Three essays on econometrics
This dissertation is composed of three chapters on modern econometric topics. Chapter 1 studies the problem of making inference on structural parameters in instrumental variables regression with weak instruments. It has become well known in the literature that the instrumental variables estimates are strongly biased and the Wald type test statistics are nonpivotal and thus could have zero coverage probability when the instruments selected are very weak. Using a local-to-zero assumption for the coefficients of instruments, Chapter 1 shows that likelihood type statistics for testing hypothesis on the structural parameters are asymptotically (boundedly) pivotal, thus valid inference can be made using the asymptotic (bounding) distribution of the likelihood type statistics. Characteristics of the confidence sets for the structural parameters are also analyzed.Chapter 2 develops a Bayesian time series model of multiple structural changes, which allows changes in both the time trend and the variance term. In spite of the complex structure the model allows, it is shown in Chapter 2 that the Bayesian Gibbs sampling technique can be employed to estimate the model in a straightforward way. The model selection problem regarding the number of structural changes is also considered using the posterior odds ratio.Chapter 3 presents a high order Markov switching model, where the underlying high order Markov chain is modeled after Raftery's parsimonious formulation. The model is used to investigate the statistical distributions of daily foreign exchange rate data. For most exchange rates high order Markov switching appears to exist in the data. However, the forecasts from the high order Markov switching models do not have obvious advantage over alternative models such as the first order Markov switching model and GARCH model with conditionally t-distributed errors.
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