I am writing a project for financial research support of a specific item and the public announcement asks me for the institution's TIN number (Tax Identification Number) or the Value Added Tax Identification Number (VAT) of the company the sells the item. I'm trying to contact the company that is located in USA, but they take too long to respond. I have its FEI number that came in an invoice. Is this FEI number equivalent to the TIN number? So, is it the same to provide the FEI number in place of the TIN or VAT number?
I don't fully understand what it is that you are trying to do or what you are being asked for. However, I believe that the answer is yes, they are the same.
Employers in the U.S. have a number that is typically called the Federal Employer Identification Number, typically abbreviated FEIN or just EIN. This number is one type of Tax Identification Number (TIN) used in the U.S.
Value Added Tax Identification Numbers (VATIN) are used by European countries and other countries, but are not used in the U.S.
If you are being asked for a particular American institution's TIN, I believe that you should give that institution's EIN.