Tax evasion is a serious problem in developing countries because of the tiny administrative capacity of authorities and the size of the informal sector. Even in more developed economies, say, the Southern European ones, tax evasion is part of daily life. Again, administrative capacity is lacking. One could even argue it is a problem in the United States seeing the tiny auditing staff of tax authorities and the complexity of the tax code. Tax auditors have thus to define priorities.
Mirco Tonin studies the rules that Italy and Bulgaria instituted. In Italy, businesses and self-employed people reporting revenues below some level are subject to higher scrutiny. The idea is thus not to go after those who declare to be big fish, but rather those who may hide it. And making it known that there is such a threshold induces people to declare more to tax authorities. In Bulgaria, authorities are after employees and firms that declare too little in social security contributions. This is also forcing them to declare more to avoid scrutiny.
Tonin uses a model of imperfect monitoring to figure out whether such threshold rules make sense. And yes, they improve tax revenue, as those who have higher true income declare more than the threshold, and those below become more truthful. Now all you need to do is figure out where to put the threshold to equalize marginal tax revenue and marginal auditing cost, possibly adjusted by the dead-weight cost of taxation and for observable characteristics of the tax payer.