We have a culture to gift when we are invited to birthday party, marriage ceremony or bridal party

I'm not sure what your question is. Are you asking if you should bring a gift to a wedding or birthday party? If you attend the party, it's customary to bring a gift. Was there another part you find confusing?

Are you asking if you should still go to the party, if you cannot afford the gift?

It is acceptable to give even an inexpensive gift.
There is an expression "It's the thought that counts."
This means the most important part of the tradition, is that you give something.
It does not have to be an expensive thing.

It might make a difference depending on where the person lives.

Yes. Sorry I did assume that this was directed at American culture.

Yikes! I'm not telling anyone to go into debt, I agree a gift need not be expensive. On many invitations often the host specifically ask that gifts not be given, they only want the pleasure of your company. On the flip side, if you accept someone's hospitality, it would be rude to suggest you are disappointed with whatever is served.