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What did I leave out? Omitted variables in regression and qualitative comparative analysis

Abstract

Social scientists often face a fundamental problem: Did I leave something causally important out of my explanation? How do I diagnose this? Where do I look for solutions to this problem? We build bridges between regression models and qualitative comparative analysis by comparing diagnostics and solutions to the problem of omitted variables and conditions. We then discuss various approaches and tackle the theoretical issues around causality which must be addressed before attending to technical fixes. In the conclusions, we reflect on the bridges built between the two traditions and draw more general lessons about the logic of social science research.

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Notes

  1. In QCA, the term of ‘omitted variables’ is not used, also because it is inappropriate to speak about ‘variables’ (see fn. 2). However, for reasons of readability, we use this expression not only for our discussion on regression, but also when we deal with QCA.

  2. This is more than just a linguistic matter of taste. Set-theoretic methods, such as QCA, do not look at variables but model various degrees of case membership in sets. The difference between the two understandings does not so much result in different values of the variable or the set membership, respectively, but lies in the perspective: variables look at a characteristics, while sets group cases according to a given case property. Sets, therefore, are very closely linked to concepts.

  3. An instrumental variable has first and foremost a technical definition, contrary to the conceptual approach we followed when dealing with the proxy.

  4. The tilde indicates the negation of a condition.

  5. The superficiality consists in the fact that our description simplifies actual XY plots a bit. There can also be inconsistent cases in the upper right and lower left corner, namely those below the diagonal. However, for the argument made here, this is not important.

  6. Since the extreme situation is already that every case has its ‘own’ explanation, there cannot be more explanatory paths than cases, unless we allow for values of ‘unique coverage’ being zero.

  7. Another source for this phenomenon might be the generally low number of cases.

  8. One may ask at this point whether it is then justified to lower expectations for large N QCAs and whether a low-expectation large N QCA is really desirable.

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Acknowledgements

We would like to thank the reviewers and the EPS co-editor Daniel Stockemer for their comments and suggestions. We also thank Fabrizio Gilardi, Jonathan C. Kamkhaji, Gabriel Katz and the participants to the ‘cake for comments’ seminar series 2016–2017 at the University of Exeter. We are grateful to Francesca Farmer for checking style and grammar. Research for this project was funded by the ERC project 694632 Protego, Procedural Tools for Effective Governance, and by the Goethe University of Frankfurt.

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Correspondence to Claudio M. Radaelli or Claudius Wagemann.

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Radaelli, C.M., Wagemann, C. What did I leave out? Omitted variables in regression and qualitative comparative analysis. Eur Polit Sci 18, 275–290 (2019). https://doi.org/10.1057/s41304-017-0142-7

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  • DOI: https://doi.org/10.1057/s41304-017-0142-7

Keywords

  • Causality
  • Econometrics
  • Qualitative comparative analysis
  • Research design
  • Regression analysis