A test of Wagner’s hypothesis for the Ghanaian economy

Figures & data

Table 1. Unit root test

	ADF (C)	ADF (C + T)^2	P-P (C)	P-P (C + T)	KPSS (C)	KPSS (C + T)
Series	t-value	t-value	t-value	t-value	t-value	t-value
lnYt	−1.9786	−0.5194	2.6059	−0.0128	0.8658	0.2293
lnGt	-1.1195	−3.0238	0.9319	−28,517	2.8662	0.3707
∆lnYt	−4.8695^a	−4.2224^a	−4.8695^a	−5.4236^a	0.5843^a	0.1111^a
∆lnGt	−6.9818^a	−7.3569^a	−9.0536^a	−9.5123^a	0.1749^b	0.0632^b

Note: The Mackinnon (1996) critical values for ADF test are used. Critical values with C (C + T) at the 5% significance is −2.92 (−3.4987) and at the 1% significance is −3.56 (−4.14). The critical values for KPSS with C (C + T) at the 10% significance are 0.347 (0.12); 5% significance is 0.463 (0.15) and at the 1% significance is 0.739 (0.22). ^{a, b} and ^c indicate significance at 1%, 5% and 10%, respectively. KPSS, Kwiatkowski et al. (1992, Table 1) refers to testing the null hypothesis of stationarity against the alternative of unit root. C = constant and C + T = constant and trend. ∆ represents first difference.

Table 2. Johansen cointegration test results

Panel A
Hypothesized no. of CE(s)	Trace Statistic	0.05 Critical Value	P-value^e
r = 0	19.3152^b	15.4947	0.0117
r > 1	0.0019	3.8415	0.9615
Panel B
Hypothesized no. of CE(s)	Max-Eigen Statistic	0.05 Critical Value	P-value
r = 0	19.5133^b	14.2646	0.0067
r > 1	0.0019	3.8415	0.9615

^bDenotes rejection of the hypothesis at the 0.05 test level

^eMacKinnon-Haug-Michelis (1996) p-value

Table 3. Long-run and short-run elasticities

Panel A: Long-run elasticities, Dependent Variable, lnYt
Independent variables	Coefficients	Standard error	t-ratio	P-values
C	22.7177	0.5191	43.7598	0.0000
lnGt-1	0.1856	0.0669	2.7750	0.0077^b
Policyt-1	0.4618	1.3048	0.3539	0.7249^b
Panel B: Short-run elasticities Dependent Variable, ∆lnYt
∆lnGt	0.0061	0.0078	0.7835	0.4370
Policy	−0.0684	0.0379	−1.8018	0.0776
ECTt-1	−0.0365	0.0048	−7.5721	0.0000^a

Note: ^{a, b} and ^c indicate significance at 1%, 5% and 10%, respectively.

Table 4. Granger non-causality tests

Null Hypothesis	Modified Wald statistics	P-value	Decision
lnYt↛lnGt	0.0636	0.9687	Fail to Reject
lnGt↛lnYt	6.6692	0.0356	Reject^b
Diagnostic tests
LM (2)	6.0244 [0.1973]^a
Hetero (1)	31.4263 [0.1419]^a
J-B Normality	17.5878 [0.0015]

Note: Note: ↛ Implies does not cause. ^{a, b} and ^c indicate significance at 1%, 5% and 10%, respectively. LM: Lagrange multiplier test of residual serial correlation. ARCH: autoregressive conditional heteroscedasticity test of residuals. Heteroscedasticity: This is based on the regression of squared residuals on squared fitted values. Normality is based on a test of skewness and kurtosis of residuals. The values in the parenthesis are the p-values.

Table

Dependent Variable	Function	F- test statistic
Model 1	F (lnY|lnG)	16.8319^a
Model 2	F (lnG|lnY)	9.5333^b
Asymptotic critical values
1%		5%		10%
I (0)	I (1)	I (0)	I (1)	I (0)	I (1)
5.6970	6.9870	4.000	5.0570	3.2700	4.2600

Note: ^{a, b} and ^c denotes significance levels at 1%, 5% and 10%, respectively. Source of critical values: Narayan (2005, p. 1988).

Table

Model Diagnostics of ARDL	F-Statistics	P-value
LM (3)	1.6934^a	[0.1469]
ARCH (3)	1.4726^a	[0.2232]
J-B Normality	17.5327	[0.0002]
Ramsey’s RESET (2)	5.7165^a	[0.0059]

Note: LM: Lagrange multiplier test of residual serial correlation. ARCH: autoregressive conditional heteroscedasticity test of residuals. Heteroscedasticity: This is based on the regression of squared residuals on squared fitted values. Normality is based on a test of skewness and kurtosis of residuals. ^{a, b} and ^c denotes significance levels at 1%, 5% and 10%, respectively.

  Lag Selection Criteria for the Augmented VAR and model diagnostics test statistics

Lag	LogL	LR	FPE	AIC	SC	HQ
0	-114.1068	NA	0.671555	5.277580	5.358679	5.307655
1	42.71810	292.2645*	0.000646*	-1.669004*	-1.425706*	-1.578778*
2	46.01567	5.845694	0.000668	-1.637076	-1.231578	-1.486698
3	49.78812	6.344586	0.000678	-1.626733	-1.059036	-1.416204
4	50.85888	1.703475	0.000779	-1.493585	-0.763690	-1.222905
5	53.56845	4.064350	0.000834	-1.434929	-0.542835	-1.104098
6	58.28047	6.639675	0.000820	-1.467294	-0.413000	-1.076311

Note: NA denotes not applicable and * denotes the chosen lag

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