IDEAS home Printed from
   My bibliography  Save this paper

Regressions, Short and Long


  • Philip Cross

    (Georgetown University)

  • Charles F. Manski

    (Northwestern University)


We study the problem of identification of the long regression E(y|x,z) when the short conditional distributions P(y|x) and P(z|x) are known but the long conditional distribution P(y|x,z) is not known. This problem often arises when a researcher utilizes data from two separate data sets. (A leading example is the ecological inference problem of political science, where voting behavior across electoral districts is observed from administrative records, the demographic composition of voters within a district is observed from census data, and the researcher wants to infer voting behavior conditional on district and demographic attributes.) We isolate an identification region containing feasible values of the long regression, and show that this region forms a sharp bound on the long regression. The identification region can be calculated precisely when y has finite support. When y has infinite support we characterize two sets, one that contains the identification region, and one that is contained by it. Following this completely nonparametric analysis, we examine the identifying power yielded by exclusion restrictions across distinct covariate values. Such restrictions cause the identification region to shrink, in many cases to a single point. To illustrate the theory, we pose and address this hypothetical question: What would be the outcome if the 1996 U.S. presidential election were re-enacted in a population of different demographic composition, ceteris paribus?

Suggested Citation

  • Philip Cross & Charles F. Manski, 2000. "Regressions, Short and Long," Econometric Society World Congress 2000 Contributed Papers 0385, Econometric Society.
  • Handle: RePEc:ecm:wc2000:0385

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. A. Meltzer & Peter Ordeshook & Thomas Romer, 1983. "Introduction," Public Choice, Springer, vol. 41(1), pages 1-5, January.
    2. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    3. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    4. A. P. Thirlwall, 1983. "Introduction," Journal of Post Keynesian Economics, Taylor & Francis Journals, vol. 5(3), pages 341-344, March.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
    2. Peter Sandholt Jensen & Allan H. W├╝rtz, 2006. "On determining the importance of a regressor with small and undersized samples," Economics Working Papers 2006-08, Department of Economics and Business Economics, Aarhus University.
    3. Tatiana V. Komarova & Denis Nekipelov & Evgeny Yakovlev, 2011. "Identification, data combination and the risk of disclosure," CeMMAP working papers CWP38/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Mullin, Charles H., 2006. "Identification and estimation with contaminated data: When do covariate data sharpen inference?," Journal of Econometrics, Elsevier, vol. 130(2), pages 253-272, February.
    5. Timothy G. Conley & Giorgio Topa, 2003. "Identification of local interaction models with imperfect location data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(5), pages 605-618.
    6. Dang, Hai-Anh & Lanjouw, Peter & Luoto, Jill & McKenzie, David, 2014. "Using repeated cross-sections to explore movements into and out of poverty," Journal of Development Economics, Elsevier, vol. 107(C), pages 112-128.

    More about this item


    Access and download statistics


    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:ecm:wc2000:0385. 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: (Christopher F. Baum). General contact details of provider: .

    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 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.

    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.