Population shifts absolutely have consequences for state governments. The most important of these are economic consequences.
In the "Rust Belt," for example, jobs have been disappearing for decades. They have been leaving this area and heading to the "Sun Belt" or even overseas. This has a huge impact on the government of states such as Michigan. These governments are left with populations that suffer from more poverty than before even as the government lacks the tax base to use to try to address the problems these people face.
This is one way in which population shifts affect state governments economically.
Already for decades wealth persons internationally relocate to other countries in order to avoid high taxes. There is a strong correlation between how high the taqx level is and how much tax is actually being levied by a country. Have for example a look at http://www.switzerland-family-office.com/international-relocation.html. A clear example how wealthy persons are focussing on this issue. In the last 20 years over a 100.000 persons have internationally relocated from the Netherlands to Belgium to avoid high taxation in the Netherlands, wih severe financial impact on the Dutch office budget.
Some governments do not have good settlement planning strategies, as the result, this causes migration of people from villages to town!
This kind of migration, of course affect very much the ecnomic activities of the departed area.
This has been affecting lots od developing countries as most of them have poor management skills on how to equally allocate the wealth!