Sample Selection Bias

Sample selection bias arises when the sample on which you estimate the model is not a random draw from the population, and the selection process is correlated with the outcome's unobservables. Then OLS on the selected sample produces a biased coefficient — it estimates the relationship among the selected, not the population relationship. The classic example is the Mroz returns-to-education regression, which can only be estimated on women observed in the labour market.

When to use

Flag selection bias whenever the dataset implicitly drops observations on a non-random criterion: women's wage data condition on labour-force participation; firm recall outcomes condition on the firm existing in the data; PS_2's fertility data drops women with zero children because childs = NA. The standard fix is the Heckman Selection Model, which models both the selection equation (who enters the sample) and the outcome equation jointly, recovering an unbiased estimate via the Inverse Mills Ratio correction term.