Three essays on econometrics

In Chapter 2, new time and frequency domain tests for the presence of a unit root are developed. For the time domain tests, moving average processes of a finite, known order are assumed for the error terms. For the frequency domain tests, general assumptions allowing for stationary and weakly dependent error processes are given. The limiting distributions of the feasible GLS tests are derived under the MA(1) errors in the time domain. This theory is extended to the higher order moving average processes satisfying the invertibility condition. The limiting distributions of the full and band spectrum tests in the frequency domain are also derived. All of these limiting distributions are shown to be free of nuisance parameters. These results demonstrate some of the advantages of the GLS in terms of stable size and good power properties for a wide variety of error generating mechanisms.;In Chapter 3, tests for a unit root based on the Hausman principle are developed. The ordinary least squares estimator and the pseudo IV estimator using the current variable as an instrument are employed to formulate test statistics. The limit distributions of these tests are expressed as inverses of the squared Brownian functionals which have not been used to test for a unit root. Coefficient tests using the pseudo IV estimators are developed.;In Chapter 4 general formulae for the finite sample and asymptotic distributions of the instrumental variable estimators and the Wald statistics in a simultaneous equations model are derived. It is assumed that the coefficient vectors of both endogenous and exogenous variables are only partially identified. The effect of partial identification on the finite sample and asymptotic distributions of the estimators and the Wald statistics is analyzed by isolating identifiable parts of the coefficient vectors using the rotation of the coordinate system developed in Phillips. The pdf's of the estimators and the Wald statistics are illustrated by simulation method. (Abstract shortened with permission of author.).