(i) With crossholding between B and C that will reduce transparency, hence higher information asymmetry. If the Manager of the pyramid is also the controlling shareholder then he can also reduce his risk of personal portfolio for diversifying across B and C while retaining overall control of these companies.(ii) For the pyramid structure one other aspect is to make sure Manager of these companies will also be under control by the company A.With crossholding between key companies at lower level of the pyramid under A's control this would ensure that decision made by these subsidiaries will not deviate from A's direction by a Manager in one particular subsidiary. Deviation from the A's corporate directive is only possible when many Managers of subsidiaries are acting in concert.
If the controlling shareholder in A has personal interests in B and C that pyramid structure is likely built for reason (i) If the crossholding between B and C are by way of company shares then it is likely that it is for reason (ii) Another way could be by examining dividend payout and the ownership/control ratio. However in the stock market there are many other factors that may affect dividend trend.