CAUSAL ANALYSIS AFTER HAAVELMO

Haavelmo's seminal 1943 and 1944 papers are the first rigorous treatment of causality. In them, he distinguished the definition of causal parameters from their identification. He showed that causal parameters are defined using hypothetical models that assign variation to some of the inputs determining outcomes while holding all other inputs fixed. He thus formalized and made operational Marshall's (1890)ceteris paribus analysis. We embed Haavelmo's framework into the recursive framework of Directed Acyclic Graphs (DAGs) used in one influential recent approach to causality (Pearl, 2000) and in the related literature on Bayesian nets (Lauritzen, 1996). We compare the simplicity of an analysis of causality based on Haavelmo's methodology with the complex and nonintuitive approach used in the causal literature of DAGs-the "do-calculus" of Pearl (2009). We discuss the severe limitations of DAGs and in particular of the do-calculus of Pearl in securing identification of economic models. We extend our framework to consider models for simultaneous causality, a central contribution of Haavelmo. In general cases, DAGs cannot be used to analyze models for simultaneous causality, but Haavelmo's approach naturally generalizes to cover them.

[1]  S. Lauritzen,et al.  Chain graph models and their causal interpretations , 2002 .

[2]  J. Robins.  A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[3]  Halbert White,et al.  Settable Systems: An Extension of Pearl's Causal Model with Optimization, Equilibrium, and Learning , 2009, J. Mach. Learn. Res..

[4]  J. Pearl.  [Bayesian Analysis in Expert Systems]: Comment: Graphical Models, Causality and Intervention , 1993 .

[5]  Greg Goth.  Judea Pearl Interview: A Giant of Artificial Intelligence Takes on All-Too-Real Hatred , 2006, IEEE Internet Computing.

[6]  Joshua D. Angrist,et al.  Mostly Harmless Econometrics: An Empiricist's Companion , 2008 .

[7]  Peter Spirtes,et al.  Directed Cyclic Graphical Representations of Feedback Models , 1995, UAI.

[8]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[9]  T. Speed,et al.  Recursive causal models , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[10]  J. Heckman.  The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models , 1976 .

[11]  Rosa L. Matzkin.  Nonparametric Identification in Structural Economic Models , 2013 .

[12]  T. Sargent,et al.  FORMULATING AND ESTIMATING DYNAMIC LINEAR RATIONAL EXPECTATIONS MODELS , 1980 .

[13]  Halbert White,et al.  Causality, Conditional Independence, and Graphical Separation in Settable Systems , 2012, Neural Computation.

[14]  Michael I. Jordan.  Graphical Models , 2003 .

[15]  P. Holland.  Statistics and Causal Inference , 1985 .

[16]  E. Tamer.  Incomplete Simultaneous Discrete Response Model with Multiple Equilibria , 2003 .

[17]  R. Rohh.  ALTERNATIVE METHODS FOR EVALUATING THE IMPACT OF INTERVENTIONS An Overview , 2001 .

[18]  Ronald A. Howard,et al.  Readings on the Principles and Applications of Decision Analysis , 1989 .

[19]  A. Philip Dawid,et al.  Separoids: A Mathematical Framework for Conditional Independence and Irrelevance , 2001, Annals of Mathematics and Artificial Intelligence.

[20]  George Berkeley,et al.  A treatise concerning the principles of human knowledge, 1734 , 1971 .

[21]  Ilya Segal,et al.  Solutions manual for Microeconomic theory : Mas-Colell, Whinston and Green , 1997 .

[22]  James J. Heckman,et al.  1. The Scientific Model of Causality , 2005 .

[23]  James J. Heckman,et al.  Econometric Mediation Analyses: Identifying the Sources of Treatment Effects from Experimentally Estimated Production Technologies with Unmeasured and Mismeasured Inputs , 2013, Econometric reviews.

[24]  Jin Tian,et al.  On the Identification of Causal Effects , 2015 .

[25]  H. Simon,et al.  Causal Ordering and Identifiability , 1977 .

[26]  W. Newey,et al.  Instrumental variable estimation of nonparametric models , 2003 .

[27]  Michael Margolis.  Endangered options and endangered species : what we can learn from a dubious design Preliminary and , 2012 .

[28]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[29]  Michael Heidelberger,et al.  Nature From Within: Gustav Theodor Fechner And His Psychophysical Worldview , 2004 .

[30]  Richard Blundell,et al.  Endogeneity in Nonparametric and Semiparametric Regression Models , 2022 .

[31]  Steffen L. Lauritzen,et al.  Causal Inference from Graphical Models , 2001 .

[32]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1995 .

[33]  J. Heckman.  Dummy Endogenous Variables in a Simultaneous Equation System , 1977 .

[34]  G T Fechner.  Outline of a new principle of mathematical psychology (1851) , 1987, Psychological research.

[35]  J J Heckman,et al.  Local instrumental variables and latent variable models for identifying and bounding treatment effects. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Rosa L. Matzkin.  NONPARAMETRIC IDENTIFICATION , 2012 .

[37]  J. Felson,et al.  Statistical Models and Causal Inference: A Dialogue with the Social Sciences , 2011 .

[38]  Judea Pearl,et al.  Comment: Graphical Models, Causality and Intervention , 2016 .

[39]  A. Chesher,et al.  Simultaneous equations for discrete outcomes: coherence, completeness, and identification , 2012 .

[40]  J. Robins,et al.  Alternative Graphical Causal Models and the Identification of Direct E!ects , 2010 .

[41]  D. Cox,et al.  Complex stochastic systems , 2000 .

[42]  D. Rubin.  Statistics and Causal Inference: Comment: Which Ifs Have Causal Answers , 1986 .

[43]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[44]  Rosa L. Matzkin.  Identification in Nonparametric Simultaneous Equations Models , 2008 .

[45]  M. Sobel.  Discussion: ‘The Scientific Model of Causality’ , 2005 .

[46]  J. Heckman,et al.  Econometric Causality , 2008 .

[47]  F. Galton.  Note to the memoir by Professor Karl Pearson, F. R. S., on spurious correlation , 2022, Proceedings of the Royal Society of London.

[48]  James J. Heckman,et al.  Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New Environments , 2007 .

[49]  Judea Pearl,et al.  A Theory of Inferred Causation , 1991, KR.

[50]  Jin Tian,et al.  A general identification condition for causal effects , 2002, AAAI/IAAI.

[51]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1994 .

[52]  Rosa L. Matzkin.  Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity , 2012 .

[53]  G. Yule.  On the Correlation of total Pauperism with Proportion of Out-Relief , 1895 .

[54]  T. Haavelmo,et al.  The probability approach in econometrics , 1944 .

[55]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[56]  Olav Reiersöl,et al.  Confluence analysis by means of instrumental sets of variables , 1945 .

[57]  J. Heckman,et al.  A Simultaneous Equations Linear Probability Model , 1985 .

[58]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[59]  T. Koopmans,et al.  The Identification of Structural Characteristics , 1950 .

[60]  James J. Heckman,et al.  Econometric Evaluation of Social Programs, Part I: Causal Models, Structural Models and Econometric Policy Evaluation , 2007 .

[61]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[62]  Illtyd Trethowan.  Causality , 1938 .

[63]  Yimin Huang.  A Study Of Identifiability In Causal Bayesian Networks 1 Version 0 . 3 , 2006 .

[64]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[65]  P. Spirtes,et al.  Causation, prediction, and search , 1993 .

[66]  James L. Powell,et al.  Estimation of semiparametric models , 1994 .

[67]  T. Haavelmo.  The Statistical Implications of a System of Simultaneous Equations , 1943 .

[68]  E. Vytlacil.  Independence, Monotonicity, and Latent Index Models: An Equivalence Result , 2002 .

[69]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[70]  J. Pearl.  Causal diagrams for empirical research , 1995 .

[71]  James J. Heckman,et al.  The Principles Underlying Evaluation Estimators with an Application to Matching , 2008 .

[72]  P. Humphreys,et al.  The Grand Leap1 , 1996, The British Journal for the Philosophy of Science.

[73]  F. E..  Principles of Economics , 1890, Nature.