(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).

References

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.

Глава 8. Контрфактивные суждения: глубинный анализ миров, которые могли бы существовать

Annotated Bibliography

The definition of counterfactuals as derivatives of structural equations was introduced by Balke and Pearl (1994a, 1994b) and was used to estimate probabilities of causation in legal settings. The relationships between this framework and those developed by Rubin and Lewis are discussed at length in Pearl (2000, Chapter 7), where they are shown to be logically equivalent; a problem solved in one framework would yield the same solution in another.

Recent books in social science (e.g., Morgan and Winship, 2015) and in health science (e.g., VanderWeele, 2015) are taking the hybrid, graph-counterfactual approach pursued in our book.

The section on linear counterfactuals is based on Pearl (2009, pp. 389–391), which also provides the solution to the problem posed in note 12. Our discussion of ETT is based on Shpitser and Pearl (2009). Legal questions of attribution, as well as probabilities of causation, are discussed at length in Greenland (1999), who pioneered the counterfactual approach to such questions. Our treatment of PN, PS, and PNS is based on Tian and Pearl (2000) and Pearl (2009, Chapter 9). A gentle approach to