VARIANCE-COMPONENTS STRUCTURES FOR THE EXTREME-VALUE AND LOGISTIC DISTRIBUTIONS WITH APPLICATION TO MODELS OF HETEROGENEITY

Two new classes of probability distributions are introduced that radic ally simplify the process of developing variance components structures for extreme-value and logistic distributions, When one of these new v ariates is added to an extreme-value (logistic) variate, the resulting distribution is also extreme value (logistic). Thus, quite complicate d variance structures can be generated by recursively adding component s having this new distribution, and the result will retain a marginal extreme-value (logistic) distribution. It is demonstrated that the com putational simplicity of extreme-value error structures extends to the introduction of heterogeneity in duration, selection bias, limited-de pendent- and qualitative-variable models. The usefulness of these new classes of distributions is illustrated with the examples of nested le git, multivariate risk, and competing risk models, where important gen eralizations to conventional stochastic structures are developed. The new models are shown to be computationally simpler and far more tracta ble than alternatives such as estimation by simulated moments. These r esults will be of considerable use to applied microeconomic researcher s who have been hampered by computational difficulties in constructing more sophisticated estimators.