## _wp0807

## Source details

**Canonical URL:** [_wp0807](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0807.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0807.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0807.pdf.json)

---

### I. MOTIVATION
- Central question: Can tax rate cuts increase revenues?
- Empirical motivation: Russian flat tax experiment — introduction of flat 13 percent personal income tax replacing prior rates 12, 20 and 30 percent; tax exempt income increased.
  - PIT revenues increased 46 percent in nominal terms and 26 percent in real terms during the next year.
  - PIT revenues rose from 2.4 percent to 2.9 percent of GDP — a more than 20 percent increase relative to GDP.
  - PIT revenues continued to 3.3 percent the following year, a further 14% gain relative to GDP.
  - Average effective PIT rate increased from 11.2 percent to 11.8 percent.
  - Official estimates showed compliance increased from 72.4 percent to 74.0 percent.
- Key intuition: tax compliance spillovers — aggregate taxpayer behavior determines how much time the tax authority can dedicate to any individual taxpayer; evaders “tie down” the tax authority’s limited capacity, protecting each other. Small cuts in tax rates can trigger large increases in honest reporting via these spillovers.
- Purpose: identify theoretical conditions under which tax rate cuts can increase compliance sufficiently to raise tax revenues; build a general equilibrium model with heterogeneous taxpayers and endogenous audit probabilities.

### Model construction overview
- Step 1: Endogenize audit probability using Sah (1991) endogenous crime approach.
  - Tax authority fixed time endowment τ to audit a unit volume of taxpayers.
  - Auditing honest taxpayers takes τ_h time; auditing and prosecuting tax evaders takes τ_e time.
  - Assume τ_e > τ_h and τ < τ_h.
  - Auditing time differences generate externality: more evasion reduces audit probability for each individual.
- Step 2: Endogenize labor supply using a linear quadratic model for closed-form solutions.
  - Agents choose labor and whether to declare income.
  - Caught evaders pay due taxes and penalties proportional to the tax revenues evaded.
  - Under this setup, taxpayers evade less when the tax rate is lower, ceteris paribus.
- Step 3: Introduce heterogeneous taxpayers differing in "shame" (φ) — utility cost of punishment/public humiliation or prison.
  - Heterogeneity ensures tax changes produce continuous changes in revenues.
  - Both homogeneous and heterogeneous setups can produce multiple equilibria (appendix).

### Key theoretical mechanisms and implications
- Endogenous enforcement → compliance spillovers:
  - Auditing evaders consumes more tax authority time, lowering audit probability for others.
  - Tax cuts reduce gains from evasion faster than potential costs, reducing evasion incentives.
  - Reduced evasion increases effective tax base; revenues can rise even with small labor supply responses.
- Labor supply effects:
  - Model nests labor supply responses; compliance effects can dominate supply-side effects.
  - Under standard RBC parameters income effects may dominate, so joint analysis of compliance and supply channels is necessary.
- Policy intuition:
  - Tax rate cuts can increase the effective tax rate by improving compliance — gaining revenue largely from previously noncompliant taxpayers while reducing burden on law-abiding taxpayers.
  - Additional revenues could be used to cut taxes further or increase government spending.

### Assumptions and modeling choices
- Risk neutrality assumed.
- Penalties proportional to tax revenues evaded.
- Heterogeneity via "shame" parameter φ with cross-sectional distribution F and mean E[φ] = 1.
- Time endowment τ fixed and limited relative to auditing needs.

### Main analytical results
- Endogenous enforcement + taxpayer heterogeneity + labor supply choice can generate:
  - Large increases in declared incomes and tax revenues following modest tax cuts due to compliance spillovers.
  - The Laffer curve phenomenon even when labor supply responses are very small.
  - Potential for multiple equilibria in some specifications.

### Audit capacity and audit probability (Section 2)
- Audit capacity μ:
  - μ = τ / (λ τ_e + (1 − λ) τ_h) (equation (2))
  - Note: 0 < μ < 1 because τ < τ_h < τ_e.
- Since total mass of taxpayers is unity, μ is also the probability of being audited.
- Audit probability is inversely related to the volume of tax evaders λ.

### Taxpayer problem, evasion condition, and comparative statics
- Utility and production:
  - u(c, c) = c − 1/2 A c^2 (equation (3)); y = c.
  - Tax rule: pay γ < 1/2 fraction of income y.
- Evading features:
  - Fraction λ evades; evading requires fixed effort E.
  - If caught, evaders pay taxes plus punishment π φ times taxes γ y.
  - φ heterogeneous with distribution F and mean E[φ] = 1 (equation (5)).
- Honest taxpayer:
  - c = (1 − γ) / A (equation (7)).
  - u_h = 1/2 (1 − γ)^2 / A (equation (8)).
- Evader optimal labor (interior positive-part):
  - c = μ / (1 − μ γ (1 + π φ)) / A (equation (10)).
  - u_e = 1/2 ( [1 − μ γ (1 + π φ)]_+ )^2 / A − E (equation (11)).
- Cheating condition:
  - Cheating iff 1/2 ( [1 − μ γ (1 + π φ)]_+ )^2 / A − E ≥ 1/2 (1 − γ)^2 / A (equation (12)).
  - Interior case threshold:
    - 1 − μ γ (1 + π φ) ≥ sqrt( (1 − γ)^2 + 2 A E ) (equation (13)).
    - φ ≤ φ̄(μ, γ, π) ≡ (1/π) [ 1 − sqrt( (1 − γ)^2 + 2 A E ) / (μ γ) − 1 ] (equation (14)).
- Signs of comparative statics for φ̄:
  - ∂φ̄/∂μ < 0, ∂φ̄/∂E < 0, ∂φ̄/∂π < 0, ∂φ̄/∂A < 0, ∂φ̄/∂γ > 0.

### Equilibrium condition and properties
- Mass of evaders implied by behavior:
  - λ̃(μ; γ, π) = F(φ̄(μ, γ, π)) (equation (15)); λ̃(μ) decreasing in μ.
- Mass of evaders implied by audit capacity:
  - λ̂(μ) = (τ/μ − τ_h) / (τ_e − τ_h) (equation (16)).
- Equilibrium μ solves:
  - λ̃(μ; γ, π) = λ̂(μ; τ, τ_h, τ_e) (equation (17)).
- Properties:
  - λ̂(μ) → ∞ as μ → 0; λ̂(1) = (τ − τ_h) / (τ_e − τ_h) < 0.
  - Both λ̃ and λ̂ decreasing in μ; with continuous F there is an odd number of intersections (at least one).
  - Multiple equilibria possible; analysis focuses on unique-intersection cases for simplicity.
- Comparative statics:
  - Changes in τ, τ_h, τ_e shift λ̂; only ratios τ_h/τ and τ_e/τ matter.
    - Increasing τ (holding τ_h, τ_e fixed) moves λ̂ upward → intersection moves right (higher μ) and down (fewer evaders).
    - Increasing τ_e or decreasing τ_h (ceteris paribus) makes evasion harder to persecute.
  - Changes in γ, A, E, π move λ̃:
    - Increasing γ shifts λ̃ upward → more evaders and lower audit probability.
    - Increasing A, E, or π shifts λ̃ downward → fewer evaders and higher audit probability.

### Illustrative numerical example and non-linear responses
- Parameters: A = 1, E = 0.1, γ = 0.115, π = 3, τ = 1, τ_h = 20, τ_e = 50.
  - If everyone honest, tax authority could audit 1/20 = 5% of the population.
- φ lognormally distributed with underlying normal variance = 1 and E[φ] = 1.
- Example equilibrium:
  - Equilibrium evasion: somewhat less than 34.6% of taxpayers evade.
  - Audit probability μ in equilibrium: around 3.3%.
  - Comment: these tax gaps are roughly twice as large as the 16.3% IRS (2006) estimate for the United States.
- Responses to small tax rate changes (±1% from γ = 11.5% i.e., 11.615% and 11.385%):
  - A 1% tax rate cut → new equilibrium evasion = 8.9% of taxpayers.
    - Interpretation: a 1% tax rate cut results in a 40% increase in tax compliance.
  - A 1% tax rate increase → 51.3% of taxpayers evading.
- Responses to larger 5% tax rate changes (to 10.92% and 12.07%):
  - Large tax rate cut almost completely eliminates tax evasion.
  - Large tax rate hike raises non-compliance to 77.4%.
- Response to changes in τ (audit capacity):
  - 5% increase in τ (to 1.05) → equilibrium evasion lowered to 23.9%.
  - 5% decrease in τ → evasion rises to 43.6%.
  - 50% increase in τ (to 1.5) → eliminates tax evasion completely in the example.
  - 50% decrease in τ → evasion rises to 87.7%.
- Laffer curve and revenue implications:
  - Tax revenues as a function of the official tax rate display a Laffer curve: revenues increase with γ until γ = 12%, then fall.
  - Laffer effect here arises from changes in compliance, not labor supply:
    - Implied tax revenue (if everyone honest) is increasing when γ < 1/2, so labor supply effects do not cause the Laffer effect.
    - The percentage of honest taxpayers falls dramatically when γ exceeds 12%.
  - Effective tax rates can increase when the official tax rate is cut because higher compliance makes evaders pay more; honest taxpayers pay less while government revenues increase.

### Conclusions, policy insights, and recommended research directions
- Main theoretical finding:
  - Tax rate cuts can increase tax compliance sufficiently that tax revenues increase in the short run.
  - Two channels for tax rate cuts to affect revenues:
    - Affecting the tax base (labor supply).
    - Affecting compliance with tax rules — the model emphasizes this channel and shows it can dominate.
- Conditions for compliance-based Laffer effect:
  - Tax authorities need medium strength relative to official tax rates:
    - If tax authorities are strong relative to official rates, compliance is dominant and tax changes have little effect on compliance.
    - If tax authorities are weak, tax changes will not induce compliance.
    - At medium enforcement strength, tax rates can be pivotal and small tax cuts can trigger large compliance increases.
- Policy trade-offs:
  - Trade-offs between improving enforcement (more resources or higher punishments) and cutting official tax rates to improve compliance.
  - Depending on circumstances, tax rate cuts may be preferred over strengthening enforcement, or vice versa.
- Suggested avenues:
  - Consider sequencing: rely initially on compliance effects while building enforcement capacity.
  - Extend the model to multiple periods to study dynamic implications and optimal timing.
  - Empirical research should incorporate compliance effects into Laffer-curve investigations.

### Appendix highlights
- Comparative statics for φ̄ assume γ < 1/2, A, E > 0 and γ ≤ 1/2 + A E (equation (18)); algebra confirms derivative signs.
- Multiple equilibria:
  - Can arise; example with underlying normal variance = 0.5 (Figure 8).
  - If agents very similar, marginal tax changes can lead to equilibrium switching.
  - In some parameterizations, increasing audit capacity could perversely increase tax evasion in the middle equilibrium; comparative statics depend on relative slopes of λ̂ and λ̃.

*Source: _wp0807 - 1. Equilibrium; 2. The tax authority audits taxpayers randomly until its time endowment is exhausted.*

### 1. Equilibrium...............................................................................................11

### 1. Equilibrium...............................................................................................11

### I. MOTIVATION
- Central question: Can tax rate cuts increase revenues?
- Empirical motivation: Russian flat tax experiment — introduction of flat 13 percent personal income tax replacing prior rates 12, 20 and 30 percent; tax exempt income increased. Reported outcomes:
  - PIT revenues increased 46 percent in nominal terms and 26 percent in real terms during the next year.
  - PIT revenues rose from 2.4 percent to 2.9 percent of GDP — a more than 20 percent increase relative to GDP.
  - PIT revenues continued to 3.3 percent the following year, a further 14% gain relative to GDP.
  - Average effective PIT rate increased from 11.2 percent to 11.8 percent.
  - Official estimates showed compliance increased from 72.4 percent to 74.0 percent.
- Key intuition proposed: tax compliance spillovers — aggregate taxpayer behavior determines how much time the tax authority can dedicate to any individual taxpayer; evaders “tie down” the tax authority’s limited capacity, protecting each other. Small cuts in tax rates can trigger large increases in honest reporting via these spillovers, potentially increasing revenues.
- Purpose of the paper: identify theoretical conditions under which tax rate cuts can increase compliance sufficiently to raise tax revenues; build a general equilibrium model with heterogeneous taxpayers and endogenous audit probabilities.

### Model construction overview (three-step setup)
- Step 1: Endogenize probability of tax audits using Sah (1991) endogenous crime approach.
  - Tax authority has fixed time endowment τ to audit a unit volume of taxpayers.
  - Auditing honest taxpayers takes τh time; auditing and prosecuting tax evaders takes τe time.
  - Assume τe > τh.
  - The total time endowment τ is insufficient to audit the unit volume of honest taxpayers, i.e. τ < τh.
  - Auditing time differences generate an externality: more evasion reduces audit probability for each individual.
- Step 2: Endogenize labor supply within taxpayers’ decisions using a linear quadratic model to obtain closed-form solutions.
  - Agents decide labor supply and whether to declare income.
  - Caught evaders pay due taxes and penalties proportional to the tax revenues evaded.
  - Under this setup, taxpayers evade less when the tax rate is lower, ceteris paribus.
  - Empirical support: Clotfelter (1983) finds evasion increases with the tax rate.
- Step 3: Introduce heterogeneous taxpayers differing in "shame" — utility cost of punishment/public humiliation or prison.
  - Sufficient heterogeneity ensures tax changes produce continuous changes in revenues.
  - Both homogeneous and heterogeneous setups can produce multiple equilibria (appendix).

### Key theoretical mechanisms and implications
- Endogenous audit probabilities create compliance spillovers:
  - Auditing evaders consumes more of the tax authority’s limited time, lowering audit probability for others.
  - If taxes are cut, gains from evasion fall faster than potential costs, reducing evasion incentives.
  - Reduced evasion increases the effective tax base and can increase tax revenues even with small labor supply responses.
- Labor supply effects:
  - Model nests labor supply responses, but finds that compliance effects can dominate supply-side effects; small labor supply changes suffice for large revenue effects.
  - Under standard RBC parameters income effects may dominate (consumers increase labor supply when taxes increase), highlighting the need for joint analysis of compliance and supply channels.
- Policy intuition:
  - Tax rate cuts can increase the effective tax rate by improving compliance — gaining revenue largely from previously noncompliant taxpayers while reducing burden on law-abiding taxpayers.
  - Additional revenues could be used to cut taxes further or increase government spending at policymakers' discretion.
- Distinction from prior literature:
  - Prior empirical work often abstracts from endogenous compliance (Heckman 1983; Feldstein 1995, 2002; Fisman and Wei 2004). This model provides a channel distinct from classic labor-supply explanations of the Laffer effect.

### Assumptions and modeling choices (explicit)
- Risk neutrality assumed for tractability (noting Allingham and Sandmo (1972) show risk aversion can alter evasion responses).
- Penalties proportional to tax revenues evaded are assumed (weakest assumption for the paper’s purposes); literature distinguishes penalties proportional to evaded tax vs. concealed income.
- Heterogeneity captured via costs of evasion ("shame"); alternative specifications (costs differing directly) produce qualitatively equivalent results.
- Time endowment τ captures long-term capacity building needs of the tax authority; τ is fixed and limited relative to auditing needs.

### Main analytical results (summary)
- Endogenous enforcement + taxpayer heterogeneity + labor supply choice can generate:
  - Large increases in declared incomes and tax revenues following modest tax cuts due to compliance spillovers.
  - The Laffer curve phenomenon even when labor supply responses are very small.
  - Potential for multiple equilibria in some specifications.

### Numerical exploration and calibration intent
- The paper numerically explores:
  - Tax cuts and tax enforcement measures.
  - How Laffer curve shapes emerge under the model.
  - The interaction between compliance and labor supply channels for revenue outcomes.
- The model is intended to be a framework for future calibrations that can separately identify compliance vs. labor supply effects.

*Source: _wp0807 - 1. Equilibrium...............................................................................................11*

### 2. The tax authority audits taxpayers randomly until its time endowment is exhausted.

### _wp0807 - 2. The tax authority audits taxpayers randomly until its time endowment is exhausted.

### Audit capacity and audit probability
- Audit capacity μ is defined by
  - μ = τ / (λ τ_e + (1 − λ) τ_h) (equation (2))
  - Note: 0 < μ < 1 because τ < τ_h < τ_e.
- Since total mass of taxpayers is unity, μ is also the probability of being audited.
- Consequence: the probability that an individual taxpayer is audited is inversely related to the volume of tax evaders λ.

### Compliance decision and labor choice
- Taxpayers maximize utility
  - u(c, c) = c − 1/2 A c^2 (equation (3)), where c is consumption and c is labor.
- Production technology: y = c.
- Tax rule: taxpayers are required to pay a γ < 1/2 fraction of income y in taxes.
- Tax evasion features:
  - A fraction λ of the population evades taxes.
  - Evading requires fixed effort E (independent of income).
  - If caught, evaders pay taxes plus a punishment of π φ times taxes γ y, where
    - π is the general punishment level,
    - φ is a heterogeneous “shame” parameter with cross-sectional distribution F and mean E[φ] = 1 (equation (5)).
- Honest taxpayer choice:
  - First-order condition yields c = (1 − γ) / A (equation (7)).
  - Honest utility: u_h = 1/2 (1 − γ)^2 / A (equation (8)).
- Evader expected choice under audit probability μ:
  - Optimal labor when positive:
    - c = μ / (1 − μ γ (1 + π φ)) / A, with positive-part operator (equation (10)).
  - Evader expected utility:
    - u_e = 1/2 ( [1 − μ γ (1 + π φ)]_+ )^2 / A − E (equation (11)).
- Cheating condition:
  - Taxpayer cheats iff 1/2 ( [1 − μ γ (1 + π φ)]_+ )^2 / A − E ≥ 1/2 (1 − γ)^2 / A (equation (12)).
  - Focusing on the interior case where the positive-part is nonzero, cheating holds iff
    - 1 − μ γ (1 + π φ) ≥ sqrt( (1 − γ)^2 + 2 A E ) (equation (13)),
    - Equivalent threshold for φ:
      - φ ≤ φ̄(μ, γ, π) ≡ (1/π) [ 1 − sqrt( (1 − γ)^2 + 2 A E ) / (μ γ) − 1 ] (equation (14) as given).
- Comparative statics for the threshold φ̄:
  - ∂φ̄/∂μ < 0 (higher audit probability reduces evasion).
  - ∂φ̄/∂E < 0 (higher evasion cost reduces evasion).
  - ∂φ̄/∂π < 0 (higher punishment reduces evasion).
  - ∂φ̄/∂A < 0 (higher disutility of work reduces evasion via lower income).
  - ∂φ̄/∂γ > 0 (higher tax rate increases evasion).

### Equilibrium and comparative statics
- Mass of evaders implied by behavior (for given μ):
  - λ̃(μ; γ, π) = F(φ̄(μ, γ, π)) = F( (1/π) [ 1 − sqrt( (1 − γ)^2 + 2 A E ) / (μ γ) − 1 ] ) (equation (15)).
  - λ̃(μ) is decreasing in μ.
- Mass of evaders implied by audit capacity:
  - λ̂(μ) = (τ/μ − τ_h) / (τ_e − τ_h) (equation (16)).
- Equilibrium μ solves
  - λ̃(μ; γ, π) = λ̂(μ; τ, τ_h, τ_e) (equation (17)).
- Properties of equilibrium:
  - λ̂(μ) → ∞ as μ → 0; λ̂(1) = (τ − τ_h) / (τ_e − τ_h) < 0 (given τ < τ_h < τ_e).
  - Both λ̃ and λ̂ are decreasing in μ; with continuous F there is an odd number of intersections (at least one).
  - Multiple equilibria are possible; for simplicity analysis focuses on cases with a unique intersection.
- Comparative statics by parameter:
  - Changes in τ, τ_h, τ_e shift λ̂: only ratios τ_h/τ and τ_e/τ matter.
    - Increasing τ (holding τ_h, τ_e fixed) moves λ̂ upward → intersection moves right (higher μ) and down (fewer evaders).
    - Increasing τ_e or decreasing τ_h (ceteris paribus) makes evasion harder to persecute.
  - Changes in γ, A, E, π move λ̃:
    - Increasing γ shifts λ̃ upward → more evaders and lower audit probability.
    - Increasing A, E, or π shifts λ̃ downward → fewer evaders and higher audit probability.

### Illustrative example (numerical parametrization)
- Parameter values used: A = 1, E = 0.1, γ = 0.115, π = 3, τ = 1, τ_h = 20, τ_e = 50.
  - Interpretation examples from these parameters:
    - Punishment equals three times the evaded taxes (π = 3).
    - If everyone honest, tax authority could audit 1/20 = 5% of the population.
- Distributional assumption:
  - φ is lognormally distributed with underlying normal variance = 1 (and mean constraint E[φ] = 1 pins down the location).
- Example equilibrium (Figure 1):
  - Equilibrium evasion: somewhat less than 34.6% of taxpayers evade taxes.
  - Audit probability μ in equilibrium: around 3.3%.
  - Comment: these tax gaps are roughly twice as large as the 16.3% IRS (2006) estimate for the United States.
- Response to tax rate changes:
  - Small tax rate change ±1% from γ = 11.5% (i.e., 11.615% and 11.385%):
    - A 1% tax rate cut leads to new equilibrium evasion of 8.9% of taxpayers.
    - Interpretation: a 1% tax rate cut results in a 40% increase in tax compliance.
    - A 1% tax rate increase leads to 51.3% of taxpayers evading taxes.
  - Larger 5% tax rate changes (to 10.92% and 12.07%):
    - Large tax rate cut almost completely eliminates tax evasion.
    - Large tax rate hike raises non-compliance to 77.4%.
  - Implication: strong non-linearities and potential equilibrium switching; small changes can cause large compliance responses.
- Response to changes in tax authority time endowment τ:
  - 5% increase in τ (to 1.05):
    - New equilibrium evasion lowered to 23.9%.
  - 5% decrease in τ:
    - Evasion rises to 43.6%.
  - 50% increase in τ (to 1.5):
    - Eliminates tax evasion completely in the example.
  - 50% decrease in τ:
    - Evasion rises to 87.7%.
  - Interpretation: changes in enforcement capacity can have effects similar to tax rate cuts, but operate through different channels.
- Laffer curve and revenue implications (Figures 6 and 7):
  - Tax revenues as a function of the official tax rate display a Laffer curve: revenues increase with γ until γ = 12%, then fall.
  - The Laffer effect here arises from changes in compliance, not labor supply:
    - Implied tax revenue (if everyone honest) is increasing when γ < 1/2, so labor supply effects do not cause the Laffer effect.
    - The percentage of honest taxpayers falls dramatically when γ exceeds 12% (right scale).
  - Effective tax rates can increase when the official tax rate is cut because higher compliance makes evaders pay more; honest taxpayers pay less while government revenues increase.

### Conclusions and policy insights
- Main theoretical finding:
  - Tax rate cuts can increase tax compliance sufficiently that tax revenues increase in the short run.
  - Two channels for tax rate cuts to affect revenues:
    - Affecting the tax base (labor supply) — classical channel.
    - Affecting compliance with tax rules — emphasized in this model.
  - In this model the compliance channel can dominate, producing a short-run Laffer effect.
- Conditions for compliance-based Laffer effect:
  - Tax authorities need medium strength relative to official tax rates:
    - If tax authorities are strong relative to official rates, compliance is dominant and tax changes do not much affect compliance.
    - If tax authorities are weak, tax changes will not induce compliance.
    - At medium enforcement strength, tax rates can be pivotal and small tax cuts can trigger large compliance increases.
- Policy trade-offs and recommendations:
  - There are trade-offs between improving enforcement (more resources or higher punishments) and cutting official tax rates to improve compliance.
  - Depending on circumstances, tax rate cuts might be preferred over strengthening enforcement, or vice versa; welfare analysis is feasible within the model.
  - Suggested avenues for policy and research:
    - Consider sequencing: rely initially on compliance effects while building enforcement capacity.
    - Extend the model to multiple periods to study dynamic implications and optimal timing of compliance and enforcement measures.
    - Empirical research should incorporate compliance effects into Laffer-curve investigations (complementing labor-supply focused studies).
- Applicability to country types:
  - Countries with high official tax rates and relatively weak tax authorities may benefit from tax rate cuts to improve compliance.
  - The framework may also apply to countries with high rates and apparently strong enforcement in absolute terms, and to low-tax countries with weak enforcement.

### Appendix highlights
- Comparative statics for φ̄:
  - Assumption: γ < 1/2, A, E > 0 and γ ≤ 1/2 + A E (equation (18)).
  - Algebra confirms sign results for derivatives of φ̄ with respect to parameters.
- Multiple equilibria:
  - Multiple equilibria can arise; example shown by changing underlying normal variance to 0.5 (Figure 8).
  - If agents are very similar, marginal tax changes can lead to equilibrium switching.
  - In some parameterizations, increasing audit capacity could perversely increase tax evasion in the middle equilibrium; comparative statics depend on relative slopes of λ̂ and λ̃.

*Source: _wp0807 - 2. The tax authority audits taxpayers randomly until its time endowment is exhausted.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp0807.pdf_