Investigation of the time-dependent dynamics between government revenue and expenditure in China: a wavelet approach

Figures & data

Figure 1. Government revenue and expenditure as percentage of GDP.

Table 1. Unit root test without structural break at levels.

Variables		ADF	PP	DF-GLS	ERS	KPSS
GR/GDP	Constant	−1.113	−4.809***	−0.482	2.603**	0.345
	With trend	−1.290	−4.819***	−0.3	4.848**	0.329***
GE/GDP	Constant	−0.927	−6.558***	−0.558	1.371	0.353*
	With trend	−1.171	−6.626***	−0.363	.989***	0.320***

Notes: GR/GDP denotes government revenue ratio to GDP in log; GE/GDP denotes government expenditure ratio to GDP in log. Lags are selected based on the Schwarts information criteria. Single (*), double (**) and triple asterisks (***) indicate statistical significance at 10%, 5% and 1% levels, respectively. ADF, PP, DF-GLS, ERS and KPSS are Augmented Dickey-Fuller test, Phillips-Perron test, Dickey-Fuller Test with GLS Detrending, Elliot, Rothenberg, and Stock Point Optimal (ERS) Test and the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test, respectively. ADF, PP and DF-GLS have null hypothesis is that the series has a unit root while KPSS null hypothesis is that the series is stationary. Barlett kernel is used for PP, ERS and KPSS. Critical values are presented in Table 3 below.

Table 2. Unit root test without structural break at 1st difference.

Variables		ADF	PP	DF-GLS	ERS	KPSS
GR/GDP	Constant	−5.500***	−22.608***	−0.248	3.042**	0.224
	With trend	−7.698***	−23.791***	−1.767	8.774	0.076
GE/GDP	Constant	−5.906***	−34.716***	−0.170	3.736*	0.377*
	With trend	−8.171***	−37.993***	−1.318	10.099	0.051

Notes: GR/GDP denotes government revenue ratio to GDP in log; GE/GDP denotes government expenditure ratio to GDP in log. Lags are selected based on the Schwarts information criteria. Single (*), double (**) and triple asterisks (***) indicate statistical significance at 10%, 5% and 1% levels, respectively. ADF, PP, DF-GLS, ERS and KPSS are Augmented Dickey-Fuller test, Phillips-Perron test, Dickey-Fuller Test with GLS Detrending, Elliot, Rothenberg, and Stock Point Optimal (ERS) Test and the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test, respectively. ADF, PP and DF-GLS have null hypothesis is that the series has a unit root while KPSS null hypothesis is that the series is stationary. Barlett kernel is used for PP, ERS and KPSS. Critical values are presented in Table 3 below.

Table 3. Critical values of the unit root tests.

Models	ADF			PP			DF-GLS			ERS			KPSS
	1%	5%	10%	1%	5%	10%	1%	5%	10%	1%	5%	10%	1%	5%	10%
Constant	−3.78	−2.88	−2.58	−3.48	−2.89	−2.58	−2.58	−1.94	−1.62	1.93	3.14	4.24	0.74	0.46	0.35
With trend	−4.03	−3.44	−3.15	−4.02	−3.44	−3.15	−3.53	−2.99	−2.70	4.17	5.65	6.82	0.22	0.15	0.12

Notes: ADF, PP, DF-GLS, ERS and KPSS are Augmented Dickey-Fuller test, Phillips-Perron test, Dickey-Fuller Test with GLS Detrending, Elliot, Rothenberg, and Stock Point Optimal (ERS) Test and the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test, respectively.

Table 4. Unit root test with on endogenous structural break: Zivot-Andrews Test.

Variables	Level	Break point (level)	1st difference (constant)	Break point (1st difference)	Result
GR/GDP	−3.586	1991q2	−8.918***	1996q1	I(1)
GE/GDP	−3.418	1998q1	−9.096***	1997q1	I(1)

Notes: GR/GDP denotes government revenue ratio to GDP in log; GE/GDPdenotes government expenditure ratio to GDP in log. Lag selection is based on T-Test. Triple asterisks (***) indicate statistical significance at 1% level. Critical values with a structural break in the intercept at the 1% levels is −5.34. Critical value with a structural break in both the intercept and trend at the 1% level is −5.57.

Table 5. Unit root test with two endogenous structural breaks: Clemente-Montanes-Reyes test.

Variables	Min t in level	Break point (level)	Min t in 1st difference	Break point (1st difference)	Result
GR/GDP	−2.534	B.P.1: 1990q1	−20.143***	B.P.1: 1995q2	I(1)
		B.P.2: 2001q4		B.P.2: 2008q2
GE/GDP	−2.367	B.P.1: 1991q1	−7.403***	B.P.1: 2007q2	I(1)
		B.P.2: 1999q2		B.P.2: 2008q2

Notes: GR/GDP denotes government revenue ratio to GDP in log; GE/GDP denotes government expenditure ratio to GDP in log. B.P.1 and B.P.2 denote the first and second break point, respectively. Triple asterisks (***) indicate statistical significance at 1% level. The 1% critical value with two breaks is −5.960.

Table 6. Unit root test with one structural break: Lee Strazicich LM unit root test.

Variables	Min t in level	Break point (level)	Min t in 1st difference	Break point (1st difference)	Results
GR/GDP	−4.094*	B.P.: 1997q1	−13.225***	B.P.: 1983q2	I(0)
GE/GDP	−3.844	B.P.: 1992q3	−8.259***	B.P.: 2011q2	I(1)

Notes: GR/GDP denotes government revenue ratio to GDP in log;GE/GDP denotes government expenditure ratio to GDP in log. B.P. denotes a break point. Single (*), double (**) and triple asterisks (***) indicate statistical significance at 10%, 5% and 1% levels, respectively. The critical values at 1, 5 and 10% level of significance are −4.73, −4.19 and −3.91, respectively.

Table 7. Unit root test with two structural breaks: Lee Strazicich LM unit root test.

Variables	Min t in level	Break point (level)	Results
GR/GDP	−5.718**	B.P.1: 1984q4	I(0)
		B.P.2: 1997q1
GE/GDP	−5.39**	B.P.1: 1983q3	I(0)
		B.P.2: 1992q1

Notes: GR/GDP denotes government revenue ratio to GDP in log; GE/GDP denotes government expenditure ratio to GDP in log. B.P.1 and B.P.2 denote the first and second break point, respectively. Double (**) asterisks indicate statistical significance at 5% level. The critical values at 1 and 5% level of significance are −5.91 and −5.38, respectively.

Table 8. Toda-Yamamoto causality test results.

Hypothesis	Chi2	Prob. > chi2
GE $\to$ GR	12.753	0.013
GR $\to$ GE	15.801	0.003

Notes: GR denotes government revenue ratio to GDP in log and GE denotes government expenditure ratio to GDP in log.

Figure 2. Time series plot and wavelet decomposition of the government revenue as a share of GDP.

Figure 3. Time series plot and wavelet decomposition of the government expenditure as a share of GDP.

Table 9. Unit root test using wavelet filtered data (wavelet details).

Variables	Wavelet scales	ADF	PP	DF-GLS	ERS	KPSS
GR/GDP	1	−5.679***	−44.672***	0.337	26.890	0.192
	2	−3.951***	−16.098***	0.336	5.583	0.092
	3	−3.459***	−2.313	−3.865***	4.581	0.139
	4	−2.435***	−3.155**	−1.699	2.166**	0.109
	5	−1.867**	−1.497	−1.483	6.962	0.236
GE/GDP	1	−5.078***	−89.934***	0.237	11.866	0.045
	2	−4.000***	−17.374***	−0.436	8.005	0.069
	3	−2.646***	0.023**	−1.078	12.289	0.037
	4	−2.875***	−3.170**	−0.915	4.376	0.084
	5	−2.126**	0.337	−1.826	5.365	0.174

Notes: GR/GDP denotes government revenue in log; GE/GDP denotes government expenditure in log. Lags are selected based on the Schwarts information criteria. ***denotes 1% level of significance. ADF, PP, DF-GLS, ERS and KPSS are Augmented Dickey-Fuller test, Phillips-Perron test, Dickey-Fuller Test with GLS Detrending, Elliot, Rothenberg, and Stock Point Optimal (ERS) Test and the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test, respectively. ADF, PP and DF-GLS have null hypothesis is that the series has a unit root while KPSS null hypothesis is that the series is stationary. Barlett kernel is used for PP, ERS and KPSS. The critical values of the tests with constant are presented in Table 3.

Table 10. Granger causality test results using wavelet details.

Hypothesis	Wavelet scales (lag length)	F-statistic	Prob.
GE $\nrightarrow$ GR	1 (7)	0.25788	0.9693
GR $\nrightarrow$ GE		0.83694	0.5576
GE $\nrightarrow$ GR	2 (14)	1.4213	0.1455
GR $\to$ GE		3.623	2.268e-05
GE $\nrightarrow$ GR	3 (7)	0.98684	0.4413
GR $\nrightarrow$ GE		1.5679	0.1455
GE $\to$ GR	4 (8)	3.2217	0.0017
GR $\to$ GE		2.8518	0.0048

Notes: GR denotes government revenue ratio to GDP in log and GE denotes government expenditure ratio to GDP in log.