How much money will US get by arm-twisting?

Were the numbers plucked from thin air, or are they based on solid fact?

Of the $20.9 billion extra that Congress predicts the new tax bill will raise in fiscal 1983, $6.7 billion is accounted for by ''compliance'' provisions, which are designed to cajole taxpayers into paying what they already owe.

But critics say tougher enforcement just isn't going to raise that much money.

''There are a lot of assumptions (in the tax bill) that are questionable,'' says Larry Wachtel, a vice-president at the Bache Halsey Stuart Shields brokerage house.

Of these compliance provisions, the largest is withholding on dividends and interest, which is predicted to bring in $4.3 billion next year that would not otherwise be paid. In fact, this is the largest revenue-raising item in the entire bill.

The appearance of this provision is something of a surprise, considering its political unpopularity. (When President Carter proposed it in 1980, the House shot it down, 401 to 4.) But by providing a large chunk of estimated revenue, this withholding negates the need for an even more unpopular measure - an oil or energy tax.

Groups that would be burdened by the provision, however, claim the figures are exaggerated.

''The withholding plan as written cannot raise more than $1.2 billion in fiscal 1983, as opposed to the official estimate of $4.3 billion,'' says Roy Green, chairman of the United States League of Savings Associations.

Mr. Green says the costs of setting up a withholding system will cut into depository institutions' own taxable income, lowering Treasury revenues. But his main point is that financial institutions will need six to nine months to gear up for withholding. This time lag, he claims, will cut deeply into 1983's projected revenue, because much of the money raised by the provision is to come from accelerated cash flow, rather than catching tax cheaters.

A lawyer with the Joint Committee on Taxation confirms that accelerated payments account for two-thirds of the $4.3 billion in projected revenue, with increased compliance making up one-third - although the ratio will reverse itself after next year.

''What we're getting in '83 is revenue we would have otherwise gotten in '84, '' he says.

Others say they don't find the figures on dividend and interest withholding too far off. Jerome Kurtz, commissioner of the IRS from 1977 to 1980, says the revenue estimates - based on an IRS study - are probably fairly accurate.

Figures for the tax bill's other compliance provisions - requiring employers to expand their reporting of employee income, and tougher penalties for cheating - are what he objects to.

''I would have to say those estimates are very, very soft,'' he says.

These miscellaneous get-tough measures are estimated to raise $2.3 billion in 1983. Mr. Kurtz claims the figure was essentially plucked from thin air. The IRS took numbers on the amount of unreported dividends and interest, he says, and arbitrarily interpreted them as an indicator of all unreported income.

''Questionable methodology,'' he grumbles, that ''substantially exaggerates the problem.''

As he points out, however, ''no one will ever know'' if any of the figures are inflated, since all tax revenues get thrown into the same pot.

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