THE LOSS OF AGRICULTURAL LAND. A REPLY 81

UNCERTAINTY, IRREVERSIBILITY AND THE LOSS OF AGRICULTURAL LAND: A REPLY

Ian Hodge

University of Cambridge* Kennedy has suggested two alternative approaches to the problem of making irreversible decisions about land use in the face of uncertainty. The first essentially maintains the framework adopted in my original paper and the second treats it as a dynamic programming problem. The purpose of this reply is to examine the reworking of the original example and to discuss the plausibility of the decision structure.

Kennedy correctly points out that the original criterion of minimising the maximum expected loss does not imply risk neutrality. He goes on to suggest an alternative approach, analysing the second decision stage, at year 20, first. In doing so, he takes the value of P at year 20 as being equal to P, or $1. But if the value of Po = $1, given the growth rates of (g) and their respective probabilities (p) indicated in Table 1, then the expected value of P,, = 1.021. It is thus necessary to adjust the value of the preservation option for each growth rate to take account of the first 20 year period. The results with a 10 per cent discount rate are shown in Table 1.

Table 1 Adjusted Optimal Stage-2 Decisions and Returns

Growth Probability Present Value of Returns ($) Optimal Rate Expected

Return

0.02 0.1 18.946 10.00 18.946 1.895 (gl f P ) Preserve Develo-o Optimal (8

~~. 0.01 0.1 13.693 10.00 13.693 1.369 0.005 0.2 11.689 10.00 11.689 2.338 0.00 0.2 10.00 10.00 10.00 2.000

-0.005 0.2 8.572 10.00 10.00 2.OOo -0.01 0.1 7.361 10.00 10.00 1.000

1 .Ooo -0.02 0.1 5.452 10.00 10.00 -

The present value from year 1 is then calculated by adding the expected value of preservation for 20 years and the optimal present value of expected returns over all growth rates from Stage 2 onwards. This might be referred to as the

resent value of optimal preservation. The adjusted value here is $8.550 + $11.602/1.120 = $10.275. Kennedy then calculates a ‘Preservation Bias Factor’ as the amount which, when multiplied by the expected value of preservation returns, equals the present value of optimal preservation. In the example he divides the present value of optimal preservation by 10. But the expected value of preservation returns is not equal to 10, but 10.125. This is given by:

* Department of Land Economy, University of Cambridge, 19 Silver Street, Cambridge CB3 9EP.

82 IAN HODGE

This gives a preservation bias factor of $10.275/$10.125 = 1.0148. Making the same adjustments for the 5 per cent discount rate gives a preservation bias factor of $21.981/$21.060 = 1.0437. Incidentally, Kennedy discounts to year 1, while the original example discounted to year 0, but this makes little difference to the results.

This approach illustrates an alternative way of looking at the problem. This is to calculate the expected value of information (Conrad, 1980) which can only be realised if the initial decision is reversible. From Table 1, it can be seen that information has value arising from a decision to develop at Stage 2 where the growth rate is negative. This is equal to the present value of returns from development, less the present value of returns from preservation for each of the three negative growth rates, multiplied by their respective probabilites. This would then be discounted back to the present time.

Kennedy is also critical of the ‘improbable’ decision structure in the original approach. It was, of course, an extreme simplification intended to capture the essentials of the problem and the implications of the assumptions are discussed in the original paper. First, Kennedy argues that ‘Future returns are never known with certainty’. Nevertheless, in his own example he takes the annual return to development to be ‘assumed equal to $1 with certainty’. Second, and more importantly, he argues that there would normally be the option of postponing the development decision for periods of less than 20 years and suggests that it would be more natural to assume that the decision will be re- evaluated at the beginning of each year into the future. This raises two points. The original decision structure does not oblige the decision-maker to wait 20 years before the decision can be re-evaluated, but rather that 20 years must pass before the full information becomes available. Even so, in practice land- owners almost invariably do not have a free choice as to whether or not to develop agricultural land and thus cannot review the decision on an annual basis. Changes in land use are the subject of planning control. Opportunities for development are likely to occur infrequently in relation to wider planning policies, such as embodied in structure plans, green belt legislation or zoning ordinances, and, within that framework, to depend upon planning applications and appeals.

Despite all this, Kennedy’s suggestions are generally helpful. His reworking of the original problem provides a clearer exposition of the issue; the use of dynamic programming can provide a framework for exploring the implications of alternative assumptions in the context of specific decisions. None of these approaches can ‘solve’ the problem which incorporates a wide range of particularly contentious questions, such as involving the choice of discount rate, intergenerational equity and the ethics of the maintenance of the resource base, as well as a lack of relevant data. Irres ective of the availability of standard computer routines for analysing actual a ecisions, the incorporation of such ideas into the planning process depends upon their acceptance by political decision-makers. The concept of quasi-option value provides an easier means of illustrating the principles involved and thus has an important role to play.

Reference

Conrad, J. M. (1980). Quasi-option Value and the Expected Value of Information, Quurrer/.v JournalofEconomics, 94,813-820.