Analytical evaluation and application of tests for cointegration

My dissertation characterizes the properties of some of the tests for integration and cointegration. In this framework all the tests have non-standard distributions and no optimality theory is yet available to indicate the Uniformly Most Optimal test. Particular care then needs to be used when doing hypothesis testing.;Chapter 1 proposes a careful comparison of residuals based tests for the null of no cointegration and theorizes which unit root test should be used when testing for cointegration. Using local alternative parameterization, I compute the analytical power of five residuals tests. The tests are then compared in term of power and size distortions and I show that no significant improvement can be achieved by using different unit root tests than the t-test originally proposed by Engle and Granger (1987).;Chapter 2 proposes a theoretical explanation to the common empirical results in which different tests for cointegration give different answers. Using local to unity parametrization I compute the analytical power of some tests for the null of no cointegration. The tests are shown to depend on a single nuisance parameter, which is, in turn determined by the correlation at frequency zero of the independent variables with the errors of the cointegration regression. Monte Carlo experiments show that the tests can have significantly different power for different values of the nuisance parameter.;Chapter 3 is an applied paper that looks at the PPP puzzle. Whilst point estimates for mean reversion in real exchange rates suggest reasonable half-lives to shocks, it still remains uncomfortable that models without any mean reversion are often compatible with individual country pair data from the floating period. Studies that use data over very long periods or that pool data for a number of countries in a panel framework find mean reversion, but at the cost of adding additional restrictions. We examine tests for mean reversion for individual country pairs where greater power is gained through modeling other economic variables with the real exchange rate. Our results are broadly consistent with other methods to improve the power of tests for unit roots in real exchange rates, finding support for PPP.