Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis
Name
1706.01778.pdf
Description
Submitted version
Size
368.63 KB
Format
Adobe PDF
Checksum (MD5)
6b0f95db61c6f78cbbd87e164331f9f4
Author(s)
Abadie, Alberto
Athey, Susan
Imbens, Guido W
Wooldridge, Jeffrey M
Date Issued
2020
Journal
Econometrica
Publisher
The Econometric Society
Version
Original manuscript
Abstract
© 2020 The Econometric Society Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design-based. In a design-based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design-based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design-based uncertainty instead of, or in addition to, sampling-based uncertainty. We show that our standard errors in general are smaller than the usual infinite-population sampling-based standard errors and provide conditions under which they coincide.
MIT Department
Massachusetts Institute of Technology. Department of Economics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3982/ECTA12675
