Mediating Between Causes and Probabilities: the Use of Graphical Models in Econometrics

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Alessio Moneta Max Planck Institute of Economics, Jena, and Sant’Anna School of Advanced Studies, Pisa https://mail.sssup.it/~amoneta 16 June 2006 Causality and Probability in the Sciences University of Kent.

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Alessio Moneta

Max Planck Institute of Economics, Jena, and

Sant’Anna School of Advanced Studies, Pisa

https://mail.sssup.it/~amoneta

16 June 2006

Causality and Probability in the Sciences

University of Kent

Mediating Between Causes and Probabilities: the Use of Graphical Models in Econometrics
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:

A0 Yt + A1 Yt-1 + … + Am Yt-m + B0 Xt + B1 Xt-1 + … + Bn Xt-n = εt

Yt : vector of endogenous variables

Xt : vector of exogenous variables

Reduced form:

Yt = P1 Yt-1 + … + Pm Yt-m + Q0 Xt + … + Qn Xt-n + ut,

where Pi = -A0-1 Ai, Qi = -A0-1 Bi, and ut = A0-1 εt

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:

Yt = P1 Yt-1 + … + Pm Yt-m + ut

• 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:

A0 Yt = A1 Yt-1 + … + Am Yt-m + εt

where Pi = -A0-1 Ai, and ut = A0-1 εt

• Problem of identification once again.
Inductivist approaches
• Granger Causality (1969, 1980). xt causes yt iff:

P(yt \yt-1,yt-2 ,… , xt-1,xt-2 ,…,Ω) ≠P(yt \yt-1,yt-2 ,… ,Ω)

• Probabilistic conception of causality: xt causes yt if xt renders yt 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