IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v88y2020i1p265-296.html
   My bibliography  Save this article

Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis

Author

Listed:
  • Alberto Abadie
  • Susan Athey
  • Guido W. Imbens
  • Jeffrey M. Wooldridge

Abstract

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.

Suggested Citation

  • Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2020. "Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis," Econometrica, Econometric Society, vol. 88(1), pages 265-296, January.
  • Handle: RePEc:wly:emetrp:v:88:y:2020:i:1:p:265-296
    DOI: 10.3982/ECTA12675
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA12675
    Download Restriction: no

    File URL: https://libkey.io/10.3982/ECTA12675?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Charles F. Manski, 2013. "Response to the Review of ‘Public Policy in an Uncertain World’," Economic Journal, Royal Economic Society, vol. 0, pages 412-415, August.
    2. Angus Deaton, 2010. "Instruments, Randomization, and Learning about Development," Journal of Economic Literature, American Economic Association, vol. 48(2), pages 424-455, June.
    3. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, November.
    4. Alberto Abadie & Susan Athey & Guido Imbens & Jeffrey Wooldridge, 2017. "When Should You Adjust Standard Errors for Clustering?," Papers 1710.02926, arXiv.org, revised Sep 2022.
    5. Liran Einav & Amy Finkelstein & Paul Schrimpf, 2015. "The Response of Drug Expenditure to Nonlinear Contract Design: Evidence from Medicare Part D," The Quarterly Journal of Economics, Oxford University Press, vol. 130(2), pages 841-899.
    6. Charles F. Manski & John V. Pepper, 2018. "How Do Right-to-Carry Laws Affect Crime Rates? Coping with Ambiguity Using Bounded-Variation Assumptions," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 232-244, May.
    7. Karthik Muralidharan & Paul Niehaus, 2017. "Experimentation at Scale," Journal of Economic Perspectives, American Economic Association, vol. 31(4), pages 103-124, Fall.
    8. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    9. Lu, Jiannan, 2016. "On randomization-based and regression-based inferences for 2K factorial designs," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 72-78.
    10. Munnell, Alicia H. & Geoffrey M. B. Tootell & Lynn E. Browne & James McEneaney, 1996. "Mortgage Lending in Boston: Interpreting HMDA Data," American Economic Review, American Economic Association, vol. 86(1), pages 25-53, March.
    11. Henry S. Farber, 2015. "Why you Can’t Find a Taxi in the Rain and Other Labor Supply Lessons from Cab Drivers," The Quarterly Journal of Economics, Oxford University Press, vol. 130(4), pages 1975-2026.
    12. White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-170, February.
    13. Alberto Abadie & Guido W. Imbens & Fanyin Zheng, 2014. "Inference for Misspecified Models With Fixed Regressors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1601-1614, December.
    14. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    15. repec:adr:anecst:y:2008:i:91-92:p:09 is not listed on IDEAS
    16. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    17. Manski, Charles F., 2013. "Public Policy in an Uncertain World: Analysis and Decisions," Economics Books, Harvard University Press, number 9780674066892, September.
    18. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2014. "Finite Population Causal Standard Errors," NBER Working Papers 20325, National Bureau of Economic Research, Inc.
    19. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(2), pages 451-470, April.
    20. Alberto Abadie & Guido W. Imbens, 2008. "Estimation of the Conditional Variance in Paired Experiments," Annals of Economics and Statistics, GENES, issue 91-92, pages 175-187.
    21. Stefano DellaVigna & Attila Lindner & Balázs Reizer & Johannes F. Schmieder, 2017. "Reference-Dependent Job Search: Evidence from Hungary," The Quarterly Journal of Economics, Oxford University Press, vol. 132(4), pages 1969-2018.
    22. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    23. Micere Keels & Greg Duncan & Stefanie Deluca & Ruby Mendenhall & James Rosenbaum, 2005. "Fifteen years later: Can residential mobility programs provide a long-term escape from neighborhood segregation, crime, and poverty," Demography, Springer;Population Association of America (PAA), vol. 42(1), pages 51-73, February.
    24. Joshua D. Angrist, 1998. "Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants," Econometrica, Econometric Society, vol. 66(2), pages 249-288, March.
    25. Rema Hanna & Sendhil Mullainathan & Joshua Schwartzstein, 2014. "Learning Through Noticing: Theory and Evidence from a Field Experiment," The Quarterly Journal of Economics, Oxford University Press, vol. 129(3), pages 1311-1353.
    26. Peter M. Aronow & Cyrus Samii, 2016. "Does Regression Produce Representative Estimates of Causal Effects?," American Journal of Political Science, John Wiley & Sons, vol. 60(1), pages 250-267, January.
    27. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2017. "Sampling-based vs. Design-based Uncertainty in Regression Analysis," Papers 1706.01778, arXiv.org, revised Jun 2019.
    2. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    3. Guido W. Imbens, 2020. "Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics," Journal of Economic Literature, American Economic Association, vol. 58(4), pages 1129-1179, December.
    4. Jeffrey D. Michler & Anna Josephson, 2022. "Recent developments in inference: practicalities for applied economics," Chapters, in: A Modern Guide to Food Economics, chapter 11, pages 235-268, Edward Elgar Publishing.
    5. Susan Athey & Guido Imbens, 2016. "The Econometrics of Randomized Experiments," Papers 1607.00698, arXiv.org.
    6. Susan Athey & Raj Chetty & Guido Imbens, 2020. "Combining Experimental and Observational Data to Estimate Treatment Effects on Long Term Outcomes," Papers 2006.09676, arXiv.org.
    7. Richard H. Spady & Sami Stouli, 2018. "Simultaneous Mean-Variance Regression," Bristol Economics Discussion Papers 18/697, School of Economics, University of Bristol, UK.
    8. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    9. Matthew D. Webb & James MacKinnon & Morten Nielsen, 2021. "Cluster–robust inference: A guide to empirical practice," Economics Virtual Symposium 2021 6, Stata Users Group.
    10. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    11. Ding, Peng, 2021. "The Frisch–Waugh–Lovell theorem for standard errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
    12. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    13. Bo, Hao & Galiani, Sebastian, 2021. "Assessing external validity," Research in Economics, Elsevier, vol. 75(3), pages 274-285.
    14. Mechoulan, Stéphane, 2020. "Civil unrest, emergency powers, and spillover effects: A mixed methods analysis of the 2005 French riots," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 305-326.
    15. Peng Ding, 2020. "The Frisch--Waugh--Lovell Theorem for Standard Errors," Papers 2009.06621, arXiv.org.
    16. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    17. Cl'ement de Chaisemartin & Jaime Ramirez-Cuellar, 2019. "At What Level Should One Cluster Standard Errors in Paired and Small-Strata Experiments?," Papers 1906.00288, arXiv.org, revised Sep 2022.
    18. Sloczynski, Tymon, 2020. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," IZA Discussion Papers 13283, Institute of Labor Economics (IZA).
    19. Hirschauer, Norbert & Grüner, Sven & Mußhoff, Oliver & Becker, Claudia & Jantsch, Antje, 2020. "Can p-values be meaningfully interpreted without random sampling?," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, pages 71-91.
    20. Haoge Chang & Joel Middleton & P. M. Aronow, 2021. "Exact Bias Correction for Linear Adjustment of Randomized Controlled Trials," Papers 2110.08425, arXiv.org, revised Oct 2021.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:emetrp:v:88:y:2020:i:1:p:265-296. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/essssea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.