Three studies on applying Positive Mathematical Programming and Bayesian Analysis to model US crop supply
The purpose of this dissertation is to find a practical way of obtaining a reasonable crop supply model for the US using a limited dataset. This model can then be used for forecasting and impact modeling. The method that is central to this model is Positive Mathematical Programming (PMP) that allows for the calibration of a nonlinear programming model to mimic the observations. This method is improved by implementing Bayesian Analysis to allow for the model to consider a distribution for the supply elasticity.
Using this method a national model was formed using only five years of data. While there were difficulties in forming a posterior density through manipulation of parameters, the Metropolis Hastings Algorithm ultimately allowed for the density to be simulated. Once the posterior data is simulated, a reasonable forecast could be made using this model.
This model was then improved by disaggregating the national model into a regional model. This was done through an additional variable (which is the percentage of national price responsiveness for a crop in a region) to consider in the prior density. Ultimately, regional results and elasticities are formed and the overall forecasting was improved.
Once the national and regional models have been formed, the models were tested under a variety of impact models. The response to the change in price for crops as well as yield changes in a region were done and reasonable results were found. Overall, a crop supply model was formed that produced reasonable elasticities and forecasted accurate results, thanks in part to a Bayesian approach which view parameters as distributions in the model.