Optimal Taxation under Imperfect Trust

Technical Summary: Optimal Taxation under Imperfect Trust

Problem Statement
This paper investigates the design of optimal taxation when citizens lack full confidence that the government will effectively convert tax revenue into useful public goods. In canonical Ramsey and Diamond–Mirrlees frameworks, it is typically assumed that the government transforms revenue one-for-one into public spending. However, in many real-world contexts, leakage, waste, or corruption mean that only a fraction of collected revenue materializes as public services. The authors ask how these doubts about government delivery affect optimal taxation in a standard Ramsey setting, specifically examining whether the "implicit contract" between citizens and the state alters the fundamental logic of tax design.

Methodology
The authors construct a one-period, representative-agent model that modifies the standard Ramsey framework by introducing an exogenous measure of trust.

• The Environment: A representative household chooses labor supply ($L$) and private consumption ($C$) to maximize utility $u(C, G, L)$, where $G$ is a non-rival public good. Production is carried out by a competitive firm with technology $Y = f(L)$.
• The Tax Instrument: The government finances $G$ using a single broad-based distortionary tax rate $\tau$ on the private tax base (e.g., labor income or consumption).
• The Trust Mechanism: The government is modeled as being of one of two types:
  1. Honest (probability $\theta$): Converts all tax revenue $T(\tau)$ one-for-one into the public good ($G = T(\tau)$).
  2. Opportunistic (probability $1-\theta$): Diverts all revenue, providing no public good ($G = 0$).
• Timing: The planner chooses $\tau$ first. The household then chooses $L$ and $C$ based on the expected utility, treating $G$ as a random variable determined by the government's type. The government's type is realized after the household's decisions.
• Objective: The planner maximizes expected welfare $W(\tau; \theta)$, defined as the probability-weighted sum of utilities under the honest and opportunistic scenarios.

Key Contributions
The paper integrates the literature on optimal taxation with the literature on state capacity and credibility. Its primary contributions are:

1. A Trust-Adjusted Ramsey Rule: The authors derive a modified optimality condition where the marginal value of public funds (MVPF) is scaled by the trust parameter $\theta$.
2. A Sharp Trust Threshold: The model identifies a critical cutoff for trust below which any positive tax rate reduces expected welfare, leading to a zero-tax corner solution.
3. Closed-Form Solutions: Through an isoelastic specialization, the authors provide explicit formulas mapping trust levels to optimal tax rates and public sector size, offering a tractable benchmark for applied work.

Key Results

1. The Trust Threshold for Positive Taxation
The analysis reveals a non-linear relationship between trust and taxation.

• The Cutoff: There exists a threshold $\bar{\theta}$ defined by the ratio of the marginal excess burden (MEB) to marginal revenue (MR) at the origin, adjusted by the marginal rate of substitution between public and private consumption:
  $$\bar{\theta} \equiv \frac{MEB(0)}{MR(0)} \cdot \frac{u_C^0}{u_G^0}$$
• The Zero-Tax Corner: If perceived honesty $\theta \leq \bar{\theta}$, the marginal deadweight loss of taxation exceeds the expected value of the public good. Consequently, the optimal policy is $\tau^* = 0$, even if the public good is highly valued.
• Positive Taxation: If $\theta > \bar{\theta}$, a small positive tax rate increases expected welfare.

2. The Trust-Adjusted Ramsey Rule
When trust exceeds the threshold and an interior solution exists, the classic sufficient-statistics logic of optimal taxation re-emerges but with a crucial modification. The first-order condition equates the marginal excess burden per unit of revenue to the trust-adjusted marginal value of public funds:
$$\frac{MEB(\tau^*)}{MR(\tau^*)} = \theta \cdot \frac{u_G(C(\tau^*), G(\tau^*), L(\tau^*))}{u_C(C(\tau^*), G(\tau^*), L(\tau^*))}$$
Here, the standard marginal value of public funds is multiplied by $\theta$. As trust falls, the right-hand side shrinks, forcing the optimal tax rate down toward the zero-tax threshold.

3. Isoelastic Specialization
In a specific case with logarithmic private utility and linear public good utility, the authors derive closed-form expressions:

• Threshold: $\bar{\theta} = 1/Y^*$, where $Y^*$ is the constant output level in the no-tax equilibrium.
• Optimal Tax Rate: For $\theta > \bar{\theta}$, the optimal tax rate is:
  $$\tau^*(\theta) = 1 - \frac{1}{\theta Y^*}$$
  This rate is strictly increasing and strictly concave in $\theta$. As trust approaches 1, the tax rate approaches the maximum feasible rate, and public good provision converges to the full tax base.

Significance and Policy Implications
The paper argues that government credibility is a prerequisite for efficient tax expansion.

• Sequencing of Reforms: In low-trust environments ($\theta \leq \bar{\theta}$), attempts to expand the tax base by raising statutory rates are welfare-reducing. Instead, credibility-enhancing reforms—such as improving spending transparency, strengthening audit institutions, or focusing on verifiable projects—should precede tax increases.
• Design Framework: The trust-adjusted Ramsey rule provides a compact method for incorporating government credibility into tax design. It suggests that the optimal size of the public sector is tightly linked to the degree of public trust.
• Tractability: By keeping the environment static and representative-agent, the model offers a simple benchmark that can be embedded into richer dynamic or heterogeneous-agent models, providing a clear "trust threshold" and a "trust-adjusted MVPF" for empirical calibration.

The authors conclude that while the model abstracts from dynamic reputation effects and heterogeneous compliance, the core insight remains robust: when the conversion of tax revenue into public goods is uncertain, trust acts as a critical state variable that fundamentally alters the optimal tax design, potentially shutting down taxation entirely if credibility is insufficient.