Mediating Between Causes and Probabilities: the Use of Graphical Models in Econometrics Alessio Moneta Max Planck Institute of Economics, Jena, and Sant’Anna School of Advanced Studies, Pisa 16 June 2006 Causality and Probability in the Sciences University of Kent

Outline 1. Causal inference in macro-econometrics 2. Graphical models 3. Graphical models and structural Vector Autoregressions

Causal inference in macro-econometrics Macro-econometric model: Structural form: A 0 Y t + A 1 Y t-1 + … + A m Y t-m + B 0 X t + B 1 X t-1 + … + B n X t-n = ε t Y t : vector of endogenous variables X t : vector of exogenous variables Reduced form: Y t = P 1 Y t-1 + … + P m Y t-m + Q 0 X t + … + Q n X t-n + u t, where P i = -A 0 -1 A i, Q i = -A 0 -1 B i, and u t = A 0 -1 ε t

Causal inference in macro-econometrics Problem of identification Underdetermination of theory by data Formalization of the problem of identification by Haavelmo (1944)

Deductivist approaches Cowles Commission approach: a priori restrictions dictated by “Keynesian macroeconomics” Lucas Critique (1976): the causal relations identified by the Cowles Commission are not stable (invariant under intervention) Rational expectations econometrics Calibration approach (Kydland – Prescott 1982) Problems with deductivist approaches

Inductivist approaches Sims’s (1980) Vector Autoregressions: Y t = P 1 Y t-1 + … + P m Y t-m + u t Let us the data speak, “without pretending to have too much a priori theory” Analysis of the effects of shocks on key variables (impulse response functions) Structural VAR: A 0 Y t = A 1 Y t-1 + … + A m Y t-m + ε t where P i = -A 0 -1 A i, and u t = A 0 -1 ε t Problem of identification once again.

Inductivist approaches Granger Causality (1969, 1980). x t causes y t iff: P(y t \ y t-1, y t-2,…, x t-1, x t-2,…,Ω) ≠ P(y t \ y t-1, y t-2,…,Ω) Probabilistic conception of causality: x t causes y t if x t renders y t more likely. Similarities between Suppes’s (1970) and Granger’s account Shortcomings of probabilistic accounts of causality

Graphical causal models A graphical causal model (Spirtes et al. 2000) is a graph whose nodes are random variables with a joint probability distribution subject to some restrictions. These restrictions concern the type of connections between causal relations and conditional independence relations. The simplest graphical causal model is the causal DAG. A causal DAG G is a directed acyclic graph whose nodes are random variables with a joint probability distribution P subject to the following condition: Markov Condition: each variable is independent of its graphical non- descendants conditional on its graphical parents.

Causal DAG Faithfulness condition: each independence condition is entailed by the Markov condition. Stability

Beyond DAGs Feedbacks (Richardson and Spirtes 1999); Latent variables; Non-linearity; Graphical models for time series.

Graphical causal models Logic of scientific discovery? Causal Markov Condition and Faithfulness condition are general a priori assumptions Using output of search algorithm + background knowledge to test single causal hypotheses. Synthetic approach (Williamson 2003).

Graphical models for Structural VAR Recovering structural analysis in VAR models (Swanson and Granger 1997, Bessler and Lee 2002, Demiralp and Hoover 2003, Moneta 2003). Procedure to identify the causal structure of VAR models using graphical models. This procedure uses a graphical algorithm (modified version of the PC algorithm of Spirtes-Glymour-Scheines 2000) to infer the contemporaneous causal structure starting from the analysis of the partial correlations among VAR residuals.

Empirical example VAR model in which Y = (C, I, M, Y, R, ΔP)’ quarterly US data 1947:2 – 1994:1 Output of the search algorithm: The output of the algorithm consists of 24 DAGs Testing the output of the algorithms: 8 DAGs are excluded Incorporating background knowledge Sensitivity analysis

Conclusions Mediating between deductivist and inductivist approaches Causal Markov Condition and Faithfulness Condition as working assumptions Importance of background knowledge and deductive side of causal inference Giving background knowledge an explicit causal language Possibility of testing background knowledge Under-determination problem and sensitivity analysis