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Inflation, Inflation Uncertainty and Macroeconomic Performance in Australia

Ramprasad Bhar

School of Banking and Finance The University of New South Wales

Sydney 2052, AUSTRALIA r.bhar@unsw.edu.au

and

Girijasankar Mallik School of Economics & Finance University of Western Sydney

Locked Bag 1797, Penrith South D. C. 1797, AUSTRALIA g.mallik@uws.edu.au

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Inflation, Inflation Uncertainty and Macroeconomic Performance in Australia

Abstract:

Using quarterly data this study finds that inflation uncertainty have negative and significant

effects on inflation and output growth at least after the inflation targeting. We also find that

output uncertainty has negative and significant effect on inflation. The study uses a newly

constructed oil price dummy variable as a control variable and finds that oil price changes

significantly increase the inflation uncertainty. These findings are robust and the Generalised

Impulse Response Functions corroborate the conclusions. These results have important

implications for inflation targeting (IT) monetary policy, and the aim of stabilisation policy in

general.

Keywords: EGARCH, Inflation, Growth, Inflation Uncertainty, Output Uncertainty, Impulse

Response.

JEL Classification: E31, E52, E63, E64

Inflation, Inflation Uncertainty and Macroeconomic Performance in

Australia

1. Introduction

The relationship between inflation, inflation uncertainty, growth and growth

uncertainty is crucial. According to Okun (1971) and Friedman (1977), it is through inflation

uncertainty, that high inflation can adversely affect economic growth. Okun (1971) and

Friedman in his 1977 Nobel Lecture argue that increased uncertainty reduces the information

function of price movements and hinders long-term contracting, thus potentially reducing

growth. Friedman (1977) also argues that high inflation leads to higher inflation uncertainty.

Ball (1992) formalises the positive relationship between inflation and inflation uncertainty. In

Ball’s model, the public does not know the preferences of the policy maker, but uncertainty

of the policy maker’s preferences only affects inflation uncertainty when inflation is high.

Empirical studies on growth, inflation and inflation uncertainty and growth

uncertainty relationship shows mixed result.1 Recently much attention has been given on the

relationship between inflation and its uncertainty. For example, Berument and Dincer (2005)

1 See Kormendi and Meguire, (1985), Grier and Tullock (1989), Grier and Perry (2000).

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find that inflation Granger causes inflation uncertainty for all G7 countries supporting

Friedman-Ball hypothesis. Using Markov Switching heteroscedasticity model for the G7

countries, Bhar and Hamori (2004) found that the relationship between inflation and inflation

uncertainty also depends on whether the shock is permanent or transitory. However, inflation

uncertainty Granger causes inflation only for Canada, France, Japan, the UK and the US.2

Using interactive dummy variable for inflation targeting in a uni-variate GARCH

model Kontonikas (2004) found that in the post-targeting period UK inflation is substantially

less persistent and less variable. Recently, using ARIMA-GARCH model, Payne (2009)

found that for Thailand, inflation targeting marginally reduced the degree of volatility

persistence in response to inflation uncertainty, which support Holland’s (1995) stabilization

hypothesis. Most of the above mentioned studies used univariate modelling and concentrated

only on inflation and inflation uncertainty.

Shields et al (2005) and Grier et al (2004) use bi-variate GARCH modelling to

establish the relationships between growth, inflation and inflation uncertainty and growth

uncertainty.3 Both Shields et al (2005) and Grier et al (2004) use US data and the approaches

are similar. Shield et al (2005) use variance impulse response function (VIRF) and Grier et at

(2004) use generalised impulse response function (GIRF). The findings are also similar in

both studies. They have found that inflation uncertainty reduces both output and inflation and

higher output uncertainty increases growth but reduces inflation significantly. Grier and Perry

(2000) find the same result for US. They think that Fed’s stabilization process of lowering

inflation in the case of higher inflation uncertainty is the cause of the negative relationship.

They have also found similar result for the UK and Germany, which contradicts Ball’s (1992)

hypothesis. Bank of England targeted inflation officially on October 1992. Therefore,

theoretically, the relationship between inflation and inflation uncertainty should be positive

before IT and negative after the IT. The overall result may differ depending upon the strength

of the IT. Therefore, there is a need to examine this relationship using more appropriate

methodology.

In the 1990s, many developed countries targeted explicit numerical goal of inflation4

as a key component of monetary policy and Australia was one of them. Reserve Bank of

2 Conrad and Karanasos (2005) did similar study for the USA, Japan and UK and Daal at al (2005) for emerging countries. 3 Similarly, Fountas et at (2006). 4 New Zealand was the first country to formally adopt an inflation target of 0-2% in March 1990. Australia adopted a target of 2-3% in March 1993. The other industrial countries with formal inflation targeting framework with an independent central bank are: Canada (1991), Finland (1993), Spain (1994), Sweden (1993) and the UK (1992).

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Australia (RBA) targeted inflation from March 1993. However, the word “target” does not

appear in Reserve Bank of Australia document until October 1995, but the RBA stated a

specific desired numerical outcome for the inflation5 (2-3% per annum). After sixteen year of

inflation targeting, it is definitely worth exploring the outcome of the inflation targeting

policy in Australia.

The purpose of our study is similar to that of Shield et al (2005) and Grier at el (2004),

but our approach is different. We believe that the methodology is much better suited for the

study in the following aspects. Our paper differs from the previous studies in three different

ways. Firstly, in this paper we have used multivariate EGARCH modelling which we believe

is a better approach. Uni-variate approach does not allow inflation uncertainty (standard

deviation of the inflation residual) to influence the conditional variance of growth or the

growth uncertainty to influence the conditional variance of inflation, but the multivariate

approach can take care of this problem.6 This approach also allows us to discuss time varying

correlation between inflation and output growth. Multivariate EGARCH developed by

Nelson (1991), captures potential asymmetric behaviour of inflation and output growth and

avoids imposing non-negativity constrains in GARCH modelling by specifying the natural

logarithm of the variance ( 2ln tσ ). It is no longer necessary to restrict parameters in order to

avoid negative inflation and output uncertainty.

Secondly, we have included a newly constructed oil price dummy to capture the

impact of oil price7 on inflation. Thus, this paper aims to re-examine the inflation-growth

relationship in Australia by employing a more appropriate econometric method, the

multivariate EGARCH-M8 model together with a newly constructed oil price dummy. It is

5 See Johnson (2002) and Mallik and Chowdhury (2002) for detail. 6 See, Grier et al (2004). 7 Previous studies failed to incorporate the oil price while calculating the inflation uncertainty. An increase in oil price can increase inflation directly by raising the energy cost component of inflation and indirectly by increasing the cost of production. Therefore, the inclusion of oil price dummy in this research is most appropriate. 8 There is a serious drawback in using ARCH/GARCH model to generate inflation uncertainty, because it considers the 2

t iε − , which is the square of the inflation shock. Thus, it fails to distinguish between the positive and negative deviations between inflation and estimated inflation. In other words, it implicitly assumes that the estimated inflation can deviate from the actual inflation in only one direction. We can overcome this problem by considering the Exponential GARCH (or EGARCH) model, which can take into account the positive and the negative shocks. Instead of using the square of the estimated error term as in GARCH to calculate the conditional variance (equation 2 above), EGARCH uses the ratio of estimated error and its standard deviation in actual and absolute terms. In addition, in EGARCH the conditional variance is also dependent on the lagged variance of the error term. See Nelson (1991) for detail.

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thus possible to estimate inflation uncertainty and investigate the impact of inflation on

inflation uncertainty, and hence on growth9.

Finally, we use interactive inflation targeting dummy 10 to measure the effect of

inflation targeting in Australia.

Thus, our hypotheses concerns are the following:

i) The relationships between inflation uncertainty, output uncertainty, inflation

and output growth,

ii) Effect of oil price on inflation,

iii) Effectiveness of inflation targeting in Australia.

The organisation of the paper is as follows. In section 2, the EGARCH model

specification is outlined along with the data description. In section 3, we analyse the results

and the related discussion while section 4 concludes the paper.

2. Model Specification and Data Description

A brief description is provided here for the bi-variate EGARCH model with time

varying correlations relating the growth rate in output and the inflation. We denote the

inflation by tπ , the annualized quarterly differences of the natural logarithm of tP , the

producer price index: [ ]1(ln ln ) 400t tP P−− × , and the growth rate in output by ty∆ , the

annualized quarterly differences of the natural logarithm of ty , the industrial production

index: [ ]1(ln ln ) 400t ty y −− × for the period 1957 to 2009. The data used in this study are

obtained from the International Financial Statistics of the International Monetary Fund. The

interaction of the expectation part with the risk (captured by contemporaneous standard

deviation of the residual) in the relationship is captured by the following equations:

t ,1 t 1 ,2 t 1 ,3 ,t ,4 y,t ,5 Oil,t ,6 IT,t ,ty D Dπ π − π − π π π ∆ π π ππ = α +β π +β ∆ +β σ +β σ +β +β + ε (1a)

t y y,1 t 1 y,2 t 1 y,3 ,t y,4 y,t y,5 Oil,t y,6 IT,t y,ty y D D∆ ∆ − ∆ − ∆ π ∆ ∆ ∆ ∆ ∆∆ = α +β π +β ∆ +β σ +β σ +β +β + ε (2a)

A second set of mean equations has been considered using multiplicative dummy11

for the inflation targeting to capture the effect of inflation uncertainty pre and post inflation

targeting period. These second sets of equations with interactive dummy are as follows: 9 We have also used quarterly data to substantiate the results obtained from monthly data. 10 UK targeted zero inflation (1-2.5% by 1997) on October 1992. See Mallik and Chowdhury (2002) and Johnson (2002) for detail

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( ) ( )t ,1 ,1 IT,t t 1 ,2 t 1 ,3 ,3 IT,t ,t ,4 y,t

,5 Oil,t ,t

D y D

Dπ π π − π − π π π π ∆

π π

π = α + β + δβ π +β ∆ + β + δβ σ +β σ +

β + ε (1b)

( ) ( )t y y,1 y,1 IT,t t 1 y,2 t 1 y,3 y,3 IT,t ,t

y,4 y,t y,5 Oil,t y,t

y D y D

D∆ ∆ ∆ − ∆ − ∆ ∆ π

∆ ∆ ∆ ∆

∆ = α + β + δβ π +β ∆ + β + δβ σ +

β σ +β + ε (2b)

Where, ,t y,t,π ∆σ σ are standard deviations of the residuals of the inflation and output growth

and will be considered as inflation uncertainty and growth uncertainty respectively.

,IT tD =inflation targeting dummy (=0 up to March 1993 and 1 otherwise). ,oil tD = Oil price

dummy. As we know from the experience of the 1970s, oil price increases could be an

important cause of inflation and output slowdown. Thus, we have introduced a dummy

variable for oil price ( oilD ) in the inflation equation.

The oil price dummy is constructed by first converting the oil price in local currency.

This is because an appreciating exchange rate can offset the impact of oil price increases.

When the oil price (in local currency) increased more than 4% in three periods consecutively

then we consider the dummy equal to (+1). Similarly we have used the dummy as (-1) if the

oil price decreased more than 4% in three periods consecutively. The dummy is zero

otherwise. This method of constructing the oil price dummy is an improvement over

Hamilton (2003). 12

To complete the model specification, we define covariance matrix as below:

( ),tt t

y,t~ N 0,π

∆

ε Ω Σ ε

. (3)

As indicated above by equations (1) and (2), we assume bi-directional influence in the mean

parts for both inflation and output growth rate. The extent and nature of these influences will

be determined by the data and discussed in the empirical results. With the inclusion of the

volatility terms in the mean equation allows us to reflect on Friedman’s hypothesis as well.

11 Introduction of such policy dummy are often employed in inflation equation. See Alogoskoufis (1992) and Kontonikas (2004) for detail. 12 Hamilton identified the following dates as being associated with exogenous decline in the world petroleum supply: November 1956→ 10.1%, November 1973→ 7.8%, December 1978→ 8.9%, October 1980→7.2%, August 1990→ 8.8%, Other period → 0

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tΩ indicates all relevant information known at time t, and tΣ is the time varying covariance

matrix defined below.

The diagonal elements of the ( )22× covariance matrix are given by:

2 2,t ,0 ,1 1 ,t 1 ,2 2 y,t 1 ,3 ,t 1ln( ) f (z ) f (z ) ln( )π π π π − π ∆ − π π −σ = γ + γ + γ + γ σ , (4)

2 2y,t y,0 y,1 1 ,t 1 y,2 2 y,t 1 y,3 y,t 1ln( ) f (z ) f (z ) ln( )∆ ∆ ∆ π − ∆ ∆ − ∆ ∆ −σ = γ + γ + γ + γ σ (5)

In equations (4) and (5), 1f and 2f are functions of standardized innovations. These

innovations are defined as ,t ,t ,tz /π π π= ε σ and y,t y,t y,tz /∆ ∆ ∆= ε σ . The functions 1f and

2f capture the effect of sign and the size of the lagged innovations as:

1 ,t 1 ,t 1 ,t 1 ,t 1f (z ) z E( z ) zπ − π − π − π π −= − + δ (6)

2 y,t 1 y,t 1 y,t 1 y y,t 1f (z ) z E( z ) z∆ − ∆ − ∆ − ∆ ∆ −= − + δ (7)

The first two terms in equations (6) and (7) capture the size effect and the third term

measures the sign effect. If δ is negative, a negative realisation of zt-1 will increase the

volatility by more than a positive realisation of equal magnitude. Similarly, if the past

absolute value of zt-1 is greater than its expected value, the current volatility will rise. This is

called the leverage effect and is documented by Black (1976) and Nelson (1991) among

others.

To complete the specification of tΣ in equation (3) we need to focus on the off

diagonal elements. The off diagonal elements of the covariance matrix tΣ are defined in a

manner similar to that in Darbar and Deb (2002). The key is to define a time varying

conditional correlation which when combined with the conditional variances given the

equations (4) and (5) generate the required conditional covariance. The conditional

correlation is allowed to depend on the lagged standardized innovations and transformed

using a suitable function so that it lies between ( )1,1− . This is given by the following

equation:

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, y, t , y, t , t y, t , y, t t 0 1 j, t 1 I, t 1 2 t 1t

1, 2 1, c c z z c1 exp( )π ∆ π ∆ π ∆ π ∆ − − −

σ = ρ σ σ ρ = − x = + + x + −x

. (8)

Although the function tx may be unbounded, the exponential function transformation will

restrict it to the desired range for correlation.

For a given pair of series for the inflation and the growth rate of output together with

the covariance specification, the number of parameters (35) to be estimated may be

conveniently labelled as:

,1 ,1 ,2 ,2 ,3 ,4 ,5 ,5 ,6 ,7

,0 ,1 ,2 ,3

y y,1 y,1 y,2 y,2 y,3 y,4 y,5 y,5 y,6 y,7

y,0 y,1 y,2 y,3 y

0 1 2

, , , , , , , , , , ,, , , , ,, , , , , , , , , , ,, , , , ,

c ,c ,c

π π π π π π π π π π π

π π π π π

∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆ ∆

∆ ∆ ∆ ∆ ∆

α β δβ β δβ β β β δβ β β γ γ γ γ δ

Θ ≡ α β δβ β δβ β β β δβ β β γ γ γ γ δ

(9)

The estimation of these parameters is achieved by numerical maximisation of the joint

likelihood function under the distributional assumption of this model. The optimisation is

carried out in Gauss programming environment. If the sample size is T then the log likelihood

function to be maximised with respect to the parameter setΘ is:

T T

,t1t ,t y,t t

t 1 t 1 y,t

L( ) T ln(0.5 ) 0.5 ln 0.5 π−π ∆

= = ∆

ε Θ = − π − Σ − ε ε Σ ε

∑ ∑ . (10)

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3. Empirical results

3.1 Summary Statistics

Summary statistics, tests for serial correlation and unit root test results for each

variable under study are presented in Table 1A, 1B, and 1C. Inflation and growth display

significant amounts of kurtosis and failed to satisfy Bera-Jarque (1980) tests for normality.

Ljung-Box (1979) tests for serial correlation [Q (4) and Q (12)] shows a significant amount

of serial dependence for both monthly and quarterly data. Similarly, Q2 (4) and Q2 (12) (serial

correlation in the squared data of lag 4 and 12) shows strong evidence of conditional

heteroscedasticity. Unit root test results from Augmented Dickey-Fuller (ADF), Dickey-

Fuller-GLS (DF-GLS), Phillips Perron (PP) and Kwiatkowski, Phillips, Schmidt, and Shin

(KPSS) tests suggests that all variables for both monthly and quarterly data are stationary and

therefore, I(0).

Table 1A, 1B and 1C here

3.2 Estimated bi-variate EGARCH dynamics

Table 2 reports the estimates of the parameters from the mean and variance equations

and the correlation parameters of the bi-variate EGARCH model, of inflation and output

growth with and without interactive inflation targeting dummy. Column 2 and 5 shows the

estimated coefficients of equations (1a) and (1b) (without interactive dummy). Similarly,

column 3 and 6 shows the estimated coefficients of equations (2a) and (2b) (with interactive

dummy). Multiplicative dummy is introduced via the first order lag of inflation and with

inflation uncertainty, in order to allow for changes in the slope of average lagged inflation

and inflation uncertainty after inflation targeting period. Focussing on the estimates of the

mean equation of inflation (equation (1a) and (2a)), it is clear that ,1πβ (co-efficient of past

inflation) is positive and significant implies that past inflation increases present inflation rates.

The estimated coefficient of ,2πβ (co-efficient of growth uncertainty) is insignificant for both

mean equations of inflation and ,3πβ (co-efficient of inflation uncertainty) is negative and

significant at 1% level for equation (1a) and positive and insignificant for (1b). On the other

hand, the coefficient of ,3πδβ the inflation equation (1b) is negative and significant. From the

above results, we can conclude that overall inflation uncertainty reduces inflation

significantly, but the effect of inflation uncertainty on inflation is positive before the inflation

targeting period and suggests that introducing IT, Reserve Bank of Australia has eliminated

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inflation inertia. Inflation targeting policy reversed the inflation uncertainty effect on inflation

to negative direction. That means the inflation-targeting period has detectable influence in

lowering the effect of inflation uncertainty over inflation, which supports existing related

studies13. The coefficient of the oil price dummy is positive and significant for both inflation

equation and the coefficient of the inflation targeting dummy is negative and significant for

equation (1a) implies that oil price has positive and significant effect on inflation and the

inflation in Australia has been reduced after the inflation targeting policy significantly.

Table 2 here

Similarly from the mean equations (equation (1b) and (2b)) of output growth, it can

be seen that the estimates of ,2yβ∆ (co-efficient of growth uncertainty) is positive and

significant and ,3yδβ∆ (co-efficient of inflation uncertainty after the inflation targeting period)

is negative and significant. Therefore, the output uncertainty increases output growth

significantly for the whole period and the inflation uncertainty lowers the growth

significantly after the inflation-targeting period. The negative and significant estimated value

of ,6yβ∆ (coefficient of inflation targeting dummy) indicates that growth has been reduced

after the inflation targeting period in Australia. Insignificant coefficient of oil price dummy

indicates that oil price has no effect on output growth.

The estimates of the variance equations for both inflation and output growth show that

the variance of growth and inflation are time varying, display asymmetry and exhibit

statistically significant EGARCH terms. This implies that the estimated variance equation is

well specified for both inflation and growth. The significance of the term defining the time

varying correlations indicates that a constant correlation model would be inappropriate. High

realised correlation (Figure 1) coincides with the high output growth volatility in the early

1970’s. This probably relates to the first oil price shock.

Figure 1 here

13 Using multivariate GARCH, Grier et al (2004) and Shields et al (2005) also found that overall inflation uncertainty lowers, rather than increases average inflation for the US. They however, did not use any interactive dummy to decompose the effect of inflation uncertainty after the inflation stabilization process. Using uni-variate GARCH modeling Kontonikas (2004) found that inflation uncertainty has no significant effect on inflation for U.K.

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Using bi-variate GARCH Shields et al (2005) and Grier et al (2004) find that inflation

uncertainty reduces inflation for the US, which contradicts Friedman-hypothesis. However,

Wilson (2006) use bi-variate EGARCH model and supports Friedman-hypothesis for Japan.

Such contradictory evidence seems to suggest that expected inflation is not captured correctly

by these models. More elaborate model may be necessary to capture the essence of expected

inflation e.g. Kim (1993) that allows for regime differences.

We did the same analysis using Consumer price Index (CPI) and Real Gross

Domestic Product (RGDP). The results are similar except for the effect of oil price on

inflation (calculated using CPI) is significant at 10% level and the size of the coefficient is

lower at 0.0066 than the inflation equation (calculated using PPI and IP) at 0.0131 (see Table

2 column 2). The results are consistent with the existing literature. In general oil price has

greater influence on PPI inflation than that of CPI inflation. Results will be available upon

request from the author.

3.3 Diagnostic tests

The diagnostics statistics for the model is given in Table 3. The test statistics (upper

panel) include the fifth order serial correlation in the squared standardised innovations as well

as the product of the standardised residuals from the two equations of the model. The Ljung-

Box statistics clearly demonstrate absence of any remaining heteroscedasticity. In other

words, the bi-variate model with EGARCH variance along with time varying correlations

properly addresses the heteroscedasticity in the data.

It is also known that when the model allows for asymmetric effects of residuals (as

EGARCH model facilitates), the Ljung-Box statistics may not have sufficient power. In that

situation, test statistics following Engle and Ng (1993) are more appropriate. Although the

Ljung-Box statistics indicate the absence of non-linear dependence in the standardised

innovations for the sample period, Engle and Ng test (lower panel) confirms the validity of

the Ljung-Box test. This confirms that there are no sign biases, that is, there is no asymmetry

effect. This bias could potentially affect the outcomes of the Ljung-Box test. We are thus

comfortable with the outcomes of the test. Besides, the joint test bias can be rejected at 90%

confidence level. The Engle and Ng test supports a good fit of the bi-variate EGARCH model

for the data set used in this study.

Table 3 here

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3.4 Generalised Impulse Response Analysis

In this section, we further investigate the statistical significance of innovations of the

variables under study by using Generalised Impulse Response Functions (GIRF), introduced

by Pesaran and Shin (1998). We have estimated GIRF by employing VAR, consisting of

inflation, inflation uncertainty, growth and growth uncertainty. The number of lags is

determined by AIC. The impulse response results are presented in Figure 2. Dashed lines

indicate two standard error bands representing a 95% confidence region.

Figure 2 here

In the first row in Figure 2 shows that the innovations in inflation explain the

movements of inflation, which is also explained by the positive and significant estimate

of ,1πβ . Similarly, the innovations of growth increases growth further. From the graph we can

see that the growth uncertainty reduces economic growth, increases growth uncertainty and

increases inflation uncertainty. On the other hand the innovations of inflation uncertainty

have significant mixed effect in the movements of inflation. Similarly, the innovations of

inflation uncertainty increase the movement of growth uncertainty and inflation uncertainty

significantly for a short period of time (approximately up to 2 quarters). Most of the results

substantiate the results obtained from Table 2.

4. Concluding Remarks

In this study, we have investigated the relation between inflation, growth, inflation

uncertainty and growth uncertainty using multivariate EGARCH modelling for Australia. We

have enhanced the analysis by including the inflation targeting interactive dummy to separate

the effect of lagged inflation and inflation uncertainty on inflation. It is clear from the

examination that, inflation uncertainty has negative and significant effect on inflation. On the

other hand growth uncertainty increases inflation. Newly constructed oil price dummy is

introduced in the mean equation of inflation and growth to capture the effect of oil price on

inflation and growth. Oil price has positive effect and significant effect on inflation but no

effect on growth.

These results are also substantiated using GIRF (Generalised Impulse Response

Function). The result in general supports the findings of similar study for USA by Shields et

al (2005) and Grier et al (2004), where inflation uncertainty reduces inflation.

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The inflation uncertainty which reduces growth is potentially harmful for the

economy. Oil price has significant positive influence on inflation. Therefore, it is clear from

this study that inflation itself is not good for the Australian economy. From the policy

perspective, Reserve Bank of Australia should attempt to keep inflation stable and low. The

study also confirms that the inflation targeting policy is working well and RBA should

continue with its present policy. Since oil price is also increasing inflation, the Australian

policy makers should stabilize domestic oil price through subsidization process and thus keep

inflation low and thus help boot investment, growth and employment.

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Table 1A: Summary Statistics

Mean Standard deviation

Skewness Kurtosis Normality(J. B. Test)

π 4.68 6.82 -0.68 4.84 44.32 (0.000) y∆ 2.91 4.73 -0.52 4.28 23.21 (0.000)

Table 1B: Test for Serial Correlation

(2)Q (4)Q 2 (2)Q 2 (4)Q

π 28.27 (0.000) 79.18 (0.000) 43.73 (0.000) 50.99 (0.000) y∆ 12.39 (0.002) 22.68 (0.000) 28.72 (0.000) 34.34 (0.000)

Table 1C: Unit Root test ADF DF-GLS PP KPSS π -2.28 -1.72 -11.61 0.27 y∆ -3.46 -1.88 -10.73 0.51

πσ -3.88 -2.48 -13.71 0.15

yσ∆ -3.52 -2.45 -11.55 0.13

1% C. V -3.46 -2.58 -3.46 0.74 5% C. V. -2.87 -1.94 -2.87 0.46 10% C. V. -2.57 -1.62 -2.57 0.35

Note: i) Figures in parentheses are the probabilities.

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Table 2 Parameter Estimates for the Bivariate EGARCH Model with Dynamic Correlation

Inflation (PPI) and Output Growth (IP) Inflation equation Output growth equation

Equation (1a) Equation (1b) Equation (2a) Equation (2b) Mean

equation Without interaction

dummy With interaction

dummy Without interaction

dummy With interaction

dummy

πα 0.0.0607*** (3.39) -0.0174 (-0.59) y∆α 0.0326** (2.11) 0.0241 (0.76)

,1πβ 0.3121*** (4.25) 0.2183** (2.39) y,1∆β -0.1189* (-1.73) -0.1609 (-1.46)

,1πδβ ----------- -0.0095 (-0.05) y,1∆δβ ----------- -0.1171 (-0.52)

,2πβ -0.0886 (-1.32) 0.1006 (1.28) y,2∆β 0.2178*** (3.33) 0.2376** (2.25)

,3πβ -0.8945*** (-8.21) 0.0810 (0.22) y,3∆β 0.0620 (0.67) 0.7775* (1.65)

,3πδβ ---------- -0.3551* (-1.92) y,3∆δβ ----------- -0.5536** (-2.38)

,4πβ 0.5372 (1.63) 0.7454** (2.45) y,4∆β -0.0621 (-0.25) -0.4966 (-1.22)

,5πβ 0.0210*** (3.30) 0.0131* (1.94) y,5∆β -0.0009 (-0.19) 0.0111 (1.62)

,6πβ -0.0274*** (-3.45) ----------- y,6∆β -0.0197** (-2.34) ----------

Variance equation

,0πγ -0.7939***(-14.92) -3.9290*** (-4.09) y,0∆γ -0.9580***(-17.74) -3.9332*** (-3.78)

,1πγ 0.1667** (2.20) 0.7007*** (4.17) y,1∆γ 0.1961* (1.91) 0.2977* (1.74)

,2πγ -0.0018 (-0.02) -0.1309 (-0.77) y,2∆γ 0.5055*** (2.84) 0.6180*** (3.37)

,3πγ 0.8571***(77.23) 0.2738 (1.56) y,3∆γ 0.8176*** (65.25) 0.2391 (1.25)

πδ 0.4412 (0.94) 0.5749*** (2.69) y∆δ -0.0480 (-0.24) -0.3927* (-1.70)

Half life 4.50 0.54 Half life 3.44 0.48 Relative asymmetry

0.39 0.27

Relative asymmetry 1.10 2.29

Correlation function Without interaction dummy With interaction dummy

0c 0.5417** (2.09) 0.3767* (1.67)

1c -0.2218** (-2.03) -0.9532*** (-3.48)

2c -0.7212*** (8.60) -0.0484 (-0.24) The numbers in parentheses indicate t-statistics. Half-life represents the time it takes for the shocks to reduce its impact by one-half. Relative asymmetry may be greater than, equal to or less than 1 indicating negative asymmetry, symmetry and positive asymmetry respectively. ***, ** and * indicate statistical significance at 1%, 5% and 10% level respectively.

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Table 3

Diagnostics Tests Monthly data Quarterly data Inflation

equation Output growth

equation

Inflation equation

Output growth

equation p-values for Ljung-Box Q(5) statistics

Z 0.000 0.003 0.009 0.022 Z2 0.970 0.071 0.946 0.811 Z1. Z2 0.287 0.014 p-values for Engle and Ng (1993) diagnostic tests Sign bias test 0.203 0.871 0.480 0.581 Negative size bias test 0.162 0.378 0.314 0.758 Positive size bias test 0.612 0.910 0.172 0.839 Joint test 0.630 0.437 0.594 0.410

Z represents the standardised residual for the corresponding equation i.e. either inflation or output growth rate. Z1. Z2 indicate product of the two standardised residuals. The entries are the p-values for the relevant hypotheses tests.

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Figure 1

Estimated Variance and Correlation Series for Australia

Variance Inflation (PPI)

0.000.010.020.030.040.050.060.070.08

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Variance Output Growth (IP)

0.00

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Correlation Inflation (PPI) and Output Growth(IP)

-1.00

-0.60

-0.20

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1.00

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Figure 2: Generalised Impulse Response Functions (Using Monthly data) Response to Generalised One Standard Deviation Innovations ± 2 S.E

-4

-2

0

2

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2 4 6 8 10 12 14 16 18 20

Response of INF to INF

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Response of INF to GR

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Response of INF to UNGR

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2 4 6 8 10 12 14 16 18 20

Response of INF to UNINF

-4

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2 4 6 8 10 12 14 16 18 20

Response of GR to INF

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Response of GR to GR

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Response of GR to UNGR

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Response of GR to UNINF

-.004

-.002

.000

.002

.004

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Response of UNGR to INF

-.004

-.002

.000

.002

.004

2 4 6 8 10 12 14 16 18 20

Response of UNGR to GR

-.004

-.002

.000

.002

.004

2 4 6 8 10 12 14 16 18 20

Response of UNGR to UNGR

-.004

-.002

.000

.002

.004

2 4 6 8 10 12 14 16 18 20

Response of UNGR to UNINF

-.002

.000

.002

.004

.006

2 4 6 8 10 12 14 16 18 20

Response of UNINF to INF

-.002

.000

.002

.004

.006

2 4 6 8 10 12 14 16 18 20

Response of UNINF to GR

-.002

.000

.002

.004

.006

2 4 6 8 10 12 14 16 18 20

Response of UNINF to UNGR

-.002

.000

.002

.004

.006

2 4 6 8 10 12 14 16 18 20

Response of UNINF to UNINF

Note for Figure 2A: INF=Inflation; UNINF=Inflation Uncertainty; GRIP=Growth of Industrial Production and UNGR=Growth Uncertainty

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