🚀 go-pugleaf

I  have   a basic understanding  of Granger-Simms   causality  (or, better, GS
temporal ordering). I have seen bivariate time-series tests in two flavors:

	[1] a vector autoregression (Y_0= a Y_-1 + b X_-1 + n)
	[2] two time-series regressions and a subsequent correlation
	of the residuals (Y_0 = a Y_-1 + n_t; X_0 = b X_-1 + m_t;
	if n_t-1 correlates with m_t, then "Y sort of causes X".

I presume that the first method is less restrictive than  the first, but loses
a little by mixing expected changes with unexpected changes.  (I may be wrong,
here, altogether.) Further, multivariate extensions are a bit  less natural in
the second procedure.

Most studies seem to perform either of  these analyses with  long time series.
Yet, I  have a  panel data set   with only 5 years  of  data, but thousands of
firms/people.  My question  is whether it makes much  sense  to  run the above
regressions cross-sectionally (and year-by-year or pooled),  and claim GS-like
causality.  It does appear to be different; the  relevant statement is now how
does a cross-sectional outlier  in X_{i,t-1} correlate with a  cross-sectional
outlier in Y_{i,t}.

Are   there comparable   studies   (especially if    these    studies use easy
computational/notational  methods; I am less  interested  in asymptotic theory
than I am interested in actual use).

Thanks.

/ivo welch