Measurement Error Without the Proxy Exclusion Restriction

37 Pages Posted: 3 May 2017 Last revised: 30 Jul 2019

See all articles by Karim Chalak

Karim Chalak

University of Virginia

Daniel Kim

BI Norwegian Business School

Date Written: April 26, 2019


This paper 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.

Keywords: college selectivity, college characteristics, endogeneity, exclusion restriction, differential measurement error, partial identification, proxy, sensitivity analysis

JEL Classification: C21, I23

Suggested Citation

Chalak, Karim and Kim, Daniel, Measurement Error Without the Proxy Exclusion Restriction (April 26, 2019). Karim Chalak & Daniel Kim (2019) Measurement Error Without the Proxy Exclusion Restriction, Journal of Business & Economic Statistics, DOI: 10.1080/07350015.2019.1617156, Available at SSRN: or

Karim Chalak (Contact Author)

University of Virginia ( email )

1400 University Ave
Charlottesville, VA 22903
United States

Daniel Kim

BI Norwegian Business School ( email )

Nydalsveien 37
Oslo, 0484

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics