Multinational firms arise because capital is much more mobile than labor. Since cheap labor and raw material inputs are located in other countries, multinational firms establish subsidiaries there. They are often criticized as being runaway corporations.
Economists are not in agreement as to how multinational or transnational corporations should be defined. Multinational corporations have many dimensions and can be viewed from several perspectives (ownership, management, strategy and structural, etc.)
The following is an excerpt from Franklin Root, International Trade and Investment
Ownership criterion
Some argue that ownership is a key criterion. A firm becomes multinational only when the headquarter or parent company is effectively owned by nationals of two or more countries.
For example, Shell and Unilever, controlled by British and Dutch interests, are good examples. However, by ownership test, very few multinationals are multinational. The ownership of most MNCs are uninational. (e.g., the Smith-Corona versus Brothers case)
Depending on the case, each is considered an American multinational company in one case, and each is considered a foreign multinational in another case. Thus, ownership does not really matter.