binary, as often happens in microeconometric analysis. The paper is grounded
on a rigorous mathematical definition of поп-causality, which is shown to be
easily fitted into a dynamic version of the bivariate probit model. Particular
attention is placed in including covariates into the analysis, and in specializing
the definitions for longitudinal data sets. Panel type data for heterogeneous
individuals are in fact typical in microeconometric applications.
The paper implicitly suggests so many extensions to fill up a research agenda.
To make some examples: a more parsimonious representation of the dynamics;
allowing for unobserved heterogeneity; generalizing to a multivariate setting;
mixing binary and continuous variables; analyzing the impact of time aggrega-
tion.
References
[1] Aalen, O.O., 1987, Dynamic Modelling and Causality, Scandinavian Actu-
arial Journal, 177-190
[2] Amemiya, T., 1981, Qualitative Response Models: A Survey, Journal of
Economic Literature, XIX, 1483-1536
[3] Andersen, P.K., Borgan, 0., Gill, R.D., Keiding, N., 1993, Statistical Mod-
els Based on Counting Processes, Springer Verlag, Berlin
[4] Arellano, M., and Carrasco, R., 1996, Binary Choice Panel Data Models
with Predetermined Variables, CEMFI, Working paper No. 9618
[5] Ashford, J.R., Sowden, R.R., 1970, Multi-Variate Probit Analysis, Biomet-
rics, 535-546
[6] Billingsley, P., 1986, Probability and Measure, 2nd Ed., Wiley, New York
[7] Chamberlain, G., 1982, The General Equivalence of Granger and Sims
Causality, Econometrica, 50, 3, 569-581
[8] Colombo, M., Mosconi, R., 1995, Complementarity and Cumulative Learn-
ing Effects in the Early Diffusion of Multiple Technologies, Journal of In-
dustrial Economics, XLIII, 13-48
[9] Cox, D.R., 1972, Regression Models and Life Tables, Journal of the Royal
Statistical Society, Series B, 34, 187-220
[10] Engle, R.F., Hendry, D.F., Richard, J.F., 1983, Exogeneity, Econometrica,
51, 277-304
[11] Florens, J-P., Fougère, D., 1996, Noncausality in Continuous Time, Econo-
metrica, 64, 5, 1195-1212
[12] Florens, J-P., Mouchart, M., 1982, A Note on Noncausality, Econometrica,
50, 3, 583-591
26
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