The rise or fall of long-range deficits.

Treasury Secretary Donald T. Regan says the federal deficit will amount to ''much less than $150 billion'' by fiscal year 1989. Congressional Budget Office (CBO) director Rudolph G. Penner says the deficit will be a whopping $263 billion by '89.

Who is right and does it matter?

To many economists, who say large deficits affect the economy in a variety of ways including boosting interest rates, the size of the deficit clearly matters. Even Reagan administration economists, who take a relatively limited view of the deficit's economic impact, agree its large size has boosted the US trade deficit.

The deficit's size also affects the way politicians plan for the future. For instance, Mr. Regan's estimate that the deficit will be ''under $175 billion'' in budget year 1984 and decline thereafter is a key underpinning for the Reagan administration's adamant stand against tax increases.

The administration strengthened its pledge against tax hikes Thursday morning during Regan's appearance on NBC's ''Today'' program. Regan said, ''Let's get the record straight. We have no plans now for tax increases in 1986, '87 ,'88. Would you like to try for 2000?''

This followed his testimony Wednesday before the Joint Economic Committee of Congress, during which Regan ruled out tax hikes in 1985 but refused to speculate on increases in later years.

Democratic presidential hopeful Walter F. Mondale accepts the CBO deficit estimates, charges the administration with ''cooking'' the budget books in a bid to lower the deficit, and calls for a tax hike next year.

The technique of estimating deficits is complex and requires in turn estimates of a variety of economic developments and congressional and executive-branch actions. Thus it is subject to large errors.

''It is not unusual to to be off by a large percent,'' said Bernard Markstein III, senior economist at Chase Econometrics, a large forecasting firm.

As a result, it is impossible to say with precision whether the CBO or administration budget estimates will prove closer to the mark.

But at the moment, the large economic consulting firms have deficit estimates , which, after accounting for differences in underlying assumptions, are more in line with the CBO figures.

Comparisons between administration and other estimates are hindered by the fact that the White House has delayed release of its midyear budget revision.

This document usually is unveiled each July. The delay reportedly is due to a internal dispute over what size defense spending increase to build into budget estimates for coming years.

Without more spending cuts and tax hikes, the deficit ''could keep up around says.

Chase predicts that the deficit will shrink to $147 billion in 1988 and $125 billion in '89 - assuming tax hikes of $20 billion in '86 and $30 billion in '87 . Chase's budget figures also assume cuts in nondefense spending of $3 billion in '85 and $19 billion in '86.

A June 1984 CBO study says that errors in four types of assumptions - economic, legislative, administrative, and technical - can throw a budget estimate off. The same factors that cause an individual forecast to go wrong also help explain differences between the CBO and administration budget estimates.

Economic assumptions are perhaps the most common reason why deficit forecasts are incorrect and why different forecasters come up with sharply different estimates. Deficit estimates are very sensitive both to assumptions about the course of interest rates and the economy's growth rate. Economic growth affects the government's tax revenues and unemploment compensation costs while interest rates affect the cost of carrying the federal debt.

All other things being equal, a 1 percent increase in interest rates would boost the 1989 deficit by $26 billion, the CBO says. A 1 percent rise in the economy's growth rate would trim the '89 deficit by $105 billion. The administration's projections assume slightly faster economic growth rates and much lower interest rates than the CBO.

Deficit estimates also depend on the assumptions forecasters make about when new tax or spending laws will be passed and what affect they will have. The CBO assumes that spending and tax policies now in effect will continue unchanged. The administration assumes the President's proposals will be enacted.

Deficit projections also can be skewed by faulty assumptions about administrative action. The CBO said that earlier estimates of the 1984 deficit were thrown off, among other reasons, because the Defense Department was not spending money as quickly as expected.

Finally, forecasters must estimate technical factors that are somewhat unpredictable. For instance, the CBO notes, ''no one can predict exactly how many people will apply for social security benefits next year.''