It is well known that the distributional theories for many of the commonly used unit root tests are nonstandard. This project develops an original approach to these and related distributions. The sampling distribution of a statistic is usually obtained for a given sample size. Using the conventional sampling distribution of the statistic for the purpose of statistical inference thus implies evaluation of the likelihood of a realized value of the statistic along the contour of the distribution, given by the fixed sample size. This project takes a different contour in obtaining the sampling distribution of a statistic, i.e., the contour that is given by the fixed sum of squares. For the observations from stationary time series, the sum of squares becomes a constant multiple of the sample size for large samples, so the contour of the equi-squared-sum has conventional statistical properties for statistical analysis of stationary data. But the statistical properties are different for nonstationary data. The proposed research develops this new framework for statistical inference in nonstationary panels. Specifically, it is well known that the cross-sectional dependencies in nonstationary panels are extremely difficult to handle. The nonstationary models in general have distributions that are nonstandard and dependent upon nuisance parameters. The tests in panels combine the statistics computed for each individual unit, so the problem of nonstandard distributions and nuisance parameter dependencies of the individual test statistics becomes aggravated if aggregated across individual units. Statistical inference is difficult if not impossible using standard statistical methods of inference. But if the individual test statistics are computed using the samples which have the same sum of squares across all cross-sectional units, then the models yield standard normal asymptotics free of nuisance parameters and statistical inference on these panels is now much easier.
Broader Impacts: This project will build up a new framework for the statistical analysis of the nonstationary panels, which will open up new opportunities for the econometric theorists to develop new methodologies to effectively deal with nonstationary panels. A set of new reliable tools to do inference in nonstationary panels will also be provided. Given that the use of nonstationary panels has become, and will be even more so in the future, widespread in such fields as international finance, macroeconomics, industrial organization and labor economics, the outputs from this research could have a far-reaching impact on both theoretical and empirical research in economics. To facilitate implementation of the new methods, the investigator will prepare a program package and distribute it to applied researchers.
