Heckman correction

The Heckman correction is a statistical technique to correct bias from non-randomly selected samples or otherwise incidentally truncated dependent variables, a pervasive issue in quantitative social sciences when using observational data. Conceptually, this is achieved by explicitly modelling the individual sampling probability of each observation (the so-called selection equation) together with the conditional expectation of the dependent variable (the so-called outcome equation). The resulting likelihood function is mathematically similar to the tobit model for censored dependent variables, a connection first drawn by James Heckman in 1974. Heckman also developed a two-step control function approach to estimate this model, which avoids the computational burden of having to estimate both equations jointly, albeit at the cost of inefficiency. Heckman received the Nobel Memorial Prize in Economic Sciences in 2000 for his work in this field. Statistical analyses based on non-randomly selected samples can lead to erroneous conclusions. 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.