1. Miguel A. Sanchez Villalba October 2004
Tax evasion as a coordination game. The role of expectations and externalities
Miguel A. Sanchez Villalba
October 2004

2. A short history of tax evasion
Early days: “It is sinful to deceive the government regarding taxes and duties”--The Talmud
Early 20th century: “The avoidance of taxes is the only intellectual pursuit that still carries any reward”--John M. Keynes
Late 70s: “The vast majority of the public had come to believe that everybody else was engaging in tax avoidance or outright tax evasion”--Michael J. Graetz
Expectations are crucial: not only I care about what everybody else does, but it will affect my own decisions.
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3. Road map The problem Related literature The model Results Policy
Final remarks
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4. The problem Citizen decides how much income to declare
The optimal declaration depends on the government’s type and on the economy-wide average declared income
Government’s policy rule contingent on average evasion  externalities
Heterogeneous info. sets  expectations
Coordination or “global” game
I could have the simplest case where the government audits with probability p=theta, and citizens only care about the unknown parameter theta (pure adverse selection case). The policy rule generates the externality, thus adding the problem of coordination. The agent has to form expectations over both the government’s type (theta) but also about the actions of the other citizens (average evasion).
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5. Related literature Benjamini and Maital (1983)
Difference: Uncertainty about average evasion and audit intensity
Morris and Shin (2002)
Difference: Need for coordination among agents is generated by the government
In BM: Certainty about average evasion and audit intensity lead to epidemics. By introducing noisy signals, the coordination failure can be mitigated.
In MS: The coordination failure is embedded in the agents’ utility functions. In my model, it is so only because the probability of detection (which is an exogenous and constant parameter in the standard models) is made contingent on the average evasion in the economy.
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6. My contribution
More structure to the externality: Policy rule contingent on average evasion
Systemic approach: Citizen vs. Other Citizens and vs. Government
Tax evasion as a coordination game: Citizens want to pay the government a high enough “bribe” so that it does not audit
Rationale: 1. Time inconsistency of tax agency: before returns are completed, announce a high auditing intensity, but after, it has incentives to defect. 2. Analogy to the investor game.
Caveat: Lucas critique: changing parameters of the policy rule based just on econometric data will fail to recognize the change’s effect on expectations, thus leading to an “unexpected” (for the policy-makers) new equilibrium.
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7. The model Continuum of citizens/agents ~U [0,1]
Agent i’s problem: maximize expected utility by choosing how much income to declare
No “ghosts”
Pre-tax income
Declared income
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8. If caught If not caught Utility function
Agents know every parameter of the problem except for the probability of being audited,
Risk neutrality simplifies matters significantly. Alternatively, one can find the FOCs and linearize them.
Expected probability
Expected utility
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9. Intuitively, the relative position matters:
Audit rule
Rationale: Time-inconsistency: ex-ante, announce “tough”; ex-post, act “soft”
Intuitively, the relative position matters:
* for a given average declaration, the more you declare, the less likely to be audited
* for a given declaration, the greater the average declaration, the more likely you’ll be audited
Gamma and delta are publicly known constants. We expect delta>gamma, such that the economy-wide probability of detection is a decreasing function of the average declaration.
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10. * the government’s type  hidden info.
Probability
Agent ignores
* the government’s type  hidden info.
* the average declaration  coordination
Exp. Prob.
Signals
* public
* private
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11. Agent’s problem FOC Solution
The expression in brackets is the asymptotic expectation over theta.
where and is the relative precision of the private signal
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12. Results Externality/Coordination
Note: Expected, not actual, average declaration
Comparative statics
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14. Important: sign of comparative statics for the audit rule parameters are not “obvious”  Lucas critique.
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15. Policy Tax agency maximizes net revenue where
(numerical computations in progress)
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16. Final remarks
Systemic approach: Citizen vs. Other Citizens vs. Government
Policy rule: Commitment device and externality generator
Role of expectations. Lucas critique
Moral hazard
The policy rule basically generates a counterbalance to the idea of evasion: the more one evades, the greater the prospective gain if not caught, but the greater the probability of being caught. Thus, the expected gain increases in terms of payoff but decreases in terms of likelihood of occurrence (the opposite is true for the expected loss).
From the point of view of the government, it is important to know the underlying structure that leads to the formation of expectations, as they are based on (at least theoretically) observable data (though it might be private information, and eliciting it is usually costly).
Important note: the rationality of expectations is crucial to ensure the equilibrium. This rationality is the one that leads to suboptimal results if allowing for discretion. The rule, on the other hand, is designed taking expectations into account, and so it is not the straitjacket it seems to be: given the rule, people’s best response is to choose the “right” level of evasion (not too high as in the discretion case), and the government’s best response is thus to follow the rule. Rational expectations ensure the existence of the equilibrium.
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