Farm Operating Risk and Cash Rent Determination

Abstract

This article examines farm operating risks and cash-rent determination through the use of the efficient set mathematics. The efficient set mathematics proves to be a pragmatic approach to characterizing operating risks, and the relationships between operating risks and cash-rent determination. Various separation theorems are used to postulate the relationship between operating risk and cash rents. Preliminary evidence appears to support the theoretical conclusion that operating risk and cash-rent determination are related. Under the assumption of homogeneous risk preferences, classical economic theory suggests that exogenous market forces and land productivity characteristics will set a single cash-rental value of land. There are numerous studies which have examined how land rentals vary within a region according to these exogenous factors (Ketchabaw and van Vuuren). However, if risk preferences are heterogeneous, then it is unlikely that market forces will determine a single cash rent. Although the theory of cash rent for agricultural land generally has not been cast in a stochastic framework, Johnson, and Collins and Barry have done so in the context of a generalized two-parameter single index model. These studies illustrate the fact that including cash rent in an expected value-variance (EV) framework does provide an effective approach to leveraging risk. In particular, it is shown that an EV frontier with riskless cash-rented land is linear and dominates all but one portfolio without cashrented land. However, it is important to recognize that these studies treat the cash rental rates as exogenous, and implicitly assume that the optimum portfolio choice is conditioned on this exogenous rate, an assumption which is sufficient but not necessary. The purpose of this article is to examine the relationship between risky and riskless cash-renting land and farm enterprise selection. Using the efficient set mathematics as an analytical tool, we examine various aspects of the cash-rent problem which extend the traditional Ricardian model to endogenous rent determination under risk, and alternative land tenure arrangements. In the first section, efficient set formulas are described which provide solutions to the primal and dual risk-minimizing problems. 1 The formulas are similar to those found in Roll (1977, 1980) and require only a basic knowledge of matrix algebra. The efficient set framework is then applied to cash-renting land. The results show that an exogenous cash rental rate will determine the portfolio proportions of independent risk preferences while an endogenous cash rent will be determined by the selection of crop mixes which are dependent on risk preferences. In the section preceding the conclusions, a simple econometric model is developed to provide evidence that the fundamental relationships among cash rent, risk, and return hold in practice.