Highlights
- The study extends the He and Krishnamurthy (HK) model by incorporating ambiguity aversion and rational inattention, which explains why households delegate investment decisions to specialists.
- Ambiguity aversion amplifies households’ incentive to delegate due to higher estimation risks, and this interaction can result in specialists adopting more conservative investment strategies.
- The model demonstrates that belief differences between households and specialists become more pronounced during crises, as these differences widen when the specialist’s wealth declines.
In this paper, the researchers incorporated ambiguity and information processing constraints into the He and Krishnamurthy (HK) model of intermediary asset pricing.
Intermediary asset pricing, pioneered by He and Krishnamurthy and Brunnermeier and Sannikov, proposes that financial intermediaries play an essential role in determining asset prices, primarily due to market segmentation that limits household participation. However, since households face few explicit constraints to participating in most financial markets, some have questioned the relevance of the intermediary asset pricing literature.
The researchers responded to Cochrane’s scepticism (with its focus on the limitations of conventional macroeconomic models and government interventions) by providing a micro-foundation for why households delegate decisions. Specifically, they assumed both households and specialists face limits on their ability to process information, and this is what raises rational inattention.
Specialists who run the intermediaries are assumed to have greater information processing capacity, so households can effectively purchase this additional capacity by delegating their portfolio decisions to intermediaries.
Besides introducing rational inattention, the researchers also assumed that agents in the HK model are ambiguity averse or have preferences for robustness. This was done for two reasons. First, delegation only occurs when households value information precision. Combining log utility with ambiguity aversion provides a sufficient preference condition for portfolio delegation. Also, ambiguity interacts with rational inattention, which then amplifies a household’s incentive to delegate.
The second reason is that incorporating ambiguity lets the study model yield a stationary wealth distribution, enabling quantitative assessments of the data. In contrast, the HK model features a degenerate wealth distribution in which specialists ultimately dominate. The researchers showed that ambiguity aversion tightens the intermediary’s capital constraint and magnifies its effects. The calibrated model can quantitatively account for both the unconditional and time-varying moments of asset returns, with empirically plausible concerns for robustness.
Ambiguity aversion and rational inattention both influence this filtering problem. The researchers operationalized robust filtering by supposing that agents distrust their priors, and this introduces a pessimistic drift distortion.
Households, being less efficient in processing information, experience higher estimation risk. With ambiguity, this leads to a welfare loss, motivating households to optimally delegate their investments to specialists who have greater information capacity.
Additionally, the rate at which agents can learn is constrained by their information processing capacity. Greater capacity accelerates learning and produces a lower steady-state estimation risk. Households, being less efficient in processing information, experience higher estimation risk. With ambiguity, this leads to a welfare loss, motivating households to optimally delegate their investments to specialists who have greater information capacity. Thus, households are willing to pay a lump-sum delegation fee to reduce estimation risk. The researchers showed that a small difference in information capacity can rationalize an empirically plausible up-front delegation fee.
The researchers also showed that ambiguity aversion and rational inattention interact. In the absence of ambiguity, households would not choose to delegate, as seen in the HK model with log utility, where estimation risk becomes irrelevant. Therefore, the HK model makes the extreme assumption that households must delegate to intermediaries to invest in risky assets.
In the model, however, the introduction of ambiguity concerning the unobserved state motivates households to delegate. Furthermore, ambiguity aversion amplifies a household’s incentive to delegate. That is, they are willing to pay more when they are more ambiguity averse.
The paper’s second contribution is empirical, showing that the model quantitatively matches the data.
Even when households and specialists have the same degree of ambiguity aversion, because ambiguity aversion is inversely scaled by time preference, specialists become effectively more ambiguity averse since they care more about the future.
The researchers demonstrated that introducing ambiguity about asset returns lets the model generate a stationary wealth distribution. Even when households and specialists have the same degree of ambiguity aversion, because ambiguity aversion is inversely scaled by time preference, specialists become effectively more ambiguity averse since they care more about the future. As a result, their strategically pessimistic drift distortions are greater than those of households.
In the researchers’ model, strategically pessimistic drift distortion leads to more conservative portfolio strategies, causing specialists to invest less of their wealth in risky assets. The researchers demonstrated that with reasonable parameter values, a specialist’s relatively greater pessimism offsets greater patience, resulting in a stationary wealth distribution.
The key ingredient in the HK model is that the delegation contract is subject to a moral hazard problem, resulting in a capital constraint faced by intermediaries, which requires specialists to maintain a minimum amount of ‘skin in the game’. In contrast, in the researchers’ model, belief differences were state-dependent. They widened during crises as the specialist’s wealth declined, and this led to a more binding capital constraint and an increase in the specialist’s relative risk exposure.
Furthermore, the model captured both unconditional and time-varying asset returns while endogenously generating an empirically consistent crisis frequency and persistence.
The researchers’ model quantitatively matched both the unconditional asset pricing moments and the time-varying prices of risk. Additionally, the model generated an empirically plausible probability and persistence of financial crises.
A useful extension of the model would be to introduce ambiguity and information processing constraints into the production-based asset pricing model of He and Krishnamurthy. Another extension would be to combine the analysis with the complex asset markets model of Eisfeldt et al., as they also studied the pricing implications of a model that combines ‘experts’ and ‘non-experts’. In contrast to the researchers’ model, where channel capacity differences are exogenous, agents can choose whether to become experts or not.
Becoming an expert is beneficial because it reduces idiosyncratic investment risk. The key mechanism in the model is endogenous entry and exit, and induced selection effects. However, in Eisfeldt et al’s model, funds cannot be reallocated across investors, and there is no trade in expertise. As a result, there is no moral hazard problem or capital constraint. Combining endogenous expertise, equilibrium entry and exit, portfolio delegation, and moral hazard would be challenging but also potentially fruitful.
Keywords: Ambiguity, Rational inattention, Portfolio delegation, Intermediary asset pricing, Financial crisis
* Learn more from the full research article here:
https://doi.org/10.1016/j.jet.2024.105922