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A Generalized Non-Parametric Instrumental Variable-Control Function Approach to Estimation in Nonlinear Settings

Author

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  • Kim Kyoo il

    (Michigan State University, East Lansing, USA)

  • Petrin Amil

    (University of Minnesota and NBER, Minneapolis, USA)

Abstract

When the endogenous variables enter non-parametrically into the regression equation standard linear instrumental variables approaches fail. Two existing solutions are the non-parametric instrumental variables (NPIVs) estimators, which are based on a set of conditional moment restrictions (CMRs), and the control function (CF) estimators, which use conditional mean independence (CMI) restrictions. Our first contribution is to show that – similar to CMI – the CMR place shape restrictions on the conditional expectation of the error given the instruments and endogenous variables that are sufficient for identification, and we call our new estimator based on these restrictions the CMR-CF estimator. Our second contribution is to develop an estimator for non-linear and non-parametric settings that can combine both CMR and CMI restrictions, which cannot be done in either the NPIV nor the non-parametric CF setting. This new “Generalized CMR-CF” uses both CMR and CMI restrictions together by allowing the conditional expectation of the structural error to depend on both instruments and control variables. When sieves are used to approximate both the structural function and the CF our estimator reduces to a series of least squares regressions. Our Monte Carlos illustrate that our new estimator performs well across several economic settings.

Suggested Citation

  • Kim Kyoo il & Petrin Amil, 2022. "A Generalized Non-Parametric Instrumental Variable-Control Function Approach to Estimation in Nonlinear Settings," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 91-125, January.
    • Handle: RePEc:bpj:jecome:v:11:y:2022:i:1:p:91-125:n:5
    DOI: 10.1515/jem-2021-0038
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    References listed on IDEAS

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    More about this item

    Keywords

    conditional moment restriction; instrumental variables; control function; non-parametric estimation; sieve estimation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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