Policy, Research, and External Affairs ,<
WORKING PAPERS
L Agricultural Policies
Agriculture and Rural Development
Department
The World Bank
January 1991
WPS 571
Credit's Effect
on Productivity
in Chinese Agriculture
A Microeconomic Model
of Disequilibrium
Gershon Feder
Lawrence J. Lau
Justin Y. Lin
and
Xiaopeng Luo
Not all farmers - sometimes only a minority - are constrained
in their farming operations by inadequate credit. And part of
formal credit is diverted to consumption so the effect on output
of greater supplies of formal credit might not be as large as one
would expect if one assumed that it would all be used produc-
tively.
The Policy, Research, and Extemal Affairs Complex distributes PRE Working Papers to disseminate the findings of work in progress and
to encouragc the exchange of ideas among Bank staff and all others interested in development issues. These papers carry the names of
the authors, reflect orly their viess, and should be used and cited accordingly, The findings, interpretations, and conclusions are the
authors' own. They should not be attributed to the World Bank, its Board of Directors, its management, or any of its member countries.
Policy, Rearch, and Exlornal AffaIrs
Agricultural Podlces
WPS 571
This paper - a product of the Agricultural Policies Division, Agriculture and Rural Development
Departmint - is part of a larger effort in PRE to evaluate agricultural credit policies and review
institutional designs so as to formulate better guidelines for Bank activities in rural credit. Copies are
available free from the World Bank, 1818 H Street NW, Washington DC 20433. Please contact Cicely
Spooner, room N8-035, extension 30464 (27 pages).
Many government programs want to provide actually be used for consumption and invest-
more credit to the farm sector to increase agricul- ment. Indeed, medium- and long-termn formal
tural productivity. If the marginal effect on credit is practically nil among the agricultural
productivity is small, those resources might be households in the study area. Rolled-over short-
put to better use elsewhere. term credit is sometimes used for small-scale
investments. The diversion of short-term credit
Feder, Lau, Lin, and Luo conducted an for farmn investment is about 40 percent for an
econometric analysis of the effect of credit on average household in the study area. This
output supply which recognizes that credit implies that almost a third of the forrnal credit is
markcts are not necessarily at equilibrium - so used for consumption (of current goods or
that credit rationing (with unsatisfied demand) durables).
and nonborrowing (when credit could be avail-
able) are both possible. Only about 37 percent of What conclusions does this suggest in
the farners in the study area were constrained by evaluating the probable effect of expandin,
inadcquate formal credit. Informal credit agricultural credit? First, not all farmers, and
sources provided funds for specific non-agricul- sometimes only a minority, are constrained in
tural activities that were not fungible. their farming operations by inadequate credit.
And second, greater supplies of formal credit
The results indicate that one additional yuan will be diverted in part to consumption, so the
of liquidity (credit) yielded 0.235 yuan of likely effect on output will be smaller than what
additional gross value of output. These results one might expect if all funds are assumed to be
suggest that for the area of China covered in the used productively.
study, a good part of the short-term credit may
The PRE Working Paper Series disseminates the findings of work under way in the Bank's Policy, Research, and Extemal
Affairs Complex. Anobjectiveof theseries is togetthesefindingsoutquickly, evenif presentations are less than fully polished.
The findings, interpretations, and conclusions in these papers do not necessarily represent official Bank policy.
Produced by the PRE Dissemination Center
Credit's Effect on Productivity
in Chinese Agriculture: A Microeconomic Model of Disequilibrium
by
Gershon Feder, Lawrence j. Lau,
Justin Y. Lin, and Xiaopeng Luo
,able of Contents
I. Intro Juction I
II. China's Farm Sector and Rural Credit Market 3
III. A Model of Farm Household Consumption, Production, and Investment 5
IV. Econometric Specification and Empirical Results 8
V. Implications 13
References 1 4
Footnotes 1 5
Annex 1 6
Appendix 24
1. INTR(DUCTION
Credit is an important element in agricultural productlon systems. It allows producers to
satisfy the cash needs Induced by the production cycle which characterizes agriculture:
preparation, planting, cultivation and harvesting of the crops are typically done over a period
of several months in which very little cash revenue is earned, while expenditures on materials,
purchased inputs and consumption need to be made in cash. Cash income is received a short
time after the harvest. In the absence of credit markets, farmers would have to maintain cash
reserves so as to facilitate production and consumption in the next cycle. The availability of
credit allows both greater consumptlon and greater purchased Input use, and thus increases
welfare of the farmers.
If a producer faces an infinite supply of liquidity at a given price, the production
decisions will be independent from consumption decisions, as has been shown in the household
models of Singh et al. However, asymmetric information and adverse selection typically prevail
in credit markets, giving rise to credit rationing as an optimal behavior (Stiglitz and Weiss).
Furthermore, government intervention in the form of interest rate ceilings or subsidized interest
rates is common in many countries' agricultural sertors, necessitating rationing. When credit is
rationed, some borrowers cannot obtain the amount of credit they desire at the prevailing
interest rate, nor can they secure more credit by offering to pay a higher interest rate. In
such circumstances, liquidity can become a binding constraint on many farmers' operations.
When liquidity is a binding constraint, the amounts and combinations of inputs used by a
farmer deviate from their notiornal optimal levels (the levels that would have been utilized if
liquidity were not a binding constraint). - ie marginal contribution of credit is therefore to bring
input levels closer to the optimal levels, thereby increasing output and, since the quantity of land
-2-
is fixed, yie!d. This potential gain in productivity is one motivation underlying many government
programs seeking to provide more credit to the farm sector. An Important issue in the context
of agricuiltural credit policy is the magnitude of the expected productivity gain. If the marginal
productivity effect of credit is small, then the resources may be more beneficially deployed
elsewhere. Assessment of the expected productivity gain Is not trivial because the effect of
credit is likely to differ between liquidity-constrained and unconstrained farm households.
Some studies attempt to identify the effect of credit by estimating separate production
functions or supply functions for borrowers and non-borrowers, and then proceeding to compare
the estimates (see review in David and Meyer, 1980, pp. 206-215). One major weakness of this
approach is the implicit assumption that all borrowers and all non-borrowers are respectively
homogenous with respect to their credit demand/supply situations. This assumption is often not
valid, as many non-borrowers do not borrow because they actually have sufficient liquldity from
their own resources and not because they cannot obtain credit, while some cannot borrow
because they are not credit-worthy. Similarly, the marginal effect of credit may actually be zero
for borrowers for whom liquidity is not a binding constraint.
The same criticism applies to other studies in which all sampled observations are pooled
to estimate production functions (or output supply functions) with credit as a production input
or as a supply determinant. As will be argued in a subsequent section, the supply function is
alfferent (both in parameters and in variables) depending on whether- liquidity is a binding
constraint. Estimates which do not take account of these restrictions on the specification are
therefore flawed.
The present study reports an econometric analysis of the effect of credit on output
supply which avoids some of the aforementioned pitfalls. The central feature is the recognition
that credit transactions are not necessarily in equilibrium at the household level. That is, the
amount of credit desired and tne amrourt offered are not necessar,,y equ4l so th:t creiit SL.ppy
- 3 -
rationing (with unsatisfied demand) and non-borrowing (while supply Is potentially avalIabl) arre
both possible. The analysis utilizes cross-sectional household-level data from a study area in
northeast China, obtained in a recent farm survey designed by the authors. The pian for tloe
paper is as follows: Section II provides background on the farm sector and the ru al cre sit
market In China, and describes the specific study area and data utilized in the analys.s. Section
liI discusses the formal model underlying the empirical analysis (the mathematical model ts pr e(ente 8
in an annex). It is followed by a discussion of the econometric procedure and tr e e j>cal
results In Section IV. The last section discusses the implications of the results.
II. CHINA'S FARM SECTOR AND RURAL CREDIT MARKET
China introduced a smaliolder agricultural production system in a series Of reFcrms
between the years 1979-1984. The "household responsibility system" made individua! householes,
rather than the communes to which they belonged, the decision-makers and mariagers of the C'N
farms. Individual families were allocated land by the communes on leases that run tycicairl fc'
15 years. The improved incentives brought about a significant increase in agricuwtura! cut_tc ac
in rural income (Lin). While prior to the reforrns there was only Vimited nter3act on retbe
households and financial institutions, the emergence of smalilholder ag:-!cu'tur e im;: -s t',t
households now need liquidity for seasonal production and consumption, or longer-rer . e
finance investment, construction and ceremoniai social events.
Most of agricultural households' transact,ons w;th the fcrma f ' sector ?are
the rural crecit cooperatives (RCCs).1 The interest rates for agricuitura oans tas ve 2-: -
loans) made by forma! credit institutions are fixed :by the government, vith some _a- a,
according to loan categories. In 1987, the rates of interest for agrcu!tural Scans
between 7 and 1 4 percent. The degree of intc, est subsidy is believed to Wave been s'L
There is evidence that following the introduction of r-efcr-ms the voiu;Tce of .
obtained from informal sources is substantial in China. Jiang asserts that ron-;rsl tutic'a,
sources contribute roughly half of the credit volume In rural areas. Feder et al. (1989) report
non-institutlonaTcredit shares of between one third and two thirds In several study areas. The
most common sources of informal credit In China are relatives and friends. Most of such loans
carry no Interest charges. Possible reasons for the absence of a substantial profit-motivated
informal credit market In China are discussed In Feder et al. (1990a). They include, unclear legal
status, residual ideological resisLance and absence of collateral assets.2
The present study relies on data collected in December 1987 in Gongzhuling. Gongzhuling
is located in Jilin province, within the corn belt of northeastern China, where agro-climatic
conditions dictate essentially one corn season a year. The original sample consists of 2U0
households selected at random from eight rdndomly selected townships. The information gathered
covers inputs, outputs, financial assets, credit transactions, and household characteristics.
Thirteen households are deleted after determining that tneir main activity was not agriculture or
that thei: situation was unusual (e.g., a widow maintaining a home garden plot).
The data show that nearly three quarters of the sample borrowed from formal sources
(essentially the RCCs) during the study season. The frequency of informal credit transactions
is much lower than that of formal transactions (about one fifth of the sample), and three
quarters of Lhese loans were provided free of interest. Given the significant differential
between the rates of interest on the two types of loans, this may be taken as evidence that
.nformal credit is not a good substitute for formal credit due to limited fungibility (otherwise
every borrower would exhaust his or her informal credit first before going to the RCC). The
share of formal credit in the total volume of new credit is 66.5 percent.
Table 1 presents the distribution of loans by purpose and by type of lender. It is readily
apparent that the predominant stated purpose of formal loans (all of whicn are short-term) is for
the financing of current production. Most of the informal credit is reported to have been
obtained for purposes other than production, with construction and social expenditures appearing
-5-
dominant. Informal loans contracted for these purposes, however, cannot be easily diverted to
finance day-to-7ay consumptlon or production, because the lenders, mostly relatives and friends,
can easily monitor compliance. The bulk of the fungible credit, defined as credit which is not
granted for easily monitored purposes, In the study area thus comes from the formal sector (87
percent).
Given the dominance of formal credit, a key issue for tha present study is the extent to
which its supply is a constraini on households' desired activities. The survey data collected
permit an answer to this question. Borrowing households were asked if at the go ng rates of
interest they would have liked more institutional credit than the amount they were actually
granted. Households which did not borrow were asked the reason for not borrowing. The most
common reason for not borrowing was availability of sufficient own resources. The borrowers
who indicated a desire for more credit, and the non-borrowers who responded that they could
not obtain credit, are classified as credit-constrained. As reported in Table 2, about 37 percent
of the farm households in Gongzhuling were constrained by credit accordina to this classification.
The liquidity position of credit-constrained households as compared to non-constra ned
households is compatible with intuitive expectations: They have significantly lower deposils in
financial institutions, and overall, their liquid resources per unit of land are 12 percent teIcA
those of unconstrained households.
lll. A MODEL OF FARM HOUSEHOLD CONSUMPTION, PRODUCTION AND INVESTMENT
Suppose the household considers the allocation of resources at its disoosai at :"e
beginning of the production period between the following uses: (i) current consumpt on,
investment; (iii) the purchase of variable inputs for current production (inclueing lator a'ncw
fertilizers). Variable inputs, in combination with land and existing capital, will produce this perici s
output. Investment will not mature by the time this period's output is produced, but Its
contribution to the household's welfare may be accounted for through a valuation function wlich
TABLE 1: Distribution of Loan Purposes by
Type of Lender (Percent)
P u r p o s e
Sample Prod- Farm Constr- Consump- Social Other
Size uction Equip- uction tion (Wedding
ment Funeral,
etc.)
S.U.lr ce (Number
o f L oans of Loans)
rO' rp.Sl. 209 92.3 4.3 1.9 0 1.0 0.5
l C mal 44 9.1 4.6 20.5 1 5.9 27.3 2 2.7
TABLE 2: Extent of Formal Credit Constraint
t ite Crs SamDle % Constrained
s.ze
(Nulber of Households)
.'. s ;frS 145 41.3
or' - tCr , D~n'es 42 28.3
187 37.4
summarizes tne contribution of capital to the future consumption stream. The household's Initial
endowments of-liquid resources, family labcr, capital, and lana (the latter two assumed not
convertible to liquldity during the perlod) can be augmented by borrowing at the beginning of the
period. Whether the household can borrow the entire desired amou. t or is constrained by a
binding upper limit on the availability of credit Is of considerable consequence, as it determines
whether production decisions are separable from the consumption decisions. The household is
assumed to maximize a utility function defined over consumption per family member in the current
and next period, plus the utility of future streams of consumption summarized by the valuation
function of next period's capital, per family mcember. The optimization can be carried out under
two scenarios: (I) The supply of credit is greater than or equ_l to the demand (i.e., credit
constraint not binding); and (ii) The supply of credit is less than the notional demand for credit
(credit constraint binding).
The essence of the results of such a model 3 is that under case (i) above, the supply
of output Is not affected by the level of licuidity (including credit), the size of the household'b
own family labor force or the total size of the household. The parameters of the output supply
function in this case are determined by the production function alone. Under case (ii), however,
output supply is positively affected by increases in liquidity (e.g. increased credit supply) and
in the household's labor endowment, while the effec. if total household size is indeterminate.
1,,creases in the initial endowments of land and capital would have a positive effect on output
supply in both cases (i) and (i), while they would have an indeterminate impact on input demands,
depending on substitutability. The parameters of the output supply function under case (ii) are
determined by both the production function and the utility function.
- 8 -
IV. ECONOMETRIC SPECFICATION AND EPRICAL RESULTS
The econometric model most suitable for estimating the output supply tunction with the
data avallable to us Is the switching regression model with an endooenous criterion function
described in Maddala (pp. 223-228). The model postulates fo'r any observation I
(1) Y P1 XIl + U11 iff 7 Z1 + UO < °
(2) Y21 P2 X21 + U21 iff 7 Z1 + U, > O
where X1;, X2; and Zi are vectors of exogenous or predetermined varlables, Pl, p2, and 7 are
the corresponding vectors of parameters, and U11, U21 and U1 are random disturbances. 'ii and
Y2i are two possible values of the dependent variable, only one of which is actually observed
for any given household, depending on the value of the (unknown) criterion function 7 Z1 + Ui.
The random disturbances are assumed to have a trivariate norma; distribution, Identically and
independently distributed across households. Applied to the particu!ar issue at hand, equations
(1) and (2) may be viewed as the output supply equations under a non-binding and binding
iquidity constraint respectively. The criterion for whether liquidity is binding or not is whether
the demand for credit exceeds credit sapply, and the criterion function 7 Z + U, in our case, is
the excess credit demand function (i.e., demand minus supply). Excess credit demand is not
directly observable. However, from the survey responses, we know whether a given household
is constrained or unconstrained by !iquidity. Using data on the dichiotomous responses, the
vector of parameters 7 can be estimated up to a proportionality constant by a probit procedure.
The estimated parameters are then used to generate Mills ra.-.s which are incorporated in tne
second stage estimates, where the equations (1) and (2), with their Mills ratio corrections, are
estimated by a linear regression. Under model assumptions, the estimated coefficients are
consistent and asymptotically normal, and with appropriate corrections to their estimated
variance-covariance matrix (dua to the heteroscedasticity of the stochastic disturbance terms
in the second stage estimates) can be subjected to statistical tests based on normality.
- 9 -
The einpirical specificatlon of the variables which corstitute the vector Z involves both
determinants orcredit demand and credit supply. Thus, In the case of variables which affect
both demand and supply In the same directlon, one cannot predict a priori the expected sign.
These variables are (with the expected effect on the probabillty of being credit constrained
indicated In parentheses for those with an unambiguous effect): (1) Land; (2) Capital; (3)
Number of adults (-); (4) Number of dependents;4 (5) Education; (6) Farm experience; (7) Savings
in financial Institutlons (-); (8) Total initial liquid assets (-); (9) Outstanding debt to financial
institutions (+)! (10) Total outstanding debt (+); (11) Last sedson's income (-); (12) Previous loan
default dumrry (+). In ddditbon, eight dummy variables for townships were introduced. The r asults
of the probit estimates are presented in Table :x.5 Two estirated coefficients are statistically
significantly different from zero at the 5 percent level of significance and have the theoretically
predicted sign: Savings in financial institutions and last season's income. Eighty-two percent
of the -.-servations are properly classified as being credit constrained or unconstrained, implying
a fc.irly good fit.
The reduced form output sunply equation for liquidity-constrained households, estimated
with the double-log specification, involves the folkviing variables (with the direction of trie
expected effect noted in parentheses): t1) Total liquidity 6 W; (2) Number of adults (+); (3)
Number of dependents (?); (4) Land (+); (5) Capital (+); (6) Education (+); (7) Farm experience
(+). The specification for the households not constrained by liquidiLy is similar exceot for the
first three variables, which do not theoretically belong in the reduced form for output sup,z Y.
The estimated coefficients are reported in Table 4.
In the output supply equation for constrained households, (column 1) the estimated
coefficient of the total liquidity variable is positive and statistically significantly different from
zero at the 5 percent level of significance, but the number of adults and the number of
- 10 -
TABLE 3: Estimated Coefficlents of Probit Model
(probability of being credit-constralned)
Variable a Estimated
Coe, ficlent
(t-value)
Land -.212
(.505)
Capital -.029
(.265)
Number of adults .282
(1.950)
Number of dependents .093
(.509)
Education -.101
(1.502)
Farm experience -.025
(1.666)
Savings in financial Institutions -.121
(2.223)
Total initial liquid assets .376
(1.552)
Outstanding debt to financial institutions -.053
(.977)
Total outstanding debt .057
(1.182)
Last season's income -.974
(2.973)
Previous loan default .587
(1.260)
Percent correctly predicted .820
No. of observaticns 156
a/ The equation also Included also eight township dummy variables. These are not reported.
- 11 -
TABLE 4: Estimated Coefficlents of Second Stage Switching
Regression Model for Output Supply
(Reduced Form)
(1) (2) (3)
Variable a/ Regression Credit Credit Credit
Constrained Unconstralned Unconstrained
Counter factual
(N-48) (N-108) (N-108)
Total liquidity .183 - .042
(2.951) b/ (1.261)
Number of adults .015 .001
(.641) (.004)
Number of dependents -.020 - -.005
(.538) (.247)
Land .863 .875 .846
(8.166) (18.120) (15.202)
Capital .027 .051 .052
(1.193) (3.287) (3.306)
Education -.004 .018 .018
(.261) (2.216) (2.206)
Farm experience -.028 .063 .062
(.533) (2.324) (2.250)
R2 .863 .867 .869
a/ Regressions Included also eight dummy variables for townships and the Mills ratios computed
from the first stage probit. These are not reported.
b/ Numbers in parentheses denote t-values
- 12 -
dependents do not have statistically significant estimated coefficlents. The hypothesis that all
three variablesdo not affect the supply of output for constrained households has a F-statistic
of 2.96 and Is rejected at the 5 percent level of significance, confirming the theoretical
predlctions of the model. The quantity of land Is an Important and statistically significant
determinant of output supply for constrained and unconstrained households (the estimated
coefficients of the output supply function for the latter group are reported In column 2). It
is also worth noting that capital, education and farm experlence have statistically significant
positive effects on output for the credit-unconstrained households but have statistically
Insignificant effects for the credit-constrained households. This finding suggests that capital,
education and experience are less likely to contribute to output If the farmer's choices are
constrained by iquidity.
While under the assumptions of our model it is not approprlate to estimate the output
supply equation for the unconstrained households with the inclusion of liquidity and household
composition variables (liquidity is theoretically endogenous for such households and the estimated
coefficients would be subject to simultaneity bias), we experimented with the estimation of such
a hypothetical counter-factual case on the assumption that the classification was wrong and
therefore these households were liquidity-constrained. The results (column 3 in Table 4) indicate
that none of the estimated coefficients of the first three variables are statistically significantly
different from zero (the hypothesis that all three are not significant has a F-statistic of 0.55
and cannot be rejected at any level of significance) implying that the counter-factual case is
not borne out empirically. Another experiment was the estimation of the model using the whole
sample without separation, that Is, as If all households were liquidity-constrained. The results
show that the estimated coefficient of total liquidity in the output supply equatlon would have
been about two-thirds of that in column 1. Predictions based on the wrong estimated
- 13 -
coefficients would thus lead to significantly Inaccurate assessments of the effect of credit on
output supply.-
V. NPLICATIONS
Based on the estimated coefficients, if every credit-constrained household In the sample
is given an additional credit of 17.82 yuan (equal to 1 percent of the average level of liquidity
of the credit-constrained households), the total output of these households may be projected
to increase by 201.08 yuan, or approximately 0.04 percent of the total output. Thus, on
average, one additional yuan of liquidity (credit) would yield 201.08/(17.82 x 48) - 0.235 yuan
of additlonal gross value of output. These results suggest that for the area of China covered
in the present study, a significant proportion of the short term credit provided by the rural
credit cooperatives as production ci-edit" may actually be utilized for consumDtion and
investment. Indeed, medium and long term formal credit is practically nil amongst the agricultural
households In our study areas, and a similar picture is given by aggregate statistics. Rolled-
over short term credit is sometimes utilized to finance small scale investments. A recent study
by Feder et al. (1990b) finds that the diversion of short-term credit for farm investment is about
40 percent for an average household in the study area. This, in turn, Implies that almost a third
of the formal credit is utilized for consumption (whether of current goods or durables).
The results of the study highlight two important factors which should be considered when
evaluating the likely impact of agricultural credit expansion: (i) Not all farmers, and sometimes
only a minority, are constrained in their farming operations by inadequate credit; (ii) Expanded
supplies of formal credit will be diverted in part to consumption, thus the likely output effect will
be smaller than that which is expected when all funds are assumed to be used productively.
These ideas have been propounded by the Ohio State school critics of credit supply-led
development schemes. The present paper thus provides empirical verification of these views.
- 14 -
References
David, Crlsthia and Richard Meyer. "Measuring the Farm Level Impact of Agriculture Loans," In John
Howell (ed.), Borrowers and Lenders: Rural Flnancial Markets and Institutlons In Developing
Countries, London: Overseas Development Institute, 1980.
Feder, Gershon, Lawrence J. Lau, Justin Y. Ln and Xlaopeng Luo, "Agricultural Credit and Farm
Performance in China," Journal of Comparative Economics, 13: 508-525, December 1989.
Feder, Gershon, Lawrence J. Lau, Justin Y. Lin and Xlaopeng Luo, "The Nascent Credit Market in
Rural China," Working Paper, Department of Economics, Stanford University, 1990a.
Feder, Gershon, Lawrence J. Lau, Justin Y. Lin and Xlaopeng Luo, "The Determinants of Farm
Investment and Residential Construction in Post-Reform China", World Bank, Department
of Agriculture and Rural Development, Working Paper, March 1990b.
Jiang, ShiJI, "How Are the Various Types of Non-Bank Credits in Rural Areas at Present to be
Treated?", Rural Finance Research Institute, Guangxl Zhuang Autonomous Region, July 1984.
Lin, Justin Y., "The Household Responsibility System in China's Agricultural Reform: A Theoretical
and Empirical Study," Economic Development and CulLurai Change, Supplement 36- 199-224,
April 198e.
Maddala, G.S., Limited - Dependent and Qualitative Variables in Econometrics, Cambridge: Cambridge
University Press, 1983.
Singh, lnderjit, Lyn Squire and John Strauss (eds.j, Agricultural Household Models, Baltimore: Johns
Hopkins University Press, 1986.
Stigiitz, Joseph E., and Andrew Weiss, "Credit Rationing and Markets with Imperfect Information,"
American Economic Review 71:393-410, June 1981.
- 15 -
Footnotes
The aut ors are respectively a Principal Economist at the World Bank, Professor of
Economics at Stanford University, Professor of Economics at Beijing University, and Visiting
Scholar, Cambridge University. We are Indebted to Angus Deaton for useful comments and to Shu-
Cheng Llu for research assistance.
1/ Greater detall on the credit market In rural China and In the study area Is provided in
Feder et al. 1989, 1990a.
2/ Land Is on a fifteen-year lease and until recently use rights could not be transferred.
3/ A rigorous derivation of model Implications is provided In an annex.
4/ The number of dependents plus number of adults constitute household size. While the
number of adults has an unambiguous effect, household size (and consequently the number
of dependents) does not.
5/ The households with special large scale ceremonial expenditures were not included in the
econometric analysis, as their liquidity requirements and borrowing patterns could be quite
differAnt. This reduces the sample size for the econometric analysis to 156. However,
including these households, with appropriate dummy variables and interaction terms, does
not alter the nature of the results qualitatively.
6/ This consists of cash value of product inventory, deposits in financial institutions, and
fungible formal loans. Informal credit was assumed non-fungible as observed in Section
11. Total liquidity differs from the total initial liquid assets in the orobit equation, which
do not Include current fungible credit.
7/ The equatlons should have Included output and Input prices. However, because the data
are derived from a cross-section within a confined geographical area, there is no price
variation and price variables are omitted.
ANNEX
-16 - --
A MOQEL °F HOUSEHOLD CONSUMPTION AND INVESTMENT
Suppose tc', household considers the allocation of resources at its
disposal at the beginning of the production period between the following
uses: (i) cdirrent consumption (ii) investment (iii) the purch.ase of
variable inputs. Variable inputs, in combination with land and existing
capital, will produce next period's output. Investment will not mature by
the time next period's output is produced, but its contribution to the
household's welfare is accounted for through a valuation function which
summarizes the contribution of capital to the optimal consumption stream.
The household's initial endowments of liquid resources, family labor,
capital, and land (the latter two assumed not convertible to liquidicy) can
be augmented by borrowing at the beginning of the period. Whether the
household can borrow the desired amourit or is constrained by a binding upper
limit on the availability of credit is of great consequence, as it
determines whether production decisions are separable from the consumption
decisions. Below we describe the various components of the model, and chen
set up the optimization problem.
a. Initial endowments
The household possesses initial liquid wealth (W.), physical capital
(K,), land (A) and household labor (X0). Household labor can be
approximated by the number of adults.
b. Production
Output is produced through a standard neo-classical production function
which combines initial capital, labor and land.
- 17 -
(1) Q - F(K,,X,A)
Partial derivatives are denoted by a letter subscript
dF
(e. g. , - * Fl)
ax
c. The utility function
The utility function is defined over consumption per family member in
the present period, plus the utility of future streams of consumption
summarized by the valuation function of next period's capital, per familv
member. The notation is
(2) U - Uo(CO/N) + UI(C1/N) + V(K)/N
where CO and C1 are respectively total consumption in the present period
and in the next period, K1 is capital in the next period, N is familv
size, UO and U, are current and next period utilities of consumption
and V is the capital valuation function. The cime discount factor is
omitted from the notation as it is implicit in the definition of U. and
V. The marginal utility of consumption and of capital value is assumed
decreasing, i.e., U" < 0, V" < 0.
d. Second period consumption and capital
The capital stock in the next period is simply the present stock K:
augmented by present investmene I, i.e.,
- 18 -
(3) If. V + I
Consuasion in neriod 1 is given by the value of output minus debt
repayment, i.e.,
(4) Cl - F(K ,X,A) - (l+r).L
where r is the interest rate and L is the amount of credit used. The
price of output is normalized to 1, without loss of generality.
a. The budget constraint
The total amount of liquid resources (i.e. , initial liquid wealth, plus
borrowing) have to equal the cash expenditures on current consumption, labor
costs for hired labor, and investment, i.e.,
(5) Wo + L - CO + a (X-XO) + I
where 9 is the wage rate.
The optimization problem is
(6) Max UO(CO/N) + U1(C1/N) + V(K1)/N
CO,Cl,Kl,I,L,X
subject to equations (1), (3), (4), (5)
By proper substitutions, the optimization problem can be
simplified to
- 19 -
(7) Max Uo((Wo + L I X + O.Xo)/N] + U1 ([F(K0,X,A) - (1+r)*L]/N)
I,X,L
+ V(KC + I)/N
Consider first the case where there is no binding constraint on the
amount which the household borrows.
Credit not a binding constraint
The first order conditions for opti-mi under this scenario are (assume
internal solutions)
(8) (-U; + V')/N - 0
(9) (-6*U0 + UO.F,)/N - 0
(10) (U; - (l+r).Uj], - 0
Substituting for UO in equation (9) using equation (10) and
rearranging yields
(11) Fx - 9'(l+r)
The optimal amount of labor (labor demand), say X^, can be derived
from equation (11) as a function of 0, r, Ko and A
(12) X - X' (9, r, KOO A)
Note that total labor demand does not depend on any of the parameters
of the util.ty functions, neither does it depend on family size, the number
- 20 -
of adults or initial liquidity. This is the well known separation property
of household production and consumption models as devaloped in Singh et al.
(1986). Using equation (12), the supply function of output (when credit is
not a bindifrg constraint) can be written as
(13) Q - Q (9, r, K., A)
Note that the econometric estimation of equations (12) and (13) should
not include the amount of credit as an explanatory variable, because it is
endogenously determined.
We turn now to discuss the case where the household cannot obtain as
much credit as is needed to satisfy the first order conditions (8) - (10).
One characteristic of such a situation is that equality (11) cannot hold,
and instead
(14) Fx > 9 (1+r)
Credit a binding constraint
The derivation of first order conditions for this scenario is based on
the same objective function (7), except that L (the amount of credit) is
treated as a parameter (it is determined by the supplier of credit and not
by the household). The control variables are therefore only I and X.
The first order conditions are:
(15) (-U0 t V')/N - 0
(16) (-9*Uo + Ui-F.)/N - 0
- 21 -
The Hessian of equations (15) - (16) is
U; U/N + V - N 8 U" /N21
H - [
L 9U'/Na (02U; + U; Fz, D+ Ul F.,)/Na
The determinant of H is
(17) a - (8-U`-V"/N3) + [(U"/N) + V"].(U` F2+U,.F,,)/N3 > 0
The sign of (17) is established given the concavity of UO, Ul V and
F.
The derivation of comparative statics results is discussed below. A
general observation, however, is that the input demand function (and
consequently the output supply function) depends on parameters of the
utility functions and on household size the household's labor endowmene and
liquidity (including the exogenously determined amount of credit).
A differentiation of equations (15), (16) yields the following
comparative static results, summarized in Table 1 (a fuller treatmenc .s
provided in the appendix).
An increase in the availability of credit will increase investment,
variable input use, and output of credit-constrained households, because i-
allows both increased consumption and production. The analysis can
demonstrate that an additional unit of credit will typically not be fullv
used for productive purposes (i.e. investment or inputs), but racher, a
portion will be used for increased current consumption (the so called
- 22 -
"leakage problem), due to the funSibility of credit
Table 6; Comoarative Statig Results for Credit-ConstrainedHou2ehold2
Inveatment Variable Output
Input
I X Q
Effect
On
Change
In
Credit (L) + + +
Household size (N) - ?
Household labor (X.) + + +
Initial capital (K0) 7 ? +
Land (A) ? ? +
An increase in the household size while holding the household labor
force constant (i.e., an increase in the number of dependents) will have a
negative impact on investment, while the impact on current input use and
output is undetermined. This is because the marginal utility of both
present and next period consumption is increased, while the marginal
valuation of capital is unchanged. This result would not obtain if the
capital valuation function were defined in terms of capical per household
member.
An increase in the household's labor force while holding household size
constant will lead to an increase in investment, variable input use and
output. The reason is that under a binding liquidity constraint, an
increase in the number of employees who do not need to be paid in cash has
- 3 -
an affect similar co that of increased credit supply.
Changes in the complementary inputs (capital and land) will increase
output, as one would expect intuitively. However, the impact on input use
and investment depends on the substitutability of inputs and on the nature
of the utility function.
A-PPENDIX
Derivation of ComDarative Static Results
The results below are derived for the case of a household with a
binding credit constraint. We rewrite the first order conditions (15),
(16), omitting unnecessary terms
(IA) -UO + V' - 0
(2A) -9 U' + U; F. - C
and the corresponding Hessian
;uo + N V" 9 uo1
(3A) H -
O- d U d .U' + U`-F2 U, -F.
The determinant of H is given by 6.
I - 92.N V U + (UO + N V")(UJ F+ILU> F1)
Results of a change in each parameter of the system (IA), (2A) are
obtained by differentiacion and a solution using Cramer's rule.
(i) Change in credit availability (L)
dI ulo
dl] 0
(4A) [H] dX _
dL OUO + Uj.Fx.(l+r)
- 25 -
dI U.U;(F1x + F,2.Fx - 9.(l+r)])
(5A) - - > 0
dL A
The sign is established using the concavity of U and F, and the
fact that in the case of a binding credit constraint it must hold F. >
9.(l+r) (see (14) in the text).
dX N.U".V" + (UO + N.V").UL>F .(l+r)
(6A) - - > 0
dL A
where the sign is established by the concavity of U and V. The
8Q
sign of - follows trivially, as
8L
aQ F,.dx
(7A) - - - > 0
aL dL
(ii) Change in household size N
dl - UO CO
dN
(8A) N2 [H] dX
dS J -Uo -Co + Ul Cl F1
1 dI -UO -CO *(U; F2+U, F-.) -9.U" 4U *C, -F,
(9A) - -- <
N2 dN A
- ,6 -
1 dX U" U; C1 F1 + NV". (U; C1 F, O U.C'o)
(IOA) - - .
N2 dN
dX
The sign of - cannot be established because the term
aN
U"C1 Fx-9 U C0 can be positive or negative. Consequently, the impact
on output is also undetermined.
(iii) Change in household labor (XO)
dl ~ dl (UF2+ U' Fo
(1LA) -H - L R
d.X0
dX e2.N.V".U0
(13A) H >0X
dXo A
(iv) Change in initial capital Ko
(14A) [H] [ t: ] _ [
Tyial l pt e L a in te s e - 0, ad
Typichangely initisar compitlentr intesnsKx O n h
- 27 -
dI dX
signs of -, - cannot be determined because the sign of -U; F.k
dKo dK
dQ dX
U* F, R .s not known. However, - - F, -+ Fk and it can be
dKo dKo
shown that
dQ -(1J + NVO).(Ui.Fz.FIk - U; F,,Fk) + 9.N.UO.V"(Fk + F1)
(15A) - - ->0
dKo
(v) Changes in land endowment (A)
(16A) (H] - [ F U . F
dA JUL u;FX. u; UFX F &
dI dX
As in the case of K0, the sign of - and - cannot be determined
dA dA
because the sign of -U' F1. - Ul F1 F. is not known. However
dQ dX NF. .UI V" (U1 + N.V")(U,F,.F,, -U,F F,F)
(17A) - - Fx - + F - >
dA aA a
PRE Working Paper Series
Contact
ie Author Date for paper
WPS554 Korea's Labor Markets Under Dipak Mazumdar December 1990 M. Schreier
Structural Adjustment 36432
WPS555 The Macroeconomics of Price Reform Simon Commander December 1990 0. del Cid
in Socialist Countries: A Dynamic Fabrizio Coricelli 39050
Framework
WPS556 Taxing Choices in Deficit Reduction John Baffes December 1990 A. Bhalla
Anwar Shah 37699
WPS557 1'he New Fiscal Federalism in Brazil Anwar Shah December 1990 A. Bhalla
37699
WPS558 Alternative Instruments for Kenneth M. Kletzer December 1990 J. Carroll
Smoothing the Consumption of David M. Newbery 33715
Primary Commodity Exporters Brian D. Wright
WPS559 Fiscal Policy and Private Investment Ajay Chhibber December 1990 D. Bilkiss
in Developing Countries: Recent Mansoor Dailami 33768
Evidence on Key Selected Issues
WPS560 The Persistence of Job Security in Milan Vodopivec December 1990 CECSE
Reforming Socialist Economies 37188
WPS561 The Labor Market and the Transition Milan Vodopivec December 1990 CECSE
of Socialist Economies 37188
WPS562 Anticipated Real Exchange-Rate Luis Serven December 1990 S. Jonnakuty
Changes and the Dynamics of 39076
Investment
WPS563 Empirical Investment Equations in Martin Rama December 1990 E. Khine
Developing Countries 39361
WPS564 Costs and Benefits of Agricultural Avishay Braverman December 1990 C. Spooner
Price Stabilization in Brazil Ravi Kanbur 30464
Antonio Salazar P. Brandao
Jeffrey Hammer
Mauro de Rezende Lopes
Alexandra Tan
WPS565 Issues in Socialist Economy Stanley Fischer December 1990 CECSE
Reform Alan Gelb 37188
WPS566 Measuring Outward Orientation in Lant Pritchett January 1991 K. Cabana
Developing Countries: Can It Be Done? 37947
WPS567 Macroeconomic Management and the Antulio N. Bomfim January 1991 A. Bhalla
Division of Powers in Brazil: Anwar Shah 37699
Perspectives for the Nineties
PRE Working Paper Series
Contact
6 AtAhor 3L for paoer
WPS5S8 Higher Wages for Relief Work Can Martin Ravallion January 1991 C. Spooner
Make Many of the Poor Worse Off: Gaurav Datt 30464
Recent Evidence from Maharashtra's Shubham Chaudhuri
'Employment Guarantee Scheme
WPS569 Domestic Purchase Requirements for Wendy E. Takacs January 1991 S. Fallon
Import License Allocations in Mali 37947
WPS570 Debt Concentration and Secondary Raquel Fernandez January 1991 S. King-Watson
Market Prices Sule Ozler 31047
WPS571 Credit's Effect on Producti .y in Gershon Feder January 1991 C. Spooner
Chinese Agriculture: A Lawrence J. Lau 30464
Microeconomic Model of Justin Y. Lin
Disequilibrium Xiaopeng Luo