Extensions of the back-door and front-door adjustments were first reported in Tian and Pearl (2002) based on Tian’s c-component factorization. These were followed by Shpitser’s algorithmization of the do-calculus (Shpitser and Pearl, 2006a) and then the completeness results of Shpitser and Pearl (2006b) and Huang and Valtorta (2006).

The economists among our readers should note that the cultural resistance of some economists to graphical tools of analysis (Heckman and Pinto, 2015; Imbens and Rubin, 2015) is not shared by all economists. White and Chalak (2009), for example, have generalized and applied the do-calculus to economic systems involving equilibrium and learning. Recent textbooks in the social and behavioral sciences, Morgan and Winship (2007) and Kline (2016), further signal to young researchers that cultural orthodoxy, like the fear of telescopes in the seventeenth century, is not long lasting in the sciences.

John Snow’s investigation of cholera was very little appreciated during his lifetime, and his one-paragraph obituary in Lancet did not even mention it. Remarkably, the premier British medical journal “corrected” its obituary 155 years later (Hempel, 2013). For more biographical material on Snow, see Hill (1955) and Cameron and Jones (1983). Glynn and Kashin (2018) is one of the first papers to demonstrate empirically that front-door adjustment is superior to back-door adjustment when there are unobserved confounders. Freedman’s critique of the smoking — tar — lung cancer example can be found in a chapter of Freedman (2010) titled “On Specifying Graphical Models for Causation.”

Introductions to instrumental variables can be found in Greenland (2000) and in many textbooks of econometrics (e.g., Bowden and Turkington, 1984; Wooldridge, 2013).

Generalized instrumental variables, extending the classical definition given in our text, were introduced in Brito and Pearl (2002).

The program DAGitty (available online at http://www.dagitty.net/dags.html) permits users to search the diagram for generalized instrumental variables and reports the resulting estimands (Textor, Hardt, and Knüppel, 2011). Another diagram-based software package for decision making is BayesiaLab (www.bayesia.com).

Bounds on instrumental variable estimates are studied at length in Chapter 8 of Pearl (2009) and are applied to the problem of noncompliance. The LATE approximation is advocated and debated in Imbens (2010).

Bareinboim, E., and Pearl, J. (2012). Causal inference by surrogate experiments: z-identifiability. In Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (N. de Freitas and K. Murphy, eds.). AUAI Press, Corvallis, OR.

Bowden, R., and Turkington, D. (1984). Instrumental Variables. Cambridge University Press, Cambridge, UK.

Brito, C., and Pearl, J. (2002). Generalized instrumental variables. In Uncertainty in Artificial Intelligence, Proceedings of the Eighteenth Conference (A. Darwiche and N. Friedman, eds.). Morgan Kaufmann, San Francisco, CA, 85–93.

Cameron, D., and Jones, I. (1983). John Snow, the Broad Street pump, and modern epidemiology. International Journal of Epidemiology 12: 393–396.

Cox, D., and Wermuth, N. (2015). Design and interpretation of studies: Relevant concepts from the past and some extensions. Observational Studies 1. Available at: https://arxiv.org/pdf/1505.02452.pdf.

Freedman, D. (2010). Statistical Models and Causal Inference: A Dialogue with the Social Sciences. Cambridge University Press, New York, NY.

Glynn, A., and Kashin, K. (2018). Front-door versus back-door adjustment with unmeasured confounding: Bias formulas for front-door and hybrid adjustments. Journal of the American Statistical Association. To appear.

Greenland, S. (2000). An introduction to instrumental variables for epidemiologists. International Journal of Epidemiology 29: 722–729. Heckman, J. J., and Pinto, R. (2015). Causal analysis after Haavelmo. Econometric Theory 31: 115–151.

Hempel, S. (2013). Obituary: John Snow. Lancet 381: 1269–1270.

Hill, A. B. (1955). Snow — An appreciation. Journal of Economic Perspectives 48: 1008–1012.

Huang, Y., and Valtorta, M. (2006). Pearl’s calculus of intervention is complete. In Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (R. Dechter and T. Richardson, eds.). AUAI Press, Corvallis, OR, 217–224.

Imbens, G. W. (2010). Better LATE than nothing: Some comments on Deaton (2009) and Heckman and Urzua (2009). Journal of Economic Literature 48: 399–423.

Imbens, G. W., and Rubin, D. B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press, Cambridge, MA.

Kline, R. B. (2016). Principles and Practice of Structural Equation Modeling. 3rd ed. Guilford, New York, NY.

Morgan, S., and Winship, C. (2007). Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research). Cambridge University Press, New York, NY.

Pearl, J. (2009). Causality: Models, Reasoning, and Inference. 2nd ed. Cambridge University Press, New York, NY.

Pearl, J. (2013). Reflections on Heckman and Pinto’s “Causal analysis after Haavelmo.” Tech. Rep. R-420. Department of Computer Science, University of California, Los Angeles, CA. Working paper.

Pearl, J. (2015). Indirect confounding and causal calculus (on three papers by Cox and Wermuth). Tech. Rep. R-457. Department of Computer Science, University of California, Los Angeles, CA.

Shpitser, I., and Pearl, J. (2006a). Identification of conditional interventional distributions. In Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (R. Dechter and T. Richardson, eds.). AUAI Press, Corvallis, OR, 437–444.

Shpitser, I., and Pearl, J. (2006b). Identification of joint interventional distributions in recursive semi-Markovian causal models. In Proceedings of the Twenty-First National Conference on Artificial Intelligence. AAAI Press, Menlo Park, CA, 1219–1226.

Stock, J., and Trebbi, F. (2003). Who invented instrumental variable regression? Journal of Economic Perspectives 17: 177–194.

Textor, J., Hardt, J., and Knüppel, S. (2011). DAGitty: A graphical tool for analyzing causal diagrams. Epidemiology 22: 745.

Tian, J., and Pearl, J. (2002). A general identification condition for causal effects. In Proceedings of the Eighteenth National Conference on Artificial Intelligence. AAAI Press/MIT Press, Menlo Park, CA, 567–573.

Wermuth, N., and Cox, D. (2008). Distortion of effects caused by indirect confounding. Biometrika 95: 17–33. (See Pearl [2009, Chapter 4] for a general solution.)

Wermuth, N., and Cox, D. (2014). Graphical Markov models: Overview. ArXiv: 1407.7783.

White, H., and Chalak, K. (2009). Settable systems: An extension of Pearl’s causal model with optimization, equilibrium and learning. Journal of Machine Learning Research 10: 1759–1799.

Wooldridge, J. (2013). Introductory Econometrics: A Modern Approach. 5th ed. South-Western, Mason, OH.