6Crop Responses to Climate and Weather Cross-Section and Panel Models

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99Abstract Crop choices vary by climate, e.g., Florida specializes in citrus crops while Iowa specializes in corn and soybeans. The advantage of a cross-sectional analysis is that it incorporates how farmers adapt to existing difference in average climate conditions across space. A potential downfall is omitted variable bias. A panel analysis can overcome omitted variable bias by including fixed effects to capture all additive time-invariant influences, yet does not account for the same set of adaptation possibilities.

6.1 IntroductionResearchers might be interested in the relationship between temperature and yields for various reasons: (i) to forecast a yield at a given place in a given year under exist-ing weather conditions; (ii) to simulate the effects of changes in average weather (i.e., climate) in the future. There is a clear distinction between the two. The former relies on the fact that farmers in a location have optimized their production process and adapted to the given climate. A historic time series at the specific location is sufficient to predict yields under various weather outcomes. Imagine a field in Iowa that has been in production for several years. If one were interested in predicting yields in that location, a good guess is to look at what happened to yields in previous years under various weather conditions and use that relationship in the forecast. This is an ade-quate procedure as farmers have to sow a crop before the weather is realized. For example, corn is usually sown in early spring in Iowa. There is no way to switch the crop in June if the weather turned warmer (or colder) than expected. The farmer is stuck with the crop that was initially chosen. While there are some possible adapta-tion measures even after the crop is planted (for example, increased use of irrigation or other inputs), the major decision has been made. Hence a farmer uses the existing distribution of possible weather outcomes when making the planting decision.

Chapter 6Crop Responses to Climate and Weather: Cross-Section and Panel Models

Wolfram Schlenker

D. Lobell and M. Burke (eds.), Climate Change and Food Security, Advances in Global Change Research 37, DOI 10.1007/978-90-481-2953-9_6, © Springer Science + Business Media, B.V. 200W. Schlenker420 West 118th St, New York, NY 10027email: wolfram.schlenker@columbia.edu1100W. SchlenkerThe situation is quite different if the goal is to predict the impacts of changing climate conditions. If Iowa is to become permanently warmer, farmers might find it no longer optimal to grow the same corn variety but rather switch to a longer season variety instead. If it becomes significantly warmer, farmers might prefer to switch to an entirely new crop, e.g., cotton or citrus, two crops currently grown in warmer climates. Looking at past data at a given location does not incorporate switching to a different crop variety or entirely different crop species as the analysis keeps the crop variety and crop species fixed. Using historic yield data at the loca-tion of interest therefore might give an inaccurate prediction of what farmers would to do if the climate permanently changed.

6.2 Cross-Sectional AnalysisA cross-sectional analysis of a specific crop would incorporate how a farmer switches to other crop varieties of the same crop (e.g., corn varieties). The idea is to compare corn yields in Iowa with corn yields in warmer states like Arkansas. The problem is that there are other differences between Iowa and Arkansas besides dif-ferences in climate. For example, soil quality varies a great deal between states. A cross-sectional analysis would have to account for all covariates to correctly identify the effect of climate on corn yields.If one is interested in how farmers switch crops with changing climates, a multi-nomial regression of crop choice on climatic variables, again accounting for all other confounding differences across climate zones explicitly, would identify such switching using cross-sectional data. In a multinomial regression, various crop choices are coded as separate categories. For example, outcome 1 could be growing maize, outcome 2 growing millet, and outcome 3 growing sorghum. A farmer will pick the most profitable crop for a given climate. Methodologically, each crop yield is modeled as a function of the climate variables as well as other controls and an error term. If the error terms follow an extreme value distribution, the probability for choosing each possible outcome has a closed form solution that is used in a multinomial logit regression. If the error terms are normal, the probability of choosing various alternatives has no closed form solution and can only be solved numerically (Maddala 1986). The multinomial logit technique has been applied to crop choices in South America by Seo and Mendelsohn (2008).One can even go a step further and use farmland values as the dependent variable to implicitly incorporate crop switching without limiting the analysis to certain crop types. Farmland values reflect the value of land if it is put to its most profitable use, whatever that may be. An example might illustrate this point. New York City’s Mayflower Hotel On the Park was a medium sized hotel on Central Park West at 61st Street. In the early 2000s it sold for an astonishing 400 million dollars. Why would anybody pay 400 million dollars for a medium-sized hotel? The first thing the new owner did was to knock down the old hotel and build a new luxury condominium (15 Central Park West) that reported apartment sales exceeding 1 billion dollars a