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A MONTE CARLO STUDY OF THE INCIDENCE OF PROBABILITY UNDERESTIMATION VERSUS PROBABILITY OVERESTIMATION ERRORS WITH ALTERNATIVE SAFETY FIRST MODELS (RISK)
Abstract
Modeling decision making under uncertainty continues to attract efforts of agricultural economists. A proposed model has been termed the safety first model. Safety first models are impacted by the probability of failing to achieve goals of the decision maker. Several methods have been proposed to estimate the probability of goal failure. Some methods attempt to exactly calculate the probability of concern. Other methods attempt to calculate an upper bounds on the probability. In either case, the researcher is usually forced to rely upon sample statistics when estimating probability levels. When statistical estimations of probability levels are made, two error types are possible. Underestimation error can lead to improperly accepting an alternative which violates a probability constraint. Overestimation errors can lead to rejecting an alternative which satisfies the constraint. This study examines the incidence of each error type with the proposed safety first models. Monte Carlo simulation techniques are utilized due to the mathematical complexity of closed form solutions. Five hundred samples, at each of several sample sizes, are drawn from a symmetric, a positively, and a negatively skewed distribution. The appropriate sample statistics are utilized to obtain probability estimates/limits with each safety first model. The relative incidence of the probability estimates/limits in prediction cells are reported. The relative frequencies can be utilized to approximate expected utility loss values for loss functions defined over the possible probability estimates/limits. The expected loss values can then be utilized to rank alternative safety first methods. With two specific loss functions, the study finds that the exact approximation methods generate serious underestimation errors. Other probability limit models generate large overestimation errors. Methods with intermediate results are available and perform relatively well across most sample sizes. Different loss functions may generate differing model rankings and can be approximated using the relative frequencies reported in the study.
Subject Area
Agricultural economics
Recommended Citation
ATWOOD, JOSEPH ALFRED, "A MONTE CARLO STUDY OF THE INCIDENCE OF PROBABILITY UNDERESTIMATION VERSUS PROBABILITY OVERESTIMATION ERRORS WITH ALTERNATIVE SAFETY FIRST MODELS (RISK)" (1985). ETD collection for University of Nebraska-Lincoln. AAI8602105.
https://digitalcommons.unl.edu/dissertations/AAI8602105