This article explores a model in which a union confronts many competitive workers, firms, and consumers. Under "monopoly" unionism, union coverage may be incomplete; then, union wages and employment are insensitive to product demand variation. Under "efficient" unionism, coverage can never be incomplete; some union variables necessarily vary with product demand. Preliminary evidence on the demand independence under incomplete coverage hypothesis is presented. Also, more structure is imposed and further hypotheses are derived, and the manner in which the model can be enriched to allow for a variety of union-related issues within a consistent framework is set out.

A frequent practice in empirical work is to "preanalyze" the data via various sample inclusion rules. Truncation of "outliers" is common. These procedures are a form of sample censoring imposed by the investigator. Such censoring produces effects familiar from the sample selection literature. This paper investigates the question why an investigator might want to censor a sample and what the costs are. In an empirical example, using a variance components model of a wage equation, potential inconsistency problems are highlighted. The results indicate that while the slope coefficients, <tex-math>\hatβ</tex-math>, may typically be less sensitive to censoring than the variance components, some common forms of censoring also markedly affect <tex-math>\hatβ</tex-math>. Finally, a Bayesian estimator that incorporates prior information in a flexible way was developed. The usual Bayesian procedure was reversed, by using the Bayesian estimator to recover the prior beliefs that an investigator imposes by any proposed truncation of outliers. Especially in large samples, extremely dogmatic prior beliefs may be imposed when outliers are eliminated. Prior distributions of the type developed in the paper may be used by the investigator to clarify the nature of his prior beliefs revealed by a willingness to truncate data points and to assess whether or not any proposed truncation accurately reflects thoes beliefs.