Threshold effects of fiscal decentralization on income inequality: Evidence from Vietnam

Figures & data

Table 1. Summary of test results to select the optimal number of thresholds

$H_{03}^{\ast }:{\beta }_3^{\ast }=0$	$H_{02}^{\ast }:{\beta }_2^{\ast }=0|{\beta }_3^{\ast }=0$	$H_{01}^{\ast }:{\beta }_1^{\ast }=0|{\beta }_3^{\ast }={\beta }_2^{\ast }=0$
F (7, 775) = 33.544	F (7, 782) = 37.451	F (7, 789) = 67.827
P-vvalue = 0.000	P-value = 0.000	P-value = 0.000

Source: Author calculated from RATS software

Table 2. Results of evaluating the suitability of the one-threshold PSTR model

Residual heterogeneity test, H0: ${\gamma }_2=0$
Additional	F- Statistics	p-value
G (G2, C1, C2, LGDP 1)	0.004	1.000
G (G2, C1, LGDP 1)	0.003	1.000
Testing the stability of the parameter, H0: ${\gamma }_2=0$
G (G2, C1, C2, t)	0.005	1.000
G (G2, C1, t)	0.007	1.000

Source: author calculated from RATS software

Table 3. Synthesized results of one-threshold PSTR model estimation

	Variable	Estimated coefficient	Standard Deviation (robust)
${\delta }_{0i}$
	OPENit-1	−0,002 (*)	0,001
	ISRit-1	−0,011	0,015
	CSTit-1	0,012	0,021
0 ${\beta }_{0j}$
	ED1it-1	−0,009	0,026
	ED2it-1	0,043 (*)	0,023
	RD1it-1	−0,006	0,018
	RD2it-1	−0,033 (***)	0,010
	TDit-1	0,002	0,013
	LGDP it-1	−0,037 (***)	0,005
	FDIit-1	−0,068 (***)	0,011
${\beta }_{0j}+{\beta }_{1j}$
	ED1it-1	0,418 (***)	0,080
	ED2it-1	−0,453 (***)	0,072
	RD1it-1	0,258 (***)	0,065
	RD2it-1	−0,182 (***)	0,046
	TDit-1	0,236 (***)	0,036
	LGDP it-1	0,018 (*)	0,010
	FDIit-1	0,657 (***)	0,136
$\gamma$	2.6084
c	4.2950
R^2	0.9820

Source: Author’s estimation using RATS software

Note: ${\delta }_{0i}$: With the threshold value, the estimated coefficient of the explanatory variable does not change.

${\beta }_{0j}$: The estimated coefficient of the explanatory variable varies with the threshold value at the low stage

${\beta }_{0j}+{\beta }_{1j}$: The estimated coefficient of the explanatory variable changes with the threshold value of the high stage; this is also the elasticity of income inequality according to the values of the hierarchical lagged variable.

(*), (**), and (***) denote the 10%, 5%, and 1% significance levels, respectively.

Figure 1. Logarithmic transition chart of average GDP per capita.

Table A1. Definitions and descriptive statistics of variables

Variable	Definition and descriptive statistics of variables	Source	Obs	Mean	Std. Dev.	Min	Max
Regional inequality—PW_CV	$\mathit{\text{PW}}\mathrm{\_}C{V}_{\mathit{\text{it}}}=\frac{1}{\mathit{\text{gd}}{p}_{\mathit{\text{cn}}}}\sqrt{W_i{(\mathit{\text{gd}}{p}_{\mathit{\text{cn}}}-\mathit{\text{gd}}{p}_{\mathit{\text{it}}})}^2}$	GSO	1197	0614264	1131741	0003925	1.084187
Self—financed spending—ED1	$\mathit{\text{ED}}{1}_{\mathit{\text{it}}}=\frac{S{S}_{\mathit{\text{it}}}-\mathit{\text{TR}}{R}_{\mathit{\text{it}}}}{G{S}_{\mathit{\text{it}}}}$	MOF	1197	2982339	1.38819	0002748	20.43596
Direct spending—ED2	$\mathit{\text{ED}}{2}_{\mathit{\text{it}}}=\frac{S{S}_{\mathit{\text{it}}}-\mathit{\text{TR}}{R}_{\mathit{\text{it}}}}{G{R}_{\mathit{\text{it}}}}$	MOF	1197	5450995	1.662856	0416235	23.09422
Autonomous own revenue—RD1	$E{D}_{\mathit{\text{it}}}=\frac{\mathit{\text{OT}}{R}_{\mathit{\text{it}}}+\mathit{\text{NT}}{C}_{\mathit{\text{it}}}}{G{R}_{\mathit{\text{it}}}}$	MOF	1197	2531311	8560512	0002369	11.28109
Autonomous and Shared own revenue -RD2	$\mathit{\text{ED}}{1}_{\mathit{\text{it}}}=\frac{\mathit{\text{OT}}{R}_{\mathit{\text{it}}}+\mathit{\text{ST}}{R}_{\mathit{\text{it}}}+\mathit{\text{NT}}{C}_{\mathit{\text{it}}}}{G{R}_{\mathit{\text{it}}}}$	MOF	1197	4912488	1.0639	0137896	12.69528
Autonomous own tax revenue—TD	$T{D}_{\mathit{\text{it}}}=\frac{\mathit{\text{OT}}{R}_{\mathit{\text{it}}}+\mathit{\text{ST}}{R}_{\mathit{\text{it}}}}{\mathit{\text{TT}}{R}_{\mathit{\text{it}}}}$	MOF	1197	5252298	8150781	0517608	7.013664
Openness	$\mathit{\text{OPE}}{N}_{\mathit{\text{ti}}}=\frac{\mathit{\text{EXPORT}}{S}_{\mathit{\text{it}}}+\mathit{\text{IMPORT}}{S}_{\mathit{\text{it}}}}{\mathit{\text{GD}}{P}_{\mathit{\text{it}}}\ast {10}^6}\ast \mathit{\text{EXCHANGERAT}}{E}_{\mathit{\text{it}}}$	GSO, WDI, WB	1197	69302	1.048941	0	8.941681
gdp	$\mathit{\text{gd}}{p}_{\mathit{\text{it}}}=\frac{\mathit{\text{GD}}{P}_{\mathit{\text{it}}}}{D{S}_{\mathit{\text{it}}}}\frac{1}{1+\mathit{\text{CPI}}}\ast 100$	GSO, WDI, WB	1197	16.70059	27.26411	1.726125	446.3168
Current spending rate (CSRit)	Provincial recurrent expenditure value year t/nominal provincial GDP year t	GSO, WDI, WB	1197	1490656	1087249	0093561	7268516
Investment spending rate (ISRit)	Provincial value of investment spending year t/nominal GDP of the province year t	GSO, WDI, WB	1197	0797914	0732522	0077742	8548093
Provincial foreign direct investment (FDIit)	Provincial FDI in year t/nominal GDP of the province year t	GSO, WDI, WB	1197	0442963	0965645	0	1.6984434

Source: Data statistics are over the period of 2000–2018.

Table A2. Estimated coefficients of dummy variables by year

YR 01	YR 02	YR 03	YR 04	YR 05	YR 06	YR 07	YR 08	YR 09	YR 10	YR 11	YR 12	YR 13	YR 14	YR 15	YR 16	YR 17
−4.68***	−4.81***	−4.38***	−3.81***	−3.41***	−2.80***	−2.52***	−2.20***	−1.72***	−1.12***	−0.61***	−0.02***	−0.39***	−1.25***	−1.30	0.36	−0.56
(1.28)	(1.23)	(1.17)	(1.08)	(1.06)	(0.95)	(0.86)	(0.76)	(0.66)	(0.52)	(0.44)	(0.38)	(0.31)	(0.42)	(0.54)	(0.48)	(0.39)

Source: Author’s estimation using RATS software.

Note:

The estimated coefficient and standard error have been multiplied by 100;

The robust standard error is enclosed in parentheses ();

(***) denotes significance at 1%, respectively.

Table A3. PSTR model estimation results with m = 1

Variable	Estimated coefficient	Standard Error (Robust)	T- Statistics
DMTM1	−0.003	0.001	−1.893
CDT1	−0.012	0.016	−0.751
CTX1	0.013	0.022	0.591
YR01	−0.047	0.013	−3.660
YR02	−0.048	0.012	−3.908
YR03	−0.044	0.012	−3.743
YR04	−0.038	0.011	−3.508
YR05	−0.034	0.011	−3.222
YR06	−0.028	0.010	−2.945
YR07	−0.025	0.009	−2.945
YR08	−0.022	0.008	−2.882
YR09	−0.017	0.007	−2.608
YR10	−0.011	0.005	−2.143
YR11	−0.006	0.004	−1.375
YR12	0.000	0.004	0.044
YR13	−0.004	0.003	−1.239
YR14	−0.012	0.006	−2.652
YR15	−0.015	0.005	−2.507
YR16	−0.013	0.007	−2.103
YR17	−0.008	0.005	−1.255
ED11	−0.010	0.027	−0.367
ED21	0.043	0.024	1.823
RD11	−0.007	0.019	−0.354
RD21	−0.033	0.010	−3.324
TD1	0.003	0.013	0.207
GDP 1	−0.038	0.006	−6.377
FDI1	−0.069	0.011	−6.082
ED11* G(G1.C1.GDP 1)	0.429	0.054	8.008
ED21* G(G1.C1.GDP 1)	−0.497	0.049	−10.194
RD11* G(G1.C1.GDP 1)	0.265	0.047	5.685
RD21* G(G1.C1.GDP 1)	−0.149	0.037	−4.054
TD1* G(G1.C1.GDP 1)	0.233	0.023	10.289
GDP 1* G(G1.C1.GDP 1)	0.056	0.007	8.031
FDI1* G(G1.C1.GDP 1)	0.727	0.125	5.800

Source: Author’s estimation using RATS software

Table A4. Summary of the distribution of per capita income in the high LGDP group

Year	Number of provinces in high LGDP group	$g\left(\mathit{\text{LGD}}{P}_{\mathit{\text{it}}-1},\gamma ,c\right)$	Average income (million VND/person/year)	Province/City
2000	0	< 0.5
2001	0	< 0.5
2002	0	< 0.5
2003	1	0.53	76.43	Ba Ria—Vung Tau
2004	1	0.62	88.73	Ba Ria—Vung Tau
2005	1	0.75	111.14	Ba Ria—Vung Tau
2006	1	0.80	123.41	Ba Ria—Vung Tau
2007	1	0.76	113.98	Ba Ria—Vung Tau
2008	1	0.85	141.73	Ba Ria—Vung Tau
2009	1	0.80	124.40	Ba Ria—Vung Tau
2010	1	0.85	142.66	Ba Ria—Vung Tau
2011	1	0.94	214.84	Ba Ria—Vung Tau
2012	1	0.84	143.73	Ba Ria—Vung Tau
2013	1	0.83	128.40	Ba Ria—Vung Tau
2014	1	0.91	136.86	Ba Ria—Vung Tau
2015	1	0.93	235.14	Ba Ria—Vung Tau
2016	3	(1)
2017	4	(2)
2018

Source: Author’s estimation using Excel software.

Note: (1) Binh Duong province, Ba Ria—Vung Tau province and Ho Chi Minh City with the transition function and per capita income (million VND/person/year) respectively (0.51; 0.99; 0.58) and (74.05; 370.24; 82.63)

(2) Bac Ninh province, Binh Duong province, Ba Ria—Vung Tau province and Ho Chi Minh City with the transition function and per capita income (million VND/person/year) respectively: (0.66; 0.54; 0.99 and 0.65) and (94.52; 78.39; 379.49 and 92.86).