Tenants, landlords, and soil conservation.

The relationship between tenancy and land degradation is one of the classic questions of economics, dating back to the earliest days of the discipline (Johnson [1950] for a brief survey). The conventional wisdom is that tenancy promotes land degradation: Because tenants have no material stake in maintaining the productivity of land beyond the expected life of the rental contract, they have an incentive to overexploit soils. That conventional wisdom considers soil conservation only from the perspective of tenants, ignoring actions landlords can take to protect their land. One possible course of action for landlords is to offer share rather than cash rental contracts. As Allen and Lueck (1992) pointed out and Dubois (2002) has shown formally, share tenancy reduces the short-run return to soil exploitation and can consequently mitigate overexploitation of land. This argument is in many ways the mirror image of the view held by many classical writers, who, as Johnson (1950) noted, believed that share tenancy reduced incentives for positive investment in land productivity. Share tenancy also allows renters to appropriate the gains from soil conservation that manifest themselves during the lifetime of the rental contract (McConnell 1983; Soule, Tegene, and Wiebe 2000). However, share tenancy by itself cannot generally induce first-best investment in land productivity when that investment is non-contractible and the gains from it accrue past the anticipated lifetime of the rental contract (Bardhan 1984).

The literature to date has not considered the possibility that landlords can undertake direct actions that physically limit tenants' ability to overexploit soil. Landlords can invest in conservation structures (e.g., terraces) that limit erosion. Alternatively, they can stipulate that tenants use soil-conserving practices that leave a durable imprint on the landscape (e.g., contour plowing, stripcropping, installation of vegetative buffers). In either case, tenants' compliance is verifiable at reasonable cost and therefore enforceable. Such conservation measures are typically costly, however. Moreover, they may require diversion of productive land (e.g., for buffers) or impair productivity by interfering with farm operations, thereby reducing the rent generated by the land (see, for example, LaFrance 1992 or Grepperud 1997). Thus, actions of this kind often confront landlords with tradeoffs between current rent and maintenance of productivity in the future.

This article investigates the optimal use of verifiable investments in land productivity under alternative rental contract specifications by landlords aiming to reconcile the conflicting objectives of maximizing rent in the near term versus land value over the longer run when tenants' soil exploitation is unverifiable and thus noncontractible. The problem is thus a multitask principal-agent problem (Baker 1992; Holmstrom and Milgrom 1991; Chambers and Quiggin 2000) in which the principal can take concrete actions (or stipulate enforceably that the agent do so) in addition to providing incentives. We consider optimal investment in land productivity under both cash and share rental contracts. We begin with a model of the case in which both landlord and tenant are risk neutral, so that cash rental contracts would be optimal in the absence of soil degradation problems. We subsequently extend the analysis to the case where tenants are risk averse and then to the case where landlords are risk averse, as may occur in developed countries (Huffman and Just 2004). Finally, we derive implications of the analysis for empirical work.

The Model

We use a modified version of Baker's (1992) multi-task principal-agent model to investigate the landlord's decision problem. We restrict our attention to the class of contracts that depend only on the current soil stock. Current production is a function of effort e, investment in durable conservation measures k, the initial level of soil stock [x.sub.0], and a white noise random element [epsilon](E{[epsilon]} = 0). The present value of output produced during the lease period is R(e, k, [x.sub.0]) + [epsilon]. We assume that it is increasing in effort e and soil stock [x.sub.0], decreasing in durable conservation k, and concave in all three arguments. The soil stock increases the marginal productivity of effort (letting subscripts denote derivatives, [R.sub.ex] > 0). We focus on the interesting case in which soil conservation measures impair current productivity, since landlords will always want to invest in "win-win" measures that increase current productivity while reducing soil degradation over the longer term. We thus assume that current revenue is submodular in effort and conservation, so that [R.sub.ek] < O.

We use an additive specification for the stochastic element in order to focus on pure income risk, abstracting away from production risk (i.e., the effects of effort and investment on output risk); however, it will be apparent that the results carry over to the case of multiplicative risk in which effort increases the riskiness of output as well as average output while conservation investment reduces both (Just and Pope 1978).

The cost of effort to the tenant is C(e). The cost of durable conservation measures is I(k). Both cost functions are assumed to be convex.

The value of the land at the end of the lease period is assumed to be an increasing, concave function of the soil stock at the end of the lease period, [x.sub.1], [beta][V([x.sub.1]) + [eta]], where [beta] is a discount factor and [eta] is a white noise random variable (so that E{[eta]} = 0). Again, we use the assumption of additive risk in order to focus on income risk and abstract away from production risk. The soil stock at the end of the lease period is given by the state equation

(1) [x.sub.1] = [x.sub.0] - h(e, k).

Soil degradation h(e, k) is increasing in effort e, decreasing in durable conservation measures k, and convex in both arguments. Conservation investment reduces marginal degradation due to effort ([h.sub.ek] < 0) as well as degradation in total.

Landlords are assumed to be risk neutral. Competition among tenants for land is assumed to be sufficient to ensure that landlords appropriate all expected rent generated above tenants' reservation utility. All actions are assumed to occur before the state of nature is known, that is, e and k are both chosen before [epsilon] and [eta] are realized. In other words, both productive effort and durable conservation investment are undertaken under uncertainty.

The timing of actions in the model is as follows. Landlords choose conservation investments and offer contract terms for a specified lease period. Once a tenant accepts those contract terms given the level of conservation investment, she exerts effort in production, after which states of nature and thus output and soil degradation are realized. The land reverts to the landlord after termination of the lease.

First-Best Production and Durable Conservation Investment

The first-best combination of productive effort e and durable conservation investment k maximizes the expected value of production during the lease period plus the expected present value of the land at the end of the lease period, less the costs of effort and conservation investment:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The necessary conditions defining this first-best combination are

(3) [R.sub.e] - [C.sub.e] - [beta]V'[h.sub.e] = 0

(4) [R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] = 0.

As is standard, optimal effort [e.sup.*] and durable conservation investment [k.sup.*] are set to equate the marginal net value of production during the lease with the present value of the marginal change in land value at the end of the lease period.

Production and Conservation Investment with Risk-Neutral Tenants

Assume that the tenant is risk neutral. Since effort can neither be observed directly nor inferred from either output or the condition of the land at the end of the lease period, it is noncontractible.

Cash Rental Contract

A cash rental contract induces the tenant to exert first-best effort when only output during the lease period matters. But a cash rental contract induces excessive effort when the condition of the land at the end of the lease period matters as well. The tenant chooses effort to maximize income earned during the lease period, [E.sub.[epsilon]]{R(e, k, [x.sub.0]) + [epsilon]} - C(e) - t, where t denotes the fixed rental payment. The condition characterizing this level of effort is

(5) [R.sub.e] - [C.sub.e] = 0.

The landlord chooses the cash rental payment t and the level of conservation investment k to maximize rent from the lease plus the value of the land at the end of the lease period, less the cost of conservation investment, t - I(k) + [beta][E.sub.n]{V([x.sub.0] - h(e, k)) + [eta]}, subject to the tenant's incentive compatibility and participation constraints:

(6) [e.sup.c] = arg max{[E.sub.e]{R(e, k, [x.sub.0]) + [epsilon]} - C(e) - t}

(7) [E.sub.[epsilon]]{R([e.sup.c], k, [x.sub.0])+ [epsilon]}-C([e.sup.c])-t [greater than or equal to] [u.sub.0]

where [u.sub.0] is the tenant's reservation utility.

The tenant's choice of effort under this contract, [e.sup.c], is implicitly defined by condition (5). It is decreasing in k([partial derivative] [e.sup.c]/[partial derivative]k = [R.sub.ek]/([C.sub.ee] - [R.sub.ee]) < 0 because [R.sub.ek] < 0).

The landlord chooses the cash rental payment so that the participation constraint (7) binds with equality. The landlord's optimal choice of conservation investment under a cash rental contract, [k.sup.c], is then defined by the condition

(8)

[R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] - [beta]V'[h.sub.e] [partial derivative][e.sup.c]/[partial derivative]k

= [R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] - [beta]V'[h.sub.e] [[R.sub.ek]/[C.sub.ee]-[R.sub.ee]] = 0.

To compare the equilibrium levels of effort and conservation investment under a cash rental contract with the corresponding first-best levels, consider a first-order Taylor series approximation to conditions (3) and (4) that define ([e.sup.*], [k.sup.*]) evaluated at the cash rental contract equilibrium ([e.sup.c], [k.sup.c]), which can be solved to yield

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

by the concavity of the objective function (2) in (e, k). It is evident from equation (9) that [k.sup.*] - [k.sup.c] < 0, so that [k.sup.c] > [k.sup.*]. The sign of the right-hand side of equation (10) is indeterminate, however. The first term in braces({}) is positive by the concavity of the objective function (2) in (e, k). The third term in braces is also positive under our assumptions, but the second term is negative. Thus, [e.sup.*] - [e.sup.c] may be either positive or negative, so that [e.sup.c] may be greater or less than [e.sup.*]. We can summarize this result as

PROPOSITION 1. When both landlord and tenant are risk neutral, under cash rental contracts landlords overinvest in durable conservation measures while tenants" effort may be either greater or less than the first best.

Intuitively and in line with the conventional wisdom, tenants exert too much effort because they have no reason to take into account the deleterious effects of current production on the future productivity--and hence value--of land, as is readily seen by comparing conditions (3) and (5) that define effort levels in the first best and cash rental contracts, respectively. Under cash rental contracts, landlords have no means of influencing tenants' effort levels aside from durable conservation measures. Hence, landlords invest more than is socially optimal in these measures in order to curb tenants' overexploitation of land.

Further insight can be obtained by graphical analysis. Let [L.sup.*](k, e) = {(k, e): [R.sub.k]--[I.sub.k]--[beta]V'[h.sub.k] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for first-best conservation investment and [T.sup.*](k, e) = {(k, e): [R.sub.e] - [C.sub.e] - [beta]V'[h.sub.e] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for first-best effort. The first-best equilibrium ([k.sup.*], [e.sup.*]) is an element of both sets, that is, can be found at the intersection of these two loci.

The slope of [L.sup.*] in (k, e) space is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The numerator is positive while the sign of the denominator is indeterminate, since its first term is negative while the second two are positive. The first term of the denominator is the effect of conservation investment on the marginal productivity of effort in current production. We will refer to it as the current productivity effect of conservation. The second two terms of the denominator combined are the effect of conservation investment on the marginal effect of effort on land degradation, that is, on the value of the land at the end of the lease period. We will refer to it as the land value effect of conservation. When the land value effect is greater (in absolute value) than the current productivity effect, [L.sup.*] is upward sloping, and vice versa.

The slope of [T.sup.*] in (k, e) space is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Since the denominator is negative, the slope of [T.sup.*] depends on the relative sizes of the current productivity and land value effects. As with [L.sup.*], when the land value effect is greater (in absolute value) than the current productivity effect, [T.sup.*] is upward sloping, and vice versa. (In other words, [T.sup.*] is upward sloping whenever [L.sup.*] is, and vice versa.) The concavity of the objective function (2) implies that [L.sup.*] is always steeper than [T.sup.*].

Now let [L.sup.c](k, e) = {(k, e): [R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] - [beta]V'[h.sub.e][[R.sub.ek]/([C.sub.ee] - [R.sub.ee])] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for conservation investment under a cash rental contract and [T.sup.c](k, e) = {(k, e): [R.sub.e] - [C.sub.e] = 0} denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for effort under a cash rental contract. Let (k', e') [member of] [L.sup.c] and consider [L.sup.*](k', e'). By the definition of [L.sup.c], [L.sup.*](k', e') = [beta]V'[h.sub.e][[R.sub.ek]/([C.sub.ee] - [R.sub.ee])] < 0. Since [L.sup.*] is decreasing in k, it must be true for k" such that (k", e') [member of] [L.sup.*] that k" < k', which implies that [L.sup.c] lies to the right [L.sup.*] in (k, e) space. Similarly, consider (k', e') [member of] [T.sup.c]. By the definition of [T.sup.c], [T.sup.*](k', e') = - [beta]V'[h.sub.e] < 0. Since [T.sup.*] is decreasing in e, it must be true for e" such that (k', e") [member of] [T.sup.*] that e" < e', which implies that [T.sup.c] lies above [T.sup.*] in (k, e) space.

Figures 1 and 2 compare the cash rental equilibrium with the first best in the cases where the land value and current productivity effects dominate, respectively. It can be seen from figure 1 that when the land value effect dominates, both conservation investment and effort under a cash rental contract exceed the first best. When the current productivity effect dominates, however, it is possible that effort is less than the first best while conservation investment exceeds the first best, as depicted in figure 2. When the land value effect dominates, durable conservation measures do not constitute much of an impediment to the productivity of effort in current production. As a result, even excessive investment in conservation measures does not induce a reduction in effort to the first-best level or less. In contrast, when the current productivity effect dominates, a larger reduction in the productivity of effort in current production is needed to attain any given reduction in marginal land degradation. Landlords' overinvestment in conservation, undertaken in order to curb tenants' incentives to overexploit land, may reduce the current productivity of effort enough that effort falls below the first best (figure 2).

[FIGURES 1-2 OMITTED]

Share Rental Contract

Share rental contracts can serve as a device for landlords to protect their land against degradation by mitigating tenants' incentives to overexploit soils. The marginal return to effort is lower under a share contract than under a cash rental contract because tenants appropriate only part of the rent generated during the lease period. Formally, let s denote the share of the rent kept by the tenant, so that the tenant's return during the lease period is s[R(e, k, [x.sub.0]) + [epsilon]] - C(e). The tenant's optimal choice of effort is thus defined implicitly by

(11) [R.sub.e]-[C.sub.e] =(1-s)[R.sub.e].

When investment in durable conservation measures is infeasible (so that k = 0), it is evident from a comparison of conditions (5) and (11) that the tenant's optimal choice of effort is lower under a share rental contract than a cash rental contract.

More generally, consider the landlord's choice of contract terms under a share rental system when investment in durable conservation measures is infeasible; this is a two-period version of the case analyzed by Dubois (2002). The landlord's objective is to choose the tenant's share s and fixed payment t to maximize

(12) (1 - s) [E.sub.[epsilon]] {R(e, O, [x.sub.0]) + [epsilon]} + t + [beta] [E.sub.[eta]]{V([x.sub.0] - h(e, 0)) + [eta]}

subject to the tenant's incentive compatibility and participation constraints,

(13) [e.sup.s] = arg max{s [E.sub.[epsilon]] {R(e, O, [x.sub.0]) + [epsilon]} - t - C(e)}

(14) s[E.sub.[epsilon]] {R(e, O, [x.sub.0]) + [epsilon]} - t - C(e) [greater than or equal to] [u.sub.0]

respectively. It follows from condition (11), which characterizes the tenant's optimal choice of effort, that effort is increasing in the tenant's share ([partial derivative][e.sup.s]/[partial derivative][e.sup.s] = [R.sub.e]/[[C.sub.ee] - s[R.sub.ee]] > 0).

The landlord chooses the fixed payment or wage so that the participation constraint binds. The landlord's optimal choice of the tenant's share satisfies

(15) ([R.sub.e] - [C.sub.e] - [beta]V'[h.sub.e]) [partial derivative]e/[partial derivative]s = 0

which implies, after substitution from condition (11), that

(16) [s.sup.s] = 1 [beta]V'[h.sub.e]/[R.sub.e].

The tenant's share of output is adjusted downward in order to make the tenant face the marginal cost of land degradation, i.e., the marginal reduction in the value of the land at the end of the lease period per unit of output during the lease period, [beta]V'[h.sub.e]/[R.sub.e].

Condition (15) characterizes the tenant's optimal choice of effort, [e.sup.s], as can be seen by substituting condition (16) into condition (11). It differs from condition (3) in that k = 0 (compared to k > 0 in the first best). Comparison of conditions (3) and (15) indicates that effort under a share rental contract without conservation investment will exceed the first best: The marginal return to effort during the lease period [R.sub.e] is higher than the first best because [R.sub.ek] < 0 while the marginal reduction in land value at the end of the lease period is lower because [h.sub.ek] < 0 and V" < 0. We thus have

PROPOSITION 2 (Dubois 2002). When both landlord and tenant are risk neutral, under a share rental contract with no conservation investment, effort and land degradation are lower than under a cash rental contract with no conservation investment but exceed the first best.

When investment in durable conservation measures is feasible, the landlord's objective is to choose the tenant's share s, fixed payment t, and level of conservation investment k to maximize

(12') (1- s)[E.sub.[epsilon]] {R(e,k, [x.sub.0]) + [epsilon]} + t - I(k) + [beta][E.sub.[eta]]{V([x.sub.0] - h(e, k)) + [eta]}

subject to the tenant's incentive compatibility and participation constraints,

(13') [e.sup.f] = arg max{s [E.sub.[epsilon]] {R(e, k, [x.sub.0]) + [epsilon]} - t - C(e)}

(14') s[E.sub.[epsilon]] {R(e, k, [x.sub.0]) + [epsilon]} - t - C(e)} [greater than or equal to] [u.sub.0]

respectively. As before, the tenant's optimal choice of effort is increasing in the tenant's output share ([partial derivative][e.sup.f]/[partial derivative]s = [R.sub.e][[C.sub.ee] - s[R.sub.ee]] > 0) and decreasing in conservation investment ([partial derivative][e.sup.f]/ [partial derivative]k = s[R.sup.ek]/[[C.sub.ee] - s[R.sub.ee]] > 0).

The landlord again chooses the fixed payment or wage so that the participation constraint binds. The landlord's optimal choice of the tenant's share satisfies

(15') ([R.sub.e] - [C.sub.e] - [beta]V'[h.sub.e]) ([partial derivative]e/[partial derivative]s = 0.

The landlord's optimal choice of conservation investment satisfies

(17) ([R.sub.e] - [C.sub.e] - [beta]V'[h.sub.e]) ([partial derivative]e/[partial derivative]k + [R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] = 0

which, after substitution from equation (15'), becomes

(17') [R.sub.k] - [I.sub.k] - [beta]V'[h.sub.k] = 0

It is readily apparent that conditions (15') and (17') are identical to conditions (3) and (4). We thus have:

PROPOSITION 3. When both landlord and tenant are risk neutral, share rental contracts combined with investment in durable conservation measures are capable of achieving first-best effort and conservation.

Intuitively, share rental contracts provide landlords with three instruments to influence land degradation: investment in durable conservation measures k, the output share s, and the fixed payment t. Combining investment in durable conservation measures with the rental share gives landlords two instruments for influencing effort and conservation while the fixed payment is used to ensure that the tenant receives her reservation utility. Because the number of instruments equals the number of objectives, it is feasible to attain the first best.

Production and Conservation Investment with Risk-Averse Tenants

When tenants are risk averse and effort is non-contractible, landlords face a tradeoff between insurance and incentives. The first-best contract features paying the tenant a wage sufficient to equate the expected utility of income with the tenant's reservation utility, [u.sub.0], with effort and conservation investment set at the same levels as under risk neutrality, ([k.sup.*], [e.sup.*]). But when effort is noncontractible, a fixed wage provides insurance but too little incentive to exert effort while a cash rental contract provides incentive for effort but no insurance; share rentals offer a compromise between income insurance and incentives to exert effort.

Consider a share rental contract with the tenant's output share s and a fixed payment t, so that the tenant's income during the lease period is s[R(e, k, [x.sub.0]) + [epsilon]] - t - C(e). Let U(*) be the tenant's utility of income, concave in income as usual. The tenant's level of effort is chosen to maximize the expected utility of income earned during the lease period, [E.sub.[epsilon]]{U(s[R(e, k, [x.sub.0]) + [epsilon]] - t - C(e))}. Condition (11) characterizes this choice due to the additive stochastic specification. Thus, the tenant's effort is independent of the fixed payment t, increasing in the output share s([partial derivative]e/[partial derivative]s = [R.sub.e]/(s[R.sub.ee] - [C.sub.ee])), and decreasing in conservation investment k([partial derivative]e/[partial derivative]k = - S[R.sub.ek]/(s[R.sub.ee] - [C.sub.ee])) as before.

The landlord chooses contract terms s and t plus investment in durable conservation measures k to maximize

(18) (1 - s)[E.sub.[epsilon]]{R(e, k, [x.sub.0]) + [epsilon]] + t - I(k) + [beta][E.sub.[eta]]{V([x.sub.0] - h(e,k)) + [eta]}

subject to the tenant's incentive compatibility and participation constraints,

(19) [e.sup.r] = arg max{[E.sub.[epsilon]]{U(s R(e, k, [x.sub.0]) - t - C(e)}}

(20) [E.sub.[epsilon]]{U(s[R(e, k, [x.sub.0]) - t - C(e))] [greater than or equal to] [u.sub.0],

respectively.

As before, the landlord chooses the fixed payment so that the participation constraint binds. The condition characterizing landlord's optimal choice of the tenant's share can be shown to be

(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Substituting condition (11), condition (21) implies that the optimal share satisfies

(22) [s.sup.r] = [beta]V'[h.sub.e]/[R.sub.e] + [rho]([C.sub.ee] - [s.sup.r] [R.sub.ee])/[R.sub.2.sub.e]

where [rho] [equivalent to] [E.sub.[epsilon]](U'[epsilon]}/[E.sub.[epsilon]](U'}, the correlation between the random factor [epsilon] and the marginal utility of income, is negative due to risk aversion. As in the case of risk neutrality, the tenant's share of output is adjusted downward in order to make the tenant face the marginal cost of land degradation. The tenant's share is adjusted downward further by the factor p ([C.sub.ee] - s[R.sub.ee])/[R.sup.2.sub.e] in order to mitigate the disincentive effects of risk on effort.

The condition characterizing the landlord's optimal choice of conservation investment is

(23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where h is the shadow price of the tenant's participation constraint (20) and the simplification results from the fact that the firstorder condition for the fixed payment t implies [lambda][E.sub.[epsilon]]{U'} = -1. As in the case of a cash rental contract with a risk-neutral tenant, the landlord's investment in durable conservation measures is adjusted to take into account its effects on the tenant's effort in production during the lease period. In contrast to the case of a cash rental contract with a risk-neutral tenant, the adjustment aims at increasing effort, which tends to be excessively low due to risk aversion and the use of risk sharing in the face of moral hazard.

Conditions (21) and (23) together define the equilibrium levels of conservation investment [k.sup.r] and effort [e.sub.r] under this contract. It is clear that they are not equivalent to conditions (3) and (4), which define the first-best levels of conservation investment and effort even when tenants are risk averse. We thus have:

PROPOSITION 4. When tenants are risk averse, share rental contracts combined with investment in durable conservation measures are not capable of achieving first-best effort and conservation.

To compare the equilibrium levels of conservation investment and effort under a share rental contract with the first best when tenants are risk averse, consider a first-order approximation to conditions (3) and (4) around the equilibrium levels of conservation and effort under the share rental contract, ([k.sup.r], [e.sup.r]), which can be solved to yield

(24) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(25) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The sign of [k.sup.*] - [k.sup.r] is indeterminate, indicating that landlords may either over- or underinvest in durable conservation measures. In contrast, [e.sup.*] - [e.sup.r] is positive, indicating that effort is always less than the first best, as one would expect.

Further insight can again be obtained by graphical analysis. Let [L.sup.r](e, k) denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for conservation investment (23) and [T.sup.r](k, e) denote the set of combinations of conservation investment and effort levels satisfying the necessary condition for effort (21). Let (k', e') [member of] [L.sup.c] and consider [L.sup.*](k', e'), the set of conservation investment and effort levels that satisfy the necessary condition for first-best effort under risk neutrality. By the definition of [L.sup.c], [L.sup.*](k', e') = [rho]s[R.sub.ek]/[R.sub.e] > 0. Since [L.sup.*] is decreasing in k, it must be true for k" such that (k", e') [member of] [L.sup.*] that k" > k', which implies that [L.sup.c] lies to the left of [L.sup.*] in (k, e) space. Similarly, consider [T.sup.*], the set of conservation investment and effort levels that satisfy the necessary condition for first-best conservation investment under risk neutrality, evaluated at (k', e') [member of] [T.sup.r]. By the definition of [T.sup.r], [T.sup.*](k', e') = [rho](s[R.sub.ee]--[C.sub.ee])/[R.sub.e] > 0. Since [T.sup.*] is decreasing in e, it must be true for e" such that (k', e") [member of] [T.sup.*] that e" > e', which implies that [T.sup.c] lies below [T.sup.*] in (k, e) space.

Figures 3 and 4 compare the share rental equilibrium with the first best under risk neutrality in the cases where the land value and current productivity effects dominate, respectively. It can be seen from figure 3 that when the land value effect dominates, both conservation investment and effort under a share rental contract with a risk-averse tenant are less than the first best. When the current productivity effect dominates, however, it is possible that conservation investment exceeds the first best while effort is less than the first-best level, as depicted in figure 4.

[FIGURES 3-4 OMITTED]

As before, share rental contracts with risk-averse tenants provide landlords with three instruments to influence land degradation: investment in durable conservation measures k, the output share s, and the fixed payment t. The output share and fixed payment combined influence land degradation indirectly by determining the tenant's level of income risk, which influences effort. The need to use risk sharing to counteract moral hazard results in a level of effort lower than that which maximizes the value of output during the lease period--although it may be higher than the first-best level when land degradation is taken into account. Investment in durable conservation measures lowers the marginal productivity of effort in current production and thus serves to reduce effort further. As a result, effort is always lower than the first best. As with risk-neutral tenants, the optimal output share is adjusted downward by a factor equal to [beta] V'[h.sub.e]/[R.sub.e]. When the land value effect dominates, a change in conservation investment lowers this adjustment factor; when the current productivity effect dominates, a change in conservation investment increases it. Thus, when the land value effect exceeds the current productivity effect, the landlord relies more heavily on output sharing, inducing a risk effect that lowers effort and thus the need for conservation investment. But when the current productivity effect exceeds the land value effect, the landlord relies less heavily on output sharing and may thus need to increase conservation investment above the first-best level in order to limit land degradation.

Production and Conservation Investment with Risk-Averse Landlords

In developed countries like the United States (and in contrast to developing countries), many farm landlords are retired farmers, the spouses of deceased farmers, or absentee landlords, all of whom can be plausibly characterized as risk averse (Huffman and Just 2004). It turns out that the results of the preceding sections carry over qualitatively to situations where landlords are risk averse.

First-Best Effort and Conservation Investment

The first-best levels of effort and conservation ([e.sup.**], [k.sup.**]) in this case maximize [E.sub.[epsilon]]{W(R(e, k, [x.sub.0]) + [epsilon] - C(e) - I(k))} + [beta] [E.sub.[eta]]{W(V([x.sub.0] - h(e, k)) + [eta])} where W(.) is the landlord's utility of income, assumed concave and stationary over time. The necessary conditions characterizing the first-best levels of effort and conservation investment for a risk-averse landlord are

(26) [E.sub.[epsilon]{W'}([R.sub.e] - [C.sub.e])} - [beta][E.sub.[eta]]{W'}}V'[h.sub.e] = 0

(27) [E.sub.[epsilon]{W'}([R.sub.k] - [I.sub.k])} - [beta][E.sub.[eta]]{W'}}V'[h.sub.k] = 0

These conditions differ from those of a risk-neutral landlord only in weighting income during the lease period and land value at the end of the lease period differently. Specifically, one would expect the expected marginal utility of income during the lease period [E.sub.[epsilon]]{W'} to exceed the expected marginal utility of the value of land at the end of the lease period [E.sub.[eta]]{W} because the value of land V(*) likely exceeds income generated during the lease period R(*) - C(*) - I(*), suggesting that risk-averse landlords prefer greater effort and less conservation investment than risk-neutral landlords.

Cash Rental Contract

If tenants are risk neutral, risk-sharing considerations suggest the optimality of cash rental contracts. Under a cash rental contract, the tenant's level of effort [e.sup.ca] is defined by equation (5). The landlord chooses the cash rental payment [t.sup.ca] so that the participation constraint (7) binds with equality. The landlord's optimal choice of conservation investment [k.sup.ca] is then defined by the condition

(28) [E.sub.[epsilon]{W'}([R.sub.k] - [I.sub.k])} - [beta][E.sub.[eta]]{W'}V' ([h.sub.k] + [h.sub.e] [partial derivative][e.sup.ca]/[partial derivative]k) = 0

which is the same as equation (8) except for the differential weighting of income during the lease period compared to land value at the end of the lease period. A first-order Taylor series approximation to the equilibrium conditions (5) and (28) yields expressions for ([k.sup.**] - [k.sup.ca]) and ([e.sup.**] - [e.sup.ca]) equivalent to equations (9) and (10), respectively, with [E.sub.[eta]]{W'V'} replacing V', [[E.sub.[eta]]{W"(V').sup.2] + W'V"} replacing V", and the second-order condition for the first best under risk aversion replacing [OMEGA]. We thus have:

PROPOSITION 5. When the landlords are risk averse and tenants are risk neutral, under cash rental contracts landlords overinvest in durable conservation measures while tenants' effort may be either greater or less than the first best.

It follows that the graphical analyses in figures 1 and 2 also illustrate the comparison of the cash rental equilibrium with the first best in the case of risk-averse landlords.

Cash rental contracts achieve optimal risk sharing when landlords are risk averse but do nothing to attenuate tenants' incentives for overexploiting soils. As before, landlords have no means of influencing tenants' effort levels other than installing or requiring durable conservation measures and thus overinvest in these measures in order to limit excessive land degradation.

Share Rental Contract

When landlords are risk averse and tenants are risk neutral, risk-sharing considerations suggest that share rental contracts would be suboptimal. But share rental contracts also attenuate tenants' incentives for exerting effort and hence overexploiting the land. As in the case of risk-neutral landlords, adding rent sharing to the set of instruments at the landlord's disposal permits attainment of the first best. The tenant's optimal level of effort, [e.sup.fa], is characterized by equation (11) as before. The landlord chooses the fixed payment [t.sup.fa] to ensure that the tenant's participation constraint (14') binds with equality. The landlord's respective optimal choices of the tenant's share [s.sup.fa] and conservation investment [k.sup.fa] then satisfy the conditions

(29) [[E.sub.[epsilon]] {W'} ([R.sub.e] - [C.sub.e]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.e]] [partial derivative]e/[partial derivative]s = 0

(30) [E.sub.[epsilon]] {W'} ([R.sub.k] - [I.sub.k]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.k]] + [[E.sub.[epsilon]] {W'} ([R.sub.e] - [C.sub.e]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.e]] [partial derivative]e/[partial derivative]k = 0.

As in the risk-neutral case, it is readily apparent that conditions (29) and (30) are equivalent to conditions (26) and (27), respectively. We thus have:

PROPOSITION 6. When the landlords are risk averse and tenants are risk neutral, share rental contracts combined with investment in durable conservation measures are capable of achieving first-best levels of effort and conservation.

The optimal share allocated to the tenant is

(31) [s.sup.fa] = 1 - [E.sub.[eta]]{W'}/[E.sub.[epsilon]]{W'} [beta] V'[h.sub.e]/[R.sub.e]

a close analog of equation (16) with the adjustment for the marginal cost of land degradation [beta] V'[h.sub.e]/[R.sub.e] weighted by the marginal utility of wealth at the end of the lease period relative to the marginal utility of income during the lease period. The arguments above suggest that this ratio is less than one, so that the tenant's share is higher when the landlord is risk averse than when the landlord is risk neutral. Such an outcome is as one would expect, since if overexploitation of soil were not an issue it would be optimal to make the tenant the residual claimant of all income during the lease period.

Risk-Averse Tenants

When both landlord and tenant are risk averse, one would expect to find share rental contracts. As in the case of a risk-neutral landlord, the tenant's incentive compatibility and participation constraints are given by conditions (19) and (20). The landlord chooses the fixed payment [t.sup.ra], the rental share [s.sup.ra], and the level of conservation investment [k.sup.ra] to maximize [E.sub.[epsilon]]{W((1 - s)[R(e, k, [x.sub.0]) + [epsilon]] + t - 1(k))} + [beta][E.sub.[eta]]{W(V([x.sub.0] - h(e, k)) + [eta])} subject to conditions (19) and (20). As before, the landlord chooses the fixed payment so that the participation constraint binds. The respective conditions characterizing the landlord's optimal choices of the tenant's share and conservation investment can be shown to be

(32) [E.sub.[epsilon]]{W'} ([R.sub.e] - [C.sub.e]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.e]] [R.sub.e] / [C.sub.ee] - s [R.sub.ee] + [E.sub.[epsilon]]{W'} ([tau] + [rho]) = 0

(33) [E.sub.[epsilon]]{W'} ([R.sub.k] - [I.sub.k]) - [beta] [E.sub.[eta]] {W'} V' [h.sub.k]] - [E.sub.[epsilon]]{W'} ([tau] + [rho]) s [R.sub.ek]/[R.sub.e] = 0

where [tau] = [E.sub.[epsilon]] {W' [epsilon]}/[E.sub.[epsilon]] {W'} is the correlation between the random factor [epsilon] and the landlord's marginal utility of income.

It is clear that equations (32) and (33) are not equivalent to equations (26) and (27), hence:

PROPOSITION 7. When the landlords and tenants are both risk averse, share rental contracts combined with investment in durable conservation measures are not capable of achieving first-best levels of effort and conservation.

The intuition here is the same as in the risk-neutral landlord case. The three instruments available to the landlord are not sufficient to meet the four objectives of optimal risk sharing, effort, conservation, and ensuring that the tenant receives her reservation utility.

The optimal share allocated to the tenant in this case is

(34) [s.sup.ra] = 1 - [beta] [E.sub.[eta]] {W'} V' [h.sub.e]/[E.sub.[epsilon]] {W'} [R.sub.e] + ([tau] + [rho]) ([C.sub.ee] - [s.sup.ra][R.sub.ee])/[R.sup.2.sub.e].

As in the case of a risk-averse tenant and risk-neutral landlord, the tenant's share is adjusted downward to make the tenant face the marginal cost of land degradation and to mitigate the disincentive effect of risk on effort. In this case, though, the latter adjustment takes into account the landlord's risk aversion as well as the tenant's.

Finally, the close similarity of equations (32) and (33) to equations (21) and (23) suggests that, as in the case of a risk-neutral landlord and risk- averse tenant, effort under the share rental contract is less than the first best for a risk- averse landlord while conservation effort may be greater or smaller than the first best and that figures 3 and 4 illustrate the possible equilibrium outcomes in this case.

Implications for Empirical Work

Propositions 1-7 indicate that landlords' choices of rental contract form and investment in durable conservation measures are more complex than those predicted on the basis of tenants' incentives alone. When landlords and tenants are both risk neutral, the analysis suggests that there should be no difference in conservation investments made by owner-operators and those made under share rental contracts, while those made under cash rental contracts should be higher than those made under share rental contracts or under owner operation. The same patterns apply when both landlords are risk averse and tenants are risk neutral--except that the level of conservation investment is likely to be lower than under risk neutrality, for reasons of risk bearing alone. And when tenants are risk averse, conservation investment under rental contracts may be higher or lower than under owner operation.

These differences in performance suggest that rental contract choice and conservation investment are more appropriately treated as simultaneous choices, that is, the choice of whether to rent as well as the form of rental contract should be treated as endogenous rather than exogenous. To see why, consider the case where both landlord and tenant are risk neutral. (The analysis is easily extended to cases involving risk aversion.) Let [W.sup.f] and [W.sup.c] be the landlord's expected present value of income under share and cash rental contracts, respectively, with optimal conservation investment and contract terms and [W.sup.s] be the landlord's maximized expected present value of income under a share with no conservation investment. Let [m.sup.f], [m.sup.c], and [m.sup.s] be the respective transaction costs associated with these contract specifications; they cover such items as the costs of verifying output (in the case of share contracts) and collecting rent, differences in the tax treatment of income and property, etc. For simplicity, assume they are independent of the maximized value of income, so that the present value of expected net income under contract type j = f, c, s is [W.sup.j] = [m.sup.j]

The landlord selects the contract that generates the highest present value of expected net income. Suppose, for example, that conservation investment is contractible and not prohibitively costly, so that [W.sup.f] - [m.sup.f] > [W.sup.s] - [m.sup.s]. In this case the landlord chooses a cash rental contract when [W.sup.c] - [m.sup.c] > [W.sup.f] - [m.sup.f]. Since [W.sup.f] > [W.sup.c] by propositions (1) and (3), the landlord will choose a cash rental contract only when [m.sup.f] - [m.sup.c] > [W.sup.f] - [W.sup.c] > 0, share rental contracts have higher transaction costs than cash rental contracts and the difference in transaction costs between the share and cash rental contracts with optimal conservation investment exceeds the difference in the present value of expected income.

One implication of this analysis is that correlations between rental status and conservation investment observed in empirical studies may be biased by endogenous matching, as has been shown to occur in empirical studies of agency and risk (see, for example, Prendergast 2002 or Ackerberg and Botticini 2002). (1) The empirical findings of Allen and Lueck (1992) and Dubois (2002) provide support for treating contract choice as endogenous. Both studies found that share rental contracts are more prevalent than cash rental contracts or owner operation in situations where land is highly vulnerable to degradation. Future studies of the impacts of tenure on conservation practice adoption should thus at least test for the endogeneity of contract choice.

The conditions for landlords to prefer cash to share rental contracts are more likely to be met when the tenant's optimal share under a share rental contract, [s.sup.f] = [s.sup.s], is close to 1, so that the share rental contract closely resembles a cash rental contract. By equation (16), the tenant's optimal share is close to 1 when [beta] V'[h.sub.e]/[R.sub.e] is close to zero. This analysis suggests certain hypothesis about likely correlations between contract terms and conservation investment. Landlords are more likely to offer cash rental contracts with investments in durable conservation measures in areas where land is less sensitive to soil degradation (V' is small), soils are less vulnerable to degradation ([h.sub.e] is small), and conservation measures are relatively cheap (I(k) is small for all k). Conversely, they are more likely to offer share rental contracts combined with investments in durable conservation measures in areas where the value of land is highly sensitive to soil degradation (V' is large) and soils are highly vulnerable to degradation ([h.sub.e] is large). They are more likely to offer share rental contracts without investments in durable conservation measures or operate land themselves in areas where the value of land is highly sensitive to soil degradation and soils are highly vulnerable to degradation but where durable conservation measures are either physically inappropriate ([h.sub.k] is small in magnitude for all k) or excessively costly (I(k) is large for all k), so that [W.sup.s] - [m.sup.s] > max{[W.sup.f] - [m.sup.f], [W.sup.c] - [m.sup.c]}.

Conclusion

The impact of tenancy on investment in soils has concerned economists from earliest days of the discipline. It has long been argued that tenants tend to overexploit land, but that conventional wisdom has been derived largely without consideration of landlords' actions, which are the focus of this article. Previous studies have shown that share contracts can mitigate tenants' overexploitation of soil and provide empirical evidence indicating that landlords prefer share contracts on land at greater risk of degradation (Allen and Lueck 1992; Dubois 2002). We examine what happens when landlords can invest in durable conservation measures (or enforceably stipulate that tenants do so) in addition to choosing between cash rentals, share rentals, and owner operation. We show that when tenants are risk neutral, landlords overinvest in conservation under cash rental contracts but can achieve first-best levels of output and protection against land degradation when conservation investment is combined with share rental. When tenants are risk averse, however, the first best is unattainable. Conservation investment combined with share rental results in output levels below the first best, while equilibrium conservation investment may be greater or less than the first best.

These results imply that contract form and conservation investments are likely made simultaneously, so that econometric studies of conservation practice adoption that treat rental status as exogenous are likely subject to selection bias. For that reason, future empirical studies of conservation investment should consider tenure status as potentially endogenous.

A final note: The model analyzed in this article assumes that competition among tenants is sufficient to permit landlords to appropriate the full rent generated during the lease period. In some areas, though, there may be more competition among landlords for suitable tenants than the reverse (e.g., areas in developed countries with aging and declining farm populations). A formal analysis of this case is beyond the scope of this article. Intuitively, though, one might expect bargaining between landlords and tenants in such situations to give tenants a share of the long run gains from soil conservation, conceivably enough to attain first-best levels of both effort and conservation investment even under cash rental contracts. Further examination of this case is likely to be of interest.

I am grateful for the helpful suggestions of Bob Chambers, Ramon Lopez, Tigran Melkonyan, Lars Olson, and three anonymous Journal reviewers. Responsibility for any errors is mine alone.

[Received April 2005; accepted July 2006.]

References

Ackerberg, D.A., and M. Botticini. 2002. "Endogenous Matching and the Determinants of Contract Form." Journal of Political Economy 110:564-90.

Allen, D., and D. Lueck. 1992. "Contract Choice in Modern Agriculture: Cash Rent versus Crop-share." Journal of Law and Economics 35:397-426.

Baker, G. 1992. "Incentive Contracts and Performance Measurement." Journal of Political Economy 100:598-614.

Bardham, P. 1984. Land, Labor, and Rural Poverty: Essays in Development Economics. New York: Columbia University Press.

Chambers, R.G., and J. Quiggin. 2000. Uncertainty, Production Choice, and Agency. New York: Cambridge University Press.

Dubois, P. 2002. "Moral Hazard, Land Fertility and Sharecropping in a Rural Area of The Philippines." Journal of Development Economics 68:35-64.

Grepperud, S. 1997. "Soil Conservation as an Investment in Land." Journal of Development Economics 54:455-67.

Holmstrom, B., and P. Milgrom. 1991. "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design." Journal of Law, Economics, and Organization 7:24-52.

Huffman, W.E., and R.E. Just. 2004. "Implications of Agency Theory for Optimal Land Tenure Contracts." Economic Development and Cultural Change 52:617-42.

Johnson, D.G. 1950. "Resource Allocation under Share Contracts." Journal of Political Economy 58:111-23.

Just, R., and R.T. Pope. 1978. "Stochastic Specification of Production Functions and Economic Implications." Journal of Econometrics 7:67-86.

LaFrance, J.T. 1992. "Do Commodity Prices Lead to More or Less Soil Degradation?" Australian Journal of Agricultural Economics 36:57-82.

Lichtenberg, E. 2004. "Cost-Responsiveness of Conservation Practice Adoption: A Revealed Preference Approach." Journal of Agricultural and Resource Economics 29:420-35.

Lynne, G.D., J.S. Shonkwiler, and L.R. Rola. 1988. "Attitudes and Farmer Conservation Behavior." American Journal of Agricultural Economics 70:12-19.

McConnell, K.E. 1983. "An Economic Model of Soil Conservation." American Journal of Agricultural Economics 65:83-89.

Myrra, S., E. Ketoja, M. Yli-Halla, and K. Pietola. 2005. "Land Improvements under Land Tenure Insecurity: The Case of pH and Phosphate in Finland." Land Economics 81:557-69.

Prendergast, C. 2002. "The Tenuous Trade-off between Risk and Incentives." Journal of Political Economy 110:1071-1102.

Soule, M.J., A. Tegene, and K.D. Wiebe. 2000. "Land Tenure and the Adoption of Conservation Practices." American Journal of Agricultural Economics 82:993-1005.

(1) Most empirical studies of soil conservation investment focus on conservation tillage, which typically lowers operating cost and hence should be a "win-win" option equally attractive to both landlords and tenants, all else equal. The few studies that examined durable conservation investments obtained somewhat contradictory results. Lynne, Shonkwiler, and Rola (1988) found that Florida growers who rented part (but not all) of the land they operated used a larger number of durable conservation practices than either pure renters or pure owner-operators but no significant difference in conservation practice adoption between pure renters and pure owner-operators. Lichtenberg (2004) found that the share of operated land rented by Maryland farmers had no statistically significant influence on the likelihood of adopting any of seven durable conservation measures. Myrra et al. (2005) found statistically significant differences between soils in owned and leased land in soil pH in all of Finland and in soil phosphorus in northern, but not southern Finland. Soule, Tegene, and Wiebe (2000) found statistically significant differences in the likelihood of one or more of three durable conservation practices between owner-operators, share renters, and cash renters. A comparison of predicted adoption probabilities calcul