## An Introduction to Causal Inference (2009)

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Citations: | 29 - 13 self |

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@MISC{Pearl09anintroduction,

author = {Judea Pearl},

title = {An Introduction to Causal Inference},

year = {2009}

}

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### Abstract

### Citations

7048 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
- Pearl
- 1988
(Show Context)
Citation Context ...social science (Goldberger, 1973; Duncan, 1975), the potential-outcome framework of Neyman (1923) and Rubin (1974), and the graphical models developed for probabilistic reasoning and causal analysis (=-=Pearl, 1988-=-; Lauritzen, 1996; Spirtes et al., 2000; Pearl, 2000a). Although the basic elements of SCM were introduced in the mid 1990’s (Pearl, 1995), and have been adapted widely by epidemiologists (Greenland e... |

1369 | The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations
- Baron, Kenny
- 1986
(Show Context)
Citation Context ...s to predict behavior under a rich variety of conditions. Yet despite its ubiquity, the analysis of mediation has long been a thorny issue in the social and behavioral sciences (Judd and Kenny, 1981; =-=Baron and Kenny, 1986-=-; Muller et al., 2005; Shrout and Bolger, 2002; MacKinnon et al., 2007) primarily because structural equation modeling in those sciences were deeply entrenched in linear analysis, where the distinctio... |

1117 |
Causality: Models, Reasoning, and Inference
- Pearl
- 2000
(Show Context)
Citation Context ...ability, instrumental variables, intervention, explanation, attribution, and so on. The former can, while the latter cannot be defined in 1 The methodology of “causal discovery” (Spirtes et al. 2000; =-=Pearl 2000-=-a, Chapter 2) is likewise based on the causal assumption of “faithfulness” or “stability” – a problemindependent assumption that constrains the relationship between the structure of a model and the da... |

1103 |
Numerical Modelling of the
- S, ERRAUD, et al.
- 2000
(Show Context)
Citation Context ...e (Goldberger, 1973; Duncan, 1975), the potential-outcome framework of Neyman (1923) and Rubin (1974), and the graphical models developed for probabilistic reasoning and causal analysis (Pearl, 1988; =-=Lauritzen, 1996-=-; Spirtes et al., 2000; Pearl, 2000a). Although the basic elements of SCM were introduced in the mid 1990’s (Pearl, 1995), and have been adapted widely by epidemiologists (Greenland et al., 1999; Glym... |

1066 |
Econometric Analysis of Cross Section and Panel Data
- Wooldridge
- 2002
(Show Context)
Citation Context ...nships of this type explain the slow acceptance of causal analysis among health scientists and statisticians, and why most economists and social scientists continue to use structural equation models (=-=Wooldridge, 2002-=-; Stock and Watson, 2003; Heckman, 2008) instead of the potential-outcome alternatives advocated in Angrist et al. (1996); Holland (1988); Sobel (1998, 2008). On the other hand, the algebraic machiner... |

1012 |
The central role of the propensity score in observational studies for causal effects
- Rosenbaum, Rubin
- 1983
(Show Context)
Citation Context ...ematically to diagrams of any size and shape, thus freeing analysts from judging whether “X is conditionally ignorable given S,” a formidable mental task required in the potential-response framework (=-=Rosenbaum and Rubin, 1983-=-). The criterion also enables the analyst to search for an optimal set of covariate—namely, a set S that minimizes measurement cost or sampling variability (Tian et al., 1998). All in all, one can saf... |

746 |
Structural Equations with Latent Variables
- Bollen
- 1989
(Show Context)
Citation Context ...o nonparametric models and graphs Structural equation modeling (SEM) has been the main vehicle for effect analysis in economics and the behavioral and social sciences (Goldberger, 1972; Duncan, 1975; =-=Bollen, 1989-=-). However, the bulk of SEM methodology was developed for linear analysis and, until recently, no comparable methodology has been devised to extend its capabilities to models involving dichotomous 7 A... |

496 |
Causation, Prediction, and Search
- Spirtes, Glymour, et al.
- 1993
(Show Context)
Citation Context ...ect” as a general capacity to transmit changes among variables. Such an extension, based on simulating hypothetical interventions in the model, was proposed in (Haavelmo, 1943; Strotz and Wold, 1960; =-=Spirtes et al., 1993-=-; Pearl, 1993a, 2000a; Lindley, 2002) and has led to new ways of defining and estimating causal effects in nonlinear and nonparametric models (that is, models in which the functional form of the equat... |

468 |
Estimating causal effects of treatments in randomized and non randomized studies
- Rubin
- 1974
(Show Context)
Citation Context ...y of the judgments upon which the analysis so crucially depends. How does one recognize causal expressions in the statistical literature? Those versed in the potential-outcome notation (Neyman, 1923; =-=Rubin, 1974-=-; Holland, 1988), can recognize such expressions through the subscripts that are attached to counterfactual events and variables, e.g. Yx(u) orZxy. (Some authors use parenthetical expressions, e.g. Y ... |

441 |
Graphical models in applied multivariate statistics
- Whittaker
- 1990
(Show Context)
Citation Context ..., is defined procedurally by β Δ = E(Y |do(x0 +1))−E(Y|do(x0)) = δ δ E(Y |do(x)) = δx δx E(Yx). Naturally, all attempts to give β statistical interpretation have ended in frustrations (Holland, 1988; =-=Whittaker, 1990-=-; Wermuth, 1992; Wermuth and Cox, 1993), some persisting well into the 21st century (Sobel, 2008). 324.2 Explicating Causal Assumptions This is the second most neglected step in causal analysis. In t... |

429 |
Identification of causal effects using instrumental variables
- Angrist, Imbens, et al.
- 1996
(Show Context)
Citation Context ...Sobel (1998, 2008). On the other hand, the algebraic machinery offered by the counterfactual notation, Yx(u), once a problem is properly formalized, can be extremely powerful in refining assumptions (=-=Angrist et al., 1996-=-; Heckman and Vytlacil, 2005), deriving consistent estimands (Robins, 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl, 2000), and combin19 The opaqueness of counter... |

417 | Discrete Multivariate Analysis: Theory and Practice
- Bishop, Fienberg, et al.
- 1975
(Show Context)
Citation Context ...ans a century ago (Pearson et al., 1899; Yule, 1903) analyzed by statisticians for half a century (Simpson, 1951; Blyth, 1972; Cox and Wermuth, 2003) lamented by statisticians (Good and Mittal, 1987; =-=Bishop et al., 1975-=-) and wrestled with by statisticians till this very day (Chen et al., 2009; Pavlides and Perlman, 2009). Still, to the best of my knowledge, Wasserman (2004) is the first statistics textbook to treat ... |

217 |
Equivalence and synthesis of causal models
- Verma, Pearl
- 1990
(Show Context)
Citation Context ...cs and the behavioral and social sciences (Goldberger, 1972; 4 Additional implications called “dormant independence” (Shpitser and Pearl, 2008) may be deduced from some graphs with correlated errors (=-=Verma and Pearl, 1990-=-). 10Duncan, 1975; Bollen, 1989). However, the bulk of SEM methodology was developed for linear analysis and, until recently, no comparable methodology has been devised to extend its capabilities to ... |

205 | A theory of inferred causation - Pearl, Verma - 1991 |

186 |
Conditional independence in statistical theory
- Dawid
- 1979
(Show Context)
Citation Context ...en the causal effect P (y|do(x)) = P ∗ (Yx = y) can readily be evalu17 The notation Y ⊥X|Z stands for the conditional independence relationship P (Y = y, X = x|Z = z) =P (Y = y|Z = z)P (X = x|Z = z) (=-=Dawid, 1979-=-). 38ated to yield P ∗ (Yx = y) = ∑ P z ∗ (Yx = y|z)P (z) = ∑ P z ∗ (Yx = y|x, z)P (z) (using (34)) = ∑ P z ∗ (Y = y|x, z)P (z) (using (31)) = ∑ P (y|x, z)P (z). (35) z The last expression contains n... |

172 | Causal diagrams for empirical research
- Pearl
- 1995
(Show Context)
Citation Context ...ted, or the language in which those assumptions are cast. The structural theory that we use in this survey satisfies the criteria above. It is based on the Structural Causal Model (SCM) developed in (=-=Pearl, 1995-=-, 2000a) which combines features of the structural equation models (SEM) used in economics and social science (Goldberger, 1973; Duncan, 1975), the potential-outcome framework of Neyman (1923) and Rub... |

162 | Observational Studies - Rosenbaum - 2002 |

153 |
A new approach to causal inference in mortality studies with sustained exposure periods - Application to control of the healthy worker survivor effect
- Robins
- 1986
(Show Context)
Citation Context ...cted to interventions on a single variable; it is applicable to simultaneous or sequential interventions such as those invoked in the analysis of time varying treatment with time varying confounders (=-=Robins, 1986-=-; Arjas and Parner, 2004). For example, if X and Z2 are both treatment variables, and Z1 and Z3 are measured covariates, then the post-intervention distribution would be P (z1,z3,y|do(x),do(z2)) = P (... |

145 |
On the Application of Probability Theory to Agricultural Experiments. Essay on Principles
- Neyman
- 1923
(Show Context)
Citation Context ...the reliability of the judgments upon which the analysis so crucially depends. How does one recognize causal expressions in the statistical literature? Those versed in the potential-outcome notation (=-=Neyman, 1923-=-; Rubin, 1974; Holland, 1988), can recognize such expressions through the subscripts that are attached to counterfactual events and variables, e.g. Yx(u) orZxy. (Some authors use parenthetical express... |

143 | Correlation and Causation - Wright - 1921 |

140 | Mediation in experimental and non-experimental studies: New procedures and recommendations
- Shrout, Bolger
- 2002
(Show Context)
Citation Context ...f conditions. Yet despite its ubiquity, the analysis of mediation has long been a thorny issue in the social and behavioral sciences (Judd and Kenny, 1981; Baron and Kenny, 1986; Muller et al., 2005; =-=Shrout and Bolger, 2002-=-; MacKinnon et al., 2007) primarily because structural equation modeling in those sciences were deeply entrenched in linear analysis, where the distinction between causal and regressional parameters c... |

136 | All of statistics : A concise course in statistical inference brief contents - Wasserman |

132 |
JM: Causal diagrams for epidemiologic research. Epidemiology
- Greenland, Pearl, et al.
- 1999
(Show Context)
Citation Context ...Pearl, 1988; Lauritzen, 1996; Spirtes et al., 2000; Pearl, 2000a). Although the basic elements of SCM were introduced in the mid 1990’s (Pearl, 1995), and have been adapted widely by epidemiologists (=-=Greenland et al., 1999-=-; Glymour and Greenland, 2008), statisticians (Cox and Wermuth, 2004; Lauritzen, 2001), and social scientists (Morgan and Winship, 2007), its potentials as a comprehensive theory of causation are yet ... |

122 |
Planning of Experiments
- Cox
- 1958
(Show Context)
Citation Context ...he verbal description with which investigators justify assumptions. For example, the assumption that a covariate not be affected by a treatment, a necessary assumption for the control of confounding (=-=Cox, 1958-=-, p. 48), is expressed in plain English, not in a mathematical expression. Remarkably, though the necessity of explicit causal notation is now recognized by many academic scholars, the use of such not... |

117 | Recent developments in the econometrics of program evaluation
- Imbens, Wooldridge
- 2009
(Show Context)
Citation Context ... standard in epidemiology research (Robins, 2001; Petersen et al., 2006; VanderWeele and Robins, 2007; Hafeman and Schwartz, 2009; VanderWeele, 2009) yet still lacking in econometrics (Heckman, 2008; =-=Imbens and Wooldridge, 2009-=-). 41implies that the corresponding background variables, UY and {UZ1,...,UZk }, are independent in P (u). These assumptions can be translated into the potential-outcome notation using two simple rul... |

115 |
A Probabilistic Theory of Causality
- Suppes
- 1970
(Show Context)
Citation Context ... The unification of the graphical, potential outcome, structural equations, decision analytical (Dawid, 2002), interventional (Woodward, 2003), sufficient component (Rothman, 1976) and probabilistic (=-=Suppes, 1970-=-) approaches to causation; with each approach viewed as a restricted version of the SCM. 2. The definition, axiomatization and algorithmization of counterfactuals and joint probabilities of counterfac... |

112 | Nonparametric bounds on treatment effects - Manski - 1990 |

104 |
The interpretation of interaction in contingency tables
- Simpson
- 1951
(Show Context)
Citation Context ...ons, a vocabulary that differs substantially from the one Bayesian statisticians have been accustomed to articulate. The classical example demonstrating this linguistic obstacle is Simpson’s paradox (=-=Simpson, 1951-=-) – a reversal phenomenon that earns its claim to fame only through causal interpretations of the data (Pearl, 2000a, Chapter 6). The phenomenon was discovered by statisticians a century ago (Pearson ... |

100 | Causality: Models - Pearl - 2000 |

95 | Comment: Graphical models, causality, and intervention
- Pearl
- 1993
(Show Context)
Citation Context ...city to transmit changes among variables. Such an extension, based on simulating hypothetical interventions in the model, was proposed in (Haavelmo, 1943; Strotz and Wold, 1960; Spirtes et al., 1993; =-=Pearl, 1993-=-a, 2000a; Lindley, 2002) and has led to new ways of defining and estimating causal effects in nonlinear and nonparametric models (that is, models in which the functional form of the equations is unkno... |

94 | Identifiability and exchangeability for direct and indirect effects. Epidemiology 3(2):143 - Robins, Greenland - 1992 |

93 |
The Statistical Implications of a System of Simultaneous Equations
- Haavelmo
- 1943
(Show Context)
Citation Context ...cient in an equation, and redefine “effect” as a general capacity to transmit changes among variables. Such an extension, based on simulating hypothetical interventions in the model, was proposed in (=-=Haavelmo, 1943-=-; Strotz and Wold, 1960; Spirtes et al., 1993; Pearl, 1993a, 2000a; Lindley, 2002) and has led to new ways of defining and estimating causal effects in nonlinear and nonparametric models (that is, mod... |

85 |
Causal Inference without Counterfactuals (with Discussion
- Dawid
- 2000
(Show Context)
Citation Context ...y to the joint statement “Y would be y if X = x and Y would be y ′ if X = x ′ .” 14 Such concerns have been a source of objections to treating counterfactuals as jointly distributed random variables (=-=Dawid, 2000-=-). The definition of Yx and Yx ′ in terms of two distinct submodels neutralizes these objections (Pearl, 2000b), since the contradictory joint statement is mapped into an ordinary event, one where the... |

73 | Direct and indirect effects
- Pearl
(Show Context)
Citation Context ... scientific knowledge. Additional graphical and counterfactual conditions for identification are derived in Pearl (2001) Petersen et al. (2006) and Imai et al. (2008). In particular, it can be shown (=-=Pearl, 2001-=-) that expression (42) is both valid and identifiable in Markovian models (i.e., no unobserved confounders) where each term on the right can be reduced to a “do-free” expression using Eq. (26) and the... |

72 |
Causal Ordering and Identifiability
- Simon
- 1953
(Show Context)
Citation Context ...remain constant. A system of such functions are said to be structural if they are assumed to be autonomous, that is, each function is invariant to possible changes in the form of the other functions (=-=Simon, 1953-=-; Koopmans, 1953). 133.2.1 Representing interventions This feature of invariance permits us to use structural equations as a basis for modeling causal effects and counterfactuals. This is done throug... |

71 | The Analysis of Randomized and Non-Randomized AIDS Treatment Trials Using a New Approach to Causal Inference in Longitudinal Studies - ROBINS - 1989 |

68 |
Causal inference, path analysis, and recursive structural equation models
- Holland
- 1988
(Show Context)
Citation Context ...ments upon which the analysis so crucially depends. How does one recognize causal expressions in the statistical literature? Those versed in the potential-outcome notation (Neyman, 1923; Rubin, 1974; =-=Holland, 1988-=-), can recognize such expressions through the subscripts that are attached to counterfactual events and variables, e.g. Yx(u) orZxy. (Some authors use parenthetical expressions, e.g. Y (0), Y (1), Y (... |

67 |
Process analysis: Estimating mediation in treatment evaluations
- Judd, Kenny
- 1981
(Show Context)
Citation Context ..., therefore, enables us to predict behavior under a rich variety of conditions. Yet despite its ubiquity, the analysis of mediation has long been a thorny issue in the social and behavioral sciences (=-=Judd and Kenny, 1981-=-; Baron and Kenny, 1986; Muller et al., 2005; Shrout and Bolger, 2002; MacKinnon et al., 2007) primarily because structural equation modeling in those sciences were deeply entrenched in linear analysi... |

66 |
Introduction to structural equation models
- Duncan
- 1975
(Show Context)
Citation Context ...is based on the Structural Causal Model (SCM) developed in (Pearl, 1995, 2000a) which combines features of the structural equation models (SEM) used in economics and social science (Goldberger, 1973; =-=Duncan, 1975-=-), the potential-outcome framework of Neyman (1923) and Rubin (1974), and the graphical models developed for probabilistic reasoning and causal analysis (Pearl, 1988; Lauritzen, 1996; Spirtes et al., ... |

66 |
Introduction to Econometrics
- Stock, Watson
(Show Context)
Citation Context ...e explain the slow acceptance of causal analysis among health scientists and statisticians, and why most economists and social scientists continue to use structural equation models (Wooldridge, 2002; =-=Stock and Watson, 2003-=-; Heckman, 2008) instead of the potential-outcome alternatives advocated in Angrist et al. (1996); Holland (1988); Sobel (1998, 2008). On the other hand, the algebraic machinery offered by the counter... |

65 |
Influence diagrams for causal modelling and inference
- Dawid
(Show Context)
Citation Context ... comprehensive theory of causation are yet to be fully utilized. Its ramifications thus far include: 1. The unification of the graphical, potential outcome, structural equations, decision analytical (=-=Dawid, 2002-=-), interventional (Woodward, 2003), sufficient component (Rothman, 1976) and probabilistic (Suppes, 1970) approaches to causation; with each approach viewed as a restricted version of the SCM. 2. The ... |

65 | Axiomatizing causal reasoning
- Halpern
(Show Context)
Citation Context ... the condition Y = y, regardless of concurrent interventions, say do(Z = z), that may be applied to variables other than Y . Equation (33) generalizes (31) to cases where Z is held fixed, at z. (See (=-=Halpern, 1998-=-) for proof of completeness.) 5.2 Problem formulation and the demystification of “ignorability” The main drawback of this black-box approach surfaces in problem formulation, namely, the phase where a ... |

65 | Using matching, instrumental variables, and control functions to estimate economic choice models. The Review of Economics and Statistics 86: 30–57
- Heckman, Navarro-Lozano
(Show Context)
Citation Context ...n (2009) goes as far as stating that refraining from conditioning on an available measurement is “nonscientific ad hockery” for it goes against the tenets of Bayesian philosophy (see (Pearl, 2009b,c; =-=Heckman and Navarro-Lozano, 2004-=-) for a discussion of this fallacy). 40ing data from experimental and nonexperimental studies (Pearl, 2000a). The next subsection (5.3) presents a way of combining the best features of the two approa... |

61 |
Probabilistic Causality
- Eells
- 1991
(Show Context)
Citation Context ...-level causes (e.g., “Drinking hemlock causes death”) and singular or unit-level causes (e.g., “Socrates’ drinking hemlock caused his death”), which many philosophers have regarded as irreconcilable (=-=Eells, 1991-=-), introduces no tension at all in the structural theory. The two types of sentences differ merely in the level of situation-specific information that is brought to bear on a problem, that is, in the ... |

61 | Probabilistic evaluation of sequential plans from causal models with hidden variables - Pearl, Robins - 1995 |

60 | Structural equations, treatment effects, and econometric policy evaluation
- Heckman, Vytlacil
- 2005
(Show Context)
Citation Context ... the other hand, the algebraic machinery offered by the counterfactual notation, Yx(u), once a problem is properly formalized, can be extremely powerful in refining assumptions (Angrist et al., 1996; =-=Heckman and Vytlacil, 2005-=-), deriving consistent estimands (Robins, 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl, 2000), and combin19 The opaqueness of counterfactual independencies expla... |

59 | Probabilistic Reasoning - Pearl - 1988 |

56 | Recursive causal models - Kiiveri, Speed, et al. - 1984 |

56 | Causal inference from graphical models
- Lauritzen
- 1999
(Show Context)
Citation Context ...ts of SCM were introduced in the mid 1990’s (Pearl, 1995), and have been adapted widely by epidemiologists (Greenland et al., 1999; Glymour and Greenland, 2008), statisticians (Cox and Wermuth, 2004; =-=Lauritzen, 2001-=-), and social scientists (Morgan and Winship, 2007), its potentials as a comprehensive theory of causation are yet to be fully utilized. Its ramifications thus far include: 1. The unification of the g... |

56 | A general identification condition for causal effects
- Tian, Pearl
(Show Context)
Citation Context ...me varying treatments), conditional policies, and surrogate experiments were developed in Pearl and Robins (1995), Kuroki and Miyakawa (1999), and Pearl (2000a, Chapters 3–4). A more recent analysis (=-=Tian and Pearl, 2002-=-) shows that the key to identifiability lies not in blocking paths between X and Y but, rather, in blocking paths between X and its immediate successors on the pathways to Y . All existing criteria fo... |