1

Discussion Paper Series No.145

Analysis of Migration Decisions ofChinese Japonica Rice Farmers:
Estimation of Internal Wage on
Output Supply Using Agricultural Household Model
Mitsuo Inada a *, and Hiromi Yamamoto b
a Graduate School of Economics, Kyoto University,

Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501, Japanb Faculty of Economics, Chuo University,

742-1 Higashinakano, Hachioji, Tokyo 192-0393, Japan
July 2010* Corresponding author, Tel: +81-75-753-3463. Fax: +81-75-753-7115

E-mail addresses: mitsuo.inada@ft3.ecs.kyoto-u.ac.jp (M. Inada),
yamah@tamacc.chuo-u.ac.jp (H. Yamamoto).
☆
The authors are indebted to Kimio Morimune, Yoshihiko Nishiyama, and Ryo Okui.
We would like to thank Kohtaro Hitomi, Hisatoshi Hoken, Toshifumi Kuroda, Motoi
Kusadokoro, Deqiang Liu, Ryoshin Minami, and Suguru Miyazaki for their valuablecomments. We also thank Naoya Hatta, Takuma Kobayashi, Chunfa Liu, Takahiro
Yuzuki, and Dongxue Zhang for their support.

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SummaryThis paper examines the migration decisions of Chinese Japonica rice farmers interms of wage gaps. We use a non-separable agricultural household model to estimate
the internal wages of the output supply. As a result, internal wages, which denote thereservation wages of Japonica rice cultivation, are substantially lower than market
wages in Japonica rice production and the wage levels in township and village
enterprises. Furthermore, we find that internal wages are substantially lower than thewage levels in the urban construction sector. Finally, we analyze the separation property
in this agricultural household model. The test for equality of means between internal
and market wages is rejected at a 1 % level of significance. We conclude that an efficientlabor market does not yet exist in rural China.
JEL classification: J31, Q11, R23
Keywords: Migration, Wage gap, Internal wages, Agricultural Household Model

1.

Introduction
After 1978, the decollectivization of the People‟s Commune System and theintroduction of the Household Responsibility System enormously changed rural China.
One of the biggest changes was the start of a massive migration of rural surplus labor.
Under the collective farming system, redundant labor in agricultural production had
been prohibited from leaving rural areas. However, in the early 1980‟s, after the
introduction of the Household Responsibility System, rural labor rapidly flowed into
urban industrial sectors and Township and Village Enterprises (TVEs). In the 1990‟s, as
intense competition among TVEs occured, a number of TVEs exited the market. At thesame time, surplus labor was allowed to migrate from villages to urban areas withoutchanging household registration (hukou) status. As a consequence, rural residents who
worked in urban areas rapidly increased. According to the National Bureau of Statisticsof China,1 the number of migrant workers exceeded 145.3 million at the end of 2009. On
the other hand, a shortage of workers surfaced in the Pearl River delta region in 2004.
After that, the entire eastern coastal region faced the same situation. Cai (2007a, and2007b) argued that surplus labor had disappeared from the entire country, meaning thatthe turning point discussed in Lewis (1954) had been exceeded. The controversy grew
concerning whether the Chinese economy had already reached its turning point.
The Lewis model assumes that surplus labor migrates from the rural agricultural1

http://www.stats.gov.cn/tjfx/fxbg/t20100319_402628281.htm

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to the urban industrial sector. But migration also happens among rural agricultural
sectors. In China, after 1998, The Data Collection of the National Farm Production

Costs and Returns recorded the working hours of workers who migrate among rural
agricultural sectors. Their hours have been increasing.
Why did migration occur from rural to various other sectors? In the empiricalliterature, analyses have been conducted in two different ways. First, a set of papers
investigated wage gaps among sectors. Some used Lewis model to estimate wage gaps
between rural and industrial sectors (e.g., Yang and Zhou (1999), Meng (2000), andMinami and Ma (2009)). Others used the agricultural household (hereafter AH) model toevaluate reservation wages in agricultural sectors (e.g., Cook (1999), Hoken (2000), andZeng (2005)). The authors who utilized the AH model also analyzed the wage gap bycomparing reservation wages with wage levels in industrial and non-agricultural sectors.
Second, another set of papers analyzed the effect of relevant variables on migration
decisions. Zhao (1997) and Zhang, Huang and Rozelle (2002) studied the effects ofeducation on migration decisions. Zhu (2002) used published income data to examine theeffect of income gaps between rural and urban areas on migration decisions. Wu and Yao(2003) analyzed the effect of the characteristics of Chinese institutions on migration
decisions. Others analyzed the effects of education and such characteristics as family
members, household, and community on migration decisions (e.g., Hare (1999, 2002),
Zhao (1999), and Lu and Song (2006)).
This paper is most closely related to the estimation of the wage gap using the AH
model. Papers conducted by the first method2 use published macro and micro data toestimate farmer‟s on-farm wage levels. In macro data analysis, Yang and Zhou (1999)
used panel data for 1987-1992 collected from the China Statistical Yearbook (CSY) andrural and urban household surveys and examined whether economic reforms reduced
rural-urban segmentation. They employed the Lewis model to estimate the marginalvalue productivity of labor (MVPL) in the agricultural sector, TVEs, and state-owned
enterprises (SOEs) at the national level. Their result shows that the MVPL in SOEs ishigher than in the rural industries and agricultural sectors. This suggests that sectoral
wage disparities cause migration from agricultural sectors to TVEs and SOEs.
Consequently, they concluded that economic reforms failed to correct urban bias. Meng
(2000) used panel data for 1984-1990 collected from CSY and a survey conducted by the
Rural Development Center of China and the World Bank on 300 TVEs. He also employed
the Lewis model to compare MVPL in TVEs with agricultural returns to labor. The
comparison result indicates that the agricultural returns to labor is substantially lower
In these papers, they refer to working in the non-agricultural sector without moving
away from their place of residence as “non-farm work”. On the other hand, work in theurban industrial sector by moving away from their place of residence is “migration”. In
this paper, we refer to both as “migration” in a broad sense.
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4than the wage level in TVEs. The wage gap was increasing. Minami and Ma (2009) used
time series-cross section data for 1990-2005 from the China Rural Statistical Yearbook(CRSY). They also utilized Lewis model to compare MVPL in agricultural sector with thelevel of subsistence wage. (the net per capita income for rural residents and per capita
rural household expenditures) They showed that MVPL is substantially lower thansubsistence wage. They concluded that agricultural sector in China still have surplus
labor, which implies that the Lewisian turning point had not been yet exceeded.
In micro data analysis, Cook (1999) used household survey data conducted in
Shandong Province in 1990 and employed an AH model to estimate production functions
in agricultural and non-agricultural sectors. The household data included crops (wheat,corn, and cotton), fruit cultivation, and animal husbandry. She found the marginal
return in agricultural sectors is substantially lower than the marginal returns in
non-agricultural sectors. Furthermore, the result shows the marginal return in
non-agricultural sectors approximate the non-agricultural wage rate and indicates thatthe labor market in this region might be efficient in the non-agricultural sector.
Hoken (2000) used household surveys conducted in Hubei Province in 1979 and1985 and employed an AH model to analyze the migration decisions of farmers fromagricultural to non-agricultural sectors. One of his contributions is to estimate thehusband and wife production function of crop cultivation. Using MVPL to calculate theannual income level of crop cultivation, he found that its income level in 1979 was higher
than non-agricultural wages for both genders. However, in 1985, the income level in crop
cultivation was substantially lower than non-agricultural wages. This is consistent withthe rise of the Gini coefficient between 1979 (0.197) and 1985 (0.257) in this region.
Hoken argues that the expansion of the non-agricultural sectors resulted from economic
reform and a corresponding reallocation of labor, which caused an income disparity
among households. On the other hand, he also analyzed the effect of education levels oncrop cultivation and the non-agricultural labor supply and showed that education forboth genders is not significantly positive in crop cultivation. But in the non-agriculturallabor supply, the wife‟s level of education is significantly positive, but not the husband‟slevel.
Zeng (2005) used a North and Northeast China Living Standard Survey coordinatedby the World Bank in 1995. The data includes agricultural production and crop
cultivation. He employed an AH model to analyze the effect of the non-agricultural labor
supply on production efficiency and simultaneously analyzed the production efficiency ofthe non-agricultural labor supply. The result shows that variables related to thedifferences of human capital (e.g., education and job training) affect the labor supply of
the non-agricultural sectors. Zeng also argues that a free transaction of farmland
accelerates the labor supply in non-agricultural sectors.

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Note that these studies employ the AH model with a separable property, whichmeans that a farmer‟s production decision is independently determined regardless of his
preferences and endowments. It assumes that a competitive market exists. However, weneed to examine whether the assumption is appropriate. Cook (1999) carried out aequality test of the means between the marginal revenue product of labor in on-farm andoff-farm work. The result shows that the returns to labor in agriculture are lower than
the returns to labor in other non-agricultural activities. Hoken (2000) verified the effectof family characteristics on the non-agricultural labor supply. Consequently, since
education and expanded family variables affect the non-agricultural labor supply, theseparation property is rejected. Hoken concludes that efficient labor allocation is notalways achieved in the sample region. Zeng (2005) also analyzed the effect of family
characteristics on the non-agricultural labor supply and confirmed that the separation
property is rejected because the variables of human capital affect the labor supply in the
non-agricultural sectors.
As seen above, most previous literatures used data that included a broad
agricultural sector, and assumed that migration decisions are homogeneous among
various types of farmers. However, differences might exist in production technology andmigration decisions among agriculture, forestry, fishery, and animal husbandry.3 In
micro data analysis, Hoken (2000) and Zeng (2005) estimated the production function ofcrop cultivation. But naturally differences are seen in production and consumption
decisions among farmers of rice, wheat, corn and others. None of the papers analysed
migration decisions in a specific crop cultivation. At the same time, these papers
analyzed migration decisions from agricultural to non-agricultural and urban industrial
sectors. None analyzed migration decisions from relatively poor agricultural to relatively
rich agricultural sectors.
This paper utilizes the non-separable AH model constructed by Sonoda andMaruyama (1999) to analyze Chinese farmers engaged in Japonica rice cultivation.4
Based on estimation of the production function, we calculate the reservation wages ofJaponica rice farmers to examine migration decisions in terms of wage gaps among

In the definition of the Chinese statistics, “agriculture” in a broad sense includes not
only agricultural production but also forestry, fishery, and animal husbandry. For
example, in CSY “agriculture” describes nong lin mu yu (agriculture, forestry, animalhusbandry and fishery). Additionally, “farmer” (nong min) indicates inhabitants in rural
areas in all Chinese statistics. It does not always mean that “farmers” indicate labors
who only engage in on-farm work. In recent years, CRSY published the classified data bysector.
4 After the implementation of the household responsibility system for management (baogan dao hu), farmers in China could voluntarily select which farm products to produce.
Therefore, if we analyze farmer production decisions using micro data, we must consider
sample selection bias. However, we ignore this problem, because we are examining
aggregate production decisions at the provincial level.
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6sectors using macro data. To analyze this argument, we compare reservation wages withmarket wages in the production of Japonica rice, wages in TVEs, and wages in the urban
construction sector. Sonoda and Maruyama (1999) demonstrated that the reservation
wages on the output supply are lower than market wages of rice cultivation in Japan.
The result provides a general explanation of migration decisions from agricultural tovarious sectors in terms of wage gaps.
In this paper, we assume that migration opportunities are constrained. Under thisassumption, we can estimate the reservation wages on the output supply, and conduct a
separability test of the AH model. The estimation method in the AH model and theseparability test in our AH model are discussed below.
The remainder of the paper is organized as follows. Section 2 reviews the theoreticalbackground of the AH model and constructs an AH model based on Sonoda andMaruyama (1999). Section 3 describes the data and the compilation method of thevariables. Section 4 presents the estimation method and the empirical results. Section 5shows the calculation of internal wages of Japonica rice cultivation and the test resultsof the separable property of our AH model. Finally, Section 6 provides some concluding
remarks.

2.

Model

2.1. Theoretical background
The AH model prototype was formed by Tschajanow (1923), who argued that
agricultural production decisions depend on consumption choices of peasant farmers.
Under the influence of Tschajanow‟s analysis, Tanaka (1951) established the AH model
as a subjective equilibrium model, which Nakajima (1956) extended to analyze imperfectagricultural input markets. Yori (1971) also developed an analysis of imperfectagricultural production markets. On the other hand, in western academic societies,
based on the insightful work of Becker (1965), researchers constructed an AH model.
Japanese papers had not been fully recognized because they were only published inJapanese. However, Singh et al. (1986) introduced early works written in Japanese as
the founding work in the AH model that analyzed imperfect labor markets. Strauss andThomas (1995) also described Tanaka (1951) and Nakajima (1957) as pioneering works
that ranked with Becker (1965).
As mentioned previously, the AH model has two types: a separable and anon-separable model. The former has a separable property in which production andconsumption decisions are independently determined under the competitive markets.
Imagine that the rice market is competitive. Then the results of the following two

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behaviors are identical in their consumption decisions: to consume goods produced bythemselves and to consume goods purchased from markets. The price of rice is stabilized
under a competitive market.
On the other hand, in the non-separable model, production decisions cannot be
separated from consumption decisions under imperfect markets because household
preferences influence the former. Non-separable models are frequently utilized by the
analysis of agricultural households in developing countries because we can incorporate
various types of markets failures and imperfect markets in this model.5
In this paper, we assume imperfect labor markets in China. Controversy continues
whether a competitive labor market has already emerged in rural China.6 But none ofthe papers show that an efficient labor market has emerged in the entire country. In
reality, minimum wages among provinces remain unequal. Therefore, when we conductmacro data analysis, assuming that the labor market is not efficient might be practical.
We also assume that migrant wage employment is constrained. The first paper thatincorporated constrained migrant employment into the AH model is Arayama (1986). He
first assumes unconstrained off-farm employment under competitive labor and productmarkets to analyze the time allocation of Japanese farmers. Although the estimatedresult is consistent with the actual time allocation in off-farm employment, theseparable property is strongly rejected. In response to the result, Arayama assumes
constrained off-farm employment due to the following two reasons. First, farmers
maintain a certain level of working hours in on-farm work. Second, there are few
opportunities to find off-farm employment in some regions. Under these assumptions,the separable property is supported by the test.
Sonoda and Maruyama (1999) extend these studies to analyze the effect of internal
wages on output supply using the AH model with constrained off-farm wage employment
and show that a rise in the price of rice decreases rice output by the internal wage
effect.7
As mentioned above, we assume that migrant wage employment is constrained,
based on Sonoda and Maruyama (1999) and that migrant wage employment isconstrained in China for the following reasons. First, farmers work in TVEs or urban
For example, Udry (1998) employs a non-separable AH model to analyze inefficientlabor and land market. Kurosaki and Fafchamps (1998) also utilize a non-separable AH
model to analyze market failures for which a complete set of contingent securities does
not exist.
6 For example, Parish, Zhe, and Li (1995) demonstrate that an efficient labor market
has emerged around big cities and the east coastal region. On the other hand, Yao (1999)shows that farmers who want to work in the non-agricultural sector face entrance andtime rationing in labor markets. Johnson (1995) argues that the entrance of the urban
labor market is restricted for rural migrants, due to deficiencies in social benefits,
medical services and educational systems for migrant workers.
7 In this paper, we use internal wage as a synonym for reservation wage.
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sectors in the off-farm season. 8 Second, the deficiencies in social benefits, medical
services, and educational systems for migrant children discourage farmers from moving
to urban areas. For these reasons, we consider that migrant wage employment offarmers is constrained.
2.2 Model
Next, we construct a AH model that deeply reflects Sonoda and Maruyama (1999).
The welfare function of households presented as follows:(1)
W  U (C1 , C2 , Z ),where U () , C1 ,C 2 , and Z denote the utility function, the amount of a home-produced
good, purchased goods, and leisure, respectively. The welfare function is assumed to bewell behaved in the usual sense. The household allocates its endowed time. We also
assume the migrant wage employment is constrained:(2)
L2  Te  Z  L1  L = constant,where L1 , L2 , Te , and L denote the hours of on-farm work, migrant work, leisure, theendowed time, and the maximum hours of migrant work, respectively. The constrainedhousehold budget satisfies:(3)
pC1  pC2  wZ  S  TAX  M ,where p, p, w, S , and TAX denote the price of a produced good, purchased goods, andthe market wage, savings, and taxes, respectively. M denotes the entire income of thehousehold defined as:

M  wTe    V ,where   pX  wL1  qF  OC.

(4)

Equation (4) shows that the household‟s entire income consists of the value of endowed
time ( wTe ), the profit function of home-produced good (  ), and unearned income ( V ).
The revenue of home-produced good (  ) is defined above. q, F and OC denote theprice of material inputs, their quantity, and other costs. The household produces aquantity of Y . The quantity of produced good C1 does not exceed the quantity of Y .

Y is bounded by production possibility:
Y  f ( L1 , F ; K , T ),(5)

In fact, the number of migrant workers who spend whole of the year working inanother sector or district (including entire family exoduses (ju jia li cun) ) is huge inmicro level. According to the Department of Rural Surveys National Bureau of Statistics(2005), the number of entire family exoduses was 24.7 million in 2004. This accounts forabout 20% of the number of migrant workers. But, we ignore the decision of year roundmigration in this paper. Because we consider aggregate production decisions, we don‟t
assume that the hours of on-farm work equals zero.
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where K and T denote the capital input and planting area of a home-produced good.
Production function f () is assumed to be well behaved in the usual sense.9
The following are the Kuhn-Tucker Lagrange optimality conditions: / L1     ( pf / L1  w)  0
 / F  ( pf / F  q)  0(6.1)

 / C1  U / C1  p  0 / C2  U / C2  p'  0 / Z  U / Z    w  0

(6.3)
(6.3)

 /   pf ( L1 , F , K , T )  wL1  qF  OC  pC1  p' C2  wZ  S  TAX  0 /   L  Te  Z  L1  0,

(6.6)

(6.2)
(6.4)
(6.4)
(6.5)
(6.5)
(6.7
(6.7)

where they are assumed to satisfy the nonnegative conditions in each variable.
Equations (6.1), (6.3), and (6.5) imply thatp

U / Z w   /   pf / L1 .
U / C1(7)

We define w   /   w  w and w  as the reservation wages of the output supply.10
Why is w  w satisfied theoretically? Sonoda and Maruyama (1999) adopted theefficiency wage hypothesis proposed by Shapiro and Stiglitz (1984). The efficiency wage
hypothesis in the context of the non-separable AH model means that employers pay
workers higher wage ( w ) than their reservation wage ( w * ) for on-farm work to
encourage workers not to shirk. If they are caught by shirking and fired, they have to
pay a penalty between their reservation wage of on-farm work and their market wage.
At the same time, imagine that workers follow suit. Now, workers who become
unemployed are willing to work for wages lower than the market wage. But theemployer doesn‟t want to hire at the lower wage, because he or she thinks that workers
will inevitably shirk under the market wage level. Therefore, workers believe theiremployment is constrained by market wages including efficiency pay. It seems true thata wage gap exists between the agricultural sector and the non-agricultural and urban
sectors in China.
The entire income and profit function based on reservation wages can be rewritten
as follows:M *  w * Te  (w  w*)L   * V ,(4.1)

If we analyze the micro data, then we must consider the production minimum goal in adual price system. Under the system, farmers receive incentive for higher cultivation,
because they can freely sell their products after achieving the production target. We
ignore this to consider aggregate production decision.
10 Sonoda and Maruyama (1996) explain that μ/λdenotes the amount of discount thatcan be allowed. If they cannot utilize the opportunity of off-farm employment, they must
input all their working hours in on-farm work. In this case, their marginal product of thelabor or their demand wage level is lower than the market wage. The amount of discountturns out to be μ/λ.
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 *  pX  w * L1  qF  OC.
The second term of the right hand side in Equation. M * presents the difference of thevalue of the maximum hours of migrant work in terms of w and w  . Consequently,
Equation (4.1) is identical with M *  w * L1  wL2  w * Z . 11 Finally, Equation (7)offers a useful device to test whether the household‟s migration employment isconstrained, because when the migration hours are constrained, reservation wage w 
influences the household‟s production and consumption decisions.
3. Data Compilation Method and Sources
The data used in this paper are mainly taken from the Data Collection of the Na-tional Farm Production Costs and Returns and the Data Collection of the National Farm
Production Costs and Returns: After the Establishment of a Nation 1953-1997 Vol.2.
(FPCRS hereafter). According to Chen and Niu (1989), the aim of the national costsurvey of farm production was to collect the cost data of inputs in agricultural
production. After 1949, the survey was conducted by the State Development Planning
Commission, because the data are essential to determine the prices of agricultural
products. The survey is now continued by the National Development and Reform
Commission. In the sampling method, they select typical prefectures in each product.
Then in each prefecture, villages or groups of villages are selected. Finally, farmhouseholds are chosen among the villages.12
The observations cover periods from 1992 to 2008. The data compilation method of
the variables is shown in Table 1. We used the data from Liaoning, Jilin, Heilongjiang,
Hebei, Jiangsu, Anhui, Henan, and Yunnan Provinces. The sample size was 135.13 The
following variables were employed in the production decision; the output of Japonica riceis used as the explained variable. Explanatory variables include capital input, working
hours, material input, and the planting area of Japonica rice.

4. Estimation Strategy and Empirical Results
We first estimate the production functions in each province and then conductpooling regression using all observations. In these estimations, the production functionis specified by the following form:

We can also solve a non-separable AH model with internal wage. See Sonoda andMaruyama (1996, and 1999).
12 In the early 1990‟s, Colby, Crook, and Webb (1992) pointed out that the reliability ofthe survey data has been questioned. For example, the sample size is extremely small
for the non-randomness of the sample.
13 The data of Jiangsu in 1992 is absent.
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Table 1. Definitions of Variables in Production Decision
Variable
Unit
SymbolCompilation method
Output of Japonica rice KilogramY
We use a category of output of Japonica rice.

Capital input

Working hours

Hour

Material input

K

Capital input is evaluated by dividing its cost by thecapital price index. The total cost is calculated by
the sum of the costs of farm implements, farmmachinery, and animal labor. The capital priceindex is constructed by weighing individual prices
with their respective shares in the total cost.

L1

We used the published data of hours of family labor.
But, before 1997, total hours of farm labor are only
available. Total hours of farm labor include
working hours of hired labor and family labor. For
convenience, we constructed the data of hours of
hired labor in the following manner. First, weannually calculated the ratio of hours of hired labor
to total hours of farm labor from 1998 to 2008. Then
we produced the hours of hired labor by multiplying
the published total hours of farm labor from 1992 to1997 by the average ratio of hours of hired labor.
Finally, we generated hours of family labor by
subtracting hours of hired labor from total hours offarm labor.

F

The material input is calculated by dividing thetotal cost of material input by the material priceindex. The total cost of material input is the sum of
the costs of seeds and seedlings, pesticide, chemicalfertilizer, agricultural film, and fuels. The material
price index is calculated by weighing individual
prices with their respective cost shares of the total
cost. The price of seeds and seedlings is obtained by
dividing the cost by the quantitiy in each year. The
price of pesticide in 1994 is absent. Therefore, weused the price of pesticide and its appliances insteadof the price of pesticide.
We take the planted areas from the Historical

Outline of National Agricultural Statistics
Planting area of Japonica
HectarericeT(http://www.agri.gov.cn/sjzl/nongyety.htm). We canonly use data for three years: 2001-2003. First, we
calculated three-year averages of the ratio of theplanting areas of Japonica rice to the planting areasof rice. Then we made absent data by multiplying
the ratio by the planting area of rice.

Notes: (1) We use 1992 as the base year by which the price indices of the capital and material input
were calculated. The price data are obtained from the Market Statistical Yearbook of China(1993-2003) and CRSY (2004-2008).
(2) The data were adapted from FPCRS . In these data, all variables are deflated by unit planting areas.
To use planting area as a variable, we multiplied each variable by the planting areas of Japonica rice.
(3) Farm machinery and animal labor are only utilized in agricultural production.

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log Y   0  1 log L1   2 log K   3 log F   4 log T  u,(8)

where  0 denotes a constant term and u an error term.
Second, we analyze the panel fixed and random effects with the following estimation
model:

logYit     log L1it   log K it   log Fit   log Tit   i   t   it ,(9)where i and t show indices of provinces and years,  means a constant term,  iaunobserved time invariant province effect,  t a common regional trends and  it anerror term. We carry out a Hausman (1978) specification test on the panel data to
determine whether to employ a fixed or a random effect.14
The estimated coefficients are shown in Tables 2 and 3. In Table 2, the OLS resultsin each province show that the small sample size seriously affects the regression. In
Table 3, it shows that all coefficients are statistically significant in the pooling
regression. In this estimation, the negative effects caused by the shortage of
observations are seemingly avoided. The coefficients of 1 and  , which aresignificant in this regression are positive. Table 4 shows the estimated result in previous
studies that utilized macro panel data for comparison. The elasticitiy of working hours
in two-way fixed effect model is close to the results of Tian and Wan (2000) and Zhang
and Fan (2001). We briefly describe the general condition of Japonica rice production inpresent China to understand the estimated result. The output of Japonica rice graduallyrose during the observation period. On the other hand, the working hours of Japonica
rice farmers in on-farm work have decreased due to the increase of migrant work.
Material input rose rapidly because of the infertile land in China. In particular, theinput of agricultural chemicals rose greatly. In recent years, agricultural machines
replaced draft animals. It might improve production efficiency of capital. However,capital input increased during the period, because agricultural machinery, which issuitable for natural conditions in China, has been underdeveloped. Finally, the plantedarea of Japonica rice cultivation decreased. Under these circumstances, the estimatedelasticities of each explanatory variable in a two-way province fixed effect model seemreasonable.15

14
15

We calculated robust Hausman test statistic proposed by Wooldridge (2002).
We conducted a Hausman specification test as a pretest of the random effects

specification. The result supports a fixed effect model. In addition, Guggenberger (2010)
showed that the size distortion is caused mainly by the poor power properties of thetest. In that sense, it is reasonable to use the coefficient of two way fixed effect model.

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Table 2 Estimated Results of Equation (8)Liaoning
Constant-1.4464(2.2080)
Log (working hours)
0.0647(0.1489)
Log (capital input)-0.0534(0.1139)
Log (material input)
0.0542(0.0752)
Log (planting area)
1.4845***(0.3742)
Observation17
R-squared
0.9228Adjusted R-squared
0.8970Constant
Log (working hours)
Log (capital input)
Log (material input)
Log (planting area)
Observation
R-squared

Jiangsu
1.2358-0.4325-0.1686-0.2725
1.9914**16
0.9398Adjusted R-squared

0.9179(0.8367)(0.3801)(0.1842)(0.2033)(0.7168)

Jilin
3.7216***-0.1892**
0.077
0.02370.8306***170.98480.9797Anhui
0.352-0.00650.1806**-0.0891.1822***170.9372

Heilongjiang(0.5132)
1.5244(0.0741)-0.0035(0.0457) 0.2068**(0.0438)-0.0165(0.0906) 0.8746***170.98910.9854(1.1963)(0.2193)(0.0731)(0.1328)(0.3019)0.9163

Note: Significance: * 10 percent, ** 5 percent, and *** 1 percent.
Standard errors are shown in parentheses.

Henan-3.5461
0.157-0.1947
0.12422.0339**170.69200.5894(0.9436)(0.1176)(0.0830)(0.1031)(0.1809)(2.4761)(0.1580)(0.1841)(0.1829)(0.6761)

Hebei
1.8071***-0.2447
0.25360.13031.0022170.88710.8494
Yunnan-2.1326
0.242
0.3867***-0.0535
1.1042***170.79890.7319(0.5343)(0.4227)(0.2551)(0.1731)(0.6391)(2.3714)(0.1824)(0.1128)(0.1505)(0.3575)

14

Table 3 Estimated Results of Equations (8) and (9)(1)
Constant
2.1085***(0.2088)(2)
1.3529**(0.4239)(3)
1.8407***(0.2797)

Log (working hours)

0.1103**(0.0393)

0.0534(0.0367)

0.0504(0.0314)Log (capital input)
Log (material input)
Log (planting area)
Province fixed effects
Province random effects
Province year effects
Observation
R-squared
Robust Hausman test

0.2438***0.0956**
0.5588***
No
No
No
135
0.9866(0.0674)(0.0347)(0.1123)

0.1430**-0.0072
0.9269***
Yes
No
No
135
0.9836(0.0430)(0.0342)(0.0752)(0.0458)(0.0364)(0.0711)(5)
1.4221***(0.3431)0.1253**(0.0534)
0.0758(0.0511)0.054(0.0558)
0.8242***(0.0647)
No
Yes
Yes
135
0.9859F(4, 7)=16.40
Prob>F=0.0012
Notes: Significance: * 10 percent, ** 5 percent, and *** 1 percent.
Standard errors are shown in parentheses. We compute standard errors that are robust to clustering by provinces.
Constant
Log (working hours)
Log (capital input)
Log (material input)
Log (planting area)
Province fixed effects
Province random effects
Province year effects
Observation
R-squared
Robust Hausman test

(4)
0.8840*0.1547**0.05
0.04770.9093***
Yes
No
Yes
135
0.98470.1654***-0.00150.8247***
No
Yes
No
135
0.9844F(4, 7)=16.37
Prob>F=0.0012(0.3925)(0.0624)(0.0423)(0.0491)(0.0594)

15

Table 4 Estimated Result of Production Function in Previous Studies
Estimated elasticity
Authors Data source Dependent variable Period capital labor material land
Tian and
Yield of Japonica
0.021～ 0.139～
FPCRS
1983-1996
Wan
rice per 1 mu.
0.086
0.238
Zhang
Adjusted VA of0.167, 0.173, 0.081, 0.408,
CRSY, etc.
1979-1997
and Fangrain cultivation
0.247
0.234
0.140
0.143
Kang
and Liu

FPCRS

Output of Japonica
rice

1992-2002

-0.17

-0.05

0.2

0.96

Sources: Tian and Wan (2000, p.167 Table 3), Zhang and Fan (2001, p.386 Table 5), Kang and
Liu (2005, p.29 Table2).
Notes: (1) VA is an abbreviation for Value Added.
(2) 1 mu equals one-fifteenth hectare.
(3) Zhang and Fan (2001) use a generalized maximum entropy approach. Kang and Liu (2005)
estimate the stochastic frontier model. In terms of specifications of the production function,
Zhang and Fan use translog and Cobb-Douglas types, and Tian and Wan, and Kang and Liutranslog type.

5.

Estimation of Internal Wages and Test of Separable Property of AH Model

5.1 Estimation of internal wages
Internal wages are estimated by the following relation:

w*  ̂ pYˆ / L1 ,(10)

where Ŷ is a theoretical value of Y . As a result of a Hausman specification test, we
adopted the estimated coefficients in a two-way fixed effect model. The estimated results
are shown in Table 5. The estimated internal wages on Japonica rice production supply
are substantially lower than market wages in each province. The internal wages in theeast coastal and northeastern regions are relatively higher than those of the central andinternal regions. Since planted areas are extensive in northeastern China, relatively
capital intensive farming is conducted. In the east coastal regions, relatively capitalintensive farming might also be conducted because of the lower capital input prices.
Table 6 compares the estimated internal wages in the previous studies. The internal
wages of Japonica rice production are higher than the internal wages of agricultural
production and crop cultivation. One possible reason why the internal wages of Japonica
rice production supply are relatively higher than other crop cultivation is that the unit
price of Japonica rice is higher than other crops.
Next, we examine the migration of peasants from Japonica rice cultivation to TVEs
and the urban sector. As proxies of the wage levels in TVEs and the urban sector, we
utilize the annual wages of TVEs and the urban construction sector. For wages in the

16urban construction sector, we chose Beijing, Shanghai, and Guangdong because they are
the major destination cities for migrant labors. For convenience, we calculated theannual maximum internal wage level by multiplying the estimated internal wage by 365(days) minus 62 (holidays) times 8 (hours). Table 7 shows the results. Consequently, theinternal wages are substantially lower than the wage levels in TVEs and the urban
construction sector except Heilongjiang.16 17

Table 5 Estimated Internal Wage (unit:Yuan/hour)
Province
Internal wage
Market wage(*)
Liaoning
1.640
3.357
(0.800)(0.771)
Jilin
1.605
2.782
(1.089)(0.933)
Heilongjiang 2.060(1.101)3.490(1.674)Hebei
1.177(0.366)
3.206(1.801)
Jiansu1.589(0.741)3.314(1.169)Anhui
0.913(0.378)3.512(1.191)Henan
0.927(0.515)2.432(1.418)
Yunnan0.648(0.280)2.384(0.794)All
1.318(0.811)3.058(1.329)Minimum
0.207
0.925
Maximum
4.446
8.650
Source: (*) We adopted market wages from the data published
in FPCRS . But since the data are unavailable for 1992 to 1997,
we estimated them by deflating existing market wages by therural residents consumer price index. The consumer priceindex is obtained from CRSY .
Note: Standard errors are shown in parentheses.

Table 6 Estimated Results of Internal Wages in Previous Studies (unit: Yuan/hour)
Author
Data
Area
Year Internal wage Std.Dev
MinMax
Zouping county,
Cook agiruculture
1990
1.231
1.032
0.239
9.91
Shandong
agriculrure, Northern Hebei,
1.56,
0.02,
18.57,
Zeng
1995
1.13, 0.33
cropnortheast Liaoning
0.56
0.003
6.13
Sources: Cook (2000, p.32 Table 5), Zeng (2005, p.148 Table 6-7).
Notes: (1) Cook (2000) used agricultural data, including wheat, corn, cotton, vegitables, fruit,and animal husbandry. Zeng (2005) used agricultural data, including crop, vegitables, fruit,and animal husbandry.
(2) The elasticities of working hours are 0.097 in Cook (2000), 0.16 (agriculture) and 0.03
(crop) in Zeng (2005).

The higher internal wages in Heilongjiang seem reasonable, because large scale andmechanized farming is prevalent there.
16

17

Table 7 Estimated Internal Wages and Wages in TVEs(*）and Urban Construction Sector(**) (unit: Yuan/year)
Liaoning
Jilin
Heilongjiang
Hebei
Jiangsu
1992 1358.2 1910.1 1131.1 1428.3
1524.51852.1 1803.9×
1689.8
1993 1505.4 2302.8 1278.4 1813.7
1693.62181.11178.3
1935.41347.02449.8
1994 2949.2× 2891.6 2020.6 3142.0 3027.3× 2388.3
2472.1
2500.92304.23110.1
1995 3782.6× 3462.7 3472.3× 3116.1 3556.5× 3043.5
3455.73541.82789.33991.6
1996 3699.1 3864.0 3208.3 3051.1
3502.03623.03161.24026.72813.24843.2
1997 3041.3 4167.8 2777.2 3151.0 3611.5× 3706.8
3017.94024.33025.54513.6
1998 3279.5 4392.9 3024.5 10081.0 5459.1
4173.52798.94404.33195.94960.7
1999 3209.8 4462.1 2872.5 3741.5
4484.45796.82624.44718.92865.55515.7
2000 2809.5 4638.2 2766.7 3830.7 4291.7× 3524.7
2046.04890.02427.15852.02001 3259.5 5184.3 2916.7 4244.4
3269.73600.92296.84951.02906.46172.4
2002 2865.9 5884.4 2436.0 4744.7
3315.44215.01954.15491.12703.58117.1
2003 3353.5 6803.0 2623.6 5279.4 4531.6× 4485.1
2420.45653.83866.58973.5
2004 4989.3 6943.4 6533.1× 5495.9 6533.6× 5690.9
3680.85604.65707.89465.52005 6084.9 8147.4 6483.1× 6265.2 7076.7× 5657.9
3063.26240.35806.6 12025.0
2006 7135.1 8821.9 7881.8× 6497.2 9291.5× 6043.3
4172.06723.85999.9 14759.7
2007 6384.2 11882.9 6804.5 8482.4 8925.8× 7788.8
3927.18862.46668.4 14867.6
2008 7865.1 13632.6 7917.2 11290.4 10777.6× 10666.1
4414.210257.97218.0 17741.5
Ave. 4056.0 5846.6 3213.6 5038.5
3321.34614.02917.75030.43852.87959.9Anhui
Henan
YunnanBeijingShanghai Guangdong
1992 807.4 1362.1 779.3 1471.9
502.1
1486.23558.04448.04627.01993 1177.0 1694.8 1040.8 1808.0
677.2
1930.14677.05861.05846.01994 1697.6 2346.3 1765.1 2341.4
984.3
2000.06820.08296.07198.01995 1855.1 3525.8 2133.4 3049.3
1268.62607.98451.09996.08110.01996 1896.4 4530.2 1887.1 3586.3
1562.72697.09642.011666.08614.01997 1960.8 4466.4 1502.3 4198.8
1392.53291.510111.012722.08982.01998 2249.4 4970.2 1547.7 4165.0
1604.14006.410777.012458.09239.01999 2090.2 5550.2 1716.8 4168.2
1361.34282.711644.013689.09738.02000 1397.5 5068.4 1105.6 4445.5
1158.24726.912275.014332.010922.0
2001 1547.7 5429.3 1584.2 4549.2
1223.34863.513840.016270.011592.0
2002 1790.1 5620.4 1366.2 4816.8
1345.14937.414455.0
18361.012365.0
2003 2138.0 6147.3 1554.0 5470.4
1386.15181.016730.0
20801.013961.0
2004 2837.2 6915.7 3852.6 6307.4
2067.5 20081.8 20606.0
24330.014980.0
2005 3062.9 7282.0 3600.9 7028.2
2095.85931.523300.025972.016795.0
2006 3020.8 9436.4 4076.9 7867.0
2313.36412.927830.027440.0
18842.0
2007 3884.9 10551.2 4117.6 10356.4 2754.0
5858.234015.030075.020906.0
2008 4207.6 10550.7 4566.3 11747.6 3007.0 11415.1 39320.0
31686.022917.0
Ave. 2213.0 5614.5 2246.9 5139.9
1570.85394.715767.7
16964.912096.1

Sources: (*) CSY , China Town and Village Enterprises Yearbook , China Town and Village

Enterprises and Agricultural Products Processing Industry Yearbook.
(**) Statistical Yearbook of Beijing, Statistical Yearbook of Shanghai and Guangdong Statistical
Yearbook.
Notes: (1) We present the annual internal wages of Japonica rice cultivation in the left and annual
wage level in TVEs in right, respectively. The annual wage levels in TVEs are obtained by dividing
the amount of wages by total number of workers.
(2) Annual wages in TVEs consist of the following firms: TVEs (1992-1996), collective and private
firms (1997), collective and private firms and individual businesses (getihu ) (1998- 2001), anddomestic and foreign enterprises (after 2002). We can see abnormal values for wages in TVEs
(Jilin in 1998 and Yunnan in 2004). The others seem reasonable.
(3) We selected the annual wages in the urban construction sector as the annual average wages in
the construction sector.
(4) If estimated internal wage outperform wage in TVEs, we mark with a symbol ×.

18

5.2 Separable property test in AH model

Tablel 8 Tests of the Equality of Internal Wages and Market Wages Received by Market
Participants

Internal wage vs market wagelog wi hourly*  1.0862  1.1482 log wi market( 0 . 092 )R 2 : 0 . 5870

( 0 . 083 ) F ( 2 ,133 )  404 . 67

Internal wage vs wage levels in TVEs

log wi yearly *  1.7401  0.727 log wi TVEs
( 0 . 571 )R 2 : 0 . 4675

( 0 . 067 ) F ( 2 ,133 )  126 . 17

Note: Standard errors are shown in parentheses.
Following the method of Sonoda and Maruyama (1999), we first estimate thefollowing equation presented by Skoufias (1994):

ln wi j *  a  b ln wi k ,(11)where wi j * (i  1...n, n  135) stands for the internal wages of Japonica rice cultivation
on hourly and yearly bases, j = hourly and yearly, wi k is the market wages of Japonica
rice cultivation and wages in TVEs, k = market and TVEs. Then we conducted the joint
hypothesis test as follows: null hypothesis H 0 : a  0 and b  1 , alternative hypothesis

H 1 : a  0 or b  1 . We obtained the estimated equations shown in Table 8. The F
statistics of both equations rejected the null hypothesis at a 1 % level of significance.
Next, we tested whether the averages of the internal wages are statistically lower
than the market wage averages in Japonica rice cultivation and TVEs. The difference
between the two wages is defined as Di  wi  wi * . The test statistic for paired sample
is 18:
1t  n 2 ( D / s D ) ~ t (n  1),(12)

where D and s D show sample means and sample standard errors of Di . Thesestatistics are 21.86 and 10.32, which are rejected at a 1 % level of significance. Therefore,18

We conducted the test of whether two groups of wages are statistically independent.
1
2

1
2

The test statistic is T   (n  2) /(1   ) which is distributed as t (n  2), where denotes correlation between two wages. These statistics are, 12.25 and 8.37, which arerejected at a 1 % level of significance. It indicates that two groups of wages are notstatistically independent.
2

19

the mean of the internal wages proves to be significantly lower than that of the market
wages.19

6.

Conclusion
In this paper, we estimated the internal wages of Chinese Japonica rice production

supply in eight provinces and analyzed the cause of migration in China in terms of wage
gaps among sectors. We found that the means of internal wages is significantly lower
than that of market wages in Japonica rice cultivation and TVEs. The result shows thatthe separable property is rejected in this AH model. As for the comparison of wages ineach sector, we also discovered that internal wages are substantially lower than market
wages in the urban construction sector. We showed that migration to each sector iscaused by the wage gap.
These results show that Japonica rice farmers in eight provinces still have surplus
labor, so that they chose migration to earn a higher income than the Japonica ricecultivation. On the other hand, the working hours in Japonica rice production have been
decreasing, and output has been increasing because of the large input of agriculturalchemicals and the replacement of animal labor by agricultural machinery. If agricultural
machinery suitable to China‟s natural conditions is developed and spread over the entire
country, the output could be further increased. Farmland improvement is also important.
For example, soil conservation and land irrigation would enhance production efficiency.
The most important aspect of the Chinese agricultural sector is to develop efficient labormarkets. Optimal allocation of labor forces will accelerate labor productivity and develop
capital intensive agricultural industries in the near future. To establish efficient labormarkets, the immediate concerns are to allow migrant workers to have permanent
residences in urban areas. The central government needs to create a new system inwhich migrants have the same social benefits, medical services, and educational systems
for migrant children as urban residents.

We also conducted paired sample Wilcoxon signed rank test which is thenonparametric methods to test whether median of the difference of two groups are equal.
The test statistics are 9.18 and 10.08, which is rejected at a 1 % level of significance.
Therefore, the null hypothesis of no difference between the two wages is strongly
rejected.
19

20

Table 9 Descriptive Statistics of Production Decision
OutputWorking hours Capital
Material
Planting area
Province
Mean Std.Dev Mean Std.Dev Mean Std.Dev Mean Std.Dev Mean Std.Dev
Liaoning
8.311 0.167 6.438 0.128 5.519 0.336 5.813 0.257 6.272 0.115
Jilin
8.269 0.204 6.408 0.195 5.683 0.410 5.474 0.210 6.281 0.197
Heilongjiang 9.084 0.468 6.917 0.179 6.658 0.707 6.385 0.204 7.217 0.371
Hebei
6.844 0.277 5.311 0.337 4.017 0.217 4.727 0.307 4.727 0.262
Jiansu9.481 0.210 7.646 0.243 6.902 0.581 7.298 0.279 7.395 0.178
Anhui
7.663 0.283 6.259 0.154 5.016 0.582 5.257 0.400 5.849 0.176
Henan
6.418 0.185 5.272 0.248 3.350 0.423 4.296 0.179 4.548 0.109
Yunnan8.084 0.187 7.224 0.195 5.101 0.305 5.295 0.190 6.110 0.087
All
7.929 0.922 6.357 0.753 5.206 1.137 5.466 0.870 5.990 0.889
Note: We set 1992 as the base year. All variables take logarithms.

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