Axcess Volatility And The Asset Pricing Exchange Rate Model With Unobservable Fundamentals

This paper presents a method to test the volatility predictions of the textbook asset-pricing exchange rate model, which imposes minimal structure on the data and does not commit to a choice of exchange rate “fundamentals.” Our method builds on existing tests of excess volatility in asset prices, combining them with a procedure that extracts unobservable fundamentals from survey-based exchange rate expectations. We apply our method to data for the three major exchange rates since 1984 and find broad evidence of excess exchange rate volatility with respect to the predictions of the canonical asset-pricing model in an efficient market.

We present tests of excess volatility of exchange rates that impose minimal structure on the data and do not commit to a choice of exchange rate fundamentals. Our method builds on existing volatility tests of asset prices, combining them with a procedure that extracts unobservable fundamentals from survey-based exchange rate expectations. We apply our method to data for the three major exchange rates since 1984 and find broad evidence of excess volatility with respect to the predictions of the canonical asset-pricing model of the exchange rate with rational expectations.

The present study builds upon the seminal work of Engel and West [2005, Journal of Political Economy 113, 485-517] and in particular on the relationship between exchange rates and fundamentals. The paper discusses the well-known puzzle that fundamental variables such as money supplies, interest rates, outputs etc. provide help in predicting changes in floating exchange rates. It also tests the theoretical result of Engel and West (2005) that in a rational expectations present-value model, the asset price manifests near-random walk behaviour if the fundamentals are I(1) and the factor for discounting future fundamentals is near one. The study explores the direction and nature of causal interdependencies and cross-correlations among the most widely traded currencies in the world, their country-specific fundamentals and their US-differentials. A new VAR/VECM-GARCH multivariate filtering approach is implemented, whilst linear and nonlinear non-causality is tested on the time series. In addition to pairwise causality testing, several different groupings of variables are explored. The methodology is extensively tested and validated on simulated and empirical data. The implication is that although exchange rates and fundamentals appear to be linked in a way that is broadly consistent with asset-pricing models, there is no indication of a prevailing causal behaviour from fundamentals to exchange rates or vice-versa. When nonlinear effects are accounted for, the evidence implies that the pattern of leads and lags changes over time. These results may influence the greater predictability of currency markets. Overall, fundamentals may be important determinants of FX rates, however there may be some other unobservable variables driving the currency rates that current asset-pricing models have not yet captured.

The NBER Macroeconomics Annual provides a forum for important debates in contemporary macroeconomics and major developments in the theory of macroeconomic analysis and policy that include leading economists from a variety of fields. The papers and accompanying discussions in NBER Macroeconomics Annual 2007 address exchange-rate models; implications of credit market frictions; cyclical budgetary policy and economic growth; the impacts of shocks to government spending on consumption, real wages, and employment; dynamic macroeconomic models; and the role of cyclical entry of new firms and products on the nature of business-cycle fluctuations and on the effects of monetary policy.

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).

This paper develops and estimates a continuous-time model of a financial market where investors' trading strategies and the specialist's rule of price adjustments are the best response to each other. We examine how far modeling market microstructure in a purely rational framework can go in explaining alleged asset pricing ànomalies.' The model produces some major findings of the empirical literature: excess volatility of the market price compared to the asset's fundamental value, serially correlated volatility, contemporaneous volume-volatility correlation, and excess kurtosis of price changes. We implement a nonlinear filter to estimate the unobservable fundamental value, and avoid the discretization bias by computing the exact conditional moments of the price and volume processes over time intervals of any length.

We estimate a multivariate unobserved components stochastic volatility model to explain the dynamics of a panel of six exchange rates against the US Dollar. The empirical model is based on the assumption that both countries' monetary policy strategies may be well described by Taylor rules with a time-varying inflation target, a time-varying natural rate of unemployment, and interest rate smoothing. Compared to the existing literature, our model simultaneously provides estimates of the latent components included in a typical Taylor rule specification and the model-based real exchange rate. Our estimates closely track major movements along with important time series properties of real and nominal exchange rates across all currencies considered, outperforming a benchmark model that does not account for changes in trend inflation and trend unemployment. More precisely, the proposed approach improves upon competing models in tracking the actual evolution of the real exchange rate in terms of simple correlations while it appreciably improves upon simpler competitors in terms of matching the persistence of the real exchange rate.

Concludes the role of asset prices in monetary policy is one of the most important, and difficult, questions confronting central banks.