UC San Diego

Many economic variables are observed to be highly persistent (Nelson and Plosser (1982)). In hypothesis testing, the nearly integrated regressor may cause a huge size distortion. The first chapter examines this problem in the predictive regression setting. We show how the rejection of hypothesis test is caused in the presence of a highly persistent regressor, by using four typical empirical settings including predicting stock returns. The rejections may not indicate predictability or rejection of the model. The second chapter considers cointegration when the regressor has a near but not exact unit root. Elliott (1998) pointed out that when the data is not exactly integrated, the test statistics will be severely biased. We examine the relevance of this explanation in four empirical settings. We will show that the rejection of the test in the presence of a near unit root variable is a common problem. We also consider alternative procedures. The third chapter examines alternative testing procedures in the predictive regression setting. One is a variable- addition method by Toda and Yamamoto (1995). Others are Supbound t-test, Bonferroni t-test, and Bonferroni Q-test. In terms of power, Bonferroni Q-test outperforms