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N U M B E R 6 C M I WO R K I N G PA P E R J U N E 2 0 17 Photo: xx Photo: xx A U T H O R S Clive Bell Chr.

Michelsen Institute (CMI) University of Heidelberg Magnus Hatlebakk Chr.
Michelsen Institute (CMI) Usufructuary Mortgages as a Source of Funds in Need: Some Theory and an Empirical Investigation Usufructuary Mortgages as a Source of Funds in Need: Some Theory and an Empirical Investigation CMI Working Paper number 6 June 2017 Authors Magnus Hatlebakk Clive Bell Graphic designer Kristen Børje Hus Cover photo flickr user Ishwar Yadav (Creative Commons license) Keywords usufructuary mortgage agrarian contracts Orissa JEL Classification D13 D14 D86 Q12 Q15 ISSN 0804-3639 (print) ISSN 1890-5048 (PDF) ISBN 978-82-8062-651-6 (print) ISBN 978-82-8062-652-3 (PDF) www.cmi.no CMI WORKING PAPER 6, JUNE 2017 Table of Contents Abstract 1 Introduction 2 The Model 2.1 Borrowers 2.2 Lenders 2.3 Borrowers and lenders: non-random factors 2.4 Equilibrium 3 Selling as a Further Option 4 Empirical Modelling 5 The Data 5.1 The incidence and duration of contracts 5.2 The hypotheses: a preliminary examination 6 Mortgages and Land Accumulation 6.1 Econometric analysis 7 Conclusions 8 Appendices 8.1 Appendix A.
Lenders 8.2 Appendix B.

Borrowers and lenders: non-random factors 8.3 Appendix C. Selling as a further option References Table 1.

Mortgage contracts per village in 2013 Table 2.

Mortgage contracts in the panel Table 3.

Landholdings (acre) for sub-groups according to mortgage status in 2013 1 2 4 6 11 11 12 13 14 16 17 19 22 24 27 28 29 31 33 36 37 38 39 Table 4.

Mortgage decisions: contractual status in 2001 40 Table 5.
Land accumulation 41 CMI WORKING PAPER 6, JUNE 2017 ABSTRACT This paper develops a theoretical framework in which the borrower, who mortgages out, and the lender, who mortgages in, a parcel of land reach their decisions when credit and land markets function imperfectly.

The results cover what conditions and factors govern the decision to contract in the first place, and when and whether to repay or agree to a sale.
The empirical investigation deals with such contracting in Orissa, based on a panel household survey over the period 2000–2013.

Almost 20 percent had contracts in 2013, the borrowers’ chief need being to marry off a daughter, followed by coping with serious illness and bad harvests.

The sums were quite large, indicating that these contracts offered the parties opportunities beyond those available through other forms of credit transactions.
Mortgaging also appeared to promote the transfer of ownership rights from relatively land- rich to land-poor households.

CMI WORKING PAPER 6, JUNE 2017 1 Introduction In close-knit societies, wherein markets may be far from perfect, transactions in goods and services are often bundled together in so-called interlinked contracts (Bardhan, 1980; Basu, 1983).

This practice may be a response to market failures, as the contract- ing parties seek ways of expanding the total surplus.
Then again it may enable the powerful to extract more surplus from the weak.
In contrast to ties between credit and tenancy, labour and marketing, the usufructuary mortgage is a contractual form that has received little attention – from economists at least –, despite the fairly prominent place it sometimes ﬁnds in India’s rural economy.1 The owner of a parcel of land borrows a sum of money, and in exchange, transfers to the creditor all rights to its use and the resulting income until such time as the former repays the entire sum borrowed.
The owner keeps the title deed, and thus the unrestricted option to recover the said rights when his circumstances permit.

The parties therefore exchange monetary claims at two points in time, with an exchange of claims on the services of land as interest in the interim, including the lender’s option to lease the parcel back to the borrower.
An alternative arrangement, in principle, is for the owner to take a normal loan from the lender, who then rents in the land in question, using the interest payments to meet the rent in a book-keeping transaction.

In eﬀect, the two parties would have de-linked the two contracts, each paying the standard interest and rental rates.

Why, then, do usufruct mortgage contracts arise?


The borrower is wholly free to decide when to repay, though this option may also be available, at least to a degree, in standard loan contracts.

The borrower also keeps the title document, which may already have been 1Perrott (1909) provides an interesting discussion of informal credit at the beginning of the 20th century.
More recent contributions are Shibli (1993) and the indirect discussion in Swaminathan (1991), where it is considered as just one of many sources of credit.

For treatments of various other forms of tying see, for example, Braverman and Stiglitz (1982), Bell and Srinivasan (1989), and Mukherjee and Ray (1995).

2 used as collateral to secure a formal loan.


The other chief beneﬁt arises from the fact that the sum involved is typically quite large, such as would be needed to deal with a very damaging shock or heavy unavoidable expenditure.

Such a sum may not be obtainable as a standard loan, especially if intended to ﬁnance marriage or cope with a serious illness or a poor harvest.
To oﬀer such a contract, however, the borrower must have available ‘excess’ land in relation to what is considered necessary, in some sense, to meet the family’s needs.

For his part, the lender may be keen to cultivate a larger holding; but the rental market may be thin, and the land purchase market even thinner.
Excess family labour in relation to the family’s current holding not only makes mortgaging in attractive, but may also provide the means to put together the sum needed to make a satisfactory oﬀer.

Households with relatively little land are also often relatively poor.

Buying land outright at once can therefore lie beyond their grasp, and so make mortgaging in a good alternative.
This option gives play, furthermore, to an opportunistic motive: if the borrower experiences another negative shock, then the lender may expect to buy the land at a low price at some point in the future.

The object of this paper is to develop and analyze a theoretical model of mortgage contracting in a risky environment, and then to apply it empirically in an investigation of households’ behaviour in upland Orissa, a semi-arid tract that is socially and eco- nomically backward.
The data stem from a series of survey rounds, which started in 2001 and continued, with breaks of varying length, until the two most recent rounds, which covered the calendar year 2013.

The original sample comprised 240 households, 8 drawn from each of 30 villages themselves drawn from spatial clusters.

Over the course of time, some households split, dissolved or migrated permanently.

Of the orig- inal households, 216 were traced and interviewed in 2013.
Joining them were another 59 households generated by the splitting of households in the interim, and four others added by the survey team that conducted the round in 2010, yielding a total sample of 279 households in the closing round.

The market was quite active: 51 households had 3 extant mortgage contracts in 2013, with both sides of the transaction almost equally represented.

The plan of the paper is as follows.


The model is developed in Section 2, with treat- ments of the borrower’s and lender’s decisions in Sections 2.1 and 2.2, respectively, an analysis of the eﬀects of variations in non-random factors in Section 2.3, and a discussion of market equilibrium in Section 2.4.
To complete the theoretical analysis, Section 3 deals with the possibility that the lender will, at some point, acquire own- ership of the mortgaged parcel, which involves a step beyond enjoying the user rights indeﬁnitely because the borrower never repays.

Section 4 summarizes these ﬁndings in a form designed to structure and support the empirical analysis.
Introduced by a brief account of the surveys and the sample, Section 5 provides, ﬁrst, a descriptive analysis of the incidence and duration of contracts, as well as what sort of households contract, and second, a preliminary examination of the hypotheses, paying particular attention to households’ motives and the adverse shocks they suﬀer.
Section 6 complements the latter with an econometric analysis of the households’ contractual choices and whether these led, in the course of time, to a redistribution of ownership holdings.

The main conclusions are drawn together brieﬂy in Section 7.
2 The Model A risk-averse household endowed with labour and possibly land and other assets allo- cates them so as to produce a stream of income, which varies stochastically not only with the vagaries of the weather, pests and market prices, but also with the family members’ state of health.

Bouts of illness can render them unﬁt to work, and some ailments may require outlays on medical treatment.

The same holds for the family’s draught animals.


At worst, a family member may die: part of the family’s total endow- ment of labour is lost, the funerary rites must be observed and the attendant, socially necessary expenditures incurred.

Draught animals, too, are mortal, and theft is not 4 altogether rare.

If lost, an animal must be replaced or draught-power services hired.

Both involve extra outlays relative to the status quo ante.
Marriages, especially of daughters, are also expensive aﬀairs if families observe social custom, as they almost invariably do.

That the event will occur is taken for granted, but the timing depends on the search for a suitable partner and subsequent negotia- tions, which can fail (Bailey, 1957).

Here too, then, there is an element of uncertainty where the level of extraordinary, unavoidable expenditures in any particular period is concerned.
For simplicity, deﬁne income to be net of outlays on marriage and funerary rites, as well as those on medical treatment.

Income is derived from two sources.

First, there are the plots of land to which the household has both title and full usufructuary rights, including those to rent out.

To these must be added any further plots that have been mortgaged in with like rights.

The sum of the two will be called the usufructuary holding.

Second, there are all other sources, including, in particular, labour.
Let λht denote the total area of household h’s ownership holdings, μht (≤ λht) the net area it mortgages out, and κht its non-land endowment.

Land unencumbered by an existing mortgage contract is necessary if the household is to mortgage out; μht < 0 indicates that land is mortgaged in.

The size of the usufructuary holding in period t is λht − μht.

Households that own no land may therefore cultivate by lending to acquire usufructuary rights.
Let the variate Yht denote the household’s total (net) income in period t, and let it be i.i.d.

over all periods, so that Yht is stationary and serially independent.

Given the endowments λht and κht, and the mortgaged area μht, let Yht have the continuous, diﬀerentiable distribution function Fh(yht; κht, λht, μht), whose support [y1 h, y2 h] depends, in general, on (κht, λht, μht).

The following assumption is very weak.

Assumption 1.
Assumption 1.

Distributions associated with larger usufructuary holdings and non-land endowments ﬁrst-order stochastically dominate those associated with smaller ones.

5 Let the household’s preferences over lotteries conform to the expected utility hypoth- esis, with the strictly concave von Neumann-Morgenstern utility function u(yht).
The expected utility of the lottery Yht is y2 h Ω(Yht) = u(yht) dFh(yht; ·) ≡ Ω(Yh), (1) y1 h where the assumptions on Yht imply Ω(Yht) = Ω(Yh) ∀ t. The present value of the stream of expected utilities arising from {Yht}t=∞ t=0 for any ﬁxed (κh, λh, μh) is V (Yh) ≡ ∞ t=0 δt h · Ω(Yh) = Ω(Yh)/(1 − δh), (2) where δh is the household’s discount factor.

The state wherein a household never engages in this form of contracting (μht = 0 ∀t ≥ 0) is an important reference case.
Such a household obtains V (Yh(μ = 0)), whereby Ω(Yh(μ = 0)) > Ω(Yh(μh > 0)) in virtue of Assumption 1.

The shocks that time brings may, however, make a mortgage contract attractive.

Social custom and severe unexpected setbacks may force some households to seek funds to cover them.

Other households may have suﬃcient funds to lend, in which event, there will be a basis for trade.

These two groups are indexed by i and j, respectively.
2.1 Borrowers Households may be able, from time to time, to put a little aside to deal with minor contingencies; but such a reserve will not normally serve to deal with the problem that arises when net income turns out to be very low in relation to essential current expen- ditures.

One option is for the household’s members simply to tighten their belts, but this may involve austerity to the point of real hunger and deprivation.
Alternatively, the household may try to cope by taking out a loan on conventional terms, perhaps secured by some form of collateral if it has any acceptable to lenders.

Yet such a loan may not be on oﬀer, or if available, its terms unacceptably onerous.
6 A third option, if the household owns land and can ﬁnd a contractual partner with enough funds, is to mortgage out a parcel of its land: in exchange for the sum mi, it gives up the right to cultivate a parcel of area μi until it has repaid the whole of mi to the creditor who provides it.

In the interim, the creditor will enjoy the usufructuary rights instead of interest.
The borrowing household enjoys not only the immediate relief of having additional funds, but also the option of reclaiming these rights whenever it is able to scrape together the sum mi at some point in the future, a task that will usually require a stroke of good luck, especially with an endowment eﬀectively reduced by the mortgaged parcel in the interim.2 Suppose household i enters into such a contract at time t = k, having drawn yik(μ = 0).
(In what follows, the index i and the corresponding endowments κi and λi are suppressed whenever no ambiguity would arise, and a zero in parentheses indicates no mortgaging activity.)

If the household repays the loan in period t = l (≥ k + 1), the contract will yield a stream of net income from period t = k onwards that arises from the process {yk(0) + m, Yk+1(μ), Yk+2(μ), .

.

.

, Yl(μ) − m, Yl+1(0), .

.

.


}, μ ≤ λk, whereby the realization yl(μ) in period l must be suﬃciently good to make the concur- rent sacriﬁce of m worthwhile.

We proceed by backward induction.

Let the household have an outstanding contract at t = τ .

It draws yτ .

If it pays oﬀ m, it will consume yτ − m in the current period and resume the stationary stream yielded by F (y; 0) thereafter.
If it decides to continue the mortgage arrangement, it will consume yτ in the current period and obtain a draw from 2Renting out a parcel in the usual way will also yield income, but will not fully serve.

‘English’ rental contracts, in which a ﬁxed rent is paid in advance are rather rare in developing countries, and the payment is limited to the coming season alone, so its receipt is unlikely to cover a big expenditure.
Sharecropping contracts are the usual form, though ﬁxed rents payable after harvest – albeit converted into sharecropping terms in the event of a generally poor crop – are also observed; they both suﬀer the salient, twin drawbacks that payment is made at the end of the season and its level is stochastic.

7 the distribution F (y; μ) in the next period, at the close of which it will face anew the decision of whether to continue.
Denote by yr the smallest realisation of yτ at which the household is indiﬀerent between these two courses of action.

Since the setting is a stationary one, yr will be the critical value of yt in all periods.
The value, as assessed at t = τ , of the stream of expected utilities yielded by continuing with the mortgage, given this choice of yr, is u(yτ ) + δSτ , where the value of the stream from t = τ + 1 onwards is yr y2(μ) Sτ = u(y)dF (y; μ) + u(y − m)dF (y; μ) + δ(1 − πi)Sτ +1 + πiδV (Y (0)) y1(μ) yr and πi ≡ 1 − F (yr; μ) is the probability that a loan outstanding at the close of the last period will be repaid at the close of the current period.
Since the setting is stationary, Sτ = Sτ +1, so that yr ⎡ ⎢ ⎣ y1(μ) Sτ = y2(μ) u(y)dF (y; μ) + u(y − m)dF (y; μ) + πiδV (Y (0)) yr ⎤ ⎥ ⎦ (1−δ(1−πi)) ∀τ.

(3) The alternative course of action is to repay m out of yτ , which yields u(yτ − m) + δV (Y (0)).
Recalling (2), the household will therefore be indiﬀerent between repaying and continuing when where u(yr) − u(yr − m) = δ · Ω(Y (0)) − Γ 1 − δ(1 − πi) ≡ δQm i (m, μ), yr y2(μ) Γ ≡ u(y)dF (y; μ) + u(y − m)dF (y; μ) y1(μ) yr (4) (5) is the expected utility of the lottery Yt(μ) with the trigger value yr inducing repayment of m.

Eq.

(4) implicitly deﬁnes yr as a function of δ and (κ, λ, μ), which generate the distributions F (y; 0) and F (y; μ).

The l.h.s.
The l.h.s.

is the ‘cost’ of belt-tightening in order to repay out of current net income.

The r.h.s is the gain from regaining F (y; 0) in the next period; its value is independent of t. 8 Observe that given m, μ, δ, F (y; 0) and F (y; μ), there may exist no yr ∈ [y1(μ), y2(μ)] that satisﬁes (4).

If the only solution is smaller than y1(μ), then repayment will follow with certainty in the next period.
This will come about if the loan is suﬃciently small in relation to the productivity of the plot that is mortgaged to obtain it, though the borrower’s rationality places limits on how disproportionately large the latter can be, both magnitudes being known ex ante.

If, at the other extreme, there is a unique yr > y2(μ), then repayment will never occur.
As we shall see in Section 3, this does not necessarily imply that the borrower sells the plot for the sum m, though if m, as the price, is high enough, that will be the right option.

The remaining possibility is that there exists a yr ∈ [y1(μ), y2(μ)] that satisﬁes (4).

Proposition 1.

The trigger value yr is unique for any oﬀer (m, μ).

It is increasing in m, κ and λ, and decreasing in μ.

Proof : see Appendix.

The conditions for yr ∈ [y1(μ), y2(μ)] are also established therein.
The larger is m, the greater becomes the attraction of waiting for a good realisation of net income, and in the limit, of eﬀectively selling the plot in question for m by choosing yr > y2(μ) and never repaying.

The larger is μ, the greater is the desire to get back the plot by repaying as soon as possible.

Larger endowments imply lower probabilities of very poor realisations of net income, and hence make it less pressing to repay.
Having established the critical value of yt for repayment decisions that are time- consistent, the next step is to determine whether the said contract is attractive at the outset, at t = k. Given the draw yk from F (y; 0), the household will be indiﬀerent between accepting the contract and making do with yk if, and only if, u(yk + m) − u(yk) = δQm i .

(6) where the r.h.s.


now represents the cost that is incurred by exchanging the superior distribution F (y; 0) for F (y; μ) until at least the trigger value yr is realised, and thus m repaid, in some future period.

Recalling that Qm i is independent of both t and the draw yk, it follows from the strict concavity of u that given (m, μ), there is a unique 9 value of yk satisfying (6), which is denoted by ym ∀k.

The level of m and the trigger values ym and yr are closely related.
From (4) and (6), we have u(ym + m) − u(ym) = u(yr) − u(yr − m), which yields at once: Proposition 2.

The trigger value for repayment, yr, exceeds that for entering into the contract, ym, by the amount of the loan: ym + m = yr. Mortgaging out is a way of smoothing the adverse shock expressed by a low realisation of yk.

Its (net) advantage over simply belt-tightening is Δm i ≡ [u(yk + m) − u(yk)] − δQm i (m, μ).
(7) The strict concavity of u implies that the relief provided by a loan of given size m, as expressed by [u(yk + m) − u(yk)], is increasing and convex as yk falls, that is, as the magnitude of the adverse shock increases.

It is seen from (7) that if u(y1(0) + m) − u(y1(0)) < δQm i , then the mortgage contract will be rejected in favour of belt- tightening; and if u(y2(0) + m) − u(y2(0)) > δQm i , the contract will be accepted.
The remaining possibility is that there exists an ym ∈ [y1(0), y2(0)], and the decision then follows according as the draw yk from F (y; 0) exceeds or falls short of ym.

The eﬀect of a small increase in m on Δm i , for a given plot μ, is ∂Δm i ∂m = [u(yk + m) − u(yk)] − δ · ∂Qm i ∂m < 0, where the negative sign follows from the strict concavity of u, Proposition 1 and ∂Qm i /∂yr > 0 (see the proof of Proposition 1).
There remains the important question of how changes in the endowment λ inﬂuence p(ym, λ) = F (ym; μ = 0), the probability that the household will accept the oﬀer (m, μ).

We have ⎛ ∂p ∂λ = f (ym) ∂ym ∂λ + ⎜ ⎝−f (y1) ∂y1 ∂λ + ⎞ ∂f (y) ∂λ ⎟ ⎠ , dy y2(λ) y1(λ) (8) where f (y) is the density function of y.

The expression in parentheses is negative in virtue of Assumption 1.

Against this, however, the trigger value ym is increasing 10 in λ, in virtue of Propositions 1 and 2.
The same holds for changes in κ.

Whether households with larger endowments are more or less likely to accept a given oﬀer in the event of an adverse shock cannot be determined without recourse to much stronger assumptions.

2.2 Lenders Suppose household j enjoys such a good draw yjk in period k that it considers lending the sum mj in order to mortgage in a suitable plot of land if the opportunity arises.
If it concludes such a contract, it will enjoy an augmented stream of net income with the distribution function Fj(yjt; μ < 0) until the loan is repaid in full.

Fj(yjt; μ < 0) ﬁrst- order stochastically dominates Fj(yjt; μ = 0) , and the advantage it confers will depend, inter alia, on the degree of complementarity in production of j’s existing endowments and additional land.
Cultivation is not the only source of risk, however; for the timing of repayment, and hence the length of the lease, is for the borrower to decide, and this is a random variable.

Recalling Section 2.1, the probability that the loan will be repaid in any period after t = k is constant, at πi .

Other than the plot associated with Fj(yjt; μ < 0), this is the borrower’s sole characteristic that matters to the lender.

We assume that the latter is able to estimate πi exactly.
The details of the analysis are found in Appendix A.

The main result is that the trigger value for lending m, ym j , is increasing in κj and λj.

2.3 Borrowers and lenders: non-random factors The foregoing analysis concentrates on borrowing and lending decisions arising from shocks to net income, with the distinction between the distributions Fi and Fj involving, in particular, μ < 0 and μ > 0, respectively.

Yet systematic factors are also at work in inﬂuencing whether a household borrows or lends.
Let these express themselves as 11 variations in net income such that each realisation of the variate Yt is augmented by the parametric amount ai or aj as appropriate.

Proposition 3.

The trigger value yr is increasing in ai if δi[Ω(Y (μ > 0) + ai − m) − Ω(Y (μ > 0) + ai)] > [u(y1 + ai − m) − u(y1 + ai)] and u > 0, that is, there is a preference for positively skewed distributions.

Proof : see Appendix B.


It is also shown that, in keeping with intuition, households which have sources of income that are rather substantial and fairly sure, such as gov- ernment or regular employment, are more likely to oﬀer mortgage loans.

2.4 Equilibrium Households interested in a mortgage contract must ﬁnd suitable partners.

In the nature of things, the potential pool thereof is largely conﬁned to the village itself or those in the near neighbourhood.
This implies, in turn, that these households’ net incomes are positively correlated.

Even so, sickness, deaths, marriages and the like will normally produce enough contemporaneous variation to yield a real chance of ﬁnding a potential partner, as the data themselves suggest.

Household i, having suﬀered a bad draw, seeks a sum of about mi and is prepared to mortgage out a particular plot in order to obtain it.
Most landowning households have a few plots, but each is registered and is therefore legally indivisible, which is what counts for mortgage contracts.

Household i therefore has only very few options in this regard.

Household j, which has just enjoyed a good draw, contemplates lending mj or thereabouts.

Villagers know much about their neighbours’ business, so there is a good chance that i and j will discuss the possibility of a deal.

For i, the oﬀer of mj must lie suﬃciently close to mi.
For j, the essential point is whether the plot on oﬀer will yield a suﬃciently attractive Fj(yjt; μ < 0) and its likely duration, which depends on the agreed level of m and the size of the plot.

If mi and mj lie somewhat far apart and 12 i possesses more than one plot, the parties can consider the other options where the particular plots are concerned.

There will also be some room for varying the amount of the loan, but this is almost surely limited by i’s immediate needs.
At all events, there will be scope for bargaining.

If i and j fail to agree, they have the option of seeking out other prospective partners.

Failing success there, i must attempt to get a standard loan or, worse still, resort to belt-tightening.

For j, there is the choice between padding out the savings account and making merry in the present.

These ‘outside’ options will play the usual role when i and j bargain over the precise terms of a usufructuary mortgage.
3 Selling as a Further Option The possibility that the borrower is certain never to repay, as expressed by the rational choice of a trigger value yr exceeding y2 i , emerged in Section 2.1.

We now pursue this further by introducing a formal sale, with a change of land title, as an explicit option.

It is important here to distinguish between simply leaving the usufructuary rights with the lender and formally assigning him or her full ownership rights.
For possession of the land title usually confers other advantages, the plot’s value as a form of collateral being most prominent among them.

If an unencumbered plot is sold outright for the amount v, then in a stationary environment, the same plot when already mortgaged for the amount m should command the additional amount v − m in negotiations leading to the lender obtaining the title.

The argument proceeds as in Section 2.


Household i draws yτ at t = τ and, having mortgaged a plot for m earlier, is confronted with the decision of whether to repay, continue for another period, or sell for the additional amount v − m and so settle for {Yt(λi − μ)} thereafter.

We conjecture that each of these choices is associated with a sub-interval of [y1 i (μ), y2 i (μ)], whereby the union of the sub-intervals covers the whole 13 support, but one or two of the sub-intervals may be null.
If a sub-interval is null, the corresponding choice will never be made.

Intuition suggests that selling will occur, if at all, only for suﬃciently bad draws (or very large sums v − m), repayment only for suﬃciently good ones, and continuing for intermediate values.

A detailed analysis is found in Appendix C. 4 Empirical Modelling Summarizing Sections 2 and 3, borrowers and lenders have stochastic incomes that depend on the assets whose usufructuary rights they control.
The lender’s usufructuary landholding will increase through the mortgage contract, the borrower’s will decline.

For the borrower, the immediate beneﬁt of the loan must be purchased at the cost of an inferior distribution function of income in the future.

In the model, the borrower considers taking up a loan when experiencing a negative income shock, whereas the lender manages to scrape together the loan thanks to a positive one.
The conclusion of a mortgage contract will not, therefore, be a very common event, since a match is needed among fairly close neighbors.

Repayment will take place, in the model, when the borrower gets a suﬃciently strong positive shock.

Full transfer of property rights – an outright sale – will happen if the borrower suﬀers another suﬃciently serious negative shock.

On this basis, we formulate a set of empirical hypotheses, all ceteris paribus.
• Larger endowments (of land and human capital) reduce the need to borrow to ﬁnance any given outlay, and hence the need to mortgage out.

• Households with relatively few assets are more likely to borrow, and hence to mortgage out; but they must own land in order to mortgage out.

• Successive negative income shocks will lead, ﬁrst, to mortgaging out, and then to a transfer of ownership.

14 • A household needs a positive shock to become a lender.
• Those with little or no land are more likely to be lenders.

We now elaborate somewhat on both parties’ motives and actions, leading to a set of more reﬁned hypotheses.

The lender will ﬁnance the loan either from own savings, perhaps from work outside the village, or by taking a loan himself.

In both cases, the informal credit market is available as the outside option.

He can either lend some of his earnings, or repay an outstanding informal loan, or not take up a new one.
Similarly, he may, in principle, either rent (or sharecrop) in the parcel of land.

So the act of mortgaging in (and lending) is particular, in the sense that he has to come up with a relatively large sum up front.

Given the relatively high interest rates in the informal loan market, he will probably do this by saving, rather than taking a loan.

Obtaining this sum can be a planned event: for example, the family may spend the lean season as laborers in a town.
We thus expect the following ﬁndings: (H:La), lenders (who mortgage in land) have small (or no) landholdings, in keeping with Proposition 3 ; and (H:Lb), they had a relatively large income just prior to closing the mortgage contract.

An alternative possibility is that lenders already have large land-holdings and mort- gage in land in the hope that the borrower will be unable to repay the loan.

In this event, they will have the option of oﬀering to buy the land – at a low price.
As discussed above, there seems to be some evidence in the data for this kind of land accumulation.

But as we shall see, the lenders did not own much land at the outset; so they may have bene opportunistic, but were not normally wealthy.

Mortgage contracts may, in fact, work as a mechanism to redistribute land away from households with large ownership holdings.

Those who mortgage out also decline the outside option.
In choosing this contract, they may be motivated by possessing more land than they are able or willing to cultivate themselves, lacking suﬃcient labor or having better income-earning possibilities for 15 family members.

If so, it appears that a standard sharecropping or ﬁxed rent contract would be the better option.

A more likely motive, therefore, is the need for a large sum of money, with the possession of land satisfying only a necessary condition for getting it.
Why, then, do they choose this type of loan, instead of using the land title as collateral to obtain a bank loan and keeping the user rights?

The bank may refuse to give (additional) loans for non-productive purposes; and standard informal loans carry very high interest rates.
If, therefore, mortgaging out is the last resort, we should expect to ﬁnd the following: (H:Ba), borrowers have relatively large land-holdings; (H:Bb), borrowers have existing loans; and (H:Bc), borrowers have an acute need for (even more) money.
5 The Data The original sample comprised a total of 240 households in upland Orissa, with 8 households drawn from each of 24 villages in Balangir District and a further 6 villages in Kalahandi District.3 The survey work involved the following rounds: several rounds during 2001-2004, covering most seasons in the period kharif 2000 through kharif 2004; a single round in 2010 covering kharif 2009, this time with a shorter questionnaire; and another in 2013, once more with a long questionnaire, with a follow-up in 2014, including equally extensive interviews with trading partner households and covering the calendar year 2013.
In 2013, we found 216 of the original households.

Many of them had split since the original rounds, and we interviewed all 59 splits that we found.

For the split households, we try to avoid double-counting, particularly of land-holdings.

For some parts of the analysis, we keep only the core household, which will have the largest landholding and whose head was normally the eldest son in the original rounds.

3For a description of the region, the villages and the survey design, see van Dillen (2008).
16 5.1 The incidence and duration of contracts Of the 279 households in the 2013 round,4 50 are landless.

Twenty-one of the latter farm, with a total of 35 plots of land under cultivation (median holding one acre, mean 1.6 acres); the other 29 do not.

Twelve landowning households do not cultivate, so there are 238 (229 + 21 − 12) cultivating households.

Landowning households cultivate a total of 538 plots, 408 of which are owned.
Of all owned plots 50 are cultivated by others, 32 of which are contracted under usufruct mortgages.

These 32 plots (35 acres in all) are part of the total of 26 mortgaged-out contracts, which are held by 24 households.

Seventy-two of the 573 (35 + 538) plots under cultivation are owned by others.

Again, the usufruct mortgage is the most common arrangement: 33 plots (totalling 37 acres) are mortgaged in by 29 households (26 from the original sample5).
The second most common contractual type is sharecropping, while pure ﬁxed-rent contracts are rather few in number (six plots leased in and three out).

Overall, there is more leasing in, mortgaging and sharecropping alike, than out.

This is to be expected even in a fairly large random rural sample, as some landowners live in towns.
There are 59 (26 + 33) extant mortgage contracts in all, involving 51 households, of which 48 belong to the original sample,6 with at least one of the said 48 present in 21 of the 30 villages (see Tables 1 and 2).

In this group of 21 villages, the median and (rounded) mean number of contracts are both 3 (59/21 = 2.8); the median and (rounded) mean number of households is holding at least one contract is 2 (48/21 = 2.3).

The distributions are shown in Table 1.


Since the sample size is only 8 households per village, an average of two households having such a contract is not a small number, 4Four new households were added to the original sample in the 2010 round, so that the 2013 round comprised the 216 originals found in 2013, the 59 splits and the said 4.
5In the ﬁnal sample, we end up with 25, since a split household that had a mortgage-in contract in 2013 is not that split of the original household with the largest landholding in 2013.

6There are 47 in the ﬁnal sample, see above.

17 and it points to a rather active market in this kind of transaction.

This invites the question, why are no contracts observed in almost one-third of the villages surveyed?
One might suspect that this has something to do with location and commercialization: whereas conditions in remote villages might favor mortgages, they may have disappeared in centrally located ones.

However, inspection of the spatial network indicates that this is not the case.

Kendumundi village, for example, is nearby the town of Titlagarh, and has two households that mortgage out land.
One may argue that these households mortgage out precisely because they have urban occupations; but if so, then someone else (presumably a neighbor) must be willing to mortgage in land, and thus lend to a fellow villager with an urban job.

(Tables 1 and 2 about here.)

The duration of such contracts is of central interest, as is their frequency over time.
Sixteen of the above-mentioned 48 households in the original sample having a contract in 2013 also had extant contracts at some stage during the early period from kharif 2000 to kharif 2004.

The reported starting dates of contracts indicate how quickly they were repaid.

In 2013, this date was reported for 57 out of the 59 contracts.

The mean date was 2010, the median was 2011, and the earliest date was 2001, with only four loans taken up in 2004 or earlier.
Extant contracts in 2013 having already lasted an average of 3 years, one might guess that loans are repaid, on average, after about 6 years, but the true value depends on the actual (stochastic) process.

In the rounds covering the period 2000-2004, both the median and mean starting years were 2001.

Most of the contracts seem to have been recorded already in the ﬁrst 2001 round, which canvassed both seasons of the agricultural year 2000-01.
Among those contracts, the median starting year was 2000 and the mean 1999, which seems to point to a shorter period until repayment, on average, at that time.

Only half of the 2001 loans were recorded as repaid in 2004, but this may be due to gaps in information on repayment in the ﬁnal round.

The data convey the general impression that people mortgage the 18 land for some years, and in some cases it changes ownership.
5.2 The hypotheses: a preliminary examination Table 3 reports summary statistics of ownership holdings for the three subgroups de- ﬁned by households’ usufruct contractual status in 2013, together with 95-percent conﬁdence intervals and signiﬁcance levels for comparisons of the means of contracting and non-contracting groups.7 Two households mortgage both in and out, and some households have multiple contractual partners, so the numbers of observations in the table do not add up to 279.
For completeness, we also report the statistics for those linked households that have mortgage contracts with households in our primary sam- ple, that is, for those contractual partners not belonging to our sample whom we were able to identity and interview.

(Table 3 about here) Starting with the sample of 279 households, we use the 223 that have no mortgage contract as the reference group.
As can be seen from Table 3, those that mortgage in land own less land on average, while those that mortgage out own more: indeed, there is no overlap between the conﬁdence intervals for the respective means of 1.4 acres and 3.4 acres.

There are similar ﬁndings for the linked samples, i.e., those that have mortgage contracts with the original sample, except that those mortgaging out have even more land.
This is not surprising, since households with more land are more likely to have multiple partners and thus have a larger probability of contracting with any randomly sampled household.

We thus have support for hypotheses H:La and H:Ba.

One must own land to be able to mortgage out, and those lacking land of their own 7With only 30 clusters, the use of clustered standard errors has pitfalls.

We report the larger standard error of the two, which in most cases is the clustered one, throughout the paper.
In this table, the non-clustered standard error is larger for the two small mortgage-out samples, where there are, respectively, 18 (in 13 clusters) and 19 (in 10 clusters) observations, so the clustered standard errors are probably biased.

19 may wish to mortgage in.

It is, however, a ﬁnding with a twist: the land-poor were lending money to the land-rich.
Returning to the possible motives of the land-rich to borrow from land-poor neighbors in exchange for such user rights, there is, in principle, the alternative of using the land title as collateral to secure a bank loan.

One stratagem is to use the land as collateral twice, ﬁrst, by depositing the title with the bank as collateral for a formal loan, and then transferring the user rights to the lending household to get an informal one.

There is some evidence that points to such behavior.
The 25 households that mortgage out have a total of 61 loans (with a median size of Rs.10,000) for which full details about the lender are available; all 25 must have at least one loan, and 17 of them reported having more than one.

Of the remaining 254 households, 82 have no loans and 91 have more than one.
Borrowers who mortgage out land have more loans than borrowers who do not: the null of homogeneity of the distributions (0 + 8, 17) and (82 + 81, 91) is decisively rejected (χ2 = 9.930, χ2 0.01(1) = 6.635).

This indicates some support for hypothesis H:Bb, that is, the usufruct mortgage is only one of many available options to which those mortgaging out resort.
Borrowers who mortgage out also take out larger loans – the median is Rs.40,000, compared with Rs.18,000 for the others (again, among those who have any loans at all).

The type of lender is known for 26 of the 32 usufruct mortgage-out loans.

All are informal lenders: 16 loans come from relatives, friends or neighbors, seven from moneylenders, two from landlords and one from a trader.

The 35 additional loans taken by the same borrowers come from more diverse lenders, similar to the other borrowers.
Where purpose is concerned, the usufruct loans are over-represented when it comes to medical expenses and a daughter’s marriage, but when all loans taken by these borrowers are examined together, the medical loans are not over-represented.

Thus, only loans for a daughter’s marriage are over-represented among borrowers who mortgage out land.

Yet only 9 of the 26 usufruct loans have marriage as the declared purpose.
If we construe marriage as a sudden need for credit, then there is some 20 support for hypothesis H:Bc.

This brings us to the role of negative shocks, information on which is available only for the period 2000-2004.

Six of the 26 households that mortgaged out (and thus took out the associated loan) reported no shocks at all.
Of the others, 17 reported that the mortgage was linked to marriage, seven had health problems (the same proportion as other households), and 12 experienced bad weather (again similar to other households).

Thus, these 20 households suﬀered, on average, about two misfortunes over the period in question.

Among the 22 households that mortgaged in land (and thus granted loans), 13 reported no shocks at all.

There were no marriages (just 3 in the remaining sample).
Seven of the nine that did report suﬀering a shock had health problems, and only four reported bad weather (note that this group of 22 had less land).

In the whole sample, a total of 22 marriages are reported, and 17 of these households mortgaged out land.

We conclude that land is frequently mortgaged out to ﬁnance a daughter’s marriage, but also that other adverse shocks play a role in forcing this option.

In what sense, however, can marriage be interpreted as a shock?
One may argue that whereas a marriage is very likely to happen, its timing is uncertain.

The family must ﬁnd an appropriate groom, followed by the additional complication that, according to tradition, there are auspicious dates for marriage.

While contemplating these tasks, there are two possible strategies to raise the funds.

One can invest in assets that can be sold at the right time: gold and cattle are readily tradable, land less so.
Or one can wait and then borrow – potentially through a usufructuary mortgage – when the time does come.

But why is there this close link between mortgage and marriage?

Marriage entails a large, one-time cost, and though there may be other large outlays during the lifetime of a family, marriage is still the most frequent such event in village economies.
Thus the high correlation between marriage and usufruct mortgage contracts may just reﬂect the fact that marriage is an almost unavoidable rite of passage, and does not necessarily imply that mortgaging out is linked only, and then potentially by social custom, to marriage.

There is, moreover, the mitigating eﬀect that when the daughter 21 leaves the household, it may need less land, if only for a while, which in turn makes mortgaging out more attractive.
6 Mortgages and Land Accumulation We turn to the possibility that lending by mortgaging in is a means of accumulating land.

We do not have direct information, but any household that mortgaged in land in the early period and owned more land in the closing period is a candidate.
Among the 22 panel households that mortgaged in land during the ﬁrst rounds, 11 had accumulated one acre or more by the close, whereas among the 194 that constitute the rest of the original panel sample of 216 households, only 44 managed as much.

Indeed, the null of homogeneity of the distributions (11, 11) and (150, 44) for the two groups is rejected with a test of size 0.01 (χ2 = 7.770, χ2 0.01(1) = 6.635).
The mean accumulations are −0.06 and 0.52 acres, with robust standard errors of 0.158 and 0.300, respectively; the diﬀerence of 0.58 acres is signiﬁcant with a test of size 0.06.

To complete the picture, of the 22 that had mortgaged in, four lost and 13 gained land in the interim.

Ten were landless in 2001, and six of them had land in 2013.

The normal gain was one acre.


It is less straightforward to compare declines in land holdings among those that mortgaged out, since the splitting of households – and of the original holding among brothers – is not a rare event, so any observed decline may result from a combination of causes.

Among the 26 panel households that reported mortgaging out in the early period, 11 had lost one acre or more by the close, while among the remaining 190, 44 had done likewise.
The null of the homogeneity of the distributions (15, 11) and (146, 44) is rejected at conventional levels (χ2 = 4.419, χ2 0.05(1) = 3.84).

To complete the picture for those mortgaging out, 10 gained and 14 lost land.

The median holding was 4 acres in 2001, and the median holding for the said 14 dropped from 5 to 1 acres.

All 26 still owned land in 2013, the median having fallen to 2.8 acres.
So from both sides of these transactions, it appears that a mortgage contract may lead to as a 22 transfer of ownership.

If this is the case, then we would expect to ﬁnd that the land-poor lenders had good non-farm incomes, while the land-rich borrowers had particularly low incomes, or high costs.
An examination of non-farm incomes during the three ﬁrst seasons canvassed (kharif 2000 through kharif 2001) reveals that the 10 households that mortgaged out during the period 2000-04 and lost one acre or more up to 2013 had lower incomes in those three seasons than other groups.

The middle seven of this group of 10 had lower non-farm incomes in 2000-01 than the 12 households that mortgaged in early on and had accumulated one acre of land or more by the close.
If, however, we compare all those which mortgaged out with all those which mortgaged in, we ﬁnd no diﬀerence.

This pattern is consistent with mortgaging out being chieﬂy motivated by pressing and substantial ﬁnancial need.

For relatively poor people with more land but limited non-farm income, it is also a way to for them lose land over time.

We now test more systematically the idea that mortgage transactions operated so as to redistribute landownership in the manner described above.
Since a household’s initial contractual status should aﬀect its subsequent (net) accumulation of land, this needs to be investigated as a ﬁrst step.

We employ a regression framework, using infor- mation on the initial conditions and state variables reported in the 2001 interviews.

All extant mortgages reported during the three seasons in question are included.

We then use the 2013 data to measure households’ subsequent accumulation of land.
Excluding two outliers,8 both the median and the mean landholding are the same, respectively, in 2001 and 2013.

For the sample as a whole, therefore, there is no land accumula- tion.

Thus households bought, sold and divided land, but without altering the central measures of the distribution.

8The 99-percentile for landownership in 2001 is at 12 acres.

Two households had, respectively, 22 and 30 acres in 2001, and lost, respectively, 16 and 27 acres between 2001 to 2013.
23 6.1 Econometric analysis We have the following latent function: zi = z(land ownership, family labor, education, caste) + ui.

The probability of mortgaging out we may write as P (mortgage out) = P (zi > K1), and the probability of mortgaging in as P (mortgage out) = P (zi ≤ K0).

The ﬁrst speciﬁcation involves estimating the two equations separately using OLS.

This implic- itly means that the group of observations formed by mortgage-out together with no mortgage is the combined control for mortgage-in.
An alternative is to estimate the two equations jointly using a multinomial logit model, with no mortgage as the control.

We report marginal eﬀects, so that they can be compared to the OLS ﬁndings.

Finally, we assume that the two equations are the same, but with K0 < K1, which means that we estimate an ordered probit model.

Again the marginal eﬀects are compared to no mortgage.

The ordered probit model implicitly assumes that the marginal eﬀects have the same size, but opposite signs.
We summarize what the analysis of the preceding sections leads us to expect.

Larger endowments (land owned, labor, education) induce a lower probability of borrowing (mortgaging out).

That is to say, as land owned decreases, then cet.

per.

the prob- ability of mortgaging out increases.

This cannot continue without limit, however; for owning some land is a necessary condition for the action of oﬀering to mortgage it.
Hence, if the size of the holding is suﬃciently small and the response function is con- tinuous, the probability of mortgaging out must be decreasing in that endowment.

Conversely, for suﬃciently small ownership holdings, culminating in landless house- holds, the probability of mortgaging in will be increasing therein.

Thus, there should be an inverse-U shaped eﬀect of own land on mortgaging out and a U-shaped eﬀect of own land on mortgaging in.
Family labor and education will increase (decrease) the probability of mortgaging in (out); and caste may shift preferences for mortgaging (both in and out).

Finally, mortgaging in may lead to accumulation of land.

24 The results for the mortgage decision are reported in Table 4.

The ﬁndings are robust across the diﬀerent econometric speciﬁcations and conform largely to expectations.
For mortgaging out, the relation is concave and ﬁrst increasing (see columns 2 and 5), with an implied turning point at about 9 acres,9 close to the top end of landholdings.

For mortgaging in, the function is convex and ﬁrst decreasing (see columns 1 and 4), though the estimated coeﬃcients are much less precise.

The OLS estimates, the more precise of the two, imply a turning point of 11.5 acres.
The ordered probit estimates (see column 3) are consistent with these ﬁndings, with an implied turning point of just over 10 acres.

These turning points are not so precisely estimated as to warrant strong assertions that households with more than 10 acres or so are less likely to mortgage out; for only 12 of the whole sample owned 6 acres or more.

Of the four owning 8.75 acres or more, one mortgaged out; but just one of the eight owning between 6 and 8.75 acres did so.
We conclude that over the actual distribution of ownership holdings, and all else being equal, households with small to modest holdings are likely to mortgage out to neighbors with even smaller ones.

In contrast to the predictions, family size has no eﬀect on these decisions, even when controlling for the number of dependants and working-age members.

Human capital, as measured by educational attainment, however, appears to increase the probability of mortgaging in.
This implies some support for the hypothesis of an opportunistic motive for mortgaging, if some education is needed to make and execute a long-term plan of acquiring full ownership.

The ﬁnding that tribal people are less active on both sides of the market – particularly in mortgaging out – is consistent with received wisdom about social customs in upland Orissa.

(Table 4 about here) To close, we investigate whether mortgaging in land in 2001 appears to have been a stepping stone towards accumulating land.
To test this, we estimate land ownership 9Both coeﬃcients are signiﬁcant at conventional levels in the logit speciﬁcation.

The turning point is 0.070/(2 × 0.004) = 8.75.

25 in 2013 as a function of landownership in 2001 and the area of land mortgaged in during 2001, adding the area mortgaged out for completeness (see Table 5).

It should be remarked that the descriptive statistics discussed above are richer in content than the following regression analysis.
For a parametric relation between initial and closing landholdings in the latter only summarizes the changes in land distributions discussed above.

Recall, in particular, that the land distribution within the panel stays basically the same: individual households just switch positions.
Thus, we cannot interpret the estimated parameter for initial land (acres01), whose value is smaller than one, as indicating that there will be growing concentration of land ownership, which would indeed happen if the estimated function described the transitions of a single household.

The estimated value merely indicates that land in fact tends to stay in the family over time, but that there is also some trade in land.
Controlling for initial land ownership, the coeﬃcient on the area mortgaged in dur- ing the early period is positive, quite large and statistically highly signiﬁcant, which supports the hypothesis that mortgaging in constitutes a long step on the way to ac- cumulating land.

This is the main ﬁnding, and it is robust to the introduction of other regressors.

It is also reassuring that the coeﬃcients on all three land variables vary relatively little across the speciﬁcations in Table 5.
Controlling for (administrative) block eﬀects is important to this ﬁnding.

Of the 22 households mortgaging in, 16 were residents of Titlagarh and Kesinga blocks, with the remaining 6 households spread over the other three.

In the absence of block dummies as controls, the coeﬃcient of land mortgaged in is both smaller and no longer statistically signiﬁcant at conventional levels.

Where the other endowments are concerned, larger families in 2001 are associated with larger ownership holdings in 2013.
There is, however, something of a surprise: controlling for all these factors, families with many adult men in 2001 had less land in 2013.

Perhaps India’s growing urban sector oﬀered them better opportunities.

26 (Table 5 about here) 7 Conclusions The usufruct mortgage oﬀers some clear advantages over other forms of contracts in risky environments when insurance and credit markets are very imperfect, if at all ac- tive.

These advantages are, however, double-edged in some respects.
When mortgaging out a parcel of land, the borrower obtains a goodly sum to deal with an immediate need and can choose when to repay the loan; but future events may well turn out so adversely that he never does so.
The lender enjoys the user rights until the loan is repaid in full, an action over whose timing he has no control; but there is always the possibility – and hope – that the borrower will eventually decide that repayment will be simply too painful and agree to a transfer of ownership, perhaps with the inducement of an additional payment.
The theoretical framework developed and analyzed in this paper contains all these elements and yields some results concerning what conditions and factors govern the decision to contract in the ﬁrst place and, subsequently, when and whether to repay or agree to a sale.

The situation on the ground, in upland Orissa, illustrates and substantially bears out these ﬁndings.

By deﬁnition, a household must own land in the ﬁrst place to be able to mortgage out land and thus obtain a loan so secured.
The chief pressing need is to marry oﬀ a daughter, but those arising from serious ill-health and bad harvests are also important.

Many of the households that mortgaged out in the early period had smaller ownership holdings at the close, and the losses were substantial, though none became landless.

Those households that mortgaged in were mostly land-poor at the outset, though evidently able to raise the money needed to oﬀer the required loan.
They may indeed have had an opportunistic motive, as this group had accumulated land ten years later.

27 Almost 20 percent of the households in the sample had extant mortgage contracts in 2013, and complementing this strong level of activity, all the sums involved were quite large.

These facts indicate that such contracts oﬀered the parties opportunities beyond those available through other forms of credit transactions.
Mortgage contracts also appear to operate as a mechanism that frequently leads to the full transfer of ownership rights from relatively land-rich to land-poor households.

There are, of course, other processes aﬀecting the distribution of land, especially the splitting of holdings among brothers.

In the villages surveyed, however, the overall distribution of ownership holdings has remained largely unchanged over time.

8 Appendices Proof of Proposition 1.

Deﬁne ξ(yr, m) ≡ u(yr)−u(yr−m).


Since u is strictly concave, ξ is positive, decreasing, continuous and strictly convex for all yr, with lim yr→∞ ξ = 0.

Now consider Qm i , which is clearly continuous in yr. Diﬀerentiating w.r.t.

yr, we obtain ∂Qm i ∂yr = δ[Qm i + u(yr − m) − u(yr)] · F (yr; μ) (1 − δ(1 − πi))2 > 0 ∀yr ∈ (y1(μ), y2(μ)).
(i) If ξ(y1(μ), m) < δQm i (y1(μ), m, μ), then ξ and δQm i will not intersect in the interval [y1(μ), y2(μ)], and the loan will be repaid for certain in the next period.

(ii) If ξ(y1(μ), m) > δQm i (y1(μ), m, μ) and ξ(y2, m) < δQm i (y2, m, μ), then ξ and δQm i will intersect exactly once, at yr, in the interval [y1(μ), y2(μ)].

(iii) If ξ(y2(μ), m) > Qm i (y2(μ), m, μ), then ξ and δQm i will not intersect in the interval [y1(μ), y2(μ)] and the loan will never be repaid.
Turning to the behaviour of the trigger value yr in relation to loan size m, diﬀeren- 28 tiating (4) totally, holding μ constant, collecting terms and rearranging, we have ⎛ y2(μ) u(yr − m) − u(yr) + ∂Qm i ∂yr dyr = ⎜ ⎝u(yr − m) − δ 1 − δ(1 − πi) u(y − m)dF (·; μ) yr ⎞ ⎟ ⎠ dm.

It is seen that the expression multiplying dyr is positive.
That multiplying dm is also positive iﬀ (1 − δ)u(yr) + δu(yr − m) dF (·; μ) > δ u(y − m)dF (·; μ), y2(μ) y2(μ) yr yr which certainly holds in virtue of the strict concavity of u.

It follows that yr is increasing in m. Analogously, yr is decreasing in μ iﬀ ∂Qm i /∂μ > 0.

We have ∂F (yr; μ) ∂Qm ∂Γ i ∂μ = ∂μ ∂μ 1 1 − δ(1 − πi) Qm i − .

It follows from Assumption 1 that ∂F (yr; μ)/∂μ > 0 ∀yr ∈ (y1, y2) and is zero oth- erwise.
Γ is the expected utility of the lottery Y (μ > 0) with optimal repayment behaviour.

It is surely decreasing in μ; for the usufructuary holding becomes smaller and the resulting F is ﬁrst-order stochastically dominated.

Thus, yr is decreasing in μ.

The same argument applies, mutatis mutandis, to changes in the endowment λ with μ constant: yr is increasing in λ. Q.E.D.

8.1 Appendix A.
8.1 Appendix A.

Lenders Proceeding as in Section 2.1, the value of the resulting stream of expected utilities yielded by the contract, as assessed at t = k, is u(yjk − mj) + δjSjk, where πiΩ(Yj(μ < 0) + mj) + (1 − πi)Ω(Yj(μ < 0)) + πiVj(Yj(0)) 1 − δj(1 − πi) Sjk = (9) and Ω(Yjt(μ < 0)) = Ω(Yj(μ < 0)) ∀t.

It should be noted how the borrower’s choice of πi weights the various branches of the lender’s outcome-tree in which repayment occurs, whereby πi is evaluated at mi = mj .
29 The alternative is simply to consume the windfall at once in period k, which yields a stream whose present value is u(yjk) + δjVj(Yj(0)) .

Noting (2), it is seen that the lender will be indiﬀerent between these two courses of action if, and only if, u(yjk) − u(yjk − mj) = δj[πiΩ(Yj(μ < 0) + mj) + (1 − πi)Ω(Yj(μ < 0)) − Ω(Yj(0))] 1 − δj(1 − πi) , (10) where the r.h.s.
is independent of t. It is proved in Proposition 3 that, for each mj, there is a unique value of yjk satisfying (10), which is denoted by ym j ∀k.

The expression in brackets in the numerator on the r.h.s.

is decreasing in each of the endowments κj and λj in virtue of Assumption 1 and the strict concavity of u.

Inspection of the l.h.s.

then reveals that ym j is increasing in κj and λj.


Analogously to (7), the net advantage of oﬀering the loan is Δm j ≡ [u(yjk−mj)−u(yjk)]+ δj[πiΩ(Yj(μ < 0) + mj) + (1 − πi)Ω(Yj(μ < 0)) − Ω(Yj(0))] 1 − δj(1 − πi) .

(11) For any given plot of land, an increase in mj involves a direct cost, as represented by the term [u(yjk − mj) − u(yjk)], but it also yields pay-oﬀs in the future.
First, when repayment does occur – if it ever does –, yjt is very likely to be lower than the favourable realisation yjk that induced the household to lend in the ﬁrst place.

Secondly, and more importantly, an increase in mj will induce the borrower to choose a higher trigger value of yr, and so a lower value of πi.
Not only does this lower the eﬀective discount rate for outcomes in which repayment is made, but it also increases the probability of enjoying the augmented process {Yt(μ < 0)} for more periods.

While these particular advantages are unlikely, by themselves, to oﬀset the direct cost in full, they will certainly temper it.
It remains to establish how changes in the endowments aﬀect the attractiveness of lending m for μ. Analogously to pi(ym i , λi) = F (ym i ; μ = 0) for a borrower to accept the oﬀer (m, μ), we have pj(ym j , λj) = 1 − F (ym j ; μ = 0) is the probability that lender j will make it.

Analogously to (8), the fact that the trigger value ym j is increasing in each of 30 the endowments makes the signs of the derivatives ∂pj/∂λj and ∂pj/∂κj ambiguous.

8.2 Appendix B.
8.2 Appendix B.

Borrowers and lenders: non-random factors Starting with putative borrowers, (4) becomes, on introducing the suﬃx i, u(yr + ai) − u(yr + ai − m) = δ · Ω(Yi(0) + ai) − Γ(ai) 1 − δ(1 − πi) ≡ δQm i (ai).

(12) Diﬀerentiating totally and rearranging terms, it is shown in the Appendix that yr is increasing in ai if, and only if, δi(Γ − Ω(Yi(0) + ai)) > (1 − δi(1 − π))[u(yr + ai − m) − u(yr + ai)].
(13) This condition states that the diﬀerence between the expected marginal utility of the lottery Γ and that of Yi(0) exceeds the diﬀerence between the marginal utility of net income evaluated at yr with repayment and that without, the diﬀerences weighted by the discount factors δi and (1 − δi(1 − π)), respectively.

The l.h.s.

will be large, cet.

par., if the plot mortgaged out is large, so that Yt(μ = 0) is much superior to Γ, which relates to Yt(μ > 0).

The r.h.s.
The r.h.s.

depends on the curvature of u over the interval (yr + ai − m, yr + ai) and the discount factor adjusted for repayment.

It is seen that the expressions on both sides of condition (13) attain a maximum when yr = y1.

This observation leads to Proposition 3.

Proof of Proposition 3.

The trigger value now relates to the variate Yt, but with each realisation augmented by ai, so that ξ ≡ u(yr + ai) − u(yr + ai − m).

We have ∂ξ ∂ai = u(yr + ai) − u(yr + ai − m) < 0.
The response of Qm i (ai) to changes in ai, holding yr constant, is ∂Qm i (ai) ∂ai = Ω(Y (0) + ai) − yr y1(μ) u(y + ai)dF (y; μ) − y2(μ) yr u(y + ai − m)dF (y; μ) 1 − δi(1 − πi) 31 < 0, since F (y; 0) ﬁrst-order stochastically dominates F (y; μ) when μ > 0.

Hence, yr is increasing in ai if, and only if, δi · ∂Qm i /∂ai − ∂ξ/∂ai < 0, which condition may be written as (13): δi(Γ − Ω(Y (0) + ai)) > (1 − δi(1 − πi))[u(yr + ai − m) − u(yr + ai)].
The partial derivative of the l.h.s.

w.r.t.

yr is −δi[u(yr + ai − m) − u(yr + ai)]F (yr; μ).

The corresponding expression for the r.h.s.

is −δi[u(yr + ai − m) − u(yr + ai)]F (yr; μ) + (1 − δi(1 − πi))[u(yr + ai − m) − u(yr + ai)]; so that the r.h.s.

of (13) is decreasing more strongly in yr than the l.h.s.
if, and only if, [u(yr + ai − m) − u(yr + ai)] < 0, and this holds in turn if u > 0.

Q.E.D.

Turning to the net advantage of borrowing over belt-tightening, (7) becomes Δm i ≡ [u(yik + m + ai) − u(yik + ai)] − δiQm i (ai).

(14) The expression in brackets on the r.h.s.

of (14) is decreasing in ai, since u is strictly concave.

It becomes arbitrarily close to zero as ai becomes arbitrarily large; the same holds for Qm i (ai).

Diﬀerentiating w.r.t.
ai, we obtain = [u(yik + mi + ai) − u(yik + ai)] − δi · ∂Qm i (ai) ∂ai + ∂Qm i (ai) ∂yr · ∂yr ∂ai , (15) ∂Δm i ∂ai where Ω(Y (μ = 0) + ai) − ∂Qm i (ai) ∂ai = yr y1(μ) u(y + ai)dF (y; μ) − 1 − δi(1 − πi) y2(μ) yr u(y + ai − mi)dF (y; μ) < 0 in virtue of the fact that F (y; 0) ﬁrst-order stochastically dominates F (y; μ > 0), and ∂Qm i (ai) ∂yr = [δiQm i (ai) + u(yr + ai) − u(yr + ai − mi)] · ∂F (yr + ai; μ)/∂ai 1 − δi(1 − πi) > 0.
Proposition 3 establishes suﬃcient conditions for yr to be increasing in ai ; but the sign of ∂Qm i (ai)/∂a renders that of ∂Δm i /∂ai ambiguous.

On balance, however, it is very 32 likely that households that enjoy a large certain component of net income will resort to belt-tightening in the face of a bad draw yk.

Putative lenders are concerned with Δm j ≡ [u(yjk + aj − mj) − u(yjk + aj)] + δj[Ω(Yj(μ) + mj + aj) + (1 − πi)Ω(Yj(μ) + aj) − (Ω(Yj(0)) + aj)] 1 − δj(1 − πi) , (16) where μ < 0.
The ﬁrst expression in brackets on the r.h.s is negative and goes to zero as aj becomes arbitrarily large.

The second expression is positive.

Diﬀerentiating w.r.t aj, we have ∂Δm j ∂aj = [u(yjk + aj − mj) − u(yjk + aj)] + δj[Ω(Y (μ) + mj + aj) + (1 − πi)Ω(Y (μ) + aj) − (Ω(Y (0)) + aj)] 1 − δj(1 − πi) .

(17) The ﬁrst term on the r.h.s is positive, since u is strictly concave.

Assumption 1 and the strict concavity of u imply that the second term is negative.
It is seen that the strict concavity of u implies that lending in exchange for usufructuary rights becomes more attractive relative to immediate consumption as aj increases provided m is suﬃciently large.

8.3 Appendix C. Selling as a further option We deﬁne ys yr y2 i (μ) Γs ≡ u(yit + v − m)dFi(yit; μ) + u(yit)dFi(yit; μ) + u(yit − m)dFi(yit; μ), y1 i (μ) ys yr (18) noting that one or two of the sub-intervals [y1 i (μ), ys], [ys, yr] and [yr, y2 i (μ)] may be null, where μ ∈ (0, λi].
The analogue of Sτ is Στ = Γs + δ[πr i V (Yi(0)) + πs 1 − δi(1 − πr − πs) i V (Yi(μ))] ≡ Σ ∀τ, (19) 33 where πr i = y2 i (μ) yr dFi(yit; μ) and πs i = ys y1 i (μ) dFi(yit; μ).

The value of continuing is u(yiτ ) + δΣ.

The value of repaying, and so reclaiming Fi(yit; 0), is u(yiτ − m) + δV (Yi(0)).

The borrower will be indiﬀerent between these two courses of action if, and only if, u(yiτ ) − u(yiτ − m) = δ · Ω(Yi(0)) + δπs[V (Yi(0)) − V (Yi(μ))] − Γs 1 − δi(1 − πr − πs) .
(20) It should be noted that the r.h.s.

depends on ys as well as yr; for if the choice is to continue, then the option of selling will be open in the next period.

The corresponding condition for the choice between selling and continuing is u(yiτ + v − m) − u(yiτ ) = δ · Γs + δπr[V (Yi(0)) − V (Yi(μ))] − Ω(Yi(μ)) 1 − δi(1 − πr − πs) .

(21) That between selling and repayment is u(yiτ + v − m) − u(yiτ − m) = δ[V (Yi(0)) − V (Yi(μ))] .
(22) Given (m, v, δ, Fi(yit; 0), Fi(yit; μ)), there is a unique value of yiτ that satisﬁes this last condition, though it need not lie in [y1 i (μ), y2 i (μ)].

Whether continuing with the contract is better or worse than selling or repaying at yiτ is an open question.

It will be useful to start by deriving conditions under which selling will never be chosen; for the setting then reduces to that analysed in Section 2.
(The suﬃx i may now be dropped, since what follows concerns only the borrower, who can block any attempt by the lender to force a sale or repayment.)

Suppose, therefore, that πs = 0 and the corresponding contribution of selling to Γs is also zero.

Recalling (5), (21) yields the following condition that continuing will be (weakly) preferred to selling: u(yτ + v − m) − u(yτ ) ≤ δ · δπr[V (Y (0)) − V (Y (μ))] + Γ − Ω(Y (μ)) 1 − δ(1 − πr) .

Since u is strictly concave, the l.h.s.


attains a minimum at yτ = y1(μ).

Hence, if u(y1(μ) + v − m) − u(y1(μ)) ≤ δ · δπr[V (Y (0)) − V (Y (μ))] + Γ − Ω(Y (μ)) 1 − δ(1 − πr) , (23) 34 selling will indeed never be chosen over continuing, and a unique value of yr will trigger the decision to repay, if at all.

Denote this value of yr by yr(c) Now suppose that condition (23) is just violated at yτ = y1(μ) and that yr(c) is not in the immediate neighbourhood of y1(μ).
Then, by continuity, the gain from selling over continuing will be small and there will exist a ys corresponding to yr(c) that is close to y1(μ).

It further follows that there exists a pair (ys, yr) close to (y1(μ), yr(c)) such that the borrower is indiﬀerent between selling and continuing, and prefers both to repaying.

From (22), it is seen that this conﬁguration will hold only if u(yτ +v −m)−u(yτ −m) > δ[V (Y (0)) − V (Y (μ))].
This involves relatively large values of m and v − m, and a plot that is not so productive as to involve a big diﬀerence between V (Y (0)) and V (Y (μ)).

It has been proved above that ys and yr move in opposite directions where condition (20) is concerned.

Hence, as condition (23) is more strongly violated, both πr and πs will increase, and the probability of continuing correspondingly reduced.
Indeed, it is possible that there exists a yτ ∈ (y1(μ), y2(μ)) such that condition (22) holds: the borrower sells for all worse draws and repays for all better ones.

This conﬁguration is most likely to hold when the additional sum v − m is suﬃciently large and repaying m is not too onerous.

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DOI: 10.1080/09578810802464912.

36 Table 1.

Mortgage contracts per village in 2013 contracts villages hh villages Table 2.
Mortgage contracts in the panel 2001-04 2013 (N=240) (N=216) (N=279) Households Contracts Original Households Contracts Mort-in Mort-out (N=51) (N=60) hh (N=47) (N=51) (N=59) 2001-04 2001-04 Mortgage-in Mortgage-out 24 28 30 30 25 24 29 24 33 26 7 (1) 2 7 The sample of 279 households in 2013 are the 216 + 59 splits from those households + four households added in 2009.

Table 3.
Landholdings (acre) for sub-groups according to mortgage status in 2013 Group: 25-percentile landless (%) median mean N 75-percentile Original sample: Mortgage in and matched Mortgage out and matched 33 17 25 15 15 12 0 0 No mortgage (ref) 223 21 Linked sample: Match and mort-in 17 Match and mort-out 18 24 0 0.5 0.5 1.4 1.0 0.5 0.5 2.5 1.0 1.0 2.8 2.0 1.3 1.0 4.0 1.4* (0.8-2) 1.4 (0.5-2.2) 3.4** (2.2-4.7) 3.0 (1.5-4.5) 2.0 (1.6-2.4) 1.1** (0.5-1.7) 5.1*** (3.0-7.2) 2.1 2.0 5.0 4.5 3.0 1.9 6.0 Significantly different from reference category at ** 5%-level, * 10%-level.
95-% confidence interval in parenthesis.

Table 4.
Mortgage decisions: contractual status in 2001 (1) OLS (2) OLS (3) (4) (5) oprobit mlogit mlogit VARIABLES mort-in mort-out mortgage mort-in mort-out acres - 0.046* 0.073*** 0.061*** - 0.034 0.070*** (0.026) (0.026) (0.020) (0.032) (0.021) acres-sq 0.002 - 0.004 - 0.003* 0.000 - 0.004** (0.002) (0.003) (0.002) (0.005) (0.002) scheduled tribe - 0.012 - 0.116** - 0.051 - 0.014 - 0.121** (0.036) (0.050) (0.036) (0.037) (0.058) education-head 0.015* - 0.006 - 0.010 0.014** - 0.005 (0.008) (0.009) (0.007) (0.007) (0.007) family-size 0.014 - 0.020 - 0.016 0.012 - 0.016 (0.016) (0.013) (0.011) (0.016) (0.015) workagefem - 0.018 0.041 0.028 - 0.027 0.032 (0.025) (0.032) (0.021) (0.029) (0.021) workagemale 0.007 - 0.038 - 0.022 0.015 - 0.035 (0.029) (0.027) (0.017) (0.025) (0.024) Observations R-squared 214 0.101 214 0.131 214 0.093 214 0.179 214 0.179 *** p<0.01, ** p<0.05, * p<0.1.
Bold if familysize+workagemale is significant (column 5: significant at 12%-level).

Cluster-adjusted standard errors in parentheses.

Block-dummies included.

Marginal effects.

Table 5.
Land accumulation OLS OLS OLS variables acres01 acres13 acres13 acres13 0.689*** 0.677*** 0.683*** (0.078) (0.079) (0.080) acres01-mortgaged-in 0.261*** 0.234*** 0.218*** (0.091) (0.081) (0.076) acres01-mortaged-out 0.281 0.360 0.330 (0.404) (0.364) (0.371) scheduled tribe 0.459(*) 0.359 (0.273) (0.287) education-head family-size workagefem - 0.012 (0.028) 0.225** (0.083) 0.263 (0.182) workagemale - 0.625*** Observations R-squared (0.150) 214 0.534 214 0.478 214 0.472 *** p<0.01, ** p<0.05, * p<0.1.
Bold if familysize+workage is significant.

Cluster-adjusted standard errors in parentheses.

Block-dummies included.

Marginal effects.

6 This paper develops a theoretical framework in which the borrower, who mort- gages out, and the lender, who mortgages in, a parcel of land reach their decisions when credit and land markets function imperfectly.

The results cover what con- ditions and factors govern the decision to contract in the first place, and when and whether to repay or agree to a sale.
The empirical investigation deals with such contracting in Orissa, based on a panel household survey over the period 2000–2013.

Almost 20 percent had contracts in 2013, the borrowers’ chief need being to marry off a daughter, followed by coping with serious illness and bad harvests.

The sums were quite large, indicating that these contracts offered the parties opportunities beyond those available through other forms of credit trans- actions.
Mortgaging also appeared to promote the transfer of ownership rights from relatively land-rich to land-poor households.

Keywords: usufructuary mortgage agrarian contracts Orissa Chr.

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