Testing for Specification Bias with a Flexible Fourier Transform Model for Crop Yields

The literature on climate risk and crop yields is currently focused on the potential for highly non-linear marginal effects, essentially modeling the threshold effects with a yield function that maps weather inputs into crop yields. Implicit in this line of research is the assertion that the traditional quadratic model of crop yield suffers from specification bias. This article examines this assumption by using the Flexible Fourier Transforms (FFT) to allow for global flexibility in the weather effects while also maintaining the traditional quadratic model as a nested model specification. In order to speak to the global flexibility of FFT, as well as to provide both robustness to outliers and information on the scale effects of weather variables, this article compares FFT with restricted cubic spline (RCS) and quadratic models in a quantile regression framework. Using U.S. county-level data on corn, soybeans, and winter wheat from 1975 to 2013, we find that while the threshold effects are largely captured by the traditional quadratic model, we statistically reject the hypothesis that the quadratic model is sufficiently flexible. We find that, under the more flexible FFT functional forms, at lower temperatures there is a greater positive impact of marginal increases in temperature on yield than with the quadratic model, which suggests a different yield-temperature relationship than found in much of the literature on threshold effects of temperature on crop yields, and is more consistent with the positive effects of minor temperature increases found in some of the Ricardian climate effect literature.