Empir Econ (2013) 45:1333–1350 DOI 10.1007/s00181-012-0650-9
Inflation uncertainty, growth uncertainty, oil prices, and output growth in the UK Ramprasad Bhar · Girijasankar Mallik
Received: 2 May 2010 / Accepted: 19 August 2012 / Published online: 7 November 2012 © Springer-Verlag Berlin Heidelberg 2012
Abstract This study examines the transmission and response of inflation uncertainty and output uncertainty on inflation and output growth in the UK using a bi-variate EGARCH model. Results suggest that inflation uncertainty has positive and significant effects on inflation before the inflation-targeting period, but that the effect is significantly negative after the inflation-targeting period. On the other hand, output uncertainty has a negative and significant effect on inflation and a positive effect on growth, while oil price rises significantly increase inflation for the UK. Results also indicate that inflation uncertainty significantly reduces output growth before and after the inflation-targeting period. These findings are robust and the Generalized impulse response functions corroborate the conclusions. These results have important implications for an inflation-targeting monetary policy, and for stabilization policy in general. Keywords
Inflation · Inflation uncertainty · EGARCH · Impulse response
JEL Classification
E31 · E52 · E63 · E64
1 Introduction The examination of the impact of inflationary expectations is crucial, as it is through inflation uncertainty that high inflation can adversely affect economic growth. Okun
R. Bhar School of Banking and Finance, The University of New South Wales, Sydney 2052, Australia e-mail:
[email protected] G. Mallik (B) School of Economics & Finance, University of Western Sydney, Locked Bag 1797, Penrith South DC NSW 1797, Australia e-mail:
[email protected]
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(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) formalizes the positive relationship between inflation and inflation uncertainty. In Ball’s model, the public does not know the preferences of the policy maker, but this only affects inflation uncertainty when inflation is high. Empirical studies on growth, inflation and inflation uncertainty, and growth uncertainty relationship show mixed results.1 Recently, much attention has been given to the relationship between inflation and its uncertainty. For example, Berument and Dincer (2005) find that inflation Granger causes inflation uncertainty for all G7 countries supporting the Friedman–Ball hypothesis. However, inflation uncertainty Granger causes inflation only for Canada, France, Japan, the UK, and the US.2 By means of GARCH modelling for monthly and quarterly data, Kontonikas (2004) finds that inflation uncertainty has no significant effect on inflation for the UK. Berument et al. (2010) conclude that the response of inflation to inflation volatility is significantly positive in Turkey. According to Fountas et al. (2004), inflation raises inflation uncertainty for all European countries except Germany, and inflation uncertainty does not cause negative output effects except for the UK. Using a time-varying GARCH framework for 12 EMU countries, Caporale and Kontonikas (2009) find that the euro has a significant impact on the relationship between inflation and its uncertainty; moreover, the Friedman–Ball link between inflation and inflation uncertainty becomes weaker3 in a number of countries. 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.4 They use US data, and the approaches and findings are similar. Shields et al. (2005) use a variance impulse response function (VIRF) and Grier et al. (2004) use a generalized impulse response function (GIRF). They find that inflation uncertainty reduces both output and inflation, and higher output uncertainty increases growth but reduces inflation significantly. By means of the GARCH-M method, Grier and Perry (2000) find that the conditional variance of inflation significantly lowers average output growth in the United States, as argued by Friedman (1977). They suggest that the US Federal Reserve’s stabilization process of lowering inflation where there is initially high inflation uncertainty is the cause of the negative relationship. They find similar results for the UK and Germany, which appear to contradict Ball (1992) hypothesis. The Bank of England targeted inflation officially from October 1992. Theoretically, the relationship between inflation and inflation uncertainty should be positive and inflation uncertainty should have a positive effect on inflation; but, this
1 See Kormendi and Meguire (1985), Grier and Tullock (1989), Grier and Perry (2000), and Golob (1994). 2 Conrad and Karanasos (2005) have conducted a similar study for the US, Japan, and the UK; and Daal
et al. (2005) for emerging countries. 3 In a cross country analysis, Wright (2009) finds that term premiums decline internationally in countries
that apparently reduce inflation uncertainty. 4 Similarly, Fountas et al. (2004, 2006) and Bhar and Hamori (2004).
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should reduce after the inflation-targeting period when the volatility of inflation should decrease because the main aim of IT is to stabilize inflation. The overall result may differ depending upon the success of the inflation-targeting strategy. The purpose of our study is similar to that of Shields et al. (2005) and Grier et al. (2004), but our approach is different. We believe that the methodology we have used is better suited for the study in several respects. Our paper differs from the previous studies in three ways. First, in this paper, we have used bi-variate EGARCH modelling, which allows us to discuss time-varying correlation between inflation and output growth. Bi-variate EGARCH, developed by Nelson (1991), captures potential asymmetric behaviors of inflation and output growth and avoids imposing non-negativity constrains in GARCH modelling by specifying the natural logarithm of the variance (ln σt2 ). It is no longer necessary to restrict parameters to avoid negative inflation and output uncertainty. Second, we have included a newly constructed oil price dummy to capture the impact of oil price5 on inflation. Thus, this paper is able to re-examine the inflation-growth relationship in the UK by employing a more appropriate econometric method, the multivariate EGARCH-M6 model. The use of higher frequency data makes it possible to use the EGARCH-M model to estimate inflation uncertainty and investigate the impact of inflation on inflation uncertainty, and hence on growth.7 Third, we use an interactive inflation-targeting dummy8 to measure the effect of IT in the UK. Our hypotheses concern the following: (i) The relationships between inflation uncertainty, output uncertainty, inflation, and output growth; (ii) Effect of oil prices on inflation; (iii) Effectiveness of IT in the UK. The organization of the paper is as follows: in Sect. 2, the EGARCH model specification is outlined along with the data description. In Sect. 3, we analyze the results and the related discussion. Section 4 concludes the paper.
5 Previous studies have failed to incorporate the oil price while calculating inflation uncertainty. An increase in the 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. 6 There is a serious drawback in using ARCH/GARCH model to generate inflation uncertainty because 2 , which is the square of the inflation shock, and thus fails to distinguish between it considers the εt−i
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 overcome this problem by considering the Exponential GARCH (or EGARCH) model, which can take into account both positive and negative shocks. Instead of using the square of the estimated error term as in GARCH to calculate the conditional variance (Eq. 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 dependent on the lagged variance of the error term. See Nelson (1991) for details. 7 We have also used quarterly data to substantiate the results obtained from monthly data. 8 The UK targeted zero inflation (1–2.5 % by 1997) on October 1992. See Mallik and Chowdhury (2002)
and Johnson (2002) for details.
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2 Model specification and data description A brief description is provided here for the bi-variate EGARCH model with timevarying correlations relating to the growth rate in output and the inflation. We denote logarithm inflation by πt , the annualized monthly differences of the natural of Pt , the producer price index9 (PPI): (ln Pt − ln Pt−1 ) × 1200 for monthly data and annualized quarterly differences of the natural logarithm of the PPI, (ln Pt − ln Pt−1 ) × 400 for quarterly data. Similarly, the growth rate in output is differences of the signified by yt , the annualized monthly and quarterly natural logarithm of yt , the industrial production index: (ln yt − ln yt−1 ) × 1200 for monthly data and (ln yt − ln yt−1 ) × 400 for quarterly data for the period 1957–2009.10 The data used in this study are obtained from the International Financial Statistics of the International Monetary Fund and seasonally adjusted. The interaction of the expectation portion with the risk (captured by contemporaneous standard deviation of the residual) in the relationship is captured by the following equations: πt = απ + βπ,1 + δβπ,1 DInf,t πt−1 + βπ,2 + δβπ,2 DInf,t πt−2 +βπ,3 yt−1 + βπ,4 yt−2 + βπ,5 + δβπ,5 DInf,t σπ,t +βπ,6 σy,t + βπ,7 DOil,t + επ,t (1) yt = αy + βy,1 + δβy,1 DInf,t πt−1 + βy,2 + δβy,2 DInf,t πt−2 +βy,3 yt−1 + βy,4 yt−2 + βy,5 + δβy,5 DInf,t σπ,t +βy,6 σy,t + βy,7 DOil,t + εy,t
(2)
where σπ,t , σy,t are standard deviations of the residuals of the inflation and output growth and will be considered as inflation uncertainty and growth uncertainty, respectively. Dinf,t = inflation-targeting dummy11 (= 0 up to October 1992 and 1 otherwise). Doil,t = Oil price dummy. As we know from the experience of the 1970s, oil price increases can be an important cause of inflation and output slowdown. Thus, we have introduced a dummy variable for oil price12 (Doil ) in the inflation equation. 9 In fact, there is not much difference between the use of CPI and PPI. We have conducted the analysis
using both, and obtained similar results. Most papers in this area such as Shields et al. (2005), Grier and Perry (2000) and Grier et al. (2004) have used PPI. According to Grier and Perry (2000), “optimal number of lags varies slightly for inflation equations depending on the sample period and whether the PPI or the CPI is used to calculate inflation.” Wright (2009) calculates inflation uncertainty using survey-based data. 10 The period of study of monthly data is January 1957–January 2009; and 1957 quarter 1–2008 quarter
4 for quarterly data. 11 Inclusion of inflation targeting dummy in a growth and inflation equation is acceptable for UK. Many
researchers including Kontonikas (2004), Gurlaynak et al. (2010) and others used such dummy to see the effectiveness of inflation targeting on growth and inflation. 12 In general, oil price can cause both inflation and growth, but fluctuations in crude oil prices have less
effect on the inflation rate than they had ten or twenty years before. However, if the oil price increases more than 4 % consecutively over three periods, then it can influence inflation and thus growth: hence our oil price dummy. For example, Hanabusa (2009) finds that oil price can cause growth in Japan, and Hooker (2002) find that oil price changes had a substantial, direct contribution to core inflation in the US before 1981, but have had little or no pass-through effect since that time.
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Inflation uncertainty, growth uncertainty, oil prices
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The oil price dummy is constructed by first converting the oil price into local currency. This is because an appreciating exchange rate can offset the impact of oil price increases. When the oil price (in local currency) increases more than 4 % in three consecutive periods, we consider the dummy equal to (+1). Similarly, we use the dummy as (−1) if the oil price decreases more than 4 % in three consecutive periods. The dummy is zero otherwise. This method of constructing the oil price dummy is an improvement over Hamilton (2003).13 To complete the model specification, we define the covariance matrix as below:
επ,t ∼ N (0, t ) εy,t t
(3)
As indicated above by Eqs. (1) and (2), we assume bi-directional influences 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 will be discussed in the empirical results; the inclusion of the volatility terms in the mean equation also allows us to reflect on Friedman’s hypothesis. t indicates all relevant information known at time t, and t is the time-varying covariance matrix defined below. The diagonal elements of the (2 × 2) covariance matrix are given by 2 2 ) = γπ,0 + γπ,1 f 1 (z π,t−1 ) + γπ,2 f 2 (z y,t−1 ) + γπ,3 ln(σπ,t−1 ) ln(σπ,t 2 ln(σy,t ) = γy,0
2 + γy,1 f 1 (z π,t−1 )+γy,2 f 2 (z y,t−1 ) + γy,3 ln(σy,t−1 )
(4) (5)
In Eqs. (4) and (5), f 1 and f 2 are functions of standardized innovations. These innovations are defined as z π,t = επ,t /σπ,t and z y,t = εy,t /σy,t . The functions f 1 and f 2 capture the effect of sign and the size of the lagged innovations as f 1 (z π,t−1 ) = z π,t−1 − E(z π,t−1 ) + δπ z π,t−1 f 2 (z y,t−1 ) = z y,t−1 − E(z y,t−1 ) + δy z y,t−1
(6) (7)
The first two terms in Eqs. (6) and (7) capture the size effect and the third term measures the sign effect. If δ is negative, a negative realization of z t−1 will increase the volatility by more than a positive realization of equal magnitude. Similarly, if the past absolute value of z t−1 is greater than its expected value, 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 t in Eq. (3), we need to focus on the off diagonal elements. The off diagonal elements of the covariance matrix t 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 by Eqs. (4) and (5), generates the required conditional covariance. The conditional 13 Hamilton identified the following dates as 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 periods → 0.
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correlation is allowed to depend on the lagged standardized innovations and is transformed using a suitable function so that it lies between (−1, 1). This is given by the following equation: σπ,y,t = ρπ,y,t σπ,t σy,t , ρπ,y,t = 2
1 1 + exp(−ξt )
− 1,
ξt = c0 + c1 z j,t−1 z I,t−1 + c2 ξt−1
(8)
Although the function ξt 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 ⎫ ⎧ απ , βπ,1 , δβπ,1 , βπ,2 , δβπ,2 , βπ,3 , βπ,4 , βπ,5 , δβπ,5 , βπ,6 , βπ,7 ,⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ γπ,0 , γπ,1 , γπ,2 , γπ,3 , δπ , ⎪ ⎪ ⎪ ⎪ ⎬ ⎨ αy , βy,1 , δβy,1 , βy,2 , δβy,2 , βy,3 , βy,4 , βy,5 , ≡ δβy,5 , βy,6 , βy,7 , ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ , γ , γ , γ , δ , γ ⎪ ⎪ y,0 y,1 y,2 y,3 y ⎪ ⎪ ⎭ ⎩ c0 , c1 , c2
(9)
The estimation of these parameters is achieved by numerical maximization of the joint likelihood function under the distributional assumption of this model. The optimization is carried out in a Gauss programming environment. If the sample size is T, then the log likelihood function to be maximized with respect to the parameter set is L() = −T ln(0.5π ) − 0.5
T t=1
ln | t | − 0.5
T
επ,t εy,t t−1
t=1
επ,t εy,t
(10) Using the definitions above, we can also define two other useful quantities. The persistence of volatility may also be quantified by an examination of the half life (HL), which indicates the time period required for the shocks to reduce to one half of their original size: HL =
ln(0.5) , i = π, y ln |γi,3 |
(11)
The asymmetric effect of standardized innovations on volatility may be measured as derivatives from Eqs. (6) and (7). Relative asymmetry is defined as | − 1 + δi |/(1 + δi ), where i = π, y. This quantity is greater than, equal to, or less than 1 for negative asymmetry, symmetry, and positive asymmetry, respectively.
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Inflation uncertainty, growth uncertainty, oil prices
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Table 1 Summary statistics Mean
Standard deviation
Skewness
Kurtosis
Normality(J. B. Test)
Monthly data π
4.87
7.14
1.54
7.34
738.98 (0.000)
y
1.34
13.20
−0.26
3.71
20.27 (0.000)
Quarterly data π
4.59
6.49
−1.24
20.22
2623.98 (0.000)
y
1.24
7.03
−0.02
7.87
205.74 (0.000)
Table 2 Test for serial correlation Q(4)
Q(12)
Q 2 (4)
Q 2 (12)
513.34 (0.000)
1285.80 (0.000)
175.27 (0.000)
5191.80 (0.000)
13.92 (0.008)
27.95 (0.006)
195.27 (0.000)
215.08 (0.000)
97.69 (0.000)
240.05 (0.000)
56.13 (0.000)
59.39 (0.000)
8.86 (0.065)
20.53 (0.058)
59.62 (0.000)
91.06 (0.000)
Monthly data π y
Quarterly data π y
3 Empirical results 3.1 Summary statistics Summary statistics, tests for serial correlation and unit root test results for each variable under study for monthly and quarterly data, are presented in Tables 1 2, and 3. Inflation and growth display significant amounts of kurtosis and fail to satisfy Bera and Jarque (1980) tests for normality. Ljung and Box (1979) tests for serial correlation [Q (4) and Q (12)] show 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) show strong evidence of conditional heteroskedasticity. 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 suggest that all variables for both monthly and quarterly data are stationary and, therefore, I(0) or integrated of order zero. 3.2 Estimated bi-variate EGARCH dynamics In Eqs. (1) and (2) a multiplicative dummy14 is introduced via the first and second lag of inflation and with inflation uncertainty, to allow for changes in the 14 Introduction of such policy dummies are often employed in inflation equations. See Alogoskoufis (1992)
and Kontonikas (2004) for detail.
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R. Bhar, G. Mallik
Table 3 Unit root test ADF Constant term only
DF-GLS Constant term only
PP Constant term only
KPSS Constant term only
Monthly data π
−2.57
−3.90
−21.76
0.61
y
−5.03
−1.94
−27.27
0.44
σπ
−7.46
−6.09
−13.01
0.53
σy
−7.84
−5.74
−10.39
0.68
5 % C. V.
−2.87
−1.94
−2.87
0.46
Quarterly data π
−3.56
−2.69
−11.47
0.43
y
−5.55
−5.24
−12.28
0.54
σπ
−4.92
−4.72
−11.13
0.25
σy
−4.28
−3.81
−10.23
0.45
5 % C. V.
−2.87
−1.94
−2.87
0.46
Note: (i) Figures in parentheses are the probabilities, (ii) C.V denotes critical value
slope of average lagged inflation and inflation uncertainty after IT for both monthly and quarterly data. The estimates of the equations are reported in Table 4, which also reports the estimates of the variance equation and the correlation parameters of the bi-variate EGARCH model introduced in Eqs. (1) and (2). Focusing on the estimates of the mean equation of inflation for monthly and quarterly data, it is clear that βπ,5 (co-efficient of inflation uncertainty), βπ,6 (co-efficient of growth uncertainty), and βπ,7 (co-efficient of oil price dummy) for the inflation equation (columns 3 and 4 in Table 4) are all significant at least at the 1 % level. The positive estimate of βπ,5 at 0.8855 for monthly and 0.9240 for quarterly data, and the negative estimate of βπ,6 at −0.4098 for monthly and −0.3755 for quarterly data, imply that inflation uncertainty increases inflation and growth uncertainty reduces inflation significantly. Positive estimated coefficients (for the oil price dummy) of βπ,7 at 0.0143 and 0.0058, for monthly and quarterly data, respectively, indicate that the oil price has a positive and significant effect on inflation for the UK. This is an important finding. For the monthly inflation equation the coefficients of the multiplicative dummy variables and lagged inflation (δβπ,1 , δβπ,2 ) are significant and have opposite signs, but for the quarterly data their sum is negative and significant at 1 % level, indicating that inflation persistence declined under inflation targeting (IT). The negative and significant estimated value of δβπ,5 at −0.7147 indicates that inflation uncertainty has a negative effect after the inflation-targeting period, which suggests that by introducing IT the Bank of England has eliminated inflation inertia. Using an interactive dummy on inflation uncertainty, our result suggests that overall inflation uncertainty has a significantly positive effect on inflation and a negative effect after the inflationinflation-targeting period. This means that the inflation-targeting period has had a detectable influence in lowering the effect of inflation uncertainty over inflation, which
123
0.9240*** (851.84)
0.1157** (2.51)
−0.1792** (−2.20)
0.0094 (0.66)
−0.0081 (−0.55)
0.8855***(78.93)
−0.7147*** (−16.66)
−0.4098*** (−5.58)
0.0143*** (4.50)
βπ,2
δβπ,2
βπ,3
βπ,4
βπ,5
δβπ,5
βπ,6
βπ,7
−0.3950*** (−14.05)
0.2891*** (5.49)
0.1319*** (2.88)
0.9350*** (211.80)
0.3769*** (2.97)
10.32
0.45
γπ,0
γπ,1
γπ,2
γπ,3
δπ
Half life
R. A
Variance equation
−0.0245** (−2.29)
0.3909*** (6.65)
δβπ,1
0.27
2.87
0.5768*** (8.25)
0.7856*** (45.72)
0.0092 (0.16)
0.9366*** (24.90)
−1.442***(−11.34)
0.0058*** (4.78)
−0.3755*** (−4.22)
−0.1553(−1.07)
0.0606*** (3.53)
−0.2683*** (−3.89)
0.1113*** (3.16)
−0.3954*** (−3.32)
0.0492*** (7.86)
0.0620 (1.41)
βπ,1
0.0128*** (2.96)
0.0440***(5.97)
απ
Mean equation
R. A
Half life
δy
γy,3
γy,2
γy,1
γy,0
βy,7
βy,6
1.51
12.06
−0.2037 (−1.61)
0.9442*** (383.90)
0.1264*** (4.17)
0.1035*** (3.15)
−0.240*** (−19.28)
0.0088* (1.81)
0.5483* (16.13)
−0.9064***(−195.4)
−0.8899***(−253.9)
βy,5 δβy,5
−0.0585* (−1.62)
−0.1951*** (−5.26)
0.3811*** (7.82)
−0.0240 (−0.61)
−0.0055 (−0.06)
−0.0239 (−0.27)
0.0093 (1.19)
βy,4
βy,3
δβy,2
βy,2
δβy,1
βy,1
αy
Monthly data
Monthly data
Quarterly data
Output growth equation
Inflation equation
Table 4 Parameter estimates for the bivariate EGARCH model with dynamic correlation U.K. inflation (PPI) and output growth rate
40.23
3.29
−0.9515*** (−27.9)
0.8102*** (42.6)
0.1418*** (4.11)
0.5272*** (6.54)
−1.0891*** (−9.39)
−0.0064 (−1.52)
0.9319*** (18.90)
−0.8820*** (−14.2)
−0.7980*** (−8.17)
0.1178** (2.40)
0.2026*** (3.04)
0.0268 (0.14)
−0.0777 (−0.76)
0.4719* (1.78)
−0.0606 (−0.56)
−0.0025 (−0.59)
Quarterly data
Inflation uncertainty, growth uncertainty, oil prices 1341
123
123 0.0381 (0.47) 0.9085*** (14.51)
−0.0720*** (−2.67) −0.9048*** (−115.76)
c2
Note: (i) The numbers in parentheses indicate t-statistics. Half-life represents the time it takes for a shock to reduce its impact by one half. (ii) Relative asymmetry (RA) may be greater than, equal to or less than 1, indicating negative asymmetry, symmetry and positive asymmetry respectively. (iii) ***, ** and * denote significance at 1, 5 and 10 % levels respectively
0.0102 (0.66)
0.0204 (0.12)
For quarterly data
c1
For monthly data
Correlation function
c0
Table 4 continued
1342 R. Bhar, G. Mallik
Inflation uncertainty, growth uncertainty, oil prices
1343
supports existing related studies.15 The overall result concurs with Friedman (1977) hypothesis. Similarly, from the mean equation of output growth for both monthly and quarterly data, it can be seen that the estimate of βy,5 (co-efficient of inflation uncertainty) is negative and significant, and of δβy,5 (co-efficient of inflation uncertainty after the inflation-targeting period) is negative and significant. Therefore, inflation uncertainty lowers growth significantly, both before and after the inflation-targeting period. The significant estimated value of βy,6 (coefficient of growth uncertainty) indicates that growth uncertainty has positive and significant effects on growth in U.K. The insignificant coefficient of the oil price dummy indicates that oil price has no effect on output growth. Therefore, inflation uncertainty increases inflation significantly for the whole period and the effect has been reduced after IT. On the other hand, the inflation uncertainty reduces growth significantly, while growth uncertainty decreases inflation significantly. The oil price has a significantly negative effect on inflation and no effect on 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 relative asymmetry for the inflation equation is less than 1, indicating positive interaction between the innovations of the previous period and the current level of volatility. This relationship is, however, reversed for the output growth equation. The persistence in volatility is measured by the parameters γπ,1 , γy,1 . These values are less than both the variables, which is a necessary condition for the volatility process to be stable. The magnitude of these parameters suggests a tendency for volatility shocks to persist. Using the HL parameter, the volatility persistence can be expressed in monthly or quarterly terms. The HL results indicate that the output growth equation exhibits slightly longer decay time for both data frequencies; this indicates that the output variable is more sluggish in adjusting to past innovations. The significance of the term defining the time-varying correlations indicates that a constant correlation model would be inappropriate. High realized correlation (Fig. 1a, b) coincides with the high output growth volatility in the early 1970s. This probably relates to the first oil price shock. Using bi-variate GARCH, Shields et al. (2005) and Grier et al. (2004) find that inflation uncertainty reduces inflation for the US, which contradicts the Friedman hypothesis. However, Wilson (2006) uses a bi-variate EGARCH model and finds support for the Friedman hypothesis for Japan. Such contradictory evidence seems to suggest that expected inflation needs a careful modelling approach. Our joint modelling via an EGARCH setup is one way of addressing the issue; using a regime-switching framework, Kim (1993) proposes an alternative way. 15 Grier et al. (2004) and Shields et al. (2005) find that inflation uncertainty lowers, rather than increasing, average inflation for the US. They did not use an interactive dummy, and therefore could not decompose the effect of inflation uncertainty before and after the inflation stabilization process. Moreover, the US did not target inflation as a central bank policy. Using uni-variate GARCH modelling, Kontonikas (2004) finds that inflation uncertainty has no significant effect on inflation for the UK.
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Inflation Variance 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 Jan-09
Jan-06
Jan-03
Jan-00
Jan-97
Jan-94
Jan-91
Jan-88
Jan-85
Jan-82
Jan-79
Jan-76
Jan-73
Jan-70
Jan-67
Jan-64
Jan-61
Jan-58
0.00
Output Growth Variance
Jan-09
Jan-06
Jan-03
Jan-00
Jan-97
Jan-94
Jan-91
Jan-88
Jan-85
Jan-82
Jan-79
Jan-76
Jan-73
Jan-70
Jan-67
Jan-64
Jan-61
Jan-58
0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00
Inflation Output Growth Correlation
Jan-09
Jan-06
Jan-03
Jan-00
Jan-97
Jan-94
Jan-91
Jan-88
Jan-85
Jan-82
Jan-79
Jan-76
Jan-73
Jan-70
Jan-67
Jan-64
Jan-61
Jan-58
0.40 0.30 0.20 0.10 0.00 -0.10 -0.20 -0.30 -0.40
Fig. 1 a Estimated variance and correlation series for UK (for monthly data), b estimated variance and correlation series for UK (for quarterly data)
3.3 Diagnostic tests The diagnostics statistics for the model are given in Table 5. The test statistics include the fifth-order serial correlation in the level and squared standardized innovations, as
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Inflation Variance
Mar-07
Mar-04
Mar-01
Mar-98
Mar-95
Mar-92
Mar-89
Mar-86
Mar-83
Mar-80
Mar-77
Mar-74
Mar-71
Mar-68
Mar-65
Mar-62
Mar-59
0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00
Output Growth Variance 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 Mar-98
Mar-01
Mar-04
Mar-07
Mar-98
Mar-01
Mar-04
Mar-07
Mar-95
Mar-92
Mar-89
Mar-86
Mar-83
Mar-80
Mar-77
Mar-74
Mar-71
Mar-68
Mar-65
Mar-62
Mar-59
0.00
Mar-95
Mar-92
Mar-89
Mar-86
Mar-83
Mar-80
Mar-77
Mar-74
Mar-71
Mar-68
Mar-65
Mar-62
Mar-59
Inflation and Output Growth Correlation 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10
Fig. 1 continued
well as the asymmetry test statistics following Engle and Ng (1993). The Ljung-Box statistics indicate the absence of linear and non-linear dependence in the standardized innovations for the sample period. The Engle and Ng test confirms the validity of the Ljung-Box test in that there are no sign biases: that is, there is no asymmetry effect.
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Table 5 Diagnostics tests Monthly data Inflation equation
Quarterly data Output growth equation
Inflation equation
Output growth equation
P values for Ljung-Box Q(5) statistics Z
0.010
0.073
0.013
0.247
Z2
0.139
0.649
0.124
0.507
Z1 · Z2
0.516
0.951
P values for Engle and Ng (1993) diagnostic tests Sign bias test
0.905
0.827
0.537
0.584
Negative size bias test
0.988
0.806
0.995
0.807
Positive size bias test
0.730
0.253
0.817
0.583
Joint test
0.141
0.379
0.030
0.805
Z represents the standardized residual for the corresponding equation; i.e. either inflation or output growth rate. Z 1 · Z 2 indicate product of the two standardized residuals. The entries are the p values for the relevant hypothesis tests
Any such bias could potentially affect the outcomes of the Ljung-Box test. We are thus comfortable with the outcomes of the test. In addition, 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 to the available data set.
3.4 Generalized impulse response analysis In this section, we further investigate the statistical significance of innovations of the variables under study using GIRF, introduced by Pesaran and Shin (1998). We have estimated GIRF by employing VAR, consisting of inflation, inflation uncertainty, growth, and growth uncertainty for both monthly and quarterly data. The number of lags is determined by AIC. The impulse response results are presented in Fig. 2a (for monthly data) and b (for quarterly data). Dashed lines indicate two standard error bands representing a 95 % confidence region. The second row of both Fig. 2a, b shows that the innovations in growth uncertainty explain significantly the movements of growth, growth uncertainty, inflation, and inflation uncertainty. From the graph, we can see that growth uncertainty reduces economic growth and increases inflation and inflation uncertainty. The innovation in inflation explains the movements of inflation and inflation uncertainty significantly. On the other hand, the innovations of inflation uncertainty significantly increase the movements of inflation and have a long-lasting effect (approximately up to 30 months). 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 6 months). The results are similar for both monthly and quarterly data.
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Response of GR to UNGR
Response of GR to INF
15
15
15
10
10
10
5
5
5
0
0
0
-5
-5
-5
5 10 15 20 25 30 35 40
5 10 15 20 25 30 35 40
Response of GR to UNINF 15 10
Response of UNGR to GR
5 10 15 20 25 30 35 40
Response of UNGR to UNGR
.002
.002
.001
.001
.000
.000
5 0
-.001
-.001
-5 5 10 15 20 25 30 35 40
Response of UNGR to INF
5 10 15 20 25 30 35 40
5 10 15 20 25 30 35 40
Response of UNGR to UNINF
.002
.002
.001
.001
.000
.000
-.001
-.001
Response of INF to GR 8 6 4 2 0
5 10 15 20 25 30 35 40
-2 5 10 15 20 25 30 35 40
Response of INF to UNGR
5 10 15 20 25 30 35 40
Response of INF to INF
Response of INF to UNINF
8
8
8
6
6
6
4
4
4
2
2
2
0
0
0
-2
-2
-2
5 10 15 20 25 30 35 40
Response of UNINF to GR
5 10 15 20 25 30 35 40
5 10 15 20 25 30 35 40
Response of UNINF to UNGR
Response of UNINF to INF
.0020
.0020
.0020
.0015
.0015
.0015
.0010
.0010
.0010
.0005
.0005
.0005
.0000
.0000
.0000
-.0005
-.0005
-.0005
5 10 15 20 25 30 35 40
5 10 15 20 25 30 35 40
5 10 15 20 25 30 35 40
Response of UNINF to UNINF .0020 .0015 .0010 .0005 .0000 -.0005 5 10 15 20 25 30 35 40
Fig. 2 a Generalized impulse response functions (using monthly data): response to one standard deviation innovations ± 2 S.E. Note: INF inflation, UNINF inflation uncertainty, GRIP growth of industrial production, UNGR growth uncertainty
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R. Bhar, G. Mallik Response of GR to GR
Responseof GR to UNGR
Response of GR to INF
8
8
8
6
6
6
4
4
4
2
2
2
0
0
0
-2
-2
-2
-4
-4
-4 2 4 6 8 10 12 14 16 18 20
2 4 6 8 10 12 14 16 18 20
Response of GR to UNINF
2 4 6 8 10 12 14 16 18 20
Response of UNGR to GR
Response of UNGR to UNGR
8
.006
.006
6
.004
.004
.002
.002
4 2 0 -2 -4
.000
.000
-.002
-.002 -.004
-.004 2 4 6 8 10 12 14 16 18 20
Response of UNGR to INF
2 4 6 8 10 12 14 16 18 20
2 4 6 8 10 12 14 16 18 20
Responseof UNGR to UNINF
Response of INF to GR
.006
.006
6
.004
.004
4
.002
.002
.000
.000
-.002
-.002
-.004
2 0 -2
-.004 2 4 6 8 10 12 14 16 18 20
2 4 6 8 10 12 14 16 18 20
Response of INF to UNGR
2 4 6 8 10 12 14 16 18 20
Response of INF to INF
Response of INF to UNINF
6
6
6
4
4
4
2
2
2
0
0
0
-2
-2
-2
2 4 6 8 10 12 14 16 18 20
Response of UNINF to GR
2 4 6 8 10 12 14 16 18 20
2 4 6 8 10 12 14 16 18 20
Response of UNINF to UNGR
Response of UNINF to INF
.012
.012
.012
.008
.008
.008
.004
.004
.004
.000
.000
.000
-.004
-.004
-.004
-.008
-.008
-.008 2 4 6 8 10 12 14 16 18 20
2 4 6 8 10 12 14 16 18 20
2 4 6 8 10 12 14 16 18 20
Response of UNINF to UNINF .012 .008 .004 .000 -.004 -.008 2 4 6 8 10 12 14 16 18 20
Fig. 2 b Generalized impulse response functions (using quarterly data): response to one standard deviation innovations ± 2 S.E. Note: INF inflation, UNINF inflation uncertainty, GRIP growth of industrial production, UNGR growth uncertainty
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4 Concluding remarks In this study, we have investigated the relation between inflation, growth, inflation uncertainty, and growth uncertainty by bi-variate EGARCH modelling for the UK. We have also included an inflation-targeting interactive dummy to separate the effects of lagged inflation and inflation uncertainty on inflation. A 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. We can conclude that inflation uncertainty increases inflation, but that the effect of inflation uncertainty on inflation is negative after the IT. On the other hand, growth uncertainty reduces inflation and increases growth. The oil price has a positive and significant effect on inflation, but no effect on growth. These results are also substantiated using GIRF. The findings of this study strongly support the Friedman hypothesis (1977) for the UK. The result in general contradicts the findings of similar studies for the US by Shields et al. (2005) and Grier et al. (2004), who find that inflation uncertainty reduces inflation. Inflation and inflation uncertainty, which increase inflation further and reduce growth, are potentially harmful for the economy. The oil price has a significant positive influence on inflation. From a policy perspective, the Bank of England should attempt to keep inflation stable and low. This study confirms that the inflation-targeting policy is working well and the Bank of England should continue with this strategy. Since oil prices are increasing inflation, UK policy makers might seek avenues to stabilize the domestic oil price or offset any significant upward movements through other cost-reducing measures. References Alogoskoufis G (1992) Monetary accommodation, exchange rate regimes and inflation persistence. Econ J 102:461–480 Ball L (1992) Why does high inflation raise inflation uncertainty?. J Monet Econ 29:371–388 Bera A, Jarque C (1980) Efficient tests for normality, heteroscedasticity and serial independence of regressions. Econ Lett 6:255–259 Berument H, Dincer NN (2005) Inflation and inflation uncertainty in the G-7 countries. Phys A 34(8): 371–379 Berument H, Yalcin Y, Yildirim JO (2010) The inflation and inflation uncertainty relationship for Turkey: a dynamic framework, Empir Econ, Published online, 16 June, 2010 Bhar R, Hamori S (2004) The link between inflation and inflation uncertainty: evidence from G7 countries. Empir Econ 29:825–853 Black F (1976) Studies of stock market volatility changes. Proc Am Stat Ass Bus Econ Stud Sect 177–181 Conrad C, Karanasos M (2005) On the inflation-uncertainty hypothesis in the USA, Japan and the UK: a dual long memory approach. Jpn World Econ 17:327–343 Caporale GM, Kontonikas A (2009) The Euro and inflation uncertainty in the European Monetary Union. J Int Money Finance 28:954–971 Daal E, Naka A, Sanchez B (2005) Re-examining inflation and inflation uncertainty in developed and emerging countries. Econ Lett 89:180–186 Darbar SM, Deb P (2002) Cross-market correlations and transmission of information. J Futur Mark 22:1059–1082 Engle RF, Ng VK (1993) Measuring and testing the impact of news on volatility. J Finance 48:1749–1778 Fountas S, Ioannidis A, Karanasos M (2004) Inflation, inflation uncertainty and common European Monetary Policy. Manchester School 72(2):221–242
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