Causality Triangle Presentation


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  • Attention getter : … What we have  many accounts; new methods (eg, Bayes nets) BUT lots of confusion about kind of questions What we want  well defined domains; clear answers; promising epistemology My task : in my Phd I face those problems too. So (i) state domains and corresponding questions clearly; (ii) sketch features of a promising epistemology Take Home Message : In the epistemology of causality (i) variation is the bottom-line concept, (ii) specific causal assumptions guarantee the causal interpretation
  • The talk is divided into 2 parts. Part 1 states different causal domains and corresponding questions. Part 2 addresses the epistemology of causality. Part 1 is a necessary preliminary work for Part 2. My hope, distinctions made in Part 1 be useful generally for the debate on causality.
  • Many recent accounts try to give a general and comprehensive understanding, then suffer knock-down objections. Seems to me: never clear what the question is, and objections often depend on this lack of clarity. Metaph  epistem  method questions; unfair to raise, say, metaph objection to epistem account … Questions and answers might overlap, but clearly perspective differs. Work in one field can help in getting sensible answers in others. Eg: Hausman-Woodward: causality is invariance under intervention – is that a metaph, epistem, or method claim?
  • Metaph studies nature of things  metaph of causality wonders what in fact causality is . Look at questions … searching for a definition as answer. Answers vary form ontic accounts (Salmon-Dowe): causation is transfer of a conserved quantity in the interaction of 2 causal process. Epistemic accounts (Williamson): causation is a mental construct. Cartwright: causes are capacities
  • Epistem addresses the problem of human knowledge  epistem of causality wonders how we know about causal relations. NB: anthropocentric (quite Kantian) perspective: knowledge of causal relations depends on the agent, on agent’s concepts etc. Question 2 might be given a metaph answer, in which case it is begging the question (from epistem point of view). Question 3 clearly overlaps with method.  on the one hand need of formal characterization of invariance, independence, etc; other hand, epistemol speculation on these notions.
  • Methodology addresses the problem of method  methodology of causality wonders what methods for the discovery and confirmation of causal relations. Adequacy of H-D or Induc is matter for epistem, but developments of algorithms is matter for methodology. Developing new methods science needs epistemological supervision. Do models make sense? Why? Questions concern concepts, notions, not mere technicalities. ________ Now domains are clearly distinguished. Shall confine to EPISTEMOLOGY .
  • Want to confine discussion to epistemology of causality, in particular to epistemology of causal modelling. Need further border: only social sciences. Won’t address problems of demarcation, social science very broadly conceived. Roughly, consider where structural models are employed. My bottom-up strategy: from analysis of case studies and statistical models, raise epistemological questions, end up with philosophical morals. Question 1: rationale of causality  not a definition but scheme of reasoning. So, not what causality is, but thanks to what notion we come to know about causal relations. Question 2: the rationale of variation still suffers the problem of validity of causal interpretation. This is bcz I don’t content with metaph argument to guarantee causation. But there is a meaningful epistemological justification. Shall give u arguments to support variation rationale. 1. structural eq models, 2. covariance structure models, 3. Suppes’ probabilistic theory. Goal: to show that the notion of variation is involved.
  • (recall meaning of structural equation) How to interpret the equation: variations in X accompany variations in Y; variations in Y are determined by variation in X (plus effect of errors …) Betas quantify the variations. Structural parameters quantify the extent to which a variation in X affects Y
  • (recall CSM: 2 models. covariances among variables in the MM are explained by relations among a fewer number of var in the SM) Measuring covariances = measuring joint variations. In the SM just saw how the rationale of variation is involved.
  • Roughly, the cause is positively relevant for the effect, a preventative is negatively relevant for the effect. In either case, inspection of inequality. The cause (or the preventative) produces a variation in the probability of the effect. Otherwise it is nothing. Evaluating statistical relevance relations means estimating variations.
  • Worth emphasising that variation is not a further condition to impose. BUT it is the bottom-line concept of causality. Why not invariance? Bcz (i) still ask: invariance of what  of a variation. (ii) invariance is a condition imposed for the variation to be causal. Consider regularist accounts (Hume …) so, why not regularity? Same thing, regularity of what? The regular constant conjunction is a conjunction of a variation. So, there is a further concept beyond regularity. Far from being a trivial claim … it is fundamental, for otherwise confuse invariance to be the key notion for causation. It is not. It is a condition on smth else.
  • Nonetheless, there’s an obvious objection to the rationale of variation. Consider two traditional examples: See level in Venice, bread prices in England both monotonically increased in last 100 years The number of storks and birth rate both increased in Alsace in the same period However, those joint variations don’t seem to be causal. The metaphysician would argue that these are not genuine correlations just picked up the wrong correlation. So, if not metaph, what guarantees the causal interpretation? (here we go with the second question)
  • Let’s examine causal models carefully. The following features might be distinguished. I shall go through them one by one. We’ll see that causal interpretation is granted thanks to specific causal assumptions. If there’s time, go through a case study to show u how those features are exemplified.
  • To begin with, we dispose of knowledge of the causal context. i.e. not start from a tabula rasa. In the causal context the conceptual hypothesis is stated: it is a causal claim about the link btw 2 conceptual variables Worth emphasising that truth of conceptual hyp is not ascertainable by a priori analysis of concepts, but demand for empirical testing.
  • When statistical assumptions are satisfied the conditional distribution correctly describes how variables covary, but no causal interpretation is allowed yet.
  • These are untested assumptions. They play important role. Direction of time, causal asymmetry (= if A causes B, B not cause A), causal priority (=causes precede effects in time) helps in causal ordering, i.e. time order in which variables are observed. Causal mechanism is not tested into the causal model, e.g. in studying the effects of prolonged smoking on lung cancer, the physical mechanism leading from smoking to cancer is simply assumed. Determinism is more debatable. Structural equations can be considered deterministic functions where probabilities come in through the lack of knowledge. NB from epistemological perspective don’t need to solve once and for all the quarrel determinism or indeterminism? Det or indet causality? Det might be considered methodological assumption, heuristic principle leading onward …
  • Consider now these assumptions. These are causal bcz are constraints o the causal relation. Linearity and separability tell how the causal relation should be. In particular separability enable to separate effects due to endogenous variables and errors. Cov suff conveys idea that indep var are direct causes of the dep var, and by “no confounding” we assume that no irrelevant var are included and that all relevant var are taken into account. By non causality of errors we impose that only indep var have causal import on the dep var Also stability of distribution means that the parametrization is sufficiently stable. Invariance condition states that the causal relation itself be sufficiently stable, i.e. not accidental. Invariance condition allow predicting effects of changes and interventions.
  • Objective: analysing possible causal paths between health and socioeconomic status. Methods: apply Granger-causality to test for the absence of causal links from socioeconomic status to health innovation and mortality, and from health conditions to innovation in wealth. N.B. Granger-causality defined in negative form (give ex) so conceptual hyp and results are about absence of causal links Results: the hypothesis of no causal link from health to wealth is generally accepted, whereas the hypothesis of no causal link from wealth to health is generally rejected. This case study is indeed particularly instructive because it exemplifies almost every feature sketched above.
  • links between health and socioeconomic status have been the object of numerous studies; the association holds for a variety of health variables and alternative measures of socioeconomic status. b) the authors expect the hypothesis of non-causality from health to wealth to be accepted, and the hypothesis of non-causality from wealth to health to be rejected. These hypotheses are put forward for empirical testing
  • the statistical analysis fits generally the approach of Granger Granger-causality is based on regression methods, so it satisfies standard statistical assumptions. In particular, it is a linear procedure. [granger-causality: time series data set. Correlation of variables with histories of other variables.]
  • Granger-causality: the past history of a variable Y t-1 causally determines the current value of the variable Y. So, in testing whether health conditions have a causal impact on wealth, it is assumed that health history determines wealth current events, and vice versa in testing from wealth to health. Granger explicitly assumes that the future cannot cause the past. Indeed, this is a metaphysical assumption about the temporal asymmetry of causation. Asymmetry of causation plus determinism allow that a series can be predicted exactly from its past term.
  • Structure of the causal relation: for sufficiently brief time intervals,will not depend on contemporaneous variables, so “instantaneous causality” is ruled out Covariate sufficiency: the components of Y form a causal chain. By focusing on first-order Markov processes, only the most recent history conveys information. Hence, all and only the components in Y t-1 are direct causes of Y. Invariance condition: invariance assumption is defined through the validity of the model: the model is valid for a given history Y t-1 if it is the true conditional distribution of Yt given this history. That is, the conditional distribution must hold across different analysed panels.
  • In Part 1 we distinguished 3 causal domains where different questions are addressed. Metaph deals with the ontology of causality, aim to give a definition of causality = what causality is, what causal relata are. Epistem deals with our epistemic access to causal relation, what concepts give us knowledge of causal relations, but also provides a critical supervision on methodology, where, “formal” questions of method for the discovery and confirmation of causal relations are addressed. Given this trichotomy, confine discussion to epistemology. Suggested that in causal modelling (i) variation is the bottom-line concept, i.e. the rationale of causality; (ii) causal assumptions guarantee the causal interpretation. To conclude : distinction of causal domains is necessary, and given the distinction I offered, a promising epistemology can be sketched.
  • Causality Triangle Presentation

    1. 1. Variations and Causal Assumptions Epistemological Remarks on Causal Modelling Federica Russo Université Catholique de Louvain Centre for Philosophy of Natural and Social Science (LSE)
    2. 2. Overview <ul><li>Different Causal Domains </li></ul><ul><ul><li>Metaphysics </li></ul></ul><ul><ul><li>Epistemology </li></ul></ul><ul><ul><li>Methodology </li></ul></ul><ul><li>The Epistemology of Causality </li></ul><ul><ul><li>The Rationale of Causality </li></ul></ul><ul><ul><ul><li>Structural Equation Models </li></ul></ul></ul><ul><ul><ul><li>Covariance Structure Models </li></ul></ul></ul><ul><ul><ul><li>Suppes’ Probabilistic Theory </li></ul></ul></ul><ul><ul><li>Causal Arrows in Causal Assumptions </li></ul></ul><ul><ul><ul><li>Features of Causal Models </li></ul></ul></ul><ul><ul><ul><li>Health & Wealth: an Example </li></ul></ul></ul>
    3. 3. Different Causal Domains <ul><li>A general and comprehensive account </li></ul><ul><li>of causation? Forget it! </li></ul><ul><li>Different causal questions lead to </li></ul><ul><li>different causal domains </li></ul>Metaphysics Epistemology Methodology
    4. 4. Different Causal Domains: Metaphysics <ul><li>Metaphysics studies </li></ul><ul><li>the nature of things </li></ul><ul><li>Questions: </li></ul><ul><ul><li>What is causation? </li></ul></ul><ul><ul><li>What are causal relations? </li></ul></ul><ul><ul><li>… </li></ul></ul><ul><li>Answers: </li></ul><ul><ul><li>From ontic causal processes to </li></ul></ul><ul><ul><li>epistemic mental representations </li></ul></ul><ul><ul><li>… </li></ul></ul>
    5. 5. Different Causal Domains: Epistemology <ul><li>Epistemology studies origin, nature, </li></ul><ul><li>and limits of human knowledge </li></ul><ul><li>Questions : </li></ul><ul><ul><li>What epistemic access to causal relations? </li></ul></ul><ul><ul><li>When are correlation causal? </li></ul></ul><ul><ul><li>Is invariance/structural stability/Markov condition </li></ul></ul><ul><ul><li>enough for causation? </li></ul></ul><ul><ul><li>… </li></ul></ul><ul><li>Answers : </li></ul><ul><ul><li>From invariance to variation, </li></ul></ul><ul><ul><li>Overlaps with methodology </li></ul></ul><ul><ul><li>… </li></ul></ul>
    6. 6. Different Causal Domains: Methodology <ul><li>Methodology is the study of </li></ul><ul><li>methods of scientific inquiry </li></ul><ul><li>Questions: </li></ul><ul><ul><li>Hypothetico-deductive or inductive methods? </li></ul></ul><ul><ul><li>How to characterise invariance? </li></ul></ul><ul><ul><li>New methods: Bayes Nets? Decision Analysis? </li></ul></ul><ul><ul><li>… </li></ul></ul><ul><li>Answers: </li></ul><ul><ul><li>Let the practising scientists speak … </li></ul></ul><ul><ul><li>with philosophers’ epistemological supervision </li></ul></ul>
    7. 7. The Epistemology of Causality <ul><li>Research Domain: </li></ul><ul><ul><li>Causal Modelling in the Social Sciences, e.g.: </li></ul></ul><ul><li>Epidemiology: Smoking & Lung Cancer </li></ul><ul><ul><ul><li>Demography: Mother’s education & </li></ul></ul></ul><ul><ul><ul><li>Child Survival </li></ul></ul></ul><ul><ul><ul><li>Econometrics: Health & Wealth </li></ul></ul></ul><ul><ul><ul><li>… </li></ul></ul></ul><ul><li>Questions: </li></ul><ul><li>What Rationale for Causality? </li></ul><ul><li>What Guarantees the Causal Interpretation? </li></ul>
    8. 8. Variation: the Rationale of Causality <ul><li>Structural Equation Models: </li></ul><ul><li>Y= β X +  </li></ul><ul><li>Variations in X accompany Variations in Y </li></ul><ul><li> s quantify those variations </li></ul>
    9. 9. Variation: the Rationale of Causality <ul><li>Covariance Structure Models: </li></ul><ul><li>Measurement Model </li></ul><ul><li>+ </li></ul><ul><li>Structural Model </li></ul><ul><li>Causal relations in the Structural Model explain covariances (= co- variations ) </li></ul><ul><li>in the Measurement Model </li></ul>
    10. 10. Variation: the Rationale of Causality <ul><li>Suppes’ Probabilistic Theory: </li></ul><ul><li>Pr (Effect | Cause) > Pr (Effect) </li></ul><ul><li>The cause produces a variation </li></ul><ul><li>in the probability of the effect </li></ul>
    11. 11. <ul><li>Variation is the bottom-line concept </li></ul><ul><li>of causality, </li></ul><ul><li>is not a further condition on models </li></ul><ul><li>Why not invariance ? </li></ul><ul><li>Invariance of what? Of a variation … </li></ul><ul><li>Why not regularity ? </li></ul><ul><li>Regularity of what? Of a variation … </li></ul>
    12. 12. Nonetheless … <ul><li>See Level in Venice & Bread Prices in England </li></ul><ul><li>Storks & Birth Rate in Alsace </li></ul><ul><li>Those variations don’t seem to be causal… </li></ul><ul><li>Hence, </li></ul><ul><li>What guarantees the causal interpretation? </li></ul>
    13. 13. Causal Arrows in Causal Assumptions <ul><li>Features of Causal Models: </li></ul><ul><ul><li>Knowledge of the causal context </li></ul></ul><ul><ul><li>Conceptual hypothesis </li></ul></ul><ul><ul><li>Statistical assumptions </li></ul></ul><ul><ul><li>Extra-statistical assumptions </li></ul></ul><ul><ul><li>Causal assumptions </li></ul></ul>
    14. 14. Causal Arrows in Causal Assumptions <ul><li>Knowledge of the causal context: </li></ul><ul><ul><li>Previous studies, scientific theories, </li></ul></ul><ul><ul><li>background knowledge </li></ul></ul><ul><li>Conceptual hypothesis: </li></ul><ul><ul><li>The causal claim stating </li></ul></ul><ul><ul><li>the causal link to test </li></ul></ul>
    15. 15. Causal Arrows in Causal Assumptions <ul><li>Statistical assumptions: </li></ul><ul><ul><li>Linearity </li></ul></ul><ul><ul><li>Normality </li></ul></ul><ul><ul><li>Non measurement error </li></ul></ul><ul><ul><li>Non correlation of error terms </li></ul></ul><ul><ul><li>… </li></ul></ul>
    16. 16. Causal Arrows in Causal Assumptions <ul><li>Extra-statistical assumptions: </li></ul><ul><ul><li>Direction of time </li></ul></ul><ul><ul><li>Causal asymmetry </li></ul></ul><ul><ul><li>Causal priority </li></ul></ul><ul><ul><li>Causal ordering </li></ul></ul><ul><ul><li>Causal mechanism </li></ul></ul><ul><ul><li>Determinism </li></ul></ul><ul><ul><li>… </li></ul></ul>
    17. 17. Causal Arrows in Causal Assumptions <ul><li>Causal assumptions: </li></ul><ul><ul><li>Structure of the causal relation </li></ul></ul><ul><ul><ul><li>Linearity </li></ul></ul></ul><ul><ul><ul><li>Separability </li></ul></ul></ul><ul><ul><li>Covariate sufficiency </li></ul></ul><ul><ul><li>No confounding </li></ul></ul><ul><ul><li>Non causality of error terms </li></ul></ul><ul><ul><li>Stability </li></ul></ul><ul><ul><li>Invariance condition </li></ul></ul><ul><ul><li>… </li></ul></ul>
    18. 18. Health & Wealth: an Example <ul><li>Adams et al. (2003), “Healthy, Wealthy, and Wise” </li></ul><ul><li>Journal of Econometrics, 112, pp.3-56. </li></ul><ul><li>Objective : analysing possible paths between health and socioeconomic status </li></ul><ul><li>Methods : Granger-causality augmented with invariance condition </li></ul><ul><li>Results : no causal link health  wealth accepted </li></ul><ul><li>no causal link wealth  health rejected </li></ul>
    19. 19. Health & Wealth <ul><li>Knowledge of the causal context: </li></ul><ul><ul><li>Links health-wealth studied by far and large </li></ul></ul><ul><ul><li>The association widely holds </li></ul></ul><ul><li>Conceptual hypothesis: </li></ul><ul><ul><li>Health doesn’t cause Wealth </li></ul></ul><ul><ul><li>Wealth causes Health </li></ul></ul>
    20. 20. Health & Wealth <ul><li>Statistical assumptions: </li></ul><ul><ul><li>Granger-causality is based on </li></ul></ul><ul><ul><li>regression methods, </li></ul></ul><ul><ul><li>hence it satisfies standard </li></ul></ul><ul><ul><li>statistical assumptions </li></ul></ul>
    21. 21. Health & Wealth <ul><li>Extra-statistical assumptions: </li></ul><ul><ul><li>Causal priority and causal ordering </li></ul></ul><ul><ul><li>the past history of Y t-1 determines </li></ul></ul><ul><ul><li>the current value of Y </li></ul></ul><ul><ul><li>Asymmetry of causation </li></ul></ul><ul><ul><li>Granger-causality assumes that </li></ul></ul><ul><ul><li>the future cannot cause the past </li></ul></ul>
    22. 22. Health & Wealth <ul><li>Causal assumptions: </li></ul><ul><ul><li>Structure of the causal relation & </li></ul></ul><ul><ul><li>Covariate sufficiency </li></ul></ul><ul><ul><li>Granger-causality rules out instantaneous causation; </li></ul></ul><ul><ul><li>the components of Y form a causal chain </li></ul></ul><ul><ul><li>where in Y t-1 are causes of Y </li></ul></ul><ul><ul><li>Invariance condition </li></ul></ul><ul><ul><li>test for causality: are model parameters </li></ul></ul><ul><ul><li>invariant among panels? </li></ul></ul>
    23. 23. To sum up … <ul><li>Metaphysics: “objects” of causality </li></ul><ul><li> </li></ul><ul><li>Epistemology: epistemic access to causality </li></ul><ul><li> </li></ul><ul><li>Methodology: methods to discover/confirm </li></ul><ul><li>causal relations </li></ul><ul><li>The Epistemology of Causality </li></ul><ul><ul><li>Variation is the bottom-line concept </li></ul></ul><ul><ul><li>Causal assumptions guarantee </li></ul></ul><ul><ul><li>the causal interpretation </li></ul></ul>
    24. 24. <ul><li>Selected Readings: </li></ul><ul><ul><li>Hausman D. (1998), Causal Asymmetries . </li></ul></ul><ul><ul><li>Holland P.W. (1986), “Statistics and Causal Inference”, JASA 81. </li></ul></ul><ul><ul><li>Pearl J. (2000), Causality. </li></ul></ul><ul><ul><li>Stone R. (1993), “The Assumptions on which Causal Inferences Rest”, JASA 55. </li></ul></ul><ul><ul><li>Suppes P. (1970), A Probabilistic Theory of Causality. </li></ul></ul><ul><ul><li>Williamson J. (2004), Bayesian Nets and Causality. </li></ul></ul>Many thanks to Jon Williamson for useful discussions Comments? Mail to: [email_address] [email_address]