Macrofinancial linkages and income distribution in the South African economy

Figures & data

Figure 1. Plots of the Gini index (left) and the top 10% income share (right), for the period 1980–2019.

The plots are based on data from the World Inequality Database.

Table 1. Unit root test results.

		DF-GLS test				Unit root with breakpoint test
	Time series in levels		Time series in first differences		Time series in levels			Time series in first differences
Variables	Intercept	Intercept and trend	Intercept	Intercept and trend	Break in intercept	Break in trend	Break in both	Break in intercept	Break in trend	Break in both
LINV	−1.764*	−2.220	−3.736***	−3.852***	−3.949	−3.490	−3.075	−5.172**	−4.657**	−5.074
LCONS	0.368	−2.283	−4.839***	−5.355**	−4.857	−5.564***	−5.779***	−6.166***	−5.863***	−6.063***
LGDP	0.821	−1.954	−3.704***	−4.119***	−3.112	−2.586	−2.483	−5.675***	−5.675***	−5.714**
LCRED	0.078	−0.622	−1.437	−5.039***	−2.292	−2.899	−2.951	−5.165**	−4.992**	−5.025
LHPI	−2.319**	−2.831	−2.212**	−2.707	−4.775	−3.590	−4.562	−4.239	−4.052	−5.519**
LSPI	0.485	−3.191**	−5.123***	−6.146***	−3.994	−3.786	−4.253	−6.786***	−6.589***	−6.819***
LEXR	0.510	−1.435	−4.445***	−4.911***	−5.472***	−5.070***	−5.098	−5.574***	−5.214***	−6.241***
LINTR	−0.851	−1.890	−1.713*	−2.905*	−5.878***	−3.838	−4.520	−7.521***	−7.357***	−7.614***
LINCOME10	0.630	−1.752	−5.381***	−5.579***	−3.414	−2.328	−2.602	−7.537***	−6.108***	−7.875***
LWS	−2.152**	−2.086	−2.297**	−3.338**	−4.561	−4.292	−4.612	−5.004**	−4.931**	−5.138
LPS	−1.714*	−1.460	−1.834*	−2.951*	−4.574	−3.811	−4.614	−7.079***	−5.614***	−5.935***
LROP	−1.770*	−1.766	−2.048**	−3.018*	−3.267	−4.175	−5.076	−5.513***	−4.681**	−5.004

***, **, * indicate significance levels at 1%, 5% and 10% respectively. The variables are in logarithmic form and are defined as; LINV-investment, LCONS-consumption, LGDP-real GDP, LCRED-credit growth, LHPI-house prices, LSPI-stock prices, LEXR-exchange rates, LINTR-interest rates, LINCOME10-income inequality, LWS-wage share, LPS-profit share and LROP-rate of profit.

Source: Authors’ estimations using EViews.

Table 2. Bounds-test results.

Outcome variable	Function	F-statistic	Outcome
Investment model
(1) LINV	f(LGDP, LCRED, LSPI, LINTR, LEXR, LINCOME10, LPS)	14.2854***	Cointegrated
(2) LINV	f(LGDP, LCRED, LSPI, LINTR, LEXR, LINCOME10, LROP)	11.4527***	Cointegrated
Consumption model
(1) LCONS	f(LCRED, LHPI, LSPI, LINTR, LINCOME10, LWS, LPS)	13.4241***	Cointegrated

***, **, * indicate significance levels at 1%, 5% and 10% respectively.

Source: Authors’ estimations using EViews.

Table 3. Critical values.

Significance level:	1%		5%		10%
No. of regressors:	k = 7		k = 7		k = 7
Bounds:	I(0)	I(1)	I(0)	I(1)	I(0)	I(1)
F-statistic
Sample size: n
35	3.841	5.686	2.753	4.209	2.300	3.606
40	3.644	5.464	2.676	4.130	2.260	3.534
Asymptotic	2.960	4.260	2.320	3.500	2.030	3.130

I(0) – lower nonstationary bound and I(1) – upper stationary bound. F-test critical values for 35–40 sample size obtained from Narayan (2005).

Table 4. Long-run investment results: LINV.

Variable	Coefficient		Std. Error		t-statistic		Prob.
	(1)	(2)	(1)	(2)	(1)	(2)	(1)	(2)
LGDP(−1)	2.355***	3.325***	0.471	0.890	5.004	3.736	0.000	0.001
LCRED(−1)	−0.417***	−0.526**	0.130	0.232	−3.206	−2.269	0.003	0.030
LSPI	0.162*	0.045	0.086	0.125	1.881	0.361	0.069	0.721
LINTR	0.805***	0.993***	0.199	0.359	4.050	2.763	0.000	0.009
LEXR	0.271***	0.134	0.096	0.164	2.831	0.816	0.008	0.420
LINCOME10(−1)	−0.241	−0.821	0.796	1.297	−0.303	−0.633	0.764	0.531
LPS	1.887***		0.317		5.954		0.000
LROP		1.763***		0.476		3.699		0.001

***, **, * indicate significance levels at 1%, 5% and 10% respectively. Std. Error-Standard Error. Prob.-Probability value. Lag structure and model selection method: Schwarz Information Criterion. Model selected for (1) and (2): ARDL(1,1,1,0,0,0,1,0). The standard errors are Newey-West heteroskedasticity and autocorrelation corrected (HAC).

Source: Authors’ estimations using EViews.

Table 5. Short-run investment results: ΔLINV.

Variable	Coefficient		Std. Error		t-statistic		Prob.
	(1)	(2)	(1)	(2)	(1)	(2)	(1)	(2)
ΔLGDP	−0.044	0.118	0.221	0.235	−0.200	0.502	0.842	0.619
ΔLCRED	0.659***	0.702***	0.075	0.084	8.769	8.340	0.000	0.000
ΔLSPI	0.069*	0.013	0.037	0.036	1.887	0.364	0.070	0.719
ΔLINTR	0.345***	0.291***	0.0891	0.094	3.868	3.102	0.001	0.004
ΔLEXR	0.116**	0.039	0.049	0.053	2.331	0.743	0.027	0.464
ΔLINCOME10	−0.840***	−0.889***	0.195	0.215	−4.304	−4.141	0.000	0.000
ΔLPS	0.808***		0.123		6.544		0.000
ΔLROP		0.516***		0.092		5.623		0.000
ECT	−0.428***	−0.293***	0.036	0.027	−11.996	−10.741	0.000	0.000
Constant	−17.897***	−15.714***	1.487	1.457	−12.036	−10.782	0.000	0.000
Regression diagnostics
	Model (1)				Model (2)
R-squared		0.876		R-squared		0.852
Adjusted R-squared		0.825		Adjusted R-squared		0.792
Std. Error of regression		0.025		Std. Error of regression		0.027
Sum squared resid		0.017		Sum squared resid		0.020
F-stat		17.39		F-stat		14.147
Prob (F-stat)		0.000		Prob (F-stat)		0.000
DW stat		1.897		DW stat		1.799

ECT – error correction term. ***, **, * indicate significance levels at 1%, 5% and 10% respectively. Std. Error-Standard Error. Prob.-Probability value. Lag structure and model selection method: Schwarz Information Criterion. Model selected: for (1) and (2): ARDL(1,1,1,0,0,0,1,0). The standard errors are Newey-West heteroskedasticity and autocorrelation corrected (HAC).

Source: Authors’ estimations using EViews.

Table 6. Long-run consumption results: CONS.

Variable	Coefficient	Std. Error	t-statistic	Prob.
LCRED	0.110***	0.018	6.026	0.000
LHPI(−1)	0.060***	0.016	3.781	0.001
LSPI	0.001	0.011	0.135	0.893
LINTR	−0.082**	0.037	−2.241	0.032
LINCOME(−1)	−0.609***	0.131	−4.636	0.000
LWS(−1)	0.254***	0.049	5.208	0.000
LPS	0.048	0.042	1.129	0.267

***, **, * indicate significance levels at 1%, 5% and 10% respectively. Std. Error-Standard Error. Prob.-Probability value. Lag structure and model selection method: Schwarz Information Criterion. Model selected: ARDL(1,0,2,0,0,2,1,0). The standard errors are heteroskedasticity and autocorrelation corrected (HAC) by the Newey-West method.

Source: Authors’ estimations using EViews.

Table 7. Short-run consumption results: ΔCONS.

Variable	Coefficient	Std. Error	t-statistic	Prob.
ΔLCRED	0.089***	0.016	5.509	0.000
ΔLHPI	0.111***	0.015	7.497	0.000
ΔLHPI(−1)	−0.052***	0.014	−3.668	0.001
ΔLSPI	0.001	0.009	0.135	0.894
ΔLINTR	−0.067***	0.025	−2.641	0.014
ΔLINCOME10	−0.087*	0.049	−1.755	0.089
ΔLINCOME10(−1)	0.369***	0.061	6.074	0.000
ΔLWS	0.067**	0.032	2.093	0.045
ΔLWS(−1)	0.205***	0.045	4.608	0.000
ΔLPS	0.039	0.038	1.032	0.312
ECT	−0.810***	0.069	−11.778	0.000
Constant	1.777	0.150	11.830	0.000
Regression diagnostics
R-squared		0.864
Adjusted R-squared		0.789
Std. Error of regression		0.006
Sum squared resid		0.001
F-stat		11.702
Prob (F-stat)		0.000
DW stat		1.759

ECT – error correction term. ***, **, * indicate significance levels at 1%, 5% and 10% respectively. Std. Error-Standard Error. Prob.-Probability value. Lag structure and model selection method: Schwarz Information Criterion. Model selected: ARDL(1,0,2,0,0,2,1,0). The standard errors are heteroskedasticity and autocorrelation corrected (HAC) by the Newey-West method.

Source: Authors’ estimations using EViews.

Figure 2. Plots of cumulative sums of recursive residuals and cumulative sums squares of recursive residuals: investment models.

The upper and bottom plots relate to the first and second investment models respectively.

The straight lines indicate the critical bounds at 5% significance level.

Source: Authors’ estimations using EViews.

Figure 3. Plots of cumulative sums of recursive residuals and cumulative sums squares of recursive residuals: consumption model.

The straight lines indicate the critical bounds at 5% significance level.

Source: Authors’ estimations using EViews.

Table 8. Diagnostic tests.

Test		test-statistic	p-value
	Investment model (1)
Serial Correlation LM Test:	Obs*R-squared	0.076	0.963
Heteroskedasticity Test:	Obs*R-squared	8.257	0.690
Normality Test:	Jarque-Bera	0.938	0.626
	Investment model (2)
Serial Correlation LM Test:	Obs*R-squared	0.561	0.755
Heteroskedasticity Test:	Obs*R-squared	8.029	0.711
Normality Test:	Jarque-Bera	1.620	0.445
	Consumption model
Serial Correlation LM Test:	Obs*R-squared	1.175	0.556
Heteroskedasticity Test:	Obs*R-squared	12.028	0.525
Normality Test:	Jarque-Bera	0.483	0.785

The serial correlation test results are based on the Breusch-Godfrey Serial Correlation LM (Lagrange Multiplier) Test under the null hypothesis of no serial correlation at up to 2 lags. The heteroskedasticity results are based on the Breusch-Pagan-Godfrey Test under the null hypothesis of homoskedasticity. The test-statistics follow a Chi-square distribution.

Source: Authors’ estimations using EViews.

Figure 4. Responses of investment (linv), consumption (lcons) and real GDP (lgdp) to unit shocks to credit growth (lcred), interest rates (lintr), house prices (lhpi), stock prices (lspi) and exchange rates (lexr).

Source: Authors’ estimations using R.

Figure 5. Responses of investment (linv), consumption (lcons) and real GDP (lgdp) to unit shocks to the wage share (lws), profit share (lps) and income inequality (lincome10).

Source: Authors’ estimations using R.

Figure 6. Responses of real GDP (lgdp) to consumption (lcons) and investment (linv), and responses of rate of profit (lrop) to consumption (lcons) and investment (linv).

Source: Authors’ estimations using R.

Table A1. Data description and sources.

Variable	Measure/indicator	Source of data
Real Gross Domestic Product (GDP)	GDP at market prices (constant prices-2015, seasonally adjusted, Rand millions)	South African Reserve Bank
Investment (INV)	Gross fixed capital formation (constant prices-2015, seasonally adjusted) – divided by real GDP by the authors	SARB
Consumption (CONS)	Final consumption expenditure by households (constant prices-2015, seasonally adjusted) – divided by real GDP by the authors	SARB
Credit (CRED)	Total credit extended to the private sector by monetary financial institutions – divided by real GDP by the authors	SARB
House prices (HPI)	Real house price indices	OECD database
Stock prices (SPI)	Real share price indices	OECD database
Exchange rate (EXR)	Nominal effective exchange rate against the most important currencies (Index, 2015 = 100)	SARB
Long-term interest rates (INTR)	Long-term government bond related interest rates	International Financial Statistics (IMF) database
Top 10% income share (INCOME10)	Top 10% income share of pre-tax national income	World Inequality Database
Adjusted wage share (WS)	Compensation of employees to GDP at factor cost	SARB
Profit share (PS)	Country-level profit shares, (net profit income/net output)	World Profitability Dashboard (Basu et al. 2022)
Rate of profit (ROP)	Country-level profit rates, (net profit income/capital stock)	World Profitability Dashboard (Basu et al. 2022)

SARB – South African Reserve Bank; OECD – Organisation for Economic Cooperation and Development; IMF – International Monetary Fund.

Table B1. Summary of descriptive statistics.

Variable	Mean	Maximum	Minimum	Std. Dev.	Obs.
INV	15.290	19.786	11.393	2.525	40
CONS	58.683	65.718	48.893	4.661	40
GDP	3092441.	4583667.	2032312.	887921.5	40
CRED	29.487	84.432	1.459	26.201	40
HPI	81.520	120.464	51.943	22.281	40
SPI	33.368	108.757	1.975	35.843	40
EXR	399.537	1490.032	89.269	403.571	40
INTR	12.059	16.901	7.722	3.330	40
INCOME10	0.545	0.650	0.460	0.0729	40
WS	43.636	51.941	37.334	3.863	40
PS	29.179	36.867	20.652	4.969	40
ROP	11.335	16.123	6.897	2.616	40

Sample: 1980–2019. All data in levels (i.e. not in log or differenced form). Obs.- number of observations. Std. Dev.-standard deviation. INV-investment, CONS-consumption, GDP-real GDP in market prices, CRED- domestic credit to private sector, HPI-house price index, SPI-stock price index, EXR-exchange rates, INTR-interest rates, INCOME10-top10% income share, WS- private wage share, PS-profit share, & ROP-rate of profit.

Source: Authors’ estimations using EViews.

Narayan, Paresh K. 2005. “The Saving and Investment Nexus for China: Evidence from Cointegration Tests.” Applied Economics 37 (17): 1979–1990. https://doi.org/10.1080/00036840500278103.

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Basu, Deepankar, Julio Huato, Jesus L. Jauregui, and Evan Wasner. 2022. “World Profit Rates, 1960–2019.” Review of Political Economy: 1–16. https://doi.org/10.1080/09538259.2022.2140007.

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Data availability statement

The various data associated with this paper can be found in the South African central bank (SARB) website, the Organisation for Economic Cooperation and Development and the International Financial Statistics databases, the Word Inequality Database, and the World Profitability Dashboard.