Location: Water Management Research
2012 Annual Report
The first year of this project was to develop the structure of the models for both the intra-seasonal problem and intra-seasonal problem assuming a single field for which a single-aged vine was planted. The research conducted in year two has focused on management decisions at the level of multiple fields, which could, depending on the scenario analyzed, represent the holdings of a single grape producer or a whole region. The field is assumed to be uniformly planted with vines of the same age, yet a farm or region is comprised of multiple fields of different age classes. Analysis at the producer or regional level then varies primarily with the age of the vines on the different fields. In economic terminology, representing the problem in this way could be classified as a vintage capital model. Such models are useful for understanding the effect of aging capital on production levels and the optimal replacement schedule. Thinking of vine area planted in this manner allows us to investigate how the biological aspects of wine grapes affects optimal water use, new plantings and removals over time. Given a working model of these dynamics, we can then estimate water demand for wine grapes and use this to evaluate the impact of various scenarios with different levels of water availability and institutional arrangements.
In order to validate the results of vintage capital model we’ve created, it is useful to compare the results generated by the model to the relevant literature; however, there are very few economic studies of perennial crops comparable to this one. The one theoretical paper we identified as being relevant predicts, assuming profit-maximizing behavior and the desire of producers to smooth consumption over time, the regional model will eventually converge to a steady-state in which equal land area will be devoted to each age class of vines. Testing various versions of our regional model, from most abstract to most realistic, shows, regardless of the area devoted to the different vintages initially planted, acts exactly as predicted by the theory. While this exercise relies on many simplifying assumptions and produces results that one would not expect to hold in reality, it is an important check on the theoretical economic foundations of our model.
Further refinements of the model includes the use of alternate utility functions and the ability of farmers to borrow and save. Utility functions are at the heart of most economic analyses. The reason they are important in the current study is they allow for more realistic behavior than strict profit maximization with respect to issues such as the desired variability of income over time. In particular, a profit-only approach implies that it may be optimal for farmers to exhibit extreme borrowing and saving behavior. To limit such unrealistic behavior, we have combined a utility function with the ability to borrow at increasingly high interest rates as debt increases. By doing this, we eliminate, for instance, the possibility that the model will find it optimal to remove and replant all vines in response to a drop in grape prices or several years of water shortages. Furthermore, by allowing our modeling approach to include utility functions, as well as profit functions, we can represent growers as individual agents through the use of a utility function, or large scale firms as profit-maximizing entities through the use of a profit function; we will allow ourselves the flexibility to evaluate either approach.
In considering the inter-seasonal model, representing the age structure of vines in a vintage capital model raises some computational problems. The standard approach to dynamic optimization of economic problems of sufficiently small size is to use computational methods such as Dynamic Programming (DP). However, the vintage approach taken here leads to a high-dimensional problem which is not computationally feasible using DP. For that reason, we have employed a computational algorithm which is not recursive but optimizes over a given planning horizon in a way that approximates recursive methods. Such methods have been used in other papers and for the present analysis have led to consistent, logical, and robust results.
While much progress has been made on the inter-seasonal model, we are returning to the intra-seasonal model to further develop this element of the project. The structure of the intra-seasonal model has been developed, yet the decision rule within the model as to how to manage the vine needs updating. Previously, we used an evapotranspiration (ET)-water relationship based on agronomic research and multiple process models associated with intra-seasonal vine management based on a simplified decision rule related to an allowable lower bound on soil moisture. We are in the process of updating this model to better represent the intra-seasonal management objectives confronting growers and vineyards, with particular attention to the ratio of yield to end-of-year pruning weight. Again, we will use generic parameters from the literature that relate seasonal evapotranspiration (ET) to applied water rates and salinity until the updated parameters from the field experiments is provided.