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The interpretation of 2SLS with a continuous instrument: a weighted LATE representation

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  • Luis Antonio Fantozzi Alvarez
  • Rodrigo Toneto

Abstract

This note introduces a novel weighted local average treatment effect representation for the two-stages least-squares (2SLS) estimand in the continuous instrument with binary treatment case. Under standard conditions, we obtain weights that are nonnegative, integrate to unity, and assign larger values to instrument support points that deviate from their average. Our representation does not require instruments to be discretized nor relies on limiting arguments, such as those used in the definition of the marginal treatment effect (MTE). The pattern of the weights also has a clear interpretation. We believe these features of the representation to be useful for applied researchers when communicating their results. As a direct byproduct of our approach, we also obtain a representation of the 2SLS estimand as a weighted average of treatment effects among ``marginal compliance'' groups, without having to resort to the threshold-crossing representation underlying the MTE construction. As an application, we consider the interpretation of ``event-study 2SLS'' specifications with continuous instruments.

Suggested Citation

  • Luis Antonio Fantozzi Alvarez & Rodrigo Toneto, 2024. "The interpretation of 2SLS with a continuous instrument: a weighted LATE representation," Working Papers, Department of Economics 2024_11, University of São Paulo (FEA-USP).
    • Handle: RePEc:spa:wpaper:2024wpecon11
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    File URL: http://www.repec.eae.fea.usp.br/documentos/Alvarez_Toneto_11WP.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Instrumental variables; Local average treatment effects; Event-study;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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