Whether it's arguing over Mitt Romney and President Obama's plans for Medicare, or Paul Ryan's budget, or which candidate will best control the debt, a lot of the discussion this election has made one unspoken assumption: the president can determine the budget.

Obviously, the president has a lot of sway over the budget. He's a formal part of the budget-writing process, for one thing. Ever since the Budget and Accounting Act of 1921, the president has been required to submit a formal budget request to Congress, including estimates of tax revenue and spending for the coming fiscal year. But how much power does that amount to in practice?

To find out, I tried comparing the proposed tax revenue and spending included in each president's budget requests from 1923 to 2011 to the actual amounts collected in taxes and spent by the government each of those years. This isn't a perfect metric - presidents often tailor requests to what they think Congress will accept - but it gives a sense of how much Congress and non-presidential forces are affecting things. Here's how much revenue and spending changed from what the president requested (data here):

On average, spending went up 4 percent from what the president requested and revenue went up by 2.2 percent. What caused this? Well, the 1930s and 40s for one thing. Spending was over 70 percent higher than requested by the president during the Great Depression, as the Roosevelt administration requested emergency funds in excess of what his budget requested, and spending and revenue doubled due to spending on World War II, increased taxes to fund that spending, and additional revenue scooped up due to the extreme economic growth in that period.

So let's confine ourselves to the last 50 years (1962 to 2011) to exclude the FDR administration, which wasn't really reflective of the budget history of the United States.

That's a much more uniform picture. But even here, outlays were an average of 2 percent higher than the president's request, while revenues were 1.46 percent lower. Based on Obama's latest request, that's a spending increase of $76.6 billion and a revenue loss of $42.4 billion. That's a lot of money. So what's going on there? For one thing, Congress often deviates from presidential policy and could have chosen to increase spending and taxes relative to what the president requested. This is clearly what happened to spending during the 1980s, where Democrats in the House pushed spending above what Ronald Reagan requested.

The changes could also reflect bad revenue predictions. For example, George W. Bush's budget requests understated how much his tax cuts would reduce revenue. Economic trends are important too, as recessions pushed down revenue in the early 1980s, early 1990s, and late 2000s, and the unbudgeted stimulus and bailouts of 2008-09 pushed up spending.

Are there ideological or party patterns that affect the size of these swings? Surprisingly few, actually. The party in control of the presidency and Senate doesn't correlate significantly with the size and direction of changes in either spending or revenue, nor does the ideological stance of the presidency and Senate as measured by DW-NOMINATE, a system for quantitatively comparing legislators' ideological stances. The degree of Senate polarization (as measured by the difference in the average DW-NOMINATE scores of the two parties) doesn't seem to matter either, nor does having different parties controlling the White House and Congress.

In fact, there are only three variables that seem to make a real difference: the rate of GDP growth, the average ideological score of the House, and the degree of polarization in the House. Each additional point of GDP growth means 1 percent lower spending and 0.85 percent more revenue, which makes sense given that the government spends less on unemployment insurance and has more income to tax when the economy's growing faster.

But the House findings are what's really interesting here. A House that's 0.1 points more conservative on DW-NOMINATE - or about how much more conservative the House got after Republicans took over in 1995 - is associated with a 7.5 percent decrease in spending and a 4.26 percent decrease in revenues. The party in control of the House isn't statistically significant, but it comes very close to being so. Further, if the two parties' DW-NOMINATE scores grow 10 percent further apart, that's associated with a 5 percent increase in revenue, but no change in spending.

I honestly have no idea what to make of the idea that political polarization is associated with revenue increasing relative to presidents' requests. Perhaps polarization prevents Congress from doing things that hurt growth; the recent economic success of Belgium, which didn't have a government during the worst of the financial crisis, would support that theory.

In any case, conservatives can take solace that electing their candidates seems to get the results they want. More than any other political factor, making the House more conservative pushes both spending and taxes down. Of course, the flip side is that making it more liberal pushes spending and taxes up. Elections: they have consequences!