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The economic growth of a nation hinges on its growth of the stock of physical, and human capital and the

level of technology it uses in the production of goods and services. Growth in physical capital stock is

generally considered an important determinant of economic growth but the growth theories predict that

The attributes of workers that can potentially enhance their productivity in any productive activity are called

human capital. Workers accumulate these attributes mostly through investments. Becker (1965) and Mincer

(1984) developed the early human capital theories. These theories explain the role of human capital in the

production process and the incentives to invest in skills, in the form of schooling, on-the-job investments,

and training. Their analysis emphasizes the productivity-enhancing role of human capital.

tasks, but to help workers cope with changes, disruptions and especially the adoption of new technologies.

This literature found a stronger correlation between economic growth and levels of human capital than

between economic growth and changes in human capital. Benhabib and Spiegel (1994) suggest that this

may be for the reason that the most important role of human capital is not to increase the productive capacity

in current activities but to facilitate the adoption of new technology.

Human capital represents people's investment in acquiring skills, education and training that raise their

productivity. The theory that explains the economic behaviour of people towards the acquisition of

education and training as an investment is called human capital theory. Human capital theories given by

in human capital enhances the productivity of other factor inputs which raises economic growth. Their

models explain that the rate of economic growth depends on the rate of human capital accumulation.

Narayan & Smith (2004) found that human capital, income and export are co-integrated when export is

used as a dependent variable, but they are not co-integrated when human capital or income is used as a

dependent variable.

Thus, in economic growth literature, both bi-directional and unidirectional causality is suggested between

human capital and economic growth.

The neoclassical growth models brought the role of technology into prominence for long-run economic

cause technological changes. Scientific research and education are complements and reinforce each other.

They are fountainheads of all types of innovations in a country. For a country with a large educated

population base, it is much easier to learn, disseminate and adopt any new knowledge or innovation. India

is one of the few countries which have successfully developed a big educated population base by adopting

the policy of free and compulsory education for all children till the age of 14.

Hence, we aim to analyze if India has reaped the benefits of high economic growth from the policy of

expanding education by providing free and compulsory education to its populace.

The primary objective of this article is to test causal relationships between physical capital, human capital

Firstly, it uses the modern econometric technique of the ARDL bound testing model developed by Pesaran

& Shin (1999) and Pesaran et al., (2001) to examine the long-run relationship among the above three

variables. Secondly, it uses the Penn World Table data on the human capital index which is much broader

than any other measure of it, as a substitute for human capital. Finally, it uses time series observations

which are long enough to validate the estimated parameters.

variables. In section 3, we describe the variables included and how they have been constructed, the data

economic growth in France, the United Kingdom, Sweden, and Japan as well as a bidirectional relationship

in Italy and Australia.

Bils & Klenow (2000) also addressed the relationship between the above two variables and found that, in

the cross-country correlation, the causal impact of education on economic growth is as strong as the reverse

In both Pakistan and India, Abbas (2000) discovered a large and positive correlation between human and

material capital. Using the impulse response function, Haldar & Mallik (2010) discovered that investments

in education had a positive and statistically significant influence on investments in health and increase GNP

per capita. Tamura (2006) discovered that the young adult death rate was favourably correlated with the

fertility rate, and adversely correlated with both education level and rate of return from education.

Hanushek (2013) contends that raising educational standards help emerging countries prosper economically

over the long term. According to Zang & Lihuan (2011), postsecondary education is more crucial for

boosting China's economic growth than primary or secondary education.

The time series data on Gross Domestic Product (GDP) at constant 2011 national prices (in mil. 2011 US$),

Physical Capital (PC) stock at constant 2011 national prices (in mil. 2011 US$), and Human Capital (HC)

index, based on years of schooling and returns to education for the period 1972-2019, are analyzed in this

article. Each of these three variables was transformed into the natural log and denoted by the letters y, pc,

and hc, respectively. The data on all of the aforementioned variables were compiled from the Penn World

Tables, version 10.01 (Feenstra et al., 2015).

To perform the bounds test of co-integration among the variables y, pc and hc, the conditional ARDL error

correction model involving variables y, pc and hc are specified as follows:

Hypotheses:

We estimate the Toda & Yamamoto (1995) test of causality between variables if they are cointegrated based

on the aforementioned relationships. The extended VAR model, which serves as the foundation for this

test, is defined as follows:

where dmax is the maximum order of integration of a variable among all the variables.

applied on the time series data of each variable. Both the tests show that only y is stationary at the first

difference while the other two variables are not stationary at either level or the first difference (table 1).

* Shows level of significance at 1% and ** at 5%.

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However, all the three variables are found to be stationary at the first difference when we apply

Zivot-Andrews (Zivot & Andrews, 1992) unit root test allowing for one break in both intercept & trend.

Hence, we find that the ARDL modelling is appropriate for examining a long-run relationships between

these variables (Table 2).

*& ** denote the level of significance at 1%. & 5% respectively. Lags selected by the BCI criterion are

given in the brackets.

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For applying the ARDL model, variables must be integrated maximum of order 1. We applied Augmented

statistic reveal that there is co-integration among the variables only when y is used as a dependent variable.

The F-statistic value of 7.43961 with y as the dependent variable is higher than the 5% I(1) critical bound.

Because y is the dependent variable, the null hypothesis that there is no long-run link between y, pc, and hc

is rejected. The F-statistic value of 3.85872 with pc as the dependent variable is below the 5% I(0) critical

bound. Since pc is the dependent variable, we could not reject the null hypothesis that there is no long-term

link between y, pc, and hc. Similar to this, the value of F-statistic 2.99925 with hc as the dependent variable

is below the 5% I(0) critical bound. As a result, the test does not successfully refute the null hypothesis that

there is no long-term link between the three variables (Table 3).

For checking the validity of the ARDL model involving co-integrated variables, we estimate the ARDL

(8, 4, 8) Error Correction model and apply the diagnostics check for the model adequacy. Table 4 displays

the outcomes of the error correction model. For the confirmation of a long-run relationship between the

three variables y, pc, and hc with y as the dependent variable, the value of the Error Correction Term (ECTt-

1) coefficient  in equation (7) must be negative and significant (Table 4).

The value of coefficient of the error correction is -0.99210 which is negative as expected and also

statistically significant at 1%. Moreover, the absolute value of it is very close to 1. Hence, the results of the

estimated Error Correction Model validate the long-run relationship among these three variables (Table 4).

The table below shows the findings of the long-term associations between the three variables. The pc and

hc coefficients are positive as predicted and significant at 1%. As a result, pc and hc have a positive

relationship with y. To put it another way, increasing physical and human capital has a favourable effect

on economic growth (Table 5).

of the recursive residuals. It displays cumulative sum plots with 5% critical lines. If the graph of the

cumulative total passes any of the two critical lines, this test shows parameter instability. The 5%

total factor productivity, driven by, among others, knowledge and technology transfers due to trade