Silviase/jgov_v1.4_full_ann huggingface dataset:
during the period from 1965–1970 to 2005–10. Figure 12 shows the positive relation between terms of trade and growth rate in India. In contrast, no such clear relation is apparent for China in Figure 12.

## [Figure 12 inserted here]

The ratio of exports plus imports to GDP is regarded as reflecting the degree of external openness. The regression in column 3 of Table 13 shows a significant positive coefficient for the external openness index. The estimated coefficient of external openness is 0.00005693621 $ (2.35) $ . $ ^{12} $

The partial relation between growth rate and the external openness is presented in Figure 13. Several countries have remarkably high values such as more than 300 per cent. Therefore, the figure is divided into a left panel for the entire world and a right panel limiting the sample countries to those with the openness index from 0 per cent to 100 per cent. This figure also presents the historical trend of external openness in India and China. As Table 2 shows, the external openness of India increased from 9.04 per cent to 45.9 per cent during 1965–2005. India's openness ratio has risen remarkably, especially after 1990. China's openness ratio also rose from 36.0 per cent to 63.7 per cent during 1990–2005. China's openness is greater than India's.

## [Figure 13 inserted here]

The polity score drawn from the Center for Systemic Peace's Polity IV project reflects the extent of qualities of governing authority from dictatorship to democracy. The polity score includes components reflecting competitiveness of executive recruitment, openness of executive recruitment, constraints on chief executives, regulation of participation, and competitiveness of political participation. In this study, the original score of -10 to +10 was revised to 0 to 10, with 0 denoting the worst and 10 denoting the best level of democracy.

The regression includes this democracy index, its own square, and its own cube. The results show a significant nonlinear effect of the democracy on economic growth. The estimated coefficients of the democracy index, its own square, and its own cube are, respectively, -0.010946744 (-2.59), 0.00217649398 (2.41), and -0.0123252181 (-2.23). The growth rate decreases as the democracy index increases from 0 toward 3.6. Then the growth rate increases as the democracy index increases from 3.6 to 8. Again, the growth rate decreases as the democracy index increases from 8.
index increases from 8 to 10. The maximum value of the growth rate is at 0 of the democracy index and minimum value of growth rate is at 3.6 of the democracy index. $ ^{13} $

The partial relation between economic growth and the democracy index is presented in Figure 14. The growth rates of low-democracy vary more than those of high-democracy. A group of low-democracy countries includes both China, which is the country with the most growth, and sub-Saharan African countries, which are growing less. To elucidate the complex relation between political regimes and economic growth might require some caution about simple conclusions drawn from a point estimation of coefficients obtained by OLS. Consequently, a scatter diagram can provide useful graphical information about the democracy–growth relation.

## [Figure 14 inserted here]

The regression equation for the 1-th percentile of the unexplained growth rate of per-capita GDP based on the democracy index and its square in the data shown in Figure 14 is the following.

$$ \begin{aligned}Unexplained Growth=&0.0808***+0.0120***Democracy-0.0007247**(Democracy)^{2}\\&(11.08)\quad(3.57)\quad(-2.35)\end{aligned} $$

NOB=651, Pseudo $ R^{2}=0.1550 $

The regression equation for the 99th percentile of the unexplained growth rate is shown below.

Unexplained Growth =0.0808***-0.0221***Democracy+0.0018235*** (Democracy) $ ^{2} $

(11.08) (-3.17) (3.19)

NOB=651, Pseudo $ R^{2}=0.1801 $

These results tell a different story. Although the growth rate of the highest growing countries is determined in a U-shaped manner by democracy, the growth rate of the least growing countries is determined as an inverted U-shaped manner by democracy.

This figure also presents the historical trend of the democracy index for India and China.
As Table 2 shows, in contrast to other explanatory variables, the democracy index has not varied in either country. India's index was 9.0–9.5 during 1965–2005. China's index was 1.5 during 1990–2005. India's democracy index is remarkably higher than China's.

The regression includes a constant term and time dummies for the nine periods to 1965–1970 to 2005–2010. The reference period of time dummies is 1960–1965. The later six period dummies 1980–1985 to 2005–2010 are significant and negative. Results show that the overall growth rate of the world economy declined after 1980.

Figure 15 presents the estimated mean of growth rate obtained using the estimated constant term interacting with time dummies at the right axis and the simple average of the growth rate at the left axis. Both growth rates peak in 1965–1970 and then reach troughs in 1980–1985. After 1985, both rates increase modestly. The growth rate of India grew steadily from 1980, remaining higher than the overall growth rate of the world economy from 1980. It is again noteworthy that China's growth rate is much higher than those of India and the world economy.

## [Figure 15 inserted here]

### 3.4 Robustness of Basic Growth Regression

The basic growth regression described in the previous section might be adversely affected by endogeneity bias, partly because of the possible correlation between the unobservable country-fixed effects and the explanatory variables. To address this issue, the fixed effects model is applied to eliminate the country-fixed effect. The regression results of columns 1–4 of Table 4 show that, even controlling for the country-fixed effect, no evidence exists of a relation between urbanization and economic growth. Turning to column 5 of Table 4, the estimated coefficients of the schooling years are negative, but not significant. However, the p value for chi-squared test of joint significance of slope coefficients of schooling years and its square is 0.0276. That result confirms that human capital has significant effects on economic growth. All other main explanatory variables have significant coefficients with the same sign, as shown in column 3 of Table 3. Consequently, the results of fixed-effect regression are not at all inconsistent with those of basic growth regression.

## [Table 4 inserted here]

Although they have the same sign, the degree of the estimated coefficient differs. For example, the overestimated variables in the basic regression compared with the fixed-effect regression are the square of schooling years, with 54 per cent more coefficient value, schooling
years with 51 per cent more value, total fertility rate with 11 per cent more value, the cube of the democracy index with 9 per cent more value, the investment rate with 8 per cent more value, and the square of the democracy index with 3 per cent more value. The estimated coefficients of schooling years with nonlinear effects imply that the schooling years beyond two years raise the GDP growth rate. The estimated coefficients of democracy index implies that the growth rate decreases as the democracy index increase from 0 to 3.6; then the growth rate increases as the democracy index increases from 3.7 to 8.7. Again, the growth rate decreases as the democracy index increase from 8 to 10. The maximum value of the growth rate is at 0 of the democracy index; the minimum value of the growth rate is at 3.7 of the democracy index. These nonlinear relations shown in the fixed-effect regression are not substantially different from those of the basic regression.

The underestimated variables in the basic regression relative to the fixed-effect regression are the government consumption ratio with 20 per cent less coefficient value, life expectancy at birth with 18 per cent less value, initial per-capita GDP with 17 per cent less value, inflation rate with 14 per cent less value, external openness ratio with 13 per cent less value, change in terms of trade with 7 per cent less value, and democracy index with 1 per cent less value.

Consequently, endogeneity bias caused by the possible correlation between the unobservable country-fixed effects and the explanatory variables generates overestimation or underestimation of coefficients of the explanatory variable, more or less. The estimated coefficients from the fixed-effect regression and basic regression, however, do not differ substantially. We infer that the reliability of the results of basic growth regression becomes greater.

## Concluding Remarks

Over the past few decades, the Indian economy has grown rapidly compared to the world’s economies. This study clarified patterns and features of long-term economic growth in India using growth regression analysis. The following main findings can be pointed out.

First, the results of growth regression support the conditional convergence hypothesis. In contrast, both India's growth rate and income level have increased, breaking the convergence hypothesis. Second, growth regression shows health capital, investment ratio, and external openness contributing to economic growth. Results show that life expectancy at birth, the investment ratio and the export–import ratio were improved in India. Thirdly, the growth regression suggests that human capital has a nonlinear effect on economic growth. It is noteworthy that schooling years beyond three years raise the growth rate. Both schooling years and growth rates have increased in India. Fourth, it is supported by the growth regression that the total fertility
rate has a negative effect on growth. It has also been observed in India that the growth rate increased as the total fertility rate declined. Fifth, the growth regression shows that government consumption reduces the growth rate. Contrary to the regression results, both India's growth rate and government consumption have increased. Sixth, according to results drawn from the growth regression, inflation has a negative effect on the growth rate. However, no clear relation is apparent between inflation and growth in India. Seventh, the growth regression results show that the improvement of terms of trade contributes to economic growth. The same was observed in India, where terms of trade fluctuated over time. Finally, growth regression results imply that democracy and economic growth have a nonlinear complex relation and that the relation differs depending on the position of the distribution of growth rates: while in the highest group the growth rate and democracy are U-shaped, in the lowest group they are inverted U-shaped. No clear relation is apparent between democracy and growth in India where India's status of democracy has varied only slightly.

Economic growth is important. With one-third of the India's total population living below the poverty line, long-term high economic growth will contribute to improvement of the well-being of the populace. Our findings show that well-being itself, such as life expectancy at birth and schooling years, has a beneficial effect on economic growth. A virtuous cycle of prosperity involving economic growth and well-being is more important for India.
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Figure 1

The Dynamics of the Neoclassical Growth Model
Figure 2

Absolute Convergence in the Neoclassical Growth Model
Figure 3

Conditional Convergence in the Neoclassical Growth Model

Panel A: Different Saving Rates

Panel B: Different Population Growth Rates
Figure 4

Simple correlation between the growth rate of per capita GDP and log of initial per-capita GDP.
Figure 5

Partial relation between the growth rate of per-capita GDP and log of initial per capita GDP.
Figure 6

Partial relation between the growth rate of per-capita GDP and upper-level schooling years.
Figure 7

Partial relation between the growth rate of per-capita GDP and inverted value of life expectancy at birth.
Figure 8

Partial relation between the growth rate of per-capita GDP and total fertility rate.
Figure 9

Partial relation between the growth rate of per-capita GDP and government consumption to GDP.
Figure 10

Partial relation between the growth rate of per-capita GDP and investment to GDP.
Figure 11

Partial relation between the growth rate of per-capita GDP and inflation rate.
Figure 12

Partial relation between the growth rate of per-capita GDP and change in terms of trade.
Figure 13

Partial relation between the growth rate of per-capita GDP and external openness ratio.
Figure 14

Partial relation between the growth rate of per-capita GDP and democracy index.
Figure 15

Growth Rates during 1960–2010
Table 1

Descriptive Statistics and Expected Sign of Growth Regression

Variable	Mean	S.D.	Min	Max	Source	Expected sign
Annual growth rate of per capita GDP	0.020901	0.0277236	-0.077573	0.138937	WDI & GDF	-
Log of initial per capita GDP	7.409063	1.456383	4.744932	10.61152	WDI & GDF	Negative
Change in terms of trade	-0.0003132	0.0551926	-0.308356	0.309547	Barro and Lee (1994), WDI & GDF	Positive
Inflation rate	0.1200026	0.2157444	-0.043022	2.22353	WDI & GDF	Negative
Total fertility rate	4.068003	1.921397	1.14	8.27	WDI & GDF	Negative
Government consumption ratio	14.51339	5.396524	4.08	40.6	WDI & GDF	Negative
Investment ratio	22.33189	7.213002	4.84	66.5	WDI & GDF	Positive
External openness ratio	70.24896	48.26262	8.43	431	WDI & GDF	Positive
1/(Life expectancy at birth)	0.0162308	0.0030151	0.012121	0.034602	WDI & GDF	Negative
Democracy index	6.067588	3.415694	0	10	Polity IV	?
Upper-level schooling years	1.949184	1.557857	0.043	8.056	Barro and Lee (2013)	Positive
Urban agglomerated population ratio	24.55164	18.27939	0	100	World Urbanization Prospects	?
Urban population ratio	47.6638	23.36899	2.294	100	World Urbanization Prospects	?

Note 1: These panel data cover observations for 23 countries in 1960-1965, 39 countries in 1965-1970, 59 countries in 1970-1975, 67 countries in 1975-1980, 48 countries in 1980-1985, 56 countries in 1985-1990, 59 countries in 1990-1995, 61 countries in 1995-2000, 120 countries in 2000-2005, and 119 countries in 2005-2010.

Note 2: Expected sign is drawn from the previous studies shown in footnotes 4 and 6-13.
Table 2 Data for China and India

Variable	Country	1965-1970	1970-1975	1975-1980	1980-1985	1985-1990	1990-1995	1995-2000	2000-2005	2005-2010
Annual growth rate of China	0.1036	0.0732	0.0862	0.1019
per capita GDP	India	0.0225	0.0055	0.0071	0.0276	0.0360	0.0299	0.0408	0.0501	0.0638
Log of initial per capita GDP	China	5.971262	6.489205	6.855409	7.286192
India	5.26269	5.375278	5.402678	5.438079	5.575949	5.755742	5.905362	6.109248	6.359574
Change in terms of trade	China	0.000000	-0.003961	-0.027393	-0.023844
India	-0.027248	-0.012443	-0.063016	0.024671	0.011514	0.046022	-0.015392	0.009758	0.038045
Inflation rate	China	0.1210	0.0174	0.0134	0.0280
India	0.0622	0.1114	0.0388	0.0892	0.0746	0.1000	0.0728	0.0390	0.0837
Total fertility rate	China	2.12	1.81	1.71	1.64
India	5.69	5.32	4.92	4.52	4.14	3.76	3.35	2.99	2.74
Government consumption ratio	China	15.2	14.4	15.2	13.7
India	8.91	9.47	10.1	10.5	12.1	11.5	11.8	11.8	10.9
Investment ratio	China	39.3	38.8	38.8	43.8
India	15.0	16.1	18.8	18.9	21.8	23.5	25.1	26.6	35.9
External openness ratio	China	36.0	38.0	51.5	63.7
India	9.04	8.43	12.9	14.1	13.1	17.8	22.8	29.6	45.9
1/(Life expectancy at birth)	China	0.014306	0.014124	0.013966	0.013774
India	0.021231	0.019802	0.018587	0.017825	0.017361	0.016978	0.016529	0.016051	0.015601
Democracy index	China	1.5	1.5	1.5	1.5
India	9.5	9.5	9.0	9.0	9.0	9.0	9.5	9.5	9.5
Upper-level schooling years	China	1.398	1.854	2.298	2.706
India	0.211	0.273	0.522	0.785	0.957	1.150	1.273	1.432	1.614
Urban agglomerated population ratio	China	14.19	17.74	23.64	27.32
India	9.97	10.63	11.41	12.29	13.06	14.01	14.84	15.85	16.72
Urban population ratio	China	26.44	30.96	35.88	42.52
India	18.79	19.76	21.33	23.10	24.35	25.55	26.61	27.67	29.24
Table 3

Regression for annual growth rate of per capita GDP

Independent variable	(1)	(2)	(3)
Log of initial per capita GDP	-0.010678665	-0.010478348	-0.009753098
(6.25)***	(6.42)***	(6.95)***
Change in terms of trade	0.099725032	0.100014692	0.100387293
(4.10)***	(4.14)***	(4.17)***
Inflation rate	-0.016248543	-0.016156654	-0.015365661
(3.43)***	(3.44)***	(3.32)***
Total fertility rate	-0.006823	-0.006881247	-0.006765639
(4.76)***	(4.78)***	(4.75)***
Government consumption ratio	-0.000667124	-0.000632891	-0.000664318
(2.54)**	(2.45)**	(2.51)**
Investment ratio	0.000745331	0.000739132	0.000738823
(2.98)***	(2.98)***	(2.96)***
External openness ratio	5.77231E-05	5.58079E-05	5.69362E-05
(2.42)**	(2.36)**	(2.35)**
1/(Life expectancy at birth)	-2.21803	-2.22951	-2.28121
(3.01)***	(3.02)***	(3.05)***
Democracy index	-0.011100604	-0.010942424	-0.010946744
(2.56)**	(2.53)**	(2.59)**
(Democracy index)²	0.002190142	0.002151512	0.002176494
(2.39)**	(2.34)**	(2.41)**
(Democracy index)³/100	-0.012269806	-0.011975205	-0.012325218
(2.19)**	(2.12)**	(2.23)**
Upper-level schooling years	-0.005846181	-0.005448386	-0.00504295
(1.80)*	(1.78)*	(1.60)
(Upper-level schooling years)²	0.000986954	0.000923958	0.000896137
(2.39)**	(2.39)**	(2.25)**
Urban agglomerated population ratio	8.43491E-05
(1.03)
Urban population ratio	8.12123E-05
(0.99)
1965-1970 dummy	0.004384338	0.004394625	0.00421406
(0.95)	(0.96)	(0.91)
1970-1975 dummy	-0.002581883	-0.002627022	-0.002890901
(0.49)	(0.50)	(0.55)
1975-1980 dummy	-0.004942937	-0.005036779	-0.005341155
(0.86)	(0.88)	(0.93)
1980-1985 dummy	-0.030577011	-0.030673538	-0.031098867
(5.98)***	(6.04)***	(5.98)***
1985-1999 dummy	-0.019757402	-0.019840701	-0.020197373
(3.07)***	(3.11)***	(3.10)***
1990-1995 dummy	-0.024792394	-0.024779299	-0.025009051
(4.34)***	(4.36)***	(4.36)***
1995-2000 dummy	-0.022823731	-0.02272799	-0.022842623
(3.86)***	(3.88)***	(3.86)***
2000-2005 dummy	-0.018111016	-0.017823258	-0.018236434
(3.03)***	(3.03)***	(3.05)***
2005-2010 dummy	-0.026234225	-0.025882281	-0.026401349
(4.06)***	(4.06)***	(4.09)***
Constant	0.18621079	0.185897317	0.1832629
(7.35)***	(7.36)***	(7.46)***
Observations	651	651	651
Adj. R-squared	0.37	0.37	0.37

Cluster-robust t statistics in parentheses

* significant at 10%; ** significant at 5%; *** significant at 1%