Using OLS to Test for Normality
Ben-Gurion University of the Negev - Department of Economics
July 14, 2012
Yitzhaki (1996) showed that the OLS estimator of the slope coefficient in a simple regression is a weighted average of the slopes delineated by adjacent observations. The weights depend only on the distribution of the independent variable. In this paper I demonstrate that equal weights can only be obtained if and only if the independent variable is normally distributed. This necessary and sufficient condition is used to develop a new test for normality which is distribution free and not sensitive to outliers. The test is compared with standard normality tests, in particular, the popular Jarque-Bera test. It is shown that the new test provides a better power for testing normality against all classes of alternative distributions. Finally, the test is applied to check normality in time-series data from major international financial markets.
Number of Pages in PDF File: 16
Keywords: regression weights, Jarque-Bera test, Kolmogorov-Smirnov test
JEL Classification: C10
Date posted: July 19, 2012