TWO out of three Greek workers either understate their earnings or fail to disclose them to the taxman altogether, according to Stephen Hall, an adviser to the Bank of Greece. Last year an estimated 24% of all economic activity in Greece went undeclared to evade tax and regulation, well above the European average of 19%.

The IMF, which was in Athens this week to check up on Greece’s public accounts, would like to bring more of this activity into the sunlight, to boost government revenues. After a calamitous recession in which the economy shrank by 30%, government debt now stands at 174% of GDP; the budget deficit last year was almost 13% of GDP. But there is a risk that an overly aggressive tax-raising drive will compound the problem.

Greeks, even more than their counterparts elsewhere, feel that their taxes are wasted. One study, using data from the 1990s, put Greece’s “tax morale” fourth-lowest of 26 countries. Greece’s public sector is more corrupt than that of any other EU state, according to Transparency International, a pressure group. Satisfaction with public services is extremely low. No wonder, then, that many Greeks have few qualms about not paying their share.

Greece also has high self-employment, which tends to lead to bigger underground economies. It is relatively easy for those working for themselves to evade income tax and social-security contributions. Greeks have plenty of incentive to do so: government levies account for 43% of labour costs, compared with the rich-country average of 26%.

A big shadow economy, naturally, crimps government revenue. Each percentage-point increase in the underground economy’s share of GDP lifts the debt-to-GDP ratio by 0.4 percentage points, according to a recent study of 11 European countries. Before Greece joined the euro, it was able to reduce its debts through high inflation. With monetary policy now in the hands of the European Central Bank, that option is no longer available: inflation has been negative for more than a year.

Lots of shady activity may also be bad for growth. Shadowy firms find it hard to borrow, which limits their productivity. According to Francesco Pappada of the Einaudi Institute of Economics and Finance many small firms in Greece deliberately avoid taking out loans because it involves being more transparent. Unproductive firms pay low wages.

The IMF wants Greece to learn from Peru, which in the 1990s tackled tax evasion by creating a small, well-trained task force. Eliminating the many exemptions and loopholes in its labyrinthine tax system will help, by making it possible to lower rates, thereby reducing the incentive to cheat. On October 6th the government unveiled a budget that included tax cuts. Greece may also refine its definition of tax fraud in an attempt to catch more evaders.

But the taxmen must tread with care. Over 25% of Greeks are officially unemployed; the shadow economy is a lifeline to many of them, notes Friedrich Schneider of Johannes Kepler University. Two-thirds of shadow earnings are spent almost immediately at businesses that do pay tax. Too severe a crackdown on tax evasion might put all that in jeopardy. Take a law passed in 2011 but yet to be implemented, which mandates that certain workers use time clocks to monitor their working hours. It may simply discourage bosses from hiring, thus bringing in little revenue while lowering incomes.

Greece should instead try to coax shadowy businesses into the open. Mr Schneider wants to see short-term tax exemptions for those who work a second job at night. Mr Pappada wants Greece to offer tax breaks to small businesses that take out loans. Both schemes would encourage workers and firms to register with the government, making it easier to shrink the shadow economy over time.

The best cure, though, would be a sustained economic expansion. According to the European Commission, Greece will grow by 0.6% this year and 2.9% next. Unemployment in the second quarter of 2014 was 3.6% lower than a year before. As unemployment falls and wages rise, the urge to go underground will wane. At any rate, that is what happened from 1993 to 2003, when growth averaged 2.5% a year and the shadow economy shrank by a third.