[Attention getter] what is missing in probabilistic theories of causality? [Need] A goal of sc (nat or soc) is to establish causal relations. Traditionally, what does philosophy have to offer? probabilistic theories crucial objections we need a more sophisticated apparatus that enable to establish causal relations causal modelling. [Task] My PhD on causal modelling, 1) try to disclose the rationale of causality, 2) be clear as to what guarantees the causal interpretation. So, here, argue that causal modelling does provide this more sophisticated apparatus we are looking for. [Main message] causal modelling provides a rich apparatus that enables to establish causal relations much better than probabilistic theories of causality
The overall idea of the talk is 1) to give some general background and basic notions both of PT and CM; then 2) to work on one example typical of PT and on of CM and show what is missing in PT. Finally, from this analysis I’ll try to draw some epistemological morals. Roughly: causal context, assumptions, H-D methodology … model building stage + test stage enable us to make explicit what is missing in PT. OSS. The point is epistemological, NOT normative (yet). Descriptive though critical.
PTs have been developed in slightly diff manners by diff philosophers over last decades. Suffice to recall pioneers Suppes and Good, quite recently Eells, of course Salmon, Cartwright etc. Considerable diff, yet there are a couple of common features they share. Explain main features of PT. Probability raising requirement causes do not necessitate their effects, just raise prob of occurrence of effect. Temporal precedence of the cause. (metaph assumption about causation, integrated in the definition of cause) To demand that cond prob be greater than uncond prob is tantamount to employing a statistical relevance measure. not statistical characterization of causality itself (would be a ontological commitment to inderteministic causality), rather, statistical characterization of how to establish causal relation. statistical characterization for epistemic purposes, not metaphysical ones. Specially Suppes provides definition of several types of cause (spurious, direct, indirect, negative …). For the present discussion does not matter present all of them. More, focus on main feature of theory.
Instead of presenting ex showing how promising and successful PT is, start off with controversial ex. Intended to pinpoint difficulties for PT. Graph depicts probabilistic (causal?) relations. Two paths: 1) C - P + T ; 2) C + T C might eventually *lower* P(T) through path 1). Apparent inconsistency btw inequality 1) and 4). Leads to hasty conclusion: PT will not do. Further defences say that this causal story is too unsophisticated, more accurate analyses would dissolve inconstistency. Well, don’t have a real case study, so I can’t tell whether this is true. However, if we stick to a mere probabilistic characterization of causal relations, surely inconsistency doesn’t go away. my point is that some important things are missing in PT .. Let me show what it is First, present causal modelling, then go over a case study.
Explain ex: fertility survey; var X 1 , X 2 , X 3 and Y are observed; relations btw var expressed mathematically as in the eq, pictorially as in the graph. CM= Set of equation associated with a graph. In the graph: nodes, arrows In the equations: variables, parameters Causal interpretation of graph and equations controversial. E.g in Bayes Nets, debate on validity of CMC supposed to grant causal iterpretation; probl of det – indet in structural eq. BUT this is the top of iceberg … causal models, made of: number of assumptions (statistical – e.g. linearity, normality of distributions, causal – e.g. correlation -var, stability, invariance, metaphysical – e.g. direction of time, asymmetry, causal priority), in model building stage background theories, causal context, -- this guide formulation of: conceptual hypothesis, choice of variables testing stage: hypothetico-deductive methodology
Causal models model properties of a social system* model relations btw these properties, represented by variables. *soc. System= roughly, a given population – e.g. in fertility survey before, a given pop in developing countries Causal models statistically model causal relations statistical causality To model its properties = to give a scheme, a skeleton of how these properties or characteristics (Education, #children, age …) relate. Possibility: think the graph = scheme of underlying causal mechanism that governs the soc system. BUT this causal mech is NOT modelled in terms of spatio-temporal processes and interactions (Salmon) – it is statistically modelled** **Stat Modelled = by means of statistical concepts of correlation, constant conjunction, screening-off … Structural models (designed for causal analysis) uncover stable relations btw properties CM aims at detecting causal rel brw properties, explain the dynamic of the system through its causes. WHY? bcz knowledge of causes allows us to explain, predict, intervene on society.
Objective: analysing possible causal paths between health and socioeconomic status. Methods: apply Granger-causality – which I’ll shortly introduce - 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 most of the features – i.e. assumptions, methodology – mentioned (and just mentioned.
Explain through the graph the idea behind Granger-Causality Next, explain features of the statistical model, and point out that these features are clearly missing in PT. Collect data about health history and wealth history of people Want to know whether these histories causally affect present health and wealth events Granger-causality is defined through the negation: X does not cause Y if (in prob terms) P(Y|X) = P(Y) Granger-causality tests absence of causal relation Here, test absence of causal link: 1) health wealth 2) wealth health In Granger terms: 1) P(health events|wealth history) = P(health events) 2) P(wealth events|health history) = P(wealth events)
Now I’ll show what *more* this causal model has rather than a mere probabilistic characterization 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) Conceptual hyp = causal claim stating causal link to test. 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. Statistical assumptions, e.g.: Linearity Normality Non measurement error Non correlation of error terms
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. OSS.: among extra-statistical assumptions we can also find: Direction of time Causal mechanism Determinism
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. OSS. Among causal assumptions we can also find: No confounding Non causality of error terms
Analysis of case study shows why a simple probabilistic characterization is not enough to establish causal relations (as the example for PT shows …) The point seems to be at the same time epistemological and methodological. Methodological we need more sophisticated formal tools than probability inequalities. On the other hand, epistemological: causal models are accompanied by non-formal elements. Some of the assumptions in causal models are of course metaphysical. Nothing bad in this – metaphysics guides (in some sense) epistemic access to causal relations. About background. Causal relations do not come out from tabula rasa. Causal analysis always has a starting point. Background also help in assessing the reasonableness of the causal interpretation. Causal interpretation two issues: 1) formal constraints given in the structure of model, 2) background; the background is by itself enough to rule out causality in the correlation btw storks and births rates. H-D methodology – methodological and epistemological import. Methodological accent on confirmation rather than discovery test causal relations. Epistemological causal relations to be tested arise from a background
Main intuitions of PT: Probabilistic (statistical) characterization of causal relations Time does enter the definition of cause
Belgian Society May05
From Probabilistic Theories of Causality to Causal Modelling Bringing causal theory to maturity Federica Russo Institut Supérieur de Philosophie, Université Catholique de Louvain Centre for Philosophy of Natural and Social Science, London School of Economics
Overview <ul><li>Probabilistic Theories of Causality </li></ul><ul><ul><li>Background and basic notions </li></ul></ul><ul><ul><li>An example: pills, pregnancy and thrombosis </li></ul></ul><ul><li>Causal Modelling </li></ul><ul><ul><li>Background and basic notions </li></ul></ul><ul><ul><li>An example: health and wealth </li></ul></ul><ul><li>Epistemological Morals </li></ul>
Probabilistic theories of causality <ul><li>Causes raise the probability of effects </li></ul><ul><ul><li>P(E|C) > P(E) </li></ul></ul><ul><li>Causes precede effects in time </li></ul><ul><ul><li>P(E t’ |C t ) > P(E t’ ) , t’ > t </li></ul></ul><ul><li>Statistical relevance is a basic notion </li></ul>
An example: contraceptive pills, pregnancy, thrombosis <ul><li>P (T | C) > P (T) </li></ul><ul><li>P (T | P) > P (T) </li></ul><ul><li>P (P | C) < P (P) </li></ul><ul><li>P (T | C) < P (T) </li></ul>C ontraceptive pills P regnancy T hrombosis + + -
Causal modelling What is a causal model? X 1 age X 2 education X 3 age at marriage Y number of children 1 2 12 13 23 3
Causal modelling <ul><li>A causal model: </li></ul><ul><li>models the properties </li></ul><ul><li>of a social system </li></ul><ul><li>detects causal relations </li></ul><ul><li>between the properties of the system </li></ul><ul><li>explains the dynamic of the system </li></ul><ul><li>through its causes </li></ul>What does a causal model do?
<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 : analyzing 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>An example: health and wealth
Health and wealth Health history Socio-economic history Health events Socio-economic events
<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>Health and 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>Health and 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>Health and 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 components 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>Health and wealth
Epistemological morals <ul><li>What is missing in probabilistic theories of causality? </li></ul><ul><ul><li>Rich apparatus of assumptions </li></ul></ul><ul><ul><li>Background theories and knowledge </li></ul></ul><ul><ul><li>Hypothetico-deductive methodology </li></ul></ul>
To sum up <ul><li>Probabilistic theories of causality are right in the main intuitions </li></ul><ul><li>Nonetheless, they face crucial objections </li></ul><ul><li>Causal modelling has a more elaborated apparatus </li></ul><ul><li>Assumptions, hypothetico-deductive methodology and the background </li></ul><ul><li>enable us to establish causal relations </li></ul>
To draw some conclusions… <ul><li>A philosophical analysis of causal modelling can bring causal theory to maturity </li></ul><ul><li>Such an analysis unveils neglected epistemological and methodological aspects that enable us to establish causal relations </li></ul><ul><li>Philosophy is perfectly on time to get engaged in an active dialogue with science </li></ul>
Selected references <ul><li>Good I.J. (1961-62), “A Causal Calculus”, in BJPS. </li></ul><ul><li>Humphreys P. (1989), The Chances of Explanation. </li></ul><ul><li>Pearl J. (2000), Causality. </li></ul><ul><li>Suppes P. (1970), A Probabilistic Theory of Causality. </li></ul><ul><li>Williamson J. (2005), Bayesian Nets and Causality. </li></ul><ul><li>Woodward J. (2003), Making Things Happen. </li></ul><ul><li>Wunsch G. (1988), Causal Theory and Causal Modelling. </li></ul>Comments? Mail to [email_address] Interested in further material? Check out http://www.geocities.com/russo_fede