Hillary Clinton's proposed tax increases are likely not enough to pay for the new spending programs she has called for, according to outside independent analyses.

The Democratic presidential candidate has made a point of finding offsets for new programs, pledging last week that she would not add a "penny" to the rising national debt. Yet nonpartisan estimates of Clinton's tax-and-spending plans cast doubt on that claim and suggest that under realistic assumptions Clinton's plans could add between a few hundred billion and one trillion dollars to projected deficits. A new analysis published Tuesday illuminates the math.

The Tax Policy Center, a nonpartisan Washington think tank, released estimates of the revenue that Clinton's new taxes on high earners and companies would bring in, including some that take into account the impact that the tax changes would have on economic growth.

In a "static" analysis, one that doesn't consider what the taxes would do to the economy, Clinton's tax plan would raise enough taxes to cut deficits by about $1.58 trillion over the next decade. That would be just short of the $1.65 trillion in new spending programs Clinton has called for, as tallied by the Committee for a Responsible Federal Budget.

However, the shortfall would be larger in a "dynamic" analysis that takes into account the impact on economic growth from sharply higher tax rates and the fact that income would be shifted from individuals to the government and the resulting influence on jobs and taxes.

Taking those effects into account, the Tax Policy Center reckons that Clinton's tax plans would reduce deficits over the next 10 years by $1.53 trillion. Using a different model, one maintained by the Penn-Wharton Budget Model, the tax plan raises even less: $1.47 trillion. That result would imply that Clinton's total fiscal plans would add about $180 billion to deficits over 10 years — a small amount, by federal government standards, but more than a penny.

Those results, however, could be overly optimistic.

Another independent organization, the Tax Foundation, ran its own model and computed that Clinton's plan would raise only $663 billion over 10 years, taking macroeconomic effects into account. If that were the case, Clinton's new revenue would fall short of her new spending by a trillion dollars — a nontrivial amount.

All three models are meant to give a sense of what changes in tax law would do, much as the models that Congress' in-house budget agencies do.

They reach different conclusions because of different assumptions and because of what they do and do not take into account.

For example, the Tax Foundation's model emphasizes the lessened incentives for work and investing that Clinton's tax plan would generate by raising tax rates. On the other hand, it downplays the benefits that would result from the same taxes lowering the federal debt, reducing the cost of borrowing across the economy.

In contrast, the Penn-Wharton Budget Model places more emphasis on the dynamics of the federal debt and how individuals would plan around changes in their own taxes and in interest rates affected by government borrowing. As a result, because Clinton's tax plan, apart from her spending plans, lowers the debt, interest rates would fall, allowing individuals and companies to borrow more easily to finance new spending and investment.

The online simulator of the candidates' plans, director Kent Smetters pointed out Tuesday, does allow users to see what would happen if greater federal spending were taken into effect: Because spending and taxes cancel each other out in that case, the debt wouldn't fall as much, interest rates would remain higher, and revenue would be lower, making it more difficult for Clinton's math to add up.

Taking the spending side into consideration introduces new wrinkles, however. Tax Policy Center analyst Ben Page noted Tuesday that some of the spending changes Clinton has proposed "could be productive." For instance, most economists believe that upgrading U.S. infrastructure, as the Democrat has proposed, would aid commerce and boost growth. That effect likely would not change the fact that incorporating spending plans into the estimates would make Clinton's deficits appear bigger, Page noted, but it would make the calculation more complicated.