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Selection of Efficient Monetary Equilibria Through Aggregate Real Savings-Based Taylor Rule

This paper demonstrates that while a standard inflation-targeting Taylor rule controls the price level, it often leads to inefficient monetary equilibria in overlapping generations economies, whereas a rule incorporating both an inflation ceiling and a relative aggregate real savings floor successfully guides the economy toward efficient monetary equilibria.

Original authors: Leandro Lyra Braga Dognini

Published 2026-07-09

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CC BY 4.0

Original authors: Leandro Lyra Braga Dognini

Original paper licensed under CC BY 4.0 (http://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

Imagine an economy as a giant, endless relay race where people are born, run a short leg, and then pass the baton to the next generation. In this race, the "baton" is money, and the "fuel" is the goods people produce and consume.

This paper tackles a famous puzzle in economics called the Hahn Problem: Why does paper money have value at all? In a world where money doesn't grow trees or pay dividends, why do people accept it? The author argues that money only becomes valuable if people are willing to save some of their fuel today to help the next generation run tomorrow.

Here is the breakdown of the paper's findings using simple analogies:

1. The Problem: The Race Without a Finish Line

In many economic models, the race never ends. If everyone just spends everything they have right now and saves nothing, the economy gets stuck. There is no reason to hold onto paper money because it can't be used to buy anything in the future if no one is saving.

The author proves that if the economy is "prone to savings" (meaning people naturally want to set aside some resources for the future), then money will have value. It becomes the tool that connects the young generation (who have goods) with the old generation (who need goods).

2. The Trap: Too Many Equilibria

The paper points out a chaotic problem: Without a referee, this race has too many possible outcomes.

Scenario A: Everyone saves a lot, money is valuable, and everyone is happy (Efficient).
Scenario B: Everyone saves almost nothing, money is worthless, and the economy stalls (Inefficient).

If the government just says, "We will print money and set interest rates," it doesn't actually force the economy into the happy scenario. It's like a referee shouting "Go!" but not telling the runners which path to take. The runners might accidentally choose the path where everyone starves.

3. The Old Solution: The "Inflation Target" (The Speed Limit Sign)

Traditionally, governments use a rule called a Taylor Rule that acts like a speed limit sign. It says: "If inflation (the speed of prices) goes above our target, we raise interest rates to slow down."

The paper argues this is like a driver trying to hit a specific speed (e.g., exactly 60 mph).

The Flaw: If the driver tries to hit exactly 60 mph, they might accidentally steer the car into a ditch (an inefficient economy). Even if they stay on the road, they might end up in a slow, foggy valley where the car runs poorly, rather than the open highway where it runs efficiently.
The Risk: If the target is set too low (trying to go 60 mph when the road is icy), the car might stop completely, and no stable outcome is possible.

4. The New Solution: The "Ceiling and Floor" (The Guardrails)

The author proposes a better rule, a Taylor Rule based on Savings. Imagine the economy is a boat on a river. Instead of trying to steer the boat to a specific speed, you install guardrails.

The Ceiling (Inflation Ceiling): This is the top rail. If the water (prices) rises too high, the rule kicks in to push it back down. It doesn't demand a specific speed; it just says, "Don't go over the edge."
The Floor (Savings Floor): This is the bottom rail. This is the paper's big innovation. It says, "The amount of water in the boat (savings) must never drop below this line."

Why this works:
If the government ensures that the "savings floor" is never breached, it forces the economy to stay in the "happy" zone.

If people try to save too little (which leads to the bad, inefficient outcome), the rule automatically raises interest rates to encourage them to save more.
It acts like a safety net that catches the economy before it falls into the "inefficient" pit.

The Takeaway

The paper concludes that while the old method (aiming for a specific inflation number) can keep prices stable, it often leads the economy to a "sub-optimal" state where resources are wasted.

The new method (setting a maximum for inflation and a minimum for savings) is superior because:

It prevents prices from spiraling out of control (The Ceiling).
It guarantees that the economy stays in a "rich" state where money has value and resources are shared efficiently (The Floor).

In short: Don't try to drive the economy at a precise speed. Instead, build guardrails that prevent the car from crashing (high inflation) and prevent it from stalling (low savings). This ensures the race continues smoothly and efficiently forever.

Technical Summary: Selection of Efficient Monetary Equilibria Through Aggregate Real Savings-Based Taylor Rule

Problem Statement
The paper addresses the Hahn (1965) problem: identifying the conditions under which a monetary equilibrium (an equilibrium where fiat money holds value) exists in a general equilibrium model. Specifically, it focuses on consumption-loan overlapping generations (OLG) economies without durable assets, cash-in-advance constraints, or transaction costs. While previous literature has offered solutions based on specific frictions or stationary assumptions, this paper investigates the existence of efficient (Pareto optimal) monetary equilibria in a general, non-stationary setting with heterogeneous households. Furthermore, it addresses the issue of equilibrium indeterminacy inherent in OLG models, where multiple equilibria often exist, and explores how interest rate rules (specifically Taylor rules) can act as selection mechanisms to guide the economy toward efficiency.

Methodology
The analysis is conducted within a discrete-time, non-stationary consumption-loan OLG model. The economy consists of households living for two periods with heterogeneous endowments and preferences. The paper utilizes the following theoretical tools:

Generalized Cass Criterion: The paper extends the existence results of Dognini (2026b) by employing a generalized form of the Cass (1972) criterion. Instead of assuming uniformly bounded endowments, it utilizes inequalities associated with deep projections of consumer theory manifolds. The criterion is expressed as:
$\sum_{t=1}^{\infty} \left( \|p_t\| \sum_{h \in G_t} \|e^h_t\| \right)^{-1} = \infty$
where $p_t$ represents price vectors and $e^h_t$ represents endowments.
Definition of "Prone-to-Savings" Economies: A key conceptual contribution is the formalization of economies "prone to savings." In these economies, low relative aggregate real savings can only occur if real return rates are small relative to the growth rate of first-period endowments.
Taylor Rule Analysis: The paper models a government that influences the economy through nominal interest rates ( $r_t$ ). It analyzes the stability of equilibria under different feedback rules (Taylor rules) that adjust nominal rates based on inflation and real savings. The analysis distinguishes between the set of all equilibria ( $H_G$ ) and the subset of stable equilibria ( $S_T$ ) relative to a specific rule $T$ .

Key Contributions

Generalization of Existence Results: The paper generalizes the definitions and existence theorems from Dognini (2026b) by replacing the standard Cass criterion with the more general form (2). This allows for a broader class of economies where endowments are not uniformly bounded.
Characterization of Efficient Equilibria: It is proved that in "prone-to-savings" economies, non-vanishing relative aggregate real savings fully characterize efficient monetary equilibria. Specifically, an equilibrium is inefficient if and only if the limit of the ratio of aggregate real savings to aggregate first-period endowments approaches zero as time goes to infinity.
Selection Mechanism via Taylor Rules: The paper demonstrates that while discretionary monetary policy increases the cardinality of equilibria (indeterminacy), Taylor rules act as selection mechanisms that exclude incompatible equilibria.
Superiority of Savings-Based Rules: The paper introduces a novel Taylor rule that incorporates a "relative aggregate real savings floor" alongside an inflation ceiling. It contrasts this with a standard inflation-targeting rule.

Results

Existence: Under Assumptions 1–6 (including bounded intraperiod growth rates and the generalized Cass criterion), the set of Pareto optimal equilibria ( $H^{PO}$ ) is non-empty and compact.
Indeterminacy: In the absence of a specific rule, monetary policy increases the degree of indeterminacy. Any monetary policy sequence can be associated with a set of real allocations, but without a rule, the economy lacks a mechanism to select a specific path.
Inflation Targeting Limitations: A Taylor rule based solely on an inflation target (reacting to deviations from a specific target $\pi^*$ ) can successfully bound inflation and stabilize the economy. However, the paper demonstrates via Example 1 that such a rule often leads to inefficient equilibria. Furthermore, if the target is set too low relative to economic shocks or growth prospects, the set of stable equilibria may become empty.
Inflation Ceiling and Savings Floor: A Taylor rule based on an inflation ceiling ( $\pi_t \leq \pi^*$ $π_{t} \leq π^{*}$ ) and a relative aggregate real savings floor ( $\sum sh / \sum \|e^h\| > \tau^*$ $\sum s h / \sum ∥ e^{h} ∥ > τ^{*}$ ) yields superior results.
- If the ceiling is not set too low, stable equilibria exist.
- If the savings floor is not set too high, the rule excludes equilibria where real returns tend toward zero (the hallmark of inefficiency in this model).
- Consequently, this rule guides the economy toward efficient monetary equilibria, whereas a pure inflation-targeting rule generally does not.

Significance and Claims
The paper claims to provide a solution to the Hahn (1965) problem for a broad class of non-stationary OLG economies by showing that if an economy is "prone to savings," money has value and leads to efficient allocations.

The primary significance lies in the policy implication regarding interest rate rules. The author argues that the standard Taylor rule (inflation targeting) is insufficient for ensuring efficiency in these models because it does not account for the real return rates necessary to sustain intergenerational transfers. Instead, the paper proposes that a rule incorporating a relative aggregate real savings floor is a more robust mechanism. This floor acts as a real component (analogous to a GDP target but theoretically grounded in savings behavior) that prevents the economy from settling into inefficient, low-return equilibria. The paper posits that monitoring real savings is a more feasible and effective policy tool than targeting "trend real GDP," which is difficult to measure accurately.

The results suggest that to achieve efficient monetary equilibria, policymakers should not merely target a specific inflation rate but should maintain an inflation ceiling and ensure that aggregate real savings do not fall below a critical threshold, thereby sustaining positive real return rates.

1. The Problem: The Race Without a Finish Line

2. The Trap: Too Many Equilibria

3. The Old Solution: The "Inflation Target" (The Speed Limit Sign)

4. The New Solution: The "Ceiling and Floor" (The Guardrails)

The Takeaway

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