| This dissertation presents three essays on asset pricing and econometrics. The first chapter identifies rare events and long-run risks simultaneously from a rich data set (the Barro-Ursua macroeconomic data set) and evaluates their contributions to asset pricing in a unified framework. The proposed model of rare events and long-run risks is estimated using a Bayesian Markov-chain Monte-Carlo method, and the estimates for the disaster process are closer to the data than those in the previous studies. Major evaluation results in asset pricing include: (1) for the unleveraged annual equity premium, the predicted values are 4.8%, 4.2%, and 1.0%, respectively; (2) for the Sharpe ratio, the values are 0.72, 0.66, and 0.15, respectively.;The second chapter, coauthored with Robert J. Barro, estimates the coefficient of relative risk aversion, gamma, by exploring the influence of rare disasters on the equity premium. The premium depends on the probability and size distribution of disasters, gauged by proportionate declines in per capita consumption or gross domestic product. Long-term national-accounts data for 36 countries provide a large sample of disasters of magnitude 10% or more. A power-law density provides a good fit to the size distribution. The observed premium of 5% generates an estimated gamma close to 3, with a 95% confidence interval of 2 to 4. The results are robust to uncertainty about the values of the disaster probability and the equity premium.;The third chapter studies the estimation and testing of ARMA(1, 1) models with root cancellation using a new method called "global approach." With this approach, it shows the asymptotic distributions of the maximum likelihood estimator, gives a complete classification of asymptotic identification categories for all the drifting sequences of parameters, and reveals how the strength of identification of parameters change with the sample size and the sum of the autoregressive (AR) and moving average (MA) parameters. A novel statistic is proposed for conducting joint tests on the AR and MA parameters, which is straightforward to calculate and has some desirable properties. |
