Correlations versus Causation

  • Heather Brown


In this chapter, we introduce the concept of correlation versus causation. We show how to estimate a simple multivariate regression model using as an example the relationship between body mass index and wages. We outline how models estimated by ordinary least squares will be unbiased if certain conditions are met that are unlikely to be the case in most real-world scenarios. Next, we outline the different types of bias that you are likely to encounter when estimating. Finally, we introduce an instrumental approach as one method for estimating causal relationships.


Correlation Causation Endogeneity Omitted variable bias Reverse causality Instrumental variable 

References and Further Reading

  1. Bernal, J. L., Cummins, S., & Gasparrini, A. (2017). Interrupted time series regression for the evaluation of public health interventions: A tutorial. International Journal of Epidemiology, 46(1), 348–355.Google Scholar
  2. Cragg, J. G., & Donald, S. G. (1993). Testing identifiability and specification in instrumental variable models. Econometric Theory, 9(2), 222–240.CrossRefGoogle Scholar
  3. Han, E., Norton, E. C., & Powell, L. M. (2011). Direct and indirect effects of body weight on adult wages. Economics & Human Biology, 9(4), 381–392.CrossRefGoogle Scholar
  4. Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4): 1029–1054. JSTOR 1912775. CrossRefGoogle Scholar
  5. Kontopantelis, E., Doran, T., Springate, D. A., Buchan, I., & Reeves, D. (2015). Regression based quasi-experimental approach when randomisation is not an option: Interrupted time series analysis. BMJ, 350, h2750.CrossRefGoogle Scholar
  6. Sargan, J. D. (1958). The estimation of economic relationships using instrumental variables. Econometrica, 26(3): 393–415. JSTOR 1907619.
  7. Stock, J. H., & Yogo, M. (2002). Testing for weak instruments in linear IV regression.Google Scholar
  8. University of Essex. Institute for Social and Economic Research, NatCen Social Research, Kantar Public. (2016). Understanding society: Waves 1-6, 2009–2015 [data collection], 8th ed. UK Data Service. SN: 6614,

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Heather Brown
    • 1
  1. 1.Newcastle UniversityNewcastle upon TyneUK

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