Measurement Error Without the Proxy Exclusion Restriction

Karim Chalak () and Daniel Kim

Journal of Business & Economic Statistics, 2021, vol. 39, issue 1, 200-216

Abstract: Abstract–This article studies the identification of the coefficients in a linear equation when data on the outcome, covariates, and an error-laden proxy for a latent variable are available. We maintain that the measurement error in the proxy is classical and relax the assumption that the proxy is excluded from the outcome equation. This enables the proxy to directly affect the outcome and allows for differential measurement error. Without the proxy exclusion restriction, we first show that the effects of the latent variable, the proxy, and the covariates are not identified. We then derive the sharp identification regions for these effects under any configuration of three auxiliary assumptions. The first weakens the assumption of no measurement error by imposing an upper bound on the noise-to-signal ratio. The second imposes an upper bound on the outcome equation coefficient of determination that would obtain had there been no measurement error. The third weakens the proxy exclusion restriction by specifying whether the latent variable and its proxy affect the outcome in the same or the opposite direction, if at all. Using the College Scorecard aggregate data, we illustrate our framework by studying the financial returns to college selectivity and characteristics and student characteristics when the average SAT score at an institution may directly affect earnings and serves as a proxy for the average ability of the student cohort.

Date: 2021
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1080/07350015.2019.1617156 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:39:y:2021:i:1:p:200-216

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UBES20

DOI: 10.1080/07350015.2019.1617156

Access Statistics for this article

Journal of Business & Economic Statistics is currently edited by Eric Sampson, Rong Chen and Shakeeb Khan

More articles in Journal of Business & Economic Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().