On the causal interpretation of statistical models in social research Alessio Moneta & Federica Russo

The dawn of history of causal modelling Staunch causalists Quetelet, Durkheim, Wright …, Blalock, Duncan, … Moderate skeptics Pearl, Heckman, Hoover, … … and the evergreen question: When and how can we draw causal conclusions from statistics? 2

This presentation Alessio Statistical vs Causal Information Associational vs Causal Models Federica Interpreting statistical models causally: – Truthmakers vs Validity – Epistemic way out 3

Important distinction (1) Associational models Causal models

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Example Associational model: Engel curves: measure of the dependence of expenditure (Y) on income (X) Regression functions: Y = f (X) + e Cannot be used to sustain counterfactual Causal model: Demand system: system of equations in which consumer behaviour is modeled as based on theory of utility maximization. Estimated and tested ex post. Used to sustain counterfactuals

Important distinction (2) Statistical Information A summary of data Inferential statistics (sample to population) Adequate and parsimonious description of the phenomenon Statistical dependence Causal Information Opening the ‘black box’ From association to causation Statistical information to provide the formalised empirical evidence Background ‘constraints’ Tests 7

Statistical dependence Statistical independence: X ind. Y iff f(X,Y) = f(X) f(Y) Conditional ind.: X ind. Y given Z iff f(X,Y|Z) = f(X|Z) f(Y|Z) Measures of dependence: correlation Pearson’s correlation coefficient: Corr(X,Y) = Cov (X,Y) / [Var(X) Var (Y)] 1/2

From association to causation Background constraints: theoretical knowledge (e.g. about exogeneity) institutional mechanisms (e.g. central banks) temporal priority rules of inference (Markov and Faithfulness)

All nice but … A vicious circle introduced? Not quite … How much background knowledge? Just the right amount … Cfr. “inductivist” and “deductivist” approaches in econometrics 10

interpreting What’s interpreting a statistical model causally?

truthmakers The philosophers’ hunt for truthmakers … that is … that is, what makes a causal claim true Difference-makers Probabilistic, counterfactual, manipulation Mechanisms 12

Anything wrong with the hunt? Conceptual analysis in philosophy of causality What explicates the concept of ‘causality’ What makes causal claims true What is causality, metaphysically Conceptual analysts failed to distinguish between evidence and concept lost on the way epistemic practices 13

interpreting What’s interpreting a statistical model causally? An epistemic activity …

In the footprints of epistemic theorists Evidence and concept Evidential pluralism: difference-making and mechanistic considerations Conceptual monism: causation is an inferential map Causality: an epistemic category to interpret the world rather than a physical relation in our ontology 15

Interpreting Interpreting in causal terms … … is deciding whether a model is valid or not Making successful inferences Not merely dependent on the physical existence of mechanisms Mechanisms have explanatory import Mechanistic and difference-making evidential components are tangled 16

The causal interpretation is model-dependent Causal conclusions depend on the statistical information and machinery from which they are inferred Not a bad thing after all Causation is not a ‘all or nothing’ affair Nor a ‘once and for all’ affair 17

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