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Inflation and growth
Economics Letters North-Holland
23
22 (1986) 23-26
INFLATION AND GROWTH An Empirical Note H. LEON University of Kent at Canterbury, Canterbury CT2 ?NS, UK Received
21 May 1986
In time series modelling, concepts of causality relationship using Jamaican data. The existence
and co-integrability are relevant. This note examines of a long-run relationship is found to be tenuous.
the growth-inflation
1. Introduction Empirical studies of the growth-inflation relationship have used both time series and cross-sectional data [see Bhatia (1960) Thirlwall and Barton (1971)]. If we accept the conventional wisdom that cross-sections indicate Iong-run trends whereas time series show short-run trends, then the relevant concept, in the time series context, is whether there exists a long-run relationship between growth and inflation. This paper examines the growth-inflation relationship for Jamaica using the concepts of causality and co-integrability. 2. Concepts It is generally assumed that in the linear formulation of the growth-inflation relationship, causality runs from inflation to growth; thus inflation is exogenously determined independently of growth. Geweke et al. (1983) show that Granger-causality can be implemented using a modified Sims approach of regressing one stationary series on its own lags and the future, current and past values of another stationary series. The null hypothesis that the dependent variable does not cause the right-hand side independent variable is rejected if the coefficients on the future (lead) variables are non-zero. In the simple bivariate case, the notion of co-integrability [Granger and Engle (1985)] requires the existence of some constant a, such that
(1)
c* = z, - ax,,
defined on a pair of series (zC, xI) of the same order of integrability, is a stationary series - LYis called the co-integrating parameter. A series is integrable of order d, Z(d), if it needs to be differenced d times to achieve stationarity, Z(0) being a stationary series. Thus, a pair of Z(1) series are co-integrable, and a long-run relationship, z, = ffx,,
obtains,
if the residuals
0165-1765/86/$3.50
of the co-integrating
0 1986, Elsevier Science Publishers
regression
(l), are Z(0).
B.V. (North-Holland)
24
3. Methodology
The order of integrability of each series is obtained through the application of a test for unit roots [Dickey and Fuller (1981)]. The causality regressions are then run on the corresponding stationary series, for an assumed lag structure. In the co-integrating case, the order of integrability provides a check that the relevant variables defining the long-run relationship are Z(1). The residuals of the co-integrating regression are then tested for stationarity.
4. Results
’
The OLS result of the linear regression relationship with significant coefficients,
of output
growth (Y) on inflation
(P)
indicates
a negative
Y = 0.08 - 0.63 P, (5.96) (5.43)
R2= 0.51,
(3
D.W.
s.e. = 0.05,
= 1.28.
Does inflation cause growth? Table 1 provides evidence that the rates of growth of both prices and output are I(1) series. Table 2 indicates that the null hypotheses that inflation does not cause growth, and growth does not cause inflation cannot be rejected. The null hypothesis that the residuals of the growth-inflation regression is Z(1) is not rejected, implying that growth and inflation are not co-integrable. We note, however, that the reverse equation
Table 1 Likelihood
ratio statistics
Prices ACPI A’CPI A3CPI Output A RGDP A’RGDP A3RGDP Output-inflation AR1
for unit root tests
@I
@2
@3
6.20 1.15 26.30 ’
4.53 3.20 20.53 ’
4.81 4.50 30.55 B
1.09 1.65 6.64 b
0.70 1.56 4.28
1.02 1.58 6.41 ’
4.42 ’
3.45
4.69
1.20
5.04 c
7.55 b
residual
Inflatm - output resrducrl AR2 a Significant b Significant ’ Significant
at 1 percent. at 5 percent. at 10 percent.
’ Data used covers the period 1953-1981;
Source:
IFS Yearbook
1982
H. Leon / Table 2 Causality
test: D;mestic
AP=u+pT+
inflatip;
&AP,_,+ ,=’
$P) and growth
c ,--I
(Y); a
variable AY
AP C
- 0.008
T
25
S,AY,_,+r,
Dependent
Regressors
Inflation and growth
(0.43)
-0.11 (0.62)
0.002 (1.28)
0.17 (1.35)
- 0.01 (0.43) - 0.0002 (0.10)
- 0.01 (0.49) 0.0002 (0.12)
0.17 (0.51)
- 0.44 (1.21)
- 0.55 (1.94)
0.07 (0.42)
0.39 (0.23)
0.07 (0.25)
- 0.02 (0.09)
- 0.76 (4.19)
- 0.72 (4.23)
- 0.30 (0.61)
- 0.50 (1.71)
0.12 (0.72) - 0.33 (1.94)
0.11 (0.56)
0.57 (0.31)
- 0.33 (1.39)
-0.37 (1.72)
- 0.54 (2.82)
- 0.52 (2.79)
- 0.55 (1.92)
- 0.61 (2.41)
0.02767 2.77
RSS LM(2) a ‘t’ statistics
- 0.27 (1.39)
are in parentheses.
0.028579 2.11
LM(2) is Lagrange
Multiplier
0.04718 4.08 Test Statistic
0.04795 3.37
for serial correlation
up to 2nd order-distributed
at the 5 percent
level, that the residuals
x2(2).
(i.e., inflation are a random
regressed on output) walk with drift.
rejects the null hypothesis,
5. Conclusions This note contends that, in the time series context, the relevant question pertaining to the growth-inflation relationship is whether a long-run formulation exists. The empirical results show that whilst the OLS results obtain a negative relationship with significant coefficients, the assumptions of unidirectional causality and the existence of a long-run relationship are far from convincing. The possibility exists, however, that output growth and inflation are jointly determined in a simultaneous equation system.
26
H. Leon / Infkttion und growth
References Bhatia, R.J., 1960, Inflation, deflation and economic development, IMF Staff Papers 8, 101-114. Dickey, D.A. and W.A. Fuller, 1981, Likelihood ratio statistics for autoregressive time series with a unit root, Econometrica 49, 1057-1072. Geweke, J., R. Meese and W.T. Dent, 1983, Comparing alternative tests of causality in temporal systems: Analytic results and experimental evidence, Journal of Econometrics 21, 161-194. Granger, C.W.J. and R.F. Engle, 1985, Dynamic model specification with equilibrium constraints: Co-integration and error correction, Discussion paper, UCSD. Thirlwall, A.P. and C.A. Barton, 1971, Inflation and growth: The international evidence, Banca Nazionale Del Lavoro Quarterly Review 98, 3-15.
23
22 (1986) 23-26
INFLATION AND GROWTH An Empirical Note H. LEON University of Kent at Canterbury, Canterbury CT2 ?NS, UK Received
21 May 1986
In time series modelling, concepts of causality relationship using Jamaican data. The existence
and co-integrability are relevant. This note examines of a long-run relationship is found to be tenuous.
the growth-inflation
1. Introduction Empirical studies of the growth-inflation relationship have used both time series and cross-sectional data [see Bhatia (1960) Thirlwall and Barton (1971)]. If we accept the conventional wisdom that cross-sections indicate Iong-run trends whereas time series show short-run trends, then the relevant concept, in the time series context, is whether there exists a long-run relationship between growth and inflation. This paper examines the growth-inflation relationship for Jamaica using the concepts of causality and co-integrability. 2. Concepts It is generally assumed that in the linear formulation of the growth-inflation relationship, causality runs from inflation to growth; thus inflation is exogenously determined independently of growth. Geweke et al. (1983) show that Granger-causality can be implemented using a modified Sims approach of regressing one stationary series on its own lags and the future, current and past values of another stationary series. The null hypothesis that the dependent variable does not cause the right-hand side independent variable is rejected if the coefficients on the future (lead) variables are non-zero. In the simple bivariate case, the notion of co-integrability [Granger and Engle (1985)] requires the existence of some constant a, such that
(1)
c* = z, - ax,,
defined on a pair of series (zC, xI) of the same order of integrability, is a stationary series - LYis called the co-integrating parameter. A series is integrable of order d, Z(d), if it needs to be differenced d times to achieve stationarity, Z(0) being a stationary series. Thus, a pair of Z(1) series are co-integrable, and a long-run relationship, z, = ffx,,
obtains,
if the residuals
0165-1765/86/$3.50
of the co-integrating
0 1986, Elsevier Science Publishers
regression
(l), are Z(0).
B.V. (North-Holland)
24
3. Methodology
The order of integrability of each series is obtained through the application of a test for unit roots [Dickey and Fuller (1981)]. The causality regressions are then run on the corresponding stationary series, for an assumed lag structure. In the co-integrating case, the order of integrability provides a check that the relevant variables defining the long-run relationship are Z(1). The residuals of the co-integrating regression are then tested for stationarity.
4. Results
’
The OLS result of the linear regression relationship with significant coefficients,
of output
growth (Y) on inflation
(P)
indicates
a negative
Y = 0.08 - 0.63 P, (5.96) (5.43)
R2= 0.51,
(3
D.W.
s.e. = 0.05,
= 1.28.
Does inflation cause growth? Table 1 provides evidence that the rates of growth of both prices and output are I(1) series. Table 2 indicates that the null hypotheses that inflation does not cause growth, and growth does not cause inflation cannot be rejected. The null hypothesis that the residuals of the growth-inflation regression is Z(1) is not rejected, implying that growth and inflation are not co-integrable. We note, however, that the reverse equation
Table 1 Likelihood
ratio statistics
Prices ACPI A’CPI A3CPI Output A RGDP A’RGDP A3RGDP Output-inflation AR1
for unit root tests
@I
@2
@3
6.20 1.15 26.30 ’
4.53 3.20 20.53 ’
4.81 4.50 30.55 B
1.09 1.65 6.64 b
0.70 1.56 4.28
1.02 1.58 6.41 ’
4.42 ’
3.45
4.69
1.20
5.04 c
7.55 b
residual
Inflatm - output resrducrl AR2 a Significant b Significant ’ Significant
at 1 percent. at 5 percent. at 10 percent.
’ Data used covers the period 1953-1981;
Source:
IFS Yearbook
1982
H. Leon / Table 2 Causality
test: D;mestic
AP=u+pT+
inflatip;
&AP,_,+ ,=’
$P) and growth
c ,--I
(Y); a
variable AY
AP C
- 0.008
T
25
S,AY,_,+r,
Dependent
Regressors
Inflation and growth
(0.43)
-0.11 (0.62)
0.002 (1.28)
0.17 (1.35)
- 0.01 (0.43) - 0.0002 (0.10)
- 0.01 (0.49) 0.0002 (0.12)
0.17 (0.51)
- 0.44 (1.21)
- 0.55 (1.94)
0.07 (0.42)
0.39 (0.23)
0.07 (0.25)
- 0.02 (0.09)
- 0.76 (4.19)
- 0.72 (4.23)
- 0.30 (0.61)
- 0.50 (1.71)
0.12 (0.72) - 0.33 (1.94)
0.11 (0.56)
0.57 (0.31)
- 0.33 (1.39)
-0.37 (1.72)
- 0.54 (2.82)
- 0.52 (2.79)
- 0.55 (1.92)
- 0.61 (2.41)
0.02767 2.77
RSS LM(2) a ‘t’ statistics
- 0.27 (1.39)
are in parentheses.
0.028579 2.11
LM(2) is Lagrange
Multiplier
0.04718 4.08 Test Statistic
0.04795 3.37
for serial correlation
up to 2nd order-distributed
at the 5 percent
level, that the residuals
x2(2).
(i.e., inflation are a random
regressed on output) walk with drift.
rejects the null hypothesis,
5. Conclusions This note contends that, in the time series context, the relevant question pertaining to the growth-inflation relationship is whether a long-run formulation exists. The empirical results show that whilst the OLS results obtain a negative relationship with significant coefficients, the assumptions of unidirectional causality and the existence of a long-run relationship are far from convincing. The possibility exists, however, that output growth and inflation are jointly determined in a simultaneous equation system.
26
H. Leon / Infkttion und growth
References Bhatia, R.J., 1960, Inflation, deflation and economic development, IMF Staff Papers 8, 101-114. Dickey, D.A. and W.A. Fuller, 1981, Likelihood ratio statistics for autoregressive time series with a unit root, Econometrica 49, 1057-1072. Geweke, J., R. Meese and W.T. Dent, 1983, Comparing alternative tests of causality in temporal systems: Analytic results and experimental evidence, Journal of Econometrics 21, 161-194. Granger, C.W.J. and R.F. Engle, 1985, Dynamic model specification with equilibrium constraints: Co-integration and error correction, Discussion paper, UCSD. Thirlwall, A.P. and C.A. Barton, 1971, Inflation and growth: The international evidence, Banca Nazionale Del Lavoro Quarterly Review 98, 3-15.