On Technological Change in Crop Yields

Technological changes in agriculture tend to alter the mass associated with a segment or subpopulation of the yield distribution as opposed to shifting the entire distribution upwards. We propose modeling crop yields using mixtures with embedded trend functions to account for potentially different rates of technological change in different subpopulations of the yield distribution. By doing so we can test some interesting and previously untested hypotheses about the data generating process of yields. For example: (1) is the rate of technological change equivalent across subpopulations; and (2) are the probabilities of subpopulations constant over time? Our results -technological change is not equivalent across subpopulations and probabilities have not changed significantly over time -have implications for modeling yields. While we consider the impacts for rating crop insurance contracts, accurate modeling of technological change is relevant to issues such as food sustainability, economic development, feeding a rapidly growing world population, biofuels markets and policy, and climate change. July 2013 Working Paper Series 13-02 Institute for the Advanced Study of Food and Agricultural Policy Department of Food, Agricultural and Resource Economics OAC University of Guelph Tor Tolhurst, former M.Sc. student and current Research Associate, Department of Food Agricultural and Resource Economics, University of Guelph ([email protected]). Alan Ker, Professor and Chair, Department of Food Agricultural and Resource Economics, University of Guelph ([email protected]). The authors would like to thank the Ontario Ministry of Agricultural and Food, the Ontario Ministry of Rural Affairs, and the Institute for the Advanced Study of Food and Agricultural Policy (Department of Food, Agricultural and Resource Economics, OAC, University of Guelph) for their generous financial support. Introduction Crop yields are agriculture’s principle unit of productivity measurement and, as a result of numerous changes in technology, agriculture has experienced dramatic and widespread yield increases over the past 75 years. These advances impact food sustainability, economic growth, world hunger, energy markets, and our ability to mitigate or enhance potential climate change effects. The rate of technological change has been exclusively measured at the mean implying technological developments result in a location or location-scale shift of the yield distribution. However, evidence in the crop science literature indicates technological developments alter the mass associated with a segment or subpopulation of the yield distribution (e.g. Barry et al. 2000; Dunwell 2000; Ellis et al. 2000; Badu-Apraku, Menkir and Lum 2007; De Bruin and Pederson 2008; Gosala, Wania and Kang 2009; Edgerton et al. 2012). For example, triplestacked seeds were developed to increase resilience to a variety of pests as well as high winds thereby reducing mass in the lower tail (Edgerton et al. 2012). In contrast, racehorse seeds were developed to increase mass in the upper tail under relatively optimal growing conditions (Lauer and Hicks 2005). These developments suggest that the rate of technological change may vary across subpopulations and the probability of those subpopulations may change as well. We propose modeling crop yields using a mixture of normals to account for the different subpopulations or components of the yield distribution. This is not new as others have first estimated a trend and then using the residuals estimated a mixture of two normals (e.g. Ker 1996; Goodwin, Roberts and Coble 2000; Woodard and Sherrick 2011). However, the mixture model is more flexible than previously employed in that it can accommodate different rates of technological change within different components and as such can be used to model yields without limiting technological change to location or location-scale shifts of the yield distribution. To illustrate and provide some intuition for the proposed model we present in Figure 1