On Mis-measured Binary Regressors: New Results And Some Comments on the Literature, Third Version

Francis DiTraglia () and Camilo Garcia-Jimeno ()
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Francis DiTraglia: Department of Economics, University of Pennsylvania
Camilo Garcia-Jimeno: Department of Economics, University of Pennsylvania

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

Abstract: This paper studies the use of a discrete instrumental variable to identify the causal effect of an endogenous, mis-measured, binary treatment. We begin by showing that the only existing identification result for this case, which appears in Mahajan (2006), is incorrect. As such, identification in this model remains an open question. We first prove that the treatment effect is unidentified based on conditional first-moment information, regardless of the number of values that the instrument may take. We go on to derive a novel partial identification result based on conditional second moments that can be used to test for the presence of mis-classification and to construct simple and informative bounds for the treatment effect. In certain special cases, we can in fact obtain point identification of the treatment effect based on second moment information alone. When this is not possible, we show that adding conditional third moment information point identifies the treatment effect and the measurement error process.

Keywords: Instrumental variables; Measurement error; Endogeneity; Binary regressor; Partial Identification (search for similar items in EconPapers)
JEL-codes: C10 C18 C25 C26 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2015-10-31, Revised 2015-11-24
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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