Control function (econometrics)

control function
Control functions (also known as two-stage residual inclusion) are statistical methods to correct for endogeneity problems by modelling the endogeneity in the error term.wikipedia
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Heckman correction

Heckit modelHeckman selection correctionHeckman selection model
Famous examples using the control function approach is the Heckman correction.
Heckman also developed a two-step control function approach to estimate this model, which reduced the computional burden of having to estimate both equations jointly, albeit at the cost of inefficiency.

Instrumental variables estimation

instrumental variableinstrumental variablestwo-stage least squares
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.

Endogeneity (econometrics)

endogenousendogeneityreverse causality
Control functions (also known as two-stage residual inclusion) are statistical methods to correct for endogeneity problems by modelling the endogeneity in the error term.

Errors and residuals

residualserror termresidual
Control functions (also known as two-stage residual inclusion) are statistical methods to correct for endogeneity problems by modelling the endogeneity in the error term.

Econometrics

econometriceconometricianeconometric analysis
The approach thereby differs in important ways from other models that try to account for the same econometric problem.

Inverse element

invertibleinverseinverses
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.

Exogeny

exogenousexogenicexogenously
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

longitudinal datapanel(panel)
Panel data use special data properties to difference out unobserved heterogeneity that is assumed to be fixed over time.

James Heckman

James J. HeckmanHeckmanNobel Prize winning economist James Heckman
Control functions were introduced by Heckman and Robb, although the principle can be traced back to earlier papers.

Rafael Robb

Rafael RobRobb
Control functions were introduced by Heckman and Robb, although the principle can be traced back to earlier papers.

Discrete choice

discrete choice analysisDiscrete choice modelsnested logit
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.

Homogeneity and heterogeneity

heterogeneoushomogeneousheterogeneity
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.

Rubin causal model

potential outcomescausal modelcausal modeling from observational data
In a Rubin causal model potential outcomes framework, where Y 1 is the outcome variable of people for who the participation indicator D equals 1, the control function approach leads to the following model

Statistical assumption

assumptionsStatistical assumptionsdistributional assumption
The original Heckit procedure makes distributional assumptions about the error terms, however, more flexible estimation approaches with weaker distributional assumptions have been established.

Higher-order function

higher-order functionshigher order functionfunctional form
This latter approach, however, does implicitly make strong distributional and functional form assumptions.