Human capital development and income inequality in Indonesia: Evidence from a nonlinear autoregressive distributed lag (NARDL) analysis

Figures & data

Figure 1. Income inequality in Indonesia—1970-2019.

Figure 2. Human capital index of Indonesia—1970-2017.

Table 1. Summary statistics

	Mean	Std. Dev	Min	Max	Observations
Indonesia
IE	43.3500	1.7539	41.5000	47.4000	50
HC	1.9567	0.3633	1.3549	2.4168	50
CPI	45.5565	48.5234	1.1553	151.1767	50
EMP	80.8789	26.6607	36.0930	131.1707	50
RGDPC	1,866.5800	884.3963	730.9584	3,877.3830	50
TO	50.5471	10.9742	28.6826	96.1862	50
URBR	35.7937	12.7488	17.0710	55.9850	50
LEC	63.3817	5.6001	52.5500	72.7160	50

Notes: IE stands for income inequality (Gini index), HC stands for human capital index, RGDPC stands for real GDP per capita, CPI stands for consumer price index, EMP stands for employment (in millions), TO stands for trade openness, URBR stands for urbanisation rate, and LEC stands for life expectancy.

Table 2. ADF and PP unit root test results

Variable	Level			First Difference
	ADF	PP	KPSS	ADF	PP	KPSS
	t-statistics	t-statistics	t-statistics	t-statistics	t-statistics	t-statistics
IE	−1.2298	−3.2067**	0.2065**	−3.8521***	−3.6747***	0.0648
HC	−0.9790	−0.9869	0.1122	−2.0320*	−4.3780**	0.1009
CPI	−1.5512	−1.7088	0.2141**	−2.6015*	−5.5759***	0.0835
EMP	−3.1047**	−3.7376***	0.2192***	−6.2147***	−6.2112***	0.1010
RGDPC	−2.6130	−0.7625	0.1150	−5.0360***	−5.0447***	0.0969
TO	−3.3086**	−3.2227***	0.3342	−8.7898***	−8.8426***	0.2872
URBR	−4.4462***	−2.6036*	0.3342	−3.6060***	−3.5024*	0.0972
LEC	0.3973	−3.3485***	0.8999***	−4.5417***	−3.4472***	0.1122

Notes: IE stands for income inequality (Gini index), HC stands for human capital index, RGDPC stands for real GDP per capita, CPI stands for consumer price index, EMP stands for employment (in millions), TO stands for trade openness, URBR stands for urbanisation rate, and LEC stands for life expectancy. The coefficients shown are T-statistics. The unit root is the null hypothesis of the Augmented Dickey-Fuller (ADF) and Phillips–Perron (PP) tests, and stationarity is the null hypothesis of the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test. Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

Table 3. Cointegration tests (human capital index as the proxy for human capital development)

		Dependent variable (income inequality) Indonesia
ARDL bounds test, Pesaran et al. (2001)		8.5223***
Diagnostic checks
Serial (1)—Lag 2		2.1214 (0.3462)
Serial (2)—Lag 4		5.0172 (0.2855)
Narayan (2005) (K = 7, n = 46)	Lower Bound	Upper Bound
1%	3.383	4.832
5%	2.504	3.723
10%	2.131	3.223
	F- Statistics	P-value
Long-Run Asymmetry Test	10.5593**	0.01325

Note: The cointegration test statistics are compared to the critical values reported by Narayan (2005) for samples with fewer than 100 observations. The Breusch-Godfrey LM test statistics for no serial correlation are serial (1) and serial (2). The numbers in parentheses indicate the p-values. *, **, and *** denote significance at 10%, 5%, and 1% levels, respectively.

Figure 3. NARDL multiplier graph.

Table 4. NARDL estimates of the impact of human capital development on income inequality

		Dependent variable (income inequality)
		I. Long-run relationship		II. Short-run relationship
		Coefficients	P-value	Coefficients	P-value
Intercept		45.3617***	0.0001	0.0481	0.5919
ECT (−1)		-	-	−0.31282***	0.0001
lnHC^+		−5.6550**	0.0127	−1.4951***	0.0007
lnHC^−		2.6253**	0.0361	2.6810***	0.0017
lnCPI		0.0604***	0.0001	−0.0102	0.2879
lnRGDPC		0.0015**	0.0106	0.0009**	0.0220
lnEMP		0.0119	0.4564	0.0175	0.1712
lnTO		0.0199*	0.0682	0.0087***	0.0008
lnURBR		−0.3552***	0.0095	0.4277***	0.0081

Notes: IE stands for income inequality (Gini index), HC+ stands for human capital index increases, HC- stands for human capital index decreases, RGDPC stands for real GDP per capita, CPI stands for consumer price index, EMP stands for employment (in millions), TO stands for trade openness, and URBR stands for urbanisation rate. The coefficients shown are the T-statistics from the EViews software application. The Akaike Information Criterion was used to select the best lag structure for the NARDL model (AIC). Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

Figure 4. Cusum and cusum squares diagrams.

Table 5. Cointegration tests (life expectancy as the proxy for human capital development)

		Dependent variable (income inequality) Indonesia
ARDL bounds test, Pesaran et al. (2001)		10.5382***
Diagnostic checks
Serial (1)—Lag 2		1.1892 (0.3199)
Serial (2)—Lag 4		0.9849 (0.1873)
Narayan (2005) (K = 6, n = 44)	Lower Bound	Upper Bound
1%	3.4240	4.8800
5%	2.5500	3.7080
10%	2.1700	3.2200

Note: The cointegration test statistics are compared with the critical values reported by Narayan (2005) for samples with fewer than 100 observations. The Breusch-Godfrey LM test statistics for no serial correction are serial (1) and serial (2). The p-values are indicated by numbers in parentheses. *, **, and *** denote significance at 10%, 5%, and 1% levels, respectively.

Table 6. ARDL estimates of the impact of human capital development on income inequality (life expectancy as a proxy for human capital development)

		Dependent variable (Life expectancy)
		I. The Long-run relationship		II. The Short-run relationship
		Coefficients	P-value	Coefficients	P-value
Intercept		78.5810***	0.0001	−0.2984	0.1745
ECT (−1)		-	-	−0.1539***	0.0001
lnLEC		−1.1390***	0.0005	−2.8548	0.0001
lnCPI		0.0128*	0.0723	0.0236**	0.0399
lnRGDPC		−0.0001	0.9682	0.0002	0.6233
lnEMP		0.2757	0.4533	0.0365	0.3990
lnTO		0.0364**	0.0285	0.0058***	0.0070
lnURBR		0.1986**	0.0220	0.1218	0.2359

Notes: IE stands for income inequality (Gini index), LEC stands for life expectancy, RGDPC stands for real GDP per capita, CPI stands for consumer price index, EMP stands for employment (in millions), TO stands for trade openness, and URBR stands for urbanisation rate. The coefficients shown are T-statistics. The Akaike Information Criterion (AIC) was used to select the best lag structure for the ARDL model (AIC). Symbols ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively.

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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Narayan, P. 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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