to remove the trend and the noise froma series.

5. If the HP filter is used to extract the non-trend components of the series then the correla-tions among the cyclical components are sig-nificantly negative since 1973 (–0.67 for 1974–1984, and –0.61 since 1984), though equal tozero prior to 1973.

6. The conclusion that inflation and unemploy-ment are not cointegrated is not changed whenmore lags are added to the augmented Dickey-Fuller regression, or when a trend is added tothe regressions.

7. Geweke and Meese (1981) show that theSchwarz criterion has optimal properties.

8. This does not deny that there may be someproblems with our estimate of inflation ex-pectations, but better estimates are not avail-able over our estimation period. We haveexperimented with including the Melbourne

Table A1 Moving-Average Filter Weights

Lag BP632 LP32

0 0.27766 0.04066

1 0.22040 0.04065

2 0.08376 0.04061

3 –0.05212 0.04054

4 –0.11835 0.04045

5 –0.10123 0.04034

6 –0.04218 0.04020

7 0.00161 0.04003

8 0.00150 0.03984

9 –0.02786 0.03963

10 –0.05014 0.03939

11 –0.04229 0.03913

12 –0.01193 0.03885



Institute’s survey measures of inflation expec-tations in some of our regressions when thesedata are available, but these do not affect ourresults. A problem with this measure is that itappears to be biased—overestimating inflationfor much of the 1990s for example.

9. We will return to estimates of the NAIRU inthe next section of the paper.

10. The F-statistic tends to explode as one ap-proaches the beginning or the end of the sam-ple.

11. Further details of the bootstrap simulationsare available from the authors.

12. We are here using a distinction between theNAIRU, relating inflation and unemployment,and the natural rate, relating to equilibrium inthe labour market. See Rogerson (1997) forsome discussion of some terminological issuessurrounding this distinction.

13. For example, if (1) contains 2 lags, then (2)must have 3 lags.

14. Individually, each of the relevant βs are notsignificantly different from zero, though it isnot possible to determine whether their sum inany regression is different from zero.

15. Further details can be found in Baxter andKing (1995). Baxter (1994) uses these filters toexamine the link between real interest differen-tials and real exchange rates.

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