Livestock disease indemnity design when moral hazard is followed by adverse selection.

The outbreak of disease in domestic livestock herds is an economic problem and potential human health risk. Diseases that are highly contagious or have human health implications are often the target of government eradication programs. Farm-level public policies under these programs range from bounties for infected livestock to whole herd depopulation and farm decontamination. (1)

When livestock are taken by the government for public health or economic reasons, the Fifth Amendment of the U.S. Constitution specifies that just compensation must be provided for this private property taken for public use. This compensation takes the form of indemnity payments. The current federal compensation level is defined by the Animal Health Protection Act, Subtitle E of the Farm Security and Rural Investment Act of 2002. This requires compensation to be based on the fair market value, as determined by the Secretary of Agriculture, adjusted for any other compensation received for the event (e.g., disaster payments or perhaps even private market insurance). States may also offer compensation in the form of indemnities.

This article focuses on the structure of indemnity payments, currently the primary form of public compensation, as the key mechanism for providing farm-level incentives to invest in biosecurity and to report when one's herd becomes infected. These actions have been fundamental issues of concern within public agencies responsible for livestock disease outbreak response (Ott 2006). However, it is not clear that existing indemnity programs adequately address the issues. Existing indemnity payments represent an implicit insurance policy for livestock producers (at least with respect to the diseases for which indemnities are paid), but are really more akin to ad hoc disaster payments due to the lack of risk classification and underwriting involved. Indeed, these payments do not have the desirable risk pooling properties associated with insurance; there are no premiums based on the risk represented by an insured as part of a portfolio of policies, and all taxpayers fund the indemnities. Accordingly, the current structure of indemnities may not generate the desired level of private risk mitigation, thereby undermining the government's livestock disease risk management objectives.

Prior economic research dealing with livestock disease (e.g., Bicknell, Wilen, and Howitt 1999; Mahul and Gohin 1999; Kuchler and Hamm 2000; Horan and Wolf 2005; Hennessy 2007) has also ignored incentive compatibility, at least in the presence of asymmetric information. (2) We use a principal-agent model to examine incentive compatibility in the presence of information asymmetry between the government and individual farmers. (3) Individuals have private information about preventive biosecurity measures they adopt on their farms prior to outbreak (ex ante), and following outbreak (ex post) they possess private information about the disease status of their herd. We investigate how indemnities can be developed to ensure incentive compatibility between the government and private decision makers, and how these incentives influence the occurrence and magnitude of a disease epidemic. Our focus is on farm-level biosecurity choices and reporting of disease status.

A Model of On-Farm Decision Making

We develop a capital valuation model of the livestock enterprise fashioned after that of Hennessy (2007), who adapted the efficiency wage model of Shapiro and Stiglitz (1984) to the problem of livestock disease management. Our farmer decision model departs from Hennessy (2007) by (a) introducing risk aversion on the part of a single farmer (only briefly addressed by Shapiro and Stiglitz 1984), (b) considering biosecurity and disease reporting decisions (whereas Hennessy focused exclusively on biosecurity), and (c) by considering the role of indemnity payments in farmer decisions. A diagram of the decision-making process described below is provided in figure 1. The farmer is risk averse with an instantaneous utility function U([omega]), where U' > 0 and U"< 0. Wealth, to, is contingent on the disease state and farmer choices in our model.

Let [theta] [member of] [0, 1] be a random variable denoting the farmer's within-herd disease prevalence rate, defined as the proportion of animals that would test positive, whether clinically or subclinically infected. We partition the range of [theta] to indicate that the farmer will either be susceptible (noninfected, with [theta] = 0) or infected ([theta] > 0) at any given point in time, as the farmer will face different choices and incentives depending on whether his or her herd is infected or not. Once infected, however, the magnitude of [theta] matters.

We denote the susceptible state by the subscript S and the infected state by the subscript 1. In the susceptible state ([theta] = 0) farmers must choose their biosecurity effort level, b. Biosecurity reduces the probability of transitioning to the infected state, [P.sub.SI](b), such that [partial derivative][P.sub.SI](b)/[partial derivative]b [less than or equal to] 0. Biosecurity also reduces the expected magnitude of a disease outbreak, should one occur. The conditional probability density function of [theta] is denoted g([theta] | b), such that G([theta] | b) is the twice continuously differentiable conditional cumulative distribution function with [partial derivative] G([theta] | b)/[partial derivative]b [greater than or equal to] 0 [for all] b. The conditions imposed on G mean that G satisfies first-order stochastic dominance in the sense that the cumulative density for a given level of infection is nondecreasing (the desirable outcome) in biosecurity. (4)

The farmer has a baseline profit flow when disease-free, gross of any biosecurity investment, denoted by [[pi].sub.0]. Biosecurity efforts are made at a constant per-unit cost of w. These costs are incurred only in the susceptible state because, once infected, there is no incentive to maintain these efforts. (5) The utility of wealth in the susceptible state can therefore be expressed as

(1) [U.sub.S] = U([[pi].sub.0] - bw).

[FIGURE 1 OMITTED]

In the infected state ([theta] > 0), the farmer must decide whether to report infection. Disease reporting is modeled as a mixed strategy, denoted r [member of] [0, 1] (where r = 1 means always report and r = 0 means never report). Reporting results in government testing, verification of infection, and culling of infected animals to eradicate the disease. The farmer is compensated for any culled animals with a government transfer denoted by [tau]([theta]). Culling results in two types of losses for the farmer--a loss of asset value [[lambda].sub.G]([theta]) ([[lambda].sup.'.sub.G]([theta]) > 0) associated with the livestock itself and consequential losses from business interruption [[chi].sub.G]([theta]) ([[chi].sup.'.sub.G] ([theta]) > 0). Business interruption losses may vary widely depending on the characteristics of the individual operation affected and possibly disease characteristics. For instance, the presence or absence of breeding stock or having high fixed costs associated with a specific capital asset (e.g., a dairy or egg-laying operation) could contribute to the magnitude of business interruption losses. The sum [[lambda].sub.G]([theta]) + [[chi].sub.G]([theta]) - [tau]([theta]) represents the farm's net disease costs per unit time. The farmer's instantaneous utility when he/she reports, denoted by the superscript R, is therefore given by [U.sup.R.sub.I]([[pi].sub.0] - [[lambda].sub.G]([theta]) - [[chi].sub.G]([theta]) + [tau]([theta])). The transition rate of returning to the susceptible state is [h.sub.G] [less than or equal to] 1, so that cumulative expected indemnity payments are [tau]([theta])/[h.sub.G]. (6)

When a farmer does not report disease, then detection is still possible via government disease surveillance activities. Surveillance activities detect nonreported infection with exogenous probability q and fail to detect nonreported infection with probability (1 - q). (7) Detection leads to government culling of infected animals. Compensation in this case is given by [tau]([theta]) - f. The term [tau]([theta]) is the same as occurs under reporting. The term f can be viewed as a fine for not reporting. In what follows, we simply refer to [tau]([theta]) as the government transfer and f as the fine.

If the infection goes undetected by government surveillance, the farmer will attempt private culling of infected animals, with costs [[lambda].sub.F]([theta]) < [[lambda].sub.G]([theta]) and [[chi].sub.F]([theta]) < [[chi].sub.G]([theta]) (where [[lambda].sup.'.sub.F]([theta]) > 0 and [[chi].sup.'.sub.F]([theta]) > 0). (8) In this case there is no indemnity payment. Rather. privately culled animals are sold at salvage value [sigma]([theta]). Whether infection is discovered by the government or not, all infected farms that do not report incur asset value losses and associated consequential losses due to culling (as occurs under reporting). We assume private culling is less effective than government culling, resulting in a smaller transition rate to the susceptible state than if reporting had occurred, that is, [h.sub.F] < [h.sub.G].

Given this specification, the expected instantaneous utility from not reporting is given by q[U.sup.D.sub.I]([[pi].sub.0] - [[lambda].sub.G]([theta]) - [[chi].sub.G]([theta]) + [tau]([theta]) - f) + (1 -q) [U.sup.ND.sub.I]([[pi].sub.0] - [[lambda].sub.F]([theta]) - [[chi].sub.F]([theta]) + [sigma]([theta])), where the superscript D denotes the diseased farm is detected and the superscript ND denotes the diseased farm is not detected. The overall expected utility of wealth in the infected state, conditional on the current level of infection, can therefore be expressed as

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

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