Looking on the internet deeply has found these results:

establish identity is the most popular phrase on the web.

construct identity 137,000 results on the web	establish identity 1194,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
We must construct our identity! A strong one! It is so contrived, the way Eastern Europeans are continuously trying to construct their identity. Or should she try to construct some kind of dwarf identity, get involved in the Little People of America, become aware of what was happening for dwarfs? We should regard the European Constitutional Treaty as being, above all, a great chance to construct a shared European identity. Europe does not need to create an enemy overseas in order to construct its own political identity. Algeria is also defined by remarkable aspirations to construct a society which reconciles its identity, fundamental freedoms and development which will benefit all people.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

construct identity

137,000 results on the web

establish identity

1194,000 results on the web

More popular!

We must construct our identity! A strong one!
It is so contrived, the way Eastern Europeans are continuously trying to construct their identity.
Or should she try to construct some kind of dwarf identity, get involved in the Little People of America, become aware of what was happening for dwarfs?
We should regard the European Constitutional Treaty as being, above all, a great chance to construct a shared European identity.
Europe does not need to create an enemy overseas in order to construct its own political identity.
Algeria is also defined by remarkable aspirations to construct a society which reconciles its identity, fundamental freedoms and development which will benefit all people.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.