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Before President Obama signed health care reform into law, we never saw a full estimate of the bill's costs. We saw countless estimates, from the CBO and elsewhere, of the bill's cost to the budget, which was a product of smart message control by Obama and the Democrats. Focusing only on the costs to the budget gave the bill's supporters a rhetorical advantage, and allowed them to produce very persuasive graphs, like this one that Menzie Chinn created and Paul Krugman, among others, reposted:

Those are CBO or other official estimates of the effect on the budget of, from left to right, the two Bush tax cuts, the war in Iraq, and the ACA (see Menzie Chinn's post for the documentation). You can disagree that the bill will cut the deficit, but then you have to find another credible source that disagrees with the CBO's projection. Your argument is not going to be as persuasive as this very simple graph. 

The cost of the bill to the budget, though, is not the only relevant cost. As the Cato Institute's Michael F. Cannon has noted, the Democrats learned from the experience with the Clinton health care reform attempt to avoid official estimates of the bill's cost full cost -- the cost to the government and to the private sector. There are provisions in the bill that require private citizens to spend their own funds on health care, most importantly the "individual mandate" that makes purchasing insurance a legal obligation for everyone. Cannon's simplified explanation of how this works:

Another gimmick pushes much of the legislation's costs off the federal budget and onto the private sector by requiring individuals and employers to purchase health insurance.  When the bills force somebody to pay $10,000 to the government, the Congressional Budget Office treats that as a tax.  When the government then hands that $10,000 to private insurers, the CBO counts that as government spending.  But when the bills achieve the exact same outcome by forcing somebody to pay $10,000 directly to a private insurance company, it appears nowhere in the official CBO cost estimates - neither as federal revenues nor federal spending.  That's a sharp departure from how the CBO treated similar mandates in the Clinton health plan.  And it hides maybe 60 percent of the legislation's total costs.  When I correct for that gimmick, it brings total costs to roughly $2.5 trillion (i.e., $1 trillion/0.4). 

[Emphasis mine.] Of course, this is not an official estimate. It's just Cannon's back-of-the-envelope estimate of the bill's cost assuming that the ratio of government to total spending that the CBO reported for the Clinton bill (that is, 4 to 10) also applies to the Obama bill. 

RAND recently released an analysis of the reform bill that included cost estimates for the law's effect on personal health care expenditures. Using their house model, they found that between 2014 and 2019, cumulative personal spending on medical services would increase 2 percent, or $548 billion, compared with the status quo. 

The study's estimates of the Obama bill's impact on the number of uninsured were similar to those of the CBO, meaning that the comparison is an apt one: 

The $548 billion increase in personal health care expenditures is the result of the mix of incentives that households face when deciding whether or not to buy insurance, under the provisions of the reform: mandates, subsidies, penalties, etc. In other words, RAND is predicting that people will purchase $548 billion worth of insurance policies because it is newly economical for them given the measures in the health care bill. That could be because they would be able to access subsidies that make a policy they've wanted all along newly affordable, or because of the cost of uninsurance penalties. Note that this estimate only includes consumption of medical services. 

The RAND study also estimates that individuals and companies would pay $87 billion in penalties for lack of insurance.

This is the only serious nonpartisan estimate of ACA's effect on private spending on health care that I've seen. Adding the $548 billion estimate to the $900 billion that RAND found the government would spend, the total cost of the Democrats' health care bill is roughly $1.45 trillion for spending on health insurance alone. Add in the provisions of the bill that aren't related to health insurance, and you arrive at a figure that is as close to Cannon's figure as to the CBO's.