Physical and Human Capital Formation, Exports, and Long-term Economic Growth: A

Causality Analysis for China

Zhongyi Tang

Introduction

In the past few decades, China has experienced dramatic economic growth. Many literature

tries to examine why China has grown so fast in order to generalize this example for other

developing countries to study. Some of them suggest that opening up the market and outward

trade policy increased economic growth(McNab and Moore(1998)). Essentially, the major

idea is that there is bidirectional causality existing between exports, FDI and economic

growth( Shan and Sun(1998), Liu, Burridge and Sinclair(2002), Mah(2005)). However, other

literature argue that it is not just a export-led growth or investment-led growth story, but other

additional factors, like investment in physical capital and R&D, also accounts for China’s

growth(Herrerias and Orts(2010)). Meanwhile, other literature took a newer standpoint and

looked at the impact of overall capital accumulation, not just physical capital but human

capital, on economic growth. They found the causal relationship among human capital

accumulation, exports, and economic growth (Chuang(2000)).

Another literature has also done thorough analysis of the role of physical and human capital

formation. Ding and Knight(2011) uses cross-province dataset spanning three decades to

explain why China, as a whole, and indeed all its provinces, has grown so fast. They found

that fixed capital investment and secondary school enrollment are positively correlated with

growth in GDP per capita. The results provide evidence of conditional convergence over

reform period. One possible explanation for conditional convergence is that relatively poor

provinces have lower stocks of physical and human capital, so that the marginal product of

capital is higher investment in capital construction and investment in innovation have

significant impacts on growth. Investment and investment-driven improvement in technology

are important for China’s growth. The results suggest that holding other variable constant, a

one percentage increase in the ratio of enrollment in higher education to population leads to

higher GDP per capita growth by 3.6 percentage point.If private fixed investment had

remained at its 1978 level and secondary school enrollment reduce to half, China’s growth

rate would have been down to 1.2%.so, both the quantity and composition of physical and

human formation are potentially important to China’s rate of economic growth. In addition,

Grossman and Heplman (1993) explaines that in endogenous growth theory, international

trade, especially exports, is viewed as an important source of human capital augmentation,

technological change and knowledge spillover across countries.

Since most paper perform time series analysis concerning the causal relationship among

export, FDI and economic growth and Ding and Knight(2011) used panel data, then there is

few literature that has conducted time series analysis on exports, physical and human capital

accumulation. This paper investigates the long term relationship among economic growth,

exports, physical capital formation and human capital accumulation and potential causal

relationship among them in the case of China. To examine the long-term relationship, the

Johansen cointegration test is performed and if there exists at least one cointegrating vector,

then Vector Error Correction Model can be run to see whether there is a short-term

equilibrium.

The paper is followed by the theoretical framework, unit root test analysis, cointegration

analysis, causality test and conclusion.

Theoretical Framework

To examine the long-term relationship among economic growth, exports, physical capital

formation and human capital accumulation, OLS regression should be run on the following

model:

f(GDP) = f(exports, physical capital, human capital)

However, since they are all macro variables and may be nonstationary, which causes the

regression to be spurious, we need to perform unit root tests and if we can find cointegration

among them, then a short-run model can be obtained by VECM.

The sample has period from 1960 to 2013. The data of GDP and physical capital is from

World Bank and the data of exports and human capital is from China Data Center.

To measure human capital, there are two choices of variables: Secondary Education(SEC)

and Higer Education (UGRAD). SEC is defined as the number of regular secondary

enrollment per million. UGRAD is defined as the number of undergraduate per million

populations.

The export variable, EXPORT, is defined as export as the percentage of GDP.

The economic growth variable, GDP, is defined as GDP per capita.

The physical formation variable is measure by gross fixed capital formation (% GDP).

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

60 65 70 75 80 85 90 95 00 05 10

GDP

From the plot above, we can see GDP with the shape of exponential growth, so we adopt the model by

taking the log. Therefore, LGDP, instead of GDP, is used in the rest of the paper.

0

400

800

1,200

1,600

2,000

60 65 70 75 80 85 90 95 00 05 10

SECONDARY

Also, the plot of SEC seems to have very turbulent number and outliers, so we should take the log of SEC.

Therefore, variable LSEC are used in the rest of the paper.

Unit Root Test Analysis

TABLE 1. Unit Root Test

ADF PP KPSS Zivot-Andrews

LGDP 7.0257 -4.0813** 0.2527 ** -6.9214**

EXPORT 2.7268 2.7268 0.2129 ** -4.1486

GFCF -3.8932 ** -5.7175** 0.1294 -5.4921**

LSEC -4.1212 ** 0.8229 0.0989 -5.6545**

UGRAD -0.8594 0.2403 ** -4.1205

D(LGDP) -3.8363 ** - 0.1751** -7.6354**

D(EXPORT) -6.2960 ** -6.4260** 0.0465 -8.7700**

D(GFCF) - - -

D(LSEC) - - -

D(UGRAD) -3.2331** 0.0894 -6.6867**

Note: ** denotes significance at 5% level.

The critical values for 1%,5%,10% of ADF test are, respectively, -2.61, -1.95 and -1.62.

The critical values for 1%,5%,10% of KPSS test are, respectively, 0.216, 0.146 and 0.119.

The critical values for 1%,5%,10% of PP test are, respectively, -4.141, -3.4969 and -3.1775.

The critical values for 1%,5%,10% of Zivot-Andrews test are, respectively, -5.57, -5.08 and -4.82.

Since all four variables, LGDP, EXPORT, GFCF, and LSEC, are all macro variables and by

looking at their plots over time, we suspect that they might not be stationary. Nonstationarity

could potentially cause spurious regression. As a result, ADF, PP, KPSS and Zivot-Andrews

unit root tests are performed on every variable. This paper follows the Doldado-Sosvilla

procedure to determine whether constant or trend will be included.

When we perform four different unit root tests on the variable, LGDP, ADF test without

constant or trend indicates that we fail to reject the null hypothesis and it appears that the

time series is nonstationary in the level form, which is consistent with confirmatory KPSS

unit root test with both constant and trend. By taking first difference, ADF shows that LGDP

becomes stationary. However, PP test with constant and trend and Zivot-Andrews test with 1

lag suggest that we can reject the null hypothesis of having an unit root and it seems that

LGDP is stationary. In addition, KPSS test suggests that LGDP in the first difference form is

still not stationary (0.1751>0.146). Therefore, we obtain mixed results and since PP test

corrects for the potential serial correlation and Zivot-Andrews takes structural break into

account, then these two tests are more powerful and it seems that LGDP is integrated of order

zero.

From the table above, we can see that results from four unit root tests on export variable are

very consistent. Results from ADF test without trend or constant, PP test without trend or

constant, and Zivot-Andrews test on the level of export leads to failure to reject the null

hypothesis of not having an unit root. In the KPSS test with both constant and trend on the

level form of export, we reject the null hypothesis of stationarity. Therefore, it seems that

variable EXPORT is nonstationary. By taking the first difference, we can then reject the null

hypothesis of ADF, PP and Zivot-Andrews unit root tests and it appears that the first

difference is stationary, so EXPORT is integrated of order one. Meanwhile, KPSS test is run

to confirm that export in the first difference form is stationary.

The results from four unit root tests on variable, GFCF, are also very consistent. ADF, PP,

and Zivot-Andrews tests suggest that we fail to reject the null hypothesis and GFCF seems to

be stationary in the level form. For the variable, LSEC, results from ADF and Zivot-Andrews

test suggest that we reject the null hypothesis of having an unit root, which is confirmed by

KPSS. However, PP unit root test suggests that we fail to reject the null hypothesis. As data

itself is turbulent, then inconsistent unit root test results are expected. There exists multiple

structural breaks in the time period of the data, so in this case, Zivot-Andrews test is a more

powerful test and it seems that LSEC is integrated of order 1.

Lastly, for variable, UGRAD, there are consistent results from four different unit root tests.

ADF, PP and Zivot-Andrews tests indicate that we fail to reject the null hypothesis and

UGRAD seems to be nonstationary in the level form. Result from KPSS confirmatory test

allows us to reject the null hypothesis of stationarity. Therefore, it seems that UGRAD is

nonstationary in the level form. However, from the table, we can see the first difference of

UGRAD is stationary since we reject the null hypothesis of having an unit root in the ADF,

PP and Zivot-Andrews test and fail to reject the null hypothesis of not having an unit root in

KPSS. Thus, KPSS seems to be integrated of order one.

Since some variables are not stationary in the level form, then ordinary least square

regression may be spurious. We then want to know whether there exists long-term

relationship between them so that the combination of I(1) variables becomes I(0). Even

though from the unit root analysis, variables are found to be integrated of order 0 or 1, we

still can perform cointegration analysis because Johansen Cointegration methodology can

handle variables with different integrated order.

Cointegration Analysis(1)

From previous sections of theoretical framework, we use two different variables to measure

human capital accumulation: LSEC(the enrollment of Secondary Education) and

UGRAD(the number of undergrad per million). Therefore, the cointegration analysis is

perform on two different models.

The first cointegration analysis attempts to examine the long-term relationship between

LGDP, EXPORT, GFCF and LSEC. By running VAR models on these four variables, we

select lag =2 as the optimal lag length by comparing Schwartz criterion. Then, Johansen

cointegration tests are perform with exogenous dummy variables.

TABLE 2.

Trace Maximum Eigenvalue

M2 M3 M4 M2 M3 M4

None 66.71* 50.79* 82.735* 30.176* 30.18* 42.46*

At most 1 35.95* 20.61 40.27 21.29 15.085 29.73*

At most 2 14.65 5.526 10.53 14.05 5.19 8.71

Following Pantula principle, we can see from table above that trace and maximum eigenvalue

lead to two different model selections: model 2 with two cointegrating vectors or model 4

with two different cointegrating vectors. Since model 4 implies intercept in both CE and VAR

and linear trend just in CE, then by the nature of the variables, we believe model 2 is a better

fit.

VECM(1)

Since we have shown that there is long-term relationship between LGDP, EXPORT, GFCF

and LSEC, we can obtain the short-term relationship by running Vector Error Correction

model(See full model in Appendix).

TABLE 3. Long-term model

Cointegrating Eq: CointEq1 CointEq2

LGDP(-1) 1.000000 0.000000

EXPORT(-1) 0.000000 1.000000

GFCF(-1) 0.455663 -40.68290

[ 1.65658] [-2.39251]

LSEC(-1) -7.435910 493.5649

[-2.64345] [ 2.83828]

C 36.33118 -2466.223

[ 2.95673] [-3.24667]

Since coefficients in the table above are normalized, we should interpret the coefficients with

reverse signs. Then, it seems that the relationship between economic growth and physical

capital accumulation is negative, which does not make economic sense. VECM takes all

variables as endogenous variables, but they might not be. So, we can use Johansen test again

to test for weak exogenousity. By imposing restrictions, we found out that variables EXPORT

and LSEC to be weakly exogenous.

With the context of economic theory, we infer that the first cointegrating relationship exists

among LGDP, EXPORT, and LSEC because export usually encourages economic growth and

increase the return of skilled labor, which implies increasing return of education investment

and motivates the enrollment rate of secondary education. The second cointegrating

relationship exists between LGDP and GFCF since they are both endogenous in the model.

Then, from the table below, we can tell that by controlling both EXPORT and LSEC as

weakly exogenous, in the first cointegrating equation, the relationship among LGDP,

EXPORT, and LSEC is positive. In the second cointegrating equation, the relationship

between LGDP and GFCF is positive.

TABLE 4.

Cointegrating Eq: CointEq1 CointEq2

LGDP(-1) -2.840866 -0.109676

EXPORT(-1) -0.036376 0.019702

GFCF(-1) 0.555476 -0.153213

LSEC(-1) -1.601520 1.210056

C 10.84598 -4.819603

The short-term model is determined by the lowest Schwartz SC and we get:

D(LGDP)=-0.015*EC1-0.0187*EC2+0.1873*D(LGDP(-1))+0.001503*D(EXPORT(-1))+0.

008547*D(GFCF(-1))+0.016248*D(LSEC(-1))+0.068*D1+0.041*D2-0.0155*D3

From equation above, we know the adjustment rate of two cointegrating equations are

respectively 1.5% and 1.87% of the deviation from LGDP every year.

Granger Causality(1)

By Granger Causality Block Test, we only find GFCF granger cause LGDP under the

significance level of 5%. It implies physical capital formation motivates economic growth.

Dependent variable: D(LGDP)

Excluded Chi-sq df Prob.

D(EXPORT) 0.271971 1 0.6020

D(GFCF) 5.194262 1 0.0227

D(LSEC) 0.154165 1 0.6946

All 5.525557 3 0.1371

Cointegration Analysis(2)

The second cointegration analysis attempts to examine the long-term relationship between

LGDP, EXPORT, GFCF and UGRAD. By running VAR models on these four variables, we

select lag=2 as the optimal lag length by lowest Schwartz criterion.

Trace Maximum Eigenvalue

M2 M3 M4 M2 M3 M4

None 70.31* 44.54 59.19 30.29* 20.93 23.5

At most 1 40.02* 23.62 35.67 20.78 13.39 20.46

At most 2 19.23 10.224 15.21 13.35 9.76 13.34

Following Pantula principle, trace stat and maximum eigenvalue suggest that model 2 (only

intercept in CE) should be chosen, but they suggest different number of cointegrating vectors.

However, they both indicate that there exists a least one cointegrating vector. Therefore, we

know there must be long-term relationship between LGDP, EXPORT, GFCF and UGRAD.

Then, we proceed to test on short-term relationship with VECM.

VECM(2)

By running Vector Error Correction Model, we get

LGDP EXPORT GFCF UGRAD

1 0.002 -0.1174 -0.000461

(-0.32) (-2.99) (-0.48)

Since results are normalized, it means all else equal, export influences LGDP negatively.

However, it is not statistically significant. Also, we assume all four variables are endogenous,

which may not be true. As a result, we can use Johansen test to test for weakly exogenousity.

By imposing restriction on the VECM, it seems that EXPORT and UGRAD are weakly

exogenous. Then, we get the following long-term relationship:

LGDP EXPORT GFCF UGRAD

1 0.145 -0.193 -0.00211

(1.43) (-3.05) (-1.36)

The coefficient of export suggests the negative relationship between export and LGDP, but

again, it is not statistically significant. Meanwhile, the negative relationship can be explained

the way we defined export as shares of GDP and increasing share of export in GDP is not

necessarily a good thing. The variable, UGRAD, is not statistically significant, but the

coefficient implies the positive impact of UGRAD on LGDP. Since the best fit short-term

model is the one with lowest Schwarz SC, then the dependent variable of the short term

model is D(LGDP). However, the coefficient for the error correction term is positive. It

implies there is no short-term equilibrium existing between LGDP, EXPORT, GFCF and

UGRAD.

Granger Causality(2)

Dependent variable: D(LGDP)

Excluded Chi-sq df Prob.

D(EXPORT) 1.197185 2 0.5496

D(GFCF) 1.887805 2 0.3891

D(UGRAD) 6.339824 2 0.0420

All 10.98008 6 0.0890

Dependent variable: D(EXPORT)

Excluded Chi-sq df Prob.

D(LGDP) 1.357263 2 0.5073

D(GFCF) 3.607239 2 0.1647

D(UGRAD) 15.09940 2 0.0005

All 25.00246 6 0.0003

Dependent variable: D(GFCF)

Excluded Chi-sq df Prob.

D(LGDP) 8.155066 2 0.0169

D(EXPORT) 0.161257 2 0.9225

D(UGRAD) 2.809167 2 0.2455

All 10.78260 6 0.0953

From Table above, UGRAD granger cause LGDP and EXPORT. LGDP granger cause GFCF.

It implies that the increasing number of people with undergraduate degree helps economic

growth and export. To have sustainable growth, export is transiting from selling cheap,

industrialized products into selling products with higher technology content. Meanwhile,

LGDP granger cause GFCF, which indicates that good economy performance has a positive

impact on fixed capital formation, which is also physical capital accumulation.

Conclusion

By using different measurements of education, we examine whether long-term relationships

exist in two different. Essentially, the question we are asking is that whether there are

long-term relationship among economic growth, export, physical capital accumulation.

Johansen cointegration tests indicate that the long-term relationship exists no matter which

measure we use to capture human capital accumulation. In the case of China, rapid growth in

export and growth in physical capital formation have contributed to economic growth.

When we use enrollment in secondary education per million to measure human capital

accumulation, we do not find it cause economic growth but find this education attainment

variable is determined by other variables. However, we have found clear evidence that

physical capital accumulation motivates economic growth.

When we use number of undergraduate per million population as a measure of higher

education attainment, we find that more people with a undergraduate degree motivates

economic growth. In other word, higher human capital accumulation, especially in higher

education, can be a new source of motivation for China to grow rapidly. After all, even

though the number of undergraduate has increased significantly in these few decades, the

ratio of number of undergraduate to population in China is still much lower than most

developed countries. In the second model, we also find that increase economic growth leads

to more physical capital accumulation, which can be explained by the fact that good economy

attracts both foreign investors and domestic investor.

One important message from this paper is that we do not see clear causality between export

and economic growth. It agrees with some of the literature that the rapid growth in China

need more explanation other than simply export-led growth theory. In the long-term, export

could not sustain the rapid growth and it even may cause imbalance of current account.

Moreover, the importance of human capital accumulation, especially in higher education, is

overlooked. Even though increased percentage of the population who have enrolled in a

secondary school implies a strong base for skilled labor, which gives an advantage to exports,

population with higher education is a larger momentum for continuing economic growth.

After all, China is “shifting away from investment towards consumption”. Moreover,

technology innovation and entrepreneurship are greatly encouraged by the government. It is

not hard to see that human capital accumulation of higher education will be crucial for China

to keep current growth rate or even have a higher growth rate.

There is more room this paper can improve. First, the variable for secondary education only

measures the number of enrollment into secondary school. This number is actually influenced

by many other factors, like one-child policy. However, the variable that measures the ratio of

people with at least secondary school degree to the population does not have data available

for 1960-2013. Second, during the time period of the sample, many important events have

happened and changed the structure of the market and economy. We used three dummy

variables to capture the effect, but it will make more economic sense to study the period after

1978 since before 1978, China economy is closed. If there are more advanced techniques to

control for the break or there are more available data, the conclusion will be more

convincing.

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