It won’t be impossible for pay for substantial individual tax rate reductions by cutting tax expenditures. But it will be very, very hard. The challenges are political, administrative, economic, and, in a key way, mathematical. While “broadening the base and lowering the rates” is a goal often advanced by politicians and economists, a new study by my Tax Policy Center colleagues Jim Nunns, Bob Williams, Eric Toder, and Hang Nguyen  shows just how tough it would be to accomplish. One of the biggest and least understood challenges is the interaction between rates and tax preferences. In short, deductions, exemptions and the like lose their value as rates fall. Thus, the very act of cutting rates shrinks the pile of money Congress has available to pay for those rate reductions. To understand why, first think of it first from the taxpayer’s point of view.  A $100 tax deduction is worth $35 to a taxpayer who is in today's top bracket of 35 percent, but would be worth only $28 if that rate is cut to 28 percent.  From government’s perspective (to oversimplify a bit), eliminating that deduction would produce $35 today but only $28 if rates are cut. To see what this means, my TPC colleagues looked at what would happen if Congress slashes individual tax rates by 20 percent across the board and eliminates the Alternative Minimum Tax, two elements of a much broader tax reform proposed by Mitt Romney. As a result, the Treasury would collect about $320 billion less in individual income taxes in 2015 than under today’s tax rules (aka current policy). Thus, if Congress wants to generate the same amount of revenue,  it would need to reduce individual tax expenditures by $320 billion (Of course, it could find the money elsewhere—say, by cutting spending or raising corporate taxes-- but that’s another story). The math is unforgiving. By lowering rates Congress reduces the total value of individual tax preferences by about $200 billion—from $1.3 trillion under current policy to less than $1.1 trillion. And that means it would need to cut those tax expenditures by nearly one-third ($320 billion out of $1.1 trillion) to make up the revenue lost by the tax cuts. If Congress wants to generate the same amount of money as current law, the hole would be much deeper. Lawmakers would have to cut tax preferences by $730 billion. In the real world, coming up with those bucks is even harder than that. Because many of these tax subsidies are deeply ingrained in the economy, Congress is likely to phase them out slowly. In addition, taxpayers will adjust their own behavior in response to these tax changes. Both would further reduce the amount of revenue from base-broadening. Then, there is the matter of what is administratively and politically feasible. To sort through this, TPC divided tax expenditures into four buckets—each less likely than the next to face cuts. The first, where changes are most likely, comprises preferences such as itemized deductions and non-retirement fringe benefits. This includes popular deductions for mortgage interest, charitable gifts, and the exclusion for employer-sponsored health insurance so scaling these back would be a heavy lift. But curbing other preferences would be even tougher. The second group includes investment and savings incentives such as low rates for capital gains and preferences for contributions to retirement accounts. The third tranche includes credits for low-income families with children and the partial exclusion of Social Security benefits. The last pot--and most untouchable-- are exclusions for income such as imputed rent on owner-occupied housing and combat pay. TPC figures that if all of the offsetting revenues came from Group 1 only, those tax preferences would have to be slashed by 72 percent to prevent the rate cuts from adding to the current policy deficit (assuming people don’t change behavior). Just as vexing, if Congress cuts that bundle of tax breaks across the board while trimming rates by 20 percent and eliminating the AMT, the Tax Code becomes much less progressive. On average, the highest-income 5 percent would pay less tax while those in all other income groups would pay more. About the only way Congress could fix that huge distribution problem would be to raise tax rates on capital gains and dividends—an idea strongly opposed by Romney and most congressional Republicans. Broadening the base and cutting tax rates is a great idea. But the message from this paper is simple: It sounds a whole lot easier than it is.