| The first two papers of this dissertation discuss state space models and their relationship to standard econometric models. Special note is made of the relationship between multivariate time series, and dynamic unobservable component models with state space models. Estimation techniques for state space models are discussed, and a general solution to the estimation problem based on the Kalman filter is suggested. It is shown that the innovations from the filter can be used to form a likelihood function, which can then be maximized to yield estimates of the parameters of the model. A scoring algorithm for this maximization is derived. Diagnostic tests for the model are also suggested. Finally, the method is used to estimate a multivariate time series model of metropolitan wage rates, using a time series of cross section sectoral wage rates from the Los Angeles area.;The third paper derives a test for a varying coefficient in the standard linear regression model. Under the null the coefficient is constant, while under the alternative it is assumed to follow a stable first order Markov process. The hypothesis testing problem is complicated by the presence of the Markov transition parameter, which is identified only under the alternative. The problem is solved by considering a sequence of Lagrange multiplier test statistics, which are indexed by the unidentified Markov parameter, and relies heavily on the work of R. B. Davies. A bound on the size of the test for any critical value is also given. The test is shown to be simple to carry out, since the main ingredients of the statistic are the ordinary least squares residuals.;The fourth paper is an empirical investigation of housing prices. The data are a time series of cross section housing prices for University City, a suburb of San Diego. The data were complied from multiple listings and span a seven year period. The model developed relates the price of a house to its specific characteristics and an unobserved time varying base price. A dynamic model of the base price is also specified. The model is estimated using two different techniques, a two-step fixed effect method, and a dynamic multiple indicator multiple cause or DYMIMIC method, which was developed in the first two papers. The properties of the estimates from both methods are contrasted, and the DYMIMIC method is shown to be superior. The results show that while the level of rents have a significant effect on the base price, mortgage, property and income tax rates provide no significant explanatory power. Possible explanations for this finding are given. |
