📈 economics

Trust as a Differential Filter: A Theory of Prepaid Contractual Form Across Societies

This paper theorizes that institutional trust functions as a differential filter on prepaid contractual forms rather than expenditure levels, demonstrating how the choice between direct deposits and vouchers determines market regimes, reveals risk weights, and shows that custodial mandates are superior to voucher substitution in mitigating true risk.

Original authors: Luoluo Gu

Published 2026-08-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Luoluo Gu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the modern world, paying for a service before receiving it is a routine part of daily life. We buy gym memberships, load value onto transit cards, or purchase bundles of hair salon visits. Yet, the way people pay for these future services varies dramatically depending on where they live. In some places, consumers happily hand over cash to be held in a merchant's account, trusting that the money will be there when they return. In others, that same group of people refuses to leave cash in a merchant's hands, preferring instead to buy a voucher for a specific number of sessions. This difference is not about how much money people have or how cheap the services are. It is about trust. Specifically, it is about how much people trust the institutions and laws that protect them if a business fails. When trust in the system is high, people treat prepaid money like a deposit. When trust is lower, they treat it like a purchase of goods, even if the economic value is identical.

A new study by Luoluo Gu from the University of the Thai Chamber of Commerce explores this divide, offering a clear explanation for why these two different worlds exist and what happens when they collide. The research focuses on a psychological phenomenon known as mental accounting, where people categorize money differently depending on how it is labeled. To a consumer, a balance in a merchant's account feels like "my money" that is being held by someone else, which triggers a deep fear of loss if that person runs away. A voucher for ten sessions, however, feels like "goods" that have already been bought; if the merchant disappears, the consumer feels they have lost a service they were promised, but the psychological sting is different. The study argues that this subtle shift in perception acts as a filter, determining which type of contract a society will use.

The researchers built a model to test how this filter works across different levels of trust. They found that in societies with strong institutional safeguards, such as reliable courts and strict regulations, the "money" account works fine. People are willing to deposit funds because they trust the system will protect them. In societies with weaker safeguards, that same trust is missing. Here, consumers will happily buy a voucher for a set number of sessions but will refuse to deposit the equivalent amount of cash into a merchant's account. The study proves that this difference is not caused by a lack of money or liquidity. Even when people have the cash to pay, the form of the contract changes based on their trust in the system. The researchers showed that this gap in acceptance is a direct measure of the trust margin in a society.

The paper also looks at what happens when merchants try to adapt to this lack of trust. In the middle ground, where trust is neither high nor low, the market often settles into a state where vouchers replace cash deposits. The study demonstrates that this substitution is not a clever adaptation that protects consumers; it is actually a trap. Because the legal protection for a voucher is often the same as for a cash deposit—if the merchant goes bankrupt, both are usually lost—the consumer gains no real safety by switching to a voucher. Instead, they lose the flexibility of having cash that could be used elsewhere. The study calculates that in these intermediate trust environments, this switch destroys about six percent of the value for everyone involved, simply because people are paying a psychological cost to avoid a risk that the voucher does not actually eliminate.

The researchers also examined how these markets evolve over time. They found that trust is not a fixed number but a living thing that reacts to business failures. If merchants start defaulting on their promises, trust erodes quickly, and the market can shift from accepting cash deposits to rejecting them entirely. However, the study suggests that this collapse is not inevitable. It shows that a specific type of government rule, one that requires merchants to hold a portion of customer funds in a secure, third-party account, can act as a powerful substitute for trust. This kind of mandate does not just make people feel safer; it actually makes the system safer by reducing the real risk of loss. The model indicates that even a small amount of this protection can be enough to push a society from the "voucher" world back into the "cash deposit" world, restoring a more efficient and valuable way for people to pay for services.

Ultimately, the study provides a map for understanding why prepaid markets look so different around the globe. It explains that the choice between a cash balance and a service voucher is a precise reflection of a society's confidence in its own rules. In high-trust environments, the system works smoothly, and people use flexible financial tools. In low-trust environments, the system is too fragile for cash, and people retreat to rigid, specific promises. The most important finding is that the middle ground, where people use vouchers to avoid risk, is not a stable or safe solution. It is a costly compromise that leaves everyone worse off. The research suggests that the best way to fix this is not to wait for trust to grow naturally, but to implement rules that lower the actual risk, allowing the market to return to the more efficient form of payment.

Technical Summary: Trust as a Differential Filter: A Theory of Prepaid Contractual Form Across Societies

Problem Statement
Prepaid consumption is ubiquitous, yet the contractual form it takes varies systematically across societies. In high-trust environments (e.g., China, Nordic countries), consumers predominantly use stored-value accounts (financial-type contracts, $M_3$ ), where funds are deposited as abstract monetary claims. In intermediate-trust environments (e.g., Thailand), consumers often reject stored-value deposits but readily accept service vouchers (property-type contracts, $M_2$ ) of identical monetary value. Standard price theory cannot explain this divergence, as the economic value is equivalent. The paper posits that institutional trust acts not merely as a gatekeeper to the level of prepayment, but as a differential filter on the form of the contract. The central question is how institutional trust, mediated by mental accounting, drives the substitution between financial claims and service entitlements, and what the welfare implications of this substitution are.

Methodology and Model Structure
The paper develops a discrete-time bilateral market model ( $M = \langle C, F, K, T \rangle$ ) integrating institutional economics, contract theory, and behavioral psychology.

Contract Typology and Risk Encoding:
Contracts are classified by the nature of the consumer's right. The critical distinction is between:
- $M_3$ (Stored Value): An unsecured monetary claim ( $\omega(M_3)=1$ ).
- $M_2$ (Service Voucher): A claim to specific service units ( $\omega(M_2)=\omega_2 < 1$ ).
  The model relies on Assumption 1 (Mental-Accounting Risk Ordering): Consumers perceive $M_3$ as strictly riskier than economically equivalent $M_2$ due to "double-entry" mental accounting. $M_3$ is encoded as "my money" (asset account), triggering loss aversion upon default. $M_2$ is encoded as "purchased goods" (consumption account), triggering regret over foregone consumption. Since loss aversion is stronger than regret, the perceived risk weight $\omega_2 < 1$ .
Trust Dynamics:
- Institutional Trust ( $\Theta$ ): An exogenous parameter representing the quality of legal enforcement and generalized trust.
- Effective Trust ( $\hat{\Theta}(t)$ ): An endogenous variable evolving via a law of motion (Eq. 6). It reverts to $\Theta$ at rate $\alpha_+$ but erodes proportionally to the market default rate $r(t)$ via a contagion coefficient $\beta$ . This creates an "erosion wedge" where sustained trust falls short of the institutional parameter.
- Acceptance Rule: A consumer accepts contract $k$ if their trust in the merchant exceeds a threshold: $Tr > \omega(k)\tau_i + PR$ , where $\tau_i$ is the individual caution threshold and $PR$ is perceived risk. Because $\omega(M_2) < \omega(M_3)$ , vouchers clear a lower trust bar.
Merchant Behavior:
Merchants adaptively choose contract forms based on a churn trigger. They prefer stored value ( $M_3$ ) if the share of their accepting customers who take $M_3$ exceeds their relative retention advantage on money-denominated claims ( $\bar{\xi}_j$ ). This retention advantage arises because $M_3$ balances are harder for merchants to "divert" (via inflation or price hikes) compared to fixed service units, mirroring the logic of in-kind lending.

Key Contributions and Theoretical Results

Identification of the Trust Margin (Theorem 1):
The paper provides a formal identification strategy to distinguish trust effects from liquidity constraints. Under an equal-expenditure design (holding monetary stakes constant), the liquidity gate is identical for both forms. Any residual divergence in acceptance rates ( $\bar{A}_{M2} > \bar{A}_{M3}$ ) is strictly attributable to the trust-threshold differential. This allows for the estimation of the "separation band"—the population segment that accepts vouchers but rejects stored value—without modeling the liquidity gate.
Orthogonality of Penetration and Form-Split (Proposition 1):
The paper proves that prepaid penetration (total volume) and the form-split (ratio of vouchers to stored value) are Fisher-orthogonal parameters. Penetration is driven by liquidity and income, while the form-split is driven solely by the trust surplus. This implies that the trust margin can be estimated independently of liquidity constraints.
Equilibrium Trichotomy (Theorem 3):
The model characterizes three distinct long-run regimes based on the sustained trust surplus ( $T^*$ ):
- High-Trust Regime: $T^* > \text{median}(\tau)$ . Stored value dominates ( $\pi^*_{M3} > 0.5$ ).
- Low-Trust Regime: $T^* < \omega_2 \tau_{0.01}$ . Prepayment collapses; spot transactions dominate.
- Intermediate-Trust Regime: $\omega_2 \text{median}(\tau) < T^* < \text{median}(\tau)$ . A "substitution regime" emerges where vouchers dominate stored value ( $\pi^*_{M2} > \pi^*_{M3}$ ).
  The paper proves global convergence to these regimes from any initial configuration within a bounded number of adjustment rounds (Proposition 6).
Welfare Analysis: Adaptation vs. Trap (Proposition 8):
The paper challenges the view that voucher substitution is a protective adaptation. If objective recovery rates are equal across forms (both are unsecured claims), substitution is a welfare trap. Consumers who switch to vouchers forgo fungibility (transferability, divisibility) without gaining risk reduction. The intermediate regime destroys approximately 6% of the prepaid stake in aggregate welfare loss.
Policy Implications (Proposition 9):
A custodial mandate (escrow) is shown to be superior to market substitution. By lowering the true risk of stored value (rather than just the perceived risk), an escrow requirement can shift the market from the intermediate regime to the high-trust regime. The optimal coverage level exceeds the level required merely to eliminate substitution, as it also restores the financing value of prepayment to merchants.
Endogenous Trust and Multiplicity (Section 5):
When trust is endogenized (default rates depend on stored-value acceptance), the system admits multiple equilibria and path dependence. However, the paper notes that the feedback strength required for bistability (tipping points) is not supported by the paper's own calibration, suggesting that while multiple equilibria are theoretically possible, the specific tipping narrative may be limited by the model's primitives.

Significance and Claims
The paper claims to provide a unified framework linking institutional environments to the psychological encoding of financial risk. Its primary significance lies in:

Reframing Trust: Moving beyond trust as a binary gatekeeper to trust as a differential filter that sorts contractual forms.
Empirical Strategy: Offering a rigorous method (Theorem 1) to identify trust effects in cross-societal data by controlling for liquidity via equal-stake designs.
Policy Critique: Demonstrating that market-driven substitutions (vouchers) in intermediate-trust societies are inefficient and that regulatory interventions (escrow) are necessary to restore welfare and market depth.
Generalizability: The theory applies to any society where institutional trust levels differ and consumers choose between financial and property-type prepaid contracts, generalizing the observed divergence between China (stored-value dominant) and Thailand (voucher dominant).

The paper remains modest regarding its claims on endogenous trust dynamics, explicitly reporting that the calibration does not support the strong feedback strength required for bistability, thereby treating the "tipping" narrative as a theoretical possibility rather than a calibrated result.

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