Non-classical measurement error with false positives and negatives

ABSTRACT

Non-classical measurement error caused by false positives and false negatives produces biased and inconsistent estimates in a regression. This is the case whether the mismeasured variable is a dependent or an explanatory variable, and having an IV does not always work. To tackle these limitations, this paper shows that proper adjustment of the mismeasured variable of interest produces consistent estimates. The paper also discusses alternatives when the key inputs to adjust the mismeasured variable are not known.

KEYWORDS:

• Non-classical measurement error
• false positives
• false negatives

JEL CODES:

• C80
• C01
• C40
• C49

Disclosure statement

No potential conflict of interest is reported by the author.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

¹ Available here: https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases

² Schmitz, Rob. ‘Germany Is Conducting Nationwide COVID-19 Antibody Testing’. NPR, 21 April 2020. Accessed 22 April 2020. https://www.npr.org/sections/coronavirus-live-updates/2020/04/21/839594202/germany-is-conducting-nationwide-covid-19-antibody-testing

³ Romo, Vanessa. ‘New York Starts “Aggressive” Coronavirus Antibody Testing In Quest To Reopen Economy’. 20 April 2020. Accessed 22 April 2020. https://www.npr.org/sections/coronavirus-live-updates/2020/04/20/839429603/new-york-starts-aggressive-coronavirus-antibody-testing-in-quest-to-reopen-econo

⁴ Although, given the novelty of these tests, it is likely that the FPR and FNR are only approximations.

⁵ E.g. Dave et al. (2020a); Chernozhukov, Kasaha, and Schrimpf (2020); Hsiang et al. (2020); Dave et al. (2020b); Courtemanche et al. (2020); Abouk and Heydari (2020); Goodman-Bacon and Marcus (2020)

⁶ But might need to be further adjusted, e.g., Bendavid et al. (2020).

⁷ Since the expected value of E$\left[\frac{1}{1-\hat{q}-\hat{r}}\right]$ in general does not equal $\frac{1}{1-E\hat{q}-E\hat{r}}$.

⁸ See proof in the appendix.

⁹ = 1