That is the subject of a new paper by Devin Caughey, Christopher Warshaw, and Yiqing Xu (pdf). It turns out that before the 1980s it hardly mattered at all which party controlled a state government. These days it matters much more, but how much?
Even today, for example, electing a Democratic rather than Republican governor should be expected to increase monthly welfare payments by only $1-2 per recipient, and to increase by just half a percentage point the proportion of policies on which a state has the liberal policy option. These effects are small relative to policy differences across states. They are also small relative to the partisan divergence in legislative voting records. These results thus partially assuage the normative concern that partisan polarization has led to extreme policy swings, degrading the congruence between policy outcomes and citizens’ preferences.
OK, you can all go home and relax now…and just to be clear, these estimates are adjusting for what is already the ideology of the state.
Some other things to note from this paper:
1. The effect of having a Democratic governor seems to be rising.
2. Whatever Democratic governors accomplish, they accomplish in their first two years in office. Policy effects do not seem to cumulate over time.
3. “The estimated policy effect of a switch in unified party control is one-twentieth the size of the typical difference between states…”
The bottom line? Worry about the culture people, not about the election.