Question

"What are the consequences of heteroscedasticity and multicollinearity in regression? What are possible remedies"?

Answer 1

When heteroscedasticity is present in data, then estimates based on Ordinary Least Square (OLS) are subjected to following consequences:

1. We cannot apply the formula of the variance of the coefficients to conduct tests of significance and construct confidence intervals.
2. If error term ($\mu_i$) is heteroscedastic, then the OLS estimates do not have the minimum variance property in the class of unbiased estimators, i.e. they are inefficient in small samples. Furthermore they are asymptotically inefficient.
3. The estimated coefficients remain unbiased statistically. That means the property of unbiasedness of OLS estimation is not violated by the presence of heteroscedasticity.
4. The forecasts based on the model with heteroscedasticity will be less efficient as OLSestimation yield higher values of the variance of the estimated coefficients.

Suppose that you find the evidence of existence of heteroscedasticity. If you use the oLS estimator, you will get unbiased but inefficient estimates of the parameters of the model. Also, the estimates of the variances and covariances of the parameter estimates will be biased and inconsistent, and as a result hypothesis tests will not be valid. When there is evidence of heteroscedasticity, econometricians do one of the two things:

• Use OLS estimator to estimate the parameters of the model. Correct the estimates of the variances and covariances of the OLS estimates so that they are consistent.
• Use an estimator other than the OLS estimator to estimate the parameters of the model.