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Impacts of Migration on HouseholdProduction Choices: Evidence fromChinaChenggang Wanga, Nicholas Radab, Lijian Qinc & Suwen Pand

a Department of Agricultural and Applied Economics, Texas TechUniversity, & Texas A&M AgriLife Research and Extension Centerat Lubbock, Texas, USAb Market and Trade Economics Division, USDA’s Economic ResearchService, Washington DC, USAc Department of Economics, Anhui University of Finance andEconomics, Bangbu, Chinad World Agricultural Economic and Environmental Services,Columbia, Missouri, USAPublished online: 02 Jan 2014.

To cite this article: Chenggang Wang, Nicholas Rada, Lijian Qin & Suwen Pan (2014) Impacts ofMigration on Household Production Choices: Evidence from China, The Journal of DevelopmentStudies, 50:3, 413-425, DOI: 10.1080/00220388.2013.866221

To link to this article: http://dx.doi.org/10.1080/00220388.2013.866221

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Impacts of Migration on Household ProductionChoices: Evidence from China

CHENGGANG WANG*, NICHOLAS RADA**, LIJIAN QIN† & SUWEN PAN‡

*Department of Agricultural and Applied Economics, Texas Tech University, & Texas A&M AgriLife Research and ExtensionCenter at Lubbock, Texas, USA, **Market and Trade Economics Division, USDA’s Economic Research Service, WashingtonDC, USA, †Department of Economics, Anhui University of Finance and Economics, Bangbu, China, ‡World AgriculturalEconomic and Environmental Services, Columbia, Missouri, USA

Final version received September 2013

ABSTRACT The great migration from Chinese farms to cities during the past several decades ranks among themost economically consequential of modern population movements. We use a national sample of rice-producingChinese households to examine the effects of that migration on agricultural production. Our assessment involvesevaluating four alternative theories of labour market equilibrium in the framework of an expanded agriculturalhousehold model. Migration’s farm production impacts appear to be slight, not on account of farm labour marketperfections or remittance-financed technological improvements, but by substituting a reduction in leisure andother low-return activities for lost labour.

1. Introduction

The impact of migration on agriculture has important policy implications in less developed countries,where policy-makers face the dual task of facilitating food production for an underfed population andproviding inexpensive labour for emerging industries. If labour migration from farm to industryreduces agricultural output, the consequent food-price inflation can weaken industrial competitiveness(Ray, 1998, p. 353). The purpose of the present analysis is to evaluate the impact of agricultural labourmigration on farm production choices. To examine this issue, we employ a national dataset of Chineserice-producing farm households. We further offer a new econometric approach for studyingmigration’s impact on farm decisions, one that is particularly useful when instrumental-variableestimation is precluded by a scarcity of instruments.

The development economics literature suggests varying theories of farm labour’s migration impacts onagricultural production. Lewis (1954) and Ranis and Fei (1961) argue farm labour is generally over-abundant in less-developed countries, so farm production is little affected by labour movement. Theagricultural household model (AHM) predicts similarly that farm production choices are independent ofconsumption and off-farm employment (Singh, Squire, & Strauss, 1986). The new economics of labourmigration (NELM) postulates that, while productive labour lost to non-farm sectors reduces farm produc-tion in the short run, migrant remittances home can compensate for the loss by financing new farmtechnology (Stark & Bloom, 1985). Each of these theories is examined in our application to Chinese rice-producing farm households. We hypothesise that rural labour is underutilised, such that agricultural labourmigration has not significantly affected rice-producing farm households’ production choices.

Correspondence Address: Chenggang Wang, Texas Tech University, PO Box 42132, Lubbock, TX 79409, USA. Email:chenggang.wang@ttu.eduThe views expressed are those of the authors and may not be attributed to the Economic Research Service or the United StatesDepartment of Agriculture.

The Journal of Development Studies, 2014Vol. 50, No. 3, 413–425, http://dx.doi.org/10.1080/00220388.2013.866221

© 2013 Taylor & Francis

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The employed econometric framework alleviates a principal concern in the empirical literature ofmigration’s effects on farm household behaviour: missing-variable bias. Such bias arises from thesimultaneity of the household’s migration, production and consumption decisions, and the most widelyadopted solution is instrumental-variable estimation (de Brauw & Giles, 2008; Lucas, 1987; Rozelle,Taylor, & de Brauw, 1999). This technique can, in theory, correct missing-variable bias, but itfrequently is limited by a dearth of powerful instruments. Lacking valid instruments, our approachis to narrow the set of missing variables and search for ways to control for them. More specifically, weanalyse four probable equilibria in an expanded agricultural household model and identify in each ofthem the required control variables when regressing household production choices on migrant employ-ment. Then, through empirical tests, we determine the equilibrium most representative of our sample’sdata generating process.

Upon selecting the optimal equilibrium, we assume the existence of an urban–rural wage gap. Wefurther assume that a household’s decision to release a member for migrant employment is determinedby household labour quality and urban job market conditions, but not by agricultural marketconditions or technological constraints. In a regression of household production choices on migrantemployment, therefore, missing agricultural market and technological factors will not lead to seriousestimation bias. The econometric task is thus reduced to controlling for household and villagecharacteristics affecting both farm and migrant labour supply.

Our results indicate that migrant employment sacrifices Chinese household rice production by anegligible amount. The modesty of this loss does not appear to be explained by the agriculturalhousehold model’s proposition that lost family labour can be substituted for by hired labour in aperfect labour market. Nor does it appear to be explained by the new economics of labour migration’sargument that households invest off-farm income in new technology to compensate for lost productionwhen labour migrates. Rather, it appears rice-producing households have demonstrated an ability andwillingness to reallocate their time from leisure and other low-return activities to production,compensating for a large portion of the lost labour. Our findings thus echo the notion of surpluslabour proposed by Lewis (1954) and Ranis and Fei (1961).

The remainder of the article is structured as follows. The next section describes the four labourmarket equilibria, and is followed by Section 3, which details the data and descriptive statistics.Section 4 specifies our econometric approach, Section 5 examines the results, and Section 6 concludeswith a discussion of the research findings and possible policy implications.

2. Labour Market Equilibria

We assess four equilibria in the agricultural household model (AHM) framework, each relating to adifferent set of assumptions on the perfection of agricultural labour markets and the existence of off-farm labour constraints. The AHM is particularly useful for this exercise because of its role inexamining the market efficiency, labour demand and food supply implications of agriculturalhousehold behaviour.1 A key feature of our model, missing in traditional AHMs, is the presence ofheterogeneous off-farm labour markets in which wages may be greater than the agricultural wage.Such a feature enables us to account for the urban–rural wage differentials widely observed in lessdeveloped countries and which have provided a foundation of dualistic economic development models(Lewis, 1954; Ranis & Fei, 1961).

2.1. Equilibrium I: Agricultural Labour Market Perfection, No Off-Farm Labour Constraint

Suppose the agricultural labour market is perfect in the sense that family and hired labour areperfectly substitutable in farm production and that the market is large enough for a household tobuy and sell as much labour as it wishes at the market wage. Suppose also that, while off-farmlabour markets are heterogeneous, all household members can find off-farm jobs matching theirpersonal traits, albeit at wages reflecting their personal productivities. Such intra-household

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productivity heterogeneity implies that a rational household would send to off-farm work its mostproductive member first, its second-most productive member second, and so on. In other words,intra-household productivity heterogeneity implies decreasing marginal returns to off-farm laboursupply. To formalise this assumption in continuous time, let M denote the total amount of time thathousehold members spend on off-farm work. Let wf ðM ; α; βÞ denote the household’s off-farm wagefunction, which decreases in M and depends on a vector α of household demographic and humancapital characteristics and a vector β of off-farm labour demand factors. The household’s totalearnings from off-farm employment is the integral of that wage function over off-farm employmenttime:

R ¼ GðM ; α; βÞ ¼Z M

0wf ðm; α; βÞdm (1)

where m is the integration variable for M. Off-farm wage is positive, wf > 0, and decreases with time

worked, dwf

dm < 0. Therefore, the off-farm earnings function is increasing and concave inM : GM > 0 and GMM < 0.

The agricultural household’s time allocation decision is made jointly with its consumption andproduction decisions. Suppose the household maximises a twice continuously differentiable quasi-concave utility function

UðC; S; αÞ (2)

subject to the budget constraint

C þ wS ¼ I (3)

where C is consumption, S leisure, w the market wage of agricultural labour and I the household’sbudget constraint or full income. Full income is composed of a time endowment, agriculturalproduction profit, net off-farm income and exogenous income:

I ¼ wTðαÞ þ pY � wL� rK þ R� wM þ E (4)

where TðαÞ is the time endowment, Y is output, L is on-farm labour, K non-labour inputs, M off-farmlabour, R off-farm income, E exogenous income, p output price, w agricultural wage and r non-labourinput prices.

The agricultural input–output relationship is governed by a twice continuously differentiable andconcave production function

Y ¼ QðL;K; θÞ (5)

in which θ is a vector of farmland characteristics and technology constraints determining productiveefficiency.

The above utility maximisation problem can be solved recursively: full income (Equation 4) isfirst maximised subject to production function (Equation 5) and off-farm earnings (Equation 1).Utility function (Equation 2) is then maximised subject to budget constraint (Equation 3), where fullincome I is now the maximised income obtained in the first stage.2 Solving the full model givesequilibrium consumption, input and output quantities, and off-farm employment. We focus in thefollowing only on the production and off-farm employment choices with which our empiricalanalysis is concerned.

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At equilibrium, marginal returns to on- and off-farm employment each equal the agriculturalwage:

pQlðL�;K�; θÞ ¼ w ¼ wf ðM �; α; βÞ (6)

Solving the two marginal equalities in Equation (6) yields equilibrium on-farm employmentL� ¼ Lðp;w; r; θÞ and off-farm employment M � ¼ Mðw; α; βÞ. Because off-farm employmentopportunities are assumed unlimited at each wage, optimal off-farm labour supply is such thatthe wage of the last unit of off-farm labour equals its opportunity cost, namely agricultural wagew. Because the latter is exogenously determined in a perfect agricultural labour market, off-farmemployment is independent of household production decisions. Further, household farm labourdemand L� in this model is, again because of agricultural wage’s exogeneity, independent of off-farm employment. Indeed, so are non-labour input demand K� ¼ Kðp;w; r; θÞ and output supplyY � ¼ Y ðp;w; r; θÞ. That is, off-farm employment and agricultural production are mutuallyindependent.

Imagine now the dataset generated under this equilibrium is used to regress agricultural inputs(L� and K�) and output (Y �) against off-farm employment (M �). Although our above analysis suggeststhe right-hand and left-hand variables in each of these three regressions are independent of oneanother, a spurious correlation may arise between them unless agricultural wage w is controlled for,since w is part of the equilibrium expressions for L�; K�, Y �, and M�.

2.2. Equilibrium II: Agricultural Labour Market Imperfection, No Off-Farm Labour Constraint

The assumption of agricultural labour market perfection is, however, intuitively inconsistent withreality in less developed countries, and has been rejected in a large body of empirical analysis (forexample, Barrett [1996], Carter [1984], Jacoby [1993], Kevane [1994], and Udry [1998]; exceptionsare Benjamin [1992] and Pitt and Rosenzweig [1986]). We therefore now relax this assumption, butmaintain that of unlimited off-farm employment opportunity. Several variants of agricultural house-hold models have emerged in the literature to explore possible types of farm labour market imperfec-tion. Pitt and Rosenzweig (1986) attempt to account for the peak season, when farm labour supplymost fails to meet demand. Benjamin (1992) examines the case in which family and hired labour arenot equally efficient. A common element of these models is that market imperfection implies theopportunity cost of family labour is, rather than exogenous market wage w, a shadow wage endogen-ously determined in the household’s time allocation decision. In such a case, our equilibrium condition(Equation 6) becomes

pQlðL�;K�; θÞ ¼ wSðp; r; θ; α; β;EÞ ¼ wf ðM �; α; βÞ (7)

where wS is the shadow wage and is a function of the full set of exogenous variables ðp; r; θ; α; β;EÞ in thefarm household’s utility maximisation program. Therefore, our equilibrium expressions now become: farmlabour quantity L� ¼ Lðp; r; θ; α; β;EÞ; non-labour input quantity K� ¼ Kðp; r; θ; α; β;EÞ; outputY � ¼ Y ðp; r; θ; α; β;EÞ; and off-farm employment M � ¼ Mðp; r; θ; α; β;EÞ.

If the data are generated by this type of equilibrium, the associations between off-farm employment(M �) and production choice variables (L�;K�; and Y �) are likely to be the convoluted outcomes of avariety of environmental effects such as agricultural input and output price changes ðp; rÞ, productivitydifferences (θ), demographic and human capital changes (α), and variations in off-farm employmentopportunity (β) and exogenous income (E). When some of these environmental variables are missing,estimation bias may arise in regression analyses of off-farm employment’s effects on farm productionchoice variables.

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2.3. Equilibrium III: Agricultural Labour Market Perfection, Non-Binding Off-Farm LabourConstraint

Both types of equilibrium described above assume all household members can find off-farm jobsmatching their skills. That assumption implies unemployment would never be observed in rural areas:every household member of working age participates in agricultural production or non-farm work; anassumption inconsistent with observed rural unemployment worldwide. Benjamin (1992) examined avariant of the agricultural household model in which a non-agricultural employment opportunity islimited. This assumption may be expressed as:

M � � �Mðα; βÞ: (8)

Constraint �Mðα; βÞ is determined either by demand factors in the off-farm labour markets for which ahousehold member qualifies or by institutional and informational market barriers. When non-agricul-tural jobs are scarce, household members qualified for off-farm positions and whose per-hourproductivity exceeds the agricultural wage spend the remainder of their time in agricultural productionor unemployment. One example of this constraint is China’s hukou, or dual-residence registrationsystem. This institutional barrier to free rural–urban labour migration impairs rural residents’ access tourban employment. The system has been, and still is, used to determine qualifications for urban workopportunities and welfare programmes.

When the constraint of Equation (8) is binding, two additional types of equilibrium may arise,depending upon whether the agricultural labour market is perfect. When the market is perfect, thefollowing equilibrium condition holds:

pQlðL�;K�; θÞ ¼ w < wf ðM � ¼ �Mðα; βÞÞ (9)

Note that the positive wage gap between off- and on-farm employment in this equilibrium indicatesthat the household will supply more off-farm labour when such opportunity arises. The equilibriumquantity of off-farm employment is now a binding constraint M� ¼ �Mðα; βÞ. Because the agriculturallabour market is assumed perfect, the household’s production choices under the present equilibrium(Equation 9) are identical to that of a profit-maximising agricultural firm: L� ¼ Lðp;w; r; θÞ;K� ¼ Kðp;w; r; θÞ; and Y � ¼ Y ðp;w; r; θÞ. Thus, as in Equilibrium I, agricultural production andoff-farm employment under this equilibrium (Equation 9) are mutually independent. Unlike inEquilibrium I, however, agricultural wage w affects only agricultural production choices, not off-farm employment. Empirically these properties imply that there should not exist correlations betweenproduction choice variables L�; K�; and Y � on off-farm employment M �.

2.4. Equilibrium IV: Agricultural Labour Market Imperfection, Binding Off-Farm Labour Constraint

In the absence of a perfect farm labour market and when the off-farm employment constraint isbinding, the final equilibrium condition that may arise pertains to time allocation:

pQlðL�;K�; θÞ ¼ wSðp; r; θ; α;E; �Mðα; βÞÞ < wf ðM � ¼ �Mðα; βÞÞ (10)

In this case, the opportunity cost of family labour is not the exogenously determined market wage; itis, rather, the shadow wage, which depends on the household’s consumption, production andemployment decisions. Because of the binding constraint on off-farm employment, the returns tosuch employment remain higher than to on-farm employment. Solving the above equilibriumcondition gives the equilibrium quantities of agricultural labour L� ¼ Lðp; r; θ; α;E; �Mðα; βÞÞ, non-labour inputs K� ¼ Kðp; r; θ; α;E; �Mðα; βÞÞ, output Y � ¼ Y ðp; r; θ; α;E; �Mðα; βÞÞ and off-farmemployment M� ¼ �Mðα; βÞ.

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Consider now the empirical implications of this equilibrium. First, production conditions (p; r; θ)and exogenous income (E) affect agricultural input demands and output supply (L�;K�; Y �) but notoff-farm employment (M �). This clearly is the result of the binding off-farm employment constraint.Empirically it means no estimation bias arises when p; r; θ are excluded from the regressions ofL�;K�; and Y �on M �. And because off-farm employment (M �) appears in the equations of agriculturalinput demands and output supply (L�;K�; Y �) but not vice versa, their association represents theimpact of the former on the latter.

Second, demographic and human capital characteristics α affect both production choicesL�;K�; and Y � and off-farm employment M �. They affect the former because, under the assumptionof agricultural labour market imperfection, hired labour may require additional incentives to eliciteffort or because hired labour is insufficient to meet the demand. They affect the latter because theydetermine the types of off-farm employment for which the household members are qualified. Theempirical implication of this property is that, in order to avoid estimation bias, household demographicand human capital factors α must be included as independent variables in regressions ofL�;K�; and Y �against M �.

Finally, availability of and access to off-farm employment opportunity β affects both(L�;K�; and Y �) and M �. But unlike household characteristics α, β affects the former only becauseit affects the latter. Therefore, no estimation bias arises when β is excluded from the regressions ofL�;K�; and Y �on M �. Moreover, β can serve as an instrument when data on household characteristicsα are missing. An excellent example of such an instrumental variable is given by de Brauw and Giles(2008), who use a rural Chinese’s receipt of the identification card (necessary for urban employment)as an instrument in their analysis of rural-to-urban migration’s impact on farm behaviour.

In short, the above equilibrium analysis suggests serious missing-variable bias may arise inregressions of production choices on off-farm employment, especially when the agricultural labourmarket is imperfect. Recognising the complex ways in which household production and employmentdecisions are interrelated, the literature has often treated such bias with instrumental-variable techni-ques (de Brauw & Giles, 2008; Lucas, 1987; Rozelle et al., 1999). The above analysis shows that analternative approach is feasible if the data are generated under Equilibrium IV. In this case, theomitted-variable bias arises only when household demographic and other non-agricultural character-istics variables are lacking. Fortunately, such variables are frequently available in household surveydata.

2.5. Equilibrium Selection Conditions

In determining under which equilibrium the data are generated, we apply two sets of conditions. Thefirst is:

dL�

dα¼ 0 (11)

which holds true in Equilibria I and III but not in II and IV. When the agricultural labour market isperfect (Equilibria I and III), changes in household demographic composition and non-agriculturalcharacteristics do not affect production choices. The second set is:

dM �

dp¼ 0;

dM �

dw¼ 0 (12)

which holds true under all but Equilibrium II. Equation (12) says off-farm employment is independentof agricultural output price and wage. This holds under Equilibria III and IV because the off-farmemployment constraint is assumed binding. It holds as well under Equilibrium I – where no suchconstraint is binding but the agricultural labour market is assumed perfect – because the exogenouslygiven farm wage separates production from off-farm employment decisions.

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In our present application, Equilibrium IV is favoured against the three alternatives because it ismost representative of less developed countries due to the persistence of observed rural–urban wagegaps and the frequently missing or fragmented rural labour markets. Equilibrium IV is selected if thecondition of Equation (11) is rejected and the condition of Equation (12) is not rejected.

3. Data and Descriptive Statistics

The data employed are drawn from the national household surveys conducted by the Research Centrefor the Rural Economy (RCRE) at China’s Ministry of Agriculture and span the 2006–2007 timeperiod. A detailed discussion of the RCRE surveys can be found in Benjamin et al. (2005). The surveyquestionnaire framework has remained largely unchanged over the last two decades, minor changesmade only when the government needed new information. For example, the RCRE began recently tocollect data on individual household members’ employment conditions in order to understand thelivelihood status of migrant workers.

The 2006–2007 rice-producing household sample provides a balanced panel of 1,207 householdswhose main crop is rice from 79 villages in 13 major rice-producing provinces.3 Table 1 divides thesehouseholds into China’s six rice ecological zones (Zhu, 2000). Contrasting each zone’s productionshares to the corresponding representation in our sample indicates all six zones are well represented byour sample.

Table 2 presents summary statistics of the key variables in our sample. Household rice productionvariables include rice output, land area planted to rice, rice yield, family and hired labour in riceproduction and costs of such rice production inputs as chemicals, seed, electricity and irrigation,cattle and machinery. Non-rice labour includes non-rice farm labour, in-village non-farm labour andmigrant labour. All labour variables are measured in person-days worked. The rice production andlabour variables are the primary dependent variables in the subsequent econometric analysis.Independent variables include wage of hired labour, lagged rice price, household size and numberof working-age family members, defined as those aged between 16 and 65. Rice price data areprovince-specific and derived from provincial crop budgets compiled by the National Bureau ofStatistics of China (2008).

Descriptive statistics of the sample presented in Table 2 depict an average rice-producing farmhousehold comprised of 4.2 people, of which 3.4 are working-age family members (WAFMs). Thisrice-producing household employs 3.2 months of family labour and hires 0.44 months of labour toachieve 442 kilograms/mu of rice. Rice production requires 110 person-days of labour, about half ofthe time devoted to non-rice farm production, and two weeks longer than in-village non-farm

Table 1. Sample distribution of household observations across rice ecological zones

Rice ecological zone(production shares)

Number of villages inthe sample

Number of householdsin the sample

Sample shares of householdobservations

North-east (2.9%) 18 296 24.50%North (3.4%) 2 52 4.30%Central (69.9%) 37 477 39.50%South (15.7%) 11 211 17.50%South-west Plateau (7.6%) 6 111 9.20%North-west (0.5%) 5 60 5.00%Total 79 1,207 100%

Notes: Our rice-producing household sample consists of 2,414 observations on 1,207 households in which rice isthe main crop in years 2006 and 2007. Our sample covers Heilongjiang, Jilin and Liaoning provinces in the North-east zone; Henan and Shandong in the North; Zhejiang, Fujian, Hubei, Chongqing, and Sichuan in Central China;Guangxi in the South; Yunnan in the South-west Plateau; and Shaanxi in the North-west. The production shares invarious rice ecological zones are from Zhu (2000).

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activities. The household spends 255 days outside the village for migrant jobs which generate 8,010yuan of income.

4. Econometric Approach

Our empirical strategy is twofold: we first test our data against the conditions of Equations (11) and(12) to determine which equilibrium characterises China’s rice-producing farm households, and thenemploy the selected equilibrium to evaluate the impact of migrant employment on farm productionchoices.

It is likely that exogenous household decision-making constraints, such as institutional, geographi-cal and informational barriers, could affect both agricultural production and migration. A village closerto cities, for example, may have better access to both migrant jobs and agricultural markets. We usevillage dummies in our regressions to control for such unobserved factors. In addition, it is likely thatthe household’s human capital and other characteristics could affect both agricultural and migrationdecisions. Households with more working-age family members are likely to be more productive inboth farming and migrant jobs. To control for such factors and other household specific effects, weinclude two human capital variables, household size and number of working-age family members, andfirst-difference the data.

4.1. Equilibrium Testing

To determine under which equilibrium our sample is generated, we test our data by estimating thefollowing:

ΔY1i ¼ Ω0 þ Ω1ΔWi þ Ω3ΔPi þ Ω3ΔHSi þ Ω4ΔWAFMi þ δ� Di þ εi; i ¼ 1; � � � ; 1207 (13)

where ΔY1 stands for the first-differenced production and labor choice variables, rice yield, planted ricearea, total rice labour, family rice labour, hired rice labour and migrant labour. The independent variablesare also first-differenced and include hired-labour’s wage ΔW , the lagged rice price ΔP, household sizeΔHS, the number of working-age family members ΔWAFM and a vector of village dummies D.

Table 2. Descriptive statistics

Variable (unit) Mean Std dev. Min. Max.

Rice output (kg) 2,750.3 3,137.1 1.0 46,830.0Planted rice area (mu) 6.3 7.1 0.2 100.0Rice yield (kg/mu) 441.5 139.1 0.7 1100.0Family rice labour (person-days) 96.5 67.5 3.0 604.0Hired rice labour (person-days) 13.2 12.0 1.0 210.0Total rice labour (person-days) 109.7 75.3 4.0 716.0Seed cost in rice (yuan) 113.6 173.5 0.0 6,900.0Electricity and irrigation cost in rice (yuan) 274.7 465.6 3.0 8,916.0Chemicals cost in rice (yuan) 146.6 177.6 4.0 3,017.0Cattle cost in rice (yuan) 190.7 191.2 5.0 2,283.0Machinery cost in rice (yuan) 295.0 345.9 2.0 8,400.0Non-rice farm labour (person-days) 226.6 199.3 0.0 1,238.0In-village non-farm labour (person-days) 94.7 163.6 0.0 1,420.0Migrant labour (person-days) 254.8 269.1 0.0 1,500.0Migrant income (yuan) 8,009.8 12,722.7 0.0 180,000.0Hired labour wage (yuan/day) 36.1 8.4 5.8 70.0Lagged rice price index 83.0 8.4 71.2 100.3Household size (headcount) 4.2 1.4 1.0 13.0Working-age family members (headcount) 3.4 1.1 1.0 8.0

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Ωi; i ¼ 0; � � � ; 5 represent the intercept and coefficients to be estimated on the price and householdcharacteristics, and δ is a vector of coefficients on the village dummies. The error term ε is assumedindependent and identically distributed.

4.2. Testing Migration’s Impact on Household Production Choices

Upon selecting the appropriate equilibrium, we test the impact of migrant’s employment on householdrice production choices. In doing so, we alter Equation (13):

ΔY2i ¼Ψ0 þ Ψ1ΔMLi þ Ψ2ΔMIi þ Ψ3ΔWi þ Ψ4ΔPiþ Ψ5ΔHSi þ Ψ6ΔWAFMi þ δ� Di þ "i; i ¼ 1; � � � ; 1207 (14)

where ΔY2 is now the first differenced dependent variables, family rice labour, hired rice labour, non-rice farm labour and in-village non-farm labour. The first differenced independent variables build uponEquation (13) and now include migrant labour ΔML and migrant income ΔMI . The other independentvariables and coefficients are interpreted identically to those in Equation (13). Note that, if EquilibriumIV is selected, coefficients Ψ1 and Ψ2 respectively represent the impact of migrant labour and migrantincome on agricultural production choice variables.

5. Examining the Results

Equations (13) and (14) are estimated using StataIC 12.1. Results from Equation (13) are available inTable 3, and Equation (14) results in Table 4.

Table 3. Equilibrium testing

Rice yieldPlanted rice

areaTotal ricelabour

Family ricelabour

Hired ricelabour

Migrantlabour

Hired labour wage –1.18** 0.07** 0.41* 0.61*** –0.20*** –0.78(0.45) (0.02) (0.20) (0.18) (0.04) (0.78)

Lagged rice price 127.00*** 0.01 –3.08 –4.47 1.39 7.24(17.40) (0.95) (7.69) (6.93) (1.52) (30.16)

Household size –3.07 0.02 –6.33* –6.53** 0.20 –14.10(6.04) (0.33) (3.08) (2.40) (0.53) (10.46)

Number of WAFMS –1.87 0.47 6.32* 5.86* 0.47 82.11***(6.99) (0.38) (3.08) (2.78) (0.61) (12.11)

R2 0.40 0.11 0.18 0.20 0.10 0.16Adjusted R2 0.36 0.04 0.13 0.15 0.04 0.10

Chemicals cost Seed cost Elec. and irr. cost Cattle cost Machinery cost

Hired labour wage –0.12 –0.12 –0.68 1.14** 0.07(0.61) (0.84) (0.95) (0.46) (1.28)

Lagged rice price –31.57 –19.54 17.40 44.92** –27.43(23.61) (32.58) (37.05) (17.95) (49.63)

Household size –4.08 –4.12 6.24 7.38 –11.32(8.19) (11.30) (12.85) (6.23) (17.22)

Number of WAFMS 15.10 5.18 9.52 5.49 23.07(9.48) (13.08) (14.88) (7.21) (19.93)

R2 0.07 0.31 0.08 0.24 0.16Adjusted R2 0.00 0.26 0.02 0.18 0.10

Notes: WAFM stands for working-age family members. Elec. and irr. cost stands for electricity and irrigation costs.*indicates statistical significance at the 5 per cent level, **at the 1 per cent level and ***at the 0.1 per cent level.

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5.1. Equilibrium Selection

The results presented in Table 3 strongly support Equilibrium IV against its alternatives. Recall theassumptions underlying that equilibrium are (a) agricultural labour market imperfection and (b) bindingmigrant employment constraints. We reject that the data are generated in a perfect agricultural labourmarket if the condition of Equation (11) fails to hold; that is, if demographic variables such as householdsize and number of working age family members affect a household’s rice labour supply. Results incolumns 4, 5, and 6 of Table 3 suggest that our data are indeed generated under an imperfect labour market.For example, we find that a household’s total rice labour increases by 6.3 person-days with the addition ofeach working-aged family member, but decreases by 6.3 days with the addition of each new non-working-aged household member. This latter result is logical in that each new household member, holding all otherfactors fixed (for example, working-age family members), reduces the household’s total working days inthe rice field by diverting a labourer for child or elderly care. By evaluating the role of family and hiredlabour separately, we further find the impact of household demographic changes on total rice labour isdriven by adjustments in family labour; hired labour does not adjust to balance total rice labour whenfamily labour is lost. Because household demographic characteristics do significantly affect a household’slabour supply, we reject the assumption that China’s rice labour markets are perfect and, therefore, mayomit Equilibria I and III from further analysis.

Table 4. Effects of migrant labour and income on household production choices under Equilibrium IV

Rice yield Family rice labour Hired rice labour Non-rice farm labour Planted area

Migrant labour –0.04* –3.3e-03 2.0e-03 –0.14*** 3.4e-03***(0.02) (0.01) (1.7e-03) (0.02) (1.0e-03)

Migrant income 1.76e-04 –1.3e-04 –8.6e-05*** 1.7e-04 –4.4e-05**(3.0e-04) (1.2e-04) (2.7e-05) (3.3e-04) (1.7e-05)

Hired labour wage –1.23** 0.62*** –0.18*** –0.48 0.08***(0.45) (0.18) (0.04) (0.49) (0.02)

Lagged rice price 127.30*** –4.45 1.37 10.92 –0.02(17.38) (6.93) (1.51) (18.89) (0.94)

Household size –3.74 –6.51** 0.27 18.15** 0.09(6.04) (2.41) (0.53) (6.57) (0.33)

Number of WAFMS 1.37 6.26* 0.39 31.39* 0.24(7.13) (2.84) (0.62) (7.75) (0.39)

R2 0.40 0.20 0.11 0.31 0.12Adjusted R2 0.36 0.15 0.05 0.26 0.05

Chemicals cost Seed cost Elec. and irr. cost Cattle cost Machinery cost

Migrant labour –4.0e-04 0.01 –0.05 –0.01 –0.02(0.03) (0.04) (0.04) (0.02) (0.05)

Migrant income 9.1e-04* –2.9e-04 3.0e-05 5.8e-05 –6.9e-04(4.1e-04) (5.7e-04) (6.5e-04) (3.1e-04) (8.7e-04)

Hired labour wage –0.25 –0.07 –0.72 1.12* 0.15(0.61) (0.85) (0.96) (0.47) (1.29)

Lagged rice price –31.56 –19.60 17.77 44.97** –27.30(23.57) (32.60) (37.05) (17.96) (49.65)

Household size –4.52 –3.87 5.51 7.25 –11.25(8.19) (11.33) (12.87) (6.24) (17.25)

Number of WAFMS 14.22 4.83 13.66 6.02 25.31(9.67) (13.38) (15.20) (7.37) (20.37)

R2 0.07 0.31 0.08 0.24 0.16Adjusted R2 0.01 0.26 0.02 0.18 0.10

Notes: WAFM stands for working-age family members.*indicates statistical significance at the 5 per cent level, **at the 1 per cent level and ***at the 0.1 per cent level.

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The remaining two Equilibria, II and IV, are now evaluated against the condition of Equation (12).This condition assumes that agricultural output and input prices affecting rice profitability do not affecta household member’s decision to become a migrant labourer because exogenous migrant employmentconstraints are binding and the return on migrant labour is higher than farm labour. We fail to rejectEquation (12) because neither the hired labour wage nor the lagged rice price significantly affects thedecision to become a migrant labourer. Stated differently, any increase in farm labour wages or theprevious year’s rice price does not induce migrant labourers to remain on-farm. As such, the migrantlabour constraint is binding and Equilibrium IV is selected for further analysis.

In the interest of broadening our understanding of the household’s production decision-makingprocess, we additionally regress five input expenditures, relating to chemicals, seeds, electricity andirrigation, cattle and machinery, on the same four independent variables in Equation (13).4 The picturedepicted by the entire set of results in Table 3 suggests a Chinese rice-producing household which, inresponse to rising wages, hires less labour will increase family labour and cattle use, increase the areaplanted to rice, but experience lower yields. One interpretation of these results is that hired labourersspecialising in rice production are more efficient than family labourers employing greater animaldrafting power. In response to higher rice prices, that same household achieves higher yields andemploys more cattle services. Interestingly, as rice prices induce greater yields, it does not appear to bedue to investments in new seed/fertiliser/irrigation technologies. It may be that higher rice pricesstimulate greater farmer effort and more intensive use of cattle power to achieve higher profits.

5.2. Migration-Induced Time Reallocation

The family rice labour regression in column 3 of Table 4 show that a migrant’s employment has noimpact on family rice labour. When a family member, who would have otherwise worked in riceproduction, migrates to a city, the household reallocates time from other activities – including non-ricefarming, in-village non-agricultural employment and leisure – to make up for the lost labour. In suchan event, as shown in column 4 of Table 4, no additional labour is hired to make up for the lost familyrice labour.

In contrast to these two sets of results, column 5 suggests that the decision to migrate for employ-ment does significantly affect non-rice farm labour. For every 100 person-days of labour lost tomigrant employment, the household will reduce non-rice farm labour by 14 days. The remaining 86days represent the loss of leisure time or local non-farm activity.

The results in Table 4 imply that, up until 2007, a significant amount of underutilised labourpersisted among Chinese rice-producing households. Migrant employment appears to have had nosignificant effect on the labour supply to these households’ main crop, and only slightly affected thelabour supply to sideline farm and nonfarm activities. Most of the time spent performing migrant jobswould therefore have been used in leisure. The breakdown of the household time allocation reveals therice-producing Chinese household’s subjective ordering, according to labour’s marginal householdutility contribution, of the four activities to which time is allocated. In descending order, they aremigrant employment, rice production, non-rice farm production and leisure.

5.3. Evaluating Migration’s Income Effect

Migrant income is significant in the hired labour rice regression presented in Table 4. The negativeeffect of migrant income on hired rice labour suggests that migrant income likely has been used topurchase hired-labour-substituting inputs, such as the labour-saving technology pesticide. The input costregressions presented in the bottom panels of Table 4 show that the chemicals input is the only oneaffected by migrant income. A household with the sample-mean migrant income will spend 7.8 yuan forchemicals and use 0.68 fewer days of hired labour. Although these numbers are rather small, thesubstitution makes economic sense considering that 0.68 day of hired labour will cost a household 25yuan (computed with the sample-mean wage), significantly higher than the increased chemicals cost.

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Migrant income has no significant effect on investments to such capital goods as cattle, machineryand irrigation equipment. This indicates, in contrast with the positive income effect on an in-villagenon-farm activity, that rice production in China is not constrained by a lack of capital. Small patches ofland and low grain prices do not yet appear to justify substantial private investment in mechanisationand other increased uses of capital goods. The lack of a capital constraint is further supported by therice-producing household’s increased use of the predominant capital good, cattle, in the face of a risein the lagged rice price, regardless of the amount of migrant income available.

Lucas (1987) and Rozelle et al. (1999) have tested the new economics of labour migration (NELM)by examining the overall effects of labour withdrawal and remittances on agricultural productivity.Using aggregate time series data from five African countries, Lucas (1987) found farm-to-industrylabour migration had reduced crop production in the short run but migrant remittances had boostedcattle herd sizes in the long run. Similar evidence for the NELM was found in Rozelle et al’s (1999)analysis of a cross-section of 787 farm households in two northern Chinese provinces. Our analysisfinds no evidence of increased capital use driven by migrant income. Our results are more in line withde Brauw and Giles (2008) who, with data drawn like ours from the RCRE national survey, find noassociation between migration and productive asset investment.

Although we see no evidence in favour of the NELM, we do not reject it either. As Taylor andMartin (2001) note, migration’s investment-boosting effects depend on the availability of investmentopportunities, which in turn depend on local conditions. Our overall assessment of income effects invarious household activities suggests unavailability of profitable investments to Chinese rice farmers,whose prospects are limited by small, fragmented farm holdings.

Given the rather inconsequential effects of migration on rice input use described above, it is notsurprising to find that migration has had a negligible impact on rice yield (Table 4). For every 100person-days of migrant labour withdrawn from agriculture, rice yields are reduced by 4 kg per mu.And migrant’s income has had no effect on rice yield at all.

6. Discussion

It is well recognised in the development economics literature that agriculture plays a synergistic role indevelopment, supplying labour to industry and surplus food to the industrial labour force.Understanding the relationships between these resource flows is of great importance to policy-makersin less developed countries. This article offers a new econometric approach for studying migration’simpacts on agricultural production. Our analysis indicates that China’s rice-producing households haveresponded to labour departures in a manner highly consistent with the agricultural household model,albeit under a type of equilibrium to which the literature has paid inadequate attention. Migrationappears to promise a much higher return than farming and other sideline activities in rural China. Inthe face of increased labour withdrawal, however, Chinese rice farmers have managed to keep theirmain crop unaffected by cutting back on leisure and non-rice production labour, an indication ofunderutilised agricultural labour in rural China. With negligible opportunity cost, therefore, migrationremains a powerful engine of income growth and poverty reduction in rural China.

Continual off-farm employment and income growth seems, on the other hand, to have brought littleproduction improvement to China’s rice farmers. While rice production stability is good news toChina’s policy-makers, inactive productive investments in the face of rising off-farm income isunfortunate evidence of a dearth of profitable investment alternatives for rural Chinese. A balancedgrowth that benefits both the rural and urban population begs for further land-market reform to unleashland’s productive potential, and greater research and extension efforts to develop better farmtechnology.

Notes

1. For a review of applications, the reader is referred to Singh et al. (1986).

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2. For a more formal treatment, the reader is referred to Strauss (1986).3. A household’s main crop is rice if the number of days worked in rice production is larger than that in any other crop.4. Quantity data are not available for these inputs.

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