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).