Null (mathematics)

Abstract: Adjustments for making multiple comparisons in large bodies of data are recommended to avoid rejecting the null hypothesis too readily. Unfortunately, reducing the type I error for null associations increases the type II error for those associations that are not null. The theoretical basis for advocating a routine adjustment for multiple comparisons is the "universal null hypothesis" that "chance" serves as the first-order explanation for observed phenomena. This hypothesis undermines the basic premises of empirical research, which holds that nature follows regular laws that may be studied through observations. A policy of not making adjustments for multiple comparisons is preferable because it will lead to fewer errors of interpretation when the data under evaluation are not random numbers but actual observations on nature. Furthermore, scientists should not be so reluctant to explore leads that may turn out to be wrong that they penalize themselves by missing possibly important findings.

Abstract: In this paper we describe a method for testing the null of no cointegration in dynamic panels with multiple regressors and compute approximate critical values for these tests. Methods for non-stationary panels, including panel unit root and panel cointegration tests, have been gaining increased acceptance in recent empirical research. To date, however, tests for the null of no cointegration in heterogeneous panels based on Pedroni (1995, 1997a) have been limited to simple bivariate examples, in large part due to the lack of critical values available for more complex multivariate regressions. The purpose of this paper is to fill this gap by describing a method to implement tests for the null of no cointegration for the case with multiple regressors and to provide appropriate critical values for these cases. The tests allow for considerable heterogeneity among individual members of the panel, including heterogeneity in both the long-run cointegrating vectors as well as heterogeneity in the dynamics associated with short-run deviations from these cointegrating vectors.

Abstract: The endogenous two-break unit root test of Lumsdaine and Papell is derived assuming no structural breaks under the null. Thus, rejection of the null does not necessarily imply rejection of a unit root per se, but may imply rejection of a unit root without break. Similarly, the alternative does not necessarily imply trend stationarity with breaks, but may indicate a unit root with breaks. In this paper, we propose an endogenous two-break Lagrange multiplier unit root test that allows for breaks under both the null and alternative hypotheses. As a result, rejection of the null unambiguously implies trend stationarity.