A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

Seojeong Lee

No 2015-01, Discussion Papers from School of Economics, The University of New South Wales

Abstract: Under treatment effect heterogeneity, an instrument identifies the instrument-specific local average treatment effect (LATE). If a regression model is estimated by the two-stage least squares (2SLS) using multiple instruments, then 2SLS is consistent for a weighted average of different LATEs. In practice, a rejection of the overidentifying restrictions test can indicate that there are more than one LATE. What is often overlooked in the literature is that the postulated moment condition evaluated at the 2SLS estimand does not hold unless those LATEs are the same. If so, the conventional heteroskedasticity-robust variance estimator would be inconsistent. However, 2SLS standard errors based on the conventional variance estimator have been reported even when the overidentifying restrictions test is rejected. I propose a consistent estimator for the asymptotic variance of 2SLS by using the result of Hall and Inoue (2003) on misspecified moment condition models. This can be used to correctly calculate the standard errors regardless of whether there are more than one LATE or not.

Keywords: local average treatment effect; treatment heterogeneity; two-stage least squares; variance estimator; model misspecification (search for similar items in EconPapers)
JEL-codes: C13 C31 C36 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2015-01
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs (2018)
Working Paper: A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs (2018)
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