01/07/2009
Yet Another Look at Pest Damage and Pesticide Productivity

Yet Another Look at Pest Damage and Pesticide Productivity

Using the Lichtenberg-Zilberman-Fox-Weersink damage specification, we develop a short-run, supply-response framework based on rational producer behavior in the presence of damage agents.

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Since the contribution of Lichtenberg and Zilberman (1986), the econometric specification of production systems that involve damage-control inputs has been widely debated. By and large, within agricultural economics, this debate has centered on the proper specification of the production role that pesticides play. Even the most casual reading of this literature highlights two salient characteristics. First, the debate focuses almost exclusively on the representation of damage-control inputs in single-output, plant-based production systems. And, second, the primary emphasis is on properly measuring pest damage to planned (maximal) output and the marginal productivity of pesticides.

The interest in the marginal productivity of pesticides is easy to understand. Economic efficiency dictates that the marginal social benefit from applying pesticides be equated to marginal social cost. The marginal productivity of pesticides is an important component of marginal social benefit.

It seems equally obvious why economists should be interested in measuring pest damage to output. Certainly, proper modelling of the economic damage caused by pests requires proper modelling of output damage. But output damage, considered alone, does not measure accurately the producerís private cost of pests.

Output damage, as traditionally defined, instead measures pest damage to maximal potential output realized from a given bundle of inputs. A more appropriate economic measure of the producerís private cost of pests is the producerís profit (quasi rent) loss due to pests. Conventional damage measures are an important component of this private cost, but they do not fully capture it. In fact, as we show, that for rational profit maximizers conventional output damage measures systematically misstate the revenue and profit losses associated with the presence of pests.

The cause of the divergence between the traditional pest-damage measure and the producerís private cost of pests is easy to trace. The former does not capture the economic adjustments to input use and production practices that rational economic decisionmakers make when using damage-control inputs. It simply measures physical damage to planned output, holding all inputs fixed, that actual pest infestations incur. The latter measure, on the other hand, accounts for rational actions taken to ameliorate pest damage, and thus captures the actual economic losses to farmers.

The implications of a possible divergence between traditional pest-damage measures and the actual economic loss due to pests are potentially important on a number of levels. First, and most simply, it is important in and of itself in empirical economics to get the numbers right. Second, and perhaps more importantly, the social costs and benefits of damage-control inputs are important matters of public concern. Many damage-control agents, such as pesticides, are often thought to have social costs (or benefits) that diverge from the private costs (or benefits) of individuals making decisions about their level of application. Thus, they have become a natural target for public regulation. Informed public regulation requires an accurate accounting of private, as well as social, costs and benefits. If the traditional measure of pest damage does not capture the producerís private cost of pests, sound policy making requires, at a minimum, that it be adjusted so that it does.

Following Lichtenberg and Zilberman (1986), Chambers and Lichtenberg (1994), and Fox and Weersink (1995), this paper develops a method for measuring quasi-rent losses due to pests and implements the method empirically using a panel-data set for Greek olive production. Our method has a number of important by- products, which merit independent study on their own. It yields both a measure of the marginal productivity of pesticides and pest damage to planned (maximal) output. The latter is the conventional damage measure considered in the literature. But because the method also provides a measure of the economic damage associated with the presence of pests, that economic damage is decomposable into its component parts, one of which includes damage to planned output. In addition, our method allows one to determine how pesticide application biases the optimal use of other variable inputs, how it a§ects the structure of quasi rents collected by quasi-fixed factors of production, and the general optimal supply-response characteristics of a farmer confronting pests.

In what follows, we first develop the basic production model. The damage specification follows the path- breaking work of Lichtenberg and Zilberman (1986), as extended by Fox and Weersink (1995) to allow for the potential presence of increasing marginal returns to the damage-control agent. The basic production model is then incorporated into a short-run supply response framework based on rational producer behavior. Here, we follow Chambers and Lichtenberg (1994) and develop a dual representation of the supply-response system associated with the Lichtenberg-Zilberman-Fox-Weersink specification of the damage-control technology.

A dual representation of the supply-response system is used because it facilitates measurement of the economically rational response producers make in the presence of pests. A primal representation, which is often used to obtain traditional damage measures, retards accurate measurement of such e§ects. And practical measurement from a primal system is only available after the inversion of first-order conditions associated with optimal behavior. This inversion process, because of its numerical nature, necessarily intro- duces yet another form of approximation error. The guiding principle is simple. The producerís profit loss is the appropriate measure of the economic loss due to pests. Therefore, we model the focus of our interest directly rather than indirectly as a primal approach would require.

After the representation is developed, we then show how to decompose the economic damage associated with the presence of pests, how to measure the shadow prices of damage-control agents, how to measure how pesticide application biases variable input use, and how pesticide application a§ects the relative returns to quasi-fixed factors of production. An econometric specification of our theoretical model follows, and that econometric specification is fit using a panel data set on Greek olive producers. The empirical results are then presented and thoroughly discussed, and the paper concludes. 

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