On Technological Change in Crop Yields

Technological changes in agriculture tend to alter the mass associated with segments or components of the yield distribution as opposed to simply 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 components 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 components, and (2) are the probabilities of components constant over time? Our results-technological change is not equivalent across components and probabilities tend not to have changed significantly over time-have implications for modeling yields. We find estimated conditional yield densities are quite different when unique trend functions are embedded inside the mixture components versus estimating the same mixture with detrended data. Also, we prove different rates of technological change in different components lead to nonconstant variance with respect to time (i.e., heteroscedasticity). We present two applications of the proposed yield model. The first application considers climate determinants of component membership, where our results are consistent with the literature for climate determinants of yields. The second application compares the proposed yield model to USDA's current rating methodology for area-yield crop insurance contracts and finds the proposed model may lead to more accurate rates.