Statistical analyses based on non-randomly selected samples can lead to erroneous conclusions and poor policy. The Heckman correction, a two-step statistical approach, offers a means of correcting for non-randomly selected samples.
Heckman discussed bias from using nonrandom selected samples to estimate behavioral relationships as a specification error. He suggests a two-stage estimation method to correct the bias. The correction uses a control function idea and is easy to implement. Heckman’s correction involves a normality assumption, provides a test for sample selection bias and formula for bias corrected model.
Suppose that a researcher wants to estimate the determinants of wage offers, but has access to wage observations for only those who work. Since people who work are selected non-randomly from the population, estimating the determinants of wages from the subpopulation who work may introduce bias. The Heckman correction takes place in two stages.
In the first stage, the researcher formulates a model, based on economic theory, for the probability of working.