Econometrics - Heteroscedasticity - Ch.9 Gujarati - 2020

This video is based on Chapter 9 of D.N. Gujarati & Porter’s : Essentials of Econometrics. The Topic discussed is the Problem of Heteroscadasticity in Regression and its analysis. I have discussed the following issues:

1. Nature of the problem of Heteroscadasticity: How is a rule rather than an exception in Cross Sectional data

2. Consequences of Heteroscadasticity:

a. No effect on Linearity & Unbiased property of OLS
b. The OLS estimates have no longer the minimum variance- there is bias in the estimation of parameters as well as the SE of regression (Sigma), the latter is cause for the former.
c. Hypothesis Testing becomes unreliable as the parameters are biased.

Need to use Weighted Least Squares instead of OLS (which gives equal weights to all errors)

3. Detection of Heteroscadasticity:

a. Graphical Examination of Residuals:

Residual Squares are regressed on Each Explanatory variable or Estimated Y (Y hat) - If there exists a pattern in the graph, it suggests towards presence of Heteroscadasticity.

b. Park Test: Formalized version of Park Test :

The log (Squares of Residuals) is regressed on log (Independent Variable) or log (Estimated Y), assuming that the error term of this regression (v) is Homoscadasticity.
If the coefficient of the above regression is significant- it shows there is significant relationship between error and independent variables & hence the indication towards Heteroscadasticity.

c. Glejser Test :

Similar to Park Test, however instead of Squared Residuals, we take absolute values of errors in this test, and regress them on multiple functional forms of independent variable.

d. White's General Heteroscadasticity Test:

i. Estimating the Residuals from OLS
ii. Run an Auxiliary Regression: Residual Squares are regressed on explanatory variables, their squares, cross products, other functional forms. With the null that each parameter is zero (Homoscadasticity). Obtain the R square from this regression.
iii. n*R square has a Chi Square distribution with degrees of freedom equal to no. of parameter (minus 1) in the auxiliary regression. If this statistic is significant, it indicates towards presence of Heteroscadasticity

e. Goldfelt-Quandt Test:

In this test we assume that the variance behaves monotonically with independent variables. We divide the data into 2 parts, removing the "C" middle observations, Where ' C = 3/8 * Observations'.

We then run 2 regressions on 2 sets of data and calculate the F statistic using their respective RSS, if F statistic is significant- it points towards Heteroscadasticity.

4. Remedial Measures :

a. If Error variance is known - Then use WLS - by dividing the entire original regression equation with the known error

b. If the Error Variance is not known - we need to estimate or have an idea about it through graphical method and transform the original regression in such a way that the new error is Homoscadasticity.

c. Re specification of the model also at times dampens the effects of Heteroscadasticity


This Chapter is extremely important from the point of examination for Semester IV students of Economics Hons. & BBE of Delhi University. While students of Masters, MBA, UGC-NET, IES Exam would also find it useful in their course of preparation.

My Best Wishes & Happy Learning😊

The Pink Professor
Siddharth Rathore
Assistant Professor
Department of Economics
Gargi College
University of Delhi