The dynamic relationship between government debt, fiscal consolidation, and economic growth in South Africa: A threshold analysis

Figures & data

Table 1. Economic variables

Economic variables	Description	Sourced
$GDP$	Gross domestic product	IMF (2020)
$AOLR$	Average output labour ratio	SARB (2023)
$AKR$	Average output capital ratio	SARB (2023)
$GD$	Domestic government debt	SARB (2023)
$G{D}^2$	Domestic government debt squared	Calculated
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}tgr$	Time-varying elasticity for total government revenue	Buthelezi and Nyatanga (2023)
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}g$	Time-varying elasticity for government expenditure	Buthelezi and Nyatanga (2023)
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB$	Time-varying elasticity for both total government revenue and government expenditure	Buthelezi and Nyatanga (2023)

Data source: SARB (2023) and IMF (2020).

Table 2. Descriptive statistics

Variable	Obs	Mean	Std. Dev.	Min	Max
$GDP$	43	.255814	2.60926	−7.7	4.4
$AOLR$	43	394311.4	38075.04	331804	453484
$AKR$	44	177527.5	19037.5	149586	204700
$GD$	44	37.22682	11.20625	21.99	73.18
$G{D}^2$	44	1508.562	1027.835	483.5601	5355.313
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}tgr$	44	−1.356591	12.22918	−47.3	49.72
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}g$	44	5.259546	45.5113	−247.4	67.85
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB$	44	6.616136	56.26286	−297.13	115.1

Table 3. Matrix of correlation

Variables	$\mathit{G}\mathit{D}\mathit{P}$	$\mathit{A}\mathit{O}\mathit{L}\mathit{R}$	$\mathit{A}\mathit{K}\mathit{R}$	$\mathit{G}\mathit{D}$	$\mathit{G}{\mathit{D}}^2$	$\mathit{t}\mathit{v}\mathit{p}\mathrm{\_}\mathit{t}\mathit{g}\mathit{r}$	$\mathit{t}\mathit{v}\mathit{p}\mathrm{\_}\mathit{g}$	$\mathit{t}\mathit{v}\mathit{p}\mathrm{\_}\mathit{C}\mathit{A}\mathit{P}\mathit{B}$
$GDP$	1.00
$AOLR$	0.25	1.00
$AKR$	0.38	0.38	1.00
$GD$	0.16	0.16	0.11	1.00
$G{D}^2$	0.16	0.16	0.16	0.98	1.00
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}tgr$	−0.18	−0.18	−0.06	0.012	0.01	1.00
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}g$	0.12	0.12	0.18	0.10	0.12	−0.84	1.00
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB$	0.13	0.13	0.16	0.08	0.09	−0.90	0.99	1.00

Note that the economic variable is the same with different notation $tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}tgr=tvp\mathrm{\_}tgr$, $tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}g=tvp\mathrm{\_}g$ and $tvp\mathrm{\_}elstcy\mathrm{\_}CAPB=tvp\mathrm{\_}CAPB$.

Table 4. Dickey–Fuller and Phillips–Perron test for unit root

Variables		Dickey–Fuller				Phillips–Perron
		Test	1%	5%	10%	Test	1%	5%	10%
GDP	Z(t)	−4.710	−3.634	−2.952	−2.610	−4.710	−3.634	−2.952	−2.610
$d.AOLR$	Z(t)	−3.639	−3.641	−2.955	−2.611	−3.639	−3.641	−2.955	−2.611
$AKR$	Z(t)	−4.093	−3.641	−2.955	−2.611	−4.093	−3.641	−2.955	−2.611
$d.GD$	Z(t)	−3.902	−3.634	−2.952	−2.610	−3.902	−3.634	−2.952	−2.610
$d.G{D}^2$	Z(t)	−4.211	−3.634	−2.952	−2.610	−4.211	−3.634	−2.952	−2.610
Estimated economic variables
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}tgr$	Z(t)	−6.515	−3.634	−2.952	−2.610	−6.515	−3.634	−2.952	−2.610
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB\mathrm{\_}g$	Z(t)	−6.253	−3.648	−2.958	−2.612	−6.253	−3.648	−2.958	−2.612
$tvp\mathrm{\_}elstcy\mathrm{\_}CAPB$	Z(t)	−6.392	−3.634	−2.952	−2.610	−6.392	−3.634	−2.952	−2.610

Notes: MacKinnon approximate p-value for Z(t) = 0.0000, Number of Obs = 42.

Table 5. Threshold regression estimation

Estimation	(1)	(2)	(3)
Region1	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$
$tvp\mathrm{\_}elstcy\mathrm{\_}capb$	−0.158*
	(−2.57)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}tgr$		−1.364**
		(−2.84)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}g$			−0.201**
			(−2.86)
$\mathrm{\_}cons$	3.714***	0.807	3.839***
	(3.33)	(0.88)	(3.55)
Region2	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$
$tvp\mathrm{\_}elstcy\mathrm{\_}capb$	−0.00173
	(−0.24)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}tgr$		0.00179
		(0.06)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}g$			−0.00332
			(−0.37)
$\mathrm{\_}cons$	−1.534	−2.080*	−1.553
	(−1.83)	(−2.51)	(−1.88)
Region3	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$
$tvp\mathrm{\_}elstcy\mathrm{\_}capb$	0.00638
	(0.44)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}tgr$		−0.0658
		(−1.19)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}g$			0.00535
			(0.31)
$\mathrm{\_}cons$	0.207	0.166	0.219
	(0.42)	(0.39)	(0.45)
Threshold	1	2	3
$gd\mathrm{\_}thr\mathrm{\_}1$	29.000	28.7400	29.0000
$gd\mathrm{\_}thr\mathrm{\_}2$	30.620	30.3100	30.6200
Statistics	1	2	3
$odr\mathrm{\_}1ssr$	222.9307	205.9457	215.9071
$odr\mathrm{\_}2ssr$	202.2691	169.9869	195.2831
N	42	42	42

Notes: t Statistics are in parentheses. *p < 0.05, **p < 0.01, ***p < 0.001.

Table 6. 2SLS model estimation

Estimation	(1)	(2)	(3)	(4)	(5)	(6)
Variables	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$
$\mathit{A}OLR$	−0.000254***	−0.000257***	−0.000273***	−0.000249***	−0.000294***	−0.000228***
	(−6.72)	(−16.28)	(−9.05)	(−5.85)	(−10.56)	(−9.53)
$AKR$	0.000289***	0.000307***	0.000316***	0.000270***	0.000341***	0.000267***
	(6.43)	(13.80)	(9.42)	(5.22)	(9.89)	(8.00)
$GD$	0.341***	0.455***	0.441***	0.377***	0.397***	0.358***
	(8.58)	(11.09)	(6.76)	(4.88)	(8.41)	(6.17)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb$	−0.127***	−0.0870***	−0.0944***	−0.124**	−0.101**	−0.0874***
	(−3.29)	(−3.55)	(−3.31)	(−3.14)	(−2.97)	(−3.49)
$dmmy\mathrm{\_}gd\mathrm{\_}30$	−1.144
	(−1.09)
$dmmy\mathrm{\_}gd\mathrm{\_}50$		4.052***
		(3.85)
$dmmy\mathrm{\_}gd\mathrm{\_}70$			3.299
			(1.66)
$dmmy\mathrm{\_}gd\mathrm{\_}30\mathrm{\_}40$				−0.516
				(−0.85)
$dmmy\mathrm{\_}gd\mathrm{\_}40\mathrm{\_}50$					3.081***
					(4.59)
dmmy_gd_50_60						−2.855**
						(−2.82)
_cons	30.48***	20.13***	25.31***	30.72***	32.48***	24.22***
	(4.48)	(7.93)	(5.69)	(5.11)	(7.36)	(8.03)
N	26	26	26	27	27	26

Notes: t Statistics are in parentheses. *p < 0.05, **p < 0.01, ***p < 0.001.

Table 7. Threshold domestic government debt, GDP and fiscal consolidation

Estimation	1	2	3
Economic variables	$\mathit{G}DP$	$\mathit{G}DP$	$\mathit{G}DP$
$AOLR$	−0.000282***	−0.000262***	−0.000284***
	(−6.82)	(−6.64)	(−6.81)
$AKR$	0.000312***	0.000285***	0.000316***
	(6.16)	(5.74)	(6.28)
$GD$	0.806***	0.668***	0.813***
	(3.86)	(3.85)	(3.71)
$G{D}^2$	−0.00439*	−0.00314*	−0.00440*
	(−2.47)	(−2.30)	(−2.33)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb$	0.0192
	(1.36)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}tgr$		−0.128***
		(−3.35)
$tvp\mathrm{\_}elstcy\mathrm{\_}capb\mathrm{\_}g$			0.0184
			(0.99)
_cons	25.72***	26.54***	25.53***
	(5.85)	(6.57)	(5.86)
N	27	27	27

Notes: t Statistics in parentheses. *p < 0.05, **p < 0.01, ***p < 0.001.

IMF. (2020). Cyclically adjusted balance. Retrieved 11-08-, 2022, from https://www.imf.org/external/datamapper/GGCB_G01_PGDP_PT@FM/ADVEC/FM_EMG/.

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