IDEAS home Printed from
   My bibliography  Save this article

Uniform consistency in causal inference


  • James M. Robins


There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934). Spirtes (1994), Spirtes et al. (1993) and Pearl & Verma (1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are 'pointwise consistent', but 'uniformly consistent' tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as BIC or AIC. The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • James M. Robins, 2003. "Uniform consistency in causal inference," Biometrika, Biometrika Trust, vol. 90(3), pages 491-515, September.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:3:p:491-515

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.


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

    Cited by:

    1. Daniel Commenges & Anne Gégout-Petit, 2009. "A general dynamical statistical model with causal interpretation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 719-736.
    2. Chen, Pu & Hsiao, Chih-Ying, 2010. "Looking behind Granger causality," MPRA Paper 24859, University Library of Munich, Germany.
    3. Mendonça, Mário Jorge & Loureiro, Paulo R.A. & Sachsida, Adolfo, 2012. "The dynamics of land-use in Brazilian Amazon," Ecological Economics, Elsevier, vol. 84(C), pages 23-36.
    4. Lima, Elcyon Caiado & Maka, Alexis & Céspedes, Brisne, 2008. "Monetary Policy, Inflation and the Level of Economic Activity in Brazil After the Real Plan: Stylized Facts from SVAR Models," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 62(2), October.
    5. Klimova, Anna & Uhler, Caroline & Rudas, Tamás, 2015. "Faithfulness and learning hypergraphs from discrete distributions," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 57-72.
    6. Chen, Pu, 2010. "A time series causal model," MPRA Paper 24841, University Library of Munich, Germany.
    7. repec:sbe:breart:v:31:y:2011:i:1:a:3410 is not listed on IDEAS

    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:oup:biomet:v:90:y:2003:i:3:p:491-515. 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: (Oxford University Press) or (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.

    We have no references for this item. You can help adding them by using 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.