| This thesis is a collection of three independent essays in econometrics.;The first essay uses the empirical characteristic function (ECF) procedure to estimate the parameters of mixtures of normal distributions and switching regression models. The ECF procedure was formally proposed by Feuerverger and Mureika (1977), Heathcote (1977). Since the characteristic function is uniformly bounded, the procedure gives estimates that are numerically stable. Furthermore, it is also shown that the finite sample properties of the ECF estimator are very good, even in the case where the popular maximum likelihood fails to exist.;The second essay applies White's (1982) information matrix (IM) test to a stationary and invertible autoregressive moving average (ARMA) process. Our result indicates that, for ARMA specification, the derived covariance matrix of the indicator vector is not block diagonal implying the algebraic structure of the IM test is more complicated than other cases previously analyzed in the literature (see for example Hall (1987), Bera and Lee (1993)). Our derived IM test turns out to be a joint specification test of parameter heterogeneity (i.e. test for random coefficient or conditional heteroskedasticity) of the specified model and normality.;The final essay compares, using Monte Carlo simulation, the generalized method of moments (GMM) and quasi-maximum likelihood (QML) estimators of the parameter of a simple linear regression model with autoregressive conditional heteroskedastic (ARCH) disturbances. The results reveal that GMM estimates are often biased (apparently due to poor instruments), statistically insignificant, and dynamically unstable (especially the parameters of the ARCH process). On the other hand, QML estimates are generally unbiased, statistically significant and dynamically stable. Asymptotic standard errors for QML are 2 to 6 times smaller than for GMM, depending on the choice of the instruments. |
