I've read in a paper that I can't find araing right now that supermajority requirements (in state budgets) tend increase deficit spending because more "pork barrel" interest are included.
If we extended that notion in practical terms to the federal level, cohabitation (to borrow a term from European politics) between majorities from different parties in Senate vs House, as well having a president from a party that doesn't have a majority in both houses seem to be an equivalent condition.
So, is there empirical evidence whether one-party budgets narrow the deficit more than party mixtures (in the three places that participate in making the budget: House/Senate/Presidency)?
N.B such a study would not be entirely trivial because deficits also depend on tax income and so on how the economy is doing. I've also read that deficits generally go down in boom/growth times, although the recent Trump years may be an exception. Also, things like wars may be a factor too on the spending side, i.e. there are confounding factors to consider.
