If the University accepted my credits for economics, mathematics or statistics courses that I took at another institution, then will they automatically be credited towards my economics degree at Columbia?

No. You must apply for transfer credit approval from the individual departments in order for these credits to count towards the economics major. In the case of economics classes and Calculus I (from an American university or college), you must apply for transfer credits from the department of economics. For courses in mathematics (other than Calculus I) or statistics, you must get approval from these departments and have them notify the economics department regarding your transfer credits.