There is no "shadow government", as in not a building that says "shadow government"... However, there is a conglomerate of people that pull the strings on those on the government...they are easy to find, it is not rocket science. Just follow the money...find the people that either print or control the flow of money (in our stupidity in the U.S. we neither control or print the money)... They are the ones that run the country, simple as that.
So in essence, they are the "shadow government"...we the people have zero say. This is why so many presidents starting with Washington was always so serious in keeping these people out of the country. They warned future presidents and leaders about the dire consequences through writings and memoirs...
Then these people behind the scenes bought all the mainstream media (news/entertainment) to keep people dumb, lazy and distracted (this was taken from Hitlers playbook, give people some free shit without work, keep them distracted with trivial things and create an imaginary Boogeyman to fight)...they saw how well it worked there is no need to change it.
This is not a conspiracy theory or opinions...they are simple facts for all to see if they would like. If we all woke up tomorrow, there would be a revolt by sundown.