# 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.