Essays in model uncertainty

This dissertation studies insurance arrangements and dynamics of asset prices in environments where models may be potentially misspecified. The first two chapters use Hansen-Sargent multiplier preferences to represent agents' doubts regarding the underlying model as sets of probability distributions that are statistically hard to discriminate. The last chapter investigates model misspecification from a statistical standpoint. It allows for time variation in the parameters governing dynamics of risk factors, risk exposures, and market price of risk and further estimates the model using US asset market data.;The insights in the first two chapters come from how doubts interact with wealth heterogeneity. The setting effectively delivers an endogenous component to disagreements (across agents) about the likelihood of future states as a function of the differences in agents' wealth shares. This opens up a new insurance motive that affects how agents trade, and prices that clear insurance markets. In chapter 1, we mainly focus on an exchange economy with aggregate risks and complete markets. The main findings documents how the effects of the doubts driven insurance channel accumulate over time. This is summarized by the changing wealth distribution. The limiting outcomes are contrasted with the Friedmanian conjecture which argues that agents who have incorrect priors do worse in the long run. Although this conjecture holds when agents trust their models, introducing doubts can substantially alter conclusions. A key primitive that turns out to be relevant is the inter temporal elasticity of substitution. Depending on this parameter, small amount of doubts may either ameliorate or amplify the effects on wealth inequality that come from heterogeneous priors. In addition, the transient wealth dynamics deliver countercyclical prices of risk and generates motives for trading on news shocks. The analysis in chapter 1 relies on the presence of aggregate risk.;In chapter 2 we study implications of model misspecification in environments with no aggregate risk but idiosyncratic risk that is privately observed and hence uninsurable. The focus here is on market incompleteness; we study two cases, first where we restrict markets such that agents only trade a risk-free bond and the second, where we characterize optimal incentive compatible insurance arrangements. The key finding is that, relative pessimism, or the likelihood of states which have low utility for a particular agent, is diminishing in wealth. Having a large amount of wealth in assets that yield non-contingent return, lowers the volatility of consumption and consequently concerns for misspecification for richer agents. Lastly, in contrast to settings where agents do not have doubts, optimal insurance with private information cab be consistent with bounded long run inequality.;The last chapter is a statistical inquiry into understanding the time-variation in asset returns in post-war US data through a lens of a multi-factor asset pricing model. It extends the standard settings with constant parameters to incorporate time variation in parameters that allows one to infer changes in extent, composition and price sensitivity of risks. The setup is kept tractable to permit the use of a Gibbs Sampler for estimation and inference. The findings give a narrative of movements in post-war US equity premium and market price of risks through their low frequency components.