I see several studies on optimal tax audit that assume the revelation principle (Myerson, 1981) on a tax game. The conventional tax game refers to a taxpayer who has a true income (private information) and reports a taxable income for a tax agency. The taxpayer has incentives to report a taxable income which is lower than the true income, so to pay less taxes. If the tax agency caches the taxpayer in a probable audit, the tax agency observes the true income, requires the payment of the full tax plus a fine over the evaded taxes. In this case, the taxpayer problem is to maximise the expected net income after taxes. The tax agency problem is to design a policy to maximise tax revenues subjected to costly audits, over the full population of taxpayers. Everything fine up to now.
Nonetheless, for the analysis of the tax agency problem, several studies declare that they assume the classical revelation principle by Myerson (1981), so to simplify the analysis. For example, on the study of Border and Sobel (1987) entitled Samurai Accountant: A Theory of Auditing and Plunder, they state (page 526 of the study):
"Without loss of generality we can restrict attention to incentive compatible direct revelation schemes, i.e. those in which the agent truthfully announces his wealth and makes a payment (which for convenience we will call a tax) based on his announcement to the principal and the principal chooses the probability of auditing based on reported wealth."
This whole sentence does not make so much sense for me: if the tax policy is equivalent to a direct revelation scheme that makes the taxpayer report truthfully, true income and reported income are the same (Nash equilibrium), so tax audits would be unnecessary. At the same time, we know that tax audits are necessary, for the taxpayers would have strong incentives to evade if there are no tax audits. In this case, I understand that the tax policy is not equivalent to a direct revelation scheme, so the revelation principle would not be applicable to this case.
So, what am I missing here?
The revelation principle is a theorem that comes from social choice theory and is only valid under very limited conditions; if the strategies of the agents are connected with costs, it only applies to a very limited extent. It does not provide convincing results for explaining real tax evasion processes. There are numerous better model approaches, such as those presented by Sandmo.
See also:
https://mpra.ub.uni-muenchen.de/89257/
https://www.jstor.org/stable/41790296
If I understand your question correctly, perhaps the direct revelation scheme works largely because the audit regime *is* effective and operating in a tax supportive environment. That is, taxpayers will evade taxes in the absence of audits. In the presence of the audits of some, perhaps taxpayers act conservatively to avoid the audit and penalties.
The conservatism may even be behavioral rather than strictly rational. (See Tversky and Kahnemann, Prospect theory/losses loom larger than gains). In earlier research, we found that t/ps dread owing money. https://www.emerald.com/insight/content/doi/10.1108/S1058-7497(2012)0000020004/full/html?utm_source=TrendMD&utm_medium=cpc&utm_campaign=Advances_in_Taxation_TrendMD_1
So, perhaps, if there's no penalty, the temptation to evade overtakes a t/p. If there's both a financial penalty risk and also an audit risk, and a t/p dreads that uncertainty, and avoiding those problems is sufficient for the direct revelation model to work in most cases.
But, also look to the environment. The UK did some interesting behavioral tax work where they reminded t/ps that most of their neighbors had paid their (fair share) of taxes already, and that boosted compliance. I believe Alm may have done academic research in this area. So, peer pressure seems and perhaps culture also play a role in this.
Yea, so I analysed this and reflected for some time. For one thing, it is true that the revelation principle is applicable only to a limited set of phenomena, under strong conditions.
On the other hand, according to the conditions required for the revelation principle to be applied, I found that there EXISTS an audit mechanism which compels all taxpayers to report truthfully. However, this equilibrium is sterile and mostly useless, for this mechanism refers to an audit scheme with an audit probability going towards zero, and a tax fine going towards infinity; this is the only Nash equilibrium I found.
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