While the first essay in this series questioned the limitations of agents under the RREEMM model, this second work utilizes the technical exposition of Minford and Peel (2002) to challenge the very definition of rationality as a purely cognitive component. We analyze how mathematical solution methods intrinsically rely on exogenous “terminal conditions” to avoid explosive paths or “bubbles” that are, paradoxically, consistent with individual internal rationality. We maintain that these conditions do not represent learning mechanisms or behavior modeled within the agent, but constraints arbitrarily imposed from outside the system to force stability. We argue that the mathematical necessity of these conditions demonstrates that “rationality” is not a self-sufficient property of the agent’s mind, but an emergent result dependent on institutional design. The stability of the saddlepath is achieved not through perfect cognition, but through an institutional scaffolding that restricts the set of possible expectations, paving the way for a conception of macroeconomics based on rules rather than individual omniscience.
Keywords: Cognitive indeterminacy | Terminal conditions | Exogenous constraints | RREEMM | Rational bubbles | Minford & Peel
In our previous analysis, we established that the rational expectations hypothesis imposes an implausible processing burden. However, the problem runs deeper than a mere lack of “RAM” in agents’ brains. By descending into the operational mechanics of macroeconomic models presented by Minford and Peel (2002), we encounter an ontological revelation: rationality, understood as an internal and isolated optimization process, is mathematically insufficient to generate economic order.
By detailing how these models are solved, the authors reveal—seemingly unwittingly—that the agent’s internal consistency is not enough to anchor expectations. This essay argues that the “terminal conditions” required to close these models are tacit proof that rationality does not reside inside the individual’s head, but in the external constraints surrounding them.
Minford and Peel (2002) demonstrate that in Rational Expectations models with Future Variables (REFV), internal mathematical consistency allows for multiple outcomes. The authors admit that, without imposing external restrictions, the models “would merely assert in effect that ‘anything can happen provided it is expected, but what is expected is arbitrary’”.
This finding is devastating for the traditional conception of rationality. If an agent is “perfectly rational” (cognitively) and yet can mathematically justify an explosive hyperinflation trajectory (rational bubble) just as well as a stable one, then the cognitive component alone is incapable of discriminating between order and chaos.
From the perspective of the RREEMM agent, this implies that the concept of “rationality” as a cognitive attribute is incomplete. The mind cannot, through pure logical introspection, deduce the unique equilibrium. The evidence that “any path is possible” suggests that what economists call a “coordination failure” is actually a failure in the definition of rationality: they have attempted to model as a mental process what is in reality a process of institutional dependency.
To illustrate that isolated cognition cannot solve the economic problem, we analyze the dynamic model presented by Minford and Peel (2002). This system incorporates adjustment costs and future expectations:
Money Demand: \[m_{t} = p_{t} + y_{t} - \alpha(E_{t}p_{t+1} - p_{t})\]
Phillips Curve (Aggregate Supply): \[y_{t} - y^{*} = \frac{1}{\delta}(p_{t} - E_{t-1}p_{t}) + \mu(y_{t-1} - y^{*})\]
Money Supply: \[m_{t} = \overline{m} + \epsilon_{t}\]
The mathematical solution reveals the “saddlepath property,” where “any deviation from this [unique] path is unstable”.
Here lies the central critique of rationality as a cognitive component. For the agent to “hit” the saddlepath using only their mind, they would need to:
This confirms that stability cannot arise from the agent’s cognition. If rationality were purely cognitive, the agent would be justified in riding a speculative bubble (which is mathematically consistent). The fact that models assume the agent does not do this implies they are tacitly assuming the existence of something beyond cognition.
To prevent the model from exploding, the literature introduces the “terminal condition.” Minford and Peel use the example of a hyperinflation where agents eventually switch to barter, forcing the government to change its policy. They explicitly admit: “These arguments appeal to forces not explicitly in the model”.
It is fundamental to distinguish the nature of this solution: stability is not endogenous (it does not arise from the agent’s behavioral equations), but strictly exogenous. In the standard model, the agent does not “learn” to discard the bubble nor develop an institution to contain it; simply, the modeler introduces a manual mathematical constraint (“the government will not allow this”) to prune unwanted trajectories. Therefore, the rationality we observe is not a property of the agent’s mental model, but an artifact of the mathematical model’s design.
By imposing a terminal condition, the modeler is admitting that the agent’s brain is insufficient to fix expectations. An “external force” is required (a credible monetary rule, a law, a social norm). Therefore, what started as questioning a cognitive limitation is reinterpreted as an institutional necessity. The “rationality” we observe in markets is not the product of superior mental calculation, but of an institutional environment that prunes the unstable branches of the decision tree.
The solution methods exposed by Minford and Peel reinforce this view:
In both cases, the agent’s success is not due to their information processing capacity (cognitive component), but because the model has gifted them the final structure of the game (institutional component). Experimental evidence from Smith (2003) confirms that without these clear external structures, real human agents (with bounded rationality) do not magically converge to equilibrium; they need rules and institutions to guide learning.
The analysis of Minford and Peel’s (2002) methods allows us to close the questioning initiated in the first essay. “Perfect rationality” is not only psychologically unrealistic (as seen with RREEMM), but it is mathematically indeterminate without external help.
The inevitable conclusion is that we must abandon the idea that rationality is an internal or cognitive attribute of the individual. Macroeconomic stability does not arise from minds calculating the infinite, but from institutions (terminal conditions) that make the future predictable. However, in current models, these institutions are not modeled; they are simply assumed as exogenous forces. This validates the shift towards the institutional: if cognition is fragile and mathematics are indeterminate, the next theoretical step is not to continue assuming these rules as given, but to explicitly model how agents build and learn them.
AI Tools Used The authors utilized large language models (LLMs) exclusively as research and synthesis assistants. Specifically, Gemini Flash 2.5 (Google, 2025) and NotebookLM (Google, 2024) were employed to analyze the source text “Advanced Macroeconomics” by Minford & Peel and synthesize the technical arguments regarding RE solution methods. All interpretive analysis connecting these technical methods to the behavioral framework of the first paper remains the sole work of the authors.