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A first-stage test for instrumental variables quantile regression

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  • Javier Alejo
  • Antonio F. Galvao
  • Gabriel Montes-Rojas

Abstract

This paper develops inference procedures to evaluate the validity of instruments in instrumental variables (IV) quantile regression (QR) models. We first derive a first-stage regression for the IVQR model, analogue to the least squares case, which is a weighted least-squares regression. The weights are given by the density function of the conditional distribution of the innovation term in the QR structural model, conditional on the exogenous covariates and the nstruments. The first-stage regression is a natural framework to evaluate the instruments since we can test for their statistical significance. In the QR case, the instruments could be relevant at some quantiles but not for others or at the mean. Monte Carlo finite sample experiments show that the tests work as expected in terms of empirical size and power. Two applications illustrate that checking for the statistical significance of the instruments at di↵erent quantiles is important.

Suggested Citation

  • Javier Alejo & Antonio F. Galvao & Gabriel Montes-Rojas, 2020. "A first-stage test for instrumental variables quantile regression," Asociación Argentina de Economía Política: Working Papers 4304, Asociación Argentina de Economía Política.
    • Handle: RePEc:aep:anales:4304
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    References listed on IDEAS

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    More about this item

    Keywords

    quantile regression; instrumental variables; first-stage;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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