Can we use the portion of an economy that’s nationally-owned or privately-owned as a proxy for how socialistic or capitalistic it is, respectively?

We know that the USA has a GDP of $30.6T a year.

• There are some portions of this GDP that's produced by commonly-owned assets, like the Post Office, the highways department, the armed forces, the public school teachers, etc. Can't we add all their output produced and divide by the total GDP and get an idea of how socialized this economy is?

Can we use the portion of an economy that's nationally-owned or privately-owned as a proxy for how socialistic or capitalistic it is, respectively?