Habits and Uncovered Interest Parity Puzzle: Theory and Estimation

Description

Currency exchange market has the largest daily trading volume among all financialmarkets. Yet, it has a very robust empirical regularity, known as uncovered interestparity (UIP) puzzle. That is a currency with relatively high interest rate tends toappreciate in short term. This is the empirical foundation for the practice of carry trade.It is until recently that equilibrium asset pricing models are able to explain this puzzle.These recent models include habit formation of Campbell and Cochrane (1999) andlong-run risks of Bansal and Yaron (2004). As pointed out by Fama (1984), any potentialexplanation of this puzzle requires the risk premium to be stochastic. Habit formationmodels the time-varying risk prices by preferences shock that is perfectly correlatedwith the consumption shock, whereas long-run risks model achieves this by a jointassumption on recursive preferences and stochastic growth rate and volatility ofconsumption.However, there is one major issue for both models; they have difficulty to extend intomulti-agent settings due to an aggregation issue. In the single-agent setting, thisaggregation issue is circumvented because the representative agent’s optimalconsumption is the same as exogenous consumption. This convenience is broken in amulti-agent setting. This is why most of the international versions of both models arebuilt by simply putting several (typical two) closed economies together. There are nointeractions among the closed economies. Another issue is that both models suffer somedegree of intractability. The original habit formation model has to rely on numericalsolution and the long-run risks model has to use log-linear approximations.In this project, based on the success of these two models, we intend to propose a modelwith preferences shock and stochastic volatility of consumption growth but without theaggregation issue. The model has potential to explain the UIP puzzle because it hasmany important features that are shown to be important by the extensive studies of theUIP puzzle. In addition, our model enjoys closed-form solutions. This enables us toconduct rigorous empirical investigations, e.g., likelihood based estimation and test, onasset pricing issues. In contrast to the common practice in this literature, a calibration-simulationis usually used to show the model’s ability to explain the empiricalregularities. This method not only is less rigorous but also offers less details on theeconomics. Our empirical studies should shed new light on the implications of UIP puzzle and other empirical regularities.