heterogeneous impact of farmer credit: an empirical investigation based on ivqr model

Systems Engineering - Theory & PracticeVolume 27, Issue 2, February 2007Online English edition of the Chinese language journal

Cite this article as: SETP, 2007, 27(2): 68–75

Heterogeneous Impact of Farmer Credit: An EmpiricalInvestigation based on IVQR ModelZHU Xi1,∗, LI Zi-nai2

1. Antai College of Economics & Management, Shanghai Jiao Tong University, Shanghai 200052, China

2. School of Economics and Management, Tsinghua University, Beijing 100084, China

Abstract: This article empirically estimates the economic impact of farmer credit by IVQR model, which takes both the heterogeneous

effect and the endogenous problem into account, using a survey data of 3,000 households from rural China in 2003. Our results show

that both formal and informal credit significantly contribute to the farmers’ operational income on the whole. However, its impact is

heterogeneous on the outcome distribution. The credit does not significantly contribute to the outcome of the poorest and richest farmers,

but it benefits the middle and low income farmers, for whom the output elasticity is about 0.08. Since the rural credit allocation leans to

rich farmers in China, there exists efficiency loss. The estimators obtained by 2SLS and QR both involve apparent biases.

Key Words: IVQR; farmer credit; economic impact

1 Introduction

Credit is one of most important factors in farmers’ pro-duction. Access to working capital or investment credit of-fered by rural financial institutions can substantially accel-erate the adoption of modern agricultural technologies andproduction patterns, permit rural entrepreneurs to take ad-vantage of investment opportunities, enhance the farmers’ability of bearing risk, and help farmers to smooth consump-tion when faced with income shocks. For these reasons, ruralcredit really matters for income growth and poverty reduc-tion, which attracts the attention of several governments andeconomists.

Existing literature focused on the credit rationing ofrural financial market, as well as the credit behavior offarmers[1−5]. This article focuses on the economic impact offarmer credit. Evaluating the contribution of credit is a rathertough job. Firstly, the endogeneity of borrowing cannot beavoided in most cases. Generally speaking, the credit sta-tus is determined by the interaction of the farmers’ demandbehaviors and the banks’ or informal lenders’ supply behav-iors. It does not happen randomly, and its amount is not ran-domly determined, either. Whether a farmer borrows or notand the amount he borrows show apparently the character-istics of self selection. It is not clear whether the measuredcredit effect reflects the borrowing constraint or the unob-servable characteristics of a borrower. McKernan (1996)[6]

stated that the presence of bias caused by the self-selection ofborrowers in credit program may bias the assessment of ben-efits of these programs by as much as 100%. Secondly, thereexists great heterogeneity among different types of farmers.The credit effect always differs for different level incomefarmers. Farmers earning different levels of income have dif-

ferent talents, and therefore, the use and efficiency of creditare also different. These factors make the measurement ofcredit effect quite sophisticated.

Nonetheless, some economists successfully estimatedthe credit effect (Carter and Weibe, 1990; Kochar, 1997;Binswanger and Khandker, 1995; Carter, 1988; Feder etal., 1990; Pitt and Khandker, 1998; Krandker and Faruqee,2003; Foltz, 2004; and Li, 2004 et al)[3−4,7−13]. The mainmethodologies applied until now can be summarized intotwo kinds. One is the IV method, which uses instrumen-tal variable to control the selection bias caused by endo-geneity. Binswanger and Khandker (1995), Krandker andRaruqee (2003), and Li (2004) applied such models[7,11,13].The other one is the endogenous switching regression model,which groups farmers by credit rationed or not, estimatesthe credit ration model (usually by the probit model) at thefirst stage, and then estimates the credit effect for both ra-tioned and non-rationed farmer at the second stage. Feder etal (1990)[9] and Foltz (2004)[12] applied such strategies. Allthese works prove the importance of credit to the farmers’income and welfare.

Although the literature has provided abundant referenceto understand the economic impact of credit, there is onecommon drawback, which is that these focus on the analysisof measures of central tendency: the mean or the median.While the mean and median impacts are interesting and im-portant measures in determining the credit impact, these arenot sufficient to fully characterize the impact of the credit(except under very restrictive conditions such as homogene-ity). In particular, these are non-informative about the im-pact of the credit on other points in the income distribution(perhaps more interesting) when the credit effect is hetero-geneous. Since policy makers may be particularly concerned

Received date: December 6, 2005∗ Corresponding author: Tel: +86-021-52301263; E-mail: [email protected] item: Supported by the National Natural Science Foundation of China (No.70573057)Copyright c©2007, Systems Engineering Society of China. Published by Elsevier BV. All rights reserved.

ZHU Xi, et al./Systems Engineering – Theory & Practice, 2007, 27(2): 68–75

about the impact of credit on the middle and lower part of thewealth distribution, understanding the whole distributionalimpact of credit is especially interesting from a policy per-spective. In addition, knowledge of the distributional impactof credit provides a clearer picture of the factor that is drivingthe mean results.

As the estimator of the mean effect, the analysis of thedistributional effects is complicated by the possibility that afarmer chooses whether or not to borrow, and how much toborrow based on his unobserved ability and the supplier’sdecision. One estimator that will capture complete charac-terization of the heterogeneous effect given the credit exo-geneity is the quantile regression estimator of Kroenker andBassett (1978)[14]. However, the self-selection of the bor-rowing state makes the conventional quantile regression es-timator inappropriate.

This article contributes to the extensive set of exist-ing literature of the credit impact by analyzing the impactof credit on the entire wealth distribution. We employeda model and an estimator developed by Chernozhukov andHansen (2001, 2005)[15−16], i.e., IV quantile regression toovercome both the endogeneity and the heterogeneity. Cher-nozhukov and Hansen (2001) demonstrated that their esti-mator is consistent under endogeneity and treatment effectheterogeneity[15]. Thus, this article provides an importantsupplement to the study discussed above, which focuses onestimating the economic impact of credit on the center ofthe outcome distribtution. We also provide the conventionalestimation of 2SLS(IV) for comparison.

The remaining sections of this article are organized asfollows: Section 3 reviews the model of quantile treatmenteffects of Chernozhukov and Hansen(2001), and applies it toan outcome model containing credit[15]. Section 4 describesthe data used in this empirical analysis. Section 5 providesan introduction to the econometric model and its estimationmethod. Section 6 presents the estimation results from theIVQR method, and compares these to the estimators of 2SLSand QR. Section 6 concludes the article.

2 Instrumental variable model for quantiletreatment effects

In the following sections, we briefly introduce theestimation of quantile regression by Koenker and Bassett(1978), and then present the assumptions and main impli-cations of the instrumental variables model of quantile treat-ment effects developed in Chernozhukov and Hansen (2001).Then, we show how an outcome model of farmers’ credit ef-fects may be embedded in this framework.

2.1 Brief Introduction of quantile regression

While there are several features of the distributions ofpotential outcomes that may be interesting, we can focus onthe quantiles of potential outcomes Y conditional on covari-ates X ,

QY (τ |x) = inf y|F (y|x) ≥ τ

Given the random sample yn, n = 1, · · · , N, for anyτ ∈ (0, 1), the quantile of potential outcomes Y can be ob-

tained by solving the optimization problem as follows:

minq∈R

N∑n=1

ρτ (yn − q(xn)) (1)

where, ρτ (u) = u × (τ − 1 (u < 0)). Linear conditionalquantile function is often applied in practice. Let X ∈ RK ,β ∈ RK , the problem becomes

minβ∈RK

N∑n=1

ρτ (yn − x′nβ) (2)

2.2 Instrumental quantile treatment model

The model is developed within the conventional po-tential (latent) outcome framework. Potential real-valuedoutcomes are indexed against treatment d and are denotedby Yd. For example, Yd is an individual’s outcome whenq (d, x, τ). Treatment d takes values in a subset of Rl,D. The potential outcomes Yd are latent because giventreatment D, the observed outcome for each individual isY ≡ YD, that is, only one component of potential outcomesvector Yd = q (d, x, Ud) is observed for each individual.

While we are interested in the different effects of treat-ment d on the marginal distribution of the potential outcome,the quantile treatment effect (QTE) is a very useful tool. De-note the quantiles of potential outcomes conditional on co-variates X by

QYd(τ |x) , τ ∈ (0, 1)1.

then, define the quantile treatment effects (QTE) that sum-marize the difference among the quantiles under differenttreatments (e.g. Doksum (1974)):

QYd(τ |x) − QYd′ (τ |x) , or ∂QYd

(τ |x) /∂d

If D is an exogenous variable, we can use the conven-tional quantile regression by Koenker and Bassett (1978).However, typically, D is selected in relation to Yd in-ducing endogeneity, so that the conditional quantile of Ygiven the selected treatment D = d, denoted by QY (τ |d, x),is generally not equal to the quantile of potential or latentoutcome QYd

(τ |x). This makes the conventional quan-tile regression inappropriate for the estimation of QYd

(τ |x).Chernozhukov and Hansen (2001) extended the model ofstandard quantile regression, which uses instrumental vari-able dealing with endogeneity.

Build the model from the basic Skorohod representa-tion of latent outcomes Yd, which yields for each d givenX = x

Yd = q (d, x, Ud) , where Ud →d U (0, 1) (3)

and q (d, x, τ) = QYd(τ |x) is the conditional τ -quantile of

latent outcome Yd.The variable Ud is responsible for the heterogeneity of

outcomes for individuals with the same observed character-istics x and treatment d. It determines their relative rankingin terms of the potential outcomes. Hence, we will call it therank variable, and may think of it as representing some un-observable innate ability or level of preference. This allowsinterpretation of the quantile treatment effect as the treat-ment effect for people with a given rank in the distribution

1 QYd(τ |x) = inf Yd|F (Yd|x) ≥ τ .


of ability or preference (Ud), making quantile analysis aninteresting tool for describing and learning the structure ofheterogeneous treatment effects.

The model consists of five main assumptions (some arerepresentations) that hold jointly. Given a common proba-bility space (Ω, F, P ), X represents covariates and Z repre-sents excluded instruments, and the following A1-A5 condi-tions hold jointly:A1 Potential Outcomes Given X = x , for each d, for someUd →d U (0, 1),

Yd = q (d, x, Ud)

where, q (d, x, τ) is strictly increasing and left-continuous inτ .A2 Independence Give X = x, Ud is independent of Z.A3 Selection Given X = x, Z = z, for unknown functionδ and random vector V ,

D ≡ δ (z, x, V )

A4 Rank similarity For each d and d′, given (V, X, Z), Ud

is equal in distribution to U ′d.

A5 Observed Variables consist of⎧⎨⎩

Y ≡ q (D, X, UD) ,D ≡ δ (Z, X, V ) ,

X, Z.

where, UD =∑

d∈D I (D = d) · Ud.Chernozhukov and Hansen (2001) discussed the identi-

fication conditions, the estimation method, and its statisticalinference based on the above assumptions. Their estimatoris consistent under endogeneity.

2.3 Instrumental Variable Quantile Regression Modeland Economic Effect of Credit

Assumption A1-A5 provides a plausible framework toanalyze the economic effect of farmer credit. First, we setthe farmers’ outcome model as follows:

Yd = q (d, X, Ud) , Ud → U (0, 1)

where, τ → q (d, X, τ) is the conditional quantile functionof outcome Yd, d ∈ l min, l max represents the farmers’loan volume2, X represents other covariates that affect theoutcome, and Ud is an unobserved random variable. As dis-cussed above, Ud can be used to represent the unobservableability. Farmers maximize their expected outcome under thecredit constraints:

D = arg maxd∈D

Eq (d, x, Ud)s.t. d ≤ S (x, z, v) (4)

where, S (x, z, v) is the lenders’ supply function. Then, loanvolume can be solved as D = δ (Z,X, V ), where, Z is aninstrumental variable, which affects the farmers’ loan vol-ume, but is uncorrelated with the farmers’ personal abilityUd. Z and X are observed, and V is an unobserved informa-tion component that depends on rank Ud and also includes

other unobserved variables that affect the participation state.Function δ is unknown. Thus, this model is a special case ofthe IVQR model. In this model, the independence conditionA2 only requires that Z is independent of Ud, conditional onX . It does not require Z to be independent of V , which iscloser to reality. The rank similarity condition A4 indicatesthat given the information in (V, X, Z) employed to make theselection of loan volume D, the expectation of any functionof rank Ud does not vary across the loan volume states, thatis, ex-ante, conditional on (V,X, Z ), the rank may be con-sidered to be the same across potential treatments, but the re-alized, ex-post, rank may be different across treatment states.From the econometric perspective, here it just requires thatunobservable heterogeneous variable (farmer’s ability) willnot vary systematically across the treatment states. Thus, wecan interpret the quantile treatment effect as the treatment ef-fect holding the level of unobserved heterogeneity constantacross the treatment states:

q (d, x, τ) − q (d′, x, τ)= q (d, x, Ud) − q (d′, x, U ′

d) |Ud=U ′d=τ

Since changes in Ud across d are assumed to be asys-tematic, the quantile treatment effect summarizes not onlythe distributional impact but also the actual likely treatmenteffect.

3 Data and stylized facts

We used data from a sample of 3,000 rural house-holds’ survey conducted in 2003. The data collection isconsigned to Rural Investigation Institution of Chinese localstatistical bureau. We adopted a four-stage sampling strat-egy (province-county-town-village), and obtained 3,000 ru-ral households’ samples from the population. The data pro-vide detailed information about the farmers’ economic andwelfare status as well as credit behaviors. The main sourceof farmer credit is from two channels: formal and informal.The former includes the loan from bank and credit unions(Chinese two main formal rural financial institutions), whilethe latter includes loans from relatives, friends, and informalfinancial institutions. Our data shows that credit is mostlydevoted into agricultural production and other productive ac-tivities, regardless of the source from where the farmer getsthe credit. 69.4% of the formal credit is devoted into produc-tive activities, while 53.9% for informal credit, and 58.1%for all credit. Apparently, formal credit is more often usedin productive ways as compared to informal credit. How-ever, the total amount of formal credit devoted to productiveways is less than the amount of informal credit devoted tothe same ways. Thus, it can be known that informal creditsubstantially contributes to the Chinese farmers’ income andwelfare, which is neglected by many studies3. Our studywill take both kinds of credit into account; this is one of thecontributions of this article.

The available financial resources significantly lean torich farmers. Figure 1 illustrates the income distribution ofcredit among the sample farmers. The x axis represents thefarmer’s operational income, and the y axis represents the

2 Unlike conventional treatment model, the loan volume here could be continuous. The IVQR model also applies to continuous endogenous treatmentvariable.

3 Some scholars have been awared of the importance of informal finance, such as Lirui (2004).


Figure 1. Income distribution of farmer credit

proportion of credit that they obtained when compared to thetotal amount. Each point on the curve represents the creditproportion received by the farmers whose incomes are be-low the level. If credit is allocated equally, the accumulatedcredit curve must be superposed with the diagonal. In reality,the accumulated credit curve substantially deviates from di-agonal line. The 15% lowest income farmers get only 6.0%of the total credit, while the 30% highest income farmersget nearly half (48.3%) of the total credit. There is a strongtrend of credit concentration given to richer farmers. Thiscan be the rural money suppliers’ rational choice because ofthe specific characteristics of farm credit, such as small vol-ume, high risk, lack of efficient mortage, etc. By lending toricher borrowers, the suppliers can reduce risks.

4 Econometric model specification and estimation

4.1 Credit outcome model: estimation and statisticalinference

To capture the effects of farmer credit on the farmer’sincome, we estimate the log-linear credit outcome model ofthe form

QYd|X (τ) = dα (τ) + X ′β (τ)

where, d indicates the farmer’s credit volume, and is instru-mented for by the farmer’s debt ex-ante. Here, the quantileeffect of credit on the outcome is in the form of outcomeelasticity, which indicates the increased proportion of out-come induced by each 1% increase of loan volume on thegiven outcome level.

While there is only one endogenous variable and themodel is just-overidentified, the IVQR estimator for a givenquantile may be computed as follows:

1. Run a series of standard quantile regressions ofY − Dαj on covariate X and instrument Z where αj is agrid over α.

2. Take the αj that minimizes the absolute value of thecoefficient on Z as the estimate of α, α. The estimates of β,β, are then the corresponding coefficients on X .

Chernozhukov and Hansen (2001) showed that underregularity conditions and for θ ∈ [α, β′]′,

√n

(θ − θ

)→d N

(0, J−1Ω

(J−1

)′)

where, for Ψ = [Z, X ′]′ and ε = Y − Dα − X ′β, ε =Y − Dα − X ′β and J = E [fε (0|D,X, Z) Ψ [D, X ′]].

For details, refer to Chernozhukov and Hansen (2001).

4.2 Variables selection

There are several available measures for the farmeroutcome. Here, we choose household operational income,which is the income generated by product or service fromhousehold operation activities in all industries, to representthe outcome. As mentioned above, farmer credit is mainlydevoted to productive ways, and therefore, this variable canbe a good indicator of the credit’s economic impact4. Theoutcome model takes the form of Cobb-Douglas productionfunction. Besides the farmer’s credit, the dependent vari-ables also include the farmer’s land, the productive fixedcapital, the highest education of adult man, the highest ed-ucation of adult woman, the age of householder, the sex ofhouseholder, etc. To control the possible interference causedby the farmer’s village geographic and economic environ-ment, we use the geography of the village and the agricul-tural product price of the village as the control variables5.The outcome, loan volume, and factors are in the form oflog value, so that the coefficient indicates the correspondingoutcome elasticities.

Choosing an appropriate instrumental variable is veryimportant, since it matters whether we can estimate the crediteffect well and correctly. By cautious consideration (includ-ing the availability of data), we choose the farmer’s debt ex-ante as the instrument of credit. The farmer’s debt ex-antegets a great deal of consideration when the money suppli-ers decide whether to lend, but it has no correlation with thefarmer’s individual ability, and therefore, it satisfies the re-quirements of instrumental variables.

5 Empirical results

5.1 Estimation of OLS and 2SLS

Table 1 lists the estimation results of the OLS and 2SLSmethods. These estimates serve as a benchmark of quan-tile and instrumental quantile regression estimates presentedlater. In addition, it contains important economic meanings.Indeed, in the case of a constant treatment effect, these es-timates will be sufficient to fully characterize the distribu-tional impact of the treatment.

The estimate results show that it fits the theoretical ex-pectation quite well. The farmer’s land, productive capi-tal, education all have significant positive effect on his op-erational income, and are statistically significant. The out-come exhibits increasing returns to scale with regard to land.The operational income of households whose head is manis higher than that of households whose head is woman.The village’s economic environment (indicated by the vil-lage agricultural price) also has positive externality to thelocal farmer’s outcome.

The coefficient of credit is significantly positive in bothOLS and 2SLS models. This confirms the positive effect of

4 Here we do not use farmer’s net income as outcome measure. Net income is a pseudo-profit indicator which deducts the cost of input. But we only have thefarmers’ cross sectional data of one year. Generally the cost of input which supported by credit could not be recovered in one year, so using the net incomeindex could underestimate the credit impact on outcome.

5 Price of agricultural products reflects the village’s market environments and economic conditions, so it is an appropriate index which indicates generaleconomic environment of a village. Refer to Krandker(2003), lirui(2004). Here use price of village’s crops, vegetables, fruits, meats and aquatic products,indexed by pc , pv, pf, pm, pfi.


Table 1. Economic effect of farmer credit: OLS and 2SLS

estimations

VariableOLS 2SLS

Coef. Std. Coef. Std.Loan 0.014*** 0.004 0.094*** 0.025Land 0.086*** 0.013 0.081*** 0.014Land sq 0.040*** 0.004 0.021*** 0.007Proca 0.144*** 0.008 0.144*** 0.008Edu m 0.035*** 0.013 0.020 0.015Edu wm 0.044*** 0.012 0.050*** 0.013Age head 0.0002 0.001 0.001 0.001Sex head 0.278*** 0.077 0.316*** 0.084Phys v 0.172*** 0.026 0.212*** 0.031Pc 0.326*** 0.051 0.323*** 0.055Pf 0.074*** 0.013 0.067*** 0.015Pv 0.020 0.018 0.038** 0.020Pm −0.004 0.004 −0.006 0.005Pfi 0.020*** 0.004 0.019*** 0.005Const. 6.542*** 0.119 6.415*** 0.134

Note: ∗∗∗ indicates coefficient sigincance at 1% level, while∗∗ indicates 5%, ∗ indicates 10%.

credit on the farmer’s operational income. However, the twoestimators differ considerably. Apparently, the OLS estima-tor underestimates the economic effect of farmer credit be-cause of the neglect of endogeneity of loan. Suppose thecredit effect on each point of income distribution is constant,then the outcome elasticity is 0.094 for all farmers accord-ing to the 2SLS estimates, that is, each 1% increase of creditinduces 0.1% increase of the farmer’s operational income.The marginal effect is 0.859, indicating that each 100 yuanincrease of credit induces 86 yuan increase of operationalincome.

5.2 QR and IVQR estimates

The results obtained by OLS and 2SLS regression pro-vide a rough estimation of the credit effect on the outcome.However, these are silent on the distributional characteris-tics of the credit effect. To further explore the credit effect,we estimate both the standard quantile regression and the in-strumental variable quantile regression. Figure 2 providesthe QR and IVQR estimates (for the coefficient and stan-dard error, see table 2). The x axis represents the incomedistribution of farmers, and the y axis represents outcomeelasticities.

Figure 2. Credit effect on outcome: QR and IVQR estimates

Our estimates provide some interesting results. Firstly,the estimates obtained by the QR model (below 0.012) areconsiderably lower than that of the IVQR model (between0.065 and 0.090). This is similar to the case of the OLSmodel, which suggests that the neglect of endogeneity will

lead to severe estimation bias. Secondly, the credit effect onthe outcome exhibits great differences among farmers whoearn different levels of income. Particularly, the credit effectis not significant for the poorest (15%) and richest (30%)farmers, that is, because of the heterogeneity induced by in-dividual ability and household condition, et al, the credit ef-fect also exhibits apparent characteristics of heterogeneity.For the poorest farmers, the credit can be mainly used to af-ford instant payment such as living consumption, medicalpayment, or tuition fees, et al. Even when such emergentneeds do not appear, the farmers cannot fully utilize credit tomake investment and production, since they generally lackessential capitals, or skills. Thus, credit does not have sig-nificant effect on these farmers. For the richest farmers, theirliquidity constraint is not binding. They can acquire capitalfor production and investment by self accumulation. Theyprobably use the credit in non-productive ways, and thus,the credit does not have a significant effect on these farmers,either.

For the middle and low income farmers (whose in-comes are ranked between 15% and 70%), the outcomeelasticities lie between 0.065 and 0.095, which are statisti-cally significant. It confirms that these farmers encountercredit restraints, and credit supplies relax their liquidity con-straint. The credit they acquire accelerates their investmentand production activities and efficiently promotes the out-come growth.

According to the estimated credit effect on outcome,if the credit resource allocation leans to middle and low in-come farmers, the farmers’ total income can be increased.Unfortunately, this is not true in reality. As we analyzedin Section 3, Chinese credit largely leans to richer farmers.Although the middle and low income farmers have efficientdemand for loan, they face severe credit constraints. It maybe a rational choice for the money suppliers to lend more tothe richer borrowers, but it really raises the cost of lendingmoney to middle and low income farmers.

Our conclusion is similar with the work of Khandkerand Faruqee (2003), who found that the credit impact ishigher for smallholders than for larger holders in Pakistan,and nevertheless, large holders receive the bulk of rural fi-nance. However, they use the methodology of grouping sam-ple households (according to the land scale of farmers) andregress the same model for each group. This is not an idealmethod since it loses a great amount of sample information.Besides, it can only roughly analyze the three groups (large,middle, small holders). Especially, it keeps silent about thesituation of the poorest households. In contrast, the IVQRmodel not only substantially utilizes the sample information,but also fully captures the credit effect on the economic out-come distribution.

Another interesting finding is the difference of the2SLS and IVQR estimates. Theoretically, 2SLS estimatesare obtained by assuming the constant credit effects on theincome distribution. To some extent, it can be taken as an av-erage of all the credit effects on the income distribution. By2SLS, the outcome elasticity of credit is 0.10. From figure1, it is clear that the 2SLS estimates are considerably largerthan the IVQR estimates. This may cause confusion. In fact,the high income farmers show very high outcome elasticity


Table 2. Credit effect on income distribution: QR and

IVQR estimates

QuantilesQR IVQR

Coef. Std. Coef. Std.0.05 0.012 0.008 0.030 0.0340.1 0.010* 0.006 0.045 0.0300.15 0.008* 0.005 0.075*** 0.0290.2 0.008* 0.004 0.090*** 0.0240.25 0.010** 0.004 0.075*** 0.0250.3 0.007* 0.004 0.070*** 0.0240.35 0.006* 0.004 0.065*** 0.0240.4 0.007** 0.004 0.080*** 0.0240.45 0.007** 0.004 0.080*** 0.0240.5 0.007* 0.004 0.085*** 0.0250.55 0.006* 0.004 0.085*** 0.0270.6 0.006 0.004 0.080*** 0.0300.65 0.006 0.004 0.075** 0.0320.7 0.010*** 0.004 0.070** 0.0310.75 0.007* 0.004 0.090 0.0560.8 0.010** 0.004 0.140 0.1060.85 0.011** 0.005 0.185 0.1770.9 0.012** 0.006 0.165 0.1300.95 0.014* 0.007 0.150 0.145

Note: ∗∗∗ indicates coefficient significance at 1% level, while ∗∗

indicates 5%, ∗ indicates 10%.

of credit in scale, although they are not statistically signifi-cant. Since 2SLS cannot separate these farmers from all, ittends to overestimate the credit effects.

To describe the credit effect on middle and low incomefarmers (ranked between 15% and 70%), we computed thearithmetic average with respect to this income interval. Formiddle and low income farmers, the average outcome elas-ticity of credit is about 0.08, and the average marginal effectis 0.69, that is, each 100 yuan increase of credit can induce70 yuan increase of the farmers’ operational income.

6 Conclusions

This article empirically estimates the economic effectof farmer credit using the IVQR model, which takes bothheterogeneity and endogeneity into account, using a surveydata of 3,000 households from rural China in 2003. Al-though the credit effect literature has been aware of the en-dogeneity problem, the heterogeneity of credit effect has notbeen given due attention. Our IVQR model fully capturesthe characteristics of credit effect on income distribution,confirming the existence of heterogeneity, and provides ev-idence of the lack of credit access for the middle and lowincome farmers in China. These are the main contributionsof this article.

Informal credit has made a non-negligible contributionto Chinese farmers’ investment and production (even moreimportant than formal credit). Unlike the former studies, ourmodel incorporates the informal credit as an important partof farmer credit. The results show that credit contributes tothe farmers’ income siginificantly on the whole, regardlessof whether it is from formal or informal source. However,its impact exists heterogeneity on the distribution of income.The credit does not significantly contribute to the outcomeof the poorest and richest farmers, but it benefits the middleand low income farmers, for whom the output elasticity is

about 0.08.

These findings provide adequate policy implications.Firstly, both formal and informal credit contribute to the in-vestment and production of Chinese farmers. To boost thefarmers’ income and develop rural economy, the governmentshould deepen the reform of rural financial market to estab-lish an instant and efficient market. Besides reconstruct-ing the rural formal financial institutions, the governmentshould pay more attention to the role of informal finance.If we establish an enable policy environment and support-ive legal and regulatory framework, the flourishing of ruralinformal finance can make the credit demand of farmers tobe met in a better way. The diversification of the rural fi-nancial system can be remunerative for the farmers’ incomeand welfare. Secondly, in view of boosting the farmers’ in-come, developing rural micro finance institutions (RMFI) isessential. These institutions have better mechanisms to dealwith adverse selections or moral hazards in the rural finan-cial market, and thus, are more adaptive to the characteris-tics of farmer credit, especially for the middle and low in-come farmers. By doing so, the middle and low incomefarmers can acquire more credit devoted to investment andproduction, which will increase their income. Since the out-come elasticities of credit for these farmers are larger thanthe others, the allocation of financial resource will be moreefficient. Last but not least, for the poorest farmers, the gov-ernment should consider other alternative ways to help them,since credit does not seem to work well in improving theirincome.

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heterogeneous impact of farmer credit: an empirical investigation based on ivqr model

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