A recent seminar presentation at UL by Prof. Denis Jansen and a conversation with Dr Tom Arbuckle today convinced me that a better, more algorithmic way to establish statistical causality in a a connected system would be something like directed acyclic graph theory, so I'm putting these resources in one place while I get my thinking right on the matter.
Definition. A directed acyclic graph (DAG) is a directed graph that contains no cycle.
Why is this useful for economists? Consider the standard consumption function, which looks like this:
This just says output (
) is a linear combination of present consumption (
) times the marginal propensity to consume of out of present income, (
), and the propensity to spend out of past income (
).
But why should this causal structure hold? Why isn't there a non linear interaction between the various vectors being represented? Why not simply ask the data to help figure out statistical causality for us?
We can use a DAG to help us try. The DAG works because by imposing a DAG structure on, say, the columns of Ireland's National Accounts, it will give rise to a partial order 
on its vertices, where 
exactly when there exists a directed path from 
to 
in the DAG.
Cool papers on this really new field are mostly by Kevin Hoover in economics, with David Bessler in Agricultural Economics. Anybody who knows of more papers in economics in this area, please email me.
If you want to manipulate a DAG to get a handle on the idea, click here.
Papers
Selva Demiralp, Kevin D. Hoover, and Stephen J. Perez, "A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression", Oxford Bulletin of Economics and Statistics, 2008
Kevin Hoover, "Economic Theory and Causal Inference," forthcoming in Uskali Mäki, editor Handbook of the Philosophy of Economic, (one volume of the Handbook of the Philosophy of Science, Dov Gabbay, Paul Thagard, and John Woods, general editors. Amsterdam: Elsevier/North-Holland.)
Kevin Hoover, "Automatic Inference of the Contemporaneous Causal Order of a System of Equations," Econometric Theory, 21(1), 2005, pp. 69-77.
Matthew C. Stockton & Oral Capps Jr. & David A. Bessler, 2008. "Samuelson´s full duality and the use of directed acyclical graphs," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 167-191, May.
Haesun Park & James W. Mjelde & David A. Bessler, 2007. "Time-varying threshold cointegration and the law of one price," Applied Economics, Taylor and Francis Journals, vol. 39(9), pages 1091-1105.
Zijun Wang & David A. Bessler, 2006. "Price and quantity endogeneity in demand analysis: evidence from directed acyclic graphs," Agricultural Economics, International Association of Agricultural Economists, vol. 34(1), pages 87-95, 0
.
