What is "control function"

n. an operation that controls the recording or processing or transmission of interpretation of data; "a control operation started the data processing" [syn: control operation]

Controls functions are statistical methods to correct for endogeneity problems by modelling the endogeneity in the error term. The approach thereby differs in important ways from other models that try to account for the same econometric problem. Instrumental variables, for example, attempt to model the endogenous variable X as an often invertible model with respect to a relevant and exogenous instrument Z. Panel data use special data properties to difference out unobserved heterogeneity that is assumed to be fixed over time.

Control functions were introduced by Heckman and Robb, although the principle can be traced back to earlier papers. A particular reason why they are popular is because they work for non-invertible models (such as discrete choice models) and allow for heterogeneous effects, where effects at the individual level can differ from effects at the aggregate. Famous examples using the control function approach is the Heckit model and the Heckman correction.