resulting in a fuzzy clustering of the I firms in K clusters or derived groups. Thus, one
is interested in simultaneously estimating the mixing proportions ðl k Þ, regression
coefficients ð bjk Þ, variances ð s2
k Þ and posterior probabilities of membership ðP ik Þ ,soas
to maximize equation (3) or (4) subject to the constraints in equations (5) – (8), given a
value of K ; _y; and _X : The technical details of this estimation procedure are described
in Appendix 1.