Causality in Time Series - ClopiNet

Moneta Chlass Entner HoyerA traditional approach to address such questions hinges on the explicit use of apriori economic theory. The gist of this approach is to partition a causal process ina deterministic, and a random part and to articulate the deterministic part such as toreflect the causal dependencies dictated by economic theory. If the formulation of thedeterministic part is accurate and reliable enough, the random part is expected to displayproperties that can easily be analyzed by standard statistical tools. The touchstoneof this approach is represented by the work of Haavelmo (1944), which inspired theresearch program subsequently pursued by the Cowles Commission (Koopmans, 1950;Hood and Koopmans, 1953). Therein, the causal process is formalized by means ofa structural equation model, that is, a system of equations with endogenous variables,exogenous variables, and error terms, first developed by Wright (1921). Its coefficientswere given a causal interpretation (Pearl, 2000).This approach has been strongly criticized in the 1970s for being ineffective inboth policy evaluation and forecasting. Lucas (1976) pointed out that the economictheory included in the SEM fails to take economic agents’ (rational) motivations andexpectations into consideration. Agents, according to Lucas, are able to anticipate policyintervention and act contrary to the prediction derived from the structural equationmodel, since the model usually ignores such anticipations. Sims (1980) puts forth anothercritique which runs parallel to Lucas’ one. It explicitly addresses the status ofexogeneity which the Cowles Commission approach attributes (arbitrarily, accordingto Sims) to some variables such that the structural model can be identified. Sims arguesthat theory is not a reliable source for deeming a variable as exogenous. More generally,the Cowles Commission approach with its strong a priori commitment to theory,risks falling into a vicious circle: if causal information (even if only about direction)can exclusively be derived from background theory, how do we obtain an empiricallyjustified theory? (Cfr. Hoover, 2006, p.75).An alternative approach has been pursued since Wiener (1956) and Granger’s (1969)work. It aims at inferring causal relations directly from the statistical properties of thedata relying only to a minimal extent on background knowledge. Granger (1980) proposesa probabilistic concept of causality, similar to Suppes (1970). Granger definescausality in terms of the incremental predictability (at horizon one) of a time seriesvariable {Y t } (given the present and past values of {Y t } and of a set {Z t } of possible relevantvariables) when another time series variable {X t } (in its present and past values) isnot omitted. More formally:{X t } Granger-causes {Y t } if P(Y t+1 |X t , X t−1 ,...,Y t ,Y t−1 ,...,Z t ,Z t−1 ,...) P(Y t+1 |Y t ,Y t−1 ,...,Z t ,Z t−1 ,...)(1)As pointed out by Florens and Mouchart (1982), testing the hypothesis of Grangernoncausality corresponds to testing conditional independence. Given lags p, {X t } doesnot Granger cause {Y t }, ifY t+1 ⊥ (X t , X t−1 ,..., X t−p ) | (Y t ,Y t−1 ,...,Y t−p ,Z t ,Z t−1 ,...,Z t−p ) (2)106