This article addresses the issue of specification of econometric selectivity models and suggests approaches for the correction of selectivity bias. Our approaches provide ways to specify selectivity models without the assumption of multinormal distribution. Some flexible function forms for the correction of selectivity bias in the regression equation are derived. All the models considered can be estimated by simple consistent two stage methods. Our approaches provide simple procedures for the testing of selectivity bias without imposing restrictive distributional assumptions and also tests for the normality assumption.