Essays in multivariate time series analysis with applications to the movement of real average earnings in the United States economy

The three dissertation chapters utilize and expand methods of multivariate time series analysis including Seemingly Unrelated Regressions (SUR) with autocorrelated errors and the Vector Error Correction Model (VECM) to explore how macro movements in the US economy differentially impact the incomes of subgroups of the population defined by race, gender, and education.;The first chapter derives the maximum likelihood form of the Parks estimator and shows that this estimator dominates all other forms of the Parks estimator, in terms of small sample efficiency. The Parks estimator is asymptotically efficient for SUR models with autocorrelated errors.;The second chapter examines the problem of hypothesis testing in a SUR model with autocorrelated errors and shows that there is no need to trade efficiency for lower level distortion as has been suggested in the literature. Through Monte Carlo experiments, I demonstrate that bootstrapping an asymptotically pivotal test statistic is the correct method for hypothesis testing in this model. I apply this estimation technique to an empirical model previously presented in the literature which compares the differential impact in the response of earnings in subgroups of the population defined by race and gender to movements in the macro economy. I test the hypothesis that there is no differential impact across subgroups using the bootstrap technique along with asymptotic techniques including the Beck-Katz method. Using asymptotic critical values, I reject the null hypothesis regardless of which estimator is used. However, using the bootstrap technique which suffers from the least level distortion, I fail to reject the null hypothesis.;The third chapter re-evaluates the traditional way we model how incomes of subgroups of the population respond to changes in the macro economy. By separating shocks to the macro economy according to their time series behavior, I show that differential impacts on incomes from movements in the macro economy are permanent. In this analysis I use the Vector Error Correction Model which allows for a common trend in earnings and GDP. The findings from this chapter give mixed results when describing the relationship between productivity growth and increased income inequality in the United States.