Identification of Local Treatment Effects Using a Proxy for an Instrument
نویسنده
چکیده
The method of indirect least squares (ILS) using a proxy for a discrete instrument is shown to identify a weighted average of local treatment e¤ects. 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 e¤ects 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. Speci cally, an individuals proxy can depend on others instrument and the proxy need not a¤ect the treatment nor be exogenous. In special cases such as with binary instrument, ILS using any suitable proxy for an instrument identi es local average treatment e¤ects.
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Instrumental Variables Methods with Heterogeneity and Mismeasured Instruments
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