AN ANALYSIS OF AGGREGATION BIAS IN QUADRATIC SPATIAL EQUILIBRIUM MODELS: AN APPLICATION TO FEDERAL MILK MARKETING ORDERS
Abstract
Spatial equilibrium models have been used to analyze various aspects of the agricultural sector. Development of these models has demanded aggregation of data for the economic entities represented. Aggregation of data used in spatial equilibrium models will generally cause the introduction of error in the solution. This aggregation error must be considered whenever a complex economic system made up of numerous individual producers and consumers is represented by data assumed common to large segments of that system. The focus of this research is the federal milk marketing order system. A quadratic programming model was developed to represent the production, processing and consumption sectors. The production sector is represented by 61 areas consisting of 45 direct ship and 16 supply plant areas. The model also includes 45 processing centers and 45 final consumption areas. These production/consumption activities were linked together via transportation activities in the model. The model utilized a quarterly time framework. A major purpose of this research was to evaluate the severity of the bias introduced by various types of aggregation using data from the federal milk marketing order systems. The research will provide analysis of accumulated error for numerous types of aggregation as well as specific analysis of the following aggregation schemes. (1) The effects of spatial aggregation are evaluated by comparing base model solutions levels for spatially separated production/consumption sectors with a non-separated model. The non-separated case is modeled by removing all transportation costs between the sectors. (2) The effects of temporal aggregation are evaluated by comparing the results of a model based on annual economic relationships with the summed results of a quarterly representation. (3) A third type of error analyzed is introduced by the number of alternative autonomous supply and demand regions represented. Errors arising from this type of aggregation are analyzed by using alternative supply and demand elasticities for the production and consumption regions. A second purpose is to provide information on which to base geographic price structures for the federal milk marketing order system. The stability of these geographic price structures under varying conditions is also examined. The results of this study can be summarized as follows: (1) Spatial aggregation of production and consumption areas affected the total solution levels very little. However, levels for specific production and consumption areas are significantly affected. (2) A quarterly time framework appears to introduce no significant bias when aggregated to annual production/consumption levels. (3) Aggregation or areas with different supply and demand elasticities bias solution levels in proportion to the range of elasticities relative to an average elasticity estimate for supply and demand relationships. (4) Model solutions suggest the existence of multiple geographic price bases. This is in conflict with the current single base pricing mechanisms. (5) Aggregation errors appear to be non-cumulative in nature. Errors introduced by various aggregations do not compound one another. Therefore, once an aggregation level has been identified for a specific type of bias, alternative aggregation decisions can be made with little concern for accumulating errors.
Degree
Ph.D.
Subject Area
Agricultural economics
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