ISSN 1471-0498

DEPARTMENT OF ECONOMICS

DISCUSSION PAPER SERIES

CAN THE AUGMENTED SOLOW MODEL EXPLAIN CHINA’S ECONOMIC GROWTH? A CROSS-COUNTRY PANEL DATA

ANALYSIS

Sai Ding and John Knight

Number 380 January 2008

Revised February 2008

Manor Road Building, Oxford OX1 3UQ

1

Can the Augmented Solow Model Explain China's Economic Growth? A

Cross-Country Panel Data Analysis

Sai Ding

Department of Economics

University of Oxford

Manor Road Building

Oxford OX1 3UQ

Email: sai.ding@economics.ox.ac.uk

and

John Knight

Department of Economics

University of Oxford

Manor Road Building

Oxford OX1 3UQ

Email: john.knight@economics.ox.ac.uk

Abstract China's economy grew at an average annual real growth rate of 9 percent over the

last three decades. Despite the vast empirical literature on testing the neoclassical model of

economic growth using data on various groups of countries, very few cross-country

regressions include China and none of them particularly focuses on the explanation of China's

remarkable economic growth. We attempt to fill this gap by utilizing panel data on 146

countries over the period 1980-2000 to examine the extent to which the growth difference

between China and other countries can be explained by the augmented Solow model. The

estimates are based on system GMM estimation which allows for unobserved country-

specific effects, measurement error, and endogeneity problems of regressors. We find that, in

spite of the restrictive assumptions involved, the Solow model augmented by both human

capital and structural change provides a fairly good account of international variation in

economic growth. In particular, physical capital investment, changes in the structure of

employment, conditional convergence, and population growth are the main sources of the

growth difference between China and many other countries.

Keywords China; Augmented Solow model; Cross-country growth regression

JEL Classification O11 ∙ O47

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1. Introduction

Few countries have been able to match the pace of China's sustained economic growth.

Since the start of economic reform in 1978, China has maintained a remarkable growth rate.

According to official Chinese statistics, the average GDP growth rate during the period 1979-

2000 was 9.2%, and it accelerated to 10.1% between 2000 and 2006. Despite the controversy

over the reliability of the official figures of real output growth, the fact that China has grown

fast is beyond dispute. Being the world's largest developing country, with one-fifth of the

world population, China's growth has contributed significantly to the reduction of global

income poverty and inequality by lifting over 200 million people out of $1 per day poverty in

the past three decades.

While China's economic growth over the reform period has received much attention in

the economic literature, research has focused mainly on relatively narrow topics such as

issues of growth convergence or divergence among provinces, determinants of cross-

provincial growth variation, and assessment of the sustainability of China's growth, all of

which are based on data for China only. Although these studies are crucial for understanding

the growth patterns within China, they can only hint at why China as a whole could grow so

rapidly and at the key factors driving the growth difference between China and other

countries.

This paper attempts to fill the gap in the literature by incorporating China into a cross-

country growth study based on a neoclassical framework. The distinguishing features of the

study are fourfold. Firstly, our preferred model is a revised cross-country specification of the

augmented Solow model which allows for cross-country differences in productivity growth

as measured by structural change. Secondly, we adopt the dynamic panel data approach to

control for unobserved country-specific effects and potential endogeneity and measurement

error problems of regressors in the growth regressions. Thirdly, by classifying countries at

similar levels of development into the same sample, we attempt to partially control for the

differences in technology and institutions and alleviate the problem of parameter

heterogeneity. Fourthly, by isolating the influence of potential outliers which are identified

using robust regression techniques, we are able to concentrate on the most coherent part of

the dataset. In brief, our efforts in allowing for international variations in productivity growth

and in dealing with the problems of parameter heterogeneity, measurement error, endogenous

regressors and outliers in the cross-country growth regression make the estimates consistent

and robust.

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We find that the augmented Solow model predicts China's economic growth rate

accurately, and there are four main determinants of China's relative success. Capital

formation has played a major role in China's economic growth, and this view of investment-

driven growth does not contradict out-of-equilibrium neoclassical growth theory. Economic

growth has been intertwined with productivity-enhancing structural change throughout

China's post-reform development process. Conditional convergence also contributes

significantly to growth differences between China and other countries. Lastly, the low

population growth rate resulting from the restrictive population policy makes an important

contribution to China's growth performance relative to many other developing countries.

The remainder of the paper is organised as follows. Section 2 briefly summarises the

neoclassical growth theory and its empirical formulation in a cross-country growth context,

which includes the textbook Solow model, the Solow model augmented with human capital,

and the augmented Solow model with structural change. Section 3 reviews the cross-country

empirical literature on the augmented Solow model. Section 4 provides some background on

China's economic reform and places its post-reform growth in comparative perspective.

Section 5 describes the data used for variable construction, sample classification, and

econometric methodology in estimating cross-country growth regressions. Section 6

interprets the estimation results for each model and predicts the growth difference between

China and the rest of the world. Section 7 draws conclusions.

2. Solow model in the cross-country growth regressions

2.1 The textbook Solow model

The Solow (or neoclassical, or exogenous) growth model has been widely used as a

theoretical framework for understanding cross-country growth patterns. By assuming

diminishing returns to capital and exogenous rates of saving, population growth and

technological progress, the model predicts that the long-run economic growth rate is

exogenously determined by the rate of technological progress and that adjustment to stable

steady-state growth is achieved by endogenous changes in factor accumulation.

Following the modern empirical growth literature, starting with the framework of

Mankiw, Romer and Weil (1992), hereafter MRW, the Cobb-Douglas production function

with constant returns to scale can be written as

, (2.1)

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where is output, is capital, is labour, is labour-augmenting technological progress,

and is the share of capital in total output. and are assumed to grow exogenously at rates

and respectively, so that

(2.2)

. (2.3)

Assuming that is the constant fraction of output that is saved and invested, and defining

output and stock of capital per unit of effective labour as and ,

respectively, the evolution of is given by

, (2.4)

where is the rate of depreciation. It is evident that converges to its steady state value

. (2.5)

The steady-state capital-labour ratio is related positively to the saving rate and negatively to

the population growth rate. Solving the equation for the steady state, substituting (2.5) into

the production function and taking logs, gives steady-state income per worker as

. (2.6)

In the Solow version of the neoclassical model, the steady state income level of a country is

thus determined by the country's saving and labour force growth rates and parameters of

technology.

MRW assumed that efficiency growth ( ) and depreciation rate of capital ( ) are the

same across countries, but allowed the initial level of efficiency to vary randomly

across countries owing to differences in resource endowments, technology, institutions,

climate, and so on. Their justification for a common rate of technical progress across

countries is that technology, as a public good, is freely available to individuals and can be

transferred instantaneously across national borders. However, despite being a useful

simplification, this assumption contradicts the fact that diffusion of new technology can be

costly or time-consuming, especially for developing countries. Further discussion of this

assumption will follow. In order to capture the different initial levels of efficiency across

countries, MRW assumed that

, (2.7)

where is a constant and is a country-specific shock. Then the empirical specification of

steady-state income per worker is

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. (2.8)

Hence, according to MRW, differences in the steady state income levels across countries are

controlled for by the inclusion of saving and population growth rate variables in the

regression. Equation (2.8) assumes that all countries are currently in their steady states or that

departures from steady states are random across countries. However, this assumption might

be problematic in empirical testing, especially when a large number of developing countries

are included. It is of more interest to consider the equation describing the out-of-steady-state

growth behaviour.

One important short-run implication of the Solow model is conditional convergence,

which is derived from the assumption of diminishing returns to capital. The model predicts

that each economy converges to its own steady state and that the speed of this convergence

relates inversely to the distance from the steady state (Barro and Sala-i-Martin, 2004). Hence

a lower starting value of real income per worker tends to generate a higher growth in GDP

per worker, once the determinants of steady state are controlled for.

Let be the steady-state level of income per effective labour given by equation (2.8),

and let be the actual value at time . Approximating around the steady state, the speed of

convergence is given by

, (2.9)

where is the rate of convergence, given by . Then equation (2.9)

implies

, (2.10)

where is income per effective labour at some initial date. Subtracting from both

sides and substituting for leads to the following approximation

. (2.11)

Equation (2.11) is formulated in terms of income per effective labour, whereas in

implementation it has to be reformulated in terms of income per worker. Substituting the

following expression for income per effective labour

(2.12)

into equation (2.11) gives

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,

(2.13)

where and is the rate of convergence. Equation (2.13) captures the dynamics

of a country's growth rate towards the steady state. Thus, in the Solow model the growth of

income per worker is a function of the initial level of income and the determinants of the

ultimate steady state.

2.2 The augmented Solow model with human capital

In order to capture the explicit role of human capital in determining economic growth,

MRW augmented the Solow model by including accumulation of human capital as well as

physical capital. The Cobb-Douglas production function is specified as

, (2.14)

where is the stock of human capital, is the share of human capital in total output, and all

other variables are defined as before. The assumption implies that there are

decreasing returns to capital as a whole. MRW assumed that the fractions of income invested

in physical capital and human capital are constant at the rates of and respectively, and

that both types of capital depreciate at a common rate . The evolution of the economy is

determined by

(2.15a)

, (2.15b)

where , and are quantities per effective unit of labour.

Solving these equations for steady state gives

and . (2.16)

Substituting (2.16) into the production function and taking logs, gives steady-state income per

worker as

. (2.17)

Approximating around steady state, MRW showed that growth of output per worker in this

model is given by

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, (2.18)

where and the convergence rate is given by .

MRW also presented an alternative way to express the role of human capital in

determining economic growth. Combining (2.17) with the equation for the steady-state level

of human capital given in (2.16) yields an equation for economic growth per worker as a

function of the rate of investment in physical capital, the rate of population growth, and the

level of human capital as

, (2.19)

where is the steady-state level of human capital as defined by equation (2.16).

Therefore, MRW provided two possible ways to examine the effect of human capital

on economic growth. The first is to estimate the reduced form of the augmented model by

including the rate of human capital accumulation in the regression based on equation (2.18).

The second way is to estimate equation (2.19), in which the level of human capital is added to

the regressors. These alternative regressions predict different coefficients on the saving and

population growth variables.

2.3 The augmented Solow model with structural change

One major criticism of MRW's specification of the Solow model is that it is not

accurate to interpret the assumption of exogenous technology as a statement that technology

or total factor productivity (TFP) grows at the same exogenous rate in all countries (e.g.

Easterly and Levine, 2001; Gundlach, 2007; Klenow and Rodríguez-Clare, 1997; McQuinn

and Whelan, 2007). It is argued that models for growth in GDP per worker should allow

productivity growth to vary across countries.

Temple and Wöβmann (2006) developed an empirical model to examine the impact of

labour reallocation on aggregate productivity growth and they augmented the conventional

growth regressions based on the MRW framework so as to allow for structural change. Their

basic idea is that changes in the structure of employment will raise aggregate productivity

when the marginal product of labour varies across sectors. If the marginal product of labour is

lower in agriculture, then the movement of agricultural workers to sectors where the marginal

product is higher will raise total output. Since this additional output is produced without

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change in the total input of capital and labour, the reallocation of labour raises aggregate

productivity.

It is a general equilibrium model of production with two sectors (a rural agricultural

and an urban non-agricultural sector) and two factors (capital and labour). Total output is

given by

, (2.20)

where is the relative price of the urban sector good; and are output quantities in

agriculture and non-agriculture; and is a GDP price deflator.

The production function in each sector has constant returns to scale and is given by

, (2.21a)

, (2.21b)

where and are TFP in agriculture and non-agriculture respectively. Assuming that

workers are paid their marginal products gives

, (2.22a)

, (2.22b)

where and are wages in agriculture and non-agriculture respectively; and the

subscript denotes the partial derivative with respect to labour. Capital also receives its

marginal product in both sectors, i.e. , where is the rental rate on

capital and the subscript is the partial derivative with respect to capital.

This model assumes that any observed effects of reallocation arise because of marginal

product differentials and that the propensity to migrate depends on the ratio of wages in the

two sectors. Migration will cease when the intersectoral wage ratio falls to a level denoted by

, so the long-run migration equilibrium is

, (2.23)

where .

The relationship between the extent of structural change and wage ratio can be

expressed as

, (2.24)

where is the migration propensity, defined by , where is the share of

agricultural employment in total employment; and is the speed of adjustment to the long-

run equilibrium. The 'odds ratio' for migration is increasing in the wage gap between the two

sectors. Rearranging (2.24) gives

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, (2.25)

so the extent of current wage ratio can be deduced using information on the observed pace of

structural change. In this model, the wage differential varies across countries according to the

value of .

By assuming that the speed of adjustment ( ), the equilibrium differential ( ) and the

labour share in total output ( ) are constant across economies, Temple and Wöβmann

(2006) derived the following expression for the aggregate Solow residual

, (2.26)

where is the nominal output share for agriculture at time t, or ; is the

labour share in total output, or ; and is the share of non-agricultural employment

in total employment, or .

In the presence of an intersectoral wage differential, the aggregate Solow residual can

thus be decomposed as a weighted average of the sectoral TFP growth rates plus the 'growth

bonus' obtained by reallocating labour to a sector where its marginal product is higher. Since

the migration propensity is related to the extent of structural change as measured by ,

equation (2.26) implies a convex relationship between growth and structural change. The

intuition is that the growth impact of a given extent of structural change will be greatest in

those countries experiencing more rapid structural change, as these are also the countries in

which the intersectoral wage differential is greatest. Note that the two structural change terms

in equation (2.26) will disappear when there is no wage differential in equilibrium, ,

and the adjustment process in response to disequilibrium is instantaneous, .

Since it was not possible to measure capital stocks at the sectoral level, Temple and

Wöβmann (2006) treated sectoral TFP as unobservable and relied on a vector to capture the

cross-section variation in aggregate TFP growth that is not due to structural change, as

follows

, (2.27)

where is a vector of determinants of aggregate TFP growth including initial level of

aggregate TFP and regional differences in technology and institutions proxied by regional

dummies; and the structural change terms are defined as

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(2.28a)

. (2.28b)

Temple and Wöβmann (2006) then extended MRW's model by including the structural

change terms derived above to proxy the varying productivity growth across countries. Given

the Cobb-Douglas production technology in equation (2.14), TFP growth is equal to the

growth rate of efficiency ( ) times the exponent on the efficiency index ( ). In the

presence of wage differentials, TFP growth is a function of structural change terms as shown

in equation (2.27). Then the extension of MRW's model takes the form

, (2.29)

where is a vector of explanatory variables including rates of saving, physical and human

capital accumulation. Thus, the specification of equation (2.29) is a hybrid of the Solow

model with an aggregate production function and a two-sector framework with sectoral

product differentials. In such a two-sector world, aggregate efficiency is unlikely to be the

same for all countries, even when they have access to the same technologies.

Despite its approximations and limits, this model has a number of comparative

advantages. Firstly, compared with the conventional MRW models described in the first two

sections, equation (2.29) allows for cross-country variation in productivity growth by taking

into account the effect of labour reallocation between sectors with different productivity.

Secondly, unlike the use of accounting methods to measure TFP growth, this model does not

involve the task of measuring the capital stock, which might be problematic for developing

countries.

When replacing the assumption that the labour share in output, , is the same across

countries by an assumption that all countries have the same Cobb-Douglas technologies in

agriculture, Temple and Wöβmann (2006) constructed a second set of structural change terms

(2.30a)

, (2.30b)

where is the share of agriculture in total value added. This alternative set of structural

change terms adds , i.e. the share of agriculture in value added divided by the share of

employment.

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3. Literature Review

The simple theoretical framework provided by MRW has been very influential and

much cited in the cross-country growth regression literature. By assuming that the rates of

saving and population growth are independent of the residual term, MRW tested both the

textbook and augmented Solow model using OLS in a single cross-section regression

framework. They concluded that an augmented Solow model with accumulation of both

human and physical capital provides an excellent explanation for international income

disparities, i.e. about 80 percent of the cross-country variation in income per capita can be

explained using just three variables: population growth, and investment rates of physical and

human capital. Moreover, by examining the dynamics of the economy out of steady state,

MRW found evidence that countries converge to their respective steady states at about the

rate that the augmented Solow model predicts, holding population growth and capital

accumulation constant. Their results are based on three samples with a maximum of 98

countries over the period 1960-1985, but none of them includes China.

A large body of subsequent empirical research has been stimulated by MRW's seminal

work. Islam (1995) criticized their approach in two major aspects. First, the single cross-

section regression is unable to deal with the unobservable country-specific aspect of the

aggregate production function, thereby generating omitted variable bias. Second, the

justification for OLS estimation is not convincing because the ignored term - which

captures country-specific production technology, resource endowment, institutions and so on

- is very likely to be correlated with other explanatory variables in the regression. These two

effects produce an upward bias on the lagged output term and thus a downward bias in the

implied convergence speed. Therefore, Islam (1995) adopted a panel data approach, which

considers the growth process over shorter consecutive intervals, to study cross-country

growth in general, and the issue of convergence in particular, using MRW's sample. By

treating the differences in the initial efficiency term as fixed effects, Islam (1995) found

higher rates of conditional convergence and lower values of the elasticity of output with

respect to capital, which are more in conformity with their commonly accepted empirical

values. Contrary to MRW's key empirical result that differences in technical efficiency have

only a small role in explaining cross-country income variation, this study highlighted the role

of the term as an empirically important determinant of the steady state level of per

capita income. However, although the use of panel techniques to control for the country-

specific effect represents an advance, the within-group estimator may also provide biased and

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inconsistent estimates in a dynamic panel data model with finite time series observations, due

to the correlation between the transformed error term and the lagged dependent variable.

Caselli et al. (1996) highlighted another source of inconsistency in MRW's work. They

argued that at least a subset of the explanatory variables are expected to be endogenous, and

that this problem may lead to unreliable estimated coefficients and convergence rates. They

therefore recommended using a panel data, generalized method of moments (GMM)

estimator to take into account both the omitted variable and endogeneity bias in the cross-

country growth regressions. By focusing on a subsample of 97 countries of Barro and Lee's

(1994) dataset for the period 1960-85 (excluding China), they found that correcting for both

biases in the augmented Solow model induces a significant jump in the estimate of

convergence rate from 2-3 percent to about 10 percent per annum. They suggested that the

high rate of convergence implied by the first-differenced GMM estimator favours an open

economy version of the neoclassical growth model, with high factor mobility.

Bond et al. (2001), however, claimed that the first-differenced GMM estimator can be

poorly behaved in the cross-country growth regressions because lagged levels of the variables

are only weak instruments for subsequent first-differences when the time series are persistent

and the number of time series observations is small. They interpreted the high convergence

rates obtained by Caselli et al. (1996) as the result of the serious bias on the initial income

term created by the first-differenced GMM estimator in the presence of weak instruments.

Bond et al. (2001) then recommended using a more efficient system GMM estimator in the

empirical growth literature. Interestingly, using the same dataset as Caselli et al. (1996), their

system GMM results of the augmented Solow model indicated a rate of convergence around

2 percent per annum, which is similar to the standard cross-section finding.

Hoeffler (2002) focused on a specific question: can the augmented Solow model

explain Africa's growth experience? Using a sample of 98 countries (excluding China) for the

period 1960-90 and comparing various estimation methods including OLS, the fixed effect

model, the first-differenced GMM, the system GMM and the instrumental variable method,

she found that system GMM is the preferred estimator for the augmented Solow model. She

then regressed the residuals obtained by system GMM estimation on the Africa dummy and

found the coefficient to be insignificant. This suggested that the augmented Solow model can

fully account for Sub-Saharan Africa's low growth performance when unobservable country-

specific effects and the endogeneity of regressors are controlled for using the system GMM

estimation method.

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While the cross-country growth regression studies discussed above all point to factor

accumulation as the main driving force in economic growth, another strand of growth

literature pinpoints the importance of TFP in explaining international differences in levels

and growth rates of output per worker. This literature, associated primarily with Klenow and

Rodríguez-Clare (1997), Hall and Jones (1999) and Easterly and Levine (2001), uses the

growth accounting approach. By adopting a Mincer regression methodology to estimate

human capital stocks, Klenow and Rodríguez-Clare (1997) found that roughly 90 percent of

international differences in output growth are attributable to differences in TFP growth. Hall

and Jones (1999) discovered a large amount of variation in the level of the Solow residual

across countries and emphasized the role of social infrastructure (institutions and government

policies) in determining the cross-country variation in capital accumulation, TFP and output

level. Using both 'level accounting' and 'variance decomposition of growth' approaches,

Easterly and Levine (2001) found that the major empirical regularities of economic growth

indicate an important role for the residual rather than for factor accumulation. They

concluded that the cross-country growth evidence does not support the neoclassical growth

model, with its assumption of diminishing returns to capital and constant returns to scale.

Two recent papers in the special issue for the 50th Anniversary of the Solow Growth

Model in Oxford Review of Economic Policy disagree with the conclusion of the growth

accounting literature that the neoclassical model fails to fit the data in the cross-country

growth literature. Gundlach (2007) argued that the empirical cross-country growth evidence

is perfectly in line with the Solow model, but it appears to be in conflict with the MRW's

augmentation of the Solow model. He believed that the fundamental insight of the Solow

model is not adequately captured by the empirical specification employed by MRW, because

it does not allow for cross-country variation in technology. Instead, he adopted an alternative

specification of the Solow model which allows for international variation in technology

conditional on a constant capital-output ratio. Following the work of Acemoglu et al. (2001),

Gundlach (2007) employed a measure of the risk of expropriation as a proxy variable for

international differences in the quality of institutional technologies and a measure of settler

mortality in the former colonies in the early nineteenth century as an instrument variable to

account for the potential endogeneity of the quality of institutions. Using the sample of

Caselli et al. (1996), he found a significant positive effect of variation in institutional quality

on the level of development and concluded that the international variation in output per

worker can be explained by international differences in technology broadly conceived,

conditional on a constant capital-output ratio. Solow (2007) commented that it is misleading

14

for this paper to assume that all the observations describe steady state, and he suggested some

more direct measure of technological level for each country, such as industrial electricity

consumption per unit of output or the number of computers, instead of using the conventional

measure of institutional quality.

McQuinn and Whelan (2007) carried this general line of thinking in a different

direction: the assumption of an exogenous growth rate of technological progress in the Solow

model does not imply that TFP grows at the same rate across countries as assumed by MRW.

The apparent importance of the role of factor accumulation in explaining cross-country

growth differentials and the low speed of convergence are reflections of the unsatisfactory

nature of the MRW assumption about technology, rather than being due to a failure of the

Solow model itself. Using data for 96 countries (including China) over the period 1960-2000,

they adopted a new approach to estimate the speed of conditional convergence based on the

adjustment of the capital-output ratio towards its equilibrium rather than the dynamics of

output per worker. They found that the estimated convergence rates are around 6-7 percent

per annum, which is above the widely cited 2 percent stylized fact. Their methodology does

not rely on the questionable assumption of a constant rate of technological progress

everywhere, but it does require the construction of data on capital stock and assumptions

about the depreciation rate.

Temple and Wöβmann (2006) employed a sample of 76 developed and developing

countries (excluding China) for the period 1960-96 to test the effect of structural change on

both cross-country output growth and TFP growth. They found clear evidence for structural

change effects associated with marginal product differences and concluded that structural

change in the form of reallocation of labour can account for a significant fraction of the

observed variation in both output and productivity growth. In addition, there was evidence

that the extent of dualism has declined over time. Their results remained intact when a

number of robustness checks were performed. Since their analysis is based on a single cross-

section framework, there is room for further extension to a more complicated panel data

model.

In brief, despite the vast empirical literature on testing the neoclassical model of

economic growth using data on various groups of countries, very few cross-country

regression analyses include China and none of them focuses on the explanation of China's

remarkable economic growth relative to other countries. We attempt to fill this gap by

utilizing panel data on 146 countries over the period 1980-2000 to examine the extent to

which the growth difference between China and other countries can be explained by the

15

augmented Solow model. Instead of using the growth accounting approach - based on several

assumptions about unknown parameters - to take account of varying technology growth

across countries, we will follow the methodology developed by Temple and Wöβmann

(2006) to incorporate structural change terms into the augmented Solow model to capture the

role of productivity growth in cross-country growth regressions. This extended neoclassical

growth model is fully compatible with our research motivation, which attempts to explain the

transitory differences in growth rates between China and other countries rather than focusing

on variation in the steady-state level of income.

4. Background to China's remarkable post-reform economic growth

4.1 China's gradualist approach to reform

The Chinese economy has grown at a rapid pace since the start of its economic reform

policies in 1978. It has been a process of ‘crossing the river by groping for the stepping

stones’, as described by Deng Xiaoping: no stereotype reform package was adopted in

advance. The reforms were incremental but hardly slow: huge changes have occurred in less

than three decades, as China has moved from central planning towards a market economy. It

is relevant that China’s was a surplus labour economy par excellence. Labour was

underemployed on the farms and in the urban state enterprises: government preferred

unemployment to be disguised and shared rather than open and threatening. New sectors

could be expanded with little or no loss of output elsewhere.

The first stage of economic reform (1978-85) concentrated on the rural areas. The

communes were disbanded and individual incentives were restored. Farming households

(then 82 percent of the population) were given use-rights to collectively-owned land under

long term leases, and the right to sell their marginal produce on the open market. Rural non-

farm enterprises were permitted, and they stepped in to produce the light manufactures that

the urban state-owned enterprises (SOEs) generally failed to supply. Rural credit constraints

encouraged household saving. Rural production rose rapidly as farms became more efficient,

as surplus farm labour was used more productively in rural industry, and as rural

entrepreneurship, saving and investment responded to the new opportunities. In 1978 the

rural labour force totalled 306 million. During the period 1978-85 total employment in rural

industry grew by 42 million (two-thirds of rural labour force growth), and rural real income

per capita increased at a rate of 15 percent per annum.

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The second stage of economic reform (1985-93) was an incremental process of

reforming the urban economy, in particular the SOEs which were gradually given greater

managerial autonomy. The principal-agent problem inherent in state ownership limited the

efficiency of SOEs but increasing competition from other market participants – initially

village and township enterprises and later domestic and foreign privately-owned enterprises –

grew steadily. The third stage of economic reform (1993- ) was ignited by Deng Xiaoping’s

‘southern tour’ to mobilise support for more radical reforms. The private sector - for the first

time acknowledged and accepted - was invigorated. Moreover, administrative and regulatory

reform of rural-urban migration, the banking system, the tax system, foreign trade, and

foreign investment lifted various binding constraints on economic growth. For instance, when

the delayed effects of the one-child family policy slowed down the growth of the urban-born

labour force from the mid-1990s, the relaxation of restrictions on temporary rural-urban

migration permitted continued rapid growth of the urban economy. Employment in

agriculture began to fall in absolute terms (from 340 million) in the early-1990s, and urban

employment, 183 million in 1993, rose by 73 million over the next decade, mainly as a result

of rural-urban migration.

Figure 4.1 reflects China’s rapid growth of GDP per capita, averaging 8.5 percent per

annum over the period 1978-2005. The figure also shows a cyclical pattern of growth, more

marked in the first and second stages of reform than in the third stage. Two peaks are evident,

in 1984-5 and 1992-3, respectively reflecting the outcome of agricultural reforms and the

green light given to capitalism. The growth rate troughed in 1989-90 owing to a surge of

inflation and social unrest.

In summary, the reforms created institutions and incentives that had been lacking in

the socialist planned economy. They improved both static allocative efficiency and dynamic

factor accumulation. Growth was also facilitated by the absorption of the abundant resource,

labour, into the expanding, more productive, activities. There was drastic movement towards

the economy’s production frontier and dramatic movement of the frontier: together they

produced a remarkably high average rate of economic growth over the period of economic

reform.

4.2 China's economic growth in comparative perspective

We compare China with the main regions of the world economy (Table 4.1). We do so

in terms of variables that suggest hypotheses for testing: the growth in GDP per capita, the

level of GDP per capita, the investment-output ratio, the share of agriculture in GDP, and the

17

growth rate of population. The table provides information at ten-year intervals over the period

1980-2000, the average for that period, and the change between 1980 and 2000.

For China, as for other countries, our measure of GDP is based on the World Bank’s

constant price (year 2000) PPP US dollar equivalents, rather than official Chinese statistics.

China’s annual average growth of GDP per capita over the 20 years (8.4 percent) is four

times that of the high-income economies (2.1 percent), and is much higher than that of Sub-

Saharan Africa and Latin America and the Caribbean (-0.6 percent and 0.6 percent

respectively). China’s sustained growth rate is indeed remarkable.

In 1980 China had a lower level of GDP per capita than any of the regions included in

Table 4.1, although by 2000 it had overtaken South Asia and Sub-Saharan Africa. The

intuition is that China was initially further away from its equilibrium GDP per capita, and that

forces of convergence would thus enable it to grow relatively fast. This hypothesis requires

testing.

China’s growth performance has been associated with an extremely high investment

rate. Gross capital formation as a proportion of GDP (averaging 36 percent) is remarkable for

such a poor country (Table 4.1), reflecting high household saving rates and large capital

inflows. We see that the four other regions managed to invest only about 20 percent of their

GDP. A large part of the answer to the question ‘why does China grow so fast?’ might be

‘because it invests so much’. That must be a core hypothesis of our enquiry.

Rapid economic growth was inevitably associated with rapid structural change in the

Chinese economy, as industrialisation proceeded. The share of agriculture in GDP fell from

30 percent (higher than elsewhere) in 1980 to only 15 percent in 2000 (Table 4.1). The fall

(by 15 percentage points) was greater than in other regions; indeed, beyond South Asia, the

fall was less than 4 percentage points in the slow-growing regions of the world. The change

in China’s sectoral composition of output involved the reallocation of labour from low

average labour productivity (and possibly zero marginal productivity) agriculture to high

productivity industry. According to the official Chinese data, the agricultural labour force fell

from 71 percent of the total in 1978 to 46 percent in 2000. The associated increase in average

labour productivity can be expected to have raised the growth rate.

China has implemented a draconian population policy since the late 1970s. Despite the

controversy over the humanity of the ‘one child family policy’, it has been efficient in

reducing fertility and slowing down the rate of population growth. This reduced the pressure

on the land and on other scarce resources. By contrast, other regions of the developing world

18

have experienced higher rates of population growth (Table 4.1). We hypothesise that China’s

growth of GDP per capita benefited from its restrictive population policy.

Human capital can raise the individual productivity of workers and improve the

adaptability, allocative efficiency, and technical level of an economy. Based on the Barro and

Lee (2001) data on international educational attainment, we find that China's average years of

schooling in total population aged over 15 (5.6 years) was much lower than that of high-

income economies (8.6 years), but higher than that of South Asia (3.1 years) and Sub-

Saharan Africa (2.9 years), and on a par with that of Latin America and the Caribbean (5.5

years) over the period 1980-2000. The pattern of annual growth rate of average years of

schooling shows opposite results: the average annual growth rate of China (1.5 percent) was

faster only than that of high-income economies (1.2 percent) and slower than those of other

developing country groups. Therefore, we expect that China’s rapid economic growth relative

to other developing countries is partly due to the level of education, while that relative to the

high-income economies can be partly explained by the growth rate of human capital over the

reform period.

5. Data and empirical methodology

5.1 Data and sample

Our empirical analysis is based on several data sets of worldwide aggregate series,

including Penn World Table (PWT), World Bank World Development Indicators (WDI) and

Statistical Database of the Food and Agriculture Organization of the United Nations (FAO).

Given the presence of cyclical effects, we opt for five-year time intervals which are less

sensitive to temporary factors associated with business cycles than yearly data and maintain

more time series variation than the ten-year interval setup. The observations in our sample are

either the average value or initial value over each five-year period in order to reduce the

influence of business cycle fluctuations and alleviate the problem of parameter heterogeneity.

The sample period we choose is 1980-2000, corresponding roughly to the post-reform period

in China.

We employ real GDP chain per worker (RGDPWOK) from PWT 6.2, which is

adjusted for purchasing power parity and based on a chain index. The workforce is defined as

working age population, i.e. the population aged 15-64. Despite potential measurement error

in the workforce data, we prefer the per worker variable to the per capita variable. The

dependent variable is the change in the logarithm of real GDP per worker at five-year

19

intervals, and the initial level of income on the right-hand side is measured by real GDP per

worker data, starting in 1980, 1985, ... and ending in 2000.

Following MRW, Islam (1995), Caselli et al. (1996) and Hoeffler (2002), we proxy the

share of saving by the share of investment in real GDP, which can be obtained from PWT

6.2. The time series are averaged over 1980-1984, 1984-1989, ... , 1995-1999.

WDI (September 2006 edition) data on total population and fraction of the population

in the age group 15-64 allow us to calculate the working-age population for each country.

The average rate of growth of the workforce is computed as the difference between the

natural logarithms of the working-age population at the end and beginning of each period and

dividing this difference by the number of years. The working-age population growth rates are

averaged over 1980-1984, 1984-1989, ... , 1995-1999.

Rather than follow MRW, Caselli et al. (1996) and Bond et al. (2001) using the

secondary-school enrolment rates to proxy the rates of investment in schooling, we rely on

the average level of human capital data provided by Barro and Lee (2001). Both Gemmell

(1996) and Temple (1999a) argued that school enrolment rates may conflate human capital

stock and accumulation effects and can be a poor proxy for either. The human capital

measure we use is average years of schooling in the total population aged over age 15, which

provides a direct measure of the stock of human capital at the beginning of each five-year

period.

FAO provides annual data on total labour force and agricultural labour force

respectively, making the calculation of agricultural share of employment possible for most

countries. After comparing the employment data for China from FAO with that from China

Labour Statistical Yearbook compiled by the National Bureau of Statistics of China (NBS),

we find a large discrepancy between these two sources (see Table A1 in Appendix). The

computed agricultural share of employment based on FAO data turns out to be stagnant in the

post-reform period, which contradicts the dramatic changing sectoral composition of GDP

and the trend towards industrialization in China. NBS data on employment reflect the pattern

of rapid reallocation of labour from low-productivity agriculture to high-productivity industry

and services, and is more consistent with the observed structural change. The NBS

employment data have been successfully used in research on the labour market in China and

this gives further credence to its reliability. It will therefore be used in our analysis. The

annual data on agricultural share of value added are available from WDI. The quinquennial

beginning-period data on both employment share and value added share for each country are

used to construct the structural change terms.

20

We consider three samples of countries in this paper (see Table A2 in Appendix).

Sample I comprises all countries available from PWT 6.2 except those receiving a grade 'D'

in terms of data quality. As pointed out by MRW, the problem of measurement error is likely

to be extremely serious for these countries and variables can be badly measured. By

eliminating these least reliable data from our sample, we are left with a sample of 146

developed and developing countries.

Sample II contains all developing countries and four East Asian Tigers1 in our non-

grade-D sample. Temple (1999a) mentioned that integrating developed and developing

countries in a single empirical framework is not without its problems since institutions and

growth processes in developing countries can be different from those in countries already

near the technological frontier. We incorporate four East Asian Tigers into this sample for

two reasons. Firstly, China shares some economic growth patterns with these countries owing

to cultural similarities, geographic location and similar economic development strategies.

Secondly, these four economies were classified as the developing countries in 1980, the

beginning of our sample period. This sample contains 111 countries after excluding OECD

and non-OECD high-income economies from Sample I.

Sample III comprises 61 large developing countries with more than 5 million

population and four East Asian Tigers, where grade D data are also excluded. These countries

are believed to have much in common with China. By grouping countries with similar

features into the same sample, we expect to control for the difference in technology and

institutions and alleviate the problem of parameter heterogeneity. The disadvantage is the

relatively small sample size.

5.2 Empirical methodology

Since judging whether countries are in their steady states or not might be difficult and

problematic in practice, our empirical analysis will focus on growth rather than income

equation in order explicitly to consider the transitional dynamics through the inclusion of

initial income.

The growth regression approach encounters the omitted variable problem associated

with the unobservable initial level of technology. In a single cross-section growth regression,

this omitted term is left within the residual term. Since variations in technical efficiency

across countries are likely to be correlated with other explanatory variables, estimates of

1 Hong Kong, Taiwan, South Korea and Singapore.

21

regressors in a conditional convergence regression are biased and inconsistent. Panel data

methods make it possible to control for the unobserved country-specific effect by treating

initial efficiency as a time-invariant fixed effect and eliminating its influence through a time-

dimensional transformation. Another advantage of the panel over the cross-section regression

is the alleviation of the endogeneity problem through the inclusion of lags of regressors as

instruments. Both the GLS estimator used in Barro and Sala-i-Martin (2004) and the GMM

estimator employed by Caselli et al. (1996), Hoeffler (2002) and Bond et al. (2001) are

efficient in correcting for some of the endogeneity problem. The panel data technique also

allows for the differences in the aggregate production function across individual countries

and utilizes more information than cross-section methods. Given these appealing features, we

will rely on panel data methods to estimate the cross-country growth regressions in this

paper.

Following Bond et al. (2001), our equations (2.13), (2.18), (2.19) and (2.29), can be

generalized in the following panel data model

, (5.1)

for and , where is the log difference in real GDP per worker

over a five-year period, is the logarithm of real GDP per worker at the beginning of

each period, and is a vector of other characteristics measured either at the beginning of

each period or as an average over each five-year period. In this paper, we maintain the MRW

idea of a common world technology trend representing advancement of knowledge, while

also allowing for the variation in productivity growth associated with structural change. In the

empirical application of the textbook Solow model (equation 2.13), consists of the

logarithm of investment rate and the logarithm of the population growth adjusted by common

exogenous rate of technical change and common depreciation rate, the sum of which is

assumed to be 0.05. In the Solow model augmented by human capital (equations 2.18 and

2.19), also includes the logarithm of average years of schooling or the log difference in

the average years of schooling to proxy the stock and accumulation of human capital

respectively. In the Solow model augmented by both human capital and structural change

(equation 2.29), the linear and non-linear structural change terms are added in . In

addition, the unobserved heterogeneity in the initial level of efficiency is reflected by the

country-specific effects, . The time dummy, , is expected to capture global shocks

affecting aggregate production functions across countries. Both the country- and time-effects

22

may also reflect country-specific and period-specific components of measurement errors

(Bond et al., 2001).

Estimating equation (5.1) is equivalent to estimating a dynamic panel data model with

a lagged dependent variable on the right-hand side as

, (5.2)

for and . In the context of cross-country growth regressions, our

data is featured by a large number of countries over a small averaged time-series period .

The use of panel data methods in general, and dynamic panel data models in particular,

is not without its own problems. Barro (1996) pointed out that the use of time series variation

may introduce unwanted business cycle effects and the transformation used to eliminate fixed

effects may exacerbate the effects of measurement errors. Temple (1998) also emphasized

that measurement error and influential outliers remain serious difficulties in panel data

applications.

Moreover, the presence of country-specific effects, , implies several econometric

problems relating to estimation of dynamic panel data models with the presence of a lagged

dependent variable on the right-hand side. Since is a function of , it immediately

follows that is also a function of . The correlation between the lagged dependent

variable and the time-invariant country-specific effects renders the OLS estimator biased and

inconsistent even if the are not serially correlated. In the cross-country growth

regressions, the OLS estimate of the coefficient of initial income term, , is likely to be

biased upward due to the positive correlation between and (Hsiao, 1986). For the

fixed effects estimator, the within-groups transformation wipes out the time-invariant by

subtracting out the time series means of each variable for each country. But ,

where , can still be correlated with even if the are

not serially correlated. Nickell (1981) showed that the unbiasedness and consistency of

within-groups estimator in a dynamic panel will depend upon being large. However, in the

typical growth regression with small , the estimate of the coefficient of initial income term,

, is likely to be seriously biased downwards (Nickell, 1981). Bond et al. (2001) and Hoeffler

(2002) suggested that a consistent estimate of is expected to lie in between the upper bound

provided by the OLS estimates and lower bound given by the within-groups estimates.

The growth regression using the first-differenced GMM estimator is first differenced to

eliminate the effect of initial efficiency and then lagged levels of the right-hand-side variables

23

are used as instruments in the first-differenced equations. However, Bond et al. (2001)

indicated that the first-differenced GMM estimator is subject to a large downward finite

sample bias particularly when the number of time series observations is small, as the lagged

levels of variables are only weak instruments for subsequent first-differences. Instead, they

recommended using a system GMM estimator with superior finite sample property developed

by Arellano and Bover (1995) and Blundell and Bond (1998). The system GMM estimator

combines the standard set of equations in first-differences with suitably lagged levels as

instruments, with an additional set of equations in levels with suitably lagged first-differences

as instruments. By adding the original equation in levels to the system, Arellano and Bover

(1995) and Blundell and Bond (1998) found dramatic improvement in efficiency and

significant reduction in finite sample bias through exploiting these additional moment

conditions. Bond et al. (2001) also claimed that the potential for obtaining consistent

parameter estimates even in the presence of measurement error and endogenous right-hand-

side variables is a considerable strength of the GMM approach in the context of empirical

growth research. As a consequence, a panel-data system GMM estimator will be our

preferred estimation method.

6. Estimation results

6.1 The textbook Solow model

We start by estimating the textbook Solow model as described by equation (2.13) in

Table 6.1. Note that all estimated standard errors are corrected for heteroskedasticity and time

dummies are included in each regression. Regarding the system GMM estimation, initial

level of income is treated as predetermined variable and both investment rates and population

growth rates are treated as potentially endogenous variables. Several studies have found that

the two-step standard errors tend to be biased downwards in finite samples (Arellano and

Bond, 1991; Blundell and Bond, 1998). By applying a correction to the two-step covariance

matrix derived by Windmeijer (2005), we find very similar results obtained from the one-step

and two-step GMM estimators. In this paper, to conserve space we report only the

heteroskedasticity-robust one-step system GMM results.

[Table 6.1 here]

The coefficients on initial income have the expected negative sign and are highly

significant for all three samples using various estimation methods, indicating strong evidence

of conditional convergence. The OLS estimate of the lagged dependent variable is biased

24

upward and the implied convergence rate, , is quite low (about one percent per annum). On

the contrary, the within-groups estimate is biased downwards in our short panel and

associated with a higher convergence rate (about 8 percent per annum). Our preferred system

GMM estimate of the coefficient on initial income lies comfortably between the approximate

upper and lower bounds, and suggests a convergence rate in the range of 2-4 percent per

annum. Moreover, the GMM results offer no evidence of second-order serial correlation in

the first-differenced residuals for all estimation. This is important because, according to

Arellano and Bond (1991), the presence of first-order autocorrelation in the differenced

residuals does not imply that the estimates are inconsistent, while the presence of second-

order autocorrelation does. Given the presence of heteroskedasticity-consistent standard

errors, the Hansen J test of over-identifying restrictions is employed to evaluate the overall

validity of the set of instruments and the Difference-Sargan statistic is calculated to test for

the validity of additional instruments used by the system GMM estimator compared with the

first-differenced one. Neither test detects any problem with instrument validity.

The investment rate has a significantly positive effect on the growth of GDP per

worker in all regressions even after controlling for unobserved country-specific effects and

allowing for the likely endogeneity of investment. However, we fail to identify a significantly

negative correlation between population growth and the growth of income per worker in this

textbook Solow model. Besides, the restriction that the coefficients of the investment and

population growth variables are equal in magnitude but opposite in sign, indicated by

equation (2.13), is rejected in Sample II. Hence, the results reported in Table 6.1 do not seem

to accord with the prediction of this model.

One possible reason for the poor performance of the basic Solow model might be the

presence of influential outliers which plague our dataset. Detection of outliers is important in

the cross-country growth regression when a large number of heterogeneous countries are

included in the same sample (Temple, 1999b). Particularly, in the dynamic panel data

framework, the use of a lagged dependent variable guarantees that an outlier in the dependent

variable will also show up as a bad leverage point in the independent variables. Temple

(1999a) suggested that single-case diagnostics like Cook's distance measure, the Studentized

residuals and DFITS are likely to miss groups of outliers or wrongly identify representative

observations as outlying. Therefore, we rely on the robust regression technique, iteratively

reweighted least squares (RWLS), to identify possible outliers and then omit these from our

OLS, within-groups and system GMM estimation. RWLS assigns a different weight to each

observation with zero or lower weights given to observations with large residuals. After

25

removing 13 unrepresentative observations2 (with weights less than 0.5) from the whole

sample, we are able to restrict the influence of these outliers and focus on the most coherent

part of the dataset.

[Table 6.2 here]

The robust estimates of the textbook Solow model are presented in Table 6.2. Omitting

the outliers from our samples results in two major changes: a rise in the R-squares of OLS

and within-groups estimation and a decline in the estimated standard errors of most

regressors, both of which indicate better goodness of fit of the regressions. However, the

awkward results that the population growth variables are wrongly signed and the adding-up

restrictions are rejected remain unchanged.

[Table 6.3 here]

The other parameter of interest in the basic Solow model is the elasticity of output with

respect to capital ( ), which can be obtained from the restricted version of equation (2.13)

where savings and population growth enter as a difference as shown in Table 6.3. From now

on, to save space we report only the results of consistent system GMM estimator with outliers

removed. We find that imposing the restriction does not affect the estimates of the initial

income much, so that the corresponding convergence rates, , are almost the same as those

from unrestricted estimation (in the range 2-4 percent per annum). The positive and

significant coefficients on the difference between savings rate and population growth rate

support the predictions of the Solow model. However, the estimates of the elasticity of output

with respect to capital, , are found to be above 0.5 for all three samples, which are higher

than the model-suggested-value of capital share of income, 0.33. Therefore, for the same

reason as MRW, we reject the textbook Solow model based on our robust system GMM

panel data estimation.

6.2 The Solow model augmented with human capital

The role of education in determining economic growth is an area of dispute in the

cross-country growth empirics. MRW found a significantly positive effect of human capital

on growth, while other studies (Pritchett, 1999; Krueger and Lindahl, 2001) claimed that

increases in measured educational attainment are not related to output growth especially in

developing countries.

2 They are: Kuwait, 1995; Congo, Republic of, 2000; Cameroon, 1985; Zambia, 1995; Jordan, 1990; Rwanda,

1980; Sierra Leone, 2000; Iran, 1980; Swaziland, 1990; Jamaica, 1980; Ireland, 2000; Uruguay, 1985; and

Paraguay, 1980.

26

[Table 6.4 here]

In Table 6.4, we estimate equation (2.18) which incorporates the log difference of

average years of schooling as a proxy for the accumulation of human capital as well as

equation (2.19) which includes the logarithm of average years of schooling as a measure of

the level of human capital respectively. In addition, following Gemmell (1996) who claimed

that higher output growth may result from both larger initial stocks of human capital and a

faster rate of human capital accumulation, we test a third specification which augments the

Solow model with both the stock and accumulation of human capital. In the system GMM

estimation, we treat the initial level of human capital as a predetermined variable and the

growth rate of human capital as a potentially endogenous variable, as fast-growing economies

are likely to devote a higher proportion of their resources to educational investment. We find

that when the two human capital variables enter the Solow formulation individually, neither

the level nor the change of human capital proves to be significant for all three samples, which

is consistent with the many studies that have failed to find a robust correlation between

educational attainment and output growth. Interestingly, when we simultaneously incorporate

both the stock and accumulation of human capital into the regressions, the level of human

capital becomes highly significant and positive for all samples; besides, Wald tests suggest

strong evidence of joint significance of both human capital variables even in Sample II and

III where only developing countries are included. Hence, our results provide support for a

role of both the initial stock and subsequent growth of human capital in fostering faster

output growth even in less developed countries, which is in contrast to the so-called 'Pritchett

hypothesis' (Pritchett,1999; Temple, 2001).

Compared with the textbook Solow model, inclusion of the human capital in the

regressions leads to two major changes. First, the population growth term which has been

wrongly signed previously becomes negative and strongly significant for all samples except

for one regression in Sample II. Second, these unrestricted regressions do not lead to rejection

of the adding-up hypotheses3 as predicted by equation (2.18) and (2.19). Both results imply

better performance of the augmented than of the basic Solow model. In addition, the

coefficients of initial income and investment rate are all signed in a manner consistent with

the model and the estimated rates of convergence are around 2 percent per annum for all

samples when the human capital is included. The hypothesis of no second order serial

3 In equation (2.18) where the growth rate of human capital is included, the adding-up restriction refers to the

hypothesis that the three coefficients other than the one on lagged output sum to zero; in equation (2.19) where

the level of human capital is included, the restriction is that the coefficients on the rates of investment and

population growth are opposite in sign and equal in absolute value.

27

correlation in the first-differenced residuals is not rejected for any of the GMM estimations.

Moreover, the Hansen test does not reject the validity of overall instruments and the

Difference Sargan test does not reject the validity of the additional instruments used

compared to first-differenced GMM.

[Table 6.5 here]

In order to calculate the physical capital's share of income ( ) and human capital's

share of income ( ), we estimate the restricted version of the augmented Solow model as

shown in Table 6.5. We find that in both cases where growth rate of human capital or the

level of human capital is included, our estimates suggest , justifying the

assumption of decreasing returns to the set of reproducible factors of production, a key

assumption of the neoclassical Solow model. Comparatively speaking, the estimates of the

elasticity of output with respect to physical capital and human capital are more plausible

when the change of human capital is included, which solves the problem of the

extraordinarily high capital share of income obtained from the textbook Solow model. This

result casts doubt on the common view that the growth rate of human capital in the form of

first differences is too noisy to be informative about the actual change in schooling over time

(Krueger and Lindahl, 2001). Unfortunately, we are unable to compute and in the case of

simultaneous inclusion of stock and accumulation of human capital owing to the lack of

structural form of the theoretical model. Note that the estimates of other parameters are not

much affected by restricted, rather than unrestricted, estimation.

6.3 The augmented Solow model with structural change

We now further supplement the augmented Solow model with the structural change

terms to test whether labour reallocation makes a significant contribution to economic growth.

Table 6.6 presents the system GMM results with the first set of structural change terms,

and . According to Temple and Wöβmann (2006), there is a convex

relationship between growth and structural change as the growth impact of a given extent of

structural change appears to be greatest in those countries experiencing more rapid structural

change. We attempt to test this hypotheses in a dynamic panel data model.

[Table 6.6 here]

Being aware of the endogeneity nature of the extent of structural change, i.e. periods of

more rapid economic growth are also periods of expanding opportunity for rural workers and

of rapid structural transformation, we treat both the linear and non-linear structural change

terms as potentially endogenous variables in the GMM estimation. Although

28

and are not individually significant, there is strong evidence of joint significance for

all samples according to the Wald test. Moreover, inclusion of the structural change terms in

the regressions also leads to the individual significance of the growth rate of human capital in

Sample I and level of human capital in Sample II, which are absent in the models where only

human capital variables are included. When both the level and accumulation of human capital

are simultaneously added in the regressions together with structural change terms, the

coefficient of level of human capital is strongly significant and positive for all three samples

and both human capital variables are jointly significant at the 5 percent level in Sample I and

roughly the 10 percent level in Sample II. Besides, all other parameters like initial income,

investment rate and population growth rate are all correctly signed and highly significant in

every regression. There is also no evidence of second order serial correlation in the first-

differenced residuals and neither Hansen test nor Difference Sargan test rejects the validity of

instruments, suggesting the consistency of the system GMM estimators being used. The

estimated convergence rate, , remains stable around 2 percent per annum on average for

each sample.

[Table 6.7 here]

The results become even better when we add the second set of structural change terms,

and , into the cross-country growth regressions. Recall that the

alternative set of structural change variables captures both structural change in employment

and sectoral transformation in total value added. In Table 6.7, not only are both structural

change terms jointly significant but also the non-linear term, , itself remains highly

significant and positive in every regression and each structural change term appears strongly

individually significant in sample II and III where only developing countries are involved.

Reflecting the very different sectoral structures and patterns of structural change in developed

and developing countries, our results show that the role of structural change in determining

economic growth is stronger in the case of developing countries. In addition, the persistently

significant term further justifies Temple and Wöβmann (2006)'s hypothesis that the

growth effect of structural change is nonlinear.

Another change associated with employing the second set of structural change terms is

the further improvement of the performance of human capital variables. When both level and

growth rate of human capital are simultaneously included in the regressions, they appear

jointly significant for all three samples as revealed by the Wald test. In particular, besides the

significant and positive association between cross-country differences in the initial

29

endowment level of education and subsequent output growth, changes in education also

explain part of the variation in changes in output in Sample I.

In brief, our system GMM results strongly support the extended version of the

augmented Solow model with both human capital and structural change, as developed by

Temple and Wöβmann (2006). The movement of labour across sectors is an essence of the

development process, and this needs to be captured in the cross-country growth regressions.

6.4 Growth and growth difference predictions

The good performance of the augmented Solow model allows us to assess the

contribution of capital accumulation and structural change to the international variation in

economic growth. By adopting a simple accounting approach used by World Bank (1993),

we attempt to provide an explanation for China's growth rate and the dramatic growth

difference between China and other country groups based on our model predictions.

[Table 6.8 here]

The model we employ for prediction is the one augmented by both level and growth

rate of human capital as well as structural change terms given in Table 6.6. We choose the

estimates of Sample III when we compare China with Sub-Saharan Africa and opt for Sample

I when we later account for the predicted growth difference between China and all other

country groups in the world.

Table 6.8, using PWT 6.2, shows that the actual average annual growth rate of output

per worker in China over the period 1980-2000 was 7.2 percent. Our model predicts that

output per worker in China grew at an average rate of 6.3 percent per annum, which is 88

percent of the actual growth rate. The unexplained residual (0.9 percent per annum)

represents the TFP growth that is not accounted for by the model. It could be due to a

combination of pushing out the technology frontier and moving towards the frontier. We are

able to claim that our augmented Solow model - capturing initial income, investment,

population growth, level and growth of human capital as well as structural change - is

successful in predicting China's growth rate.

Table 6.8 also presents a detailed decomposition of the difference in the growth

predictions for China and Sub-Saharan Africa. The actual annual growth rate for Sub-Saharan

Africa is 0.4 percent, whereas the model predicts that the region grew at an annual rate of 0.7

percent. This slight overprediction implies a negative TFP growth for Sub-Saharan Africa

that is not accounted for by our model. The actual and predicted annual growth differences

between China and Sub-Saharan Africa are 6.8 percent and 5.6 percent respectively. Hence,

30

the model captures 82 percent of the actual growth difference between them. When the

predicted growth difference between China and Sub-Saharan Africa is decomposed, we find

that capital investment is the most important component (accounting for 54 percent of the

total). Capital accumulation has traditionally been viewed as an inferior source of growth, in

that capital deepening is subject to diminishing returns and will eventually run out of steam.

This has not been true for China's high investment rates for two reasons. Firstly, investment is

a major carrier of structural change: structural transformation requires investment in new,

normally high-productivity activities. In China, employment growth in the high-productivity

industrial and service sectors is determined by the rate of investment in those sectors. The

new job opportunities are largely filled by migrant workers from the low-productivity

agricultural sector. Secondly, the slow convergence rate predicted by our model, roughly 2

percent per annum, implies that the average time an economy spends to cover half of the

distance between its initial position and its steady state is about 35 years 4, and that it would

take about 70 years for three-quarters of the gap to vanish. Even if there are diminishing

returns to investment, the role of capital accumulation in driving economic growth can persist

for decades during the economic transition to the long-run equilibrium.

As far as other variables are concerned, the fact that the average growth rate of human

capital in China was slightly below that in Sub-Saharan Africa over the period 1980-2000

leads us to predict that their growth difference would be smaller by 0.2 percent. Contributions

to that difference came from China's slower population growth (24 percent), higher level of

human capital (11 percent), conditional convergence gain (17 percent) and its more dramatic

structural change (12 percent).

[Table 6.9 here]

Using this methodology, we are able to account for the predicted growth differences

between China and other major country groups as shown in Table 6.9 based on estimates of

Sample I. Growth prediction for China and growth difference prediction between China and

Sub-Saharan Africa are also reported as a robustness check: we find that our prediction

results remain stable when different sample estimates are employed. Our main findings for

the other country groups are as follows. Firstly, conditional convergence, the basic property

of the Solow model, has considerable explanatory power for the growth difference across

countries, ranging from 25 percent between China and South Asia to 103 percent between

China and the high-income economies. Secondly, China invests more than other economies,

4 According to equation (2.10), the time for which is halfway towards satisfies the condition

.

31

which accounts for 43 percent of the predicted growth difference between China and East

Asia and the Pacific, 40 percent in the case of South Asia, and 26 percent in the case of Latin

America and the Caribbean. By stimulating structural change, high investment rates are not

only a cause of economic growth but also a symptom of productivity improvement. Thirdly,

reallocation of labour from low- to high-productivity sectors is another source of China's

economic growth. The joint contribution of linear and non-linear structural change terms to

the predicted growth difference ranges from 8 percent between China and Latin America and

the Caribbean to 14 percent between China and other East Asian countries. Fourthly, the

slower population growth rate of China also contributes to its faster growth relative to other

developing countries (accounting for 7 percent of the predicted growth difference between

China and Latin America and the Caribbean; 3 percent in the case of South Asia; and one

percent for East Asia and the Pacific). Fifthly, the level of human capital explains 17 percent

of the predicted growth difference between China and South Asia. Compared with the other

country groups shown in Table 6.9, the level of human capital in China is still quite low.

Lastly, the growth rate of human capital contributes positively to the predicted growth

difference of China with the high-income economies, but its contribution is tiny.

In brief, we find that physical capital accumulation, structural change, conditional

convergence and population growth explain the vast majority of the difference in the growth

rates of output per worker between China and other country groups. There is still room for

China to expand its investment in human capital in order to sustain and further accelerate its

economic growth, in relation to other countries.

7. Conclusion

In this paper, we have examined the role of the augmented Solow model in explaining

China's remarkable post-reform economic growth rate, both absolute and relative to the rest

of the world. Following Temple and Wöβmann (2006), we allowed productivity growth to

vary across countries in models of growth in GDP per worker. We extended Temple and

Wöβmann's cross-section analysis to the dynamic panel data analysis using a robust and

consistent system GMM estimator. Firstly, we found that the extended version of the

augmented Solow model provides a good explanation of China's economic growth, i.e. we

were able to predict a growth rate that was 88 percent of its actual growth rate using the

variables of initial income level, investment rate, population growth rate, level and growth

rate of human capital and structural change.

32

Secondly, this model is also a valuable means of understanding the large and persistent

differences in growth rates between China and other countries. China's relatively good

performance is mainly due to accumulation of physical capital, to improvements in factor

productivity through structural change, to conditional convergence and to slower population

growth rate. The level of education is crucial to the growth difference between China and

other developing countries in Sub-Saharan Africa and South Asia, while the growth rate of

human capital contributes to the growth difference between China and high-income

economies, but the magnitude is not as large as we expected.

China's experience also shows that rapid growth is indeed possible with imperfect

institutions, but it is important in these circumstances that the government addresses the

institutional obstacles to growth as they become apparent. The reform of rural and urban

institutions from 1978 onwards loosened various binding constraints on growth and helped

unleash previously untapped market forces. The augmented Solow model captures the effects

of factor accumulation and structural change. Because our panel data analysis eliminates

country-specific effects, it is silent on the role of several underlying variables such as

institutions, research and development, financial depth and openness of the economy, each of

which is potentially important in the growth process (see, for instance, Quah, 2000).

Moreover, since some variables in our growth equations may themselves need to be

explained if we are to discover the ultimate drivers of growth (see, for instance, Blomström et

al., 1996), it is sensible also to investigate their determinants in China. These will be our next

tasks in modelling China's economic growth.

33

Data source: World Bank, World Development Indicators 2006 Database.

0

2

4

6

8

10

12

14

16

Per

cen

tage

(%)

Figure 4.1 China Annual GDP Per Capita Growth Rates

34

Table 4.1 International Comparison of Key Variables

1980

1990

2000

Average during

1980 - 2000

Change between

1980 and 2000

GDP per capita growth rate per annum (%)

China 6.46 2.29 7.64 8.43 1.18 South Asia 3.87 3.42 2.36 3.33 -1.50

Sub-Saharan Africa 1.07 -1.76 0.79 -0.59 -0.28

Latin America and the Caribbean 3.87 -1.39 2.41 0.57 -1.46

High Income Economies 0.46 2.26 2.83 2.06 2.37

GDP per capita per annum (constant 2000 $)

China 186.44 391.65 949.18 476.44 762.74 South Asia 235.32 327.86 449.60 329.11 214.28

Sub-Saharan Africa 589.60 530.75 515.38 528.72 -74.22

Latin America and the Caribbean 3565.73 3258.70 3852.41 3481.26 286.68 High Income Economies 17304.14 21916.68 26368.33 21419.46 9064.19

Share of gross capital formation in GDP (%)

China 35.19 34.74 32.76 36.04 -2.43

South Asia 18.73 22.83 23.53 21.98 4.80 Sub-Saharan Africa 24.76 17.75 17.28 18.99 -7.48

Latin America and the Caribbean 24.54 19.39 21.07 20.91 -3.47

High Income Economies 24.62 22.94 22.03 22.25 -2.59

Share of agriculture in GDP (%)

China 30.09 27.05 14.83 24.35 -15.26

South Asia 37.15 30.67 24.16 30.90 -12.98 Sub-Saharan Africa 18.72 19.61 18.49 19.61 -0.23

Latin America and the Caribbean 10.16 8.97 6.67 9.01 -3.49

High Income Economies 3.97 2.81 1.79 2.84 -2.18

Population growth rate per annum (%)

China 1.25 1.47 0.71 1.06 -0.54

South Asia 2.46 2.14 1.83 2.08 -0.63 Sub-Saharan Africa 3.11 2.88 2.49 2.77 -0.62

Latin America and the Caribbean 2.31 1.84 1.51 1.87 -0.80

High Income Economies 0.84 0.84 0.82 0.76 -0.02

Average years of schooling over age 15 (year)

China 4.77 5.85 6.36 5.61 1.59 South Asia 2.48 3.24 3.76 3.13 1.28

Sub-Saharan Africa 2.24 2.93 3.40 2.89 1.16

Latin America and the Caribbean 4.86 5.54 6.18 5.53 1.32

High Income Economies 7.82 8.64 9.30 8.58 1.48

Average annual growth rate of average years

of schooling (%)

China 1.66 3.36 0.78 1.48 -0.87

South Asia 6.31 3.73 1.96 3.25 -4.35

Sub-Saharan Africa 3.48 2.97 1.27 2.47 -2.22 Latin America and the Caribbean 2.65 1.41 0.93 1.56 -1.72

High Income Economies 2.01 1.36 0.71 1.18 -1.31

Data source: Human capital variables are from Barro and Lee (2001); and other variables are from

World Bank, World Development Indicators 2006 Database.

35

Table 6.1 The Textbook Solow Model (Unrestricted)

Sample I: 146 countries Sample II: 111 countries Sample III: 61 countries

OLS Within

Groups

System

GMM OLS

Within

Groups

System

GMM OLS

Within

Groups

System

GMM

Constant 0.111

(0.099)

3.103**

(0.536)

0.703*

(0.427)

0.295**

(0.116)

3.043**

(0.509)

0.718*

(0.441)

0.253

(0.211)

1.959**

(0.605)

0.721

(0.464)

-0.047** (0.009)

-0.347** (0.053)

-0.151** (0.032)

-0.045** (0.009)

-0.327** (0.050)

-0.111** (0.051)

-0.070** (0.012)

-0.291** (0.060)

-0.189** (0.053)

0.111**

(0.017)

0.097**

(0.039)

0.231**

(0.050)

0.107**

(0.017)

0.102**

(0.043)

0.248**

(0.049)

0.134**

(0.022)

0.145**

(0.054)

0.211**

(0.046)

-0.051 (0.041)

0.013 (0.111)

-0.062 (0.091)

0.019

(0.038) 0.117** (0.054)

0.099 (0.105)

-0.052 (0.082)

-0.122 (0.107)

-0.192 (0.122)

0.181 0.301 0.172 0.305 0.266 0.325

-3.64

[0.000]

-3.40

[0.001]

-2.60

[0.009]

-0.67

[0.501]

-0.71

[0.480]

-1.03

[0.305]

Hansen Test p value 0.337 0.449 0.999

Difference Sargan p value 0.309 0.429 1.000

Implied 0.009 0.085 0.033 0.009 0.079 0.024 0.015 0.069 0.042

Restriction p value 0.219 0.373 0.126 0.003 0.001 0.001 0.372 0.853 0.892

No. of observations 524 524 524 379 379 379 234 234 234

Note: Heteroskedasticity-consistent standard errors are in parentheses; the test statistics for first and second order correlation are given by and

respectively and the -values are in brackets; instruments used for first-differenced equations in System GMM are , and

; additional instruments used for levels equations in SYS-GMM are , and ; ** and *

indicate that the coefficient is significantly different from zero at the 5 and 10 percent significance level respectively.

36

Table 6.2 The Textbook Solow Model (Outliers removed; Unrestricted)

Sample I: 146 countries Sample II: 111 countries Sample III: 61 countries

OLS Within

Groups

System

GMM OLS

Within

Groups

System

GMM OLS

Within

Groups

System

GMM

Constant 0.181**

(0.081)

2.962**

(0.438)

0.891**

(0.366)

0.292**

(0.114)

2.988**

(0.477)

0.986**

(0.416)

0.256

(0.215)

1.883**

(0.595)

0.702

(0.466)

-0.051** (0.008)

-0.307** (0.042)

-0.161** (0.028)

-0.046** (0.009)

-0.318** (0.047)

-0.128** (0.045)

-0.074** (0.011)

-0.284** (0.057)

-0.202** (0.056)

0.124**

(0.015)

0.114**

(0.034)

0.243**

(0.049)

0.118**

(0.016)

0.106**

(0.039)

0.225**

(0.046)

0.154**

(0.020)

0.171**

(0.050)

0.209**

(0.048)

-0.029 (0.036)

0.117** (0.047)

-0.016 (0.091)

0.025

(0.038) 0.131** (0.045)

0.127 (0.106)

-0.045 (0.085)

-0.096 (0.109)

-0.243** (0.119)

0.239 0.359 0.218 0.358 0.339 0.381

-3.67

[0.000]

-3.26

[0.001]

-2.60

[0.009]

-0.53

[0.596]

-0.74

[0.457]

-1.26

[0.208]

Hansen Test p value 0.489 0.524 0.998

Difference Sargan p value 0.641 0.360 0.953

Implied 0.009 0.073 0.035 0.009 0.077 0.027 0.015 0.067 0.045

Restriction p value 0.018 0.000 0.032 0.001 0.001 0.001 0.245 0.543 0.799

No. of observations 511 511 511 368 368 368 230 230 230

Note: Heteroskedasticity-consistent standard errors are in parentheses; the test statistics for first and second order correlation are given by and

respectively and the -values are in brackets; instruments used for first-differenced equations in System GMM are , and

; additional instruments used for levels equations in SYS-GMM are , and ; ** and *

indicate that the coefficient is significantly different from zero at the 5 and 10 percent significance level respectively.

37

Table 6.3 System GMM Estimation on the Textbook Solow Model (Outliers removed; Restricted)

Sample I Sample II Sample III

146 countries 111 countries 61 countries

Constant 0.578*

(0.349)

0.525

(0.473)

0.751*

(0.439)

-0.158**

(0.028)

-0.133**

(0.047)

-0.199**

(0.055)

- 0.185**

(0.041)

0.148**

(0.037)

0.212**

(0.044)

-3.50

[0.000]

-3.03

[0.002]

-2.71

[0.007]

-0.67

[0.505] -0.96

[0.339] -1.23

[0.218]

Hansen Test p value 0.519 0.360 0.998

Difference Sargan p value 0.428 0.205 0.959

Implied 0.034 0.029 0.044

Implied 0.539 0.527 0.516

No. of observations 511 368 230

Note: Heteroskedasticity-consistent standard errors are in parentheses; the test statistics

for first and second order correlation are given by and respectively and the -

values are in brackets; instruments used for first-differenced equations in System GMM

are , and ; additional instruments used for levels

equations in SYS-GMM are , and ; ** and *

indicate that the coefficient is significantly different from zero at the 5 and 10 percent

significance level respectively.

38

Table 6.4 System GMM Estimation on the Augmented Solow Model with Human Capital (Outliers removed; Unrestricted)

Sample I: 146 countries Sample II: 111 countries Sample III: 61 countries

(1) (2) (3) (1) (2) (3) (1) (2) (3)

Constant -0.392

(0.332)

-0.531*

(0.304)

-0.175

(0.301)

-0.081

(0.305)

-0.343

(0.278)

-0.009

(0.317)

-0.161

(0.305)

-0.206

(0.282)

-0.079

(0.325)

-0.105**

(0.024)

-0.096**

(0.024)

-0.111**

(0.024)

-0.106**

(0.029)

-0.061**

(0.027)

-0.088**

(0.030)

-0.096**

(0.031)

-0.093**

(0.029)

-0.102**

(0.029)

0.161** (0.039)

0.131** (0.038)

0.119** (0.032)

0.164** (0.037)

0.145** (0.033)

0.131** (0.029)

0.142** (0.035)

0.137** (0.036)

0.127** (0.032)

-0.377**

(0.135)

-0.438**

(0.148)

-0.316**

(0.139)

-0.243**

(0.116)

-0.231**

(0.101)

-0.167

(0.123)

-0.256**

(0.099)

-0.305**

(0.079)

-0.253**

(0.093)

0.027

(0.041)

0.090** (0.037)

0.069

(0.046)

0.095** (0.039)

0.068

(0.045)

0.078** (0.039)

0.201

(0.152)

0.169

(0.118)

0.221

(0.139)

0.145

(0.111)

0.034

(0.141)

0.104

(0.099)

Joint significance test for

&

6.06

[0.048]

6.83

[0.033]

6.37

[0.042]

-3.61

[0.000]

-3.91

[0.000]

-3.98

[0.000]

-3.65

[0.000]

-3.79

[0.000]

-4.03

[0.000]

-2.72

[0.006]

-2.61

[0.009]

-2.84

[0.005]

-1.10

[0.270] -1.17

[0.241] -1.18

[0.238]

-1.11 [0.269]

-1.02 [0.310]

-1.07 [0.283]

-0.87

[0.385] -0.91

[0.364] -0.91

[0.362]

Hansen Test p value 0.989 0.966 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Difference Sargan p value 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Implied 0.022 0.02 0.024 0.022 0.013 0.018 0.02 0.02 0.22

Restriction p value 0.131 0.661 0.522 0.411 0.296 0.392

No. of observations 378 375 375 266 263 263 184 184 184

Note: Heteroskedasticity-consistent standard errors are in parentheses; the test statistics for first and second order correlation are given by and

respectively and the -values are in brackets; instruments used for first-differenced equations are , , ,

and ; additional instruments used for levels equations are , , , and

; ** and * indicate that the coefficient is significantly different from zero at the 5 and 10 percent significance level respectively.

39

Table 6.5 System GMM Estimation on the Augmented Solow Model with Human Capital (Outliers removed; Restricted)

Growth Rate of Human Capital Level of Human Capital

Sample I Sample II Sample III Sample I Sample II Sample III

146 countries 111 countries 61 countries 146 countries 111 countries 61 countries

Constant -0.512*

(0.287)

-0.383

(0.281)

-0.123

(0.278) Constant

-0.031

(0.199)

0.042

(0.234)

0.084

(0.264)

-0.091**

(0.024)

-0.073**

(0.027)

-0.087**

(0.030)

-0.105**

(0.028)

-0.099**

(0.028)

-0.098**

(0.032)

- 0.138**

(0.035)

0.144**

(0.034)

0.139**

(0.034) -

0.193**

(0.040)

0.170**

(0.035)

0.155**

(0.032)

- 0.264** (0.108)

0.147* (0.087)

0.107 (0.091)

0.056

(0.042) 0.066

(0.046) 0.065

(0.047)

-4.11

[0.000] -3.62

[0.000] -2.68

[0.007]

-3.73 [0.000]

-3.47 [0.001]

-2.66 [0.008]

-1.11

[0.268]

-1.16

[0.244]

-0.85

[0.393]

-0.92

[0.357]

-1.03

[0.304]

-0.79

[0.432]

Hansen Test p value 0.985 1.000 1.000 Hansen Test p value 0.984 1.000 1.000

Difference Sargan p value 1.000 1.000 1.000 Difference Sargan p value 1.000 1.000 1.000

Implied 0.019 0.015 0.018 Implied 0.022 0.021 0.021

Implied 0.279 0.396 0.417 Implied 0.648 0.632 0.613

Implied 0.535 0.404 0.321 Implied 0.188 0.245 0.257

No. of observations 375 263 184 No. of observations 378 266 184

Note: Heteroskedasticity-consistent standard errors are in parentheses; the test statistics for first and second order correlation are given by and

respectively and the -values are in brackets; instruments used for first-differenced equations are , , ,

and ; additional instruments used for levels equations are , , , and

; ** and * indicate that the coefficient is significantly different from zero at the 5 and 10 percent significance level respectively.

40

Table 6.6 System GMM Estimation on the Augmented Solow Model with Human Capital and Structural Change 1 (Outliers removed; Unrestricted)

Sample I: 146 countries Sample II: 111 countries Sample III: 61 countries

(1) (2) (3) (1) (2) (3) (1) (2) (3)

Constant -0.295

(0.306)

-0.546**

(0.272)

-0.243

(0.276)

-0.056

(0.305)

-0.324

(0.262)

-0.052

(0.287)

-0.066

(0.299)

-0.067

(0.243)

-0.057

(0.276)

-0.098** (0.021)

-0.078** (0.017)

-0.099** (0.019)

-0.103** (0.022)

-0.068** (0.016)

-0.092** (0.023)

-0.099** (0.023)

-0.092** (0.023)

-0.096** (0.023)

0.151**

(0.031)

0.129**

(0.031)

0.110**

(0.026)

0.143**

(0.031)

0.143**

(0.028)

0.122**

(0.027)

0.129**

(0.029)

0.111**

(0.029)

0.109**

(0.027)

-0.302**

(0.119)

-0.368**

(0.121)

-0.308**

(0.111)

-0.224**

(0.099)

-0.238**

(0.086)

-0.205**

(0.090)

-0.246**

(0.085)

-0.269**

(0.063)

-0.245**

(0.079)

0.042

(0.031)

0.071** (0.028)

0.072** (0.033)

0.072** (0.034)

0.040

(0.036)

0.053* (0.033)

0.192*

(0.106)

0.129

(0.086)

0.101

(0.094)

0.056

(0.077)

0.043

(0.113)

0.062

(0.088)

0.864

(0.996) 0.425

(1.026) 0.501

(0.993)

1.128 (0.901)

0.916 (0.998)

1.131 (0.851)

0.581

(0.827) -0.375 (0.979)

0.397 (0.879)

2.774

(2.716)

4.357

(2.748)

4.329

(2.857)

2.011

(2.356)

2.747

(2.638)

2.284

(2.458)

3.064

(2.292)

6.563**

(2.851)

3.732

(2.473)

Joint significance test for

&

7.57

[0.023]

4.55

[0.103]

2.74

[0.255]

Joint significance test for H &

16.07

[0.000]

16.84

[0.000]

19.16

[0.000]

15.44

[0.000]

17.39

[0.000]

20.02

[0.000]

14.72

[0.001]

20.28

[0.000]

18.51

[0.000]

-3.79

[0.000] -4.10

[0.000] -4.08

[0.000]

-3.61 [0.000]

-3.71 [0.000]

-3.75 [0.000]

-2.93

[0.003] -2.80

[0.005] -2.89

[0.004]

-0.95

[0.345]

-1.11

[0.268]

-1.15

[0.250]

-1.02

[0.307]

-1.09

[0.274]

-1.13

[0.257]

-0.77

[0.441]

-0.87

[0.385]

-0.90

[0.366]

Hansen Test p value 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Difference Sargan p value 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Implied 0.021 0.016 0.021 0.022 0.014 0.019 0.021 0.019 0.02

No. of observations 373 370 370 261 258 258 179 179 179

41

Table 6.7 System GMM Estimation on the Augmented Solow Model with Human Capital and Structural Change 2 (Outliers removed; Unrestricted)

Sample I: 146 countries Sample II: 111 countries Sample III: 61 countries

(1) (2) (3) (1) (2) (3) (1) (2) (3)

Constant -0.087

(0.294)

-0.542**

(0.263)

-0.044

(0.285)

0.132

(0.328)

-0.169

(0.311)

0.235

(0.315)

0.334

(0.285)

0.057

(0.225)

0.289

(0.253)

-0.128** (0.022)

-0.102** (0.020)

-0.124** (0.021)

-0.110** (0.021)

-0.071** (0.016)

-0.109** (0.021)

-0.117** (0.021)

-0.101** (0.016)

-0.110** (0.018)

0.154**

(0.029)

0.127**

(0.035)

0.117**

(0.028)

0.147**

(0.028)

0.146**

(0.029)

0.124**

(0.026)

0.118**

(0.028)

0.120**

(0.030)

0.103**

(0.025)

-0.310**

(0.129)

-0.461**

(0.128)

-0.294**

(0.128)

-0.173

(0.120)

-0.191*

(0.119)

-0.139

(0.110)

-0.150

(0.088)

-0.224**

(0.092)

-0.155*

(0.083)

0.090** (0.031)

0.109** (0.032)

0.089** (0.031)

0.105** (0.032)

0.049

(0.034)

0.054** (0.026)

0.118

(0.103)

0.164*

(0.098)

0.080

(0.080)

0.096

(0.082)

-0.001

(0.105)

0.052

(0.078)

0.441

(0.982) 0.774

(0.947) 0.586

(0.877)

1.625 (1.059)

1.588* (0.987)

1.174 (0.918)

2.985** (0.669)

3.277** (0.717)

2.787** (0.693)

0.173**

(0.056)

0.228**

(0.064)

0.205**

(0.051)

0.134**

(0.057)

0.127**

(0.062)

0.159**

(0.054)

0.208**

(0.052)

0.208**

(0.058)

0.217**

(0.055)

Joint significance test for

&

11.81

[0.003]

10.50

[0.005]

4.83

[0.089]

Joint significance test for H2 &

11.42

[0.003]

15.71

[0.000]

19.87

[0.000]

10.28

[0.006]

9.15

[0.010]

12.70

[0.002]

33.60

[0.000]

27.62

[0.000]

33.75

[0.000]

-3.75

[0.000] -3.92

[0.000] -4.02

[0.000]

-3.60 [0.000]

-3.52 [0.000]

-3.53 [0.000]

-2.70

[0.007] -2.56

[0.011] -2.59

[0.010]

-0.92

[0.358]

-1.07

[0.283]

-1.01

[0.311]

-0.95

[0.344]

-1.06

[0.287]

-1.00

[0.318]

-0.67

[0.500]

-0.74

[0.458]

-0.79

[0.427]

Hansen Test p value 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Difference Sargan p value 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Implied 0.027 0.022 0.026 0.023 0.015 0.023 0.025 0.021 0.023

No. of observations 355 352 352 250 247 247 170 170 170

42

Table 6.8 Growth and Growth Difference Prediction between China and Sub-Saharan Africa (Based on Sample III Estimation)

Variable (1)Parameter

estimates

(2) Mean value of

China (per annum)

(3) Mean value of

SSA (per annum)

(4) Mean difference

(China vs SSA)

(5) Difference in predicted

growth (China vs SSA)

(6) Percentage of total predicted

growth difference (China vs SSA)

(4) = (2) - (3) (5) = (1) * (4)

-0.096 1.554 1.655 -0.101 0.010 17.2 0.109 0.662 0.386 0.276 0.030 53.7

-0.245 -0.760 -0.704 -0.056 0.014 24.3 0.052 0.345 0.232 0.113 0.006 10.6

0.062 0.015 0.016 -0.001 0.000 -0.2 0.397 0.011 0.004 0.007 0.003 4.9

3.733 0.001 0.000 0.001 0.004 7.3

Actual annual growth rate and growth rate difference

0.072 0.004 0.068

Total annual predicted

growth rate and growth rate

difference

0.063 0.007 0.056

Percentage of annual actual

growth rate and growth

difference that is predicted

87.62

82.44

Note: The difference in the sample means of a variable between regions X and Y equals the average value in region X minus the average value in region Y;

the difference in predicted growth between region X and Y attributable to a certain variable is equal to the difference in the sample means of that variable

between region X and Y times the estimated coefficient on that variable from the regression; the total difference in predicted growth between region X and Y equals the sum of the differences in predicted growth attributable to all variables contained in the regression including constant and time dummies.

43

Table 6.9 Growth Difference Prediction between China and Other Country-Groups (Based on Sample I Estimation):

Percentage Components of the Difference in Predicted Growth Rates

Variable Parameter estimates

Mean value of China

China vs All

Other

Countries

China vs High

Income

Economies

China vs

Sub-Saharan

Africa

China vs Latin

America and the

Caribbean

China vs East

Asia and the

Pacific

China vs South Asia

-0.099 1.554 73.4 103.0 29.2 59.2 59.4 24.9 0.110 0.662 24.6 10.1 42.5 26.0 43.4 40.2

-0.308 -0.760 -12.5 -44.0 24.1 6.9 1.1 3.4 0.071 0.345 -1.9 -11.2 11.7 -0.2 -3.4 17.4

0.130 0.015 -0.6 0.8 -1.3 0.0 -0.4 -4.8 0.501 0.011 5.3 7.7 4.5 4.0 6.1 5.7

4.329 0.001 4.7 5.2 6.1 3.6 8.4 7.4

Actual annual growth rate / growth rate difference

0.072 0.061 0.058 0.066 0.067 0.051 0.044

Predicted annual growth

rate/ growth rate difference

0.069 0.058 0.055 0.063 0.063 0.046 0.048

Percentage of annual actual

growth difference predicted

95.8 94.5 94.7 95.6 94.2 88.7 107.9

Note: All other countries consist of 145 countries in Sample I except China, which also includes Europe and Central Asia that is not reported in this table; the high-income economies include 39 high-income OECD and

non-OECD members; Latin America and the Caribbean contains 26 countries; East Asia and the Pacific

comprises 14 countries excluding China; and South Asia includes 7 countries.

44

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47

Appendix

Table A1. Employment Data for China

NBS Data FAO Data

Total Employment (Unit: 10 000

person)

Employment in Agriculture (Unit: 10 000

person)

Share of Agricultural Employment

Total Labour Force

(Unit: 10 000 person)

Labour Force in Agriculture (Unit: 10 000

person)

Share of Agricultural

Labour Force

1978 40152 28318 70.53% 52946 39565 74.73% 1979 41024 28634 69.80% 54017 40140 74.31% 1980 42361 29122 68.75% 55104 40718 73.89% 1981 43725 29777 68.10% 56258 41459 73.70% 1982 45295 30859 68.13% 57429 42209 73.50% 1983 46436 31151 67.08% 58636 42980 73.30% 1984 48179 30868 64.07% 59897 43787 73.10% 1985 49873 31130 62.42% 61224 44636 72.91% 1986 51282 31254 60.95% 62630 45538 72.71% 1987 52783 31663 59.99% 64106 46485 72.51% 1988 54334 32249 59.35% 65618 47452 72.32% 1989 55329 33225 60.05% 67116 48404 72.12% 1990 64749 34117 52.69% 68563 49312 71.92% 1991 65491 34956 53.38% 69524 49652 71.42% 1992 66152 34795 52.60% 70413 49928 70.91% 1993 66808 33966 50.84% 71248 50151 70.39% 1994 67455 33386 49.49% 72056 50343 69.87% 1995 68065 33018 48.51% 72858 50518 69.34% 1996 68950 32909 47.73% 73657 50678 68.80% 1997 69820 33095 47.40% 74446 50820 68.26% 1998 70637 33232 47.05% 75223 50939 67.72% 1999 71394 33493 46.91% 75979 51034 67.17% 2000 72085 33355 46.27% 76711 51100 66.61%

Note: (1) NBS Data are from China Labour Statistical Yearbook (2003), complied by National Bureau of

Statistics of China (NBS) and Ministry of Labour and Social Security of China; NBS definition on

agricultural employment is the number of employment in farming, forestry, animal husbandry and fishery; and NBS definition on total employment is the number of employment in farming, forestry,

animal husbandry and fishery; mining and quarrying; manufacturing; production and supply of

electricity, gas and water; construction; geological prospecting and water conservancy; transport, storage, post and telecommunications; wholesale and retail trade and catering services; finance and

insurance; real estate trade; social services; health care, sporting and social welfare; education, culture

and arts, ratio, film and television; scientific research and polytechnic services; government agencies,

party agencies and social organizations; and others. (2) FAO data are from Statistical Database of the Food and Agriculture Organization of the United

Nations. FAO definition on labour force in agriculture (economically active population in agriculture)

is that part of the economically active population engaged in or seeking work in agriculture, hunting, fishing or forestry; and FAO definition on total labour force (economically active population) is the

number of all employed and unemployed persons (including those seeking work for the first time). It

covers employers, self-employed workers, salaried employees, wage earners, unpaid workers assisting

in a family, farm or business operation, members of producers' cooperatives, and members of the armed forces.

48

Table A2. Samples in this paper

All Countries in PWT 6.2 (188 countries)

Country Isocode

PWT Order

Region

Sample I (146)

Sample II (111)

Sample III (61)

Afghanistan AFG 1 SA 1 1 1 Albania ALB 2 EUCA 1 1 0 Algeria DZA 3 MENA 0 0 0 Angola AGO 4 SSA 0 0 0 Antigua ATG 5 HIE 1 0 0 Argentina ARG 6 LAC 1 1 1 Armenia ARM 7 EUCA 1 1 0 Australia AUS 8 HIE 1 0 0 Austria AUT 9 HIE 1 0 0 Azerbaijan AZE 10 EUCA 1 1 1 Bahamas BHS 11 HIE 1 0 0 Bahrain BHR 12 HIE 1 0 0 Bangladesh BGD 13 SA 1 1 1 Barbados BRB 14 LAC 1 1 0 Belarus BLR 15 EUCA 0 0 0 Belgium BEL 16 HIE 1 0 0 Belize BLZ 17 LAC 1 1 0 Benin BEN 18 SSA 1 1 0 Bermuda BMU 19 HIE 1 0 0 Bhutan BTN 20 SA 0 0 0 Bolivia BOL 21 LAC 1 1 1 Bosnia and Herzegovina BIH 22 EUCA 1 1 0 Botswana BWA 23 SSA 1 1 0 Brazil BRA 24 LAC 1 1 1 Brunei BRN 25 HIE 1 0 0 Bulgaria BGR 26 EUCA 1 1 1 Burkina Faso BFA 27 SSA 1 1 1 Burundi BDI 28 SSA 1 1 0 Cambodia KHM 29 EAP 0 0 0 Cameroon CMR 30 SSA 1 1 1 Canada CAN 31 HIE 1 0 0 Cape Verde CPV 32 SSA 0 0 0 Central African Republic CAF 33 SSA 0 0 0 Chad TCD 34 SSA 0 0 0 Chile CHL 35 LAC 1 1 1 China CHN 36 EAP 1 1 1 Colombia COL 37 LAC 1 1 1 Comoros COM 38 SSA 0 0 0 Congo, Dem. Rep. ZAR 39 SSA 0 0 0 Congo, Republic of COG 40 SSA 1 1 0 Costa Rica CRI 41 LAC 1 1 0 Cote d`Ivoire CIV 42 SSA 1 1 1 Croatia HRV 43 EUCA 1 1 0 Cuba CUB 44 LAC 0 0 0 Cyprus CYP 45 HIE 0 0 0 Czech Republic CZE 46 EUCA 1 1 1 Denmark DNK 47 HIE 1 0 0

49

Djibouti DJI 48 MENA 0 0 0 Dominica DMA 49 LAC 1 1 0 Dominican Republic DOM 50 LAC 1 1 1 Ecuador ECU 51 LAC 1 1 1 Egypt EGY 52 MENA 1 1 1 El Salvador SLV 53 LAC 1 1 0 Equatorial Guinea GNQ 54 SSA 0 0 0 Eritrea ERI 55 SSA 0 0 0 Estonia EST 56 EUCA 1 1 0 Ethiopia ETH 57 SSA 1 1 1 Fiji FJI 58 EAP 1 1 0 Finland FIN 59 HIE 1 0 0 France FRA 60 HIE 1 0 0 Gabon GAB 61 SSA 1 1 0 Gambia, The GMB 62 SSA 1 1 0 Georgia GEO 63 EUCA 1 1 1 Germany GER 64 HIE 1 0 0 Ghana GHA 65 SSA 1 1 1 Greece GRC 66 HIE 1 0 0 Grenada GRD 67 HIE 1 0 0 Guatemala GTM 68 LAC 1 1 1 Guinea GIN 69 SSA 1 1 0 Guinea-Bissau GNB 70 SSA 0 0 0 Guyana GUY 71 LAC 0 0 0 Haiti HTI 72 LAC 0 0 0 Honduras HND 73 LAC 1 1 0 Hong Kong HKG 74 HIE 1 1 1 Hungary HUN 75 EUCA 1 1 1 Iceland ISL 76 HIE 1 0 0 India IND 77 SA 1 1 1 Indonesia IDN 78 EAP 1 1 1 Iran IRN 79 MENA 1 1 1 Iraq IRQ 80 MENA 0 0 0 Ireland IRL 81 HIE 1 0 0 Israel ISR 82 HIE 1 0 0 Italy ITA 83 HIE 1 0 0 Jamaica JAM 84 LAC 1 1 0 Japan JPN 85 HIE 1 0 0 Jordan JOR 86 MENA 1 1 0 Kazakhstan KAZ 87 EUCA 1 1 1 Kenya KEN 88 SSA 1 1 1 Kiribati KIR 89 EAP 1 1 0 Korea, Dem. Rep. PRK 90 EAP 1 1 1 Korea, Republic of KOR 91 HIE 1 1 1 Kuwait KWT 92 HIE 1 0 0 Kyrgyzstan KGZ 93 EUCA 1 1 0 Laos LAO 94 EAP 0 0 0 Latvia LVA 95 EUCA 1 1 0 Lebanon LBN 96 MENA 1 1 0 Lesotho LSO 97 SSA 0 0 0 Liberia LBR 98 SSA 0 0 0

50

Libya LBY 99 MENA 1 1 0 Lithuania LTU 100 EUCA 1 1 0 Luxembourg LUX 101 HIE 1 0 0 Macao MAC 102 HIE 1 0 0 Macedonia MKD 103 EUCA 1 1 0 Madagascar MDG 104 SSA 1 1 1 Malawi MWI 105 SSA 1 1 1 Malaysia MYS 106 EAP 1 1 1 Maldives MDV 107 SA 1 1 0 Mali MLI 108 SSA 1 1 1 Malta MLT 109 HIE 0 0 0 Mauritania MRT 110 SSA 1 1 0 Mauritius MUS 111 SSA 1 1 0 Mexico MEX 112 LAC 1 1 1 Micronesia, Fed. Sts. FSM 113 EAP 1 1 0 Moldova MDA 114 EUCA 1 1 0 Mongolia MNG 115 EAP 0 0 0 Morocco MAR 116 MENA 1 1 1 Mozambique MOZ 117 SSA 0 0 0 Namibia NAM 118 SSA 0 0 0 Nepal NPL 119 SA 1 1 1 Netherlands NLD 120 HIE 1 0 0 Netherlands Antilles ANT 121 HIE 1 0 0 New Zealand NZL 122 HIE 1 0 0 Nicaragua NIC 123 LAC 1 1 0 Niger NER 124 SSA 0 0 0 Nigeria NGA 125 SSA 1 1 1 Norway NOR 126 HIE 1 0 0 Oman OMN 127 MENA 1 1 0 Pakistan PAK 128 SA 1 1 1 Palau PLW 129 EAP 1 1 0 Panama PAN 130 LAC 1 1 0 Papua New Guinea PNG 131 EAP 0 0 0 Paraguay PRY 132 LAC 1 1 0 Peru PER 133 LAC 1 1 1 Philippines PHL 134 EAP 1 1 1 Poland POL 135 EUCA 1 1 1 Portugal PRT 136 HIE 1 0 0 Puerto Rico PRI 137 HIE 0 0 0 Qatar QAT 138 HIE 1 0 0 Romania ROM 139 EUCA 1 1 1 Russia RUS 140 EUCA 1 1 1 Rwanda RWA 141 SSA 1 1 1 Samoa WSM 142 EAP 1 1 0 Sao Tome and Principe STP 143 SSA 0 0 0 Saudi Arabia SAU 144 HIE 0 0 0 Senegal SEN 145 SSA 1 1 1 Serbia and Montenegro SCG 146 EUCA 1 1 1 Seychelles SYC 147 SSA 0 0 0 Sierra Leone SLE 148 SSA 1 1 0 Singapore SGP 149 HIE 1 1 1

51

Slovak Republic SVK 150 EUCA 1 1 0 Slovenia SVN 151 HIE 1 0 0 Solomon Islands SLB 152 EAP 1 1 0 Somalia SOM 153 SSA 0 0 0 South Africa ZAF 154 SSA 1 1 1 Spain ESP 155 HIE 1 0 0 Sri Lanka LKA 156 SA 1 1 1 St. Kitts & Nevis KNA 157 LAC 1 1 0 St. Lucia LCA 158 LAC 1 1 0 St.Vincent & Grenadines VCT 159 LAC 1 1 0 Sudan SDN 160 SSA 0 0 0 Suriname SUR 161 LAC 0 0 0 Swaziland SWZ 162 SSA 1 1 0 Sweden SWE 163 HIE 1 0 0 Switzerland CHE 164 HIE 1 0 0 Syria SYR 165 MENA 1 1 1 Taiwan TWN 166 HIE 1 1 1 Tajikistan TJK 167 EUCA 0 0 0 Tanzania TZA 168 SSA 1 1 1 Thailand THA 169 EAP 1 1 1 Togo TGO 170 SSA 0 0 0 Tonga TON 171 EAP 1 1 0 Trinidad &Tobago TTO 172 LAC 1 1 0 Tunisia TUN 173 MENA 1 1 1 Turkey TUR 174 EUCA 1 1 1 Turkmenistan TKM 175 EUCA 0 0 0 Uganda UGA 176 SSA 0 0 0 Ukraine UKR 177 EUCA 1 1 1 United Arab Emirates ARE 178 HIE 0 0 0 United Kingdom GBR 179 HIE 1 0 0 United States USA 180 HIE 1 0 0 Uruguay URY 181 LAC 1 1 0 Uzbekistan UZB 182 EUCA 0 0 0 Vanuatu VUT 183 EAP 1 1 0 Venezuela VEN 184 LAC 1 1 1 Vietnam VNM 185 EAP 1 1 1 Yemen YEM 186 MENA 0 0 0 Zambia ZMB 187 SSA 1 1 1 Zimbabwe ZWE 188 SSA 1 1 1

Note: 'EAP': East Asia and Pacific; 'EUCA': Europe and Central Asia; 'LAC': Latin America & the

Caribbean; 'MENA': Middle East and North Africa; 'SA': South Asia; 'SSA': Sub-Saharan Africa;

and 'HIE': High-Income Economies include both high-income OCED members and non-OECD members. Country groups by region and income are based on definition of World Bank.