Rational Expectations Under Knightian Uncertainty — An Overview
An overview of my series that explains how to model rational expectations under Knightian uncertainty arising from unforeseeable structural change
In a series of four posts, I have explained the details of Roman Frydman’s and my new working paper, titled Rational Expectations of Inflation Undergoing Unforeseeable Change.
This post provides an overview and a summary of the four posts.
Part 1: Modeling Rational Expectations in Real-World Markets Requires Acknowledging Knightian Uncertainty
The first post explains our main motivation for developing KMH. It begins with the observation that the economy’s structure undergoes structural changes over time, and that we cannot perfectly foresee these changes, even in probabilistic terms, as they are nonrepetitive.
As Frank Knight argued a century ago, such unforeseeable structural change implies that we face Knightian uncertainty, which cannot be reduced ex ante to a probability distribution.
In the paper, we argue that economists must open their theoretical models to Knightian uncertainty to represent the expectations of rational individuals in real-world markets adequately. By doing so, economists acknowledge that rational individuals in real-world markets face Knightian uncertainty and consequently cannot have perfect probabilistic knowledge.
The following post explains the details of this motivation.
Part 2: How Can We Formalize Unforeseeable Change and Knightian Uncertainty in Economic Models?
In the second post, I explain how the Knight-Muth hypothesis (KMH) provides a tractable and empirically testable formalization of unforeseeable structural change in a simple New Keynesian Phillips curve that relates inflation to an exogenous output gap.
It does so by assuming the parameter representing the pass-through of the output gap to inflation shifts intermittently between nonrepetitive regimes restricted to lie within an interval. This provides a simple formalization of Knightian uncertainty: the model’s conditional expectation of future inflation is inherently unknowable ex ante. The model can, however, be estimated ex post.
The following post explains the details and how it gives rise to Knightian uncertainty about future inflation within the model.
Part 3: Formalizing Model-Consistent Expectations Under Knightian Uncertainty
In the third post, I explain how the Knight-Muth hypothesis formalizes model-consistent expectations in a model with Knightian uncertainty arising from unforeseeable change.
In models with only probabilistic risk, the rational expectations hypothesis (REH) represents model-consistent expectations with a model’s conditional expectation of future outcomes. In a KMH model with Knightian uncertainty, however, REH is inapplicable because the model’s conditional expectation of future outcomes is inherently unknowable at the time individuals form expectations.
Instead, KMH represents model-consistent expectations in terms of the model’s conditional expectation of future outcomes, but where subjective parameters replace the model’s unknowable actual future parameters.
Importantly, we leave the determination of the subjective parameters and how they shift over time to be exogenously determined. We do, however, restrict them to lie within the same interval as the unknowable actual future parameters.
Thereby, KMH acknowledges that an economist cannot know exactly how rational market participants subjectively assess future changes in forming inflation expectations, and that they might rely on fundamental factors as well as psychological and other factors outside the model.
The following post motivates and explains the mathematical details of KMH’s model-consistent inflation expectations in the simple New Keynesian Phillips curve model.
Part 4: Rational Expectations Under Knightian Uncertainty vs. Probabilistic Risk
In the final post, I explain the difference between KMH’s rational expectations under Knightian uncertainty and REH’s rational expectations under probabilistic risk.
KMH’s theoretical representations of rational expectations differ from REH’s because opening an economic model to Knightian uncertainty renders perfect probabilistic foresight inherently impossible.
To summarize, KMH represents rational expectations under Knightian uncertainty as:
Diverse, even when based on the same information, as there are many rational ways to map the information into expectations.
Driven by fundamental factors, but also influenced by psychological factors.
Deviating from ex post outcomes in unforeseeable ways, so that the bias of ex post forecast and their correlation with ex ante information shift in unforeseeable ways over time, even when individuals have access to full information.
In contrast, REH represents rational expectations under probabilistic risk as:
Identical when based on the same information, as there is only one rational way to map the information into expectations.
Only driven by fundamental factors, while the influence of psychological factors is interpreted as irrationality.
Only deviating from ex post outcomes by a random error, so that their ex post forecast errors are unpredictable, assuming that individuals have access to full information.
The final post below explains these differences in detail. Moreover, it explains how recognizing the importance of Knightian uncertainty enables KMH to reconcile the assumption that individuals in real-world markets are rational with key features characterizing survey-based expectations.