Rational Expectations Under Knightian Uncertainty — Part 1
Why an adequate theoretical representation of rational expectations in real-world markets requires opening economic models to Knightian uncertainty
In my new working paper with Roman Frydman, we present a new theoretical approach to formalizing unforeseeable change and rational expectations in the presence of Knightian uncertainty arising from such change.
The paper is titled Rational Expectations of Inflation Undergoing Unforeseeable Change.
We call our theoretical approach the Knight-Muth hypothesis (KMH), because it combines Frank Knight’s argument that “true” uncertainty—nowadays referred to as Knightian uncertainty—arises from unforeseeable structural change with John Muth’s hypothesis that economists can acknowledge that individuals are rational by representing their expectations as consistent with the predictions of the economist’s model.
We could, however, have referred to our approach simply as rational expectations under Knightian uncertainty.
This post is the first in a series that breaks down and explains the key elements of our approach and its implications.
In this post, I focus on the motivation for our paper. That starts with an observation worth elaborating on.
The Economy Undergoes Structural Changes That We Cannot Foresee
We start the paper with the observation that
the economy undergoes nonrepetitive structural changes whose consequences and timing cannot be fully understood in advance.
We argue that these changes are an essential feature of market economies:
Major structural changes are engendered not only by economic policy shifts, geopolitical conflict, pandemics, and various other factors, but also by modern market economies’ essential feature: incentivizing profit-seeking participants to seek new ways to allocate their resources. Ultimately, participants’ innovation changes the economy’s structure in ways that are not repetitive of past changes.
We are currently in a period with major structural changes in the economy. Some of these changes are caused by the re-election of Trump, others by Russia’s attack on Ukraine. The COVID-19 pandemic provides another recent example of major shifts in aggregate demand and supply.
The explosive rise of AI represents an alternative example of a present technological innovation that, among other things, is creating new services and changing the demand for labor, and which will undoubtedly continue to do so in the future in ways we cannot yet imagine.
These very different events share a common feature: they cause the economy to shift from one structure to the next. In other words, the structural changes are nonrepetitive.
Building on Frank Knight’s insights, we argue in the paper that recognizing this nonrepetitiveness is crucial because it limits what we can know about the future:
This nonrepetitiveness renders the structural change unforeseeable: no one can objectively know, even in probabilistic terms, when and how the economy’s structure will change and thus how structural change will affect future economic outcomes.
In other words, because AI is a true innovation that shifts the economy to a structure we have not observed before, we cannot objectively know today exactly how it will impact the economy in the future, even in probabilistic terms. This is what we mean when we refer to structural change as unforeseeable.
The important consequence of unforeseeable change is that our knowledge of the future is inherently imperfect.
Beyond its sheer complexity, that is what distinguishes the economy from playing roulette: unforeseeable structural change renders our knowledge of future economic outcomes inherently imperfect, while the constancy of the roulette gives us perfect probabilistic knowledge of it (or at least we can achieve that by studying probability and statistics).
It is useful to emphasize what we don’t mean when we refer to structural change as unforeseeable.
By unforeseeable, we do not mean that no one could have foreseen the possibility that Trump’s re-election or the invention of AI would occur and lead to structural changes in the economy, or that no one could make probabilistic predictions about these changes.
All we are arguing is that before such changes occur, no one can objectively know when they will occur and what their impact on the economy will be.
That does not rule out making predictions about these changes, or even relying on complex statistical analyses of historical data to make these predictions. But these predictions are ultimately guesses. The unforeseeable change in the economy implies that we cannot know from statistical analyses of historical data what its future structure will be.
Another point worth emphasizing is that by unforeseeable change, we do not mean that the economy’s structure changes all the time and in ways such that there are absolutely no regularities over time. If that were the case, any form of economic modeling would be useless. Additionally, we should not be able to identify any form of stability in economic time-series data, which is clearly not the case empirically.
Representing Rational Expectations Requires Opening Economic Models to Unforeseeable Change
Most economists I speak with agree that the economy’s structure undergoes unforeseeable structural changes, at least rarely.
Most economic models, however, abstract from unforeseeable change. They do so by formalizing the economy’s structure to either remain constant or switch between repetitive regimes in ways that can be foreseen probabilistically.
Relying on such models, the rational expectations hypothesis (REH) is widely considered the way to represent the expectations of rational individuals.
In proposing REH, John Muth (1961) argued that economists should acknowledge that individuals are rational by representing their expectations as consistent with the predictions of the economist’s model. After all, the model represents the economist’s hypothesis about how the economy works. If this hypothesis is correct and individuals are rational, their expectations should correspond to the model’s predictions. Thus, REH represents rational individuals’ expectations by the model’s conditional expectation of future outcomes.
Roman and I argue in the paper, however, that:
although REH models specify participants’ expectations as consistent with the models’ predictions, (…) they do not represent expectations of rational participants in real-world markets.
We argue that this is because REH relies on models that assume the economy’s structure remains constant or switches in foreseeable ways between repetitive regimes, which I have also written about here. Thus, they abstract from unforeseeable change and assume that the future is a probabilistic replica of the past.
Our argument is not about whether these assumptions are realistic.
Instead, we argue that REH’s representation of rational expectations is too narrow to characterize the expectations of rational individuals in real-world markets. Effectively, they assume that rational expectations in real-world markets can be represented the same way as rational expectations of the roulette.
This is because REH models assume that the future is a probabilistic replica of the past. Thereby, they assume that individuals face only probabilistic risk and can have perfect probabilistic foresight of the future. By representing individuals’ expectations as consistent with these predictions, REH models reduce rational expectations to perfect probabilistic foresight.
We argue that unforeseeable structural change—even if it occurs very rarely—renders such perfect probabilistic foresight inherently unattainable in real-world markets. In other words, perfect probabilistic foresight is possible when playing roulette, but not when assessing the value of AI companies or predicting future inflation in real-world markets undergoing unforeseeable change.
Thus, we argue that adequately characterizing the expectations of rational individuals in real-world markets
requires that economists formalize structural change as unforeseeable and specify participants’ expectations as consistent with the Knightian uncertainty arising from such change.
This is our motivation for developing the Knight-Muth hypothesis, which does exactly that.
Building unforeseeable change into economic models is important not because it makes them more realistic, but because it changes our understanding of rational expectations. It leads to predictions about rational expectations that differ substantially from REH’s predictions. That enables accounting for key features of survey-based expectations and reconciling them with individuals’ rationality. That, however, is the topic for the next posts.