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TRYGVE HAAVELMO AND THE EMERGENCE OF CAUSAL CALCULUS

Published online by Cambridge University Press:  10 June 2014

Judea Pearl*
Affiliation:
University of California, Los Angeles
*
*Address correspondence to Judea Pearl, University of California, Los Angeles, Computer Science Department, Los Angeles, CA, 90095-1596, USA; e-mail: [email protected].

Abstract

Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had (and still have) to overcome and lays out a logical framework that has evolved from Haavelmo’s insight and matured into a coherent and comprehensive account of the relationships between theory, data, and policy questions. The mathematical tools that emerge from this framework now enable investigators to answer complex policy and counterfactual questions using simple routines, some by mere inspection of the model’s structure. Several such problems are illustrated by examples, including misspecification tests, nonparametric identification, mediation analysis, and introspection. Finally, we observe that economists are largely unaware of the benefits that Haavelmo’s ideas bestow upon them and, to close this gap, we identify concrete recent advances in causal analysis that economists can utilize in research and education.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Angrist, J., Imbens, G., & Rubin, D. (1996) Identification of causal effects using instrumental variables (with comments). Journal of the American Statistical Association 91, 444472.CrossRefGoogle Scholar
Angrist, J.D. & Pischke, J.-S. (2010) The credibility revolution in empirical economics: How better research design is taking the con out of econometrics. Journal of Economic Perspectives 24,330.CrossRefGoogle Scholar
Balke, A. & Pearl, J. (1995) Counterfactuals and policy analysis in structural models. In Besnard, P. & Hanks, S. (eds.), Uncertainty in Artificial Intelligence 11, pp. 1118. Morgan Kaufmann.Google Scholar
Balke, A. & Pearl, J. (1997) Bounds on treatment effects from studies with imperfect compliance. Journal of the American Statistical Association 92, 11721176.CrossRefGoogle Scholar
Bareinboim, E. & Pearl, J. (2012) Controlling selection bias in causal inference. In Lawrence, N. & Girolami, M. (eds.), Proceedings of the 15th International Conference on Artificial Intelligence and Statistics (AISTATS), pp. 100108. JMLR.Google Scholar
Bareinboim, E., Tian, J., & Pearl, J. (2014) Recovering from selection bias in causal and statistical inference. Technical report R-425, Department of Computer Science, University of California, Los Angeles, CA. Forthcoming Proceedings of the Twenty-Eighth Conference on Artificial Intelligence (AAAI-14). Available athttp://ftp.cs.ucla.edu/pub/stat_ser/r425.pdf.CrossRefGoogle Scholar
Brito, C. & Pearl, J. (2002) Generalized instrumental variables. In Darwiche, A. & Friedman, N. (eds.), Uncertainty in Artificial Intelligence, Proceedings of the Eighteenth Conference, pp. 8593. Morgan Kaufmann.Google Scholar
Brito, C. & Pearl, J. (2006) Graphical condition for identification in recursive SEM. In Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence, pp. 4754. AUAI Press.Google Scholar
Campbell, D. & Stanley, J. (1963) Experimental and Quasi-Experimental Designs for Research. Wadsworth Publishing.Google Scholar
Cartwright, N. (1989) Nature’s Capacities and Their Measurement. Clarendon Press.Google Scholar
Cartwright, N. (2007) Hunting Causes and Using Them: Approaches in Philosophy and Economics. Cambridge University Press.CrossRefGoogle Scholar
Chalak, K. & White, H. (2011) An extended class of instrumental variables for the estimation of causal effects. Canadian Journal of Economics 44, 131.CrossRefGoogle Scholar
Chen, B. & Pearl, J. (2013) Regression and causation: A critical examination of econometrics textbooks. Real-World Economics Review 65, 220.Google Scholar
Dawid, A. (1979) Conditional independence in statistical theory. Journal of the Royal StatisticalSociety, Series B 41, 131.Google Scholar
Engle, R., Hendry, D., & Richard, J. (1983) Exogeneity. Econometrica 51, 277304.CrossRefGoogle Scholar
Foygel, R., Draisma, J., & Drton, M. (2012) Half-trek criterion for generic identifiability of linear structural equation models. The Annals of Statistics 40, 16821713.CrossRefGoogle Scholar
Galles, D. & Pearl, J. (1998) An axiomatic characterization of causal counterfactuals. Foundation of Science 3, 151182.Google Scholar
Glymour, M. & Greenland, S. (2008) Causal diagrams. In Rothman, K., Greenland, S., & Lash, T. (eds.), Modern Epidemiology, 3rd ed., pp. 183209. Lippincott Williams & Wilkins.Google Scholar
Goldberger, A. (1992) Models of substance; comment on N. Wermuth, ‘On block-recursive linear regression equations’. Brazilian Journal of Probability and Statistics 6, 156.Google Scholar
Greenland, S. & Pearl, J. (2011) Adjustments and their consequences – collapsibility analysis using graphical models. International Statistical Review 79, 401426.CrossRefGoogle Scholar
Haavelmo, T. (1943) The statistical implications of a system of simultaneous equations. Econometrica 11, 112. Reprinted in D.F. Hendry & M.S. Morgan (eds.) (1995) The Foundations of Econometric Analysis, pp. 477–490. Cambridge University Press.CrossRefGoogle Scholar
Haavelmo, T. (1944) The probability approach in econometrics (1944). Supplement to Econometrica 12, 12–17, 26–31, 3339.Google Scholar
Halpern, J. (1998) Axiomatizing causal reasoning. In Cooper, G. & Moral, S. (eds.), Uncertainty in Artificial Intelligence, pp. 202210. Morgan Kaufmann. Also Halpern, J. (2000) Journal of Artificial Intelligence Research 12, 17–37.Google Scholar
Heckman, J. (1979) Sample selection bias as a specification error. Econometrica 47, 153161.CrossRefGoogle Scholar
Heckman, J. (2000) Causal parameters and policy analysis in economics: A twentieth century retrospective. The Quarterly Journal of Economics 115, 4597.CrossRefGoogle Scholar
Heckman, J. (2003) Conditioning causality and policy analysis. Journal of Econometrics 112,7378.CrossRefGoogle Scholar
Heckman, J. (2008) Econometric causality. International Statistical Review 76, 127.CrossRefGoogle Scholar
Heckman, J. (2010) Building bridges between structural and program evaluation approaches to evaluating policy. Journal of Economic Literature 48, 356398.CrossRefGoogle ScholarPubMed
Heckman, J. & Pinto, R. (2013) Causal analysis after Haavelmo. Technical report NBER Technical Working paper 19453, National Bureau of Economic Research, MA.CrossRefGoogle Scholar
Heckman, J. & Vytlacil, E. (2007) Econometric evaluation of social programs, part I: Causal models, structural models and econometric policy evaluation. In Handbook of Econometrics, vol. 6B, pp. 47794874. Elsevier B.V.CrossRefGoogle Scholar
Hirano, K. & Imbens, G. (2001) Estimation of causal effects using propensity score weighting: An application to data on right heart catheterization. Health Services and Outcomes Research Methodology 2, 259278.CrossRefGoogle Scholar
Hoover, K.D. (2011) Counterfactuals and causal structure. In Illari, P.M., Russo, F., & Williamson, J. (eds.), Causality in the Sciences, pp. 338360. Clarendon Press.CrossRefGoogle Scholar
Imbens, G. & Wooldridge, J. (2009) Recent developments in the econometrics of program evaluation. Journal of Economic Literature 47, 586.CrossRefGoogle Scholar
Keane, M.P. (2010) A structural perspective on the experimentalist school. Journal of Economic Perspectives 24, 4758.CrossRefGoogle Scholar
Kyono, T. (2010) Commentator: A front-end user-interface module for graphical and structural equation modeling. Technical report R-364. Available athttp://ftp.cs.ucla.edu/pub/stat_ser/r364.pdf. Master thesis, Department of Computer Science, University of California, Los Angeles, CA.Google Scholar
Leamer, E.E. (2010) Tantalus on the road to asymptopia. Journal of Economic Perspectives 24, 3146.CrossRefGoogle Scholar
Lee, J.J. (2012) Correlation and causation in the study of personality. European Journal of Personality 26, 372390.CrossRefGoogle Scholar
Lewis, D. (1973) Counterfactuals. Harvard University Press.Google Scholar
Lucas, R Jr.. (1976) Econometric policy evaluation: A critique. In Brunner, K. & Meltzer, A. (eds.), The Phillips Curve and Labor Markets, pp. 1946. CRCS, vol. 1. North-Holland.Google Scholar
Marschak, J. (1953) Economic measurements for policy and prediction. In Hood, W.C. & Koopmans, T. (eds.), Studies in Econometric Method, pp. 126. Cowles Commission Monograph 10. Wiley and Sons, Inc.Google Scholar
Morgan, S. & Winship, C. (2007) Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research). Cambridge University Press.CrossRefGoogle Scholar
Nevo, A. & Whinston, M.D. (2010) Taking the dogma out of econometrics: Structural modeling and credible inference. Journal of Economic Perspectives 24, 6982.CrossRefGoogle Scholar
Neyman, J. (1923) Sur les applications de la thar des probabilities aux experiences Agaricales: Essay des principle. English translation of excerpts by Dabrowska, D. & Speed, T. (1990) Statistical Science 5, 463472.Google Scholar
Oster (2013) Unobservable selection and coefficient stability: Theory and validation. Technical report, National Bureau of Economic Research.CrossRefGoogle Scholar
Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.Google Scholar
Pearl, J. (1993) Comment: Graphical models, causality, and intervention. Statistical Science 8, 266269.CrossRefGoogle Scholar
Pearl, J. (1994) A probabilistic calculus of actions. In de Mantaras, R.L. & Poole, D. (eds.), Uncertainty in Artificial Intelligence 10, pp. 454462. Morgan Kaufmann.Google Scholar
Pearl, J. (2000) Causality: Models, Reasoning, and Inference. Cambridge University Press. 2nd ed., 2009.Google Scholar
Pearl, J. (2001) Direct and indirect effects. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, pp. 411420. Morgan Kaufmann.Google Scholar
Pearl, J. (2004) Robustness of causal claims. In Chickering, M. & Halpern, J. (eds.), Proceedings of the Twentieth Conference on Uncertainty in Artificial Intelligence, pp. 446453. AUAI Press.Google Scholar
Pearl, J. (2009a) Causality: Models, Reasoning, and Inference, 2nd ed.Cambridge University Press.CrossRefGoogle Scholar
Pearl, J. (2009b) Myth, confusion, and science in causal analysis. Technical report R-348, University of California, Los Angeles, CA. Available athttp://ftp.cs.ucla.edu/pub/stat_ser/r348.pdf.Google Scholar
Pearl, J. (2010a) The foundations of causal inference. Sociological Methodology 40, 75149.CrossRefGoogle Scholar
Pearl, J. (2010b) An introduction to causal inference. The International Journal of Biostatistics 6, Iss. 2, Article 7; doi:10.2202/1557–4679.1203. Available at http://ftp.cs.ucla.edu/pub/stat_ser/r354–corrected–reprint.pdf.CrossRefGoogle ScholarPubMed
Pearl, J. (2010c) On the consistency rule in causal inference: Axiom, definition, assumption, or theorem? Epidemiology 21, 872875.CrossRefGoogle ScholarPubMed
Pearl, J. (2010d) Review of N. Cartwright ‘Hunting causes and using them’. Economics and Philosophy 26, 6977.CrossRefGoogle Scholar
Pearl, J. (2011a) Graphical models, potential outcomes and causal inference: Comment on Lindquist and Sobel. Statistics in Medicine 58, 770771.Google Scholar
Pearl, J. (2011b) Principal stratification a goal or a tool? The International Journal of Biostatistics 7, Iss. 1, Article 20; doi:10.2202/1557-4679.1322. Available at http://ftp.cs.ucla.edu/pub/stat_ser/r382.pdf.CrossRefGoogle ScholarPubMed
Pearl, J. (2011c) Understanding bias amplification. American Journal of Epidemiology 174, 12231227; doi:10.1093/aje/kwr352.CrossRefGoogle ScholarPubMed
Pearl, J. (2012a) The causal foundations of structural equation modeling. In Hoyle, R. (ed.), Handbook of Structural Equation Modeling, pp. 6891. Guilford Press.Google Scholar
Pearl, J. (2012b) The causal mediation formula – a guide to the assessment of pathways and mechanisms. Prevention Science 13, 426436; doi:10.1007/s11121–011–0270–1.CrossRefGoogle Scholar
Pearl, J. (2014) Interpretation and identification of causal mediation. Technical report R-389, Department of Computer Science, University of California, Los Angeles, CA. Available athttp://ftp.cs.ucla.edu/pub/stat_ser/r389.pdf. Forthcoming Psychological Methods, 2014.CrossRefGoogle Scholar
Pearl, J. (2013a) Lindear models: A useful “microscope” for causal analysis. Journal of Causal Inference 1, 155170.CrossRefGoogle Scholar
Pearl, J. (2013b) Reflections on Heckman and Pinto’s ‘causal analysis after Haavelmo’. Technicalreport R-420, Department of Computer Science, University of California, Los Angeles, CA. Available athttp://ftp.cs.ucla.edu/pub/stat_ser/r420.pdf. Working paper.CrossRefGoogle Scholar
Pearl, J. & Bareinboim, E. (2011) Transportability of causal and statistical relations: A formal approach. In Proceedings of the Twenty-Fifth Conference on Artificial Intelligence (AAAI-11). Available athttp://ftp.cs.ucla.edu/pub/stat_ser/r372a.pdf.Google Scholar
Pearl, J. & Paz, A. (1986) On the logic of representing dependencies by graphs. In Proceedings of the Canadian AI Conference, Montreal, Ontario, Canada, pp. 9498.Google Scholar
Pearl, J. & Verma, T. (1987) The logic of representing dependencies by directed graphs. In Proceedings of the Sixth National Conference on Artificial Intelligence, pp. 374379. Morgan Kaufmann Publishers.Google Scholar
Pearl, J. & Verma, T. (1991) A theory of inferred causation. In Allen, J., Fikes, R., & Sandewall, E. (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, pp. 441452. Morgan Kaufmann.Google Scholar
Phiromswad, P. & Hoover, K.D. (2013) Selecting instrumental variables: A graph-theoretic approach. Available at SSRN: http://ssrn.com/abstract=2318552 or http://dx.doi.org/10.2139/ssrn.2318552.CrossRefGoogle Scholar
Richard, J. (1980) Models with several regimes and changes in exogeneity. Review of Economic Studies 47, 120.CrossRefGoogle Scholar
Rosenbaum, P. & Rubin, D. (1983) The central role of propensity score in observational studies for causal effects. Biometrika 70, 4155.CrossRefGoogle Scholar
Rubin, D. (1974) Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66, 688701.CrossRefGoogle Scholar
Rubin, D. (2009) Author’s reply: Should observational studies be designed to allow lack of balance in covariate distributions across treatment group? Statistics in Medicine 28, 14201423.CrossRefGoogle Scholar
Rubin, D. (2010) Reflections stimulated by the comments of Shadish (2010) and West and Thoemmes (2010). Psychological Methods 15, 3946.CrossRefGoogle ScholarPubMed
Shpitser, I. & Pearl, J. (2008) Complete identification methods for the causal hierarchy. Journal of Machine Learning Research 9, 19411979.Google Scholar
Simon, H. & Rescher, N. (1966) Cause and counterfactual. Philosophy and Science 33, 323340.CrossRefGoogle Scholar
Sims, C.A. (2010) But economics is not an experimental science. Journal of Economic Perspectives 24, 5968.CrossRefGoogle Scholar
Spanos, A. (2010) Theory testing in economics and the error-statistical perspective. In Mayo, D.G. & Spanos, A. (eds.), Error and Inference, pp. 202246. Cambridge University Press.Google Scholar
Spirtes, P., Glymour, C., & Scheines, R. (1993) Causation, Prediction, and Search. Springer-Verlag.CrossRefGoogle Scholar
Stock, J. & Watson, M. (2011) Introduction to Econometrics, 3rd ed.Addison-Wesley.Google Scholar
Strotz, R. & Wold, H. (1960) Recursive versus nonrecursive systems: An attempt at synthesis. Econometrica 28, 417427.CrossRefGoogle Scholar
Vansteelandt, S. & Lange, C. (2012) Causation and causal inference for genetic effects. Human Genetics 131, 16651676. Special Issue on Genetic Epidemiology: Study Designs and Methods Post-GWAS.CrossRefGoogle ScholarPubMed
Verma, T. & Pearl, J. (1990) Equivalence and synthesis of causal models. In Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, Cambridge, MA. Also in Bonissone, P., Henrion, M., Kanal, L.N., & Lemmer, J.F. (eds.) (1991) Uncertainty in Artificial Intelligence 6, pp. 255–268. Elsevier Science Publishers, B.V.Google Scholar
Wermuth, N. (1992) On block-recursive regression equations (with discussion). Brazilian Journal of Probability and Statistics 6, 156.Google Scholar
White, H. & Lu, X. (2010) Robustness checks and robustness tests in applied economics. Technical report, Department of Economics, University of California, San Diego, CA. Discussionpaper.Google Scholar