Sensitivity Analysis of an OLS Multiple Regression Inference with Respect to Possible Linear Endogeneity in the Explanatory Variables, for Both Modest and for Extremely Large Samples

Richard Ashley () and Christopher Parmeter

Econometrics, 2020, vol. 8, issue 1, 1-24

Abstract: This work describes a versatile and readily-deployable sensitivity analysis of an ordinary least squares (OLS) inference with respect to possible endogeneity in the explanatory variables of the usual k -variate linear multiple regression model. This sensitivity analysis is based on a derivation of the sampling distribution of the OLS parameter estimator, extended to the setting where some, or all, of the explanatory variables are endogenous. In exchange for restricting attention to possible endogeneity which is solely linear in nature—the most typical case—no additional model assumptions must be made, beyond the usual ones for a model with stochastic regressors. The sensitivity analysis quantifies the sensitivity of hypothesis test rejection p -values and/or estimated confidence intervals to such endogeneity, enabling an informed judgment as to whether any selected inference is “robust” versus “fragile.” The usefulness of this sensitivity analysis—as a “screen” for potential endogeneity issues—is illustrated with an example from the empirical growth literature. This example is extended to an extremely large sample, so as to illustrate how this sensitivity analysis can be applied to parameter confidence intervals in the context of massive datasets, as in “big data”.

Keywords: robustness; exogeneity; multiple regression; inference; instrumental variables; large samples; big data (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2225-1146/8/1/11/pdf (application/pdf)
https://www.mdpi.com/2225-1146/8/1/11/ (text/html)

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:gam:jecnmx:v:8:y:2020:i:1:p:11-:d:333196

Access Statistics for this article

Econometrics is currently edited by Ms. Jasmine Liu

More articles in Econometrics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().