Empirical studies in economics and finance often face the difficulty that the data is correlated and heterogeneous or heavy-tailed in some unknown fashion. Many estimators of parameters of interest remain valid and interesting even under the presence of correlation and heterogeneity or heavy tails, but it becomes considerably more challenging to correctly estimate their sampling variability. Several methods have been proposed in econometrics to deal with the problem of heteroskedasticity and correlation. The typical approach is to use consistent variance estimators. While powerful and quite general, in many cases, the approach leads to tests that have poor finite sample properties. More recently, a number of inference procedures have been developed that do not rely on consistency of the variance estimator. In many settings, these procedures have better finite sample properties than the methods based on consistent variance estimation. However, their performance is still problematic in a number of heteroskedasticity and dependence setups. Development of new robust approaches to inference under heterogeneity and correlation with a wide range of applicability is, therefore, of significant interest in modern econometrics. This project focuses on further analysis and applications of the t-statistic based approaches to robust large sample inference and on development of general related procedures that rely on conservativeness of test statistics employed in the analysis. In particular, it develops robust tests for equality of two or more parameters of interest using general results on conservativeness of Behrens-Fisher statistic for testing equality of two means and its extensions. The project focuses on the analysis of conservativeness properties of ratios of Gaussian quadratic forms, F-statistics, variance ratio statistics, empirical autocorrelation coefficients and Dickey-Fuller and Phillips-Perron test statistics under heteroskedasticity and dependence in observations. These results are employed to develop robust approaches to testing equality of model parameters, robust tests for random walks, uncorrelatedness, stationarity and unit roots, and tests for structural breaks. The statistical approaches proposed are used to develop robust inference procedures for various economic and financial variables and indices. In particular, they are applied to analysis of the asymptotics and robust confidence intervals for Sharpe ratio and other financial indices and also for a number of commonly used poverty, inequality and concentration measures under dependence, heterogeneity and heavy tails.
Broader Impacts: The project integrates research and education by including research results into the syllabus of graduate and undergraduate courses the investigator is teaching and by collaborating with student research assistants on the numerical parts of the study. The results obtained in the project will be disseminated broadly in publications in peer-reviewed journals and in discussion papers. They will also be presented at conferences and seminars on economics, finance and statistics and at meetings of professional societies in these fields. The project benefits society at large in several important ways. In particular, one of the main planned outcomes of the study is a toolbox of statistical approaches that are of importance to researchers and students in many different areas of knowledge where heterogeneity and dependence in data are typically encountered. In addition, the analysis provides reliable statistical methods for making sound economic and financial decisions, including those related to poverty reduction and income distribution.
