Symmetric and asymmetric impact of public investment on private investment in South Africa: Evidence from the ARDL and non-linear ARDL approaches

Figures & data

Figure 1. Public Investment and Private Investment in South Africa (1980–2018).

Source: Own compilation from World Bank Development Indicators (2021)

Table 1. Stationarity Test for all Variables

	Dickey-Fuller Generalized Least Square (DF-GLS)
Variable	Level					First Difference
	Without Trend		With Trend			Without Trend		With Trend
PrvI	−1.07		−1.36			−2.70***		−3.93***
PubI	−0.60		−1.05			−4.49***		−5.27***
Y	−0.84		−1.79			−3.51***		−3.89***
CRED	−0.62		−1.52			−5.88***		−6.00***
INT	−0.48		−1.56			−2.76***		−4.89***
INF	−1.40		−2.85			−5.35***		−5.59***
TO	−1.43		−2.39			−5.67***		−6.15***
	Phillips-Perron (PP)
	Level					First Difference
	Without Trend		With Trend			Without Trend		With Trend
PrvI	−2.12		−1.89			−3.81***		−3.84***
PubI	−2.05		−0.99			−5.44***		−6.06***
Y	−0.60		−1.81			−3.87***		−3.35***
CRED	−1.59		−0.70			−6.24***		−7.66***
INT	−5.45***		−5.25***			__		__
INF	−1.39		−2.85			−9.49***		−10.42***
TO	−1.86		−3.12			−6.47***		−7.08***
	Zivot-Andrews (ZAURoot)
	Level					First Difference
	Without Trend	Time Break		With Trend	Time Break	Without Trend	Time Break	With Trend	Time Break
PrvI	−4.33	2005		3.75	1991	−5.65***	2009	−5.34***	2009
PubI	−3.29	1990		−3.82	1990	−7.10***	1996	−6.95***	1995
Y	−4.04	2004		−3.23	1990	−6.17***	2009	−6.43***	2009
CRED	−1.79	2011		−2.34	2006	−10.47***	1992	−10.74***	1992
INT	−3.24	1994		−3.37	1994	−7.90***	2000	−9.50***	2000
INF	−3.60	1993		−3.63	2003	−6.84***	2007	−6.93***	2007
TO	−3.90	1989		−3.65	1990	−7.23***	2009	−7.06***	2009

Notes: *** denotes stationarity at 1% significance level

Table 2. BDS Test for Nonlinearity

Variables	Dimension 2		Dimension 3		Dimension 4		Dimension 5		Dimension 6
	BDS Statistic	P-value	BDS Statistic	P-value	BDS Statistic	P-value	BDS Statistic	P-value	BDS Statistic	P-value
PrvI	0.142***	0.000	0.226***	0.000	0.266***	0.000	0.279***	0.000	0.280***	0.000
PubI	0.175***	0.000	0.296***	0.000	0.391***	0.000	0.453***	0.000	0.487***	0.000
Y	0.153***	0.000	0.246***	0.000	0.295***	0.000	0.317***	0.000	0.312***	0.000
Cred	0.188***	0.000	0.313***	0.000	0.402***	0.000	0.460***	0.000	0.499***	0.000
Int	0.091***	0.000	0.148***	0.000	0.173***	0.000	0.189***	0.000	0.189***	0.000
Inf	0.118***	0.000	0.198***	0.000	0.264***	0.000	0.296***	0.000	0.315***	0.000
To	0.106***	0.000	0.160***	0.000	0.173***	0.000	0.178***	0.000	0.163***	0.000

Notes: *** denote statistical significance at 1% level

Table 3. Bounds F-test for Cointegration Results

ARDL Model			NARDL Model
F-Statistic	Cointegration Status		F-Statistic			Cointegration Status
6.981***	Cointegrated		4.120**			Cointegrated
Pesaran et al. (2001), p.300, Table CI(iii) Case III	Asymptotic critical values for ARDL Model
	10%		5%			1%
	I(0)	I(1)	I(0)		I(1)	I(0)	I(1)
	2.12	3.23	2.45		3.61	3.15	4.43
	Asymptotic critical values for NARDL Model
	10%		5%			1%
	I(0)	I(1)	I(0)		I(1)	I(0)	I(1)
	2.03	3.13	2.32		3.5	2.96	4.26

Notes: ** and *** denote statistical significance at 5% and 1% level.

Table 4. Results of Long-Run and Short-Run Estimation

Dependent Variable is PrvI
	ARDL (Model 1)		NARDL (Model 2)
Regressor	Coefficient	T-ratio [p-value]	Coefficient	T-ratio [p-value]
Panel A: Long-Run Results
$PubI$	1.9975***	4.543 [0.000]	_	_
$Pub{I}^{+}$	_	_	−1.174	−0.888 [0.387]
$Pub{I}^{-}$	_	_	1.157*	1.908 [0.075]
$Y$	0.0023***	3.063 [0.007]	−0.004***	3.457 [0.003]
$CRED$	0.0691**	−0.844 [0.408]	0.102***	3.975 [0.001]
$INT$	−0.1242	−0.346 [0.733]	0.071	0.670 [0.512]
$INF$	−0.0277	1.652 [0.114]	0.096	0.710 [0.488]
$TO$	−0.1912**	0.086 [0.933]	−0.129	−1.732 [0.103]
Panel B: Short-Run Results
$C$	−2.0634	−0.754 [0.461]	−4.273***	−6.941 [0.000]
$\mathrm{\Delta }PrvI\left(-1\right)$	0.5288***	3.956 [0.001]	0.379***	3.404 [0.004]
$\mathrm{\Delta }PrvI\left(-2\right)$	0.5302***	3.011 [0.008]	_	_
$\mathrm{\Delta }PubI$	1.2825***	3.495 [0.003]	_	_
$\mathrm{\Delta }Pub{I}^{+}$	_	_	−0.280	−0.524 [0.608]
$\mathrm{\Delta }Pub{I}^{+}\left(-1\right)$	_	_	1.531**	2.693 [0.016]
$\mathrm{\Delta }Pub{I}^{-}$	_	_	1.822***	5.156 [0.000]
$\mathrm{\Delta }Y$	0.0014***	2.922 0.010]	−0.002*	−2.047[0.057]
$\mathrm{\Delta }CRED$	−0.0019	−0.1000 [0.922]	0.010	1.077 [0.297]
$\mathrm{\Delta }CRED\left(-1\right)$	−0.0943***	3.816 [0.001]	−0.033*	−2.055 [0.057]
$\mathrm{\Delta }INT$	−0.0798	−1.380 [0.186]	0.156***	4.491 [0.000]
$\mathrm{\Delta }INF$	−0.2575***	−2.863 [0.011]	−0.122***	−2.926 [0.010]
$\mathrm{\Delta }INF\left(-1\right)$	−0.1116	1.674 [0.112]	−0.105**	−2.807 [0.013]
$\mathrm{\Delta }TO$	0.1772***	3.598 [0.002]	0.054	1.669 [0.115]
$\mathrm{\Delta }TO\left(-1\right)$	0.1081**	2.231 [0.040]	_	_
$ECM\left(-1\right)$	−0.6420***	−8.131 [0.000]	−0.743***	−6.883 [0.000]
Test Statistic		ARDL	NARDL
R- Squared		0.881	0.897
R-Bar-Squared		0.834	0.844
F-Statistic [Prob]		18.952 [0.000]	16.763 [0.000]
DW Statistic		2.209	2.121
Akaike info criterion		1.441	1.401
Schwarz info criterion		1.895	1.973

Notes: *, ** and *** denote statistical significance at 10%, 5% and 1% levels, respectively

_+ and _- denotes positive and negative shocks

Table 5. Long- and Short-Run Asymmetry Results

Country	Test	F-statistic	P-value	Decision
South Africa	WLR	8.394**	0.011	Asymmetric
	WSR	3.824*	0.068	Asymmetric

Notes: $W_{LR}$ is long-run asymmetric test; W_SR is short-run asymmetric test; **and * signifies significance at 5% and 10% level.

Table 6. Diagnostic Tests Results

LM Statistics	ARDL	NARDL
Normality	0.233 [0.890]	0.270 [0.874]
Serial Correlation	0.679 [0.422]	1.393 [0.281]
Heteroscedasticity	0.372 [0.970]	0.353[0.984]
Functional Form	2.403 [0.141]	2.626 [0.126]

Notes: Normality test using the Jarque-Bera test; Serial correlation using the Lagrange Multiplier test; Heteroscedasticity using the Breusch-Pagan-Godfrey test and Functional form; the value in parenthesis is p-values.

Figure 2. Plot of Dynamic Multiplier Graph.

Figure 3. Plot of CUSUM and CUSUMQ.

Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16(3), 289–326. https://doi.org/10.1002/jae.616

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Data availability statement

The data that support the findings of this study are available upon reasonable request.