Three essays on exchange rate dynamics and model uncertainty

At least since Knight (1921), economists have suspected that the distinction between risk and `uncertainty' might be important in economics. However,Savage (1954) showed this distinction is meaningless if agents adhere to certain axioms, which seem to be normatively compelling. Savage's SubjectiveExpected Utility (SEU) model became the dominant paradigm in economics, and remains so to this very day. Still, suspicions that the distinction matters never really died. The Ellsberg Paradox (1961) first raised doubts about the SEU model. Then, Gilboa and Schmeidler (1989) showed how to modifySavage's axioms so that the distinction does matter. In their model, agents entertain a set of priors, and optimize against the worst-caseprior. Finally, Hansen and Sargent (2008) operationalized this new approach by linking it to the engineering literature on `robust control'. My dissertationapplies the Hansen-Sargent framework to the foreign exchange market. I show that if we think of market participants as confronting both uncertainty andrisk, then we can easily explain several well known empirical puzzles in the foreign exchange market.The second chapter of my dissertation, entitled "Robustness and Exchange Rate Volatility", was published in the Journal of International Economics in 2013, and is coauthored with my supervisor, Prof. Kenneth Kasa. This paper uses the monetary model of exchange rates. It assumes investors are aware of their own lack of knowledge about the economy. They respond to their ignorance strategically, by constructing forecasts that are robust to model misspecification. We show that revisions of robust forecasts are more sensitive to new information, and can easily explain observed violations of Shiller's variance bound inequality.The third chapter, entitled "Model Uncertainty and the Forward Premium Puzzle", was published in the "Journal of International Money and Finance" in 2014. It studies a standard two-country Lucas (1982) asset-pricing model. The main objective is to understand the determinants of observed excess return in the foreign exchange market. The paper shows that Hansen-Jagannathan (1991) volatility bounds can be attained with both reasonable degrees of risk aversion and empirically plausible detection error probabilities. Hence, excess returns in the foreign exchange market appear to be primarily driven by a `model uncertainty premium' rather than a risk premium.The fourth chaper, entitled "Robust Learning in the Foreign Exchange Market", was recently revised and resubmitted to the "Canadian Journal of Economics". Following Hansen and Sargent (2010), it assumes agents cope with uncertainty by both learning and by formulating robust decision rules. Agents entertain two competing models, differing by the persistence of consumption growth. As in my previous paper, agents continue to doubt the specification of each model. It shows that robust learning can not only explain unconditional risk premia in the foreign exchange market, but can also explain the cyclical dynamics of risk premia. In particular, an empirically plausible concern for model misspecification and model uncertainty generates a stochastic discount factor that uniformly satisfies the spectral Hansen-Jagannathan bound of Otrok et. al. (2007).

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