We used as an alternative measure of economic importance a Chebyshev polynomial expansion in the share of affiliates, revenue, and employees as a functional form of the independent variable. The idea is that a high-order polynomial may approximate most functional forms (Kolsarici and Vakratsas 2015). The economic importance, k, of firm i to country m at year t has the following form:
where t_(li..lk)is the relative frequency of the categorical variables for the firms in the treatment group and c_(li..lk) is the corresponding number for the firms in the control group. A magnitude of L(t,c)=0 means perfect balance while a magnitude of 1 represents perfect separation.
The analyses included expansions up to the 20th degree, opting for third-order polynomial based on the Bayesian information criterion (BIC). The results using this variable are presented in table 2.