Explain again:
1) Why does Mississippi and New Mexico receive from the federal government more than they pay to the federal government in taxes?
2) Why does New Jersey and California receive from the federal government less than they pay to the federal government in taxes?
3) What do these facts imply about which of these states are the more productive and which are less productive?
Exactly correct. States are not taxed. Citizens are taxed.
Mississippi and New Mexico do not pay into the federal government. Their citizens do. We do not know how much more an individual citizen may pay or receive from the federal government.
It is true that some states receive less federal dollars than their citizens pay. This is especially likely in highly populated States, because federal expenditures are for the whole country, not for each state. It would be expected that highly populated states would receive less federal dollars per person.
If a citizen living in California pays a lot of Federal taxes, then retires, pays little taxes, and moves to Alaska where they then receive lots of social security and medicare dollars, then the federal dollars have moved from California to Alaska.
As States do not pay federal taxes, it is irrational to attribute federal gains and losses by state rather than by individual.
Moreover, as I have stated, a great many people move between states.