Effects of sample size on MOTAD and Target MOTAD solutions

Abstract

This study examines the effects of sample size on MOTAD and Target MOTAD solutions. Data sets based on historical observations are generated with a multi-variate normal random deviate generator. A representative Montana dry-land grain farm supplied the historical data. Ten data sets of each sample size (10, 20, 30, 40, 50, and 70 observations per activity) are generated and input into both of the linear risk models. All of the MOTAD models arrived at feasible solutions. Considerable instability was observed in the objective function values and basis activity levels for even the largest samples (at the lower deviation levels). However, as sample size increased the MOTAD results tended to be more stable. Several of the Target MOTAD models were infeasible due to the specified deviation and/or target income levels. In the feasible Target MOTAD models, stability of the objective function values and basis activity levels was noted when sample sizes were 30 observations or larger. Feasible Target MOTAD models resulted in considerably larger objective function values than comparable MOTAD models. The feasibility problems of the Target MOTAD specification serve to illustrate theoretical problems of the traditional MOTAD model.