Estimating within-herd preventive spillovers in livestock disease management.

Farm managers take biosecurity precautions against diseases that are not present and mitigate the effects of diseases that are present. In doing so, managers weigh the costs of prevention, illness, and control. If each disease is considered as an independent event (i.e., by making biosecurity and health management decisions on a disease-by-disease basis), the full scope of disease management actions are ignored. We define a preventive spillover as existing whenever a health management or biosecurity practice yields preventive returns for more than one disease. These spillovers may be difficult to identify, and the result from the perspective of farm management decision-making is a known investment for an unknown benefit with respect to other diseases.

The objective of this article is to model and empirically estimate spillovers of farm biosecurity practices in order to provide an accurate accounting of their preventive benefits. Preventive spillovers are empirically demonstrated when the adoption of a practice reduces the expected herd prevalence of multiple diseases.

Disease Management Decisions

Livestock disease can lower output by increasing the mortality rate or reducing the efficiency of inputs, result in premature culling, and lower weight gain or reproductive performance, among other consequences. Prevention and control practices are inputs to the production process. Maximizing profits occurs where the marginal value product of prevention and control equals the marginal cost of the input. In the veterinary literature, it is common practice to consider on-farm disease management on a disease-by-disease basis, in large part because observational or case-control studies are designed to identify management "risk factors" for infection. From an economic standpoint, estimation of disease control functions should take into account the potential for disease management practices to affect the prevalence of multiple diseases, so that resources can be allocated efficiently.

Preventive spillovers may be thought of as either multi-product outputs of individual management practices or as input externalities, which may be either positive or negative. If management practices are viewed as livestock production inputs, then the notion of preventive spillovers suggests that biosecurity practices are nonallocable factors in the sense that shares of the input cannot be allocated to the prevention of a specific disease or set of diseases and not to others.

Consider a vector of K practices x which are nonallocable with respect to disease prevention "output" and denote by [y.sub.d] the prevalence (continuous in the unit interval) of a particular disease d. Then an individual management practice yields a preventive return to an individual disease whenever [partial derivative][y.sub.d]/[partial derivative][x.sub.k] < 0. While in general [X.sub.k] may be continuous (e.g., the amount of antibiotic administered or nutritional supplement in a feed ration), the practices in our empirical application are binary (i.e., they are either practiced or not). To establish empirically whether individual practices yield preventive outputs, we undertake an analysis similar in spirit to the estimation of disease control functions in Chi et al. (2002), but depart from their approach by selecting an econometric model which ensures that predicted herd prevalence falls in the unit interval and controls for individual farm heterogeneity. Our approach makes a further contribution by estimating the determinants of disease management adoption. The preventive spillovers are estimated via a two-stage econometric procedure. The fractional response to preventive measures is estimated in the first stage, and adoption of the measure is estimated in the second stage as a function of avoided economic damages. This article extends previous research (Gramig, Wolf, and Lupi 2006) by considering multiple diseases and controlling for preventive spillovers in disease management practice adoption.

Stage I in our framework estimates a set of disease control functions, each with dependent variable equal to prevalence (a fraction) for a single disease, d, in herd i (we omit the herd-level index for notational simplicity in what follows). Explanatory variables for all disease equations take a form similar to those found in "risk factor" papers in the veterinary epidemiology literature except that the same explanatory variables are included in the estimation for each disease in order to account for the possibility of spillovers in disease management. Explanatory variables are of two types: demographic (either binary or continuous) or management practice (binary only). A vector of demographic variables, z, and of management practices, x, are considered. When a particular practice is found to be significant and negatively associated with multiple diseases, this is considered evidence of a preventive spillover. In general, spillovers need not be preventive in nature and may in fact yield preventive returns to one disease while contributing to greater infection by another pathogen. The marginal effects of the practices from Stage I are used to estimate adoption in Stage II.

In the first stage, we adopt the fractional logit model of Papke and Wooldridge (1996) with dependent variable [y.sub.d] [member of] [0, 1] for each of D diseases for which we have herd-level data, which takes the general form

E[[y.sub.d]|q[beta]] = G(q[beta]) where q[beta] = [alpha] + x[gamma] + [epsilon] (1)

contains an intercept with coefficient [alpha], a vector of explanatory variables x with coefficient vector [gamma] random error [epsilon], and G() = [LAMBDA](), the logistic CDF. The fractional logit model directly estimates the fractional response of interest for each management practice while ensuring that the predicted prevalence for a given set of practices falls in the unit interval.

In the second stage, a binary response adoption equation for each practice k found to be significant in control function (1) is estimated in the form

[x.sub.k] = 1[[??][??] + u > 0] where [??][??] = [v.sub.k] + z[[xi].sub.k] + [L.sub.k][[lambda].sub.] (2)

where 1[] denotes the indicator function and [??][??] contains an intercept, a vector of herd-specific explanatory variables z, and D dimensional vector of estimated losses from disease, [L.sub.k], based on the fractional response of prevalence to practice k for each of the D diseases. Greek letters denote associated coefficients, z is herd-specific and does not vary over d or k while [L.sub.k] varies over practice and each element is disease-specific, and u is a random error term. The significance of two or more parameters in the D-vector [[lambda].sub.k] supports a hypothesis that spillovers have a significant adoption effect.

Empirical Example

The National Animal Health Monitoring System (NAHMS) is coordinated by USDA-APHIS and regularly conducts surveys designed to estimate livestock disease prevalence for livestock industry species in the United States. The cross-sectional data from NAHMS provide detailed behavioral information at the herd level on health management and biosecurity practices along with the results of serological tests for antibodies to disease for the herds sampled. We demonstrate the two-step econometric procedure proposed for identification of preventive spillovers and analysis of the role that spillovers may play in management practice adoption using data from the 1996 NAHMS Dairy survey, which includes within-herd prevalence for Bovine Leukosis Virus (BLV) and Johne's disease (M. Paratuberculosis). Details of the survey and the importance of these particular diseases have been previously discussed elsewhere (Pelzer 1997; Ott, wells, and Wagner 1999; Ott, Johnson, and Wells 2003), and we limit our discussion to applying the empirical framework proposed and the economic interpretation of estimation results.

We utilize a complex stratified random sample of dairy herds that is representative of over 80% of the national herd and undertake the first step in the proposed econometric procedure by estimating the disease control functions (1). We first identify management practices in the dataset that represent veterinary recommendations or are identified in prior literature as "risk factors" for infection by BLV (DiGiacomo, Darlington, and Evermann 1985; DiGiacomo et al. 1986; Heald et al. 1992) and Johne's (Johnson-Ifearulundu and Kaneene 1998). We follow a modified backward stepwise procedure that is consistent with veterinary studies of management risk factors. However, because of our focus on preventive spillovers we also adopt the fractional logit model (Papke and Wooldridge 1996), in order to estimate the marginal effect of individual practices on within-herd disease prevalence in the first stage for the diseases BLV and Johne's, denoted by d = BLV, J. In our application, equation (1) takes the form

E[[y.sub.d]|q[beta] = G(q[beta]) where q[beta] = [[alpha].sub.d] + x[[gamma].sub.d] + [epsilon] (3)