Using theoretical relations as a source of econometric specifications might lead a researcher to models that do not adequately capture the statistical regularities in the data and do not faithfully represent the phenomenon of interest. In addition, the researcher is unable to disentangle the statistical and substantive sources of error and thus incapable of using the statistical evidence to assess whether the theory, and not the statistical model, is wrong. The Probabilistic Reduction Approach puts forward a modeling strategy in which theory can confront data without compromising the credibility of either one of them. This approach explicitly derives testable assumptions that, along with the standardized residuals, help the researcher assess the precision and reliability of statistical models via misspecification testing. It is argued that only when the statistical source of error is ruled out can the researcher reconcile the theory and the data and establish the theoretical and/or external validity of econometric models. Through the approach, we are able to derive the properties of Beta regression-like models, appropriate when the researcher deals with rates and proportions or any other random variable with finite support; and of Lognormal models, appropriate when the researcher deals with nonnegative data, and specially important of the estimation of demand elasticities. / Ph. D.

Following the Probabilistic Reduction(PR) Approach, this paper proposes the Student’s Autoregressive (St-AR) Model, Student’s t Vector Autoregressive (St-VAR) Model and their heterogeneous versions, as an alternative to the various ARCH type models, to capture univariate and multivariate volatility. The St-AR and St-VAR models differ from the latter volatility models because they give rise to internally consistent statistical models that do not rely on ad-hoc specification and parameter restrictions, but model the conditional mean and conditional variance jointly. The univariate modeling is illustrated using the Real Effect Exchange Rate(REER) indices of three mainstream currencies in Asia (RMB, Hong Kong Dollar and Taiwan Dollar), while the multivariate volatility modeling is applied to investigate the relationship between the REER indices and stock price indices in mainland China, as well as the relationship between the stock prices in mainland China and Hong Kong. Following the PR methodology, the information gained in Mis-Specification(M-S) testing leads to respecification strategies from the original Normal-(V)AR models to the St-(V)AR models. The results from formal Mis-Specification (M-S) tests and forecasting performance indicate that the St-(V)AR models provide a more appropriate way to model volatility for certain types of speculative price data. / Ph. D.