When Congres first discovered the underground economy a couple of years ago, the usual experts were rounded up for hearings and the predictable occurred: nothing.

Since then the debate over whether there is an underground economy has been replaced with happling over just how big it is, and the question of what to do about it is being asked with increasing urgency.

"Unless some action is taken to both eliminate incentives for underground economy participation and better enforce tax laws, then the voluntary compliance tax system will be subject to increasing strain," warns a background report prepared for the House Wednesday Group, a caucus of progressive Republicans.

Economist Peter Butmann, the best-known student of the underbelly of the economy, predicts: "We can expect the subterranean economy to prosper ightily. It will become ever more visible and ever more obvious to ever more people. How to react to it will become ever more pressing."

Suggested soluitons abound:

Supply-side advocates such as Rep. Jack Kemp (R-N.Y.) insist that the same Laffer Curve, whose tax cuts are supposed to spur productivity, also will pry open the underground economy. If taxes are lower, there's less incentive to evade them, they argue.

Liberal tax reformers such as Rep. Benjamin Rosenthal (D-N.Y.) say closing imcome tax loopholes would make the tax system more fair and rebuild respect for voluntary compliance. Eliminate tax shelters, outlaw tax havens and step up IRS audits, the liberals urge.

Former Rep. Al Ullman, (D-Ore.) for years futilely urged utilizing both remedies, slashing individual, corporate and Social Security taxes and and replacing them with a European-style value-added tax that can be tightly enforced to assure equality.

Unleash the armed forced to stop the $90-billion-a-year drug traffic, demands the Florida congressional delegation. Legalize marijuana, grow it at home, and tax it like alcohol, dreams the National Organization for the Reform of Marijuana Laws. Remove the penalties for hiring illegal aliens to bring them into the above groung economy, recommends the Reagan administration.

You can't cut taxes enough to remove all the incentives to go underground, and you can't tighten enforcement enough to make underground business impossible, respoind the economists who specialize in subterranean studies.

On the enforcement side, political objections to IRS tactics and potent special interests have blocked tax reform and compliance efforts.

Despite evidence that each additional dollar spent on IRS audits yields about $7 in tax revenue, Congress last year refused to increase the IRS budget, and the Reagan administration wants to cut it.

Congress has likewise been unwilling to order withholding of taxes on dividends and interest, though the IRS has calculated that at least $15 billion of this form of income escapes into the underground without taxation each year.

Any hope that the current Congress would rejuvenate faith in the tax system by injecting a healthy dose of fairness into its tax bill have vanished in the past few weeks. The tax bill has been described as a Christmas tree decorated with symbols of special interests. A bipartisan tax-reform effort to close a $1.3-billion-a-year loophole that lets commodity traders avoid most income taxes has been perverted by industry lobbyists.

Even without highly paid advocates, Caribbean tax havens continue to bedevil reformers by offering ways for legitimate businesses and illegal enterprises to escape taxes.

Middle Eastern investors who are negotiating to buy Financial General Bankshares Inc. of Washington have incorporated in the Netherlands Antilles, so they can avoid paying most of the taxes now paid by that bank's owners.

U.S. Customs agents in :miami say banks and shell corporations in the Antilles, Seychelles and Banamas are routinely used by drug smugglers to finance marijuana and cocaine deals and to launder illegal profits.

The likelihood that taxes can be cut enough to shift a lot of business out of the tax-free undergrund is pooh-poohed by Gutmann, the City University of New York professor who first suggested the scope of subterranean business. 4tGutmann has plotted his own curve to show that a cut in tax rates can increase above-ground economic activity and cut underground work. But ther gains will not offset the lost tax revenue, he says, not even with the help of the increased economic activity that economist Arthur Laffer predicts will come with a tax cut.

"Growth of the subterranean econmy goes hand in hand with erosion of our tax system," says Gutman;n, predicting, "the erosion process will continue.

"As voluntary self-compliance declines, the perceived unfairness of the tax system rises, since some pay the required taxes and others simply do not. This, in turn, further stimulated the subterranean economy."

Gutmann and Edward Feige of the University of Wisconsin disagree bitterly over the size of the underground economy -- Gutmann calculates 14 percent of the gross national product, while Feige says it's twice that much -- but both agree its booming.

Inflation and the well-documented "bracket creep" that forces taxpayers to tolerate higher and higher tax rates provide continuing momentum for underground growth, Feige says. "There is absolutely nothing that will stop they dynamic disequilibrium," he says.

Feige, however, says the driving force of the undergruond economy is not just economic, blaming it on "a dramatic decline in trust in government."

Underground activity is much less common in Scandinavia, where the social contract between the government and hoverned is most carefully honored, notes Feige who is pursuing his studies in Europe. The Continent's most conspicuous underground economy is in Italy, where respect for authority has been crumbling for centuries.

The pessimistic predictions of continuing underground prosperity are challenged, however, by theofficial keepers of U.S. economic statisitcs -- the Bureau of Economic Analysis of the Department of Commerce.

"I just don't see the growth," says Robert Parker, chief of the national income and wealth division of BEA.

Parker contends that much of the income that evakes taxes is eventually caught in the government statistical system, so accurate monitoring of the economy is still possible. National figures for farm income, self-employment income and other earnings known to be understated on tax returns are adjusted to reflect the cheating caught by IRS auditors, he notes.

BEA officials admit they don't count any illegal income in their official gross national product, nor do they have any way of evaluating the rapidly growing barter between businesses. The biggest weakness in the statistics, Parker concedes, is in the service sector of the economy, which is also the most rapidly growing.

Even with these weaknesses, the official statisticians insist they are missing no more than 1 or 1 1/2 percent of the nation's economic output and see no evidence of an underground boom.

"I just don't think there has been a tremendous growth," said Parker, challenging the underground estimates of Feige, Gutmann and others. "There are too many statistical problems [in their calculations] to warrant worrying about the effect."