Semiparametric Estimators for Limited Dependent Variable (LDV) Models with Endogenous Regressors

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This article reviews semiparametric estimators for limited dependent variable (LDV) models with endogenous regressors, where nonlinearity and nonseparability pose difficulties. We first introduce six main approaches in the linear equation system literature to handle endogenous regressors with linear projections: (i) 'substitution' replacing the endogenous regressors with their projected versions on the system exogenous regressors x, (ii) instrumental variable estimator (IVE) based on E{(error) × x} = 0, (iii) 'model-projection' turning the original model into a model in terms of only x-projected variables, (iv) 'system reduced form (RF)' finding RF parameters first and then the structural form (SF) parameters, (v) 'artificial instrumental regressor' using instruments as artificial regressors with zero coefficients, and (vi) 'control function' adding an extra term as a regressor to control for the endogeneity source. We then check if these approaches are applicable to LDV models using conditional mean/quantiles instead of linear projection. The six approaches provide a convenient forum on which semiparametric estimators in the literature can be categorized, although there are a few exceptions. The pros and cons of the approaches are discussed, and a small-scale simulation study is provided for some reviewed estimators.

Original languageEnglish
Pages (from-to)171-214
Number of pages44
JournalEconometric Reviews
Issue number2
Publication statusPublished - 2012 Mar


  • Endogenous regressors
  • Equation systems
  • Limited dependent variables
  • Nonparametrics
  • Semiparametrics

ASJC Scopus subject areas

  • Economics and Econometrics


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