ABASTRACT

The use of linear regression is central in applied research. However, when the base assumptions such as normality, homoscedasticity and independence of errors do not holds. Particularly, the assumption of homoscedasticity—the constancy of variance of errors often gets violated particularly in cross-sectional data. The OLS estimates in this situation though remain unbiased but they are no longer efficient, and the covariance matrix of OLS estimates becomes biased leading to wrong inferences related to hypothesis testing. Specifically, significant regressors might appear insignificant and vice versa if OLS is used under heteroskedasticity. Thus, it is especially important to evaluate this assumption via some existing tests for heteroskedasticity. One of the popular tests is the Goldfeld-Quandt (GQ, see, Goldfeld and Quandt, 1965) test which works well when there is a known break point, and one wants to assess if the variance before and after the break point is same. Rana et al. (2008) proposes a modified version of GQ—the MGQ test for the situations when there are outliers in the design matrix and shows that MGQ is a better choice when there are outliers in the data. It is emphasized that both tests, the GQ and the MGQ are designed to work for the case when the break point in variance is known. However, little is known on the performance of these tests when the break point in variance is unknown. This research takes a lead and proposes several extensions of GQ test for the case when break point in variance is unknown. Particularly, new tests have been proposed for the unknown break in variance by modifying a) the original GQ and b) the modified GQ for outliers (MGQ). The proposed tests are named supGQ and supMGQ and are designed for single but unknown split (break) in variance. The performance of these newly proposed tests is assessed via Monte-Carlo simulations and is compared with their conventional peers (GQ and the MGQ). Extensive Monte-Carlo simulations show the superiority of these newly proposed tests. A real- World example is also provided to support the analysis. The results of comparison analysis indicate that the proposed tests demonstrate significantly better performance than the existing tests.