Well, borders aren't a physical thing. So it's no so much as removing them as stop arbitrarily enforcing them.So remove them?
Right now, the type of people that would contribute to your country have an extremely difficult time doing so because the borders are "closed". The people you don't want in, stream across illegally and no one does anything about it because there are a myriad or loopholes and no enough man power to do anything about it. Then there are a whole bunch of people (most of the world) who couldn't be bothered to move there even if they were welcome.