As someone who works in public finance, I often get asked outside of my job a number of questions similar to the title of this post. Recently, I negatively commented on tax incentives given out by the state of Kentucky to build a young-earth creationist theme park. I had two basic objections. One was that I thought it promoted an unscientific view of the world, which is ironic since the state spends so much money attempting to property educate its young people in the public school system in the ways of science. The other is another point, which is the primary focus of this discussion, centering on whether or not this use of tax incentives is appropriate from a public finance perspective. Advocates of these sorts of projects almost invariably say, "Oh, but it will pay for itself.". Republicans do the same thing with tax cuts more generally while Democrats do it with transportation infrastructure and education.
Since this is such a common phenomenon, let's actually work through the math and see if it works out. First, let's confront the basic constraint, which any project or tax break must contend with: the basic laws of mathematics. Taxes, particularly on the state and local level, only capture a small fraction of economic activity. Let's be generous at the federal level and say that the government current collects 20% of GDP in taxes. It doesn't, but let's just say that it does. This means that, in a single year, for every dollars you cut taxes or increase spending, it has to produce $5 in order to recoup its cost. At the state level, it's even worse than that. Because states typically collect in the mid-high single digit percentages of tax revenue as a percent of GDP, let's pick 7% for the sake of argument, it has to generate a whopping $14 of new economic activity for each dollar forgone in revenues or increased expenditures.
Now, you might say, "Aha! But what about the later years as well?". Fair enough. Let's work through that exercise, remembering that we have to discount future revenues. Click on the image below to see the entire table. I used a theoretical economy with the government collecting 20% of GDP in taxes and did a 1% reduction in tax rates, which could also some kind of long-term economic development incentive of equivalent magnitude. This tax rate reduction is maintained through-out the ten year period since, if it is taken away the year after it is implemented, the short term boost is lost and demand was just essentially brought forward.
Even assuming a 2.5x multiplier, which is quite generous, not only does the tax cut not pay for itself initially, it never, in any given year, does so. I solved the equation to see what multiplier is needed in this long-term example, and it is 5.26x. That is simply unheard of. Using the tax rates that a state has, this becomes even more intractable. Here I show the multiplier on the table for what is needed to finance a 0.5% tax cut.
A 15.4x multiplier is simply preposterous. I would challenge anybody to find an economic paper that claims to have found anything like that for any policy.
It's actually even worse than this in many respects when you consider the opportunity cost of what else you might have elected to use an equivalent amount of money for. Basically, what you find is that the marginal impact of this in your revenue projections compared to continuing to spend it on, say, public infrastructure is that you are even further behind. That's because if that 1% of tax revenue forgone was current being used to finance some ongoing expenditure, you can no longer finance that ongoing expenditure and thus lose the GDP associated with it. This simplified example basically was meant to demonstrate what would happen if you took a budget surplus of 1% of GDP and gave it out in an ongoing tax cut or long-term economic growth incentive of some sort that came out of current tax revenues. We could work out a similar exercise for a long-term spending increase, but I don't want to clutter up this post too much. The results are very nearly the same.
Now, some programs are more effective and more cleverly structured than others and can obtain significant leveraging of private sector dollars if done properly. There are instances where the dollars deployed have a particularly powerful marginal effect where they may possibly get a development over a certain threshold of financing it would otherwise not have crossed. In those circumstances, a small amount of government financing can achieve bizarre levels of leverage. It must be noted, though, that those cases are not as common as many claim.
As a general proposition, most tax cuts and economic development programs do not "pay for themselves", but that's not necessarily an argument that they shouldn't be done. There are plenty of reasons to undertake a project or policy beyond whether or not it actually pays for itself. However, the basic rule should be that one does not undertake a project or policy because policymakers think it pays for itself.