Do both these sentences mean the same?
This type of economic policy can be harmful for a nation.
This type of economic policy can be harmful for any nation.
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There is a subtle difference.
This type of economic policy can be harmful for any nation
Any emphasizes that nations other than our own are included. You can think of this sentence as having a hidden "not just your nation" or "not just our nation" attached to it.
This type of economic policy can be harmful for a nation
This is a neutral statement that simply comments on a policy.
Yes. "A" being an indefinite article, you are not referring to a specific nation. "Any" is functioning as a pronoun (standing in for "one" country), which makes it an indefinite article in this context, again not referring to a specific nation. So while it might seem that the meanings could be different, it's really too subtle to matter.