Interlinkage of transactions and rural development

bardhan udry chapter 9

• Over the last couple of decades, the theoretical literature on rural development has sometimes emphasized the role of interlinked, often personalized, transactions between economic agents in providing a key element of the underlying institutional framework.

• Anthropologists have often pointed to the multi-stranded nature of relationships in small face-to-face communities.

• Gluckman, in his studies of tribal Africa, has called such societies ‘multiplex’, with each individual playing not one but a variety of roles in interacting with the fellow members of his community

• Bailey (1971) notes: ‘the watershed between traditional and modern society is exactly this distinction between single-interest and multiplex relationships.

• The usual examples in literature take theform of • landlord–tenant relations intertwined with creditor–borrower

relations between the same parties, or of• employers hiring workers on terms that are interlocked with

those on which the former provide credit (or land) to the latter, • or of simultaneous deals in the commodity and credit markets

between a trader and a farmer where the latter gets credit on the pre-commitment of future crop delivery to the former.

• An understanding of the nature of theserelations is clearly important in any policy agenda of institutional reforms.

The policy question• If, in our reformist zeal, we do not pay enough attention to the underlying

economic rationale of pre-existing institutions and their interconnections, and try to hack away parts of them, we may not always improve (and may even worsen) the lot of the poor tenant–labourer–borrower, the intended beneficiary of the reform programme.

• A well-intentioned land redistribution programme may, for example, be rendered counter-productive by the absence of a simultaneous programme of credit reform;

• even in credit reform, public banks spreading to reach out to the peasants may meet with limited success in the face of the potential borrower interlocked in her credit-cum-land or -labour relationship with the local lender–landlord–employer.

• Piecemeal laws trying to put a ceiling on rents or interest rates or a floor to minimum wages may be rendered ineffective by suitable readjustments of prices or selective rationing in interlinked transactions.

• On the other hand, in trying to understand the micro foundations of pre-existing institutions, we should not be blind to their adverse consequences.

• For example, the very nature of rationale for personalized interlinking may at the same time act as a formidable barrier to entry for other parties and may give the dominant partner in a transaction some additional leverage. The thin line between understanding an institution and justifying it is often blurred, particularly by careless interpreters of the theory.

The model

• In a survey of a random sample of 110 villages in East India, Bardhan and Rudra (1981) observed that about fourfifths of the villages have a system of loans by the landlord–employer in the slack season against a commitment by the peasant labourer to supply labour services in the peak season.

• Such voluntary credit–labour linkage (terminable and renewable every crop season) may be interpreted simply as an intertemporal barter transaction, ensuring a double coincidence of wants arising from the irregularities of the agricultural crop cycle.

• Many such village economies are characterized• by a dominant landlord who, because of the size of his assets and urban

connections, is able to obtain credit more cheaply than other local agents. Thus, the landlord is able to act as a financial intermediary.

• However, the landlord is also positioned as a monopolist in establishing the terms of trade between current consumption and future labour services.

• If the landlord can obtain unlimited funds at a fixed interest rate, r, then monopoly profits are earned by a two-part tariff on consumption credit.

• Labourers pay a marginal interest rate per unit of consumption credit equal to the landlord's opportunity cost plus a fixed ‘entry fee’ for the privilege of borrowing at this rate.

• The provision of labour services in future periods constitutes repayment of principal and interest, including the entry fee, on a consumption loan.

• The entry fee represents the monopoly profits on the transaction.

• Consider a stylized agrarian economy with two periods.In the first, there is no work. In the second, there is a spot labour market where labour services are traded at a given wage rate, W.

• The revenues of the single dominant landlord are a monotonically increasing and strictly concave function, F(L), of the quantity of labour employed, L.

• There is a pool of n peasants who borrow from and work for this landlord. Each peasant has an identical utility function, U(C1, C2), defined over consumptions, C1 and C2, in each of the two periods, with the usual properties of strict concavity and consumption in each period being a ‘normal' good.

• credit–labour transactions may be seen as an implicit contract specifying three items: (1) an amount of consumption credit, c, which the landlord extends to peasants during period 1;

• (2) a commitment of labour services, l, to be provided• by each peasant in period 2; and • (3) a wage, w, at which the committed labour services

are compensated. Implicit• contracts are, by assumption, costlessly enforceable.

• Consider an implicit contract (c, l, w). Each peasant has committed l units of labour to the landlord at a wage of w, and, if the peasant's second-period labour endowment is one unit, trades 1 − l units of labour at the spot wage.

• Hence under the contract, first-period consumption is equal to c, and second-period consumption is equal to wl + W(1 − l).

• Substituting these into the utility function gives the utility of the contract to peasants as

U= U(c,wl+ W(1-L)) (1)

• Profits to the landlord is given by ∏=F(L)- W(L-nl)-wln –(1+r)nc (2)• The market value of these labour services is

Wl, whereas the peasant is compensated only by an amount lw. The difference, constituting the loan repayment, we call

R=l(W-w) (3) • Using 3, 1 and 2 can be written as follows

• U= U(c,W-R) (4)• ∏= F(L)+ nR- WL- (1+r)cn (5)• From (4) and (5), one may note that these do not directly

involve the contract values of l and w, except to the extent they jointly affect R.

• This means that in equilibrium the contract wage, w, is indeterminate, depending on the number of hours worked for the landlord. From (3), a loan repayment of a given size can be made equivalently by working more hours at a smaller discount or fewer hours at a larger discount.

• Peasants can borrow from a source other than the landlord (say, the professional moneylender in the village or in the nearby small town) at an exogenous interest rate of r 0 > r ;

• similarly, they can work at the spot market at the wage rate W. These define a reservation utility of V(W,r 0) for the peasant.

• The implicit contract must ensure for the peasant a• utility level at least equal to thisreservation utility, and profit

maximization by the landlord implies that this voluntary compliance constraint must hold

• with strict equality, so that• U(c,W-R)= V(w,r0) (6)

• From (6) we can write the loan repayment as an implicit function• R = R(c, W, r0) (7)• Given exogenous values of W and r 0, the implicit function defines the

maximum repayment a peasant is willing to make for a consumption credit of c.

• Rc, the partial derivative of the function with respect to c, i.e. the peasant‘s willingness to pay for a marginal increase in consumption credit, should be equal to the peasant's intertemporal marginal rate of substitution in consumption, given by the ratio of the marginal utilities in the U function.

• Substituting the R function from (7) into (5), the landlord's profit function, and maximizing it with respect to L and c,we get

• F’(L)= W (8)

• And• Rc(c,W,r0)=1+r (9)• The eqn 8 determines the eqm value for L* and

eqn 9 detremines c* and thus the eqm value for R*

• Using Rc from (9), the opportunity cost of credit to the landlord can be equalized to the peasants' intertemporal marginal rate of substitution, so that

• U1(c,W-R)/U2(c,W-R)= 1+r

• This suggests a further interpretation of the equilibrium implicit contract.

• Suppose that the landlord charges peasants an interest rate on consumption loans of r plus an ‘entry fee' of f for the privilege of borrowing at this rate.

• A peasant will optimally choose a consumption credit, c, that satisfies the optimal intertemporal consumption condition

• U1(c,W-(1+r)c-f)/ U2(c,W-(1+r)c-f)= 1+r

• If f= R*-(1+r)c*, then the peasant will optimally choose credit c= c*

• Thus, the equilibrium implicit contract effects an outcome equivalent to a two-part tariff on consumption loans by which the landlord establishes a fixed entry fee and a marginal interest rate equal to his own cost of credit

Model 2

• now we move from the world of consumption credit for a labourer to that of production loans for a farmer.

• concave production function F(K), K- working capital that the farmer has to borrow.

• the opportunity cost of credit to the linked lender (the trader, in this case) is r, which is lower than r0, the rate that the (small) farmer faces were he to raise credit outside

• Let i be the interest rate charged by the trader lender, such that (1+i) = α(1+r)

• p= market price of output• Price offered by the trader is q= βp• α,β greater than equal to or less than 1

• So the farmer maximises his income Y wrt K• Y= βpF(K) – α(1+r)K• FOC yields• βpF’(K)=α(1+r)• The minimum income the farmer can get without

entering into the contract with the trader is• Y= max[p F(K)- K (1+r0)]• The trader maximizes his income• ∏(α,β)= (1-β)pF(K)- (1-α)(1+r)K (15)

• The first term on the right-hand side of (15) is the trader–lender‘s gain from trading and the second term is his interest income.

• So the optimal traders contract(α*β*) is given by

• α*=β*=γ=Y/ Max[pF(K)-K(1+r)] < 1

• Thus, the farmer is given an interest discount (i.e. i < r), which is compensated by the underpayment in the output

• market (q < p).• Even though the farmer faces a credit market imperfection (r0 > r),

interlinkage allows the trader to counteract the possible effect of this imperfection on the farmer's production efficiency and to squeeze the maximum

• surplus over the farmer's reservation income.64 An obvious policy conclusion is that, if our objective is to prevent

• underpayment to farmers in the output market, an intervention in the credit market may be called for; an intervention

• directly in the output market will lead to inefficiency.