An essay on multivariate macroeconometrics

Douglas Harold Willson, University of Pennsylvania


This dissertation considers the development and application of several econometric techniques to problems multivariate problems in macroeconomics. The first chapter develops spectral shape tests to test the null hypothesis that a multivariate time series is a martingale difference sequence. Spectral shape tests measure deviations of sample spectral distribution functions from their values under the null hypothesis. Under the martingale null, the univariate spectral distribution function is a diagonal line, while the cross spectral distribution function has a real part that is a diagonal line and a complex part that is zero. Existing asymptotic theory for the periodogram estimate of the univariate spectral distribution function is extended to the cross-spectral distribution function. General goodness-of-fit tests are developed that summarize all of the auto and cross-covariance properties of the data. The methodology also allows for tests based on specific ranges of frequencies. As an application, the martingale properties of eight weekly exchange rates are examined. General evidence against the martingale hypothesis is found and multivariate tests are found to be informative about deviations from the null hypothesis that are not apparent in a univariate framework. Multivariate spectral shape tests are employed in Chapter 2 to investigate the complete time series properties of post-war aggregate output for the G-7 industrialized countries. With the exception of the U.K., all countries are found to exhibit persistence equal to or excess of that implied by a random walk. Cross-spectral frequency interval tests are indicate the presence of significant international business cycles; most output time series are found to exhibit substantial cospectral power at low business cycle frequencies. Chapter 3 considers simulation methods for estimating linear latent variables with categorical indicators. These models when most (if not all) of the data are categorical, as is the case in the statistical analysis of business survey data. Full information maximum likelihood estimation is infeasible in these models due to problems associated with the calculation of multidimensional integrals. A simulation procedure is devised that avoids direct calculation of the maximum-likelihood estimates. The method is applied to a model of Swiss inventory investment behavior. The simulation method is shown to compare favorable with existing estimation techniques. The data do not provide convincing support for the production smoothing hypothesis.

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Recommended Citation

Willson, Douglas Harold, "An essay on multivariate macroeconometrics" (1990). Dissertations available from ProQuest. AAI9113870.