The damage control nature of pesticides has not been considered in any previous study on total factor productivity (TFP). Instead pesticides have been treated as a conventional input that affects output directly while in reality their contribution is rather indirect through their ability to reduce crop damage due to pest infestation and diseases. By treating pesticides as a damage control rather than an output expanding input affects the way pesticides appear in the production function. Specifically, as a damage control input, pesticides enter into the production function indirectly through either the abatement (Lichtenberg and Zilberman) or the output damage function (Fox and Weersink). Consequently, the way of calculating pesticides’ marginal product and output elasticity should be revised. In fact, the results of previous empirical studies (e.g., Lichtenberg and Zilberman; Oude Lansink and Carpentier; Oude Lansink and Silva) indicate that the marginal product of pesticides tends to be overestimated when it is modeled as a conventional rather than a damage control input.
This bias in the estimated marginal product of pesticides is going, among other things, to affect both the measurement (if output elasticities instead of cost shares are used to compute input growth) and the decomposition of TFP changes through the magnitude and the relative importance of the scale effect. However, the direction of the bias cannot be predicted with certainty: the upward bias in the estimated marginal product of pesticides results in a greater output elasticity and consequently, in an overestimation of scale elasticity compared to the case of treating pesticides as a damage control input. On the other hand, it also implies that the contribution of conventional inputs to the growth of aggregate input, defined as a weighted average over all inputs with the ratios of output to scale elasticity used as weights (Chan and Mountain), would be understated while that of pesticides would be overstated. Thus the net effect on the growth of aggregate input is undetermined a priori. This in turn implies that that the impact on the scale effect, which depends on both the magnitude of the scale elasticity and the growth of aggregate input, is ambiguous.
This paper develops a framework for analyzing the sources of TFP changes by explicitly taking into account the damage control nature of pesticides. In the proposed framework, TFP changes are decomposed into the conventional sources of growth (namely, technical change, scale effect, and changes in technical efficiency), and the damage control effect which consists of three distinct components: the first is due to changes in the initial pest infestation, the second is a spillover effect arising from neighbors’ use of preventive inputs, and the third is related to abatement effectiveness. To develop this decomposition framework we extend the output damage approach into two directions: first, we analyze the damage control nature of pesticides in the presence of technical inefficiency and second, we introduce a spillover variable into the abatement technology.