As at 17:00 / 19-11-2010
Rural Labour Reallocation and Productivity Growth in China1
Fung KWAN2
Yang ZHANG3
Shuaihe ZHUO4
Abstract
Dualism has long been a distinguished feature of many developing economies.
This paper attempts to examine the possible contributions of structural change,
measured by labour reallocation from agriculture to non-agriculture, to the
growth of total factor productivity (TFP) in China during reform. Building
upon the framework developed by Temple and WÖßmann (2006), we find that
a three-sector model is more suitable to identify the role of labour reallocation
to TFP growth in rural China.
JEL O11,
Keyword Labour reallocation, TFP growth, wage differentials
1
2
3
4
Draft and for discussion only. Please do not quote without permission from the authors.
Department of Economics, University of Macau, Macao; Email: FungKwan@umac.mo
Faculty of Business Administration, University of Macau, Macao.
Department of Economics, University of Macau, Macao.
1
1
Introduction
China had around 470 million labourers in its countryside in 2008, 50 percent
more than the figure in 1980 (Table 1). Of these, 269 million were in agriculture.
With just 122 million hectares of arable land (NBS, 2008), the Chinese
countryside seems unable to provide enough agricultural jobs for peasants.
This, together with the development of rural enterprises and other nonagricultural sectors, have attracted many agricultural labour to become engaged
in all these formal and informal activities since the economic reform in the late
1970s.
Dualism has long been a distinguished feature of many developing
economies. The primer works of Lewis (1954) and Ranis & Fei (1961) remain
important to the basic understanding of this framework. Fei & Ranis (1997)
revised and completed the whole dual economy models. The analytical
framework of dualism is based on the assumption that an economy is divided
into two sectors, the first being the traditional sector, and the second modern
sector (A popular interpretation views the dichotomy as one between
agriculture and industry). The traditional sector employs non-wage labour, or
household-based decision-making units, to produce goods for subsistence
purposes, while the modern sector contractually hires factor inputs to produce
goods for profit maximization. In the modern sector, it is also assumed that
exchange takes place through the market mechanism.
The theoretical models have been applied to study the industralization of
many countries, but surprisingly little effort has been made to China. The
application of dualism to China could at least cover the following development
issues:
(1) The existence of the surplus labour / inefficient labour in rural China;
(2) The transfer of such labour from the traditional sector to the modern
sector (the development of rural enterprises after 1978 in particular); and
(3) The output growth contributed by such labour transfer through the
growth of TFP.
This paper attempts to examine possible contributions of structural change
to the growth of total factor productivity in China. To measure structural
change, we focus on the reallocation of agricultural labour in the countryside to
both non-agriculture in the rural and urban sectors. A three-sector model is
developed to analyze the growth relationship between structural change and
productivity growth.
There have been tremendous changes of GDP composition in China over
the last three decades. During this period, the structural change of labour
market contributed positively to the employment creation. Figure 1 shows that
labour participated in agriculture dropped from nearly 60 percent in 1980 to
2
around 35 percent of total employment in 2008. Urban employment, on the
other hand, shows steady growth from some 25 percent to almost 40 percent
over the same period. More importantly, labour employment in rural nonagriculture (represented by rural enterprise workers in the early years and
employment from various non-state sectors in more recent years) expanded
from less than 10 percent in 1980 to more than 25 percent in 2008.
The rest of the paper is organized as follows. Section 2 discusses the
development of labour market of China. Brief literature of growth related to
structural change is reviewed in section 3. We derive our three-sector
framework in section 4 and present the empirical model in section 5. The initial
results are discussed in sector 6. Section 7 summaries our major findings.
Figure 1: Distribution of Labour Employment in China
80
70
Labour Share (%)
60
Urban
50
40
Rural
Agriculture
30
Rural Non‐
Agriculture
20
10
0
Source: NBS.
2
Rural Labour Market of China
Rural China appears to fit the dualistic framework reasonably well (Putterman
1992). Before 1978, the collectivized institutional framework of agriculture,
mainly represented by the rural communes and the household registration
system (hukou), was an effective mechanism for controlling the huge rural
population, in accordance with the strategic imperative of prioritizing heavy
industrial development. However, with the modification of this strategy when
the economic reform started at the end of the 1970s, rural enterprises (mainly
industrial firms) became the main non-agricultural entities that “absorbed”
rural labour. Since then, those who stayed in farming had been more successful
in engaging in farming activities under various forms of the household
3
responsibility system, especially the popular Baogan Daohu (contracting
everything to the households).
Table 1: Rural Labour & Its Composition in China (1980-2008, Selected Years)
Year
Rural
L
RE L
PE L
Ag L
Rural L
RE L
PE L
Ag L
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
1980
318.4
30.0
0.0
298.1
9.4
0.0
93.6
3.0
1985
370.7
69.8
0.0
303.5
18.8
0.0
81.9
5.1
1990
477.1
92.7
16.0
368.4
19.4
3.4
77.2
4.1
1995
490.3
128.6
35.3
326.4
26.2
7.2
66.6
5.3
2000
489.3
128.2
40.7
320.4
26.2
8.3
65.5
5.4
2005
484.9
142.7
44.9
297.3
29.4
9.3
61.3
6.1
2007
476.4
150.9
48.6
276.9
31.7
10.2
58.1
6.6
2008
472.7
154.5
49.5
268.7
32.7
10.5
56.8
6.9
(2) – (5) are in million labourers; (6) – (9) are %.
Rural L: Rural Labour, RE L: Labour of Rural Enterprises, PE L: Labour in Private Enterprises, Ag L: Agricultural
Labour.
Sources: NBS (2009), pp.112-113.
3
Brief Literature Review
There are various theoretical approaches of identifying sources of output
growth. The Solow neoclassical growth framework is considered the first
structural growth model. Mankiw et al (1992) employed in the growth equation
exogenous technology and diminishing returns to capital which provided good
explanation of output differences among countries. These models were later
extended to include human capital as input to the production for innovations,
the so-called endogenous growth models (such as Howitt, 2000). Nevertheless,
these models are criticized mainly by ignoring some other important variables.
The second approach is to use ad hoc regressions to incorporate all relevant
variables, a Barro-type regressions after Barro (1991). Such informal regressions
are popular because they can include important factors other than conventional
inputs. These reduced-form growth regressions are subject to the problem of
model uncertainty.
One of the criticisms of the growth accounting exercise is treating TFP as a
residual, which include factors like structural change, improvement in
allocative efficiency, economies of scale, and other omitted variables. The third
type of model intends to rectify this shortcoming by concentrating on the role of
technological efficiency in determining economic growth.
Studies of economic growth or dual economy models are often criticized
for ignoring the role of structural change. As confirmed by many empirical
4
studies, there exists a significant differential of marginal product of labour
across sectors in developing economies. Changes in the composition of
employment should be, therefore, considered as an independent factor of
accounting for source of economic growth.
Temple and WÖßmann (2006) attempt to incorporate structural change
terms into the augmented Solow growth model so as to capture the role of both
factor accumulation and productivity growth in variations on output growth.
In addition to the standard determinants of aggregate TFP, Temple and
WÖßmann include two approximations in their empirical models to measure
the structural change. The first is approximated by the growth of nonagricultural employment and the second is the expression of migration
propensity times the change of non-agricultural employment. This model
exhibits several advantages. Firstly, it allows the effect of labour reallocation
between sectors with different productivity into productivity growth.
Secondly, no capital stock measurement is required in this model. Finally, this
structural growth model is less subjective to the problem of model uncertainty
than the Barro-type ad hoc model.
Following this, Ding and Knight (2009) applies this framework to a crosscountry panel data analysis with system GMM estimates which includes China.
They found that this extended augmented Solow model provides a good
explanation of China’s output growth: actual annual growth of per worker GDP
at 7.2% falls with the 95% confidence interval for its predicted value (6.3%). The
unexplained residual might represent China’s efficiency gains from reform and
marketization. However, the main limitation of using this framework is its
failure to take proper account of labor movement with the rural sector. We aim
to address this problem in our model developed below.
4
The Theoretical Framework
In this paper, we develop a three-sector model to capture the effect of structural
change in China. Instead of the division between rural and urban sectors that
often used in other papers, we adopt a different framework by segmenting the
Chinese economy into three sectors: rural agriculture, rural non-agriculture and
urban sectors, respectively. There are several advantages of such division.
Firstly, the non-farm agricultural sectors enjoyed a profound development after
the agricultural reform in the end of the 1970s, and therefore labour
productivity in Chinese agricultural sector is expected to change significantly.
Second, a lot of peasants in rural China have been employed by different nonagricultural sectors since reform, initially by the rural enterprises (mainly the
township and village enterprises), and later formal and informal productions in
the countryside. Due to the job nature, marginal product of labour in
agriculture and that in rural non-agricultural are expected to be significantly
different. Thirdly, some of the rural labour is believed to work in various urban
5
formal and informal productions in the presence of the household registration
system. With China’s WTO membership in 2001, labour participate in the
urban sector is even more obvious. The work patterns are thus vary across
sectors.
The direction of labour reallocation in our three-sector model is more
complicated than that under the rural-urban migration. To simplify our
analysis, we only consider the possibility of people moving from agriculture to
rural non-agriculture or from agriculture to urban sector.
We first define the shares of labour in the three sectors
；
,
,
as
[1]
；
where the subscripts a,b,m denote rural agriculture, rural non-agriculture, and
urban sectors respectively.
The extents of structural change in rural non-agricultural sector ( ) and
urban sector ( ) are measured by
[2]
[3]
The dots refer to the derivatives of shares of labour with respect to time. The s
are alternatively interpreted as propensity to migrate.
In the long-run, it is assumed that no labour reallocation due to wage
differentials will happen. Accordingly, long-run wage s in the three sectors
have the relationships as follows.
1
[4]
1
[5]
and the parameter κ s measure the intersectoral wage ratio when labour
reallocation / migration does not occur in the long-run.
The decision to work in other sectors of individual labour is based on the
long-run and short-run wage ratio differentials. Since the scenario when wage
rates equal to marginal products of labour is hardly observable, a simplified
assumption is chosen to model such relationship. According to Temple and
WÖßmann (2006), “we can use the observed extend of structural change to infer
the magnitude of the wage differential”, and only the current ratio of wages
6
between sectors is considered. The propensity to migrate from rural agriculture
to rural non-agriculture is specified as this form:
[6]
and
1
[7]
where denotes the wage in short-run and captures the speed of adjustment
from short-run to long-run equilibrium.
indicates the difference between the
short-run and long-run wage ratio where the latter is 1. We assume
and therefore labour reallocation could occur in the short-run. Moreover, the
relationship in [6] is consistent with the fact that the propensity to migrate will
decrease as the agricultural wage increases.
Similarly, labour reallocation from rural agriculture to urban sector has
the following relationship:
[8]
1
[9]
The unobservable wage rates are expressed in terms of propensity to
migrate and other parameters:
1
[10]
1
[11]
The total production is the sum of output in three sectors:
[12]
where
and
are relative prices.
, labour , land
Given the factor inputs capital
and technology , the sectoral production functions are:
(fixed in our case)
,
,
[13]
,
,
[14]
,
,
[15]
7
If the labour markets in each sector are competitive, workers are assumed
to be paid their marginal products:
[16]
[17]
[18]
where the subscript
respect to labour.
refers to the derivative of production function with
The capital markets are assumed to be competitive and the rentals are
constant across the three sectors:
[19]
where is the rent and the subscript
function with respect to capital.
refers to the derivative of the production
When the sectoral production functions are homogenous of degree one,
the labour share and the capital share 1
are expressed as follows:
[20]
1
[21]
Take total differentiation of Eq [12] with respect to time, we have
[22]
Alternatively the aggregate output growth is written in terms of the share
of each sector:
1
[23]
where
[24]
[25]
8
With the standard Cobb-Douglas technology, the aggregate production
function can be written in the form of
1
[26]
where denotes the aggregate technology and the is the growth of total factor
productivity. Since our model has three sectors, Eqs. [22] and [26] could be
treated as the starting point of our empirical work. Let us rewrite Eq [26] as:
1
[27]
With Eqs [10] and [11], Eq [21] could be expressed in the following:
[28]
Together with Eqs. [22] and [28], Eq. [27] is further expanded into:
1
1
1
[29]
Finally the relationship between productivity growth and structural
change of labour employment is
1
1
1
11 1
21 2
Eq [30] is proved in Appendix A.
,
measured by the terms
[30]
Accordingly, the structural change is
,
, and
.
Intuitively, the aggregate TFP is decomposed into three parts. The first
part is the weighted sum of sectoral TFP growth. The second part is the labour
growth of rural non-agriculture and urban sector. The third part is the change
of disequilibrium of labour shares. If we consider the case of a two-sector
model, i.e., between agriculture and urban sectors, all the terms with subscript
will be removed. That case, Eq [30] will collapse to the dual economy models
developed by Temple and WÖßmann (2006).
9
5
The Empirical Model
We derive a consistent empirical model to estimate Eq [30] with the following
aggregate production function:
[31]
Let us denote
/
and
/
and assume
0
and
0
, where is the growth rate of technology and is the growth rate
of labour. So at the steady state can be shown that
ln
ln
ln
0
ln
ln
ln
[32]
which is proved in the Appendix B. Eq [32] implies that the economy will
converge to the state steady from the initial year. When there is no structural
change, the TFP growth in the Solow model is expressed as:
1
[33]
In the MRW model developed by Mankiw et.al. (1992), the TFP growth
rate is assumed constant. After introducing the structural change, the TFP
growth rate will be a function of several variables. Assuming ln 0 and ln
are constant across provinces, our empirical model for cross-section regression
is
ln
ln
constant
ln
ln
[34]
6
Initial Results
We begin by estimating the model of Temple and WÖßmann for 1983-2006.
The dependent variable is the natural logarithmatic ( ) difference of per capita
GDP between 1983 and 2008. The standard explanatory variables include
of
the sum of labour growth rate, production growth and deprecation (which is
assumed 5% in our case); and the of initial per capita income. The additional
independent variables are the two structural change terms introduced by
Temple and WÖßmann (2006), as defined in Eqs (A16) – (A19). All
observations are from 29 provinces for 1983 and 2008. Both the two-sector and
the three-sector models are first estimated by least squares regression, and
further re-estimated after adjusting heteroscedasticity.
10
The results of two-sector model by Temple and WÖßmann (2006) are
presented in the last three columns of Table 2. Only the two structural change
terms of the urban sectors are included. It is shown that both the ln
are statistically insignificant.
and the
We then estimate our three-sector models. With Model I, all estimated
coefficients are to our expected sign. Same for P-values except those for
. Model II supplements the Model I by dropping the
ln
and
and we find that the explanatory power of the model is very close to
Model One.
Overall, the adjusted
are very high in both models: more than 80
percent of the log difference of GDP per capita over the specified time period is
explained by this three-sector model. The three-sector framework is 19 percent
better than the Temple and WÖßmann (2006)’s two-sector specification (in
terms of adjusted ). Such initial empirical results strengthen our theoretical
specification in the case of China’s labour reallocation experience.
11
Table 2: Effects of Structural Change on TFP Growth
Three‐Sector Model
Variable
ln
ln
0 / 0
Constant
Adjusted
Two‐Sector Model
Model I
Model II
Coefficients Standard Error P Values Coefficients Standard Error P Values Coefficients Standard Error P Values
0.03
0.08
0.69
‐0.01
0.08
0.92
‐0.10
0.11
0.41
‐0.48
0.08
0.00
‐0.51
0.06
0.00
‐0.54
0.09
0.00
2.71
0.45
0.00
1.97
0.43
0.00
‐
‐
‐
1.66
0.35
0.00
2.09
0.38
0.00
1.84
0.60
0.01
‐0.18
0.15
0.22
‐
‐
‐
‐
‐
‐
0.06
0.03
0.09
‐
‐
‐
‐0.03
0.03
0.33
1.45
0.14
0.00
1.40
0.15
0.00
1.76
0.17
0.00
0.88
‐
‐
0.86
‐
‐
0.75
‐
‐
0.85
‐
‐
0.83
‐
‐
0.71
‐
‐
The white standard errors are presented. Dependent variable is the natural log difference of per capita GDP over 2008 and 1983.
The Two-Sector Model was developed by Temple and WÖßmann (2006).
12
7
Summary and Concluding Remarks
Modeling structural change, measured by the reallocation of labour
employment, to the contribution of TFP growth is both theoretically and
empirically difficult for an underdeveloped dualistic economy. Temple and
WÖßmann (2006) developed a two-sector model and found that structural
change can account for a significant proportion of any observed variations in
productivity growth.
Building upon their models, we extended the framework to better fit the
reality of China which experienced both rural industrialization and urban
industrialization during the reform period.
Since there are significant
differentials of marginal product of labour in rural agriculture, rural nonagricultural sectors and urban sectors, we propose a three-sector model and
examine the contribution of labour reallocation to the growth of total factor
productivity. Our initial results show that the specification of three-sector
model is empirically superior to the framework proposed by Temple and
WÖßmann (2006) at least in the case of China during reform.
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Appendix A
By taking the derivatives of each sectoral production functions with respect to
time, we obtain
.
[A.1]
.
[A.2]
.
[A.3]
Multiply both sides of [A.1] to [A.3] by 1
consequently,
1
1
,
1
1
and
,
[A.4]
[A.5]
1
[A.6]
The factor share of labour in Eq [20] is further extended to
[A.7]
Define
[A.8]
With Eqs [10] and [11], factor shares of labour in sector b and m become:
1
[A.9]
15
1
[A.10]
Adding up Eqs [A.4], [A.5] and [A.6]:
1
1
1
1
[A.11]
,
With Eq [1],
1
;
, Eq [A.11] becomes
1
1
1
[A.12]
By taking the derivatives of both sides of
Accordingly,
yields
.
[A.13]
The same can be applied to sectors b and m. Eq [A.12] is changed to
1
1
1 1 11
1
1
21 1 2 21
2
[A.14]
1, we get
Since
1
and
1
1
1
1
1
Denote
16
[A.15]
∆
[A16]
∆
[A17]
∆
[A18]
∆
[A19]
Together with Eq [26], we demonstrate the relationship between productivity
growth and structural change of employment in Eq [30].
Appendix B
The capital stock evolves according to
1
[B1]
where is the depreciation rate and is the investment. In the steady state, the
value of capital stock is
[B2]
Substituting the value of capital stock in the steady state into the production
function yields
[B3]
The speed of convergent is given by
ln
ln
,
1
where
[B4]
Solving the above differential equation yields
ln
1
ln
ln
0
17
[B5]
in Eq [B1], denoting
With
give Eq [34].
1
and subtracting ln
18
0 of both sides
