Variance Components Structures for the Extreme-Value and Logistic Distributions with Application to Models of Heterogeneity

Abstract

Two new classes of probability distributions are introduced that radically simplify the process of developing variance components structures for extremevalue and logistic distributions. When one of these new variates is added to an extreme-value (logistic) variate, the resulting distribution is also extreme value (logistic). Thus, quite complicated variance structures can be generated by recursively adding components having this new distribution, and the result will retain a marginal extreme-value (logistic) distribution. It is demonstrated that the computational simplicity of extreme-value error structures extends to the introduction of heterogeneity in duration, selection bias, limited-dependent- and qualitative-variable models. The usefulness of these new classes of distributions is illustrated with the examples of nested logit, multivariate risk, and competing risk models, where important generalizations to conventional stochastic structures are developed. The new models are shown to be computationally simpler and far more tractable than alternatives such as estimation by simulated moments. These results will be of considerable use to applied microeconomic researchers who have been hampered by computational difficulties in constructing more sophisticated estimators.