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Identification of Local Treatment Effects Using a Proxy for an Instrument

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  • Karim Chalak

    () (Boston College)

Abstract

The method of indirect least squares (ILS) using a proxy for a discrete instrument is shown to identify a weighted average of local treatment effects. The weights are nonnegative if and only if the proxy is intensity preserving for the instrument. A similar result holds for instrumental variables (IV) methods such as two stage least squares. Thus, one should carefully interpret estimates for causal effects obtained via ILS or IV using an error-laden proxy of an instrument, a proxy for an instrument with missing or imputed observations, or a binary proxy for a multivalued instrument. Favorably, the proxy need not satisfy all the assumptions required for the instrument. Specifically, an individual's proxy can depend on others' instrument and the proxy need not affect the treatment nor be exogenous. In special cases such as with binary instrument, ILS using any suitable proxy for an instrument identifies local average treatment effects.

Suggested Citation

  • Karim Chalak, 2010. "Identification of Local Treatment Effects Using a Proxy for an Instrument," Boston College Working Papers in Economics 738, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:738
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    Cited by:

    1. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute for the Study of Labor (IZA).

    More about this item

    Keywords

    causality; compliance; indirect least squares; instrumental variables; local average treatment effect; measurement error; proxy; quadrant dependence; two stage least squares.;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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